Recent Research in Control Engineering and Decision Making: Volume 2, 2020 [1st ed.] 9783030652821, 9783030652838

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Studies in Systems, Decision and Control 337

Olga Dolinina · Igor Bessmertny ·  Alexander Brovko · Vladik Kreinovich ·  Vitaly Pechenkin · Alexey Lvov ·  Vadim Zhmud   Editors

Recent Research in Control Engineering and Decision Making Volume 2, 2020

Studies in Systems, Decision and Control Volume 337

Series Editor Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

The series “Studies in Systems, Decision and Control” (SSDC) covers both new developments and advances, as well as the state of the art, in the various areas of broadly perceived systems, decision making and control–quickly, up to date and with a high quality. The intent is to cover the theory, applications, and perspectives on the state of the art and future developments relevant to systems, decision making, control, complex processes and related areas, as embedded in the fields of engineering, computer science, physics, economics, social and life sciences, as well as the paradigms and methodologies behind them. The series contains monographs, textbooks, lecture notes and edited volumes in systems, decision making and control spanning the areas of Cyber-Physical Systems, Autonomous Systems, Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Biological Systems, Vehicular Networking and Connected Vehicles, Aerospace Systems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power Systems, Robotics, Social Systems, Economic Systems and other. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution and exposure which enable both a wide and rapid dissemination of research output. Indexed by SCOPUS, DBLP, WTI Frankfurt eG, zbMATH, SCImago. All books published in the series are submitted for consideration in Web of Science.

More information about this series at http://www.springer.com/series/13304

Olga Dolinina Igor Bessmertny Alexander Brovko Vladik Kreinovich Vitaly Pechenkin Alexey Lvov Vadim Zhmud •

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Editors

Recent Research in Control Engineering and Decision Making Volume 2, 2020

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Editors Olga Dolinina Yury Gagarin State Technical University of Saratov Saratov, Russia Alexander Brovko Yury Gagarin State Technical University of Saratov Saratov, Russia Vitaly Pechenkin Yury Gagarin State Technical University of Saratov Saratov, Russia

Igor Bessmertny ITMO University Saint Petersburg, Russia Vladik Kreinovich University of Texas at El Paso El Paso, USA Alexey Lvov Yury Gagarin State Technical University of Saratov Saratov, Russia

Vadim Zhmud Novosibirsk State Technical University Novosibirsk, Russia

ISSN 2198-4182 ISSN 2198-4190 (electronic) Studies in Systems, Decision and Control ISBN 978-3-030-65282-1 ISBN 978-3-030-65283-8 (eBook) https://doi.org/10.1007/978-3-030-65283-8 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

This book constitutes the full papers and short monographs developed on the base of the refereed proceedings of the International Conference on Information Technologies: Information and Communication Technologies for Research and Industry (ICIT-2020), held in Saratov, Russia, in December 2020. The book “Recent Research in Control Engineering and Decision Making Volume 2, 2020” brings accepted papers which present new approaches and methods of solving problems in the sphere of control engineering and decision making for the various fields of studies: industry and research, energy efficiency and sustainability, ontology-based data simulation, smart city technologies, theory and use of digital signal processing, cognitive systems, robotics, cybernetics, automation control theory, image and sound processing, image recognition technologies, and computer vision. Particular emphasis is laid on modern trends, new approaches, algorithms, and methods in selected fields of interest. The presented papers were accepted after careful reviews made by at least three independent reviewers in a double-blind way. The acceptance level was about 60%. The chapters are organized thematically in several areas within the following tracks: • Information systems for industry and research • Models, methods, and approaches in decision-making systems • Smart city technologies and Internet of things Due to the COVID-19 quarantine measures, ICIT-2020 was held online. The conference was focused on development and globalization of information and communication technologies, methods of control engineering and decision making along with innovations and networking, smart city and Internet of things, information and communication technologies for sustainable development and technological change, global challenges. Moreover, the ICIT-2020 served as a discussion area for the actual above-mentioned topics.

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The editors believe that the readers will find the proceedings interesting and useful for their own research work. December 2020

Olga Dolinina Alexander Brovko Vitaly Pechenkin Alexey L’vov Vadim Zhmud Vladik Kreinovich Igor Bessmertny

Organization

Conference Board Chairman Alexander Rezchikov

Doctor of Engineering, Professor, Corresponding Member of Russian Academy of Sciences

Conference Board Members Alexander Sytnik

Vadim Kushnikov

Olga Dolinina Alexander Brovko

Vitaly Pechenkin Alexey L’vov Vadim Zhmud Vladik Kreinovich

Doctor of Engineering, Professor, Corresponding Member of Russian Academy of Education, Yury Gagarin State Technical University of Saratov, Russia Doctor of Engineering, Professor, Saratov Scientific Centre of Russian Academy of Sciences, Russian Academy of Sciences, Russia Doctor of Engineering, Professor, Yury Gagarin State Technical University of Saratov, Russia Doctor of Physics and Mathematics, Professor, Yury Gagarin State Technical University of Saratov, Russia Doctor of Sociology, Professor, Yury Gagarin State Technical University of Saratov, Russia Doctor of Engineering, Professor, Yury Gagarin State Technical University of Saratov, Russia Doctor of Engineering, Professor, Novosibirsk State Technical University, Russia PhD in Mathematics, Professor, University of Texas at El Paso, USA

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Igor Bessmertny Leonid Bobrov

Sergey Borovik

Ekaterina Pechenkina Lubomir Dimitrov Valery Kirilovich Uranchimeg Tudevdagva

Organization

Doctor of Engineering, Professor, ITMO University, Russia Doctor of Engineering, Professor, Novosibirsk State University of Economics and Management, Russia Doctor of Engineering, Professor, Institute for the Control of Complex Systems, Russian Academy of Sciences, Russia PhD in Cultural Anthropology, Swinburne University of Technology, Australia Doctor of Engineering, Professor, Technical University of Sofia, Bulgaria Doctor of Engineering, Professor, Zhitomir State Technological University, Ukraine Doctor of Engineering, Professor, Mongolian University of Science and Technology, Mongolia

Organizing Committee Chair Olga Dolinina

Doctor of Engineering, Professor, Yury Gagarin State Technical University of Saratov, Russia

Organizing Committee Members Alexander Sytnik

Vadim Kushnikov

Olga Toropova

Alexander Brovko

Svetlana Kumova

Doctor of Engineering, Professor, Yury Gagarin State Technical University of Saratov, Corresponding Member of Russian Academy of Education, Russia Doctor of Engineering, Professor, Saratov Scientific Centre of Russian Academy of Sciences, Russian Academy of Sciences, Russia PhD in Engineering, Associate Professor, Yury Gagarin State Technical University of Saratov, Russia Doctor of Physics and Mathematics, Professor, Yury Gagarin State Technical University of Saratov, Russia PhD in Political Science, Associate Professor, Yury Gagarin State Technical University of Saratov, Russia

Organization

Elena Kushnikova

Daria Cherchimtseva

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PhD in Engineering, Associate Professor, Yury Gagarin State Technical University of Saratov, Russia Yury Gagarin State Technical University of Saratov, Russia

Conference Organizer Yury Gagarin State Technical University of Saratov, web: www.sstu.ru, email: sstu_offi[email protected]

Co-organizers Russian Academy of Education Saratov Scientific Centre of Russian Academy of Sciences (Saratov, Russia) Institute for the Control of Complex Systems, Russian Academy of Sciences (Samara, Russia)

Conference Website, Call for Papers http://icit2020.sstu.ru

Contents

Information Systems for Industry and Research The Task of Controlling Robotic Technological Complexes of Arc Welding in Unstable States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dmitry Fominykh, Alexander Rezchikov, Vadim Kushnikov, Vladimir Ivaschenko, Alexander Sytnik, Alexey Bogomolov, and Leonid Filimonyuk Longitudinal Waves in Two Coaxial Elastic Shells with Hard Cubic Nonlinearity and Filled with a Viscous Incompressible Fluid . . . . . . . . . Lev Mogilevich and Sergey Ivanov Acceleration and Increase of Reliability of the Algorithm for Numerical Optimization of the PID-Regulators for Automatic Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vadim Zhmud, Lubomir Dimitrov, and Jaroslav Nosek PID Controller for Non-stationary Plants of Relative Second Order . . . Galina Frantsuzova and Anatoly Vostrikov Adaptive Decision Support System for Scaling University Cloud Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bakhytzhan Akhmetov, Valerii Lakhno, Boris Gusev, Miroslav Lakhno, Ivan Porokhnia, Gulnaz Zhilkishbayeva, and Madina Akhanova Application of a Combined Multi-Port Reflectometer to Precise Distance Measuring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Peter L’vov, Artem Nikolaenko, Alexey L’vov, Sergey Ivzhenko, and Oleg Balaban A Transformation-Based Approach for Fuzzy Knowledge Bases Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nikita Dorodnykh, Olga Nikolaychuk, and Aleksandr Yurin

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Mathematical Modeling of Hydroelastic Oscillations of Circular Sandwich Plate Resting on Winkler Foundation . . . . . . . . . . . . . . . . . . Aleksandr Chernenko, Alevtina Christoforova, Lev Mogilevich, Victor Popov, and Anna Popova

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Numerical Simulation Results of the Optimal Estimation Algorithm for a Turn Table Angular Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Roman Ermakov, Alexey L’vov, Anna Seranova, Nina Melnikova, and Elena Umnova Comparison of LSTM and GRU Recurrent Neural Network Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Anton Pudikov and Alexander Brovko System Analysis of the Process of Determining the Room Category on Explosion and Fire Hazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Yuliya Nikulina, Tatiana Shulga, Alexander Sytnik, and Olga Toropova Comparison of Methods for Parameter Estimating of Superimposed Sinusoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Alexey L’vov, Anna Seranova, Roman Ermakov, Alexandr Sytnik, and Artem Muchkaev Jumping Robot as a Lunar Rover: Basic Technical Solutions . . . . . . . . 152 Vadim Zhmud, Dmitry Myakhor, and Huberth Roth Fast Method for Solving the Wave Equation . . . . . . . . . . . . . . . . . . . . . 165 Vil Baiburin, Alexander Rozov, Artem Kolomin, and Natalia Khorovodova Dynamic Error Reduction via Continuous Robot Control Using the Neural Network Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Viktor Glazkov, Stanislav Daurov, Alexey L’vov, Adel Askarova, and Dmitriy Kalikhman Neural Network Modeling of the Kinetic Characteristics of Polymer Composites Curing Process . . . . . . . . . . . . . . . . . . . . . . . . . 185 Oleg Dmitriev and Alexander Barsukov A Technique for Multicriteria Structural Optimization of a Complex Energy System Based on Decomposition and Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 Ekaterina Mirgorodskaya, Nikita Mityashin, Yury Tomashevskiy, Dmitry Petrov, and Dmitry Vasiliev Emulators – Digital System Simulation on the Architecture Level . . . . . 209 Alexander Ivannikov

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Modeling the Vibrations of Elastic Plate Interacting with a Layer of Viscous Compressible Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Oksana Blinkova and Dmitry Kondratov Modeling of Process Control Algorithms for Parallel Computing Systems Using Nondeterministic Automata . . . . . . . . . . . . . . . . . . . . . . 235 Dmitry Pashchenko, Alexey Martyshkin, and Dmitry Trokoz Estimating Algorithm for Harmonics of Current and Voltage Signals When Measuring Reactive Power in Industrial Power Networks . . . . . . 250 Olga Dolinina, Olga Toropova, Elena L’vova, and Natalia Vagarina Detection of Scenes Features for Path Following on a Local Map of a Mobile Robot Using Neural Networks . . . . . . . . . . . . . . . . . . . . . . . 272 Kirill Sviatov, Alexander Miheev, Yuriy Lapshov, Vadim Shishkin, and Sergey Sukhov Development of the Geometrical Modeling Built-in Toolkit to Create Design Strategies for the Digital in-Process Models of the Aircraft Structures Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 Kate Tairova, Vadim Shishkin, and Leonid Kamalov Performance Analysis of 6-Axis Coordinate Measuring Machine . . . . . . 298 Mikhail Zakharchenko, Petr Salov, Liudmila Seliverstova, Andrew Kochetkov, and Oleg Zakharov Development of a Computer Simulation Model for Shaping the Working Surface of a Worm Wheel with a Gear Cutting Tool with Modified Producing Surface . . . . . . . . . . . . . . . . . . . . . . . . . . 308 Sergey Ryazanov and Mikhail Reshetnikov Optimization of Diagnostics and Treatment of Concomitant Strabismus Using Video Oculograph . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 Stanislav Radevich, Tatiana Kamenskikh, Alexander Postelga, Tatiyana Usanova, Dmitry Usanov, and Elena Chernyshkova Analysis of 3D Scene Visual Characteristics Based on Virtual Modeling for Surveillance Sensors Parameters . . . . . . . . . . . . . . . . . . . . 328 Vitaly Pechenkin, Olga Dolinina, Alexander Brovko, and Mikhail Korolev Analysis of the Jitter on the Eye Diagram Received with Equivalent-Time Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 Konstantin Zakharov and Ivan Reva The Bridge Design of Tensegrity Structures Using Parametric Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 Artem Bureev and Igor Ovchinnikov

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Pseudoexfoliation Syndrome, Pseudoexfoliation Glaucoma: Modern Monitoring Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 Tatiana Kamenskikh, Ekaterina Veselova, Igor Kolbenev, Elena Chernyshkova, Olga Dolinina, and Vitaly Pechenkin Models for Determining the Electric Power Consumption in the Water Recycling System at an Industrial Enterprise . . . . . . . . . . . . . . . . . . . . . 378 Ekaterina Kulakova, Vadim Kushnikov, Andrey Lazarev, and Inessa Borodich Global a Priori Inference in Algebraic Bayesian Networks . . . . . . . . . . 391 Anatolii G. Maksimov, Arseniy D. Zavalishin, and Alexander L. Tulupyev Upper Theoretical Estimate of Solving the Second Problem of Local a Posteriori Inference in Algebraic Bayesian Networks . . . . . . 404 Arseniy D. Zavalishin, Anatolii G. Maksimov, and Alexander L. Tulupyev Operational Properties Estimation Mathematical Models and Statements of Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 Alexander S. Geyda Models, Methods and Approaches in Decision Making Systems Optimization of Financial Flows in a Building Company Using an Escrow Account in the Russian Federation . . . . . . . . . . . . . . . . . . . . 427 Karolina Ketova and Daiana Vavilova Using of Digital Analysis of the Light Tones Balance in Painting . . . . . 443 Alexander Voloshinov and Olga Dolinina Classification Approach to Management of Polythematic Knowledge . . . 453 Yuliya Cherepova, Leonid Bobrov, Irbulat Utepbergenov, and Bulat Kubekov Approach to the Use of Language Models BERT and Word2vec in Sentiment Analysis of Social Network Texts . . . . . . . . . . . . . . . . . . . 462 Andrey Konstantinov, Vadim Moshkin, and Nadezhda Yarushkina Alpha-Search Algorithm for Cohesive Teams of Software Engineers . . . 474 Alexey Zhelepov and Nadezhda Yarushkina Non-parametric Bayes Belief Network for Intensity Estimation with Data on Several Last Episodes of Person’s Behavior . . . . . . . . . . . 486 Valeriia F. Stoliarova Semantic Consolidation of Data Market Digital Services . . . . . . . . . . . . 498 Anton Ivaschenko, Evgeniya Dodonova, Anastasiya Stolbova, and Oleg Golovnin

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Comparison of Behavior Rate Models Based on Bayesian Belief Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 Aleksandra Toropova and Tatiana Tulupyeva Multi-parameter Efficiency Criterion for Information Channel Models with High Information Reliability . . . . . . . . . . . . . . . . . . . . . . . 522 Dmitry Klenov, Michael Svetlov, Alexey L’vov, Alexander Sytnik, and Igor Bagaev Vector Representation of Words Using Quantum-Like Probabilities . . . 535 Aleksei Platonov, Igor Bessmertny, Julia Koroleva, Lusiena Miroslavskaya, and Alaa Shaker Development of a System Dynamics Model of Forecasting the Efficiency of Higher Education System . . . . . . . . . . . . . . . . . . . . . . . 547 Elena Kalikinskaja, Vadim Kushnikov, Vitaly Pechenkin, and Svetlana Kumova Medication Intake Monitoring System for Outpatients . . . . . . . . . . . . . . 563 Alexander Ermakov, Aleksandr Ormeli, and Matvey Beliaev Cognitive Model of the Balanced Scorecard of Manufacturing Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 Oleg Protalinsky, Anna Khanova, Irina Bondareva, Kristina Averianova, and Yulya Khanova Automated Player Activity Analysis for a Serious Game About Social Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 Boris Krylov, Maxim Abramov, and Anastasia Khlobystova Mathematical Model for Evaluating Management Processes for Implementing Electronic Document Management Systems . . . . . . . . 600 Olga Perepelkina and Dmitry Kondratov Smart City Technologies and Internet of Things «Smart Cities» as Digital Transformation Centers: The Case of Modern Russia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 Svetlana Morozova and Alexander Kurochkin Audio-Based Vehicle Detection Implementing Artificial Intelligence . . . . 627 Oleg Golovnin, Artem Privalov, Anastasiya Stolbova, and Anton Ivaschenko Methodological Foundations for the Application of Video Analytics and Incident Management Technologies in Real-Time Detection and Control Systems for Road Incidents . . . . . . . . . . . . . . . . . . . . . . . . 639 Olga Dolinina, Andrey Motorzhin, Vitaly Poltoratzky, Aleksandr Kandaurov, Sergey Shatunov, and Aleksandr Kartashev Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657

Information Systems for Industry and Research

The Task of Controlling Robotic Technological Complexes of Arc Welding in Unstable States Dmitry Fominykh1(B) , Alexander Rezchikov2 , Vadim Kushnikov1 , Vladimir Ivaschenko1 , Alexander Sytnik3 , Alexey Bogomolov1,4 , and Leonid Filimonyuk1 1 Institute of Precision Mechanics and Control, Russian Academy of Sciences, 24,

Rabochaya str., Saratov 410028, Russia [email protected] 2 V. A. Trapeznikov Institute of Control Sciences of RAS, 65 Profsoyuznaya street, Moscow 117997, Russia 3 Yuri Gagarin State Technical University, 77 Politechnicheskaya str., Saratov 410054, Russia 4 Saratov State University, 83 Astrakhanskaya street, Saratov 410012, Russia

Abstract. The article presents mathematical models and the control algorithm of robotic welding complexes of arc welding in the conditions of unstable conditions. A procedure for identifying unstable states for a mathematical model has been developed using the example of the Lorenz and Nose-Hoover attractors. An algorithm is proposed to prevent the system from transitioning to unstable states by implementing action plans. Keywords: Robot · Welding · Control · Mathematical model · Chaos · Unstable state · Technological process

1 Introduction The introduction of robotic technological complexes (RTC) for arc welding is becoming more common in global industry. As a rule, these are enterprises manufacturing cars, railway wagons, agricultural machinery, etc. At the same time, the scope of operation of robots is constantly expanding. This is due to the large number of freedom axes of the manipulator, the ability to position the welding torch in the desired spatial position, as well as the possibility of flexible programming. The welding robot is notable for its versatility of actions, as well as a high speed of transition to performing various operations. RTC can be used for welding both compact parts and large-sized workpieces of any design. The main purpose of the application of welding robots is to increase labor productivity and product quality. The economic efficiency of RTC includes improving the quality of welded joints and saving payroll. In addition, the robot can be operated in environments harmful to human health. The typical RTC is a complex single system with a large number of different components, including a manipulator, its controller, welding equipment and adaptive control © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 3–13, 2021. https://doi.org/10.1007/978-3-030-65283-8_1

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and maintenance systems of the robot. The process flow diagram of automatic welding as a control object using the example of Kawasaki robots with Fronius welding equipment is shown in the Fig. 1.

Fig. 1. The process flow diagram of automatic welding via RTC as a control object: CA – control actions, FB – feedback, ED – external disturbances

The problem of reliable operation is one of the paramount when metal constructions welding in RTC. An insufficient level of control during the process for any reason increases the risk of an accident or defective product. At present, various robots control systems have been developed and tested in practice. Significant attention in publications is given to the problem of friction stir welding quality [1–3]. For instance, authors of the article [1] show that a robot with an embedded realtime algorithm for the compensation of the lateral tool deviation can reproduce the same as a gantry-type CNC system by using friction stir welding quality. Wherein the model of an industrial robot is carried out by the classical identification technique and this is embedded in the robot controller; the corrected path is based on force measurements along the welding process in real-time. The paper [2] explores the effects of friction stir weld tool travel angle and machine compliance on joint efficiency. This model is able to

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estimate the joint efficiency of friction stir welds as a function of gap width, travel angle, and plunge depth based on tool geometry and workpiece dimensions. In [3] a friction stir weld robot for large-scale complex surface structures, which has high stiffness and good flexibility is presented. A welding trajectory planning method based on iterative closest point algorithm is used. Another popular area of research is the task of the welding path tracking [4–10]. For example, a method for the automatic identification and location of welding seams for robotic welding using computer vision [4]. For this, an algorithm for detection and localization of weld joints for robotic welding used. In the article [5] a welding robot system based on the real-time visual measurement in the different levels of the welding current describes. Here the control algorithm is based on the knowledge base for control the weld formation by regulating the welding current and wire feed rate. Likewise, [6] presents a non-contact automated data acquisition system for monitoring arc welding process based on laser ultrasonic technology. A pulse laser generates ultrasound on one side of the weld by ablation, and a non-contact electro-magnetic acoustic transducer (EMAT) placed on the opposite side of the weld detects ultrasound transmitted through the weld bead; and time required for ultrasound to travel from the laser source to the EMAT is defined by analysis these data. The versatile machine vision system for correcting off-line programmed nominal robot trajectories for advanced welding [7] uses one camera and a weld tool mounted on the robot hand. This system takes images of the weld joint from different positions and orientations, and determines the weld joint geometry in 3D using a stereo vision algorithm. The method [8] is proposed to automatically locate the weld seam between two objects in butt welding applications by having the ability to locate the weld seam on arbitrarily positioned work pieces. It was developed using images captured from a low cost web-cam and it is able to plan a robot path along the identified seam. The authors of [9] use structured lighting, in the form of a steerable cone of laser light, and to use machine vision for sensing of the weld joint location and determining the detailed three-dimensional weld joint surface geometry ahead of the welding torch. This sensory feedback is used for the off-line detection of large fixturing errors before welding starts (part finding); the real-time correction of robot paths to compensate for thermal distortion and loose part tolerances during single-and multipass welding conditions to correct for weld joint shape variations (adaptive welding). In the article [10] the problem of coordinating multiple motion devices for welding considered by focusing on the problem of coordinating a positioning table and a manipulator. The robot coordination is achieved by keeping the six-axis arm in good maneuverability position, i.e., far from its singular configurations and far from the motion limits of the six-axis arm and the motion limits of the track. This allowed the authors to obtain an analytic solution to find Cartesian positions of the track and the robot end-effector which used to generate the joint angles of the arm by inverse kinematics. Besides, a number of researchers work on remotely controlled welding scheme that enables transformation of human welder knowledge into a welding robot is proposed [11]. It is achieved by equipping the industrial robot arm with sensors to observe the welding process, including a compact 3D weld pool surface sensing system and an

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additional camera to provide direct view of the work-piece. The paper [12] presents a genetic algorithm for the traveling salesman problem is used to determine welding task sequencing. A random key genetic algorithm used to solve multi-robot welding task sequencing: multiweldline with multiple robots. Here various simulation tests for a welded structure are performed to find the combination of genetic algorithm parameters suitable to weld sequencing problems and to verify the quality of genetic algorithm solutions. Cannot be ignored an online method of quality control and assurance of welded structures [13], which can be used not only for determining the weld quality level with respect to the fatigue strength but also to be evaluated for use in improved process control, in welding power sources and robot control systems. This achieved by identification of critical points of the welds, developing welding procedures to optimize the fatigue properties of the weld, defining and setting appropriate weld requirements which contribute to a high focus on critical characteristics. The authors of [14] try to establish a correlation between the current and voltage signatures with the good weld and weld with porosity and burn through defect during the welding of carbon steel using gas metal arc welding process. By using online current and voltage sensors, data loggers, and signal processing hardware and software authors found that the probability density distributions of the current and voltage signature have a correspondence between the current and voltage signatures with the welding defect. Of interest is the iterative method proposed in [15] that has been developed using Matlab software package for robot speed optimization. This algorithm is aimed to maintain complete joint penetration while maximizing productivity by utilizing the fastest weld speed. Also noteworthy a vision-based measurement system [16] for evaluating how different conditions and algorithms impact the measuring of beveled edges. This system integrates hardware and software to image the welding plates using a single camera as visual sensor, run computer vision algorithms on a field programmable gate array board, controls the robot movements and adjust the weld pattern and welder equipment parameters. As seen, these systems are mainly aimed at ensuring compliance with welding parameters and the accuracy of the positioning of the welding torch (for example, methods and algorithms for tracking a weld: tracking using a laser sensor, optical tracking, tracking arc parameters). However, insufficient attention is paid to optimizing the operational control of the welding process, taking into account all the parameters of the technological process, including human involvement, external factors and disturbances. In addition, attention must be paid to preventing the system from transitioning to an unstable or chaotic state when a small perturbation of the boundary conditions leads to a significant change in the trajectory of the system variables in the phase space. Although RTCs usually have several stabilization circuit, and the probability of such states is extremely small, this possibility cannot be completely ruled out. In the article [17], we considered the identification of unstable states using the Lorenz attractor and the model of system dynamics [18–21]. When constructing the phase portrait, the following quality indicators were used as the basic variables: X 1 (number of defective beams per 100 units of production), X 4 (average length of defective welds per

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7

1 unit of production) and X 18 (number of beams accepted by quality control inspectors from the first presentation). The remaining variables were considered constant. In this article, we will consider other types of chaos.

2 The Mathematical Models It is not possible to determine in advance all possible unstable states. Therefore, two types of chaos were taken as a basis: the Lorentz and Nose-Hoover systems [18, 19], most often encountered in technical systems process control. In the course of further functioning of the system, the set of possible unstable states will be replenished. First, we’ll define the change of the main quality indicators X 1 , X 4 and X 18 by taking the remaining indicators as constants at which the system takes the form of a system of Lorenz equations: ⎧ dX1 ⎨ dt = σ(X4 − X1 ) dX4 dt = X1 (r − X18 ) − X4 ⎩ dX 18 dt = X1 X4 − bX18 where σ = 10, r = 28, b = 8/3, (NW f1 (X3 )f2 (X11 )f3 (X12 )f4 (X13 )) − (NS f5 (X2 )f6 (X8 )f7 (X17 )) = X4 − X1 Ldf13 (X15 )f14 (X16 ) − L ∗ f15 (X2 ) + X1 X18 + X4 r = = 28 X1   (Ab + Ld )f35 (X1 )f36 (X4 ) − Nd f31 (X6 )f32 (X7 )

σ =

b =

f33 (X8 )f34 (X14 ) + X1 X4

X18

10

= 8/3

By substituting the functional dependences f 1 , f 2 , … , f 36 to the equations for σ, r and b, we can obtain: ⎧ N X (1−X (X −X +1))−N (X −2X −X (1−X )+3) 12 13 11 17 2 17 W 3 S 8 − 10 = 0 ⎪ ⎪ X4 −X1 ⎪   ⎪ ⎪ ⎪ Ld (0, 247 − 0, 081X15 + X16 (0, 268 − 0, 088X15 )) ⎪ ⎪ ⎨ −L ∗ (0, 914 − 0, 473X2 ) + X1 X18 + X4 − 28 = 0 X1 ⎪  ⎪ ⎪ ⎪ (Ab + Ld )(1, 278 − 0, 66X + X (0, 67X − 1, 29)) − Nd (16X14 + X1 X4 4 1 4 ⎪ ⎪ ⎪ ⎪ X (X + 20X + 87) − X (X + 3X + 12) + X (4X + 116) + 518) ⎩ 7 14 8 6 7 8 8 14 X18

(1) = 8/3

Thus, for values of quality indicators which (1) will be fulfilled for, we will have the Lorenz attractor. System reduced to the Nose-Hoover attractor, will look as follows: ⎧ dX1 ⎨ dt = X4 dX4 dt = −X4 X18 − X1 ⎩ dX 2 18 dt = X4 − 1

8

D. Fominykh et al.

⎧ ⎪ NW X3 (1 − X12 (X13 − X11 + 1)) − NS (X8 − 2X17 ⎪ ⎪ ⎪ ⎪ − X2 (1 − X17 ) + 3) − X4 = 0 ⎪ ⎪ ⎨ X1 + Ld (0, 25 − 0, 08X15 + X16 (0, 27 − 0, 09X15 )) ⎪ − L ∗ (0, 91 − 0, 47X2 ) + X4 X18 = 0 ⎪ ⎪ ⎪ ⎪ X 2 + (Ab + Ld )(1, 278 − 0, 66X4 + X1 (0, 668X4 − 1, 294)) − Nd (16X14 ⎪ ⎪ ⎩ 4 + X7 (X14 + 20X8 + 87) − X6 (X7 + 3X8 + 12) + X8 (4X14 + 116) + 518) + 1 = 0 (2) Similarly to [17], the presence of a nonzero solution of one of the Eqs. (1)–(2) is a necessary condition for the existence of an unstable state. As is known [19, 20], a sufficient condition for the chaotic of the system is the positive value of the senior Lyapunov exponent: 1 δi (t) λmax (x0 ) > 0, λi (x0 ) = lim ln t→∞ t δi (0) where i = 1, 2, … 18, δi (t) is the fundamental solution to the system (1) or (2) linearized in a neighborhood of x 0 . Obtaining Lyapunov exponents is analytically difficult. For this, the Benettin algorithm was implemented, which was realized in the DEREK-ODE v.3.0 application package.

3 The Procedure of Unstable States Prevention Based on the values of the variables at which the system goes into an unstable state, it is possible to develop and implement control actions for stabilization. For this, action plans pj ∈ {P}, j = 1, 2, … , N p must be identified, the implementation of which moves the system away from unstable states: (j)

pj : s(X1 , X2 , . . . , X18 ) → s ∗ (X1 + δ1 , X2 , (j) (j) + δ2 , . . . , X 18 + δ18 ) ∀i(ρ(s∗, s˜i ) > ρ(s, s˜i )), s˜i ∈ S˜ where ρ(si , sj ) is the metric that defines a distance between states si and sj defined in [17]:  n  (j) 2 (i) (ωi (Xk − Xk ) ), ρ(si , sj ) =

k=1 (j) s, s∗ ∈ S are possible system states, s˜ ∈ S˜ are unstable states, - Xk < δk < 1−Xk , k = 1, 2, … , 18, j = 1, 2, … , N p , i = 1, 2, … , M. Consider the procedure for preventing unstable states, taking the normalized indicators of the quality of welding via the Kawasaki robots with C40 controllers and Fronius welding equipment. The current state vector will look like this:

0, 09; 0, 74; 0, 18; 0, 59; 0, 71; 0, 56; 0, 62; 0, 78; 0, 47; s0 = 0, 39; 0, 32; 0, 17; 0, 56; 0, 94; 0, 61; 0, 63; 0, 94; 0, 92

The Task of Controlling Robotic Technological Complexes

9

The following state vectors correspond to the conditions (1), (2):

0, 54; 0, 15; 0, 60; 0, 74; 0, 38; 0, 20; 0, 48; 0, 12; 0, 47; s˜1 = 0, 39; 0, 74; 0, 55; 0, 68; 0, 28; 0, 87; 0, 83; 0, 96; 0, 73

0, 15; 0, 43; 0, 21; 0, 54; 0, 80; 0, 13; 0, 17; 0, 29; 0, 91; s˜2 = 0, 21; 0, 41; 0, 35; 0, 33; 0, 74; 0, 21; 0, 41; 0, 78; 0, 24

0, 31; 0, 65; 0, 15; 018; 0, 43; 0, 59; 0, 92; 0, 17; 0, 48; s˜3 = 0, 24; 0, 68; 0, 27; 0, 58; 92; 0, 42; 0, 37; 0, 34; 0, 69 The values of Lyapunov exponents under various initial conditions are shown in Table 1. As can be seen from the Table 1 under initial conditions X 1 = 0,54; X 2 = 0,15; X 3 = 0,6; X 5 = 0,38; X 6 = 0,2; X 7 = 0,48; X 8 = 0,12; X 11 = 0,74; X 12 = 0,55; X 13 = 0,68; X 14 = 0,28; X 15 = 0,87; X 16 = 0,83; X 17 = 0,96; X 18 = 0,73, the presence of a positive Lyapunov exponent λ1 = 1.306 was revealed, which indicates the chaotic of the system. This corresponds to the following values of variables and external factors: the average number of RTC operators for the period is 4 people; the average number of RTC stops per cycle is 9; RTC scheduled maintenance work - 45%; the average number of programmers for the period is 2 people; the average number of adjusters for the period is 3 people; the average number of quality control inspectors for the period is 1 person; the average voltage deviation of the welding arc is 4 V; the average current deviation on the feed unit motor is 2.5 A; the average deviation of the manipulator from the program path is 12 mm; the availability of the necessary technological documentation - 33%; the average deviation of the protective gas pressure is 1,8 MPa; the average deviation of the compressed air pressure is 1,2 MPa; production plan for a given period - 175 units; the number of beams welded in RTC - 350 pcs.; the number of beams accepted by the quality control department and sent to the assembly - 306 pcs.; the total length of defective joints for the period is 38 m; the estimated length of defective joints for the period is 14 m; the number of beams delivered from the 1st presentation is 297 pcs; the number of acts on non-conforming products for the period is 53. Table 1. Values of Lyapunov exponents λ1 = −0,01 λ1 = 0 λ1 = 1,306 λ1 = 0 λ1 = 0 λ2 = 0 λ2 = 0 λ2 = 0 λ2 = 0 λ2 = 0 λ3 = 0 λ3 = −0,01 λ3 = −0,17 λ3 = 0 λ3 = 0 X1

0,539

0,539

0,539

0,539

0,539

X2

0,131

0,143

0,149

0,160

0,172

X3

0,620

0,620

0,620

0,620

0,620

X4

0,738

0,738

0,738

0,738

0,738

X5

0,384

0,384

0,384

0,384

0,384

X6

0,201

0,201

0,201

0,201

0,201

(continued)

10

D. Fominykh et al. Table 1. (continued) λ1 = −0,01 λ1 = 0 λ1 = 1,306 λ1 = 0 λ1 = 0 λ2 = 0 λ2 = 0 λ2 = 0 λ2 = 0 λ2 = 0 λ3 = 0 λ3 = −0,01 λ3 = −0,17 λ3 = 0 λ3 = 0 X7

0,482

0,482

0,482

0,482

0,482

X8

0,121

0,121

0,121

0,121

0,121

X9

0,467

0,467

0,467

0,467

0,467

X 10 0,392

0,392

0,392

0,392

0,392

X 11 0,744

0,744

0,744

0,744

0,744

X 12 0,551

0,551

0,551

0,551

0,551

X 13 0,676

0,676

0,676

0,676

0,676

X 14 0,282

0,282

0,282

0,282

0,282

X 15 0,870

0,870

0,870

0,870

0,870

X 16 0,833

0,833

0,833

0,833

0,833

X 17 0,962

0,962

0,962

0,962

0,962

X 18 0,731

0,731

0,731

0,731

0,731

A control system for stabilization can be developed and implemented. Consider several possible action plans to prevent the system from falling into unstable state. The most effective action plans are shown in the Table 2. As can be seen from the Table 2, the implementation of the action plan p1 will most effectively prevent the onset of unstable states in the system, since after its implementation the distance to the closest chaotic state will be 1,535, while after the implementation of plans p1 and p3 this distance will be 1,432 and 1,339, respectively. Table 2. The action plans of prevention unstable states Plan Actions

Responsible

ρ(s0 , s˜1 ) ρ(s0 , s˜2 ) ρ(s0 , s˜3 )

p1

Technologist HR-manager RTC operator Mechanic

1,535

1. Check for technological documentation at workplaces 2. Hire an additional one RTC operator 3. Fine-tune the shielding gas and cutoff value daily 4. Install protective gas pressure regulators at the inlet of the RTC

1,743

2,304

(continued)

The Task of Controlling Robotic Technological Complexes

11

Table 2. (continued) ρ(s0 , s˜1 ) ρ(s0 , s˜2 ) ρ(s0 , s˜3 )

Plan Actions

Responsible

p2

1. Carry out an intermediate quality control of the weld 2. Measure the values of the welding current by the indicators of the power source 3. Carry out scheduled maintenance according to the schedule 4. Hire an additional one programmer

RTC operator 1,432 RTC operator Adjusters & programmers HR-manager

1,834

1,760

p3

1. Monitor torch nozzle condition after cleaning 2. Make monitoring welding current values using the RTMON function 3. Hire an additional one RTC operator 4. Periodically check the relevance of documentation

RTC operator Programmers HR-manager Technologist

1,329

1,908

2,3

4 Conclusions The article describes the task of controlling the welding process in the RTC in the risk of unstable conditions based on a previously developed model of system dynamics. An algorithm for identifying unstable states for the Lorenz and Nose-Hoover attractors is proposed and justified. A procedure for preventing unstable states is proposed. The solution to the problem is illustrated by the model example. The use of the considered models and algorithms will help prevent the unstable states of the RTC. The estimated effect for the production process from the implementation of developed software is presented in the Fig. 2. Henceforward, developed models and algorithms can be improved for identifying and preventing unstable states during the technological process by using other types of chaos.

12

D. Fominykh et al.

Fig. 2. Estimated effect from the implementation of developed software

References 1. Guillo, M., Dubourg, L.: Impact & improvement of tool deviation in friction stir welding: weld quality & real-time compensation on an industrial robot. Robot. Comput.-Integr. Manuf. 39, 22–31 (2016) 2. Shultz, E.F., Cole, E.G., Smith, C.B., Zinn, M.R., Ferrier, N.J., Pfefferkorn, F.E.: Effect of compliance and travel angle on friction stir welding with gaps. J. Manuf. Sci. Eng. Trans. ASME 132(4), 0410101–0410109 (2010) 3. Wu, J., Zhang, R., Yang, G.: Design and experiment verification of a new heavy friction-stirweld robot for large-scale complex surface structures. Ind. Robot 42(4), 332–338 (2015) 4. Dinham, M., Fang, G.: Autonomous weld seam identification and localisation using eye-inhand stereo vision for robotic arc welding. Robot. Comput.-Integr. Manuf. 29(5), 288–301 (2013) 5. Shen, H.Y., Wu, J., Lin, T., Chen, S.B.: Arc welding robot system with seam tracking and weld pool control based on passive vision. Int. J. Manuf. Technol. 39(7–8), 669–678 (2008) 6. Miller, M., Mi, B., Kita, A., Ume, I.C.: Development of automated real-time data acquisition system for robotic weld quality monitoring. Mechatronics 12(9–10), 1259–1269 (2002) 7. Ryberg, A., Ericsson, M., Christiansson, A.K., Eriksson, K., Nilsson, J., Larsson, M.: Stereo vision for path correction in off-line programmed robot welding. In: Proceedings of the IEEE International Conference on Industrial Technology, pp. 1700–1705 (2010) 8. Micallef, K., Fang, G., Dinham, M.: Automatic seam detection and path planning in robotic welding. Lecture Notes in Electrical Engineering, LNEE, vol. 88, pp. 23–32 (2011) 9. Agapakis, J.E., Katz, J.M., Friedman, J.M., Epstein, G.N.: Vision-aided robotic welding. An approach and a flexible implementation. Int. J. Robot. Res. 9(5), 17–34 (1990) 10. Ahmad, S., Luo, S.: Coordinated motion control of multiple robotic devices for welding and redundancy coordination through constrained optimization in Cartesian space. IEEE Trans. Robot. Autom. 5(4), 409–417 (1989) 11. Liu, Y.K., Zhang, Y.M.: Toward welding robot with human knowledge: a remotely-controlled approach. IEEE Trans. Autom. Sci. Eng. 12(2), 769–774 (2015) 12. Kim, K.Y., Kim, D.W., Nnaji, B.O.: Robot arc welding task sequencing using genetic algorithms. IIE Trans. (Inst. Ind. Eng.) 34(10), 865–880 (2002)

The Task of Controlling Robotic Technological Complexes

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13. Stenberg, T., Barsoum, Z., Åstrand, E., Öberg, A.E., Schneider, C., Hedegård, J.: Quality control and assurance in fabrication of welded structures subjected to fatigue loading. Weld. World 61(5), 1003–1015 (2017) 14. Sumesh, A., Rameshkumar, K., Raja, A., Mohandas, K., Santhakumari, A., Shyambabu, R.: Establishing correlation between current and voltage signatures of the arc and weld defects in GMAW process. Arab. J. Sci. Eng. 42(11), 4649–4665 (2017) 15. Ericsson, M., Nylén, P.: A look at the optimization of robot welding speed based on process modeling. Weld. J. (Miami, Fla) 86(8), 238 (2007) 16. Leonardo, B.Q., Steffens, C.R., da Silva Filho, S.C., Mór, J.L., Hüttner, V., do Amaral Leivas, E., Da Rosa, V.S., da Costa Botelho, S.S.: Vision-based system for welding groove measurements for robotic welding applications. In: Proceedings - IEEE International Conference on Robotics and Automation, vol. 2016-June, pp. 5650–5655 (2016) 17. Fominykh, D.S., Kushnikov, V.A., Rezchikov, A.F.: Prevention unstable conditions in the welding process via robotic technological complexes. In: MATEC Web of Conferences, vol. 224, p. 01045 (2018) 18. Hoover, W.G.: Remark on some simple chaotic flows. Phys. Rev. E 51, 759–760 (1995) 19. Moon, F.C.: Chaotic Vibrations. Wiley, New York (1987). 309 pp. 20. Andrievsky, B., Fradkov, A.: Autom. Remote Control 4, 5 (2003) 21. Tikhonova, O.M., Kushnikov, V.A., Fominykh, D.S. with co-authors: Mathematical model for prediction of efficiency indicators of educational activity in high school. In: Proceedings of International Conference on Information Technologies in Business and Industry, Tomsk Polytechnic University, Journal of Physics Conference Series, vol. 1015, no. UNSP 032143, Tomsk (2018)

Longitudinal Waves in Two Coaxial Elastic Shells with Hard Cubic Nonlinearity and Filled with a Viscous Incompressible Fluid Lev Mogilevich1

and Sergey Ivanov2(B)

1

Yuri Gagarin State Technical University of Saratov, 77 Politechnicheskaya street, Saratov, Russia 410054 [email protected] 2 Saratov State University, 83 Astrakhanskaya Street, Saratov, Russia 410012 [email protected]

Abstract. This article investigates the influence of fluid motion on the amplitude and velocity of longitudinal deformation waves in physically nonlinear coaxial cylindrical elastic shells. The shells contain a viscous incompressible fluid as between them, as in the inner one. The model of deformation waves (used to transmit the information) is studied by using the numerical method. This work is carried out by using the difference scheme similar to the Crank-Nicholson one. The numerical experiment showed that in the absence of the fluid in the inner shell the velocity and amplitude in the shells do not change. The movement of the waves takes place in the positive direction. This means that the waves’ velocity is supersonic. It is equivalent to the behavior of the exact solutions. Therefore, the difference scheme and the system of generalized modified Korteweg-de Vries equations are adequate. The inertia of the fluid motion in the inner shell leads to a decrease in the strain wave velocity, while the influence of the fluid viscosity in the inner shell leads to a decrease in the wave amplitudes. Keywords: Nonlinear waves · Elastic cylindrical shells · Viscous incompressible fluid · Crank-Nicholson difference scheme

1

Stating the Problem

The study of the interaction of the elastic shells with viscous incompressible fluid, taking into account the wave phenomena and the influence of local terms of fluid movement inertia, was carried out in [1]. The study of the wave phenomena for coaxial elastic shells with a viscous incompressible fluid between them, was carried out in [2]. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2021  O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 14–26, 2021. https://doi.org/10.1007/978-3-030-65283-8_2

Longitudinal Waves in Two Coaxial Elastic Shells with Fluid

15

In this article, mathematical models of the wave process in infinitely long physically nonlinear coaxial cylindrical elastic shells are obtained by the perturbation method for a small parameter of the problem. They differ from the known ones due to the presence of the incompressible viscous fluid both between the shells and also in the inner shell. These models are considered on the basis of the coupled hydroelasticity problems, which are described by the dynamics equations of the shells and the incompressible viscous fluid with corresponding boundary conditions. Let us consider two infinitely long axisymmetric coaxial elastic cylindrical shells.

Fig. 1. Elastic infinitely long coaxial cylindrical shells

Let us denote: R1 is the radius of the inner surface of the outer shell; R2 is the radius of the outer surface of the inner shell; R3 is the radius of the inner surface of the inner shell; δ is the thickness of the liquid layer in the annular section of (i) the pipe; R(i) are the radii of the median surfaces; h0 are the shells’ thicknesses; (i = 1 for the outer shell, i = 2 for the inner one). In this case, the following (1)

h

(2)

h

(2)

h

relations are held: R1 = R(1) − 02 ; R2 = R(2) + 02 ; R3 = R(2) − 02 The deformation plasticity theory of A. A. Ilyushin [3,4] connects the components of the stress tensor σx , σΘ with the components of the strain tensor εx , εΘ and the square of the strain intensity εu . This connection is called hard cubic nonlinearity [5,6].  m (i) 2  E  (i) (i) ε 1 + ; ε + μ ε 0 x Θ 1 − μ20 E u   2 E  (i) m = εΘ + μ0 εx(i) 1 + εu(i) ; 2 1 − μ0 E

σx(i) = (i)

σΘ

(1)

16

L. Mogilevich and S. Ivanov

  4   (i) 2 (i) 2 (i) − μ2 εx(i) εΘ ; μ1 εx + εΘ 9 μ0 (2μ0 − 1) 2μ0 (2μ0 − 1) μ1 = 1 + ; 2 ; μ2 = 1 − 2 (1 − μ0 ) (1 − μ0 ) 2

εu(i) =

where E is Young’s modulus; m is the constant of the material, defined from the experiments on tension or compression; μ0 is the Poisson’s ratio of the shell material. We write down the relationship of the deformations’ components with elastic displacements in the form of [7] εx(i)

1 ∂U (i) + = ∂x 2



∂W (i) ∂x

2 −z

∂ 2 W (i) (i) W (i) ; ε = − Θ ∂x2 R(i)

(2)

Where x is the longitudinal  coordinate along  the median surface; z is the normal −

coordinate in the shell

(i)

h0 2

(i)

h0 2

≤z≤

; U (i) is the longitudinal elastic dis-

placement of the shell along the x axis; W (i) is the deflection of the shell positive to the center of curvature. We write down the square of the strain intensity in the form of:  (i) 2 εu

=

4 9



μ1

(i) + μ2 W R(i)

∂U (i) ∂x



+

∂U (i) ∂x

1 2

+



1 2

∂W (i) ∂x



2

∂W (i) ∂x

−

2

2 W (i) z ∂ ∂x 2

−



2

2 W (i) z ∂ ∂x 2

+ 

2

W (i) R(i) 2

(3)

We determine the forces in the middle surface of the shell and the moment by using the following formulas

(i)

Nx =

(i) h0 2



(i) h − 02

(i)

(i)

σx dz; NΘ =

(i) h0 2



(i) h − 02

(i)

(i) h0 2



(i)

σΘ dz; Mx =

(i)

σx zdz.

(4)

(i) h − 02

We write down the equations of dynamics for the shells similarly to [2]



(i) ∂ 2 U (i) (i) ∂Nx(i) ˜x (i − 1) ∂x = ρ0 h0 ∂t2 − qx + q R(i)   2 (i) (i) (i) (i) ∂ Mx ∂ ∂W 1 + + N N x 2 ∂x ∂x ∂x R(i) Θ (i) 2 W (i) = ρ0 h0 ∂ ∂t − [(−1) q + q ˜ 2 n n (i − 1)]R(i)

; (5)

where t is time; r, x are the cylindrical coordinates; ρ0 is the density of the (i) shell material; qx , qn are the stresses from the side of the liquid inside the annular section q˜x , q˜n – the stresses from the side of the liquid inside the inner shell. Substituting (1)–(4) into (5), we obtain the resolving equations as in [2].

Longitudinal Waves in Two Coaxial Elastic Shells with Fluid

1.1

17

The Asymptotic Method for Studying the Equations of the Shells Filled with the Fluid

For the wave problems, the shell is considered infinite. For the longitudinal waves, dimensionless variables and dimensionless parameters are introduced in the shell. We take for the characteristic length l - the wavelength, and um , wm - the characteristic values of elastic displacements, when W (i) = wm u3 , U (i) = um u1 , x∗ = xl , t∗ = (i)

(i)

wm =

(i) h0 ,

(i)

um =

h0 l . R(i)

c0 l t,

r∗ =

r , R(i)

(6)

 E c0 = ρ(1−μ0 ) is the propagation velocity of longitudinal elastic waves in the shell. Let us put (i)

h0 R(i) um R(i) l h(i) 0

= ε  1,

= O (1) ,

mε E

R(i) l2

2

= O (ε) ,

= O (1) ,

(i) 2 h0 l2

wm (i) = O (1) , h0 (i) 2 (i) 2 h = R0(i) 2 · Rl2

(7)

= ε3

where ε is the small parameter of the problem. To solve the system of resolving equations we apply the two-scale asymptotic expansions. We introduce the independent variables in the form of: (8) ξ = x∗ − ct∗ , τ = εt∗  2 where τ is the slow time; c = 1 − μ0 is the dimensionless wave velocity. We represent the dependent variables as an asymptotic expansion (i)

(i)

(i)

(i)

(i)

(i)

u1 = u10 + εu11 + ..., u3 = u30 + εu31 + ...

(9)

Similarly to [1,2], we obtain the system of resolving equations for the first terms of the asymptotic expansions    (i) (i) 2 2 (i)   ∂ 2 u10 m  u m 2 ∂u ∂ u10 10 + 2 1 − μ20 μ1 + μ2 μ0 + μ1 μ20 ∂ξ∂τ Eε l ∂ξ ∂2ξ +

(10)



(i)

1 − μ20 ∂ 4 u10 1 l2 qx(i) =−  4 (i) 2 2 2 ∂ ξ 2 1 − μ0 εum ρ0 h0 c0  i−1 R (−1) qn + q˜n (i − 1) . + q˜x (i − 1) − μ0 l ∂ξ

1 R2 μ20 ε l2

∂u

(i)

The obtained equations are generalized MKdV equation for ∂ξ10 . In the absence of the fluid, the right side of the equation is zero and MKdV is obtained. It is necessary to determine the right side by solving the equations of hydrodynamics.

18

1.2

L. Mogilevich and S. Ivanov

The Study of the Stresses Acting on the Shell from the Side of the Fluid Inside

In the case of the axisymmetric flow the equation of motion of the incompressible viscous fluid and the continuity equation in the cylindrical coordinate system (r, Θ, x) are written down in the form of [8]: ∂Vr ∂Vr ∂t + Vr ∂r + ∂Vx ∂Vx ∂t + Vr ∂r

+





∂ 2 Vr ∂ 2 Vr Vr 1 ∂Vr 2 + r ∂r + ∂x2 − r 2 ∂r   2 ∂ Vx ∂ 2 Vx 1 ∂p 1 ∂Vx x , Vx ∂V ∂x + ρ ∂x = ν ∂r 2 + r ∂r + ∂x2 ∂Vr Vr ∂Vx ∂t + r + ∂x = 0.

r Vx ∂V ∂x +

1 ∂p ρ ∂r

=ν

, (11)

The conditions of fluid adhesion at the boundary of the shells according to Fig. 1 at r = Ri − W (i) are satisfied in the form of [8] ∂U (i) ∂W (i) Vr = − . (12) ∂t ∂t and the conditions of velocity limitation are satisfied at r = 0. Here Vr , Vx are the projections on the axis of the cylindrical coordinate system of the velocity vector; p is the pressure in the liquid; ρ is the density of the liquid; ν is the kinematic viscosity coefficient. The stresses from the side of the liquid layer are determined by the formulas Vx =



      n(i) , n ¯ r + Prx cos −¯ n(i) , ¯i  qn = Prr cos −¯ r=Ri −W (i) 

      qx = − Prx cos −¯ n(i) , n ¯ r + Pxx cos −¯ n(i) , ¯i  r=Ri −W (i)   ∂V ∂Vr r x x ; P Prr = −p + 2ρν ∂V ; P = ρν + = −p + 2ρν ∂V rx xx ∂r ∂r ∂x ∂x .

(13)

¯ Θ , ¯i are the Here n ¯ is the normal to the middle surface of the i-th shell, n ¯r , n unit vectors (r, Θ, x) of the cylindrical coordinate system, the center of which is located on the geometric axis. If we carry the stress on the unperturbed   n(i) , n ¯ r = 1, surface of the shell, then we can also assume −¯ n = n ¯ r , cos −¯    cos −¯ n(i) , ¯i = 0. The stresses q˜x , q˜n from the side of the fluid, that is in the inner shell, are determined by the same formulas (13) in which the density of the fluid is ρ˜, the kinematic viscosity coefficient is ν˜. The Ring Section. We introduce the dimensionless variables and parameters Vr = wm cl0 vr ; Vx = wm cδ0 vx ; r = R2 + δr∗ ; p = ρνc0δR3i wm P + p0 ; ψ = Rδ2 = o (1) ; λ = wδm = o (1) ; wRm2 = wδm Rδ2 = λψ; 1 1 wm wm δ Ri δ δ Ri 2 2 l = δ Ri l = λψε ; l = Ri l = ψε .

(14)

Longitudinal Waves in Two Coaxial Elastic Shells with Fluid

19

We obtain the equations of hydrodynamics from (11) in the introduced dimensionless variables. According to (12), we obtain the boundary conditions. Assuming now δl = 0, Rδ2 = 0 (the zeroth approximation in δl is the hydrodynamic theory of lubrication [8]), similar to [2], and decomposing the pressure and velocity components in powers of a small parameter λ P = P 0 + λP 1 + ..., vx = vx0 + λvx1 + ..., vx = vr0 + λvr1 + ...,

(15)

we obtain the equations for the first terms of the expansion 0 0 2 0 0 0 ∂P 0 ˜ ∂vx + ∂P = ∂ vx ; ∂vr + ∂vx = 0; Re ˜ = δ δc0 = 0; Re ∂r∗ ∂t∗ ∂x∗ ∂x∗ l ν ∂r∗ 2 ∂r∗ and the boundary conditions

(16)

(1)

∂u3 ; vx0 = 0; where r∗ = 1 ∂t∗ (2) ∂u vr0 = − 3∗ ; vx0 = 0; where r∗ = 0 ∂t vr0 = −

(17)

We now define the stresses from the fluid on the shells in these variables. The ˜ 80% or a part of virtual memory > 20%. In most cases [3, 4], rules are created in pairs: for scaling up and down. At creating rules, it should be taken into account the cloud application hosting limitations: to make sure that the number and size of VMs are within the allowed range, do not use transitions that are not in the state graph of the ClAPP infrastructure of the university DEE, etc. All this leads to a complication of the conditions of the rules Xr .

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Start

Data input

e← Reaс(CPU, RAM, t, tb)

e=null 1 e← Proac(xt+h, h, C, t, tb) 0 Output e

End

Fig. 1. Decision making algorithm for ClAPP scaling of the university DEE

Carrying out reactive scaling, it is necessary to take into account the possibility of oscillations in the number of VMs. In order to avoid this undesirable effect, it should be carefully selected the limiting values of the scaling rules. In order the method not to issue scaling commands in response to unit load peaks, in the conditions of the rules Xr , there are used averaged indices for the last few time steps. For the same purpose, some varieties of the method issue a scaling command only if the condition Xr is met sequentially in several steps. In a set of rules R, we can add rules with conditions that are executed at a certain point in time, without reference to the level of system resources use. Such rules make it possible to scale on the eve of events that increase the ClAPP workload of the university DEE. These are, for example, certification periods and a session. To minimize costs, modifications to the rules can be made taking into account the hosting pricing policy. For example, in case of time-based billing, it makes no sense to scale ClAPP of the university DEE down within an hour after the up-scale operation. The main advantages of using the reactive scaling method with respect to the ClAPP of the university DEE with periodic load peaks is the simplicity of the method, its high speed and the ability to start operation without collecting additional information about the infrastructure. The limitations of the method include the reactive nature, which is displayed in its name. The scaling command can only be given when a lack of resources is detected, and when new resources are allocated the operation of the cloud application

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can occur in an emergency mode. Also, a complex procedure  is to set threshold values in the rules (r), as well as the selection of a scaling action S  , N . Let note that due to the large number of combinations the choice of optimal solution is a non-trivial task. The ability to use the method without additional knowledge about the ClAPP operation of the university DEE in a specific infrastructure allows the use of the described method as a reserve for more complex scaling methods. If it is impossible to make a decision about scaling using your own resources, you can use the results of the reactive scaling method. In case if ClAPP of the university DEE has a state Si , Ni , Pi  from the state graph of the cloud application infrastructure, there are possible d (i) scaling variants, where d – a function that returns the degree of the graph vertex. Let denote the set of possible scaling variants as Ei . In order to select the optimal scaling variant, we calculate the value of the criterion function G(e), e ∈ Ei as follows: G(e) = Pinf + k · Pl ,

(1)

where Pinf – the cost of maintaining the ClAPP infrastructure of the university DEE within the next tr minutes, Pl – the cost of losing one user, k – the number of users lost due to the excessive load of the cloud application during the following tr , e – the  arc of the  state   graph of the ClAPP infrastructure of the university DEE - Si , Ni , Pi , Sj , Nj , Pj , tij . The cost of maintaining the ClAPP infrastructure of the university DEE is determined as the sum of the cost of maintaining up to and after scaling. Each of the terms is calculated as the value of the tariff per minute P on the number of minutes tr − tij and tij :   Pinf = Pj · tij + Pj · tr − tij . (2) The number of users lost due to the excessive ClAPP workload of the university DEE is calculated as follows: k=

tr 

vt · ql (t),

(3)

t=1

where vt – the number of ClAPP users of the university DEE over the period of time (t; t + 1), ql (t) – the probability that the user will stop using ClAPP of the university DEE. Substituting expressions (2) and (3) in (1) we obtain a more detailed expression for calculating the criterion function: tr    G(e) = Pj · tij + Pj · tr − tij + Pl · v · ql (t).

(4)

t=1

To determine the probability of user loss ql , we use the probability distribution function, which represents the dependence of the probability of user loss on the time it takes to complete a network request F(τ ). The probability of user loss increases with the time it takes to wait for a response from the ClAPP of the university DEE. Studies [4–6] show that the number of users begins to decrease when τ > 2 s. In [5] there is shown the distribution function of the probability of user loss.

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Let denote the random variable corresponding to the time of executing one network request of ClAPP of the university DEE as R. Statistical characteristics of R depend on the ClAPP workload at a particular moment of time t and on the state of the ClAPP infrastructure. Let determine the probability of user loss through the mathematical expectation of the network query execution time M (R) :    (5) ql (t) = F M Rj,τ . In case if tij ≤ h and taking into account (5), expression (3) can be represented as follows: k=

tij 

tr h            vt · F M Rj,τ + vt · F M Rj,τ + vt · F M Rj,τ . t=tij +1

t=1

(6)

t=h+1

Considering that the prediction of the number of network requests is made in h steps, it is necessary to determine the values vt and R for the time interval [h; tr ). We use the prediction at the moment of time h for this time period, then the last term in (6) can be represented by: k=

tij 

h           vt · F M Rj,τ + vt · F M Rj,τ + (tr − h) · vh · F M Rj,τ . (7) t=tij +1

t=1

Therefore, expression (4) can be detailed using relation (7):    G(e)tij ≤ h = Pj · tij + Pj · tr − tij ⎛ t ⎞ ij     vt · F M Rj,τ ⎜ ⎟ ⎜ ⎟ + Pl · ⎜ t=1 h .   ⎟      ⎝ ⎠ vt · F M Rj,τ + (tr − h) · vh · F M Rj,τ +

(8)

t=tij +1

For the case when tij > h similar transformations lead to such results: k=

h 

             vt · F M Rj,τ + tij − h · vh · F M Rj,τ + tr − tij · vh · F M Rj,τ .

t=1

   G(e)tij > h = Pj · tij + Pj · tr − tij ⎞ ⎛ h     v · F M Rj,τ ⎠. + Pl · ⎝ t=1 t           + tij − h · vh · F M Rj,h + tr − tij · vh · F M Rj,h

(9)

(10)

Therefore, on the basis of the prediction of the number of ClAPP users of the university DEE and the average execution time of the network request, it is possible to calculate the value of the criterion function for all possible ways to scale e ∈ Ei of ClAPP at a

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time t. The scaling method with the lowest value of the criterion function is used as the selected scaling variant. The formal record of the scaling rule in DSS has the following form: if

t > tb then

   perform scaling emin G emin = min G(e), if

(11)

emin , S  = Si or emin , N = 0 then tb ← t + t

where t – current moment of time, tb – point in time at which the stabilization period ends after the last scaling operation, t – the period of rest time after ClAPP scaling of the university DEE during which new scaling operations are not carried out. In order to determine the value of the criterion function of the ClAPP scaling efficiency of the university DEE, it is necessary to have information about the number of ClAPP users per minute and about the average time of the network request. Using the DSS computational core, we will create a prediction of these values based on the prediction of the number of network requests and statistical information on the ClAPP operation of the university DEE [11, 12]. The ratio of the number of network requests to the number of unique users with a large number of users is a constant value for a particular ClAPP. Therefore, the prediction of the number of users vt can be calculated as follows [13]: vt = xt · ψu ,

(12)

where xt – prediction of the number of network requests for a period of time t, ψu – coefficient showing the frequency of requests from one user per unit of time for a specific ClAPP. The value of the coefficient ψu is determined by periodical collecting statistics on the number of unique users and the number of network requests during ClAPP operation of the university DEE. In order to predict the execution time of a network request based on the number of network requests per unit of time, it is necessary to have information about the allocated computing power. Such information is contained in the description of ClAPP infrastructure of the university DEE S, N , P, namely, the size of the VM S and their number N .. Let present possible combinations of variable values x, S and N using a hypercube of cloud application states [9, 10, 14]. The number of measurements of such a hypercube is three; an array is stored in the cells, each element of which represents the execution time of a separate network request. The cell also stores the average value of the array elements. Such a representation will speed up the calculations. To reduce the number of hypercube cells and to facilitate prediction [9, 14, 15], it is necessary to discretize the variable x, dividing the range of its values to 3–10 segments. The advantage of using a hypercube for storing data on the average time of a network request is the possibility of organizing data in such a way when it becomes possible to use information from neighboring cells in case of the absence of information in the cell describing the ClAPP state.

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In case if the increase in the execution time of the network request changes linearly at moving along one of the dimensions of the hypercube, it is possible to introduce into DSS an algorithm for determining the execution time of the network request. This algorithm allows to supplement the information about empty hypercube cells using linear interpolation. Step 1. Start of the work. Step 2. Entering information about the dimension of the hypercube of ClAPP states (kS , kN , kx ), the set of values of its cells (C) and the target state (iS, iN , ix), as well as about the search depth  z. Step 3. If CiS,iN  the value – go to the step 4, otherwise – step 5.  ,ix has Step 4. Find CiS,iN ,ix , go to step 13. Step 5. For j from 1 to z perform  the steps 6 – 11.   Step 6. If there is CiS−j,iN ,ix and has the value and if there CiS+j,iN ,ix and has the value – go tothe step 7, otherwise – go tothe step 8. Step 7. Find CiS−j,iN    ,ix + CiS+j,iN ,ix /2 , go to step 13. Step 8. If there is CiS,iN −j,ix and has the value and if there CiS,iN +j,ix and has the value – go tothe step 9, otherwise – go tostep 10. Step 9. Find CiS,iN  +j,ix /2 , go to step 13.  −j,ix + CiS,iN Step 10. If there is CiS,iN ,ix−j and has the value and if there d has the value – go to the step 11, otherwise    – go to step 5. Step 11. Find CiS,iN ,ix−j + CiS,iN ,ix+j /2 , go to step 13. Step 12. Find the undefined result. Step 13. End. A diagram of the algorithm for determining the execution time of a network request is shown on Fig. 2. By introducing a variable z, the algorithm allows prediction based on hypercube cells, the values of which are undefined. For clarity of the operation of the algorithm, the main variables are written in the corresponding blocks of the block diagram, respectively, on Figs. 1 and 2. Algorithms on Fig. 1 and Fig. 2 allow forming a classification criterion for the current operating mode of ClAPP. The procedure for forming the criterion is based on the Paige-Hinckley method and the calendar of events, which are associated with the operation of ClAPP. The ClAPP performance criterion was determined on the basis of information about the execution time of a network request, the algorithm on Fig. 2, the number of users and the cost of maintaining the infrastructure. The proposed criteria made it possible to compare and combine dissimilar metrics of ClAPP operation of the universities. Using the obtained criteria, we can evaluate the efficiency of ClAPP functioning when using different scaling strategies, as well as compare the feasibility of using different scaling methods.

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Start Data input

CiS, iN, ix exists 1 Output CiS, iN, ix 0 For j from 1 to z Output Null

CiS+j, iN, ix Exists? 1 OutPut (CiS-j, iN, ix + CiS+j, iN, ix)/2 0

0

CiS, iN+j, ix Exists? 1 Output (CiS, iN-j, ix + CiS, iN+j, ix)/2

0

CiS, iN, ix+j Exists? 1 Output (CiS, iN, ix-j + CiS, iN, ix+j)/2

End

Fig. 2. Algorithm for determining the execution time of a network request in ClAPP of the university DEE

The model and decision making algorithms described in the article for ClAPP scaling of the university DEE, as well as determining the network request execution time were implemented in a software product – a decision support system on the need to scale ClAPP of the university DEE. The DSS interface is shown on Fig. 3. In the computational core of adaptive DSS, a criterion function is used to analyze the variants for ClAPP scaling of the university DEE. This allows to get an economic assessment of the ClAPP effectiveness, which is based on the cost of maintaining the ClAPP infrastructure. Moodle systems, Blue Jeans Web conferences, the http://ideone. com portal and etc. were analyzed as cloud applications for learning programming languages. At the same time, the work was organized in heterogeneous collaboration groups. Students also had the opportunity to collaborate on Google Docs in order to create group presentations and reports on thematic projects. During the quarantine period, and the increase in the load on cloud services and applications of distance learning systems of the universities, there was made a comparison of the work offered by DSS for ClAPP scaling (based on the European University (Ukraine), Yessenov University and Abai University (Kazakhstan)) with a CloudMonix automation system.

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Fig. 3. The DSS interface on ClAPP scaling of the university DEE

Since the purpose of the work was to design the DSS computational core for scaling cloud applications of the university’s digital educational environment (DEE CA of the university), during the experiments, it was only required to qualitatively show the convergence and correctness of the algorithms shown on Fig. 1 and 2. In order to evaluate the algorithms in the DSS, it was proposed to implement the following approach: 1. For test CAs, the input data, the DEE CA configuration and the corresponding operating time were randomly selected. Test CAs were launched with a different number of nodes in the university’s DEE. Then, in the cycle, the input parameters of the problems, solved using the CAs, were randomly selected. These parameters, together with the history of previous launches, were fed to the input of the algorithms, Fig. 1 and 2. After each such request, the algorithms returned the DEE configuration and the time parameters for the execution of network requests to the DEE CA of the university. These values were saved in the history of DSS launches and were used for subsequent runs of the algorithm and decision making on scaling the university’s DEE cloud application. It is shown that the developed DSS for ClAPP scaling can increase the efficiency of the cloud application by 12–15%.

5 Conclusions Therefore, on the basis of information about the state of the cloud application of the university’s digital educational environment (DEE) there was formed an algorithm based on a set of reactive scaling rules and effectiveness assessment. The proposed algorithm allows making decisions on cloud application scaling of the university DEE. There was developed a model of the criterion function for the analysis of scaling variants, which allows to obtain an economic assessment of efficiency. This assessment is based on the cost of maintaining the cloud application infrastructure, as well as an assessment of the number of users who are forced to use the cloud application due to its overload. The

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developed algorithm can be used as a composite information technology for an adaptive decision support system for cloud applications scaling not only for universities, but also for other informatization objects. Therefore, the scientific novelty of the work lies in the improvement of the decision making method for ClAPP scaling. The improved method, in contrast to the existing ones, is based on a combination of reactive and advanced predictive approaches, taking into account data on possible peaks of ClAPP load. The proposed approach increases the capacity and efficiency of many ClAPP scaling solutions. For the first time, there was developed an adaptive decision support system for ClAPP scaling. This system provides analysis of information about the ClAPP state and implements an improved method for decision making on its scaling, which can improve the efficiency of the ClAPP operation.

References 1. Yang, S., Huang, Y.: Teaching application of computer multimedia cloud sharing technology in hand-painted performance course in colleges and universities. In: International Conference on Education Innovation and Social Science, ICEISS. Atlantis Press (2017) 2. Liu, S., Zeng, W., Li, Y.: Study on the preliminary construction of the cloud of mental health education in Chinese colleges and universities. In: 2016 International Conference on Public Management. Atlantis Press (2016) 3. Lorido-Botran, T.: Auto-scaling techniques for elastic applications in cloud environments. In: Lorido-Botran, T., Miguel-Alonso, J., Lozano, J.A. (eds.) Department of Computer Architecture and Technology, University of Basque Country, Tech. Rep., EHU-KAT-IK-09, vol. 12 (2012) 4. RightScale Cloud Management. http://www.rightscale.com/ 5. How a Slow Website Impacts Your Visitors and Sales. http://www.peer1.com/knowledgebase/ how-slow-website-impacts-your-visitors-and-sales 6. Nah, F.F.H.: A study on tolerable waiting time: how long are web users willing to wait? Behav. Inf. Technol. 23(3), 153–163 (2004) 7. How Loading Time Affects Your Bottom Line. https://blog.kissmetrics.com/loading-time/ 8. Menasce, D.: Load testing of web sites. Internet Comput. 6(4), 70–74 (2002) 9. Tamimi, A.A., Dawood, R., Sadaqa, L.: Disaster recovery techniques in cloud computing. In: 2019 IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology, JEEIT, pp. 845–850. IEEE (2019) 10. Duncan, B., Happe, A., Bratterud, A., Sen, J.: Cloud cyber security: finding an effective approach with unikernels. Security in Computing and Communications, vol. 31. IntechOpen, London (2017) 11. Akinsanya, O.O., Papadaki, M., Sun, L.: Current cybersecurity maturity models: how effective in healthcare cloud? In: CERC, pp. 211–222 (2019) 12. Srinivasan, S., Raja, K.: An advanced dynamic authentic security method for cloud computing. In: Cyber Security, pp. 143–152. Springer, Singapore (2018) 13. MacLennan, J., Tang, Z., Crivat, B.: Data mining with Microsoft SQL server 2008 (2008) 14. Savchuk, T.O., Kozachuk, A.V.: Viznachennya dotsIlnostI vikoristannya bagatovimIrnogo pIdhodu do prognozuvannya stanu tehnogenno. VimIryuvalna ta obchislyuvalna tehnIka v tehnologIchnih protsesah. Hmelnitskiy 2(47), 179–182 (2014) 15. Lakhno, V.A., Malyukov, V.P., Satzhanov, B., Tabylov, A., Osypova, T.Yu., Matus, Yu.V.: The model to finance the cyber security of the port information system. Int. J. Adv. Trends Comput. Sci. Eng. 9(3), 2575–2581 (2020)

Application of a Combined Multi-Port Reflectometer to Precise Distance Measuring Peter L’vov1 , Artem Nikolaenko2 , Alexey L’vov2(B) and Oleg Balaban2

, Sergey Ivzhenko2

,

1 Engels Experimental Design Bureau «Signal» named after A.I. Glukharev, Engels,

Russian Federation [email protected] 2 Yuri Gagarin State Technical University of Saratov, Saratov, Russian Federation [email protected], [email protected], [email protected], [email protected]

Abstract. The paper introduces a novel microwave non-contacting gauge for distance measuring based on a combined multi-port reflectometer (CMPR). The proposed measuring technique allows one to monitor hot surfaces, e.g. molten metal. The methods for CMPR calibration, measuring distance to a plane target surface and refinement of reference signal frequency are described and their advantages are considered. It is shown that the proposed measuring device enables to provide precise monitoring (up to 0.01 mm) for metallurgical works and other applications. Computer simulation results confirming the efficiency of proposed techniques are also presented in this paper. Taking into account the low cost electronic equipment needed for CMPR implementation, the authors put forward an idea of its use for design and development of relatively inexpensive meter for the flat surface displacement with sub-millimeter accuracy. Keywords: Combined multi-port reflectometer · Microwave distance meter · Calibration technique · Calibration standards · Microwave frequency refinement · Measurement accuracy · Voltage control oscillator

1 Introduction In 1972 G.F. Engen and C. Hoer proposed six-port reflectometer (SPR) for measuring a complex reflection coefficient of a microwave load [1]. The main idea of using a multiport reflectometer (MPR) was to create a low-cost alternative for an expensive vector voltmeter, which is based on complex frequency scaling and automatic gain control circuits. The SPR is a passive linear microwave device with several ports. One of its ports is used to connect a microwave generator and one is for a microwave load under test. Four other ports are used for connecting power meters (detectors having square-law transfer function) to the reflectometer. The considered approach of using SPR seemed to be very promising, and a variety of different MPR constructions was proposed and studied by many researchers in the past over 40 years (e.g. [2–5, 11–15]). The papers © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 61–75, 2021. https://doi.org/10.1007/978-3-030-65283-8_6

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introduced new constructions, signal processing techniques and calibration routines for a corresponding multi-port-based application. However, the research confronted with several difficult challenges, namely: the solution for a set of quadratic MPR equations often turns to be unstable resulting in a steady growth of measurement errors; the precise calibration routine of an SPR is complex and demands several (no less than 4) precise calibration standards (microwave loads), which reproduce precisely complex reflection coefficients in the entire measurement frequency range [6–13]. To ensure solution stability the researchers increased the complexity of SPR designs using hybrid directional couplers, phase shifters, delay circuits, etc., thus resulting in a considerable cost increase for a meter. Unfortunately, this was the only way adopted for solving calibration issues, and it included usage of high-precision standard calibration loads. As a result, precise MPR-based meters were implemented in a few highly-equipped laboratories (e.g. [12]) and an overall cost of these meters exceeds the cost of a commercial automatic network analyzers (ANA) based on a vector voltmeter [13]. The idea of creating a commercial ANA based on a SPR is still no more than “a dream”. In spite of all mentioned challenges some authors attempted to present applications for an SPR-based circuit analyzer. In [16], it was used for microwave diversity imaging. The calibration circuit included expensive Hewlett-Packard HP8510B analyzer. But calibration loads available for the authors were not precise enough and the proposed calibration technique was non-optimal overall. In [17–20] the authors used a SPR for constructing a Doppler radar and an angular meter. Both applications used such a reflectometer as a wave correlator in a phased-array radar system. However these applications could not be considered successful: the overall measurement precision is rather low. The resulting high errors have the same source – the signal processing technique is inadequate. The reason of high error levels [16–20] lies in introducing a “reference port” followed by the division of power measurements from other ports by this “reference port” power signal. A non-linear mathematical operation applied to a random numbers (sum of signal and noise) impairs the distribution law of these numbers and hence blocks the usage of statistical approach for measurement data processing. Another very interesting application of multi-port reflectometers is related to their use as transceivers for software-defined radio communication systems [21–27]. Indeed, the idea of using a simple passive device with four power meters instead of expensive receivers based on a heterodyne frequency down conversion is very attractive. But here, the authors are faced with the difficulties of multi-port calibration when working in real conditions of transmitting a communication signal through the environment against the background of significant noise and interference. So, the transceivers based on SPR were created only in experimental laboratories. In our previous works [28–30] we proposed a special type MPR for microwave parameter measurements. It comprises the conventional multi-port being connected with so-called multi-probe transmission line reflectometer (MTLR) [31]. In [28–30], it was shown that the resulting composite MPR, called by the authors “a combined multi-port reflectometer” (CMPR), allows its accurate calibration without any precise calibration standard using only the set of loads with unknown reflection parameters. Moreover,

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one can join calibration and measurement procedures for this CMPR and extend its application field drastically. In this paper, we discuss the application of a CMPR in design of non-contacting precise distance gauge, which can be used for measuring the level of a molten liquid metal in a tank. The structure of the paper is the following. Section 2 is devoted to the general problem statement and description of the known six-port based meter proposed in [32] as well as to analysis of its advantages and drawbacks. Section 3 introduces the design of a new CMPR-based distance meter for flat surfaces. Measuring and calibration procedures are described and the method for frequency refinement for the reference meter microwave signal is given. Mathematical simulation of CMPR measurement and calibration is presented in the Sect. 4. After that CMPR advantages over the SPR proposed in [32] are discussed in Sect. 5, followed by the final conclusions.

2 Problem Statement and Analysis of the Six-Port Based Distance Meter 2.1 Problem Statement In sheet-metalworking, a conventional hot-rolling machine is being replaced with more resource- and energy-efficient thin-film metal-sheet casting technology. In that process, a high-precision sensor, measuring the level of liquid steel, is needed. The requirements to be satisfied are submillimeter resolution, a range of approximately half a meter, robustness, and insensitivity to variations of temperature, humidity, dust and spurious signals, fast response, small measurement spot for good lateral resolution, remote sensing, and electromagnetic compatibility. The microwave sensor meets all of these requirements stated. The authors of [32] particularly described a SPR-based microwave meter. The corrugated horn is connected to one of the ports of a six-port as a load and is used to scan the target liquid metal plane. The operating frequency of a sensor is about 35 GHz, therefore standard interferometric or frequency-modulated continuous wave (FM-CW) techniques alone are not sufficient to meet the specifications, and a combination of both principles is used. 2.2 Analysis of a Six-Port Based Sensor Design The block-diagram of a SPR-based sensor [32] is shown in Fig. 1. It is built of a voltagecontrolled microwave generator, a frequency counter, a six-port, a calibration network and a digital signal processing (DSP) block, which is used for generator control and data acquisition. To avoid extremely stringent linearity specifications, which are essential for achieving reasonable accuracy using the FM-CW radar principle, the authors of [32] consider measuring at arbitrary frequency points. Applying this technique, the frequency must be measured very accurately and fast. To achieve this, a frequency divider module is used. The initial 35 GHz frequency is divided by 4 (that makes 8.75 GHz) and it is further measured by a high-speed asynchronous counter divided into two (high- and low-frequency) modules (see Fig. 1).

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Fig. 1. Block-diagram of the position sensor consisting of radar front-end and data acquisition: VCO is the voltage-controlled microwave oscillator; QD are the quadric detectors; A are the amplifiers; D/A and A/D are the digital-to-analog and analog-to-digital converters; DSP is the digital signal processing unit

A SPR used has a regular coaxial design. It consists of directional coupler, three 90° hybrids and a power divider. A calibration procedure corresponds to the one, presented in [9, 10] and makes use of a microwave sliding-short standard included in the calibration network. According to [32], the accuracy of the phase measurement is directly related to the accuracy of the power measurement at the four measuring ports. The detector diodes used for this power measurement exhibit a large temperature coefficient of the voltage sensitivity, which, in addition, depends on the load resistor. Therefore, the optimum resistor value for 22 °C ambient temperatures was found to achieve a nearly temperatureindependent sensitivity. A disadvantage of such a high source resistor is that it introduces thermal noise and reduces signal-to-noise ratio. To achieve high dynamic range, each detector diode is equipped with a low-noise amplifier directly attached to the detector output. This amplifier has to be designed very carefully in order to minimize additional noise. To further enhance electromagnetic immunity, the authors of the work [32] used the RF-shielded metal case in conjunction with a double-shielded cable. And finally, in order to suppress the noise a galvanic isolation of A/D converters from the signal processor via a fiber-optic transmission was used. After calibrating the six-port, it is possible to determine the complex vector of the reflected signal. The remaining error in the power measurement leads to an error in magnitude and phase of the received microwave signal. An estimate of that error propagation was obtained by a Monte Carlo simulation [32] with addition of random errors of power measurement. For a reflection coefficient having 0-dB magnitude, a power measurement error of 1% results in a maximum phase error of 5° (with maximum sufficient value of phase error ±10°). This results show that the adopted DSP technique for measured data was somehow inadequate. The resulting precision of the proposed sensor in terms of phase measurement is ±10° and leads to the level errors in distance being around ±0.12 mm. One can conclude that the desired high-level precision is reached, but to achieve error level stability the user

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should carefully and accurately adjust the sensor installation to the maximum available precision. The non-optimality of the proposed measurement and calibration techniques lies in the fact that the authors pay close attention to noise reduction (this requires engineering approach) not taking into account error reduction itself (that is, statistical approach). Therefore, a well-known engineering problem arises: additional components bring about additional noise that needs additional components to reduce its influence, etc. For example, connecting a high-value resistor to the detector output leads to additional thermal noise. The proposed solution is to determine an optimal value of resistor at a given temperature to achieve stable voltage sensitivity. And the ambient conditions at a real metal works can hardly assure the required temperature level all the time. That is why we can clearly figure out that a potential user of the proposed sensor will confront serious adjustment problems. Another set of difficult challenges is related to calibration of a SPR. In [9, 10], the calibration standard for the sliding-short had the complex reflection coefficient (CRC) magnitude of 0.997–0.998. This level of precision requires a specific sliding load that should be supplied along with the sensor installation. Moreover, the liquid metal temperature would inevitably influence the CRC of a calibration load (the distance to it is 0.5–1 m) and lower the desired accuracy. All mentioned difficulties being brought together make practical usage of the proposed sensor nearly impossible and hence its construction needs some enhancement.

3 Position Sensor Based on a Combined Multi-port Reflectometer After the structure analysis of position sensor described in previous section the new design for this sensor is proposed. At the heart of a new meter lays the CMPR concept, which has reduced architecture complexity, provided lower sensor cost and made it more stable as well as accurate. 3.1 CMPR Design and its Mathematical Models The block-diagram of the proposed sensor is shown in Fig. 2-a, and Fig. 2-b illustrates the design and concept of CMPR. It is implied to be a segment of the microwave section (waveguide, coaxial, or microstrip) with regular cross-sections and 2N measuring ports (N ≥ 4) are arranged in line along the central lengthwise axis. First N ports are strongly coupled with the field inside CMPR, thus this part of the section can be considered as a conventional MPR. The rest N ports located apart from MPR are weakly coupled with the field inside. The distances lj from these weakly coupled probes to some reference plane AA are assumed to be exactly known. The section part with these probes represents a multi-probe transmission line reflectometer, [31]. So, the CMPR should have at least 8 measuring ports. This amount of 8 is conditioned by the fact, that 4 ports in MPR allow one to solve the set of its equations both during calibration and when measuring the distance to the target plane. The rest four probes of the MTLR enable to calibrate the MTLR without using any precisely known standard. For this purpose one can use the kit of loads with unknown reflection parameters, the CRCs

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Fig. 2. Block-diagram of a CMPR-based position sensor (a) and the layout view of a CMPR concept (b): PC is the personal computer; AA is the reference plane.

of these calibration loads being estimated simultaneously during calibration procedure. The same number of MPR ports and the MTLR probes is taken for convenience and does not limit the generality of further considerations. The half of them should correspond to a MTLR system. Generally speaking, the proposed sensor can be applied to a wide array of tasks that require non-contacting position and/or shift measurements. Here we design this sensor as a position meter. In discrete in time samples of MPR ports’ and MTLR probes’ output signals are proportional to power and can be represented by the next set of equations:  2 (1) ujm = Aj am + Bj bm  + ξjm ; j = 1, 2, . . . , 2N ; m = 1, 2, . . . , M where j is the port number; m is the discrete time moment; Aj , Bj are the complex transition coefficients of the j-th port for reference and signal waves; am , bm are complex magnitudes of direct and diffused by the target surface waves at the m-th time moment correspondingly; ξjm is the additive noise in the j-th port at the m-th time. The noise values ξjm are assumed to be average zero normally distributed due to their thermal nature. The solution of the set (1) for unknown CRC phases of the examined object plane can be expressed in the following form:     (2) ϕm = arg bm am = 4π dm λ; m = 1, 2, . . . , M ,

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where λ is the known wavelength of the reference oscillator signal; d m is the distance between the horn and the surface at the m-th time moment. Hence, if one obtains the estimates for every am and bm he can find from (2) the dependence in time of distance variation to the target surface. The main problem is that all values of Aj and Bj from the set (1) are unknown and therefore should be determined during an appropriate calibration procedure. The main reason of MTLR use in the CMPR scheme (Fig. 2-b) is that it allows one to calibrate the whole reflectometer without precise calibration standards at hand. First, one should accurately determine the distances lj from the MPTL probes (having weak coupling with the electric field inside the segment) to some reference plane AA that can be chosen quite arbitrary. For example, this plane can coincide with the segment flange connected to the antenna horn. The mathematical model for the signals taken from MTLR probes is defined by the same set (1). But the regular structure of the microwave segment as well as the weak coupling of the probes make the following relations for the MTLR transmission coefficients true [28–31]:   4π · lj √ √ ; j = N + 1, N + 2, . . . , 2N , (3) Aj = αj , Bj = αj exp i λ where αj is the gain of j-th detector, i is the imaginary unit vector. Taking into account the relationships (3) one can rewrite the equation set (1) for the MTLR probes in the next form: 

 4π · lj 2 2 1 + m + ξjm ; j = N + 1, N + 2, . . . , 2N , ujm = αj am + 2m cos ϕm − λ (4)    where m = bm am . 3.2 CMPR Calibration Procedure For the calibration purposes we can use any available microwave loads with unknown CRCs. Particularly, we can just set up a horn in K ≥ 4 different positions (corresponding to the several arbitrary distances dk to the examined plane) and measure the power levels for all 2N available detectors of ports and probes. The CMPR calibration is performed in two steps [28–30]. At the first step the developed algorithm processes only signals taken from the transmission line probes. The set of Eqs. (4) for this case takes the following form:

  4π · lj + ξjk ; j = N + 1, . . . , 2N ; k = 1, 2, . . . . K, ujk = αj ak2 1 + k2 + 2k cos ϕk − λ

(5)

   where k = bk ak  is the CRC modulus of the k-th calibration load. The set (5) is to be solved for unknown values αj , ak ,  k , ϕk . The total number of unknowns is N + 3K. The number of equations in the set (5) is NK. Therefore, the unambiguous solution of this set exists if NK ≥ N + 3K, whence it follows that both the number of probes and the number of calibration loads must be at least four.

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If the number of equations in the set (5) is greater than the number of unknowns their estimates can be found by the maximum likelihood method, which is described in [33, 34]. A remarkable feature of the MTLR is that in parallel with the calibration of its detectors’ gains the CRCs of all unknown calibration loads are also estimated. The values of lj and λ are considered to be precisely known. On the second step, when the maximum likelihood estimates for values ˆ k , ϕˆ k , aˆ k are obtained, the adaptive Bayesian approach is used [28–30]. These estimates for all calibration loads are substituted into (1), and eventually this set of equations is solved by maximum likelihood method for unknown MPR complex constants, Aj and Bj . At this step we consider only the data, acquired from the MPR detectors having the numbers from 1 to N. All in all, the unknown parameters are estimated and the CMPR is finally calibrated. It is worth mentioning, that the calibration procedure should be taken only once before starting the measurement and the subsequent adjustment procedures and measurements would be automatically combined using the described method. It can be said, that the calibration and measurement are going in parallel simplifying the adjustment of the whole installation drastically. The described calibration procedure only assumes, that the value of λ should be precisely known. Unfortunately, in practice there is always a non-zero deviation for this parameter and if we avoid the fact, the total measurement accuracy would be sufficiently decreased. In order to simplify the displacement sensor design we refused to use an expensive precision frequency counter. Therefore, the adaptive refinement of the reference signal wavelength is needed. 3.3 Oscillator Signal Wavelength Adjustment Consider that there is a little deviation of reference wavelength, λ, in (3)–(5), i.e. λ = λ0 + λ,

(6)

where λ0 = 35 GHz (precisely known value) and λ is a little unknown correction (|λ|  λ0 ). If the part of CMPR corresponding to MTLR has more than 4 weakly coupled probes (the total number of CMPR ports should be no less than nine) then the iterative algorithm for finding the unknown λ is available. To account for a λ correction, i.e. the substitution (6) into (5) for any arbitrary load, gives the next set of equations:

 4π · l j   + ξj ; j = N + 1, . . . , 2N . uj = αj a2 1 +  2 + 2 cos ϕ −  λ0 1 + λ λ0 (7)   −1 The expression 1 + λ λ0 in the argument can be expanded in a Taylor series up to the linear terms, then: 

 4π · lj λ ψj + ξj ; ψ j = uj ≈ αj a2 1 +  2 + 2 cos ϕ − 1 − ; j = N + 1, . . . , 2N . λ0 λ0

(8)

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Since the absolute value of the correction λ is small as compared to λ0 , one can use the well-known approximations:



λ λ λ ψj ≈ 1, sin ψj ≈ ψj . cos λ0 λ0 λ0 Taking into account the above relationships and removing the brackets in (8) results in the following non-linear set of equations for the unknown load parameters , ϕ, a and the correction λ: (9) Making the following variable substitution in (9): ⎧ ⎧   ⎪ ⎪ q1 = a2 1 +  2 , x = αj , ⎪ ⎪ ⎪ ⎪ 1j ⎪ ⎪ 2 ⎪ ⎪ ⎨ q2 = a  cos ϕ, ⎨ x2j = 2αj cosψj , q3 = a2 λ cos ϕ, x3j = 2αj ψj λ0 sin ψj , ⎪ ⎪ ⎪ ⎪ 2  sin ϕ, ⎪ ⎪ = a q x4j = 2αj sin ψj , 4 ⎪ ⎪ ⎪ ⎪ ⎩ q = a2 λ sin ϕ, ⎩ x = −2α ψ  λ  cos ψ , j j 0 j 5 5j

(10)

One can obtain from (9) the set of linear equations for new unknown variables, qi . Since the number of unknown parameters in the set (9) is four and the number of intermediate unknowns is five there should be a non-linear constraint, which can be easily got from (10). For the sake of convenience we write the linear set in a matrix form, then: u = Xq +
,

(11)

q2 q5 − q3 q4 = 0,

(12)

where u = (uN +1 , . . . , u2N )T is the vector of measured powers from the probes;  MTLR  q = (q1 , . . . , q5 )T is the vector of unknowns to be estimated; X = xij  is the design of experiment matrix;
= (ξ1 , . . . , ξN )T is the error vector; “T” denotes a transpose matrix. An iteration algorithm for solution the Eqs. (11), (12) by maximum likelihood method, which represents the iterative estimation of parameters q is described in [28, 35, 36]. The resulting iteration process is described by the formula: qˆ (r+1) = qˆ (r) −

 −1 qˆ (r)T Gqˆ (r) XT X GT qˆ (r) ,  −1 qˆ (r)T G XT X GT qˆ (r)

(13)

where G is the matrix of quadratic form from constraint Eq. (12); r is the step number. Initial approximation for q is found as a least-squares solution for (11) without account for constraint (12):  −1   XT u . qˆ (0) = XT X

(14)

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The presented iteration algorithm usually converges quickly (no more than 2–3 steps required). After determination of the estimated vector q, the resulting correction λ is found from (10):   2   2  qˆ + qˆ 2 qˆ + qˆ 2 . (15) λˆ = 3

5

2

4

Using the described wavelength correction one can trace the wavelength during the measurement process and avoiding the use of the frequency counter without loss of the whole measurement accuracy.

4 Computer Simulation The solution algorithm for the set (1) described in [28] and [35] was implemented using software package designed in Visual Studio 10 media. It processes the digital data taken fromthemeasuringportsinrealtimeandoverlapsmeasuringandcalibrationroutineswhen the number of measuring ports is N = 10 and the number of measurements is K = 65535. The performance and efficiency of the developed algorithms and software were evaluated using computer simulation. The simulated experiments carried out by the authors of [32], who created an experimental setup of the device, which measured the coordinates of the surface under test using a conventional SPR. The true picture of the change in the position of the test surface moving from a distance of 748 mm to 853 mm from the antenna horn was simulated exactly the same as in [32]. Then these distances were recalculated into the phases of the signal, b, scattered by the test surface. Basing on the given complex amplitudes, a and b, and the given CMR ports’ coefficients, Aj and Bj , an array of output voltages was computed. After the additive random errors were added to these voltages an input array uij (1) was obtained for subsequent statistical data processing. The signal-to-noise ratio was set equal to 35 dB for MR ports and 25 dB for MTLR probes, which corresponds to their real values. The digitized signals were processed using the developed calibration and measurement algorithms [28–30, 33–36]. The obtained results of phase difference estimation for waves, a and b, were compared with the results of [32]. Figure 3 shows the measured phase dependences of the moving surface reflection coefficient and the error of its measurement on the distance from the antenna horn obtained in [32], when the results are measured using a SPR. As a result, a measurement error of less than ±10° was obtained (Fig. 3, dashed line 1), which corresponds to a distance measurement error of approximately ±0.12 mm. In practical environments, the signal path of the free-space propagation includes parasitic reflections, which distort the phase characteristics. According to the authors of [32], measuring with submillimeter resolution is only achievable if the target has a smooth surface and does not extend in the direction of the wave propagation. Moreover, the main contributions to the distortion are multiple reflections between the target and horn antenna. That is why they tried to leave out these reflections using the horn with an excellent voltage standing wave ratio (VSWR ≈ 1.02) in the forward direction as well as to take into account the inherent possible variations of the oscillator frequency using a precision frequency meter. After that it became possible to increase

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Fig. 3. Phase and phase error of CRC as a function of target distance estimated by the sensor based on SPR [32]. Dashed curve 1 – without account for multiple reflections; dashed curve 2 – phase error measured considering multiple reflections between horn aperture and target

the accuracy of the phase measurement up ±6° (Fig. 3, dashed curve 2) corresponding to an error of the distance measurement of ±0.07 mm. Figure 4 presents the results of our similar simulation experiments when measurements were carried out using proposed CMPR with the number of measurement ports equal to 10. Half of these measurement ports have weak coupling with the field inside the microwave path. Based on their output signals, an additional refinement of the generator signal wavelength has been performed in accordance with formulas (6)–(15), when the frequency could vary within 1% of the main mode. It can be seen from the last figure that the use of optimal statistical methods for processing signals from CMR ports made it possible to increase the measurement accuracy by 6–10 times without use of an expensive equipment, i.e. a precision frequency meter, antenna horn with VSWR ≈ 1.02 and a set of calibration loads for SPR. Comparing the obtained values of the phase measurement errors by the conventional six-port and the proposed multi-port we can conclude that the new method for estimating the surface coordinates is promising.

5 Discussion The design of the proposed meter is significantly simpler and, therefore, less expensive to be compared with known analogues. An increase in the number of measurement ports does not lead to a significant complication of the circuit, but the design of the MR itself is simplified drastically, the precision frequency meter being eliminated as well. In addition, there is no need for precision calibration loads. The solution algorithm of the set (1) does not impose any restrictions on the parameters ak and bk ; therefore, the modulus of the tested surface reflection coefficient can

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Fig. 4. The upper picture: phase and phase error of CRC as a function of target distance estimated by the sensors based on SPR [32] and proposed CMPR. Dashed curve 2 – phase error of SPR (taken from Fig. 3); dotted curve – phase error of CMPR. The lower picture: same CMPR phase error shown on a larger scale.

vary arbitrarily in time. This property of the described method allows one to achieve noted advantages over Doppler measuring methods. First, the measurement results are variations in time of the surface coordinate, and not changes in its velocity, which follows from (2). Therefore, this meter has greater sensitivity at low frequencies of surface oscillations (less than 5 Hz) compared with Doppler counterparts. Secondly, this feature expands the scope of the meter, because it can measure not only moving surfaces, but also static ones. The accuracy of the method is determined by the signal-to-noise ratio at the output of the MR ports. The use of simple microwave components makes it possible to achieve a ratio of 30–35 dB, which ensures phase measurement accuracy of 0.5–1° and corresponds to a distance measurement error of less than ±0.01 mm for linear displacements. Basing on the result of the Sect. 3.2 it can be argued that the self-calibration procedure of the meter can be performed with each measurement of unknown surface coordinates.

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Therefore, there are no requirements for the stability of the generator power as well as for the knowledge of phase relationships between the measuring ports. As a result, the influence of external factors on the measurement accuracy is excluded, e.g. changes in ambient pressure, temperature, humidity, etc. As already mentioned, the meter calibration procedure does not require the reflection or transmission standards. The only reference is the wavelength of the used oscillator. Therefore, it is sufficient to monitor the change in the frequency of the generator, since the wavelength of the reference signal is used in expression (2). This can be done using the estimation algorithm (4)–(9) described above.

6 Conclusions A direct method of measuring the frequency of the reference signal using the phase of the surface under test reflection coefficient with the six-port reflectometer allows one to estimate the distance to the surface with certain accuracy. The disadvantages of this approach are the requirement for a large number of high-precision measuring equipment and difficulties associated with accounting for reflections of the reference signal from the antenna. The paper proposes a statistical method for solving the equations of a combined multiport reflectometer used as a precision meter for the distance to the surface under test with sub-millimeter accuracy. The offered technique allows the use of extremely simple multi-port’s designs and does not require high-precision standards for reflectometer calibration. In this case, the measuring system becomes extremely simple to manufacture and therefore cheap. A program was developed that implements this algorithm, and on its basis a numerical simulation of the calibration as well as measurement procedures for the described meter was carried out. It showed the high efficiency of the proposed measurement technique.

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A Transformation-Based Approach for Fuzzy Knowledge Bases Engineering Nikita Dorodnykh , Olga Nikolaychuk , and Aleksandr Yurin(B) Matrosov Institute for System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, 134, Lermontov St., Irkutsk 664033, Russia [email protected]

Abstract. Fuzzy knowledge base engineering remains an important area of scientific research. The efficiency of this process can be improved due to the automated analysis of existing domain models in the form of conceptual diagrams of different types. In this paper we propose an approach for generating knowledge bases by transforming conceptual models with fuzzy factors. Resulted knowledge bases contain fuzzy rules. The proposed approach includes: a method for the automated analysis and transformation of conceptual models serialized in the XML-like formats; an extended domain-specific declarative language for describing transformation models, namely Transformation Model Representation Language (TMRL); a software module for Knowledge Base Development System (KBDS) that implements the proposed method. Our approach was used for prototyping a knowledge base for predicting degradation processes of technical systems in the petrochemical industry, in this case we developed the software module for transformation of Ishikawa diagrams that account fuzzy and uncertainty factors. Keywords: Model-driven engineering · Model transformation · Metamodel · Code generation · Fuzzy conceptual model · Fuzzy knowledge base · Fuzzy rules · TMRL · Ishikawa diagrams

1 Introduction Generative programming and model transformations [1] remain the popular ways to improve creating software, in particular, intelligent systems and knowledge bases. Model transformations play a key role in a model-driven engineering [2] when software developed on the basis of various conceptual models, for example, UML, IDEF1X, etc. There are many implementations of model-driven and transformation-based approaches in the field of intelligent system and knowledge base engineering, in particular, [3–8]. However, most of them are focused only on a certain type of models and systems, and not covered the fuzzy conceptual modeling in the form of fuzzy cognitive maps, fuzzy ER models [9], fuzzy UML models and others. In this paper we propose a transformation-based approach for processing fuzzy domain models and generation of a source code for fuzzy knowledge bases. The main our contributions are the followings: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 76–90, 2021. https://doi.org/10.1007/978-3-030-65283-8_7

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• a method for the automated creation of fuzzy rule-based knowledge bases by analyzing and transforming source fuzzy conceptual models serialized in the XML-like formats; • an extended edition of a domain-specific language called Transformation Model Representation Language (TMRL) [10] that used for describing transformations. This extension includes the support of fuzzy factors, in particular, uncertainty and fuzziness, etc.; • a software module (converter) for Knowledge Base Development System (KBDS) that implements the proposed method. Our illustrative example presents the transformation of Ishikawa diagrams [11] describing the cause-effect relationships in the field of predicting degradation processes of technical systems in the petrochemical industry. Discussion of results is presented. The proposed means can be used for prototyping model transformations (import and export) for various XML-like formats.

2 State-of-Art 2.1 Model Transformations: Background In general, a model transformation is the automatic generation of a target model from a source model, according to a set of transformation rules that describe how a model in the source language can be transformed into a model in the target language [12]. In fact, the model transformations are extension of program transformations: if a program is based on a model then this model transformation can lead to the program transformation. However, transformation approaches in these areas have differences: while program transformations are typically based on mathematically oriented concepts such as term rewriting, attribute grammars and functional programming, then model transformations usually adopt an object-oriented approach for representing and manipulating their domain models (system abstractions and/or its environment) [1]. At this connection various objects can be used for transformations: UML models, feature models, interface specifications, data and component schemas, and source codes. The model transformation can be considered from different viewpoints [8, 12], for example: • by the type of transformations (a model-to-model, M2M; a model-to-text, M2T; and text-to-model, T2M); • by an abstraction level of models (vertical, horizontal); • by a transformation direction (unidirectional, bidirectional); • by count of modeling languages used (one, two, and etc.). A four-level metamodeling architecture (schema) is used to represent the concept of a model transformation in model-driven engineering (Fig. 1) [13]. In accordance with this architecture a metamodel is one of the main concepts of model transformations, the metamodel defines a model of modeling language used to describe the transformations.

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Fig. 1. A model transformation schema form a model-driven engineering [13]

All models of the M1-level correspond to some metamodels at the M2-level. In turn, all metamodels at the M2-level correspond to a single meta-metamodel at the M3level, i.e. they are described using some meta-modeling language. The most common metamodeling languages are the followings: MOF (Meta-Object Facility), Ecore, KM3 (Kernel Meta Meta Model) and others. A meta-metamodel is a bridge between different metamodels, since it is the basis for their description. If two different metamodels correspond to one common meta-metamodel, i.e. can be described by means of the M3level, then all specific models of the M1-level based on them can be stored in a common repository and jointly processed by model transformation tools. Today, there are a set of examples of the computer-aided development of knowledge bases and intelligent systems based on principles of a model-driven engineering and model transformations [3–8]. It should be noted that these approaches are intended, mainly, for well-defined problems. However, the domain knowledge represented in the form of conceptual models in the most cases includes fuzziness: uncertainty in verbal characteristics, inaccuracy, varying degrees of confidence, lack of some data, etc. Thus, processing such information requires special methods and software. 2.2 Model Transformations: Languages and Tools Currently, model transformation techniques are based on graph grammars (graph rewriting), the category theory, and hybrid (declarative-imperative) approaches. The most popular model transformation languages are the followings: • QVT (Query/View/Transformation) is an OMG consortium specification that defines three model transformation languages: QVTc, QVTo and QVTr [14]. • ATL (ATLAS Transformation Language) is a language for describing model transformations based on QVT standard and a standardized language for describing constraints called OCL (Object Constraint Language) [15]. • VIATRA2 (VIsual Automated model TRAnsformations) is a transform language for managing graph models, this language is based on rules and patterns [16]. • GReAT (Graph REwriting And Transformation) is a language for describing model transformations based on the approach of triple graph transformations [17].

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• Henshin is a model transformation language based on graph rewriting and using template-based rules that can be structured into nested transformation units with welldefined semantics [18]. • Epsilon is a family of languages and tools for model transformations, code generation, model validation, migrations, and refactoring [19]. • XSLT (eXtensible Stylesheet Language Transformations) is a XML document conversion language [20], this language is a specification of the W3C consortium. The main disadvantage of these model transformation languages is the high qualification requirements for the end-users when developing transformation rules. In particular, a user needs to know a syntax and semantics of a certain model transformation language, which can be quite complex. The user also needs to know the metamodeling languages (e.g., MOF, Ecore, KM3, etc.) used to describe the input and output models, as well as various related (additional to the main languages) language constructs (e.g., OCL). A significant drawback of almost all model transformation languages is a tight binding to certain tools, in particular, to Eclipse platform. So, the language support in EMF (Eclipse Modeling Framework) [21] is implemented in the form of plugins. The combination of these factors complicates the practical use of these languages and tools in knowledge base and intelligent system engineering, especially when the transformation of conceptual domain models are made by non-programming users (e.g., domain experts, knowledge engineers, analysts, etc.).

3 Proposed Transformation-Based Approach We propose a transformation-based approach for development of knowledge bases that include fuzzy rules. The conceptual models containing fuzzy factors are used as a source of information. Our approach includes a specialized method and an extended domainspecific language for describing transformations; let’s describe them in the detail. 3.1 Method for Fuzzy Knowledge Base Engineering We define a transformation of fuzzy conceptual models to fuzzy knowledge bases (Fig. 2) by using the model transformation schema presented above (Fig. 1). Our transformation scheme defines a horizontal exogenous transformation [12], i.e. the source and target models are the models of a same hierarchy level, but they are defined by different modeling languages. In this connection, different languages for fuzzy conceptual modeling and knowledge representation can be used. Source conceptual models representing domain information with fuzziness are at the “M1” level. These models can be transformed into some target model of knowledge base (in our case it is the fuzzy rule-based model). At the “M2” level there are metamodels that correspond to certain source and target models of the “M1” level. These source and target models correspond to specific metamodels at the “M2” level. It should be noted that the initial and final artifacts of the transformation process are the text documents. In particular, it is assumed that source fuzzy conceptual models are represented (serialized) in the XML format. XML is the universal and most common way

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for representing and storing conceptual models, integrating software and providing the exchange of information between various applications. The final result of this transformation is a knowledge base code represented in a certain fuzzy knowledge representation language, for example, FuzzyCLIPS [22]. Therefore, the initial (preprocessing) task is a transformation of a source XML document text into a target model in accordance with the specified metamodel, i.e. translation of a specific specification to an abstract one (called as a text-to-model transformation). The main condition of this transformation is a correspondence of a source fuzzy conceptual model to a certain metamodel at the “M2” level. Let’s define the transformation model using the previously described schema (Fig. 2): MT = MMFCM , MMFRKB , T ,

(1)

where MMFCM is a metamodel for a source fuzzy conceptual model; MMFRKB is a metamodel for a target fuzzy knowledge base; T is a model transformation operator (transformation rules). A metamodel is a language model, i.e. a description of its elements and relationships that are used to create conceptual models and knowledge bases. Thus, in order to provide the transformation of a source fuzzy conceptual model to a target knowledge base code in a certain fuzzy knowledge representation language, it is necessary to describe a set of transformation rules (T ); these rules describe the correspondence between MMFCM and MMFRKB elements. Let’s clarify a transformation chain (T ) using (1): T = TFCM −FRM , TFRM −FRKB ,

(2)

where TFCM −FRM is a set of rules for transformation of a source fuzzy conceptual model to a fuzzy rule-based model; TFRM −FRKB is a set of rules for transformation of a fuzzy rule-based model to a target knowledge base code in a fuzzy knowledge representation language. Wherein: TFCM −FRM : FCMXML → FRM , where FCMXML is a source fuzzy conceptual model presented in the XML format, which is described using MMFCM ; FRM is an unified intermediate representation for storing and representing the extracted knowledge in the form of a fuzzy rule-based model. This model abstracts from the features of various knowledge representation languages when they describe knowledge, for example, FuzzyOWL, FuzzyCLIPS.

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FRM supports representation of well-defined, fuzzy facts, and its mixed use in conditions and actions of rules. FRM uses two concepts of soft computing: fuzziness and uncertainty. Fuzziness of this model is based on the theory of fuzzy sets, which represent and manipulate fuzzy facts and rules. The degree of uncertainty is represented by a numerical value (certaintyFactor) on a scale from 0 to 1. Another concept of this model is a linguistic (fuzzy) variable (FuzzyVariable). Each linguistic variable has a basic measurement scale and a set of fuzzy terms (FuzzyTermSet). This fuzzy set can have four types of descriptions: • a standard table type is a set of element pairs of a basic scale and membership function values: (x; µ(x)); • a standard analytical type is an expressed using basic analytical types of membership functions (e.g., S-function, P-function, Z-function, etc.); • expressions with modifiers (ModifyFunction) are fuzzy variables with modifiers (e.g., vary, norm, above, below, etc.) that increase or decrease the values of fuzzy variables; • linguistic expressions (LinguisticExpression) are a set of fuzzy variables with logic operators (AND, OR, NOT) and modifiers. Fuzzy facts are described with the use of these linguistic variables. Therefore this model provides definition of fuzzy slots (fuzzy slots). Rules in a fuzzy model divided into two types: simple and complex. Simple rules can contain only one antecedent (condition) and consequent (action). Moreover, if the antecedent and consequent are “clear” terms (facts) with certainty factors then the simple rule is a “clear” rule. A simple rule is a “semi-clear” rule when the antecedent is a fuzzy fact with some linguistic variable. A simple rule is a “fuzzy” rule when the antecedent and consequent are fuzzy facts. It should be noted that in this rule type a certainty factor for the rule consequent is calculated by multiplying certainty factors for the rule antecedent and the rule itself (implementation of fuzzy set operations). Complex rules can contain a different number of antecedents with various logical operators (e.g., AND) and consequents. In turn TFRM −FRKB : FRM → CodefuzzyCLIPS , where CodefuzzyCLIPS is a target code of a fuzzy knowledge base in the FuzzyCLIPS [22] format that is described using MMFRKB . A special meta-metamodel is developed for the unified representation and storing of all metamodels. This meta-metamodel abstracts from a specific metamodeling language (e.g., MOF, Ecore, KM3, etc.). It describes the main meta-entities and their relationships, and based on the Ecore specification [23]. 3.2 Extended Transformation Model Representation Language All model transformations are carried out at the level of metamodels using a domainspecific declarative language called Transformation Model Representation Language (TMRL). The TMRL grammar belongs to the class of context-free grammars (CFgrammars, for example – LL (1)) [24]. TMRL describes the elements of models in a declarative form, in particular, in the form of rules representing correspondences of metamodel elements. TMRL specifications meet the requirements of accuracy, clarity

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and completeness: all the necessary information for the considered transformations is presented; all objects of the models are well formalized; the specifications are compact enough and understandable (readable). The TMRL program consists of three main blocks: • elements and relationships of a source metamodel; • elements and relationships of a target metamodel; • transformation rules that describe the correspondence between elements of a source and target metamodels. The main TMRL elements are described in Table 1. A detailed TMRL description is presented in [10]. Table 1. The main TMRL elements. Element

Description

Source meta-model Description of a source metamodel for a modeling language (source conceptual models are presented on this language) Target meta-model

Description of a target metamodel for a knowledge representation language (a target fuzzy rule-based model is presented on this language)

Elements

Description of concepts of a source and target metamodels

Attributes

Description of concept properties of a source and target metamodels

Relationships

Description of relationships of a source and target metamodels

Transformation

The main construction describing a set of transformation rules

Rule

Description of a transformation rule that defines the correspondence between concepts or properties of a source and target metamodels

Call

An additional block for the call of existing transformation module that processes this model

In this paper we extend TMRL by adding fuzzy factors representation and processing. In particular, the followings terms are added: a linguistic (fuzzy) variable, a membership function, a fuzzy set. There are two methods for defining a membership function: in the form of a table and analytical. The following membership function types for the analytical method are defined: triangular; trapezoidal; a S-shaped spline function; a Z-shaped spline function; a linear S-shaped function; a linear Z-shaped function; a P-shaped function. A fuzzy set in TMRL described as follows: = [ ()] = table | analytical = triangular | trapezoidal | … = (a, b, c) | (a, b, c, d) | …

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Despite the simple TMRL syntax, in most typical cases a visual programming technique for the creation of TMRL programs is used. The direct manipulation of language constructs (the direct programming) is optional only. The visual programming technique involves the use of the following tools: • • • •

a parser for a source and target models formats; a visual metamodel editor; a visual transformation editor (Fig. 3); a TMRL codes generator (Fig. 4).

So, the creation of TMRL programs consists of the following main steps using this toolset: • creating a metamodel for a source fuzzy conceptual model based on an XML schema or analysis of a source fuzzy conceptual model (a reverse engineering procedure); • selecting a metamodel for target knowledge base (by default, a metamodel for a fuzzy rule-based knowledge base is implemented for a FuzzyCLIPS language); • creating transformation rules including: a structure analysis of metamodels; creating the correspondences between metamodel elements via a visual editor; automated TMRL code generation; modification of TMRL code (optional). 3.3 Verification of Model Transformations The use of model transformations requires verification of the results. In our case we suggest two methods: human expert evaluation; and formal requirements evaluation. Human expert evaluation consists of verification of the results by domain experts.

Fig. 3. An example of a GUI form of a visual transformation editor

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Fig. 4. An example of a GUI form with results of a TMRL codes generator

Formal requirements evaluation consists of the compliance of constraints for metamodels and transformation rules. The main constraints for metamodels: • • • • •

no unrelated elements; no elements without properties; no duplicate relationships; no ring relationships of the same type; no recursive relationships. The main constraints for transformation rules:

• at least one transformation rule; • the use elements of a source and target metamodels only; • correspondences between elements are created before the creation of correspondences between element properties; • no correspondences between element properties and elements themselves; • elements without correspondences can exist in the cases of a redundancy or a lack of expressive ability; • the definition of priorities of transformation rules for an interpreter; • the absence of equal priorities; • the correct sequence of priorities.

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The most of these constraints are automatically checked, so the syntactically correct models resulted. 3.4 Using TMRL Programs When Creating Software Modules Obtained TMRL programs (models) are used when creating software modules (converters) for the Knowledge Base Development System (KBDS) [25]. KBDS implements the concept of a template-based or frame-based assembly [26] when a new module is a template with blank slots, which are filled with certain content resulted from the TMRL programs (models) interpretation. A typical software module template is described as follows: MSM = MT , A, G, I ,

(3)

where MT is a TMRL program (model); A is a parser for input models (a slot for analyzer module); G is a generator of output models (a slot for generator module); I is API functions for interaction with external systems (providing access to the analyzer and generator). Wherein: A ∈ {AFCM , AFRM }, where AFCM is a analyzer (parser) for a source fuzzy conceptual models presented in the XML format; AFRM is a analyzer for a source conceptual model presented in the form of a fuzzy rule-based model. GOUT ∈ {GFRM , GFRKB }, where GFRM is a generator of a target fuzzy rule-based model; GFRKB is a generator of a knowledge base  code on FuzzyCLIPS language. I = {i1 , . . . , in }, ij = namej , commandj , j ∈ 1, n, where namej is a name of jmethod of interaction; commandj is a command for interaction method. This interaction interface provides access the external systems to functions the software module (converter). In the current version of the software the source code of modules is generated in PHP and requires refinement by the programmer for their further integration into KBDS.

4 Illustrative Example Let’s consider an example of application of our approach when creating a prototype of a fuzzy knowledge base for predicting the degradation processes of technical systems in petrochemistry. The cause-effect Ishikawa diagrams with fuzzy and uncertainty factors were used for transformations. These diagrams were based on an extended diagram template [27]. An example of a fragment of a source fuzzy Ishikawa diagram of degradation process “corrosion cracking” for a damage stage is presented in Fig. 5. This diagram includes two fuzzy factors: “pH” of “Environment” and “value” of “Residual stresses” (Fig. 6). A reverse engineering procedure was used to generate a metamodel for fuzzy Ishikawa diagrams. The analysis of the XML structure of a source fuzzy Ishikawa diagram was carried out by cyclic traversal of all nodes of the XML tree in a depth. At the same time, the names of metamodel elements corresponded to the node names; metamodel element properties corresponded to the node attributes; relationships between the

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Stress [0,9] type: heat exchange

pH : average

Environment [0,9]

Corrosion cracking [0,9]

technological inheritance: electrochemical heterogeneity of grain boundaries

type: steel

Material [0,9] orientation : longitudinal

location : on the side

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Fig. 5. A fragment of a fuzzy Ishikawa diagram of a “corrosion cracking” degradation process

1 expert

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[0, 300] MPa (0, 0) (150, 0.5) (300, 1)

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Fig. 6. Fuzzy factors: a) “pH” of “Environment”, b) “value” of “Residual stresses”

metamodel elements were determined by analyzing the nesting of XML nodes in each other. In addition, namespaces declared in a source model were taken into account in the analysis. The main result of the XML structure analysis procedure is a metamodel of a fuzzy Ishikawa diagram. This metamodel represented and edited in the visual metamodel editor (Fig. 7), in particular, relationships of “by identifier” and “part-whole” types were defined manually. The transformations for fuzzy Ishikawa diagrams were created in the visual transformation editor (an example of a GUI form of visual transformation editor is presented in Fig. 3). After clarifying fuzzy factors (e.g., “pH” and “value” (Fig. 6)), the knowledge base code on FuzzyCLIPS language was generated. A fragment of this code is presented below:

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Fig. 7. A fragment of a fuzzy Ishikawa diagram metamodel (KBDS visual metamodel editor)

(deftemplate pH 1 15 units ((average (1 0) (7 1) (10 1) (15 0) ) ) (deftemplate value 0 300 MPa ((max (0 0) (150 0.5) (300 1) ) ) ...(deffacts fuzzy-facts (pH average) (value max) )

5 Discussion In this paper we propose an approach designed for transformations of conceptual models with fuzzy factors to fuzzy knowledge bases with fuzzy rules. The direct correct comparison with other transformation-based approaches is difficult because of differences in their purposes and implementations. In this connection a qualitative comparison of some separate elements of approaches is possible, for example, transformation languages. So, the main difference between TMRL and existing models transformation languages (e.g., QVT, ATL, etc.) is its ease of use, achieved through a limited set of elements. TMRL is not an extension of other languages and does not use the constructions of other languages, as other transformation languages very often do; in particular, ATL uses the OCL. In addition, TMRL has human-readable syntax, and an additional feature of TMRL is the integration with previously developed KBDS software components.

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The proposed methods and tools can be used for prototyping transformation (import and export) modules for various intelligent systems. In particular, we used our proposals when creating a converter prototype for the XTM format (a IHMC CmapTools concept maps) for a Personal Knowledge Base Designer (PKBD) platform [28]. The XTM convertor was developed in 26 min with the aid of KBDS including solving the following tasks: • • • • • • •

creating a new software module project; generating a metamodel for source concept maps; refining the metamodel using a visual metamodel editor; creating transformation rules using a visual transformation editor; generating a TMRL code; refining a TMRL code; assembling a software module (convertor).

Obtained the metamodels and transformation rules were used for the direct programming a IHMC CmapTools plugin for PKBD. This plugin supports import and export of a IHMC CmapTools concept maps, it was developed in 3,5 h with the aid of Embarcadero Delphi XE.

6 Conclusions The efficiency of fuzzy knowledge base engineering can be improved due to the automated analysis of existing domain models in the form of conceptual diagrams of different types. In this paper we propose an approach for generating knowledge bases by transforming conceptual models with fuzzy factors. Resulted knowledge bases contain fuzzy rules. Ishikawa diagrams serialized in the XML like format are used as source conceptual models. Our approach includes: • a method for the automated creation of fuzzy rule-based knowledge bases by analyzing and transforming source fuzzy conceptual models; • an extended edition of a domain-specific language called Transformation Model Representation Language (TMRL) [10] that used for describing transformations. • a software module (converter) for Knowledge Base Development System (KBDS) that implements the proposed method. In future we plan to improve the TMRL supporting tools, and use them to create knowledge bases for solving interdisciplinary tasks of technological safety provision based on self-organization [29]. The present study was supported by the Russian Foundation for Basic Research (Grant no. 19-07-00927).

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References 1. Czarnecki, K., Helsen, S.: Feature-based survey of model transformation approaches. IBM Syst. J. 45(3), 621–645 (2006) 2. Cretu, L.G., Florin, D.: Model-Driven Engineering of Information Systems: Principles, Techniques, and Practice. Apple Academic Press, USA (2014) 3. Nofal, M., Fouad, K.M.: Developing web-based semantic expert systems. Int. J. Comput. Sci. 11(1), 103–110 (2014) 4. Kadhim, M.A., Alam, M.A., Kaur, H.: Design and implementation of intelligent agent and diagnosis domain tool for rule-based expert system. In: Proceedings of the International Conference on Machine Intelligence Research and Advancement, December 21–23, pp. 619– 622. IEEE Xplore Press, Katra (2013) 5. Ruiz-Mezcua, B., Garcia-Crespo, A., Lopez-Cuadrado, J., Gonzalez-Carrasco, I.: An expert system development tool for non AI experts. Expert Syst. Appl. 38, 597–609 (2011) 6. Shue, L., Chen, C., Shiue, W.: The development of an ontology-based expert system for corporate financial rating. Expert Syst. Appl. 36, 2130–2142 (2009) 7. Canadas, J., Palma, J., Tunez, S.: InSCo-Gen: a MDD tool for web rule-based applications. In: Web Engineering, ICWE 2009. Lecture Notes in Computer Science, vol. 5648, pp. 523–526 (2009) 8. Yurin, A.Y., Dorodnykh, N.O., Nikolaychuk, O.A., Grishenko, M.A.: Prototyping rule-based expert systems with the aid of model transformations. J. Comput. Sci. 14(5), 680–698 (2018) 9. Zhang, F., Ma, Z.M., Yan, L.: Representation and reasoning of fuzzy ER model with description logic. In: Proceedings of IEEE International Conference on Fuzzy Systems, pp. 1358–1365. IEEE Xplore Press, Hong Kong (2008) 10. Dorodnykh, N.O., Yurin, A.Yu.: A domain-specific language for transformation models. In: CEUR Workshop Proceedings (ITAMS-2018), vol. 2221, pp. 70–75 (2018) 11. Ishikawa Diagram. https://en.wikipedia.org/wiki/Ishikawa_diagram. Accessed 29 Apr 2020 12. Mens, T., Gorp, P.V.: A taxonomy of model transformations. Electron. Notes Theor. Comput. Sci. 152, 125–142 (2006) 13. Silva, A.R.D.: Model-driven engineering: a survey supported by the unified conceptual model. Comput. Lang. Syst. Struct. 43, 139–155 (2015) 14. Query/View/Transformation Specification Version 1.3. http://www.omg.org/spec/QVT/1.3/. Accessed 29 Apr 2020 15. Jouault, F., Allilaire, F., Bezivin, J., Kurtev, I.: ATL: a model transformation tool. Sci. Comput. Program. 72(1), 31–39 (2008) 16. Varro, D., Balogh, A.: The model transformation language of the VIATRA2 framework. Sci. Comput. Program. 63(3), 214–234 (2007) 17. Balasubramanian, D., Narayanan, A., Buskirk, C., Karsai, G.: The graph rewriting and transformation language: GreAT. Electron. Commun. EASST 1, 1–8 (2007) 18. Arendt, T., Biermann, E., Jurack, S., Krause, C., Taentzer, G.: Henshin: advanced concepts and tools for in-place EMF model transformations. In: Processing of the 4th International Conference on Model-Driven Engineering and Software Development (MODELSWARD 2010). Lecture Notes in Computer Science, vol. 6394, pp. 121–135 (2010) 19. Epsilon. http://www.eclipse.org/epsilon/. Accessed 29 Apr 2020 20. XSL Transformations (XSLT) Version 2.0. http://www.w3.org/TR/xslt20/. Accessed 29 Apr 2020 21. Eclipse Modeling Framework. http://www.eclipse.org/modeling/emf/. Accessed 29 Apr 2020 22. FuzzyCLIPS. https://wiki.tcl-lang.org/page/FuzzyCLIPS. Accessed 29 Apr 2020 23. Ecore. http://download.eclipse.org/modeling/emf/emf/javadoc/2.9.0/org/eclipse/emf/ecore/ package-summary.html. Accessed 29 Apr 2020

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Mathematical Modeling of Hydroelastic Oscillations of Circular Sandwich Plate Resting on Winkler Foundation Aleksandr Chernenko1 , Alevtina Christoforova2 , Lev Mogilevich1 Victor Popov1(B) , and Anna Popova1

,

1 Yuri Gagarin State Technical University of Saratov, 77 Politechnicheskaya Street, Saratov 410054, Russia [email protected], [email protected], {vic_p,anay_p}@bk.ru 2 Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia [email protected]

Abstract. Modern composite materials consist of layers with different physical properties. Three-layered composite plates or sandwich plates are widely used in aerospace industry and civil engineering. However, the issues of hydroelastic vibrations of these plates resting on an elastic foundation are not well studied. We investigated the mathematical modeling problem of hydroelastic oscillations for a three-layered circular plate interacting with pulsating viscous liquid layer. The sandwich plate was mounted on Winkler foundation and forms the bottom wall of the narrow channel. The upper wall of the narrow channel was an absolutely rigid disk. The disk and plate were coaxial and parallel to each other. The channel was filled with a pulsating viscous incompressible liquid. The plate’s kinematics was considered within the framework of the broken normal hypothesis. The radial and bending vibrations of the plate were studied on the basis of the formulation and solution of the coupled hydroelasticity problem. The hydroelasticity problem includes the dynamics equations of the plate, the dynamics equations of the liquid layer and corresponding boundary conditions. Using the perturbation method, we solved the formulated hydroelasticity problem. Using the obtained solution, we constructed and investigated frequency-dependent distribution functions of sandwich plate’s displacements. These functions allowed us to determine the resonant frequencies for radial and bending vibrations of a three-layered circular plate. Keywords: Mathematical modeling · Hydroelasticity · Oscillations · Sandwich circular plate · Viscous liquid · Winkler foundation

1 Introduction Currently, there are a lot of practical usages of multilayer structures as beams and plates in various industries, for example, civil construction, machine building, aerospace, medicine. In this regard, the development of mathematical models for studying the statics and dynamics of sandwich beams and plates is relevant. Issues of the design and © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 91–101, 2021. https://doi.org/10.1007/978-3-030-65283-8_8

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approaches to the calculation of multilayered structural elements are considered in [1– 3]. The creation of mathematical models for multilayer plates based on zig-zag theory was studied in [4, 5], and [6–8] deals with studies of sandwich beams and plates under the influence of various loads. In references [9–13], the problems for the statics and dynamics of three-layered beams and plates resting on an elastic foundation and under various types’ loads were studied based on the kinematics description of a three-layered structure in the framework of the broken normal hypothesis, which was proposed in [1]. On the other hand, studies of the homogeneous beams and plates interaction with liquid are relevant. For example, the problems of developing mathematical models for studying the hydroelastic vibrations of a circular plate in contact with an ideal fluid were considered in [14–18]. The stability and vibrations of two rectangular plates forming the walls of the channel with an ideal liquid flow were studied in [19–21]. In references [22, 23], mathematical models for bending vibrations of rectangular and circular plates interacting with a viscous liquid layer are presented. Studies of the hydroelastic response of homogeneous plates resting on an elastic foundation were carried out in [24–28]. In references [29–33], vibrations of composite and three-layer elastic elements interacting with a liquid were considered. Mathematical modeling of bending vibrations of threelayered beams and plates resting on an elastic foundation was done in [34–36]. In the proposed work, we carry out mathematical modeling for radial and bending oscillations of a circular sandwich plate resting on an elastic foundation and interacting with a pulsating layer of viscous liquid.

2 Stating the Problem In this section, we present a mathematical model for the sandwich circular plate interacting with pulsating liquid layer. Let us consider a gap between two circular walls and filled with a pulsating liquid, as shown in Fig. 1. The walls of radiuses R are parallel to each other and their centers lie on the same axis. The bottom wall is a circular sandwich plate consisting of three layers, i.e. the face-sheets perceive the main load and the core between them ensures the three-layered structure works as a single package. The upper face-sheet thickness is h1 , the bottom face-sheet thickness is h2 and the core thickness is 2c.

Fig. 1. The gap between two coaxial parallel circular walls: 1 – the upper wall is a rigid disk, 2 – the bottom wall is a circular sandwich plate, 3 – viscous liquid.

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Further, according [1] we assume the plate’s core is incompressible and lightweight, as well as, neglect its work in the radial direction. The sandwich plate clamped at its contour and resting on Winkler foundation [12]. The upper wall is an absolutely rigid disk. The liquid layer thickness between walls in the unperturbed state is h0 . At the gap edge, the liquid flows into a cavity filled with the same liquid, possessing pressure with the constant component p0 and pulsating component p* (ωt), i.e. at r = R, the liquid pressure in the gap cross-section is p0 + p* (ωt). Here ω is the pressure pulsations frequency. We believe that R  h0 and consider the liquid as incompressible and viscous one. Besides, we consider the core center of the sandwich plate as a center of cylindrical coordinate system rϕz and assume that the elastic displacements of the sandwich plate are significantly less than h0 . Taking into account the axial symmetry of the gap, we investigate the axisymmetric problem. The equilibrium equations of a three-layered sandwich plate were obtained in [1] using the broken normal hypothesis [3, 11] for describing plate’s kinematics. Applying the d’Alembert’s principle to these equations and taking into account inertia forces of the plate in the radial and normal directions, we obtained the equations of motion for the sandwich plate in the form:   ∂w ∂ 2u − M0 2 = −qzr , L2 a1 u + a2 ϕ − a3 ∂r ∂t   ∂w L2 a2 u + a4 ϕ − a5 = 0, (1) ∂r   ∂w ∂ 2w − γ w − M0 2 = −qzz , L3 a3 u + a5 ϕ − a6 ∂r ∂t where the following notation is used    ∂ 1 ∂ 1 ∂  L2 (g) = rL2 (g) , (rg) , L3 (g) = ∂r r ∂r r ∂r a1 = h1 K1+ + h2 K2+ + 2 c K3+ , a2 = c (h1 K1+ − h2 K2+ ),       1 1 2 + + + + + 2 a3 = h1 c + h1 K1 − h2 c + h2 K2 , a4 = c h1 K1 + h2 K2 + c K3 , 2 2 3       1 1 2 a5 = c h1 c + h1 K1+ + h2 c + h2 K2+ + c2 K3+ , 2 2 3     1 1 2 a6 = h1 c2 + c h1 + h21 K1+ + h2 c2 + c h2 + h22 K2+ + c3 K3+ , 3 3 3 Kk+ = Kk +

4 Gk , k = 1, 2, 3, M0 = ρ1 h1 + ρ2 h2 + ρ3 h3 . 3

Here M 0 is the cross-section mass of the sandwich plate; qzr , qzz are shear and normal stresses of the liquid layer, respectively, acting on the upper face-sheet; Gk is the shear

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modulus of the k-th layer; K k is the bulk modulus of the k-th layer; ρ k is the density of the k-th layer material; u is the radial three-layered circular plate displacement; w is the three-layered circular plate deflection; ϕ is the rotation angle of the normal in the sandwich circular plate core after deformation; γ is the Winkler foundation modulus. According [37] stresses qzr , qzz are determined by the expressions     ∂Vr  ∂Vz ∂Vz  + qzr = ρν , q = − p − 2ρν , (2) zz ∂r ∂z z=w+h1 +c ∂z z=w+h1 +c where V r , V z are the projections of liquid velocity on the coordinate axis, ρ is the density of liquid, ν is the kinematic coefficient of the liquid viscosity, p is the liquid pressure. The boundary conditions of Eqs. (1) are u=ϕ=w= r

∂w = 0 at r = R, ∂r

(3)

∂w = 0 at r = 0. ∂r

The equations of motion for a viscous incompressible liquid are represented by the Navier-Stokes equations and the continuity equation. However, according to [37], we assume the movement of the liquid in the gap as a creeping one and neglect the inertial terms in the above equations. As a result, we obtain the following equations of creeping motion for the viscous liquid layer:   2 1 ∂p ∂ Vr ∂ 2 Vr 1 ∂Vr Vr =ν + + − 2 , ρ ∂r ∂r 2 r ∂r ∂z 2 r   2 1 ∂p ∂ Vz ∂ 2 Vz 1 ∂Vz , (4) =ν + + 2 ρ ∂z ∂r r ∂r ∂z 2 ∂Vr 1 ∂Vz + Vr + = 0, ∂r r ∂z where V r , V z are the projections of liquid velocity on the coordinate axis, ρ is the density of liquid, ν is the kinematic coefficient of the liquid viscosity, p is the pressure. The boundary conditions of Eqs. (4) are the no-slip conditions Vr = 0, Vz = 0 at z = h0 + c + h1 , Vr =

(5)

∂u ∂w , Vz = at z = w + c + h1 , ∂t ∂t

and conditions for the pressure at the gap edge and the symmetry axis: p = p0 + p∗ (ωt) at r = R, r

∂p = 0 at r = 0. ∂r

(6)

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3 Solution of the Problem Let us denote the deflection amplitude of sandwich circular plate as wm  h0 and introduce small parameters ψ=

wm h0  1, λ =  1, R h0

(7)

as well as following dimensionless variables: z − c − h1 r wm ωR , ξ = , τ = ωt, Vz = wm ωUζ , Vr = Uξ , h0 R h0 ρνwm ω w = wm W , u = um U , ϕ = ϕm Φ, p = p0 + p1 (τ ) + P, h0 ψ 2

ζ =

(8)

where um is the radial displacement amplitude of the sandwich plate, ϕ m is the rotation angle amplitude of the normal in the sandwich plate core. Bearing in mind the expressions (8) and neglecting the terms of order ψ and λ [38], we presented the Eqs. (4) in the form of: ∂ 2 Uξ ∂P ∂Uξ ∂Uζ 1 ∂P = = 0, + Uξ + = 0. , ∂ξ ∂ζ 2 ∂ζ ∂ξ ξ ∂ζ

(9)

The boundary conditions (5) and (6) take a form of: Uξ = 0, Uζ = 0 at ζ = 1, Uξ = 0, Uζ = P = 0 at ξ = 1, ξ

∂W at ζ = 0, ∂τ

(10)

∂P = 0 at ξ = 0. ∂ξ

By solving the Eqs. (9) with boundary conditions (10) we obtained: ∂P ζ (ζ − 1) , ∂ξ 2   2  ∂P 3ζ − 2ζ 3 − 1 1 ∂ ξ , Uζ = ξ ∂ξ ∂ξ 12 ⎤ ⎡ ξ  1 ξ ∂Uξ  1 ∂W 6 ∂W d ξ ⎦d ξ , d ξ. P = 12 ⎣ ξ = ξ  ξ ∂τ ∂ζ ζ =0 ξ ∂τ Uξ =

ξ

0

(11)

0

By substituting the expressions (2), (7), (8) and (11) into Eqs. (1) we have written the following equations for radial and bending hydroelastic oscillations of the circular sandwich plate resting on Winkler foundation

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  ξ ∂ 2U a3 wm ∂W ρνwm ωR 6 ∂W 2 d ξ, L2 a1 um U + a2 ϕm Φ − ξ − M0 ω um 2 = R ∂ξ ∂τ ξ ∂τ h20 0

  a5 wm ∂W L2 a2 um U + a4 ϕm Φ − = 0, R ∂ξ   ∂ 2W a6 wm ∂W L3 a3 um U + a5 ϕm Φ − − γ W − M0 ω2 wm 2 R ∂ξ ∂τ ⎡ ⎤ 1 ξ 1 12ρνwm ωR2 ∂W ∗ ⎣ = p0 + p + ξ d ξ ⎦d ξ . 3 ξ ∂τ h0 ξ

(12)

0

The boundary conditions of Eqs. (12) are U =Φ =W =

∂W ∂W = 0 at ξ = 1, ξ = 0 at ξ = 0. ∂ξ ∂ξ

(13)

Bearing in mind the boundary conditions (13) we presented the solution of the Eqs. (12) in the form of eigenfunctions series for the Sturm-Liouville problem: ∞ 

u = −um

k=1

ϕ = −ϕm

   J (β ξ ) I (β ξ )  1 k 1 k + βk Qk0 + Qk (τ ) . J0 (βk ) I0 (βk )

∞  k=1

   J (β ξ ) I (β ξ )  1 k 1 k 0 + , βk Tk + Tk (τ ) J0 (βk ) I0 (βk )

(14)

∞    J (β ξ ) I (β ξ )   0 k 0 k 0 w = wm − . Rk + Rk (τ ) J0 (βk ) I0 (βk ) k=1

Here J 0 , J 1 are the Bessel function of the first kind, I 0 , I 1 are the modified Bessel function, β k is the root of the transcendental equation I 1 (β k )/I 0 (β k ) = –J 1 (β k )/J 0 (β k ) [1]. R0k , Qk0 , Tk0 mean the unknown coefficients, corresponding to the static pressure p0 and Rk , Qk , Tk are the unknown time functions, corresponding to the pulsation pressure p*. Thus, by setting the terms number in the series (14), then substituting them into Eqs. (12) and performing the re-decompositions for the remaining terms of Eqs. (12) as the eigenfunctions series, we obtain a system of linear algebraic equations for determining R0k , Qk0 , Tk0 , and a system of linear differential equations for determining Rk , Qk , Tk . Next, we consider harmonic oscillations in the main mode, i.e. we assume k = 1 and 2 d 2 Q1 = −Q1 , dd τR21 = −R1 . In this case, according to the above, we obtain the system dτ2 of linear algebraic equations a3 wm 0 R1 = 0 R a5 wm 0 R1 = 0, a2 um Q10 + a4 ϕm T10 − R a1 um Q10 + a2 ϕm T10 −

(15)

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2 J1 (β1 ) a6 wm 0 4 R1 )β1 − R3 γ wm R1 = −R3 p0 , R β1 J0 (β1 )

(a3 um Q10 + a5 ϕm T10 −

and the system of linear differential equations (a1 um Q1 + a2 ϕm T1 −

a3 w m 11 − R2 u M ω2 β Q = −R2 ρνω w 6 ∂R1 d 11 , R1 )β13 d11 m 0 m 1 1 R β1 ∂τ 11 h0 ψ 2

(a2 um Q1 + a4 ϕm T1 − (a3 um Q1 + a5 ϕm T1 − = −R3 p∗ (τ )

a5 wm 11 R1 ) β13 d11 = 0, R

(16)

a6 wm R1 ))β14 − R3 wm γ R1 + R3 wm M0 ω2 R1 R

ρvω ∂R1 31 2 J1 (β1 ) wm − 12R3 d . 2 β1 J0 (β1 ) h0 ψ ∂τ 11

Solving (15), (16) for case of p* = pm sin(ωt) we presented the radial displacement and deflection of the circular sandwich plate resting on Winkler foundation as u=−

pm R3 p0 R3 Au (0, ξ ) − Au (ω, ξ ) sin(ωt + φu (ω)), b21 b21

w=−

pm R3 p0 R3 Aw (0, ξ ) − Aw (ω, ξ ) sin(ωt + φw (ω)), 0 b21 b21

   b221 ((b12 )2 + (K11 ω)2 ) Au (ω, ξ ) =  (b11 b22 − b21 b12 )2 + (b11 K21 ω − b21 K11 ω)2  (b21 b11 )2 Aw (ω, ξ ) = (b11 b22 − b21 b12 )2 + (b11 K21 ω − b21 K11 ω)2

tgϕu (ω) =

 2 J1 (β1 ) J1 (β1 ξ ) I1 (β1 ξ ) + I0 (β1 ) β14 J0 (β1 ) J0 (β1 )  2 J1 (β1 ) J0 (β1 ξ ) I0 (β1 ξ ) − I0 (β1 ) β 5 J0 (β1 ) J0 (β1 )

(17)  ,  ,

1

K11 ω(b11 b22 − b21 b12 ) − b12 (b11 K21 ω − b21 K11 ω) , b12 (b11 b22 − b21 b12 ) + K11 ω(b11 K21 ω − b21 K11 ω) tgϕw (ω) =

b21 K11 ω − b11 K21 ω , b11 b22 − b21 b12

where Au (ω, ξ ), Aw (ω, ξ ) are frequency-dependent distribution functions of sandwich plate’s displacements and we accepted notation: b11 = a1 − a22



 b21 = (a5 a2 a4 − a3 ), b22

ρν R2 ρν R3 31 , K21 = 12 4 d11 , 4 2 2 h0 ψ β1 h0 ψ β1     2 (β ) J12 (β1 ) J J (β ) 1 4 J1 (β1 ) 4 1 1 1 31 = = 2 12 − − , d11 . J02 (β1 ) β1 J0 (β1 ) β1 J0 (β1 ) β1 J0 (β1 ) K11 = 6

11 d11

  M0 ω2 R2 a R , b = a a − a 12 2 4 3 5 11 β 2 d11 1     = a6 R + γ R3 β14 − a52 (a4 R) − M0 ω2 R3 β14 ,

a4 −

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4 Calculation Results As an example, we carried out, a numerical study of functions Au (ω, ξ ), Aw (ω, ξ ), for the gap with the following parameters: R = 0.1 m, h0 /R = 0.08, h1 /R = 0.01, h2 /R = 0.015, ρ = 103 kg/m3 , ρ1 = ρ2 = 2.7·103 kg/m3 , ρ3 = 2.15 × 103 kg/m3 , K 1 = K 2 = 8·103 Pa, K 3 = 4.7·109 Pa, G1 = G2 = 2.67·1010 Pa, G3 = 9·107 Pa, ν = 10−6 m2 /s, γ = 8·108 Pa/m. In the calculations, we considered the ratio of Au (ω, ξ ), Aw (ω, ξ ) to their values at ω = 0, i.e. we introduced the functions α u (ω) = Au (ω, ξ )/Au (0, ξ ), α w (ω) = Aw (ω, ξ )/Aw (0, ξ ). The α u (ω), α w (ω) are the amplitude frequency responses of radial displacements and deflections for the circular sandwich plate, respectively. These functions allow us to determine the resonant frequencies for the main mode of radial and bending oscillations, as well as and the oscillations amplitudes at these frequencies. The results of the calculations are presented in Fig. 2 and Fig. 3.

Fig. 2. The frequency responses α u (ω): 1 – the Winkler foundation modulus γ = 8 ×108 Pa/m, 2 – the Winkler foundation modulus γ = 0 Pa/m.

Fig. 3. The frequency responses α w (ω): 1 – the Winkler foundation modulus γ = 8 ×108 Pa/m, 2 – the Winkler foundation modulus γ = 0 Pa/m.

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5 Summary and Conclusion We have proposed a mathematical model for studying the hydroelastic response of the circular sandwich plate resting on Winkler foundation and interacting with a pulsating viscous liquid layer. Within the framework of this model, a resolving system of equations for studying radial and bending vibrations of the sandwich plate is obtained. The calculations of the hydroelastic response of the circular sandwich plate for steady-state harmonic oscillations were presented. As a result of the simulation, the importance of jointly taking into account the inertia forces of the sandwich plate in the radial and normal directions are shown since the mutual influence effect of these forces on each other is observed. We note that this effect was not found in [32–36], were only inertia forces in the normal direction were taken into account and shear stresses in a viscous fluid were neglected. In addition, a significant effect of the elastic foundation on the resonant frequencies and oscillation amplitudes of the sandwich plate is shown. Thus, we have found that, in contrast to hydroelasticity problems of the homogeneous elastic plate, in which they are traditionally limited only to the study of bending vibrations [14–28], for three-layered plates, it is important to take into account the inertial forces in the radial direction, as well as the tangential stresses in the viscous fluid layer. Acknowledgments. The study was funded by Russian Foundation for Basic Research (RFBR) according to the projects № 18-01-00127-a and № 19-01-00014-a.

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Numerical Simulation Results of the Optimal Estimation Algorithm for a Turn Table Angular Velocity Roman Ermakov(B)

, Alexey L’vov , Anna Seranova , Nina Melnikova , and Elena Umnova

Yuri Gagarin State Technical University of Saratov, Saratov, Russian Federation [email protected], [email protected], [email protected], [email protected], [email protected]

Abstract. The article presents the results of numerical modeling of the accuracy of measuring and reproducing angular velocity with precision rotary stand (turn table), based on all sensors included in it. A comparison of the estimates of the angular velocity of the turntable of the stand with three different methods is performed. The results of modeling the dynamics of the rotary sstand demonstrate a significant difference between the errors in determining the angular velocity of the platform of the stand by measuring quantities from various sensors included in its composition. Keywords: Angular velocity · Precision rotary table · Estimation · Maximum-likelihood method

1 Introduction Gyroscopic devices are widely used in orientation systems for marine objects, aviation, rocket and space technology, as well as navigation systems for studying the state of gas and oil pipelines, in inclinometry, etc. When setting up and testing precision gyroscopic devices, rotary stands (turn tables) are used, which reproduce angular velocities that can be constant or vary according to a certain law with high accuracy and stability. The creation of such stands is an independent task, the successful solution of which largely determines the progress in the development of gyroscopic instrumentation. Controlled stands (turn tables) used for the study of gyroscopic devices should have at least an order of magnitude higher accuracy than the tested devices, as well as control modes adequate to operating conditions, which should help to identify the true values of the achieved technical characteristics. Typically, the stand includes a rotary platform, an electric motor, a sensor and a control system. Precision rotary stands for reproducing angular velocities are created, as a rule, using an angle sensor [1–7]. The main disadvantage of such stands is the inability to accurately reproduce low angular velocities [1, 8–16]. As an alternative, a number of authors suggest © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 102–113, 2021. https://doi.org/10.1007/978-3-030-65283-8_9

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using inertial sensors as a sensor of the angular velocity of the stand platform. Similar stands were considered in [1, 9–16]. In the cited works, however, insufficient attention is paid to issues of estimating the error in determining the angular velocity of the rotary platform of the stand. In this paper, we present the numerical simulation results of the algorithm for optimal estimation of the turn table angular velocity based on the indications of sensors of various physical natures, given in [17].

2 The Design of the Measuring Stand The generalized diagram of the stand [17] is presented in Fig. 1.

Fig. 1. The generalized diagram of the stand

The stand consists of the next sensors: angle (2), angular velocity (4), tangential (6) and centripetal (7) accelerations, which are rigidly connected to the auxiliary platform (5) connected to the main platform (1), to which the device under test is attached (10) using a rigid shaft (3), which rotates using an electric motor (8) controlled by a control unit. Information about the angular velocity, its derivative and integral, coming from the corresponding sensors, is converted by the control unit into motor control signals. In the works [1, 9–16] no consideration is given to assessing the uncertainty of determining the angular velocity of the turn table platform. For example, the estimate

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given in [12] is of a qualitative nature; in other works, the uncertainty of the data of a single sensor is studied, and the signals of this sensor control the turntable. In works [2, 3, 5, 7], a rather detailed analysis of the uncertainty of reproduction and measurement of a plane angle was carried out. However, as was shown in [17–19], it is impossible to reliably determine small angular velocities from the readings of the angle sensor. In connection with the foregoing, in work [17] a methodology for the optimal estimation of the angular velocity of the stand rotary platform shown in Fig. 1 was proposed. To find an asymptotically effective estimate of the angular velocity in [17, 19], models of sensor errors were constructed and their properties were investigated.

3 Optimal Estimation of the Stand Angular Velocity by the Maximum Likelihood Method In work [17], the laws of the distribution of sensor errors were mismatched with the normal law (error distribution was found to be not normal), which limits the applicability of the least squares method (LSM) to determine the efficient estimate of the angular velocity of the stand platform (we cannot use the conventional LSM, since this method is based on the assumption that all measurement errors are normally distributed). In [17, 18], it was proposed to find the optimal estimate of the angular velocity of the stand turntable using the maximum likelihood method. Below, we briefly describe the essence of the method proposed in the above papers. Let yk be the output sensor responses. Then one can write the following:   (1) yk = Mk gk (ωk ) + ξk = Mk gk (ωk ) + ζk + ξk0 where ω is the angular velocity, g(ω) is the transfer function of the sensor, M are the scale coefficients of the sensors, ξ is the additive component of the error of the sensors, including systematic ξ0 and random ζ components, k = 1…m is the number of the sensor. Let us represent the angular velocity estimate obtained on the basis of the data taken from the k-th sensor as: ω˜ k = fk (yk , z1 , z2 , z3 , . . .) where the functions fk (yk , z1 , z2 , z3 , . . .) are determined by the expressions given in [17] and zi are unknown parameters. In order to determine the joint angular velocity estimator set by the turn table using the maximum likelihood method (MLM), according to the technique described in [17], first, separate ML estimates of the angular velocity are determined from the data recorded by stand-alone sensor. In [17, 19], expressions are given for the measurement error distribution of the sensors used in the turn table. Denote xk = gk (ωki ) and represent (1) in the next form: ξki = yki − Mk xk We assume that the errors ξki are independent. Let us consider the sets of normal equations that were obtained in [17] for each sensor implemented in the turn table stand.

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3.1 Angular Velocity Maximum Likelihood Estimation Using the Readings Taken from the Angular Velocity Sensor For the angular velocity sensor, taking into account the fact that in this case g(ω) = ω, we can represent (1) as y = ωˆ = M ω + ζ = M ω + (ζω + ζω0 ), were ω is true angular velocity of the tern table, ωˆ is the angular velocity sensor readings; M is the scale factor, ζ = (ζω + ζω0 ) is the angular velocity measurement error. In [17], the following expression is given for the probability density distribution of angular velocity measurement errors:      η−d η+d 1 − erf √ , (2) erf √ p(η) = 4d 2σ 2σ where erf (x) =

√2 π

x

e−t dt is the Gauss error function (Laplace integral); d and σ are 2

0

the distribution parameters defined in [17]. So, we can the following expression is for the joint probability density for a sample of N angular velocity measurements [17]:      N yi − Mω ω − d yi − Mω ω + d 1 − erf = erf WN = √ √ 4d 2σi 2σi i=1  N     N  1 yi − Mω ω + d yi − Mω ω − d erf − erf → max, √ √ 4d 2σi 2σi i=1 For further consideration it is more convenient to use the logarithm of the above likelihood function [14]:

  N      1 N yi − Mω ω + d yi − Mω ω − d L(ω) = ln(WN ) = ln erf − erf = √ √ 4d 2σi 2σi i=1



1 = N ln 4d



     N yi − Mω ω − d yi − Mω ω + d − erf . + ln erf √ √ 2σi 2σi i=1 (3)

It can be seen that (3) depends on two parameters ω and σ. An estimate of the parameter ω is further used to obtain a joint estimate; and an estimate of the parameter σ determines the weight coefficient, with which the obtained estimate of ω is included in this joint angular velocity estimate. Finally, in [17], the following set of normal equations is given for determining the estimate of the angular velocity from the readings of the angular velocity sensor and its variance: dL(ω, σ ) N1 (ω, σ ) = = 0, dω D1 (ω, σ ) N

i=1

(4)

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where



   (yi − Mω ω − d )2 (yi − Mω ω + d )2 N1 (ω, σ ) = Mω exp − − exp − ; 2σi2 2σi2      √ yi − Mω ω − d yi − Mω ω + d − erf ; D1 (ω, σ ) = π σ erf √ √ 2σi 2σi   √ 1 (yi −Mω ω−d )2 exp − − M ω − d 2 ) (y N i ω 2 2 σi dL(ω, σ ) − = √ 2 dσ π σi i=1   √ 1 (yi −Mω ω+d )2 exp − 2 (yi − Mω ω + d ) 2 σi2 − = 0. (5) √ 2 π σi

It is also proposed there to solve the system (4), (5) for ω and σ using numerical algorithms based on quasi-Newtonian methods [20]. 3.2 Angular Velocity Maximum Likelihood Estimation with the Data from Tangential and Centripetal Acceleration Sensors Expressions for angular velocity estimation using the measurement data form the sensors of centripetal and tangential components of linear acceleration are given in [17]. For the centripetal acceleration sensor these relationships are the next: ω2 r ; g ω2 r aˆ C = MC + (ζarC + aC0 ); g  ⎛ ⎞   g(ζarC + aC0 ) MC∗ + MC aC g ⎝ω − ⎠, = ωˆ C = g(ω) = r KCr r aC =

(6)

where aˆ C is the measured value of centripetal acceleration; aC is the true value of centripetal acceleration; MC is the scale factor of the centripetal acceleration sensor; MC∗ the ideal value of the scale factor of the centripetal acceleration sensor; MC is the error of the scale factor of the centripetal acceleration sensor; aC0 is the constant error component of the centripetal acceleration sensor; ζarC is a zero mean normally distributed random variable; g is the gravity projection on the accelerometers sensitivity axis; and r is the radius (the distance from the pivotal point to the center of mass of the accelerometer sensitive element). The tangential acceleration component is equal: aτ =

ε·r , g

(7)

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where aτ is the tangential acceleration; ε is the angular acceleration. That is why, the angular velocity estimator obtained from the readings of an tangential acceleration sensor over a time interval T = t n –t (n–1) , is defined by the following expression, [17]: 1 ωˆ τ [tn ] = g(ω) = T

tn tn−1

g aˆ τ dt + ωˆ τ [tn−1 ], ·r

Kτr

(8)

where T is the integral action time; Kτr is a coefficient taking into account the setup error of the tangential acceleration sensor; aˆ τ = Mτ aτ + ζaτ ; aτ is the true value of the tangential acceleration; ζaτ = aτ0 + ξaτ is a random component of the measurement error of the this acceleration, Mτ is the scale factor of the acceleration sensor. As shown in [17] the probability density distribution of both sensors errors is described by expression (2). Now we can provide the following set of normal equations for both the tangential and the centripetal acceleration sensors: dL(ω) N2 (ω) dgk (ωk ) = · = 0, dω D2 (ω) dω N

(9)

i=1

where:



   (yi − Mk gk (ωk ) − d )2 (yi − Mk gk (ωk ) + d )2 N2 (ω) =Mω exp − − exp − ; 2σi2 2σi2      √ yi − Mk gk (ωk ) − d yi − Mk gk (ωk ) + d − erf ; D2 (ω) = π σ erf √ √ 2σi 2σi     ⎧ 2 2 √ √ ⎫ 1 ηi 1 ψi ⎪ ⎪ ⎪ η ψ exp − exp − 2 N i i 2⎪ ⎬ 2 σ2 2 σ2 dL(ω, σ ) ⎨ i i =0 (10) = − √ 2 √ 2 ⎪ ⎪ dσ πσi π σi ⎪ ⎪ ⎩ i=1 ⎭

where the following notation is used: ηi = yi −Mω gk (ωk )−d ; ψi = yi −Mω gk (ωk )+d . 3.3 Angular Velocity Maximum Likelihood Estimation from the Angular Sensor Readings The angular velocity of the turn table can be calculated from the measurement data taken from the angular sensor using the next expressions obtained in [17]: ωˆ A = g(ω) =

α[n] − α[n − 1] , αˆ = α + α0 (α) + αζ T

αζ (α0 (α[n]) − α0 (α[n − 1])) ω+ , ωˆ A ∼ = ω + G ω + α T0

(11) (12)

where ωˆ A is the angular velocity ML estimation from the angular sensor readings; αˆ is the angle estimate; α0 (α) is the systematic component of the angle sensor error; αζ

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is the random component of the error of the angle sensor; α is the true value of the angle; T is the sampling period of the angular velocity estimation algorithm; T 0 is the ideal value of the period; α[n] is the value of the angle at time n; G is the master oscillator error. Estimation algorithm by the MLM for the angular sensor is defined using the following set of normal equations, [17], [19]: WN =

R N

! " ρj · Nx μj , σj ;

(13)

i=1 j=1

⎞ ⎞ ⎛ ⎛ R N N R ! " ! " L(α) = ln(WN ) = ln⎝ ρj · Nx μj , σj ⎠ = ln⎝ ρj · Nx μj , σj ⎠; (14) i=1 j=1

i=1

R #

(yi −α)2 2σij2 √ 3 2π σij

ρj (yi −α) exp

j=1 dL = dα i=1 R # N





(yi −α)2 2σij2

exp

ρj

j=1  

dL(α, σ ) = dσ

j=1 

= 0;

√ 2π σij

    ⎫ ⎧ Y Y ⎬ ρi exp σiα (2π)N ∂σ∂ det(σ ) ρi Yiα exp σiα R ⎨ # ij ij ij −√ N − 21 3 √ (2π ) det(σ )σij2 ⎭ N j=1 ⎩ (2π)N det(σ ) i=1

R # j=1

(15)

  Y ρi exp σiα

√

,

(16)

ij

(2π )N det(σ )

Yiα = (yi − α)T (yi − α); ρi are non-negative coefficients of the poly-Gaussian distribution (the sum of several Gaussian distributions with different variances and mathematical expectations), σ is N×R matrix. In practice, as a rule, scale factors M k . are known inaccurately and may change during the stand operation. The methodology for their estimation is also given in [17].

4 Technique for Turn Table Platform Angular Velocity Integral Estimation The technique for determining the angular velocity estimator of the turn table platform using the readings taken from all four sensors consists of two stages. At the first stage, the calibration of the stand is carried out; after that at the second stage, the stand reproduces the angular velocity, which is measured by all sensors. The main items of the presented technique are the following. At the first stage (calibration of the turn table): 1) For a fixed (non-rotating) stand platform, the average values of ζω0 , aC0 , aτ0 are determined, which are used as initial approximations.

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2) Then the platform is rotated at fixed angles αi with fixed angular velocities ωi , i = 1, …, M. The durations T i of the full turn cycles are measured. 3) For all sensors, the scale factors M k are calculated by the weighted least-squares method using the following expressions. $ M M   αi 0 Mk = ωi ω˜ ki − ξk ωi2 , ωi = . (17) Ti i=1

i=1

The values determined while the stand platform was motionless (step 1 above) we take for estimates of the constant components ξk0 . This completes the calibration of the stand. After the calibration procedure one can proceed to measuring process during the stand operation. So, the second stage consists in the following: 4) According to the MLM, by numerical solution of the equation sets (4)–(16) is carried out and the ML estimates of the angular velocity ωˆ k and variance σk2 are obtained. 5) Weighting coefficients pk are determined as the reciprocal values of the variances, calculated at the previous step: pk = 1/σk2 . 6) Finally, the joint angular velocity estimate calculated as the weighted average of the separate estimates of this parameter found at the step 4) using the data from all the used sensors:

ω˜ ML =

M k=1

$ pk ωˆ k

M

pk

(18)

k=1

5 Simulation Results for the Turn Table Accuracy To confirm the operability and effectiveness of the proposed method for obtaining a joint angular velocity estimate, computer simulation of sensors’ calibration and measurement processes using them was performed. First, we studied the estimation accuracy of the angular velocity for each sensor in the turn table separately. The parameters of the sensors were taken from the works [12, 19]. The results of simulation experiments with individual sensors are shown in Fig. 2. It gives the obtained simulation dependences of the errors in estimating the turn table angular velocity on the measured angular velocity itself for each type of sensors used. The first three curves refer to the angle sensor when the averaging time was: 1 s, 0.1 s, and 0.01 s (curves numbered 1, 2, and 3, respectively). The remaining three curves refer to the sensor of angular velocity, centripetal acceleration sensor, and tangential acceleration sensor (curves with the numbers 4, 5, and 6, respectively). Figure 2 shows that the accuracy of estimating the angular velocity for its small and very small values is significantly higher for the angular velocity sensor, which performs direct measurements. It should also be noted that the accuracy of the rotational speed estimation basing on the measured data from the angle sensor largely depends on the

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Fig. 2. The dependence of the individual sensors errors on the angular velocity of the turn table

averaging time. For precision stands, the necessary accuracy is achievable when the averaging period is about of several seconds [11, 21]. However, with increasing angular velocity, the superiority in the accuracy of the angular velocity sensor decreases markedly. Since modern sensors, which are tested using rotary stands, must successfully operate in a frequency bandwidth from tens to hundreds of hertz [21, 22], rotary test stands for such devices cannot be built on the basis of an angle sensor alone. Therefore, several sensors of various physical natures are used in one stand. As a result, a “switching” method was proposed [12] that consist in using at any time the sensor, which measures with maximum accuracy in a given turn table operating mode and in a specific range of angular velocities to be measured. After that, the accuracy of the joint angular velocity estimation was investigated, based on the use of all estimates obtained by individual sensors taking into account their weight coefficients in accordance with expression (18). The comparative results of computer simulation for three estimation techniques are shown Fig. 3, which presents the relative estimation error of turn table angular velocity versus its true value. The considered techniques are: 1) the switching method proposed in [12] (curve 1); 2) method of simple averaging of individual angular velocity estimates obtained by different sensors, without using weight coefficients (curve 2); 3) MLM joint estimate proposed in the paper (curve 3). In order to depict visually the efficiency gain of the MLM joint estimate before the known switching technique the difference of these estimators’ errors are shown in Fig. 3 (dashed curve 4), the ordinate axis for this curve being given on the right. As it can be seen from the picture the MLM error is less than the error of switching method in the whole considered angular velocity range. It is also clear from Fig. 3 that the technique of simple arithmetic averaging (curve 2) has the lowest accuracy of all methods since the used sensors based on various physical principles; so their accuracies may differ significantly at different segments

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Fig. 3. Comparison of the error in estimating the angular velocity by various methods

of the studied angular velocity range. Switching method and the MLM based technique demonstrate close accuracies at the low angular velocity range where the angular velocity sensor operates effectively; but their estimation results vary drastically (the switching method can be inferior in accuracy to the MLM up to 25–30%) for the range of high angular velocities where the angle and linear acceleration sensors provide more accurate estimators compared to angular velocity sensor.

6 Conclusion The article gives a brief description of a new method for estimating the angular velocity of a precision turntable based on a joint maximum likelihood estimation using a combination of data from several sensors of different physical nature. The results of computer simulations showed that the accuracy of measurement by the used sensors of angular velocity, angle rotation, centripetal and tangential components of linear acceleration depends on the mode of the turn table operation as well as the magnitude of measured angular velocity. The simulation results of the turn table dynamics demonstrate that the difference in the estimation errors of the stand platform angular velocity basing on the measurements of various sensors can be very substantial. A comparison of the angular velocity estimates of the turn table with three different approaches is performed. The technique, based on the maximum likelihood method, allows one to reduce the error in estimating the angular velocity of the stand platform in comparison with other known methods. The reduction in estimation error depends on the operation mode of the stand and may achieve the value of more than 25%.

References 1. Sinelnikov, A.E., Kudryavtsev, V.N., Pavlov, P.A.: A new Russian standard in the field of lowfrequency motion quantities measurements. In: Proceedings 9-th St.-Petersburg International

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17. Ermakov, R.V., Seranova, A.A., L’vov, A.A., Kalikhman, D.M.: Optimal estimation of the motion parameters of a precision rotating stand by maximum likelihood method. Measure. Techn. 62(2), 139–146 (2019). https://doi.org/10.1007/s11018-019-01598-x 18. Ermakov, R.V., Kalihman, D.M., L’vov, A.A., Sokolov, D.N.: Angular velocity estimation of rotary table bench using aggregate information from the sensors of different physical nature. In: Proceedings 2017 IEEE Russia Section Young Researchers in Electrical and Electronic Engineering Conference, pp. 820–825 (2017) 19. Ermakov, R.V., Kalikhman, D.M., Kondratov, D.V., Lvov, A.A.: Errors’ distribution laws analysis of sensors for the rotary tables. Matematicheskoye modelirovaniye, komp’yuternyy i naturnyy eksperiment v yestestvennykh naukakh [Mathematical modeling, computer and natural experiment in the natural sciences], 3, 9–16. (2016). http://mathmod.esrae.ru/3-19. (in Russian) 20. Gill, P.E., Murray, W., Wright, M.H.: Practical Optimization. Academic Press, London (1981) 21. Grebennikov, V.I., Kalikhman, L.Y., Kalikhman, D.M., Nahov S.F., Skorobogatov, V.V., Sapozhnikov, A.I., Smirnov, E.S.: Vibration-resistant pendulum linear acceleration meter with digital feedback. In: Proceedings 22nd St.-Petersburg International Conference on Integrated Navigation Systems, ICINS 2015, St. Petersburg, CSRI Elektropribor, pp. 368–376 (2015) 22. Ermakov, R.V., Popov, A.N., Scripal, E.N., Kalikhman, D.M., Kondratov, D.V., L’vov, A.A.: Methods for testing and test results of inertial sensors intended for operation in helicoptertype aircraft. In: Proceedings 24-th St. Petersburg International Conference on Integrated Navigation Systems, St. Petersburg, CSRI Elektropribor, pp. 335–338 (2017)

Comparison of LSTM and GRU Recurrent Neural Network Architectures Anton Pudikov

and Alexander Brovko(B)

Yuri Gagarin State Technical University of Saratov, Saratov, Russia [email protected], [email protected]

Abstract. This paper describes the comparison results of two types of recurrent neural network: LSTM and GRU. In the article the two types of RNN architecture are compared with the criterion of time consumed for test problems solving and training. Information about network training is provided in order to explain the differences in the training of LSTM and GRU RNN’s types and the final difference in time. Mathematic models of this neural network types are provided. The article includes description of software implementation of recurrent neural networks. As a result of research the numerical comparison of training and solving time is provided, and practical hints and conclusions are derived. Keywords: Recurrent neural network · Deep learning networks · Long Short-Term Memory · Gated Recurrent Unit

1 Introduction Recurrent neural networks (or RNNs) are deep learning neural networks that gain popularity as a machine learning method at present [1]. In general, the results that deep learning networks (or DNNs) can reach are better [1] than the results of alternative intelligent algorithms in a such of areas: speech recognition, computer vision, natural language processing, computer science in medicine and other. It can be concluded that deep learning is a form of learning that involves modeling or extracting data using multiple filter layers, often layers with of complex structure [1]. Such a very generalized approach is preferable at quite complex problems, examples of which are listed above and differ significantly from traditional programming algorithms, as well as from other methods of machine learning and designing neural networks. RNN as a kind of deep learning networks, which differs from other types by a directed sequence of connections between elements (network neurons). Thus, it is RNN that allows you to process sequences of events [1], a series of frames, or key points in time due to the presence of “internal memory” - a block structure within a neuron with internal connections and stored values. The specific implementation of such a block can significantly differ in different types of RNN, but its presence is a necessary condition for processing data sequences in time.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 114–124, 2021. https://doi.org/10.1007/978-3-030-65283-8_10

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The growing popularity of both deep neural networks and their subspecies (recurrent neural networks) can be explained by several factors [2]. Firstly, the widespread use of the GPU (Graphics Processing Unit) together with the CPU (Central Processing Unit) has led to the possibility of training and solving problems with such networks in a reasonable amount of time. An important role in this process was played by the emergence and dissemination of the technology of using CUDA cores (Compute Unified Device Architecture) as part of the GPU for even greater computational speedup [2]. Secondly, the emergence and filling of training sets, the dissemination of more data on which such networks can learn. It is known that even training a multilayer perceptron (the simplest form of a neuron in a deep learning network) is much more complicated and requires more data and time than training a simple perceptron [2]. This example illustrates the problem of learning deep networks in general. And, finally, thirdly - the emergence of new methods of training for these networks [3]. Detailed information about them is presented below, as well as an explanation of how important it was to solve the problems of a disappearing gradient and retraining. The structure of the article is as follows. Section 2 is devoted to a review of the structure and training features of recurrent neural networks [3]. In addition, Sect. 2 formulates tasks for comparing the time spent working with various types of RNN, provides and describes the software implementation of each type. Section 3 describes the numerical results for the time duration of executing of the considered types of network [3].

2 Method and Implementation 2.1 The Structure of RNN It has already been stated above that a recurrent neural network is one of the classes of deep learning networks. At least, this means the multilayer structure of a neuron. However, the key difference of such a network is a storage of the internal state of the neuron and the multiple, cyclical return to it [4]. This process can be implemented in a different way, but in general terms it can be represented in the form, shown in Fig. 1. The following values appear in this diagram: • (U, V, W ) - parameters on each layer. RNN, unlike other deep learning networks, uses the same parameters on each layer [4]; • xt - input at step t, represented by a moment in time. For example, x1 is a vector with one “hot state” (one-hot vector), which corresponds to the second word of the sentence being analyzed [4]; • st is the hidden state of step t. In fact, this is the memory of the network. st has a dependency represented by the function of the current input xt and previous states.

  st = f Ut + Wst−1

(1)

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Fig. 1. Sweep of RNN’s neuron.

• The function f is non-linear, for example, as tanh or ReLU. s−1 , required to calculate the hidden state number one, is initialized to zero (zero vector); • or - exit at step t. For example, in the process of predicting a word in a sentence, the output is represented by a vector of probabilities in our dictionary [4]; The using of the same parameters (U, V, W ) on each of the layers is due to the need for the input data to remain unchanged - during the operation of the network, the initial formulation of the problem should not be distorted despite the fact that the intermediate data and processes can and should differ [5]. 2.2 Training of RNN Learning of deep neural networks is a non-trivial task, differently solved at different points in the history of the development of neural networks [5]. The primary problem is the complexity and time spent on training due to the large number of layers. In 1987, Dana Ballard (PhD, University of California) developed a learning algorithm using autoencoder [6]. In fact, the autoencoder significantly reduced the amount of processed data by using linear methods, such as the principal component method. In the simplest case, the autoencoder is a hidden layer with the code h, which serves to represent the input signal x [6]. To do this, he uses the encoding function f , which converts the input signal to the code h = f (x) and the decoding function g, which restores the input values of the signals r = g (x) [6]. An approximate diagram of such an auto-encoder is shown in Fig. 2.

Fig. 2. General structure of autoencoder.

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During autoencoders usage, it is necessary to train it, which is done by the recirculation method, which implies a hierarchical integration of autoencoders in the learning process [1]. The method itself is still used as a method of teaching deep neural networks without a teacher, however, not as widely as methods with a teacher [1]. The use in 1989 of Yann LeCun to train the deep learning network of the error back-propagation algorithm (which was developed back in 1970 for related areas) was a breakthrough in this area. Learning using this method is done with a teacher; for this purpose, a learning set is necessary [1]. For example, the MNIST dataset, initially introduced in 1989, is now used for handwriting recognition. The backpropagation method of error is based on the gradient descent method. To use it, an error measure is introduced that defines the difference between the “reference” output values from the training set and the real ones [1]. Due to the change in the values of the weights in the network, the error measure is minimized, for which gradient descent is used. Its essence is the calculation of partial derivatives of the error of calculating the weights in the network and the following change in the weights to insignificant values, taking into account the gradient [1]. The process must be repeated until the output error value is reduced. In this case, the initial values of the weights of neurons in the network are set randomly. For deep neural networks, the method works in a similar way, the value of the calculated error is transmitted from one hidden layer to another through the use of a memory block [1]. However, the backpropagation algorithm has a key problem formulated in 1991, which is the problem of the vanishing gradient [1]. It stands in the fact that, if traditional activation functions are used, the propagation error signals quickly become either too small or excessively large. In practice, their reduction occurs exponentially, depending on the number of layers in the network [1]. There are several ways to solve this problem, starting from the rejection of the gradient when learning in principle (algorithms based on random values), and ending with the use of other network architectures or its included neurons. The most common and currently used architectures that solve this problem are LSTM and GRU [7]. 2.3 Types of RNN LSTM (Long Short-Term Memory) is a type of architecture of recurrent neural networks, proposed in 1997 as a solution of the problem of a vanishing gradient in the training of classic RNN types [7]. LSTM is also presented as a separate module of a complex network or layer in a multilayer network. Networks of long short-term memory do not use the activation function inside recurrent components, do not blur the stored value in time, which directly means the stability of the gradient, the absence of the disappearance effect [8]. The key concept of LSTM is a “gate” - a logistic function that serves to calculate a value in the range from 0 to 1. By multiplying by the obtained value, the network can control the admission or prohibition of information transmission within the network, or input or output [9]. By roles, the gates are divided into “input gate”, “forgetting gate”, the first of which controls the measure of using the value in the calculation, and the last - the measure of the value being stored in memory [9].

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The general structure of the LSTM layer is shown in Fig. 3.

Fig. 3. General structure of the LSTM layer.

The mathematical model of the LSTM layer is as follows (for each LSTM module). In these equations, the (n-d vectors) it , ft and ot are the input gate, forget gate, output gate at time t, Eqs. (1)–(3). it = σ(Ui ht−1 + Wi xt + bi )

(2)

  ft = σ Uf ht−1 + Wf xt + bf

(3)

ot = σ(Uo ht−1 + Wo xt + bo )

(4)

Note that these gate signals include the logistic nonlinearity σ, and thus their signals ranges are between 0 and 1. The n-d cell state vector ct and its n-d activation hidden unit ht at the current time t are in Eqs. (5)–(6): ct = ft ◦ ct−1 + it ◦ tanh(Uc ht−1 + Wc xt + bc )

(5)

ht = ot ◦ tanh(ct )

(6)

The input vector xt is an m-d vector, tanh is the hyperbolic tangent function, and ◦ in Eqs. (5)–(6), denotes a point-wise (Hadamard) multiplication operator. The GRU (Gated Recurrent Unit) networks are more general, however, they were opened much later, in 2014. In fact, the concept of GRU includes the LSTM structure and the use of fans as its basis, but the classically established use of GRU layers does

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not imply the presence of an input valve in the principle, which simplifies both the mathematical model and the parameter mechanism. That is why GRUs are often distinguished as a separate type of RNN architecture, different from LSTM, both in scientific works and sources, and in practice-oriented libraries and software products [10]. 2.4 The Statement of Tasks for Comparing of RNN Different Types The primary goal of this work is to compare the time taken to solve a certain practical problem by neural networks of different architectures. First we need to formulate both the tasks themselves and define the recurrent neural networks and layers that will be used in the process. Among the tasks most often encountered in requests of experts from various subject areas and business, the following can be identified: 1. Recognition of signs of fire in the area; 2. Recognition of the type of vehicles in different lighting conditions, various weather conditions; 3. Recognition of characters shot from different angles in different lighting conditions. This article considers the analysis of single photos through neural networks, since the analysis of a series of photos or video files requires a different algorithm base or the presence of additional software modules [11]. The experiment will be based on the use of the Tensorflow library and the Keras library, which is an add-on for Deeplearning4j, TensorFlow, and Theano. This library has software tools for constructing a neural network using layers: – fully connected (SimpleRNN); – layer with controlled recurrent unit (Gated Recur-rent Unit, GRU); – long-term short-term memory (LSTM). Thus, for testing, networks will be constructed using the following combinations of layers: 1. A recurrent network with a combination of a fully connected layer and a GRU layer; 2. A recurrent network with a combination of a fully connected and LSTM layer. 2.5 Software Implementation of RNN The program code for constructing a recurrent network using a fully connected layer and some additional ones, a detailed description of which can be omitted, is presented below:

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model = Sequential() model.add(SimpleRNN(32, kernel_initializer =initializers.RandomNormal(stddev=0.001), recurrent_initializer=initializers.Identity(gain=1.0), activation='relu', input_shape=train_images.shape[1:])) model.add(Dense(num_classes)) model.add(Activation('softmax')) model.add(Flatten())

To add a particular layer, just add it to the model using the add () function, as shown in the example above. Thus, a network architect with a fully connected and GRU layer is implemented by adding it using the code below: model.add(GRU(32, kernel_regularizer=regularizers.l2(0.001), bias_regularizer=regularizers.l2(0.001), recurrent_regularizer =regularizers.l2(0.001), activity_regularizer=regularizers.l2(0.001), kernel_constraint='max_norm', bias_constraint='max_norm', recurrent_constraint='max_norm'))

To implement a network model with a combination of fully connected and LSTM layers, you must add the code below: model.add(LSTM(32, return_sequences=True, input_shape=(10, 32)))

3 Numerical Results 3.1 Signs of Fire One of the most frequently demanded tasks for employees of various subject areas is the possibility of automatic recognition of fire. Keras enthusiasts have compiled a “kerasfire-detection” dataset that includes more than several thousand images of fire, smoke and no fire. This dataset meets the requirements of the task. Of course, the number of training epochs will, of course, directly affect the result of the experiment in terms of the accuracy of the result, however, this will not affect the final time of image analysis, only the training time. Thus, it is possible to set in advance the number of epochs that will be used within the entire experiment. Their optimal number is 20. 3.1.1 SRNN and GRU The following data were obtained as a result of the experiment (Table 1):

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Table 1. Identification of signs of fire. SRNN and GRU. Number of eras Learning set Learning time Execution time 20

2650

1080 s

14–18 s

3.1.2 SRNN and LSTM The following data were obtained as a result of the experiment (Table 2): Table 2. Identification of signs of fire. SRNN and LSTM. Number of eras Learning set Learning time Execution time 20

2650

1840 s

10 s

3.2 Vehicle Type This task is especially demanded within the framework of companies and services that are directly related to urban road traffic. In fact, it comes down to recognizing objects with a prepared training set of cars and their classes. During the search, a number of datasets were found, among them a dataset with types of cars close to our realities and containing 1,500 samples was selected. Obviously, this difference is distinguished from the previous task by a significantly larger number of recognition classes, because the time costs increase significantly. 3.2.1 SRNN and GRU The following data were obtained as a result of the experiment (Table 3): Table 3. Identification of a vehicle type. SRNN and GRU. Number of eras Learning set Learning time Execution time 20

1500

2350 s

16 s

3.2.2 SRNN and LSTM The following data were obtained as a result of the experiment (Table 4):

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1500

3000 s

8–12 s

3.3 Traffic Sign Recognition In addition to the previous task in the field of transport and traffic control, the need often arises for the intellectual recognition of road signs. However, this task is compounded by the fact that in different countries and regions the signs are significantly different, therefore, the selection and formation of the right learning set plays a special role. As part of this work, a dataset of 43 classes was used, which is distributed together with the keras library - GTSRB. It contains 39,000 training images. 3.3.1 SRNN and GRU The following data were obtained as a result of the experiment (Table 5): Table 5. Traffic sign recognition. SRNN and GRU. Number of eras Learning set Learning time Execution time 20

39000

10640 s

13 s

3.3.2 SRNN and LSTM The following data were obtained as a result of the experiment (Tables 6 and 7): Table 6. Traffic sign recognition. SRNN and LSTM. Number of eras Learning set Learning time Execution time 20

1500

12000 s

9–11 s

4 Conclusion To finalize the results of the work done, a common result table that includes the tasks, types of networks built to solve them, and the resulting time is presented below. As a result and conclusion, a number of regularities can be derived from these data:

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Table 7. Result data Task

Network architecture

Signs of fire

SRNN and GRU SRNN and LSTM

2650

1840 s

10 s

Vehicle type

SRNN and GRU

1500

2350 s

16 s

SRNN and LSTM

1500

3000 s

8–12 s

SRNN and GRU

39000

10640 s

13 s

SRNN and LSTM

39000

12000 s

9–11 s

Traffic signs

Learning set

Learning time

650

1080 s

Execution time 14 s

– the combination of a fully connected layer and GRU gives a significant increase in the learning speed, but is inferior to the combination of a fully connected layer and LSTM in speed of execution; – the value of the training set is directly proportional to the time of training, but does not correlate with the time the network solves a specific problem. For the more displayable result we present a diagram of dependence of execution time and network architecture and type of task, in Fig. 4.

Network Achcitecture

Traffic signs. SRNN and LSTM. Traffic signs. SRNN and GRU. Vehicle type. SRNN and LSTM. Vehicle type. SRNN and GRU. Signs of fire. SRNN and LSTM. Signs of fire. SRNN and GRU. 0

2

4

6

8

10

12

14

16

18

Execution Time Fig. 4. Runtime versus network type.

It is worth to say that the considered solutions and implementations are only a small part of those that were implemented as part of the history of the development of recurrent neural networks. Even more - such a widespread distribution of neural networks and their

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application in practice is possible precisely due to the large number of solutions that serve for training and application of deep neural networks.

References 1. Yakovlev, V.V., Murphy, E.K., Eves, E.E.: Neural networks for FDTD-backed permittivity reconstruction. COMPEL: Int. J. Comput. Math. Electric. Electron. Eng. 24(1), 291–304 (2005) 2. Haykin, S.: Neural Networks: A Comprehensive Foundation. 2nd edn. Prentice Hall (1999) 3. Sermanet, P., Eigen, D., Zhang, X., Mathieu, M., Fergus, R., LeCun, Y.: OverFeat: integrated recognition, localization and detection using convolutional networks. In: International Conference on Learning Representations (ICLR2014), CBLS, (Arxiv:1312.6229) (2014) 4. Dolinina, O.: Test Set generation method for debugging of neural network-based expert systems. In: Dolinina, O., Kuzmin, A. (eds.) Proceedings of International Congress on Information Technologies ICIT-12 (Information & Communication Technologies in Education, Manufacturing & Research). 6–9 June 2012, pp. 53–59. Saratov, Russia (2012) 5. Brovko, A.V., Murphy, E.K., Yakovlev, V.V.: Waveguide microwave imaging: neural network reconstruction of functional 2-D permittivity profiles. IEEE Trans. Microwave Theory Techn. 57(2), 406–414 (2009). https://doi.org/10.1109/TMTT.2008.2011203 6. Dolinina, O., Kushnikov, V., Kulakova, E.: Analysis of objective trees in security management of distributed computer networks of enterprises and organizations. In: Gaj, P., Kwiecie´n, A., Stera, P. (eds.) CN 2015. CCIS, vol. 522, pp. 117–126. Springer, Cham (2015). https://doi. org/10.1007/978-3-319-19419-6_11 7. Kumaran, D., Hassabis, D., McClelland, J.L.: What learning systems do intelligent agents need? Trends in Cognitive Sciences 20(7), 512–534 (2016) 8. Lampert, C., Nickisch, H., Harmeling, S.: Learning to detect unseen object classes by betweenclass attribute transfer. In: CVPR 2009. MiamiBeach, Florida (2009) 9. Lomonaco, V., Maltoni, D.: Core50: A New Dataset and Benchmark for Continuous Object Recognition. In CoRL, Mountain View (2017) 10. LeCun, Y., Bottou, L., Bengio,Y., Haffner, P.: Gradient-based learning applied to document recognition. In: Proceedings of the IEEE (1998) 11. Chao, J., Hoshino, M., Kitamura, T., Masuda, T.: A multilayer RBF network and its supervised learning. In: IEEE IJCNN’01. International Joint Conference on Neural Networks. Proceedings (Cat. No.01CH37222), vol. 3, pp. 1995–2000 (2001). https://doi.org/10.1109/ijcnn.2001. 938470

System Analysis of the Process of Determining the Room Category on Explosion and Fire Hazard Yuliya Nikulina(B)

, Tatiana Shulga , Alexander Sytnik , and Olga Toropova

Yuri Gagarin State Technical University of Saratov, 77, Politechnicheskaya st.„ Saratov 410054, Russia [email protected], [email protected], [email protected], [email protected]

Abstract. The task of determining the category of premises for explosion and fire hazard in accordance with regulatory documents is thoroughly considered and formalized. The authors have carried out a system analysis of the process of solving this task and proposed a domain model in the form of ontology. This article described the decision-making algorithm by a specialist who carries out the solution of the task. The article draws our attention to the main classes, subclasses, settings, properties and rules of ontology. The authors presented the results of the analysis in the form of an algorithm. The main criterion for determining belonging to a certain category is substances in the room. The domain model was created to support decision making. The results can be used to solve other problems in the design of fire protection systems. Keywords: System analysis · Ontology · Ontological engineering · Fire safety · Room category

1 Introduction One of the tasks in designing a fire alarm system is to determine the category of the room. The rules for determining categories of premises are legally established by order of March 25, 2009 No. 182 “On approval of the code of rules “Determination of categories of rooms, buildings and external installations on explosion and fire hazard” (hereinafter SP 12.13130.2009) [1]. The categories of rooms and buildings are determined based on the type of combustible substances and materials in the premises, their quantity and fire hazard properties, as well as on the basis of space-planning decisions of the premises and the characteristics of the technological processes carried out in them. The classification of buildings and premises for explosive and fire hazard is used to establish fire safety requirements aimed at preventing the possibility of a fire and providing fire protection for people and property in case of fire. The room category on explosion and fire hazard affect its equipment with an automatic fire alarm installation, an automatic fire extinguishing installation, fire resistance, area of fire compartments, the performance of equipment located indoors and other, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 125–139, 2021. https://doi.org/10.1007/978-3-030-65283-8_11

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and as a result - human safety and industrial safety equipment. Russian researchers are actively developing models of the dynamics of fire development [2–5], but there is no system analysis of specific practical problems. The task of determining the room category is relevant for all organizations involved in the design of fire alarm systems and is difficult to solve on the basis of existing regulatory documents. Formalization of the task was carried out by a system analysis of the development processes of projects to ensure the fire safety of buildings and structures in the Russian Federation and the relevant regulatory documentation conducted jointly with specialists in the field of fire safety. This article describes system analysis of the process of solving the task of determining the room category on explosion and fire hazard and proposed a domain model in the form of an ontology.

2 The Task of Determining the Room Category on Explosion and Fire Hazard According to SP 12.13130.2009 there are eight room categories (A, B, V1-V4, G and D) on explosion and fire hazard. The Table 1 below presents the room categories definitions given in [1]. Methods for determining the categories of premises A and B are established in accordance with Appendix A SP 12.13130.2009. Classification of a room into categories B1, B2, B3 or B4 is carried out depending on the quantity and method of placing the fire load in the specified room and its space-planning characteristics, as well as on the fire hazard properties of the substances and materials that make up the fire load. The division of premises into categories B1–B4 is regulated by the provisions in accordance with Appendix B SP 12.13130.2009. Table 1. The room category on explosion and fire hazard. Name of category

Characteristics of substances and materials located (circulating) in the room

A Flammable gases, flammable liquids with a flashpoint of not more than increased fire hazard 28 °C in such an amount that they can form explosive vapor-gas mixtures, when ignited, the calculated overpressure in the room develops in excess of 5 kPa, and (or) substances and materials that can explode and burn when interacting with water, atmospheric oxygen or with each other, in such a quantity that the calculated overpressure of the explosion in the room exceeds 5 kPa B explosion hazard

Flammable dusts or fibers, flammable liquids with a flash point of more than 28 °C, flammable liquids in such an amount that they can form explosive dusty or vapor-air mixtures, when ignited, the calculated overpressure in the room develops in excess of 5 kPa (continued)

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Table 1. (continued) Name of category

Characteristics of substances and materials located (circulating) in the room

V1-V4 fire hazard

Flammable and slow-burning liquids, solid flammable and slow-burning substances and materials (including dust and fibers), substances and materials that can only burn when interacting with water, atmospheric oxygen or with each other, provided that the premises in which they are located (apply), do not belong to category A or B

G Non-combustible substances and materials in a hot, hot or molten state, moderate fire hazard the processing of which is accompanied by the release of radiant heat, sparks and flame, and (or) combustible gases, liquids and solids that are burned or disposed of as fuel D reduced fire hazard

Non-combustible substances and materials when cold

The main criterion for determining belonging to a certain category is substances in the room. In accordance with the current legislation, article 27 of FZ-123 [6] clearly defines that the premises are divided into categories for fire and explosion hazard, regardless of their functional purpose. The categories of premises and buildings are determined based on the type of combustible substances and materials in the premises, their quantity and fire hazard properties, as well as on the basis of space-planning decisions of the premises and the characteristics of the technological processes carried out in them. The determination of the room categories should be carried out by sequentially checking that the premises belong to the categories listed in Table 1, from the most dangerous (A) to the least dangerous (D). According to the type of fire hazard, the following substances are allocated, which are arranged in order to reduce fire hazard: combustible gas, flammable liquid, combustible liquid, combustible dust, solid combustible substances and materials. The determination of the fire hazardous properties of substances and materials is carried out on the basis of test results or calculations by standard methods, taking into account state parameters (pressure, temperature, etc.) in accordance with paragraph 4.3 of SP 12.13130.2009. The use of officially published reference data on the fire hazard properties of substances and materials is allowed. It is also allowed to use fire hazard indicators for mixtures of substances and materials for the most dangerous component. When calculating the criteria for explosive and fire hazard, the most unfavorable variant of the accident or the period of normal operation of the apparatus should be chosen as the calculated one, in which the formation of combustible gas-, steam-, dustair mixtures involves the largest number of gases, vapors, dusts, the most dangerous with respect to the consequences of the combustion of these mixtures. If the use of calculation methods is not possible according to Appendix A.1 SP 12.13130.2009, it is allowed to determine the values of the explosion hazard criteria based on the results of the corresponding research work, agreed in the manner established to coordinate derogations from the requirements of regulatory documents on fire safety.

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3 Systems of Fire Protection: An Ontology for Determining the Room Category A system analysis of the process of determining the room category of premises in the Russian Federation and the relevant regulatory documentation was carried out jointly with specialists in the field of fire safety. To represent knowledge in this area, an ontological approach was used, which has established itself well and is used by researchers to model various subject areas, for example, [7–9]. Part of this work was presented in [10], the major focus in this paper was on comparison of ontologies in the field of fire safety and consider possible ways to use them. Based on the studies of existing ontological models, the ontology “Systems of fire protection” was created [11]. We used the Protégé [12] for building the ontology. In Fig. 1 shows the classes of this ontology associated with the concept of “Room category”.

Fig. 1. A fragment of the structure of the ontology systems of fire protection

To determine the room category, the design engineer uses the information provided by the customer and also independently performs the necessary measurements at the facility. Types of substances are defined as classes in ontology. Instances of this class are data from the reference table of materials created by the authors on the basis of reference data on the fire hazard properties of substances and materials. The type of substance for each particular instance is selected as operational data using the drop-down list. An engineer can use the existing base to enter an instance in the specific working draft or add a new one. More than 1,500 substances are introduced into the ontology as instances of the class “Material”, as well as background information necessary for calculations, such as molar mass, density, the Antoine equation parameters, etc. The Table 2 below shows a fragment of the material base sheet.

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Table 2. Fragment or reference table “Materials”. Material name

Type of fire hazard

Lower calorific value, MJ/kg

Molar mass, kg/kmol

Density, kg/m3

Flash point, °C

Maximum explosion pressure, kPa

…

Ammonia

Flammable gas

18,58

17,03

0,6

1

588

…

Acetone

Flammable liquid 31,36

58,08

790,9

−18

572

…

Petrol

Flammable liquid 44

98,2

760

−39

900

…

Paper

Solid combustible 13,4 substances and materials

…

slow-burning liquid Naphthalene

Slow-burning substances and materials

38,25

Water

Non-combustible liquids

Wood in products

Solid combustible 13,8 substances and materials

29

…

At the first stage of determining the room category for explosive and fire hazard, the specialist must to enter information about room, which include the name of the room according to the technical passport, area, room height, storage area, estimated air temperature, etc. Next, the fuel load is determined. It consists of materials and products stored in a warehouse. The types of substances are ranked by explosive and fire hazard, the calculation is carried out according to the most dangerous. For each substance, its mass is introduced, for flammable gas or vapors of flammable liquids released as a result of an accident into the room according to formulas A.6 and A.11 of Appendix A of SP 12.13130.2009. The necessary reference information, such as calorific value, critical heat flux density, etc., is also extracted from reference tables. An important task in the calculation is to determine the emergency scenario, that is, what is possibly the most unfavorable combination of circumstances with the available initial data. Then the calculation itself begins. If flammable gas is present in the room, the room is checked for belonging to category A. In accordance with the provisions of Appendix A of SP 12.13130.2009, the mass of combustible gas (m) released as a result of the calculated accident into the room is determined, the free volume of the room is determined (Vfr ), based on the reference data, the density of the combustible gas (ρg ) is calculated, as well as the stoichiometric concentration Cst .

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With the exception of a number of cases described in Appendix A of SP 12.13130.2009 [13], the explosion overpressure P (kPa) is calculated by the formula 1: m P = 1.332 ∗ 104 ∗ Vfr ∗ ρg ∗ Cst If P > 5 kPa, then the room is classified as explosive and fire hazard category A. The determination of the category of the room is completed. If  P ≤ 5 kPa, then the room does not belong to the explosive and fire hazard category A and further determination of the category of the room depending on the fire hazard properties and the number of substances and materials circulating in the room. In the event that a flammable liquid or flammable liquid is present in the room, we check for belonging to category A (B). The evaporation rate is calculated, the mass of vapors entering the room is also used previously calculated free volume of the room, based on the reference data is the vapor density and stoichiometric concentration. Then the overpressure of the explosion P (kPa) is recalculated according to the formula 2: m P = 7, 99 ∗ 103 ∗ Vfr ∗ ρg ∗ Cst Provided that  P > 5 kPa, the room is classified as explosive and fire hazard category A, if a flammable liquid is present, or category B, if the calculation was carried out for a combustible liquid. The category determination of the premises is completed. If  P ≤ 5 kPa, then the room does not belong to the explosion and fire hazard category A (B), verification continues. If there is combustible dust or fibers in the room under consideration, it is checked for belonging to category B. Similarly to the previously described cases, the calorific value of the substance (Ht ) is determined from the reference data, then the overpressure P is calculated by the formula 3: P = 47, 18 ∗

m ∗ Ht Vfr

If the excess air pressure exceeds 5 kPa, then the room belongs to categories B, otherwise the calculation continues. If there are flammable and slow-burning liquids, solid flammable and slow-burning substances and materials (including fibers), that is, in rooms in which there are flammable and gaseous and flammable liquids not belonging to categories A and B, checked in its belonging to categories B1–B4. According to Appendix B SP 12.13130.2009, the fire load Q is calculated by the formula 4: Q =

n  i=1

p

Gi QHi

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where Gi is the amount of the ith material of the fire load in kg, is equal to the mass p previously entered into the table, QHi is the net calorific value of the ith fire load material, which is extracted from the reference data. The specific fire load of the room is calculated by the formula 5: g =

Q S

where Q is the total fire load in the area, S is the storage area that was entered at the initial stage when entering data about the room. Next, the room category is determined based on the values of g and Q, if g > 2200, the category B1 is assigned to the room, the calculation is completed. If 1400 ≤ g < 2200, the preliminary room category is B2. Again, the fulfillment of the inequality Q ≥ 0.64 gt H2 is checked, where gt = 2200, H is the difference between the room height and the storage height. In the event that the calculated Q meets the inequality, the category B1 is assigned to the room, if it is not fulfilled, category B2, the calculation is completed. In the event that 180 ≤ g < 1400, the preliminary category of room B3 is established. Then, the condition Q ≥ 0.64 gt H2 is checked, where g t = 1400. If the inequality is true, the room is assigned category B2, if not, category B3. The calculation is completed. When condition 1 < g < 180 is fulfilled, the room is assigned category B4, the calculation is completed. When non-combustible substances and materials are stored in a room in a hot, hot or molten state, the processing of which is accompanied by the release of radiant heat, sparks and flames, and (or) combustible gases, liquids and solids that are burned or disposed of as fuel, the room is assigned a category D. As a rule, this category is assigned to the rooms in which the boiler rooms are located. If the results of checking for belonging to the most dangerous categories (A–G) are negative, as well as when non-combustible substances and materials are stored in a room in a cold state, category D is assigned to the room. At the output of the described algorithm, the engineer receives the result - the category of the premises for explosion and fire hazard, as well as the calculations based on which the result was obtained and the reference data necessary for the calculations.

4 Applicability of the Algorithm Consider the use of the results of a system analysis to determine the room category on specific examples. Below the article presents some examples of real tasks of the organization, which were solved using the described algorithm. Specialists constantly faced with such tasks checked the correctness of the constructed model, but also outlining suggestions on how to improve the layout and to add new functionalities. 4.1 Example 1. Definition of a Warehouse of Bulk Products Category The hotel has a warehouse of bulk products, the engineer takes a description of the premises from the technical passport of the object. The Table 3 presents the input data.

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Room parameters

Value

Description

No. 7 on the technical passport

Length

3.8 m

Width

3.3 m

Area

12.5 m2

Height

3,7 m

Storage area

9.9 m2

Storage height

2.7 m

Estimated air temperature

22 °C

There is an automatic fire extinguishing

No

Emergency ventilation available

No

Next, a combustible load is determined. It consists of materials and products stored in a warehouse. According to the information provided by the customer, Flour and Sugar are stored in the warehouse in question, it is also necessary to take into account the bags in which the products and wooden shelves are stored. The tables below provide the necessary background information (Tables 4, 5 and 6). Table 4. Fuel load “Wooden shelves” Name

value

Name of material

Wood in products

Calorific value

13.8 MJ/kg

Critical heat flux density 13.9 kW/m2 Weight

100 kg

Table 5. Fuel load “ Bags” Name

Value

Name of material Polypropylene Calorific value

45.7 MJ/kg

Weight

10 kg

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Table 6. Fuel load “ Flour” Name

Value

Name of material Flour Calorific value

16,8 MJ/kg

Weight

1500 kg

Then, the specific fire load of the warehouse is determined (Table 7). Table 7. Fuel load “Sugar” Name

Value

Name of material Sugar Calorific value

16,8 MJ/kg

Weight

1500 kg

Table 8. The fire load in the area № Name

Fuel load

Weight

Calorific value

100 kg

13.8 MJ/kg

1

Wooden shelves Wood in products

2

Bags

Polypropylene 10 kg

3

Flour

Flour

1500 kg 16.8 MJ/kg

4

Sugar

Sugar

1500 kg 16.8 MJ/kg

45.7 MJ/kg

Specific fire load is determined by the formula 5: g=

Q = 5223, 7 MJ/m2 S

where Q is the total fire load in the area 52237 MJ, S - storage area (with an area of less than 10 m2 , a value of 10 m2 is assumed) 4.9 m2 . Next, the category of the room is determined. The room does not circulate flammable gases, flammable liquids with a flashpoint not exceeding 28 °C and (or) substances and materials that can explode and burn when interacting with water, atmospheric oxygen or with each other, in such a quantity that the calculated excess the explosion pressure in the room exceeds 5 kPa, so the room does not belong to category A. No flammable dusts or fibers, flammable liquids with a flashpoint of more than 28 °C, flammable liquids in such a quantity that they can form explosive dusty or vapor-air mixtures, when ignited, the design overpressure in the room exceeds 5 kPa, therefore, the room does not belong to category B.

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Flammable (slow-burning) liquids, solid flammable (slow-burning) substances and materials, or substances and materials that can only burn when interacting with water, atmospheric oxygen or with each other, are circulated in the room, therefore the room belongs to one of category B1–B4. Conclusion: according to p.p. B.1, B.2 SP 12.13130.2009, since g > 2200 MJ /m2 , the bulk products warehouse belongs to category B1. 4.2 Example 2. Definition of the Logistics Warehouse Category Next we define the room category of the logistics warehouse. The Table 9 presents the input data. Each room’s technical-economic indicator corresponds to a data type property at the ontology. This example is more complex because in this room there is a flammable liquid and it is necessary to make more detailed calculations. Table 9. Logistics warehouse data Room parameters

Value

Description

Logistics

Length

45 m

Width

18 m

Area

810 m2

Height

6.5 m

The level of the lower zone of the overlapping trusses (cover)

5m

Storage area

320 m2

Storage height

4,5 m

Estimated air temperature

22 °C

There is an automatic fire extinguishing

No

Emergency ventilation available

No

The list of fuel loads is presented in the following tables (Table 10). Table 10. Fuel load “ White Spirit” Name

Value

Name

White spirit

Calorific value

43.97 MJ/kg

Molar mass

147.3 kg/kmol

Lower Flame Concentration Limit

0.7% vol. (continued)

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Table 10. (continued) Name

Value

Flash point

33 °C

Boiling temperature

140 °C

Fluid density

760 kg/m3

The specific area of the spill in the room

1 m2 /l

Constant Antoine A

7,13623

Constant Antoine V

2218.3

Constant Antoine Sa

273.15

Overall volume

1 m3

Volume of one container

0.01 m3

Maximum fluid temperature

40 °C

The specific heat of the liquid at the initial temperature of evaporation

2400 J /(kg • K)

Evaporation duration

3600 s

It is necessary to determine the mass of liquid spilled during the accident. According to the law [1], one container of White Spirit spills. The entire volume of the container enters the surrounding space. Thus, the volume of liquid entering the surrounding space during the spill of one container is 0.01 m3 . The mass of liquid entering the surrounding space during the spill of one container is 7.6 kg. The liquid spill area is 10 m2 . The next stage is determination of saturated vapor pressure of a liquid. The saturated vapor pressure of the liquid is determined by the formula of Antoine (6):

where A = 7,13623, B = 2218,3 Ca = 273,15. Values A, B and Ca are Antoine constants from reference table. Value t is the estimated fluid temperature 40 °C. Then it is necessary to calculate the mass of liquid vapor. The maximum temperature for the climatic zone of the city of Sochi (geographic location of the ogject) is 40 °C - not higher than the boiling point (140 °C), then, according to formulas (A.14) and (A.15) SP 12.13130.2009, the calculation of the mass of liquid vapor is performed as follows (7): √ Cl mfr , m = 0, 02 M · PN Lv where mass of the liquid released into the surrounding space mfr = 7.6 kg; molar mass of liquid M = 147.3 kg/kmol; saturated vapor pressure at the calculated liquid temperature (40 °C) PN = 1,128 kPa; specific heat of the liquid at the initial temperature

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of evaporation Cl = 2400 J /(kg · K); specific heat of vaporization of the liquid at the initial temperature of evaporation Lv calculated by the formula 8 below:

288832,6 J / kg, where Ta is initial temperature of the heated liquid (40 °C). According to the formula 7, the mass of liquid vapor is 0.017 kg. Since the liquid is heated to a flash point or higher. The coefficient Z = 0.3 according to table A.1 SP 12.13130.2009. The explosion overpressure P for substances that are not an individual combustible substance is determined by the formula 9:

0,01 kPa,

where HT is calorific value, P0 is initial pressure, KN is coefficient taking into account leakage of the room and non-adiabaticity of the combustion process. The specialist takes values from the reference tables at the otology and also takes the necessary measurements at the object. Since  P ≤ 5 kPa, then the room does not belong to the explosion and fire hazard category A. Next, according to the algorithm the premises are checked for category B. The determination of the specific fire load is carried out similarly to the first example. The location of the fire load in warehouses is regulated by law. There are strict rules and regulations for storing goods. When changing the amount of fire load, the calculation is made at maximum load. In this way, the most dangerous emergency scenario is calculated. Specific fire load is determined by the formula 5, same as in the previous example: g=

Q = 678, 2 MJ/m2 S

where the total fire load in the area Q = 217038,2 MJ, storage area S = 320 m2 (Table 11). Table 11. The fire load in the area №

Name

Fuel load

Weight

Calorific value

1

Paper napkins

Paper

1500 kg

13.4 MJ/kg

2

Rags

Cotton loose

1750 kg

15.7 MJ/kg

3

Wooden furniture

Wood in products

1500 kg

13.8 MJ/kg

4

Liquid soap

Liquid soap

200 kg

34.47 MJ/kg

5

Cardboard products

Cardboard

1000 kg

15.7 MJ/kg

6

Plastic dishes

Polystyrene

1000 kg

39 MJ/kg (continued)

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Table 11. (continued) №

Name

Fuel load

Weight

Calorific value

7

Plastic products

Polyvinyl chloride

500 kg

20.7 MJ/kg

8

Powdered Detergents

Powdered Detergents

200 kg

3.04 MJ/kg

9

Liquid detergents

Synthetic liquid detergents

200 kg

12.32 MJ/kg

10

Glass Cleaner

Glass Cleaner

200 kg

10.98 MJ/kg

11

Washing powder

Washing powder

500 kg

4.28 MJ/kg

12

Solid soap

Soap

200 kg

34.47 MJ/kg

13

Toilet paper

Paper

1500 kg

13.4 MJ/kg

14

White Spirit

White Spirit

760 kg

43.97 MJ/kg

Since 180 < g ≤ 1400 MJ /m2 and the condition Q ≥ 0.64 gt H2 is fulfilled, the Logistics warehouse belongs to category B2. 4.3 Example 3. Definition of a Lobby Category The next example is the definition of the lobby category. The main fire load in the room is a wooden decorative lining of a part of the walls. There is no other fire load. The area of the room is 148.4 m2 , the height of the room is 4.8 m. There are no flammable gases, flammable liquids and flammable liquids in the room, therefore the room does not belong to category A and B. We will check for classifying the room into categories B1–B4 for fire hazard. The specific fire load is determined by the formula 5. The lowest calorific value of wood is 13.8 MJ /kg, the weight of wood is 10 kg. Fire load will be Q = 10 * 13.8 = 138 MJ. Specific fire load g = 138 /148.4 = 0.93 MJ /m2 . The resulting value is less than the values indicated for category B4 in table B.1 SP 12.13130.2009, respectively, the lobby is classified as category D - reduced fire hazard.

5 Conclusion Thus, the formalization of the task of determining the room category for explosion and fire hazard was carried out. Based on the obtained data, a domain model in the form of an ontology is created, which is planned to be used to create a decision support system. Such a system will increase the efficiency of the design engineer. We believe that the ontology “Systems of fire protection” reduce the timing of implementation, adjustment and coordination of the project. The need to define categories is an important component of the fire safety of an object. The task of determining categorization is to reduce the risk of fires. Accordingly, increase the safety of people who work at these facilities. Moreover, the category affects

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the choice of type of fire safety. That is, what funds should be allocated, for example, for signaling, for primary fire extinguishing means, for fire fighting equipment, and so on. The model itself can also be used to solve other problems in the design of fire protection systems. It was evaluated by expert. The results were satisfactory. As a future work we plan to add some new characteristics, meet the requirements of specialists to improve the layout and to add new functionalities. Acknowledgements. The reported study was funded by RFBR, project number 20-37-90058\20.

References 1. SP 12.13130.2009: Determination of categories of rooms, buildings and external installations for explosion and fire hazards. Approved Russian Emergency Situations Ministry, 3/25/2009, # 182 (in Russian) 2. Samartsev, A.A., Rezchikov, A.F., Kushnikov, V.A., Ivashchenko, V.A., Bogomolov, A.S., Filimonyuk L.Y., Dolinina, O.N., Kushnikov, O.V., Shulga, T.E., Tverdokhlebov, V.A., Fominykh, D.S.: Fire and heat spreading model based on cellular automata theory. J. Phys.: Conf. Ser. 1015, p. 032120 (2018) 3. Samartsev, A., Ivaschenko, V., Rezchikov, A., Kushnikov, V., Filimonyuk, L., Bogomolov, A.: Multiagent model of people evacuation from premises while emergency. Adv. Syst. Sci. Appl. 19(1), 98–115 (2019) 4. Samartsev, A., Rezchikov, A., Kushnikov, V., Ivaschenko, V., Filimonyuk, L., Fominykh, D., Dolinina, O.: Software package for modeling the process of fire spread and people evacuation in premises. Stud. Syst. Decis. Control. 199, 26–36 (2019) 5. Samartsev, A.A., Ivaschenko, V.A., Kushnikova, E.V.: Combined modeling of fire and evacuation from premises. In: 2019 International Science and Technology Conference “EastConf”, EastConf 2019, pp. 8725394 (2019) 6. Technical regulation on fire safety requirements: Federal law of the Russian Federation of July 22, 2008 No. 123-FZ (as amended on December 27, 2018). (In Russian). URL: http:// www.consultant.ru/document/cons_doc_LAW_78699. Accessed 25 May 2020 7. Danilov, N., Shulga, T., Frolova, N., Melnikova, N., Vagarina, N., Pchelintseva, E.: Software usability evaluation based on the user pinpoint activity heat map. In: Silhavy, R., Senkerik, R., Oplatkova, Z.K., Silhavy, P., Prokopova, Z. (eds.) Software Engineering Perspectives and Application in Intelligent Systems. AISC, vol. 465, pp. 217–225. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-33622-0_20 8. Danilov, N.A., Shulga, T.E., Sytnik, A.A.: Repetitive event patterns search in user activity data. In: Proceedings of the 2018 IEEE Northwest Russia Conference on Mathematical Methods in Engineering and Technology (MMET NW), 10–14 September, 2018. St. Petersburg, Russia: Saint Petersburg Electrotechnical University “LETI”, pp. 92–94 (2018). (in Russian) 9. Sytnik, A.A., Shulga, T.E., Danilov, N.A.: Ontology of the “Software Usability” Domain. In: Trudy ISP RAN/Proceeding ISP RAS, vol. 30, no. 2, pp. 195–214 (2018). (in Russian) 10. Nikulina, Y., Shulga, T., Sytnik, A., Frolova, N., Toropova, O.: Ontologies of the fire safety domain. Stud. Syst. Decis. Control 199, 457–467 (2019) 11. Shulga, T.E. Nikulina, Y.V.: Ontological model of the subject area “Fire safety systems”. In: Proceedings of St. Petersburg State Technical University (TU), vol. 51, no. 77, pp. 109–114 (2019). (in Russian)

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12. Stanford University, “Proteg´ e - Stanford,” http://protege.stanford.edu/. Accessed 02 Apr 2020 13. Smolin, I.M., Poletaev, N.L., Gordienko, D.M., Shebeko, Y.N., Smirnov, E.V.: Handbook for the use of joint venture 12.13130.2009 “Definition of categories of premises, buildings and outdoor installations for explosive and fire hazard” (in Russian). http://mtsk.mos.ru/Handlers/ Files.ashx/Download?ID=22289. Accessed 10 May 2020

Comparison of Methods for Parameter Estimating of Superimposed Sinusoids Alexey L’vov1

, Anna Seranova1(B) , Roman Ermakov1 and Artem Muchkaev2

, Alexandr Sytnik1

,

1 Yuri Gagarin State Technical University of Saratov, Saratov, Russian Federation [email protected], [email protected], [email protected] 2 Martec Corporation, Las-Vegas, USA [email protected]

Abstract. The task of parameter estimation of signal components from a finite number of noisy discrete measurements is an active area of research. Different methods of signal components evaluation are used in practice, each of which has its own advantages and disadvantages. A new method for estimating signal components from a finite number of noisy discrete measurements based on the data matrix subfactorization is proposed. Comparison with one of the most popular methods described in IEEE-STD-1057, which presents algorithms for estimating the wave signal parameters from its noisy discrete time counts and with classic spectrum estimation method Periodogram is presented. Keywords: Parameter estimation · Data matrix subfactorization · Noisy discrete measurements · Periodogram · Maximum likelihood method · IEEE-STD-1057

1 Introduction Measurement-based estimation of signal parameters is a challenge in many practical signal processing problems such as high-resolution frequency, angle of arrival and time delay estimation of superimposed signals in additive noise. Let us consider the problem of parameter estimation of superimposed sinusoids in noise. Sinusoidal models in various forms are used in a variety of signal processing applications and time series data analysis. Applications of sinusoidal modelling are found, among others, in radio positioning of distant objects, communications, speech and biomedical signal processing, and geophysical exploration by seismic waves processing. A number of methods for parameter estimation of a superimposed sinusoidal model have been proposed recently, and the literature on this subject is extensive [1–10]. The difficulty of the parameter estimation problem is due to the fact that it belongs to a class of nonlinear fitting problems for the parameters. The structured factorization can often be performed based on physical properties of an application problem exposing the structure inherent to it. An appropriate use of data structure and matrix operations leads to robust estimates by properly exploiting the algebraic structure of the signal subspace. The concept of using singular value decomposition © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 140–151, 2021. https://doi.org/10.1007/978-3-030-65283-8_12

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for estimating frequencies has been utilized in the eigenstructure-assisted polynomial method (or Tufts-Kumaresan (TK) algorithm) [2]. The linear prediction TK algorithm can achieve the Cramer-Rao bound (CRB) when signal-to-noise ratio (SNR) is high. However, this algorithm is not able to estimate signal frequency efficiently at low SNR. In [3], the frequency estimation method based on joint diagonalization was proposed. The method found independent vectors that have a specific structure and span the null space of a data matrix. These vectors form matrices that are then jointly diagonalized to obtain the frequency estimates. The performance of the joint diagonalization method is only better in the SNR in terms of threshold effect than given by TK method. Besides, several methods have been proposed to improve the high noise threshold issue [4]. However, their performance is only better in the SNR of the TK algorithm threshold effect. Another method called the estimation of signal parameters via rotational invariance technique (ESPRIT) is a high resolution signal parameter estimator [5]. The matrix pencil (MP) method is similar to the ESPRIT method with its solving technique of a generalized eigenvalue problem, but the MP algorithm utilizes direct data approach [6]. It has been shown that MP method and TK polynomial method are special cases of a matrix prediction approach, but the pencil method is more efficient in computation and less sensitive to noise than TK algorithm [7]. The discussed estimation methods are parametric, or model-based. In cases when the assumed model closely approximates the reality, the parametric methods provide more accurate estimates and resolution than non-parametric techniques [1, 8]. The discrete Fourier transform (DFT) approaches are known to give satisfactory solution of the above-mentioned estimation problem; however, they require well-separated signal components [10]. In [11], performance comparison of MP method and DFT technique for high-resolution spectral estimation was considered. The performance of both techniques was studied in the presence of noise, and the results were compared with efficient estimates corresponding to CRB. It was shown that MP method provided better estimates than DFT techniques over some certain threshold of SNR [11]. Therefore, in this study, we used MP method as a benchmark for performance comparison in the threshold region. The maximum likelihood-based methods stand apart from the algebraic methods. They give excellent performance, except the fact that their computational requirements are heavy and they involve very accurate initialization [1, 9]. As we know, there are two kinds of commonly methods for power spectrum estimation, classic spectrum estimation (non-parametric method) and modern spectral estimation (parametric method). Classic spectrum estimation method basically has direct method and indirect method, direct method is also called the periodogram method, it can calculate Fourier transform modulus square of sequence directly. This paper presents an approach to the nonlinear parameter estimation problem that utilizes the maximum likelihood (ML) estimation and performs robust parameterization of a subspace-based model.

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2 Data Model and Subfactorization Algorithm The general problem of interest may be characterized using the following model: un =

M 

am esm n + ξm , n = 0, 1, 2, .., N − 1,

(1)

m=1

where N samples of observed data, un , consist of M exponentially damped sinusoids; am are unknown complex amplitudes; sm = −αm + jωm are unknown complex parameters including damping factors αm and angular frequencies ωm ; ζm are independent identically distributed white Guassian noise samples with zero mathematical expectation and unknown variance δ2 . Let us suppose that the number of samples, N, is rather large, i.e. N > M 2 . Then one can substitute the problem (1) by the following matrix representation. Form a data matrix U from the data un corrupted by noise as: ⎡

⎤ uL uL−1 · · · u1 ⎢ uL+1 uL u2 ⎥ ⎢ ⎥ U=⎢ . . .. ⎥, . . ⎣ . . . ⎦ uK−1 uK−2 · · · uK−L

(2)

where L > M , K > M . According with proposed method, U can be defined by the following relationship [12, 13]: ⎡

⎤⎡ ⎤ 1 1 ··· 1 a1 es1 L a1 es1 (L−1) · · · a1 es1 ⎢ es1 es2 · · · esM ⎥⎢ a2 es2 L a2 es2 (L−1) · · · a2 es2 ⎥ ⎢ ⎥⎢ ⎥ U=X·Q=⎢ . ⎥ +
.. .. ⎥⎢ .. .. .. . ⎣ . ⎦ . . ⎦⎣ . . . es1 L es2 L · · · esM L aM esM L aM esM (L−1) · · · aM esM L

(3)

where U: m × n is a data matrix; X: m × k and Q: k × n are unknown matrices; and
: m × n is an additive white Gaussian noise (AWGN) matrix. The generalized model (3) represents estimation procedure as a structured matrix factorization problem: given the data distorted by noise, it is necessary to find the factors containing information about unknown parameters [12]. The nonlinear data models (1)–(3) are called separable when X and Q contain different independent parameters that enter into the model linearly or nonlinearly. We call the data model semiseparable when the same parameters enter into both X and Q linearly or nonlinearly. It is worth noting that, although the data model (2) is nonlinear for the parameters taken jointly, it can be linear in each of separate matrices X and Q. Simplified ML approach based on subfactorization of the data model is introduced the redundant model (3) as separable model, depending on input decomposition factors and eigenvectors of the Gram matrix UUT and UT U. In result, finding of unknown parameters xi and qν, minimizing residual function

ε0 (X, Q) = Tr (U − XQ)T P(U − XQ) , (4)

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where P is the covariance matrix; Tr[•] is the trace operator, reduces to solving a system of linear equations regarding these decomposition coefficients. If the assumptions about the normality of the errors ξiν are fulfilled, the resulting estimates of unknown parameters are the maximum likelihood (ML) estimation, unbiased, substantial and asymptotically efficient. Optimization of the model for special cases by Gram matrix eigenvector expansion was described in [12, 13]. Mathematical modeling and application of this expansion showed good results in practice. In [14] there is the proof of the following theorem. Theorem Solution a set of non-linear Eqs. (3), where X = [x1T ,…,xNT ]T i Q = [q1 ,…,qM ]– unknown Rg(Q) = Rg(X) = m rank matrix, model coefficients, consisting of N row-vectors xiT dimension m and M column-vectors qν dimension m (N, M ≥ m); U = ||uiν || is matrix of order N × M observed values;  = [ξ1 ,…, ξM ] matrix of order N × M measurement errors, consisting of M vectors ξν , with vector components that are normally independently distributed values with zero mathematical expectations and covariance matrix P, relative to its unknown values by ML, so X and Q matrices are the solution, which satisfied (4): X = W · S−1 , Q = S · M · VT ,

(5)

where W = [w1 , w2 , . . . , wm ] is the matrix of order N × m, consists of m Gram’s matrix eigenvectors UUT ; V = [v1 , v2 , . . . , vm ] is the matrix of order M × m, consists of m Gram’s matrix eigenvectors UT U; S are the non-singular matrix of unknown decomposition coefficients, of order m × m; M = diag{μ1 ,μ2 ,…,μm } is the diagonal matrix singular values of U matrix, satisfying a following equation: ⎧ ⎡ T  ⎤⎫ m m ⎬ ⎨   j j μk wk vkT P U − μk wk vkT ⎦ , M = arg inf Tr⎣ U − (6) ⎭ µj ∈Σμ ⎩ k=1

k=1

j

j

where precise bottom is finding by any vectors µj = (μ1 ,… μm )T of length m that are the singular values of U matrix, obtained by choice m arbitrary values from  μ all singular values of this matrix. What is more, eigenvectors of W and V matrices, corresponding m singular values of U matrix, selected according with (6), and S matrix of decomposition coefficients, satisfying (4) is the one single. In expressions for separable models (5) only the decomposition coefficients making up the matrix S remains unknown, and components of the eigenvectors, of which W and V matrix consists, can be easily calculated if measurement matrix U is known. Ideally, when measurements have no errors, error matrix  is zero and Gram matrices UUT and UT U have exactly m non-zero eigenvalues (U matrix has m non-zero singular values). In real measurements there are certainly errors, so number of non-zero singular values of U matrix will be equal to the minimum of K or N. As known [16], singular are defined as correspondent eigenvalues λk of Gram’s matrix values μk of U matrix √ UUT (or UT U) μk = λk . Significantly, if measurement matrix U contains random errors, than all of non-zero singular values of U will be different [15] and there is no multiple singular values problem. Thus, if we know all λk , we can calculate all eigenvectors UUT and UT U, corresponding to this eigenvalues. The condition (6) sets the

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rule according to which the selection of the necessary singular values and corresponding eigenvalues should be carried out in order to ensure the minimum of residual function (4), i.e. solve the system (3) by ML. Substitution of found eigenvectors in (5) gives the desired estimates of maximum likelihood of calibrated parameters xi and state vectors qν , in condition, that decomposition coefficients matrix S will be found. Now then, as a result of using separable model the unknown matrix X and Q problem is reduced to the problem decomposition coefficients matrix search problem, while the number of unknowns is reduced from (N + K)m to m2 .

3 Data Model and Algorithms of IEEE-STD-1057 The IEEE Standard 1057 (IEEE-STD-1057) [17] provides algorithms for fitting the parameters of a sine wave to noisy discrete time observations. The fit is obtained as an approximate minimizer of the sum of squared errors, i.e. the difference between observations and model output. It is shown that the algorithm of IEEE-STD-1057 provides accurate estimates for Gaussian and quantization noise. In the Gaussian scenario it provides estimates with performance close to the derived lower bound. In IEEE-STD-1057, data can be modelled by the next set of equations: yn [A, B, C, ω] = A cos ω tn + B sin ω tn + C, (n = 1, . . . , N )

(7)

where A,B, and C are the unknown constants; the angular frequency ω may be known, or not, leading to models with three or four parameters, respectively; N is the number of measurements. The IEEE Standard 1057 provides algorithms both for 3-parameter (known frequency) and 4-parameter (unknown frequency) models. When the frequency in (7) is known, estimates of the unknown parameters of vector x = [A,B,C]T are obtained by a least squares fit. From expression ⎡

⎤ cosω t1 sinω t1 1 ⎢ cosω t2 sinω t2 1 ⎥ ⎢ ⎥ y = Dx, D = ⎢ .. .. .. ⎥ ⎣ . . .⎦ cosω tN sinω tN 1

(8)

where y = [y1 , y2 , …, yN ]T is measurement vector, D is the N × 3 matrix, estimations of unknown parameters can be calculated as xˆ = (DT D)−1 DT y. Let us assume that ωˆ i is frequency ω estimation in iteration i. Then serving approximate relations can be written: cosω tn ≈ cos ωˆ i tn − tn sin ωˆ tn ωi

(9)

sinω tn ≈ sin ωˆ i tn − tn cos ωˆ tn ωi ,

(10)

and

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where ω = ω − ω. ˆ Substitution (9) and (10) into (7) gives: yn [x] ≈ A cos ωˆ i tn + B sin ωˆ i tn + C − A tn ωi sin ωˆ i tn + Btn ωi cos ωˆ i tn , (11) where x i = [A, B, C, ωi ]T . Equation (11) is nonlinear in its parameters, but may be linearized using the fact that ωi ≈ 0. Putting available estimates of A and B from previous iteration, i.e.Aˆ i−1 i Bˆ i−1 that replace the corresponding unknown parameters in the two last terms of the set (9) results in an equation linear for the components of x i . Similar to (7), we may write the next relationships: ˆ i xi , y=D ⎡

cosω t1 sinω t1 1 ⎢ cosω t2 sinω t2 1 ⎢ where D = ⎢ .. .. .. ⎣ . . . cosω tN sinω tN 1

At1 ωi sinωˆ i t1 + Bt1 ωi cosωˆ i t1 At2 ωi sinωˆ i t2 + Bt2 ωi cosωˆ i t2 .. .

(12) ⎤ ⎥ ⎥ ⎥. ⎦

AtN ωi sinωˆ i tN + BtN ωi cosωˆ i tN

The set of linear Eqs. (12) is cyclically solved to achieve the required accuracy, which N  characterizes by the well-known value (yn − yn [x])2 . n=1

As the initial estimate xˆ 0 can be obtained by peak-picking the Discrete Fourier Transform (DFT) of data. As mentioned in [17], for short noisy data records or signals at low frequency the convergence problems may occur. It should be mentioned that [17] is a basic numerical method to perform sine-fitting in order to characterize a sine wave acquired by a digitizer. This algorithm determines the amplitude, phase and off-set component of the acquired signal in one, non-iterative step for a given frequency. Its major drawback is that, when the relation between the input and sampling frequencies is not correctly known, the results of the method are not reliable. The technique proposed in [17] and based on the IEEE-STD-1057 algorithm was the basis for the estimating algorithm of parameters of a several sinusoids additive mixture, which was described in [18], [27]. In these papers, a problem similar to (1)–(3) is considered, namely the next multi-sinewave signal model is employed: un = C +

M 

Am cos(ωm n + ϕm ),

(13)

m=1

where C is the signal off-set; Am and ϕm are the unknowns to be estimated. A detailed solution to problem (13) is not given here because of its cumbersomeness, but it is with this solution that the evaluation results obtained by the authors are compared in Sect. 5 of this article.

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4 Data Model and Periodogram Method The Periodogram method is based on a Fourier series model of the data, having direct access to Fourier transform X N (ejω ) of N point observation data x N (n). The power spectrum is estimated by making the square the amplitude of X N (ejω ) divided by N. N −1      2 1   jω −jω n =  x ne Pˆ per e   N

(14)

0

Periodogram is calculated efficiently and a reasonable result can be produced for a large set of data [19]. In spite of these advantages, there are a few inherent performance deficiencies of this method. The most prominent one is the spectrum leakage, resulting in the energy in main lobe of a spectrum leaks into the side lobes. The reason for this is the truncation effect, due to the assumption that the data outside observation are defaulted as zeros. It equals the result multiplying the data by a rectangular window in time domain, which breaks the correlation of the data inside and outside observation. There are two parameters to indicate the performance of window function, main lobe width and side lobe level. Rectangular window has the narrowest main lobe, corresponding to the best resolution, but the most serious leak occurs for the bad side lobe level of rectangular window. Narrow main lobe and low side lobe level are expected, but they are a couple of contradictory parameters. Hamming window and Hann window are usually adopted for the balance between these two parameters. The Welch method is a modification of Periodogram. N point observation data x N (n) is divided into M overlapping or non-overlapping segments to reduce large variance of Periodogram. Assuming there are L-point data in each segment, the appointed window is applied to each segment to reduce side lobe effect. The modified Periodogram of the ith segment is given by 

Pˆ per ejω



2 L−1  1   =  xi (n)ω(n)e−jω n  , i = 1, 2, · · · , M  U

(15)

0

where U is called normalization factor, and it is given by 1 2 ω (n) L L−1

U =

(16)

0

Based on the modified Periodogram of each segment, the power spectrum of x N (n) can be estimated by averaging M modified Periodogram M 1  ˆ i  jω  Pper e Pˆ Welch = M

(17)

i=1

It can be extended as Pˆ Welch

 2 M L−1  1    = xi (n)ω(n)e−jω n     MU i=1

0

(18)

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When the length of x N (n) is fixed, with the increase of the number of the segments, the length of data which each segment contains will decrease [20]. It is helpful to decrease the variance of estimation by using a large number of segments, but the frequency resolution of power spectrum will deteriorate due to a small quantity of data. Therefore the choice of the number of segments should be considered according to the requirement. The Periodogram method and Welch method are nonparametric methods, while the Burg method is a parametric method [21]. For parametric method, the estimation is based on the parametric model of random process. The Burg method for AR power spectrum [22] is based on minimizing the forward and backward predication errors while satisfying the Levinson-Durbin recursion. It avoids calculating the autocorrelation function, while estimates the AR parameters directly instead. For N point observation data x N (n), the pth forward and backward predication errors can be defined as f

ep (n) = x(n) +

p 

apk x(n − k)

(19)

∗ apk x(n − p + k)

(20)

k=1 f ep (n)

= x(n − p) +

p  k=1

The average power of the pth forward and backward predication errors can be defined as ρp,f =

N −1 1   f 2 ep (n) N − p n−p

(21)

ρp,b =

N −1 1   b 2 e (n) N − p n−p p

(22)

The average power of the pth predication errors can be given by ρp =

 1 ρp,f + ρp,b 2

(23)

And the pth reflection coefficient k p can be calculated by minimizing the average ∂ρ power of predication errors, making ∂kpp = 0 −2 kp =

N −1 n=p

N −1 n=p

f

b∗ (n − 1) ep−1 (n)ep−1

 2  2   f  b   (n − 1) ep−1 (n) + ep−1

And the corresponding model parameters can be calculated by ap,i = ap−1,i + kp ap−1,p−i

(24)

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ap,p = kp i = 1, 2, · · · , p − 1

(25)

The power spectrum of x N (n) can be estimated from these model parameters, and the Burg method can always produce a stable model. But the accuracy is lower for high-order model; therefore the adoption of order is important for the Burg method.

5 Experimental Results Described above methods were used in processing experimental data obtained in the study of AFC micromechanical gyroscopes [23–26]. The external view of the experimental setup is shown in Fig. 1.

Fig. 1. The experimental setup

The reference rotary table, capable of performing controlled movements according to a given law was used in the experiment. Experimental block of micromechanical gyroscopes was rigidly attached to the table platform. The platform made oscillatory movements in harmonic law with a fixed amplitude 0,5 °/c and changing frequency in the range 0,5–100 Hz. The position of the platform was recorded with high accuracy by the integrated optical sensor of the angle of the rotary table. As a result of processing experimental data by two described above methods, the estimates of the AFC and measurement errors were obtained. Test sensors have a finite passband lying inside the frequency range under investigation, the SNR ratio of the resulting signals was dependent on the oscillation frequency of the rotary table. Deviation of the estimation error of the amplitude-phase frequency response to signal-to-noise ratio and the Cramer-Rao bound [17] are shown in the Fig. 2. It can

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be seen, that the proposed method has an advantage over the method from IEEE-STD1057 [18] and Periodogram methods, and the advantage is more noticeable at low noise levels.

Fig. 2. Standard deviation of the estimation error of the amplitude-phase frequency response vs signal-to-noise ratio

6 Conclusion In this paper, we proposed a maximum likelihood solution for the problem of parameter estimation, which is based on subfactorization of the data model parameters. The subfactorization method exploits specific structure of the data matrix and finds vectors spanning singular vectors of the data matrix. As a result of processing experimental data by three described above methods, the estimates of the AFC and measurement errors were obtained. The proposed algorithm presents some advantage over the IEEE-STD1057 standard and advantages are more noticeable in low SNR cases and big advantage over the Periodogram method in all SNR cases. In addition to the above, the proposed method also has less computational complexity due to the reduction in the number of unknowns to be evaluated.

References 1. Stoica, P., Moses, R.: Introduction to Spectral Analysis, p. 427. Prentice-Hall, Upper Saddle River (1997) 2. Tufts, D.W., Kumaresan, R.: Estimation of frequencies of multiple sinusoids: making linear prediction perform like maximum likelihood. Proc. IEEE 70(9), 975–989 (1982)

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23. Seranova, A.A., Abakumov, A.V., Gutsevich, D.E., Ermakov, R.V., Livshits, D.Yu., Romadin, S.N., Sergushov, I.V., Skripal’, E.N.: Design aspects of flight and navigation systems for small UAVs of different types. In: Proceedings 24th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2017, pp. 208–217 (2017) 24. Ermakov, R.V., Popov, A.N., Scripal E.N., Kalikhman D.M., Kondratov D.V., L’vov A.A.: Methods for testing and test results of inertial sensors intended for operation in helicoptertype aircraft. In: Proceedings 24th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2017, pp. 335–338 (2017) 25. Ermakov, R.V., Seranova, A.A., L’vov, A.A., Kalikhman, D.M.: Optimal estimation of the motion parameters of a precision rotating stand by maximum likelihood method. Measure. Techniques 62(2), 139–146 (2019). https://doi.org/10.1007/s11018-019-01598-x 26. Gulevich, S.P., Sergushov, I.V., Skripal, E.N., Abakumov, A.V., Kuzmenko, I.K., Livshits, D.Yu., Shapovalova, K.D.: Aircraft high accuracy positioning during approach to a platform using laser system with the GNSS signals outage. In: Proceedings 25th Anniversary Saint Petersburg International Conference on Integrated Navigation Systems, ICINS 2018, pp. 213– 220 (2018) 27. Andersson, T., Hndel, P.: Toward a standardized multi-sinewave fit algorithm. In: Proceedings 9th European Workshop ADC Modelling Test, pp. 337–342 (2001)

Jumping Robot as a Lunar Rover: Basic Technical Solutions Vadim Zhmud1(B)

, Dmitry Myakhor1

, and Huberth Roth2

1 Novosibirsk State Technical University, Karl Marx Ave. 20, 630073 Novosibirsk, Russia

[email protected], [email protected] 2 Department of Regulatory and Control Technologies, University of Siegen, Siegen, Germany

[email protected]

Abstract. Currently, the creation of new principles for the operation and movement of mobile robots, robotics is a fundamental task, extremely important and relevant, associated with robotics and digitalization at a fundamentally new level, corresponding to the concept of “Industry 4.0”. A subtask of this direction is also the development of the most effective ways of moving these robots. Under the conditions when the first lunar rover was created, the systems of automatic stabilization of equilibrium and motion control were not sufficiently developed, it was necessary to rely on maintaining the equilibrium of the lunar rover due to the advantages of its mechanical design. In these conditions, the wheel drive was optimal. The development of robotics, mechanics, electronics, automation, and computer technology has made it possible to turn to the most effective ways of moving over rough terrain in the absence of atmosphere, and with reduced gravity, these methods can be even more effective than wheel drives. A series of jumps is seen as the most effective way to travel in conditions where flight does not provide such opportunities due to the lack of atmosphere. Jumping allows many animals to save energy and move most quickly, efficiently, overcoming ravines, using the smallest opportunities for short-term support; jumping allows them to quickly and accurately move along the slopes of the mountains, through the rubble of large stones, along the windfall. With a fairly sharp and accurate impact with flat analogues of the soles, especially with low gravity, jumping can even allow robot to overcome ravines, screes, stone blockages. In terrestrial conditions, they are effective for overcoming water barriers, swamps, quicksand, and also, as some videos with animals show, they can allow robot to successfully move through avalanches. This paper sets the task of creating an effective jumping robot to study the surface of the moon and asteroids, as well as to study hard-to-reach areas on the Earth’s surface. An exotic design and basic principles for solving this problem are proposed Keywords: Automation · Robotics · Moon rover · Planet rover · Bionics

1 Introduction Research in order to create prototypes of a jumping robot for moving under conditions close to the surface of the moon is relevant. The main factors in this formulation of the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 152–164, 2021. https://doi.org/10.1007/978-3-030-65283-8_13

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problem are all kinds of surface problems, including hidden irregularities, as well as the absence of the atmosphere. Additional factors are increased dustiness and reduced gravity. Watching video recordings of the movements of jumping desert animals showed that this method is the most economical and promising for such conditions. The proposed set of scientific and technical solutions is aimed at creating jumping balancing robots that will use one of the most effective ways of moving over the most rough terrain, used by insects (mares, cicadas, locusts, some species of spiders, fleas, etc.), amphibians (frogs), mammals (jerboas, kangaroos, lemurs, squirrels, etc., as well as all cats), birds (penguins, blackbirds, sparrows, parrots). Jumping can be the most effective way to travel on the lunar surface and the surfaces of asteroids. Development in this direction involves the most accurate and efficient connection of sensors for sensing the position of the robot relative to the gravity vector, for orientation on the ground and for the perception of other environmental details in order to fulfill the tasks. Also, the robot must have a set of executive manipulators and movers as a means of interaction of robots with the environment and computer intelligence, implemented on microprocessor controllers, as a means of matching sensors and manipulators to ensure the highest accuracy of motion control. The breakthrough development of domestic robotics requires the creation of sets of standard solutions for sensors, microcontrollers, actuators, the integrated design of such systems and ensuring their reliability and other important functional characteristics.

2 Overview of Achievements in the World There are reports in the press about the Kangaroo robot, which reproduces with excessive reliability not only the principle of movement, but also the appearance of this animal [1], other publications about the same device: [2, 3, 4]. With unnecessary external similarity, the robot does not achieve the functional identity that is required: the robot jumps only forward, the tail balance is purely symbolic, in fact it is a toy that repeats the movements of the prototype animal only on a demonstration principle, while the real robot must, first of all, form the goal of the movement and achieve it most quickly, efficiently from an energy point of view, with the correction of jumps in the case of disturbance with the movement and so on, which, of course, is not achieved in the said publications. Also, in the international literature search there are publications about the same device: [5, 6, 7, 8]. There is information about the jerboa robot [9], and other sources about the same robot: [10, 11]. This robot is not so much similar in appearance to a biological prototype, only the principle of movement is imitated. The disadvantages of this robot are identical: it simply moves forward with a certain energy of the jump, the task of achieving the set goal was not solved, the subtasks of the correction of disturbance with the aim of directed movement to the target of the next jump were not solved, the trigger is simply implemented, leading to the only jump or to serial jumping in a random direction depending on the initial orientation and on many random surface factors. All these robots realize the identical movement of both limbs, which excludes control over the choice of the direction of the jump in dynamics. Currently, the best examples of such robots to change the direction of the next jump make a turn during a stop between jumps, while jumping animals quickly change direction during the landing and repulsion phases. While maintaining the synchronism of the action of the limbs, they should not act

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completely identically, the difference in repulsive forces and the difference in orientation should allow robot to control the direction and distance of the jump, which is not in the considered analogues. Jumping in all known cases is used only to overcome obstacles, but not as the main and most effective way to move over rough terrain in a given direction [12–20]. In the nature, jumping is most often used more efficiently, in a completely different way. While maintaining the synchronism of the action of the limbs, they should not act completely identically, the difference in repulsive forces and the difference in orientation should allow robot to control the direction and distance of the jump, which is not in the considered analogues. Thus, there is currently no solution to the problem in the formulation given in this project.

3 State of the Art In every aspect except accuracy and speed, modern robotics corresponds to the tasks of creating mechanical devices moving more successfully than living organisms. Speed and accuracy can be ensured by more effective than existing automatic control systems [21–34]. The design methods of such systems have reached such heights that control of the movement of individual manipulators and many other complex technical devices is achieved with the highest accuracy and very high speed. These types of devices include all types of balancing robots, first of all, a one-wheeled unmanned robot [34]. At the same time, a balancing two-wheeled robot must provide equilibrium with respect to one degree of freedom, a balancing one-wheeled robot is much more complicated, since it has two independent degrees of freedom, and equilibrium must be ensured along these two coordinates simultaneously, and in addition, it is necessary to control the direction of movement and speed. This problem is currently being solved by many research teams. There are no reports on solving this problem in an unmanned version yet. The robot must not only maintain equilibrium, but also dispense the impulse (speed and force of influence on the support) so that the jump is directed in the right direction and that it ensures movement precisely at a given distance with high accuracy. During the flight, the robot must rearrange its components in the same way as a cat regroups in flight in order to land exclusively on its limbs. This requirement means that the robot must land simultaneously on those two or four limbs that will absorb impact energy, provide amortization and energy storage, and the conversion of the kinetic energy of convergence into potential energy. This energy must then be released again for a new leap in the form of kinetic energy. Also, the limbs should work so that the jumps, if necessary, follow continuously without a pause. During the time between landing and the next jump, such a regrouping must be carried out that the new jump is directed to a new predetermined and calculated target. That is, the springs or their analogue are compressed from the energy obtained by damping the jump from the side of the incoming movement, and are unclenched for a new jump in the direction of motion propagation. The force is transmitted not in the diametrically opposite direction with respect to where it came from, but in a new direction. Therefore, during the landing, the tasks of depreciation, energy storage and its release for the next

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jump should be solved, as well as the task of changing the direction of the jump using this energy, and the change in direction is done during depreciation and repulsion, not being allocated for stopping. An additional energy is required to be introduced into the spring mechanism, which is added to the action of the spring; phase matching is required. This force is realized in the form of a pneumatic or magnetic impact. The cocking of this striking mechanism is carried out during the flight in the jump. Thus, the task is to form a series of jumps that solve the problem of movement, provided that the number of jumps in the series can be quite large. The solution of this problem is fundamentally important for the development of robotics, the solution of related problems will allow to obtain new results also in the field of automatic control theory as testing the most modern and effective methods for designing controllers for non-linear non-stationary objects (non-stationary properties are generated by a change in the mass distribution of the robot due to rearrangement). The disturbing effect (interference) is a movement error relative to the selected path, the position of the robot will be corrected by moving the limb manipulators and the flywheel (analogue of the tail). The results can be applied in transport systems, as well as embedded in the educational process.

4 Formulation of the Problem Due to the high speed and sufficient accuracy of actually available mechanical elements, sensors and microcontrollers, modern robotics is able to work faster and more accurately by several orders of magnitude than a person can do and move even if his capabilities of perceiving all the details of this movement are exceeded. That is, an effective robot can move so fast that a person cannot follow its actions in all details, and so precisely that even the most dexterous animal could not repeat these movements. In practice, there are no walking or jumping robots that perform these manipulations more successfully than living organisms. In order to fully realize the advantages of a jumping robot, it is necessary to use all the advantages of a jump efficiently from an energy point of view. What is needed is the most effective means of depreciation, which would, like a spring, absorb fall energy, transforming it into compression energy for a new jump, then release it in the right direction. Depreciation is needed precisely in the direction of landing in order to eliminate blockage on one side. In this case, the direction of the reaction vector of the support may be inconsistent with this requirement, since it lands on a random surface, it is even possible that it is covered with dust, under which the actual surface profile is hidden. This requires the coordinated action of stabilization systems and direction control of the next jump. In wildlife, this problem is solved in such a way that the limb that previously meets the support first bends without significant reciprocal effort, until the other or three other limbs also begin to touch the surface. After that, they will bend so that the force on them is identical. This result can be achieved in part using pneumatic resistance, but this is not enough. We need an automatic control system operating on the principle of negative feedback, providing identical force on both limbs, if there are two of them, or the corresponding equality of mechanical moments from pairwise diametrically opposite limbs, so that the braking is in the opposite direction to the landing.

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Further, the jumping robot moves in the direction of the energy pulce of the completed jump, while approaching the surface, the shock absorbers absorb kinetic energy from the vertical component of the movement, damping it completely, after which they convert the potential energy back into kinetic energy, throwing the robot up. In this phase of movement, the expanding shock absorbers must set the direction of the next jump, adjusting its current direction if necessary. To correct this direction, those of the limbs that are located in the opposite direction to the direction of the required acceleration should straighten more quickly, transmitting more force, and therefore more acceleration to this edge of the robot body. In this concept, there are many automatic control systems, as in the living organism of a jumping animal, which in biological nature act due to instincts and, possibly, without the participation of the brain, and in the case of a robot, they also apparently must act partially autonomously, obeying the central processor only as a whole, that is, in the field of target designation, and not in the field of a detailed algorithm of their work.

5 Jumping Robot Project The first project of the proposed robot was developed quite carefully. Part production technology is 3D printing. The goal of the project is to create a relatively lightweight, small-sized and possibly not expensive product, the main advantages of which will be contained in the development of technical solutions for the most accurate traffic control, to solve the movement problem in the complex. Small-sized samples represent more complex problem from the perspective of effective control, since their speed is several times higher, therefore, control should be several times faster, which puts higher demands on the speed of sensors, microcontrollers, actuators and the quality of design of the mathematical model of the controller. These problems in relation to balancing two-wheeled robots have already been successfully solved, only the scaling of these methods for a new task is required. The development of design methods for controllers has reached a sufficient level to solve all the subproblems of motion control by calculating controllers by numerical optimization [31–33]. Devices of this class are fundamentally different from manned robots, which in the form of one-wheeled and two-wheeled Segways are already quite widely known and are mass-produced. Unlike a manned balancing robot, an unmanned balancing robot does not have a person who could additionally maintain balance in all directions. By analogy, readers can compare a circus acrobat that maintains balance on a unicycle. In such a device there is no system for automatically maintaining balance, and yet it can remain in balance due to the pilot’s skill. Unlike balancing on a wheel or on two wheels, the proposed robot must balance on two limbs, acting on the same principle as the legs of a kangaroo, jerboa, lemurs, moving exclusively on the ground with leaps. Without balance on two legs it is impossible to make the first jump, but this is not enough: firstly, during the flight robot must regroup so that it land again on these limbs, and secondly, it must absorb the energy of the landing temporarily, then release it for the next jump thirdly, to direct the next jump. The robot control drives should form the difference in the effects of each limb separately, for example, to jump a little to the left, it should push harder with its right foot, to jump

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to the right, it should push harder with its left leg. In other words, it is thus necessary to ensure the trajectory along which the limbs are straightened relative to the center of mass of the robot in order to jump precisely in the required direction and precisely to the required flight length, and during the flight the necessary regrouping should be carried out again. This requires detailed studies of jump mechanics. The objective of the project is to create an unmanned balancing jumping and regrouping in a jump robot. To solve this problem, the robot must have a substantially partitioned body (feline flexibility) and (or) an external balancing counterweight (like a kangaroo), the project involves the use of both of these features in the created layout, i.e. the robot will also have a body that can influence the position of the center of gravity, and a sufficiently weighty counterweight (analogue of the tail). To the greatest extent, these properties are combined by an animal known as snow leopard [34], however, this animal lands on four legs, and a kangaroo or jerboa uses only two legs for jumping. It is advisable to explore both possibilities and choose the best. We stated from the two legs. All factors that disturb the balance should be monitored, and their influence should be suppressed by the operation of automatic robot balancing systems. The problem of changing the direction of the jump in the required direction and controlling the length of the jump should also be solved. The task is not limited to the simple formation of movements that generate the jump, but should be solved in a complex: the balance of the robot before the start of the jump, at the time of preparation, during its completion, preparation of the balance during the landing, balance during and after the landing, and so on in the cycle. The balance is carried out by the action of two joint ways of maintaining it: the external flywheel (analogue of the tail) and the movement of individual elements of the body and upper limbs (analogue of the cat’s bend). Maintaining balance is critical to building a series of sustained, focused leaps. Also, the equilibrium at the stage from landing to the next jump provides bouncing not according to the laws of mechanics for a spherical elastic object (when the angle of incidence is equal to the angle of reflection), but bouncing in the right direction even when the landing is not on a strictly horizontal plane, with tilt to 30° or more in any direction. For this purpose, it is necessary to use surface recognition and the preparatory arrangement of the limbs intended for jumping, and to provide the necessary orientation of the robot during landing and repulsion. This principle of motion is not currently used in robotics in the aggregate of all the proposed technical solutions; for this reason, the totality of the required capabilities is not demonstrated. The introduction of control in order to ensure movement after a jump in a given direction, with the suppression of the influence of the plane’s inclination, similar to how real living prototypes — kangaroos, jerboas, lemurs—moves in nature, makes the problem statement unique; there are currently no such results in the world. The project does not aim to create a robot, the mechanics and appearance of which would be, as far as possible, most flashing to a particular animal, but involves the maximum copying of the principles of motion and the most effective mechanical solutions found by wildlife. Refusal to copy the creativity of wildlife is not the only possible approach, an alternative approach (maximum mechanical identity) also deserves consideration, however, in many cases it is advisable to go beyond this approach. It is not

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advisable to completely copy a kangaroo or jerboa, and this is too primitive compared to potential capabilities. But it is advisable to borrow the technology of jumping, placing the cargo in a bag, which facilitates the achievement of stability in an upright position, also using a massive tail to ensure balance. However, the excess weight of the tail can be reduced, this structure is effective in the open, but loses in the forest, in the bushes, as well as in the labyrinth of the urban environment or in some field conditions. Completely copying cats is unnecessarily difficult and insufficiently functional, since cats do not carry bags or backpacks, a cat with a load is no longer a cat, she could not move so efficiently. Ideally, a robot from all animals will be most similar to a hybrid of kangaroos and snow leopards. From the kangaroo, the principle of a jump is borrowed with the maximum reuse of the kinetic energy of landing to form a new push, the principle of tail balance is also borrowed, however, it is necessary to transfer the main burden of the balancing task in the future not to external flywheels that have no functions other than balance, but to rearrange useful elements designs. Rearrangement in flight is borrowed from the snow leopard and feline as a whole in order to land on the required limbs. In the first year of the project, the external balancing element is essential, like an snow leopard with a relatively massive tail, in the future it is necessary to get away from this “tail” like a lynx with a tail absent, but this does not interfere with providing balance in the jump and when landing. Thus, cat lemur jumps most closely meet the task, since they are carried out on two limbs, and the whole organism is used for balance purposes. The main thing in the task is a comprehensive solution, which consists not only in simulating the action of the limbs that provide movement, but in the development and implementation of the action of the entire body of the device as a whole, since only with this solution jumps give a significant advantage over other methods of movement in specific conditions of highly crossed terrain. All the necessary structural elements are made by volume printing on 3D printers. These items are made of plastic. A detailed study of the design based on the study of the mechanics of skeletons of animal prototypes (opening of animals is not required, since the Internet has enough information about the mechanism of such movements and the structure of skeletons) is one of the parts of the project. Based on mock-ups showing the main features of the mechanics of the designed robot, a preliminary design will be made containing actuators and sensors. The restriction of the direction of vision to one fixed viewing angle, as in most animals, also seems optional. It is planned to ensure a full all-round view due to a sufficient number of video cameras (at least four). The formation of such an element as a “head” in the body is not necessary, however, stabilization of the orientation of the chambers in space should be recognized as effective, similar to the nature of the case of the cheetah: despite the fact that the animal is in motion by the whole organism, the head moves along an extremely smooth trajectory, in which there are no sharp up-and-down movements, left-right and up-down turns with respect to the center of mass are practically excluded; the stabilization system (in this case, muscular) provides an independent movement, smoother and more stable than with the rest of the body. This principle is supposed to be borrowed and reproduced. This stabilization of the optical head (an analogue of the head of an animal) can be carried out on the basis of the positive experience of stabilization of a balancing robot.

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6 The First Version of the Proposed Robot The project used the results obtained during the thorough study of all the main implementation issues. All mechatronic nodes used in the robot can be found on AliExpress, and the body parts are designed for production from ABS plastic, and their overall dimensions do not go beyond the average limitations of the printing area of amateur 3D printers (200 × 200 × 200 mm3 ). Thus, the ability to implement the entire project in a conventional laboratory is fully confirmed. The option under discussion is the first step, not final, research is required to ensure balance, to ensure jumping on only two limbs, since such jumps give an advantage in speed (kangaroo, jerboa). When designing a robot, a large number of various designs of competitors was studied. In terms of the mechanism of repulsion from the surface (soil), two popular solutions are found: 1) either the development is imitated by animals using bent limbs, 2) or the push is due to telescopic legs. The most concise and promising decision was made: to transmit the force to the leg through the pneumatic piston CDJ2D. At the initial moment, the piston with forced air holds the limb in a compressed position, simultaneously pulling the elastic gum. As soon as the normally-closed electric solenoid valve opens, which holds compressed air, the leg begins to rotate around the joint, creating a catapult effect for the robot. The basic ideas of the robot’s movements are shown in Fig. 1.

Fig. 1. The main ideas of the movements of the proposed robot: the robot jump through the stages (preliminary design of the first version)

For greater balance and repulsive force, as well as the possibility of choosing the direction of the push, four limbs are used, connected to MG996R servos, with which you can set not only pitch, but also yaw. Since we use compressed air, we need a compressor, which is capable of creating a pressure of 20 bar. Even if the actual pressure is half that, it should be enough to work. Also, an air receiver from an OP-1 fire extinguisher is installed on the robot, which will store compressed air.

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To mitigate the landing, the robot legs are equipped with shock absorbers, as shown in Fig. 2. There are springs and pistons with compressed gas. Electronic components and a battery are not shown for simplicity. The presence of springs is fundamental, they are equivalent in principle to the tendons of jumping animals, which convert kinetic energy from landing into potential compression-extension energy, and then back into kinetic energy, therefore, with a large series of jumps, a minimum of energy is spent, the main energy is consumed only during the first jump, further it is needed only to correct the direction of the jump and to make up for the loss of energy.

Fig. 2. Shock absorbers to mitigate the landing and storage of kinetic energy with its conversion to potential (energy of a compressed spring) with subsequent reverse conversion to kinetic (for the next jump)

The appearance of the proposed robot without electronic components and without power sources (batteries) is shown in Fig. 3, 4, 5, 6 and 7. In the final version, instead of the “head”, a platform with video cameras will be installed (four, cameras on each side, and possibly, if necessary, also cameras pointing down and up), as well as balance sensors and other necessary sensors. For movement during the night, each camera will be equipped with a backlight based on spotlights from infrared LEDs. Weights at the ends of the forelimbs are needed only at the first stage for practicing movements. In the final version, manipulators will be installed to capture cargo and to act with them. In the area where the bag is located on a real kangaroo, batteries and a place for securing the necessary goods will be installed. The tail in the final version will have fewer elements, each subsequent knee will apparently be smaller, the elemental base is currently being selected for these details. The idea of proportional transmission of forces along all articulations of the tail is considered. In this case, it will be controlled as a whole only in two coordinates: left-right and up-down, tail control will be not only to balance the flight, but it is also possible, as in the prototype (living kangaroo) to form a temporary third limb for supports during the rack (during a long stop of the robot). All moving structural parts are connected to the housing through bearings 608-2RS. On the 3D model, they are depicted in black discs. Technological cutouts are provided in the body parts to reduce weight. All connections are made in pairs of screw-nut with a

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Fig. 3. Sketch design of the robot: side view

Fig. 4. Sketch design of the robot: rear view (half-turn)

Fig. 6. Sketch design of the robot - top view

Fig. 5. Sketch design of the robot - front view (half-turn)

Fig. 7. Sketch design of the robot: bottom view

nylon seal with a metric thread and a diameter of 3 mm. The metal products on the model are not traced for reasons of greater clarity and less information loading of the image. In the finishing project necessary for implementation, the entire structure will be worked out including each rivet and each fastening. The generalized structure of the control system is shown in Fig. 8. The task of movement of the robot will be set by the external former of the task. The central controller will analyze it and distribute the tasks of control to local

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controllers of each joint. The control system for each joint consists of a local controller, a local drive, a local motor and a local sensor. Each joint is controlled according to the principle of negative feedback. Also, balance sensors installed in all critical points and four cameras installed in the head of the robot allow it to analyze the execution of the movement task by the robot as a whole, these sensors submit their information to the central controller, which analyzes the position and movement of the robot as a whole based on this information, based on this, it transfers the corrected control commands to the local controllers. Also, the system of head stabilization is projected. It contains sensors of balance, video cameras, head stabilization controller, head stabilization driver and head stabilization motors (actuators).

Fig. 8. Design block diagram of automatic control system: OTF – Outer Task Former, CC – Central Controller, LD – Local Driver, LM – Local Motor, LS – Local Sensor, SB – Sensors of Balance, VC – Video Cameras, HSC – Head Stabilization Controller, HSD– Head Stabilization Driver, HSM – Head Stabilization Motors (actuators)

7 Discussion and Conclusions This paper has presented the results of a preliminary development of a jumping robot. The advantages of this movement are confirmed by the analysis of movements in living nature, the novelty is confirmed by the analysis of existing robots according to the most important sources of information. The expected flight range when jumping exceeds the length of the robot by 15–25 times. These indicators will be worked out on the first model. Another important indicator is energy saving, that is, the use of landing energy for a new jump by accumulating it in the springs, but the orientation of the springs during landing will be different than during take-off, which allows robot to redirect this energy to correct the course. Also, the fundamental task is to separate the repulsive moments of force along the left and right limbs, this is necessary to control the direction of the jump. It is also planned to solve the problem of automatically lifting the robot from any position due to special balancing means, mainly without using the technology of repulsion from the surface, for this purpose it is planned to use the tail manipulator. These properties are an extremely important indicator of survivability and ability to complete

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a task even as a result of an unsuccessful fall and as a result of falling into a position from which it is impossible to make another jump.

References 1. https://prohitech.ru/robot-kenguru-kontroliruemyj-zhestami-umeet-prygat-kak-ee-zhivojsobrat/ 2. http://robocraft.ru/blog/news/3067.html, http://dosoaftor.ru/2017/02/03/robot-kenguru-otfesto/ 3. https://www.dailytechinfo.org/robots/5778-noveyshiy-robot-kompanii-festo-prygayuschiybionicheskiy-kenguru-bionickangaroo.html 4. Tadayoshi, S., Junzo, K., Susumu, T., Testuo, S., Hiroshi, M., Kouji, T. Pid controller system. US Patent. US4903192A. https://patents.google.com/patent/US4903192A/en 5. https://patents.google.com/?q=G05B13%2f0275 6. https://www.festo.com/group/ru/cms/10219.htm 7. https://spectrum.ieee.org/automaton/robotics/robotics-hardware/festo-newest-robot-is-ahopping-bionic-kangaroo, https://interestingengineering.com/robotic-kangaroo-based-onthe-principles-of-nature 8. https://www.theverge.com/2014/4/6/5587564/festo-robotic-kangaroo-is-inspired-by-nature 9. https://vido.com.ua/article/11868/miru-priedstavlien-robot-tushkanchik/ 10. https://www.dailytechinfo.org/robots/6930-sozdan-robot-tushkanchik-vesma-zabavno-pod razhayuschiy-svoemu-zhivomu-prototipu.html, https://www.htbook.ru/publ/tekhnologii/ robot-tushkanchik 11. Lotfi, A.Z. US Patent. US8949170B2. System and method for analyzing ambiguities in language for natural language processing. https://patents.google.com/patent/US8949170B2/en? q=G05B13%2f0275&num=100 12. https://engineering.phys.msu.ru/ru/projects/jumping-robot 13. https://nplus1.ru/news/2016/10/07/hopping-robot 14. https://habr.com/ru/post/140850/ 15. https://focus.ua/technologies/429719-prygayushhij-robot-salto-progulyalsya-po-ulicam 16. https://www.popmech.ru/technologies/news-492922-prygayushchie-roboty-muravi-ispolz uyut-rabotu-v-komande-dlya-preodoleniya-prepyatstviy/ 17. https://polit.ru/news/2016/12/07/ps_jump/ 18. Duncan, W.H., Plecnik, M., Yim, J.K., Fearing, R.S.: Robotic vertical jumping agility via serieselastic power modulation. Sci. Robot. 1(1), eaag2048 (2016). https://doi.org/10.1126/scirob otics.aag2048 19. https://life.ru/p/943033 20. http://robotrends.ru/pub/1723/luchshie-v-mire-hodyashie-begayushie-i-prygayushie-robotyiz-ssha-uhodyat-k-yaponcam 21. Intelligent control method for pulsation vacuum sterilizer based on fuzzy control. China Patent. CN104850010. https://patents.google.com/patent/CN104850010A/en 22. JUSTIA patents. Proportional-integral-derivative (p-i-d) Pftents (Class 700/42). https://pat ents.justia.com/patents-by-us-classification/700/42 23. PID regulator circuit. China Patent. CN201732261U. https://patents.google.com/patent/CN2 01732261U/en 24. A kind of self-adaptive low-voltage difference linear constant voltage regulator of wide withstand voltage scope and chip thereof. China Patent. CN104808734B. https://patents.google. com/patent/CN104808734B/en

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25. Doicin, B., Popescu, M., Patrascioiu, C.: “PID Controller optimal tuning,” In: 2016 8th International Conference on Electronics, Computers and Artificial Intelligence (ECAI), Ploiesti, pp. 1– 4 (2016). https://doi.org/10.1109/ecai.2016.7861175, http://ieeexplore.ieee.org/stamp/stamp. jsp?tp=&arnumber=7861175&isnumber=7861062 26. Xu, L., Ding, F.: Design of the PID controller for industrial processes based on the stability margin. In: 2016 Chinese Control and Decision Conference (CCDC), Yinchuan, pp. 3300–3304 (2016). http://doi.org/10.1109/CCDC.2016.7531552, http://ieeexplore.ieee.org/stamp/stamp. jsp?tp=&arnumber=7531552&isnumber=7530943 27. Tjokro, S., Shah, S.L.: Adaptive PID Control, In: 1985 American Control Conference, Boston, MA, USA, pp. 1528–1534 (1985). https://doi.org/10.23919/acc.1985.4788858, http://ieeexp lore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4788858&isnumber=4788561 28. Díaz-Rodríguez, I.D., Oliveira, V.A., Bhattacharyya, S.P.: Modern design of classical controllers: digital PID controllers. In: 2015 IEEE 24th International Symposium on Industrial Electronics (ISIE), Buzios, pp. 1010–1015 (2015). https://doi.org/10.1109/isie.2015.7281610, http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7281610&isnumber=7281431 29. Mehta, U., Majhi, S.: On-line identification and control methods for PID controllers. In: 2010 11th International Conference on Control Automation Robotics & Vision, Singapore, pp. 1507– 1511 (2010). https://doi.org/10.1109/icarcv.2010.5707428, http://ieeexplore.ieee.org/stamp/ stamp.jsp?tp=&arnumber=5707428&isnumber=5707203 30. Ashida, Y., Hayashi, K., Wakitani, S., Yamamoto, T.: A novel approach in designing PID controllers using closed-loop data. In: 2016 American Control Conference (ACC), Boston, MA, pp. 5308–5313 (2016). http://doi.org/10.1109/ACC.2016.7526501, http://ieeexplore.ieee.org/ stamp/stamp.jsp?tp=&arnumber=7526501&isnumber=7524873 31. Zhmud, V., Liapidevskiy, A., Prokhorenko, E.: The design of the feedback systems by means of the modeling and optimization in the program VisSim 5.0/6. 2010. In: Proceedings of the IASTED International Conference on Modelling, Identification and Control. AsiaMIC 2010, 24–26 November 2010, 27–32. Phuket, Thailand (2010) 32. Zhmud, V., Yadrishnikov, O., Poloshchuk, A., Zavorin, A.: Modern key technologies in automatics: structures and numerical optimization of regulators. In: 2012 Proceedings - 2012 7th International Forum on Strategic Technology, IFOST 2012, Tomsk, Russia (2012) 33. Zhmud, V., Yadrishnikov, O.: Numerical optimization of PID-regulators using the improper moving detector in cost function. In: Proceedings of the 8th International Forum on Strategic Technology 2013 (IFOST-2013), vol. II, 28 June–1 July, pp. 265–270. Ulaanbaatar, Mongolia (2013) 34. Sablina, G.V., Stazhilov, I.V., Zhmud, V.A.: Development of rotating pendulum stabilization algorithm and research of system properties with the controller Actual problems of electronic instrument engineering (APEIE–2016). In: Proceedings of 13 International ScienceTechnology Conference, Novosibirsk: Publication House of NSTU, 2016. vol. 1, Part. 3, pp. 165–170 (2016)

Fast Method for Solving the Wave Equation Vil Baiburin , Alexander Rozov(B) , Artem Kolomin , and Natalia Khorovodova Information Security of Automated Systems, Yuri Gagarin State Technical University of Saratov, 77 Politechnicheskaya Street, Saratov 410054, Russia [email protected]

Abstract. This chapter focuses on the numerical solution of the wave equation. Partial differential equations play a key role in many fields of science and engineering. Recently, however, the emergence of massively parallel computer systems has suggested an alternative computational approach. Many classical numerical methods are not intended for multiprocessor systems. We devote this paper to the investigation of new numerical methods for solving equations in partial derivatives with parallel computer systems using. The basic idea is founded on the assumption that the mesh function is monotonous and consistently bypasses the solution area in different directions. It is demonstrated that the application of the proposed method on large meshes is more preferable than the known methods. Keywords: PDE · Parallel computer systems · Numerical method

1 Introduction The subject of partial differential equations (PDEs) is enormous. At the same time, it is very important, since so many phenomena in nature and technology find their mathematical formulation through such equations. Knowing how to solve at least some PDEs is therefore of great importance to engineers. Most simulation models in various fields of science and technology (including microwave, electronics, etc.) are based on PDE [4, 6], in particular, wave equation, heat equation, etc. We know it that the efficiency of used simulation models is determined by the speed and adequacy of numerical solutions of these equations. A solution of the wave equation is one of the most demanded problems in electronics and microwave, in particular, in the calculation and design of terahertz range generators [13]. The finite difference method (FDM) [11], the finite element method [12], is the most common among numerical methods for PDE solving [5, 7, 8]. Numerical techniques in solving scientific and engineering problems are growing importance, and the subject has become an essential part of the training of applied mathematicians, engineers and scientists. The reason is numerical methods can provide the solution while the ordinary analytical methods fail. Numerical methods have almost unlimited breadth of application. Other reason for lively interest in numerical procedures is their interrelation with digital computers. Besides, parallel computing is © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 165–174, 2021. https://doi.org/10.1007/978-3-030-65283-8_14

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a good platform to solve a large scale problem especially the numerical problem. This is proven through the successful implementation in solving hyperbolic problem. The outcomes of parallel performance measurements show that parallel computing is time saving comparatively with the sequential computing as many researchers have taken interests in developing finite difference methods that could approximate the solution of a one dimensional hyperbolic diffusion equation. Classical methods, however, have their own restrictions. Explicit methods are simple but generally suffer the disadvantage of conditional stability and low accuracy. Implicit methods, on the other hand, may possess unconditional stability and higher accuracy. Their features, however, are less amenable to parallelism. The problem of creating effective working algorithms which significantly increase the speed of calculations for the possibilities of parallel calculations is the most urgent. [16]. the researchers discussed the solution of one-dimensional Partial Differential Equations (PDEs) using some parallel numerical methods namely finite difference method and proposed method. The selected one-dimensional PDEs in order to solve the problem was hyperbolic type. Calculation programs usually based on methods connected to systems of linear equations, usually three-diagonal [3, 10]. Earlier in [1] devoted to the numerical solution of the Dirichlet problem for the Poisson equation. Authors showed the possibility of creating high-speed distributed algorithms. The method was that the values in the internal nodes of the calculation grid are determined as arithmetic mean values for three neighbouring nodes. We have implemented these methods for stationary problems. In presented paper the approach which does not suppose the solution of systems of the equations and supposes we state parallel realization of the numerical solution that as a result leads to acceleration of calculations in comparison with known methods. One purpose of this paper will be to show the possibility of creating a similar method for a non-stationary problem.

2 Materials and Methods of Research To present the core of the algorithm we seek the solution to the one-dimensional wave Eq. [14]: ∂ 2 u(x, t) ∂ 2 u(x, t) − a2 =0 2 ∂t ∂x2

(1)

where u = u(x,t) x-position, t – time, a – phase velocity, the environment resistance is not taken into account. We set auxiliary conditions [14]: u|t=0 = u(x, 0) = ϕ1 (x)

(2)

∂u |t=0 = ϕ2 (x) ∂t

(3)

Let introduce a mesh in time and in space. The mesh in time consists of time points: t = t j+1 − t j j = 0, 1, 2 .. J

(4)

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and space points: x = xi+1 − xi i = 0, 1, 2 .. I

(5)

We use Neumann conditions [7] (2), (3), discretizing the Neumann condition will be recorded as: ui0 = ϕ1i,0

(6)

t = ui1 − ui0 = ϕ2i,0

(7)

j

j

u0 = uI = 0

(8)

Mesh scheme is shown in Fig. 1.

Fig. 1. Mesh scheme. White node shows the point where function values are set on initial and boundary conditions, black indicates the points in which the function values are unknown

To solve Eq. (1), let’s assume the smoothness and monotony of the unknown function. Consider cell number 11. The value of the function at point u12 can be calculated as mean: u12 =

u01 + u11 + u02 3

(9)

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The values in nodes u22, u32 , u42 etc. can be found in the same way, at this point forward stroke ends. The reverse stroke starts in cell number 15, at that the results of calculations by the forward and reverse stroke are averaged in the corresponding internal nodes. Accordingly, this algorithm allows for parallel implementation of calculations by rows and columns in different directions.

3 Results Let compare the speed between the proposed numerical method and classical numerical methods. The classical scheme for numerical solving Eq. (1) has the following form [2]: j+1

ui

  j j j j−1 = 2(1 − λ)ui + λ ui+1 + ui−1 − ui λ =

a2 x2 t 2

(10)

We compared how quickly the proposed algorithm, and the algorithm (10) close to the known analytical solutions. Assume that: ϕ1 (x) = sin(x), ϕ2 (x) = cos(x), a = 1

(11)

The analytical solutions for case (11) are known [14]: u(x, t) = [cos(x)](at − x) + [sin(x)](at + x)

(12)

We conduct simulation for the string with the length equal to 500 mm, let the string be deflected at the initial moment of time. The simulation was carried out for interval delay in 5 s. Further, the graphics of the string position at different moments in time are shown, obtained by the proposed numerical method and analytical method. The figures show a solid line, the exact analytical solution, and the value of the numerical solution shown in circles (Figs. 2, 3, 4, 5 and 6). The performance of the parallel algorithm will be analyzed in terms of the time execution, speedup, efficiency, effectiveness and temporal performance. The measurements are defined as follow [17]. Speedup: S(p) =

t1 tp

(13)

Where t 1 – execution time for a single processor, t p – execution time using p parallel processors. Efficiency: S(p) p

(14)

Ep S(p) = ptp tp

(15)

E(p) = Effectiveness: F(p) =

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40000

30000

20000

U(X,T)

10000

0

-10000

-20000 X

Fig. 2. Comparison between analytical and numerical solutions t = 1 s.

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4000 3500 3000 2500 2000 1500 1000

0

1 22 43 64 85 106 127 148 169 190 211 232 253 274 295 316 337 358 379 400 421 442 463 484

500

X

Fig. 3. Comparison between analytical and numerical solutions at t = 2 s.

140 120 100 80 60 40 20 0 -20

1 22 43 64 85 106 127 148 169 190 211 232 253 274 295 316 337 358 379 400 421 442 463 484

170

Fig. 4. Comparison between analytical and numerical solutions t = 3 s.

Fast Method for Solving the Wave Equation 40

35

30

25

20

15

10

0

1 19 37 55 73 91 109 127 145 163 181 199 217 235 253 271 289 307 325 343 361 379 397 415 433 451 469 487

5

-5

Fig. 5. Comparison between analytical and numerical solutions t = 4 s.

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1 23 45 67 89 111 133 155 177 199 221 243 265 287 309 331 353 375 397 419 441 463 485

172

-0.5 -1 -1.5 -2 -2.5 -3 -3.5 -4 -4.5

Fig. 6. Comparison between analytical and numerical solutions t = 5 s.

Temporal performance: L(p) =

1 tp

(16)

Table 1 below shows the performance of the parallel algorithm. Table 1. Performance Nb CPUS

1

2

4

8

Time (s)

42 22

13

6

Speedup

1

1.9

3.23

7

Efficiency

–

0.95

0.81

0.86

Effectiveness

–

0.043 0.20

0.10

Temporal performance: 1

0.024 0.046 0.166

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Table 2 shows a comparison of the calculation time using the known algorithm (10) and the proposed algorithm, for different meshes. Simulations were carried out in 8 threads, in different directions (north-south, south-north, west-east, east-west) of the grid. Table 2. Solution time (time specified in sec.) Mesh size

FDM [11] Proposed Method

10000 * 10000

21

10

50000 * 50000

72

36

60000 * 60000

81

42

70000 * 70000

130

210

90000 * 90000

700

274

1300

310

900000 * 900000

1701

410

6500000 * 650000

1801

504

7000000 * 700000

2124

613

7500000 * 750000

2640

810

8000000 * 800000

2800

915

100000 * 100000

4 Conclusion As we can see from data in Table 1, the proposed method provides a significant reduction in calculation time with high accuracy of the numerical solution. Also, it is necessary to note the simplicity of implementation of this algorithm in comparison with the finite difference method, and the fact that it allows refusing from solving systems of linear algebraic equations.

References 1. Baiburin, V.B., Rozov, A.S.: Poisson equation numerical solution method based on bidirectional multiple passage of grid cells and parallel computations. In: 2019 3rd School on Dynamics of Complex Networks and their Application in Intellectual Robotics (DCNAIR 2019), pp. 19–25 (2019) 2. David, E.: Potter Computational physics Wiley-Interscience Publications (1988) 3. Evans, D.J.: The solution of periodic parabolic equations by the coupled Alternating Group Explicit (CAGE) iterative method”. Int. J. Comp. Math. 34, 227–235 (1990) 4. Feynman, R.P., Leighton, R.B., Sands, M.L.: The Feynman Lectures on Physics. AddisonWesley, Redwood City (1989) 5. Hansen, P.B.: Numerical Solution of Laplace’s Equation Electrical Engineering and Computer Science Technical Reports, pp. 168–182 (1992)

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6. Jackson, S.: Electrodynamics, MIT, Cambridge (1966) 7. Lau, N., Mark, A., Kuruganty, S.P.: Spreadsheet Implementations for Solving Boundary-Value Problems in Electromagnetics, Spreadsheets in Education (eJSiE), 4(1), Article 1 (2010) 8. Logan, D.L.: A first course in the finite element method. CL-Engineering; 5th edition (2011) 9. Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in Pascal: The Art of Scientific Computing. Cambridge University Press, Cambridge (1989) 10. Press, W.H., Teukolsky, S.A.: Multigrid methods for boundary value problems. I. Comput. Phys. 5(5), 514–519 (1991) 11. Pschenica, S.: Parallel algorithms for solving partial differential equations. J. Iowa Acad. Sci. JIAS, vol. 101(2), Article 11 (1994) 12. Reddy, J.N.: An Introduction to Nonlinear Finite Element Analysis, Oxford University Press, Oxford (2004) 13. Rozov, A.S., Baiburin, V.B.: Generation in crossed fields under parametric variation in the magnetic field. J. Commun. Technol. Electron. 61(3), 267–271 (2016) 14. Yu, V.: Egorov Partial Differential Equations IV (Encyclopedia of Mathematical Sciences). Springer (1992) 15. Strang, G.: Introduction to Applied Mathematics. Wellesley-Cambridge Press, Wellesley (1986) 16. Alias, N., Che Teh, C.R., Islam, M.R., Farahain, H.: Halal food industries based on dehydration of dic technique. In: Proceedings of the Regional Annual Fundamental Science Symposium, 8–9 June 2010, Kuala Lumpur, Malaysia, pp. 1–8 (2010) 17. Alias, A.P., Ghaffar, Z., Satam, N., Darwis, R., Hamzah, N., Islam, Md.R.: Some Parallel Numerical Methods in Solving Parallel Differential Equations, p. (2010). https://doi.org/10. 1109/iccet.2010.5485502

Dynamic Error Reduction via Continuous Robot Control Using the Neural Network Technique Viktor Glazkov1 , Stanislav Daurov1(B) , Alexey L’vov1 and Dmitriy Kalikhman2

, Adel Askarova1

,

1 Yuri Gagarin State Technical University of Saratov, Saratov, Russian Federation

[email protected], [email protected], [email protected], [email protected] 2 Branch of FSUE «Academician Pilyugin Center » – « Production Association Korpus » , Saratov, Russian Federation [email protected]

Abstract. The article presents an algorithm for planning the trajectory which goes exactly through two given points: the initial and end points. By complicating the structure of the neural network, we can plan the trajectory that will go through a specified number of points with regard to additional conditions. It is obvious that with the increase of the problem complexity, the accuracy of the solution to the problem decreases. The suggested recommendations reduce the possibility of errors in the neural network solutions. Keywords: Manipulator · Programmed motion trajectory · Motion control · Dynamic error · Neural network · Neural network control approach

1 Introduction Robotic manipulator control systems are divided into continuous (contour), discrete positional (a step by step point-to-point motion), and discrete sequencing ones with respect to a type of manipulator motions. The first type of these systems is most sophisticated, since they ensure continuous motion of an end effector along the fixed trajectory (for example, industrial modulators for arc welding and cutting, etc.). The second type of systems is used in spot welding, assembly, and manufacturing machinery servicing. The third type of robotic systems is used in the simplest robots with sequencing control [1–6]. Fundamental distinction between the continuous control and discrete positional systems consists in the fact that the former must assure not only static accuracy in the positioning points, but also dynamic accuracy of the motion along the fixed trajectory. Therefore, the transient performance and stability in discrete positional systems are estimated only for the node points, whereas at continuous control the given requirements must be ensured all along the fixed trajectory qf (t), In either case, the problem with the manipulator motion control can be solved in two stages: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 175–184, 2021. https://doi.org/10.1007/978-3-030-65283-8_15

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• designing (planning) the programmed motion trajectory; • assuring the motion along the planned trajectory in compliance with stipulations. Trajectory planning for motions of the manipulator means obtaining a set of n continuous functions for generalized coordinates of time, where n is the number of manipulator joints used to train the planned motion. The papers on robotics [2, 4–6] describe two ways for manipulator trajectory planning. The first method, known as planning based on Cartesian coordinates, is applied for the cases when the desired motion trajectory in the Cartesian space is given as the analytical function z = f (x,y). This approach allows for accurate tracking of the desired spatial trajectory. However, determination of the trajectory in the form of an analytic function would not always be possible, or would be challenging. In such cases, we can use another method, known as planning in terms of the generalized coordinates. The given method is based on the knowledge of Cartesian coordinates with discrete set of points, called nodes. Dependence of the generalized coordinates on time is approximated by various orders of polynomials. The order of the polynomial is dictated by the number of fixed points in the Cartesian space, as well as by the boundary conditions applied for the programmed trajectory. A set of numerous via points provide a near to optimum motion trajectory for the manipulator of the robot and solve the problem of avoiding collision with various obstacles in the environment. In fact, the given tens or hundreds of points are generally set by way of manual training of the manipulator. Then, even in the cases of insignificant changes in the workspace, a retraining is required. In most cases, the motion space of the manipulator contains no obstacles. Consequently, only a few points of the trajectory will be sufficient, including the initial and end points, and two or three intermediate points, defined for the cases when there are no collision constraints at the initial or end points. This type of planning is adequate for the cases, when the initial and end points vary within certain limits, as for example, in the case of object manipulation with the coordinates determined by means of robot vision systems or other types of sensors. As a result, the motion trajectory can be changed without human intervention. In the given case, the law of motion along any of the generalized coordinates is determined by a combination of polynomials of the third, fourth, and fifth orders, where the coefficients are computed from conditions of continuity of the joint coordinate, as well as its first and second time derivatives. The disadvantage of this type of planning is an unpredictable or in certain cases oscillating type of motion along the generalized coordinates between the node points, which makes it hard to predict the motion trajectory in the Cartesian space [2–5].

2 Related Work In many applications, robot is considered as work platform carrying instruments, so its positioning accuracy affects the working quality of the robot directly. At present, there are many works studying robot’s error, which are based on the parameters of the model calibration that is common establishing the Denavit–Hartenberg kinematic model [7–10]. Due to the complicated factors, confirming the multiple parameters’ error often makes the solving of the robot’s error model difficult, and the calibrated parameters are

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not always accurate. Therefore, the using of wider and easier compensation method is very beneficial to the improvement of the precision of the robot and the simplified process of calculation. A simple compensation method, using a way of mapping the structural parameters’ error to the joints’ angular parameter of the kinematics parameters is given in [11]. This method is made on the robot error compensation, so as to avoid the accuracy of the parameters’ measurement affecting the precision of the robot, which makes the error compensation effect further improve. Moreover, the dynamic error compensation method is discussed and analyzed in the cited paper, which can be designed through adding control algorithm to the software used for compensation. In most cases an Inertial Navigation Systems (INS) must be integrated with other absolute location-sensing mechanisms to provide useful information about vehicle position. As a consequence, an INS by itself is characterized by position errors that grow with time and distance. One way of overcoming this problem is to periodically reset inertial sensors with other absolute sensing mechanisms and so eliminate this accumulated error. In robotics applications, a number of systems have been described which use some form of absolute sensing mechanisms for guidance ([12, 13] for surveys; [14–17]). In [18], the integration of inertial and visual information is investigated. Methods of extracting the motion and orientation of the robotic system from inertial information are derived theoretically but not directly implemented in a real system. In [19], inertial sensors are used to estimate the attitude of a mobile robot. With the classical three-gyro, two-accelerometer configuration, experiments are performed to estimate the roll and pitch of the robot when one wheel climbs onto a plank using a small inclined plane. The primary motivation for the work [20] has been the need to develop a system capable of providing low-cost, high-precision, short time-duration position information for large outdoor automated vehicles. The approach taken in the cited paper is to incorporate in the system a priori information about the error characteristics of the inertial sensors and to use this directly in an extended Kalman filter to estimate position before supplementing the INS with absolute sensing mechanisms. A computer-controlled vehicle, which is part of a mobile nursing robot system is described in [21]. The vehicle applies a motion control strategy that attempts to avoid slippage and minimize position errors using a cross-coupling control algorithm. The design and implementation of a cross-coupling motion controller for differential-drive mobile robot is described in [22]. The idea of using a new fuzzy logic expert rule-based navigation method for fusing data from multiple low- to medium-cost gyroscopes and accelerometers in order to estimate accurately the heading and tilt of a mobile robot is introduced in [23, 24]. Presented experimental results of mobile robot runs over rugged terrain showed the effectiveness of the proposed method. This paper proposes a new neural network approach for planning the motion trajectories of the mobile robot manipulator. The main advantage of this technique is has no need in a rather sophisticated procedure connected with solving the inverse problem of dynamics to the full mathematical model of arm actuators.

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3 Methods to Reduce Dynamic Errors It is worth noting, that all the above mentioned methods for trajectory planning have a major disadvantage. These methods are based purely on robot kinematics and do not take into account the dynamic properties of a manipulator, which may result in the risk when the programmed trajectory could not be used to generate motion. 3.1 Dynamic Compensation Under Program Control Thus, the programmed trajectory and the control inputs are different notions, and can coincide only in particular cases [1, 4]. In fact, if we provide arm actuators with the programmed trajectories qf (t), calculated in accordance with the programmed trajectory of the end effector x of (t) by solving the next inverse kinematics problem qf (t) = f −1 [xof (t)],

(1)

where: x of (t) are the coordinates, which characterize the position and end effector orientation in relation to the base (absolute) coordinates; and qf (t) is the vector of the generalized coordinates of the manipulator, which correspond to a specified programmed trajectory, then the motion behavior will be characterized for deviation of the manipulator dynamics. The higher the velocity, the more serious is the dynamic error q. At zero initial velocity and acceleration, the error at the initial time point is equal to zero and changes in the process of the motion. When planning the trajectory using the generalized coordinates, avoiding the error at the end point is of critical importance. Figure 1 shows

Fig. 1. Dynamic deviation q (t) found when tracking the programmed trajectory qf (t)

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the trajectories of the robot gripper obtained from the dynamic model of the manipulator in the system SimMechanics. The solid line corresponds to the desired trajectory defined by a polynomial of the seventh order; the dotted, dash-dotted and dashed lines represent the trajectory programmed with the dynamic error. The error becomes more evident at decreasing the time of the motion from 10 s (dotted line) to 2.5 s (dashed line). The ways to reduce dynamic errors are known from the theory of automated control [1, 3, 6]. First, since we analyze the programmed control, the error can be eliminated by adding the pre-calculated dynamic compensation to the programmed trajectory, which may compensate for the specified deviation of the manipulator dynamics. As a result (see Fig. 2), the arms will train the control programs 2.4 G

2.2

Δc

qз qf q

2

Δq = q − q f

1.8 q

1.6 1.4 1.2 1 0.8 0.6 0.4

0

0.5

1

t

1.5

2

2.5

Fig. 2. Compensation of the dynamic lag

G(t) = qf (t) + c (t),

(2)

where c (t) is the dynamic compensation. Computation of the control program can be made by solving the inverse dynamics problem in terms of mathematical descriptions of actuators  A(˙q)¨q + b(˙q, q) + c(q) = QE ; , (3) QE = AD (UD ), where QE is the vector of generalized torques acting along the coordinates of the manipulator links; AD (U D ) is the operator of the system of actuators; U D is the vector of control inputs. By substituting q(t) for the given programmed trajectory qf (t), which was found in x of (t) by solving the inverse kinematics qf (t) = f −1 [xof (t)],, we will find the required control program, U Df (t).

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In Fig. 2, the solid line shows the desired coordinated joint trajectory qf , the dashed line represents the real-time trajectory with the dynamic deviation q, the dotted line G corresponds to the coordinated joint trajectory with the compensation, which due to the servo drive allows us to obtain the desired motion trajectory. 3.2 Development of Control Using Training Methods Additionally, control programs can be determined experimentally using the training methods on real robots [4–6]. There are two ways to introduce these methods of training. First, steering the continuous motion of the end effector of a robotic manipulator manually by the human operator and recording the signals from feedback sensors of actuators. To avoid interference of manipulator motors into the given process, manipulator designers must foresee a possibility to disconnect the motor from the mechanical system of a manipulator (while maintaining connection with feedback sensors). Another method is based on sequential installation of end effectors using the actuators at pre-selected points of the programmed trajectory, and recording of the feedback sensor readings, as in the case with programming systems of discrete position control. A digital interpolator is used to generate the planned trajectory between these points while simulating the pre-programmed motion. Dynamic compensation required for this type of programming is also determined experimentally by means of multi-trial simulation of the desired trajectory over a specified time [1, 4, 6]. The second way for reducing dynamic errors is based on upgrading the automatic control system performance through introduction of dynamic compensation to be formed directly while perfecting the input system of the desired programmed trajectory. Undoubtedly, the given way is considerably more sophisticated, since we ignore the priori information about the planned trajectory, though it simplifies the robot programming method, reducing it to kinematic synthesis of the programmed trajectory for actuators [5, 6]. Basically, we can provide distinction between the two versions applied in programming continuous (contour) control systems: dynamic and kinematic [1, 3]. The first version corresponds to low speeds of the end effector motion (lower than 0.5 m/s), where dynamic errors in the programmed trajectory under provided high performance of control systems can be neglected. The second version relates to higher speeds, where dynamic compensation is to be introduced into control programs, i.e. the inverse problem of dynamics, rather than kinematics used for the first version, is to be solved in analytical calculations. To improve the above programming methods based on training techniques, the novel methods introduced control of robot manipulators provided by human operators. This procedure is performed either by a three degree freedom robot arm, which is moved manually by the operator, or by computer-assisted control using a television camera mounted on the end effector of the manipulator [1]. This method does not require disconnection of the drive motors, and at the same time it upgrades the accuracy and performance of programming.

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3.3 Neural Network Approach for Trajectory Planning The conducted analysis shows that in spite of the numerous existing methods, the problem with continuous dynamic control of the manipulator is still relevant and complicated. To solve the problem, we propose a new approach which allows us to take into account the dynamic properties of the manipulator, and consequently control the manipulator at high motion speeds of the end effector. For this purpose, when planning the trajectory, we propose to use feedforward artificial neural networks. At the same time, we receive the possibility to take into account not only dynamic properties of the manipulator, but also to plan the trajectories near to the optimum in terms of the motion range in kinematic pairs, i.e. without any inaccuracies of motion. The neural network training can be performed based on the data relating the coordinates at the initial and end points of the trajectory, using the dynamic models of manipulators or a set of experimental data. Let us assume that the initial and end points of the trajectory of the grip are given. The purpose of the planning is to find the continuous function of the corresponding trajectory, which the manipulator can follow with an error: f

qi = f (qii , qi , t),

(4)

f

where qi is the i-th generalized coordinate; qii , qi are the values for generalized coordinates of the initial and end points of the trajectory; t is the time. Let us assume that the speed of the manipulator motion at the initial and end points of the trajectory equals zero. The given restriction complies with assembly operations. f A three-component vector consisting of the values qii , qi and t will be served for the input of the neural network, which approximates the function (4). To simplify the structure of the neural network, it is advisable to use a separate neural network with a single output value for each generalized coordinate. The number of neural networks, operating in parallel, will be determined by the number of joints in the manipulator. This technique allows significantly reducing the number of links in each neural network, and therefore, speeding up training procedure and improving its accuracy. The problem relating the optimal structure of the neural network is open for discussion. Based on the experimental data [4, 7], we can give recommendations referring the following: – the dimension of the input vector of the neural network approximating the function (4) equals 3, i.e. the network has 3 inputs; – the number of neurons in the hidden layer should exceed the number of inputs by 15–20 times; – the number of hidden layers should be from 1 to 3; – the number of output variables equals 1, i.e. each neural network is designed in order to find one generalized coordinate; – to achieve the required accuracy, the number of training examples should exceed the number of links in the neural network by no less than 7–10 times.

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The set of training and test data needed to train a neural network is created in the course of the following algorithm: 1. Randomly set the coordinates for initial and end points corresponding to the whole range of various trajectories. 2. Transform a set of Cartesian coordinates for the points into a set of generalized coordinates, while solving the inverse problem of kinematics. 3. Make an extended set of points for each pair of initial and end points within the space of generalized coordinates by adding a number of path points to those obtained at stage 1. 4. Test the resulting sets of points for accuracy (absence of by-movements, or overrange). 5. Accomplish the pre-planning of trajectories by approximation with polynomials of low order passing through the points obtained at stages 2 and 3. 6. Construct the table functions qik (tn ) using the coefficients of the polynomials obtained at stage 4, where qik is the “kinematic” value of the generalized coordinate i-th„ i.e. obtained without taking into account the dynamic properties of the manipulator; and tn is timing. 7. Construct the table functions qid (tn ) corresponding to the motion trajectories with account for the dynamic properties of the manipulator, using the manipulator model designed to solve the feedforward problem of dynamics, and generate the kinematic trajectories obtained at stage 5.    8. Form the training set: qid (tin ), qid (tfin ), tn ↔ qik (tn ) where qid (tin ), qid (tfin ) are the values of the generalized coordinate on the “dynamic” trajectory at the initial and final points of time, respectively; qik (tn ) is the value of the generalized coordinates   on the “kinematic” trajectory at the time point t n . The set qid (tin ), qid (tfin ), tn corresponds to the variables provided for the input of the neural network, the value qik (tn ) is provided at the output. As the values of the generalized coordinates qid (tin ), qid (tfin ) are obtained by means of the dynamic model, or by the experimental data corresponding to a particular manipulator, the neural network is trained to plan the trajectory taking into account the dynamic compensation (graph G in Fig. 2). In this case, the training trajectory (graph qf in Fig. 2) will pass through the required points. 9. The training set, obtained at stage 8, is used to train the neural networks. For the training of feedforward networks, we can use modifications of the gradient descent method or genetic algorithms. The research shows that the trained neural network is capable to solve the problems of trajectory planning under the changes in the input values within the range set during the training process. The initial and end values of the generalized coordinate can vary widely, depending on complexity of the neural network and permissible errors. Tight constraints are imposed on the motion time. When using the trained neural network, the time for the performance of the trajectory by the manipulator must equal exactly determined for the training set. However, we assume that the given time restriction is not a serious constraint in the application of the proposed method. If we take human performance, such as writing, for the standard of the coordinated motion, it can be observed that the handwriting will significantly vary depending on

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the writing speed. Both slow and quick writing standards, will noticeably distort the handwriting compared with the handwriting provided at a normal speed.

4 Conclusions This paper proposes the neural network approach for planning the motion trajectories of the manipulator. Among the advantages of the given approach is that it is devoid of a rather sophisticated procedure connected with solving the inverse problem of dynamics to the full mathematical model of arm actuators. Therefore, the computing system used to implement the neural network control algorithm may have a limited computing power. Each cycle of the algorithm requires the same number of computational operations, which makes the selection of a computing device easier.

References 1. Yurevich E.I.: Osnovy robototekhniki [Robotics Basics], 2 izd., SPb.: BHV, 302 p., Peterburg, (2005), (in Russian) 2. Fu, K.S., Gonzalez, R.C., Lee C.S.G.: Robotics: Control, Sensing Vision and Intelligence, 580 p., Mcgraw-Hill Book Company (1987) 3. Kozlov ,V.V., Makary’chev, V.P., Timofeev, A.V., Yurevich, E.Yu.: Dinamika upravleniya robotami [Robot control dynamics], 336 p., M.: Nauka, (1984), (in Russian) 4. Vukobratovic, M.: Introduction to Robotics, Springer-Verlag, 299 p. (1989) 5. Koren Y.: Robotics for Engineers, McGraw-Hill, 345 p., (1986) 6. Angeles, J.: Fundamentals of Robotic Mechanical Systems. MES, vol. 124. Springer, Cham (2002). https://doi.org/10.1007/978-3-319-01851-5 7. Guo, X., Ma, T., Zhang, Z., Li, M.: Research on smart operation method of industrial robot based on laser sensor. In: Proceedings SPIE 11378, Nano-, Bio-, Info-Tech Sensors, and 3D Systems IV, p. 1137818 (2020). https://doi.org/10.1117/12.2558480 8. Roth, Z.S., Mooring, B.W., Ravani, B.: An overview of robot calibration. IEEE J. Robot. Autom. 3(5), 377–385 (1987). https://doi.org/10.1109/JRA.1987.1087124 9. Meng, Y., Zhuang, H.: Autonomous robot calibration using vision technology. Robot. Comput. Integr. Manuf. 23(4), 436–446 (2007) 10. Du, G., Zhang, P.: Online robot calibration based on vision measurement. Robot. Comput. Integr. Manuf. 29(6), 484–492 (2013) 11. Zhang, J., Cai, J.: Error analysis and compensation method of 6-axis industrial robot. Int. J. Smart Sens. Intell. Syst. 6(4), 1383–1389 (2013) 12. Kuritsky, M.M., Goldstein, M.S. (eds.) Inertial navigation, Autonomous Robot Vehicles, Cox I. J., Wilfong G. T., Eds. New York: Springer-Verlag (1990) 13. Leonard, J.J., Durrant-Whyte, H.F.: Directed Sonar Navigation. Kluwer Academic Press, Norwell, MA (1992) 14. Ermakov, R.V., L’vov, A.A., Sadomtsev, Y.V.: Fundamentals of developing integrated digital control of precision stands with inertial sensors using signals from an angular rate sensor, accelerometer, and an optical angle sensor. In: Proceeding 23rd St. Petersburg International Conference on Integrated Navigation Systems, St. Petersburg, CSRI Elektropribor, pp. 361– 366 (2016) 15. Ermakov, R.V., L’vov, A.A., Sokolov, D.N., Kalihman, D.M.: Angular velocity estimation of rotary table bench using aggregate information from the sensors of different physical nature. In: Proceeding 2017 IEEE Russia Section Young Researchers in Electrical and Electronic Engineering Conference, St. Petersburg, Russia, pp. 585–589 (2017)

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16. Ermakov, R.V., Popov, A.N., Scripal, E.N., Kalikhman, D.M., Kondratov, D.V., L’vov, A.A.: Methods for testing and test results of inertial sensors intended for operation in helicopter-type aircraft. In: Proceeding 24-th St. Petersburg International Conference on Integrated Navigation Systems, St. Petersburg, CSRI Elektropribor, pp. 335–338 (2017) 17. Ermakov, R.V., Seranova, A.A., L’vov, A.A., Kalikhman, D.M.: Optimal estimation of the motion parameters of a precision rotating stand by maximum likelihood method. Meas. Tech. 62(4), 139–146 (2019). https://doi.org/10.1007/s11018-019-01598-x 18. ViCville, T., Faugeras, O.D.: Cooperation of the inertial and visual systems. In: (NATO AS1 Series, F63), pp. 339–350. Springer-Verlag, New York (1990) 19. Vaganay, J., Aldon, M.J.: Attitude estimation for a vehicle using inertial sensors. In: 1st IFAC International Workshop on Intellignet Autonomous Vehicles, pp. 89–94 (1993) 20. Barshan, B., Durrant-Whyte, H.F.: Inertial navigation systems for mobile robots. IEEE Trans. Robot. Autom. 11(3), 328–342 (1995) 21. Borenstein, J., Koren, Y.: Motion control analysis of a mobile robot. Trans. ASME J. Dyn. Measur. Control 109 (2), 73–79 (1986) 22. Feng, L., Koren, Y., Borenstein, J.: Cross-Coupling Motion Controller for Mobile Robots. IEEE Control Syst. Mag. 13(6), 35–43 (1993) 23. Ojeda, L., Borenstein, J.: FLEXnav: Fuzzy logic expert rule-based position estimation for mobile robots on rugged Terrain. In: Proceeding 2002 IEEE International Conference on Robotics and Automation. Washington DC, USA, pp. 317–322 (2002) 24. Glazkov, V.P., Egorov, I.V., Pchelintseva, S.V.: Exact estimates of a neural network solution for the inverse kinematics of a manipulator. Mekhatronika, avtomatizatsiya, upravlenie 11, 12–18 (2003). (in Russian)

Neural Network Modeling of the Kinetic Characteristics of Polymer Composites Curing Process Oleg Dmitriev

and Alexander Barsukov(B)

Tambov State Technical University, Tambov, Russia [email protected], [email protected]

Abstract. This article discusses the possibility and expediency of modeling the kinetic characteristics of the curing process of polymer composites (using carbon fiber as an example) based on the use of artificial neural networks. Using neural network modeling, the dependence of the kinetic function of the polymer composite on its degree of cure was obtained. The neural network operability is compared with experimental data and classical approximation methods. Keywords: Kinetic characteristics · Polymer composites · Neural networks

1 Introduction Currently, polymer composites (PC) are used in all areas of modern technology and industries, coming to replace many traditional materials. The production efficiency and quality of PC products are largely determined by their optimal temperature-time curing cycle. To optimize the curing process using a mathematical model, it is necessary to determine empirically and by calculation, many parameters of the curing process, for example, kinetic, rheological, thermophysical, and other characteristics [1–5]. There are many different methods and mathematical models for determining the kinetic characteristics of the curing process of PC [6–8]. However, not all of the kinetics models can equally accurately describe the change in the kinetic function for each specific PC curing cycle. Therefore, the search and selection of an adequate curing model requires the high qualification of the chemical technologist and a lot of time. To simplify the simulation, it is proposed to use neural networks (NN), which are currently widely used for forecasting and approximation in many fields of technical and humanitarian sciences. The aim of the work is to verify the possibility and expediency of using a neural network to predict the kinetic function ϕ(β) of PC curing. Neural networks are self-learning systems that allow effective the building of nonlinear dependencies that more accurately describe sets of experimental data. The main advantage of neural network modeling is the training and synthesis of accumulated information based on a selection of experimental data. Any information loaded into the neural network as input and output signals can be experimental or calculated data [9]. The neural network modeling method allows simplifying the modeling of curing kinetics, eliminating the selection and search for an adequate curing model. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 185–193, 2021. https://doi.org/10.1007/978-3-030-65283-8_16

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2 Mathematical Model of the Cure Kinetics of Polymer Composites We will study the characteristics of composites under conditions of one-dimensional one-sided heating of a sample of a flat shape with thermal insulation of the opposite and lateral sides (Fig. 1). This allows creating a temperature distribution in the sample similar to the temperature field of an unlimited plate. In research and production, it is impossible to completely exclude the prepreg resin flow in the direction perpendicular to the temperature gradient in the experimental setup. Therefore, we introduce the assumption about the flow of the resin along the isotherm taking into account the change in thickness L and factor resin content γ in the studied PC prepreg. Thus, to study the characteristics of the sample, we will use the mathematical model of hot pressing [10].

0 C(T,β,γ) L

x

F

q0(t)

λ(T,β,γ)

W(x,t) qL(t)

T0(t) T(x,t) TL(t)

Fig. 1. Physical model of an experimental study of the curing process of PC sample

To determine the thermophysical and kinetic characteristics, it is necessary to solve the inverse problems of heat conduction and kinetics of the process. When solving the problem, we will use as initial data the heat fluxes q0 , qL on the surfaces of the sample and temperature T (x,t). In this regard, when constructing a mathematical model of heating and curing of PCs, the boundary conditions of the second kind will be specified. Thus, the mathematical model describing the heating and curing process of the PC is similar to the model of the unlimited plate shown in Fig. 1, and is the NL system of the following partial differential equations: - heat transfer with boundary conditions of the second kind with sample thickness L changing under pressure in the presence of internal heat sources:   ∂ ∂T ∂β ∂T = λ(T , β, γ ) + γ (t)Qt , C(T , β, γ ) ∂t ∂x ∂x ∂t T ≡ T (x, t), 0 < x < L(t), 0 < t ≤ tf , T (x, 0) = g0 (x), 0 ≤ x ≤ L(0),  ∂T  = q0 (t), 0 < t ≤ tf , −λ(T , β, γ )  ∂x x=0  ∂T  −λ(T , β, γ )  = qL (t), 0 < t ≤ tf . ∂x x=L(t) - kinetics of cure

  E(β) ∂β = ϕ(β) exp − , ∂t R·T

β < 1,

(1)

(2)

(3)

Neural Network Modeling of the Kinetic Characteristics

β ≡ β(x, t),

187

0 ≤ x ≤ L(t), 0 < t ≤ tf ,

β(x, 0) = β0 (x), 0 ≤ x ≤ L(0), - squeezing of resin and compacting of the material during pressing L(t) = L(0) − Ls.rs (t) , n−1   dhi (τ ) dτ , dτ

(4)

t

Ls.rs (t) =

(5)

i=1 0

h3i (t)

dhi (t) F = −16 , i = 1, 2, . . . , n − 1, 0 < t ≤ tf , dt B · μi (t) l 3 b   L(0) · γs − γf ,  h(0) = (n − 1) · 1 − γf   Eμ , i = 1, 2, . . . , n − 1, 0 < t ≤ tf , ˜ · exp μi (t) = μ(β) R · Ti (t) γ (t) =

L(t) − L(0)(1 − γs ) , L(t)

γs = γf =

ρpr (0) Mrs (0) , ρrs Mpr (0)

ρpr .min Mrs .min ρrs Mpr .min

(6) (7) (8) (9) (10)

,

(11)

where B - shape factor of gaps between layers of fiber filler in prepreg; C - volume heat capacity, J/(m3 ·K); E - activation energy of curing, J/mol; Eμ - activation energy of viscous flow, J/mol; g - initial temperature distribution, K; h - thickness of resin layer, m; L - thickness of the product, m; Qf - full exothermic reaction heat, J/m3 ; R - universal gas constant, J/(mol·K); T - temperature, K; t - time, s; W - the rate of evolved heat of cure reaction, W/m3 ; x - spatial Cartesian coordinate, m; β - degree of cure; γ - volume resin content in prepreg; ϕ - kinetic function, 1/s; λ - thermal conductivity, W/(m·K); μ - dynamic viscosity resin, Pa·s; ρ - density, kg/m3 ; Indexes: f - finished; pr - prepreg; rs - pure resin; s.rs - squeezed out resin; s - start. To determine the kinetic characteristics, i.e. activation energy E(β) and kinetic curing function ϕ(β), we will use the rate of evolved heat of cure reaction W (x, t) = Qt

∂β . ∂t

(12)

Kinetics will be studied on thin samples of PCs whose thickness does not exceed 10 mm. For such samples, the temperature inside and on the surface is practically the same. This allows making an assumption about the same rate of the curing reaction

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throughout the entire volume of the test sample. Thus, we assume that the curing process proceeds in thickness at the average integral temperature

. Then we

will consider the distribution of the heat source over the thickness of the sample to be uniform: W (x, t) ≡ W (t).

(13)

The integral representation of the rate of evolved heat of cure reaction as a function of time is found directly from Eq. (1) taking into account the boundary conditions (Eq. 2) and has the form ⎡ ⎤ L(t) T(x,t) d 1 ⎢ ⎥ (14) C(s, β, γ) ds dx⎦. W (t) = ⎣qL (t) − q0 (t) + γ (t) L(t) dt 0 T (x,0)

The rate of evolved heat of cure reaction contains information on the kinetics of the process and is related to the kinetic equation as follows: β(t) = where Q(t) =

t

Q(t) , 0 ≤ β ≤ 1, Qt

(15)

W (t)dt - thermal effect of the curing reaction; Qt = Q(tf ) - the full

0

exothermic reaction heat; tf - cure time end. Given these assumptions, the mathematical model of kinetics for the average integral temperature Tav (t) over the thickness of the sample will take the form:   E(β) dβ = ϕ(β) exp − , β < 1, (16) dt R · Tav (t) β ≡ β(t), 0 < t ≤ tf , β(0) = β0 . For further modeling and calculation of the curing process, it is necessary to know the values of the parameters of the mathematical model (Eqs. (1)–(11)). The parameters can be found empirically by conducting physicochemical studies of the curing process of PC or by solving the corresponding inverse problems of heat conduction and kinetics of the process. In solving the inverse kinetics problem to finding the activation energy E(β) and the kinetic curing function ϕ(β) we will use experimentally measured values of the concentrations of the reacted substances or the degree of cure β. Corresponding methods and algorithms have been developed for determining thermophysical and kinetic characteristics, as well as technical equipment for their determination [10, 11]. To determine two unknown characteristics E(β) and ϕ(β) from the equation of the mathematical model of kinetics (Eq. 16), it is necessary to compose a system of two equations describing various conditions of the curing process. Thus, it is sufficient to have data on the degree of cure β(t), obtained by curing the same material which has been studied using two different temperature-time cycles T1 (t), T2 (t).

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Having logarithmized both sides of Eq. (16) and using the time dependences β(t) and Tav (t) two experiments with different heating rates, we compose a system of two linear algebraic equations for the unknown and(β) and E(β), solving which, we find the kinetic characteristics of the curing process 2 (t(β)) ln W W1 (t(β)) Tav1 (t(β)) Tav2 (t(β)) , E(β) = R Tav2 (t(β)) − Tav1 (t(β)) ⎡ ⎤ W1 (t(β)) Tav2 (t(β)) ln W2Q(t(β)) − T (t(β)) ln av 1 Q f f ⎦, ϕ(β) = exp⎣ Tav2 (t(β)) − Tav1 (t(β))

(17)

(18)

where W 1 (t(β)), W 2 (t(β)) - the rate of evolved heat of cure reaction of the samples depending on the time and degree of cure for two different temperature-time curing cycles;Tav1 (t(β)), Tav2 (t(β)) - average integral temperatures of the samples during curing for two different temperature-time cycles. For the correct simulation of the polymer curing cycle, it is necessary to approximate the kinetic function within the limits of the degree of cure from 0 to 1, and find the activation energy. The activation energy is determined experimentally and has a weak dependence on the degree of cure, so it can be represented as constant E, although there are no obstacles to using it as an experimentally measured function E(β). The kinetic function is usually approximated according to one of the models (Table 1), which is often used in chemical engineering practice [3, 6, 7]. In this work, we want to check which of the models is best suited for approximating the experimentally obtained kinetic function and if there are any ways to improve it, since the calculated optimal temperature-time curing cycle of PC depends on this. Table 1. Kinetic function approximation models Model 1

Model 2

Model 3

ϕ(β) = K(1 − β)m

ϕ(β) = Kβn (1 − β)m

ϕ(β) = K(1 − β)(1 + k0 β)

K = 1, 093 · 106

K = 1, 15 · 106

K = 1, 15 · 106

m = 1, 25

m = 1, 26

k0 = −0, 66

n = 0, 02

Where m, n – chemical reaction orders; K – chemical reaction rate constant. The reaction orders and the chemical reaction constant are determined on the basis of experimental data. They are empirically calculated constants for each individual type of PC and depend on the nature of the chemical reaction of the curing process.

3 Construction of a Neural Network for Modeling the Kinetics of Curing The choice of an adequate model of kinetic function is proposed to be performed using a neural network. To predict the kinetic function, we will use a data array that contains

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the calculated dependencies of the kinetic function ϕ(β) change on the degree of cure β according to the above formulas. To analyze the data, the neural network modeling method was used. We have built non-neural networks of three different types of neural networks: according to the Levenberg-Marquardt method, according to the Bayesian regularization method and the scaled conjugate gradient method. The simulation was carried out in the MATLAB environment using the NEURON FITTING TOOLS plugin, which will allow setting the number of neurons in the hidden layer and changing the percentage of training, test, and test samples (Fig. 2).

Fig. 2. Block diagram of a neural network

The neural network was trained using the “with the teacher” algorithms. Three vectors were specified - input values (INPUTS), target output values (OUTPUTS), and test. An experimental array of data on the change in the degree of cure of the polymer composite during curing was used as an input vector. The values of the kinetic function calculated by models 1–3 were used as the target parameter. A verification vector was randomly selected 15% of all experimental data. These data were not used in the construction of the model, but only to verify the adequacy of the NN. Each of the available training methods was used to build a neural network. The number of neurons in the hidden layer was set in the amount of 50 pieces, the training set was 70%, the control and test set was 15%. Figure 3 shows graphs of NN regression using the above algorithms, confirming its operability and performance. As can be seen from Fig. 3, the highest NN performance is achieved when training the network using the Bayesian regularization method. For further computer modeling, we will use this particular method. To determine the performance of the NN and compare the results, we will compile Table 2, in which we enter 10 random values of the degree of cure of the polymer composite, the values calculated using models 1–3 (Table 1), the neural network, and experimental values. A complete enumeration of the degree of cure values β from 0 to 1 with about 0.01 steps was carried out during the simulation. According to the simulation results, a kinetic function ln ϕ(β) was obtained depending on the degree of cure β (Fig. 4) and the calculated values are placed in Table 2. When compared with the experimentally obtained data, it turned out that the NN quite accurately predicts a change in the kinetic function values from the degree of cure at β > 0.1. The large difference between the results of modeling and the experiment in this area is associated with large errors in the experimental determination of the heat release power at the initial stage of the experiment.

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a

191

b

c Fig. 3. Neural network Regression Charts. a - Levenberg-Marquardt method, b - Bayesian regularization, c - scaled conjugate gradient method

To clearly compare the accuracy of the calculation of the kinetic function for each of the models, we find the mean squared error (MSE). It is calculated on the basis of predicted data for each of the methods and experimental data. To calculate the MSE, the cure kinetics β was calculated from 0.1 to 0.9. This range of variation in the degree of cure was chosen to minimize the influence of the error of experimental measurements on the accuracy of comparison of the presented methods. The calculation results are shown in Table 3. From Table 3 we can see that the smallest value of the MSR of the model is achieved using a neural network. Thus, its use in the process of finding the kinetic characteristics of the curing of polymer composites is justified, and also increases the accuracy of the approximation of the kinetic function.

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Degree of cure, β

Model 1

Model 2

Model 3

Neural network

Experimental data

0.003

13.837

13.950

13.845

13.048

13.900

0.017

13.852

13.926

13.884

13.520

13.883

0.164

13.693

13.661

13.682

13.718

13.680

0.251

13.563

13.484

13.535

13.613

13.542

0.347

13.397

13.268

13.337

13.452

13.371

0.467

13.147

12.957

13.059

13.142

13.118

0.642

12.653

12.378

12.559

12.607

12.622

0.743

12.239

11.924

12.128

12.165

12.208

0.835

11.685

11.356

11.711

11.743

11.656

0.967

9.661

9.531

9.638

9.704

9.645

The logarithm of the kinetic function, ln ϕ(β)

Fig. 4. The results of modeling the kinetic function

Table 3. Mean square error

Mean square error

Model 1

Model 2

Model 3

Neural network

0.0049

0.0404

0.0045

0.0036

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4 Conclusion In the course of this work, we created an NN simulating a change in the kinetic function of carbon fiber in the process of curing. This confirmed the possibility and expediency of using NN for modeling the curing process of polymer composites. However, for the functioning of the NN, it is required to determine the empirical parameters of the kinetics models. Therefore, further development of an experimental data processing system based on NN is relevant. It will allow automatic determination of all the necessary kinetic characteristics of the curing process only on the basis of experimental data, without performing intermediate calculations and choosing the right approximating models.

References 1. Struzziero, G., Teuwen, J.J.E., Skordos, A.A.: Numerical optimisation of thermoset composites manufacturing processes: a review. Compos. A 124, 105499 (2019). https://doi.org/10. 1016/j.compositesa.2019.105499 2. Liy, M., Zhuz, Q., Geubellez, P.H., Tucker, C.L.I.I.I.: Optimal curing for thermoset matrix composites: thermochemical considerations. Polym. Compos. 22(1), 118–131 (2001). https:// doi.org/10.1002/pc.10524 3. Rai, N., Pitchumani, R.: Optimal cure cycles for the fabrication of thermosetting-matrix composites. Polym. Compos. 18(4), 566–581 (1997). https://doi.org/10.1002/pc.10309 4. Shah, P.H., Halls, V.A., Zheng, J.Q., Batra, R.C.: Optimal cure cycle parameters for minimizing residual stresses in fiber-reinforced polymer composite laminates. J. Compos. Mater. 52(6), 773–792 (2017). https://doi.org/10.1177/0021998317714317 5. Baronin, G.S., Buznik, V.M., Zavrazhina, C. V., et al.: Thermophysical properties of fluoropolymer composites with cobalt nanoparticles. In: AIP Conference Proceedings. Mechanics, Resource and Diagnostics of Materials and Structures (MRDMS-2017), vol. 1915, p. 040003 (2017). https://doi.org/10.1063/1.5017351 6. Vafayan, M., Abedini, H., Ghreishy, M.H.R., Beheshty, M.H.: Effect of cure kinetic simulation model on optimized thermal cure cycle for thin-sectioned composite parts. Polym. Compos. 34(7), 1172–1179 (2013). https://doi.org/10.1002/pc.22526 7. Kumar, K.V., Safiullah, M., Ahmad, A.N.K.: Root cause analysis of heating rate deviations in autoclave curing of CFRP structures. Int. J. Innov. Res. Stud. 2(5), 369–378 (2013) 8. Poodts, E., Minak, G., Mazzocchetti, L., Giorgini, L.: Fabrication, process simulation and testing of a thick CFRP component using the RTM process. Compos. B 56, 673–680 (2014). https://doi.org/10.1016/j.compositesb.2013.08.088 9. Himmelblau, D.M.: Applications of artificial neural networks in chemical engineering. Korean J. Chem. Eng. 17(4), 373–392 (2000) 10. Mishchenko, S.V., Dmitriev, O.S., Shapovalov, A.V.: An automated system for investigation and selection of the optimum conditions of curing of thin-walled composite parts. Chem. Petrol. Eng. 29, 144–148 (1993). https://doi.org/10.1007/BF01149368 11. Dmitriev, O.S., Zhivenkova, A.A.: Numerical-analytical solution of the nonlinear coefficient inverse heat conduction problem. J. Eng. Phys. Thermophys. 91(6), 1353–1364 (2018). https:// doi.org/10.1007/s10891-018-1869-x

A Technique for Multicriteria Structural Optimization of a Complex Energy System Based on Decomposition and Aggregation Ekaterina Mirgorodskaya(B) , Nikita Mityashin , Yury Tomashevskiy , Dmitry Petrov , and Dmitry Vasiliev Yuri Gagarin State Technical University of Saratov, 77, Politechnicheskaya Str., Saratov 410054, Russia [email protected]

Abstract. A class of architectures, called group hybrid microgrid, is identified within the framework of the system approach. The connection between components of hybrid microgrids of these groups is realized by a common DC bus. Functions of inversion, accumulation and reservation by diesel generators are given to the corresponding equipment of only one hybrid microgrid. A selection algorithm of variants for decomposition of a power supply system, based on group hybrid microgrid, according to two criteria has been developed. These criteria are the minimum length of power transmission lines from generating equipment to consumers and the degree, to which consumers’ powers in load centers conform to powers of supplying them group hybrid microgrids. It is proposed to use an optimization assignment model, formulated as a Boolean linear programming model, to solve this problem. The mechanism for solution of this optimization problem, which used the genetic algorithm with the replacement of several criteria with single super criterion, is described. At the same time a procedure for the formation of a fuzzy version of the constraint mechanism is developed. An example of the problem solution with given numbers of hybrid microgrids and load centers is considered. The smallest values of criteria, obtained for different results of the decomposition of the initial hybrid microgrids’ set, are shown as a result of using of proposed algorithms. Keywords: Microgrid · Decomposition · Aggregation · Optimization assignment problem · Genetic algorithm · Fuzzy

1 Introduction Decomposition and aggregation operations are fundamental in systems analysis. The problem of decomposition of a complex system, i.e. division of a complex system into subsystems, can be used for different purposes as a simplifying of the control process, testing and design in various fields of technology, economics and sociology. Problems of criterial decomposition, results of which must satisfy certain conditions corresponding to their purposes, can be distinguished in the general problem of decomposition. The ability © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 194–208, 2021. https://doi.org/10.1007/978-3-030-65283-8_17

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to solve such problems arises due to the ambiguity of the decomposition procedure. These conditions are most often expressed by setting of one or more criteria, minimization or maximization of which corresponds to the purpose of decomposition. We can give an example of a system decomposition of non-modular equipment into subsystems in order to create an appropriate system of modular equipment. In this case criteria for the structural optimization of the equipment system are the efficiency and flexibility of production. A set of modules is formed, when this problem is solving. The aggregation of these modules allows to create not only compositions corresponding to samples of the initial system of non-modular equipment, but also units with new useful qualities. The specified combination of decomposition and aggregation procedures is a mean of structure optimizing of a complex system. An example of the first effective application of this method is the system of aggregated assembly equipment, described in [1, 2]. Thus, we can talk about multicriteria problems of structural optimization of complex systems, the solution of which is found by the consistent application (possibly multiple) of decomposition and aggregation procedures.

2 Problem Statement As an actual example we consider the following problem, arising in the design of a branched system of electric energy generation, based on HMG [3–6]. Hybrid microgrid (HMG) consists of several generation sources that receive primary energy of various physical natures and, above all, based on solar panels and wind generators. The electric energy, generated by these sources, has a different form. It is characterized by parameters with unstable values, so microgrid (MG) must contain devices, which convert it into electricity that meets existing standards. The conversion equipment contains rectifiers and impulse converters that collect energy from generation sources on a common DC bus, from which the output autonomous inverter is powered. HMG also contains batteries and diesel generators in addition to this equipment. Thus, a distributed autonomous power supply system for consumers is formed, on the basis of which a larger HMG can be compiled. The location and required powers of HMG for a specific area are determined, first of all, by its geographical and climatic features. It may be appropriate to combine some groups of compactly located MGs into a common subsystem to increase the flexibility and reliability of the power supply system, as well as simplify control systems. In this case, the connection between components of HMG can be realized by the integrated DC bus, while functions of inversion, accumulation and reservation by diesel generators are given to the corresponding equipment of only one HMG. Replacing of several inverters, rechargeable batteries and diesel generators with corresponding individual devices of total power also has economic advantages. The subsystem of HMG, obtained in this way, will be called group hybrid microgrid (GHMG). The initial system of individual HMGs can be decomposed into similar GHMGs if it necessary. An additional advantage of this separation is the ability to organize the

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redistribution of generated power between GHMGs, which is almost impossible within the initial system. In this regard, the following problem can be stated. It is necessary to design a system, based on the GHMG architecture, using the existing set of individual HMGs and set of consumers, powering from them. A similar problem makes sense when the set of consumers can be decomposed into groups of compactly placed loads, which will allow them to be powered within a single GHMG. Such decomposition is a secondary problem, a possible algorithm for solving which is given below. Mentioned load groups will be called load centers with defined coordinates. The selection of generating variants for the decomposition of the power supply system, based on GHMG in this problem, is carried out according to two criteria, which are expressed in numerical form. The first of them meets the requirement of the minimum length of power transmission lines from generating equipment to consumers. These lines include both direct current power lines from generation points to the inverter of the corresponding HMG group, and alternating current lines from group inverters to load centers, which they power supply. The second criterion characterizes the degree of correspondence between powers of load centers’ consumers and powers of GHMGs, which power them. We give the structure of the source data to obtain analytical expressions of these criteria. The set of generating HMGs, denoted below by D, is defined by following parameters. We give models for analytical expressions of these criteria. They will be used below for representation of the problem initial data and results of its solution. The set D = {di }, i = 1, N is a model of the set of initial HMGs, characterized by their powers Sid and coordinates {xi , yi }. Here N is the number of HMGs, forming the set D.   The set C = cj , j = 1, M unites load centers, characterized by total powers Sic   and coordinates ξj , ηj , j = 1, M . Results of the problem solution should be expressed, firstly, in determination of a one-to-one correspondence between M load centers cj and M selected HMGs. These HMGs, collecting electric energy from M groups of HMGs, contain inverters, which power supply loads of corresponding centers cj . Therefore these HMGs will be denoted below as IHMG. This correspondence will be represented by an M-dimensional vector f¯ , whose jth coordinate f j is equal to the number of selected IHMGs, i.e. fj = ij . The result of decomposition of the set D into subsets Dj , j = 1, M , generating electricity for load centers cj , is represented by the matrix R, consisting of M rows and N columns. Wherein  1, if HMG di ∈ Dj . Rji = 0, if HMG di ∈ / Dj Obviously, by definition Rjij = 1. Thus, the result of any decomposition of the power supply system of load centers cj from the HMG set D is represented as the vector f¯ and the matrix R.

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We will give analytical expressions of result criterion estimates of such composition. The first criterion F1 , expressing the total length of electric power transmission lines from HMGs to the load centers, is 1 (R, f¯ ) =

M 

ρ(ci , dij ) +

j=1

N M  

Rji ρ(di , dij ).

j=1 i=1

The first term of this sum expresses the total length of the energy transmission line from IHMGs to corresponding load centers. The second term is equal to the total length of energy transmission lines from HMGs to corresponding IHMGs. The second criterion F2 , expressing the correspondence degree of powers of load centers and IHMGs, has the following analytical expression. We introduce particular indicators of energy correspondence for each center cj according to the formula Sic = Sic −

N 

Sid Rji .

i=1

This value is a positive for this decomposition variant, if the center cj receives less energy than required, and a negative, if this center is power supplied with excess. Each of these cases will be evaluated by following non-negative values   Sjc , if Sjc > 0 − Sjc , if Sjc < 0 c+ c− ; Sj = . Sj = 0, if Sjc ≤ 0 0, if Sjc ≥ 0 Then the total correspondence degree will be evaluated by the criterion F2 as follows 2 = α1

M 

Sjc+ + α2

j=1

M 

Sjc− ,

j=1

where non-negative coefficients α1 and α2 such, that α1 + α2 = 1, characterize the comparative undesirability of one or another variant of the discrepancy between values of the received and required energy for this problem. Criteria can be expressed in natural units, as was done above (in length units for criterion F1 and in energy units for criterion F2 ), and in a normalized dimensionless form. It is depended on the optimization method, which used for solution of the considered problem. We naturally introduce the dimensionless normalized criterion for the first criterion, using the following formula  ρ(di , cj(i) ) n 1 = , 1 where cj(i) – the nearest load center to HMG d i .

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The normalized analog is calculated for the second criterion by the formula M 

n2 =

j=1 M  j=1

Sjc .

Sjc + 2

The optimization assignment model [7] is repeatedly used, when problem solutions of the present work are getting. The classical formulation of this Boolean linear programming model in the context of this paper has the following form. Let there be two sets of points A and B with the same number of elements N. The distances between each points ai ∈ A and bj ∈ B are equal to rij , i, j = 1, N . It is necessary to one-to-one correspond elements of these sets to each other so that the sum of distances between elements, mapped onto each other, is minimal, i.e. N 

ri,f (i) = min.

i=1

Here the function f corresponds to the required one-to-one mapping, i.e. j = f (i) is the index of an element of the set B, mapped onto an element of the set A with index i. Solving methods for this problem are described in [7, 8]. Moreover, the formal model has the form of a Boolean linear programming problem: it is necessary to find a matrix X with elements xij , i, j = 1, N such that  1, if element ai ∈ A is paired with element bj ∈ B , xij = 0 otherwise moreover N N   i=1 j=1

rij xij → min;

N 

xij = 1, i = 1, N ;

j=1

N 

xij = 1, j = 1, N .

i=1

Last two conditions signify one-to-one correspondence of sets A and B. The Boolean nature of the problem follows from the fact that all required elements of the matrix X take values 0 or 1 in this statement. The considered formulation of the model in a standard way extends to the case when the elements’ number of sets A and B is not the same, for example, N > M. In this case, the problem “expands” as follows. The set B is supplemented by (N – M) fictitious points, much more distant from points of the set A, i.e. so that for new points of the set B distances ri1 j1 , i1 = 1, N , j1 = M + 1, N are ri1 j1  max max rij . i=1,N j=1,M

Note that instead of the bijection, got between sets A and B, in the classical case, the injection of the set B into a certain subset A of the set A is obtained in the considered

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case N > M. Elements’ pairs of sets A and B, got by this injection, are used in the content of the problem. When the assignment problem is solving, fictitious elements, added to  the set B, form elements pairs of the set A A , which are not used in the content of the problem.

3 System Structure Optimization Method The stated problem has high complexity, which is determined by the large number of distribution variants for N elements of the set D over M centers of the set C even for small values of these quantities. It is easy to calculate that without taking into account the additional choice of IHMGs the number of possible options is equal to G = M N . So, for N = 7 and M = 3 the number G = 2187 and Pareto selection of optimal variants can be realized using a computer with a simple exhaustive search. However, the value of G increases sharply with increasing values of N and M. For example, the number G is greater than 16 million with N = 12 and M = 4. Two conclusions follow from this. Firstly, it is necessary to apply the most powerful algorithm of directional machine exhaustive search. A genetic algorithm (GA) has this property [9]. Secondly, initial variants of the HMGs’ distribution over load centers, which required for the algorithm realization, should be selected on the basis of some heuristic methods that allow them to obtain sufficiently qualitative criteria-based estimates. This can significantly reduce the time to find acceptable solutions. One of criteria is chosen alternately by the main one when the initial distribution variants are forming. This criteria has a determining value, while the value of the second one is either temporarily ignored or reduced requirements are imposed on it. The forming principle of the first distribution variant is that each element of the set D refers to a particular center, the distance to which is minimal. The assignment problem between sets D and C with the Euclidean metric is posed and solved for determination of the vector f¯ 0 . This metric is rij = ρ(di , cj ). We find an M-dimensional vector f¯ 0 with coordinates fi0 = ij as a solving result of this problem. The coordinate ij is the number of an element of the set D that is corresponded to the center cj of the set C in accordance with the solution of the stated assignment problem. HMG with the number ij in this distribution variant is an IHMG, which powered the load center cj , as it follows from the substantive part of our problem. The distribution matrix R0 is formed as follows. At the first step, all elements of the matrix R0 are zeroed. At the second step, a value min ρ(di , dik ) is sought for each element d j of the set D, k

i.e. it is a minimum value of the distance from this element to IHMGs, whose numbers are elements of f¯ 0 . The matrix element R0ik becomes equal to 1 as a result, i.e. the corresponding HMG is included in the set Dj , which powered the load center cj . The vector f¯ 0 and matrix R0 , formed by this way, determine the first distribution variant. At the same time this variant is optimal by the first criterion, which follows from its formation. Thus, the criterion value for this distribution variant sets its minimum possible values, while the criterion can be reduced only the first one in the   by increasing future. This optimal distribution is denoted by 1 = f¯ 0 , R0 .

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An improvement of the distribution 1 according to the second criterion can be obtained as follows. We find among those sets Dj , for which Sjc+ > 0, one, for which this value is maximal. Obviously, this set Dj+ can be called “overloaded”, since the power of corresponding HMGs is not enough to power the entire load cj . Similarly, among those sets Dj , for which Sjc− > 0, we choose one Dj− , for which this value is maximum. This set of HMGs is “underloaded”. We choose from D− one MG d i and transfer it into D+ . Each of S c+ and S c− decreases by value Sid as a result, and the second criterion decreases by value 2Sid . This transfer reduces to the transfer of 1 from the cell rj1 i to the cell rj2 i and to zeroing of the cell rj1 i of the matrix R0 . At the same time the first criterion will increase by the difference ρ(dij1 , di ) − ρ(dij2 , di ). The resulting distribution 1 will have the same vector f¯ 0 as 1 and the matrix R0 modified by the above method. Such transformations can be continued until this leads to an unacceptable increase of the first criterion. Consider the algorithm for formation of the initial distribution variant based on the priority of the second criterion and the temporary ignoring of the first one. 1.

2. 3. 4.

5. 6.

7. 8.

We order the set D by decreasing of powers Sid , forming an N-dimensional vector U¯ 0 , whose jth coordinate coincides with the number of that d i , which has received the index j in this ordering. The set C 0 = C with the power j0 = Sjc for j = 1, M is similarly ordered by decreasing of powers of the load centers, and a vector V¯ 0 with dimension M 0 = M is formed. Its jth coordinate coincides with the center number, which according to this order is in the jth place. It is assumed that v = 0, the distribution matrix R1 is zeroed. Subsequent steps of the algorithm are carried out in a cycle along v. = vvj − Residual uncompensated powers of loads’ sets C v are calculated as vv+1 j dvj , j = 1, Mv . ≤ 0 for some j, then corresponding load centers are removed from the set C v , If uv+ j because power supplying groups are considered to be formed for these centers. In this case, remaining centers form the set C v+1 , and the matrix R1 contains 1 in corresponding cells rvj uj . If μ is the number of such centers, then the number Mv+1 = Mv − μ. If Mv+1 = 0, then we go to the step 8, otherwise assume v = v + 1 and go to the step 3. The vector V¯ 0 is transformed as follows vi = vi + Mv , i = 1, Mv , i.e. coordinates with numbers i = 1, Mv are deleted, and remaining coordinates are shifted to places with lower numbers i. Freed coordinates are reset. If all coordinates of the vector V¯ 0 are equal to zero, then we go to the step 9, otherwise assume v = v + 1 and go to the step 3. If not all coordinates of the vector V¯ 0 contain nonzero elements, it means that not all MGs from D are distributed among groups of power supplying centers of the set C. In this case, MGs, whose numbers are written in nonzero elements of the vector V¯ 0 , must be distributed among already formed groups. Since these MGs, by virtue of the ordering rule of the set D, had the least power, this will not lead to a significant

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9.

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increase in the second criterion. Zero columns of the matrix R will contain 1 as a result of this step realization. It remains to form a vector f¯ since all power groups of load centers are defined, i.e. each column of the matrix R contains 1. We select for it such MG in each group, which is closest to the corresponding load center, i.e. this MG has an index ij = arg min ρ(cj , di ). i

The jth coordinate of the vector f¯ 1 is fj1 = dij as a result. 10. Values of criteria are calculated that evaluate the formed distribution, denoted hereinafter as 2 . These values are calculated according to formulas above, based on values of the matrix S 1 and vector f¯ 1 . 11. The end of the algorithm. 3.1 Crossover and Mutation A feature of the considered problem from the point of view of its solution based on GA is that it is advisable to use the matrix R as the code for the decomposition variant of the set D. In this regard, it is necessary to choose methods for realization of the basic GA operations, and first of all, crossover and mutation. We will consider these operations as an example of the decomposition of the set D into groups Dj , corresponding to load centers cj for N = 7 and M = 3. Figure 1 shows realizations of the matrix R for two variants of decomposition, which denoted by Ra and Rb . In this case, elements di , i = 1, 7 correspond to columns of matrices Ra and Rb , and groups of MG Dj , j = 1, 3 correspond to rows of these matrices. We choose the break point, indicated in bold vertical line in Fig. 1, by analogy with the crossover point, used for integer coding of chromosomes. We get two child-variants of parents from Fig. 1 as a result of the crossover. Figure 2 shows them.

Fig. 1. Matrices Ra and Rb , corresponding to two variants of decomposition

Fig. 2. Matrices Rab and Rba , corresponding to two child-variants of parents from Fig. 1

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Essentially, such transformation of matrices is equivalent to the elements’ exchange of columns d 5 , d 6 and d 7 (or, equivalent to this, of columns d 1 , d 2 , d 3 and d 4 ) between matrices Ra and Rb . Therefore this way of a crossover realization can be generalized as follows. We randomly select several columns and exchange them between two parents. We get two child-variants, corresponding to new decompositions. We select columns, corresponding to elements d 2 , d 3 and d 6 , in matrices as an example. We get new generation matrices, shown in Fig. 3, as a result.

Fig. 3. Matrices Rab and Rba , corresponding to two child-variants of parents from Fig. 1

A feature of the mutation realization in the considered problem is that any inversion in the matrix R must be accompanied by another inversion. The disappearance or occurrence of any 1 must be compensated by the corresponding occurrence or disappearance of 1 in some other cell of the matrix R, since their number in matrix R must always be equal to the number N. In this regard, the mutation algorithm is different, when 1 is inverting by 0 or 0 is inverting by 1. There should be one and only one 1 in each column of the matrix R according to the meaning of coding. This should be so, since each element of the set D should be assigned to a single group Dj during decomposition. Therefore, if 0 is inverted by 1, then 1, which existed in the same column before the mutation, should also be inverted by 0. If a primary inversion of 1 by 0 occurs in a determined column, then it is necessary to select the row of this column, into which compensating 1 should be written. A single random choice is made  for it between the initially zero elements of the column with probabilities, equal to 1 (M − 1), in the simplest case. 3.2 Selection GA is designed to solve a single-criterion problem by its meaning. Therefore we can go to single super-criterion, formed according to one of well-known methods, when multicriteria problems are solving. However, all these methods are quite subjective. Therefore we can propose the following technique, based on a fuzzy version of the restriction mechanism [10, 11], in order to avoid subjectivity. The constraint mechanism in the language of the choice function [10] is determined by the binary relation P and the given element u. It is the choice of elements x from the presented set X, which are more preferable from the point of view of the strict ordering

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relation P than the fixed element u: Cu (X ) = {x ∈ X |xPu}, moreover, u may not belong to X. Here the set Cu (X ) ⊂ X is the result of the choice. The binary relation P can be realized in various ways. It is easy to set this relation for a multicriteria choice in the form of the vector superiority of x over u, using the corresponding inequalities by all criteria. This is determined by the fact that the decision maker (DM) usually knows, which worst values ∗v of criteria Fv he can admit. So the condition ν (x) ≤ ∗v must be met for selected alternatives x for all criteria numbers v, assuming that all criteria are minimized. The selection method based on the mechanism under consideration is realized in three stages. 1st stage. Compilation of the initial Table 1, rows of which correspond to alternatives from the presented set X, and columns correspond to the test criteria. 2nd stage. Table 2 and Table 3 are compiled, basing on Table 1 as follows: columns of Table 2 are columns of Table 1, in which elements are ordered by increasing values of the criterion, i.e. the number is placed higher, if it is less. Numbers of those alternatives that occupy corresponding cells in Table 2 are placed in cells of Table 3. 3rd stage. DM analyzes Table 2 and marks for each criterion Fv (i.e. in each column) a critical boundary ∗v , which characterized the minimum value of the criterion, to which he can agree. In this case, a boundary polyline appears in the table. A similar polyline is formed in Table 3. If there is a certain number of the alternative above the polyline in this table in each column, then each such alternative suits the DM. Otherwise, it is necessary to reduce requirements by increasing all or some values ∗v . It is necessary to bring the constraint mechanism into line with the basic concepts of GA for realization it in the evolutionary method of generating alternatives. This primarily refers to the transition to a single criterion, consistent with the restrictions mechanism, as well as to the correspondence of GA population concept and the presented set X. The first problem is solved by transition to the fuzzy criterion [12]. We offer DM to + instead of one ∗ . Thus the border indicate for each criterion two boundary − v and v  −v + ∗ v is “blurred” and replaced by an interval v , v . At the same time we consider that all criteria are minimized, the boundary + v corresponds to optimistic expectations – to pessimistic. of DM, and the boundary − v We introduce the function for a quantitative assessment of the alternatives’ correspondence to DM requests for each criterion: ⎧ 1, if ν (x) > + ⎪ ν ⎪ ⎪ ⎨ − −  (x) ν ν − + . μ(x) = − + if ν (x) ≥ ν and ν (x) ≤ ν ⎪  −  ⎪ ν ν ⎪ ⎩ 0, if ν (x) < − ν Finally, the problem becomes single-criterion with the introduction of the following function μ(x) = min μν (x). This criterion μ(x) can be interpreted as a membership ν function of a fuzzy set of choices from presentation X [13].

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The following procedure is realized to solve the second formation problem of the presented set using GA. It consists of three stages too. 1st stage. The single-criterion optimization is realized consistently for each criterion Fv with using of GA. Final populations Pν of the evolutionary process of such optimizations are combined in the set = ∪ ν . ν 2nd stage. Upper boundaries  ν of each criterion values are selected, based on the analysis of criteria values for individuals of the set P. Individuals are cast off from the set along these boundaries so, that the inequality holds in the remaining set P* for any individual x and any ν: ν (x) ≤ ν . Values  ν are selected so, that the power of the set P* is sufficient for further optimization by the criterion μ(x) with using of GA. + 3rd stage. Values − v and v are assigned according to values of criteria of * individuals in the set P , with using which values of the criterion μ(x) are calculated. 3.3 Algorithms for the Formation of Load Centers Considered algorithms can also be used in cases, where energy consumers are decentralized, i.e. centers C are not defined. Therefore, it is necessary to initially structure the load, combining them into groups in a rational way, when such problems are solving. It is necessary to solve two particular problems, when load centers are forming. Firstly, it is necessary to determine the rational number of load centers M. Secondly,  it is  necessary to find the optimal location of these centers, i.e. their coordinates ξj , ηj , j = 1, M . It is advisable to proceed from the total load power S 0 and the maximum power of the existing equipment that supplies the load of these centers, when the first problem is solving. If, for example, the power of individual inverters, supplying a separate center, equal to S i , is taken to be the base, then the number M can be found by the formula   1, 2 · S0 . M = Si Here 20% power reserve of inverters is taken into account. Obviously, the general problem solution is advisable, if the number of unit loads R significantly exceeds the number of centers M. The number M can be determined by an expert method in combination with the one described above. The solution of the second problem, related to the formation of load centers, i.e. the compact location of load groups, which are advisable to power from individual GHMGs, can be obtained with using of the following heuristic decomposition algorithm for the initial set of loads: 1. The set of loads  is ordered by decreasing values of their powers, i.e. the sequence of loads D = dl | Sl+1 ≤ Sl , l = 1, L is formed. Here S l is the power of the load, received number l, according to the specified method of ordering.

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2. A sufficiently large number of the first elements of the set D is distinguished, for example, 20% of the total number of loads. An index of mutual remoteness is introduced by the formula for elements of the set D0 , formed in this way

ρ0 (dl ) = min ρ(dl , dk ), k∈J0

where ρ(dl , dk ) – Euclidean distance between loads d l and d k , i.e.  ρ(dl , dk ) = (xl − xk )2 + (yl − yk )2 , J 0 – the set of load indices from the set D0 . 3. The set is ordered by decreasing values ρ1 (dj ) = maxρ0 (dl ), l ∈ J0 . 4. We get M powerful loads, choosing the first M elements from the ordered in this way set D0 . These loads are located quite far away, both from each other and from other less powerful loads. “Initial” states of these formed centers are compiled from obtained loads dj1 , j = 1, M , numbered for definiteness in the same order that they had in the set D. Thus,  of centers consists of a single element at this step of the  each 1 1 algorithm, i.e. cj = dj , j = 1, M . The set of centers is denoted by D1 at this step of the algorithm, i.e. D1 =

M  j=1

cj1 .

 5. We suppose that v = 1; 1 = D D1 ; B = D1 . Thus, the set 1 is the set of all loads that do not fall into the set D1 , ordered by the same condition as the set D. 6. Next steps of the algorithm are realized in a loop at index v. 7. The condition v = ∅ is checked, under which fulfillment all loads are distributed in centers cjv . In this case, we go to the end of the algorithm – step 12. 8. If v = ∅, we form a set Γ v , into which include the first M elements. If the current number of elements in v is less than M, then we assume Γ v = v . The finding problem of bijection between sets Γ v and B is solved. The distance between elements g ∈ Γ v and dj1 is calculated according to the Euclidean metric. After this, the element gjv ∈ Γ v , corresponding to the element dj1 ∈ B by virtue of the received solution of the problem, is included in the new state of the   assignment v+ v th v j center, i.e. cj = c ∪ gj , j = 1, M . 9.

The condition is checked for each element gjv ∈ Γ v v+1  μ=1

μ

Sj ≥ Si ,

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where Sj – power of the element dj1 , if μ = 1, or power of the element gjv , included μ in the set cj at the μth stage, if 1 < μ ≤ v + 1. All elements dj1 , for which the last condition is satisfied, are removed from the set B. 10. If B = ∅, it means that all centers are formed, and we should go to the end of the algorithm – step 12. 11. Transition to the step 6. 12. The end of the algorithm.

4 Modelling Results Consider an example of problem solution with the following data: the number of HMGs N = 7, the number of load centers M = 3. Values of the HMGs’ powers, their coordinates, powers of load centers and their coordinates are presented in Tables 1 and 2, respectively. Table 1. Coordinates and powers of HMGs. N

1

2

3

4

5

6

7

x, km

3

5 13

16 10

9

8

y, km

10

15 15

8 10

7

3

S d , kVA 170 160 70 110 50 60 80

Table 2. Coordinates and powers of load centers. N

1

x, km

11 13

y, km

5

2

3 7

8 11

S c , kVA 29 21 12

The following smallest values of criteria 1min = 30, 14 km; 2min = 80 kVA in the case of different results of the decomposition of the set D are obtained as a result of the above algorithms. Since the total HMGs’ power from D, equal to 700 kVA, is greater than the power, consumed by the load of all three centers, equal to 620 kVA, it should be expected that the main contribution to the value of the second criterion will be the component S c− , reflecting the power reserve. Therefore, values α1 = 1, α2 = 0 are accepted in the formula for calculating of the second criterion.

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Following values c1 = 33, 3 km; c2 = 88 kVA; n1 = 37, 8 km; n2 = 104 kVA were selected as boundary values of criteria for the realization of the used selection method. Variants, having nonzero values of the normalized criterion μ, were obtained as a result of selection. Corresponding absolute and relative values of criteria for these variants are presented in Table 3. Table 3. Variants, obtained as a result of selection. N F1

F2

μ1

μ2

μ = min(μ1 , μ2 )

1 36,96

80,0 0,18 1,00 0,18

2 35,07

80,0 0,60 1,00 0,60

3 37,22 100,0 0,13 0,25 0,13 4 36,31

80,0 0,33 1,00 0,33

5 37,80

80,0 0,01 0,25 0,01

The second variant has the largest μ criterion value of 0,6 as it follows from this table. This variant corresponds to the following decomposition matrix R and the vector f¯ ⎡ ⎤ ⎡ ⎤ 100 00 11 6 ⎢ ⎥ R = ⎣ 0 0 1 1 1 0 0 ⎦; f¯ = ⎣ 4 ⎦. 2 010 00 00 Thus, the MG group, supplying the load c1 , includes HMG d 1 , d 6 and d 7 . The second group, which powers consumers from c2 , consists of HMG d 3 , d 4 and d 5 . The center c3 is powered by a single HMG d 2 . Moreover, IHMGs in these groups are d 6 , d 4 and d 2 . The absolute value of the first criterion for this decomposition variant is 35,07 km, i.e. it is 4,73 km greater than the minimum possible value. At the same time the value of the second criterion is equal to the minimum possible value of 80 kVA. This value is distributed among load centers as follows. Consumer centers c1 and c2 have a supply of energy, equal to 20 kVA, each, and c3 – 40 kVA.

5 Conclusion A class of architectures, called GHMG, is identified. The connection between HMG components is realized by a common DC bus. Functions of inversion, accumulation and reservation by diesel generators are given to the corresponding equipment of only one HMG. A distinctive feature of GHMGs is the aggregation of several inverters, rechargeable batteries and diesel generators into corresponding single devices of total power; it provides economic advantages, compared to the traditional organization of the MG functioning.

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A selection algorithm of variants for decomposition of a power supply system, based on GHMG, according to two criteria, which are expressed in numerical form, has been developed. The first of them meets the requirement of the minimum length of power transmission lines from generating equipment to consumers. The second criterion characterizes the degree, to which consumers’ powers in load centers conform to powers of supplying them GHMGs. It is proposed to use an optimization assignment model, formulated as a Boolean linear programming model, to solve this problem. The mechanism for solution of this optimization problem, which used the genetic algorithm with the replacement of several criteria with single super criterion, is described. A procedure for the formation of a fuzzy version of the constraint mechanism is developed. It avoids the subjectivity characteristic of this case. An example of the problem solution with the number of HMGs, equal to 7, and the number of load centers, equal to 3, is considered. The smallest values of criteria, obtained for different results of the decomposition of the initial HMG set, are shown as a result of using of proposed algorithms.

References 1. Kuzmichenko, B.M.: Methods and means of creating an aggregate-modular system of robotic assembly equipment in instrument and mechanical engineering. Dissertation, SGTU of Saratov (1999). (in Russian) 2. Kuzmichenko, B.M.: Structural and parametric synthesis of the technological system of assembly. In: Problems and prospects of precision mechanics and control in mechanical engineering: Proceedings of International Conference 1997, pp. 20–22. SGTU, Saratov (1997). (in Russian) 3. Ranganathan, P., Nygard, K.: Distributed Linear Programming Models in a Smart Grid. Springer, Cham (2017) 4. Jiménez-Fernández, S., Camacho-Gómez, C., Mallol-Poyato, R., Fernández, J.C., Ser, J., Portilla-Figueras, A., Salcedo-Sanz, S.: Optimal microgrid topology design and siting of distributed generation sources using a multi-objective substrate layer coral reefs optimization algorithm. Sustainability 11(1), 169–190 (2019) 5. Saharia, B., Brahma, H., Sarmah, N.: A review of algorithms for control and optimization for energy management of hybrid renewable energy systems. J. Renew. Sustain. Energy 10, 053502 (2018) 6. Schütz, T., Hu, X., Fuchs, M., Müller, D.: Optimal design of decentralized energy conversion systems for smart microgrids using decomposition methods. Energy 156, 250–263 (2018) 7. Wagner, H.M.: Principles of Operations Research: With Applications to Managerial Decisions. Prentice-Hall Inc., Englewood Cliffs NJ (1969) 8. Bundy, B.: Basic Optimization Methods. Edward Arnold Publ, Baltimore (1984) 9. Rutkovskaya, D., Pilinsky, M., Rutkovsky, L.: Neural Networks, Genetic Algorithms and Fuzzy Systems. Goryachaya liniya, Moscow (2013). (in Russian) 10. Yudin, D.B.: Computational Methods of Decision Theory. Nauka, Moscow (1989). (in Russian) 11. Statnikov, R.B., Matusov, N.B.: Multicriteria design of machines. Znanie, Moskow (1989). (in Russian) 12. Mityashin, N.P., Mirgorodskaya, E.E., Tomashevskiy, Y.B.: Special Issues of Decision Theory. SGTU, Saratov (2016). (in Russian) 13. Averkin, A.N., Batyrshin, I.Z., Blishun, A.F., Silov, V.B., Tarasov, V.B.: Fuzzy sets in models of control and artificial intelligence. Nauka, Moscow (1986). (in Russian)

Emulators – Digital System Simulation on the Architecture Level Alexander Ivannikov(B) Institute for Design Problems in Microelectronics of Russian Academy of Sciences, Moscow 124365, Russia [email protected]

Abstract. Digital system simulation on the architecture level is considered, i.e. instruction set and internal register changes emulation. Emulators is used for embedded software debugging and in the design process of new special processor development. The requirements for emulators is formalized. There is the classification of debugging features of emulators and possible ways of debugging mode implementation. The structure of emulators is described. Graph model of emulator structure is proposed. Each instruction is presented as the sequence of smaller operations. If different instructions include the same operations, such operations could be fulfilled by the same program modules. Those modules could be included into all appropriate instruction simulation parts of emulator, or emulator could include only one copy of each operation program module, and the module could be called while executing the appropriate instruction. The emulator structure determination is formalized as an extreme task. Practical methodology for emulator structure determination is proposed. Keywords: Cross system for software development · Embedded software debugging · Emulator optimization

1 Introduction When developing and debugging software for digital controllers of equipment and digital systems, so-called cross-systems are quite often used [1–3], the core of which are emulators that simulate the functioning of target digital controllers or digital systems at the architecture level, that is, sets of instructions or microinstructions, changing the contents of internal registers, making calls to I/O channels and blocks that implement any functions in hardware, as well as interrupts. In other words, emulators simulate all the features of the target system that the programmer operates in the development of software or firmware. Thus, emulators carry out simulation of digital systems at the level of architecture or microarchitecture and, in the presence of effective debugging capabilities, allows efficient debugging of software [3–6]. Emulation on instruction set level is also necessary for not ordinary architecture processor, for example, special RISC processors and processors for digital signal processing on design stage [7]. The following requirements are imposed on the model of digital systems of this level [8]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 209–222, 2021. https://doi.org/10.1007/978-3-030-65283-8_18

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1. Emulators should adequately simulate the digital system at the architecture level. 2. Emulators should allow the user to debug real-time software conveniently and efficiently, that is, provide a convenient set of debugging operations. 3. Emulators should have high performance indicators, that is, the minimum average number of instrumental computer instructions needed to simulate the execution of one instruction of the target digital system. When developing emulators, the most important issues are: – selection of a list of debugging features; – the choice of methods for organizing debugging modes; – development and optimization of the structure of the emulator.

2 Classification of Debugging Features of Emulators An important indicator of emulators is their debugging features, that is, the set of operations used when debugging software or firmware for digital systems. We will classify and analyze possible debugging operations that can be used in cross-system debugging software or firmware. We will single out the basic operations that have become almost standard for emulators and are available in almost all debugging systems. In addition, we will consider operations that can significantly increase the productivity of the developer, and are either available in part of the systems or desirable in their composition. We will carry out further consideration from the point of view of software development, although cross-system emulators at the architecture level (microarchitecture) are also used for debugging microprograms. In the latter case, microprograms act as programs, and the micro-instruction set implemented by the emulator plays the role of an instruction set. All possible debugging operations that can be used in cross-system emulators can be divided into five groups [9–11]. 1. Determining the conditions for breaking the debugged program, that is, exit it to perform any additional actions. The basic break conditions used in debugging are the execution of an instruction with a given address, as well as the execution of jump instruction or subprogram calls in case of tracing. In addition, an effective tool for debugging is to break the debugged program when accessing the memory cell with a given address or a given processor register. To debug real-time software, you must be able to break the debugged program when accessing an external device register or I/O channel with a given address, as well as at a given model time value. More difficult to implement, but giving the developer additional features, is the programmability of the break conditions. 2. Performing various actions in the event of a breakdown in a debugged program: stopping emulation, indicating the contents of memory cells, processor and external device registers, displaying labels, addresses and mnemonics of the last instruction executed, displaying the model time value. The basic ones in this group of debugging operations are stopping emulation and displaying labels, addresses or mnemonics

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of instructions of a certain group in order to trace the execution of the debugged program. The rest of the actions provided for in this group are often implemented after the emulation of the program is stopped according to special directives. 3. Viewing and editing the contents of the registers of the processor and external devices, memory cells, the values of the program time, setting the sign of one-by-one instruction execution mode during the stop of the emulation. These operations are implemented in most of the currently available cross-system emulators that operate in interactive mode. These operations can be considered basic. In addition to these basic operations, it is effective to memorize and restore the state of the program being debugged by setting the flag of remembering changes in variables with subsequent restoration of the latter. In addition, it is possible to use macros, that is, operations programmed by the user. 4. Modeling of environmental influences, namely: receipt of interrupt requests and direct access to memory, changing the contents of registers and readiness flags of external devices. These operations are necessary for debugging real-time programs. The moments of changes in external influences are set by the conditions for breaking the debugged program. 5. Performing additional operations with the debugged program as a whole, namely: – automatic or automated selection of debugging tests [12]; – symbolic execution of the program [13]; – automatic fulfillment of a debugging test set and comparison the result with the expected; – getting a graph of a debugged program [14, 15]; – automatic or automated installation of progress indicators in all branches of the program and subsequent analysis of the completeness of testing [16]. The first two operations are very difficult to implement and can be performed by a separate system. The last three operations can be implemented in a cross-system of usual complexity and help a lot in debugging.

3 Organization of Debug Modes in Cross-System Emulators Despite the fact that debugging operations are performed when not every instruction execution is simulated, but only some, the conditions for breaking the debugged program must be checked after each instruction is executed. In this regard, checking these conditions greatly affects the efficiency (speed) of the emulator. Let us analyze the various ways of organizing debugging modes from the point of view of minimizing computational costs when simulating a debugged program. The Method for Jointly Compiling a Debugged Program and Debug Directives In some cases, this method is used when debugging software for universal computers. After joint compilation of the program and debug directives, in the corresponding place of the debugged program there is a group of instruction that perform the specified debugging actions. This leads to the displacement of the instructions of the debugged

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program in the address space. In this regard, this method is used, as a rule, for debugging programs in a high-level language. The method allows you to organize debug mode only by the condition of executing instructions at a known address. In connection with the above, the use of the joint compilation method for organizing debugging modes in emulators is not effective. The method of a list of addresses, upon reaching or accessing which debugging actions are carried out or signals from the external environment are simulated. With this method, the debugging directives form an ordered list (usually in the form of a linear list structure with a pointer to the next element) of addresses, upon reaching or access to which debugging actions are performed. The list, as a rule, immediately indicates what actions need to be performed. This method of organizing debugging modes is universal and does not depend on the ratio of the bit width of the instrumental computer and the target digital system. When simulating each instruction, it is necessary to determine in one way or another whether the current address of the instruction or the address of the data used is in the list or not. In this case, computer time for the organization of the debug mode when modeling each instruction is tdb =

n2 n3 n1 tcmp + ρ1 tcmp + ρ2 tcmp + kdb tdb , 2 2 2

(1)

where n1 , n2 , n3 - the number of elements in the list of specified instruction addresses, data addresses, I/O channel addresses, respectively, when accessed, a break point is established; tcmp - time to compare the address with the one specified in the list and go to the next address of the list; ρ1 , ρ2 - the average number of data accesses in memory and input-output channels in one command, respectively; kdb - the percentage of instructions in the program being debugged, after which it is necessary to perform some debugging actions; tdb - the average execution time of debugging actions. kdb is usually quite small. In addition, the user determines what actions at the break point he needs based on, among other things, the computer time spent on them. And, finally, the last term in (1) is present in a similar form for all types of organization of debugging modes. In this regard, when comparing the methods of organizing debugging modes, this term will not be taken into account. The method of replacing an instruction at the desired address with an instruction for switching to a special subprogram. This method is widely used in resident software development systems. The instruction of the program being debugged at the break point address is stored in the reserve area of the memory, and the instruction to go to the subroutine for performing the specified debugging actions is set in its place. Moreover, at the very beginning of this subroutine, the instruction of the debugged program stored in the reserve area of memory is restored. When using this method in the emulator, the instruction of the debugged program at the address of the break point can be replaced either by an instruction to go to the selected address of the target system or by a reserved code that does not correspond to any instruction of the target digital system. In the first case, the transition to the highlighted address is a sign of access to the debugging

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routine. At the same time, the addresses used in the debugged program are subject to certain restrictions. In the second case, the allocated reserved code calls the debugging routine. In this case, means are needed to determine whether the reserved code is a sign of a break point or whether the reserved code is present in the debugged program, which should lead to an interruption on the reserved code. The method of replacing an instruction allows you to identify only the condition for simulation an instruction with a given address and is not suitable for identifying conditions for accessing data at known addresses or specified input-output channels. When a certain address is reached, the need for debugging actions is detected, but to determine the type of actions, an additional analysis of the mode signs and other data is needed. Additional Word Method. With this method, each item of data or instruction of the simulated program is given a word of features. Special features are installed for those instructions, after which it is necessary to perform debugging actions. If the required number of features is present in the feature word, it is possible to distinguish various features for different types of debugging actions and thus completely or partially identify debugging operations using the feature word. This method increases the value of used memory of the instrumental computer by (

lad + lins − 1)np , lins

where lad - the number of addressable memory units in an additional word; lins - the number of addressable memory units in an instruction; np - the page size of the memory of the target system located in the RAM of the instrumental computer. On emulating each instruction for analyzing the need to break the execution of the program being debugged it is necessary to spend the time tdb = tsel + tcj , where tsel - the execution time of the command to extract the necessary feature; tcj - the execution time of the conditional branch instruction. From the above comparative analysis of the methods for organizing debugging modes in cross-system emulators it can be seen that the most effective method for detecting a wide class of break conditions for a debugged program is address list methods and an additional word method. The faster backup code method can also be used in crosssystems if the class of specified break conditions is limited to the specified instruction addresses.

4 The Optimal Structure of Digital System Emulator Determination as an Extreme Task The algorithm of the emulator of a digital microcontroller or a single-processor digital system includes:

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– assignment of a variable that simulates the instruction counter of the target system, the initial value (start address); – selection of a value (instruction) from an array cell simulating the memory of the target system. The instruction is selected from the cell in the array indicated by the value of the instruction counter; – decryption of the instruction and the transition to a sequence of actions simulating the execution of one of the instruction of the target system; – performing actions corresponding to the simulated instruction: selecting additional words from the array simulating the memory of the target system, if the emulated instruction contains more than one word, performing actions on the models of the registers of the target system and memory cells, checking the break conditions of the simulated program, for example, by analyzing an additional word, increasing the value of the variable simulating the instruction counter of the target system, increasing the value of the clock counter of the target system; – if the simulation of the program is not completed, then go to selection of a value (instruction) from an array cell. An important indicator of the emulator is the simulation time of one instruction of the target system, or for a given instrumental computer, the average number of instrumental computer instructions executed when simulating one instruction of the target system. In addition, there may be a limitation on the amount of RAM of the instrumental computer occupied by the emulator. Therefore, when developing an emulator, it is necessary to minimize the average simulation time of one instruction of the target system while limiting the amount of RAM occupied by the emulator. With the simplest structure of the emulator, each instruction from the instruction set of the target system corresponds to its own fragment of the emulator program. In this case, with the optimal construction of the decoder, the speed will be maximum, but the amount of memory occupied will not be minimal. In order to reduce the amount of memory, it is advisable to use the same fragments of the emulator program to simulate similar instructions. In this case, one decoder of the instructions is replaced with a series of partial decoders and the latter are distributed according to the emulator program, which in certain cases can increase the total decryption time. The task of choosing the structure of the emulator is as follows: a) the presentation of algorithms for executing all the instructions of the target system in the form of a linear sequence of elementary operations and identifying a system of such operations sufficient to implement all the instructions of the target system; b) the definition of groups of instructions and subsequences of operations in them, for the implementation of which it is advisable to use the same fragments of the emulator program. The choice of such groups and subsequences uniquely determines the location of the decoders of the instruction groups (branch points in the emulator program); c) the choice of correspondence between the outputs of the decoders of instructions or groups of instructions, taking into account the relative frequency of the latter in debugged programs.

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Let us formulate the problem of choosing the structure of the emulator as extreme search. Let there be an instruction set of the target digital system K with power I, for each of which a relative execution frequency ϑi is set in debugged programs. The instruction set of modern digital systems are such that each instruction can be represented as a sequence of certain operations that does not contain cycles and transfers control back. Most instruction can be represented as a linear sequence of operations. The only exceptions are conditional branch instructions, the sequence of operations of which contain a conditional transfer of control depending on the state of the signs of results. Let us represent each conditional transition instruction as two separate commands, one of which corresponds to a transfer of control in the presence of a transition sign, and the second in its absence. Then each instruction can be represented as a linear sequence of certain operations. Representing the simulation process of each instruction ki as a sequence of distinguished operations, we form the set of operations L such that the simulation of each instruction is the sequence of operations ki = lji1 lji2 … ljin , lji ∈ L. i For each operation the RAM occupied by the software implementation mj and the average execution time tj are known. The operations of the instruction ki form the kit Bi on the set L. In mathematics a kit B can contain several samples of elements l of the set L. So, let B¯ be the kit of operations of the set L implemented in the emulator. Wherein       [#(lj , Bi ), j = 1, . . . , J, max # lj , Bi ≤ # lj , B¯ ≤ i   where # lj , Bi is the number of occurrences of the element lj in the kit Bi ; J is the cardinality of the set of operations L. As a model of the structure of the emulator, we consider the directed graph G(V, E), defined as follows. The set of vertices V = V ∪ {vstr } ∪ {vend }, where V is isomorphic to elements ¯ vstr , vend - start and end vertices. Each vertex represents a fragment of the of the kit B; emulator program that implements one of the operations lj of the set L. Let each vertex vk of the set V has the marks mj , tj - the RAM volume and the execution time of the corresponding operation lj . For vstr , vend mk = 0, tk = 0. Then each vk , vk ∈ V, has its own values mk , tk . If the operation lj is programmed in the emulator n times (n = # lj , B¯ ), then the graph G(V, E) has n vertices labeled by the values mj , tj . The edge e(j1 , j2 ) is directed from the vertex vj1 to the vertex vj2 if and only if there is an instruction ki , in the simulation of which the execution of the operation corresponding to the vertex vj2 immediately follows after the operation corresponding to the vertex vj1 . Each ki instruction defines a chain in G(V, E) connecting the vertices with the operations lji1 lji2 … ljin . Thus, the set E is divided into disjoint classes Ei i corresponding to the instructions ki . Suppose, in addition, that each class of edges Ei contains an edge directed from vstr to the first operation in the sequence ki , and an edge directed from the last operation in the sequence ki to vend (Fig. 1).  To each vertex vk we associate the relative frequency of its use ϑk = i δik ϑi , where δik = 1 if there is an edge e ∈ Ei among the edges entering vk , and δik = 0 otherwise. For the vertex vstr we take ϑ = 1. Each vertex vk in the graph G(V, E)

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Fig. 1. Graph model for emulator structure

has q immediate followers w1 , w2 , . . . , wq . For q > 1, in the emulator program, after executing the fragment corresponding to the vk vertex, a decoder is necessary (program branching). To each vertex vk we put in correspondence mkdc - the amount of decoder memory, an ordered set t1dc ≤ t2dc ≤ . . . ≤ tqdc of the decoder working times for the corresponding outputs, an ordered set of relative frequenciesusing the outputs of the decoder ϑ1dc , ϑ2dc , . . . , ϑqdc , such that for 1 ≤ p ≤ q ϑpdc = Ii=1 ϑi δpi , where δpi = 1  if vj , wp ∈ Ei , and δpi = 0 otherwise. For the vertices vk , for which q = 1, and for vend , mkdc = 0, t1dc = 0. quantities: Thus, each G(V, E) is associated with the following  vertex vk of the graph q mk , tk , mkdc , tk1dc , tk2dc , . . . , tkqdc , ϑk1dc , ϑk2dc , . . . , ϑkqdc , and vk = p=1 νkpdc , and the output of the decoder with tkpdc corresponds to a group of instructions or an instruction

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with a relative execution frequency ϑkpdc . The set of graphs G = {G} defines all possible variants of the structure of the emulator that implements a given set of instructions K based on the selected set of operations L, taking into account the selected set of debugging operations and a certain method for implementing debugging modes. Each G ∈ G has ¯ its own kit B. The total amount of memory occupied by the emulator:   mk + mkdc , mem = mop + mdc = vk ∈V

vk ∈V

where mop , mdc are the volumes of RAM occupied by software-implemented operations and decoders, respectively. Average simulation time of instruction  qk   tk ϑk + tk,p dc ϑk,p dc , tav = top + tdc = vk ∈V

vk ∈V

p=1

where top , tdc - the average time of operations and decoders. The execution time of each instruction ki operations does not depend on the structure of the decoder and is equal to I i=1

ϑi top i ,

where ϑ i is the relative frequency of the instruction; top i - the total time of the operations that make up the i-th instruction. Then I  qk tav = ϑi top i + tk,p dc ϑk,p dc . i=1

vk =V

p=1

Let us consider choosing the correspondence between the outputs of decoders and groups of instructions, taking into account the relative frequency of the latter in debugged programs. Suppose that there is a decoder on q outputs and that the decoder operating times for each output are t1 dc ≤ t2 dc ≤ . . . ≤ tq dc . q Let us show that the average operating time of the decoder tdc = i=1 ti dc ϑi will be minimal if the relative frequencies of use of its outputs are ordered as follows ϑ1 ≥ ϑ2 ≥ . . . ϑq . First of all, we show that tdc is minimum if ϑ1 is maximum. Assign the maximum relative frequency the index 1: ϑ1 = maxi (ϑi ). Let ϑ2 , ϑ3 , . . . , ϑq be ordered arbitrarily. Consider the difference in the average operating times of the decoder for ϑ1 = maxi (ϑi ) and for interchanging ϑ1 and an arbitrary frequency ϑj in the sequence: tdc (ϑ1 , ϑk2 , . . . , ϑj , . . . , ϑkq ) − tdc (ϑj , ϑk2 , . . . , ϑ1 , . . . , ϑkq ) = t1 dc ϑ1 + tj dc ϑj − t1 dc ϑj − t1 dc ϑ1   = (t1 dc − tj dc ) ϑ1 − ϑj ≤ 0, because

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q Then tdc will be minimal ϑ1 = max iq(ϑi ). And tdc = t1 dc ϑ1 + i=2 ti dc ϑi . We if q apply similar procedure to i=2 ti dc ϑi , i=3 ti dc ϑi , etc. and we find that the optimal frequency ratio is ϑ1 ≥ ϑ2 ≥ . . . ϑq . Thus, when choosing the correspondence between the outputs and groups of instructions using these outputs, it is necessary to use the output with the minimum time for the group of instructions with the maximum frequency of occurrence, the output with the minimum time from the remaining ones to use for the group of instructions with the maximum frequency of occurrence from the remaining group of instructions, and so on. The decoder on q outputs can be implemented in several ways, for example, using an operator of type IF GOTO or an operator of the calculated GOTO ( ,…, ), N, and so on. Suppose that for each of the R possible implementation methods, there are estimates of the occupied memory mrdc (q) and a set r , . . . , t r for each output. of times t1dc qdc The problem of choosing the structure of the emulator can be formulated as the following extreme task. Minimize I   qk r ϑi ton i + tk, (2) tav = p dc vk ∈V

i=1

at mdc =



 vk ∈V

p=1



mk + mrkdc ≤ Mlim , r ∈ R, G(V, E) ∈ G

(3)

where Mlim is the limit on the amount of memory occupied by the emulator. Problem (2)–(3) is an extremal integer programming task, the solution of which is based on methods of full or partial enumeration. For programmers involved in the development of emulators, the exact solution to problem (2)–(3) is very difficult. Taking into account the fact that the relative frequencies of executing commands in debugged programs vary depending on the class of debugged programs within certain limits, it is necessary to conduct a further study of problem (2)–(3) in order to create a methodology for choosing the structure of an emulator available to a programmer.

5 Choosing the Structure of a Digital System Emulator Let us consider defining groups of instructions and sequences of operations in them, for the implementation of which it is advisable to use the same fragments of the emulator program, in order to solve the extreme task (2)–(3). An emulator with a structure in which each instruction is a separate chain of operation (Fig. 2) will have maximum speed, having one decoder based on an operator of the type GOTO < …>, N.   The structure of such an emulator will be represented by the graph G 1 V1 , E1 (Fig. 2a), in which the vertices vstr and vend are connect exactly by I independent chains, where I is the cardinality of the set of the instruction set K. Each chain ki is composed of edges of class Ei . In order to reduce the amount of RAM occupied by the emulator, we apply the following procedure.

Emulators – Digital System Simulation on the Architecture Level

Fig. 2. Example of emulator structure development

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1. Assign to all the vertices of the set V the rank r as follows: r(vstr ) = 0 r, the next vertices in ki will be assigned r = 1, etc. Thus, the rank of a vertex v is equal to the distance of this vertex from vstr . To the vertex vend rank will not be assigned. 2. Consider vertices of rank r + 1, starting with r = 0. Vertices that: a) have incoming edges emanating from the same vertex of rank r; b) marked with the same operation lj - merge into one. Moreover, the average execution frequency ϑk of the newly formed vertex vk is equal to the sum of the relative frequencies of the joined vertices. We repeat step 2 sequentially for all r until there are vertices to be combined. 3. The vertices of the set V, such that there is a unique path connecting each of them with vend , we assign the rank q as follows: q (vend ) = 0; to the previous vertices in ki we assign the rank q = 1, etc. Thus, the rank of a vertex v, if assigned, is equal to the distance from this vertex to vend . 4. Consider vertices of rank q + 1, starting with q = 0. Vertices that: a) have outgoing edges that are included in the same vertex of rank q; b) marked with the same operation lj , - combined into one (Fig. 2b). Moreover, the average execution frequency ϑk of the newly formed vertex vk is equal to the sum of the relative frequencies of the combined vertices.   The resulting graph G 2 V2 , E2 completely determines the structure of the emulator, the amount of the memory and the average simulation time of each instruction due to the fact that it uniquely determines the location of the partial decoders and their characteristics taking into account methods for implementing decoders.  the selected   When passing from the graph G 1 V1 , E1 to the graph G 2 V2 , E2 , in the general case, the average time and the total volume of the memory of the decoders increase, but the volume of the memory needed for the software  decreases implementation of operations. The resulting emulator structure G 2 V2 , E2 should be taken as the initial one for the approximate solution of the extremal problem (2)–(3). For this initial approximation, for 2 and m2 . With m2 < M the chosen programming language, correspond tav max , steps can e e be taken to reduce the average simulation time of instructions by combining a number of partial decoders into one. So in Fig. 2c, for the implementation of the same operation l3 during the execution of various instructions, two identical program modules are allocated. In this case, partial decoders after l1 and l3 , each with two outputs, are replaced by one decoder after l1 with three outputs. In this case, neither the memory nor the operating time of the decoder will decrease. However, if the number of decoder outputs after l1 were more than four, then the combination of decoders would lead to a certain reduction in the memory capacity of the decoders and to a reduction in their operating time with an increase in the amount of memory occupied by program fragments of operations. The average simulation time for one instruction would decrease. However, as a rule, the gain in speed is very small.   If for an emulator with the structure G 2 V2 , E2 , m2e > Mmax , then the reduction in the occupied RAM volumecan be achieved by combining the vertices or linear sequences  of vertices of the graph G 2 V2 , E2 , located in the middle of the sequence of operations of various instructions.

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So, two vertices l11 are combined (Fig. 2d), which reduces the volume of memory operations, but requires the introduction of an additional partial decoder after l11 . In view of the proximity of the introduced estimates and their dependence on the programming language, the choice of decoders or program fragments that implement operations should be made by the programmer based on specific conditions. Thus, the engineering technique for choosing the structure of the emulator, providing an approximate solution to problem (2)–(3), includes the following steps. 1. Based on the analysis of the instruction set K of the simulated digital system, the required debugging capabilities of the emulator and the selected method of organizing the debugging modes, form the set of operations L. Represent the instructions of the set K as a linear sequence of operations from L.  2. Take for the initial approximation the structure G 2 V2 , E2 , obtained by the above 2 i m2 . method. Calculate the values of tav e 3. If m2e < Mmax , then identify possible options for combining decoders, leading to a decrease in the average simulation time of the instruction, but preserving the ratio m2e ≤ Mmax . Among the selected options, select the one that allows you to minimize the average simulation time of one command, and conduct the appropriate association of decoders, and then repeat the operation. If there is no option for combining decoders that reduces the average simulation time of the command and preserves the relation m2e ≤ Mmax , then the solution is found, and the selected structure should be considered final. If m2e > Mmax , then it is necessary to search for operations lj or chains of such operations implemented two or more times. If any, consider combining them. If, when combining, the total volume of the memory, taking into account the additional decoder,  decreases, then we should combine the corresponding vertices of the graph G 2 V2 , E2 . If, as before, me > Mmax , then the process of searching for identical operations lj and chains of such operations and their union should be continued. If there are no identical operations lj in different paths from vstr to vend (different instructions), it is impossible to reduce the amount of memory occupied by the emulator keeping the decided list of debugging capabilities, and the method of organizing debugging modes.

6 Conclusion So, the structure of emulators on instruction set level was analyzed. Graph representation of emulator structure can be used for optimization of its structure. The task of emulator structure choosing is formalized as extreme finding task. Based on it practical procedure for emulator structure development is proposed.

References 1. Zhou, J., Zhang, Z., Xie, P., Wang, J.: A test data generation approach for automotive software. In: 2015 IEEE International Conference on Software Quality, Reliability and Security – Companion, Vancouver, BC, pp. 216–220 (2015)

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Modeling the Vibrations of Elastic Plate Interacting with a Layer of Viscous Compressible Gas Oksana Blinkova1,2

and Dmitry Kondratov2,3,4(B)

1 Federal State Budget Educational Institution

of Higher Education Saratov State Academy of Law, Volskaya Str., 1, 410056 Saratov, Russia [email protected] 2 Volga Management Institute named after P.A. Stolypin - A Branch of Federal State-Funded Educational Institution of Higher Education Russian Presidential Academy of National Economy and Public Administration, Moskovskaya Str., 164, 410012 Saratov, Russia [email protected] 3 Yuri Gagarin State Technical University of Saratov, 77 Politechnicheskaya Street, Saratov 410054, Russia 4 Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia

Abstract. The rapid process of the development of technology and engineering in the modern world leads to the need to build and consider mathematical models of thin-walled elastic structural elements. The study of elastic thin-walled structures, the space between which is filled with a viscous liquid or gas, is becoming increasingly interesting. The problem of modeling the flow of a viscous compressible gas in a slotted channel consisting of two plates is considered. The first plate is absolutely rigid and performs harmonic vibrations in the vertical plane - the vibrator, the second one is an elastic plate - the stator. The mathematical model in dimensionless variables is a coupled system of partial differential equations describing the dynamics of the motion of a viscous compressible gas (NavierStokes equations and the continuity equation) flowing between two plates and an elastic beam-strip with the corresponding boundary conditions. To solve the resulting problem of the interaction of a viscous incompressible gas and an elastic linear plate, we switched to dimensionless variables of the problem. The small parameters of the problem were chosen - the relative width of the viscous gas layer and the relative deflection of the elastic stator. The small parameters of the problem made it possible to use the perturbation method to simplify the system of equations. The method for solving this problem is presented, which is a combination of the direct method for solving differential equations and the Bubnov-Galerkin method. The expression is obtained for the amplitude-frequency characteristics of the elastic stator. The study of the amplitude-frequency characteristics of the elastic stator will determine the operating modes under which the resonant phenomena occurs, and can be taken into account when constructing new structures in the modern engineering and aerospace industries. The presented mathematical model can find its application in gas-static vibration mounts and dampers. Keywords: Viscous compressible gas · Slit channel · A Beam-Strip · Elastic plate · Navier-Stokes equation · Amplitude-Frequency characteristic © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 223–234, 2021. https://doi.org/10.1007/978-3-030-65283-8_19

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1 Introduction Currently, various elastic structural elements, in particular, plates, rods and shells, are actively used in the aviation and space industry [1, 2]. These designed elements can be used as engine and fuel elements, chassis constructions, navigation devices, and others [2, 3]. In addition, elastic structural elements can be interconnected with a viscous liquid or gas, therefore, the problems of contact interaction the influence of vibrations and waves on elastic elements are solved in [4–7]. Thus, the interaction of a viscous incompressible fluid with a three-layer plate was considered in [4]. The flow of a viscous fluid between two elastic plates was considered in [5]. The dynamics of the interaction of a viscous incompressible fluid with a geometrically irregular plate was considered in [6]. The hydroelasticity of a pivotally supported plate interacting with a thin layer of a viscous incompressible fluid was considered in [7]. The problems of modeling the behavior of elastic plates that dynamically interact with a liquid or gas are continuously studied. The cases where the space between the plates is filled with a viscous incompressible fluid is considered in [8–10]. The wave effects in elastic elements interacting with a viscous incompressible fluid are considered in [8]. The pulsation of a viscous incompressible fluid in a thin channel are considered in [9, 10]. The nonlinear vibrations and stability of shells conveying water flow, nonlinear oscillations of viscoelastic plates of fractional derivative type considered in [11, 12]; the dynamics of plates under aerodynamic effects is considered in [13] and the elastic vibrations of plates under significant fluid loading are studying in [14]. In addition to the study of thin-walled structures, the study of various layered materials and multi-layer elastic structures has became more and more common for the creation of modern aircraft and mechanical engineering products. For example, the mechanics of layered viscoplasticity of structural elements was described in [15] and mathematical modeling of dynamic processes in hydrodynamic support with a three-layer stator was carried out in [16]. The formulation of the problem of modeling of interaction layer of a viscous compressible fluid with elastic three-layer stator and a rigid vibrator support was described in [17] and gidroproject supports with round elastic three-layer plate with an incompressible filler was studied in [18]. The nonlinear vibrations of nuclear fuel rods were described in [19] and the nonlinear vibrations of plates in an axial pulsating flow were considered in [20]. Nevertheless, despite regularly continuing studies of the behavior of elastic plates in dynamic interaction with a viscous compressible gas that fills the space between them, they are not studied well enough. The development of aggregates consisting of elastic thin-walled plates interacting with the surrounding layer of viscous gas involves the study of the mechanical system «plate–layer of viscous gas» dynamics. This leads to formulating and solving the problems of modeling of elastic plates and ones with a layer of viscous gas in a flat slop channel interaction dynamics. The channel is supported harmonically varying pressure, with the aim of finding and studying the amplitudefrequency characteristics of the model identifying the modes that can cause resonant phenomena, as, for example, in [21]. Thus, it is an urgent task to find the amplitude frequency characteristics of elastic structural elements interacting with a layer of viscous compressible gas in relation to gas-static vibration mounts and dampers.

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2 Statement of the Problem Let us consider a physical model of a mechanical system consisting of an absolutely rigid plate I (the vibrator) and a elastic plate II (the stator), the space III between which is filled with a viscous compressible gas (Fig. 1). The inner surface of the vibrator is considered to be flat and presents one of the walls of the slotted channel. We assume that the vibrator has an elastic suspension. The harmonic vibrations of the vibrator in the vertical direction relative to the stator arise. The motion of plate I is described by the harmonic law and has the amplitude.

Fig. 1. Physical model of a mechanical system

The stator is an elastic plate. The stator length and width (2l and b) are similar to the length and width of the vibrator. The width of the walls is considered significantly greater than their length, i.e. 2b >> 2l. It is assumed that the rigidity of the plate along the side b is much greater than its rigidity along the side 2l. All derivatives with respect to y can be neglected (i.e., the plane problem is considered below), since the planes of this model in the direction of the axis y can be considered unlimited. Viscous compressible gas III completely fills the gap space formed by the vibrator I and the elastic stator II. The thickness of the aggregate layer is much less than the length of the plates: h0 0). 4. Three-cascade model with Hamming CC metric, protective CSF-based code with m1 = 3 and PC codec in mixed mode (s = r > 0, e > 0). 5. Three-cascade model with Hamming CC metric, protective CSF-based code with m1 = 3 and PC codec in erasure handling mode (r = s = 0, e > 0). 6. Four-cascade model with Hamming CC metric, protective CSF-based code with m1 = 3, PC transformation to binary code by representing each PC symbol by L = log2 K bits and PC codec in mixed mode (s = r > 0, e > 0). 7. Three-cascade model with Hamming CC metric and correcting codecs in first and second code cascades, both codecs in mixed mode (s = r > 0, e > 0).

Information Channel Efficiency Criterion

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8. Two-cascade model with Hamming CC metric and two-dimantional code with codec C1 in transformation error handling mode (e = 0) and codec C2 in mixed mode (s = r > 0, e > 0). To reflect the features of each IC, it is suggested to represent their mathematical models as sets of generic coding-decoding cascades. The proposed approach allows to combine the most efficient known solutions with protective code ideas. With the selected approach, each mathematical model Mφ is represented as a consecutive set of coding-decoding cascades: Mφ = {Zφν }ν∈Nφ ,

(2)

where Nφ is the number of generic cascades in the φ-th model, ν is the cascade number, Zφν is the ν-th cascade of the φ-th mathematical model. Here and further on the cascade with number 1 will be called external and cascades with numbers ν ∈ [2..Nφ ]—internal. K-ary PC transformation to binary code and CC (regardless of the metric) are also considered as separate cascade types.

3

Multi-parameter Efficiency Criterion

The proposed multi-parameter relative normalized efficiency criterion for the IC mathematical models can be written in the form: ηφ =

Nη 

βc

(ηφc )

,

(3)

c=1

where ηφ is the efficiency coefficient of the φ-th model; c is the criterial parameter type; Nη is the number of criterial parameters of different types; ηφc is the φth mathematical model efficiency coefficient on the c-th criterial parameter; βc is the c-th criterial parameter weight coefficient (weight). For each efficiency coefficient on the specific (c-th) criterial parameter, one of two inequalities is fulfilled: either ∀φ : 0 ≤ ηφc ≤ 1, in this case βc > 0, or ∀φ : ηφc ≥ 1, then βc < 0. Thus, inequality 0 ≤ ηφ ≤ 1 always holds true. Analysis of various IC mathematical models made it possible to identify three criterial parameters (Nη = 3) as the most significant efficiency indicators: 1. The parameter characterizing the IC information reliability. 2. The parameter characterizing the speed of the model. 3. The parameter characterizing the structural complexity of codecs. 3.1

The Parameter Characterizing the IC Information Reliability

The main criterial parameter of the IC model is its information reliability, which is quantitatively characterized by probabilities of correct (pcr ) and false (pf r )

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reception, as well as probability of protective failure (ppf ). The efficiency coefficient for this parameter can be written as an aggregate ηφ1 , which does not explicitly depend on the correct reception probability:    γ − ln max (pf r )φ + (ppf )φ , 10−14 , (4) ηφ1 = − ln (10−14 ) where γ > 0 is the weight coefficient of the protective failure probability. It is easy to see that ∀φ : 0 ≤ ηφ1 ≤ 1 and therefore the weight coefficient β1 should be positive: β1 > 0. Coefficient (4) characterizes the proximity of noise immunity (meaningfully, command message transformation (false reception) probability) of the φ-th mathematical model to the noise immunity of remote control systems of the first category (the highest category in terms of information reliability) defined in the State Standard 26.205-88. The reception outcome probabilities and therefore, the efficiency coefficient η1 depend on the pulse noise intensity and its statistical characteristics. As primarily the case of high-intensity noise is considered, the number of noise pulses affecting the transmitted code combinations can be arbitrary, provided that ipn ≥ 3. It is assumed that the noise impulse flow satisfies the Poisson distribution: the appearance probability of exactly kpn noise impulses is calculated by the formula: k (ipn ) pn −ipn e p (kpn ) = . (5) kpn ! The physical nature of the noise impulses may vary, so the noise statistical characteristics are considered in a generic form, namely, as a tetrad pg = (pp , ps , pe , pse ), (0 ≤ pp , ps , pe , pse ≤ 1, pp + ps + pe + pse = 1) of atomic pulse interference probabilities, where: – pp is the probability of a “preserving” effect, which does not change the original alphabet symbol or the erasure symbol; – ps is the probability of a “transforming” impact, which transforms the original alphabet symbol into some other alphabet symbol (which one, depends on the CC metric) or translates the erasure symbol into a symbol 0; – pe is the probability of “erasing” effect, which translates an alphabet symbol into the “own” (corresponding) erasure symbol, or vice-versa, erasure symbol to the “own” alphabet symbol; – pse is the probability of a “transform-erasing” impact, which translates an alphabet symbol into the “alien” (non-corresponding) erasure symbol. This impact type, caused by the influence of multiple noise impulses, is placed into a separate category due to the nature of Elias decoding algorithm used in erasure channels [23,24]: the received erasure symbol is simultaneously decoded in two parallel decoding cascades (DC), being placed as symbol 0 to the one DC and as “own” alphabet character to another DC. It is assumed, that the correct alphabet symbol is placed to at least one of the DCs. When

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an “alien” erasure symbol is received instead of original alphabet symbol, the last assumption is not fulfilled, and a symbol, different from the original one, is placed to each of the DCs. Therefore, to restore the original code combination, besides the erasure error correction, an additional handling of the transformation error is needed, which requires higher code correction ability. It is also assumed, that each generic cascade, starting from the innermost (the cascade with the largest number), converts incoming generic probabilitis pg into outgoing generic probabilities pg , keeping the interference types: “preserving”, “transforming”, “erasing” and “transform-erasing”. The final reception outcome probabilities are calculated as a separate functions of the external code cascade, which depend on its incoming generic probabilities. Let us consider the generic probability conversion formulas for each type of generic cascades in details. The CC. The conversion of generic probabilities for the CC is made in three stages: 1. Having incoming probabilities pg , construct the matrix P1 , which defines the transition probabilities of symbols into each other under the influence of a single noise impulse. The constructed matrices P1 are different for CC with a Hamming metric and CC with alternative metric. 2. Having the matrix P1 , construct the matrix P , which defines the transition probabilities of symbols into each other under the influence of an arbitrary number of noise pulses taking into account the intensity ipn of their appearance. The matrix P is calculated by the formula: P =

∞ 

k

p(kpn )P1 pn ,

(6)

kpn =0

where p (kpn ) is defined by the formula (5). 3. Obtain generic output probabilities pg from the matrix P summing up the transition probabilities for all alphabet characters taking into account the probability of their appearance at the cascade input. The probabilities pg depend on presence or absence of zero signal feature in the CC: in case of zero signal feature absence in the initial alphabet, its appearance at the CC output is treated as appearance of erasure symbol. CSF-Based Code. CSF-based code usage is possible both for IC with transformation errors only as well as for the generic IC, where transformation and erasure errors are allowed. The paper [16] provides formulas for reception outcome probabilities (pcr , pf r , ppf ) of CSF-based code for both IC types. With minor changes, these formulas can be used to calculate the outgoing probabilities pg for the cascade, represented by CSF-based code using the following principle:    pp = pcr ; ps = pf r ; pe = ppf ; pse = 0 . (7)

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K-ary to Binary Code Transformation. K-ary to binary code transformation is performed using L = log2 K bits for each K-ary symbol. The output probability calculation is based on computing of wider recurring formulas— probabilities dl,hs,he , where 0 ≤ l ≤ L is the prefix of alphabet symbol binary representation, hs, he ∈ {0, 1} is the indicator of transformation or erasure error presence on the considered prefix, respectively. The relations are defined by the following formulas: ⎧ ⎪ ⎪d0,hs,he = (1 − hs)(1 − he); ⎪ ⎨d l,hs,he = dl−1,hs,he · pp + hs · (dl−1,0,he + dl−1,1,he ) · ps + ⎪ +he · (dl−1,hs,0 + dl−1,hs,1 ) · pe + ⎪ ⎪ ⎩ +hs · he · (dl−1,0,0 + dl−1,0,1 + dl−1,1,0 + dl−1,1,1 ) · pse , l > 0. As binary code does not have “alien” erasure symbol, the resulting output probabilities can be computed as    pp = dl,0,0 ; ps = dl,1,0 ; pe = dl,0,1 + dl,1,1 ; pse = 0 . (8) Correcting Code. For the cascade represented by correcting code it is assumed, that we know code word length nK , lengths of its informational (mK ) and control (kK = nK − mK ) parts, its minimal code distance dmin as well as numbers of detected (r) and corrected (s ≤ r) transformation errors, number of erasure errors (e) within code correcting ability defined by the formula (1). To find out generic output probabilities pg , it is required to know numbers of correctly received symbols (np), transformation errors (ns), erasure errors to “own” erasure symbol (ne) and erasure errors to “alien” symbol (nse) within the code word, where np + ns + ne + nse = nK . The exact error location inside the code word does not matter. Let’s define the state with given number of errors as S = (np, ns, ne, nse) and the probability of this state—as pS . It is possible to show, that the following formula is true: np ns ne ns ne nse pS = Cnp+ns+ne+nse Cns+ne+nse Cne+nse pnp p ps pe pse .

(9)

The formula (9) is used for the subsequent calculations. If the given cascade is an internal cascade, the output probabilities pg are calculated based on code correcting ability. The formulas are similar to bit error rate calculation expressions, but with separation by error type [25–27]. If an error is not corrected in the given cascade, it may be corrected in one of the cascades with lower number. Two cases are considered: when all erasure errors can be corrected (ne + nse ≤ e) and when not. In the first case, the output probabilities are calculated by formulas: ⎧  p = pS nK −max(0,ns+nse−s) ; ⎪ nK ⎪ ⎪ p,S max(0,ns+nse−s) ⎨  ps,S = pS ; nK (10)  ⎪ p = 0; ⎪ e,S ⎪ ⎩  pse,S = 0.

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In the second case not all erasure errors are corrected, so it is additionally taken into account how many erasures to “own” symbol (0 ≤ xe ≤ ne) and how many erasures to “alien” symbol (0 ≤ ye ≤ nse, xe + ye = e) are corrected. It is assumed that corrections of both types have equal probability. The subsequent transformation error fixes can be made only on those positions, where either transformation errors happen, or where erasure errors to “alien” symbol were corrected: ⎧ min(e,ne) xe ye ⎪ Cnse Cne ⎪  ⎪ p = pS nK −(ne+nse−e)−nsr ; e ⎪ p,S C nK ⎪ ne+nse ⎪ xe=max(0,e−nse) ⎪ ⎪ ⎪ min(e,ne) ⎪ xe ye ⎪ Cnse Cne ⎪ pS nsr ⎪ps,S = e ⎨ Cne+nse nK ; xe=max(0,e−nse) (11) min(e,ne) xe ye ⎪ Cnse Cne ⎪ ne−xe  ⎪ pS nK ; e ⎪ Cne+nse ⎪pe,S = ⎪ xe=max(0,e−nse) ⎪ ⎪ ⎪ min(e,ne) ⎪ xe ye ⎪ Cnse Cne ⎪ ⎪pse,S = pS nse−ye ⎩ Ce nK , xe=max(0,e−nse)

ne+nse

where nsr = max(0, ns + ye − s) is the number of transformation errors remain uncorrected. To compute the final output probabilities pg , the formulas (10) and (11) are summed up by all final states S, where np + ns + ne + nse = nK . If the given cascade is external, the outcome probabilities are calculated using the following formulas: ⎧ pcr = pS ; ⎪ ⎪ ⎪ np+ns+ne+nse=nK , ⎪ ⎪ 0≤ns+nse≤s, ⎪ ⎪ ⎪ 0≤ne+nse≤e ⎪ ⎪ ⎪ ⎨pf r = pS ; np+ns+ne+nse=nK , (12) r 0 with learning sample (6) known values of attributes amn and unknown weights pnm . In this case, the problem solution is reduced to minimizing the quality function: Q(Dψ ) =

N k=1

  L L i=1

j=1

2 aijk ρji − PAk

→ min

(8)

Approximations of the unknowns ρnm could be obtained using the quality function (8) and the gradient descent method. During this, constraints of the training set (6) are satisfied and the values PAk are obtained by substituting the found coefficients. However, this solution cannot be satisfactory. In the general case we will get the matrix Dψ which will not satisfy constraints imposed on the density matrix in quantum probability theory. These restrictions give it probabilistic properties and the possibility of using the expression (2) for contexts that have not been encountered in the training set. The constraint system is described below: ρii ≥ 0

(9)

Tr(Dψ ) = 1

(10)

2 Tr(Dψ )≤1

(11)

ρij = ρji , i = j

(12)

3.4 Regularizer Forms for Quality Functions Constraints (9) and (10) can be used for normalization of density matrix. After this, the density matrix can be used for prediction of a new system state probability. Pure state 2 ) = 1 expression is true, the system of system also can be described by (11). If Tr(Dψ

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will be in pure state. Ideal sinusoid is a good example of a pure state of the system. In our case, the pure state of the system is an ideal generalized word context, which was composed from only one context. That means the word was appeared only once. Mixed state is a superposition of several states of the system. It is corresponded to set of contexts for a target word. The expression (8) allows taking into account these constraints in the target function. Therefore, the task is reduced to minimization of quality function with regularizer: Q(Dψ ) =

N k=1

  L L i=1

ak ρji j=1 ij

2 − PAk

+ λ(Dψ ) → min

(13)

The function for regularizer must be differentiable of a Dψ variable. The regularizer can be represented as a sum of other regularizers. Each term of the sum satisfies the (9)–(12) respectively.       λ(Dψ ) = λ1 Dψ + λ2 Dψ + λ3 Dψ + λ4 (Dψ ) (14) Conditions must not be substituted into a target directly using Averson’s notation [2], because in this case the function would not be differentiable. Therefore, it is necessary to work out approximation functions, which would fit to the restrictions.  Now  it is easier  to  find acceptable differentiable approximation functions. Obviously, λ2 Dψ and λ4 Dψ can be approximated using second order polynomial. Their approximations can be represented as:     2 λ2 Dψ = (Tr Dψ − 1)   L L λ4 Dψ = i=1 j=1,i=j (ρij + ρji − 2 · Re(ρij ))2

(15)

    More natural approximation for λ1 Dψ and λ3 Dψ can be represented as exponential function, but in that case target function will optimize by regularizer data instead of basic requirement for matching probabilities PAk , because growth order O(ex ) is higher  than O(x2 ). However, it’s impossible to represent regularizers λ1 Dψ and λ3 Dψ as a second degree polynomial. Use of two quadratic splines consisting of two segments each can be a solution for this problem. Splines save growth order of regularizer that equals O(x2 ) and also save differentiability of the whole system considering   the boundary conditions imposed on the spline segments. In a basic view for λ1 Dψ spline can be represented as: ⎧  

λ11 Dψ = a1 Li=1 ρii2 , ρii ≤ 0 ⎪ ⎪  

⎪ ⎪ ⎪ λ D = b Li=1 ρii2 , ρii ≤ 0 ⎪ ⎪ 12 ψ ⎨ λ11 (0) = λ12 (0) = 0 λ1 (Dψ , a1 , b1 ) = , (16) ∂λ11 ∂λ12 ⎪ ⎪ ∂ρii (0) = ∂ρii (0) = 0 ⎪ ⎪ ⎪ 1 < a1 ≤ 2 ⎪ ⎪ ⎩ 0 < b1 < 1     where λ11 Dψ and λ12 Dψ - the left and right branches of the spline respectively, the parameters a and b are free spline parameters which set the slope of the parabolic

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branches and represent   the parameters of the regularizer. Similar system can be created for regularizer λ3 Dψ : ⎧   2      2 = a · Tr D2 − 1 , Tr D2 ≤ 1 ⎪ ⎪ λ21 Dψ 2 ψ ψ ⎪ ⎪      2   ⎪ ⎪ ⎪ 2 2 2 ⎪ ⎪ λ22 Dψ = b · Tr Dψ − 1 , Tr Dψ > 1 ⎨   ⎪ 2 λ21 (E) = λ22 (E) = 0 λ3 Dψ , a2 , b2 = , ∂λ ∂λ ⎪  21  (E) =  22  (E) = 0 ⎪ ⎪ 2 2 ⎪ ∂Tr Dψ ∂Tr Dψ ⎪ ⎪ ⎪ ⎪ ⎪ 0 < a2 < 1 ⎪ ⎩ 1 < b2 ≤ 2

(17)

Considering of new parameters of the regularizer the final expression for the target function represents as:  2   L L k ·ρ −P a + λ1 (Dψ , a1 , b1 ) Q Dψ , a1 , b1 , a3 , b3 = N ji A k k=1 i=1 j=1 ij +λ2 (Dψ ) + λ3 (Dψ , a3 , b3 ) + λ4 (Dψ ) → min

(18)

The resulting expression allows obtaining approximate values of the members of the matrix Dψ . These approximation functions don’t precisely satisfy the constraint system (9)–(12). However obtaining the corresponding matrix after minimization of the target function (18) is not a hard task, because miss quality of the functional (8) each constraint (9)–(12) can be algorithmically easily organized. That, the constraint (9) for negative diagonal elements can be satisfied by setting them to zero. For constraints (10) and (11) need to multiply resulting matrix on 1/Tr (Dψ ), the constraint (12) need to average of the real and imaginary parts of the symmetric elements of the matrix ρij and ρji among themselves. The matrix with dimension L×L can be easily calculated despite the size of matrices, because all matrices in the main expression (2) are very sparse, which leads to the fact that most elements ρij are zero and not interact in the optimization of the function (18). Using the method of stochastic gradient descent to optimize the target functional will reduce the overhead of recalculating the gradients at each point of the training sample (6). In addition, it is necessary to say that with uneven distribution of the contexts of words; it makes sense to try using statistical bootstrapping to compensate disadvantages of the small training sample with a small number of contexts and a large dictionary. In the future, it is planned investigation of the effectiveness of this model and comparison with similar models, for example, Word2Vec, Bag-of-Words or LSA, and extension of this model to the field of complex numbers, which will expand the capabilities and interpretation of the model as applied to the word-embedding problem.

4 Experimental Part To evaluate the algorithm, the well-known WordSim353 package was chosen. This corpus consists of two parts with a total number of examples, strings equal to 353. Each row of this data set is a pair of English words and a set of 16 ratings of people reflecting

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the degree of similarity of this pair of words with each other. A couple of words can get a rating from 1 to 10, where 10 means the maximum semantic similarity between words in our opinion. For the needs of evaluating the developed algorithm, we used the average value of people’s ratings for pairs of words as a reference. To perform a comparative evaluation of the developed algorithm, two text data vectorization algorithms were chosen: an algorithm based on the idea of a word bag and tf × idf statistics and the word2vec algorithm (CBoW architecture was used) as the values of the coordinates of the context vectors. For both algorithms, the cosine distance was used as a measure of the proximity of the resulting vector representations. As a training sample for algorithms, a slice of English Wikipedia was chosen (17 Mio. Words positions minus prepositions and conjunctions). As a measure for comparing the algorithms with each other, the correlation coefficient between the result of assessing the proximity of words by a person and the metric for this model was chosen. The results of the comparison of the algorithms are shown in the Table 1. Table 1. Pearson’s correlation coefficient between human assessments of words’ similarity and algorithm estimation. tf × idf Word2Vec QST Part 1 0.0831 0.1461

0.2213

Part 2 0.1023 0.1644

0.2107

5 Conclusion The article discusses the analogy between quantum tomography and the process of constructing vector representations of words for text documents. Such an analogy allows us to adapt the mathematical apparatus used to describe the process of quantum tomography, which is used to describe the statistical properties of objects with quantum-like properties. From the point of view of semantics modeling, such a mathematical apparatus allows one to take into account the properties of superposition and entanglement of word contexts that occur during vectorization of the analyzed word. In this case, the superposition is considered from the point of view of the dictionary - each individual word in the context is a semantic concept from the dictionary, and the analyzed word is, respectively, in a state of superposition of all words in its context, i.e. in a state of uncertainty about its meaning, expressed through the words of context. As for the analogy with a mixed state, the analyzed word occurs in a number of contexts, and from this point of view, the representation of a word as a density matrix should take into account the many encountered contexts as a mixture of density matrices. An analogy with entanglement can be drawn by determining the presence of a correlation of the words encountered in the analyzed contexts. Even though the proposed algorithm showed the quality of the resulting vector representations on the test sample is higher than other models, several improvements and studies are needed as part of the semantic tomography approach.

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Reducing the dimension of matrix representations. Currently, the algorithm generates high-density density matrices corresponding to the square of the dictionary size. Despite the fact that the matrix is very sparse and only diagonal and upper diagonal elements are stored (due to the symmetry of the matrix), it can still be on the order of several thousand (2–3 thousand) numbers. Of course, such redundancy must be eliminated in order to reduce computational complexity and stored volumes in memory. Transition to the field of complex numbers. Our hypothesis is that using the field of complex numbers in density matrices will improve the convergence of the target metric. However, of course, this requires a reduction in the dimension of the density matrices, since the number of system parameters will be doubled.

References 1. Harris, Z.: Distributional structure. Word 10(23), 146–162 (1954) 2. Chomsky, N.: Three models for the description of language. IRE Trans. Inf. Theory 2, 113–124 (1956) 3. Mouriño-García, M., Perez-Rodriguez, R., Anido-Rifón, L.: Bag-of-concepts document representation for textual news classification. Int. J. Comput. Linguist. Appl. 6, 173–188 (2015) 4. Heffernan, K., Teufel, S.: Identifying problem statements in scientific text. In: Workshop on Foundations of the Language of Argumentation (in conjunction with COMMA) (2016) 5. Zhang, Y., Rong, J., Zhi-Hua, Z.: Understanding bag-of-words model. A statistical framework. Int. J. Mach. Learn. Cybern. 1, 43–52 (2010) 6. Fabrizio, S.: Machine learning in automated text categorization. ACM Comput. Surv. (CSUR) 34(1), 1–47 (2002) 7. Soumya George, K., Shibily, J.: Text classification by augmenting bag of words (BOW) representation with co-occurrence feature. IOSR J. Comput. Eng. 16, 34–38 (2014) 8. Levy, O., Goldberg, Y., Dagan, I.: Improving distributional similarity with lessons learned from word embeddings. TACL 3, 211–225 (2015) 9. Jeong, Y., Song, M.: Applying content-based similarity measure to author co-citation analysis. In: Proceedings of Conference 2016 (2016) 10. Hartmann, N., Fonseca, E., Shulby, C., Treviso, M., Rodrigues, J., Aluisio, S.: Portuguese word embeddings: evaluating on word analogies and natural language tasks (2017) 11. Evangelopoulos, N., Zhang, X., Prybutok, V.: Latent semantic analysis: five methodological recommendations. Eur. J. Inf. Syst. 21(1), 70–86 (2012a) 12. Dumais, S.T.: Latent semantic analysis. Ann. Rev. Inf. Sci. Technol. 38, 189–230 (2004) 13. Evangelopoulos, N., Zhang, X., Prybutok, V.R.: Latent semantic analysis: five methodological recommendations. Eur. J. Inf. Syst. 21, 70–86 (2012b) 14. Aerts, D., Czachor, M., Sozzo, S.: Quantum interaction approach in cognition, artificial intelligence and robotics. CoRR, abs/1104.3345 (2011) 15. Hrennikov, A.J.: Vvedenie v kvantovuju teoriju informacii. Fizmatlit (2008) 16. Frommholz, I., Larsen, B., Piwowarski, B., Lalmas, M., Ingwersen, P., van Rijsbergen, K.: Supporting poly representation in a quantum inspired geometrical retrieval framework. In: Proceedings of the 3rd IIIX Symposium, August 2010 17. Piwowarski, B., Frommholz, I., Lalmas, M., van Rijsbergen, K.: What can quantum theory bring to information retrieval. In: Proceedings of the 19th ACM International Conference on Information and Knowledge Management, CIKM 2010, New York, NY, USA, pp. 59–68. ACM (2010)

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18. Sadrzadeh, M., Grefenstette, E.: A compositional distributional semantics, two concrete constructions, and some experimental evaluations. In: Song, D., Melucci, M., Frommholz, I., Zhang, P., Wang, L., Arafat, S. (eds.) Quantum Interaction, pp. 35–47. Springer, Heidelberg (2011) 19. Sordoni, A., Nie, J., Bengio, Y.: Modeling term dependencies with quantum language models for IR. In: Proceedings of the 36th International ACM SIGIR Conference on Research and Development in Information Retrieval, SIGIR 2013, New York, NY, USA, pp. 653–662. ACM (2013) 20. Khrennikov, A.: Classical and quantum probability for biologists introduction. Quantum Prob. White Noise Anal. 26, 179–192 (2010) 21. van Rijsbergen, C.J.: The Geometry of Information Retrieval. Cambridge University Press, New York (2004) 22. Melucci M., Piwowarski, B.: Quantum mechanics and information retrieval: from theory to application. In: Proceedings of the 2013 Conference on the Theory of Information Retrieval, ICTIR 2013, New York, NY, USA p. 1:1. ACM (2013) 23. Barros, J., Toffano, Z., Meguebli, Y., Doan, B.-L.: Contextual query using bell tests. In: Atmanspacher, H., Haven, E., Kitto, K., Raine, D. (eds.) Quantum Interaction, pp. 110–121. Springer, Heidelberg (2014) 24. Haven, E., Khrennikov, A.: Quantum probability and the mathematical modelling of decisionmaking. Philos. Trans. Ser. A. Math. Phys. Eng. Sci. 374, 1–3 (2016) 25. Gleason, A.M.: Measures on the closed subspaces of a Hilbert space. Indiana Univ. Math. J. 6, 885 (1957)

Development of a System Dynamics Model of Forecasting the Efficiency of Higher Education System Elena Kalikinskaja , Vadim Kushnikov , Vitaly Pechenkin , and Svetlana Kumova(B) Yuri Gagarin State Technical University of Saratov, 77 Politechnicheskaya Street, Saratov 410054, Russia [email protected]

Abstract. The aim of the article is to develop a system dynamics model that allows to analyze the effectiveness of the higher education system in modern Russia. A brief description of the existing approaches is given and a model of the dependencies of the monitoring parameters of higher education is proposed. This model is the main one in the system dynamics of J. Forrester. The model is refined through a statistical analysis of the coefficients of the influence of some monitoring parameters on others. Keywords: Educational system parameters · Measurement · Mathematical model · System dynamics

1 Introduction One of the main trends in the higher education system development in Russia are the increasing demands for educational organizations, the formation and refinement of a set of parameters that allows assessing the degree to which organizations meet these requirements. Recently, international organizations (UNESCO and OECD) begin to actively use extensive sets of indicators that describe the main characteristics of education systems at various levels. Among them there are indicators that show the level of countries expenditure on education, its accessibility, assessment of the educational system infrastructure and some others. The results of measuring the indicators of various countries make it possible to compare the parameters of educational systems. In this case, it is necessary to take into account the existence of a sufficiently serious influence of the European education system on processes in other countries and regions [1]. In Russia they use the universities effectiveness monitoring system which is partially similar to the European educational systems. Since 2013, in Russia, the activity of educational institutions of higher education has been continuously monitored [2]. The purpose of monitoring is to identify inefficient universities and their branches. For each performance monitoring indicator there are the threshold values. Information on the organization and conduct of performance monitoring and its results are published on the official portal of the Ministry of Education and © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 547–562, 2021. https://doi.org/10.1007/978-3-030-65283-8_45

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Science of Russia, as well as on a special portal (www.miccedu.ru/monitoring) where detailed analytical information for each educational organization is presented. The monitoring of 2019 was attended by 1264 educational organizations, 920 state and municipal organizations and 344 private higher education institutions, including: • • • •

555 branches; 10 federal universities; 29 national research universities; 21 participants of the project 5-100.

The number of students of the educational institutions that participated in the monitoring was 4174944. Monitoring includes an assessment of the following activities: • • • • • •

Educational activity - 15 indicators; Research activity - 16 indicators; International activities - 13 indicators; Financial and economic activity - 4 indicators; Infrastructure - 8 indicators; Staffing - 5 indicators.

Also, the monitoring system includes additional characteristics of the educational organization for each type of activity. If an educational organization (EO) does not pass the threshold values for more than 4 indicators, then measures are taken for state control over this organization’s activities and the reorganization of this EO is possible. By this system the activity of the educational institution as a whole is considered, and not the quality of training for a separate educational program (in contrast to the accreditation procedure). Separate authors analyze various approaches to the formation of an assessment of the quality of the educational process and the concept of the effectiveness of educational organizations [3]. They consider both the institutional mechanisms for regulating this process (such as the accreditation of educational programs) and various ratings. Recently, more and more attention has been paid to an independent assessment of the quality of higher education, the conduct of various public accreditations. The paper analyzes the tools of independent assessment, the quality of education, presents the results of university participation in the fourth stage of the experiment, according to an independent assessment, the quality of higher education, and typifies universities using cluster analysis [4].

2 Existing Approaches There are a large number of indicator systems that allow a comprehensive analysis of its condition and development trends. The education system and, in particular, the higher education system as an important social institutions are in the focus of attention of Russian and foreign researchers. An example of a fundamental analysis of a set of indicators is the article [5], which presents various levels of education and methods of constructing

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complexes for measuring them. This takes into account the institutional differences of systems that exist in different countries. A limited set of indicators is provided by the Federal State Statistics Service as part of the annually published statistical reports. So, according to official information, the number of qualified personnel in the higher education system over the past 10 years has significantly decreased [6, p. 194]. This fact may indicate significant trends in staff training for higher education and changes in the system itself. It is impossible to solve the problem of forming a set of indicators and methods of their analysis without building models to describe the processes occurring in the system components. In this paper, we consider the problem of changing the personnel potential of higher education and modeling the dynamics of the processes of its formation, taking into account the size of the contingent and age stratification. There are many examples of developing a set of indicators to offer a rating to a higher education institution. In general, the structure of such a complex can be described by the following diagram in Fig. 1 [7]. arameters

Fig. 1. The structure of the efficiency parameters

Simulation in the broad sense of the term in these areas encounters significant difficulties, associated with the limited methodology of scientific research in this subject area and the complexity of the studied social systems. It is obvious that in such research it is necessary to apply the methodology of natural Sciences, for example, a quantitative analysis of social processes, taking into account all the features inherent in the object of research. The construction of the model, on the one hand, makes it possible to single out the most significant factors affecting the dynamics of social, economic and (in many ways) psychological effects and phenomena and, at the same time, to exclude factors that have a slight effect on the situation. On the other hand, relying on the analysis of the obtained model, we can distinguish those data and the level of detail that would most fully characterize the system under study and the mechanisms of its development. It is such a preliminary analysis using modeling that allows us to clarify the structure of the data that is necessary for further more detailed research. The latter, in turn, will make it possible to concentrate the attention of researchers on obtaining the data really necessary for research, which can be presented in the form most suitable for further manipulations and analysis.

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3 Additive Model Using Weighted Indicators There are systems for evaluating higher education institutions, which are based on analytical characteristics that take into account various aspects of their activities. For example, in studies, a model for assessing university progress on the basis of an additive scale with weighted Indicators was proposed [8]. An example is the scale for constructing the rank of an object R, which in the general case has the following form: R = w1 × A1 + w2 × A2 + · · · + wn × An ,

(1)

where Ai (i = 1..n) is a set of indicators by which the object is evaluated; wi (i = 1..n) are the weights of the corresponding indicators. Various indicators of the university’s presence in the Internet space are considered, such as access to resources, citation, media activity and many others. It is important to note that most of these systems are built on the summation of weighted values for each indicator, which corresponds to the hypothesis of the additive property of the analytical index in the evaluation of the university. Using the proposed set of simple mathematical models, the analysis of trends in the state of the teaching staff of a higher educational institution is carried out, and on the basis of the studies conducted, some forecasts are made of the further state of the staff of a higher school, taking into account the socio-economic policy carried out by the administration of the university. The article deals with the formation of trends in age and qualification composition (in particular, the well-known problem of “aging” of teaching staff and the influx of young people into higher education [9]). Particular attention in this work paid to the following aspects: special transformation of the value of specific teaching load, which determines the professional teacher’s load, the problem of the influence of the load on the possibility of research work, the ratio of the volume of certain types of work (organizational-methodical, educational and others). The results of assessing the dynamics of changes in the wages of various categories of teaching staff in the conduct of a strategy of “rewards” and “punishments” by the university administration are presented, the relationship of the “salary and economic aspect” of the university staff with the organization of academic and scientific work is examined. The results of the study are relevant, allowing for their further practical application to assess the scientific potential of Russian universities, as well as to give a forecast of its dynamics in the near future. For such further studies, simple discrete models presented in this paper can be effectively used. The development of approaches to measuring the quality of the education system, building mathematical models of quality management is an urgent task, the solution of which will increase the degree of compliance of the education system with the state. Integrated quantitative assessments of the quality of education will not only improve the efficiency of the entire system, but also solve the problem of forecasting subsequent changes.

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4 CIPP Model One of the approaches that has been actively used for several decades in constructing a set of indicators of educational systems is the CIPP model (context, input, process, product – result) [10]. This model is a reliable analytical basis for assessing the education system both at the local – regional level and at the level of national educational systems. The context refers to a set of parameters that characterize the environment in which the education system operates. Available human, technological and financial resources, as well as the laws and rules used, form a set of parameters, designated as “Input”. A separate block of parameters allows us to evaluate the process characteristics of the educational process (the “Process”) using groups of indicators that measure its availability, the infrastructure of the learning process, and organizational structures. Efficiency (“Product” or “Result”) is measured by indicators of employment of graduates, quantitative parameters of the system. A detailed list of indicators is presented in [11]. This model allows you to take into account many of the nuances of the evaluated systems and is considered one of the most effective. The structure of the model for measuring the quality of education is presented in Fig. 2.

Context

Input Data

Process

Results Products

System Levels Fig. 2. The basic model of the educational system functioning using CIPP

The CIPP model is basic for many education systems, but it represents only a set of measurable indicators, the relationships between which can be established, but not declared in the model itself. The second drawback of the described approach is the lack of predictive capabilities in the model that reflect the dynamics of the educational process.

5 Cellular Automation Modeling There are approaches that allow you to analyze the structure of the faculty of the educational system based on various methods of mathematical modeling. An example of such an analysis is the work [12], in which the apparatus of cellular automata is used to study the dynamics of abundance and age-related stratification of PPP indicators. The analysis is based on the assertion that these parameters are similar for all regions of Russia by age groups of the staff of higher education. Using the initial statistical data, the

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authors propose a model of a class of cellular automata with discrete time, designed to simulate the dynamics of the staff of higher education and give predictive trends for the future. Within the framework of the proposed model, each homogeneous age category is modeled by one element of the cellular automaton, characterized by the number of this category, the evolution of which determined a change in the number of this age group. When building the model, the following factors were taken into account: – aging of each teacher over time (for one interval of discrete time t, a transition is made to the next age category of each element of the model); – retirement of teachers who have reached the age limit; – the departure of active employees of higher education in other industries; – the emergence of new young employees from among graduates of higher educational institutions; – defense of candidate and doctoral dissertations with the corresponding transfer of teachers to a new category (candidates of sciences or doctors of sciences). The authors point out certain problems in the construction of the model, which are associated with insufficient statistics, the shortness of the period covered by the available data, a high degree of aggregation, changes in the boundaries of age groups in the initial data, and some others. The paper presents various teaching staff parameters and shows a good agreement between the predicted values and the available ones. The proposed approach allows not only to form forecast models for faculty quality indicators, but also to link them with university ranking indicators, performance criteria. The authors point out certain problems in building the model that are associated with insufficient statistical data, the shortness of the period covered by the available data, a high degree of aggregation, changes in the age group boundaries in the initial data, and some others. The paper presents various parameters of the teaching staff and shows a good match of the forecast values with the existing ones. The proposed approach allows not only to form predictive models for staff quality indicators, but also to link them with the University’s rating indicators and performance criteria

6 Management System Model and Efficiency as an Optimization Task When developing algorithms for optimal control of the higher education system, traditional modeling approaches based on optimization methods are also used [13]. The authors formulate the task of optimizing the curriculum in terms of its maximum compliance with standards. In a formalized form, the statement of the problem is as follows: it is necessary to find such a structure D of the main professional educational program with the corresponding set of competencies K implemented by the disciplines that the objective function reaches its maximum: F(D) → max, when performing a system of restrictions, as determined by the principles of mathematical programming. That is, the task is reduced to determining the set of feasible solutions

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and finding the optimal among them. The following system of restrictions is proposed: CjD ∈ C P ∪ C PC ∪ C LM

(2)

MTB(D) ≤ MTB0 SU (D) ≤ SU0 FEI (D) ≤ FEI0 P(D) ≤ P0 RR(D) ∈ RR0 where C D , C P , C PC , C LM are respectively the competence of a particular discipline; personal competencies demanded by students; competencies arising from the requirements of a professional standard; competencies required by the labor market. MTB(D), SU(D), FEI(D), P(D), RR(D)- functions that return the values of the necessary material and technical base, staff of the university, financing of an educational institution, personality and regulatory restrictions for a given set disciplines D. In the right parts of expressions boundary normative values for these functions are set.

7 Forrester System Dynamics Model For the formation of a dynamic model of the education system, taking into account the interconnections of the elements of the educational process by a team of authors, it was proposed that J. Forrester’s world dynamics model be used to model the performance monitoring system of Russian universities [14, 15]. The model is described by a system of nonlinear differential equations of the first order, which is based on an analysis of causal relationships between predicted performance indicators. The result of this analysis is a directed graph whose vertices are the predicted characteristics, and the outgoing and incoming arcs characterize the functional relationships between them. The structural diagram of the flows of the educational process defines a system of equations, the main idea of which is to take into account the rate of influence of factors of inhibition and acceleration of the simulated processes. For variables, which are accumulations in feedback circuits, equations of the form are written: dy = y+ + y− dt

(3)

where y+ , y– are, respectively, the positive and negative rates of the speed of the variable y. including all factors causing its growth and decrease. The difficulties of applying the model are associated with the need to select scales for measuring factors, subjectively determining their role in the variability of the dependent variable, using an exclusively additive model of the mutual influence of variables. The dimension of the model depends on the number of factors considered and it is not possible to propose a single universal method for converting measurement scales taking into account the weight of their influence. Another important feature of this methodology is the additive nature of the influence of factors on dependent variables, which corresponds to empirical ideas about

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the nature of dependence, but cannot always accurately describe the essence of the process. In separate studies [16, 17], the educational process is considered as a complex system from the position of system dynamics. The Forrester Model is proposed, which is used to analyze processes in a university, to predict the development of the system as a whole. The model consists of elements: levels; threads moving content from one level to another; decision procedures that regulate the flow rate between levels; information channels connecting decision procedures with levels. Some of these flows affect parameters that are essential for the education system and therefore should be considered as the most important aspects of a systematic analysis of higher education in the Russian Federation. Due to the complexity of describing the directions of interaction of flows and their parameters, the task of constructing a model is extremely difficult to relate the real dynamics of processes to the proposed model. A positive point is the possibility of empirical verification of the proposed patterns. The advantage of such models is the presence of a relationship between expert assessments of patterns in the dynamics of the system and a possible correction of the model when new real data about the behavior of system parameters appear. Statistics are an important part for building correct computer models. One of the strengths of the education sector is the availability of reliable and extensive data arrays that can be used to fit the model to real data. The use of expert knowledge and statistical data allows us to build adequate models of the system that describes the effectiveness of the higher education system, which makes it possible to understand the current dynamics and develop more effective strategies and measures in the future. The following is an example of a model based on a study of real data obtained in the process of analyzing the educational activities of Gagarin State Technical University of Saratov.

8 Monitoring Parameters of the Higher Education System In order to propose a model of the dynamics of changes in the monitoring parameters of the effectiveness of the organization of higher education in universities, indicators are used that are described in detail in separate studies [2]. In the proposed method, the effectiveness of the educational process is such a ratio of the parameters of the university that, within the process control, does not go beyond the permissible deviations from the reference values. The monitoring includes 61 indicators; to build a system dynamics model, 40 of the most significant indicators were selected that characterize the educational, research, financial and economic activities of the university, as well as the staff. Next, each indicator is associated with the variable name (x with the corresponding number) and its brief description is given in Table 1.

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Table 1. Cost matrix of EC calculated model Indicator Description

x1

The average score of the Unified State Examination (USE) of students admitted to the first year of full-time undergraduate and specialist studies at the expense of the federal budget

x2

The average score of the USE of students admitted to the first year of full-time undergraduate and specialty studies at the expense of the federal budget, with the exception of persons who have received special rights and within the framework of the targeted admission quota

x3

Average USE score of students admitted to the first year of full-time undergraduate and specialist studies with payment of the cost of training costs by individuals and legal entities

x4

Average minimum score of the exam, students admitted to the first year of undergraduate and full-time specialization;

x5

The number of students, winners and prize winners of the final stage of the All-Russian Olympiad for schoolchildren, members of the national teams of the Russian Federation who participated in international Olympiads in general subjects in the specialties and (or) areas of training corresponding to the profile of the All-Russian Olympiad for schoolchildren or the international Olympiad, accepted for full-time education for the first course in undergraduate and specialty programs without entrance examinations

x6

The number of students, winners and prize-winners of schoolchildren’s Olympiads accepted for full-time first-year studies in undergraduate and specialty programs in the specialties and (or) areas of training corresponding to the profile of the schoolchildren’s Olympiad, without entrance tests

x7

The number of students admitted according to the results of targeted admission to the first year of full-time study in undergraduate and specialist programs

x8

The proportion of students enrolled in the first year of targeted admission to full-time undergraduate and specialty programs in the total number of students admitted to the first year in undergraduate and specialty full-time programs

x9

The proportion of the number of students (reduced contingent) studying under the master’s program in the total number of students enrolled in the educational programs of undergraduate, specialty and master’s programs

x10

The proportion of the number of students (reduced contingent), according to the master’s program, the training of scientific and pedagogical personnel in graduate school (adjunct), residency, assistant-internships in the total number of the cited contingent of students in basic educational programs of higher education

x10

The proportion of the number of students with a bachelor’s degree, specialist or master’s degree from other organizations accepted for the first year of study in the master’s programs of an educational organization, in the total number of students accepted for first year in master’s programs in full-time education (continued)

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Indicator Description

x12

The proportion of students enrolled in graduate programs, training of scientific and pedagogical personnel in postgraduate studies (postgraduate studies), residency, assistant internships with a bachelor’s diploma, a specialist’s diploma or a master’s diploma from other organizations in the total number of students enrolled in master’s programs, scientific and pedagogical training personnel in graduate school (postgraduate studies), residency, assistant internships

x13

The number of graduate students (adjuncts), residents, assistant trainees of an educational organization per 100 students (reduced contingent);

x14

The proportion of the number of students from third-party organizations in the total number of students who have been trained in an educational organization according to programs of advanced training or professional retraining

x15

The proportion of the number of students studying in the areas of undergraduate, specialization, and master’s degrees in the fields of knowledge “Engineering, Technology and Technical Sciences”, “Health and Medical Sciences”, “Education and Pedagogical Sciences”, with which agreements on targeted training, in the total number of students studying in these areas of knowledge

x16

The number of citations of publications published over the past 5 years, indexed in the information-analytical system of scientific citation Web of Science Core Collection per 100 teaching staff members (TS)

x17

The number of citations of publications published over the past 5 years, indexed in the information and analytical system of scientific citation Scopus per 100 TS

x18

The number of citations of publications published over the past 5 years, indexed in the Russian Science Citation Index (hereinafter - RSCI) per 100 TS

x19

The number of publications of the organization, indexed in the information-analytical system of scientific citation Web of Science Core Collection, per 100 TS

x20

The number of publications of the organization, indexed in the information and analytical system of scientific citation Scopus, per 100 TS

X 21

The number of publications of the organization, indexed in the information-analytical system of scientific citation of the Russian Science Citation Index, per 100 TS

x22

The total amount of research and development work

x23

The proportion of income from research and development (R&D) in the total income of the educational organization

x24

The proportion of R&D performed on its own (without involving co-contractors) in the total income of the educational organization from R&D

x25

Income from R&D (excluding budgetary funds of the budget system of the Russian Federation, state funds to support science) per one scientific research work (continued)

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Table 1. (continued) Indicator Description

x26

The number of license agreements

x27

The proportion of funds received by the educational organization from the use of the results of intellectual activity in the total income of the educational organization

x28

The proportion of the number of research workers without a scientific degree - up to 30 years, candidates of science - up to 35 years, doctors of science - up to 40 years old, in the total number of scientific research work

x29

The proportion of scientific and pedagogical workers who defended their candidate and doctoral dissertations for the reporting period in the total number of scientific research projects

x30

The number of scientific journals, including electronic ones, published by an educational organization

x31

The number of grants received for the reporting year per 100 TS

x32

Income of the educational organization from the funds from income-generating activities per one TS

x33

The share of income from funds from income-generating activities in income for all types of financial support (activities) of the educational organization

x34

The ratio of the average salary of the academic staff in an educational institution (from all sources) to the average salary in the region’s economy

x35

The income of the educational organization from all sources based on the number of students (reduced contingent)

x36

The proportion of candidate of sciences in the total number of TS

x37

The proportion of doctor of sciences in the total number of TS

x38

Proportion of candidate and doctor of sciences in the total number of TS without part-time workers and working under civil law contracts

x39

The number of candidate and doctor of sciences per 100 students;

x40

The percentage of full-time staff members in the total number of staff

9 Model of Dependencies Between Rating Indicators To establish the relationship between the indicators, experts were involved from among the university staff with at least 10 years of experience in the university. A fragment of the dependency matrix is shown in Fig. 3. There is one in the row if the parameter in the row affects the parameter in the column.

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Fig. 3. A fragment of the matrix of dependencies of the parameters of the education system

For example, parameter x 1 is the average score of the Unified State Examination taken at the university, affects the parameters x 2 , …, x 6 .. For each variable x i , i = 1..10 we can describe the nature of the functional dependence on other variables. In the most general form, in accordance with the concept of the model of the dependence of variables on factors influencing them, the equations of connection between variables could be written as follows: x2 = f2 (x1 ); x3 = f3 (x1 ); x4 = f4 (x1 , x3 ); x5 = f5 (x1 , x4 ); ... x13 = f13 (x16 , x17 , x18 , x19 , x20 ); ... x40 = f40 (x6 , x7 , x8 , x13 , x26 , x19 , x34 ); In accordance with the Forrester system dynamics approach, it is assumed that these dependencies are multiple linear in nature, which is indirectly confirmed by scattering diagrams for pairs of variables. In Fig. 4 shows a scatter plot for variables x 34 and x 13 showing a regression line. Because of the expert assessment, the adjacency matrix of the directed graph is constructed, in which the directional arc shows that the parameter corresponding to the vertex of the beginning of the arc affects the parameter corresponding to the final vertex of the arc. The dependency graph is shown in Fig. 5. For example, the fact that the parameter x 1 affects the parameters x 2 , x 3 , x 4 , x 5 , x 6 is marked on the graph by the fact that oriented arrows go to the vertices corresponding to these variables from the vertex x1 . The graph was visualized in Gephi software using the Fruchterman – Reingold algorithm (Fig. 5a). The diameter of the vertex is determined by the number of outgoing arcs (half-degree of the outcome of the vertex), that is, the more parameters depend on the parameter, the greater the diameter of the corresponding vertex. Vertices that do

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Fig. 4. Scatter plot for a pair of variables x 34 (y) and x 13 (x)

a.

b.

Fig. 5. Parameter dependency graph (a), reduced dependency graph (b)

not affect other variables have a minimum radius when rendering the graph. Such, for example, are the vertices x 11 , x 14 , x 29 .

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To clarify the type of dependence, a correlative analysis is used, as the initial data for this analysis, real data of the values of variables for the Saratov State Technical University (Russia) were taken over the past 6 years. It is assumed that when the next portion of data arrives in the developed system, the model will be refined. Table 2 (the fragment) shows the correlation matrix for all model variables. Table 2. Correlation matrix (fragment) by variables (Pearson correlation coefficient) x1 x1

x2

x3

x4

x7

1 0,967 0,713 0,873

x 2 0,967

x8

x9

x 10

0,78 0,217 0,327 0,895

x 11 0,57

1 0,793 0,757 0,616 0,002 0,874 0,895 0,042

x 3 0,713 0,793

1 0,563 0,575 0,986 0,544 0,865

x 4 0,873 0,757 0,563

0,24

1 0,314 0,206 0,327 0,856 0,841

x 7 0,078 0,616 0,575 0,314

1 0,804 0,821 0,608 0,494

x 8 0,217 0,002 0,386 0,206 0,804

1 0,538

0,04 0,282

Analyzing standardized variables, we can conclude that there is a strong correlation between the variables x 4 and x1 (r = 0,873). In a similar way, the indicators of the regression equations for the remaining functions of the model are calculated. Correlation analysis of the dependencies between performance indicators showed that many of the indicators duplicate each other with a fairly high degree of statistical significance. Some of them are the value of a simple function calculated from other indicators. The analysis of the dependencies between the indicators allowed us to go to the reduced graph of the dependencies between the indicators, shown in Fig. 4b. The vertices corresponding to indicators correlatively dependent on other indicators at the level of a correlation coefficient of 0.9 (Pearson’s correlation coefficient was used) were removed from the original graph. When developing a model of system dynamics, the following parameters external to the performance indicators were used. When developing a model of system dynamics, the following parameters external to the performance indicators were used. Fak 1 (t)- university rating; Fak 2 (t) ¬ - university region rating; Fak 3 (t) ¬ - average salary of a university graduate; Fak 4 (t), Fak 5 (t) - the ruble exchange rate against the dollar and euro, respectively; Fa6 (t) - the availability of a modern material base at the university; Fak 7 (t) - the level of training of the teaching staff of the university. Based on the reduced graph of dependencies, which determines the cause-and-effect relationships, the following system of differential equations is built in accordance with

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the Forrester model.

On the right side of this system of differential equations f 1 (x 4 ), f 2 (x 5 ), f 3 (x 6 ) and all subsequent ones are determined experimentally at the stage of primary data analysis in relation to a specific object of modeling. It is believed that these functional dependences can be approximated fairly accurately by polynomials of degree at most 3.

10 Conclusion Summarizing the presented analysis, it can be argued that each of the above analysis models has both its advantages and disadvantages. The approach based on the use of CIPP allows you to create a holistic system of indicators, the study of the measurement results of which can be carried out in the framework of multidimensional scaling and methods for processing multidimensional data. The disadvantages of this approach include the lack of an explicitly declared effect of some indicators on others, although this is known in advance. Indirectly, this effect is taken into account within individual groups of indicators. Methods of system dynamics, in turn, allow to explicitly indicate the presence of causal relationships in the complexes of indicators and predict the dynamics of the functioning of the entire system. With this approach, the process of forming a graph of cause-effect relationships and interpreting the resulting solution in terms of its compliance with the expected range of predicted values is quite time-consuming. The use of discrete automaton models (cellular automata) allows one to obtain realistic forecasts of the development of the situation, but requires a high-quality array of initial statistical data to determine the rules for the functioning of the automaton. Finally, there are examples of reducing problems to classical optimization problems. The disadvantage of this technique is a narrow class of problems that have effective mathematical algorithms for finding the optimal values; for most cases, the computational procedure remains quite time-consuming.

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In the paper a system dynamics model is proposed, which is refined by analyzing the type of dependence between variables using regression analysis. The dependency system is based on expert assessment of parameter dependencies

References 1. Pechenkin V.V., Pechenkina, E.V.: Comparative analysis of the role of universities in the formation of centers of knowledge and entrepreneurship. Actual Probl. Econ. Manag. 1 (1), pp. 112–119. ISSN 2312-5535 (in Russian) 2. Information and analytical materials on the results of monitoring the effectiveness of educational organizations of higher education. www.miccedu.ru. Accessed 3rd jan 2020 (in Russian) 3. Rudnikova, I.N.: Development of approaches to assessing the quality and effectiveness of higher education. Bull. South Ural state Univ. Series: Soc. Human. Sci. 17(1), 74–81 (2017). (in Russian) 4. Raev, K.V.: Tools and results of approbation of the multicomponent model of independent assessment of the quality of higher education. Bull. Univ. (5), 181–188 (in Russian) 5. Matheson, N., Salganik, L.H., Phelps, R.P., Perie, M., Alsalam, N., Smith, T.M.: U.S. Department of Education, national center for education statistics. education indicators: an international perspective, NCES 1996–2003, Washington, D.C.: 1996 https://nces.ed.gov/pubs96/ 96003.pdf 6. Russian statistical Yearbook. 2017: Stat. sat. / Rosstat. - P76 M., 2017 -686 p. URL: http:// www.gks.ru/free_doc/doc_2017/year/year17.pdf. (in Russian) 7. Maslova, L.D.: On systems for assessing the quality of higher education international research Journal. 3(3), 64–69. https://doi.org/10.18454/IRJ.2227-6017. https://research-journal.org/ pedagogy/o-sistemax-ocenki-kachestva-vysshego-ob/. (in Russian) 8. Karpova, G.G., Shulga, T.E., Rudnikova, I.N.: Mechanisms for evaluating the activity of universities in internet networks [Electronic resource]. Econ. Human. Sci. 11 3–13. https:// rucont.ru/efd/483346. (in Russian) 9. Koronovsky, A.A., Trubetskov, D.I., Khramov, A.E.: Population dynamics as a process that obeys the diffusion equation. Rep. Acad. Sci. 372(3). p. 397 (2000). (in Russian) 10. Cornali, F.: Effectiveness and efficiency of educational measures: evaluation practices. Ind. Rhetorical Mind. 2(3), 255–260 (2012). https://doi.org/10.4236/sm.2012.23034 11. Scheerens, J., et al. (eds.).: Measuring educational quality by means of indicators. Perspect. Edu. Qual. Springer Briefs Edu. https://doi.org/10.1007/978-94-007-0926-3_2 12. Koronovsky, A.A., Strikhanov, M.N., Trubetskov D.I., Khramov, A.E.: Analysis of changes in the scientific and pedagogical potential of the higher school of Russia. Naukovedenie, no. 2, pp. 82–102 (2002). (in Russian) 13. Krasniansky, M.N., Popov, A.I., Obukhov, A.D.: Mathematical modeling of adaptive management system of professional education. Bull. TSTU 23(2), 196–208. (in Russian) 14. Forrester, J.: Some Basic Concepts in System Dynamics. World Dynamics. Waltham, MA, Pegasus Communications, pp. 144 (1973) 15. Mathematical model for prediction of efficiency indicators of educational activity in high school. J. Phy. Conf. Ser. 1015:032143 (2018). https://doi.org/10.1088/1742-6596/1015/3/ 032143. (in Russian) 16. Kushnikov, V.A., Yandybayeva, N.V.: Management of the educational process of the university on the basis of the Forrester model. Appl. Inform. 3(33), 65–73 (2011). https://cyberleninka. ru/article/n/model-forrestera-v-upravlenii-kachestvom-obrazovatelnogo-protsessa-vuza 17. Groff, J.S.: Dynamic systems modeling in educational system design & policy. New Approach. Educ. Res. 2(2), 72–81 ISSN: 2254-7399 (2013). https://doi.org/10.7821/naer.2.2.72-81

Medication Intake Monitoring System for Outpatients Alexander Ermakov(B)

, Aleksandr Ormeli , and Matvey Beliaev

Yuri Gagarin State Technical University of Saratov, Saratov, Russia [email protected]

Abstract. The subject of this article is the developing and implementing a hardware and software complex for monitoring medication intake by outpatient patients. Unlike today’s common hardware platforms, described complex allows not only remind patients of the need to perform regular admission, but also provide the infrastructure to inform the attending physician about the status of patient medication. The article discusses the implemented hardware prototype and the implemented soft-ware, as well as a description of the current problems and planned research. Keywords: Medication intake · Internet of things · Outpatients compliance monitoring · Therapist information system

1 Introduction The evolution of modern society, especially in the context of the global COVID-19 pandemic, requires new approaches to solving old problems through the use of Internet of things technologies. The use of modern technologies will al-low us to solve the patients compliance problem of undergoing outpatient treatment in a new way. Compliance refers to the patient’s ability to take medication and undergo procedures in accordance with the schedule and regimen prescribed by the doctor. The problem of compliance has been investigated in many medical studies [1, 2]. Failure to follow the therapist recommendations, in particular the pill regimen, leads to the transformation of acute diseases into chronic ones, the appearance of antibioticresistant bacterium, ineffectiveness of treatment in general and many other problems. The main task in forming the schedule of medication in-take is to ensure the required level of concentration of the active substance in the blood, cycles of their fluctuations for a period of time sufficient for healing, but not too long in order to avoid negative effects on the body. Research shows that the reason why patients lose their medication schedule is most often due to forgetfulness. The patient can easily miss the time of taking the medication more than once in the course of treatment. Other reasons include a decrease in attention on this issue: most often in the acute phase, the patient is ready to take medications on schedule, but stops doing so in the remission phase, even with the ongoing course of treatment. Even worse – the treating doctor of such a patient has little chance to learn © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 563–574, 2021. https://doi.org/10.1007/978-3-030-65283-8_46

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about the occurrence of such a situation, since often patients in remission begin to skip control appointments, or do not re-port the true state of things regarding the schedule of medication. In this paper, we offer a comprehensive solution to this problem based on Internet of things technologies. This solution is based on the idea of tracking the facts of medicines intake by patients, storing the schedule of this reception, providing a mobile application that can take into account the schedule and re-mind the patient about it, as well as exploring the possibility of implementing this technology in existing medical systems.

2 Objectives and Methodology of the Study The main purpose of the study is to try to find out whether it is possible to implement hardware and software complex for tracking medication intake by an outpatient patient in modern medical information systems and improve the quality of treatment as a result of implementation. • • • • • • • •

On the basis of the described objective, it was necessary: Identify system requirements based on information flow analysis Analyze the current state of medicines tracking and medical information systems Design and develop a prototype hardware and software package Perform load testing and determine system scalability and fault tolerance requirements Implement this complex in the existing medical system Determine the possibility of industrial production of hardware and software Conduct field experiments and statistical analysis of their results.

At this time we are at the stage of completing the prototype development: prepared the sample of hardware and managing service that can receive and store data about the medication, and also developed a demonstration information system for patients management.

3 The Architecture of the Solution The idea of a hardware and software complex is based on the idea of combining functionality for two main users: the patient and the doctor. When developing the system, it is necessary to take into account that both users are not specialists in information technology, and therefore it is necessary to minimize the specialized actions and configuration process for both categories of users. In addition, we consider it necessary to provide two modes of operation of the application: full, in which the patient takes medication under the supervision of a therapist, and custom, in which the patient takes substances that do not require medical supervision, but require compliance with the schedule. For the patient, the main functionality of the system is a reminder: that is, the system should signal that at the moment you need to take your medication. In terms of modern technologies, this means that there must be not only some device with a light and sound alarm, but also it must be possible to pair it with the patient’s personal mobile phone. The functionality of collecting statistics from the patient’s point of view will not be

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mandatory, since they cannot make decisions about the course of their treatment, but it is important to have a schedule of expected appointments. For the therapist, the main functionality is the ability to set a schedule for taking one or more medications for all patients they working with and get information about the regularity of taking in the medical history. It should be noted that therapists can work with different information systems and the required solution must be separated from them and provide their data independently, so that existing systems can request data and send requests for the formation of a medication schedule to a specific patient. Based on the analysis, we have developed a high-level architecture of the system shown in Fig. 1.

1 1

2

1

1

3

4

5

2 6 Fig. 1. High level architecture of the system

There are six main components in the system. Number one is the medicine dispenser. In this case, the dispensers are grouped under number two. This combination shows that a single user can take multiple medications. To simplify the design of the system, it is proposed to use one dispenser for one medication type, and to be able to combine such dispensers into a single design. Thus, Fig. 1 shows two users, one of whom takes three medications and therefore has three dispensers, and the second takes one medication and therefore has one dispenser. The dispenser should be responsible for two main functions. First, it must be able to signal the need for medication. Ideally, it should support both sound and light alarms (with the possibility of disabling them). At the same time, it is necessary to minimize, in order to reduce the cost, the functionality of the dispenser, and therefore it should not store data about the reception, or about the expected schedule. Therefore, its second function will be the ability to connect to the management service, which is marked with the number three in the figure. The functionality of the management service (or rather, even a group of such services) should include interaction with the dispenser. In fact, this app should be able to track the list of dispensers that it monitors and take into account the schedules of taking medications from these dispensers. When the time for taking medication in the monitored dispenser comes, it sends a command to this device

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to activate the light and sound alarm. At the end of the control time (depending on the settings, it can be from one minute to several hours), it repeatedly requests the dispenser to get information about whether there were signs of taking the medication during the specified time period or not. The management service takes information about dispensers and their schedules from the database shown in Fig. 1 by the number four. There the managing service will store the results of the survey of dispensers. The web service shown in Fig. 5 also works with the database. The web service will be the external interface of the system. In particular, it is assumed that it will provide data on the statistics of medication intake by a certain user or dispenser, or enter information about the schedule of medication intake by a certain dispenser into the database. The presence of such a tool, independent of the user interface, allows you to work with any external systems. We also assume that the management service will be able to send the results of the dispenser survey directly to the external systems registered with it. An example of an external system is the mobile app shown at number six. The mobile app is designed for patients. In it, the patient can track the medication schedule in dispensers, receive notifications about the need for medication, and manage the medication schedule in cases where they are not managed by the attending physician. Other types of external systems are generally shown here in curly brackets. The main idea of the architecture is based on the assumption that we do not need to write a new system specifically for the solution we have proposed. With this architecture, manufacturers of medical information systems will be able to integrate the functionality of their dispensers data request into their software with minimal effort. However, we should provide our own software product for cases where the only option is to maintain two separate lists – a list in an existing medical history system and a list of patients with dispensers and medication statistics.

4 Existing Solution Before starting the developing of this system, we conducted a study of the state of the subject area and functionality of existing systems. The study showed that the task of controlling medication intake by patients has been solved for a long time, but the existing solutions do not fully meet the identified requirements. Following systems was conducted: • • • • •

GlowCap; AdhereTech; MedReady 1700; MedCenter System; Xiaomi Zayata Portable Smart Pill Dispenser.

The hardware platforms we have studied only solve the problem on the patient’s side, that is, they are dispensers with a signal function. Almost every solution found (except Xiaomi) takes into account medication intake after opening and closing the dispenser lid. The solution from Xiaomi requires a special

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device flip. Schedule tracking is implemented in different ways: there are devices that require you to download medications for each day of intake separately, and there are those that take into account the configured schedule and offer to store all medications together. All devices in one form or another have a light and sound alarm about the need for reception. The latest systems allow you to connect to a mobile phone via Bluetooth channel. However, this solution cannot be considered satisfactory, since for our purposes it means that the patient must have a mobile phone (which is not always true) and that the phone must be close to the dispenser at the time of taking the medicine. For the GlowCap system, we were able to find functionality that includes pre-ordering medicine from the pharmacy after it is finished and not quite clear mentions of the possibility of contacting a doctor via the GSM network. Based on the analysis, we can conclude that the stage of introduction of dispensers with the possibility of network interaction is a predictable and obvious next step.

5 Implementation of the Hardware Complex At the moment, we have developed a prototype of the hardware. A feature of its architecture is the layout of standardized elements widely used in the market, while the external form is sacrificed to the convenience of development. Figure 2 shows an image of the assembled device. As you can see, the device consists of two compartments – the upper one is a dispenser box with a lid where the medicine is placed. The lower compartment is a protected space for placing the microcontroller.

Fig. 2. Hardware prototype

The most common solution used to record information about taking a medicine suggests that medicine is accepted if the dispenser lid was opened and closed. We tracking opening by the KY-021 magnetic field sensor. This sensor is quite small in size compared to other solutions, and also has a short response range, which should help eliminate the possibility of a false result.

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The main logic of the device is implemented by the Arduino Uno microcontroller. The logic of the hardware complex is simple enough that we do not need to use a microcomputer, while the response speed of the microcontroller is higher, and the power consumption is lower, which allows you to increase battery life. The choice of standardized microcontrollers can be found quite large, but the Arduino line can be considered as a reference for rapid prototyping systems. A huge number of libraries have been written for Arduino that allow you to work with almost any peripherals. A large number of connection modules, expansion boards and sensors are being developed for Arduino. To develop software for Arduino, a very convenient development environment is used – the Arduino IDE, and the development language itself is look like C++, which allows you to quickly adapt to writing sketches (that is name for Arduino microcontrollers programms). For this task, we chose a specific\implementation: Arduino Uno, because it implemented the desired combination of sizes and connectivity. A separate issue is the organization of communication between the hardware complex and external services. At the moment, the market is experiencing rapid development and cheapening of communication means, which allows you to make a wide selection. After analyzing existing systems and the proposed architecture, it was decided to use the prototype to connect the dispenser via an Ethernet cable to the Internet. The main advantage of this solution is again speed and ease of prototyping. For Arduino, a standard solution is provided in the form of an Ethernet Shield W5100 expansion board, which is well protected from voltage changes, has a high data transfer rate, and has a large selection of libraries in the development environment. However, it should be noted that this solution clearly requires the patient to have a home Internet connection, and with the possibility of connecting a cable, which is not always true. In the future, we will continue to investigate this issue. In addition to the above devices, the system also includes three led sensors designed for light signaling of the device status. We will describe how they work later in this article. Figure 3 shows the scheme of Assembly of the device. The Ethernet Shield W5100 expansion board connects to a board with an Arduino Uno microcontroller. Due to the fact that the form factor of the plug-in coincides with the each other form factor, connecting can be done by placing the Ethernet Shield on Arduino board, with the Ethernet cable connector right above the USB cable connector of the Arduino Uno. After connecting, the contacts located on the Ethernet Shield start working as contacts of the Arduino Uno Board, which means that in the future it is necessary to connect all the wires to the contacts of the expansion board. To organize the operation of the led at optimal brightness, it is necessary to connect a 220  resistor to the anodes of all LEDs. Then connect the resistor and the digital output as shown in the Fig. 3. The red led indicating an Internet connection error must be connected to digital output number 8. The Yellow led indicating the need to close the device cover is connected to digital output 7. The Green led indicating the need to take medication is included in digital output 5. Ground wires are connected to the cathodes of all LEDs. The Arduino Uno Board has a limited number of connectors for connecting the ground due to which it is necessary to combine the ground for all LEDs and connect the resulting wire to the free ground on the board.

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Fig. 3. The outline of the prototype

The assembly ends by connecting the magnetic field module. For its correct functioning, it is necessary to connect the module contacts to the board contacts in the correct sequence. The contact located near the label “-” on the module board is a ground connection. It must be connected to the ground contact on the board with the microcontroller. The next contact must be connected to an empty socket on the Board marked “5V”. The last contact is necessary for reading information from the sensor and it must be connected to the digital output 9. The connection as shown on Fig. 4.

Fig. 4. Connection diagram of the magnetic field sensor

The last step is to attach the magnet to the lid of the dispenser, which will interact with the opening/closing sensor. When applied, the magnet will close two open contacts in the vacuum flask located on the magnetic field sensor.

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6 Implementation of the Software An important part of the describing complex is the implementation of software that ensures the functioning of the entire system. Currently implemented: • • • •

scripts manage the state of the microcontroller; management service; external interface of the management service; demonstration information system.

The main functionality is provided by the management service: its tasks include sending HTTP requests to the microcontroller to activate scripts and collect data, as well as sending the collected data to external systems. The service is implemented using PHP scripts and runs under the OpenServer application server. The general algorithm of the management service is as follows: 1. In the management service system configured Cron scripts that describing the schedule of medication intake. They describe the time of the next intake and the duration of waiting for the end of medication. When the time has come for intake, a POST request is sent to the address of the dispenser using a script activate LED.php. 2. When receiving a described request, the microcontroller triggers the sketch code block on the microcontroller to turn on the green led, which means that you need to take medication. The variable “lid” is set to 0, i.e. the dispenser lid was not opened yet. 3. If the lid of the dispenser was opened, the sketch block turns on yellow led, which means that the lid must be closed. The variable “lid” is set to 1, i.e. the dispenser lid is open. 4. If the lid was opened and closed, the sketch block for switching off both LEDs is triggered. The “lid” variable is set to 2, i.e. the medication is taken. 5. On the control service side, there is a pending operation the following Cron script. The next scenario lags behind by an arbitrary time, on average about an hour, then activates the script readINFO.php, which sends a signal to send data from the dispenser to the service. 6. When the microcontroller receives a signal to return data, it sends the value of the variable “cover” and turns off the light indication (if it is not off yet). 7. On the service side, the script is activated when data is received sendInfoToDB.php which sends information about the date, time, and status of medication to all registered external systems. External systems are currently registered manually. The described algorithm allows you to make a complete diagnosis of the system and use it. For test purposes, several scenarios were also developed for manually managing the service’s requests to the dispenser and visualizing them as a web form. An example of applying these scenarios is shown in Fig. 5.

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Fig. 5. Service web form

For the patient the software operation order can be represented as shown in Fig. 6. At the first step, the green led lights up, the patient opens the lid (second step) and the yellow led lights up, the patient closes the lid – no led lights up. The red led lights up if the dispenser loses connection to the control service.

Fig. 6. Dispenser lights

The interaction of the therapists with this system is carried out through the usual information system. As mentioned earlier, the management service is able to send data to a registered external system if it is able to receive incoming HTTP requests. In our work, we have implemented a demo version of such an external system. In Fig. 7, we can see a form for the therapist to keep a patient’s medical history, in which, in addition to standard

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information, presented information about the percentage of successful medicines intake by the patient.

Fig. 7. Patient view

The information on the necessary medications, dosages, and frequency of admissions are selected by the doctor when registering the medication, and then it is need to perform, in one way or another, pairing the dispenser with information about the medication in the system. In the current solution, we simplified the system and suggests that the therapist issues a dispenser with its number written on it, signs the type of medicine for this dispenser and gives it to the patient for use. The dispenser is returned by the patient after the end of the course of treatment. In addition, the external system can access or store information about all medications independently, as shown in Fig. 8. In Fig. 8, we can see the number of the dispenser passed by the doctor to the patient, the date and time of taking the medication, and the status of the reception – missed or received.

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Fig. 8. Medication intake information

7 Further Work The described complex is the basic implementation for the medication intake monitoring task. It includes both standard features of existing systems for notificating the patient about the need for medication, and more advanced features for providing information about admission to external systems. However, it should be noted that this system has several interesting scientific and practical problems. The further work with the hardware: • the Arduino system is effective for prototyping, but expensive when producing dispensers in bulk volumes. It is needed to find a cheaper, and possibly simpler analog. At a time we are exploring the possibility of applying the solution described in [3]; • the dispenser microcontroller can be powered by both mains and battery, but the battery life is lower than desired (and a minimum of a month is required). It is needed to find a way to increase the battery life; • connecting the dispenser to the management service via an Ethernet cable requires the patient to have an appropriate connector or computer with the Internet. Alternative and more convenient implementation options should be considered; • the device itself requires improvement in its appearance for distribution to patients. • The further work with the software: • it is necessary to implement a service that is independent of external data storage systems; • it is needed to implement a mobile app for the most popular operating systems; • the management service needs to be improved in order to provide flexibility in setting the medication schedule and connecting external systems;

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• it is necessary to conduct load testing and investigate the issues of scaling the system when increasing the number of dispensers served. It is necessary to implement the appropriate system architecture for the research results. In addition to all of the above, a major challenge is to determine the best way to configure and interact with the therapist and patient with the dispenser and the system, based on the assumption that it is necessary to ensure the minimum possible level of understanding of the system by users. Solving all of these tasks can help improve medical monitoring of outpatient patients.

References 1. Bosworth, H.B.: Enhancing Medication Adherence. Springer Healthcare, London (2012). https://doi.org/10.1007/978-1-908517-66-1 2. Gellman, M.: Encyclopedia of Behavioral Medicine. Springer Nature Switzerland AG, Part of Springer Nature (2020) 3. Dolinina, O., Pechenkin, V., Gubin, N., Kushnikov, V.: A petri net model for the waste disposal process system in the “Smart Clean City” project. In 3rd International Conference on Smart City Applications Proceedings, SCA 2018, Tetouan, Morocco, October 2018. https://doi.org/ 10.1145/3286606.3286786

Cognitive Model of the Balanced Scorecard of Manufacturing Systems Oleg Protalinsky1 , Anna Khanova2(B) , Irina Bondareva2 Kristina Averianova2 , and Yulya Khanova3

,

1 Moscow Energy Institute, 14 Krasnokazarmennaya St., Moscow 111250, Russia 2 Astrakhan State Technical University, 16 Tatishchev St., Astrakhan 414056, Russia

[email protected] 3 Saint-Petersburg Electrotechnical University “LETI”,

5 Professora Popova St., St. Petersburg 197376, Russia

Abstract. A balanced scorecard is a tool of strategic management, which represents a group of selected indicators of a complex organizational system, grouped by 4 perspectives (finance, clients, internal business processes, training of personnel). The formation of a balanced scorecard is a difficult and poorly formalized task in accordance with the organization’s development strategy. The article deals the method of the analysis of the balanced scorecard a priori (at a development stage of its structure) and a posteriori (monitoring of the performance of goals based on data of imitating modeling or corporate information system) based on the cognitive model of the organization. Described is the approach to a priori analysis of the structure of a Balanced Scorecard, which includes checks of balance, transparency, causal relationships between perspectives along the entire vertical of goals, vertical checks of the total number of goals of a Balanced Scorecard and vertical checks by types of indicators, horizontal checks of the number and types of indicators by perspectives. Balanced Scorecard’s analysis of a posteriori is performed after the design of the structure of Balanced Scorecard based on values of indicators received from the object of control or its simulation model. The purpose of this assessment is to compare the functioning of a manufacturing system with a Balanced Scorecard in different situations. A posteriori analysis of a balanced scorecard is a tool for evaluating the configuration of a manufacturing system. The system of criteria of an assessment of a configuration of manufacturing systems (organizations) based on the balanced scorecard is formalized. Keywords: Balanced Scorecard · Cognitive model · Risk · Synergetic effect · Manufacturing system

1 Introduction Every manufacturing system needs to be adapted in advance to changing market conditions better than competitors in order to achieve success in a complex and dynamic environment. The actions of a manufacturing system should be coordinated and aimed © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 575–586, 2021. https://doi.org/10.1007/978-3-030-65283-8_47

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at achieving certain long-term goals [1]. These goals are expressed in the form of a balanced scorecard (BSC). Using BSC enterprises can significantly improve the efficiency of their operations; it proves the analysis of the results of its use in the past 20 years [2]. Completeness, consistency, integrity are used as criteria for evaluating BSC, which are provided by BSC construction methodology. The process of assessing BSC at enterprises is not formalized and has a qualitative nature. It is usually done manually based on the experience of the management staff. Accordingly, errors and inconsistencies arise in the structure of the BSC. It is difficult for a manager to identify patterns in the ratios of the values of the BSC indicators and make effective management decisions. It is necessary to define several criteria that give a quantitative estimate of BSC in addition to the qualitative criteria that assess the BSC at the stage of goal development. The BSC analysis should include a stage of a priori control of the BSC structure after its synthesis and a posteriori assessment of the BSC indicators based on the corporate information system (CIS) database or the imitating model (IM) runs. Some of the BSC assessments are presented as subjective peer review, other estimates are based on monitoring and statistical data [3].

2 A Priori Analysis of the Structure of BSC A priori analysis is carried out during the design of the BSC before use. A priori analysis of the structure of the BSC includes verification of the balance with the strategy; verification of transparency; cause-and-effect relationships between the perspectives across the vertical targets; vertical verification of the total number of BSC goals and by types of indicators; horizontal verification of the number and types of indicators for the perspectives. The verification of the balance with the strategy (Kapi1): checked reflected in the business strategy map, competitive strategy, and the main consequences of the SWOTanalysis. It should be noted that the solution of the problem of balancing a strategy is not amenable to formalization; it cannot be solved without the participation of the human factor and is usually very specific for each organization, for each stage of its development [4]. The main way of verification of consistency is the qualitative expert assessment by the participants of the BSC development process. The verification of transparency (Kapi2) assumes that there is an opportunity to restore targets by indicators, and there is an opportunity to restore a strategy by targets. The verification of transparency is essentially laid down already at the stage of compiling information thesauruses of indicators and goals [5]. The vertical verification of the total number of indicators (Kapi3): 8 ≤ nm ≤ 25 (nm is the number of BSC indicators). The BSC should consist of at least 8 indicators (nm = 8): one delayed indicator for each component and one indicator corresponding leading one [6]. In reality, such a limited set of characteristics may not be enough for achieving success, but an excessive number of indicators inevitably leads to a “blurring” of efforts to achieve results. 20–25 indicators are optimal for the BSC (Table 1). The vertical verification of indicators types (Kapi4): 80% of non-financial indicators (logical statement Kapi41 ); internal/external ratio (logical statement Kapi42 ); diagnostic/strategic ratio (logical statement Kapi43 ).

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Table 1. Verification criteria for BSC Analysis Assessment The vertical verification Dispersion value Synergy values intervals Kapo3 Kapi3 interval Kapo1, Kapo2 Poor

(nm ≤ 7) ∨ (26 ≤ nm)

Satisfactory 8 ≤ nm ≤ 11

1 < Var ≥ 0.7

(−1 < Sy ≤ 0) ∨ (0.8 < Sy ≤ 0.1)

0.7 < Var ≥ 0.6

(0 < Sy ≤ 0.2) ∨ (0.6 < Sy ≤ 0.8)

Good

12 ≤ nm ≤ 19

0.6 < Var ≥ 0.4

(0.2 < Sy ≤ 0.4) ∨ (0.6 < Sy ≤ 0.8)

Excellent

20 ≤ nm ≤ 25

0.4 < Var

0.4 < Sy ≤ 0.6

For each logical statement of Kapi4, it can definitely be said whether it is true (logical 1) or false (logical 0). The truth table for logical statements Kapi41 , Kapi42 , Kapi43 (Table 2) is proposed for formalizing the Kapi4 estimate [7]. Table 2. The truth table for assessing Kapi4 Kapi41 Kapi42 Kapi43 Kapi4 1

1

1

Excellent

1

1

0

Good

1

0

1

Good

1

0

0

Satisfactory

0

1

1

Poor

0

1

0

Poor

0

0

1

Poor

0

0

0

Poor

The vertical verification of balance (Kapi5) checks for causal relationships between perspectives across the vertical of goals “from the bottom up”. If the achievement of the underlying result (goal) is a necessary condition for the achievement of the overlying one, then the following causal link is checked. If this is not necessary, the following options are possible: 1. If the lower goal is connected by other proven causal relationships to the upper goal, then the unconfirmed link is canceled. 2. If the connection is unique, then one of the actions is performed: • direct communication with the target located above the map. Moreover, if the goal is left without a causal relationship, it can be removed from the map;

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• one of the goals is reformulated so that the achievement of the underlying goal is a necessary condition for the achievement of the overlying one. In this case, the indicators are redesigned in accordance with the goals; • an additional goal is introduced into the strategic map, which is a necessary link between the underlying and the overlying goals. The horizontal verification of the number of indicators for perspectives (Kapi6): • indicators of perspective «Finance» Pf : 2 ≤ M Pf ≤ 4 (logical statement Kapi61 ); • indicators of perspective «Clients» Pc: 2 ≤ M Pc ≤ 8 (logical statement Kapi62 ); • indicators of perspective «internal business process» Pip: 2 ≤ M Pip ≤ 10 (logical statement Kapi63 ); • indicators of perspective «Training of personnel» Ptd: 2 ≤ M Ptd ≤ 6 (logical statement Kapi64 ). To formalize the assessment of Kapi6, a truth table is proposed for the logical statements Kapi61 , Kapi62 , Kapi63 , Kapi64 , which is similar in principle to Table 2. The horizontal verification of the balance (Kapi7) is carried out in each BSC perspective separately, based on the ratio of indicator types. Mandatory verification includes monitoring the ratio of indicators: deferred/advanced (one deferred and one advanced indicator for each component). It is necessary to take into account that the degree of achievement of the goal is determined by the resultant indicator; the activity in the operational contour is controlled by the leading indicator. Accordingly, for this node to work, it is necessary to make the leading indicator a more frequent polling period than the resulting one. Assessment Kapi1, Kapi2, Kapi5 and Kapi7 are constructed as a subjective expert assessment of the structure of the BSC.

3 A Posteriori Analysis of the Structure of BSC A posteriori analysis is carried out after the design of the BSC structure based on the values of the indicators obtained from the control object or the model. The purpose of this assessment is comparing the organization’s activities for BSC in various conditions according to the results of the simulation model runs. BSC analysis is a system configuration assessment tool. It is necessary to formulate a list of criteria for ranking various implementations of the organization configuration. The set of criteria depends on the subjective assessments of management, on the vision of the problem and the nature of the goal that the enterprise strives to achieve. For each specific area, there is a well-established set of criteria, which may vary depending on the current situation and the subjective preferences of the manager. Consider a ranking method that would determine an assessment of the implementation of activities for the BSC of some enterprise. In [8] it is argued that enterprises for assessing goals and strategies for their implementation most often use the following criteria (production): balance, synergy, team competence, specialization, growth of firm capitalization, survival, minimizing the risk of loss, success. Experts could add some criteria and refuse others. It was decided that

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in the future only criteria will be taken into account with which all experts agree. As a result, the list of criteria selected by experts: balance (Ba), risk (Ri) [9] and synergy (Sy) [10]. Evaluation of the results obtained will be made based on the variance of estimates of indicators characterizing the organization. The intervals and estimates of the variance for the selected criteria were identified. Using the expert survey (Table 1). For each BSC indicator obtained as a result of the IM run, its agreed criteria assessment is determined; this makes it possible to further unify the processing of information on indicators in the future. Then the average value of all estimates is defined as: 1  mi , nm nm

MBa =

(1)

i=1

where mi is the agreed criteria assessment of the indicator, nm is the number of BSC indicators (8 ≤ nm ≤ 25). The variance value is determined by the formula:  1 (mi − MBa )2 . nm − 1 nm

VarBa =

(2)

i=1

The evaluation of the Ba criterion is determined based on the value of Var and Table 1. Each management decision (MD) concerning the future development of an enterprise is always associated with a certain degree of uncertainty. Uncertainty can be both positive (possibility) and negative (risk) [11]. MD is based on information on potential deviations from planned targets. For individual planned values of certain indicators, individual decisions are made regarding how they are exposed to various risks. Therefore, risk has become the second criterion for analyzing BSC. In the framework of this work, the risk is calculated as a value calculated using the following formula: Ri =

nex   mf i=1

nex

 · mr ,

(3)

where mf is the number of conducive outcomes after running the simulation model for mi [12]; nex is the number of experiments performed; mr is the planned or baseline value of mi . The determination of the risk of deviation of the indicator from the base value is made similarly to the assessment of balance using dispersion, according to Table 1. The assessment of the criteria is the balance of Kapo1 and the risk Kapo2 is determined based on the value of Var in Table 1. The efficiency of business processes directly contributes to the qualification of personnel and the technologies used, which contributes to the qualitative solution of the tasks set before the organization and the achievement of competitive advantages, which ultimately leads to the planned financial indicators [13]. This is implemented in the BSC in the form of causal relationships. The resulting cumulative effect is called synergistic [14]. The synergistic effect rule states that the sum of 1 + 1 is not 2, but 3 or even more. This fully corresponds to the philosophical interpretation of the systems approach: the properties of the whole are more than just a set of properties of the parts that make up this

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whole. The criterion synergy determines the integral efficiency of the enterprise. Integral efficiency depends on how much enhances (or reduces) each evaluated indicator of the effectiveness of all others. For example, how does the training of personnel affect the success of the use of equipment, product quality, the state of finances, etc. The effect of the deviation of the indicator mk on the deviation of the indicator mi at the moment τ will be expressed by the function:

(4)

The nature of such influence can be represented as a cognitive map, which reflects the direction and relative coefficients of the influence of indicators on each other (Fig. 1).

Fig. 1. Fragment of the cognitive model of indicators

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On a cognitive map, the plus sign on arcs between vertex factors means that increasing the value of the factor-cause leads to an increase in the factor-effect, and a minus sign - increasing the value of the factor-cause decreases the value of the factor-effect [15]. A cognitive map reflects the functional structure of the situation being analyzed since a change in the value of any factor in the situation leads to the emergence of a “front” of changes in the values of the factors associated with it. The weight of an arc in a cognitive map determines confidence in the existence of a connection between vertices and is represented by a number in the interval [−1, 1]. For a causal relationship between a factor-cause and a factor-effect, positive relationship associates positive increments, and negative ones with negative increments [16]. The negative relationship is associated, respectively, with positive increments with negative, and negative with positive increments [17, 18]. Thus, it is necessary to initially create a table for all BSC indicators available in the database. The values of νij located at the intersection of the i-th row and the j-th column of the table, filled by different experts, may not coincide, so each value must be consistent. Apply the principle of unanimity here is impossible. The matching algorithm will be used. The fragment of such a table, for some indicators of BSC, is presented in Table 3. Table 3. Fragment of the matrix of the effect of BSC indicators on each other BSC indicators

Reliability loading (+)

The error rate for shipments per month (−)

+0.8

Enterprise Reputation (+)

Reduced staff percentage (−)

−0.3

−0.6

Reliability loading (+) Warehouse load factor (+)

The percentage of refusals in the implementation of the deal (−)

−0.3

Percentage of customers making a repeat deal (−)

−0.5

The percentage of refusals in the implementation of the deal (−)

+0.2

In the headings of the rows of Table 3 after the name of the indicator indicates the sign of its deviation from the norm. In accordance with it, the signs of the coefficients of influence on other indicators are adjusted. The headings of the columns at the beginning of the name of the indicator indicate the signs of deviations that are desirable for the organization.

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The resulting column coefficients are added up to calculate the synergy estimate, taking into account the desired deviation: with the desired positive deviation, the resulting amount is left unchanged, and with the desired negative deviation - multiply by −1. Then normalize the resulting sums (to the sum of absolute values) and add the resulting values [15]: Sy =

nm  i=1

i , nm  |i |

(5)

i=1

where Sy is the estimate of synergy, i is the sum of the coefficients in the i-th column,  |i | = 0 is the sum of the absolute values of the coefficients. Thus, a synergy score is obtained, having a value from −1 to 1. With a negative synergy value, we can talk about a large number of negative deviations of the indicators from the norm and we need to achieve the best values of the indicators. Estimation of synergy can be given depending on the percentage that improves the integral efficiency of the enterprise, in accordance with Table 1, which is rather conditional. But if we assume that it is accepted at the enterprise, we can find out the percentage of indicators that improve synergy and derive an assessment according to the criterion “synergy” Kapo3.

4 Evaluation of the Values and “Weights” of the Criteria a Priori and a Posteriori In conclusion, experts build a final table of estimates of a priori analysis of the structure of BSC and a posteriori analysis of BSC indicators according to selected criteria (Table 4). In the last column of Table 4 ranked criteria, because experts will need to determine their “weight”. The rank of a criterion determines what its importance is for the organization. The score of ranks can be determined by their number. The rank of criteria a priori can have a value from 1 to 7, a posteriori - from 1 to 3. The rank of criteria is determined by a group of experts of 12 people. After the experts put down the ranks of the criteria in Table 4, the sum of the ranks obtained by each criterion is determined: kpi =

J 

kpij Nexpj , i = 1, .., I ,

(6)

j=1

where kpij is the rank of the i-th criterion, determined by the j-th expert; Nexpj is the number of experts who gave this assessment to the criterion and the normalized sum of the ranks hkpi , determined by the formulas: Kapi

hkpi

= kpi /

7 

kpi (a priori analysis),

(7)

kpi (a posteriori analysis),

(8)

i=1 Kapo

hkpi

= kpi /

3  i=1

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Table 4. Evaluation criteria a priori and a posteriori Indicators

Assessment

A priori

A posteriori

Rank, kpi (inverted rank used to calculate “weight”)

The verification of the balance Excellent with the strategy (Kapi1)

7(1)

The verification of transparency (Kapi2)

Good

3(5)

The vertical verification of the total number of indicators (Kapi3)

Good

6(2)

The vertical verification of indicators types (Kapi4)

Good

5(3)

The vertical verification of balance (Kapi5)

Excellent

4(4)

The horizontal verification of the number of indicators (Kapi6)

Excellent

2(6)

The horizontal verification of the balance (Kapi7)

Satisfactory

1(7)

Balance (Kapo1)

Poor

2(2)

Synergy (Kapo2)

Excellent

3(1)

Risk (Kapo3)

Satisfactory

1(3)

 where kpi = 0. For ranking the criteria, Table 5 was compiled showing the weights of the criteria equal to the normalized sum of ranks in accordance with the collective assessment of experts separately for the criteria a priori and a posteriori. After the values and “weights” of the criteria based on the monitoring data and statistical information from the simulation model runs are determined, the options BSC BSC = (BSC 1 , BSC 2 , …, BSC nbsc ) can be evaluated a priori and a posteriori. The overall assessment of the BSC structure a priori for the considered example, api taking into account the value of each Kapi criterion and its “weight” hkpj (Table 4 and 5) can be determined: BSC api =

7 

api

Kapij · hkpj

= 0, 2 × 5 + 0, 14 × 4 + 0, 19 × 4 + 0, 18 × 4 + 0, 15 × 5 + 0, 07 × 5 + 0, 06 × 3 = 4, 32.

j=1

The overall assessment of the BSC indicators a posteriori for the considered example, taking into account the value of each Kapo criterion and its “weight” (Tables 4 and 5) can be determined by the relation: BSC apo =

3  j=1

apo

Kapoj · hkpj

= 0, 35 × 2 + 0, 24 × 5 + 0, 41 × 3 = 3, 13.

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Rank of criterion

Table 5. Rated sums of ranks for evaluating criteria a priori and a posteriori Estimations of criterion importance Criterion

7

6

5

4

3

2

1

Amount of ranks kpi

Rated sums of ranks (weight of criterion), hkpi

Kapi1

5

4

3

-

-

-

-

74

0,20

2

Kapi3

3

4

5

-

-

-

-

70

0,19

3

Kapi4

2

4

4

1

1

-

-

65

0,18

Kapi5

-

3

-

9

-

-

-

54

0,15

Kapi2

-

2

3

3

3

1

-

50

0,14

Kapi6

-

-

-

1

3

5

3

26

0,07

7

Kapi7

-

-

-

1

1 2 3

Kapo3 Kapo1 Kapo2

4 5

A priori

1

A posteriori

6

1

5

5

22

0,06

6 2 2

3 7 1

3 3 8

27 23 16

0,41 0,35 0,24

Thus, the assessment of the structure of BSC according to the selected criteria is a priori “good with a plus”, and the assessment of BSC indicators a posteriori is “satisfactory”. In Fig. 2 shows the effectiveness of the BSC analysis. The method of analysis of a balanced scorecard based on the cognitive model.

Fig. 2. Effectiveness of the BSC analysis

The conducted research allowed formulating the BSC analysis method based on a combination of a priori and a posteriori approaches:

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1. Begin a priori analysis of the structure of BSC based on the Kapi criteria. The verification of the balance with the strategy, of transparency, vertical and horizontal verification of balance based on subjective peer review. 2. The vertical verification of the total number of indicators (Table 1). 3. The vertical verification of indicators types (Table 2). 4. The horizontal verification of the number of indicators on perspectives. 5. The overall assessment of the structure of BSC is a priori, taking into account the api value of each Kapi criterion (Table 4 and 5) and its “weight” hkpj . Completion of a priori analysis of the structure of BSC. Conclusion on the synthesized structure of BSC. 6. Run a simulation model or obtain information from a manufacturing system’s (organization’s) information system. 7. Begin a BSC a posteriori analysis based on Kapo criteria. Evaluation of the balance and risk of BSC according to the results of the simulation model run (Table 1). 8. Evaluation of BSC synergy based on the cognitive model of BSC indicators (Fig. 1). 9. The overall assessment of BSC indicators is a posteriori, taking into account the value of each Kapo criterion (Table 4 and 5) and its “weight”. Completion of a posteriori analysis BSC. Conclusion on the implementation of the BSC.

5 Conclusion A new method for formalizing and assessing the patterns of ERP based on a cognitive model is proposed. It evaluates the effectiveness of the strategic management of an enterprise based on quantitative and qualitative assessments. A posteriori analysis is carried out after the design of the BSC structure based on statistical values obtained from the corporate information system of the enterprise or its simulation model. A detailed description of approaches to assessing BSC a priori is presented, which allows verifying the correctness of the BSC based on the monitoring of the number of indicators and goals of the BSC vertically and horizontally, as well as the presence of cause-effect relationships. The systems of criteria for evaluating BSC a priori are described in detail, i.e. based on the numerical values of the BSC indicators obtained from the results of the simulation model run. Developed methods for calculating all criteria and their estimates. A method for analyzing BSC based on the results of the monitoring and simulation model runs under the influence of various factors has been developed, which allows choosing the best implementation of the manufacturing system configuration.

References 1. Protalinskiy, O., Andryushin, A., Shcherbatov, I., Khanova, A., Urazaliev, N.: Strategic decision support in the process of manufacturing systems management. In: Eleventh International Conference “Management of Large-Scale System Development”, MLSD, Moscow, pp. 1–4 (2018). https://doi.org/10.1109/MLSD.2018.8551760 2. Kaplan, R.S.: Conceptual foundations of the balanced scorecard. In: Handbooks of Management Accounting Research, vol. 3, pp. 1253–1269 (2009). https://doi.org/10.1016/S1751-324 3(07)03003-9

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3. Parygin, D., Malikov, V., Golubev, A., Sadovnikova, N., Petrova, T., Finogeev, A.: Categorical data processing for real estate objects valuation using statistical analysis. IOP Conf. Ser.: J. Phys.: Conf. Ser. 1015, 032102 (2018). https://doi.org/10.1088/1742-6596/1015/3/032102 4. Theriou, N.G., Demitriades, E., Chatzoglou, P.: A proposed framework for integrating the balanced scorecard into the strategic management process. Oper. Res. Int. J. 4, 147 (2004). https://doi.org/10.1007/BF02943607 5. Strohhecker, J.: Factors influencing strategy implementation decisions: an evaluation of a balanced scorecard cockpit, intelligence, and knowledge. J. Manag. Control 27(1), 89–119 (2015). https://doi.org/10.1007/s00187-015-0225-y 6. Geyda, A.: Dynamic capabilities indicators estimation of information technology usage in technological systems. In: Dolinina, O., Brovko, A., Pechenkin, V., Lvov, A., Zhmud, V., Kreinovich, V. (eds.) Recent Research in Control Engineering and Decision Making, ICIT 2019. Studies in Systems, Decision and Control, vol. 199. Springer, Cham (2019). https://doi. org/10.1007/978-3-030-12072-6_31 7. Kaplan, R.S., Norton, D.P.: Using the balanced scorecard as a strategic management system. Harv. Bus. Rev. 74(1), 75–85 (1996) 8. Niven, P.R.: The Balanced Scorecard Step by Step: The Maximum Increase of Efficiency and Fixing Received Results. Balance Business Books, Moscow (2003). (in Russian) 9. Orlova, E.: Approach for Economic Risks Modeling and Anti-risk Decision Making in a Transport Company (2019). https://doi.org/10.2991/cmdm-18.2019.8 10. Orlova, E.: Synergetic synthesis of the mechanisms and models for coordinated control in production and economic system, pp. 783–788 (2019). https://doi.org/10.1109/CSCMP45713. 2019.8976801 11. Nedosekin, A.O., Kozlovskij, A.N.: Information model for the description of the field of properties “efficiency-risk-chance”. Inf. Space 4, 101–105 (2016). (in Russian) 12. Sandkuhl, K., Seigerroth, U.: Method engineering in information systems analysis and design: a balanced scorecard approach for method improvement. Softw. Syst. Model. 18(3), 1833– 1857 (2018). https://doi.org/10.1007/s10270-018-0692-3 13. Surnin, O., Sitnikov, P., Khorina, A., Ivaschenko, A., Stolbova, A., Ilyasova, N.: Industrial application of big data services in the digital economy. In: Information Technology and Nanotechnology, pp. 409–416 (2019). https://doi.org/10.18287/1613-0073-2019-2416409-416 14. Frischkorn, G.T., Schubert, A.-L.: Cognitive models in intelligence research: advantages and recommendations for their application. J. Intell. 6, 34 (2018). https://doi.org/10.3390/jintel ligence6030034 15. Khanova, A.A.: The synergistic effect of organizational management based on the Balanced Scorecard. Caspian Mag.: Manag. High Technol. 4, 36–41 (2010). (in Russian) 16. Augustine, M., Yadav, O.P., Jain, R.: Cognitive map-based system modeling for identifying interaction failure modes. Res. Eng. Des. 23, 105–124 (2012). https://doi.org/10.1007/s00 163-011-0117-6 17. Benkova, E., Gallo, P., Balogova, B., Nemec, J.: Factors affecting the use of balanced scorecard in measuring company performance. Sustain. MDPI Open Access J. 12(3), 1–18 (2020). https://doi.org/10.3390/su12031178 18. Prezenski, S., Brechmann, A., Wolff, S., Russwinkel, N.: A cognitive modeling approach to strategy formation in dynamic decision making. Front. Psychol. 8, 1335 (2017). https://doi. org/10.3389/fpsyg.2017.01335

Automated Player Activity Analysis for a Serious Game About Social Engineering Boris Krylov1(B)

, Maxim Abramov1,2

, and Anastasia Khlobystova1,2

1 St. Petersburg State University, St. Petersburg, Russia [email protected], {mva,aok}@dscs.pro 2 St. Petersburg Institute of Informatics and Automation of the Russian Academy of Sciences, St. Petersburg, Russia

Abstract. This article proposes a mathematical model that helps to track a player’s game actions and present them in a structured form. The gaming process is presented as a set of states that are connected by a player’s actions. Each state is a set of predicates that characterize the player’s knowledge about the game. This mathematical model was developed as a step in achieving the general goal of the research branch, which is to increase the safety of an information system from social engineering attacks by developing a serious game. This serious game is aimed at improving players’ skills in recognition and counteraction to social engineering attacks as well as at raising awareness among employees. Keywords: Graph theory · Social engineering attacks · Game environment for social engineering attacks · User protection · Information security

1 Introduction 1.1 Social Engineering Attacks Social engineering attacks are methods of security attacks in which a perpetrator manipulates the system’s user into breaking the company’s established policies to steal data, personal information, money, and even identity [3, 5, 10]. Over the years, such attack methods had gained in popularity. Social engineering attacks are becoming more and more prevalent, leaving companies to suffer the cost of their employees being deceived. On average, companies lost around $1 407 214 to phishing and social engineering attacks in 2018 according to the Ninth survey of cybercrime conducted jointly by Accenture and Ponemon Institute [6]. 85% of the companies that were participating in the study encountered social engineering attacks. It is also noted that 76% of the company employees do not have the skills to protect their data [9]. However, there are measures companies can employ to ensure their safety against malefactors. The development of approaches, methods, and models to increase the security of users from social engineering attacks was considered in studies [1, 3]. The overall goal of these studies was to develop an automated complex aimed at identifying the organization’s employees most susceptible to the social engineering attack, as well as © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 587–599, 2021. https://doi.org/10.1007/978-3-030-65283-8_48

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the most critical attack distribution scenarios. For the identified employees it is important to perform follow-up training and educating [5, 14]. The importance of educating staff on security issues or developing cybersecurity tools designed to prevent successful social engineering attacks is emphasized in [12]. A game is presumed to be one of the best means of raising awareness among company staff regarding cybersecurity and user protection from social engineering attacks. During such a game, an employee engages in a simulated social engineering attack. This form makes training not only useful but also interesting and thus more effective. The general goal of this branch of the study is to increase the protection of information systems users from social engineering attacks utilizing a serious game to train company employees in the field of cybersecurity, in particular, social engineering. The game is divided into two phases. During the first phase, the player is “performing” the social engineering attacks against the non-player characters (NPCs) while also learning the principles and features of the attacks. The player’s task is to perform multiple simulated social engineering attacks to obtain a certain file in the in-game company’s information system. And the second phase is a quiz to test the knowledge the player learned during the game. The main goal of this work is to develop a mathematical model to track a user’s actions in such a game. The novelty of the study lies in the proposal of a mathematical model that represents, the player’s story. This model is based on a graph of game environment states. Each state is a set of the facts that the player knows about an in-game information system (we will discuss the particular facts below). Each action the player performs leads to the emergence of some new knowledge. This model allows for a structured representation of the player’s story, which is used to automatically generate a test for the quiz in the second part of the game. It is also can be used to study the player’s behavior in the game. This model was designed for the serious game about social engineering attacks, however, it can be applied to other puzzle or detective video games, thus we will give a generalized description of the system, illustrated by the examples, taken from the developed serious game. 1.2 Related Works It is proposed to develop a digital serious game for educating users about social engineering attacks and thus helping to increase their awareness. Despite the apparent demand in training, surveys, etc. relatively few serious games have been developed. The main purpose of the board serious game presented by K. Beckers and S. Pape is the elicitation of the company’s vulnerabilities to the social engineering attacks [4]. It can be used as a learning tool within the company; however, it requires several people to play. Another game, “Playing safe”, which was developed by M. Newbould and S. Furnell, aims to raise awareness [11]. Authors of [15] also present an education game for helping players to get an understanding of security attacks and vulnerabilities. In paper [8] authors propose game “Riskio”. It is a card game to increase cybersecurity awareness for company employees. The players can be both the role of the attacker and the defender of critical documents of the organization, in so doing, they are in an active learning environment. Approaches suggested in [8] can be useful for the branch

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of study, however “Riskio” is a tabletop card game, not a digital serious game. Thus, these approaches should be adjusted. In the work [2] a mobile game “CybAR” is represented. It is intended to educate users about different forms of cyber-attacks and ways of avoiding them. The main goal of the “CybAR” game is to increase interest in cyber security and increase knowledge of cyber-attacks; also “CybAR” helps users to understand correct and safe behavior on the Internet. The main aim of [13] is to explore approaches of design, development, and implementation of a collectible card game (CCG) for teaching cyber security to middle school students. A similar goal is pursued in [7], however, the system is designed for elementary education. The presented theoretical approaches can be used in the further development of a serious game. 1.3 Serious Game In the developed serious game, a player interacts with the environment and learns new information based on these interactions. The player can speak with the NPCs, send them emails, and interact with the office environment. Among the key actions that can be performed by the player, there are different types of social engineering attacks, such as phishing, shoulder surfing, impersonation, or dumpster-diving. Performing the attacks in the game in a simplified form, the player learns about their principles and means of prevention. The game is designed to encourage to perform multi-pass social engineering attacks to maximize the spectrum of social engineering attacks executed during one play session. The final goal of the game is to obtain a specified file. After completing this goal, the player has to take a quiz to test his or her knowledge obtained during the game. To maximize the player’s engagement into the final quiz we propose a system that tracks player’s behavior and then formulates the quiz questions so that they correspond with the situations the player had faced during the play session. 1.4 Defining the Task: System for Tracking Player’s Behavior It is impossible to predict the player’s actions during the game session. Some of the actions the player decides to perform do not help to finish the game and are redundant (a more formal definition of redundant actions will be presented further). The player can change strategies, mix redundant actions with useful ones, and it is not clear which actions were necessary to win the game until the end of the game session. These facts make a linear representation of the player’s actions unsuitable for assessing a player’s performance. Moreover, some social engineering attacks can be skipped during the game session. It is very possible that the player has never encountered certain situations during the game session, and it was deemed unreasonable to question the player about the situations that were never encountered. Therefore, the task is to create a system that records and structures actions that help to track the player’s progression towards the goal of the game. The resulting structure

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should allow the extraction of the most useful player action for composing a quiz for the player.

2 Defining the Domain Knowledge During a game session, a player is performing actions that change the game environment state. In the developed game a state is representing a player’s knowledge. A player’s knowledge is a set of facts a player can learn about the digital environment throughout the game. The fact is considered learned when the player first accessed the in-game source of information which contains this fact. After that, the player can revisit this information via a special menu dedicated to storing acquired facts. Note that this model does not account for the player’s prior knowledge about the game that could be acquired during preceding game sessions. To describe states of player knowledge, a specific language is used. It consists of mutually disjoint sets of symbols. Constant symbols from a finite set of constant symbols C and variable symbols from an infinite set V of variable symbols can be used as terms. From a predicate symbol p ∈ P and a list of terms τ1 , τ2 , . . . , τk a Boolean-valued function, a predicate p(τ1 , τ2 , . . . , τk ), can be built. Let Q denote a set of predicates. The predicate is called ground if it does not contain any variable symbols. Facts are represented by ground predicates which compose a state s ∈ 2Q , set of ground predicates. All predicates that are not included in s are presumed to be false, in other words, the closed world assumption is adopted. In the developed game the player’s knowledge about the gaming environment is essentially the facts the player knows about the NPCs. Each character has a uniform array of predicates associated with him. Each character has a set of traits: Curiosity, Negligence, Greed, Credulity, Fearfulness, Desire to help, Technical savviness. Each trait is rated from −100 to 100 by its expressiveness and this rating affects the effectiveness of the social engineering attack. The player also gets to know the NPC’s relations with the other characters, position within the in-game company, email address, password, and even the answer to the secret question. There are also technical flags that indicate that the player had accessed NPC’s e-mail or computer. In total, for 5 characters that are in the game, 95 predicates represent different facts about the game (7 trait ratings, 4 relationships, 1 secret question answer, 1 “knows the password partly”1 , 1 “knows the full password”, 1 position, 1 e-mail address, 1 name, 1 “has access to the NPC’s mail”, 1 “has access to the NPC’s computer” for each character). All these facts compose the game state, which the player can change by performing actions.   Definition 1 (Player action). A player action is a triple a, fpre (a), feff (a) , where a is an action symbol, fpre (a) ∈ 2Q is a set of preconditions, feff (a) ∈ 2Q is a set of action effects. Preconditions are used to describe an action applicability to certain states. Sometimes the player makes well-informed decisions and takes a certain action knowing how 1 We use two predicates to describe the player’s knowledge of the NPC’s password because during

the game it is possible to learn only some characters in the password by using shoulder surfing mechanic.

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effective it would be. However, sometimes the player can perform actions without some prior knowledge. To illustrate this, the set of preconditions is divided in two parts: esseness (a), and negligible preconditions, denoted as f neg (a). tial preconditions, denoted as fpre pre For example, the player can access the NPC’s e-mails via password, however, the player can guess the password, thus physical access to the in-game computer is an essential precondition, but prior knowledge of the NPC’s password is negligible. ess (a) ∪ f ∗neg The action a is called fully applicable to a state s, if fpre (a) ⊆ s. If fpre pre neg neg (a) ⊆ s, where f ∗pre (a) = ∅ and is the subset of fpre (a) (i.e. not all negligible preconditions are satisfied in the state s), then the action is called partially applicable. If ess (a) ⊆ s, then the action is technically applicable. Partial applicability is weaker than fpre the full applicability, but stronger than technical. When calculating a suitable set of preconditions, we always operate under the assumption that the player always makes well-informed decisions and considers all the information available. This assumption does not distort the resulting structure. Even if the player overlooks some facts when deciding, the action is still being performed at a given moment in time, and there is no way to know the player’s reasoning to perform this action. Thus, the best reasoning is stored and if the player does not know it, he or she may learn it during the question phase. The result of applying the action a to the state sn is the state sn+1 = sn ∪ feff (a). When the game is started, starting state is denoted as so = ∅. Actions performed by the player modify the game environment state. It is assumed that the player is actively trying to complete the game, thus a terminal state will eventually be reached, concluding the game session. Definition 2 (Terminal state). A terminal state is the state that satisfies finishing conditions fterm i.e. st ∩ fterm = ∅. Finishing conditions are a set of predicates, that if true, indicate the completion of the game by the player. Finally, it is possible to define an action graph construction problem using the definitions from above. Definition 3. (Action graph construction problem) An action graph construction problem is the tuple (Q, A, s0 , P, fterm ), where. • • • • •

Q is a finite set of predicates. A is a finite set of player’s actions. s0 is a starting state. P is a sequence of player’s actions. fterm is a set of finishing conditions.

The sequence P consists of actions, performed by the player in the environment. Each action changes the state of the environment, creating a sequence of full states s1 , s2 , s3 , . . . , sterm . Every action ai ∈ P is applicable to the state si . The solution to the given problem 3 is an action graph.   Definition 4 (Action graph). An action graph is the tuple s0 ∪ S prt , E , where S part is a set of partial environment states and E is a set of arrows, the tuple that consists of the

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  part part ordered pair of partial states pi , pi+1 and the symbol a∗ ∈ A ∪ {u}, where u is a special union symbol. The first item in the ordered pair is the arrow’s tail, the second is the arrow’s head, the symbol a∗ is used to distinguish arrows. A partial environment state is the result of the application of the player’s action ai to the starting state s0 , the result of the application of the player’s action to another partial state, or some union of the partial states. The partial state that represents the union of the several other partial states is called combo state. These are the only graph vertices that has the in degree higher than 1. There are two types of arrows in the set E. The first type is arrows that are associated with player’s actions, i.e. a∗ = ai . The action ai must be at least technically applicable part ∈ S part that is the arrow’s tail. The head of such arrow is the state to the state si part part pi+1 = si ∪ feff (a). Arrows of the second type connect partial states to a combo state, and the combo state value is the result of the union of all its direct predecessors. in these arrows a∗ = u. An action graph is a directed graph with no loops, cycles, or multiple arrows that have the same source and target partial states2 . Each arrow represents an action and each part node — a partial environment state. It is important to note that si = ∪ij=1 sj .

3 Action Graph Construction During the game, the player performs actions thatchange  the state of the  environment. Each time the player performs an action, a triple a, fprei (a) , feff (a) is created. a is an action symbol used to distinguish different actions between themselves. A set of sets {fprei (a)}m i=0 is used to describe all possible preconditions from strongest to the weakest. A set of predicates feff is the effect of the action. This triple is added to the processing queue. To process a new action the following algorithm is used:     1. Retrieve the triple a, fprei (a) , feff (a) from the queue3 . 2. Linearly check the list of full environment states to determine the earliest full state to which the action is applicable with the preconditions fpre0 (a). This way the search area on the graph is reduced. Each action in action sequence corresponds with the full state. If si is the desired earliest state, then to add a new edge to the graph, partial part part need to be checked. If the desired full state was not found, states s1 , . . . , si preconditions must be weakened, and the search has to be restarted. Repeat until the desired full state is found. The applicability of the action to at least one of the full states is guaranteed by the fact that it is impossible to perform an action if its essential preconditions are not satisfied. 2 If the player learns the same information from 2 different actions, the system stores the one that

the player performed first. 3 The action extracted from the queue is guaranteed to provide the player some new information.

If f eff (a) ∈ s, where s is a current state of the game environment, the action a is considered redundant and is not recorded.

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3. Linearly check graph nodes from 0 to i until one of them does not satisfy preconditions, that were chosen on step 2 (These preconditions are denoted as fprek ). (a) If such partial state is found (let sl denote it), create a new node with the state sn+1 = sl ∪ feff (a) (n being the number of all partial states in the graph). Create the arrow that connects sl and sn+1 and mark it with the action symbol. (b) If there is no such node in the graph, construct the node that represents the union of partial states. i.

part

For each node sj

part

, where j ∈ {1, . . . , i}, check if sj

∩ fprek (a) = ∅, and

part sj

to the unification list. if it is so, add ii. Construct the node that represents the union of all states on the unification list and create arrows from all the states in the list to this new combo state (Denoted as scombo ). iii. Create a new node which represents the state sn+1 = scombo ∪ eff (a) and mark the arrow with the action symbol. 4. Check if the created node is a partial terminal state. If not, check if the new full state is a terminal state. If it is, construct a combo-state that represents the partial terminal state. Figures 1, 2, and 3 illustrate the operation of the algorithm. In these examples, states of the environment, preconditions and effects are described by a set of four predicates, represented by bit sequences.

Fig. 1. The action a2 is applied to the state s1

Fig. 2. The action a3 is applied to the state s0 with weaker preconditions

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Fig. 3. Action a4 is applied to a combo-state

For better illustration of the algorithm let us assign a fact to each bit. In this example, the player is attacking a character named John. Here is what each bit represents: 1. 2. 3. 4.

“Player knows John’s password” “John is very gullible” “Player knows John’s full name” “Player knows John’s email”

On the Fig. 1 it is presented how the action is added to the graph. The player somehow learned that John is very gullible and decided to speak with John. In private conversation, the player learns John’s full name and email address. On the Fig. 1 this conversation is represented by the action a2. The Fig. 2 showcases the situation when the action is not applicable with the stronger preconditions but is applicable with the weaker ones. Note that action has precondition {0; 0; 0; 0} which is equivalent to the starting state. This set can be generated only if the action has no essential preconditions. In this example, the player takes another approach. To learn John’s full name and email, he or she uses the mailing list and finds John’s name and address. This is the action a3 on the Fig. 2. The player may know John’s full name, but it is not necessary, the player can find John’s address using only his first name. Figure 3 illustrates the construction of a combo state. The action a4 cannot be applied to any state in the graph specifically, but it can be applied to the union of the states s1 and s2. Thus, the combo state is constructed, and the action is applied to it. The action a4 is an actual attack in this example. To get John’s password, the player writes him a phishing mail. The player knows that John is gullible, thus a phishing attack will be highly effective. The player also needs to know John’s full name and address to make a believable phishing letter (the process of making the letter is automated, the player does not write anything by himself). Thus the action a4 requires a combo-state. After the action graph is constructed using the algorithm outlined above, it is possible to extract the strategy the player used to reach the terminal state.

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4 Action Graph Utility 4.1 Player Strategy Extraction In the developed game the action graph is primarily used for determining the player’s strategy and to ensure that all the questions in the test are related to it. To achieve this a simple algorithm is proposed. Consider the action graph A shown in the Fig. 4. The finishing conditions in this example is {0; 0; 0; 0; 1}, in other words, the game reached its terminal state if the last bit in the sequence is 1.

Fig. 4. Graph A

In this example, the player is attacking Claire and there are 5 facts in the knowledge domain: 1. 2. 3. 4. 5.

“The player knows Claire’s name.” “The player knows Claire’s answer to a secret question.” “The player knows Claire’s e-mail address.” “The player knows Claire’s password.” “The player has access to Claire’s e-mail.”

Figure 4 illustrates a player’s strategy when attacking Claire. The sequence of actions {a1, a2, a3, a4, a5} changes the state of player’s knowledge, however, not all of them are required to reach the goal. To find the winning strategy, the following algorithm is used: 1. Mark terminal node as visited and put all the nodes preceding it in the queue. 2. Get one element from the queue. 3. If the element is not marked, mark it and put all the elements preceding it in the queue (if the element is a starting node, no vertex is added to the queue). Otherwise, the node should be ignored. 4. Check if the queue is empty. If it is not, go to step 2. 5. Extract all the marked elements and convert them to a required data type such as a list or a graph.

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The edges that connect the marked elements make up a player’s strategy. Figure 5 demonstrates what states were marked by the algorithm in the graph A. As you can see, to get Claire’s password the player only needed to perform actions {a1, a3, a5}.

Fig. 5. Graph A with player’s strategy

Actions that are not marked by the algorithm are considered redundant. After the winning strategy was extracted, we can use an action to make a quiz. The action symbol is used to choose the topic of one of the predefined questions, and the preconditions and effects are used to customize the chosen question. As it was mentioned above, each fact in the developed game can be traced to the NPC. Using the effects of the actions it is possible to determine which NPC was subject to a player’s attack. Preconditions are the circumstances in which the attack has happened, thus they can be used to customize the answers. For example, the player can access Claire’s e-mail by finding her paper with Claire’s password written on it, or just by guessing if the password is too simple. In these two situations, the player learns Claire’s password under different circumstances, but the question regarding the situation is the same: “How did you manage to learn Claire’s password?” (Instead of Claire there can be the name of any other NPC). The thing that changes is the right answer. In the first case, the right answer may be “Because Claire is keeping her password written on a paper, which is extremely dangerous.” And in the second case it is “Because her password was too simple, I was able to just guess it.” And if the player a uses phishing attack or a virus on Claire the system can change answers in the test accordingly or choose a different question. It is presumed that by designing the system in such a way, we increase the player’s engagement in the test. Because the player is taking not just some test, but the test about himself or herself, the player hopefully will be interested to return and play again to see other questions. However, this approach does not require a complex system to structure the player’s actions. There are two reasons for such an intricate system to be implemented. Firstly, by using just the winning strategy to make tests for the player, we limit the number of customized questions, so the player cannot see most of them in his or her first game session. Secondly, it is assumed that the player was more mindful of the actions in the winning strategy than the redundant ones. That is because it is hard to win a puzzle game by randomly doing something. The player must study the game and the characters, to

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attack them effectively, because ineffective attacks will fail, and the player will not be able to win. 4.2 Composite Action Graph Another especially useful application of the action graphs is a merge of several action graphs into one composite action graph. If each action graph represents one player’s game session, the composite action graph represents the multitude of game sessions. It allows the developers to study players’ behavior in the game and to determine the most popular strategies. There are two major differences between an action graph and a composite action graph. Firstly, the composite action graph can have multiple terminal states, while the action graph always has only one. Secondly, each edge on the composite action graph is assigned a counter, that is used to showcase how often the player chooses one action or the other. To showcase the operation of the proposed algorithm, the graph A from Fig. 4 and graph B from Fig. 6 are used. Note that these graphs have different terminal vertices. For the sake of simplicity, a1 = b1, a2 = b2, a3 = b3. These actions connect the same partial states, however, in the game action that does so may have varying action symbols, making them essentially different actions.

Fig. 6. Graph B

To merge two graphs into one the following algorithm is proposed: 1. Copy all the nodes and edges from graph A to a composite graph. Assign to all edges counter with the value 1. 2. For each node in graph B check if the composite graph already holds thenode with the same state. If not, add this state to the composite graph. 3. For each arrow in graph B, check if the arrow is present in the compositegraph. If so, increase its counter by 1. Otherwise, create a new arrow. The result of the application of this algorithm to graphs A and B is illustrated on the Fig. 7. A composite action graph can be used to study the game itself. By composing several graphs into one, we can see what strategies were popular among the players and what

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Fig. 7. Result of merging graphs A and B

design problems we may have in the game. For example, if the players chose only shoulder surfing as their main password acquiring strategy and forsake other social engineering attacks (shoulder surfing attacks have higher counter values than any other type of attack), we may want to make peeking passwords more difficult to push the players toward other strategies.

5 Conclusion This article describes the system that tracks a player’s actions and structures them. This system was developed as part of the serious game about social engineering attacks but can be applied to other puzzle or detective games. Knowing what actions, the player performed and in what order allows the game to choose context-specific questions about a player’s game session. The structured form allows identifying redundant actions and player strategies, thus allowing the game to recognize certain behavior patterns and provide the player a reward. It is also useful to identify problems in the game design and analyze players’ behavior. The theoretical and practical significance of the study lies in building the foundation for the development of a gaming environment designed to improve staff skills in the field of protection against social engineering attacks. A further area of the research may be to study the actions of non-player characters, develop appropriate artificial intelligence systems, and develop the more complex player’s test system.

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Acknowledgments. The research was carried out in the framework of the project on state assignment SPIIRAN No 0073–2019–0003, with the financial support of the RFBR (project No 20–07– 00839 Digital twins and soft computing in social engineering attacks modeling and associated risks assessment; project No 18–01–00626 Methods of representation, synthesis of truth estimates and machine learning in algebraic Bayesian networks and related knowledge models with uncertainty: the logic probability approach and graph systems).

References 1. Abramov, M.V., Tulupyeva, T.V., Tulupyev, A.L.: Social Engineering Attacks: social networks and user security estimates. SUAI, St. Petersburg (2018). 266 p. (in Russian) 2. Alqahtani, H., Kavakli-Thorne, M.: Design and evaluation of an augmented realitygame for cybersecurity awareness (CybAR). Information 11(2), 121 (2020). https://doi.org/10.3390/ info11020121 3. Azarov, A.A., Tulupyeva, T.V., Suvorova, A.V., Tulupyev, A.L., Abramov, M.V., Usupov R.M.: Social Engineering Attacks: the Problem of Analysis. Nauka Publ., St Petersburg (2016). 349 p. (in Russian) 4. Beckers, K., Pape, S.: A serious game for eliciting social engineering security requirements. In: 2016 IEEE 24th International Requirements Engineering Conference (RE), Beijing. 16–25 (2016). https://doi.org/10.1109/RE.2016.39 5. Peltier, T.R.: Social engineering: concepts and solutions. Inf. Syst. Secur. 15, 13–21 (2006). https://doi.org/10.1201/1086.1065898X/46353.15., 4.20060901/95427.3 6. Bissell, K., LaSalle, R., Dal Cin, P.: The Cost Of Cybercrime. NinthAnnual Cost of Cybercrime Study (2019). https://www.accenture.com/acnmedia/PDF-96/Accenture-2019-Costof-Cybercrime-Study-Final.pdf. Accessed 12 June 2020 7. Giannakas, F., Papasalouros, A., Kambourakis, G., Gritzalis, S.: A comprehensive cybersecurity learning platform for elementary education. Inf. Secur. J. A Global Perspect. 28(3), 81–106 (2019). https://doi.org/10.1080/19393555.2019.1657527 8. Hart, S., Margheri, A., Paci, F., Sassone, V.: Riskio: a serious game for cybersecurity awareness and education. Compute. Secur. 95, (101827) (2020). https://doi.org/10.1016/j.cose.2020. 101827 9. Russian companies lost 1.26 billion rubles on social engineering, Kommersant, https://www. kommersant.ru/doc/4215008. Accessed 23 May 2020 10. Makhutov, N.A. (ed.): The security of Russia. Legal, social economic and scientifictechnical aspects. IHPF “Knowledge”, Moskow (2018). 1016 p. (in Russian) 11. Newbould, M., Furnell, S.: Playing Safe: a prototype game for raising awarenessof social engineering. In: Australian Information Security Management Conference, pp. 24–30 (2009). https://doi.org/10.4225/75/57b4004e30de7 12. Types of Social Engineering Attacks in 2020, SolarWinds MSP. https://www.solarwindsmsp. com/blog/types-of-social-engineering-attacks-in-2020. Accessed 22 May 2020 13. Thomas, M.K., Shyjka, A., Kumm, S., Gjomemo, R.: Educational design research for the development of a collectible card game for cybersecurity learning. J. Format. Des. Learn. 3(1), 27–38 (2019). https://doi.org/10.1007/s41686-019-00027-0 14. Abass, Islam: Social engineering threat and defense: a literature survey. J. Inf. Secur. 09, 257–264 (2018). https://doi.org/10.4236/jis.2018.94018 15. Yasin, A., Liu, L., Li, T., Wang, J., Zowghi, D.: Design and preliminary evaluation of a cyber Security Requirements Education Game (SREG). Inf. Software Technol. 95, 179–200 (2018)

Mathematical Model for Evaluating Management Processes for Implementing Electronic Document Management Systems Olga Perepelkina1(B)

and Dmitry Kondratov1,2,3

1 Russian Presidential Academy of National Economy and Public Administration,

164 Moskovskaya Street, Saratov, Russia [email protected], [email protected] 2 Yuri Gagarin State Technical University of Saratov, 77 Politechnicheskaya Street, Saratov, Russia 3 Saratov State University, 83 Astrakhanskaya Street, Saratov, Russia

Abstract. The activity of the executive bodies of the State power consists in making management decisions within the framework of the implementation of their powers. The effectiveness of this process is determined by the document flow and records management system (SEDD). The introduction of the SEDD is one of the priorities of the authorities of various levels, the successful implementation of which will ensure the transition to a higher level of their functioning. However, the implementation of the electronic document and office management system in the authorities is not fast enough. Thus, the relevance of the study is caused by the importance of increasing the efficiency of the electronic document circulation system in the executive bodies of the state power, which becomes possible only when applying mathematical models, modern and reliable algorithms and complexes of quality assessment programs according to certain criteria. The purpose of the study is to develop mathematical models, a software complex to improve the performance of executive bodies of state power. The authors have determined that the object of the study simulation is an electronic document circulation system. The main objectives of document flow modeling in executive bodies of state power are: to increase efficiency of management activity; accelerate the movement of documents; to reduce labour input of documents processing. The authors use the formalization method. The main conclusion of the research is, that by mean of using mathematical modeling, a mathematical model of business process optimization was built in the course of implementing an electronic document flow and office management system in the executive bodies of state power. A software package has been developed based on it software complex “Evaluation of management processes from the implementation of SEDD” has been developed in the programming environment C #, which is an object-oriented programming language and is based on a strict component architecture and implements advanced code security mechanisms. Keywords: Digitalization · Digital economy · Digital public administration · Digital transformation · Electronic document management system · Implementation evaluation criteria · Evaluation of the effectiveness of electronic © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 600–612, 2021. https://doi.org/10.1007/978-3-030-65283-8_49

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document management and office management systems · Mathematical modeling · Modeling object · Development of a program complex

1 Introduction The implementation of the activities of Russia on introduction of electronic document management systems and administration (SEDD) began in the mid 90-ies. However, mass introduction of SEDD began only in the XXI century, and in many state and commercial structures to the introduction of SEDD started only in recent years. The development of SEDD is constrained by the framework of traditional technology for working with documents and document management, this is on the one hand, and on the other, weak integration with other information technologies and systems used in the management of organizations [1–3]. Nowadays most of the developing countries use a traditional paper documents management system (DMS), but also the electronic form of the documentation has increased including e-mails, web pages, and database packages, which have been stored in workstations and servers. For integrated data gathering in an institution or organization, electronic document management system (EDMS) often becomes one of the most required tools for management. However, this requirement should be implemented carefully depending on the institution or organization need. Therefore, organization should have an EDMS for creating, keeping and organizing data in the organization and handle all synchronization process [4]. The study of process management, processes of internal and external document flow, information flow, SEDD, and the study of problems related to the workflow involved many scientists, for example, I.L. Bachilo, D.A. Divers, T.A. Polyakova, I.M. Brines, N. And. Solovianenko, S.I. Semiletov, A.A. Fatyanov, P.O. Khalikov, A.B. Shamraev, and foreign D. SCOM, R. hills etc. You can agree with the opinion expressed in the work Fabrizio Errico, Università del Salento, Angelo Corallo, Rita Barriera, Marco Prato that nowadays, every organization have to manage several documents and the number and volume of these will grow more and more, causing a substantial increase in management costs and slowing down the process of recovering useful information at the desired time. Document Management Systems (DMS) are currently a very hot topic because companies can significantly improve their efficiency and productivity through their adoption and use. Solution presented a document management solution based on a semantic classifier and a semantic search engine, able to support a company in the correct management, archiving and research of documents. A Case Study approach is used through which has been analyzed potential benefits for companies, such as the reduction of problems related to the loss of paper documents and the costs related to their management, the resolution for the recovery and archiving of paper and/or thimble documents and the reduction of search time [5]. An office automation system means any automated system designed to solve the tasks of office management, regardless of the object of automation, whether it be a state authority, a commercial bank, a trading company or any other organization. It is important

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that this organization carry out office work, and that it be carried out in accordance with the requirements put forward by Russian law, which allows you to clearly outline the range of tasks to be solved [6]. At present, digital technologies, innovative business models penetrate into all spheres of society, having a significant impact on the economy, forming qualitative structural changes in it. It is possible to agree with the view expressed by many researchers that mankind has entered a new era of global change thanks to digitalization and other technological changes [7–10]. As a result, the digital economy is formed as a subsystem of the traditional economy, characterized by the active use of digital technologies and the circulation of specific electronic goods. Digitalization is introduced into all social processes and increasingly depends on the people‘s successful life and there is a largescale implementation of digital technologies into the work of government organizations and structures [11]. The document lives in anticipation of major changes in the company Aktivterm digital transformation. And they are connected primarily with the necessity to use more complex and systemic solutions, involving no separate operations management, and all phases, stages and operations [12, 13]. The tasks of the federal project “Digital State Administration” of the national program impose requirements into the activities of state authorities and local selfgovernment bodies, as well as organizations under their jurisdiction for digital transformation of the state (municipal) service, namely the introduction interdepartmental legally significant electronic document circulation with the use of electronic signature, based on unified infrastructure, technological and methodological solutions with a period of execution - 31.12.2024 [14]. In order to implement the tasks set, it is necessary for all state authorities and local self-government bodies (hereinafter referred to as “the Authorities”) to use electronic document circulation and record-keeping systems (hereinafter referred to as “SEDD”). However, the implementation of the electronic document management system is not fast enough, which is largely due to the lack of a clear system for monitoring the effectiveness of the implementation of electronic document management and office management, which prevents rapid adjustment and appropriate changes in the system. In such a case, all authorities must use the same electronic document management system or electronic document management system to easily communicate with each other, which is a particularly relevant issue in the transition of authorities to Russian software. The search for possible ways to create a unified electronic document flow system requires an analysis of the effectiveness of the system implementation, which is one of the main tasks of our study. The results of the analysis will help to select the optimal strategy of using the electronic document circulation system in the authorities, which can be recommended for optimization of the electronic government system [15]. The search for possible ways to create a single SEDD requires the analysis of the effectiveness of the implementation of the system, which is one of the main tasks of our study. The results of the analysis will help to choose the optimal strategy of SEDD use in the Authorities.

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2 Research Methods The results of the study are based on the use of theory of system analysis, methods of structural analysis and design, method of formalization, mathematical modeling, modern technologies of data storage and processing. The methodology of the study relies on the results of discrete mathematics, the theory of object-oriented design. To obtain theoretical results, deductive reasoning, construction of practical models, which is implemented by mathematical modeling methods, are carried out. The development of the software product is carried out by using object-oriented programming language - C #.

3 Results and Discussion Modeling is the process of developing abstract models of a system, where each model represents your opinion or perspective of that system. Under the modeling usually refers to the performance of the system using some graphical notation, which is now almost always based on notations in the unified modeling language (UML). Simulation is widely used in various spheres of human activity, especially in the areas of design and management, where special processes are making efficient decisions on the basis of the received information. A mathematical model is a set of equations or other mathematical relationships that reflect the main properties of the studied object or phenomenon within the accepted speculative physical model and characteristics of its interaction with the environment on the spatial temporal boundaries of its location. Currently, mathematical models are used in many branches of modern science. Mathematical models are tools to describe a variety of problems. The range of these tasks is very wide, includes various areas of human activities: education, research activities, technical design, mechanics, medicine, Economics, ecology, etc. Correctly constructed mathematical model allows to describe the most significant relationships between the objects, predict object behavior in different conditions, to evaluate different parameters dependencies, to predict the negative consequences, then determine the best solution [16]. Consider the definition of “mathematical model”. In a short article by A. N. Tikhonov’s mathematical encyclopedia this term is defined as an approximate description of some class of external phenomena, expressed by mathematical symbols. The mathematical model is defined as an object - the Deputy of the object - the original, providing a study of some properties of the original [17]. In the work of A. D. Myshkis [18] defines a mathematical model as a system of equations, or an arithmetic of ratios, or geometric shapes, or a combination of both, the study of which by means of mathematics should answer questions about the properties of some set of properties of a real world object. Consequently, mathematical modeling is the construction and study of mathematical models. In A. A. Lyapunov, mathematical modeling is an indirect, practical or theoretical study of the object which is studied is not itself directly of interest to us object, and some auxiliary natural or artificial system (the model), which is in a

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accordance with an objective knowable object that can replace it in certain relations, and giving in its study, eventually, information about the simulated object [19]. In their work, under the mathematical modeling we mean the process of establishing the actual object of a particular mathematical object called a mathematical model. The main purpose of modeling the optimization of business processes implementation of SEDD are the following indicators: productivity of administrative activities; accelerate the movement of securities; reducing labor costs for processing securities. The simulation object of our study is SEDD. The main objectives of modeling of document flows in executive bodies of state power (hereinafter - IOGV) are: to increase efficiency of management activity; to accelerate the movement of documents; to reduce labour input of documents processing. In recent years, there has been a significant increase in the volume of documents in the authorities. In this regard, one of the most important tasks now in the public administration system is to streamline the process of case management, which is the key to maintaining and increasing the productivity of the employees of the authorities. The analysis of the time spent on paper and electronic document circulation carried out in the authorities of the Penza region showed that on average, an IOGV employee spends six times more time creating a document on paper than on its electronic image. Electronic document circulation significantly reduces the travel time of documents between the Government of Penza region and the authorities, as well as saves budgetary money spent on the purchase of paper. To assess the level of use of SEDD the authorities is possible using various indicators, such as estimating the cost of SEDD and functional characteristics, efficiency of use, etc. The effect of the introduction of electronic document management system can be time-divided into two parts: the direct effect of the implementation of the system, associated with the savings on materials, staff time, etc., the indirect effect associated with the benefits to the functioning of the organization that gives electronic document management system (transparent management, discipline control, accumulation of knowledge etc.). The second group of effects includes timeliness and speed of decision-making; faster document processes (harmonization, approval, etc.), optimization of processes related to document flow; improvment their transparency and control over information flows and processes in IOGV. The decision of problems of quality management implementation SEDD possible in the case of the use of mathematical modeling, including constructing mathematical models of optimization of business processes implementation of SEDD. Indeed, effective quality management is impossible without replacing the subjective descriptions of rigorous objective evaluations of the implementation of SEDD that allows to make the method of constructing the mathematical model. There are many different types of models and associated modeling languages of different aspects and different types of systems. Since different models serve different purposes, the classification models may be useful for choosing the right type of model for the intended purpose and application.

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We will define the basic types of mathematical modeling: formal and informal models; physical and abstract models; descriptive and analytical models (analytical models can be further classified into dynamic and static patterns); system models; computer modeling. Building a model of optimization of business processes implementation of SEDD possible with the help of graph model. Using graph models or graph language allows not only to simulate the processes and to work with them, but also to carry out operations on processes operations on graphs. For example, through the use of graph operations from simple processes to model more complex as a set of simple, as a separate process the necessary part of the process, and similar operations [20]. The model represented by sets of participants, actions and States of documents can be represented as matrices. The relationship between the States of the documents, the actions available to participants, and scenarios can also be described by matrices. Logical modeling of SEDD. The purpose of this type is the development of a set of UML diagrams that reflect different aspects of the logical model of SEDD. The implementation of large-scale, complex SEDD is a time-consuming and longterm process, requiring a significant amount of resources. Their development and adaptation to specific tasks, the development of universal design solutions using advanced information technologies becomes an urgent task, which cannot be solved without the use of systems analysis and mathematical modeling methods [21–24]. Mathematical models tend to be the basis for the development of software packages using software tools that are used, including for management tasks. Imagine the optimization of business processes in the implementation of SEDD in the form of a mathematical model. When optimizing business processes when implementing SEDD to the Authorities, the following criteria are the current indicators: – – – – – – – – – – – – –

Total share of documents registered in SEDD,%; Percentage of incoming documents registered in SEDD,%; Percentage of outgoing documents registered in SEDD,%; Share of organizational and administrative documents registered in SEDD,%; Average number of documents generated by 1 employee per month, pcs.; Time spent on creating internal documents during electronic document flow, hour/month; Time spent on creating internal documents with mixed workflow, hour/month; Paper time per month, hour; Time spent on electronic document circulation per month, hour; Reference time spent by employees for full electronic document flow per month, hour; Actual time spent by employees with mixed workflow per month, hour; Saving time per month, hour; Economic effect when using SEDD (rate release), units.

However, when implementing SEDD in IOGV, as well as when optimizing the number of full-time staff of IOGV, the issue of optimization of business processes - reduction of employees (full-time units) who are engaged in business management in IOGV (economic effect in the use of SEDD, release of job rates in IOGV) is relevant.

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We will present the optimization of business processes when implementing SEDD in the form of a mathematical model. To do this, we introduce criterion values (constants): – – – – – – – – – – – – – – – – – – – – – – – – –

Total number of employees, persons – A. Number of employees working with electronic documents (in SEDD), persons – C. Number of IOGV employees registered in SEDD, persons – B. Number of employees working with paper documents (not registered in SEDD), persons – E. Total documents (total number of documents in IOGV (electronic and paper), pcs. – D. Total documents in SDDS (number of electronic documents in databases (VCD, ISCD, GNI, ORD, OG), pcs. – ED. Number of paper registration cards, pcs. – BD. Total share of documents registered in SEDD,% - ED%. Total incoming documents, pcs - Dvx. Total incoming documents registered in SEDD, pcs. - EDvx. Percentage of incoming documents registered in SEDD,% - EDvx%. Total outgoing documents, pcs. - Dix. Total outgoing documents in electronic form, pcs. - EDix. Percentage of outgoing documents registered in SEDD,% - EDix%. Total organizational and administrative documents, pcs. - Dor. Share of organizational and administrative documents registered in SEDD,% - Dor%. Average number of documents generated by 1 employee per month, pcs. - Dcr. Time spent creating internal documents during electronic document flow, hour/month - V vned. Time spent creating internal documents with mixed workflow, hour/month - V vnd. Time spent on paper workflow per month, hour/month - V d. Time spent on electronic document circulation per month, hour - V ed. Reference time spent by employees for full electronic document flow per month, hour - V eed. Actual time spent by employees with mixed workflow per month, hour - V fd. Saving time per month, hour - V e. Economic effect when using SEDD (rate release), persons - S ek.

Using criteria values, we will build a mathematical model optimization of business processes when implementing SEDD. The mathematical calculation is presented in the following form S ek . Where: Average number of documents generated by 1 (one) employee per month, pcs. (Dcr ): Dcr =

D A

(1)

Paper time per month, hour (V d ): Vd = E ∗ Dcr ∗ 0, 25

(2)

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Time spent on electronic document circulation per month, hour (V ed ): Ved = C ∗ Dcr ∗ 0, 08

(3)

Reference time spent by employees for full electronic document flow per month, hour (V eed ): Veed = A ∗ Dcr ∗ 0, 08

(4)

Actual time spent by employees with mixed workflow per month, hour (V fd ): Vfd = Vd + Ved

(5)

Saving time per month, hour (V e ): (6) Economic effect when using SEDD (rate release), units (S ek ): Sek = Ve /176

(7)

The constructed mathematical model (after performing the necessary transformations) is presented in the following form:

(8)

So, the developed model is designed to simulate and predict the indirect effect (which is most difficult to estimate when implementing SEDD) related to the advantages for the functioning of the organization provided by SEDD (transparency of management, control of executive discipline, possibility of knowledge accumulation, etc.). The model allows the head of the Authority to make management decisions taking into account the factors of influence. The software complex “Evaluation of management processes from the implementation of SEDD”(software complex “Evaluation of management processes from the implementation of SEDD”) based on the designed mathematical model was made. The software complex “Evaluation of management processes from the implementation of SEDD” is designed to assess the effectiveness of SEDD implementation in the Authorities at various levels, in organizations (enterprises), as well as it can be applied in organizations engaged in implementation of electronic document circulation. The development of the software complex “Evaluation of management processes from the implementation of SEDD” used an object-oriented programming language, C

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#, which is based on a strict component architecture and implements advanced code security mechanisms. The software complex “Evaluation of management processes from the implementation of SEDD” is designed to run on operating systems such as Windows XP and above (including Windows 10). The block diagram of the software complex “Evaluation of management processes from the implementation of SEDD” is given in Fig. 1.

Fig. 1. The block diagram of the software complex “Evaluation of management processes from the implementation of SEDD”

Consider the functionality of the software complex “Evaluation of management processes from the implementation of SEDD” Figure 2 shows the software complex “Evaluation of management processes from the implementation of SEDD” interface. Here is a description of the main sections of the software complex “Evaluation of management processes from the implementation of SEDD”, which contains 2 sections: “Data” and “Calculation.” The section “Data” is used to enter the necessary information for calculation and contains the following indicators, which are presented in Fig. 3.

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Fig. 2. The interface of the software complex “Evaluation of management processes from the implementation of SEDD”

Fig. 3. The section “Data” of the interface of the software complex “Evaluation of management processes from the implementation of SEDD”

When entering the necessary data, the user can either enter the data from the keyboard himself or use the import of the previously completed file in .xls format. After the import is completed (or the data is filled manually - at the user ‘s choice), the data is automatically calculated and the charts are built (each chart can be selected by the user). The user can also add or remove the year and print the information if necessary.

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The section “Calculation” software complex “Evaluation of management processes from the implementation of SEDD” is used to perform calculations, the indicators of which are presented in Fig. 4.

Fig. 4. The section “Calculation” of the software complex “Evaluation of management processes from the implementation of SEDD”

The software complex “Evaluation of management processes from the implementation of SEDD” is designed to assess the effectiveness of SEDD implementation in the Authorities at various levels, in organizations (enterprises), as well as it can be applied in organizations engaged in implementation of electronic document circulation. The certificate on the state registration of the computer programs No. 2019612943 for a program complex is received. Date of state registration in the Register of Computer Programs - 05.03.2019.

4 Conclusion Thus, the result is a software system designed for “ Evaluation of management processes from the implementation of SEDD “ on the basis of the mathematical model of optimization of business processes implementation of SEDD that allows you to evaluate different parameters of the dependencies and to determine the economic effect of the introduction of SEDD. The software complex “Evaluation of management processes from the implementation of SEDD” is designed to assess the effectiveness of SEDD implementation in the Authorities at various levels, in organizations (enterprises), as well as it can be applied in organizations engaged in implementation of electronic document circulation. The use of the software package “ Evaluation of management processes from the implementation of SEDD” allowed the Ministry of industry of the Penza region to

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implement measures to optimize the number of full-time employees who are engaged in office management.

References 1. Avtomatizatsiya dokumentooborota — osnova dokumentatsionnogo obespecheniya upravleniya: InterTrast URL: http://www.intertrust.ru/products/companymedia/biznesreshen iya/dokumentatsionnoe-obespechenie-upravleniya/. (data obrashcheniya: 14.07.2020). (In Russian) 2. Kuznetsov, S.L.: Deloproizvodstvo na kompyutere: Kompyuternyye tekhnologii v deloproizvodstve / S.L. Kuznetsov. - M.: ZAO « Biznes-shkola « Intel – Sintez » . - s.232 (2008). (In Russian) 3. Larin, M.V.: Upravleniye dokumentatsiyey i novyye informatsionnyye tekhnologii / Larin, M.V.: - M.: Nauchnaya kniga. 137s (2008). (In Russian) 4. Ismael, A., Okumus, I.: Design and implementation of an electronic document management system. Mehmet Akif Ersoy Üniversitesi Uygulamalı Bilimler Dergisi. 1. 9–17 (2017). https:// doi.org/10.31200/makuubd.321093 5. Fabrizio, E., Corallo, A., Barriera, R., Prato, M.: Dematerialization archiving and recovery of documents: a proposed tool based on a Semantic Classifier and a Semantic Search Engine. 297–301. https://doi.org/10.1109/ICITM48982.2020.9080389 6. Efimova, O.A.: Modern system of office automation In the torture of the analysis and classification. Efimova, O.A., the Secretarial de-lo.-2000.– No. 4.–pp. 37–42 7. Pshenichnikov, V.V.: Prospects and risks of the use of electronic money in the context of digitalisation of the economy. Bulletin of Saint-Petersburg State Economic University. No. 1 (109). pp. 39–45 (2018) 8. Volkova A.A., Plotnikov V.A., Rukinov M.V. Digital Economy: Essence of the Phenomenon, Problem and Risks of Formation and Development. Administrative Consulting. 2019;(4):38– 49. (In Russ.) https://doi.org/10.22394/1726-1139-2019-4-38-49 9. Decree of the President of the Russian Federation dated 09.05.2017 No. 203 “On The strategy for the development of the information society in the Russian Federation for 2017–2030 » 10. Resolution of the Government of the Russian Federation of 28.07.2017 No. 1632-R “On approval Of the program for the development of the digital economy of the Russian Federation 11. Decree of the President of the Russian Federation dated 07.05.2018 No. 204 “On national goals and strategic objectives for the development of the Russian Federation for the period up to 2024 » 12. Zhurikhin E. Elektronnyy dokumentooborot: vozmozhnosti ispolzovaniya i vnedreniya/ E. Zhurikhin// Upravlyayem predpriyatiyem. 2012. № 12(23). S. 1–7. (In Russian) 13. Satton M. Dzh. Korporativnyy dokumentooborot. – M.: Azbuka. 2002. 448 s. (In Russian) 14. The national programme “Digital economy of the Russian Federation” approved the minutes of the meeting of the Presidium of the presidential Council of the Russian Federation for strategic development and national projects of 04 .06.2019 No. 7 15. Perepelkina O., Kondratov D. (2019) Mathematical Modeling of Electronic Records Management and Office Work in the Executive Bodies of State Administration. In: Dolinina O., Brovko A., Pechenkin V., Lvov A., Zhmud V., Kreinovich V. (eds) Recent Research in Control Engineering and Decision Making. ICIT 2019. Studies in Systems, Decision and Control, vol 199. Springer, Cham 16. Borgoyakov T. G., lozitska E. V. Mathematical modeling: definition, applicability of the models of educational process // Internet-journal “science of SCIENCE” Volume 9, No. 2 (2017) http://naukovedenie.ru/PDF/82TVN217.pdf (access is free). Tit. screen. Yaz. eng., eng

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17. Sovetov B. Y., Yakovlev S. A. Modeling of systems [Text]: textbook. for universities, 3rd ed., Rev. and extra - M.: Higher. wk., 2001. - 343 p. - p. 6 ISBN 5-06-003860-2 18. Myshkis A. D. elements of the theory of mathematical models [Text] - 3-e Izd., Rev. - M.: Komkniga, 2007. - 192 p. ISBN 978-5-484-00953-4 19. Novikov I. B. philosophical questions cybernetic modeling [Text] - M., Znanie, 1964 20. Krukovsky M. Y. Software complex system support composite workflow based on process models // Matematicheskiy i systems. - 2016. - No. 1. – P. 81–92 21. Chen H. Business Intelligence and Analytics: from Big Data to Big Impact / H. Chen, R. H. L. Chiang, V. C. Storey // MIS Quarterly : Management Information Systems. – 2012. – Vol. 36, No. 4. – P. 1165 – 1188 22. The Evolution, Challenges, and Future of Knowledge Representation in Product Design Systems / S. K. Chandrasegaran [et al.] // Computer-Aided Design. – 2013. – Vol. 45. – P. 204 – 228. https://doi.org/10.1016/j.cad.2012.08.006 23. Ghani, E. K. Development of Integrated Information Management System Service Quality Model in an Accounting Faculty / E. K. Ghani, K. Muhammad, J. Said // International Journal of Business and Social Science. – 2012. – Vol. 3, No. 7. – P. 245 – 252 24. Anvari, A. An Investigation of Innovation in Higher Educational Environments A Consideration of Five Substructures (Technical, Administrative, Information Systems, Information Technology and Knowledge Management) / A. Anvari, G. A. Alipourian, R. M. A. TalebBeidokhti // Middle-East Journal of Scientific Research. – 2012. – No. 11 (9). – P. 1278 – 1285. https://doi.org/10.5829/idosi.mejsr.2012.11.09.3780

Smart City Technologies and Internet of Things

«Smart Cities» as Digital Transformation Centers: The Case of Modern Russia Svetlana Morozova(B)

and Alexander Kurochkin

Faculty of Political Science, St. Petersburg State University, Smolny St., 1/3, 191124 St. Petersburg, Russia [email protected]

Abstract. The article is devoted to studying the experience of implementing Smart City projects in modern Russia in the context of global process of digital transformation of economical and social interactions. The conceptual part of the Smart City technologies is analyzed, at the same time as its practical implementation in decision making processes. Particular attention is paid to the projects, aimed at maximizing of effectiveness and quality of Citizens to Government interactions by means of digital platforms and online services. The analysis of such projects currently being implemented in the Russian Federation has led to the conclusion that the availability of digital technologies for the majority of citizens is not enough. In addition, there is still a significant digital divide at both the cross-regional and cross-social group levels, which is largely determined by a low level of awareness and willingness to innovate in the economy and public life. Recommendations regarding the active involvement of citizens in urban development issues in order to improve the efficiency of urban governance are presented. Keywords: Urban governance · Smart city · Digital transformation · Information and communication technologies · Innovative infrastructure

1 Introduction The dominant economic and demographic relevance of cities in the modern world poses fundamentally new challenges for the sphere of urban development. The dynamics of urban population growth is comparable today with the pace of information and communication technologies development and, accordingly, the growth in the volume of information produced and consumed. If in the 1900s. The urban population of the planet was no more than 200 Mio. People, then by the end of the 1990s it exceeded 3.5 billion people, and by 2050 with the current dynamics of resettlement (daily up to 200 thousand people), it will reach 70% of the total [1]. By the end of the 21st century, the urban population of the Earth is projected to grow to 8 billion people, with a total population of 10 billion. Under such conditions, for example, India will have to build one Chicago a year to satisfy the demand of new citizens for housing, and China has already announced plans to build annually 20 new © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 615–626, 2021. https://doi.org/10.1007/978-3-030-65283-8_50

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cities per year (totaling more than 12 Mio. Inhabitants) to accommodate future dwellers [2]. The denser the communication space of a modern city becomes, the more connections are present and their structure are more complex, the more likely breakthroughs in the innovative development of the city are and the higher its global competitiveness is. «Cities are the lack of physical space between people and companies. They are intimacy, density, neighborhood. They allow us to work and have fun together…., accelerate innovation, connecting smart citizens with one another,… Become portals through which contact is made between markets and cultures» [3]. But on the other hand, rapidly growing urban agglomerations significantly expand the range of problems that they inevitably face in their development: the growth of lowskilled labor, excessive density, transport problems, growing environmental pressure, changing demands of residents and businesses on the quality of the urban environment and services. Under these conditions, there is a gradual revision of approaches to urban development management, which is increasingly based on advanced technological solutions, digitalization and platforming. Ideally, there is a transition to an integrated digital urban ecosystem that responds to emerging challenges, contributes to meeting the needs of all participants (residents, businesses, authorities, etc.), as well as provides more efficient integration of individual components of urban infrastructure. For a conceptual understanding of such a transition, the term «smart city» is used. This concept is interpreted differently, but in any approach, the key role is given to information and telecommunication technologies that help to support the current processes of urban life more efficiently and solve emerging problems through the involvement of citizens, business and authorities. This article is based on the definition proposed by experts of the International Telecommunication Union (ITU) following a detailed analysis of more than 100 approaches to this concept. «A smart sustainable city is an innovative city that uses information and communication technologies (ICTs) and other means to improve quality of life, efficiency of urban operation and services, and competitiveness, while ensuring that it meets the needs of present and future generations with respect to economic, social, environmental as well as cultural aspects» [4]. In this vein, the sustainability of digital urban development is of particular importance, which is understood as the ability of the urban management system to keep changes in the urban environment within the given parameters, quickly restoring balance, adequately responding to external influences and preserving its own integrity and identity. Based on network, institutional, structural-functional and comparative scientific approaches this article proposes desirable conditions for the effective smart city technology implementation and recommendations on the active involvement of citizens in smart urban development issues.

2 Theoretical Framework and Methods As noted above, «Smart cities» has become the most popular notion for the future city development, and is also becoming a globally recognized term, replacing or co-existing

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with ones in other languages. The «smart city» has displaced the «sustainable city» and «digital city» as the word of choice to denote ICT-led urban innovation, and new modes of governance and urban citizenship [5]. The concept of «smart city» is one of the most widespread up-dated concepts which contains ideas about the future of the cities and ways their problems should be solved. Mark Deakin defines the «smart city» as one that utilizes ICT to meet the demands of the market (the citizens of the city), and states that community involvement in the process is necessary for a «smart city» [6]. Agreeing with Husam Al Waer’s ideas in the research «From intelligent to smart cities» [7], he draws attention to factors that constitute the «smart city» definition: applying a wide range of electronic and digital technologies to communities and cities; using ICT to transform life and working environments within the region; embedding ICTs into government systems; introducing practices that bring ICTs and people together to enhance the innovation and knowledge they offer. Rudolf Giffinger and his co-authors define «smart city» as «Regional competitiveness, transport and Information and Communication Technologies economics, natural resources, human and social capital, quality of life, and participation of citizens in the governance of cities» [8]. Caragliu and Nijkamp emphasize that «a city can be defined as ’smart’ when investments in human and social capital and traditional (transport) and modern (ICT) communication infrastructure fuel sustainable economic development and high quality of life, with wise management of natural resources, through participatory action and engagement» [9]. As the Spanish economist, the expert in the field of «smart» cities Gildo Seisdedos remarks, the «smart city» concept means the efficiency reached on the basis of intellectual management and integrated by ICT as well as active participation of citizens in the city development [10]. Thus, two key components of the smart city concept can be distinguished: infrastructural and participative. These components are undoubtedly interconnected, but the final effectiveness of the implementation of a smart city project depends primarily on the degree of balance in their implementation. There is no coincidence that the famous urbanist J. Jacob noted: «Big cities are only capable of giving something to everyone when everyone takes part in their creation» [11]. Of great importance is also a discussion on combining the goals of technological development of cities, digitalization of the economy and social life (which makes them «smart») and the principles of sustainable development, ensuring high-quality ecology, development of urban public spaces and commons. We find an original solution to this problem in the proposal to combine two qualitative characteristics: sustainability and smart in one definition of smart sustainable city. A Smart sustainable city is defined as «an innovative city that uses ICTs and other means to improve quality of life, efficiency of urban operation and services, and competitiveness, while ensuring that it meets the needs of present and future generations aspect to economic, social, environmental as well as cultural aspects» [12]. An accurate description of a sustainable city was given by Manuel Castells, who referred to those cities in which «its conditions of production do not destroy over time the conditions of its reproduction» [13]. It is also quite common in the literature evaluation of sustainable urban development in terms of «achieving a balance between the

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development of the urban areas and protection of the environment with a view to equity in income, employment, shelter, basic services, social infrastructure and transportation in the urban areas» [14]. To sum up, it is important to remark that creating the conditions for city development, providing uniformity of economic and social development of the country’s territories due to growth of their own competitiveness becomes a key challenge today. The relations of interaction and cooperation are based on the most effective use of limited resources (primarily intellectual) and that is why they play the key role here. «Smart cities» can be defined as the systems integrating the following directions (axes) within uniform city space [8]: • • • • • •

Smart Economy; Smart Mobility; Smart Environment; Smart People; Smart Living; Smart Governance.

These 6 axes have to be connected to traditional regional and neoclassical theories of city growth and development. A key feature of the methodology of our analysis is the combination of network, institutional and comparative scientific approaches to urban governance. The network approach allowed us to consider the process of development and implementation of intelligent systems as a network interaction of all stakeholders (urban citizens, local communities, public and non-profit organizations, professional associations, representatives of large, small and medium-sized businesses, representatives of government bodies). The government should act as an initiator of such interactions, ensuring the identification of the interests of all participants and exercising control over their activities. The comparative approach enabled a value analysis of theoretical substantiations of the smart city concept and innovation projects of implementing the smart city model in public urban governance. In addition to the above humanitarian methods of scientific analysis, we used the method of statistical research, which allowed us to identify the specifics of the development of smart city technologies in Russian urban management.

3 Statement of the Problem For the successful implementation of the smart city strategy it is necessary to have, first, a progressive, modern institutional environment, a developed infrastructure, including ICT infrastructure and its readiness for innovation, monitoring, data collection, data processing, and complex decision making. Secondly, an important condition is the presence of a developed city management system with smart users, a high level of management system readiness for changes, ensuring the consumption of services in the conditions of their digitalization, as well as stimulating its further development.

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Innovation culture in Russia faced with problem of low awareness and readiness to implement innovations in the economy and public life. Therefore, one of the paramount tasks of Russia’s strategy of digital transformation is the implementation of initiatives to improve the quality of the innovative culture in the country. For the successful implementation of the smart strategy, it is important to prepare citizens for life in a smart city. In this article we will offer our recommendations on the active involvement of citizens in smart urban development issues in order to improve the efficiency of public governance in the sphere of innovations.

4 Discussion In Russia the Smart City project is aimed at improving the global competitiveness of cities, creating an effective urban management system, creating safe and comfortable living conditions for citizens. It is based on the following key principles: • • • • •

human orientation; manufacturability of urban infrastructure; improving the quality of urban resource management; comfortable and safe environment; focus on economic efficiency, including the service component of the urban environment [15].

The main tool for implementing these principles is the widespread adoption of advanced digital and engineering solutions in urban public governance. The Smart City project is officially implemented in the Russian Federation by the Ministry of Construction and Housing and Communal Services of the Russian Federation as part of the national projects «Housing and Urban Environment» and «Digital Economy». A working group for the implementation of the Smart City project has been created under the Ministry of Construction and Housing and Communal Services of the Russian Federation, which includes representatives of all interested federal and regional authorities, representatives of housing and communal services, major technology developers, expert community, universities and centers of competencies, as well as leading international experts [15]. Thus, the goal of the Smart City project in Russia is not only to digitally transform and automate processes, but also to comprehensively improve the efficiency of urban infrastructure. With the support of Rostec, Rosatom and Rostelecom, the National Competence Center of the Smart City project was created, which is engaged in the development, implementation and popularization of technologies, equipment, programs aimed at improving the digitalization of the urban economy, as well as preparing and providing promoting international cooperation projects on housing policy, urban development and natural resource management, especially concerning the creation and functioning of smart cities.

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It is important to note that smart city projects implemented to date all over the world have their own specifics. Some of them are highly specialized and aimed at solving specific problems, for example, protecting natural resources, strengthening environmental sustainability and improving the efficiency and quality of natural resource management through the use of the latest technologies. The most successful example of the implementation of the described strategy is Amsterdam. Amsterdam’s Smart City project aims to reduce emissions, save energy and leverage technological advances to optimally transform the urban environment. The Amsterdam authorities, in collaboration with local businesses and corporations, have tested the most sustainable solutions (energy efficient lighting, waste reduction, etc.) on Utrechtsestraat, the city’s main shopping street. As a result, energy consumption at Utrechtsestraat has been reduced by 10%. Other projects are more multipurpose and aim to transform a wide range of urban functions into smart ones. For example, the Smart City Seoul project is being carried out with the aim of transforming traditional urban governance into smart ones and improving the quality of life. It is a people-oriented or human-centric project, which aims to implement as many smart technologies as possible, but also to create a more collaborative relationship between the city and its citizens [16]. It should also be noted that the smart city projects differs in Europe and Asia. European countries usually have a social dimension, while Asian countries have a technological dimension [17]. So, London is the smartest city when it comes to human capital and international relations (passenger traffic at airports, number of hotels and restaurants), and one of the best metropolises in terms of transport, economy, management and urban planning. Whereas Tokyo, the smartest city in the Asia-Pacific region and hosting the 2021 Olympics, is working to introduce the most advanced security measures including facial recognition technology and the use of self-driving taxis to transport athletes and tourists. London, New York, Paris, Tokyo, Reykjavik, Copenhagen, Berlin, Amsterdam, Singapore and Hong Kong are the smartest cities in the world, according to Cities in Motion Index 2020, prepared by the University of Navarra Business School in Spain (IESE Business School) [18]. Moscow took only the 87th place in the ranking. In the study, cities were assessed based on the following indicators: the economy, human capital, international projection, urban planning, the environment, technology, governance, social cohesion and mobility and transportation. The results of this rating allow us to conclude that the leaders in the development of smart city technologies are, for the most part, the largest megacities in the world with a high level of labor productivity, human capital, quality of life, economic development and innovation. These cities are densely populated and attractive for tourists, what necessitates the optimal transformation of the urban environment through the use of the latest technologies in the field of urban and transport mobility, safety, environmental protection, and improving the efficiency of urban management and planning. Thus, on the one hand, the transformation of traditional urban functions into smart ones is the most important achievement of urban management in the context of globalization and digitalization, on the other hand, it is, rather, a forced necessity.

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5 Results In order to identify the specifics of the development of smart city technologies in Russian urban management, we analyzed the implemented to date «smart» projects presented on the official smart city platform, named «Solution Bank» [19]. The study was based on a quantitative and qualitative analysis of the platform’s content. To achieve this goal, we used the method of statistical research, consisting of the following main stages: statistical observation, summary, data analysis. We chose a type of discontinuous observation to obtain the information needed to date and carried out statistical observation using external secondary data (open access database). So, within a month we reviewed 364 projects, studied their characteristics, goals and business schemes. We also evaluated expected and achieved effects from the projects’ implementation, thus identifying their effectiveness. The analyzed projects offer smart solutions to problems related to various areas of the urban environment: information city and systems (180 projects), security (47), energy efficiency (41), transport (40), water supply (14), heat supply (11), energy supply (10), ecology (10), construction (6), waste (5). Using MS Excel, we have made a simple summary of the results. Based on the information received, we have determined the smartest cities in Russia: Moscow (96 projects), St. Petersburg (64), Yekaterinburg (47) and Novosibirsk (39). We have also identified the most extensive «smart» projects being implemented in Russia, which are presented in Table 1. Table 1. The most extensive Russian «smart» projects Smart Project

Cities

Content

Smart Meter

140

A system of integrated energy accounting, a «transparent» system of payments and the possibility of tariff regulation. For the rapid deployment of the developed infrastructure of such systems, it is proposed to use the existing infrastructure of mobile operators (as an example) with a wide range of presence in the Russian Federation

Wireless metering of electric energy WAVIoT

88

A system of wireless collection of indications and management of electricity and water supply resources

Server for data collection and storage

87

Autonomous system for collecting data from household and domestic appliances for metering gas, water, electricity based on the BBT-x communication module

The Smart-Subscriber hardware and software complex

87

It performs integrated home automation control and ensures the coordinated operation of all engineering systems in the house

Source: Author’s own work.

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Instruments for financing the above projects are contracts, concessions, subsidies, grants, own funds. Despite the fact that Russian projects in the field of digital modernization of cities are mostly often connected with the electric power industry, the evidence of which is provided by the above statistics, such areas as transport, mobility, and public safety are also reflected in smart projects: • Organization of a system of cashless payment for travel in public transport based on transport and / or bank payment cards (20 cities) • The ITLINE informing system (17 cities) is a connecting link between public transport and passenger throughput. ITLINE stop displays work automatically and update information online. Due to the large amount of memory, the board is able to store information on more than 60 public transport routes in a buffer. • Automated Transport Management Information System (8 cities). The transport management information system is a high-tech software package that is a key component of monitoring and control systems for moving objects using data from satellite navigation systems. • Integrated IT System for Public Transport - Smart Bus (5 cities). It increases road safety, makes transport more accessible and convenient for passengers. A comprehensive IT system is installed on the vehicle, which brings together a media center, video surveillance system, GLONASS system and various sensors. Existing initiatives are mostly local and cover a narrow range of infrastructure modernization tasks. As for large-scale technological initiatives aimed at comprehensive modernization and transformation of the management system throughout the city, at the moment in Russia such projects are implemented only as part of g‘reenfield initiatives («Skolkovo», Moscow Region; «SMART City» Kazan; «Academic» Yekaterinburg). Higher specialized project is, for example, the portal «The best doctors of our city», which was launched in Nizhny Novgorod: the Internet resource provides detailed information about the best doctors, and visitors can choose the specialist they need through the built-in multi-factor search system. In addition, portal staff can arrange a consultation with a selected doctor for visitors. Another forward-looking segment in the field of local solutions is projects on the intellectualization of individual components of urban infrastructure, for example, the development of a free wireless Internet network in Moscow public transport or the launch of smart pedestrian crossings in Tyumen. The technological basis for the implementation of the latest initiative has become an integrated warning system for identification and video recording of violations of the passage of pedestrian crossings, developed by scientists of the Institute of Transport of the Tyumen State Oil and Gas University. One of the most dynamically developing smart city segments in Russia is the services that ensure the participation of citizens in the formation of the urban development agenda. Such a project, for example, is the Moscow platform «Active Citizen». The platform was launched in 2014 at the initiative of the Moscow Government to conduct open referenda in electronic form. According to the platform, today in «Active Citizen» more than two million users are registered, more than 4,000 votes have been taken and more than 121 Mio. Votes have been counted. To ensure the transparency of the project, the

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developers have provided a number of mechanisms that allow participants not only to monitor the overall dynamics of the voting results online, but also to control the reliability of the results [20]. Another digital platform for citizen engagement in urban development is the omnichannel communication system of citizens and government agencies. It covers 33 Russian cities. The omnichannel communication system is designed to automate the interaction of the region executive authorities and local governments with citizens on issues of informing about urban facilities in a certain territory, the quality of work on these facilities, and also processing residents’ appeals on problematic topics. This project, developed using highly advanced technologies, allows residents of the region to take part in the development of an urban environment aimed at improving the quality of life, and the government increases its openness and level of satisfaction from the population using a convenient and modern internet resource with mobile applications. Despite the government activities in the past five years to involve citizens in urban governance, they can hardly be called effective. Many projects do not receive appropriate feedback from citizens. The reasons for this are found not only in the problems of the innovative and political culture, mentioned earlier, but also in the absence of the quality and availability of the ICT city infrastructure in some regions of Russia. As shown by comparative studies of smart sustainable cities in the world, carried out in recent years, sustainable development is ensured primarily by the long-term nature of providing project implementation with resources that cannot be attracted exclusively from the state [12, 21]. Successful world experience in implementing smart city technologies analyzed in this study also emphasizes the need to attract large-scale investments in the realization of smart projects. Therefore, the government needs to strengthen public-private partnerships in this sector. It is equally important to prepare citizens for life in a modern and technological city. The public authorities of the city, which seeks to become smart, need to work in the following areas: 1. Applying strategies of informing citizens at the regional and federal levels, making information on smart cities mechanisms available in popular media and Websites; 2. Providing more opportunities for citizens to get Internet connection and increase wi-fi coverage. 3. Providing conditions for training citizens how to work in smart city system, including the creation of a support services with specially trained specialists in order to give personal support to citizens in using the smart city services. 4. Increasing the citizens’ motivation to use smart city technologies by using information mechanism and improving feedback. One should bear in mind the fact that efficiency of process and improvement of smart city technologies also depend on use of available experience, both domestic and foreign.

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6 Conclusion Having reviewed the largest and most needed smart projects in Russia, the following conclusions should be drawn: 1. The smartest Russian cities are: Moscow (96 projects), St. Petersburg (64), Yekaterinburg (47) and Novosibirsk (39), what allows us to conclude about: • a relatively small number of cities in Russia active using smart technologies for urban development, • a unequal distribution of «smart» urban projects in the territory of the Russian Federation, • a strict correlation of the region / city innovative infrastructure preparation level and the number of implemented digital technologies (all the cities listed above are large scientific centers). 2. Such areas as electric power industry, transport, mobility, and public safety are mostly required in the field of digital modernization of Russian cities. 3. Existing smart initiatives are mostly local and cover a narrow range of infrastructure modernization tasks. 4. Large-scale technological initiatives aimed at comprehensive modernization and transformation of the management system throughout the city are implemented only as part of greenfield initiatives. 5. Innovation culture in Russia faced with problem of low awareness and readiness to implement innovations in the economy and public life, so one of the most dynamically developing smart city segments in Russia is the services that ensure the participation of citizens in the formation of the urban development agenda. An effective model for the smart city technology implementation is the one, which would comply with the following conditions: First, it is necessary to ensure the quality and availability of the ICT city infrastructure. It is about creating the necessary technological infrastructure at the state level and equalization the technological conditions for innovation at the level of individual regions and municipalities (modern types of wired and wireless communications, a sufficient number of public Internet access points, the availability of public databases, etc.). Public-private partnerships should be strengthened for large-scale investment aimed at the development of innovative projects and their implementation. Second, smart city should be based on making network of «smart» devices available to all users; meeting the citizens’ demand or creating services that bring the highest value. Particular attention should be paid to the development of educational policies aimed at adapting citizens to life in a smart city, which should include both the formation of innovative attitudes in society and the development and teaching of new methods for searching, processing and analyzing information. Moreover, smart city must be adapted for people with disabilities. It is important to use international experience in this field. So, leading technology companies and civil

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society organizations (AT&T, World Enabled and Microsoft) participated in the development of G3ict - the global initiative on inclusive information and communication technologies «Smart Cities for All» (SC4A), which aims to eliminate the digital divide for persons with disabilities and older persons in smart cities around the world [22]. These conditions can be used by local authorities as a key to implementing smart city technologies. Acknowledgements. The research and publication is funded by Russian Foundation for Basic Research (project №19–011-00792 «Evaluation of social and political effects of new technologies of urban development in the context of the current stage of the administrative reform of the Russian Federation»).

References 1. Abouchakra, R., Khoury, M.: Government for a New Age. Infinite Ideas, United Kingdom (2015) 2. Townsend, E.: Smart Cities: Big Data, Civil Hackers, and the Search for a New Utopia. W. W. Norton & Company, New York (2013) 3. Glaser, E.: Triumph of the City. How Our Greatest Invention Makes Us Richer, Smarter, Greener, Healthier, and Happier. Penguin Press, New York (2011) 4. Focus Group on Smart Sustainable Cities (2015). https://www.itu.int/en/ITU-T/focusgroups/ ssc/Pages/default.aspx. Accessed 10 Jul 2020 5. Moir, E., Moonen, T., Clark, G.: What are Future Cities? Origins, Meanings and Uses. Government Office for Science, London (2014) 6. Deakin, M.: From intelligent to smart cities. In: Deakin, M. (ed.) Smart Cities: Governing, Modelling and Analysing the Transition, pp. 15–33. Taylor and Francis, London (2013) 7. Deakin, M., Al Waer, H.: From intelligent to smart cities. J. Intell. Build. Int. From Intell. Cities Smart Cities 3(3), 140–152 (2011). Taylor and Francis 8. Giffinger, R., Fertner, C., Kramar, H., Kalasek, R., Pichler-Milanovic, N., Meijers, E.: Smart cities – Ranking of European medium-sized cities. Centre of Regional Science, Vienna, (2007). https://www.smart-cities.eu/download/smart_cities_final_report.pdf. Accessed 10 Jul 2020 9. Caragliu, A., Del Bo, C., Nijkamp, P.: Smart cities in Europe. J. Urban Technol. 18(2), 65–82 (2011) 10. Seisdedos, G.: Qué es una Smart City? BIT Num. Math. 188, 35–37 (2012) 11. Jacobs, J.: The Death and Life of Great American Cities. Random House, New York (1961) 12. Huovila, A., Bosch, P., & Airaksinen, M.: Comparative analysis of standardized indicators for Smart sustainable cities: what indicators and standards to use and when? In: Cities, vol. 89, pp. 141–153 (2019). https://www.matchup-project.eu/wp-content/uploads/2019/04/201901_ Comparative-analysis-on-strùandardised-indicators_VTT.pdf. Accessed 10 Jul 2020 13. Castells, M.: Urban sustainability in the information age. City 4(1), 118–122 (2000) 14. Ahvenniemi, H., Huovila, A., Pinto-Seppä, I., Airaksinen, M.: What are the differences between sustainable and smart cities? Cities 60(A), 234–245 (2017) 15. «Smart Cities» project. https://russiasmartcity.ru/about. Accessed 10 Jul 2020 16. Seoul Smart City Initiatives & Strategies. https://we-gov.org/wp-content/uploads/2017/11/ 13-KWEAN-Seoul-Presentation-for-Beyoglu-Final.pdf. Accessed 10 Jul 2020

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17. Morozova, S., Maltseva, D.: Developing an effective model for the smart city technology: implementation as a part of new urban governance. In: EGOSE: International Conference on Electronic Governance and Open Society: Challenges in Eurasia. Communications in Computer and Information Science book series, vol. 1135, pp. 32–40 (2020). https://link.spr inger.com/chapter/https://doi.org/10.1007/978-3-030-39296-3_3. Accessed 10 Jul 2020 18. IESE Cities in Motion Index 2020. https://media.iese.edu/research/pdfs/ST-0542-E.pdf. Accessed 10 Jul 2020 19. Russia Smart City, Bank Solutions. https://russiasmartcity.ru/projects. Accessed 10 Jul 2020/07/10. 20. Active Citizen. https://ag.mos.ru/home. Accessed 10 Jul 2020 21. Smart cities: digital solutions for a more livable future. McKinsey & Company (2018). https:// www.mckinsey.com/industries/capital-projects-and-infrastructure/our-insights/smart-citiesdigital-solutions-for-a-more-livable-future. Accessed 10 Jul 2020 22. Smart Cities for All. https://smartcities4all.org/. Accessed 10 Jul 2020

Audio-Based Vehicle Detection Implementing Artificial Intelligence Oleg Golovnin1(B)

, Artem Privalov1 , Anastasiya Stolbova1 and Anton Ivaschenko2

,

1 Samara University, 34, Moskovskoye Shosse, Samara 443086, Russia

[email protected] 2 Samara State Technical University, 244, Molodogvardeyskaya Str, Samara 443100, Russia

Abstract. This paper presents a method for audio-based vehicle detection within the urban traffic flow analysis in Smart Cities. The proposed technology implements artificial neural networks to recognize and count vehicle sounds on audio recordings using mel-frequency cepstral coefficients. Nowadays there are a lot of different approaches for sound recognition but convolutional neural networks (CNN) have the greatest accuracy among the others. In this study, we compared CNN to a classic multilayer perceptron in the case of audio events recognition. The method was tested on the UrbanSound8K dataset and a mixed dataset combined by authors to be similar to actual conditions. Evaluation of possible intelligent solutions using the same UrbanSound8K dataset demonstrated that CNN have higher classification accuracy: 92.0% for CNN against 87.6% for multilayer perceptron. For the mixed dataset CNN presented the average vehicle detection accuracy of about 84.2%. Therefore, the proposed method allows simplification of traffic surveillance and reducing its costs and total information processing time. Keywords: Traffic flow · Sound recognition · CNN · MFCC

1 Introduction Nowadays one can say with confidence that the information technologies of the Smart City have changed a lot in the life of a city dweller; and these positive changes are becoming even more visible every day. Implementation of Smart City technologies in practice requires a deep analysis of various characteristics that describe the functioning of the urban environment, and, in particular, traffic flows as having the highest impact on the transport function and city infrastructure. Online processing and analysis of the traffic flow characteristics are possible only with an advanced technical supply. Information about the current state of traffic flows is traditionally collected using various technical facilities, for example, loop detectors and radars. However, the recent increase in the number of video cameras on the urban streets makes it possible to use video records to analyze traffic flows. This approach has certain drawbacks since video recordings contain redundant information and require significant costs for data processing, storage, and analysis. It seems promising to use the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 627–638, 2021. https://doi.org/10.1007/978-3-030-65283-8_51

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audio signal instead captured by Smart City’s video cameras or microphones, since the audio signal is less redundant and does not depend on visibility conditions. The purpose of this work is the development and experimental testing of a method for detecting acoustic emission of vehicles in audio recordings as a part of the traffic flow analysis. The method is planned for implementation under the Smart City framework. The proposed method for detecting patterns of acoustic emission from vehicles uses melfrequency cepstral coefficients (MFCCs) to identify the classification features using an artificial neural network. Two classes of neural networks are considered: multilayer perceptron (MLP) and convolutional neural network (CNN).

2 State-of-the-Art For successful traffic management, it is necessary to determine the density of traffic using the technologies of video analysis [1, 2]. To solve the problem of detecting vehicles, lidar-based computer vision methods are often used [3]. As a rule, the proposed solutions include two stages [4]: research and evaluation of lidar methods, and then training and tuning of neural networks to improve detection quality. Detection and monitoring of vehicles in real-time are one of the difficult problem domains where CNN demonstrate high efficiency and performance in the field of detection and identification of objects [5, 6]. In [7], there is conducted a review of CNN-based vehicle detection methods for monitoring a traffic situation. Note that CNN are used not only for the analysis of video images but also for aerial photographs [8]. A separate area for research is the task of detecting vehicles in video and images at night. So, in [9], a detection method is proposed, which is based on video and laser data processing. This technology uses the Gabor filter and the support vector method. To analyze video records in order to determine traffic, a wavelet transform is implemented in [10]. Spectral analysis methods are used for pre-processing and postprocessing of data for vehicles detection. For example, in [11], fast Fourier transforms and prescribed smart solutions enhance traffic detection of non-contact microwave radars. The wavelet transform is used for image preprocessing in traffic monitoring systems, where it highlights the characteristics of the vehicles [12]. Widespread methods for detecting vehicles in aerial photographs have many applications for vehicle monitoring [13] and urban planning [14, 15]. The analysis of aerial photos has certain difficulties because of the small size of the objects, the complex background, and the different orientation of the images. Effective methods are significantly different from the methods for detecting objects in images from the ground. In [12], to solve this problem, the authors propose a new CNN structure with double focal loss, and the authors of [16] propose a method for obtaining rotation-invariant descriptors. The considered technologies use video data and images as initial data [17], which is often redundant and requires large resources to process. The use of audio analysis is a promising way to identify vehicles since it does not require expensive recording devices and a large amount of memory for data storage. In addition, such an important indicator as poor illumination does not affect the quality of data. The work [18] demonstrates the possibilities of classifying vehicles by analyzing audio signals. The authors of [19] developed a system for detecting vehicles by the sound

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signal received from two microphones located on the sidewalk. Analysis of audio signals based on a combination of frequency, time, and frequency-time characteristics is used to identify dangerous events on the roads, such as drifts, accidents, in conditions of poor visibility [20]. It is shown in [21] that for detecting events by the sound the combination of gammatone frequency cepstral coefficients and discrete wavelet transform coefficients can be used. The estimation of the traffic flow by the audio signal is carried out using the support vector regression method in [22]. Assessment of the traffic by analyzing the total acoustic signal received from the smartphones based on a wavelet packet transform is given in [23].

3 Audio-Based Vehicle Detection Method 3.1 General Information In order to efficiently and accurately recognize audio events that describe the appearance of a vehicle of various kinds, the following method was proposed, consisting of five steps, described below The first step is the conversion of the original audio signal into a set of frames with overlapping. The second step is pre-processing, which includes filtering and window weighing. This step is necessary for spectral smoothing of the signal. In this case, the signal becomes less susceptible to various noises arising during processing. In addition, during pre-processing, the audio is resampled, as well as its conversion to one channel. The bit depth is also normalized, so the values range from -1 to 1. This removes the complexity of data processing because different audio files can have different bit ranges. The third step is to extract the necessary features. In the third step, the signal redundancy is reduced, the most relevant information is highlighted, and irrelevant information is eliminated. The patterns describing the audio signal are combined into one vector, on the basis of which further classification takes place. As symbols, it is proposed to use mel-frequency cepstral coefficients extracted from the audio signal. MFCCs summarize the frequency distribution according to window size, so we can analyze both the frequency and time characteristics of the sound. These audio presentations make it possible to identify the characteristics necessary for classification. At the fourth step, the post-processing of the attributes occurs. After extracting the patterns of the signal for their further use, the patterns are normalized so that each component of the feature vector has an average value and a standard deviation of 1. Dimension reduction is used to significantly increase the speed and accuracy of the learning process, and the accuracy of machine learning algorithms, due to getting rid of an excess of patterns and highlighting significant patterns. It is proposed to use the principal component method at this step since it makes it possible to reduce the dimension of the feature vector by identifying independent components, which maximally covers the scatter for all events. At the last fifth step of the proposed method, a training model is selected. For various types of audio events, it is worthwhile to select a specific classifier, because this

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can provide a large increase in accuracy in the classification process. The paper discusses the use of a multilayer perceptron and a convolutional neural network as a classifier. 3.2 Calculation of Mel-Frequency Cepstral Coefficients We detail some aspects of the presented method in part of MFCCs calculation. It is necessary to reduce the problem for N -numbers to the problem with a smaller number. For N = pq, p > 1, q > 1 over the field of complex numbers we introduce εv = e2π i/v , εvv = 1, where v is any number. Discrete Fourier Transform is used:  p−1 q−1 q−1 ij p−1 (kq+j)i (1) bi = akq + εN = εN akq+j εpki . k=0

j=0

j=0

k=0

Next, each bi is calculated: bi = ε−i

2

N −1 j=0

ε(i+j)

2 /2

ε−j

2 /2

aj .

(2)

The algorithm for obtaining MFCCs is constructed as follows: first we get the spectrum of the original signal (x[n], 0 ≤ n < N ): Xa (k) =

N −1 n=0

x(n)e−

2π i N kn

,0 ≤ k < N

(3)

The resulting spectrum is displayed on a chalk scale. To do this, we use the windows located on the chalk axis: ⎧ 0, k < f (m − 1) ⎪ ⎪ ⎪ ⎨ k−f(m−1) , f (m − 1) ≤ k < f (m) (m)−f (m−1) . (4) Hm (k) = (f(f(m+1)−k) ⎪ (f (m+1)−f (m) , f (m) ≤ k < f (m + 1) ⎪ ⎪ ⎩ 0, k > f (m + 1) The frequencies f(m) are obtained from the equality:

m f (m) = 700 10 2595 − 1 .

(5)

Next, we calculate the energy of each window: S(m) = ln(

N −1 k=0

|Xa (k)|2 Hm (k), 0 ≤ m < M ,

(6)

where M is the number of filters we want to get. After that, a discrete cosine transform is applied to obtain a set of MFCCs:   M −1 π n(m + 0.5) ,0 ≤ n < M. (7) c[n] = S(m) cos m=0 M

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3.3 Artificial Neural Networks Specification As mentioned above, we use a multilayer perceptron and a convolutional neural network as a classifier. Such a comparison is needed to conclude how the choice of classifier affects the result of the method. The MLP was chosen because it is a classical architecture and is the first choice as a network architecture when a new area of problems is considered for the solution of which a neural network can be applied. The CNN architecture is proposed as an alternative to the MLP, because the CNN architecture is widely used in the task of classifying images, and this area is adjacent to the problem that is considered in this paper. The architecture of the used MLP consists of three layers: input, hidden, and output layers. The activation function is ReLU because it is the best choice for neural networks with a similar architecture: f (x) = max(0, x)

(8)

The CNN is organized in three dimensions: width, height, and depth. The vertices in one layer are not necessarily connected to all the vertices of the next layer. The model optimizer is Adam. The ReLU function is also used as an activation function for convolutional layers. The activation function in the output layer is Softmax. The function converts a vector z of dimension K into a vector σ of the same dimension, where each coordinate σi of the resulting vector is represented by a real number in the interval [0,1] and the sum of the coordinates is 1. The coordinates σi are calculated as follows: ezi σ (z)i = K

k=1 e

zk

.

(9)

4 Results 4.1 Dataset Preprocessing For testing the proposed method, the Urbansound8K data set is used [24]. The UrbanSound8K dataset consists of 8732 short (less than 4 s) fragments of city sounds, which are divided into 10 classes, while the class labels are not balanced. The training and test samples consist of.wav files and metadata describing them, stored in a .csv table. Each sample represents the amplitude of the wave in a particular time interval, where the depth in bits determines how detailed the sample is. Therefore, the data that we will analyze for each sound fragment, in fact, is a one-dimensional array or a vector of amplitude values. First, buffering occurs with overlapping in the source file. The following is the signal preprocessing. To convert the data into spectrogram representations, we used the LibROSA library [25], which is an open-source package implemented in Python. Figure 1 shows an example of the shape of an audio signal passing by car, and Fig. 2 – of a truck.

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Fig. 1. Acoustic emission of a car

Fig. 2. Acoustic emission of a truck

From the visual analysis, it is clear that it is difficult to identify the difference between the classes of vehicles. Also, the shape of the car has similarities with street music, and the sound of children playing. It is also worth noting that most instances of the sample have two audio channels (stereo sound), although some have only one audio channel. The easiest way to avoid this problem is to combine the two channels into one, by averaging the two channels. 4.2 UrbanSound8K Dataset Study To compare the efficiencies of MLP and CNN architectures, we trained the networks with these architectures on the same data set. After training, the classification accuracy was measured and the neural network was selected with the greatest accuracy. The MFCCs is used as a feature extraction tool. First, we extract the MFCCs from the instances for each frame with a window size of several milliseconds. MFCCs summarize the frequency distribution according to window size, therefore, both frequency and time characteristics of sound can be analyzed. A similar representation of audio identifies the

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characteristics for classification. The following is the post-processing of the received characteristics. Figure 3 shows the spectrograms obtained without and with scaling coefficients for a car, and in Fig. 4 – for a truck.

Fig. 3. Spectrogram for a car

Multilayer Perceptron. To begin with, we considered a simple structure of a neural network – MLP. The construction of the MLP is performed using Keras and TensorFlow. The first layer is the input. Each sample contains 40 MFCCs, so the layer has a shape of 1 × 40. The first two layers have 256 neurons, and the activation function is ReLU. The exclusion level set to 50% to regularize the neural network during training, which leads to obtaining a network with better predictions. The output layer has 10 neurons that correlate with the number of feature classes in the data set. The activation function for this class is Softmax. Softmax makes the output sum close to 1, so the output values can be interpreted as probabilities. Then the model will make its forecast based on which option has the greatest probability. The results of testing the recognition accuracy of the MLP in the test and training samples are 87.6% and 92.5%, respectively. The accuracy is quite high, as well as a slight difference between samples (about 5%). Thus, the results show the MLP was not retraining.

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Fig. 4. Spectrogram for a truck

A graph of the classification accuracy versus the number of epochs is presented in Fig. 5.

0.9

Accuracy of classificaon

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1

11

21

31

41

51

61

71

81

91

Number of epochs Fig. 5. The accuracy of classification vs. the number of epochs (MLP)

Convolutional Neural Network. MLP training has shown quite a good result. However, it is worthwhile to find out if another network architecture can achieve even higher

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accuracy. CNN shows a good result in the classification of images, so this architecture was chosen to verify the assumption. Since the CNN requires that the number of inputs be equal, we zero out the vectors so that they all become the same size. The network model also remains consistent, with 4 convolutional layers and a dense output layer. The number of filters for convolution filters is defined as 16, 32, 64, and 128. The size of the core is 2x2 because the window size, in this case, is 2. The first layer takes the form 40, 174 by 1, where 40 is the number of MFCCs, 174 is the number of frames, taking into account the filling, and 1 is the number of channels. The activation function for convolutional layers is, as in the previous model, ReLU, and the exclusion level set to 20%. Each convolutional layer has a 2-by-2 sub-sampling layer. All of the subsampling layers are connected to one with the averaging layer, which supplies the averaged data to the output layer. Sub-sampling layers can reduce the dimension of the model (by reducing the number of parameters and sequential calculations), which leads to a decrease in training time and reduces retraining. The output layer is identical to the output layer of the MLP. Figure 6 shows a graph of the classification accuracy versus the number of training epochs.

0.97

Accuracy of classification

0.96 0.95 0.94 0.93 0.92 0.91 0.9 0.89 0.88 0.87 1

11 21 31 41 51 61 71 81 91 101 111 121 131 141 151

Number of epochs Fig. 6. The accuracy of classification vs. the number of epochs (CNN)

The results of testing the recognition accuracy of the CNN in the test and training samples are 92.0% and 98.2%, respectively. The accuracy increased by 6% for the training and about 4% for the test samples. Although the difference between them has

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increased (up to 6%), this value is not so great that it is an indicator of the fact that during training the CNN was not retraining.

4.3 Mixed Dataset Study. We tested the CNN on other data sets containing sounds of passing vehicles of varying quality and duration. Thus, we tried to simulate a real situation. Table 1 shows the parameters of the method when using trained CNN for a control set of data taken from open sources. Table 1. Classification accuracy on open-source data set Tittle

Number Number Classification of vehicles of classified vehicles accuracy, %

Record 1

68

65

92.5

Record 2

43

43

100.0

Record 3

10

10

100.0

Record 4

14

13

92.9

Record 5

33

30

90.9

Record 6

68

65

92.5

Record 7

22

18

81.8

Record 8

3

103

100.0

Record 9

55

50

90.9

Record 10 46

53

86.8

Table 2 shows the results of testing on the data recorded by the authors. Table 2. Classification accuracy on authors’ data set Tittle

Number of vehicles

Number of classified vehicles

Classification accuracy, %

Personal record 1

15

13

86.7

Personal record 2

7

7

100.0

Personal record 3

33

30

90.9

Personal record 4

46

35

76.1

Personal record 5

18

9

50.0

Personal record 6

13

7

53.8 (continued)

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Table 2. (continued) Tittle

Number of vehicles

Number of classified vehicles

Classification accuracy, %

Personal record 7

18

15

83.3

Personal record 8

24

20

83.3

Personal record 9

68

55

80.9

Personal record 10

34

17

50.0

Thus, the resulting accuracy on the mixed data set (open-source and authors’), which is similar to actual conditions, was 84.2%.

5 Conclusion In this paper, we proposed and investigated the method for patterns detection of vehicle acoustic emission in audio recordings using CNN and MFCCs. Studies conducted using MLP and CNN on the UrbanSound8k data set. The better results were presented by CNN that has higher classification accuracy: 92.0% against 87.6% by MLP. In addition, a study was conducted on the authors’ data set recorded, and mixed by audio files taken from open data sources. The resulting accuracy on the mixed data set using the CNN was 84.2%. A certain decrease in accuracy on the mixed set relative to the UrbanSound8k data set is due to the authors’ audio recordings have overlapping of sound emission from several vehicles at the same time. In additional, the results achieved on the classification accuracy (92.0% on the UrbanSound8k data set, 84.2% on the mixed data set) exceeds the classification accuracy of 73.5% achieved by the authors in the previous work [26], when MFCCs were not used. As a result, the proposed method is recommended for Smart City applications to simplify the traffic surveillance and reduce the costs and total information processing time.

References 1. Swathy, M., Nirmala, P., Geethu, P.: Survey on vehicle detection and tracking techniques in video surveillance. Int. J. Comput. Appl. 160(7), 22–25 (2017) 2. Ostroglazov, N., Golovnin, O., Mikheeva, T.: System analysis and processing of transport infrastructure information. CEUR Workshop Proceedings 2298, 144071 (2018) 3. Li, B., Zhang, T., Xia, T.: Vehicle detection from 3d lidar using fully convolutional network. arXiv preprint arXiv 1608.07916 (2016) 4. Asvadi, A., Garrote, L., Premebida, C., Peixoto, P., Nunes, U.: Multimodal vehicle detection: fusing 3D-LIDAR and color camera data. Pattern Recogn. Lett. 115, 20–29 (2018) 5. Bautista, C., Dy, C., Mañalac, M., Orbe, R., Cordel, M.: Convolutional neural network for vehicle detection in low resolution traffic videos. In: 2016 IEEE Region 10 Symposium, pp. 277–281. IEEE (2016)

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6. Gao, S., Jiang, X., Tang, X.: Vehicle motion detection algorithm based on novel convolution neural networks. Curr. Trends Comput. Sci. Mech. Autom. 1, 544–556 (2017) 7. Manana, M., Tu, C., Owolawi, P.: A survey on vehicle detection based on convolution neural networks. In: 3rd IEEE International Conference on Computer and Communications, pp. 1751–1755. IEEE (2017) 8. Qu, T., Zhang, Q., Sun, S.: Vehicle detection from high-resolution aerial images using spatial pyramid pooling-based deep convolutional neural networks. Multimedia Tools Appl. 76(20), 21651–21663 (2016) 9. Zhang, R., You, F., Chen, F., He, W.: Vehicle detection method for intelligent vehicle at night time based on video and laser information. Int. J. Pattern Recognit Artif Intell. 32(04), 1850009 (2018) 10. Golovnin, O., Stolbova, A.: Wavelet analysis as a tool for studying the road traffic characteristics in the context of intelligent transport systems with incomplete data. Trudy Spiiran 18(2), 326–353 (2019) 11. Ho, T., Chung, M.: An approach to traffic flow detection improvements of non-contact microwave radar detectors. In: 2016 International Conference on Applied System Innovation, pp. 1–4. IEEE (2016) 12. Tang, Y., Zhang, C., Gu, R., Li, P., Yang, B.: Vehicle detection and recognition for intelligent traffic surveillance system. Multimedia Tools Appl. 76(4), 5817–5832 (2015) 13. Razakarivony, S., Jurie, F.: Vehicle detection in aerial imagery: a small target detection benchmark. J. Vis. Commun. Image Represent. 34, 187–203 (2016) 14. Audebert, N., Le Saux, B., Lefèvre, S.: Segment-before-detect: Vehicle detection and classification through semantic segmentation of aerial images. Remote Sens. 9(4), 368 (2017) 15. Tang, T., Zhou, S., Deng, Z., Zou, H., Lei, L.: Vehicle detection in aerial images based on region convolutional neural networks and hard negative example mining. Sensors 17(2), 336 (2017) 16. Ma, B., Liu, Z., Jiang, F., Yan, Y., Yuan, J., Bu, S.: Vehicle detection in aerial images using rotation-invariant cascaded forest. IEEE Access 7, 59613–59623 (2019) 17. Peppa, M., Bell, D., Komar, T., Xiao, W.: Urban traffic flow analysis based on deep learning car detection from CCTV image series. In: SPRS TC IV Mid-term Symposium “3D Spatial Information Science–The Engine of Change”, pp. 499–506. Newcastle University (2018) 18. Yang A., Goodman E.: Audio Classification of Accelerating Vehicles (2019) 19. Kubo, K., Li, C., Ishida, S., Tagashira, S., Fukuda, A.: Design of ultra low power vehicle detector utilizing discrete wavelet transform. In: Proceeding of ITS AP Forum, pp. 1052–1063. (2018) 20. Almaadeed, N., Asim, M., Al-Maadeed, S., Bouridane, A., Beghdadi, A.: Automatic detection and classification of audio events for road surveillance applications. Sensors 18(6), 1858 (2018) 21. Waldekar, S., Saha, G.: Analysis and classification of acoustic scenes with wavelet transformbased mel-scaled features. Multimedia Tools and Appl. 79 1–16 (2020) 22. Lefebvre, N., Chen, X., Beauseroy, P., Zhu, M.: Traffic flow estimation using acoustic signal. Eng. Appl. Artif. Intell. 64, 164–171 (2017) 23. Vij, D., Aggarwal, N.: Smartphone based traffic state detection using acoustic analysis and crowdsourcing. Appl. Acoust. 138, 80–91 (2018) 24. Dataset UrbanSound8k. https://urbansounddataset.weebly.com/urbansound8k.html. Accessed 04 Jun 2020 25. LibROSA, https://librosa.github.io/librosa/. Accessed Accessed 04 Jun 2020 26. Golovnin, O., Privalov, A., Pupynin, K.: Vehicle Detection in Audio Recordings by Machine Learning. In: 2019 International Multi-Conference on Industrial Engineering and Modern Technologies, pp. 1–4. IEEE (2019)

Methodological Foundations for the Application of Video Analytics and Incident Management Technologies in Real-Time Detection and Control Systems for Road Incidents Olga Dolinina1(B) , Andrey Motorzhin2 , Vitaly Poltoratzky3 , Aleksandr Kandaurov3 , Sergey Shatunov3 , and Aleksandr Kartashev3 1 Yuri Gagarin State Technical University of Saratov, Saratov, Russia

[email protected] 2 Company “Satellite SoftLabs”, Saratov, Russia 3 Company “AMT-GROUP” (Company Group “TransNetIQ”), Moscow, Russia

Abstract. The article describes the official methodology adopted in Russia for the calculations of the risks of the traffic accidents. The statistics of the traffic accidents is considered. It is shown that the key reason of the accidents is traffic violation by the drivers and that’s why it is necessary to implement the system of the “smart traffic” for the on-line control of the traffic on the base of the video detection and transport analytics which detects the drivers’ state, state of the roadbed, traffic violation and accidents. This paper describes methods and solutions of the “smart traffic” currently used in Russia and suggested the way of control of the traffic accidents. Keywords: Traffic accidents · Smart traffic · Video detection · Control of incidents · Efficiency of the traffic control

1 Introduction The importance of transport in the life of modern society can hardly be overestimated: the role of the transport system of any state is similar to the circulatory system of the body – every failure in its functioning is fraught with social and economic losses. The price of any incident is human life and material and financial costs. The most important mode of transport is automobile. In Russia, the length of public roads was about 1.6 million km, the share of road transport in the total passenger turnover was 22,1%, and freight turnover was 4,6%. At the same time, motor transport has the most emergencies: the number of road traffic accidents (RTAs) in road transport in 2018 amounted to 168,1 thousand (58,3% of the total number of accidents in all modes of transport), the number of deaths in these incidents – 18,2 thousand people. (11,8%). The distribution of accidents by type is shown in the Table 1. Three quarters of all accidents (77%) occurred in cities and towns, with the share of dead and injured being 47,8% and 74%, respectively. Information about the types of accidents in 2018 [1] is give in the Table 1. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 639–655, 2021. https://doi.org/10.1007/978-3-030-65283-8_52

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O. Dolinina et al. Table 1. Types and percentage of road traffic accidents in 2018 Type of accident

Quantity Percentage

Collision of vehicles

51022

42,70%

Vehicle rollover

9714

8,10%

Hitting a standing vehicle

3438

2,90%

Passenger fall

4687

3,90%

Pedestrian collision

32488

27,20%

Hitting a barrier

8201

6,90%

Hitting a cyclist

4584

3,80%

Hitting an animal

322

0,30%

Cartage accident

17

0,01%

4902

4,10%

Other type of accident

A number of deaths in road accidents in Russia per one million people in 2018 amounted to 124 people. For comparison, in the European Union, the countries with the lowest mortality on the roads in 2018 were Great Britain (28 deaths per million), Denmark (30), Ireland (31) and Sweden (32). The highest mortality rates were found in Romania (96), Bulgaria (88), Latvia (78) and Croatia (77). According to the traffic police data, in 2019 in Russia the total number of accidents amounted to 164,4 thousand, 16981 people died and 210877 people were injured. Despite a slight decrease in the total number of accidents, the significant increase (by 11,7%) in the number of accidents involving public road transport engaged in bus transportation, and for all indicators (see Table 2) [2, 3], is alarming. The main reason for the accident is a violation of traffic rules by drivers – 89,2%. In total, due to traffic violations by drivers of vehicles last year, 146,688 traffic accidents occurred. In the period from January to October 2019 alone, 5598 accidents involving buses occurred in Russia, which is 12% more than in the same period in 2018. Unfortunately, the situation with road accidents with buses has not fundamentally changed for almost four years. In 2019, 5,535 accidents were caused by bus drivers. As a result of such accidents, 246 people were killed, 8795 were injured. The main causes of accidents due to violation of the rules by drivers are: – – – – – – – –

failure to comply with the order of intersections – 20%; wrong choice of distance between vehicles – 10%; violation of the rules of passage of pedestrian crossings – 9,2%; departure into oncoming traffic lane – 8,4%; speed mismatch to specific traffic conditions – 5,8%; violation of the requirements of traffic signals – 2,7%; excess of the established speed of movement – 2,3%; violation of the rules for overtaking – 1,3%.

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Table 2. Traffic accidents and injuries in them, with the participation of public road transport by mode of transport in 2019 Indicator

Russian federation Accidents Died

Accident involving public road transport bus

Injured

Total number

Total

Passengers Total

Passengers

6926 +11,7%

359 +0,3%

62 –26,2%

10307 7461 +11,1% +11,4%

6725 +10,5%

329 +7,2%

53 +17,8%

9656 +8,5%

7000 +9,0% 5501 +5,7%

–Including– Regular transportation with passengers disembarking at designated stopping points

Regular transportation in urban 5618 traffic with passengers disembarking +9,5% in any place not prohibited by traffic rules

155 12 +34,8% +9,1%

7512 +5,6%

Transportation in urban traffic on orders

41 +36,7%

4 +300%

74 44 +23,3% +51,7%

Regular transport in the suburban

693 +13,2%

67 16 –16,3% +23,1%

1261 829 +13,9% +12,3%

Commuter transportation on orders

37 +54,2%

5 0 –64,3% –100%

128 73 +36,2% +25,9%

Regular transportation in intercity (international) traffic

420 +21,7%

106 –5,4%

935 652 +31,3% +39,9%

Transportation in intercity (international) traffic

117 20 9 +129,4% –62,3% –73,5%

0

24 +14,3%

443 +2,1%

341 +9,9%

Such a significant number of accidents caused by drivers, driving under the influence of alcohol or drugs (only from April 1 to May 11, 2020 revealed 35,5 thousand motorists who got behind the wheel while intoxicated), the aggressive behavior on the roads necessitates the improvement of mechanisms control the behavior of drivers on the road. In Russia, the concept of hazardous driving has been introduced into the Rules of the Road, which is the repeated commission of one or more subsequent actions, if these actions entailed the creation by the driver of a road traffic situation where his movement and (or) the movement of other road users in the same direction and at the same speed poses a threat of death or injury to people, damage to vehicles, structures, goods or other material damage. Outside Russia there is also the “3D reason” – drunk, drugged and dangerous, what means driving under the influence of drugs or drugs and dangerous driving, while the most significant fines are imposed for dangerous driving. It should be noted that in addition to a direct violation of traffic rules by drivers, the causes of traffic accidents are also:

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– the physical impossibility of preventing drivers of traffic accidents caused by other vehicles and pedestrians; – physical fatigue of drivers associated with non-compliance with the regime of work and rest; – accidents with drivers (heart attacks, acute attacks of chronic diseases, etc.); – distraction of drivers (acts of unlawful interference, accidents in the passenger compartment, etc.). The second concomitant cause of an accident is a violation of the requirements for the operational condition of roads and railway crossings. Unsatisfactory road conditions were recorded in 48,259 traffic accidents. In such accidents, 4317 people died and 61637 people were injured. The main types of unsatisfactory road conditions include the absence, poor distinguishability of the horizontal marking of the carriageway (51%), lack of winter maintenance (13,7%), lack of road signs (21,9%) and pedestrian fences in the required places (9,8%), improper use, poor visibility of road signs (9,4%) [4]. In third place among the causes of the accident is a violation of the rules of the road by pedestrians. The share of such accidents is 10,56%. The share of accidents due to the operation of technically faulty vehicles is also significant. Accidents in which technical malfunctions of vehicles were recorded, or conditions under which their operation is prohibited, amounted to 4,14% of the total. In general, traffic accidents cause Russia and its society not only social and demographic, but also significant material and economic damage. One third of those killed in road accidents are people of the most active working age (26–40 years), and about 20% of the victims become disabled. The country’s annual economic losses from road accidents amount to about 2 percent of the gross domestic product and are comparable in absolute terms with the gross regional product of such constituent entities of the Russian Federation as the Krasnodar Territory or the Republic of Tatarstan. A similar picture exists in many countries of the world — average road accident costs at the country level are about 3% of GDP [5].

2 Approach to Assessing the Economic Losses from the Road Accidents It should be noted that now in Russia there is no single approved methodology for assessing economic losses from road accidents. In 2001–2005, in domestic practice, a methodology was used to assess the calculation of the standards of socio-economic damage from road accidents. According to this technique, the magnitude of socio-economic damage resulting from a traffic accident includes several components: damage resulting from deaths and injuries; damage resulting from damage to vehicles; damage resulting from damage to the cargo; damage resulting from road damage. However, the approach prescribed in this document has a number of significant drawbacks (the standards used in international practice and the availability of statistical data are not taken into account) and is outdated.

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Modern domestic and foreign methodological approaches to assessing the economic losses from the road accidents are described in sufficient detail in the articles “Study of foreign methods and domestic practices for determining the economic damage caused by death as a result of an accident” [6], “Approaches and methods for assessing socioeconomic damage from road traffic accidents” and others. In different countries, these approaches are different, or rather different combinations of these approaches. But the main are two approaches. The first is the assessment of damage from the point of view of the theory of human capital, when the monetary assessment of the benefits that society will bear from preserving human life and health with a certain set of socio-economic characteristics is taken as the basis. The second approach is the assessment of damage in terms of the willingness of the population to pay for improving the quality of life and public safety [8]. In the general case, damage caused as a result of an accident can be considered as a combination of direct costs directly related to the accident, indirect costs and intangible losses. The first includes expenses on medical care, rehabilitation of victims, administrative, police, legal expenses, etc., the second – the costs borne by society from the reduction in the number of economically active population as a result of death, as well as full or partial disability, to the third – losses of an emotional nature: pain, sadness, grief, loss of quality of life, etc. Direct and indirect costs can be calculated in monetary terms using existing methods. Less obvious and more time consuming to calculate intangible losses [9]. Most of the existing methods are based on models of the theory of human capital and the willingness of the population to pay for risk reduction. To some extent, when calculating the economic losses from road accidents, the methodology for calculating the economic losses from mortality, morbidity and disability can be used [7] and a unified methodology for determining the amount of expenses for restoration in respect of a damaged vehicle [4]. Another option is the Methodology for assessing economic damage from death, disability and injuries as a result of an accident, the main approaches of which are shown in Fig. 1. In the analytical review “Socio-economic consequences of road traffic accidents in the Russian Federation” a simplified methodology for the valuation of damage caused by deaths and injuries in traffic accidents is presented, the initial information for calculations of which is the damage standard for 2006 (calculated according to P-03112100-050200), as well as the size of the traffic accidents (TA) and the number of people employed in the economy. In various documents, scientific papers and the media, the economic damage from road accidents is estimated from 2% to 5% of our country’s TA and the wide variation in estimates is precisely explained by the existence of a large number of diverse approaches, methods and recommendations. Russia’s gross domestic product for 2019 amounted to 110,046 trillion rubles, and therefore, even if 2% of GDP is adopted as the normative value, the economic damage from road accidents in Russia is more than 2.2 trillion rubles [10], a huge number, which indicates that this remains one of the acute socio-economic and demographic problems in Russia, requiring the intensification of the efforts of the state, business community and citizens. It should be noted that the state authorities of the Russian Federation and its constituent entities are taking measures to improve the organization and safety of road traffic by introducing modern digital and navigation

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Fig. 1. Calculation procedure considering the gender and age structure of dead and injured

technologies in the operation of road transport and improving control and supervision activities based on their use. Under these conditions, the participating countries of the Third World Ministerial Conference on Road Safety in February 2020 in the Stockholm Declaration committed themselves to encouraging and stimulating the development, application and implementation of existing and future technologies and other innovations to expand the coverage and improve all aspects of road safety movements from accident prevention to emergency response and the provision of medical care in case of injuries.

3 Smart Traffic as the Solution of the Problem In particular, the most important steps in improvement of the traffic management making it the smart one are: • equipping vehicles with satellite navigation equipment, emergency call systems, tachographs with video surveillance systems; • creation and commissioning of the GAIS “ERA-GLONASS”, regional navigation and information systems, the “Platon” charging system; • deployment of video recording systems for traffic violations and weight and weight control; • implementation of components of intelligent transport systems and hardware systems “Safe City”, etc. Of course, there is a certain effect from the implementation of each of these systems, but today it is time to achieve a synergistic effect from the integrated use of advanced

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technologies in order to prevent accidents or minimize its negative consequences for the life and health of citizens, the state of transport complex facilities (if the incident is happened). One of the possible ways to achieve such a synergistic effect is the transition from automated systems for recording traffic incidents to automated systems for detecting and managing traffic incidents in real time, based on the use of video detection technologies and transport analytics. Such systems using cameras can automatically recognize events in the passenger compartment of the vehicle (deviations in driver behavior, riots among passengers, things left behind), on the road network (large crowds and riots on the street, a person lying down) and highways (accident, vehicle fire, traffic jam/congestion, a pedestrian knocked down, the appearance of obstacles or ground failures on the road, for example, a fallen tree or pole). The use of additional sources of information (sensors of various physical nature and panic buttons in the vehicle interior and transport infrastructure objects, data from the ERA-GLONASS and 112 systems, etc.) can significantly expand both the range of detected incidents and the range of typical algorithms their automated mining. Currently, damage reduction from the consequences of incidents in the road transport complex is achieved, mainly, by the following set of organizational and technical measures: • driver control; • road condition monitoring; • identification of violations of traffic rules and the identification of accidents. So, the main methods for controlling the driver are: pre-trip and post-trip medical examinations, traffic control by the traffic police, traffic controllers. In addition, a unified system of electronic digital waybills is introduced in the Russian Federation, which allows controlling the rules for the transport of passengers and goods. Information environment is created where, in the automatic mode, visual information on the driver’s condition before and during the vehicle’s movement can be recorded also in real time [11, 12]. As the main technical means of driver control, CCTV cameras are used, including those with video analytics functions. Unfortunately, they do not have quick response mechanisms from dispatching, operational services and emergency response services. The main methods for monitoring the condition of the roadway are: visual inspection, automated monitoring by mobile complexes, video surveillance, data collection from road users. As the main technical means, automated mobile complexes for monitoring the condition of the roadbed and road infrastructure facilities [13], specialized social networks (https://dorogi-onf.ru), video surveillance equipment on the roads (http://www. cud59.ru). The condition of roads is also studied using unmanned aerial vehicles [14, 15]. The most promising from the point of view of the rapid detection of incidents on the roads and in transport are the methods and means of photo and video recording of traffic violations and the detection of road incidents. The main methods are: reports of road accident participants, eyewitnesses, police officers; automated incident detection, including ERA GLONASS; video monitoring.

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Means – telephone and radio communications, social networks, special hardware and software systems for detecting incidents on the road network [16], means of surveillance video surveillance on the roads (http://www.cud59.ru). Unfortunately, about the presented methods and means, despite the fact that they individually solve the tasks assigned to them to ensure the effective and safe operation of transport and road infrastructure facilities, there is a major and serious drawback: they do not allow operational, in real time, identify the prerequisites for the occurrence of incidents and the incidents themselves and promptly organize their elimination. In this regard, in scientific and technical articles and publications, articles and studies are increasingly appearing on methods and means of quickly detecting incidents on the roads through artificial intelligence technologies and video analytics. In addition, there are more and more projects, startups related to this topic. According to Berg Insight research [17], the video telematics market is growing at a rate of 15,6% per year. So, in 2019 in the United States there were installed 1,6 million active video telematics systems, in Europe – 1 million. According to forecasts, in 2024 the market in Europe and the USA will grow to $ 1,5 billion. According to this study, one of the largest suppliers of such systems is Lytx [18]. The main tasks solved by their systems are driver identification, identification of dangerous driving and warning the driver in real time about dangerous driving behavior. In addition to Lytx, a notable player in this market is the Trafficvision solution. The solution is based on video analysis of a video stream from video cameras and allows you to automatically detect: • • • • •

oncoming traffic; slow motion (slower than a given speed for a certain time); a stopped car or mechanical obstruction on the road; pedestrian on the road; traffic jam if traffic jam has reached a certain fraction of the visible length of the road.

The solution of the Citylog company (www.citilog.com) offers the solution of the following tasks: • automatic detection of incidents; • collection of traffic information; • intersection management (adaptive control based on data from video cameras). MediaVMS solution integrates several technologies of intelligent transport systems: • • • • •

video analytics; automatic detection of incidents; license plate recognition; traffic data; smart traffic as control of intersections, smart traffic lighting.

Valerann (www.valerann.com/solutions) is a startup that creates an artificial intelligence-based traffic control system. It is based on special sensors built into the

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roadbed and collecting traffic information, using data mining and artificial intelligence, transmitting information wirelessly. The system collects, analyzes traffic data, predicts dangerous traffic situations. Brisksynergis (brisksynergies.com) based on an analysis of the interaction between traffic participants, analyzes the organization of traffic, identifies incidents that did not happen by a lucky chance, in order to make changes to the organization of traffic: • real-time incident prediction, collision risk assessment; • analysis of road safety/road infrastructure; • analysis of user behavior on the road. System I2V (www.i2vsys.com) based on the existing road video cameras networks and video analytics provides information about the incidents: – – – – – – – – – – – – – – – – –

Automatic fire detection; Advanced Motion Detection; Perimeter Tripwire; Abandoned Object Detection; Determination of the disappearance of an item; Zone Intrusion Detection; Boundary Loitering Detection; Intelligent People Counting; Crowd Counting and Detection; Object Classification; Attribute Search; Vehicle Speed Detection; Stopped Vehicle Detection; Wrong Way Detection; No Helmet Detection; Automatic Traffic Counting and Classification; Vehicle counting and classification system for integration with toll systems on toll roads, for online monitoring and offline analysis.

Let’s consider the “classic” response scheme for various incidents in the transport (road) system of a typical city agglomeration. In the event of an incident more often participants or witnesses of it exist (including video surveillance equipment) who, using available means (phone call, SMS, mobile application, service radio, the operation of specialized detectors, etc.), report the incident to a certain abstract center (this can be a dispatch center in the event of an incident on board of a passenger vehicle or another incident witnessed by a bus driver, it can be a traffic safety center or a call reception dispatch center of System-112 if an accident/traffic accident occurred on a street urban agglomeration road network with the participation of road or rail transport, it can be a control point in the event of cracks/failures/flooding on the infrastructure of artificial road structures (bridges, overpasses, tunnels), etc.). The center staff receives an incident report, verifies its reliability, first classifies it and must perform a certain series of actions according to the scenario (regulation rules)

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of the typical proceeding for the fixed incident. Moreover, depending on the severity of the incident itself, as well as possible consequences, in order to minimize them, the center employee should organize (if necessary) high-quality and operational interaction with other services. Not only the size of the resulting material damage, but also human lives often depends on the correct and timely actions of the center’s personnel. In the course of analytical studies in the period 2018–2020, a number of existing systems for managing (responding) incidents in the transport complex in the regions of the Russian Federation were analyzed. One of the result of the study was detection of the following systems flaws: – low speed and reliability of incident detection (in some cases, eyewitnesses/participants cannot reach the relevant services due to insufficient call center capacity and “busy telephone syndrome”); – most of the functions of notification and coordination of services in resolving incidents are performed manually, by telephone; – “watching and seeing is not the same thing” – the majority of video cameras located on the street-road network of the city agglomeration operate in archive mode without any analytical processing in the operator rooms (in this case, incident data is mainly claimed by incident participants only for their requests when providing information to the group of traffic accident analysis or to the court); – the relatively low level of wages of dispatch center personnel causes staff turnover in key responsible positions, while an employee with insufficient qualifications (little experience) may act reflexively at the time of a serious incident, violating established regulations and instructions. Despite the undoubted advantages and effects of existing and promising methods and means of identifying incidents on the road network and transport, their main drawback, which does not fully ensure road safety, is the fragmentation, lack of comprehensive technology and systems for detecting road incidents and their premises and management coordinated development and mitigation with the possibility of big data analytics and predictive analytics. In this regard, in order to increase the efficiency and reliability of identifying incidents on the street-road network of urban agglomerations and managing them, it is proposed to consider the possibility of using methods and means for automatically detecting incidents based on video recording technologies, video analytics and machine learning (based on the mathematical apparatus of neural networks) to ensure automatic incident detection in the form of a distributed video analytics platform (video surveillance and incident detection). At the same time, in order to increase the efficiency of the procedure of direct testing and coordination of participants, it is advisable to ensure the integration of the video analytics platform with the incident management system. Thus, the implementation of a real-time applied incident management system is proposed. It should be noted that the main problem of the most existing video analytics systems is the high frequency of false positives, which quickly reduces the economic effect of the technology. The problem is gradually being solved by improving video analysis algorithms, automatic testing on special test benches and ranking events by importance. Another problem is the significant cost of the system integration and implementation of

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video analytics. The role of this factor is reduced due to the emergence of open standards such as ONVIF (Open Network Video Interface Forum), simplification of calibration procedures and video analytics settings. The main functional steps for responding to an incident subject to the implementation of a full-cycle incident management system are (see Fig. 2):

Begin Detec on of the incident Classifica on (download)

Video

Selec ng a scenario

No fica on of par cipants Appointment of responsible persons common Сommon informa informa on on space space Сrea ng a list of ac ons Сontrol of task deadlines Resolving an incident No fica on of elimina on Сlosing the incident card Сollec on and centralized storage of data about the incident Sta s cal evalua on of results Аnalysis of the prerequisites, tasks for the preven on End

Fig. 2. Algorithm of the main functional steps for responding to an incident subject to the implementation of a full-cycle incident management system

1.

detection (fixing) of the incident;

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2. 3. 4. 5. 6.

7. 8. 9. 10. 11. 12.

13. 14.

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classification, loading of a video fragment (if possible); determination of the most optimal scenario (regulation) of development/elimination of consequences. notification of officials and responsible persons proceeding the documents of the road incidents (if necessary); the appointment of responsible persons (central coordinator, delegation of responsibility to hierarchically superior units (if necessary); organization of a common information space for data collection and coordination of actions (formation of an incident card and a dynamic conference communication group (if necessary); the formation of a list of actions/tasks for each proceeding area; control of the deadlines for completing tasks by each participant, the formation of recommendations (if necessary); the elimination of an incident according to its type under the regulations; notice of rectification; closing the incident card; collection and centralized storage of incident data (photo, video, audio materials from the scene of the incident, aggregation of various reports on the actual actions of the participants); statistical evaluation/analysis of the results of mining (assessment of personnel efficiency); analysis of the prerequisites, the formation of tasks for prevention.

A number of similar pilot projects are currently being implemented in the Russian Federation, with the successful implementation of real-time detection and control systems of the road incidents. An example is TransNetIQ’s solutions, which have proven their success in a number of regions (Perm Territory, Kursk, Ryazan regions) based on using real-time passenger transport cameras (via the mechanisms of a hybrid video analytics system based on neural network processing). TransNetIQ system allows: • on-line detection of the traffic incidents based on the vide-cameras data; • monitoring the physical state and driving style of drivers; • video surveillance inside passenger vehicles to provide data to authorized bodies (with the ability to search for the necessary video clips by time and georeferencing events/incidents); • integration with ERA-GLONASS and System-112 systems; • integration with specialized social networks for additional detection of potential incidents (events); • decision support based on the objective data (video and photo materials from the scene of the incident, including online, an objective picture of the effectiveness of the actions of all participants involved in the development of the incident); • an expanded adaptive system of recommendations for personnel actions in accordance with the approved regulations; • the possibility of retraining neural network sensors during the operation of the system based on feedback from employees of the dispatch center.

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• systems for detecting and managing traffic incidents, while ensuring real-time availability The effectiveness of such systems was tested during experimental testing, including through urban exercises. The comparison was carried out on two cohorts of road incidents on ground urban passenger transport. As a result of pilot implementations of the full-cycle incident management systems, the following effect is noted: – reduced response time and incident handling (up to 40%); – increasing the efficiency of informing management about incidents and the progress of their development (up to 40%); – improving the quality of incident handling (up to 20%); – reduction of time for incident handling by dispatching personnel of organizations involved in liquidation of consequences of incidents (up to 30%). At the same time, such systems provide effective coordination of actions of transport organizations and emergency services in response to incidents (Figs. 3 and 4).

Fig. 3. An example of an accident detector on board of the passenger bus

In conclusion, it should be noted that the resolution of emergency situations is one of the basic tasks of any management process. In different countries, the same management tasks are being solved, but the methods for solving them differ. The article “Features of National Management” identifies the American, Japanese and Russian management

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Fig. 4. An example of an accident detector by a traffic control video camera

models. The unconditional and recognized leader who has been exporting his management practices for over 100 years is the American management model. This model has the most developed conceptual apparatus, which is also used in other national management models. One of such universal concepts, the analogues of which are present in all control models, is the concept of “incident”. In their historical circumstances, each of the above management models was formed on its dominant incident management scenario: – the Japanese model was built on a scenario to prevent incidents, eliminate the causes before they start generating incidents; – the American model was built on a scenario to quickly eliminate incidents until they turned into a crisis situation; – the Russian model was built on a scenario to quickly eliminate crisis situations until they turned into a disaster Each of these models has its own advantages and disadvantages; inevitably, in each model, to one degree or another, there are also scenarios that are more characteristic of another control model. Of course, regardless of the management model, the best way to deal with incidents is to prevent them, that is, to create conditions that exclude or at least minimize the likelihood of incidents. But in the case when the incident nevertheless becomes a reality, the effectiveness of measures taken to eliminate both the incident itself and its onset and/or potential consequences is crucial. In solving these problems in Russia, the best foreign incident management practices are increasingly being introduced. It is also important that with a large flow of incidents, the response to some incidents must be postponed to a later time. That is, incidents must be ranked according to the

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scale of possible consequences, and, consequently, the urgency and scale of the reaction to them. With regard to the management of road incidents, this means the special importance of the rapid detection and ranking of incidents according to the degree of (potential) damage to the health of the participants of the incidents, and their socio-economic consequences. As experience shows, the time to bring emergency traffic information to the accident using traditional means (telephone) takes at least 5–10 min. Significantly reduces this time the commissioning of the ERA-GLONASS system, but the low percentage of equipping vehicles with emergency call devices, as well as their failure in certain conditions (for example, in case of minor accidents) determine the special role of video surveillance systems (video recordings) and video analysts in the process of managing incidents in automobile transport, especially taking into account the significantly increasing number of photo and video recording cameras annually (as of the end of 2019, there are 12,5 thousand pieces of stationary cameras only). In the modern sense, the essence of incident management processes consists in the implementation of automated algorithms for collecting data about traffic incidents, detecting events based on this information, and creating and working out options (performing a sequence of measures) for optimal response to them. The basis for the implementation of these algorithms is an integrated intellectual processing of data got from video surveillance systems, satellite navigation and other sources, as a result of which answers must be obtained not only to the questions “WHAT?” (what happened and under what conditions), “WHERE?” (in what place and in what environment), “WHEN?” (at what time and under what seasonal and diurnal features)?”, as well as a strategy and tactics for responding to the incident [6, 7]. At the same time, the answer to the eternal Russian question “WHAT TO DO?” must be formulated in one or more scenarios. It should be noted a number of related factors that can reduce the cost of implementing video analytics and incident management systems. These include: – a significant number of cameras installed on federal highways and the road network of settlements in order to control traffic. Requirements for installation locations and technical specifications are normatively established in national standards (GOST R 57144–2016 & GOST P 57145–2016). An affordable price and a short payback period contribute to a significant annual increase in the number of photo and video recording complexes (the price of a stationary complex of video and video recording violations varies between 2 million and 5 million rubles, the payback period is 3–5 months. In 2019, the number of fines for motorists increased to a record high - more than 142 million fines were issued to Russian drivers, and the total amount of fines exceeded the milestone of 100 billion rubles); – equipping vehicles with satellite navigation equipment and emergency call devices in accordance with the technical regulations of the Customs Union “On the safety of wheeled vehicles”. The requirements for these on-board devices are also established in interstate and national standards; – the presence in the regions of significant computing power that can be used (traffic management centers, regional navigation and information systems, etc.).

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4 Conclusion Thus, for the implementation of traffic incident management systems, only an increase (if necessary) in server capacities, the development of a scientific and methodological apparatus and special software are needed. The effects of the introduction of photo and video recording technologies, video analytics and satellite navigation in the systems for detecting and managing traffic incidents are: • reducing the time to bring information about transport incidents to emergency operations services (due to the automatic detection and detection of events); • reducing the number of employees involved in incident analysis today and reducing the influence of the “human factor” on the quality of video detection processes (due to the implementation of automatic processes); • ensuring the rational use of forces and means of emergency operational services (by detecting, ranking incidents and using optimal response algorithms for them); • reducing mortality in road accidents (by increasing the efficiency of the distribution of forces and emergency medical facilities and units of the Ministry of Emergencies of Russia when planning measures to prevent accidents and eliminate their consequences); • reducing economic losses from traffic incidents (by preventing the occurrence and timely response to accidents and other incidents, as well as organizing automated information for road users). Ultimately, the implementation of automated systems for managing of the traffic incidents will increase the safety of passengers and goods, the efficiency of transport work by carriers, the stability and quality of public transport services.

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Author Index

A Abramov, Maxim, 587 Akhanova, Madina, 49 Akhmetov, Bakhytzhan, 49 Askarova, Adel, 175 Averianova, Kristina, 575 B Bagaev, Igor, 522 Baiburin, Vil, 165 Balaban, Oleg, 61 Barsukov, Alexander, 185 Beliaev, Matvey, 563 Bessmertny, Igor, 535 Blinkova, Oksana, 223 Bobrov, Leonid, 453 Bogomolov, Alexey, 3 Bondareva, Irina, 575 Borodich, Inessa, 378 Brovko, Alexander, 114, 328 Bureev, Artem, 350 C Cherepova, Yuliya, 453 Chernenko, Aleksandr, 91 Chernyshkova, Elena, 320, 367 Christoforova, Alevtina, 91 D Daurov, Stanislav, 175 Dimitrov, Lubomir, 27 Dmitriev, Oleg, 185 Dodonova, Evgeniya, 498 Dolinina, Olga, 250, 328, 367, 443, 639 Dorodnykh, Nikita, 76

E Ermakov, Alexander, 563 Ermakov, Roman, 102, 140 F Filimonyuk, Leonid, 3 Fominykh, Dmitry, 3 Frantsuzova, Galina, 39 G Geyda, Alexander S., 411 Glazkov, Viktor, 175 Golovnin, Oleg, 498, 627 Gusev, Boris, 49 I Ivannikov, Alexander, 209 Ivanov, Sergey, 14 Ivaschenko, Anton, 498, 627 Ivaschenko, Vladimir, 3 Ivzhenko, Sergey, 61 K Kalikhman, Dmitriy, 175 Kalikinskaja, Elena, 547 Kamalov, Leonid, 286 Kamenskikh, Tatiana, 320, 367 Kandaurov, Aleksandr, 639 Kartashev, Aleksandr, 639 Ketova, Karolina, 427 Khanova, Anna, 575 Khanova, Yulya, 575 Khlobystova, Anastasia, 587 Khorovodova, Natalia, 165 Klenov, Dmitry, 522

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 O. Dolinina et al. (Eds.): ICIT 2020, SSDC 337, pp. 657–659, 2021. https://doi.org/10.1007/978-3-030-65283-8

658 Kochetkov, Andrew, 298 Kolbenev, Igor, 367 Kolomin, Artem, 165 Kondratov, Dmitry, 223, 600 Konstantinov, Andrey, 462 Korolev, Mikhail, 328 Koroleva, Julia, 535 Krylov, Boris, 587 Kubekov, Bulat, 453 Kulakova, Ekaterina, 378 Kumova, Svetlana, 547 Kurochkin, Alexander, 615 Kushnikov, Vadim, 3, 378, 547 L L’vov, Alexey, 61, 102, 140, 175, 522 L’vov, Peter, 61 L’vova, Elena, 250 Lakhno, Miroslav, 49 Lakhno, Valerii, 49 Lapshov, Yuriy, 272 Lazarev, Andrey, 378 M Maksimov, Anatolii G., 391, 404 Martyshkin, Alexey, 235 Melnikova, Nina, 102 Miheev, Alexander, 272 Mirgorodskaya, Ekaterina, 194 Miroslavskaya, Lusiena, 535 Mityashin, Nikita, 194 Mogilevich, Lev, 14, 91 Morozova, Svetlana, 615 Moshkin, Vadim, 462 Motorzhin, Andrey, 639 Muchkaev, Artem, 140 Myakhor, Dmitry, 152 N Nikolaenko, Artem, 61 Nikolaychuk, Olga, 76 Nikulina, Yuliya, 125 Nosek, Jaroslav, 27 O Ormeli, Aleksandr, 563 Ovchinnikov, Igor, 350 P Pashchenko, Dmitry, 235 Pechenkin, Vitaly, 328, 367, 547 Perepelkina, Olga, 600 Petrov, Dmitry, 194 Platonov, Aleksei, 535

Author Index Poltoratzky, Vitaly, 639 Popov, Victor, 91 Popova, Anna, 91 Porokhnia, Ivan, 49 Postelga, Alexander, 320 Privalov, Artem, 627 Protalinsky, Oleg, 575 Pudikov, Anton, 114 R Radevich, Stanislav, 320 Reshetnikov, Mikhail, 308 Reva, Ivan, 341 Rezchikov, Alexander, 3 Roth, Huberth, 152 Rozov, Alexander, 165 Ryazanov, Sergey, 308 S Salov, Petr, 298 Seliverstova, Liudmila, 298 Seranova, Anna, 102, 140 Shaker, Alaa, 535 Shatunov, Sergey, 639 Shishkin, Vadim, 272, 286 Shulga, Tatiana, 125 Stolbova, Anastasiya, 498, 627 Stoliarova, Valeriia F., 486 Sukhov, Sergey, 272 Svetlov, Michael, 522 Sviatov, Kirill, 272 Sytnik, Alexander, 3, 125, 522 Sytnik, Alexandr, 140 T Tairova, Kate, 286 Tomashevskiy, Yury, 194 Toropova, Aleksandra, 510 Toropova, Olga, 125, 250 Trokoz, Dmitry, 235 Tulupyev, Alexander L., 391, 404 Tulupyeva, Tatiana, 510 U Umnova, Elena, 102 Usanov, Dmitry, 320 Usanova, Tatiyana, 320 Utepbergenov, Irbulat, 453 V Vagarina, Natalia, 250 Vasiliev, Dmitry, 194

Author Index Vavilova, Daiana, 427 Veselova, Ekaterina, 367 Voloshinov, Alexander, 443 Vostrikov, Anatoly, 39 Y Yarushkina, Nadezhda, 462, 474 Yurin, Aleksandr, 76

659 Z Zakharchenko, Mikhail, 298 Zakharov, Konstantin, 341 Zakharov, Oleg, 298 Zavalishin, Arseniy D., 391, 404 Zhelepov, Alexey, 474 Zhilkishbayeva, Gulnaz, 49 Zhmud, Vadim, 27, 152