Hybrid Metaheuristics in Structural Engineering: Including Machine Learning Applications 9783031347276, 9783031347283

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Studies in Systems, Decision and Control 480

Gebrail Bekdaş Sinan Melih Nigdeli   Editors

Hybrid Metaheuristics in Structural Engineering Including Machine Learning Applications

Studies in Systems, Decision and Control Volume 480

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.

Gebrail Bekda¸s · Sinan Melih Nigdeli Editors

Hybrid Metaheuristics in Structural Engineering Including Machine Learning Applications

Editors Gebrail Bekda¸s Department of Civil Engineering Istanbul University - Cerrahpa¸sa Istanbul, Türkiye

Sinan Melih Nigdeli Department of Civil Engineering Istanbul University - Cerrahpa¸sa Istanbul, Türkiye

ISSN 2198-4182 ISSN 2198-4190 (electronic) Studies in Systems, Decision and Control ISBN 978-3-031-34727-6 ISBN 978-3-031-34728-3 (eBook) https://doi.org/10.1007/978-3-031-34728-3 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 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

In structural engineering design, engineers search for a better design than before. Also, reaching this design must be faster than before. In this case, to consider all design constraints, it is needed to use iterative methods. As iterative methods, metaheuristics are a very useful tool. Instead of generating new metaheuristics, several features of the existing ones may be combined to generate hybrid algorithms. Thus, an improvement in convergence and best optimum results may be provided. In addition to that, machine learning techniques can be used or combined with metaheuristics as a hybrid method. In that case, prediction models can be developed to save time without making an iterative process. This book includes reviews and applications of hybrid metaheuristic algorithms and machine learning used in structural engineering. It contains 14 chapters including an overview and introduction. 14 of 13 chapters are presented in two parts, namely, Part I: Hybrid Metaheuristics and Part II: Machine Learning. In Part I, a review and seven structural engineering applications including reinforced concrete, truss structures, tuned mass damper, composite structures, and dam structures are given. In Part II, two reviews and four machine learning applications about structural engineering problems, reinforced concrete, and building information modeling are given. Istanbul, Türkiye March 2023

Gebrail Bekda¸s Sinan Melih Nigdeli

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Contents

Introduction and Overview: Hybrid Metaheuristics in Structural Engineering—Including Machine Learning Applications . . . . . . . . . . . . . . Gebrail Bekda¸s and Sinan Melih Nigdeli

1

Hybrid Metaheuristics The Development of Hybrid Metaheuristics in Structural Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aylin Ece Kayabekir, Sinan Melih Nigdeli, and Gebrail Bekda¸s Optimum Design of Reinforced Concrete Columns in Case of Fire . . . . . U˘gur Günay, Serdar Ulusoy, Gebrail Bekda¸s, and Sinan Melih Nigdeli Hybrid Social Network Search and Material Generation Algorithm for Shape and Size Optimization of Truss Structures . . . . . . . . . . . . . . . . . . M. Saraee, A. Jafari, D. Yazdani, M. Baghalzadeh Shishehgarkhaneh, B. Nouhi, and S. Talatahari

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Development of a Hybrid Algorithm for Optimum Design of a Large-Scale Truss Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Melda Yücel, Gebrail Bekda¸s, and Sinan Melih Nigdeli

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Structural Control Systems and Tuned Mass Damper Optimization by Using Jaya and Hybrid Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Muhammed Ço¸sut, Sinan Melih Nigdeli, and Gebrail Bekda¸s

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Manta Ray Foraging and Jaya Hybrid Optimization of Concrete Filled Steel Tubular Stub Columns Based on CO2 Emission . . . . . . . . . . . 111 Celal Cakiroglu, Kamrul Islam, and Gebrail Bekda¸s Optimum Design of Dam Structures Using Multi-objective Chaos Game Optimization Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 A. Jafari, M. Saraee, B. Nouhi, M. Baghalzadeh Shishehgarkhaneh, and S. Talatahari

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Contents

Machine Learning The State of Art in Machine Learning Applications in Civil Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Yaren Aydin, Gebrail Bekda¸s, Ümit I¸sıkda˘g, and Sinan Melih Nigdeli Machine Learning Application of Structural Engineering Problems . . . . 179 Ayla Ocak, Sinan Melih Nigdeli, Gebrail Bekda¸s, and Ümit I¸sıkda˘g Modeling Civil Engineering Problems via Hybrid Versions of Machine Learning and Metaheuristic Optimization Algorithms . . . . . 199 Vahdettin Demir, Esra Uray, and Serdar Carbas Comparison of Multilayer Perceptron and Other Methods for Prediction of Sustainable Optimum Design of Reinforced Concrete Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Yaren Aydın, Gebrail Bekda¸s, Sinan Melih Nigdeli, Ümit I¸sıkda˘g, and Zong Woo Geem Artificial Intelligence and Deep Learning in Civil Engineering . . . . . . . . . 265 Ayla Ocak, Sinan Melih Nigdeli, Gebrail Bekda¸s, and Ümit I¸sıkda˘g Deep Learning-Based Framework for Reconstruction and Optimisation of Building Information Models Containing Parametric Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Vincent J. L. Gan

Introduction and Overview: Hybrid Metaheuristics in Structural Engineering—Including Machine Learning Applications Gebrail Bekda¸s

and Sinan Melih Nigdeli

Abstract For the first chapter of the book entitled “Hybrid Metaheuristics in Structural Engineering—Including Machine Learning Applications”, an introduction and overview chapter is given. This chapter includes the importance of optimization in civil engineering as an introduction. Then, metaheuristics are defined as a general frame. Then, machine learning is mentioned. Finally, an overview of the content of the book was given. Keywords Optimization · Metaheuristic algorithms · Hybrid algorithms · Structural engineering · Machine learning

1 Introduction Important factors must be addressed during the design of an engineering structure. These key factors are economics, safety, usage, and architecture. It is not enough to consider one or just a few of these important factors to validate that a design is an optimally designed object. A perfectly done engineering design must consider all of these important aspects to meet the needs of individuals. In this case, an engineer is under a heavy burden to think through all the problems to find the perfect balance between these factors that have generally opposite effects on design objectives. Only experienced engineers can handle all the elements with near perfection. To take these factors into account, various measures should be established and these should be formulated in the design. Since these factors are interrelated, design problems are often non-linear. Because of that, various methods that are specific to the design problem must be developed. Because of their non-linearity, these problems can be approximately addressed using conventional methods. Due to the increasing demands G. Bekda¸s (B) · S. M. Nigdeli Department of Civil Engineering, Istanbul University - Cerrahpa¸sa, 34320 Avcılar, Istanbul, Turkey e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Bekda¸s and S. M. Nigdeli (eds.), Hybrid Metaheuristics in Structural Engineering, Studies in Systems, Decision and Control 480, https://doi.org/10.1007/978-3-031-34728-3_1

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and the advantages of technology, we need a design that is beyond an approximate solution. A few nonlinearities can be handled with difficulty or approximation, or a classical solution cannot be derived without the assumption of a few factors. In this case, experience will have an important role in good design. For a precise and optimal design, the evaluation of the design phases must be iteratively repeated and it can be done by using an algorithm. Civil engineering produces products that are directly effective on individuals. It is one of the fundamental engineering disciplines. For that reason, civil engineers’ products must be economical, safe, and comfortable. In that case, optimization has become a necessity. Civil engineering has many applications, as all designs that provide a living environment fall within the scope of civil engineering. Optimization is needed for all sub-branches of civil engineering including structural engineering, structural mechanics, building materials, building management, geotechnical engineering, transportation engineering and hydraulics. As examples, the applications cover water resources, superstructure and infrastructure projects, stabilization of landfills and soil improvement, public transportation and resources, traffic in transportation, etc. Civil engineering designs are affected by environmental conditions and the world has different geographical areas with different resources and different natural disaster risks. While the most important issue in the design of civil engineering applications is safety, other issues are the preferability index. Structural mechanics theory and experimental research for the safety of designs have been formulated in various arrangements. Although the theory and experiments are generally the same in the regulations, the standards are different in different countries or there are different standard annexes in different countries due to the material production quality, workmanship quality and specific natural disasters in the region. Legislative differences are compounded by the demands of people and social authorities, including resource opportunities in a region. In this case, the optimum design for one region or person may not be the best acceptable design for another. Therefore, these factors are considered specific design constraints and design variable ranges. Optimizing a mechanical engineering product and a civil engineering structure can differ greatly in assigning optimum design results. Generally, using continuous design variables is the best option in search of the best variables. A machine part or an object can be produced in a factory with precise dimensional values. Preciselysized building construction cannot be achieved at a construction site. In this case, discrete variables may be used for structural design or continuous values should be rounded to the practical size. In this case, the exact optimum design can never be used for structural design. Especially, the construction of reinforced concrete structures involves pouring concrete on site and placing the fixed-sized reinforcements that are available in local markets. This situation requires design variables to be assigned specific values. Therefore, the reinforcing steel dimensions should be selected from the dimensions defined by the designer during the optimization processes. In addition,

Introduction and Overview: Hybrid Metaheuristics in Structural …

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profile dimensions for steel structures are produced according to the fixed dimensions of local markets. The optimum design of structures includes the best possible dimensions and design detail practical in construction. In the regulation, design rules have to be defined as design constraints. These constraints can only be calculated if the values of the design variables are known. For that reason, minimization of an objective function is not possible using linear mathematical methods and the optimization problem of finding the best variables is a nonlinear problem. Also for nonlinear methods, the existence of various design constraints (stress limits, shear capacity, minimum and maximum limits, and ductility conditions) and variables (cross-section size and amount of reinforcement for different stress and section types) makes optimization problem to be complex. In this case, numerical optimization methods using iterative analysis are suitable for optimization. Metaheuristic-based optimum design methodologies have been developed for civil engineering problems. In general, these algorithms formulate a process, event or behavior from social life or nature. Similarly, every process, event or behavior has an ultimate purpose, such as optimization objectives in engineering problems. As a first experimental idea, Galilei Galileo worked in 1665 to improve the shape of beams as optimization [1]. Academically, early iterative computational efforts to optimize a beam to minimize the weight of beams were made by Haug and Krimser [2] using design constraints of stress and deflection. Venkaya [3] proposed a search procedure that uses energy criteria to optimize structures including beams, frames and trusses while fully considering the design constraints on the dimensions, stress and displacement of the members under multiple loading conditions. For the optimum design of reinforced concrete (RC) beams, Friel [4] developed an optimum design formulation for the ratio of steel considering that the reinforced concrete beam is subjected to moment only. Chou [5] optimized the depth and bending reinforcement area of reinforced concrete T-beam sections using the Lagrange multipliers method. Krishnamoorthy and Munro [6] proposed a linear programming model that optimizes reinforced concrete frames for constraints about compatibility, limited ductility, stability, and serviceability. Kirsch [7] developed a three-level iterative methodology for cost optimization of a multi-span continuous RC beam. Lakshmanan and Parameswaran [8] determined span-to-effective depth ratios to avoid trial-and-error approaches in the optimum bending design of reinforced concrete sections. Prakash, Agarwala and Singh [9] developed simple optimization techniques for single and double-reinforced beams, T-beams and eccentrically loaded columns. Hoit, Soeiro and Fagundo [10] used augmented Lagrange multipliers and nonlinear programming techniques to minimize the weight of frames. Chakrabarty [11] proposed a model using geometric programming and Newton–Raphson methods for optimization with various constraints. Al-Salloum and Siddiqi [12] obtained a closed-form solution for the area and depth according to the cost and strength parameters by taking the derivatives of the augmented Lagrangian function. Chung and Sun [13] used computational methods including sequential linear programming and gradient projection method for reinforced concrete beams. Adamu et al. [14] proposed a continuous-type optimality criteria method for RC beams.

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2 Metaheuristics The word metaheuristic is derived from the Greek word heuriskein, which means to find or explore, and the word meta, which means upper, advanced, advanced, etc. Many real-world applications have many more complex factors and parameters. Also, the constraints that will affect the behavior and solution of the system, require a specific approach generated via basic scientific thinking of optimum resources in any field [15]. Additionally, the complexity of the problem directs us to iteratively search for any possible solution or combination of solutions. Therefore, finding suitable solutions for the problem within an acceptable duration becomes the main success. Due to that, the uncertainty and irregular structure of metaheuristic approaches can be solutions for various applications and problems that may need a long time to solve. Generally, heuristic algorithms rely on local search procedures around the existing solution and a better solution is iteratively tried to be found. This search is usually terminated when the first local optimum is achieved. On the other hand, metaheuristic methods combine some heuristic approaches and provide better solutions than the previously found local optimums via local search [16]. The main components of any metaheuristic algorithm are concentration/ exploitation and diversification/discovery. Diversification is researching the entire search area and producing various solutions Concentration means focusing on the search (local search) in that region, using the knowledge of the chosen solution by searching for the best available solutions in any region, and choosing the best candidate solutions. While randomization is beneficial in diversifying solutions, it avoids being trap in the local optimum. The diversification phase enables the algorithm to explore the search space more efficiently [17]. On the other hand, these methods are inspired by various things. These may be natural features, special abilities of living things in their lives, some physical and chemical events, evolution/genetic processes and natural events. When we look at nature in general, it is understood that living things have characteristics that are innate or developed for various purposes such as survival, nutrition, and the continuation of species. It is possible to show many examples of these, such as the fox making use of the earth’s magnetic field while hunting, the chameleon changing color to hide from danger, the cuckoo using other birds’ nests for the continuation of its species, the hedgehog stretching themselves and throwing their thorns in danger. When all these processes are examined, it is seen that living things change their defense or attack mechanisms in accordance with the conditions, and they use a kind of heuristic optimization specific to the species that enables them to use the limited opportunities they have in the most appropriate time and manner in order to maintain their vital activities [18]. These intuitive optimization processes of living things in nature have attracted the attention of researchers working on basic sciences and have produced various algorithms that express these processes mathematically.

Introduction and Overview: Hybrid Metaheuristics in Structural … Table 1 Trajectory-based metaheuristic algorithms

Table 2 Evolutionary-based metaheuristic algorithms

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Algorithm

Abbreviation Year Reference

Simulated annealing

SA

1983 [19]

Tabu search

TS

1989 [20]

Variable neighborhood search VNS

1997 [21]

Guided local search

GLS

1998 [22]

Iterative local search

ILS

2003 [23]

Algorithm

Abbreviation

Genetic algorithm

Year

Reference

GA

1992

[24]

Differential evaluation DE

1997

[25]

Clonal selection algorithm

CSA

2000

[26]

Harmony search

HS

2001

[27]

Backtracking search algorithm

BSA

2013

[28]

Stochastic fractal search

SFF

2015

[29]

Across neighborhood search

ANS

2016

[30]

The oldest metaheuristics are trajectory-based ones. As given in Table 1, these algorithms include simulated annealing inspired by the annealing process of metal and tabu search using the human brain. The mostly used metaheuristics are evolutionary-based that are generally inspired by genetics. Also, an evolution process can be formulated. For example, harmony search imitated from the music that is tried to be better for the audience. Common evolutionary-based algorithms are listed in Table 2. Most of the metaheuristic algorithms are nature inspired. As a subcategory, the algorithm may use a different source in nature. As listed in Table 3, the subcategories are bio-inspired, swarm-based, plant-based, physics/chemistry-based and humanbased. Metaheuristics have different inspirations and all processes are formulated with different formulations, but the phases of processes may show similar formulations. In that case, problem-solving is more important than imitation. Thus, different features of these algorithms can be combined to generate a new hybrid algorithm without the need for a metaphor as an inspiration. The period that will be orientated on the scientific problem will be the future period [92].

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Table 3 Nature-based metaheuristic algorithms Algorithm

Abbreviation

Subcategory

Year

Reference

Particle swarm optimization

PSO

Swarm-based

1995

[31]

Artificial bee colony

ABC

Bio-inspired

2005

[32]

Ant colony optimization

ACO

Bio-inspired

2006

[33]

Glowworm swarm optimization

GSO

Swarm-based

2006

[34]

Shuffled frog leaping algorithm

SFLA

Bio-inspired

2006

[35]

Invasive weed optimization

IWO

Plant-based

2006

[36]

Seeker optimization algorithm

SOA

Human-based

2006

[37]

Imperialistic competitive algorithm

ICA

Human-based

2007

[38]

Biogeography based optimization

BBO

Human-based

2008

[39]

Firefly algorithm

FA

Bio-inspired

2008

[40]

Intelligent water drops

IWD

Swarm-based

2008

[41]

Monkey algorithm

MA

Bio-inspired

2008

[42]

Cuckoo search

CS

Bio-inspired

2009

[43]

Group search optimizer

GSO

Swarm-based

2009

[44]

Hunting search

HS

Swarm-based

2009

[45]

Chemical reaction optimization

CRO

Physics/chemistry-based

2009

[46]

Bat algorithm

BA

Bio-inspired

2010

[47]

Charged system search

CSS

Physics/Chemistry-based

2010

[48]

Cuckoo optimization algorithm

COA

Bio-inspired

2011

[49]

Teaching–learning-based optimization

TLBO

Human-based

2011

[50]

Krill herd algorithm

KHA

Bio-inspired

2012

[51]

Migrating birds optimization

MBO

Swarm-based

2012

[52]

Black hole algorithm

BH

Physics/chemistry-based

2013

[53]

Dolphin echolocation

DE

Bio-inspired

2013

[54]

Animal migration optimization

AMO

Swarm-based

2013

[55]

SDA optimization algorithm

SDA

Bio-inspired

2014

[56] (continued)

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Table 3 (continued) Algorithm

Abbreviation

Subcategory

Year

Reference

Artificial root foraging algorithm

ARFA

Plant-based

2014

[57]

Chicken swarm optimization

CSO

Bio-inspired

2014

[58]

Flower pollination algorithm

FPA

Plant-based

2014

[59]

Radial movement optimization

RMO

Swarm-based

2014

[60]

Spider monkey optimization

SMO

Bio-inspired

2014

[61]

Elephant search algorithm

ESA

Bio-inspired

2015

[62]

Grey wolf optimizer

GWO

Bio-inspired

2015

[63]

Jaguar algorithm

JA

Bio-inspired

2015

[64]

Locust swarm algorithm

LSA

Swarm-based

2015

[65]

Moth-flame optimization

MFO

Bio-inspired

2015

[66]

Vortex search algorithm

VSA

Physics/chemistry-based

2015

[67]

Water wave optimization

WWA

Physics/chemistry-based

2015

[68]

Ant lion optimizer

ALO

Bio-inspired

2015

[69]

African buffalo optimization

ABO

Swarm-based

2015

[70]

Lightning search algorithm LSA

Physics/chemistry-based

2015

[71]

Crow search algorithm

CSA

Bio-inspired

2016

[72]

Electromagnetic field optimization

EFO

Physics/Chemistry-based

2016

[73]

Joint operations algorithm

JOA

Swarm-based

2016

[74]

Lion optimization algorithm

LOA

Bio-inspired

2016

[75]

Sine cosine algorithm

SCA

Physics/chemistry-based

2016

[76]

Virus colony search

VCS

Bio-inspired

2016

[77]

Whale optimization algorithm

WOA

Bio-inspired

2016

[78]

Red deer algorithm

RDA

Bio-inspired

2016

[79]

Phototropic optimization algorithm

POA

Plant-based

2018

[80]

Coyote optimization algorithm

COA

Swarm-based

2018

[81]

Owl search algorithm

OSA

Bio-inspired

2018

[82]

Squirrel search algorithm

SSA

Bio-inspired

2018

[83] (continued)

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Table 3 (continued) Algorithm

Abbreviation

Subcategory

Year

Reference

Social engineering optimizer

SEO

Human-based

2018

[84]

Emperor penguin optimizer

EPO

Bio-inspired

2018

[85]

Future search algorithm

FSA

Human-based

2019

[86]

Emperor penguins colony

EPC

Swarm-based

2019

[87]

Thermal exchange optimization

TEO

Physics/chemistry-based

2019

[88]

Bio-inspired

2019

[89]

Harris Hawks optimization HHO Political optimizer

PO

Human-based

2020

[90]

Heap-based optimizer

HBO

Human-based

2020

[91]

3 Artificial Intelligence and Machine Learning Machine learning, one of the sub-disciplines of artificial intelligence, is the process of focusing on various methods and algorithms for providing learning activity by computers. Here, in the machine learning process, when a sample data set is given to any system, learning can be performed by generating information about the data and the connections/relationships between the data. In this context, the concept of machine learning can be defined as the development of systems that can learn, feel and create a reaction/response for a situation by enabling machines, computers, software and even robots to perform many activities that can only be done by a person with real intelligence and mind. Machine learning has become important in many working disciplines, especially in recent years, and in this context, smart systems, software and tools have been developed by using various learning techniques and algorithms. In this sense, the machine learning technology in question can be used by researchers, designers, engineers, etc. during the acquisition of some necessary outputs or the finding of parameters/information. In addition to providing ease of use for anyone or anyone interested in this field, it provides many advantages in terms of cost and time savings and efficient expenditure of labor. Thanks to the machine learning processes carried out, time and effort are saved by leading the necessary activities in the scientific field as well as in many areas of daily life. These methods have been used in several health services including determining mental health [93–95], estimating the probability of occurrence of some diseases [96–98], detecting cancerous cells in organisms [99–101], etc. On the other hand, the engineering discipline is one of the fields where machine learning applications are already being used and are becoming more widespread day by day. In this context, estimating the water demand for existing users [102, 103], energy planning to ensure efficiency [104, 105] and obtaining some mechanical properties of structural materials [106–108] can be given as recent examples.

Introduction and Overview: Hybrid Metaheuristics in Structural …

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In structural engineering, machine learning is generally used with metaheuristic algorithms to generate a hybrid process. In this process, metaheuristics are employed for the optimization and data of several design constants are generated. Then, this data is used in machine learning. Thus, an artificial intelligence model that predicts optimum results of a case of design constants without a rerun of the iterative process is generated to save time. Examples of these applications are estimating the optimal model parameters of structural elements [109–111] and estimation of optimized mechanical parameters for tuned mass dampers (TMD) [112–114].

4 Overview of the Book Content The book entitled “Hybrid Metaheuristics in Structural Engineering—Including Machine Learning Applications” is organized into two parts. The first part is about the optimization of structural engineering using hybrid metaheuristics. Chapter 2 summarised the recent developments in structural optimization using hybrid metaheuristics. Then, reinforced concrete columns are optimized via a hybrid algorithm by considering the case of fire. Chapters 4 and 5 are about the optimization of truss structures. As Chap. 6, a passive structural control that is tuned mass damper is optimized via hybrid metaheuristics. A concrete-filled steel tubular (CFST) structure optimization is explained in Chap. 7. A multi-objective optimization of dam structures is presented in Chap. 8. The second part is related to prediction applications using machine learning. As the first chapter of the second part, the current state of art in machine learning in civil engineering is presented as Chap. 9. Then, several structural engineering applications such as tubular column and I-beam optimization examples are presented for the machine learning prediction model in Chap. 10. In Chap. 11, metaheuristic optimization algorithms and machine learning techniques are hybridized to present civil engineering problems. Chapter 12 presents a prediction application for the eco-friendly optimum design of reinforced concrete columns. Then, a review of artificial intelligence and deep learning is given in Chap. 13. Finally, a deep learning application about building information modeling is generated in Chap. 14.

References 1. Galilei, G.: Dialogues Concerning Two New Sciences. Northwestern University Press, Evanston, IL (originally published in 1665) (1950) 2. Haug, E.J., Kirmser, P.G.: Minimum weight design of beams with inequality constraints on stress and deflection. J. Appl. Mech. 34(4), 999–1004 (1967) 3. Venkayya, V.B.: Design of optimum structures. Comput. Struct. 1(1–2), 265–309 (1971) 4. Friel, L.L.: Optimum singly reinforced concrete sections. J. Proc. 71(11), 556–558 (1974, November)

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Hybrid Metaheuristics

The Development of Hybrid Metaheuristics in Structural Engineering Aylin Ece Kayabekir, Sinan Melih Nigdeli, and Gebrail Bekda¸s

Abstract In engineering designs, the variables in the problems are needed to define by checking several constraints. In that case, the problem is a nonlinear one that needs several iterations when the best suitable solution is wanted. To find the best solution, several algorithms may be employed to iteratively search for the optimum solution. These algorithms are inspired by happening or processes to provide different formulations. As the current trend, multiple algorithms are combined to update efficient features instead of using a metaphor. In this chapter, a review is presented for hybrid metaheuristics in structural engineering applications. Keywords Hybrid algorithms · Structural engineering · Optimization · Metaheuristics · Constraints

1 Introduction At the start of life, people tried to solve problems to invent something. Then, they need to consider additional factors to eliminate negative issues in the first design. As time progress, engineers must make this design perfect and optimum. To find the best balance between constraints and factors that are the design objectives, it is needed to try several iterations and these iterations can be automatically done by several algorithms. Metaheuristics have great importance in this solution. According to Sörensen et al. [1], the development of metaheuristics can be given in five periods. The first period was named the pre-theoretical period. Heuristics are essentially used by the human brain, but it is not studied. In this period, humans copied several previously solved problems to solve new ones that are essential to A. E. Kayabekir Department of Civil Engineering, Istanbul Geli¸sim University, Avcılar, Istanbul, Turkey S. M. Nigdeli (B) · G. Bekda¸s Department of Civil Engineering, Istanbul University - Cerrahpa¸sa, 34320 Avcılar, Istanbul, Turkey e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Bekda¸s and S. M. Nigdeli (eds.), Hybrid Metaheuristics in Structural Engineering, Studies in Systems, Decision and Control 480, https://doi.org/10.1007/978-3-031-34728-3_2

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living and surviving. For that reason, the heuristic belongs to the human and these algorithms can be mentioned as artificial intelligence. After World War II, a new period called “the early period” starts and the principles such as analogy, induction, and auxiliary problem are mentioned. As an analogy, the problem was tried to be solved by another problem. As induction, the learned techniques are used, and finally, the problem was transformed into smaller problems as an auxiliary problem. After 1980, the method-centric period started. In this period, several metaheuristics such as Tabu Search [2], Genetic Algorithm [3, 4], and Simulated Annealing [5] were developed. After 2000, the framework gains more interest instead of solving the problem. Thus, the number of metaheuristic methods showed a great increase. After the 80s, the metaphor used in the development of the algorithm showed more interest. Opposite to that, solving the problem is more scientifically important. For that reason, the future will be the scientific period. In this period, more complex and challenging problems will be needed to be solved. For that reason, great effort must be given to find the exact method that is the best for the problem. This situation can be provided by hybridizing the effective known features of existing algorithms instead of proposing new ones that are similar to previous algorithms. This chapter includes a brief definition of metaheuristic algorithms. Then, the objectives and constraints in structural engineering are summarized. Then, the applications using hybrid algorithms are reviewed in structural engineering.

2 Metaheuristic Algorithms and Optimization In engineering design and optimization, the key method that is used are metaheuristics. It provides a formalized generation of design variables to find the coded objective functions that are penalized for constraint violation. In short, a design variable (x i ) is searched within defined minimum (x min ) and maximum (x max ) values by using randomization. As the most basic formulation, Eq. (1) can be given as a linear search with a random parameter shown as ε. xi = xmin + ε(xmax − xmin )

(1)

Equation (1) is generally used in the definition of initial values and special features of algorithms were used to update this solution. A general flowchart is shown in Fig. 1.

The Development of Hybrid Metaheuristics in Structural Engineering Fig. 1 A general flowchart for metaheuristic algorithms

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START

Define problem constants, algorithm parameters and ranges of design variables

Randomly generate the initial solutions

Modify the existing solutions by using the features of the algorithms

NO

Are the stopping criteria provided?

YES

STOP

3 The Structural Optimization Problems The engineering optimization aims to find a set of design variables (x i ) that minimize or maximize objective function ( f (x)) according to several constraints that may be equality (h(x) = 0) or inequality (g(x) ≤ 0) functions. In this section, possible objectives and constraints in structural engineering are mentioned.

3.1 Objective Function Weight (W ) is one of the objective functions that is needed to minimize to maximize material amount or decrease the self-weight. Also, it may be efficient for transportation or use in space. The second objective is cost. It can be also directly related to weight, but composite materials with different costs (especially in reinforced concrete structures) show different situations since the costs of different materials are different, too. Thirdly, the response such as deflection or stress of structural members can be considered as objectives. The response of structures can be also considered as a second objective or as a constraint.

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The efficiency of the use of additional system in design can be used as an objective function. Especially, for structural control systems, the efficiency of response reduction can be maximized to make a perfectly tuned control system. Finally, environmental factors such as CO2 emission minimization can be used as an objective to find a sustainable design.

3.2 Design Constraints As the design constraint of structure, several rules are given in the design codes. One of the factors in engineering design is not to exceed stress capacity. The stress capacity must be checked for different sections and types including normal (axial) stress and shear stress. As seen in Fig. 2, the buckling load (N) must be checked for slender structural systems. For steel members, the fatigue of the member under cycled load must be checked as a constraint. Also, deflections must be limited and member sections may be wanted to be in a specific range according to design codes. Fig. 2 Buckling

N

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4 Review of Structural Engineering Applications Using Hybrid Algorithms In 2008, a hybrid Harmony search algorithm using sequential quadratic programming was presented by Fesanghary et al. [6] for the optimization of engineering problems. The hybrid approach was implemented for various benchmark problems. According to this, the proposed approach was capable to find quality results and was successful in terms of required fitness function numbers. Kaveh and Talatahari [7] proposed a hybrid algorithm combined harmony search (HS) scheme, particle swarm optimizer, and ant colony optimization (ACO). The analyzes done for truss and frame systems revealed that the proposed method is effective to obtain optimal solutions to continuous or discrete optimization problems. For the optimum design of fuzzy-PID controllers, the combination of PSO and Evolutionary Programming (EP), was investigated by Chiou and Liu [8]. In this study, it was shown that fuzzy-PID controllers using the PSO-EP method have been successful in evaluating indices such as the rise time, settling time, peak time, maximum overshoot, and Integral of Absolute Error. Sandesh and Shankar [9] introduced a hybrid method based on PSO and Genetic Algorithm (GA). The method runs for the identification of damages in a thin plate due to multiple cracks. In this application, although a single PSO was to be fast and hybrid method provided more accurate damage prediction. In another study, PSO was hybridized with a simultaneous perturbation stochastic approximation (SPSA) algorithm by Seyedpoor et al. [10] for structural optimization. The benchmark examples on truss systems that were solved by various methods, indicated that SPSA-PSO combination was successful in terms of quality of optimum results and structural analyses. In 2011, Plevris and Papadrakakis [11] investigated the improved PSO method using the gradient-based quasi-Newton sequential quadratic programming (SQP) method. The performance of the method was analyzed on the various truss system and, it was concluded that the proposed method obtained better optimum solutions according to other methods such as PSO, GA, SQP. The Genetic algorithm was hybridized with Nelder Mead simplex was presented by Rahami et al. [12] and then used to minimize the weight of truss structures. Analysis results showed that robust optimization results were obtained with the hybrid algorithm. Another truss optimization was done by Hadidi et al. [13]. In the optimization process, PSO and Simulated Annealing (SA) combination (PSO-SA) was utilized to prevent the stuck local minimum problem. The efficiency of the PSO-SA was tested on several benchmark examples. This investigation demonstrated that PSO-SA was efficient and provide computational advantages regarding standard PSO and several heuristic algorithms. Also, Lee et al. [14] used a PSO-SA hybrid algorithm for the Sliding mode control of isolated bridges. In this investigation, the hybrid algorithm outperformed PSO as well.

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Kaveh and Talatahari [15] combined PSO with the charged system search (CSS) for the optimum design of structures. Three structures including containing a truss, a frame, and a grillage system were optimized with a developed hybrid algorithm (PSO-CSS). Generally, PSO-CSS found better solutions considering computational costs according to CSS, PSO, and other advanced heuristic methods like GA, BB-BC, evolution strategies (ESs), ACO, and harmony search (HS). In 2013, multi-objective design problems including benchmark functions and a welled beam were solved by Rachid and Rajae [16]. The optimization process was carried out with the combination of the Normal Boundary Intersection approach (NBI) and the Simulated Annealing Simultaneous Perturbation (SASP) method. It resulted that, the NBI-SASP combination provided a well-distributed Pareto front and was successful to solve real-world application problems. Pholdee and Bureerat [17] carried out a multi-objective optimization process via incorporation (RPBIL-DE) of differential evolution (DE) and population-based incremental learning (RPBIL) for truss systems. RPBIL-DE was tested on several examples solved by some other multi-objective evolutionary algorithms (MOEAs). Results of the examinations showed that DE improved performance of RPBIL and RPBIL-DE have better performance compared to other techniques. For the size and geometry optimization of truss structures, Shojaee et al. [18] proposed a method based on discrete PSO and the method of moving asymptotes (MMA). The analysis shows that the method has effectively accelerated the convergence rate capability. In addition to these studies, several hybrid methods have been developed to solve truss problems such as HS-PSO [19], cellular automata-PSO [20], GA-phenotypical probabilistic local search algorithm [21]. Amini and Ghaderi [22] suggested using HS with ACO to determine the optimum location of dampers attached to structures. Numerical examples showed that hybridized search algorithm improved the convergence rate. Khajehzadeh et al. [23] integrated the firefly algorithm (FA) with sequential quadratic programming (SQP). The hybrid method was tested on the design optimization of reinforced concrete (RC) foundations and it outperforms FA. Glowworm swarm optimization (GSO) was combined with Simulated Annealing (SA) by García-Segura et al. [24]. In the numerical example, the cost and CO2 emissions of a concrete I-beam were minimized, and the hybrid algorithm was more efficient and provided more convergence rate than GSO. Long et al. [25] proposed that the Pattern search method incorporate into the cuckoo search (CS) algorithm to enhance approximation capability. The developed method implemented several benchmark problems. According to the analysis results, the proposed algorithm was effective, efficient, and robust in solving structural design optimization problems. A hybrid algorithm including the advantages of PSO and CSS was presented by Talatahari et al. [26] for the seismic design optimization of steel frames. In the seismic design process, four performance levels were considered to minimize structural costs. Two building frameworks were optimized with the hybrid algorithm as well as GA,

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ACO, PSO, and PSACO. The optimum results showed that the presented hybrid algorithm found a better seismic design. Liu et al. [27] developed a hybrid procedure using finite element analysis, Neural networks, GA, and the Monte-Carlo method to evaluate the reliability of cable-stayed bridges. The method was tested on two numerical examples. According to this, the hybrid procedure provided accuracy satisfactorily and was efficient in calculations. A hybrid evolutionary approach combining gravitational search algorithm (GSA) and pattern search (PS) was presented by Khajehzadeh et al. [28] for multi-objective optimization of retaining walls. The hybrid approach is employed for two objective functions i.e. total cost and amount of embedded CO2 emissions. The comparative analysis indicates that the presented approach provided better computational efficiency and robustness than standard GSA and some other methods. For the optimum reinforced concrete (RC) design against seismic excitations, the PSO algorithm using an intelligent regression model (IRM) was presented by Gharehbaghi and Khatibinia [29]. The hybrid method was applied to 9- and 18-story RC frames under earthquake loads for the minimum cost. It was concluded that IRM was effective to predict average time-history responses (ATHR) of structure and reduce the time of the optimization process. Hadidi and Rafiee [30] introduced a hybrid algorithm combining Harmony Search (HS) and Big Bang-Big Crunch (BB-BC) for the design optimization of semi-rigid connection steel frames. The optimization process was to search optimum sections and connections of beams and columns to minimize cost. Three benchmark optimization problem was solved proposed approach. According to the results, it was observed that the introduced method outperform classical BB-BC and HS methods. An investigation was carried out by Akın and Aydo˘gdu [31] to calculate the minimum weight of design steel space frames. In the optimization process, TLBO and HS collaboration (hTLBO-HS) was utilized. Analysis results demonstrated that hTLBO-HS was found better solution than standard HS. In 2016, Babaei and Sanaei [32] developed a hybrid method using ACO and GA for multi-objective optimization of braced frames. In the optimization process, optimum cross sections of structural members and optimum topologies of the braces were searched to provide minimum weight and minimum displacement. Analysis results demonstrated that the developed method was capable to obtain optimum topologies and sections. Khajehzadeh [33] investigated a hybrid optimization method based on pattern search with the gravitational search algorithm (GSA) for RC retaining walls. The example done for minimum embedded CO2 emissions revealed that the hybrid method performs better than GSA in terms of efficiency and robustness. In another study conducted in 2016, Sheikholeslami et al. [34] solved the minimum cost problem of the retaining wall. It has developed a higher-performance solution method by combining the firefly algorithm with HS. For the reduction of computational effort, the upper bound strategy (UBS) was also included in the optimization process. The proposed method was effective to find the minimum cost with a lower number of analyses.

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Kaveh and Shokohi [35] optimized castellated beams by hybridizing Colliding Bodies Optimization (CBO) and PSO to obtain minimum cost. The hybrid method developed in this study was applied to 3 different benchmark problems and its performance was compared with existing methods. Hybridization of CBO and PSO generally provided less cost. Maheri et al. [36] proposed the PSO-GA hybrid technique to find the optimum size and topology that provide the minimum weight of trusses. As a result of analyses carried out on several benchmark problems, the PSO-GA hybrid method achieved better solutions with better convergence compared to GA, PSO, and other hybrid methods. Hybrid HS using Global-best PSO search and neighborhood search was introduced by Cheng et al. [37]. The method was tested on the optimum design of truss structures. Analyzes results show that the proposed method generally was superior to other optimization methods used for comparison in terms of optimum results and convergence rate. For a more effective, robust, and cheaper design of spatial structures, a hybrid methodology consisting of genetic programming and local search methods was proposed by Assimi et al. [38]. Hoseini Vaez and Fallah [39] investigated damage detection with its location and its severity in thin plates. For that reason, a hybrid approach based on GA and PSO was developed. In the optimization process, the objective function was formulated considering natural frequencies and the mode shapes of the structure and minimized. According to evaluations done on the three different plates for four damage scenarios, it was observed that the proposed approach provides less error index in comparison to GA and PSO. A hybrid algorithm including modified PSO and modified GSA was developed by Chutani and Singh [40] for the cost minimization of RC frames. Analysis results revealed that the modified hybrid algorithm improved the performance of PSO and GSA by overcoming the limitations of the algorithms. Jiale [41] optimized structural sensor configuration for civil engineering problems. The optimization process was carried out by simulated annealing-genetic algorithm combination and the optimum number and position of the sensor were obtained. In 2018, Nelder–Mead local search operator was incorporated into the genetic programming algorithm by Assimi and Jamali [42] to find the optimum topology and size of truss structures considering static and dynamic constraints. The proposed algorithm was employed for some optimization problems with continuous and discrete design variables. It was observed that the hybrid algorithm performed better generally than other methods used in the optimization of the numerical examples. Design optimization of large-scale dome truss structures was done by Kaveh and Ilchi Ghazaan [43]. For that reason, the vibrating particle system algorithm, multidesign variable configuration cascade optimization, and an upper-bound strategy were combined. Comparative analyzes showed that the proposed hybrid combination had powerful search capability and was suitable for structural engineering problems. In 2019, a methodology using the plant growth simulation algorithm and particle swarm optimization was developed by Jiang et al. [44] for structural optimization.

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The method tested on a pre-stressed spatial steel dome, was found to be effective and applicable for structural optimization. Huang et al. [45] suggested combining PSO and cuckoo search (CS) to determine the damage to structures under noise and temperature environments. The numerical analysis was done for the simply supported beam. The suggested method has superior performance than PSO and CS algorithms. Total potential optimization employing hybrid metaheuristics using fundamentals of JA and phases of FPA and TLBO algorithms was investigated by Bekda¸s et al. [46]. In this study, four different hybrid methods were developed; i.e. JA using Lévy flights, JA using Lévy flights and linear distribution, JA with consequent student phase, and JA with probabilistic student phase (JA1SP). These hybrid methods were also compared with DE, PSO, and HS considering large-scale truss analysis problems (Fig. 3). Comparative analysis revealed that JA1SP provides better convergence to a global optimum. Jafari et al. [47] presented a hybrid optimization method that enhances the performance of elephant herding optimization (EHO) via the cultural algorithm (CA). The hybrid algorithm (EHOC) was employed for mathematical optimization problems and to minimize the truss weight. Analysis results show that EHOC has efficient convergence capability and provides better solutions in comparison to EHO and CA. In the other study conducted by Jafari et al. [48], the PSO algorithm was improved by using the cultural algorithm. Developed methods provide effective solutions and convergence rates for the optimum design of truss structures. For the cost minimization of the waffle slab, mouth-brooding fish (MBF) and colliding bodies optimization (CBO) algorithms were hybridized by Shayegan et al. [49]. Comparing the performance of the proposed method with MBF, CBO, harmony search (HS), PSO, democratic particle swarm optimization (DPSO), charged system search (CSS), and enhanced charged system search (ECSS), it was concluded that the proposed method is effective to obtain an optimum solution. Han et al. [50] presented a hybrid algorithm named (MSFWA) combining moth search (MS) and fireworks algorithms (FWA). MSFWA was effective and provide fast approximation in solving several benchmark functions and engineering design problems. García et al. [51] optimized cost and CO2 emissions for counterfort retaining walls. In the optimization process, a method based on Cuckoo Search Algorithm and k-Means Operator which is a machine learning algorithm was employed. This application showed that k-Means Operator provided significant quality solutions and the proposed method found the superior result according to HS. A technique, a hybrid form of ant lion optimizer, and an improved Nelder–Mead algorithm were suggested to detect structural damage by Chen and Yu [52]. For the verification of the hybrid technique, benchmark functions, two numerical simulations including a two-story rigid frame, and 31-bar planar truss structures were utilized and experimental validation for the simply supported beam was carried out. According to these, it was claimed that the proposed technique was successful to determine the location and severity of the damage.

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Fig. 3 Truss structures analyzed via hybrid algorithms [46]

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In addition to the optimization problems presented above, many research articles have been done on the truss optimization problem. For this purpose, several hybrid algorithms were proposed such as the invasive weed optimization-shuffled frogleaping algorithm [53], TLBO-HS [54, 55], PSO-GA [56] and firefly algorithmoptimality criteria [57]. Kayabekir et al. [58] developed a hybrid procedure (HHS) combining the local search phases of HS and the global search phase of the FPA to minimize total potential energy for structural systems. In this study, HSS applied to solve plane stress members (Fig. 4) and compared several metaheuristics such as s HS, FPA, TLBO, and JA. As a result, HSS reached the best solutions quickly. In the other study, four different hybrid algorithms using HS, TLBO, FPA, and JA were proposed by Toklu et al. [59]. The hybrid algorithms were employed for the total potential optimization of tunnel structures (Fig. 5). According to the analysis results, it was observed that Total Potential Optimization via hybrid algorithms increased the capacity of solving the problem.

Fig. 4 Plane-stress members [58]

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Fig. 5 The tunnel system [59]

An adaptive version of HS was hybridized with JA to get rid of stuck-in local optimum by Yücel et al. [60] for the optimum cost of RC retaining walls. A comparative analysis conducted by several metaheuristic algorithms demonstrated that adaptive-hybrid HS can achieve optimum solutions using fewer population numbers. Kaveh et al. [61] combined Harris Hawks Optimizer (HHO) with the Imperialist Competitive Algorithm (ICA) to enhance the exploration performance of HHO. The performance of the developed hybrid algorithm was tested by several benchmark optimization problems employing nature-inspired algorithms. These comparisons showed that the hybrid algorithm is efficient in structural optimization. Similarly, the HHO algorithm was improved by teaching the learning-based optimization (TLBO) algorithm to get rid of the trap in the local optimum. Examinations on benchmark functions and engineering optimization problems demonstrated to increase in the global performance capability of the proposed method [62]. Three ANN (artificial neural network) models were developed by different optimization algorithms; i.e. PSO, Archimedes optimization algorithm (AOA), and sparrow search algorithm (SSA), to estimate the shear capacity of reinforced concrete deep beams by Barkhordari et al. [63]. It has been observed that among hybrid models, the PSO model can achieve more precise results by using a lower neuron and hidden layer. In the other study, Grey Wolf Optimization (GWO) improved via PSO was implemented for static and dynamic crack identification of two-dimensional plates [64]. The comparative analysis demonstrated that the improved GWO (IGWO) outperforms than original GWO in terms of the accuracy of results. IGWO and GWO were also used for the prediction of ANN parameters. In this application, IGWO provided a better estimation of crack length as well.

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Firouzi et al. [65] conducted a study using optimization algorithms such as Harris hawk optimization (HHO), electrostatic discharge algorithm (ESDA), pathfinder algorithm (PFA), and Henry gas solubility optimization (HGSO), and hybrid versions of the algorithms to detect cracks in cantilever beams. In the hybrid version of algorithms, Nelder–Mead (NM) algorithm is included in the optimization process. According to comparative analyzes, Hybrid algorithms outperformed in the prediction of crack capability. Kayabekir et al. [66] proposed metaheuristic-based hybrid design procedures to optimize active tuned mass dampers (ATMDs) added to structures under earthquake excitations (Fig. 6). For the generation of hybrid algorithms, four different metaheuristic algorithms; i.e. Harmony search (HS), Flower pollination (FPA), Teaching Learning Based Optimization (TLBO), and Jaya (JA) are combined. The slime mold algorithm (SMA) is hybridized with the sine cosine algorithm to avoid getting stuck in the local search space by Örnek et al. [67]. The proposed method was employed for various benchmark functions and optimization problems such as the design of a cantilever beam, pressure vessel, 3-bar truss, and speed reducer problems. As a result of these applications, the hybrid algorithm has superior convergence than standard sine cosine and SMA algorithms. Similarly, Chauhan et al. [68] also hybridized the SMA and AOA algorithms against less internal memory and slow convergence. The hybrid method has better performance than classical SMA and AOA on various real-world problems such as the design of spring, pressure vessel, welded beam, and three-bar truss. In 2023, Cao [69] presented a hybrid constraint-handling method considering the Deb rule and the mapping strategy for the optimum size and shape of truss structures. According to the results of the comparative analysis, it was seen that the Hybrid CHT method is one of the effective methods that can be used in solving such problems.

5 Conclusion As seen from the literature review about structural optimization using a hybrid metaheuristic algorithm, the subject is the latest trend in optimization. Hybrid algorithms are effective in finding the optimum solution by eliminating back draws of existing algorithms and adding new features of other algorithms. In the future, hybridization will be more effective since the huge increase in the number of metaheuristic algorithms. According to the no-free-lunch theorem, there is no superior algorithm that can perfectly solve all problems. Also, the performance of the algorithm may show differences according to design constant cases. For that reason, humans will always need new ways to find the best solution for their current interests.

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Fig. 6 Structure with ATMD [66]

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Optimum Design of Reinforced Concrete Columns in Case of Fire U˘gur Günay, Serdar Ulusoy, Gebrail Bekda¸s, and Sinan Melih Nigdeli

Abstract When designing load-bearing reinforced concrete components, external factors such as fire should be taken into account in addition to horizontal and vertical forces. Parameters such as cross-section of the reinforced concrete components, concrete cover, material properties and quantity of the concrete steel affect significantly the fire resistance of the reinforced concrete section exposed to fire. In this study, optimal cross-sections are obtained for 30, 60 and 90 fire duration taking into account the different cross-sections and concrete cover of the reinforced concrete column. The method for calculating the optimal sections of reinforced concrete columns is the modified metaheuristic algorithm, which is a combination of Flower Pollination Algorithm (FPA) with Jaya Algorithm (JA). The behavior of reinforced concrete column in case of fire is investigated according to EN-1992-1-2 (Eurocode 2: Design of reinforced concrete structures-Part 1–2: General rules—Structural fire design). The Eurocode offers 3 different methods for the fire design of concrete structures (simplified, advanced calculation methods and the tabulated date). In this study, optimal results are obtained in the tabulated date section. Thus, some limitations in EN-1992-1-2 such as minimum reinforcement cross-sectional area and column buckling length have been overcome. Keywords Reinforced concrete column · Fire design · Metaheuristic algorithm · Optimization · Eurocode 2

U. Günay · S. Ulusoy Department of Civil Engineering, Turkish-German University, 34820 Beykoz, Istanbul, Turkey e-mail: [email protected] S. Ulusoy e-mail: [email protected] G. Bekda¸s · S. M. Nigdeli (B) Department of Civil Engineering, Istanbul University - Cerrahpa¸sa, 34320 Avcılar, Istanbul, Turkey e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Bekda¸s and S. M. Nigdeli (eds.), Hybrid Metaheuristics in Structural Engineering, Studies in Systems, Decision and Control 480, https://doi.org/10.1007/978-3-031-34728-3_3

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1 Introduction Fire is a rapid combustion event that occurs when three main factors come together, referred to as the fire triangle in the literature. The three main factors in this event accompanied by flames are combustible material, oxygen and heat source. At the end of this combustion process, carbon monoxide (CO), which can be fatal for many living beings, is formed as a combustion product of oxygen and carbon in burning materials. A further fatal effect of this phenomenon can be seen in the damage it causes to the failure of buildings. In recent years, especially in large cities, the incidence and damages caused by this effect have been increasing with the growing density of building stock per unit area. In the 10 year period between 2011 and 2020, over 13 million fire incidents were recorded across the United States, resulting in over 30,000 fatalities [1]. As the statistics show, the importance of the design and protection of buildings against fire is getting vital. The strength properties of concrete and structural steel materials, which are the two main components of reinforced concrete structural elements, have an important connection with temperature change. In particular, it is undeniable that a sudden effect such as fire, which rises above 1000 °C (Fig. 1) in short periods, leads to rapid heating of the materials themselves depending on their thermal properties, thus causing sharp changes in their behavior [2]. In a study on the fire resistance of concrete specimens with different compressive strengths, it was observed that the specimens lost more than half of their compressive strength at 600 °C and more than 75% of their tensile strength at room temperature (20 °C) [3]. On the other hand, in another study on the behavior of the other main element, structural steel, at high temperatures, a strength loss exceeding 80% was observed in the strength of 12 mm diameter structural steel with a yield strength of 426 MPa at normal temperatures (Fig. 2) [4]. It should be noted here that this temperature does not reach all points of the column at the same time and this loss of strength is not in the whole element. Attention should be paid to spalling, which is one of the most important factors that cause this spread to accelerate. Resilience capacity in the context of a fire disaster reflects the ability to prevent a fire from occurring and to limit the initial damage if a fire does occur. When protection methods are considered in order to limit this damage, two main headings, active and passive protection, emerge. While active protection requires an external intervention, passive protection can be seen as measures taken in the design and manufacture of building elements. Systems such as audible warning systems, smoke detection systems, and automatic fire sprinklers that are already in the building before the fire and are activated during the fire can be given as examples of active protection systems. The design of building elements, fire compartments, fire walls, paints that increase resistance to heat and thermal barrier building elements made of polypropylene fiber can be examples of passive protection. In addition to protecting the structural steel in reinforced concrete elements against corrosion, the concrete cover also protects against events such as fire, which cause high temperatures and greatly reduce the ductility of steel. Concrete, which plays a

Optimum Design of Reinforced Concrete Columns in Case of Fire

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Fig. 1 ISO 834 standard fire curve (ISO, 1975) Fig. 2 Stress–strain graph of structural steel at elevated temperatures [4]

major role in resistance against pressure, which is one of the main tasks of elements such as columns, causes loss of cross-section as a result of pouring. This can lead to an increase in stress and result in the collapse of the structure. Many factors such as aggregate type and quantity, concrete cover and water content affect the spalling. The water and moisture in the concrete tend to expand with increasing temperatures and move to a volume larger than the volume of the voids inside. This leads to explosive spalling, which is the most important type of spalling [5]. For this reason, the spread

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of heat is accelerating and protection methods to reduce this spread are becoming very important. The studies and the codes implemented as a result of these studies prioritize the geometry of the concrete in order to design the structural elements resistant to a certain fire duration. In addition to obtaining the required cross-section for design, it is also economically very important to determine the optimum value of the size of this cross-section. When the numerical calculation of fire resistance of reinforced concrete columns was checked through an experimental study, the strength time prediction was quite acceptable, but the displacement prediction could not be made accurately because the analytical models of the material behavior of concrete and steel were inadequate [6]. A study investigating the restraint of thermal expansion of a reinforced concrete column shows that the fully restrained columns are slightly beneficial for the fire performance of the column as the surrounding structural elements can transfer part of the load to other columns as they normally would [7]. A study of 80 column specimens with different reinforcement ratios and geometry showed that reinforcement ratio and cross-section size are very important parameters in fire resistance [8]. Another study with columns exposed to 400–800 °C showed that the distance between the reinforcement and the edge of the concrete was at least 20 mm and the cross-sectional separation was at least 100 mm, which made a sharp difference in increasing the fire resistance, and it was said that the use of stirrups also provided a significant increase [9]. In a study on high-strength concrete (HSC) columns, it was shown that the fire performance was longer than that of normal-strength columns and a concrete cover of at least 30 mm was recommended for the fire resistance of HSC [10]. In a study investigating the effect of Fibre-Reinforced Polymer (FRP) wrapped concrete columns on fire resistance, a total of 6 columns of 3.81 m length and 0.4 m diameter, two of which were wrapped with FRP, were exposed to a standard fire [11]. The study showed that the wrapped columns achieved a 5 h ULC-S101 fire endurance rating. In a study that investigate the effect of reinforcement with only fibers and not FRP, with 99 normal and HSC columns, explosive spalling, which is the most important spalling type, was observed in the first 45 min in all elements and it was seen that the use of polypropylene fiber was instrumental in reducing spalling up to 22% [12]. A study investigating the relationship between the crosssectional shape of the element and fire resistance was conducted with 9 different cross-sectional columns, 3 of which were L, 3 of which were T and 3 of which were +type, and the highest strength was found in the T type cross-section, while the lowest strength was found in the +type with the highest surface area [13]. In the behavior of concrete-filled steel slender columns under the effect of 30–120 min fire, the columns with a height/diameter ratio of 20, 30 and 40 obtained significantly higher strength than the columns with a ratio of 20. As the slenderness increased, a significant increase in the decrease in strength was observed [14]. In a study on the fire resistance of reinforced concrete columns produced with recycled aggregate (RA), the strength of the elements produced from normal concrete under the same axial load was lower than that produced with RA [15]. The reason for this is that the penetration of heat is more difficult in elements produced with RA. It investigated

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the fire resistance of columns with 50, 100 and 150 mm stirrup spacing and found that as the stirrup spacing increased, significant decreases in strength were observed due to the decrease in load-carrying capacity and the possibility of spalling [16]. However, the early crack formation was observed in columns with frequent stirrups. In a study investigating the fire effect of reinforced concrete columns with seismic damage history, 6 columns were exposed to 120 min of fire. As a result of the research, it was observed that the fire resistance of the columns with seismic damage history decreased dramatically and collapse occurred after 120 min of fire, while the columns in the control group did not experience any collapse [17]. In another study that aims to investigate the relationship between eccentricity and fire resistance, loaded reinforced concrete columns with eccentricities of 20 and 40 mm. Increasing the eccentricity by 100% resulted in a 200% increase in spalling and a 43% decrease in strength [18]. There are many studies in the literature about the optimization of reinforced concrete structural components or structures. The optimum diameter of the reinforced concrete column, the optimum dimensions of the reinforced footing, the minimum structural cost of the reinforced concrete retaining wall are determined using metaheuristic algorithms [19–22]. Different metaheuristic Algorithms such as Flower Pollination Algorithm (FPA), Jaya algorithm (JA), Teaching–LearningBased optimization (TLBO), Harmony search (HS) algorithm and modified Harmony search algorithm are used to calculate the optimum cross-section of T-shaped or rectangular reinforced concrete beam, a post-tensioned reinforced concrete cylindrical wall, reinforced concrete cantilever soldier piles and reinforced concrete deep beams considering Carbon emission [23–28].

2 Design of Reinforced Concrete Column According to Eurocode 2 In EN 1992-1-2 [29], many calculation methods related to fire design and resistance of reinforced concrete structures are proposed. Among these, the advanced calculation method uses Fourier differential equations and numerical methods such as finite element and finite volume to calculate the heat transfer in structural elements. As a result of these calculations, the temperature value at any point of the structural element at any point in time, for example the point where the reinforcement is located, can be calculated. These values for specific sections are already available in Annex A of EN 1992-1-2. The effect of this thermal change in sections on the mechanical response is also calculated. In another method, the simplified calculation method, a faster calculation can be made using the temperature profiles available in Annex A. Apart from these two methods, a tabulated data section is presented. Table 5.2 in Eurocode 2 with certain cross-sections is available in this section. In a study, 82 fire tests were performed on columns using the database from which Table 5.2 was created and Formula (5.7) in Eurocode 2 was derived from regression analysis of the

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results of these tests [30]. Therefore, this formula is presented in the EC under the tabulated data section. The table method can be used to obtain the minimum cross-section and concrete cover values of the columns at certain loading conditions (μfi = 0.2, μfi = 0.5 and μfi = 0.7) for fire durations from R30 to R240. Linear interpolation can be applied for values not shown in the table. These values depend on the exposure of one or more surfaces of the element to fire (Table 1). In order to use Table 5.2, columns must have the following values: • Effective length of the column in fire condition: l0,fi ≤ 3 m, • 1st degree eccentricity value in case of fire: e = M 0Ed,fi /N 0Ed,fi ≤ emax ; recommended emax value = 0.15h, • Reinforcement area ratio: As < 0.04Ac . must be met. Here, the effective length l0,fi of the column under fire effect is considered equal to the length l in the non-fire condition. l is the distance between the axes where the columns meet the beams; if the floor where the column is located is the intermediate floor, the l0,fi value is taken as 0.5l, and if it is the upper floor, it is taken between 0.5l and 0.7l. In the same way, the eccentricity value in the fire-free condition can also be used in the calculation in case of fire. The main determining factor in the table, μfi , the load utilization factor in the fire condition, is the ratio of the axial load rating N Ed.fi of the column in the fire condition to the axial load rating N Rd in the normal condition. N Rd can be calculated according to 1992-1-1. / μfi = NEd.fi NRd

(1)

Table 1 Minimum column dimensions and axis distances for columns with rectangular or circular section Standard fire resistance

Minimum dimensions (mm) Column width bmin /axis distance a of the main bars Column exposed on more than one side

Exposed on one side

μfi = 0.2

μfi = 0.5

μfi = 0.7

μfi = 0.7

R 30

200/25

200/25

200/32 300/27

155/25

R 60

200/25

200/36 300/31

250/46 350/40

155/25

R 90

200/31 300/25

300/45 400/38

350/53 450/40a

155/25

R 120

250/40 350/35

350/45a 450/40a

350/57a 450/51a

175/35

R 180

350/45a

350/63a

450/70a

230/55

R 240

350/61a

450/75a

–

295/70

a

Minimum 8 bars

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EC states that the reduction factor ηfi can be used instead of μfi . The reason for this is to assume that the design force N Ed is equal to the axial load resistance N Rd , in other words, to assume that the column is performing at full capacity and to design safely. EC states that ηfi can be taken as 0.7 for simplification but gives the following equations for detailed calculation. In the following equations, the live load value is Qk,1 and the fixed load value is Gk , γ Q,1 = 1.5 and γ G = 1.35 are taken as safety coefficients. ηfi = NEd.fi /NEd

(2)

NEd,fi = G k + ψfi Q k,1

(3)

NEd = γG G k + γQ,1 Q k,1

(4)

It is possible to make a rapid design with Table 5.2 in Eurocode 2 (Table 1). However, the fire resistance duration of most of the sections already designed cannot be clearly determined because they are not included in Table 5.2. Equation (5.7) in Eurocode 2 can give the fire resistance time of a given section by taking into account the effect of the load level Rηfi , the effect of the distance between axes Ra , the effect of the column length Rl , the effect of the cross-section size Rb and the effect of the reinforcement Rn . These effects are calculated with the formulas given below. Rηfi = 83[1.00 − μfi ((1 + ω))/((0.85/αcc ) + ω)]

(5)

Ra = 1.60(a − 30)

(6)

( ) Rl = 9.60 5 − lo,fi

(7)

Rb = 0.09b'

(8)

Rn = 0 (n = 4) or Rn = 12 (n > 4)

(9)

With the combination of the above effects, Eq. (5.7) is determined as follows. ) )1.8 (( R = 120 Rμfi + Ra + Rl + Rb + Rn /120

(10)

R gives the fire resistance time of the column element and the inputs in the above equations are subject to the following constraints and formulas. • A is the distance between axes of longitudinal reinforcement; 25 mm ≤ a ≤ 80 mm,

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• l o,fi is the effective length of the column in case of fire; 2 m ≤ lo,fi ≤ 6 m (l o,fi less than 2 m shall be taken as 2). • b' for rectangular sections = Ac /(b + h), for circular columns = Φ column ; 200 mm ≤ b' ≤ 450 mm; h ≤ 1.5b,

• ω, mechanical reinforcement ratio at normal temperature conditions = (Asfyd )/ (Acfcd ), • α cc coefficient for long-term effects on compressive strength; α cc = 0.85

3 Hybrid Metaheuristic Algorithm Flower Pollination Algorithm (FPA), which is inspired by the properties of flowers while considering changes in color and smell, have been developed by Yang [31]. The creation of local pollination and global pollination situations in the algorithm ensures that optimal results of the engineering problems are achieved. In this study, Flower Pollination Algorithm is used to compute the optimum cross-section of the reinforced concrete column in case of fire. The phases of the optimization process can be summarized as follows: • First Step: Identify the design variable of the reinforced concrete column in case fire (shown in Table 2) • Second Step: Produce randomly the candidate cross-sections of the reinforced column and the associated total weight • Third Step: Give a start for optimization process with FPA • Fourth step: Replace present candidate cross-sections using local or global pollination taking into account the cross-sections with the lowest total weight • Fifth Step: Carry on process in step 4 for 10,000 iterations • Last Step: Complete the optimization process.

Table 2 Design variables of reinforced concrete in case of fire Explanation

Symbol

Unit

Min. value

Max. value

Width

b

mm

200

450

Height

h

mm

200

450

Compressive strength of concrete

f ck

MPa

16

50

Yield strength of steel

f yk

MPa

420

500

Clear cover

cnom

mm

30

45

Specific gravity of reinforced concrete

Γ

kg/m3

2300

2800

Buckling length in fire

l fi

m

2

6

Degree of utilization in case of fire

μfi

–

0.2

0.7

Fire duration

T

min

30

90

Optimum Design of Reinforced Concrete Columns in Case of Fire

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A simple algorithm called Jaya [32], which has no specific check parameters, are developed by Rao after the effectiveness of the TLBO [33] in optimization problems. Jaya algorithm aims to be near to the best solution by avoiding the convergence to the worst solution. The mathematical expression of local, global pollination and Jaya algorithm are given in Eqs. (11), (12) and (13), respectively. g* is the best present cross-section, w* is the present worst cross-section, xit+1 is the newly produced cross-section, xit is the present cross-section, r 1 and r 2 are two random numbers between 0 and 1, L is a Lévy distribution, ε is the linear distribution, x tj and xkt are two randomly chosen cross-sections. ) ( xit+1 = xit + ε x tj − xkt

(11)

( ) xit+1 = xit + L xit − g ∗

(12)

( ( ) ) xit+1 = xit + r1 g ∗ − abs(xit ) − r2 w ∗ − abs(xit )

(13)

A hybrid algorithm is proposed to find the optimum cross-section of the reinforced concrete columns by integrating a part of Jaya Algorithms to FPA. The code of these generated algorithms is written in Matlab [34]. The global pollination equation is removed from FPA’s codes and the Jaya algorithm equation is added in its place. The Flowchart diagram of the hybrid algorithm is given in Fig. 3.

4 Numerical Examples Optimum results of the reinforced concrete column with different cases are obtained, which are shown in Table 3 as a numerical example. In the first case, the duration of the fire is accepted as 90 min. In this case, the clear cover is 40 mm and the number of reinforcement bars is over 4. Also, this situation corresponds to both cross-section types, square and circular. Height and width values for a square section are equal to the diameter for a circular section. In the second and third cases, the fire duration of the examined cross-section is 60 min and the number of reinforcement bars is again over 4. Both case 2 and case 3 shows the situation resulting from the use of different clear covers. In the second case, the clear cover is 35 mm, while in the third case, 40 mm is taken. In the following cases, the number of reinforcement bars is taken as 4. These cases are investigated under 30, 60 and 90 min fire exposure with a clear cover between 30 and 45 mm. The optimum cross-section values of the reinforced concrete column according to the hybrid metaheuristic algorithm for different cases are presented in Figs. 4 and 5. In Case 1, the optimum height and width of the column vary between 200 and 442 mm according to different loading conditions factors and buckling length. In case 1, no optimum cross-section is calculated if the loading condition factor (μfi ) is greater

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Fig. 3 Flowchart diagram of hybrid algorithm

than 0,6 and the buckling length (l0,fi ) is greater than 4 m. Optimum cross-section values decrease by rising the number of bars in the cross-section. The importance of the clear cover is visible from the comparison of cases 5 and 6. For example, the optimum width and height for a buckling length of 3 m and a load capacity of 0.7

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Table 3 Cases for reinforced concrete columns in case of fire Clear cover (mm)

Fire duration (min)

Case 1

40

90

Case 2

35

60

Case 3

30

60

Case 4

40

90

Case 5

35

60

Case 6

30

60

Case 7

30

30

Cases

Corner bars

are increased from 329 to 418 mm. In case 7, the optimum cross-section is available for all loading condition factors and buckling length.

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Fig. 4 Optimum results of reinforced column cross-section under cases 1, 2 and 3

Fig. 5 Optimum results of reinforced column cross-section under cases 4, 5, 6 and 7

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5 Results and Conclusion In this study, a hybrid metaheuristic algorithm is proposed for the optimum design of the reinforced concrete column in case of fire according to Eurocode 2. The results of this study are as follows: • Although the design of column elements in case of fire according to Eurocode 2 is simple using Table 5.2, it is not possible to obtain economical cross-sections. The values in the table are prepared for α cc = 1,0. This also results in higher values for E d,fi . The optimum cross-section for the reinforced column under different fire conditions is calculated by using Eq. (5.7) in Eurocode 2 and metaheuristic algorithms. • Equation (5.7) in Eurocode is permissible to design rectangular columns with lo,fi < 6. This value is limited to 6 m in Table 5.2. The effects of the buckling length, loading condition factor, clear cover, fire time and the number of reinforcements bar on the optimum cross-section are shown through numerical examples. • If the hybrid algorithm and the FPA algorithm are compared, both algorithms give the same results. However, the hybrid algorithm achieves the optimal result in a shorter time. This shortens the calculation time. This situation turns out to be an important factor when investigating the fire situation of larger three-dimensional structures.

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Hybrid Social Network Search and Material Generation Algorithm for Shape and Size Optimization of Truss Structures M. Saraee, A. Jafari, D. Yazdani, M. Baghalzadeh Shishehgarkhaneh, B. Nouhi, and S. Talatahari

Abstract Metaheuristic algorithms (MH) are widely used in engineering applications due to their global search capabilities and independence from gradient information. Truss structures are commonly used in structural design, and the best solution typically involves minimizing the weight while ensuring adequate strength and stiffness. To achieve this goal, several hybrid MH algorithms have been proposed by combining the strengths of two or more algorithms. In this paper, we propose a hybrid social network search (SNS) and material generation algorithm (MGA) for truss structure optimization. The main levels as parallel and series levels are defined for the hybrid algorithm. The proposed algorithm is evaluated using several benchmark truss structures, and the results demonstrate its superiority over other state-of-the-art MH algorithms. Keywords Social network search · Material generation algorithm · Truss structure · Structural optimization

M. Saraee · A. Jafari · S. Talatahari (B) Department of Civil Engineering, University of Tabriz, Tabriz, Iran e-mail: [email protected] D. Yazdani Department of Computer Engineering, Mashhad Branch, Azad University, Mashhad, Iran M. B. Shishehgarkhaneh Department of Civil Engineering, Monash University, Clayton, VIC 3800, Australia B. Nouhi · S. Talatahari Faculty of Engineering & IT, University of Technology Sydney, Ultimo, NSW 2007, Australia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Bekda¸s and S. M. Nigdeli (eds.), Hybrid Metaheuristics in Structural Engineering, Studies in Systems, Decision and Control 480, https://doi.org/10.1007/978-3-031-34728-3_4

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1 Introduction Structural optimization problems have emerged as one of the most active subfields of structural engineering. Optimization entails minimizing or maximizing a function and monitoring the system’s performance. Designers created a plethora of knowledge-based models to get a model with better qualities. Metaheuristic (MH) algorithms are searching strategies that employ higher-level methodologies to perform search operations to find optimum results. These approaches have earned a lot of interest due to their tremendous potential for modeling engineering issues in instances where traditional techniques have failed to provide a solution. They are more capable of global search than traditional optimization algorithms and do not need gradient information [1]. Some of the prominent and novel MH algorithms are Genetic Algorithms (GAs) [2], Particle Swarm Optimization (PSO) [3], Chaos Game Optimization (CGO) [4, 5], Energy Valley Optimizer (EVO) [6], Charged System Search (CSS) [7–10], Crystal Structure Algorithm (CryStAl) [11, 12], Bat Algorithm (BA) [13], Grey Wolf Optimizer (GWO) [14], Whale Optimization Algorithm (WOA) [15], Nutcracker Optimization Algorithm (NOA) [16], Cuckoo Search (CS) [17], Fire Hawk Optimizer (FHO) [18, 19], Plant Competition Optimization (PCO) [20], Salp Swarm Algorithm (SSA) [21], Atomic Orbital Search (AOS) [22, 23], Jellyfish Search (JS) [24], Krill Herd (KH) [25], Black Widow Optimization (BWO) [26], Special Relativity Search (SRS) [27], and Fusion–Fission Optimization (FuFiO) [28]. Furthermore, the hybrid version of MH algorithms—which are two or more algorithms that work in tandem and complement one another for creating a beneficial synergy [29]—has been developed and proposed for different purposes [30–37]. A structural optimization issue involves the structure system’s weight minimization by using various parameters, like layout and size, as the decision variables. Cross-sectional areas and nodal coordinates of the structure are used as the deciding factors in size and layout optimization, respectively [38]. Truss structures are made of stiff elements that are pin-connected at the joints and solely provide axial forces. Truss structures are made up of rigid beams that are joined together with pins and only exert axial forces. With this simple shape, trusses could be deemed as a group of connected three-dimensional segments, where each element has exactly two ends and each joint can fit any number of beams [39]. The best solution in truss optimization is typically understood to be achieving the desired structure while using the least amount of material and the best structural configuration to sustain the design loads and, thereby making the design effective regarding weight and strength/stiffness. Within a predetermined structural typology, this also indirectly lowers construction costs [40]. Generally speaking, to optimize truss structures, the topology is often changed beginning with a ground structure, which is the collection of all feasible member placements between the truss nodes, and the design factors include the sizes of the member cross sections [41]. Over the last few years, MH algorithms have been employed in truss optimization problems. Kazemzadeh Azad and Aminbakhsh [42] employed one of the novel MH

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algorithms called guided stochastic search (GSS) in dealing with large-scale steel truss structure optimization problems. Awad [43] used a political optimizer (PO) algorithm for seven different truss structure optimization problems; According to the results, the PO algorithm surpasses various cutting-edge optimization approaches in small- or medium-sized structural systems regarding algorithmic stability, optimized weight, and convergence rates. Li et al. [44] proposed an improved version of the chicken swarm optimization (CSO) algorithm for ameliorating the design effectiveness of the truss optimization. Azizi et al. [5] employed the chaos game optimization (CGO) algorithm in dealing with truss structures’ shape and size optimization, in which they evaluated the capability of the CGO algorithm on five different largescale truss structures. Pierezan et al. [45] employed the modified version of the coyote optimization algorithm (MCOA) for truss structure optimization problems considering discrete variables. Khodadadi and Mirjalili [46] employed the generalized normal distribution optimization (GNDO) approach for the weight optimization of truss structures. Lemonge et al. [47] utilized the improved differential evolution (IDE) algorithm for spatial and plane truss optimization problems. Jawad et al. [48] employed the artificial bee colony (ABC) algorithm in dealing with members’ size and layout optimization of truss structures. However, some research works have employed the hybrid version of MH algorithms in truss optimization problems. Liu and Xia [49] suggested a novel hybrid intelligent genetic algorithm (HIGA) for the sake of improving the truss optimization problems’ efficiency. Furthermore, for truss structures’ weight minimization, Yücel et al. [50] proposed a hybrid optimization algorithm regarding miscellaneous MH algorithms, consisting of flower pollination algorithm (FPA), teaching–learning-based optimization (TLBO), and Jaya algorithm (JA). Omidinasab and Goodarzimehr [51] proposed a novel hybrid version of the GA and PSO algorithm in coping with truss structure optimization problems considering discrete design variables. Kaveh and Talatahar [52] developed a hybrid version of the ant colony and PSO algorithms for truss optimization problems. Table 1 summarizes some recent hybrid algorithms applied for solving truss structure optimization problems. In the current research work, the optimization of truss structures is deemed using a new hybrid algorithm based on Social Network Search (SNS) algorithm and Material Generation Algorithm (MGA). SNS was proposed by Talatahari et al. [68] and it is inspired by users’ efforts to increase their reputation on social networks by modeling their emotions, such as Imitation, Conversation, Disputation, and Innovation, in the actual world while expressing their thoughts. Furthermore, MGA was proposed by Talatahari et al. [69]. Several advanced and fundamental features of material chemistry, including the arrangement of chemical compounds and chemical processes in the production of new materials, are employed as inspiration for the MGA. The 37-bar, 52-bar, and 72-bar truss structures—three of the field’s benchmark problems—are regarded as design examples for purposes of computation. The main purpose of this research is to assess the capability of the proposed algorithm in dealing with the optimization of complex truss structures and compare its results with other well-known metaheuristic oprimization algorithms.

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Table 1 List of some of the hybrid algorithms in truss structure optimization problems No

References

Year

Algorithms

Optimization purposes

1

[53]

2023

PSO, SQP, and FE

Optimum design of truss structures

2

[54]

2023

CHT and MRFO

Truss structures’ size and shape optimization

3

[55]

2023

DE and Jaya

Size optimization of truss structures

4

[56]

2022

ICA and BBO

Optimum design of spatial truss structures

5

[57]

2022

TLBO and CSS

Minimization of truss structures’ weight

6

[58]

2022

PSO and GA

Minimization of truss structures’ weight

7

[59]

2022

AOA and DE

Optimum design of truss structures considering frequency constraints

8

[60]

2022

DE and SOS

Size, shape, and topology optimization of truss structures

9

[61]

2021

DE and SOS

Size and shape optimization of truss structures considering frequency constraints

10

[62]

2021

PSO and CA

Optimum design of truss structures

11

[63]

2021

FPA and DE

Size optimization of truss structures

12

[64]

2021

HS and Jaya

Minimization of large-scale truss structures’ weight

13

[65]

2020

IWO and SFLA

Optimum design of truss structures

14

[66]

2020

TLBO and HS

Optimum design of space trusses

15

[67]

2019

EHO and CA

Minimization of truss structures’ weight

PSO: particle swarm optimization; SQP: sequential quadratic programming algorithm; FE: finite element method; ICA: Imperialist Competitive Algorithm; BBO: biogeography-based optimization; TLBO: teaching–learning-based optimization; CSS: charged system search; GA: genetic algorithm; CHT: constraint-handling technique; MRFO: manta ray foraging optimization; AOA: arithmetic optimization algorithm; DE: differential evolution; SOS: symbiotic organisms search; CA: cultural algorithm; FPA: flower pollination algorithm; EHO: elephant herding optimization; HS: harmony search; IWO: invasive weed optimization; SFLA: shuffled frog-leaping algorithm

The rest of this research work is structured as follows: the statement of optimum design of structures and a summary of the SNS and MGA algorithms are represented in Sect. 2. Section 3 explains the new hybrid approach. The problem statement and numerical investigations are presented in Sects. 4 and 5. Finally, the core findings of this research are provided in the last section.

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2 Utilized Methods 2.1 Social Network Search The human species is a sociable species that strives to interact with one another continuously. Social networks are virtual tools that were developed for this purpose as a result of technological advancements. The suggested SNS algorithm replicates the interactive attitude of social network users in order to increase their fame. The user’s perspective may be influenced by other perspectives including Imitation, Conversation, Disputation, and Innovation. Imitation implies that the opinions of other users are appealing since users often attempt to emulate one another while expressing their thoughts. Conversation indicates that people may converse and use other viewpoints. In the Disputation, people may debate and discuss their viewpoints with a group of other users. Finally, Innovation reveals that individuals occasionally discuss topics related to their novel ideas and experiences on social networks. It is possible to represent imitation mood mathematically as: X i (new) = X j + rand(−1, 1) × R

(1)

R = rand(0, 1) × r

(2)

r = X j − Xi

(3)

where, X j shows jth user’s view’s (position) vector; X i elucidates ith user’s view’s vector; rand(0, 1) and rand(−1, 1) represent vectors in intervals [0, 1] and [−1, 1] randomly. R represents the shock radius, which expresses the effect of the jth user and is measured as a multiple of r . . In the second mood (Conversation), users get an understanding of events from various points of view, and ultimately, because of the variety in viewpoints, they may create a new understanding of the issue using the following equation: X i (new) = X k + R

(4)

R = rand(0, 1) × D

(5)

) ( ) ( D = sign f i − f j × X j − X i

(6)

where, X k illustrates the problem’s vector because that was randomly selected to be discussed; R is chat’s impact, which is based on differences in viewpoints and signifies a shift in their opinions about the problem (X k ); D elucidates the difference among users’ viewpoints, and there are no input parameters for this calculation of view differences; rand(0, 1) represents a vector in the range [0, 1] randomly; in a

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conversation, X j clarifies the vector of the perspective of a randomly selected user, of) the ith user. Furthermore, sign while X i represents the vector of the opinion ( demonstrates the sign function and sign f i − f j compares f i and f j to identify the movement direction of X k . However, the third mood (Disputation) describes a scenario in which users explain and defend their perspectives on situations to other individuals. In this mood, a subset of users is selected at random to participate as a commenter or group members, and their perspective is then used to inform the new viewpoint in dispute. These features are described mathematically as follows: X i(new) = X i + rand(0, 1) × (M − AF × X i ) ∑ Nr M=

t

Xt

Nr

AF = 1 + r ound(rand)

(7)

(8) (9)

where, X i shows the ith user’s view vector; a random vector in the range [0, 1] is returned by rand(0, 1). M demonstrates the opinions’ mean of group members or commenters. The Admission Factor, or AF, is a randomly generated number that may either be 1 or 2. It represents the users’ tendency to insist on their opinions while speaking with others. rand elucidates a number in the range [0, 1] randomly, while r ound(.) shows a function that rounds its input to the closest integer value. The size of the group of commentators, Nr , is a random integer between 1 and Nuser , where Nuser shows the network users’ number or Network size. Finally, in the last mood (Innovation), users sometimes share the results of their opinions and experiences. Each of a subject’s distinctive characteristics may have an impact on how well the issue is understood. As a consequence, by altering the perception of just one of them, the subject’s overall meaning will also be altered, leading to the development of a fresh perspective. These features are described mathematically as follows: xid(new) = t × x dj + (1 − t) × n dnew

(10)

n dnew = lbd + rand 1 × (ubd − lbd )

(11)

t = rand 2

(12)

where, D shows the variables’ number in the issue, and d is the dth variable that is chosen from the range [1, D] randomly. There are two random numbers in the range [0, 1] called rand 1 and rand 2 . The dth variable’s minimum and maximum values are lbd and ubd , respectively. The novel concept about the dth dimension of the issue is represented by n dnew . x dj shows the current notion offered by another user concerning the dth variable, and the ith user wants to modify it due to a novel thought (n dnew ). d . The novel perspective of the dth dimension will eventually be formed as xi(new)

Hybrid Social Network Search and Material Generation Algorithm …

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d Meanwhile, change in one dimension (xi(new) ) affects the whole notion and might be deemed a new perspective to convey. This procedure could be represented as follows:

] [ X i(new) = x1 , x2 , x3 . . . .xid(new) . . . .x D

(13)

2.2 Material Generation Algorithm Material is a concoction of several components made up of the substances that make up the cosmos and have mass and volume. The procedure of generating novel materials involves the capacity of several components to combine to produce novel materials with greater functionality and increased energy levels. To better a material’s functionality and regulate its unique qualities, materials are created on an atomic, nano, micro, or macro scale. Furthermore, chemical reactions and chemical mixtures are used to modify materials chemically. Hence, compounds, reactions, and stability—three fundamental ideas in material chemistry—were taken into account in developing the MGA. A variety of materials (Mat) made up of various periodic table elements (PTEs) are identified by MGA. In this method, a variety of materials (Mat n ) that include certain components designated as decision variables are taken j into consideration as solution candidates ( P T E i ). These two features are presented mathematically as follows: ⎤ ⎡ ⎤ j P T E 11 P T E 21 · · · P T E 1 · · · P T E d1 Mat 1 ⎢ Mat ⎥ ⎢ P T E 1 P T E 2 · · · P T E j · · · P T E d ⎥ ⎢ ⎢ 2⎥ 2 2 2 ⎥ 2 ⎢ . ⎥ ⎢ ⎥ { ...... . . .. ⎢ . ⎥ ⎢ ⎥ ... . . ⎢ . ⎥ ⎢ ⎥ i = 1, 2, . . . , n. Mat = ⎢ ⎥=⎢ ⎥, j ⎢ Mat i ⎥ ⎢ P T E i1 P T E i2 · · · P T E i · · · P T E id ⎥ j = 1, 2, . . . , d. ⎢ . ⎥ ⎢ ⎥ ...... . . .. ⎢ . ⎥ ⎢ ⎥ ⎣ . ⎦ ⎣ ⎦ ... . . 1 2 j d Mat n PT En PT En · · · PT En · · · PT En (14) ⎡

Each material (solution candidate) has d elements (decision variables), and n j materials are thought of as solution candidates. Furthermore, P T E i is set at random in the first phase of the optimization process, while the decision variable boundaries are established according to the issue under consideration. The PTEs’ starting positions in the search space are determined randomly as follows: j P T E i (0)

=

j P T E i,min

) ( j j + U ni f (0, 1). P T E i,max − P T E i,min ,

{

i = 1, 2, . . . , n. j = 1, 2, . . . , d. (15)

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where, the initial value of the jth element in the ith material is determined by j j j P T E i (0); P T E i,min and P T E i,max are the jth decision variable of the ith solution candidate’s minimum and maximum permissible values, respectively; U ni f (0, 1) elucidates an integer within the range [0, 1] randomly. The probability theory is used to simulate the processes of losing, gaining, or sharing electrons for the chosen PTEs. To do this, a chemical molecule, which is regarded as a new PTE, is configured as follows using a continuous probability distribution for each PTE: P T E knew = P T E rr21 ± e− , k = 1, 2, . . . , d.

(16)

where, the probabilistic component represented by e− is used to model the process of losing, gaining, or sharing electrons, and is expressed as a normal Gaussian distribution in the mathematical model. The novel material is denoted as P T E knew . r1 and r2 are random integers uniformly distributed in the intervals [1, n] and [1, d], respectively. P T E rr21 represents a randomly selected PTE from the material Mat. A new material, denoted as Mat new1 , is generated using the newly generated PTEs and is added as a new solution candidate to the original material list (Mat) in the following manner: [ ] Mat new1 = P T E 1new P T E 2new · · · P T E knew · · · P T E dnew , k = 1, 2, . . . , d. (17) Regarding the randomly picked starting element (P T E rr21 ), the probability of choosing a new element (P T E knew ) is stated as follows: ( ) −(x−μ)2 1 f P T E knew |μ, σ 2 = √ .e 2σ 2 , k = 1, 2, . . . , d. 2π σ 2

(18)

where, μ represents the distribution related to the randomly chosen PTE’s (P T E rr21 ) mean, median, or expectation; the natural logarithm’s natural base, also known as the Naperian base, is e; σ and σ 2 are the standard deviation and variance, respectively. Finally, since various materials might engage in the reactions to varying degrees, a participation factor (p) is also computed for each material. This characteristic is presented mathematically as follows: ∑l Mat new2 =

m=1 ( p m .Mat m j ) , ∑l m=1 ( p m j )

j = 1, 2, . . . , l.

(19)

where, Mat new2 shows the new material formed by the chemical reaction idea. Mat m represents the mth randomly picked material from the original Mat; pm is the normal Gaussian distribution for the mth material participation factor.

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3 Hybrid Method Hybrid algorithms are created when two or more algorithms are combined in order to create a new algorithm that has the best features of each algorithm. By combining two or more algorithms, those weaknesses can be mitigated, resulting in a stronger and more efficient algorithm that can solve complex problems faster and more accurately. Additionally, hybrid algorithms are also capable of scaling more effectively, meaning they can be used for more complex problems. Therefore, hybrid algorithms are highly valuable when it comes to solving problems such as finding the optimal structural design, where accuracy and speed are crucial. We present a novel hybrid algorithm that combines social network optimization and Material Generation Algorithm, which is called SNS-MGA in this chapter. The SNS-MGA algorithm is defined in accordance with the parallel-series concept. In other words, the SNS-MGA combines the best features of both serial and parallel systems. The hybrid algorithm considers the following levels: Level (1) Parallel Level: The two algorithms are executed separately and in parallel in the first step. During this step, half of all iterations considered for the hybrid algorithm are considered. Level (2) Series Level: In the second step, the two algorithms are combined. We use the results of the first level as the initial solution to the algorithms at this level. Using the following equations, we are able to obtain new solutions based on the concepts of both algorithms: X i(new) = X j + rand(−1, 1) × rand(0, 1) × (X j − X i )

(20)

( ) ( ) X i(new) = X k + rand(0, 1) × sign f i − f j × X j − X i

(21)

(∑ X i(new) = X i + rand(0, 1) ×

Nr t

Nr

Xt

) − (1 + r ound(rand)) × X i

d xi(new) = rand 2 × x dj + (1 − rand 2 ) × {lbd + rand 1 × (ubd − lbd )}

xi(new) = xrr12 ± e−

(22) (23) (24)

∑l X new =

m=1 ( p m .Mat m j ) ∑l m=1 ( p m j )

(25)

A half-number of iterations is reached at the end of this step. Figure 1, sumurize the levels of the hybrid algorihm.

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Define problem

SNS

MGA

Parallel Step

Combination of SNS and MGA

Series Step

Fig. 1 The levels of the hybrid algorithm

4 Problem Statement In this part, the generic formulation of structural design optimization issues is described, along with a weight minimization approach that takes frequency design constraints into account. The structure’s total weight is calculated for the objective function. In size optimization problems, the design variables are the cross-sectional areas of structural components, while in shape optimization problems, the design variables are the nodal coordinates of structures. These characteristics can be expressed mathematically as follows: W eight(A, X ) =

∑e i=1

ρi L i (xi )Ai , i = 1, 2, . . . , n

(26)

ω j ≥ ω∗j , j = 1, 2, . . . , p

(27)

ωk ≤ ωk∗ , k = 1, 2, . . . , p

(28)

up

Al ≤ Al , l = 1, 2, . . . , n

(29)

xmlow ≤ xm ≤ xmup , m = 1, 2, . . . , r

(30)

where, A is a vector with a total number of structural components that includes the design variables for the structural elements’ cross-sectional areas. The nodal coordinate design variables are represented by the vector X , where r shows the total number of nodes in the structure. ρi and L i elucidate the materials’ density and structural components’ length, respectively; ωk and ω j show the structure’s kth and jth natural frequency including the overall number of p frequencies. Structure’s kth and jth natural frequency’s upper and lower bounds are represented by ωk∗ and ω∗j , up respectively. Al demonstrates the lth member’s (Al ) cross-sectional area’s upper and up variables for the mth node’s (xm ) nodal coordinates are xmlow and xm , respectively. Because structural design optimization is a constraint optimization issue, the optimization process should be carried out using a constraint handling approach.

Hybrid Social Network Search and Material Generation Algorithm …

59

Consequently, this study employs the penalty constraint handling technique with the following penalty function: f penalt y (A) = (1 + ε1 .ϑ)ε2 × W eight(A, X ) ϑ=

∑q i=1

(31)

max{0, gi (A, X )}

(32)

where, q shows the design constraints’ overall number; ε1 and ε2 stand for the control values used to calculate the penalty value throughout the optimization procedure; gi (A) is the ith design constraint.

5 Design Examples In the current research work, 5 different truss structures, including 37, 52, and 72-bar trusses, are considered for optimization purposes. Table 2 represents their physical characteristics, while their descriptions are described as follows.

5.1 Describing the Examples 5.1.1

37-Bar Truss Structure

In the first design example, a truss structure with 20 nodes and 37 structural members is taken into consideration as a procedure of size and shape optimization simultaneously. While a total of 19 design variables are chosen for the size and shape optimization of the structure, the constraint restrictions of 20, 40, and 60 Hz for the first three natural frequencies of the structure are considered. Figure 2a is a graphical depiction of this structure. Table 2 Features of the truss structures

37-bar

52-bar

72-bar

Elasticity modulus (N/ m2 )

2.1 × 1011

2.1 × 1011

6.8 × 1010

Steels’ density (kg/ m3 )

7800

7800

2770

Lower bound (m2 )

0.0001

0.0001

0.645 × 10−4

0.001

0.001

20 × 10−4

10

50

2770

Upper bound

(m2 )

Added mass (kg)

60

(a)

(b)

(c)

Fig. 2 Graphical view of the selected structure

M. Saraee et al.

Hybrid Social Network Search and Material Generation Algorithm …

5.1.2

61

52-Bar Truss Structure

This design example, which includes 52 structural elements and 21 nodes, is the second shape and size optimization issue in this work. Five shape and eight size design factors are taken into account concurrently while the optimization methods are being performed. While taking into account the constraint restrictions of 15.961 and 28.648 Hz for the structure’s first two natural frequencies, all of the free nodes are allowed to move with a maximum tolerance of ±2 (m). Figure 2b is a graphical depiction of this structure.

5.1.3

72-Bar Truss Structure

This truss structure, which has 72 members and 20 nodes with constraint constraints of 4 and 6 Hz for the first and third natural frequencies of the structure, is the second size optimization problem in this study. Figure 2c is a graphical depiction of this structure.

5.2 Numerical Results In this sub-section, we provide a comprehensive overview of the optimum results of the selected truss design problems. We also present the best results and convergence histories of the optimization procedures, based on 30 independent runs conducted for statistical validity. To ensure that our findings are reliable, we compare the results of our proposed algorithm with those of other metaheuristic approaches found in the literature.

5.2.1

37-Bar Truss Structure

Table 3 presents the best results obtained by the SNS-MGA algorithm for the 37bar truss design problem, based on 30 independent optimization runs conducted for comparative purposes. The table also includes results from other optimization methods in the literature, and statistical results are provided to ensure a fair comparison. According to the results obtained, the new algorithm achieves an optimal weight of 359.917 kg for the 37-bar truss structure, which is very close to the weight achieved by other methods. However, the new algorithm is significantly more computationally efficient than other algorithms, and it requires only 3000 analyses to arrive at the final result. The new algorithm also provides a mean weight of 361.25 kg across 30 independent runs, with a standard deviation of 1.68, demonstrating its reliability. The convergence history of the hybrid algorithm for the 37-bar truss problem is depicted in Fig. 3. The figure indicate that the algorithm was able to converge to the optimum design very fast. This improved efficiency was achieved by the algorithm’s ability to

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quickly identify the optimal locations for the truss bars, as well as the optimal lengths for the bars. Consequently, the algorithm was able to identify the best solution for the structure quickly, while also reducing the number of analyses required to reach the final outcome.

5.2.2

52-Bar Truss Structure

Table 4 presents the best results obtained by the new algorithm and other metaheuristic optimization methods in the literature for the 52-bar truss design problem. The results indicate that the hybrid algorithm provides the best optimum weight of 193.93 kg with a mean wieght of 197.68 kg. These results demonstrate the effectiveness of the proposed algorithm in addressing complex truss design problems and meeting multiple design constraints, including simultaneous shape and size optimization. In Fig. 4, the convergence history of the SNS-MGA is shown for the 52-bar truss design problem. The convergence history demonstrates that the algorithm is able to quickly find the optimal solution to the problem. The results show that the algorithm is a promising approach for solving truss design problems. Furthermore, the results exhibit the effectiveness of the new algorithm in achieving the desired optimization results in a faster and more efficient manner.

5.2.3

72-Bar Truss Structure

SNS-MGA’s convergence history is illustrated in Fig. 5 as it tackles a 72-bar truss design example. A convergence history of the best optimization runs is presented in the figure. The figure shows that the optimization process converges to a near-optimal solution after only a few iterations. The optimization process is efficient, converging quickly to the optimal design, and the solution is stable, meaning that it remains close to the optimal value despite changes in the design parameters. As a result of the speed of the algorithm for detecting the optimal space, the new algorithm is able to reach an acceptable result after only 500 analyses. This highlights the effectiveness of the new algorithm and ensures that the design can be optimized rapidly and effectively without compromising accuracy. In Table 5, the best results are presented for various metaheuristic approaches, including SNS-MGA, in solving the 72-bar truss problem. In addition to the optimal design variables, the table also provides the corresponding statistical results. The results show that SNS-MGA was able to achieve the best results among the different approaches tested. Additionally, the new algorithm results in a mean weight of 325.26 kg across 30 independent runs. The results obtained using the SNS-MGA algorithm are the best among all other approaches, highlighting its robustness and efficiency. The statistical results demonstrate that SNS-MGA was able to achieve better results in terms of mean weight, compared to other approaches. These results also indicate that SNS-MGA has a higher degree of reliability and accuracy, which makes it the reliable choice for optimal design.

1.1998

1.6553

1.9652

2.0737

1.2086

1.5788

1.6719

1.7703

1.8502

3.2508

1.2364

1.0000

2.5386

1.3714

1.3681

2.4290

1.6522

1.8257

Y3 , Y19 (m)

Y5 , Y17 (m)

Y7 , Y15 (m)

Y9 , Y13 (m)

Y11 (m)

A1 , A27 (cm2 )

A2 , A26 (cm2 )

A3 , A24 (cm2 )

A4 , A 25 (cm2 )

A5 , A23 (cm2 )

A6 , A21 (cm2 )

A7 , A22 (cm2 )

A8 , A20 (cm2 )

A9 , A18 (cm2 )

1.9526

2.0009

1.8254

1.2642

1.5962

1.3655

1.0000

1.1201

2.8932

2.3050

Wei et al. [71]

Wang et al. [70]

Design variables

2.1214

1.1246

4.6850

1.4819

1.2751

1.7182

2.3476

1.1568

2.6797

2.0856

1.8812

1.5929

1.3978

0.9637

Gomes [72]

Table 3 Final results for the 37-bar truss problem

1.7033

1.2223

2.1881

1.0883

1.4057

3.3281

1.1871

1.1107

3.2031

1.5971

1.5334

1.4464

1.2409

0.8415

Miguel [73]

1.4771

1.3588

2.4264

1.1975

1.2610

2.5955

1.0091

1.1098

2.9838

1.6679

1.6086

1.5063

1.3270

0.9392

Farshchin et al. [74]

1.5172

1.5100

2.3170

1.1423

1.2139

2.5958

1.0042

1.0005

2.9913

1.7590

1.6871

1.5645

1.3803

0.9830

Goodarzimeher et al. [75]

1.4618

1.3706

2.4843

1.2030

1.2387

2.6633

1.0005

1.0007

2.9219

1.7509

1.6727

1.5273

1.3289

0.9598

Tejani et al. [76]

1.5124

1.3791

2.4757

1.2097

1.1640

2.5221

1.0023

1.0019

2.8228

1.7942

1.6897

1.5559

1.3707

1.0037

This study

1.6276

1.3864

2.4104

1.5877

1.0109

3.1940

1.0033

1.0163

2.9038

1.7203

1.6687

1.5698

1.3867

0.9598

(continued)

1.5216

1.4176

2.5629

1.2736

1.0001

2.6010

1.0057

1.0023

2.9773

1.7346

1.6633

1.5353

1.3638

1.0001

Hybrid Social Network Search and Material Generation Algorithm … 63

Wang et al. [70]

2.3022

1.3103

1.4067

2.1896

1.0000

366.50

NA

NA

NA

Design variables

A10 , A19 (cm2 )

A11 , A17 (cm2 )

A12 , A15 (cm2 )

A13 , A16 (cm2 )

A14 (cm2 )

Best (kg)

Mean

SD

NFEs

Table 3 (continued)

NA

9.03

NA

368.84

1.0000

1.4049

1.2358

1.8294

1.9705

Wei et al. [71]

12,500

4.26

381.20

377.20

3.3276

1.2563

1.2021

2.9817

3.8600

Gomes [72]

20,000

0.52

362.04

361.50

1.0269

2.8499

1.4074

1.0100

3.1885

Miguel [73]

5,000

0.26

360.37

360.05

1.0004

2.9217

1.3199

1.1295

2.5648

Farshchin et al. [74]

12,000

0.49

360.83

359.96

1.0000

2.4934

1.2739

1.2112

2.2722

Goodarzimeher et al. [75]

12,000

0.47

360.23

359.88

1.0000

2.3831

1.3491

1.2758

2.4432

Tejani et al. [76]

3,000

1.24

361.05

359.92

1.0003

2.3443

1.2929

1.2715

2.5330

This study

4,000

2.97

364.852

360.865

1.0000

2.0673

1.3721

1.0293

2.3594

3,000

1.68

361.25

359.917

1.0001

2.4191

1.2790

1.1810

2.4711

64 M. Saraee et al.

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Fig. 3 Convergance history for the 37-bar truss obtained by the hybrid algorithm Table 4 Final results for the 52-bar truss problem Design variables

Lin et al. [77]

Wei et al. [71]

Gomes Miguel Farshchin Tejani Goodarzimeher This [72] [78] et al. [74] et al. [76] et al. [75] study

Z A (m)

4.3201 5.8851 5.5344 6.4332 5.9531

5.7624

5.9140

5.9033

X B (m)

1.3153 1.7623 2.0885 2.2208 2.2908

2.3239

2.2207

2.1243

Z B (m)

4.1740 4.4091 3.9283 3.9202 3.7037

3.7379

3.7092

3.7405

X F (m)

2.9169 3.4406 4.0255 4.0296 3.9660

3.9842

3.9375

3.9048

Z F (m)

3.2676 3.1874 2.4575 2.5200 2.5001

2.5121

2.5002

2.5013

A1 –A4 (cm2 )

1.00

1.0988

1.0001

1.0095

1.0000 0.3696 1.0050 1.0002

A5 –A8 (cm2 )

1.33

2.1417 4.1912 1.3823 1.0962

1.0031

1.1864

1.2488

A9 –A16 (cm2 )

1.58

1.4858 1.5123 1.2295 1.2252

1.1956

1.2602

1.2636

A17 –A20 (cm2 ) 1.00

1.4018 1.5620 1.2662 1.4555

1.4563

1.4384

1.4369

A21 –A28 (cm2 ) 1.71

1.9110 1.9154 1.4478 1.4172

1.3773

1.4006

1.3796

A29 –A36 (cm2 ) 1.54

1.0109 1.1315 1.0000 1.0003

1.0055

1.0008

1.0019

A37 –A44 (cm2 ) 2.65

1.4693 1.8233 1.5728 1.6204

1.7397

1.5530

1.5893

A45 –A52 (cm2 ) 2.87

2.1411 1.0904 1.4153 1.3296

1.3084

1.3979

1.3859

Best (kg)

298.00 236.04 228.38 197.53 193.18

195.49

193.342

193.629

Mean

NA

214.66

198.875

197.68

NA

234.30 212.80 197.87

SD

NA

37.462 5.22

NFEs

NA

NA

17.98

5.79

11,270 10,000 15,000

14.14

4.21

4.95

4,000

3,000

3,000

66

Fig. 4 Convergance history for the 52-bar truss obtained by the hybrid algorithm

Fig. 5 Convergance history for the 72-bar truss obtained by the hybrid algorithm

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Table 5 Final results for the 72-bar truss problem Design variables

Miguel [78]

Farshchin et al. [74]

Tejani et al. [76]

Goodarzimeher et al. [75]

This study

A1 –A4 (cm2 )

3.3411

3.4188

3.6957

3.3434

3.5862

A5 –A12 (cm2 )

7.7587

7.9263

7.1779

7.9841

7.8450

A13 –A16 (cm2 )

0.6450

0.6450

0.6450

0.6450

0.6450

(cm2 )

0.6450

0.6450

0.6569

0.6450

0.6452

A19 –A22 (cm2 )

9.0202

8.0143

7.7017

7.9805

7.7377

A23 –A30 (cm2 )

8.2567

7.9603

7.9509

7.8631

7.9276

A17 –A18

A31 – A34

(cm2 )

0.6450

0.6450

0.6450

0.6450

0.6452

A35 – A36 (cm2 ) 0.6450

0.6450

0.6450

0.6450

0.6451

A37 – A40 (cm2 ) 12.045

12.7903

12.3994

12.6510

12.6649

A41 – A48

(cm2 )

8.0401

8.1013

8.6121

7.7268

7.9628

A49 – A52 (cm2 ) 0.6450

0.6450

0.6450

0.6450

0.6463

A53 – A54 (cm2 ) 0.6450

0.6473

0.6450

0.6450

0.6450

A55 – A58

(cm2 )

17.4615

17.4827

17.2382

17.2305

A59 – A66 (cm2 ) 8.0561

8.1304

8.1502

8.1914

8.0091

A67 – A70 (cm2 ) 0.6450

0.6450

0.6740

0.6450

0.6463

(cm2 )

17.380

0.6450

0.6451

0.6550

0.6450

0.6450

Best (kg)

327.691

327.575

325.558

324.348

324.209

Mean

329.890

327.693

331.122

325.569

325.26

SD

2.59

0.1250

4.227

0.9503

1.231

NFEs

10,000

15,000

4,000

2,500

3,000

A71 – A72

6 Conclusion This paper presented a novel hybrid algorithm, combining the Social Network Search and Material Generation Algorithm, for optimization of truss structures. The proposed hybrid SNS and MGA (SNS-MGA) demonstrated remarkable performance in dealing with various truss optimization problems, with the results showing its superiority over other existing optimization techniques. The SNS-MGA algorithm leverages the strengths of both Social Network Search and Material Generation Algorithm to efficiently explore the solution space and converge to the optimal solution. The algorithm ensures the satisfaction of constraints, such as the natural frequencies of truss structures, by incorporating these constraints into the optimization process. To assess the capability of the proposed Hyb SNS-MGA for truss structures’ shape and size optimization, three benchmark problems with varying numbers of bars (37, 52, and 72) were considered. The optimization procedure considered frequency constraints as limits, which are commonly encountered in truss design. Multiple optimization runs were performed to ensure the statistical significance of the results, and a comparative analysis with other algorithms in the literature was conducted.

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The outcomes show that the SNS-MGA algorithm can find optimum designs for the truss structures.

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Development of a Hybrid Algorithm for Optimum Design of a Large-Scale Truss Structure Melda Yücel, Gebrail Bekda¸s, and Sinan Melih Nigdeli

Abstract In the present study, the optimum design of a structural model as a 72-bar truss was handled to detect the minimum weight. By this scope, the main objective function value as the total weight is tried to be minimized through that all bar members of the truss structure were optimized without grouping to observe section areas by considering as design parameters. Within this process, two different metaheuristics including nature-inspired, and swarm-based algorithms known as the flower pollination algorithm (FPA) and the Jaya algorithm (JA) were combined and hybridized to enhance the optimization performance of JA. On the other hand, it is observed and detected that the performances of algorithms show an increment in which iteration and population numbers. With this respect, it became more suitable and effective that the optimization process is implemented with the best-selected algorithm in terms of optimal performance, and successful parameters for the algorithm can be determined to observe numerous design variables belonging to an extremely large-scale structural model. Keywords Metaheuristics · Flower pollination algorithm · Jaya algorithm · Hybridization · Truss structures

M. Yücel Institute of Graduate Studies, Istanbul University - Cerrahpa¸sa, 34320 Avcılar, Istanbul, Turkey G. Bekda¸s · S. M. Nigdeli (B) Department of Civil Engineering, Istanbul University - Cerrahpa¸sa, 34320 Avcılar, Istanbul, Turkey e-mail: [email protected] G. Bekda¸s e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Bekda¸s and S. M. Nigdeli (eds.), Hybrid Metaheuristics in Structural Engineering, Studies in Systems, Decision and Control 480, https://doi.org/10.1007/978-3-031-34728-3_5

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1 Introduction While structural design problems are tried to overcome, some conditions require to be controlled, or some assumptions or acceptances must be applied for the designing of structures. The main cause is that real engineering problems are not linear, and due to that these always cannot suit a specific line/solution or equation. In other saying structural models in real life have nonlinearity behavior. In this regard, to make true the mentioned requirements or expressions can be considered like a task, which must be realized by structural engineers. Therefore, some issues such as engineers’ experience and knowledge, etc. play an important role to obtain the best conditions for designs. However, this is not possible to realize to find the most proper solution with classical hand calculations. Also, computer design programs should be applied iteratively by engineers. But these have time-consuming stages and cannot be turned back when any error is made. For this reason, it is always not possible to say that these are the best solutions or the rightest designs. In recent times, advanced computer-codding applications or calculation methods are performed to ensure the models are optimal by preventing these problems. Optimization methodologies are one of these, and the usage of metaheuristic methods based on nature, physical or chemical processes of materials, human memory, or genetics came into prominence in this process. Because, these are very easy to use, effective, understandable, and successful in finding the best solution, because of have quick stages and error controllability advantages. From this point of view, civil especially structural engineering is one of the widespread application areas of metaheuristics. For example, the best cross-section can be determined, or the optimal steel bar area can be found for a beam or column, the weight or cost can be minimized for any structural member, the optimum amount of structural materials can be analyzed, etc. In this regard, in the mentioned structural engineering area, optimization applications are realized by utilizing many different metaheuristic algorithms. For instance, genetic algorithm (GA) [1], artificial bee colony algorithm (ABC) [2], teaching– learning based optimization (TLBO), harmony search (HS) and bat algorithm (BA) [3], particle swarm optimization (PSO) combined with HS [4]; Jaya algorithm (JA) [5]; crow search algorithm (CSA) [6], TLBO and flower pollination algorithm (FPA) [7], GA and PSO [8], and hybrid approach based on HS [9] were benefited to minimize of cost and/or structural mass via determining of optimum properties belonging to structural members as beam, column, footing etc. including reinforced concrete, steel composite materials; ant colony optimization (ACO) algorithm [10], charged system search algorithm (CSS) [11], biogeography-based optimization algorithm (BBO) [12], PSO algorithm [13]; more than five metaheuristics [14], black hole algorithm (BH) [15] are handled about determination of the lowest carbon emission rate besides minimum cost by optimizing of geometry for retaining walls with different structural designs; HS [16]; GA [17, 18], FPA [19, 20]; FPA, TLBO and JA [21], differential evolution (DE) algorithm [22]; CSA, whale optimization algorithm (WOA), and grey wolf optimization (GWO) [23] are also investigated for optimum

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designing of some devices like tuned mass or liquid dampers, base-isolation systems, active control mechanisms etc., which are benefited to control and damp of dynamical effects as wind forces. On the other respect, in the structural engineering area, there also exist numerous optimization applications realized for suitable and proper designs, which can provide the required design targets like not exceeding the allowable compression and tension stresses to prop the nodal displacements for truss structures at a specific level, etc. In this regard, various applications have been realized for truss systems, which makes possible either structural weight and also cost minimization or optimal placement for node points (layout optimization), besides topology optimization. One of these is a study conducted by Çerçevik et al. [24] where size and shape optimization was realized in the way of minimization of weight under multiple natural frequency constraints by using the firefly algorithm (FA) and HS for different truss structures. Vu [25] and also Kaveh and Ghazaan [26] benefited from the methods, which are known as DE and vibrating particles systems (VPS), respectively, for optimizing truss structures (by providing minimum weight) to improve their dynamic performance of them under frequency constraints, too. On the other hand, a method was proposed to find the optimum truss structures with minimum weight by using three variations of CSA [27]. Furthermore, various applications related to the topology optimization of trusses were tackled with different metaheuristics. For example, Cui et al. [28] also carried out an application for topology optimization by benefiting from GA with the prevention of local buckling constraints besides overlapping of bars that it is previously accomplished by controlling design constraints such as displacement and stress. At the same time, Hosseinzadeh et al. [29] examined the combination of a metaheuristic method called an electromagnetism-like mechanism algorithm with an approach as migration strategy (EM-MS) to make real optimization for layout and size belonging to five different truss models under natural dynamic frequency constraints. PSO was utilized to generate the best truss structure with the aim of sizing and layout arrangement by optimizing of cross-sectional areas of bars and coordinates of each node, besides providing minimum weight through conforming to different design conditions and laws [30]. In addition to these, two different algorithms were arranged as a hybrid tool by integrating GWO and DE intended for optimization of fully-stressed truss structure as shape (geometrical) and size besides topology [31]. Within the scope of this study, intended for the lightest 72-bar truss structure, section areas belonging to each of the bar members are tried to find with an optimization approach by developing a hybridized version of nature-inspired and populationbased metaheuristic methods, that was generated with the usage of two kinds as Jaya algorithm and Flower pollination algorithm. The current problem is based on an extremely large-scale structural design model and the consideration of this effective and precise method is required to analyze it. At the same time, it is aimed that the best/suitable process time is determined with the evaluation of various iteration numbers and population numbers by applying two different cases for observation of optimum section area results and minimum weight values, besides collaboration of optimization methods with each other.

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2 Jaya Algorithm and Flower Pollination Algorithm Jaya algorithm (JA), which is named after a Sanskrit word that meant victory, was first proposed by Rao in 2016. Also, the working logic of JA is based on glorification, which has an approach to reaching the best point by going far from the worst point [32]. However, the Jaya algorithm can search the solutions between only the best and worst solutions namely points. For this reason, the other solutions sometimes can be ignored, while the optimistic solutions are trying to find. Although the taking time for the operation of the optimization process is pretty short, and adjusting specific parameters is not required similar to other metaheuristics, it cannot be so effective and successful to find the best solution optimally. In this meaning, there is one formulation to be used in the optimization process by JA as below Eq. (5.1): | | |) |) ( ( X i,new = X i, j + rand X i,gbest − | X i, j | − rand X i,wor st − | X i, j |

(5.1)

where rand function provides to generate a random number ranging between 0 and 1. Also, X i,new and X i, j means to the value of the new namely updated and jth (old) solution among the whole population corresponding to ith design variable, respectively. Moreover, X i,gbest and X i,wor st are the best and worst solutions’ values for this variable in terms of the objective function. The flower pollination algorithm (FPA), which was proposed by Xin-She Yang in the year of 2012, was created by taking as the basis of an approach depending on the pollination capability of flowers. In this algorithm, there are several conditions to be applied for mathematical optimization problems. These consist of the type of pollination as global or local search, constancy of flower, selection of search by using switch probability parameter (sp), etc. [33]. While the optimization process is realized, two alternative scenarios can be applied according to the value of the FPA parameter expressed as sp (∊[0,1]), which determines the search type through be tuned this value. Here, the first one is known as global search, which becomes possible between only different flowers of the same plants by any pollinators including fish, insects, birds, etc., or wind through applying ´ (Eq. (5.2)). Also, the local search can realize in a random distribution called L evy own structure of a specific flower. These processes can be expressed via Eq. (5.3) as mathematical. ) ( 1 1 + (rand)−1.5 e(− 2rand ) (5.2) Lé vy = √ 2π ) ( { if sp > rand X i, j + Lé vy( X i,gbest − X)i, j Global search (5.3) X i,new = Local search else X i, j + rand X i,m − X i,n Here, X i,m and X i,n present the two different random solutions (mth and nth) selected from the population community.

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3 Hybridization of Metaheuristics In the current study, two different population-based metaheuristic algorithms were combined by benefiting from some properties and searching behaviors of them. In this respect, the flower pollination algorithm (FPA) and JA were combined and transformed into a hybrid method symbolized as JA&FPA. These metaheuristic optimization algorithms also have some inspirations including natural life processes and community-based properties. For example, FPA used the pollination ability of flowers with the help of pollinators like flies, insects, wind, etc. to simulate optimization processes for solving especially nonlinear reallife problems. In this scope, to generate an advanced and powerful methodology for both overcoming this kind of problem and developing the performance with the success of the JA algorithm, a different approach was proposed by combining the basic phase of JA and the local search phase of the FPA method. In this meaning, the details for the working principle of the hybridized algorithm as JA&FPA is presented as a flowchart in Fig. 1 [34].

Fig. 1 Flowchart for JA&FPA hybrid algorithm

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4 Design of Truss Structure In this book chapter, a structural model as a large-scale truss with 72-bar was investigated to generate the best design namely the optimal model by minimizing the total weight. In Fig. 2, the details of the structural model in terms of geometry, and design parameters can be seen as a plan, and 3-d display, respectively. In this chapter, two different cases for optimization modeling of truss structure were realized to determine the minimized structural weight by finding the best parameters of structure as cross sections of bars. In this regard, the design properties as parameters and constants are presented in Table 1. On the other hand, different constraint functions and limitations were handled for designing structures in the way of providing suitability to design requirements. Two different constraints were utilized for nodes and bars as controlling displacements, and compressive together with tensile stresses, respectively (Table 2). For this reason, the multiple loading conditions are applied on nodes of the truss that are given in Table 3. Moreover, the best parameter values as optimum results for all design properties can be ensured without exceeding any constraints by applying the penalization of objective functions. Fig. 2 Design model and variables of the 72-bar truss structure [35]

Table 1 Design details for optimum design of truss structure Property

Symbol

Limit/value

Unit

Design parameters

Cross-section of bars

Abar

0.1–3.0

inch2

Design constants

Elastic modulus

Es

107

psi

Weight per unit of volume for steel

ρs

0.1

lb/inch3

Number of bars

–

72

–

Number of nodes

–

20

–

Development of a Hybrid Algorithm for Optimum Design …

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Table 2 The design constraints applied on nodes of truss Structural member

Description

Constraints

Unit

Displacement

Nodes All

Constraints for displacements arisen on nodes

Bars A1–72

Constraints for stresses arising on bars

δ < |∓0.25|

inch

Compression stress

Tension stress

σc > −25000

σt < +25000

psi

Table 3 Values of the multiple loading conditions on nodes Case

Node

Loading

Unit

Px

Py

Pz

1st

17

5000

5000

−5000

2nd

17

0

0

−5000

18

0

0

−5000

19

0

0

−5000

20

0

0

−5000

lb/inch2

5 Numerical Investigations for 72-Bar Truss In the current chapter, an optimization process was designed for the modeling of a truss model with 72-bar. In this respect, the optimization process was applied in two different cases by adjusting algorithm parameters. Also, all of these processes were applied with the usage of both the independent algorithm as JA and the hybrid algorithm as JA&FPA. In this regard, firstly, for the 1st and 2nd cases, the changing of iteration and population numbers are evaluated in terms of detection of the best weight, respectively. Here, in the 1st case (Fig. 3, Tables 4 and 5), the range of iteration numbers is taken in 500–120,000 in the way of applying a total of 34 different alternatives (by using constant population as 20). As to the 2nd case (Fig. 4, Tables 6 and 7), population numbers are evaluated as 3, 5, and 10–30 by increasing 10 together with 100,000 iteration numbers constantly. These two cases were presented below sections, respectively.

6 Conclusions In the current study, a large-scale structural model of a 72-bar truss was tried to optimize by providing the best weight value as minimized. For this reason, all of the design parameters as structural bar sections were obtained as optimized by utilizing

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M. Yücel et al. 440.0000 420.0000

Minimum weight (lb)

400.0000 380.0000 360.0000 340.0000 320.0000 300.0000 Iteration number JA&FPA JA

Fig. 3 The changing of the minimized weight values along iteration numbers is increasing

an advanced metaheuristic algorithm called JA&FPA. Moreover, two different optimization cases were arranged by benefiting variable values of population and also iteration numbers towards the classic version of JA and JA&FPA hybrid algorithm, too. According to the obtained results for the 1st case as changing of iteration numbers, the most successful algorithm is JA&FPA in terms of the minimization of total structural weight (304.9611 lb). Although JA&FPA used fewer iteration steps according to classical JA, it can be more effective for the minimization of weight. On the other hand, in the 2nd case, the change in population numbers is evaluated in terms of obtaining of best weight values. At this time, the most effective algorithm is JA&FPA like the 1st case. Between the results of minimized weights provided by JA and JA&FPA, there is an extremely significant difference at 3.15 lb. In this respect, JA performance can be extremely improved in terms of minimizing the total weight. However, it can be thought that the most successful case is changing population numbers. Because the best value for total weight is smaller in comparison to the case changing of iteration numbers. Moreover, the convergence performance of the JA&FPA algorithm is more steady in the minimization of weight for the truss model. Also, JA&FPA can reach the mentioned best results more quickly than the classic version of JA.

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Table 4 The best optimization results are determined by JA besides evaluations of statistical parameters Bar

Min. weight

Bar

Min. weight

Bar

Min. weight

Bar

Min. weight

A1

1.7610

A19

1.7005

A37

0.4587

A55

0.2786

A2

0.1001

A20

0.2652

A38

0.2979

A56

0.4252

A3

2.3456

A21

2.1035

A39

0.7212

A57

0.5699

A4

0.1388

A22

0.2594

A40

0.2695

A58

0.3839

A5

0.1000

A23

0.7451

A41

0.1000

A59

0.8746

A6

0.7444

A24

0.1010

A42

0.8071

A60

0.1000

A7

0.1001

A25

0.7679

A43

0.1000

A61

0.6557

A8

0.8090

A26

0.1090

A44

0.7615

A62

0.1000

A9

0.8284

A27

0.1477

A45

0.7403

A63

0.1000

A10

0.1006

A28

0.7604

A46

0.1000

A64

0.6670

A11

0.7184

A29

0.1000

A47

0.7712

A65

0.1002

A12

0.1005

A30

0.7143

A48

0.1000

A66

0.8415

A13

0.1000

A31

0.1000

A49

0.1007

A67

0.1000

A14

0.1000

A32

0.1003

A50

0.1001

A68

0.1000

A15

0.1000

A33

0.1000

A51

0.1000

A69

0.1000

A16

0.1001

A34

0.1000

A52

0.1000

A70

0.1000

A17

0.1000

A35

0.1000

A53

0.1000

A71

0.9089

A18

0.1000

A36

0.1002

A54

0.1025

A72

0.1000

Best weight

305.0709

Mean weight 305.0895 Std. dev. for best weight

0.0088

Population number

20

Iteration number

100,000

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Table 5 The best optimization results were determined by the hybrid algorithm as JA&FPA besides evaluations of statistical parameters Bar

Min. weight

Bar

Min. weight

Bar

Min. weight

Bar

Min. weight

A1

1.7927

A19

1.6370

A37

0.4280

A55

0.1018

A2

0.1000

A20

0.2863

A38

0.3177

A56

0.2905

A3

2.3597

A21

2.1013

A39

0.7421

A57

0.3825

A4

0.1047

A22

0.2934

A40

0.3108

A58

0.5742

A5

0.1002

A23

0.7289

A41

0.1001

A59

0.3722

A6

0.7205

A24

0.1014

A42

0.7805

A60

0.9184

A7

0.1009

A25

0.7713

A43

0.1008

A61

0.1005

A8

0.8056

A26

0.1256

A44

0.7211

A62

0.6607

A9

0.8062

A27

0.1345

A45

0.7443

A63

0.1000

A10

0.1002

A28

0.7719

A46

0.1007

A64

0.1002

A11

0.7177

A29

0.1067

A47

0.7875

A65

0.6386

A12

0.1004

A30

0.7131

A48

0.1003

A66

0.1005

A13

0.1000

A31

0.1005

A49

0.1000

A67

0.8983

A14

0.1005

A32

0.1000

A50

0.1008

A68

0.1019

A15

0.1001

A33

0.1000

A51

0.1000

A69

0.1000

A16

0.1003

A34

0.1001

A52

0.1001

A70

0.1000

A17

0.1002

A35

0.1001

A53

0.1002

A71

0.1029

A18

0.1007

A36

0.1005

A54

0.4280

A72

0.8984

Best weight

304.9611

Mean weight 304.9869 Std. dev. for best weight

0.0138

Population number

20

Iteration number

65,000

Development of a Hybrid Algorithm for Optimum Design …

83

1150.0000 1050.0000

Minimum weight (lb)

950.0000 850.0000 750.0000 650.0000 550.0000 450.0000 350.0000 250.0000

3

5

10

20

30

Population number JA&FPA

JA

Fig. 4 The decreasing of the minimized weight values along population numbers is changing Table 6 The best optimization results are determined by JA besides evaluations of statistical parameters Bar

Min. weight

Bar

Min. weight

Bar

Min. weight

Bar

Min. weight

A1

3.000

A19

1.7026

A37

0.4795

A55

0.2547

A2

0.100

A20

0.2542

A38

0.2724

A56

0.4011

A3

2.996

A21

2.1343

A39

0.7603

A57

0.6282

A4

0.1437

A22

0.1632

A40

0.3548

A58

0.4259

A5

0.1001

A23

0.7034

A41

0.1001

A59

0.9128

A6

0.7017

A24

0.1000

A42

0.7733

A60

0.1001

A7

0.1000

A25

0.7822

A43

0.1000

A61

0.6461

A8

0.8203

A26

0.1000

A44

0.7812

A62

0.1000

A9

0.7531

A27

0.1403

A45

0.7428

A63

0.1000

A10

0.1056

A28

0.7297

A46

0.1000

A64

0.5976

A11

0.6775

A29

0.1000

A47

0.7651

A65

0.1000

A12

0.1205

A30

0.7099

A48

0.1000

A66

0.8322

A13

0.1002

A31

0.1000

A49

0.1000

A67

0.1000

A14

0.1000

A32

0.1000

A50

0.1000

A68

0.1000

A15

0.1000

A33

0.1000

A51

0.1000

A69

0.1000

A16

0.1000

A34

0.1000

A52

0.1004

A70

0.1000

A17

0.1000

A35

0.1000

A53

0.1000

A71

0.8671 (continued)

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Table 6 (continued) Bar

Min. weight

Bar

Min. weight

Bar

Min. weight

Bar

Min. weight

A18

0.1000

A36

0.1000

A54

0.1000

A72

0.1015

Best weight

308.4800

Mean weight 308.5093 Std. dev. for best weight

0.0141

Population number

10

Iteration number

100,000

Table 7 The best optimization results were determined by the hybrid algorithm as JA&FPA besides evaluations of statistical parameters Bar

Min. weight

Bar

Min. weight

Bar

Min. weight

Bar

Min. weight

A1

1.8660

A19

1.6899

A37

0.4019

A55

0.2990

A2

0.1025

A20

0.2955

A38

0.3272

A56

0.3654

A3

2.2738

A21

1.9927

A39

0.7335

A57

0.5858

A4

0.1044

A22

0.3047

A40

0.2857

A58

0.3911

A5

0.1047

A23

0.7584

A41

0.1030

A59

0.9106

A6

0.6863

A24

0.1018

A42

0.8213

A60

0.1021

A7

0.1009

A25

0.7334

A43

0.1034

A61

0.6489

A8

0.8113

A26

0.1283

A44

0.7317

A62

0.1001

A9

0.8057

A27

0.1168

A45

0.7177

A63

0.1001

A10

0.1035

A28

0.7707

A46

0.1075

A64

0.6523

A11

0.7305

A29

0.1000

A47

0.8072

A65

0.1025

A12

0.1039

A30

0.7399

A48

0.1036

A66

0.9197

A13

0.1002

A31

0.1009

A49

0.1006

A67

0.1055

A14

0.1004

A32

0.1000

A50

0.1000

A68

0.1008

A15

0.1005

A33

0.1000

A51

0.1000

A69

0.1001

A16

0.1021

A34

0.1002

A52

0.1030

A70

0.1003

A17

0.1000

A35

0.1009

A53

0.1003

A71

0.8822

A18

0.1005

A36

0.1016

A54

0.1000

A72

0.1037

Best weight

305.3269

Mean weight 305.4213 Std. dev. for best weight

0.0406

Population number

30

Iteration number

100,000

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22. Deastra, P., Wagg, D., Sims, N.: Optimum design of a tuned-inerter-hysteretic-damper (TIHD) for building structures subject to earthquake base excitations. In: EURODYN 2020: Proceedings of the XI International Conference on Structural Dynamics. September 2020. European Association for Structural Dynamics (EASD), pp. 1501–1509 (2020) 23. Çerçevik, A.E., Av¸sar, Ö., Hasançebi, O.: Optimum design of seismic isolation systems using metaheuristic search methods. Soil Dyn. Earthq. Eng. 131, 106012 (2020) 24. Miguel, L.F.F., Miguel, L.F.F.: Shape and size optimization of truss structures considering dynamic constraints through modern metaheuristic algorithms. Expert Syst. Appl. 39(10), 9458–9467 (2012) 25. Vu, V.T.: Weight minimization of trusses with natural frequency constraints. In: 11th World Congress on Structural and Multidisciplinary Optimisation. 7–12 June 2015, Sydney, Australia (2015) 26. Kaveh, A., Ghazaan, M.I.: Vibrating particles system algorithm for truss optimization with multiple natural frequency constraints. Acta Mech. 228, 307–322 (2017) 27. Javidi, A., Salajegheh, E., Salajegheh, J.: Enhanced crow search algorithm for optimum design of structures. Appl. Soft Comput. 77, 274–289 (2019) 28. Cui, H., An, H., Huang, H.: Truss topology optimization considering local buckling constraints and restrictions on intersection and overlap of bar members. Struct. Multidiscip. Optim. 58(2), 575–594 (2018) 29. Hosseinzadeh, Y., Taghizadieh, N., Jalili, S.: Hybridizing electromagnetism-like mechanism algorithm with migration strategy for layout and size optimization of truss structures with frequency constraints. Neural Comput. Appl. 27(4), 953–971 (2016) 30. Mortazavi, A., To˘gan, V., Nuho˘glu, A.: Weight minimization of truss structures with sizing and layout variables using integrated particle swarm optimizer. J. Civ. Eng. Manag. 23(8), 985–1001 (2017) 31. Panagant, N., Bureerat, S.: Truss topology, shape and sizing optimization by fully stressed design based on hybrid grey wolf optimization and adaptive differential evolution. Eng. Optim. 50(10), 1645–1661 (2018) 32. Rao, R.: Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int. J. Ind. Eng. Comput. 7(1), 19–34 (2016) 33. Yang, X.S.: Flower pollination algorithm for global optimization. In: International Conference on Unconventional Computing and Natural Computation. Springer, Berlin, Heidelberg, pp. 240–249 (2012) 34. Yücel, M., Bekda¸s, G., Nigdeli, S.M.: Optimization of truss structures with sizing of bars by using hybrid algorithms. In: International Conference on Intelligent Computing & Optimization. Springer, Cham, pp. 592–601 (2021, December) 35. Bekda¸s, G., Yucel, M., Nigdeli, S.M.: Evaluation of metaheuristic-based methods for optimization of truss structures via various algorithms and Lèvy flight modification. Buildings 11(2), 49 (2021)

Structural Control Systems and Tuned Mass Damper Optimization by Using Jaya and Hybrid Algorithms Muhammed Ço¸sut, Sinan Melih Nigdeli, and Gebrail Bekda¸s

Abstract In this section, as well as explaining the building control systems and their properties, the displacement and acceleration values were found in the case that TMD is not used and TMD is placed, according to the earthquake record that affects the building most negatively, by affecting past earthquake records on the single degree of freedom system. By using the Matlab & Simulink programs, the displacement optimization was performed according to the time history domain using the Hybrid (TLBO-Jaya) and Jaya algorithms. In this optimization process, firstly, the TMD mass was determined as 5% of the mass of the structure, after that. the constant values, constraint values and the necessary information for the algorithm were entered to solve the system. Optimal intervals were determined by assigning the TMD period and damping ratio as variables. In the case of optimization of the single degree of freedom system, it is seen that there are great differences in displacement and acceleration in the system. Furthermore, while for the same system operated using different algorithms, the values of the Hybrid algorithm and the Jaya algorithm for variables under loadings were compared for system. Keywords Structural control system · Passive tuned mass damper · Metaheuristic algorithm · Optimization · Jaya algorithm · Hybrid algorithm

1 Introduction Circumstances such as building design systems, different types of structures, material development and techniques [1], which continue to develop from the past to the present, reveal that there are significant increases in the performance of the system to be designed. Such developments are constantly renewing themselves and will M. Ço¸sut · S. M. Nigdeli (B) · G. Bekda¸s Istanbul University - Cerrahpa¸sa, 34320, Avcılar ˙Istanbul, Turkey e-mail: [email protected] G. Bekda¸s e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Bekda¸s and S. M. Nigdeli (eds.), Hybrid Metaheuristics in Structural Engineering, Studies in Systems, Decision and Control 480, https://doi.org/10.1007/978-3-031-34728-3_6

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contribute to the sustainability of the system [2] by ensuring that the system is designed safely [3] and continues its life, even in cases such as the most undesirable ground conditions and the seismic characteristics of the location. Although buildings built or planned to be built (there are certain limitations in their designs according to their intended use) are designed under the building design standards of the country in which they are located, it is seen that the effectiveness of the system and the behaviour of the system against external loads affecting the building will change if some building control systems are used. Building control systems may differ according to the type of building, its design, or the protection of the system from which loads. In other words, while rubber-based isolation is used in some structures, active, passive or mixed control systems are used in some structures. After the most suitable system is selected by considering the costs of this usage diversity, the compatibility between the structure and the control system used is examined in detail by using analysis programs, and its suitability is checked. In some cases, it can be used by choosing special structural materials due to the location characteristics of the structure rather than the cost. The implementation of selections in this way is carried out to ensure that the structures remain on the safe side under dynamic loads such as earthquakes or winds. Accordingly, earthquake and wind load risk reduction will be realized. Bekda¸s and Ni˘gdeli [4] found the optimum parameter values of the TMD system under seismic loads using Harmony Search. Farshidianfar and Soheili [5] analysed the TMD calculations of high-rise buildings according to the Tabas and Kobe earthquakes using Ant Colony Optimization. Araz and Kahya [6] performed the displacement optimization of serial-tuned mass dampers using the Simulated Annealing method. Ni˘gdeli and Bekda¸s (2014) [7] made mass damper optimization to prevent the collision of adjacent buildings under earthquake effects. In this chapter, the types of building control systems that can be used in different building types are explained, and in addition, in case of using TMD in a single degree of freedom system, the displacement optimization is carried out by applying the Hybrid [8] and Jaya [9] algorithms. In this optimization process, FEMA P-695 [10] far-fault data, which has 44 different earthquake records affecting the system, were used and the earthquake record with the most adverse conditions for the structure was selected and its design was provided. While creating the algorithms, all the necessary data for the analysis of the system were written into the program and the displacement optimization was done according to the time domain.

2 Vibration The oscillation of a certain speed and magnitude under the force of a system is called vibration. While vibrations can occur in many different ways on the structure, it is expected that the structure will dampen by reacting to these vibrations. Structural vibrations are divided into some classes. There are different types of these classifications: undamped free vibration motion, damped free vibration motion, undamped forced vibration motion and damped forced vibration motion. While free vibration

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is created by giving the initial motion to the structure, forced vibration is created by applying varying forces. In the case of free vibration movement of the undamped system, it is a type of movement that does not have any external forcing and damping feature on the structure, and the vibration movement continues from the moment it starts. The free vibration motion of the damped system is the damped motion without any external force on the structure. In any loading affecting the structure, the structure will absorb the energy after vibrating for a certain period. In the forced vibration motion of the undamped system, there is no damping when there is an external force. In the forced movement of the damped system, there is external stress as well as damping. Transient vibrations are called the highest dynamic loadings that occur due to impact and explosion effects. However, stable vibrations are studied in general at periodic loadings.

3 Structure Control Systems The natural damping values of traditional structures are very low; therefore, in the case of using mechanical materials, the damping rate value of the system is increased, allowing it to perform better against seismic loads [11, 12]. Although the structures are designed considering sufficient strength, sufficient rigidity, and sufficient ductility, sudden loads such as earthquakes and strong winds are possible structural risks and extra precautions should be taken [13, 14]. While possible wind formations can be predicted in some regions, such winds have started to be seen frequently even in regions where no strong winds are expected with climate change. The damping systems, which started to be used in the field of the mechanical industry in the 1950s, started to be applied to high-rise buildings in 1969. Before being used in high-rise buildings, it was created in low-rise buildings and adapted to high-rise buildings. Here are some of the processes and work involved in making it more harmonized: • Madsen et al. [15] had a solution which is dampers in shear walls to transform the control system from to low-rise building to a high-rise building • Integration of dampers in the outrigger system is proposed [16–19]. • Kidokoro [20] suggests that the self-mass damper is inspired by the pendulum movement and clock. Figure 1 delineates the structure reaction diagram when the control system is applied and not applied. In the case of using building control systems in buildings that may be subjected to any loading, it ensures that the relative floor displacement of the structure is reduced, and thus, the structure is designed to remain on the safe side without damage under the impact of seismic forces. In addition, in the case of using seismic isolation;

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Seismic Loads

Structure

Structure

Reaction

Fig. 1 Structure reaction diagram

No Structural Control System

With Structural Control System

Seismic Izolation System

Fig. 2 Structure motions

the interaction between the structure and the ground decreases, the relative floor displacements decrease, and at the same time, with the decrease of the structureground interaction, a decrease in the acceleration value felt in the building is observed. The damper type and properties should be designed according to the displacement value of the structure as a result of the calculations and by finding certain distances between adjacent buildings to prevent collisions. Figure 2 shows three different buildings which have various properties such as no control system, with the control system as well as with seismic isolation. It can be observed when a structural control system is utilized, displacement is less than the building which no structural control system.

3.1 Passive Control System The passive control system is placed at the base, inside or on the structures. By extending the construction period thanks to viscoelastic and friction tools [21], it increases the energy absorption capacity of the structure against earthquakes or different external loads, while ensuring the preservation of the equilibrium state of the structure, preventing regional stresses in the sections and ensuring the safety of the structure. Minimizing the damages that will occur in the structure depends on

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the mechanical property of the material to be used and will ensure that the vibration levels decrease proportionally [22]. There are several different types of passive energy dampers and specifications; bending metal dampers, friction-type dampers, tuned mass dampers and tuned liquid dampers, viscous and viscoelastic dampers. Each of them has different properties and performs energy distribution according to the property that it is good. To exemplify, Taipei 101 and CN Tower TV Antenna building can be seen in Fig. 3. Tuned Mass Damper (TMD) TMD, the vibration control device [23] found by Frahm in 1909, ensures that the vibrations remain at certain levels in the system in which it is used. As a result of the studies, Den Hartog presented the formulas which are Eqs. (1) (frequency ratio, f opt respect to mass ratio, μ) and (2) (damping ratio, ξ d ) for dampers in 1928. Warburton defined the frequency and damping ratio in Eqs. (3) and (4) in 1982. Sadek et al. [24] developed these equations and used them in 1997. With the development of the system over time, it has started to be applied more efficiently in building systems. This system is a structural control system created as a result of connecting the spring and damping element, which are in harmony with each other, to a mass. Since TMD generally performs well against wind and earthquake loads, it will be quite appropriate to use it in structures exposed to such loads. The working principle of this structural element is that the structure will make certain displacements in a certain direction under seismic loads. Vibrating at the same frequency as the structure, the TMD moves in the opposite direction of the movement of the structure, compressing the spring element and the energy acting on

(a) Fig. 3 a Taipei 101, b CN Tower TV Antenna

(b)

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the system together with the damping element is damped to a certain extent. In this way, it has been observed that there is a significant reduction in the displacement of the structure. f opt = √ ξd = f opt √ ξd =

1 1+μ

(1)

3μ 8(1 + μ) ( ) 1 − μ2 = 1+μ

(2)

(3)

μ(1 − μ4 ) 4(1 + μ)(1 − μ2 )

(4)

While Fig. 4 illustrates how the TMD system is applied, Table 1 shows the buildings which are applied TMD. There are several buildings that TMD is utilized to design and built. To stay safe, designers prefer to use this mass damper system in their structure. Tuned Liquid Damper (TLD) The TLD working principle is similar to the TMD working principle. TLD is created by putting a certain amount of liquid (usually water) into the tank connected to the Fig. 4 TMD application

kd md cd

Storey: n

Storey: 2

Storey: 1

GROUND

Structural Control Systems and Tuned Mass Damper Optimization … Table 1 TMD applications

93

Structure

Height-Length (m)

Location

Year

CN Tower TV Antenna

553

Toronto, Canada

1973

John Hancock Tower

240

Massachusetts, USA

1976

Chifley Tower

209

Sydney, Australia

1993

Al Taweelah

70

Abu Dabi, UAE

1993

Hotel Burj Al-Arab

321

Dubai, UAE

1997

Petronas Twin Towers

452

Kuala Lumpur, Malaysia

1998

Akashi Kaikyo Bridge

3911

Honshu-Shikoku, Japan

1998

Park Tower

257

Chicago,ABD

2000

Taipei 101

508.2

Taipei, Taiwan

2003

Almas Tower

360

Dubai, UAE

2008

Tokyo Skytree

634

Tokyo, Japan

2012

23 Marine

392

Dubai, UAE

2012

Shanghai Tower

632

Shanghai, China

2014

432 Park Avenue

426

New York, USA

2015

Ping an Finance Center

599

Shenzhen, China

2017

system. Although the movement of the TMD mass increases the damping ratio of the structure, a TLD absorbs structural energy through the viscous actions of liquid and wave break. Friction Type Dampers Friction, which has a significant mechanism to dissipate energy, has been used in automotive brake systems to distribute kinetic energy for a long time. The development of this system which is used in construction contributes to transforming from kinetic energy to heat energy; therefore, the building will absorb energy under the effects of earthquake or wind excitation. This damping system is used with a crosslink arrangement of metals and steel alloys. Friction damper application can be used as Fig. 5. Yielding Metal Dampers In energy dissipation, the use of inelastic behaviour is provided by utilizing the hysterical behavior of metals. They are designed to endure the bending, shearing and axial forces resulting from floor offsets. Metal dampers are generally designed as

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Fig. 5 Friction damper application

rectangular, triangular, or X-shaped, and importance is given to the equal distribution of stresses in the material [25]. Working in the system for a long time, and being resistant to heat differences and environmental conditions makes its use widespread. Some metal dampers are shown in Fig. 6. Viscoelastic Dampers When viscoelastic dampers are utilized in the structure, they contribute to not only increasing the damping ratio but also rise the lateral rigidity. It transforms the energy provided in shear stresses caused by plate movements into damping energy. The Fig. 6 Metal damper applications

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situation caused by the movements between the metal plates used in the system works with the stretching principle of the elastomers. Its first application was used to prevent vibrations in aircraft. After that, the system structure was developed and started to be used in lots of engineering fields, and it is widely used in civil engineering. The Twin Towers, which were first used in civil engineering, were completed in 1969 [26]. Viscous Dampers Situations that might damage the structure, such as stresses that may occur under the influence of earthquake and wind loads, and stresses at the junction points, are reduced by viscous movement. In the viscous damper, the fluid contained in the piston chamber is converted into heat energy with the movement and displacement of the liquid and its absorption is made. As a fluid material; silicone, lead or oil are used.

3.2 Active Control System Active control systems contribute to reduction quantities such as structure deflection, forces, acceleration as well as velocities [27]. They are designed with control computers separately from TMD. It makes calculations using algorithms according to the force magnitudes affecting the structure and determines the movement, direction and intensity of the control system. The change of these properties is done through the properties of the system, namely the stiffness change and the mass damper. Some of the most important reasons for using active control systems are: • It ensures that the vibrations remain at a certain level according to the load that will affect the structure. • It takes up less space compared to passive mass dampers. • While passive control systems are calculated and designed according to the preexperienced load, active control systems determine the behaviour of the system according to the magnitude of the force when the force acts on the structure. • Preservation of valuable materials inside the building Some problems encountered when using these systems are: • Late detection of seismic loads, • The energy source to which the control system is connected must provide continuous energy, • The cost is too high. • The structures to be applied are not linear • Some uncertainties in the structure parameters Table 2 gives information about the buildings which are used for ATMD.

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Table 2 The ATMD’s applications Structure

Height (m)

Location

Year

Ando Nishikicho

68

Tokyo, Japan

1993

C Office Tower

130

Tokyo, Japan

1993

Kansai International Airport

86

Osaka, Japan

1993

Rokko Island Procter and Gamble

117

Kobe, Japan

1993

Incheon International Airport Control Tower

100.4

Incheon, Kore

2001

Shanghai World Financial Centre

492

Shanghai, China

2008

Canton Tower (Guangzhou TV Tower)

600

Guangzhou, China

2010

The active control system consists of active tuned mass damper, active beam control, and active rigidity control. In addition, the operating principle of the active control system is shown in Fig. 7. Active Tuned Mass Damper (ATMD) The ATMD system developed towards the end of the twentieth century began to be applied in building systems. It is one of the control systems developed against the seismic force effects of high-rise buildings. The fact that it can be adjusted through the actuator and sensor used in the system enables this system to work more efficiently than other systems. In addition, it performs effectively in most mode situations due to its wide frequency range. Figure 8 shows the ATMD application.

Sensors

Calculation of Loads

Load Operators Control Force

Seismic Loads

Structure

Structure Reaction Fig. 7 Active control system principle of work

Structural Control Systems and Tuned Mass Damper Optimization … Fig. 8 ATMD application

97

kd cd

md

actuator Sensor

Storey: n

Storey: 2

Storey: 1

GROUND Active Tendon Control The system, which consists of prestressed cables and actuators, sends signals to the control mechanism through sensors placed in different parts of the structure. As a result of the forces acting on the structure, the sensors in this control mechanism will apply the necessary force to reduce the loading after calculating using algorithms according to the signal status of the loading. In this way, the self-adjustment of the system according to the magnitude of the forces acting on the structure plays an important role in preventing the structures from being damaged or collapsing under any load. The active beam control system shows in Fig. 9.

Fig. 9 Active beam control system

X(t)

Cable

Actuator X(t)

u(t)

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Fig. 10 Active rigidity control application

Active Rigidity Control It creates a reaction against the incoming loads by changing the properties between the beam and the conjunction. This response is determined and created as a result of the calculation by the computer by taking the signal of the forces acting on the structure. This system, which is used in high-rise buildings, consists of cylinders and valves and reacts against the seismic loads. The opening status of the valve may differ according to the floors. In other words, while the valve is open on one floor, the valve can be closed on other floors. The fact that the valves are closed or open in this way ensures the formation of rigidity differences on the floors. Figure 10 describes the active rigidity control system.

3.3 Semi-Active Control System The semi-active control system was recommended in about the 1920s. Active control systems require a lot of energy to function properly and to prevent this [28], the semiactive control system can be used. The working principle of these systems, which can be supported by batteries and are not affected by power cuts in the building, is to provide a time-varying control force by changing the characteristics of the damping system. Examples of these systems are magnetorheological dampers. A magnetorheological damper is a system filled with magnetorheological fluid that is controlled by a magnetic field, usually using an electromagnet. This allows the damping properties of the shock absorber to be constantly controlled by varying the strength of the electromagnet. As the density of the electromagnet increases, the viscosity of the fluid in the damper increases.

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3.4 Hybrid Control System Hybrid control systems are created by using Passive control and Active control systems together. Increasing the performance of the system under loads affecting the structure [29] and the desire to reduce the costs of the system used is the most important reasons for the creation of this system. It is created by adding a sensor, actuator and controller to the passive control system. With the examinations, the fact that the active control tools can be adjusted according to the load affecting the structure and that the passive control systems are safer have been beneficial in the effective use of mixed control systems. This has 2 different types of systems which are a Hybrid mass damper (HMD) as well a Hybrid seismic isolation (HSI). Figure 11 illustrates the HMD in which the TMD connects the structure, after that the ATMD links to the TMD.

4 Metaheuristic Algorithms Algorithms developed by being inspired by many different events in nature [30] are called metaheuristic algorithms. Teaching–learning based optimization (TLBO) is inspired by the communication of teachers and students, Flower pollination optimization (FPA) is inspired by local and global pollination of flowers, Ant colony optimization (ACO) is inspired by the movements of ants and the fluid they secrete in reaching the target, Harmony search (HS) is inspired by the harmonious combination of notes to create an effective and beautiful piece of music, while Shark smell optimization (SSO) is inspired by sharks using their advanced sense of smell to find their prey. These algorithms have been created as a result of formulating many different situations by observing them and are used extensively in fields such as Fig. 11 HMD system

Actuator Spring

ATMD

TMD

Damping

Structure

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engineering, economics, software, and computers in general. When these algorithms are used in optimization problems, they can reach the objective function in different iteration numbers and in different times depending on the number of variables of the problem and the size of the data to be examined. In addition, some algorithms reach the objective function in a shorter time due to the formulas they contain, while some algorithms reach the objective function in a shorter iteration and time than other algorithms due to the 2-phase comparison system.

4.1 Jaya Algorithm Jaya algorithm which is developed by Rao in 2016 is one of the most frequently used algorithms for engineering problems today. One of the most important reasons why it is preferred so much is that it does not need control parameters [30], while the second most important feature is that it can reach the objective function in a short time by determining the best and worst values of the objective function in the iteration stage and using it to calculate the variables in the problem. The equation of Jaya is illustrated in Eq. (5). There are necessary to find several values to calculate the variable’s new value. X i, j is the value of the candidate solution, X i,gbest is the best value of an objective function, X i,gwor st is the worst value of the objective function; in addition, all values which are used to find new variable is in the initial matrix. Also, rand () is assigned randomly. | | |) |) ( ( ' X i,new = X i, j + rand() X i,gbest − | X i, j | − rand() X i,gwor st − | X i, j |

(5)

4.2 Hybrid Algorithm Hybrid algorithms [31] are created when the developed metaheuristic algorithms are combined with each other in 2 or more phases. It can be created using many different algorithms, and in this way, much more efficient results can be obtained in the optimization of problems compared to other algorithms. These results show that better results can be obtained if the difference between the number of iterations reached by the objective function and the mean standard deviation values are compared, rather than the difference in the objective function value. Some hybrid algorithms are TLBO-Jaya, TLBO-FPA (Teaching–Learning Based OptimizationFlower Pollination Algorithm), ACO-GA (Ant Colony Optimization-Genetic Algorithm), GAAP (Hybrid Ant Colony-Genetic Algorithm) as well as DE-BBO (Hybrid Differential Evolution- Biography-Based Optimization). There are several Hybrid Algorithm, and a lot of metaheuristic algorithms can be combined to generate Hybrid Algorithms. One of them is TLBO-Jaya. TLBO has 2

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phases, whereas Jaya has 1 phase. That is why, the equation of Jaya is used in TLBO process by replacing the learning phase. Teaching phase equations are shown Eqs. (6) and (7). X i,or talama is the mean value for the objective function. | |) ( X i,new = X i, j + rand() X i,gbest − | X i, j | − (T F)X i,or talama

(6)

T F = r ound(1 + rand())

(7)

Equation (8) is known as the learning phase in TLBO while Eq. (9) is used in the Jaya algorithm process. In Eq. (8), a and b are assigned randomly. In order to generate Hybrid Algorithm, the learning phase might be removed by Jaya’s equation, which is shown in the equations as an arrow. ) ( AFa < AFb , X i, j + r ()( X i,a − X i,b ) AFa > AFb , X i, j + r () X i,b − X i,a | | |) |) ( ( + rand() X i,gbest − | X i, j | − r () X i,gwor st − | X i, j | {

X i,new = '

X i,new = X i, j

(8) (9)

5 Numerical Example By using a Tuned Mass Damper in a single-degree-of-freedom system, the effect on the structure and the changes in systemic movements were examined. Displacement differences and changes in the acceleration of the force acting on the structure were compared without using the control system and in the case of using the control system. In addition, the necessary codes for this system have been written separately for both the Jaya algorithm and Hybrid algorithms. The hybrid algorithm was created as a result of the combination of TLBO and Jaya algorithm and consists of 2 phases. It uses Jaya algorithm and learner phase of TLBO. Figures 12 and 13 show the single degree of freedom’s (SDOF) TMD application. Table 3 displays structure features which are mass, damping coefficient and rigidity. Table 4 illustrates the constraint and intervals which can change by changing structure features like structure period. According to the given structure properties, the structure period is found as 0.288 s. Earthquakes that are from FEMA P695 [10] are used for the given structure. Table 5 gives information about FEMA far-fault earthquake record, which provides us to control the name of the earthquake as well as their motions. Looking at this table in more detail, San Fernando earthquake, which was in 1971, is the earliest one.

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Fig. 12 TMD application for SDOF: system-1

u+ud kd md

u

cd

m c k 2

k 2

P(t) Fig. 13 TMD application for SDOF: system-2

u

P(t) kd

k

md

m cd

c u

Table 3 Structure features

Table 4 TMD design properties and constraint

Symbol

Value

u+ ud

Unit

m

2924

Kg

c

1581

Ns/m

k

1,390,000

N/m

Explanation

Values and intervals

TMD mass

(Structure mass) * 5%

TMD Max. Damping Ratio

0.5

TMD Min. Damping Ratio

0.01

Max. TMD period

1.5 x (Structure Period)

Min. TMD period

0.5 x (Structure Period)

Stroke capacity constraint

g(X ) = st_ max

max(|xd−x N |)T M Dwith |x N |T M Dwithout

≤

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All these earthquakes occurred between 1971 and 1999. In addition, they have two components, acceleration value as well velocity value. Furthermore, the maximum displacement for all earthquakes was recorded, and they are shown in Table 6. The earthquake which is DUZCE/BOL000 in the table was chosen to design the control system since the maximum displacement occurs. Also, Table 6 shows the displacement of 100 iterations results for Hybrid and Jaya Table 5 FEMA earthquake record Earthquake Year No

Record information Earthquake Location

Motions

Component-1

Component-2

PGAmax (g) PGVmax (cm/ s)

1

1994 Northridge

NORTHR/ MUL009

NORTHR/ MUL279

0.52

63

2

1994 Northridge

NORTHR/ LOS000

NORTHR/ LOS270

0.48

45

3

1999 Duzce, Turkey

DUZCE/ BOL000

DUZCE/ BOL090

0.82

62

4

1999 Hector Mine

HECTOR/ HEC000

HECTOR/ HEC090

0.34

42

5

1979 Imperial Valley

IMPVALL/ H-DLT262

IMPVALL/ H-DLT352

0.35

33

6

1979 Imperial Valley

IMPVALL/ H-E11140

IMPVALL/ H-E11230

0.38

42

7

1995 Kobe, Japan KOBE/ NIS000

KOBE/ NIS090

0.51

37

8

1995 Kobe, Japan KOBE/ SHI000

KOBE/ SHI090

0.24

38

9

1999 Kocaeli, Turkey

KOCAELI/ DZC180

KOCAELI/ DZC270

0.36

59

10

1999 Kocaeli, Turkey

KOCAELI/ ARC000

KOCAELI/ ARC090

0.22

40

11

1992 Landers

LANDERS/ YER270

LANDERS/ YER360

0.24

52

12

1992 Landers

LANDERS/ CLW-LN

LANDERS/ CLW-TR

0.42

42

13

1989 Loma Prieta LOMAP/ CAP000

LOMAP/ CAP090

0.53

35

14

1989 Loma Prieta LOMAP/ G03000

LOMAP/ G03090

0.56

45

15

1990 Manjil, Iran MANJIL/ ABBAR–L

MANJIL/ ABBAR–T

0.51

54

16

1987 Superstition SUPERST/ Hills B-ICC000

SUPERST/ B-ICC090

0.36

46 (continued)

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Table 5 (continued) Earthquake Year No

Record information Earthquake Location

Component-1

Motions Component-2

PGAmax (g) PGVmax (cm/ s)

SUPERST/ B-POE360

0.45

36

17

1987 Superstition SUPERST/ B-POE270 Hills

18

1992 Cape Mendocino

CAPEMEND/ CAPEMEND/ 0.55 RIO270 RIO360

44

19

1999 Chi-Chi, Taiwan

CHICHI/ CHY101-E

CHICHI/ CHY101-N

0.44

115

20

1999 Chi-Chi, Taiwan

CHICHI/ TCU045-E

CHICHI/ TCU045-N

0.51

39

21

1971 San Fernando

SFERN/ PEL090

SFERN/ PEL180

0.21

19

22

1976 Friuli, Italy

FRIULI/ A-TMZ000

FRIULI/ A-TMZ270

0.35

31

algorithms. Looking at the table in more detail, the displacements are decreased considerably by TMD. Therefore, the structure is not influenced too much by any dynamic loads, so the safety of the construction increases. 50 and 100 iterations were used for the optimization process to reach objective function, which is related to the period of TMD and the damping ratio of TMD. It can obviously be seen that displacement values without TMD are higher than the structure which are utilized TMD. Hybrid and Jaya algorithms have the same displacement for 100 iterations with 10 population numbers (Table 6) whereas they have different displacement results for 50 iterations with 5 population numbers. When 100 iterations were chosen for the optimization, Jaya and the Hybrid algorithm reached the objective function. Thus, the result of displacements by using TMD was found same for these algorithms. Nevertheless, when 50 iterations were chosen for the optimization, Jaya and the Hybrid algorithm did not reach the objective function. Therefore, the result of displacements was found different for these algorithms. In order to compare Hybrid and Jaya algorithms, optimization was repeated 10 times and saved maximum displacement for 50 iterations with 5 population numbers. After 10 runs, the maximum displacement and minimum displacement are chosen. In addition, mean and standard deviation are found in these displacement results. Table 7 delineates the values of the results. Maximum displacement was found for the Hybrid and Jaya algorithms, at about 0.0602 m and 0.0707 m respectively. Minimum displacement was found for the Hybrid and Jaya algorithms, at roughly 0.0419 m and 0.0466 m respectively. The mean of 10 runs’ displacement was computed for the Hybrid and Jaya algorithm, at approximately 0.05 m and 0.0547 m respectively. Therefore, the mean of

Structural Control Systems and Tuned Mass Damper Optimization … Table 6 Earthquakes and their maximum displacement without TMD and by using TMD

Earthquake no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Components

105

Maximum displacemen No TMD

With TMD

All runs

For 100 iterations

1

0.0271

0.0169

2

0.0377

0.0263

1

0.0229

0.0171

2

0.0236

0.0189

1

0.0455

0.0435

2

0.0213

0.0211

1 2

0.0160 0.0304

0.0113 0.0183

1

0.0206

0.0129

2

0.0201

0.0175

1

0.0617

0.0356

2

0.0288

0.0275

1

0.0350

0.0281

2

0.0463

0.0267

1

0.0079

0.0074

2

0.0115

0.0095

1

0.0146

0.0118

2

0.0361

0.0311

1

0.0087

0.0060

2

0.0097

0.0078

1

0.0148

0.0096

2

0.0198

0.0120

1

0.0287

0.0244

2

0.0212

0.0198

1

0.0732

0.0424

2

0.0212

0.0163

1

0.0400

0.0271

2

0.0289

0.0237

1

0.0277

0.0260

2

0.0396

0.0339

1

0.0204

0.0137

2

0.0151

0.0095

1

0.0250

0.0179

2

0.0169

0.0144

1

0.0302

0.0222 (continued)

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Table 6 (continued)

Earthquake no.

19 20 21 22

Components

Maximum displacemen No TMD

With TMD

All runs

For 100 iterations

2

0.0469

0.0376

1

0.0275

0.0189

2

0.0191

0.0142

1

0.0275

0.0263

2

0.0323

0.0196

1

0.0195

0.0133

2

0.0110

0.0088

1

0.0300

00205

2

0.0205

0.0163

Table 7 Values after 10 runs for 50 iterations with 5 populations numbers Maximum Displacement

Minimum Displacement

Mean

Standard Deviation

HYBRID

0.060226463

0.041869342

0.049886476

0.008663872

JAYA

0.0707

0.046601362

0.054665278

0.01239423

Hybrid algorithm was found to be closer than the Jaya algorithm in terms of objective function result, which was 0.452 m. Standard deviation results were found according to objective function displacement. The standard deviation of Hybrid and Jaya algorithms were calculated, at about 0.00866 and approximately 0.0124 respectively, which were too close to zero. Nevertheless, the Hybrid algorithm is getting closer to zero compared to those of Jaya. Maximum and minimum displacements are shown in Table 7. The results of these displacements in terms of variables which are period and damping ratio demonstrated in Table 8. It can obviously be seen that different period and damping ratio values were found due to displacements. Table 9 shows the results according to 100 iterations. It can be seen that Hybrid and Jaya which reached the objective function algorithm results have the same period and damping ratio. The period was found as 0.379, and also the damping ratio was found as 0.454 for 100 iterations with 10 population numbers in both Jaya and Hybrid algorithms. The earthquake acceleration figure can be seen in Fig. 14. Algorithm results were used to find changes between displacement and accelerations. When the optimization reaches the objective function, period and damping ratio are found as 0.379 s and 0.454 respectively. Figure 15 and Fig. 16 are demonstrated. For time histories and displacement and acceleration are observed at lower values thanks to using TMD.

Structural Control Systems and Tuned Mass Damper Optimization … Table 8 Period and damping ratio results for displacements (5 population and 50 iteration numbers)

HYBRID

JAYA

Table 9 Hybrid and Jaya algorithm results

Displacements

Period (s)

Damping ratio

Maximum Displacement

0.3556

0.2092

Minimum Displacement

0.2852

0.1422

Maximum Displacement

0.2145

0.2202

Minimum Displacement

0.3423

0.4758

100 iterations

Explanation No control system TMD

Fig. 14 Earthquake acceleration (DUZCE/ BOL000)

107

Period (s)

Damping ratio

0.288

–

HYBRID

0.379

0.454

JAYA

0.379

0.454

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M. Ço¸sut et al.

Fig. 15 Displacement of structure (DUZCE/BOL000)

Fig. 16 Total acceleration (DUZCE/BOL000)

6 Conclusion Although the structure is built in accordance with the regulations, some loading situations that are not taken into account in the design can cause regional damage by creating excessive stresses on the system elements when the structure is encountered, which triggers a collapse situation. Prevention of these and similar situations have been carried out with building control systems. There are varieties of building control systems that can be placed in many locations of the building, which makes it easy to add these systems to pre-built buildings later. When these systems are added to the structure; they can reduce the interaction between the structure and the ground, they can reduce the relative stories displacements (allowing the displacements to remain at a certain level), the structure will prevent the structure from being damaged by

Structural Control Systems and Tuned Mass Damper Optimization …

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reducing the acceleration and speed of the acting load. By increasing the construction period at a certain rate through the systems it contains, it will ensure that the structure remains on the safe side. Optimization of the TMD system was performed using Hybrid and Jaya algorithms. As a result of this, the period and damping ratio value of TMD were found depending on the amount of iteration. In addition, the displacement as well as acceleration of the structure were found and shown on graphs. It is clearly seen in the graphs that the displacement and acceleration values generated in the structure when no control system is used in the structure will take much larger values than in the case of using TMD in the structure. Therefore, the structure will remain on the safe side with a significant reduction in structure displacements and acceleration values. Furthermore, the results of TMD can be found Jaya and Hybrid algorithms which reached objective function in about 100 iterations. Looking at the Hybrid and Jaya algorithm for different iteration numbers which are 50 iterations with 5 population numbers, they have not reached the objective function. Moreover, this optimization was repeated 10 times and saved for both algorithms. It was seen that the Hybrid algorithm approached the objective function better than Jaya algorithm. As a consequence, reaching the objective function is affected by iteration and population numbers as well as algorithm types.

References 1. Isalgue, A., Lovey, F.C., Terriault, P., Ferran, Martorell, Torra, R.M., Torra, V.: SMA for dampers in civil engineering. Mater. Trans. 47 (3), 682–690 (2006) 2. Vu, K.D.T., Nguyen, B.N.: Sustainable material awareness, belief and readiness in housing development. Built Environment Journal 18(2), 88–96 (2021) 3. Utsev, T., Tiza, M.T., Sani, H.A., Sesugh, T.: Sustainability in the civil engineering and construction industry: a review. J. Sustain. Constr. Mater. Technol. 7(1), 30–40 (2022) 4. Bekda¸s, G., Ni˘gdeli, S.M.: Estimating optimum parameters of tuned mass dampers using harmony search. Eng. Struct. 33(9), 2716–2723 (2011) 5. Farshidianfar, A., Soheili, S.: Ant colony optimization of tuned mass dampers for earthquake oscillations of high-rise structures including soil–structure interaction. Soil Dyn. Earthq. Eng. 51, 14–22 (2013) 6. Araz, O., Kahya, V.: Design of series tuned mass dampers for seismic control of structures using simulated annealing algorithm. Arch. Appl. Mech., 4343–4359 (2021) 7. Nigdeli, S.M., Bekdas, G.: Optimum tuned mass damper approaches for adjacent structures. Earthq. Struct. 7(6), 1071–1091 (2014) 8. Liao, T.W.: Two hybrid differential evolution algorithms for engineering design optimization. Appl. Soft Comput. 10, 1188–1199 (2010) 9. Rao, R.V.: Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int. J. Ind. Eng. Comput. 7, 19–34 (2016) 10. FEMA P-695. Quantification of Building Seismic Performance Factors. Washington 11. Montuori, R., Nastri, E., Piluso, V.: Theory of plastic mechanism control for eccentrically braced frames with inverted Y-scheme. J. Constr. Steel Res. 92, 22–135 (2015) 12. Zeynali, K., Monir, H.S., Mirzai, N.M., Hu, J.W.: Experimental and numerical investigation of lead-rubber dampers in chevron concentrically braced frames. Arch. Civil Mech. Eng. 18(1), 162–178 (2018)

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13. Davalos, C., Escudero, C., Cano, G., Hernandez, V., Cruz, S.: Damage modelling of hysteretic energy dissipative devices in building seismic response control. Researchgate 73, 1883–1890 (2017) 14. Bekda¸s, G., Ni˘gdeli, S.M.: Mass ratio factor for optimum tuned mass damper strategies. Int. J. Mech. Sci. 71, 68–84 (2013) 15. Madsen, L.P.B., Thambiratnam, D.P., Perera, N.J.: Seismic response of building structures with dampers in shear walls. Comput. Struct. 81(4), 239–253 (2003) 16. Ahn, S. K., Min, K. W., Lee, S. H., Park, J. H., Lee, D. G., Oh, J. G.: Control of Wind-Induced Acceleration Response of 46-Story R.C. Building Structure Using Viscoelastic Dampers Replacing Outrigger System. In CTBUH Conference Seoul, 504–509 (2004). 17. Smith, R.J., Willford, M.R.: The damped outrigger concept for tall buildings. Struct. Design Tall Spec. Build. 16(4), 501–517 (2007) 18. Joung, J., & Kim, D.: Experimental and Numerical Studies of a Newly Developed Semiactive Outrigger Damper System. In CTBUH 9th World Congress Shanghai 2012 Proceedings, 790–796 (2011). 19. Asai, T., Chang, C.M., Phillips, B.M., Spencer, B.F., Jr.: Real-time hybrid simulation of a smart outrigger damping system for high-rise buildings. Eng. Struct. 57, 177–188 (2013) 20. Kidokoro, R.: Self Mass Damper (SMD): Seismic Control System Inspired by the Pendulum Movement of an Antique Clock. In The 14th World Conference on Earthquake Engineering, (2008). 21. Öncü-Davas, S., Alhan, C.: Realibility of semi-active isolation under far-fault earthquakes. Mech. Syst. Signal Process. 114, 146–164 (2019) 22. Aldemir, A., Ersin, A.: Depreme Dayanıklı Yapı Tasarımında Yeni Yakla¸sımlar. Türkiye Mühendislik Haberleri Sayısı 435, 81–89 (2005) 23. Bekda¸s, G., Ni˘gdeli, S.M.: Estimating optimum parameters of tuned mass dampers using harmony search. Eng. Struct. 33, 2716–2723 (2011) 24. Sadek, F., Mohraz, B., Taylor, A.W., Chung, R.M.: A method estimating the parameters of tuned mass dampers for seismic applications. Earthq. Eng. Struct. Dynam. 26(617), 617–635 (1997) 25. Sahin, ¸ M.: Depreme Dayanıklı Yapı Tasarımında Pasif ve Aktif Kontrol Sistemleri. Tasarım Kuram, Sayı 1, 60–65 (1999) 26. Kayabekir, A.E., Bekda¸s, G., Ni˘ggeli, S.M., Geem, Z.W.: Optimum design of PID controlled active tuned mass damper via modified harmony search. Applied Science 10, 2976 (2020) 27. Pourzeynali, S., Lavasani, H.H., Modarayi, A.H.: Active control of high-rise building structures using fuzzy logic and egentic algorithms. Eng. Struct. 29, 346–357 (2007) 28. Gkatzogias, K.I., Kappos, A.J.: Semi-active Control Systems in Bridge Engineering: A Review of the the Current State of Practise. Struct. Eng. Int. 26(4), 290–300 (2016) 29. Wang, L., Nagarajaiah, S., Shi, W., Zhou, Y.: Seismic performance improvement of baseisolated structures using a semi-active tuned mass damper. Eng. Struct. 271, 114963 (2022) 30. Bekda¸s G., Nigdeli M. N., Yücel M., Kayabekir A. E.: Yapay Zeka optimizasyon Algoritmaları ve Mühendislik Uygulamaları. Seçkin Yayıncılık, Ankara (2021) 31. Ting, T.O., Yang, X.S., Cheng, S., Huang, K.: Hybrid metaheuristic algorithms: past, present and future, recent advances in swarm intelligence and evolutionary computation, studies in computational. Intelligence 585, 71–83 (2015)

Manta Ray Foraging and Jaya Hybrid Optimization of Concrete Filled Steel Tubular Stub Columns Based on CO2 Emission Celal Cakiroglu, Kamrul Islam, and Gebrail Bekda¸s

Abstract Concrete-filled steel tubular (CFST) columns exhibit favorable characteristics and have been studied extensively particularly through experiments. However, the CO2 emission in the production process of these structural members should be reduced to minimize the environmental impact. At the same time, the performance of these structures should be kept at a satisfactory level. This can be achieved using metaheuristic optimization algorithms. The most commonly used indicator of structural performance for CFST columns is the ultimate axial load carrying capacity (Nu ). This quantity can be predicted using various equations available in design codes and the research literature. However, most of these equations are only applicable within certain parameter ranges. A recently developed set of equations from the CFST literature was applied for the prediction of Nu due to its improved ranges of applicability. Furthermore, novel metaheuristic algorithms called Manta Ray Foraging Optimization and, Jaya algorithm are applied to the cross-section optimization of rectangular CFST columns. The improvement of the structural dimensioning under Nu constraint was demonstrated. The objective of optimization was to minimize the CO2 emission associated with the fabrication of CFST stub columns. For different concrete classes and load capacities, the optimum cross-sectional dimensions have been obtained. Keywords Metaheuristic optimization · CFST columns · Axial compressive strength · Jaya · Manta ray foraging

C. Cakiroglu Department of Civil Engineering, Turkish-German University, Beykoz, 34820 Istanbul, Turkey e-mail: [email protected] K. Islam Department of Civil, Geological and Mining Engineering, Polytechnique Montréal, Montréal, Canada e-mail: [email protected] G. Bekda¸s (B) Department of Civil Engineering, Istanbul University - Cerrahpa¸sa, Avcılar, 34320 Istanbul, Turkey e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Bekda¸s and S. M. Nigdeli (eds.), Hybrid Metaheuristics in Structural Engineering, Studies in Systems, Decision and Control 480, https://doi.org/10.1007/978-3-031-34728-3_7

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1 Introduction High ductility, rapid construction, and increased strength are a few of the qualities making concrete-filled steel tubular (CFST) columns preferable in structural design. However, it should be noted that the concrete constituents and steel constituents of CFST columns can have considerable amounts of CO2 emission associated with their production process. In line with the efforts of the construction industry to reduce its carbon footprint design engineers should consider carbon emissions as an additional factor besides the structural performance. The production of 1 kg of steel and 1 kg of concrete are known to cause an emission of approximately 1.38 kg and 0.12 kg of CO2 respectively [1]. Furthermore, Arama et al. [2] showed that the concrete volume has a more decisive effect on the CO2 emission compared to the steel weight. Table 1 shows the amounts of CO2 emission related to different classes of concrete. Based on extensive experimental studies various methods are developed and included in the design codes to predict the load-carrying capacity (Nu ) of CFST columns. However, for most of these methods, certain ranges of applicability are defined so that they are not recommended to be used for variable values outside of these ranges. For instance, the equations included in the AISC 360-16 code [3] are recommended only for fy ≤ 525 MPa and for 21 MPa ≤ fc ' ≤ 70 MPa. The widely accepted definition of Nu is the maximum axial compressive load if this load level is reached at an axial strain of less than 1%. If the maximum load is observed at greater strain levels, then Nu is defined as the load level at 1% axial strain [4–6]. The ultimate axial load carrying capacity prediction equations developed by Wang et al. [6] obtain the Nu value by adding the structural capacities of the steel casing and the concrete core as shown in Eq. 1 for circular CFST stub columns. Nu = Ns + Nc ,

(1) '

N s = ηs f y A s , N c = ηc f c A c ,

(2)

) 0.14D < 1, ηs = 0.95 − 12.6 t [ ) ( )0.04 ( ) ]( t f y 0.51 D ' 0.1 fc ηc = 0.99 + 5.04 − 2.37 >1 t D f c' f y−0.85 ln

(

(3)

(4)

In Eq. 1, Ns and Nc stand for the load-carrying capacities of the steel casing and the concrete inner part respectively. In Eq. 2, As and Ac are the areas of the steel Table 1 CO2 emission of different concrete classes (Fantilli et al. [1]) Concrete class CO2 emission

[kg/m3 ]

C25

C40

C60

C80

215

272

350

394

Manta Ray Foraging and Jaya Hybrid Optimization of Concrete Filled …

113

tube and the concrete core cross-sections respectively. Under the axial load, the steel casing exerts a confining force on the concrete core which in turn causes the steel wall thickness to decrease due to hoop stresses. Also, due to being a thin-walled structure, the steel casing is prone to local buckling which adversely affects Nu . In Eq. 2, ηs is a reduction factor that introduces these adverse effects into the overall structural capacity. On the other hand, the confinement by the steel casing has a favorable effect on the capacity of the concrete core. This favorable effect is quantified by the amplification factor ηc in Eq. 2. The equations for ηs and ηc are given in Eqs. 3,4. In Eq. 3, D and t are the diameter and wall thickness of the steel casing respectively as depicted in Fig. 1. Table 2 shows the ranges of parameters in which Eq. 1 is valid. Equations 1 and 2 are also applicable to columns with rectangular cross-sections. In case of rectangular cross-sections, ηs and ηc are calculated as in Eqs. 5 and 6. ( ' )2 ) ( D ηs = 0.91 + 7.31 · 10−5 f y − 1.28 · 10−6 + 2.26 · 10−8 f y , t ηc f c' Ac ,

ηc = 0.98 + 29.5( f y )

−0.48

( K s0.2

(a)

t fy (D ' f c' )

)1.3 (6)

(b)

Fig. 1 a Circular CFST cross-section; b rectangular CFST cross-section

Table 2 Parameter ranges for which Eqs. (1–7) are applicable [6]

(5)

Diameter to thickness ratio

12 ≤ D/t ≤ 150

Width to thickness ratio

12 ≤ B/t ≤ 100

Height to width ratio

1 ≤ H/B ≤ 2

Yield stress of the steel tube

175 MPa ≤ fy ≤ 960 MPa

Compressive strength of the concrete

20 MPa ≤ fc ≤ 120 MPa

Steel wall thickness [mm]

3 ≤ t ≤ 30

'

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( ) 1 B − 2t 2 Ks = 3 H − 2t

(7)

'

In Eqs. 5 and 6, D is the√equivalent diameter of the rectangular cross-section ' which is calculated as D = B2 + H2 where B and H are the width and height of the cross-section respectively as shown in Fig. 1b. Due to the rectangular shape of the cross-section the concrete confinement is not as effective as in the circular form. This lack of concrete confinement in rectangular cross-sections is quantified with the equivalent confinement coefficient K s in Eq. 7.

2 Optimization Methodology Metaheuristic optimization techniques are finding broad application in numerous areas of engineering. To give a few examples of these applications the works of Geem et al. [7–9] on water network design and vehicle routing, Kayabekir et al. [10, 11] on reinforced concrete retaining walls and plane stress systems, and Cakiroglu et al. [12–15] on laminated composite plates, steel plate girders and retaining walls can be mentioned. Furthermore, physics-inspired optimization algorithms such as the atom stabilization algorithm [16–18], particle swarm optimization [19–22], genetic algorithm [23] and evolutionary optimization algorithms [24, 25] have been widely implemented in the optimization of various engineering systems. The following sections introduce the algorithms implemented in this study for the optimal design of rectangular CFST stub columns.

2.1 Jaya Optimization In this study, a novel metaheuristic algorithm called the Jaya algorithm was implemented to find the cross-sectional properties of a CFST column that lead to the minimum CO2 emission. The Jaya algorithm was developed by Rao [26] as a generalpurpose optimization technique. The major difference of this algorithm compared to the other state-of-the-art metaheuristic techniques is that the Jaya algorithm does not depend on parameters that need to be tuned by the user. This is a great advantage since it opens up the possibility of integration of this algorithm into the structural design process by engineers that are not necessarily experts in the field of optimization. A flowchart of the Jaya algorithm is given in Fig. 2.

Manta Ray Foraging and Jaya Hybrid Optimization of Concrete Filled …

115

Fig. 2 Flow chart of the Jaya algorithm

The algorithm starts with the creation of an initial population where each randomly generated population member represents a candidate for the optimum solution. In the process of minimizing the CO2 emission, the side lengths of the rectangular crosssection and the wall thickness are the design parameters while the yield stress of steel and concrete compressive strength are kept constant throughout the optimization process. In the case of circular cross-sections, the side lengths are replaced by the outer diameter. In the Jaya optimization, each member of the population is an array of design variables taking values within their predefined domain of allowable values. In this process, Nu is kept above a certain predefined value which becomes one of the optimization constraints. Additional constraints are introduced on the crosssectional dimensions as well. These variables can take any value continuously within their predefined constraints. Once the initial population is generated, all members of the population go through a Jaya iteration step which is described in Eq. 8. | |) | |) ( ( Xt+1 = xti + r1 g∗ − |xti | − r2 gw − |xti | i

(8)

In Eq. 8 xi t is the candidate solution vector in the t-th iteration, r1 , r2 ∈ (0,1) are random numbers and g*, gw are the best- and worst-performing members of the population respectively. After every iteration the newly generated vector xi t+1 is compared to gw with respect to its CO2 emission value and in case the new vector performs better, it replaces gw gw . Every newly generated vector is controlled with respect to its Nu value and dimensions. In case a cross-sectional dimension is outside its predefined upper and lower bounds this dimension is set equal to its lower or

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upper bound. After this operation if the Nu Nu value of the new vector is below the lower bound for Nu then the newly generated vector is discarded.

2.2 Manta Ray Foraging Optimization (MRFO) This algorithm is inspired by the intelligent foraging strategies of manta rays that feed on planktons. The foraging strategies of Manta rays can be classified as chain foraging, cyclone foraging, and somersault foraging [27]. The MRFO technique combines the mathematical models of the chain foraging, cyclone foraging and somersault foraging strategies of manta rays in one algorithm. Like many other metaheuristic optimization algorithms, the starting point of MRFO is the generation of a random population that fulfills certain optimization constraints. Afterward, the algorithm enters into a loop of incremental improvements of this population. In every iteration, the algorithm branches into one of cyclone or chain foraging based on the value of a random variable in that particular iteration. Once the cyclone or chain foraging operation is completed the population goes through somersault foraging after which the values of the newly generated vectors are compared to the upper and lower bounds. In case they exceed one of these boundaries they are assigned values equal to the boundary values. Newly generated vectors replace old ones in case they perform better. The chain foraging strategy is based on the motion of manta rays in a head-to-tail foraging chain toward areas with high plankton concentration. In this process every population member except for the one in front of the chain (the first member) moves towards the best performing member of the population and towards the individual directly in front of it. The mathematical description of this motion is given in Eq. 9 where N denotes the size of the population and r ∈ (0, 1). A graphical depiction of the chain foraging process is given in Fig. 3. { xit+1

=

) ( t ) ( t − xit ) + α(xbest − xit )ifi = 1 xit + r (xbest t t − xit + α xbest − xit ifi > 1 xit + r xi−1 √ α = 2r |log(r)|

(9) (10)

In cyclone foraging manta rays move in a spiral pattern towards the plankton. In addition to their motion towards the plankton, also each manta ray in the foraging chain moves toward the individual in front of it. The cyclone foraging step further branches into exploration and exploitation phases depending on the current number of iterations. In the beginning stages of the algorithm the exploration operation is performed in order to search for the global optimum. Equation 11 describes the exploratory operation in cyclone foraging.

Manta Ray Foraging and Jaya Hybrid Optimization of Concrete Filled …

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Fig. 3 Chain foraging process

{ xit+1

=

) ( t ) ( t t + r (xrand − xit) + β( xrand − xit) ifi = 1 xrand t t t + r xi−1 − xit + β xrand − xit ifi > 1 xrand β = 2er1

T−t+1 T

· sin(2πr1 )

t xrand = LB + r0 (UB − LB)

(11) (12) (13)

In Eqs. 11 and 12, t and T are the current and maximum number of iterations respectively and r1 ∈ (0, 1). In Eq. 13, r0 is another random number in (0,1) which is used in generating a random vector between the lower bound vector LB and the upper bound vector UB. On the late stages of the iterations when t/T > r0 ∈ (0, 1), the exploitation operation is carried out which is described in Eq. 14. { xit+1 =

) ( t ) ( t t + r (xbest − xit ) + β(xbest − xit )ifi = 1 xbest t t t + r xi−1 − xit + β xbest − xit ifi > 1 xbest

(14)

Finally, after all population members go through the chain foraging and cyclone foraging phases, the somersault phase begins. In this phase the population members settle in a new position between their previous positions and another position symmetrical with respect to the position of the best population member. Mathematically somersault iteration can be described as in Eq. 15 where S is the somersault factor which determines the somersault range. In this study S is initialized as S = 2. t xit+1 = xit + S(r2 xbest − r3 xit )

(15)

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In this study a new hybrid algorithm has been proposed by combining the Jaya and Manta ray foraging algorithms. The Jaya iteration formula given in Eq. 8 has been implemented in the exploration phase of the algorithm whereas the somersault iteration given in Eq. 15 has been implemented in the exploitation phase.

3 Result Analysis This section presents the steps of the CO2 emission minimization for rectangular CFST stub columns. The optimization process is visualized for C25, C40, and C60 concrete classes separately. For each concrete class different lower bound values for the ultimate axial load capacity (Nu,min ) are set and these values serve as optimization constraints that guarantee a minimum level of acceptable structural performance. In addition to Nu,min also dimensional constraints are in place in all stages of the optimization. Using the Jaya algorithm, the cross-sectional width and height as well as the steel casing wall thickness of the member are optimized while keeping Nu above Nu,min at all times. The objective of the optimization is the CO2 emission resulting from the production of a CFST stub column with unit height. In Fig. 4 the results of the Jaya optimization are presented at four different levels of Nu,min for columns with rectangular cross-section and a concrete class of C25. The curves in Fig. 4 show CO2 emissions associated with the best performing member in all of the population at each iteration step. From Fig. 4 it is clear that after the first 25 iterations a convergence of the minimum CO2 emission is observed at all levels of Nu,min . For the Nu,min threshold values of 5000 kN, 4000 kN and 2000 kN this convergence is observed as early as after the first 10 to 20 iterations. Table 3 presents a list of the minimum CO2 emission values together with the corresponding cross-sectional dimensions for a constant yield stress of 800 MPa for the steel casing. Figures 4, 5, and 6 visualize the development of the minimum CO2 emissions obtained through the Jaya optimization process using C25, C40, and C60 concrete classes respectively. For each concrete class the optimization process is repeated at four different levels of the ultimate axial load capacity constraint Nu,min . The crosssectional configurations which do not satisfy the Nu,min constraints are not included in the population of solution candidates during the Jaya iterations. In these optimizations the cross-sectional height (H), width (B), and the thickness of the steel casing (t) are the optimization variables, and modifying these dimensions leads to changes in the concrete and steel volumes needed to manufacture the CFST stub columns which in turn leads to different amounts of CO2 CO2 emissions. For each concrete class and Nu,min constraint the corresponding cross-sectional dimensions are listed in Table 3. Using the Jaya algorithm, average values of 50.4 kg, 48 kg, and 42.5 kg could be obtained as minimum CO2 emissions corresponding to C25, C40, and C60 concrete classes respectively.

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(a)Nu,min = 6000kN

(b)Nu,min = 5000kN

(c)Nu,min = 4000kN

(d)Nu,min = 2000kN

Fig. 4 Jaya optimization of a rectangular cross-section with respect to CO2 emission (C25) Table 3 Minimum CO2 emissions for rectangular cross-section (Jaya) Concrete class

Nu,min [kN]

Min. CO2 emission [kg]

B [mm]

H [mm]

t [mm]

C25

6000

71.6

169

249

7.3

5000

59.1

118

183

9

4000

47.3

98

152

8.9

2000

23.6

70

108

6.2

6000

67.7

233

275

4.8

5000

56.5

212

251

4.3

4000

45.2

190

225

3.9

2000

22.6

126

153

3

6000

59.4

262

279

3

5000

49.6

229

247

3

4000

40

194

214

3

2000

20.8

115

135

3

C40

C60

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(a)Nu,min = 6000kN

(b)Nu,min = 5000kN

(c)Nu,min = 4000kN

(d)Nu,min = 2000kN

Fig. 5 Jaya optimization of a rectangular cross-section with respect to CO2 emission (C40)

(a)Nu,min = 6000kN

(b)Nu,min = 5000kN

(c)Nu,min = 4000kN

(d)Nu,min = 2000kN

Fig. 6 Jaya optimization of a rectangular cross-section with respect to CO2 emission (C60)

Manta Ray Foraging and Jaya Hybrid Optimization of Concrete Filled …

(a)Nu,min = 6000kN

(b)Nu,min = 5000kN

(c)Nu,min = 4000kN

(d)Nu,min = 2000kN

121

Fig. 7 Manta ray foraging—Jaya hybrid optimization of a rectangular cross-section with respect to CO2 emission (C25)

Figures 7, 8, and 9 visualize the development of the minimum CO2 emissions obtained through the Manta ray foraging—Jaya hybrid algorithm using C25, C40, and C60 concrete classes respectively. The optimal cross-sectional dimensions obtained through this hybrid algorithm have been listed in Table 4. For concrete classes C25. C40, and C60 optimal cross-sectional dimensions corresponding to four different lower bounds of the axial load carrying capacity have been obtained. These lower bound values have been varied between 6000 and 2000 kN as listed in Table 4. The CO2 CO2 emission values corresponding to each optimal design have been listed in Table 4. Using the Manta ray foraging—Jaya hybrid algorithm, average values of 50.3 kg, 48 kg, and 42.5 kg could be obtained as minimum CO2 emissions corresponding to C25, C40, and C60 concrete classes respectively.

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(a)Nu,min = 6000kN

(b)Nu,min = 5000kN

(c)Nu,min = 4000kN

(d)Nu,min = 2000kN

Fig. 8 Manta ray foraging—Jaya hybrid optimization of a rectangular cross-section with respect to CO2 emission (C40)

(a)Nu,min = 6000kN

(b)Nu,min = 5000kN

(c)Nu,min = 4000kN

(d)Nu,min = 2000kN

Fig. 9 Manta ray foraging—Jaya hybrid optimization of a rectangular cross-section with respect to CO2 emission (C60)

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Table 4 Minimum CO2 emissions for rectangular cross-section (Manta ray foraging—Jaya hybrid) Concrete class

Nu,min [kN]

Min. CO2 emission [kg]

B [mm]

H [mm]

t [mm]

C25

6000

70.9

225

302

5.4

5000

59.3

118

207

8.2

4000

47.3

98

152

8.8

2000

23.6

69

108

6.3

6000

67.7

231

276

4.8

5000

56.5

211

250

4.4

4000

45.2

190

225

3.9

2000

22.6

126

153

3

6000

59.4

262

279

3

5000

49.6

229

247

3

4000

40

194

214

3

2000

20.8

94

168

3

C40

C60

4 Conclusion CFST members find widespread applications in the area of structural engineering because of the enhanced mechanical properties that these members possess. However, the production process of the concrete constituents and steel constituents of these structures can be linked to considerable amounts of CO2 emissions. To reduce the carbon footprint associated with the construction industry, there is an ongoing effort to reduce the CO2 CO2 emission caused by the production of various construction materials. At the same time, it is the responsibility of structural design engineers to guarantee the performance of structures such as CFST columns in an optimum way so that they satisfy certain load carrying capacity requirements. These requirements led to an increasing interest in the application of meta-heuristic optimization techniques to structural optimization problems in recent years since these techniques can solve many engineering problems more effectively. The Jaya optimization algorithm is a newly developed meta-heuristic algorithm that was shown to be suitable to tackle structural design optimization problems. In this study the Jaya algorithm has been combined with the Manta ray foraging algorithm which is another newly developed metaheuristic algorithm and a hybrid algorithm has been proposed. These algorithms have been applied to the problem of CO2 emission minimization by varying the cross-sectional dimensions while keeping the structural capacity above a certain level. The class of the core concrete was shown to have a significant influence on the CO2 emission. The configurations with C60 concrete class had the least amount of CO2 emission whereas, it was observed that the configurations with less concrete compressive strength exhibited greater CO2 emission. Further research in this field can include the study of CFST columns concerning the changes in the cross-sectional slenderness properties and column heights. Also, concrete-filled double skin steel

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tubular column behavior can be investigated. Furthermore, the behavior of different materials such as fiber-reinforced composites as outer casing can be analyzed.

References 1. Fantilli, A.P., Mancinelli O., Chiaia B.: The carbon footprint of normal and high-strength concrete used in low-rise and high-rise buildings. Case Stud. Constr. Mater. 11, 1–7, e00296 (2019) 2. Arama, Z.A., Kayabekir, A.E., Bekda¸s, G., Geem, Z.W.: CO2 and cost optimization of reinforced concrete cantilever soldier piles: a parametric study with harmony search algorithm. Sustainability 12(15), 1–24, 5906 (2020) 3. American Institute of Steel Construction (AISC): Specification for Structural Steel Buildings; AISC 360-16. American Institute of Steel Construction, Chicago, IL, USA (2016) 4. Tao, Z., Wang, Z.B., Yu, Q.: Finite element modelling of concrete-filled steel stub columns under axial compression. J. Constr. Steel Res. 89, 121–131 (2013) 5. Uy, B., Tao, Z., Han, L.H.: Behaviour of short and slender concrete-filled stainless steel tubular columns. J. Constr. Steel Res. 67(3), 360–378 (2011) 6. Wang, Z.B., Tao, Z., Han, L.H., Uy, B., Lam, D., Kang, W.H.: Strength, stiffness and ductility of concrete-filled steel columns under axial compression. Eng. Struct. 135, 209–221 (2017) 7. Geem, Z.W.: Harmony search optimisation to the pump-included water distribution network design. Civ. Eng. Environ. Syst. 26(3), 211–221 (2009) 8. Geem, Z.W.: Particle-swarm harmony search for water network design. Eng. Optim. 41, 297– 311 (2009) 9. Geem, Z.W., Lee, K.S., Park, Y.: Application of Harmony Search to Vehicle Routing. Am. J. Appl. Sci. 2, 1552–1557 (2005) 10. Kayabekir, A.E., Arama, Z.A., Bekda¸s, G., Nigdeli, S.M., Geem, Z.W.: Eco-friendly design of reinforced concrete retaining walls: multi-objective optimization with harmony search applications. Sustainability 12(15), 1–30, 6087 (2020) 11. Kayabekir, A.E., Toklu, Y.C., Bekda¸s, G., Nigdeli, S.M., Yücel, M., Geem, Z.W.: A novel hybrid harmony search approach for the analysis of plane stress systems via total potential optimization. Appl. Sci. 10, 1–15, 2301 (2020) 12. Cakiroglu, C., Bekda¸s, G., Geem, Z.W.L.: Harmony search optimisation of dispersed laminated composite plates. Materials 13(12), 1–13, 2862 (2020) 13. Cakiroglu, C., Bekda¸s, G., Kim, S., Geem, Z.W.: Optimisation of shear and lateral–torsional buckling of steel plate girders using meta-heuristic algorithms. Appl. Sci. 10(10), 1–14 3639 (2020) 14. Cakiroglu, C., Islam, K., Bekda¸s, G., Kim, S., Geem, Z.W.: Metaheuristic optimization of laminated composite plates with cut-outs. Coatings 11, 1235 (2021). https://doi.org/10.3390/ coatings11101235 15. Cakiroglu C., Islam K., Bekda¸s G., Nehdi M.L.: Data-driven ensemble learning approach for optimal design of cantilever soldier pile retaining walls. Structures 51, 1268–1280 (2023). https://doi.org/10.1016/j.istruc.2023.03.109 16. Biswas, A., Mishra K.K., Tiwari, S. and Misra, A.K.: Physics-inspired optimization algorithms: a survey. J. Optim. 2013, Article ID 438152, 16 pages, (2013). (ESCI) 17. Biswas, A.: Atom stabilization algorithm and its real life applications. Journal of Intelligence and Fuzzy Systems (JIFS), IOS Press 30(4), 2189–2201 (2016) 18. Biswas, A., Biswas, B. and Mishra, K.K.: An atomic model based optimization algorithm. In: 2nd International Conference on Computational Intelligence & Networks (CINE 2016), pp. 63–68. Bhubaneswar (11 Jan. 2016) 19. Biswas, A., Kumar, A., and Mishra, K.K.: Particle swarm optimization with cognitive avoidance component. In: 2nd International Conference on Advances in Computing, Communications and Informatics (ICACCI-2013), pp 149–154, Mysore, India (22–25 Aug. 2013a)

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Optimum Design of Dam Structures Using Multi-objective Chaos Game Optimization Algorithm A. Jafari, M. Saraee, B. Nouhi, M. Baghalzadeh Shishehgarkhaneh, and S. Talatahari

Abstract This chapter aims to present a novel methodology for determining the optimal shape of double-curvature arch dams. The proposed approach differs from previous research by employing a multi-objective optimization approach, which generates a set of Pareto solutions instead of a single solution. The authors use the MOCGO algorithm, a multi-objective version of the standard Chaos Game Optimization (CGO) algorithm, to achieve this goal. The methodology involves the use of parallel-working APDL-MATLAB codes that model, analyze, and obtain the fitness functions of the arch dam, and interface with the MOCGO algorithm at every step of the optimization process. The results were compared with MoPSO, NSGA-II, and MoCSS approaches, and findings show that the proposed algorithm has the potential to provide effective and robust solutions for finding the optimal shape of double-curve arch dams. Keywords Multi-objective Chaos Game Optimization · Double curvature arch dam · Optimum design

1 Introduction Arch dams are concrete structures with a base less than half its height and rely on its curve to transmit some of the water load laterally into the valley margins. Arch dams may only have one-fifth of the concrete of gravity dams of the same size. Arch dams can be modeled and designed with a single or double curve [1]. Due to A. Jafari · M. Saraee · S. Talatahari (B) Department of Civil Engineering, University of Tabriz, Tabriz, Iran e-mail: [email protected] B. Nouhi · S. Talatahari Faculty of Engineering & Information Technology, University of Technology Sydney, Ultimo, NSW 2007, Australia M. B. Shishehgarkhaneh Department of Civil Engineering, Monash University, Clayton, VIC 3800, Australia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Bekda¸s and S. M. Nigdeli (eds.), Hybrid Metaheuristics in Structural Engineering, Studies in Systems, Decision and Control 480, https://doi.org/10.1007/978-3-031-34728-3_8

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several influential factors in double-curvature arch dam geometry, the complexity of numerical modeling, and the need for high computing costs, their design is categorized as a complicated task. Finding the optimal solution for such tough challenges is more difficult when various designs must be executed. The nonlinear character of the relevant objective function and constraints of the arch dam optimization issue and the need to incorporate diverse boundary conditions necessitate adopting unique optimization techniques in dealing with this problem, considering some primary constraints [2]. The behavior constraint is one of the most significant constraints. Natural frequencies are essential factors that influence how dynamically the arch dams behave. Various restrictions should be placed on the natural frequency range to decrease the vibrational domain and avoid the resonance phenomena in the dynamic response of arch dams [3]. Conventionally, the shape of an arch dam is designed using the designer’s expertise, model testing, trial-and-error, and deterministic solution methods. Because of limitations such as needing an appropriate starting point, the possibility of attaining an inadequate local minimum, necessitating objective function continuity and differentiability, and having poor performance when dealing with large-scale practical and intricate situations, metaheuristic (MH) algorithms have gained much popularity among academics in dealing with shape optimization problems in arc dams. The designer should choose numerous schemes with varied patterns and change them to create various acceptable shapes to get a superior shape [4]. Zacchei and Molina [5] used the Bayesian theorem hypothesis to optimize a Spanish double-arch dam’s shape. Aalami, Talatahari [2] employed the multi-objective charge system search algorithm for double curvature arch dams’ shape optimization considering natural frequencies and concrete volume. Seyedpoor, Salajegheh [6] used the simultaneous perturbation stochastic approximation (SPSA) algorithm for arc dams’ shape optimization. Zhang, Li [7] employed the so-called trial-load approach Xiamen Arch dam’s shape optimization. Fengjie and Lahmer [8] utilized the genetic algorithm (GA) in dealing with model-based shape optimization of arch dams; they concluded that it is possible to find a reliability-based design that guarantees the safety and serviceability of newly constructed arch dams. Takalloozadeh, Takalloozadeh [9] used the prominent particle swarm optimization (PSO) method to solve arch dams’ shape on unsymmetrical valleys. Wang, Zhao [10] proposed a novel methodology consisting of a sequential Kriging surrogate model and GA for arch dams’ shape optimization. Furthermore, Talatahari, Aalami [11] evaluated the arch dam’s optimum shape’s failure costs using the Hybrid Charged System Search algorithm. Talatahari, Aalami [12] proposed a multi-objective optimization approach for the design of arch dams, which aims to simultaneously minimize two objectives: the stress state and the concrete volume required for the construction of the dam body. Multi-objective optimization (MOO) refers to the process of optimizing multiple objective functions concurrently in the field of multi-criteria decision-making. This approach is used to solve complex problems that involve multiple objectives, and the goal is to find a set of solutions that are optimal for all objectives simultaneously [13]. Multi-objective optimization is widely used in various fields such as engineering [14– 17], economics [18], and environmental management [19, 20], where decisions need

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to be made concerning multiple and often conflicting criteria. It allows decisionmakers to consider different aspects of the problem simultaneously, and find the best possible solution that satisfies all objectives. In other words, MOO is a useful technique for optimizing solutions in various conditions where multiple objectives need to be considered. One of the main challenges is dealing with contradictions and non-conformities that arise due to the existence of multiple objectives [21, 22]. This chapter utilizes a Multi-objective Chaos Game Optimization (MOCGO), for shape optimization of double-curved arch dams considering the frequency and concrete volume. Chaos Game Optimization (CGO) was developed by Talatahari and Azizi [23] and is inspired by the fractals self-similarity and chaos game theory. The concrete volume of the dam body, which should be minimized, and the various natural frequencies of the arch dam, which should be maximized, are the two other objective functions in the optimization problem.

2 Optimization Problem Formulation In the current research work, two different objectives are deemed as follows [2].

2.1 Concrete Volume The arch dam’s concrete volume ought to be minimized. It might be identified by integration on the dam’s surfaces as follows [2]: ¨ |yu (x, z) − yd (x, z)|d A

Minimi ze : f it1 (X ) =

(1)

A

where, yd (x, z) and yu (x, z) show the arch dam’s downstream and upstream surfaces; A displays the region that results from projecting the body of the arch dam on an xz plan.

2.2 Natural Frequency The arch dam’s natural frequencies ought to be maximized by the following equation: Maximi ze : f it2 (X ) = f rn n = 1, 2, . . . , n f r

(2)

where, n f r elucidates the natural frequencies’ number. X , design variables, can be defined as follows:

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X = {s, β, tc1 . . . tcn+1 , r u 1 . . . r u n+1 , r d 1 . . . r d n+1 }

(3)

X comprises 2 + 3(n + 1) shape characteristics of the arch dam, where n shows the dam height divisions’ number. Numerous constraints, including geometrical and stability constraints, are taken into consideration in this optimization problem. Equation (4) should be met to guarantee that the dam’s downstream and upstream faces do not cross over one another. Additionally, the slope of the overhang at the upstream and downstream sides of the dam should meet Eq. (5) in order to build amenities and have smooth cantilevers across the height of the dam, as follows: rdi ≤ rui →

rdi − 1 ≤ 0, i = 1, 2, . . . , 6 rui

s ≤ salw →

s sahw

−1≤0

(4) (5)

where, S = cot(α) is the slope of the overhang at the downstream and upstream sides of the dam, and rdi and rui elucidate the radius of curvature at the ith level in the z-direction. For the previously indicated parameter, salw is the allowed absolute value. The following equation must be accurate for the dam’s sliding stability: ϕl ≤ ϕ ≤ ϕu

(6)

where, ϕ shows the arch dam’s central angle at the ith level in the z-direction, which ranges from 90° to 130° across the dam’s height. There are also a few geometric criteria for double-curvature arch dams. One polynomial of second order is provided in the equation below, and it is used to calculate the curve of the upstream boundary illustrated in Fig. 1a:

g(z) =

γ2 −γz 2βh

(7)

where, h shows the dam’s height and z is the elevation at which the upstream face’s slope equals zero (βh). The thickness of the crown cantilever may be calculated using a polynomial function by segmenting the dam height into n equal parts. tc (z) =

n+1 ∑

L i (z)tci

(8)

i=1

where, tci demonstrates the thickness of the centre vertical section at the level it and z is a Lagrange interpolation formula. z could well be represented as:

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Fig. 1 Schematic of arch dam: a Crown Cantilever profile b parabolic shape of an elevation

n+1 ∏

L i (z) =

m=1,m/=i

z − zm zi − z

(9)

where, z i shows the ith level’s z coordinate. The horizontal portion of a parabolic arch dam is shaped by the following two parabolas, as illustrated in Fig. 1b, for the goal of a symmetrical canyon and arch thickening from crown to abutment. x2 + g(z) 2ru (z)

(10)

x2 + g(z) + tc (z) 2rd (z)

(11)

yu (x, z) = yd (x, z) =

where, the parabolas of the upstream and downstream faces are yu (x, z) and yd (x, z), respectively. According to the following equations of the nth order, ru and rd are the radius of curvature for the upstream and downstream curves in the z-direction and may be interpolated by L i (z). ru (z) =

n+1 ∑ i=1

L i (z)rui

(12)

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rd (z) =

n+1 ∑

L i (z)rdi

(13)

i=1

where, rui and rdi are, respectively, the relevant ru and rd values at the controlling levels.

3 Developed Method 3.1 Single Objective Chaos Game Optimization Single objective Chaos Game Optimization (CGO) was inspired by Euclidean fractals, which is a branch of Mathematics, [11]. The aim of using chaos game theory is to find the patterns of points by rolling a die many times to predict later points. Talatahari and Azizi [11] used the chaos game theory to introduce CGO. The CGO algorithm is explained briefly using the Sierpinki triangle as a simple example as follows: The beginning process of the CGO algorithm is started by considering three points as the vertices of the main triangle. Each of the vertices and the roll are contributed specific color. By rolling the die depending on what color comes up, the random points which are named seeds moved half the distance toward which color comes up. And by rolling the die for the second time, previous results are utilized for the positions of the next seed. In several iterations, depending on problems the Sierpinki triangle is organized as depicted in Fig. 2. The mathematical explanation of CGO is as follows: The primary positions of the eligible point are defined by a random value as follows: ) { i = 1.2. . . . .n ( j j j j xi (0) = xi.min + rand. xi.max − xi.min . (7) i = 1.2. . . . .d j

The primary eligible positions are noted by xi (0) and also the minimum and maximum permitted values by considering the search space boundary for the ith

Fig. 2 Different scales of Sierpinski triangles

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j

solution and the jth decision variable are noted xi.min xi.max . And rand is considered in a limitation between [0 1]. It is worth mentioning that each of the solution candidates, X i , in the search process uses three special points as the vertices of the Sierpinki triangle: the position of the best solution candidates (G B), the position of the mean values of some acceptable primary points M G i and solution candidateX i . For regenerating new triangles to find new points, the CGO algorithm utilized 3 seeds and a die. The seed was defined in the X i , G B and the M G vertices respectively as depicted in Fig. 3. Based on which seed was positioned on the vertices and which colors come up, the seeds moved toward the G B or the M G i or X i . These processes were formulated as follows: Seed i1 = X i + αi × (βi × G B − γi × M G i ) i = 1.2. . . . .n

(8)

Seed i2 = G B + αi × (βi × X i − γi × M G i ) i = 1.2. . . . .n

(9)

Seed i3 = M G i + αi × (βi × X i − γi × G B) i = 1.2. . . . .n

(10)

Fig. 3 Position update for seeds in the search space, [11]

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Fig. 4 Update the position of the fourth seed in the search space, [11]

where, αi ,βi , γi are a random integer of 0 or 1 to define the seeds’ movement limitations and rolling a die possibility. It is worth mentioning that,αi as exploitation and exploration controller could be adjusted by following relations: ⎧ ⎪ ⎪ ⎨

Rand 2 × Rand αi = ⎪ (δ × Rand) + 1 ⎪ ⎩ (∊ × Rand) + (ε)

(11)

where, Rand, δ.ε, were utilized as a random number in the range of [0 1]. In addition, the mutation phase in CGO is considered as shown in Fig. 4. The mutation phase was formulated as follows: ( ) Seed i4 = X i xik = xik + R . k = [1.2. . . . .d]

(12)

where, k is considered as a random integer in the range of [1 d] and also R was utilized as a uniform random number in the range of [0 1].

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3.2 Multi-Objective Chaos Game Optimization The Multi-Objective Chaos Game Optimization, abbreviated as MOCGO, uses the following concepts [24, 25]: The algorithm utilizes an archive that contains all non-dominated Pareto optimal responses. An archive controller is an essential component when a solution is archived or when the archive is full. Additionally, only a limited number of solutions are allowed to save in the archive. As part of the optimization process, we compare non-dominated solutions obtained up to each step with the existing archive. With the leader selection feature, the current best solutions from the archive are selected as the search’s leaders. An archive member is omitted from the grid mechanism and a new solution is added. Increasing the number of solutions in a hypercube increases the probability of removing a solution. A solution is randomly deleted from the most crowded segments in the archive, if it is full, in order to make space for a new solution. When it is necessary, a solution can be added outside the hypercubes in an exceptional circumstances. To accommodate the new solutions, all components are extended. This allows several alternative solutions to have their components changed. By increasing the number of segments, the algorithm can create more distinct solutions and better identify which solutions are most crowded. This allows the algorithm to more accurately determine which solutions should be removed in order to make room for new ones. Furthermore, extending the components allows the algorithm to adapt to situations where it is necessary to create alternative solutions with different components.

4 Numerical Results This study aims to assess the effectiveness of the MOCGO methodology by utilizing the Morrow Point arch dam as a benchmark problem. To achieve this goal, a numerical model of the dam-reservoir system is established. The accuracy and validity of the proposed model are then confirmed by comparing it with experimental and analytical findings from previous literature. Finally, the developed methodology is employed to optimize the problem. In order to apply the MOCGO algorithm to optimize the dam, objective functions are established. Based on the previous research work [2], this paper utilizes the inverse of frequencies multiplied together as the second objective function: f it2 (X ) =

n fr ∏ 1 n = 1, 2, . . . , n f r f rn n=1

(13)

Similar to [2], in this study, the first 10 natural frequencies of the dam-reservoir system are utilized. By using a limited number of natural frequencies, the optimization process becomes more tractable and computationally feasible, while still

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capturing the essential aspects of the system’s performance and safety. The selection of the specific frequencies to be included in the optimization process depends on various factors, such as the dam’s design, location, and potential hazards.

4.1 Arch Dam Modeling [2] The analysis of the arch dam in this study is conducted using a hybrid approach, which combines parallel working MATLAB and Ansys Parametric Design Language (MATLAB-APDL) codes as shown in Fig. 5. The lower and upper bounds of the design variables are determined using established design approaches, as described in reference [26]. This study utilizes a finite element model for accurately simulating the behavior of an arch dam-reservoir system. The model incorporates 8-node solid elements to model the dam body and an 8-node fluid element to represent the reservoir. The model considers only the interaction between the dam and reservoir and assumes a rigid foundation rock. The dam is modeled as a linear 3D structure, while the fluid medium is assumed to be homogeneous, isotropic, irrotational, and inviscid with linear compressibility. The fluid–structure interaction (FSI) effects are considered between the reservoir and dam body, as well as the reservoir walls. The number of nodes and elements may vary during the optimization process, depending on changes in the dam’s dimensions and mesh generation requirements for each analysis, [2].

Fig. 5 Arch dam finite element modeling

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4.2 Results and discussion In addition to the proposed MOCGO, three well-studied multi-objective optimization methods, namely the multi-objective particle swarm optimization (MoPSO) [27], the non-dominated sorting genetic algorithm (NSGA-II) [28] and multi-objective charged system search [2] were also selected to compare the performance of the new algorithm. To ensure fairness in the comparison of these methods, twenty runs were executed with different random initial populations, and the best-obtained solutions were recorded as the final design. To ensure computational equivalence, the same number of search iterations and population size were used for all algorithms. The Pareto fronts of all algorithms are displayed in Fig. 6. These diagrams show the Pareto fronts in which the concrete volume of the dam body ( fit 1 ) and a combination of reversed frequencies (fit 2) are the main objectives of the problem. From Fig. 6, it is clear that almost all points obtained by MOCGO are better than the previous ones found in ref. [2] using MoPSO, NSGA-II, and MoCSS. Extreme values of the Pareto solutions are provided in Table 1. In addition, Fig. 7 shows the corresponding volume-frequency diagrams obtained by each method. According to this figure, the new algorithm is capable of finding better results in many parts of the search space. The improvement can be attributed to the fact that the new algorithm is capable of exploring a larger area of the search space before settling on a solution. Furthermore, this algorithm is more efficient in terms of time and resources because there is no need to adjust any parameters. To make a fair comparison of the results and make informed decisions based on decision-maker criteria, the researchers considered five different scenarios, with coefficients ranging from 0.1 to 0.9, [2]. The results of the decision-making process are presented in Table 2. In MOCGO, the best volumes are produced for scenarios A, B, and C, whereas in MoCSS, the best volumes are produced for scenarios D and E, which is not so far off from the result of MOCGO. This suggests that both MOCGO and MoCSS are able to effectively optimize for a range of decision-maker criteria.

5 Conclusion An optimization algorithm based on the multi-objective chaos game has been used for determining the optimal shape of double-curvature arch dams in this chapter. It involves the development of a set of parallel-working APDL-MATLAB code modules for modeling, analyzing, and obtaining the fitness function of the arch dam, as well as interacting with MOCGO at each step of the optimization process. For the optimal shape of double-curve arch dams, this approach is expected to provide effective and robust solutions. The first objective function is the concrete volume, while the second objective function is a combination of reversed natural frequencies of the dam. The optimal design strategies of the dam are obtained by minimizing the two objective functions simultaneously. The MOCGO technique is used to tackle the problem.

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Fig. 6 Pareto front of all methods

Table 1 Comparison of the results obtained by selected algorithms Optimization methods

MoCSS, [2]

NSGA-II, [2]

MoPSO, [2]

MOCGO

Obtained extreme values

fit1

fit2

fit1

fit2

fit1

fit2

fit1

fit2

Vol (1e5)

1.099

3.340

1.099

3.288

1.099

3.280

1.110

2.928

Fr1

2.572

2.922

2.514

2.924

2.572

2.918

2.487

2.908

Fr2

3.104

3.305

3.101

3.304

3.104

3.302

3.080

3.275

Fr3

3.691

4.332

3.708

4.326

3.691

4.326

3.634

4.245

Fr4

4.433

5.196

4.421

5.167

4.433

5.196

4.384

5.056

Fr5

5.015

6.171

4.845

6.160

5.015

6.174

4.883

6.083

Fr6

5.689

6.664

5.572

6.675

5.689

6.638

5.506

6.556

Fr7

6.699

7.362

6.568

7.360

6.699

7.364

6.513

7.322

Fr8

7.008

7.716

6.943

7.712

7.008

7.713

6.936

7.677

Fr9

7.370

7.784

7.376

7.782

7.370

7.786

7.374

7.730

Fr10

7.460

7.885

7.404

7.878

7.460

7.886

7.340

7.869

The MOCGO approach can achieve a trade-off between the two objective functions. In order to demonstrate the effectiveness of the proposed methodology, it has been applied to the Morrow Point dam, and the results obtained by the MoCSS, MoPSO,

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b)

c)

d)

e)

f)

f)

Fig. 7 Pareto fronts of all methods; a fit1-Fr1, b fit1- Fr2, c fit1- Fr1, d fit1- Fr4, e fit1- Fr5, f fit1Fr6, g fit1- Fr7, h fit1- Fr8, i fit1- Fr9, j fit1- Fr10

and NSGA-II methodologies are compared with those obtained by the proposed methodology. Findings suggest that MOCGO outperforms its competitors.

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g)

h)

i)

j)

Fig. 7 (continued)

Importance of criteria

[0.3,0.7]

[0.1,0.9]

C1 < C2

C1 C2

C1 > C2

A

B

MoPSO, [2]

[0.7,0.3]

[0.5,0.5]

C1 > C2

C1 ≈ C2

B

C

[0.9,0.1]

C1 >> C2

A

NSGA-II, [2]

[0.7,0.3]

[0.5,0.5]

C1 > C2

C1 ≈ C2

B

C

[0.9,0.1]

C1 >> C2

Possible priority weights

A

MoCSS, [2]

Scenario

271,749.572

314,937.556

132,956.454

171,357.449

226,966.502

269,714.224

306,734.745

109,942.578

150,206.901

198,943.337

264,968.249

306,505.148

Vol

2.902

2.920

2.643

2.779

2.881

2.904

2.918

2.571

2.72

2.84

2.90

2.91

Fr1

3.275

3.296

3.132

3.180

3.237

3.273

3.292

3.10

3.15

3.21

3.26

3.29

Fr2

Selected solution by MTDM

Table 2 Different possible scenarios corresponding solutions

4.259

4.311

3.852

4.025

4.156

4.248

4.302

3.69

3.93

4.10

4.24

4.30

Fr3

5.040

5.156

4.548

4.729

4.858

5.005

5.122

4.43

4.62

4.80

5.00

5.12

Fr4

6.109

6.165

5.326

5.885

6.025

6.101

6.145

5.01

5.65

5.97

6.09

6.14

Fr5

6.503

6.616

5.716

5.908

6.324

6.481

6.603

5.69

5.80

6.12

6.52

6.61

Fr6

7.356

7.362

6.838

7.155

7.344

7.353

7.360

6.70

6.98

7.31

7.35

7.35

Fr6

7.636

7.701

7.246

7.339

7.418

7.620

7.690

7.00

7.31

7.34

7.61

7.69

Fr7

7.848

7.877

7.633

7.708

7.774

7.830

7.870

7.46

7.67

7.72

7.84

7.86

Fr10

(continued)

7.748

7.778

7.435

7.694

7.724

7.740

7.759

7.36

7.55

7.72

7.73

7.76

Fr8

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[0.5,0.5]

[0.3,0.7]

[0.1,0.9]

C1 ≈ C2

C1 < C2

C1 C2

C1 ≈ C2

C1 < C2

C1 > C2

A

MOCGO

E

Possible priority weights

Importance of criteria

Scenario

Table 2 (continued)

127,080.347

165,531.618

206,805.547

229,625.894

271,186.374

150,504.796

181,474.149

227,666.621

Vol

2.645

2.787

2.870

2.886

2.905

2.754

2.824

2.886

Fr1

3.124

3.189

3.240

3.256

3.282

3.143

3.187

3.240

Fr2

Selected solution by MTDM

3.855

4.065

4.167

4.205

4.278

3.908

4.033

4.160

Fr3

4.592

4.733

4.874

4.947

5.064

4.610

4.747

4.864

Fr4

5.422

5.972

6.085

6.086

6.116

5.678

5.929

6.031

Fr5

5.762

5.970

6.219

6.358

6.536

5.813

5.971

6.354

Fr6

6.787

7.129

7.353

7.377

7.364

6.977

7.191

7.342

Fr6

7.242

7.378

7.403

7.479

7.674

7.306

7.334

7.425

Fr7

7.543

7.689

7.743

7.753

7.750

7.533

7.675

7.722

Fr8

7.601

7.699

7.748

7.788

7.856

7.671

7.713

7.767

Fr10

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Machine Learning

The State of Art in Machine Learning Applications in Civil Engineering Yaren Aydin, Gebrail Bekda¸s, Ümit I¸sıkda˘g, and Sinan Melih Nigdeli

Abstract Machine learning (ML) is one of the methods used by the artificial intelligence approach. Machine learning is used to teach machines how to handle data more efficiently. The purpose of machine learning is to learn from the data. Thanks to machine learning, a certain result can be reached without the need for an expert on the subject. It has very common usage areas from the financial sector to e-mail analysis. Machine learning is also widely used in civil engineering. In this study, machine learning is explained in historical development, and general terms and the studies that have been done are summarized. Keywords Machine learning · Supervised learning · Unsupervised learning · Algorithms · Performance metrics

1 Introduction In recent years, machine learning has become the basis of information technologies and has become a part of life. Machine learning (ML) includes algorithms developed to find the model and its parameters that best represent the available data. Learning is the acquisition of knowledge, skills, and abilities from experience gained through trial and error [1]. Artificial intelligence (AI) eliminates the programmer and the Y. Aydin · G. Bekda¸s (B) · S. M. Nigdeli Department of Civil Engineering, Istanbul University - Cerrahpa¸sa, Avcılar, 34320 Istanbul, Turkey e-mail: [email protected] Y. Aydin e-mail: [email protected] S. M. Nigdeli e-mail: [email protected] Ü. I¸sıkda˘g Department of Informatics, Mimar Sinan Fine Arts University, Si¸ ¸ sli, 34427 Istanbul, Turkey e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Bekda¸s and S. M. Nigdeli (eds.), Hybrid Metaheuristics in Structural Engineering, Studies in Systems, Decision and Control 480, https://doi.org/10.1007/978-3-031-34728-3_9

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Fig. 1 Artificial intelligence, machine learning, and deep learning scope chart [2]

expert by imitating a certain part of the human brain. As a result of the progress of artificial intelligence applications, machine learning, and its applications have emerged. Although traditional programming can imitate human behavior to a certain extent, when it comes to artificial intelligence, the concepts of machine learning and deep learning (DL) often come to mind instead of traditional programming. The relationship between these concepts is as follows (Fig. 1). Artificial intelligence can be defined as the imitation of human cognitive features such as learning and problem-solving by machines [3]. Artificial intelligence applications generally include machine learning and deep learning sub-fields. Machine learning, known as predictive analytics or statistical learning, is an area of research at the intersection of AI and computer science [4]. Machine learning is an approach that predicts that algorithms that automatically extract information from existing data become better with experience and that with less programmer intervention, improvement with experience increases. More specifically, machine learning is concerned with automatically detecting meaningful patterns in data and using the detected patterns for specific tasks [5]. The overall goal of machine learning is to recognize patterns in data that inform how unseen problems are treated. For instance, in a complex self-driving car, a computer learning about hazards must transform large amounts of data from sensors to determine how it should control a car [6]. Machine learning is a multi-disciplinary field with a wide array of research areas strengthening its presence. ML can easily overcome the complexity of real-world problems. Machine learning can be applied to design and program open algorithms with high-performance output, such as email spam filtering, traffic prediction, face and shape detection, and medical diagnostics. As can be seen in Fig. 2, ML is used in various fields. Traditional programming is based on the computer execution of sequences of commands entered by the programmer. Machine learning is based on learning. In traditional programming, the inputs and the operations to be applied to these inputs are coded one by one by the programmers as commands. But in machine learning, the inputs and outputs are given by the programmers, and the operations to be done to achieve the desired outputs of these applications are found by the computer and

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Fig. 2 Application fields of machine learning [7]

Fig. 3 Generalized machine learning methodology [8]

recorded in a data structure called a model. The stages of developing a machine learning model are given in Fig. 3.

2 Historical Development of Machine Learning The terms artificial intelligence and machine learning have been studied and applied by various expert groups for over 60 years. The mathematical foundations of machine learning are based on algebra, statistics, and probability [9].

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The concept of neural networks was born in 1943 with the work of McCulloch, a logician, and Pitts, a neuroscientist, at the earliest [10]. They created the first mathematical model of a neural network. In 1949, Donald Hebb published The Behavior Organization, which introduced theories about the interaction between neurons so important to advancing machine learning [11]. In 1950 Alan Turning created the “Turning Test” to test the intelligence of machines. To pass the turning test, the machine must be able to convince a human that it is talking to a human and not a machine. In 1952, Samuel created a machine that can play and self-learning Chess was demonstrated to the public on television [12]. And ML first coined with Arthur Samuel [13] in 1959 pioneered various machine learning techniques [14]. In 1967, Cover and Hart proposed the Nearest Neighbour Algorithm, which can be considered the beginning of Pattern Recognition [15]. In 1979, Stanford students invented the Stanford Cart, a remote-controlled car that could move autonomously and sense and avoid objects [16]. Machine learning has advanced further after 1990 and has become the most successful method used by the artificial intelligence approach and present technology terms [17]. In 2006, Geoffery Hinton coined the term deep learning to describe a new neural network architecture that uses multiple layers of neurons for learning. In 2012, Google’s Jeff Dean developed GoogleBrain, a deep neural network that recognizes patterns in video and images. In 2017, Google proposed smartphones based on ML and DL algorithms, such as Google Lens and Google Nexus. Apple presented the Home Pod, an interactive machine-learning device [9]. Machine learning has become an important method in decision-making and the most successful subfield of AI. Thanks to ML, large data sets can be easily processed and a decision-making mechanism can be provided between these sets. ML technology is developing and new algorithms are written by researchers in many fields from medicine to industry, from technology to art [18].

3 Machine Learning Types Training is the process of automatic model building and training data is the data used for training purposes. Thanks to the trained model, skills are gained regarding the mapping of input variables to output and predictions can be made for new inputs. [19]. The model is trained and tested with the test data set and the predictions made are evaluated [8]. If sufficient accuracy and evaluation metrics are obtained, the model is considered complete. Otherwise, the model is retrained by evaluating the metrics and using options such as adding/removing variables, increasing the data set, or reducing the size. After this stage, the model is evaluated again and the steps are repeated until the demanded results are obtained. Machine learning is a highly multidisciplinary field that builds on ideas from statistics, computer science, engineering, and crowded scientific also mathematical disciplines [20]. Many applications such as fraud detection, text, and document classification, speech processing applications, credit card, computer vision, network attack

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Fig. 4 Types of machine learning (adapted from [24])

detection, and self-driving car applications are performed with machine learning. The problems are tackled using machine learning techniques [21]. Machine learning systematically applies algorithms to synthesize fundamental relationships between data and information [22]. According to the learning types, machine learning has four groups supervised learning, unsupervised learning, reinforcement learning, and semi-supervised as unsupervised learning, supervised learning, semi-supervised learning, and reinforcement learning [23]. Machine learning types are given in detail in Fig. 4.

3.1 Supervised Learning The supervised learning model works based on the input–output example. A model is developed with samples consisting of input and output parameters. While training the models, labeled data is used. The aim of this learning is that the machine can learn the path to a known result by experiencing a particular result [25]. After establishing the relationship between the input and output parameters, the model is tested and its success in estimating the data it did not know before is checked. The supervised learning workflow is shown in Fig. 5. Supervised learning has applications such as predictive analysis based on regression and classification, natural language processing, automatic image classification, and sentiment analysis [27].

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Fig. 5 Supervised learning workflow [26]

3.1.1

Performance Evaluation of Supervised Learning

Cross Validation Cross-validation (CV) is a data resampling method used to assess the true prediction error of the model and to adjust its parameters [28]. Cross-validation is used to deal with generalization and overfitting errors. The current dataset is split into training and testing, which will be used in the learning process and performance evaluation, respectively [29]. CV has purposes such as estimating the performance of the learned model using a single algorithm from the available data and comparing the performance of two or more different algorithms [30]. The various CV charts differ in the way they split the sample data. The most widely used method is k-fold cross-validation [31]. K-Fold Cross Validation K-fold cross-validation decomposes the folds into layers so that the class distribution of records in each layer is approximately the same as the initial data. It is usually recommended that k should be 10 for relatively low bias and variance. [32]. In the first iteration in Fig. 6, 1 box in the blue part is tested and 9 boxes are trained. Thus, the first iteration ends and the success rate is achieved. The same process is applied to the other iterations so that all of the data enters both training and testing. Stratified K-Fold Cross Validation In this cross-validation method, folds are created with a criterion. In general, the criterion is to create folds in the form of an equal proportion of the result variable. For example, in Fig. 7, 3 diabetics and 7 non-diabetics in every 10 rows were selected as the criteria for diabetes. Thus, validation is created by creating a constancy in the resulting output. The proportions of the class to be classified are equally distributed on each floor.

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Fig. 6 10-Fold cross-validation [33]

Fig. 7 Stratified 5-fold cross-validation [34]

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(a)

(b)

Fig. 8 a Classification, b regression [38]

Leave One Out Cross Validation Leave-Out-One-Out (LOO) CV is straightforward as the training dataset is created by including all individuals except one, while the test set contains the individual not included. Therefore, there are different training and test sets for each individual in the whole dataset. This method wastes minimum data as only one individual is removed from the training set [35].

Train Test Split The most accurate machine learning algorithm is tried to be selected by making basic modeling experiments on the training dataset. It consists of the observations that are sampled the most over this data set [36]. The data set is divided into training and test sets (usually with ratios of 0.7/0.3) and the success of the model is measured. Using the training data, the best values of the control parameters of the various machine learning models used are determined. While the data set is distributed as training and test data set in certain ratios, irregularities that may occur negatively affect the performance of the model. To solve this problem, Stone [37] developed the k-fold cross-validation method in 1974. When more data is needed, the data is divided into two training data and test data. To test how well it learns, the machine is presented with test data, which is 30% of the data it has never seen before. Using accuracy measurement metrics, the machine’s predicted value is compared with the actual value, and the result is how many percent correct guesses are obtained. The two most common types of supervised learning are classification and regression (Fig. 8). In classification, entries are categorized into a particular class. In regression, the label is continuous and the relationships between the variables are looked at [25]. The main difference between classification and regression is that their outputs are categorical and numerical respectively.

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In traditional supervised learning, learning is performed from a large number of training examples. Each training example has a label indicating the desired output for the event described in the example. In the classification problem, the label indicates the category in which the relevant sample is included, while in the regression; refers to a real-valued output such as temperature, altitude, or price [39].

3.2 Unsupervised Learning Unsupervised learning is referred to as descriptive or undirected classification. Unsupervised learning is learning where data without labeled output is available. [40]. Some of the features that algorithms learn come from the data [41]. Unsupervised learning discovers hidden patterns in the data [42]. Since no system controls the learning according to the entered data, the machine determines the output itself [25]. Let X = (x 1 , …, x n ), be a set of n samples (or points), with x i ∈ X for all i ∈ [n] T := {1,2, …, n}. It is often convenient to define (n × d) − matrix X = (x iT )i∈[n] containing data points as rows. In this case, the purpose of unsupervised learning is to find interesting structures in the X data [43]. The most common types of unsupervised learning are clustering and dimensionality reduction are shown in Fig. 9.

3.2.1

Clustering

Clustering is the grouping of observations according to similar characteristics. Instead of classifying or predicting the value of a target variable, clustering algorithms attempt to divide the entire dataset into relatively homogeneous subgroups.

(a) Fig. 9 a Clustering, b dimensionality reduction [38]

(b)

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Thus, similarity to observations within the cluster is increased while similarity to observations outside the cluster is minimized [44]. Clustering is more difficult than supervised classification as there are no labels attached to the patterns in clustering. In supervised classification, labels allow data objects to be grouped as a whole. Since there are no labels in clustering, it is difficult to determine to which group a model belongs [45].

3.2.2

Dimensionality Reduction

Dimension reduction is the task of reducing the number of inputs. Dimension reduction is the task of reducing the number of inputs. Dimension reduction techniques facilitate the utilization of data for successful learning. This pre-processing is done to make the data more ready for use before applying it to another algorithm [46].

3.3 Semi-Supervised Learning A semi-supervised learning model is a combination of supervised and unsupervised models. These areas of machine learning can also be fruitful with data mining, where unmarked data that is already retrieved data tagged is a process. The standard methods of supervised machine learning algorithms are for the labeled datasets, and each record contains result information [47]. Only a subset of the training data is labeled [48]. This learning improves learning performance by using a limited amount of labeled data and a large amount of unlabeled data [49].

3.4 Reinforcement Learning The training data is only given as feedback in the form of reward and punishment to an AI agent with interaction. This feedback improves performance on the learned task [50]. It is based on trial and error and has no output [51]. In this learning, the goal of the model is to win the most rewards [25]. The learning system of the robot is the reward-punishment system it receives according to the situation it encounters. The schematic form of reinforcement learning is in Fig. 10. There are different algorithms already developed for reinforcement learning problems. The most well-known use of reinforcement learning is models developed for playing games and controlling robots [3].

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Fig. 10 Reinforcement learning [42]

4 Machine Learning Algorithms 4.1 Random Forest (RF) Random Forest was proposed by Leo Breiman in 1997 [52]. Random forest is based on a supervised learning technique. This algorithm is an ensemble learning method. It can be used both in classification and regression. The parameters of the random forest are not complex. It is based on the logic of using a combination of many tree estimators instead of using a single classifier tree to eliminate problem complexity and improve model performance [53]. With more trees, it shows better performance [54]. As a result of the combination of many tree estimators, some trees may make correct predictions while others may produce incorrect predictions. Although this may seem like a disadvantage, all trees can predict the correct output when combined. RF has decision trees that examine subsets of the given dataset. It averages the input dataset to improve the prediction accuracy [55]. It is an extension of the bagging predictor algorithm [56]. The schematic representation of the RF algorithm is given in Fig. 11.

4.2 Decision Tree (DT) The best performance of the decision tree in speed and frequency has made it the most widely used machine learning technique by researchers in classification. Decision trees usually operate in two stages, the tree creation, and classification stages. It was during classification the rules for classification are applied from the tree. The process of deciding root to leaf followed the branches [42]. The diagram in Fig. 12 below shows decisions and results in a tree format of a decision tree.

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Fig. 11 Random forest example [42]

Fig. 12 Structure of a decision tree [57]

4.3 Naive Bayes (NB) This classification algorithm supports Bayes’ theorem and assumes that features within classes are irrelevant [58]. It is based on the fact that if the class is known, the properties can be predicted correctly and if the class is not known, the properties given by the Bayes rule can be predicted for the given class [42]. While it has advantages such as computing the training fast and showing success, it also has the disadvantage that the success of the results of analysis depends on the records [42].

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Fig. 13 Support vector machine [61]

4.4 Support Vector Machine (SVM) Support vector machine can be used for classification and regression problems [58]. SVM is used in many fields, including bioinformatics and the analysis of chemical data [59]. The SVM has good sensitivity even with a small number of samples and performs well [60]. SVM classifies data points by finding a hyperplane in ndimensional space. [54]. The margin is the largest distance between data points and the goal is to find the plane with the maximized margin. A margin among the classes was drawn (Fig. 13). Edges are also considered to maximize the distance between the edge and the class, minimizing classification errors [25].

4.5 K-Nearest Neighbors (KNN) The KNN algorithm was first mentioned by Fix and Hodges in 1951 and Cover and Hart advanced the algorithm in 1967 [62]. KNN algorithm can be easily used in classification and regression problems. The disadvantage is that the success decreases when the data size increases [42]. The algorithm predicts the class of its unlabeled neighbors using its labeled neighbors. The k parameter and the distance affect the performance of the model. [25]. The KNN algorithm works by classifying each new sample from its K-nearest neighbor according to the majority tag. This method works well at a reasonable distance and with a small number of data points in the training set [31]. A simple KNN example on a two-dimensional plane is shown in Fig. 14. In the example, the nearest neighbors for K = 3 and K = 8 of a new data point in a two-class dataset are specified. When the majority voting method is applied, it is seen that the new sample is included in Class 2 for both cases [42].

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Fig. 14 K-nearest neighbor algorithm example demonstration [42]

4.6 Logistic Regression (LR) Logistic regression is used to get the probability ratio in the occurrence of various illustrative variables. It allows various illustrative variables to be analyzed concurrently, meantime decreasing the effect of confusion factors [63].

5 Evaluation of Classifier Performances Confusion matrix, performance metrics, and AUC-ROC curve approaches are used to evaluate classification methods [64]. The confusion matrix allows the performance of the classification to be evaluated. Performance metrics are determined according to the correct and incorrect numbers of class predictions.

5.1 Confusion Matrix The confusion matrix is used to determine which of the methods used to measure the quality of algorithms used in machine learning classification studies gives better results. By using confusion matrices, the relationships between the reference data, that is, the ground truth data, which are accepted as correct, and the automatic classification results corresponding to these data can be categorically compared with each other [65]. The confusion matrix is one of the common methods used to measure machine learning model performance. The success of the model and the errors caused by the classifier are shown in the form of a table in matrix format. This matrix is a 2-dimensional table. One of the dimensions shows the actual values, while the other

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Fig. 15 Confusion matrix

shows the predicted values. Although it is mostly used in binary classification problems, a Confusion Matrix can also be created in multi-class classification problems. It is a good measure by which models can explain the overlap in class properties and which classes are most easily confused. The Confusion Matrix for binary classification is shown in Fig. 15. The confusion matrix has actual values in the rows and predicted values in the columns. TP (True Positive) indicates the case of correctly predicting positive observations with a positive true class value. FP (False Positive) indicates the case when observations with negative true class value are correctly predicted as positive. TN (True Negative) indicates the case when observations with a negative true class value are correctly predicted as negative. FN (False Negative) shows that observations with positive true class values are incorrectly evaluated as negative as a result of the prediction [66]. The sum of these four values gives the total number of samples to be classified.

5.2 Performance Metrics 5.2.1

Accuracy

The most common and simple way to measure model performance is model accuracy [67]. The confusion matrix is used when calculating accuracy. Accuracy =

TP +TN T P + T N + FP + FN

(1)

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As can be seen from Eq. 1, it is a measure of how often the classifier makes a correct prediction. In analyses using classification algorithms, it is not sufficient to examine only the accuracy rate as a success criterion. It may not give correct information, especially in unbalanced datasets.

5.2.2

Recall (True Positive Rate) (TPR)

The recall metric is an indicator of falsely predicted true positives. In a multiclass and unbalanced classification problem, it is the ratio of true positives to the sum of true positives and false negatives [68]. The calculation of the recall value is shown in Eq. 2. Recall =

5.2.3

TP T P + FN

(2)

Specificity (False Positive Rate) (FPR)

The specificity corresponds to the proportion of negative data points that are considered false positives relative to all negative data points [69]. The specificity is obtained by dividing the false positive by the sum of the false positive and true negative. Speci f icit y =

5.2.4

FP FP + T N

(3)

Precision

The Precision performance metric, also known as a positive predictive value, is a measure of how accurately predicted from all classes. It is desired and expected to be as high as possible. This metric determines how many of the positive estimates are truly positive. Precision value is especially important when False Positive (FP) prediction is costly. Precision is the ratio of true positives to the sum of true positives and false positives [68]. The calculation of the precision value is shown in Eq. 3. Precision indicates how many of all predicted positive examples were predicted correctly. Pr ecision =

TP T P + FP

(4)

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F1 Score

More accurate results are obtained when recall and precision metrics are evaluated together. For this purpose, the F1 score is defined. The F1 score is calculated by taking the harmonic mean of recall and precision [67]. F1 Scor e = 2 ∗

5.2.6

Pr ecision ∗ Recall Pr ecision + Recall

(5)

Receiver Operating Curve (ROC)

The ROC curve is a graph of positive false rate and recall of tests. The ROC curve is often a form of performance evaluation for different kinds of classification problems. The AUC values found in the ROC curve determine the overall accuracy values. It shows how accurately the models used in the ROC curve can classify. When it is desired to evaluate the methods used in the ROC curve, how close or 1 the AUC values of the methods used in the model are, these values help to determine the most suitable model [67]. A graph is created with TPR on the y-axis and FPR on the x-axis. The curve passing through the graph in Fig. 16 and the area under the curve are important. The area under this curve is called Area Under Curve or Are Under the ROC Curve. Success can be calculated from the size of this area. Based on this, the matrix works. The value of the ROC curve with a perfectly straight line is 1.0. If the field is cut in the middle with a 45-degree line (50% success), it is a very unsuccessful prediction. Fig.16 ROC and AUC [66]

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As advantages of the ROC curve, the ROC curve shows all possible cut-off points, and the tests can be visualized in a graph according to the ROC curve. For these reasons the evaluation is facilitated, in some cases sensitivity may come to the fore or selectivity may be preferred to sensitivity. Even when these two situations are encountered, ROC curves find suitable cut-off points [71].

6 Evaluation of Regressor Performances As for the problem classification (two-class, multi-class) problem, it is mentioned above that it is used in the measurement of success (precision, recall, F1, error matrix, etc.). is working.

6.1 R2 (Coefficient of Determination) R2 is a measure of fitness for linear regression models. The R2 (coefficient of determination) shows how close the data are to the fitted regression line [69]. R2 refers to how successfully the model explains the total change and is the power of the analysis. A high R2 indicates a good regression model fit. ∑n E x plained V ariation (yi − xi )2 R = 1 − ∑i=1 =1− n 2 T otal V ariation i=1 (yi − x i ) 2

(6)

xi and yi are the predicted and actual values for the ith observation, respectively. x i is the average of predicted values, and there is n number of observations [72].

6.2 Mean Absolute Error (MAE) The absolute error is the difference between the actual and predicted value. The MAE is the average of the absolute values of each difference between the actual value and the predicted value for the sample. A lower MAE value means more success [69]. ∑n M AE =

i=1 |yi

n

− xi |

(7)

xi and yi are the predicted value and the actual value for the ith observation, respectively.

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6.3 Mean Squared Error (MSE) Mean Square Error (MSE) is commonly used and is the mean square loss per sample over the entire dataset. To calculate the MSE, all the squared losses for individual samples are added up and then divided by the number of samples. A lower value indicates better accuracy [69]. MSE =

n ∑ (yi − xi )2 n i=1

(8)

6.4 Root Mean Squared Error (RMSE) Root Mean Squared Error is the average squared root error between actual observation and output [51]. The lower the measures, the more accurate the prediction results [70]. ⌜ | n |∑ (yi − xi )2 RMSE = √ n i=1

(9)

6.5 Mean Absolute Percentage Error (MAPE) Mean absolute percentage error (MAPE) is a measure of the prediction accuracy of the method used for prediction [74]. 1 M AP E = n

∑n

i=1 |yi

yi

− xi |

× 100

(10)

7 Overfitting and Underfitting Fitting the model to the data as undersaturated or oversaturated is important because neither an under-fitting nor over-fitting model is desired for a successful machine learning model. In the visuals in Fig. 17, for example, those who have diabetes are shown with a cross and those who do not are shown with a circle. In such a case, as Fig. 17a, when

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(a) Under-fitting,

(b) Appropriate-fitting

(c) Over-fitting

Fig. 17 Schematic illustration of three models for classification [75]

the curve and these are separated and the equation of this curve is a sufficient model to make this distinction, it cannot make a very accurate classification when the shape of the curve is correct. The reason for this may be an under-trained, insufficiently trained model, the wrong algorithm chosen, etc. There is a model in this data that is not well-fitted. The equation of this line cannot be predicted very well. This problem also arises when the training data set is too small or when the population data cannot be represented. A bad model cannot make good predictions because it does not fit the training data well. This means that predictions using unseen data are weak, as people unfamiliar with the training dataset are perceived as strangers [35]. The Fig. 17b model is well-trained, although it throws a few errors. If the equation of this curve is known, a correct distinction can be made. Overfitting (Fig. 17c) occurs when the machine learning model learns the training dataset but does not perform on a new dataset. It occurs when it learns the training dataset very well but performs poorly on datasets it has not seen. Due to the overfitting problem, success with new data is not achieved and the generalizability of the model is hampered [35].

8 Machine Learning in Civil Engineering There are many studies of machine learning in civil engineering. The outcomes of these studies are beneficial for researchers in civil engineering for the timely and effective evaluation of engineering problems. It is frequently used in various sub-branches of civil engineering. In this section, recent work in the literature on machine learning in civil engineering is examined. Although machine learning has only recently been introduced in civil engineering, the results obtained are quite good.

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8.1 Structural Engineering In structural engineering, computer software using methods such as the finite element method is generally required for the calculation of design parameters. However, analyses performed with this computer software require large amounts of memory and time. By utilizing the advantages of machine learning, the results are reached in a fast and reliable way. There are studies in structural engineering such as confinement coefficients, compressive strength, carbonation, chloride diffusion, failure mode, lateral drifts, long-term deflections, behavior under seismic effects, flexural strength, axial capacity, structural damage, shear stress and plastic viscosity, optimum design, moment capacity and ductility of different materials [76–92]. The use of machine learning in structural engineering is listed in Table 1.

8.2 Geotechnical Engineering Since the experiments in geotechnical engineering are mostly carried out in the field and the laboratory, it is necessary to use approaches to determine the parameters in a short time and close to reality. In addition, since geotechnical parameters depend on many variables (environment, dynamic conditions, etc.), their calculation is more difficult with traditional methods. The use of ML in geotechnical engineering has become widespread day by day. There are studies on soil classification, correlation of parameters, pile-bearing capacity, optimum design of retaining walls, leak-off pressure, permeability coefficient, optimum drift capacity of retaining walls, compaction quality, and soil liquefaction [93–103]. Table 2 lists some of the studies carried out with machine learning.

8.3 Hydraulic Engineering As a result of global warming and climate change, it is difficult to predict hydrological data such as precipitation, floods, and rainfall in terms of time, cost, and labor. For this reason, machine learning is necessary and has recently made significant progress in hydraulic engineering. These issues such as dam flow, structural dam behavior, water demand, reservoir water balance, water quality, and groundwater pollution have been studied by machine learning [104–111]. Thanks to machine learning, structures that require high costs (such as dams) can be designed more economically and safely. The studies on the mentioned topics are listed in Table 3.

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Table 1 Machine learning studies in structural engineering Study summary

Authors

Year

M5 model trees and MT were compared to predict the confinement coefficient in rectangular columns [76]

Naeej, M., Bali, M., Naeej, M. R., & Amiri, J. V

2013

Predicting the compressive strength of high-performance concrete [77]

Chou, J. S., Tsai, C. F., Pham, A. D., & Lu, Y. H

2014

Developing a machine learning-based carbonation prediction model [78]

Taffese, W. Z., Sistonen, E., & Puttonen, J

2015

Using a hybrid machine learning model for predicting the ultimate punching shear capacity of fiber reinforced polymer reinforced slabs [79]

Vu & Hoang

2016

Building machine learning models for chloride diffusion Hoang, N. D., Chen, C. T., & 2017 prediction in cement mortar [80] Liao, K. W Using machine learning techniques to identify the classification of failure mode and the prediction of beam-column joints [81]

Mangalathu & Jeon

2018

Applying machine learning algorithms to classify the walls and predict their lateral drifts [82]

Siam, A., Ezzeldin, M., & El-Dakhakhni, W

2019

Proposing ML model to predict long-term deflections in Pham, A. D., Ngo, N. T., & reinforced concrete structures [83] Nguyen, T. K

2020

Predicting the behavior of ductile reinforced concrete frame buildings under seismic effects [84]

Hwang, S. H., Mangalathu, S., Shin, J., & Jeon, J. S

2021

Developing a machine learning algorithm to predict the compressive and flexural strengths of steel fiber-reinforced concrete [85]

Kang, M. C., Yoo, D. Y., & Gupta, R

2021

Predicting the axial capacity of fiber-reinforced polymer Cakiroglu, C., Islam, K., reinforced concrete columns [86] Bekda¸s, G., Kim, S., & Geem, Z. W

2022

Combining optimization and machine learning tools to minimize potential structural damage through optimal modeling of tuned mass dampers (TMDs) [87]

Yucel, M., Nigdeli, S. M., & 2022 Bekda¸s, G

Predicting shear stress and plastic viscosity of self-compacting concrete utilizing ensemble machine learning techniques [88]

Cakiroglu, C., Bekda¸s, G., Kim, S., & Geem, Z. W

Designing optimum (minimizing total cost of wall thickness) cylindrical walls utilizing ensemble learning methods [89]

Bekda¸s, G., Cakiroglu, C., 2022 Islam, K., Kim, S., & Geem, Z. W

2022

Developing machine learning models for predicting the Cakiroglu, C., & Bekda¸s, G shear strength of recycled aggregate concrete beams [90]

2023

Using optimization and machine learning to predict the Aydın, Y., Bekda¸s, G., design variables of an eco-friendly concrete column [91] Nigdeli, S. M., Isıkda˘g, Ü., Kim, S., & Geem, Z. W

2023

(continued)

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Table 1 (continued) Study summary

Authors

Year

Integrating machine learning method to evaluate the moment capacity and ductility of the compression yielding beam with T section [92]

Guo, B., Lin, X., Wu, Y., & Zhang, L

2023

Table 2 Machine learning studies in geotechnical engineering Study summary

Authors

Developing a Unified Soil Classification System prediction model via Random Forest algorithm [93]

Gambill, D. R., Wall, W. A., 2016 Fulton, A. J., & Howard, H. R

Puri, N., Prasad, H. D., & Correlating parameters such as density, index of compression, etc. with soil parameters determined in the Jain, A laboratory and the field via machine learning models [94]

Year

2018

Predicting the pile-bearing capacity via gaussian process regression [95]

Momeni, E., Dowlatshahi, M. 2020 B., Omidinasab, F., Maizir, H., & Armaghani, D. J

Interpreting Cone Penetration Tests data with different machine learning models [96]

Rauter, S., & Tschuchnigg, F 2021

Predicting leak-off pressure with machine learning algorithms [97]

Choi, J. C., Liu, Z., Lacasse, S., & Skurtveit, E

2021

Developing predictive models for optimal dimensions of reinforced concrete retaining walls [98]

Bekda¸s, G., Cakiroglu, C., Kim, S., & Geem, Z. W

2022

Predicting and investigating the permeability coefficient of soil with a machine learning algorithm [99]

Tran, V. Q

2022

Predicting drift capacity of RC walls via machine learning algorithm [100]

Aladsani, M. A., Burton, H., Abdullah, S. A., & Wallace, J. W

2022

Compaction quality evaluation of subgrade using machine learning model [101]

Wang, X., Dong, X., Zhang, Z., Zhang, J., Ma, G., & Yang, X

2022

Soil classification via machine learning algorithms [102]

Aydın, Y., I¸sıkda˘g, Ü., 2023 Bekda¸s, G., Nigdeli, S. M., & Geem, Z. W

Predicting soil liquefaction potential using different machine learning models [103]

Vasegh, M., Dehghanbanadaki, A., & Motamedi, S

2023

8.4 Construction Management While the construction of a building in the construction sector is still at the idea stage, the correct establishment of the time and cost model will prevent many problems in advance. This is possible with machine learning. Construction management issues such as delay risk, construction cost, project characteristics, injury severity, risk analysis, construction requirements, and leading indicators were examined with machine

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Table 3 Machine learning studies in hydraulic engineering Study summary

Authors

Predicting the amount of dam inflow by combining machine learning models [104]

Hong, J., Lee, S., Bae, J. H., 2020 Lee, J., Park, W. J., Lee, D., … & Lim, K. J

Predicting and Interpreting structural dam behavior with machine learning models [105]

Mata, J., Salazar, F., Barateiro, J., & Antunes, A

2021

Predicting water demand utilizing machine learning models [106]

Shuang, Q., & Zhao, R

2021

Simulating reservoir water balance using a machine learning algorithm [107]

Latif, S. D., Ahmed, A. N., Sherif, M., Sefelnasr, A., & El-Shafie, A

2021

Predicting the water quality classification via machine learning models [108]

Malek, N. H. A., Wan Yaacob, W. F., Md Nasir, S. A., & Shaadan, N

2022

Detection of flood with machine learning [109]

Tanim, A. H., McRae, C. B., Tavakol-Davani, H., & Goharian, E

2022

Integrating Bayesian and machine learning approaches An, Y., Zhang, Y., & Yan, X to recognition groundwater contamination source parameters [110]

2022

Predicting rainfall utilizing machine learning models [111]

2023

Baljon, M., & Sharma, S. K

Year

learning models [112–119]. Table 4 lists the studies carried out with machine learning in the construction business.

8.5 Transportation Engineering Forecasts such as road traffic accidents, traffic flow, and road pavement assessment involve complex operations. Machine learning is useful to create an efficient forecast even in complex operations. Road pavement, energy consumption, classifying vehicles, road traffic accidents, vehicular traffic flow, pavement condition, and temperature changes in asphalt mixtures, which are the fields of transportation engineering, were examined by applying machine learning. [120–127]. Table 5 lists the topics related to the use of machine learning in transport engineering.

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Table 4 Machine learning studies in construction management Study summary

Authors

Year

Predicting project delay risk using machine learning algorithms [112]

Gondia, A., Siam, A., El-Dakhakhni, W., & Nassar, A. H

2020

Predicting the construction price index by applying machine learning algorithms [113]

Nguyen, P. T

2021

Predicting delay in construction utilizing decision tree and Erzaij, K. R., Burhan, A. naïve Bayesian classification algorithm [114] M., Hatem, W. A., & Ali, R. H

2021

Classifying project features using machine learning [115]

Fan, C. L

2022

Predicting injury severity using machine learning [116]

Gondia, A., Ezzeldin, M., & El-Dakhakhni, W

2022

Analyzing risk with hybrid machine learning [117]

Fitzsimmons, J. P., Lu, R., 2022 Hong, Y., & Brilakis, I

Predicting requirements in construction projects with machine learning [118]

Golabchi, H., & Hammad, 2023 A

Producing predictions for leading indicators in different working areas and all project life cycles with machine learning [119]

Gondia, A., Moussa, A., Ezzeldin, M., & El-Dakhakhni, W

2023

Table 5 Machine learning studies in transportation engineering Study summary

Authors

Year

Predicting the properties of asphalt concrete with waste coal admixture [120]

Katanalp, B. Y., Yildirim, Z. B., Karacasu, M., & Ibrikci, T. (2019)

2019

Predicting highway energy consumption [121] Cansız, Ö. F., Ünsalan, K., & Erginer, ˙I. (2020)

2020

Classifying vehicles with machine learning [122]

Li, C., & Xu, P

2021

Assessing prediction model designs for road traffic accidents [123]

Bokaba, T., Doorsamy, W., & Paul, B. S

2022

Predicting vehicular traffic flow [124]

Olayode, I. O., Severino, A., Campisi, T., & Tartibu, L. K

2022

Evaluating pavement condition [125]

Sholevar, N., Golroo, A., & Esfahani, 2022 S. R

Modeling road traffic accidents [126]

Megnidio-Tchoukouegno, M., & Adedeji, J. A

2023

Evaluating temperature changes in asphalt mixtures [127]

Wang, X., Pan, P., & Li, J

2023

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9 Summary and Conclusions Machine learning is a trendy tool for solving all kinds of problems and it is not a method that is only useful in a specific area. In this chapter, the state of the art in machine learning applications of civil engineering is summarized. After the introduction to machine learning, a short historical summary of ML is given. In the third section of this chapter, the types of ML such as supervised learning, unsupervised learning, semi-supervised learning, and reinforcement learning are summarized. In the fourth section, several potentially used ML algorithms are mentioned. Then, the evaluation methods for ML are shortly given. After the ML methods are briefly mentioned, the state of art in the application of civil engineering is used for different branches of civil engineering. 17 papers that were done between 2013 and 2023 are listed for structural engineering. It is possible to see 11 studies in geotechnical engineering and 8 recent papers about hydraulics engineering are reviewed. 8 recent construction management papers are given in the chapter. Finally, 8 papers about transportation engineering are listed. According to the research, the number of studies in subbranches of civil engineering has a great increase in numbers to estimate optimum results or complex solutions easily.

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Machine Learning Application of Structural Engineering Problems Ayla Ocak, Sinan Melih Nigdeli, Gebrail Bekda¸s, and Ümit I¸sıkda˘g

Abstract The cross-sectional properties of the basic structural system elements, such as columns and beams, are the basic structural design elements that need to be determined sensitively. For the optimum design of such structural system elements, it is necessary to minimize the displacement and volume by optimization. In this study, the design of a tubular column and I-section beam element has been optimized, and a section prediction model has been produced by the machine learning method, which has been successfully applied in the risk and damage detection of various engineering problems. For this purpose, optimum cross-section properties were determined for different load conditions with the Jaya Algorithm (JA), which is a metaheuristic algorithm. To minimize production errors arising from workmanship in the production of structural system elements, cross-section parameters are divided into classes covering certain dimensions. Different design combinations obtained by optimization were converted into a data set and training for machine learning was applied. With the trained data, a cross-section prediction model was produced that predicts the cross-sectional properties of column and beam samples on a class basis. When the results are examined, it is understood that the prediction models to be produced with the optimum design data are suitable for use in determining the cross-sectional properties of the structural system elements. Keywords Artificial ˙Intelligence · Machine learning · Optimization · Jaya Algorithm

A. Ocak · S. M. Nigdeli · G. Bekda¸s (B) Department of Civil Engineering, Istanbul University - Cerrahpa¸sa, 34320 Avcılar, Istanbul, Turkey e-mail: [email protected] S. M. Nigdeli e-mail: [email protected] Ü. I¸sıkda˘g Department of Informatics, Mimar Sinan Fine Arts University, ˙Istanbul 34427, Turkey e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Bekda¸s and S. M. Nigdeli (eds.), Hybrid Metaheuristics in Structural Engineering, Studies in Systems, Decision and Control 480, https://doi.org/10.1007/978-3-031-34728-3_10

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1 Introduction Artificial intelligence refers to various software made to bring several features unique to the human brain to a machine. In today’s world, it is used in many areas such as health, economy, finance, media, and telecommunication. The main idea of artificial intelligence technologies emerged from the idea of intelligentizing machines. In this context, phones, tablets, computers, and similar devices that people use as communication tools have become a source of commercial income as “smart devices” by providing various human-specific features such as listening, perceiving what one hears, making suggestions, and finding directions. In recent years, artificial intelligence technologies have been successfully applied in the prediction of production materials, and risk and damage detection as a solution to engineering problems. When artificial intelligence studies in the field of engineering are examined, it is seen that it is frequently used in the detection of material strength, performance, tracking, and faults such as bearing failure detection in industrial plants, detection of superficial defects of cold rolled steel strips, monitoring of thermal events in reactors, quality control of automatic production lines, modeling of CNC machine tools [1–5]. In the field of structural engineering, it is frequently preferred for determining the capacities of structural elements and materials such as structural damage assessment, beam member bending estimation, steel plate buckling load estimation, final bearing capacity estimation of concrete-filled steel pipes, concrete compressive strength estimation [6–10]. Artificial intelligence is a technology that has a wide range of research and includes different application techniques. Among them, machine learning stands out in terms of the way it processes and uses data. Machine learning is defined as the process of gaining human-specific behaviors to a machine, just as it is at the base of artificial intelligence. The difference that makes it a different technique here is that the machine is trained with some data to gain the ability to make inferences. By entering some data into the machine, it is expected that each data will be perceived by the machine and it will be successful in estimating the new data. For this purpose, using various validation techniques, the data is divided into two training and test data, and the prediction performance of the trained data and the tested data is turned into a table. The resulting table shows how many of the correct and incorrect outputs the machine predicts as correct or incorrect, and how many incorrect or correct predictions of the incorrect result. in this way, the predictive success of the split data for training and testing becomes comparable. Machine learning is a method of generating a good predictive model that can be applied to all parts of civil engineering, including construction, transportation, mechanics, geotechnical, materials, hydraulics, and construction management. Performance in solving various problems such as the estimation of the bearing capacity of foundations and soil geotechnical parameters, the extent of water spillage effects, flood estimation, measurements and measurements of damage, estimation of seismic isolation systems under earthquake load, estimation of cracks in asphalt pavements and construction costs was supported by the operation performed [11–18]. The

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possibilities of machine learning in terms of application areas give the impression that it is suitable for the design of separation units. The design of the structural system elements that make up the column, beam, floor, and a similar structure is important in terms of building safety and cost. In machine test applications for such elements, shear, stress, and axial load capacity estimations are generally studied [19– 22]. Machine learning applications in the dimensioning of structural carrier units are a lighting method that should have an open structure specified in the literature. Optimization is a method that structural engineers often resort to getting the highest efficiency from the structural design. The aim here is to determine the most appropriate parameters in line with the objective function determined by the problem. In optimization applications, the optimum solution is sought by using various algorithms. Metaheuristic algorithms are a method used in the optimization process and are among the sub-branches of artificial intelligence. It is based on the idea of mathematical modeling of intuitive methods that can be inspired by the instinctive behavior of living things in nature as well as natural events such as pollination. Particle swarm optimization (PSO) is inspired by the swarm behavior of living things, gray wolf optimization (WAO) is inspired by the social hierarchy and hunting strategies of wolves, bat algorithm (BA) is inspired by the echolocation of bats and flower pollination algorithm (FPA) inspired by the pollination process of flowers. There are varieties inspired by different events like the artificial bee colony algorithm (ABC) inspired by the path it follows, the harmony search algorithm (HSA) inspired by the process of composing the best harmony and the teaching–learning-based optimization (TLBO) inspired by the learning and teaching process of a group of individuals [23–29]. In the studies, lattice structures, steel plate shear wall frames, retaining walls, composite plates, and similar elements were preferred as optimization methods in the optimum design [30–34]. Another heuristic algorithm is the Jaya Algorithm (JA), which was developed by Rao by reducing the two-stage TLBO algorithm consisting of a teaching and learning process to a single stage [35]. Since this algorithm consists of a single stage and does not contain a design factor, it is a simple and easily applicable, advantageous algorithm that produces fast solutions. In structural engineering, the optimization of control systems has been supported by studies that have remarkable effects on the optimum design of truss structures [36–38]. Data is one of the most important parameters to achieve high prediction success in machine learning applications. The optimum level of data to be used in the application will be an advantage for the machine to offer the best solutions. The machine learning method is divided into two main headings supervised and unsupervised. Studies with supervised learning are divided into classification or regression problems according to the type of problem and are used in algorithms accordingly. To make the workmanship easy and applicable in the design of the structural elements, the design is required to be in standard dimensions. Considering this aspect, it would be more appropriate for the design problems to divide the dimensioning models into classes and make class predictions in terms of ease of work and workmanship. Considering this situation, it is recommended to use classification algorithms of machine learning in estimating the cross-sectional dimensions of structural members.

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In this study, a machine learning model has been developed for cross-section predictions of column and beam examples, which are basic structural elements. For this purpose, the optimum design properties were determined by optimizing the structural elements under different load conditions with the Jaya algorithm. The optimization process has been completed using the Jaya algorithm on the Matlab program [39]. The obtained optimum design parameters and load cases were turned into a data set and a machine-learning method was applied. For the machine trained with optimum data, class prediction models were developed with machine learning algorithms on the Python program for column and beam examples [40]. The success and performance of machine learning algorithms were evaluated for both problems.

2 Methodology 2.1 Optimum Design of Structural System Elements with Jaya Algorithm Jaya algorithm is a metaheuristic algorithm developed by Rao in 2016 [35]. Its origin is based on the teaching–learning-based optimization (TLBO) algorithm. It has been developed by reducing the TLBO algorithm, which has two stages, to a single stage. In Jaya optimization, similar to other heuristic algorithms, the objective function of the problem is determined and the lower and upper limit values of the element properties to be optimized are introduced to the program. For elements such as columns and beams, these values are the section width, height, or thickness that is planned to be optimized. After defining the limit values of the section properties of the element to be optimized, the first solution matrix is randomly assigned between these limit values. Then, for each new solution to be produced, the best and worst solution values in the previous solution matrix are determined and used to produce new solutions. The algorithm equation used to obtain new solutions is shown in Eq. 1. | | |) | ( X i,new = X i, j + rand X i,best − | X i, j | − rand(X i,wor st − | X i, j |)

(1)

X i,new in Eq. 1 is ith variable of new solution value, X i, j is ith variable of jth value of the candidate solution in the initial matrix, X i,best and X i,wor st indicates the best and the worst solution of ith value according to the objective function, respectively. After this stage, the iteration process starts, each new solution is compared with the old solutions, and the better solution is decided. The optimum result is reached by repeating the solution updates with the amount of iteration.

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2.2 Design Parameters for Tubular Column and I-Beam Optimization Tubular columns are elements with cross-sectional properties consisting of a center and a diameter. In optimizing the cost of a tubular column under pressure, the objective function is to minimize these sections. A representative image of a tubular column is shown in Fig. 1. P in Fig. 1 denotes the pressure load, and l denotes the length of the column. In the image of the A-A section taken on the column, di represents the inner diameter, d0 , the outer diameter, d represents the center diameter and t represents the section thickness of the column. The objective function f (d, t) used in the cost minimization process for cost optimization of such columns is given in Eq. 2 [42]. Min f (d, t) = 9.8dt + 2d

(2)

In the optimization of tubular columns, it is convenient to use the axial load capacity and the buckling limit as constraints that can be defined for the design. In the axial load capacity constraint, the case that the compressive stress does not exceed the yield strength is taken into account. The equations to be used for the axial load constraint (g1 ) and column buckling constraint (g2 ) is given in Eqs. 3 and 4, respectively [42]. g1 =

Fig. 1 Tubular column and cross-section detail [41]

P −1≤0 π d tσ y

(3)

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g2 =

8 P L2 π 2 Ed t(d 2 + t 2 )

−1≤0

(4)

E given in Eqs. 3 and 4 denotes the modulus of elasticity of the material, and σ y the yield strength. In steel I profile beam designs, the height of the beam, the width and thickness of the flange, and the thickness of the web is the parameters that express the crosssectional properties of the I-shaped beams. The design of such beams is aimed to prevent the deflection of the beam against horizontal and vertical loads. Optimization of the section properties is necessary to avoid vertical displacements of the beam. In addition to the height of the I-profile beams and the flange widths, the optimization of the flange and web thicknesses is also important. Producing the material in sufficient thickness is one of the design criteria that is effective in preventing deflection. A representative illustration of an example of a steel beam with an I profile is given in Fig. 2. Figure 2, P indicates the vertical load, Q indicates the horizontal load, C L the centerline, L is the length of the beam, b is the flange width of the beam, h is the beam height, and t f and tw are the flange and web thicknesses of the beam, respectively. In the optimization of the I-section beam, it is desired to minimize the deflection of the beam. The displacement equation for a simple beam to be used in optimization is given in Eq. 5. The objective function depending on the beam sections obtained by calculating the inertia of the beam is shown in Eq. 6 [42]. f (x) =

P L3 48E I

Fig. 2 I-section beam construction and design variables [43]

(5)

Machine Learning Application of Structural Engineering Problems

(

M i n f (h, b, t w , t f ) = 48E

P L3 t w ( h−2t f ) 12

3

+

bt 3f 6

+ 2bt f

185

(

h−t f 2

)2 )

(6)

E in Eqs. 5 and 6 represents the modulus of elasticity of the material and I represents the moment of inertia of the beam. To limit the beam section properties, two different design criteria can be set for the I profile. One of them can be taken as the maximum area constraint (300 cm2 ) for the beam section and the other as the allowable moment stress (6kN/cm2 ). The recommended beam section constraint g3 is given in Eq. 7 and the moment stress constraint g4 is given in Eq. 8 [42]. ( ) g 3 = 2bt f + t w h − 2t f ≤ 300 g4 =

(

t w h − 2t f

)3

(7)

1.5 P Lh 1.5 Q Lb ( ) ≤6 ( )) + 3 ( 2 h − 2t f + 2t w b3 t + 2bt f 4t f + 3h h − 2t f w (8)

2.3 Class Prediction of Column and Beam Sections with Machine Learning Column and beam elements are carrier system parts that require precision and good workmanship. In the production of these elements, although it is possible to estimate the element dimensions at the numerical level depending on the characteristics and correlation of the data, it is advantageous to apply the class-based estimation method considering the convenience it will provide in production. Standard production of carrier system elements, taking into account the speed and practicality of production, reduces labor costs and minimizes the errors arising from the production to be made in practice. For all these purposes, classification algorithms of machine learning are suitable methods for use in education. While the classification of multiple sections separately is possible with machine learning, they can also be classified at the same time. Within the scope of this study, class-based cross-section prediction models were produced by using Logistic Regression and Decision Tree algorithms, which are machine learning algorithms, in training. The Decision tree algorithm is an algorithm that queries and branches the data and divides the data into small clusters with a tree-like appearance. The attributes of the data are expressed as nodes and the results from the test data form the branches of the tree [44]. As an example of the branching of this algorithm, when it is desired to make a prediction model on column sections, these sections are branched according to whether they are long, short, wide, or narrow, and then they are divided into short,

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Fig. 3 Decision tree example representation

long, and medium branches, while these new nodes are sufficient for the section. The answers are given to the question of whether there are any new sub-branches of the tree. An example of a decision tree for a rectangular column is given in Fig. 3. As seen in the figure, the features in the data are transformed into nodes, and the responses corresponding to these features form the branches of the tree. The logistic regression algorithm is a supervised machine learning algorithm that establishes a relationship between two data features. When estimating a dependent variable, it makes an estimation based on the least squares algorithm [45, 46]. It is a very successful method in classifications with two answers such as yes or no. Using one of the predicted factors establishes a link for the estimation of the other factor. Looking at the beam example, its use is expected to yield remarkable results if it is desired to make a dual classification as thick and thin for the flange and web widths of the beam.

3 Numerical Examples 3.1 Tubular Column In the tubular column study, a machine learning model has been developed to estimate the cross-section of the column under axial compression load. The cost minimization has been made by using the objective function in Eq. 2 of the column center diameter and section thicknesses from the Tubular column sections. The algorithm and design parameters used in the optimization and the design lower and upper limit values are given in Table 1. In the optimization process, optimum cross-section parameters were obtained for different stress, load, and column lengths, and data to be used in machine learning were obtained. Then, for classification estimation, optimum section thicknesses (A, B, C, D, E, F, G) and section center diameters were converted into 6 (H, J, K, L, M, N) different classes and made categorically. The 10 lines of the generated data set are given in Table 2, and the class distributions in the data are given in Table 3.

Machine Learning Application of Structural Engineering Problems Table 1 Optimization parameters and design limits

187

Symbol Definition

Value

mt

Maximum iteration number

10,000

pn

Population number

15 0.85 × 106

elasticity(kgf/cm2 )

E

Modulus of

L

Column length (cm)

100–500

P

External load (kgf)

100–5000

σy

Strain

tmin

Minimum section thickness (cm)

0.2

tmax

Maximum section thickness (cm)

0.9

dmin

Minimum section center diameter (cm)

2

dmax

Maximum section center diameter (cm) 14

(kgf/cm2 )

100–500

Table 2 10 rows of tubular column dataset Strain (kgf/cm2 )

Length (cm)

Load (kgf)

Thickness (cm)

Center Diameter (cm)

Fx

100

100

100

A

H

100

300

100

C

H

13.35831

100

400

500

A

J

22.22907

7.92

100

2200

400

G

K

84.28906

200

2800

100

F

J

54.39317

300

900

100

C

H

13.35831

300

4500

400

E

K

60.24811

400

1800

200

B

H

21.81489

500

800

200

A

H

14.43357

500

3500

300

A

K

36.6415

The table with the correlation matrix of the data is given in Table 4 and its graphical representation is given in Fig. 4. The cross-sectional properties of the tubular column were estimated with the created data set. Since the section center diameter and section thicknesses require two classifications, the class estimation of the two sections at the same time was investigated by applying multiple classifications. Multi-output classification is an algorithm for the simultaneous prediction of two or more features. The classification result presents two or more outputs. An example of this can give a data set about fruits. In this dataset, when one of the attributes is the type of fruit and the other is the color of the fruit, the type (apple, pear, orange) and color (yellow, orange, red) of the fruit can be estimated simultaneously with multi-classification. In the classification made, multi-output classification is applied by choosing one of the classification algorithms. In multiple-output classification applications, it is calculated by taking the precision

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Table 3 Class distribution of the dataset

Class of t

Number of data

Section intervals

A

438

0.2–0.3

B

100

0.3–0.4

C

84

0.4–0.5

D

84

0.5–0.6

E

72

0.6–0.7

F

82

0.7–0.8

G

324

0.8–0.9

Class of d

Number of data

Section intervals

H

424

2–4

J

258

4–6

K

302

6–8

L

125

8–10

M

56

10–12

N

19

12–14

Table 4 Correlation matrix for the tubular column Strain

Length

Load

Fx

Strain

1

0.1102

0.0018

−0.5249

Length

0.1102

1

−0.0014

0.5879

Load

0.0018

−0.0014

1

0.1243

Fx

−0.5249

−0.5879

0.1243

1

Fig. 4 Correlation matrix graph for a tubular column

Machine Learning Application of Structural Engineering Problems Table 5 Accuracy metrics of multi-output classification for a tubular column

189

Algorithm

Accuracy (%)

Decision tree classification

42.27

K-Nearest neighbors classification

33.23

Logistic regression

22.40

Linear discriminant analysis

34.39

Naïve Bayes

22.29

Support vector machine

29.48

values of each predicted group and finding their average. The precision table of the multi-output classification prediction models made with different machine learning algorithms is given in Table 5. Prediction models were reproduced by using the decision tree algorithm. The highest precision is given in multi-output classification to develop the prediction model separately for the two dimensions. In the separate classification, 70% of the data was allocated for training and 30% for testing was applied. Whereas in multioutput classification, training was applied to the data with tenfold cross-validation. The obtained confusion matrices are shown in Figs. 5 and 6, respectively, for the section thickness and section center diameter estimation model, and the accuracy, precision, recall, and f1 scores are shown in Tables 6 and 7, respectively. Fig. 5 Confusion matrix: thickness prediction model

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Fig. 6 Confusion matrix: center diameter prediction model

Table 6 Decision tree classification, accuracy, precision, recall, and f1-score values for thickness

Class

Precision

Recall

A

0.96

0.92

0.94

B

0.50

0.56

0.53

C

0.48

0.39

0.43

D

0.33

0.48

0.39

E

0.38

0.39

0.38

F

0.35

0.36

0.36

G

0.86

0.82

0.84

Accuracy Table 7 Decision tree classification, accuracy, precision, recall, and f1-score values for center diameter

F1-score

Class

0.72

Precision

Recall

F1-score

H

0.96

0.98

0.97

J

0.86

0.80

0.83

K

0.85

0.84

0.84

L

0.81

0.85

0.83

M

0.72

0.81

0.76

N

0.67

0.50

0.57

Accuracy

0.88

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3.2 I-Section Beam A machine learning model has been developed for the cross-section prediction of an I-section steel beam sample. The beams resist deflection by using the moment of inertia. Since beam section width and height are used in the basic parameters of the moment of inertia, it is quite difficult to determine the optimum section properties for different load situations by optimization. The optimization process usually aims to maximize the inertia of the beam based on the maximum limit. In this case, obtaining data on a wide variety of section properties, with optimization for use in machine learning for the beam, is an area to be explored. A solution to this problem can be considered by applying different objective functions. Another feature that protects I-section beams from deflection is the beam flange and web thicknesses. The main purpose of optimization here is to prevent vertical displacement of the beam against horizontal and vertical loads. In a classification of beam dimensions, the classification of I-section beam thicknesses is a viable solution to generate a predictive model for minimizing vertical displacements. In this case study, the flange and web thicknesses of an I-section beam are optimized for different load cases. The algorithm and design parameters and limits for optimization with the Jaya algorithm are given in Table 8. In the optimization process, optimum cross-section dimensions for different stress and load situations were obtained and thus these optimal dimensions were used in forming the new dataset. Then, for classification estimation, optimum section thicknesses were converted into 2 (thin and thick) different classes. 10 rows of the produced data set are given in Table 9 and the class distributions of the data are given in Table 10. Table 8 Optimization parameters and design limits

Symbol

Definition

Value

mt

Maximum iteration number

500,000

pn

Population number

15

E

Modulus of elasticity (kN/cm2 )

20,000

L

Beam length (cm)

200

P

Vertical load (kN)

100 ∼ 800

Q

Horizontal load (kN)

1 ∼ 80

σ

Moment stress (kN/cm2 )

6

h min

Minimum beam section height (cm)

10

h max

Maximum beam section height (cm)

80

bmin

Minimum beam section width (cm)

10

bmax

Maximum beam section width (cm)

50

twmin

Minimum beam web thickness (cm)

0.9

twmax

Maximum beam web thickness (cm)

5

t f min

Minimum beam flange thickness (cm)

0.9

t f max

Maximum beam flange thickness (cm)

5

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Table 9 10 rows of I-beam dataset Vertical load (kN)

Horizontal load (kN)

Height (cm)

Width (cm)

Web thickness

Flange thickness

Fx

100

1

80

50

Thin

Thick

0.002179

100

27

63

31.43

Thin

Thick

0.003777

120

19

68.60

20.54

Thick

Thick

0.005147

120

74

80

50

Thick

Thin

0.004035

140

78

80

50

Thin

Thin

0.003161

150

3

65.55

32.22

Thick

Thin

0.006583

210

3

80

34.80

Thin

Thick

0.004698

240

67

79.86

40.73

Thick

Thin

0.007783

250

24

80

50

Thick

Thin

0.008407

290

12

63.70

25.21

Thick

Thick

0.014492

Table 10 Class distribution of the dataset

Class of tw

Number of data

Section intervals

Thin

4917

0.9–2.2

Thick

596

2.2–5

Class of tf

Number of data

Section intervals

Thin

3931

0.9–2.2

Thick

1582

2.2–5

The graphical representation of the correlation matrix of the data in Table 11 is given in Fig. 7. With the created data set, a predictive model was produced with machine learning classification algorithms. Multiple classifications were performed for simultaneous estimation of both web and flange widths. The precision levels of the algorithms used in multi-output classification are shown in Table 12. The logistic regression algorithm, which gives the highest precision in multioutput classification, is also used in the estimation of web and flange thicknesses separately, and the difference between multi-output classification is examined. The Table 11 Correlation matrix for I-section beam Vertical Load

Horizontal Load

Height

Width

Fx

Vertical load

1

−0.0209

−0.0115

0.0157

0.0111

Horizontal load

−0.0209

1

−0.0126

0.0174

0.0216

Height

−0.0115

−0.0126

1

0.7252

−0.4452

Width

0.0157

0.0174

0.7252

1

−0.1895

Fx

0.0111

0.0216

−0.4452

−0.1895

1

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193

Fig. 7 Correlation matrix graph for I-section beam

Table 12 Accuracy metrics of multi-output classification for I-section beam

Algorithm

Accuracy (%)

Decision tree classification

75.81

K-nearest neighbors classification

84.44

Logistic regression

88.71

Linear discriminant analysis

87.74

Naïve Bayes

60.84

Support vector machine

60.68

estimation precision level was more successful for the separately classified web and flange thicknesses. In a separate classification, 70% of the data was allocated to training and 30% to testing, and training was applied. In multi-output classification, training was applied to the data with tenfold cross validation. Confusion matrices of the trained models are shown in Figs. 8 and 9 for web thickness and flange thickness predictions, respectively, and accuracy, precision, recall, and f1 scores are shown in Tables 13 and 14, respectively.

4 Discussion and Conclusions In this study, column and beam sections, as an example of structural system elements, are optimized for different load and stress conditions with metaheuristic algorithms. Jaya Algorithm, a metaheuristic algorithm, was used in the optimization process.

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Fig. 8 Confusion matrix for the thickness prediction model

Fig. 9 Confusion matrix for the center diameter estimation model

Table 13 Logistic regression classification, accuracy, precision, recall, and f1-score values for web thickness (tw)

Class

Precision

Recall

F1-score

Thick

1.00

0.12

0.22

Thin

0.90

1.00

0.95

Accuracy

0.91

Machine Learning Application of Structural Engineering Problems Table 14 Logistic regression classification, accuracy, precision, recall, and f1-score values for flange thickness (tf)

195

Class

Precision

Recall

Thick

0.98

0.98

0.98

Thin

0.99

0.99

0.99

Accuracy

F1-score

0.99

The optimum values obtained from the optimization, the attributes used in the optimization process, and machine learning techniques were applied, which were turned into a data set. In the column example, the section center diameter and section thicknesses are divided into 6 and 7 classes at regular intervals, and the prediction model of the machine is aimed to estimate sections in standard dimensions. The highest precision values of the column machine learning model, in which the multiple classification methods are applied, were obtained in the decision tree algorithm. A decision tree is an algorithm that can be applied to both classification and regression problems. In this study, since it is desired to create a class-based prediction model, the model was created by using the decision tree algorithm in classification. In comparison with other algorithms, it can be shown that the most successful algorithm is the decision tree because splitting into many classes results in the formation of many branches against the nodal points of the partitions. Up to 42% prediction accuracy is a good prediction success rate. Since it undertakes a successful estimation task, it may be appropriate to use this algorithm in numerical studies for regression analysis apart from classification. When the prediction model success levels of two-column section features are examined separately, it is seen that the prediction success of some classes is 96%, while the section feature of another class has a precision of around 33%. One of the main reasons for this situation is the averaging of precision values in multiple classifications. Therefore, it can be said that the machine learning method did not show a high performance due to the data characteristics, since the tubular column sample was averaged over different prediction success rates. To overcome this situation, increasing the number of data in the class with low estimation precision or extending the training period may produce a solution. In the study made with the beam example, the section width height, flange, and web thicknesses of the beam were optimized with the Jaya algorithm. In the optimization, the deflection of the beam is tried to be minimized. In the optimization to prevent deflection due to beam inertia, the section width and height values were close to the upper limit. Considering this situation, it was decided that it would be more appropriate to use the web and flange dimensioning. In the alternative solution here, beam heights and widths are used in training and a prediction model is produced by machine learning to determine the flange and web thicknesses that affect the deflection of the beam. Beam web and flange thicknesses are divided into two classes thin and thick. The logistic regression algorithm produced the most successful estimation model in the multi-output classification. The fact that the web and flange thicknesses have 2 classes is the reason why logistic regression is the classifier with the highest precision. Other classification algorithms have also provided a remarkable level of

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precision in estimating beam thicknesses. Logistic regression and linear discriminant analysis algorithms showed very close precision. The reason for this can be shown that there is a linear relationship between them due to the small number of classes and the data obtained by optimization. A logistic regression algorithm was used to classify beam thicknesses separately. In the prediction models produced, a 91% accuracy level in web thickness and a 99% accuracy level in flange thickness were obtained. However, the recall score obtained from the separate classification estimated 100% correctly when the web width was “thin”, but it was insufficient with 12% in the classification as “thick”. When the data distributions in Table 13 are examined, a noticeable disproportion in the data class distributions draws attention. Although the accuracy level is above 90%, it can be said that the reason why only 12% of the data that should be classified as “thick” are correctly classified is the insufficient number of data expressed as “thick” in web thicknesses. It is expected that this remarkable difference in the recall value will disappear by balancing the number of data. In line with the optimization and machine learning studies, it is shed light that the application of artificial intelligence methods can be successful in estimating the carrier system designs, and it is concluded that an artificial intelligence prediction model with a high level of precision can be produced if the data is well analyzed and organized.

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32. Degertekin, S.O., Lamberti, L., Ugur, I.B.: Discrete sizing/layout/topology optimization of truss structures with an advanced Jaya algorithm. Appl. Soft Comput. 79, 363–390 (2019) 33. Gandomi, A.H., Kashani, A.R., Roke, D.A., Mousavi, M.: Optimization of retaining wall design using evolutionary algorithms. Struct. Multidiscip. Optim. 55, 809–825 (2017) 34. De Almeida, F.S.: Stacking sequence optimization for maximum buckling load of composite plates using a harmony search algorithm. Compos. Struct. 143, 287–299 (2016) 35. Rao, R.: Jaya: a simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int. J. Ind. Eng. Comput. 7(1), 19–34 (2016) 36. Ocak, A., Bekda¸s, G., Nigdeli, S.M.: A metaheuristic-based optimum tuning approach for tuned liquid dampers for structures. Struct. Design Tall Spec. Build. 31(3), e1907 (2022) 37. De˘gertekin, S.O., Bayar, G.Y., Lamberti, L.: Parameter-free Jaya Algorithm for truss sizinglayout optimization under natural frequency constraints. Comput. Struct. 245, 106461 (2021) 38. Bekda¸s, G., Kayabekir, A.E., Ni˘gdeli, S.M., Toklu, Y.C.: Transfer function amplitude minimization for structures with tuned mass dampers considering soil-structure interaction. Soil Dyn. Earthq. Eng. 116, 552–562 (2019) 39. The MathWorks, Matlab R2022b. Natick, MA (2022) 40. Python Software Foundation. PYTHON 3.11.0, USA (2022) 41. Rao, S.S.: Engineering Optimization Theory and Practise, 4th edn. Wiley, New Jersey, USA (2009). ISBN: 978-0-470-18352-6 42. Bekda¸s, G., Nigdeli, S.M., Yücel, M., Kayabekir A.E.: Yapay Zeka Optimizasyon Algoritmaları ve Mühendislik Uygulamaları. Seçkin, Ankara, Turkey (2021) 43. Yang, X.S., Bekda¸s, G., Ni˘gdeli, S.M. (eds.): Metaheuristic and Optimization in Civil Engineering. Springer, Switzerland (2016). ISBN:9783319262451 44. Morales, E.F., Escalante, H.J.: A brief introduction to supervised, unsupervised, and reinforcement learning. In: Biosignal Processing and Classification Using Computational Learning and Intelligence, pp. 111–129. Academic Press (2022) 45. Harrell, F.E.: Regression modeling strategies: with applications to linear models, logistic regression, and survival analysis, vol. 608. Springer, New York (2001) 46. Mellit, A., Kalogirou, S.: Artificial intelligence techniques: machine learning and deep learning algorithms. Handbook of artificial intelligence techniques in photovoltaic systems, pp. 43–83. (2022)

Modeling Civil Engineering Problems via Hybrid Versions of Machine Learning and Metaheuristic Optimization Algorithms Vahdettin Demir, Esra Uray, and Serdar Carbas

Abstract The aim of this study is to develop hybrid solution models by integrating metaheuristic optimization algorithms and machine learning technique. These hybrid models are utilized to estimate bearing capacity of pile groups and lake levels, which are common challenges to calculate in the geotechnical and hydrology designs of civil engineering. To achieve this, Lake Bey¸sehir lake-water level observations and various pile group designs are used as a dataset, which is divided into two parts; 75% for training and 25% for testing. By employing improved hybrid models that combine metaheuristic algorithms such as harmony search, artificial bee colony, and particle swarm optimization with a machine learning technique called least squares support vector regression (LSSVR), optimal values of kernel parameters are obtained reliably and robustly. The results suggest that these hybrid models can be successfully applied to complex real-world problems, as evidenced by nine evaluation metrics, including mean absolute error (MAE), root mean squared error (RMSE), and determination coefficient (R2 ), which showed satisfactory and reasonable performance. Keywords Hybrid model · Least squares support vector regression · Metaheuristic optimization algorithms · Pile group bearing capacity · Lake level

V. Demir (B) · E. Uray Department of Civil Engineering, KTO Karatay University, Konya 42020, Türkiye e-mail: [email protected] E. Uray e-mail: [email protected] S. Carbas Department of Civil Engineering, Karamanoglu Mehmetbey University, Karaman 70200, Türkiye e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Bekda¸s and S. M. Nigdeli (eds.), Hybrid Metaheuristics in Structural Engineering, Studies in Systems, Decision and Control 480, https://doi.org/10.1007/978-3-031-34728-3_11

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1 Introduction Nowadays, as the solution to various civil engineering phenomena is affected by management and sustainability processes, the solution process developed by including this effect emerges as a complex issue. Researchers contributing to the literature have shown a great interest in applying modern artificial intelligence (AI) solution models and their hybrid versions promising potential for tackling challenging issues, to solve complex real-world engineering design problems [1, 2]. For this reason, hybrid models generated with machine learning and various optimization techniques are employed commonly by researchers in solving many intricated engineering problems. Given the robustness, reliability, and effectiveness of the hybrid models that result from the integration of optimization algorithms and artificial intelligence models, these models demonstrate the capacity to address complex nonlinear problems encountered in the field of civil engineering. Furthermore, hybrid solution models based on AI have been recently utilized in the optimization of hyperparameters in machine learning in an attempt to reduce modelling time and increase the accuracy of complex engineering problems such as civil engineering designs. Since the hyperparameters affect the behaviour and performance of the model on a vast scale, determining the appropriate parameter values is crucial [3]. Thereby, the fundamental objective of this study is to create a hybrid model by integrating an artificial intelligence model with nature-inspired metaheuristic optimization algorithms for hyperparameter optimization and subsequently investigate it to address two distinct problems in the field of civil engineering [4]. Within this scope, optimum values of γ and α kernel parameters of Least Squares Support Vector Regression (LSSVR) machine learning algorithm have been investigated by utilizing hybrid algorithms via combining the harmony search algorithm (HS), artificial bee colony algorithm (ABC), and particle swarm optimization (PSO) metaheuristic algorithms with LSSVR. In obtaining optimal values of γ and α, the datasets of lake-water levels of Lake Bey¸sehir and the pile group have been employed and the performance of the hybrid models have been evaluated with nine different metrics such as Error Sum of Squares (SSE), Mean Squared Error (MSE), Mean Root Square Error (MRSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Relative Error (MARE), Coefficient of Determination (R2 ), Variance Account Factor (VAF), and Adjusted Coefficient of Efficiency (E).

2 Design Problem Definition 2.1 Lake Level Water resources engineering is a significant field of civil engineering that studies the earth’s atmosphere and the hydrological cycle, which is the distribution and circulation of water. The main purpose of water resources engineering is to determine the

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quantity and quality of water resources within the framework of a management plan, to protect, control, and to contribute to engineering design studies for the most efficient use. Applications of water engineering include the design of hydraulic structures such as stormwater and sewer pipes, dams, flood traps, regulators, and breakwaters, management of waterways such as erosion protection and flood protection, and environmental management such as the estimation of surface waters (river or lake). In addition, hydroelectric power development, water supply, and irrigation are the main applications of water resources engineering [5, 6]. The development of accurate lake-water level prediction with hybrid solution models is important for water resource planning and management. In this study, the estimation of Lake Bey¸sehir lake-water level as a water resources engineering design problem is taken into consideration. Lake-water level forecast is a vital requirement in water management operations such as irrigation and drinking water supply management and decision-making, fishing, tourism, railroad transportation, and a variety of other recreational and socioeconomic activities [7]. Recently, techniques such as artificial intelligence models, machine learning models, and deep learning have demonstrated an extensive ability to model lake water levels without the need for experimental apparatus and complex hydro-physical models based on physical principles and mathematical equations. For a comprehensive literature review and to see the trend of current studies, the Scopus database was searched with the keywords “lake water level, forecast, and hybrid and model, and machine and learning”. It has been observed that there are 299 academic studies on similar subjects in total. These studies were limited to 5 common keywords and a relationship map was obtained for the keywords of the studies scanned using VOSviewer software [8]. A good search of the available literature shows that these investigations include applications of the neural network model, heuristic regression techniques, machine learning techniques, deep learning techniques and their hybrid models. In Fig. 11.1, while machine learning has a central position in the estimation of lake levels, it has been associated with hybrid models in recent years. In addition, it is observed that researchers have developed methods such as fuzzy logic and artificial neural network with preprocessing-hybrid models such as wavelet in the past. In recent years, methods such as deep learning and heuristic optimization algorithms like particle swarm optimization seem to attract more attention by researchers. In addition, it can be said that studies on lake-water level are closely related to water resources, climate change, and drought studies. The fact that there are studies on lakewater level and the investigation of techniques to develop them shows that the subject is up to date. In addition, advanced versions support vector regression of (SVR) such as LSSVR and optimization algorithms such as harmony search algorithm, artificial bee colony algorithm, particle swarm optimization were not used as a focus in studies distinguishes the current study from the literature. Lake-water level information can help with regional water planning, water management, hydropower plants, commercial navigation, domestic, agricultural,

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Fig. 11.1 Relationship map of keywords

industrial activities, environmentally friendly construction planning, and the sustainable life of all inhabitants of the lake basin [9]. Lake-water level fluctuation is dependent on time series that can be expressed as the results of numerous hydrological and climatological parameters such as rainfall, runoff, evaporation, temperature, groundwater and other geoscience variables [10, 11]. However, providing all these parameters in the estimation of lake-water levels and determining the impact areas of the stations is a difficult and expensive process. Instead, making estimations using past lake-water levels is more practical and economical, as well as more advantageous in terms of applicability [12]. Lake Bey¸sehir, Turkey’s largest freshwater lake, and the drinking water reservoir is located in Central Anatolia between 31°17' and 31°44' E and 37°34' and 37°59' N [13]. It is one of the most critical water sources, particularly for domestic and irrigation purposes [14]. Lake Bey¸sehir has been a first-degree Specially Protected Area since 1991, and it has been entirely surrounded by two National Parks, Bey¸sehir and Kızılda˘g, since 1993 [15]. Figure 11.2 depicts a map of the lake’s location. The lake is approximately 45 km long, 24 km wide and covering an area of 1125 m2 [16]. Lake Beysehir is a tectonic lake located between the Sultan and Anamas Mountains, which form two fault groups running northwest-southeast. Despite its tectonic origin, a karst phenomenon was responsible for its creation. The lake’s northern and southern coastlines are shallow, with an average depth of 8.5 m and a maximum observed depth of 10 m. The lake’s water level and area dramatically change from season to season and year to year. In addition to direct precipitation, Lake Beysehir is fed by small surface streams and creeks from the Sultan Mountain and the Anamas Mountain, and by flow through the Mesozoic calcareous cracks located at the bottom of the lake. Water losses from the lake occur by surface evaporation, the sinkholes in the north–south direction and the Bey¸sehir canal, which diverts the water from the

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(a)

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(b)

Fig. 11.2 Study area; a country-wide, b basin

lake for irrigation [17]. The long-term hydrology of the region shows that temperature and evaporation data have decreased, while lake-water levels, precipitation and groundwater levels have increased [18]. The trend graph of lake-water levels in the time series is given in Fig. 11.3. When Fig. 11.3 is examined, an increasing trend is observed in lake-water levels around the 1950s and 1980s, while those decrease in the following years. With the measures taken by local authorities since 2008, increasing trends are seen in the data [11, 18]. When the boxplot graph of the data is examined, there are fluctuations around 1123, on average around 1125–1121 m, according to years. This study investigates the applicability of at Least squares support vector regression with various optimization techniques (harmony search algorithm, artificial bee colony algorithm, particle swarm optimization) for Lake Bey¸sehir lake-water level estimation with input variables of historical lake-water level records.

(a)

(b)

Fig. 11.3 The time series graph a and boxplot b of Lake Bey¸sehir lake-water levels

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2.2 Pile Group Design Geotechnical engineering is a field of civil engineering that deals with the study of the behavior of earth materials, such as soil, rock, and groundwater, under various physical and environmental conditions. The primary objective of geotechnical engineering is to ensure that structures and their foundations are built safely, efficiently, and sustainably, taking into account the geological and environmental conditions of the site. Geotechnical engineers perform a wide range of tasks, including site investigation, laboratory testing of soil and rock samples, analysis and interpretation of data, design of foundations and retaining structures, slope stability analysis, and risk assessment. Comprehensive literature search according to cases in which artificial intelligence, machine learning, neural networks, and deep learning methods application in civil and geotechnical engineering have been conducted and results have been visualized via VOSviewer software for conflicting of keywords of the studies [8]. Researchers have frequently employed artificial intelligence-based methods such as artificial neural networks, machine learning algorithms, and metaheuristic optimization algorithms as seen from in Fig. 11.4 usage of them in civil engineering and geotechnical engineering. The study which is conducted by Baghbani et al. [19] shows that artificial intelligence methods have been extensively employed in geotechnical engineering topics like frozen soils and soil thermal properties, rock mechanics, subgrade soil and pavements, landslide and soil liquefaction, slope stability, shallow and piles foundations, tunneling and tunnel boring machine, dams, and unsaturated soils. The utilization of algorithm-based methods in civil and geotechnical engineering studies is observed to be extensive owing to the existence of complex real-world engineering design

Fig. 11.4 Literature review

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problems. In literature, there is the common usage of these kinds of algorithms to predict reliable design [20–22] or to achieve the optimum design of geotechnical structure [23–25]. In geotechnical engineering, pile foundations have been generally preferred as structure foundations that transmit the load to the depth of soil safely because of the need to increase living space with the growing population, especially in weakcharacterized soils. Using pile foundations, it is possible to construct multi-story buildings even though the presence of a weak soil environment. Pile group by using artificial intelligence methods [26, 27] and optimum design of pile group via metaheuristic algorithms [28, 29] were investigated and safely and prosperous results were acquired. The working principle of piles under loads involves the transfer of loads from the superstructure to the soil through the pile. When a pile is subjected to a load, it transfers the load to the soil or rock mass through skin friction and end bearing. In the case of a pile group, the behavior is more complex as the loads are shared among the piles. The interaction between the piles in a group can result in a decrease in the overall bearing capacity of the group, compared to the sum of individual pile capacities. In this study, pile group (PG) bearing capacity are considered for application of hybrid algorithms. Specifically, the design of the pile group considers an environment characterized by cohesion-less soil, where the angle of internal friction (Ø) and unit volume weight (γk ) are key factors. In the design, different soil properties and pile group dimensions which are pile diameter (D), pile length (Lk ), and space between pile center to center (S) have been considered and the pile group design is shown in Fig. 11.5. In pile group design, the single bearing capacity of a single pile is determined initially, and then the bearing capacity of the pile group is calculated considering the total number of piles in the group and group efficiency [30]. In this section,

(a) Fig. 11.5 Pile group design; a plan and b section

(b)

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Meyerhof’s method [31] is explained for single bearing capacity in homogenous sandy soil. The ultimate bearing capacity (Qu ) is calculated by summing the loadcarrying capacity of the pile point (Qp ) and frictional resistance derived from the soil-pile interface (Qs ) (Eq. 11.1). Qu = Q p + Qs

/ Q p = γk L k N q π D 2 4

/ Q lmt = 0.5Pa Nq tan(φ ' )π D 2 4 Q s = 0.5(q0 + q Lkc )π DL kc + q Lkc (L k − L kc )π DL kc

q Lkc = L kc γk K tan(δ)

(11.1)

For bearing capacity factor (Nq ), the values presented by Meyerhof [31] as depending on the variation of Ø is used. δ is soil-pile friction and its value is taken 0.8Ø in given formula. K which depends on pile type is the effective earth pressure coefficient and its value is taken as 1.3 in this formula. The load-carrying capacity of the pile point (Qp ) should not be great than Qlmt value. Here, Pa means atmospheric pressure (100 kN/m2 ). The skin frictional resistance, denoted by Qs, exhibits an increasing trend with depth during the Lkc length but becomes constant thereafter. A conservative estimation of Lkc , assuming it to be 15D, is typically employed in calculations. As a result, the skin frictional resistance qLkc attains a constant value beyond the Lkc depth. Once Qu of single pile is determined by aggregating Qp and Qs , it is advisable to apply an appropriate factor of safety (FS) ranging from 2.5 to 4 to arrive the total allowable load (Qall ) for each pile (Eq. 11.2). In this study, FS is taken as 3.0. Q all =

Qu FS

(11.2)

The pile groups are often used to distribute the loads from the structure over a larger area, which helps to reduce the stress on the individual piles and prevent them from failure. The bearing capacity of a pile group can be determined by reducing the total pile bearing capacity with a reduction factor smaller than one. The reduction factor value of η depends on various factors such as the pile group configuration, pile spacing (S), and the number of total piles in directions horizontal (Nx ) and vertical (Ny ). The bearing capacity of the pile group (Qg ), whose center-to-center distance between piles is taken as 2.5D and 3.5D may be determined via Eq. 11.3 according to Converse-Labarre formulation [30]. Q g = ηQ u N x N y ] [ / ϕ (N x − 1)N y + (N y − 1)N x ϕ = tan−1 (D S) η =1− 90 Nx N y

(11.3)

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3 Solution Algorithms 3.1 Machine Learning Algorithm 3.1.1

Least Squares Support Vector Regression (LSSVR)

In 1995, Vladimir Vapnik and his colleagues at AT&T Bell Laboratories created LSSVR, which are used to determine the nonlinear relationship between input variables and output variables with the least amount of error [32]. Then final version LSSVR proposed by Suykens and Vandewalle in 1999 and it is applied on chaotic time series forecasting [33]. Basically, the LSSVR function can be expressed as in Eq. 11.4. y(x) = w T ϕ(x) + b

(11.4)

where y is the value obtained in x, w is the coefficient vector, ϕ is the mapping function, and b is the bias term derived by minimizing the upper bound of the generalization error. LSSVR kernels include two alteration parameters (γ, α). The γ is the regularization constant and the α is the width of the radial basis function kernel. LSSVR is derived from SVR, which is an excellent technique for solving real-world problems through the use of regression, function estimation, and classification. The SVR is based on structural risk minimization (SRM), which gives the least amount of inaccuracy in forecasting challenges. It is mostly used for signal processing, pattern recognition, and nonlinear regression estimation [34]. In this current study, various hybrid LSSVR models are used for y and modeling of Lake Bey¸sehir lake-water levels. Hence, compared with traditional models, the LSSVR model is the best at eliminating noise and reduces computational labor. The hybridization of the model enables the kernel parameters (γ, α) to be obtained quickly. So, because of these advantages, conventional models can be replaced with hybrid LSSVR models.

3.1.2

Evaluation Metrics

For evaluation metrics of hybrid LSSVR models, commonly used criteria in the literature are utilized [35, 36]. These evaluation metrics usually focus on the difference between observed and predicted values. While this difference is close to zero in criteria such as RMSE and MAE, close to one in criteria such as E and R2 or close to 100 in VAF is considered a success criterion.

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Below are the equations for the evaluation metrics. (1) Error Sum of Squares (SSE) SS E =

n ∑ ( )2 i p − io

(11.5)

i=1

(2) Mean Squared Error (MSE) ⌜ | n ∑ 1| (i o − i p )2 MSE = √ n i=1

(11.6)

(3) Mean Root Square Error (MRSE) ⌜ | n ∑ 1| (i o − i p )2 M RS E = √ n i=1

(11.7)

(4) Root Mean Square Error (RMSE) ⌜ | n |1 ∑ RMSE = √ (i o − i p )2 n i=1

(11.8)

(5) Mean absolute error (MAE) M AE =

n | 1 ∑ || i p − io | n i=1

(11.9)

(6) Mean Absolute Relative Error (MARE) | n | 1 ∑ || i p − i o || M A R E = 100 n i=1 | i p |

(11.10)

(7) Coefficient of Determination (R2 ) n ∑

R =1− 2

(i o − i p )2

i=1

(i o − i o )2

(11.11)

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(8) Variance account factor (VAF) ( ) var(i p − i o ) V AF = 1 − x100 var(i p )

(11.12)

(9) Adjusted Coefficient of Efficiency (E) n | | ∑ |i o − i p |

E(%) = 1 −

i=1 n ∑

| | |i o − i o |

(11.13)

i=1

In these equations, io and ip show the observed and predicted values, respectively. n represents the number of data, and the line over io or ip represents the average. In addition, scatter plots, violin plots and Taylor diagrams are utilized in this study to compare methods. These images show graphically how closely the models match the observations [37–39]. The statistical information of the violin diagram used in the study is given in Fig. 11.6 [40]. Fig. 11.6 Statistics of the violin diagram

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3.2 Metaheuristic Optimization Algorithms Metaheuristic optimization algorithms are designed to solve complex optimization problems without requiring any initial values. One of the main advantages of these algorithms are their ability to find the approximate global solution by exploring many directions without getting stuck in a local optimum. This is achieved through a randomization process that introduces diversity into the search process, allowing the algorithm to escape from local optima. It has been successfully used in various fields, including engineering, economics, and computer science [41].

3.2.1

Harmony Search Algorithm (HS)

The HS is a robust metaheuristic optimization algorithm based on the principles of musical harmony [42]. It was first introduced in 2001 by Geem et al. as a metaheuristic optimization algorithm inspired by the process of musicians improvising to find the best harmony during a musical performance. Figure 11.7 displays a detailed flowchart outlining the steps of the HS algorithm. The HS algorithm works by maintaining a set of solutions for number of design variables (NVar), called the harmony memory (HM), which is updated at each iteration (iter) to improve the quality of the solutions. The HS algorithm generates new candidate solutions by combining existing design variables in HM whose row number is defined as harmony memory size (HMS). Harmony memory consideration rate (HMCR) and pitch adjusting rate (PAR) parameters play important roles in the improvisation of a new solution vector (NCV). If HMCR is smaller than the random number (ran) ranging between [0,1], the existing solution may update its value with a new one from HM (with the possibility of HMCR). Otherwise, the new solution is taken from the design space (DS) with the possibility of 1-HMCR. In the case of selecting the new solution from HM, it is checked whether the NCV value is replaced by its nearest lower and upper neighbours according to the possibility of PAR or 1-PAR. It is similar to how musicians might create new harmonies by combining existing musical notes since the musician performs a note from memory or a note near to in his/her mind. End of this improvisation process, the NCV quality is assessed according to objective function value. This value is added to the harmony memory matrix only if it is superior to the lowest value of the harmonic vector in the matrix, and this lowest value is replaced by the new value. Until the current iteration number reaches the maximum iteration number (max-iter), the improvisation of NCV and updating HM continue.

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Fig. 11.7 The flowchart of HS algorithm

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Artificial Bee Colony Algorithm (ABC)

Karabo˘ga [43] proposed the ABC algorithm as a metaheuristic optimization algorithm based on swarm intelligence promoting communication between individuals in the population to ensure survival and meeting basic needs such as nutrition, defence, and migration. In Fig. 11.8, the flowchart of ABC algorithm is presented, including steps and mathematical formulations [44]. The ABC algorithm begins with the definition of population size (NPop), number of food sources (NFS), and limit parameters, as well as the determination of initial food sources (xij ) for design variable (N). Employer bees are then dispatched to the food source to assess the fitness value (fitnessi ) of the food source by generating a new food source (vij ) in the vicinity of the current food source. After the fitness value of the new food source is determined using the objective function value (fi ), the better food source is selected between xij and vij , taking into account the calculated fitness value using greedy selection. If the new food source does not have a better fitness value, the solution failure counter is incremented by one. However, if the food source with a better fitness value is selected and memorized, a new solution is developed, and the solution failure counter is reset. The employed worker bees then share information about the food sources they discover near the hive with the onlooker bees, who choose their food source based on the nectar amount, location, and quality of the food sources. The onlooker bees consider the probability value (pi ) calculated based on the fitness value of the food source during the selection process. If the randomly generated number (Øij ) falls in the range [0,1] and is greater than pi , onlooker bees generate a new food source (vij ) like worker bees. The nonsolution counter is updated depending on whether the new food source is better or worse than the old food source, and this process continues until all onlooker bees are dispatched to food sources. The worker and onlooker bees continue their cycles until it is determined, by checking the non-solution counter, whether the nectar in a food source has run out. If the solution development counter exceeds the limit value, the food source is abandoned, the employed bee becomes a scout bee, and the process of searching for a random food source commences. This loop continues until the current iteration number reaches the maximum number of iterations, after which the algorithm terminates.

3.2.3

Particle Swarm Optimization (PSO)

The PSO algorithm was introduced by Kennedy and Eberhart in 1995 [45] as a swarm intelligence-based algorithm inspired by social metaphors such as flocks of fish and birds. The PSO algorithm is a meta-heuristic optimization technique that mimics the communication and foraging behaviors observed in animals. In the PSO algorithm, each individual in the swarm is represented as a particle that adjusts its position by utilizing its previous experience to attain the best position

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Fig. 11.8 The flowchart of ABC algorithm

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in the swarm, ultimately resulting in the optimal target value. Figure 11.9 illustrates a summary flowchart of the PSO algorithm. The PSO algorithm employs a set of parameters, namely c1 , c2 (accelerate constants for local and global, respectively) ω (inertia weight), NPop (population size), and the maximum number of iterations, to conduct an iterative search for an optimal outcome. Initially, the algorithm generates random positions and resets the initial velocity for each particle. Subsequently, the algorithm evaluates the objective function value in the problem definition for each particle. Based on the updated objective function value, the algorithm determines the best solution for both the individual and the swarm. The algorithm updates the velocities and positions of the individuals

Fig. 11.9 The flowchart of PSO algorithm

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over time by taking into account the values of c1 , c2 , and ω. The objective function value is calculated by considering the updated speed and location information while also ensuring adherence to the constraints. The algorithm operates until the stopping criterion, which is reaching the maximum number of iterations, is met. It is repeated until the best solutions for the individuals and the optimal solution for the swarm are obtained in each iteration.

4 Implementation of Hybrid Optimization Algorithms In this section, the employed datasets of lake-water levels of Lake Bey¸sehir and pile group bearing capacity for obtaining optimal values of γ and α to implementation of hybrid optimization algorithms, and design optimization problem are explained in detail.

4.1 Hybrid Optimization Algorithms In this study, hybrid optimization algorithms versions which are obtained by combining a metaheuristic optimization algorithm and a machine learning algorithm have been improved. While the LSSVR method has been considered as a machine learning algorithm, the HS, ABC, and PSO algorithms have been used as metaheuristic optimization algorithms given in Figs. 11.7 , 11.8, and 11.9, respectively. Improved hybrid algorithms named LSSVR-HS, LSSVR-ABC, and LSSVR-PSO have been implemented to the data sets of LL and PG problems given in this section to optimize the kernels parameters (γ and α) of the LSSVR. Figure 11.10 illustrates the flowcharts of hybrid algorithms by explaining the implementation of metaheuristic optimization algorithms with the LSSVR method.

4.2 Dataset of Lake Level(LL) In this study, forecasting of monthly lake-water levels are investigated by using four different metaheuristic optimization algorithms and LSSVR for forecasting one month ahead of water levels of Lake Bey¸sehir. The data sample consists of a 73-year (1950–2022) record of average lake-water level (m). 75% of all data is used for the training phase and 25% of the remaining and more recent data are used for the testing phase. Basic statistics of training and test data are given in Table 11.1.

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Fig. 11.10 The flowchart of hybrid algorithms

Table 11.1 Statistical information for LL problem Data set

Period

Mean

Minimum

Maximum

Standard deviation

Kurtosis coefficient

Skewness coefficient

All

1950–2022

1123.13

1121.03

1125.50

1.009

−0.862

0.265

Training

1950–2004

1123.30

1121.03

1125.50

1.034

−1.035

0.079

Testing

2004–2022

1122.67

1121.15

1124.63

0.762

−0.169

0.333

Lake-water levels from the past months (lag times) are used as input data in design problem modelling. Correlation, autocorrelation, and partial correlation analyses are performed in the literature for the number of inputs. In this study, the relationship between the data at T time and the data at T-N months is examined with autocorrelation graphs and correlation (Figs. 11.11 and 11.12). The autocorrelation graph shows that the data in the time series have strong relationships with the data in the past months. This relationship shows a decreasing trend until the 8th month and then increases until the 12th month. After the 12th month, it decreases again and the similar periodicity continues. In the study, the data up to the

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Fig. 11.11 Autocorrelation graph

Fig. 11.12 Correlation graph of LL

12th month, which is the last period of the increase, are used as input data of this study. Similarly, Fig. 11.11, the correlation graph in Fig. 11.12. shows strong and increasing correlations up to 12 months. In addition, the correlation between T and T-N months can also be seen. As a result, when both graphs were examined, it is seen

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that there is a strong relationship between the data of the past month up to 12 months and the data at time T. For this reason, a prediction model with 12 inputs from the 1st to the 12th month and 1 output that expresses the same T in the modelling is established in the study.

4.3 Date Set of Pile Group (PG) In the synthetic dataset of the pile group, input parameters of angle of internal friction (Ø), unit volume weight (γk ), pile diameter (D), pile length (Lk ), and space between pile center to center (S) are taken as input parameters to predict bearing capacity of pile group (Qg). A dataset consisting of 1200 data is created by utilizing values within the range of the lower and upper bounds of input parameters shown in Table 11.2. Based on the prescribed input parameters, Eq. 11.3 has been employed to calculate the bearing capacity of a pile group, yielding a total of 1200 distinct values. 75% and 25% of the 1200 data are used in the training phase and testing phase, respectively. It is suggested that the application of normalization in case of existing big differences in the ranges of different features [46]. For instance, normalization is useful because pile group bearing capacity and pile diameter features have different units and magnitudes. Pile group bearing capacity is typically measured in kilopascal (kPa), while pile diameter is measured in meters (m). Without normalization, the pile group bearing capacity could have a much larger range of values than the pile diameter, which could lead to bias in the analysis. To provide a similar scale between [0–1] for all features and output parameter, the data set was normalized using including min–max scaling (Eq. 11.14). '

X =

X − X min X max − X min

(11.14)

Table 11.3 presents the descriptive statistics of datasets for all, training, and testing. A correlogram which is a graphical representation of a correlation matrix is shown in Fig. 11.13 to identify patterns and relationships between features and output. Table 11.2 Data set property

Features

Lower–upper bounds

Ø

30–36°

γk

18–20 kN/m3

D

0.80–1.40 m

Lk

15-30 m

S

2.5D-3.5D

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Table 11.3 Statistical information for PG problem Data set

Data

All

1200 0.3473 0

Mean

Minimum Maximum Standard Median Kurtosis coefficient Skewness coefficient deviation 1

0.2271

0.3192

-0.6293

0.5144

Training 900

0.3472 0

1

0.2270

0.3132

-0.6713

0.5141

Testing

0.3476 0.0044

0.9805

0.2278

0.3276

-0.4938

0.5181

300

Fig. 11.13 Correlation graph of PG

While dark colored or close to 1.0 show strong correlation, light colored or close to 0.0 means that correlation is weak or uncorrelated. Also, values greater than 0.0 corresponds positive effect, and values smaller than 0.0 have a negative effect.

4.4 Design Optimization Problem As beforementioned, in this study, the LSSVR method is used to occur the hybrid versions with metaheuristic optimization algorithms which are the HS algorithm, ABC algorithm, and PSO algorithm, to optimize the kernels parameters (γ and α) that are used on the prediction model for both design problems of LL and PG. Design space (DS) by using different γ and α values ranging between [1, 100] both of them have been formed for the design optimization problem of improved hybrid solution models. The quality of initial solutions or new solutions generated randomly corresponds to objective function of the design optimization problem. Since achieving the optimum values of the parameters of LSSVR depends on the test performance of the model trained for the data sets used, the evaluation metrics given in Eqs. 11.5 to 11.13 has been considered as the objective function and constraints. Design variables, objective function, and constraints of the optimization problem are demonstrated in Eq. 11.15.

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In accordance with the provided equation, the summation of all evaluation metrics constitutes the objective function, whereas each individual metric is considered a distinct constraint. [ ]T → Design variables:− x = γ, α Minimize: → f(− x ) = R 2 + SS E + M S E + M RS E + R M S E + M AE + M A R E + V AF/100 + E Subject to: → g (− x ) = [SSE MSE MRSE RMSE MAE MARE] [1−6]

→ g[7−9] (− x ) = [1 − VAF/100 1 − E 1 − R2 ]

(11.15)

Deb’s rules which is a simple and intuitive way to evaluate the feasibility of a solution with respect to its constraints were utilized as the constraint-handling technique during the optimization procedure [47]. In this process, constraint values that don’t satisfy limits and is not equal to zero, are summed and a penalty value is obtained for each solution. To determine the optimal solution in the implementation of Deb’s Rule, three principles are employed the ensuing; (i) a feasible solution is preferred to an unfeasible one, (ii) if both designs have suitable constraints, then the design with a better objective function value is preferred, (iii) if neither design is feasible, the design with lesser constraint violation is preferred among the two. In determination of the optimum algorithms parameters for HS, ABC, and PSO algorithms like HMS, HMCR, PAR, nPop, NFS, MR, c1 , c2 , and w, pressure vessel design (PVD), which is one of the well-known benchmark engineering design problems, has been employed [48]. It is a common complex engineering design optimization problem that involves determining the minimum cost of a pressure vessel, which takes into account factors such as material, forming, and welding, while also satisfying constraints such as the thickness of the heads and shell, prescribed working pressure values, volume, and the length of the shell section (excluding the head). In this particular case, the design variables are the thicknesses of the shell (Ts ) and head (Th ), the inner radius (R), and the length of the cylindrical section of the vessel. Many trails have been conducted considering suggested values for HS [49], ABC [44], and PSO [50] algorithm parameters in the literature. Considered algorithm parameters for these analyses are given in Table 11.4. Obtained optimum results according to values in Table 11.4 are tabulated in Table 11.5.

Modeling Civil Engineering Problems via Hybrid Versions Table 11.4 Metaheuristic algorithm parameters

221

Metaheuristic Algorithm

Algorithm parameters

HS

HMS: 20, HMCR:0.95, PAR:0.40,

ABC

NPop: 50, NFS:NPop/2, limit: NFSxN, MR: 0.40

PSO

NPop: 50, c1 : 1.9, c2 : 2, w: (MaxIter-iter)/MaxIter

Table 11.5 Optimum values and comparison of the best solutions in literature for PVD problem Optimum solutions

Ts

Th

R

L

f(x) ($)

HSPS

0.8022

0.3961

41.2146

188.0063

5975.2258

ABCPS

0.8615

0.4245

44.4230

149.8970

6067.2776

PSOPS

0.778391

0.384759

40.3312

199.839

5886.1585

Kannan and Kramer [51]

1.2500

0.6250

50.000

120.0000

7198.2000

Deb [52]

0.9375

0.5000

48.3290

112.6790

6410.3810

Coello [53]

0.8125

0.4375

40.3239

200.0000

6288.7445

Çarba¸s and Saka [54]

0.8125

0.4375

42.0984

176.6366

6059.7143

PS: Present Study

5 Hybrid Optimization Algorithms Results 5.1 Optimization Analyses Improved hybrid algorithms (LSSVR-HS, LSSVR-ABC, LSSVR-PSO) have been applied for 1000 maximum iterations (MaxIter) and 30 independent run numbers for all optimization analyses. The Tables 11.6 and 11.7 present the statistical assessments obtained from optimization analyses that have fulfilled the prescribed constraints for the LSSVR-HS, LSSVR-ABC, and LSSVR-PSO algorithms for LL and PG problems, respectively. In Tables 11.6 and 11.7, there are differences between the results statistics of 30 runs and the best run. This difference shows the performance improvement of the models in reaching the optimum level. When the methods are compared, both problems show slightly differences. In this case, it can be interpreted that all three optimization techniques successfully support each other and give consistent results. In Figs. 11.14 and 11.15, fmin objective function values of 30 runs and the iteration history graph of the best run are demonstrated, respectively. Furthermore, optimal solutions of the LL problem in Fig. 11.16 and the PG problem in Fig. 11.17. are given for different hybrid algorithms. In Fig. 11.14., as the iterations change in HS for both problems, the feature of searching for the best shows more variation compared to HS and ABC. It is also seen that PSO responds less to iteration change. In Fig. 11.15, the fmin change of

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Table 11.6 Statistical results for fmin optimum values of 30 runs Problem

Hybrid algorithm

LSSVR-HS

LSSVR-ABC

LSSVR-PSO

LL

Best

3.58263571

3.58005481

3.58005481

PG

Mean

5.02602678

3.59714006

3.58005481

Worst

6.31815550

3.77392104

3.58005481

StD

0.85452026

0.04597511

0.00000000

Median

5.20494421

3.58005481

3.58005481

Best

3.04532573

3.04518859

3.04518859

Mean

3.08221120

3.04528597

3.04518859

Worst

3.14777058

3.04758083

3.04518859

StD

0.03385287

0.00043865

0.00000000

Median

3.06616057

3.04518859

3.04518859

Table 11.7 Statistical results for fmin optimum values of iterations for best run Problem LL

PG

Hybrid algorithm

LSSVR-HS

LSSVR-ABC

LSSVR-PSO

Best

3.58263571

3.58005481

3.58005481

Mean

3.59449892

3.58814613

3.58955693

Worst

3.78035587

3.95117693

5.88002689

StD

0.04719249

0.05233472

0.10416052

Median

3.58263571

3.58005481

3.58005481

Best

3.04532573

3.04518859

3.04518859

Mean

3.04534923

3.04554556

3.04535304

Worst

3.04767603

3.07543725

3.11206087

StD

0.00023503

0.00302603

0.00225448

Median

3.04532573

3.04518859

3.04518859

best run according to iteration is shown. For both problems, asymptotic change is observed after 20 iterations. Therefore, there was no need for modeling over 100 iterations. When the iteration reaches 20, significant fmin decreases are seen in both problems. Although the increase in the iteration of the problems did not show very large decreases for the HS and ABC models, the increase in the iteration for the PSO decreased the fmin value. In Figs. 11.16. and 11.17., the two kernel parameters of the LSSVR model are shown in three dimensions, with α approaching 1 and γ approaching 100 as the solution that gives the least error. While the hybrid models approach these parameters, the variable distribution is seen in LSSVR-HS, followed by LSSVR-ABC, and the model that differs least or generally remains constant in its estimation is observed as LSSVR-PSO.

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5.2 Performance of Hybrid Algorithms In the optimization analyses, the evaluation metrics given in Eqs. 11.5 to 11.13 have been considered as design constraints. The mean of 30 runs for 9 evaluation metrics obtained using hybrid algorithms which are LSSVR-HS, LSSVR-ABC, and LSSVR-PSO is demonstrated in Table 11.8 and Table 11.9 for LL and PG problems, respectively. In Table 11.8 and Table 11.9, the acceptable results are obtained for both design problems. Although the success of LSSVR is known in the literature in estimating similar problems, reaching these solutions quickly and reliably with optimization algorithms is seen as the success of this study. For example, in the study performed with LSSVR in Lake Michigan in the USA, the RMSE MAE R2 parameters are 0.0427, 0.0332, and 0.9890, respectively [9]. Obtaining results close to these criteria in this current chapter study, although not directly showing the success of the model, can show the accuracy of hybridization.

Fig. 11.14 fmin optimum values for 30 runs

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6 Discussions In this section, the solution model performances are discussed with graphs obtained using various statistics. These graphs are very good at seeing small differences between models [55]. For example, the violin graph is a graph drawn according to the statistics in Fig. 11.6., and the observed data in the first row is represented, while the following graphs are drawn according to the results obtained in the best prediction models of the optimized kernel parameters (γ, α). The similarity between these drawings shows the model performances. Another graph is the Taylor diagram, which is obtained according to the observed data, correlation, RMSE (obtained by Eq. 11.8) relationship. The observed data in the graph are represented by the red dot positioned on the x-axis, and being close to this point indicates the success of the models. In Fig. 11.20, Violin plots of the best results are given for the LL and PG problems, and in Fig. 11.21 Taylor diagram are given for the same problems. The evaluation metrics of 30 runs using LSSVR-HS, LSSVR-ABC, and LSSVRPSO algorithms have been presented in Figs. 11.18 and 11.19 for the LL and PG problems, respectively. In the LL design problem, it is very difficult to see the difference between the methods visually. This situation is also observed in the Taylor diagram by placing

Fig. 11.15 fmin optimum values versus iteration for best run I

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Fig. 11.16 Optimum values of LL problem for 30 runs; a LSSVR-HS, b LSSVR-ABC, c LSSVRPSO

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Fig. 11.17 Optimum values of PG problem for 30 runs; a LSSVR-HS, b LSSVR-ABC, c LSSVRPSO

Modeling Civil Engineering Problems via Hybrid Versions Table 11.8 Evaluation metrics of optimum design for LL problem

Hybrid algorithm LSSVR-HS LSSVR-ABC LSSVR-PSO R2

0.995619

0.995639

0.995639

SSE

0.55516

0.55262

0.55262

MSE

0.00257

0.002558

0.002558

MRSE

0.003449

0.003442

0.003442

RMSE

0.050697

0.050581

0.050581

MAE

0.032621

0.032534

0.032534

MARE

0.000029

0.000029

0.000029

VAF (%) E

Table 11.9 Evaluation metrics of optimum design for PG problem

227

99.5585 0.946905

99.5605 0.947047

99.5605 0.947047

Hybrid algorithm LSSVR-HS LSSVR-ABC LSSVR-PSO R2

0.997648

0.997655

0.997655

SSE

0.036542

0.036436

0.036436

MSE

0.000122

0.000121

0.000121

MRSE

0.000637

0.000636

0.000636

RMSE

0.011037

0.011021

0.011021

MAE

0.007512

0.007494

0.007494

MARE

0.033469

0.033363

0.033363

VAF (%) E

99.76450 0.960714

99.7652 0.960811

99.76520 0.960811

the models on top of each other. HS and PSO algorithms are superior to the observed data with a small difference, especially in terms of mean, deviation and end data in the violin graph. This difference is observed more in low data. For the PG design problem, ABC and PSO algorithms perform very close to each other in the Violin graph, whereas in HS algorithm the differences are observed when the observed data is low value. However, it is also seen that HS algorithm predicts higher values closer to the observed values than ABC and PSO algorithms. According to the Taylor diagram, the most successful results are observed in ABC, PSO and HS algorithms, respectively.

7 Conclusions In this study, LSSVR, one of the machine learning methods, and HS, ABC and PSO, which are metaheuristic optimization algorithms, are used for LL and PG, two different design problems investigated and predicted in water resources field of civil engineering. Hybrid solution models are created by using optimization techniques

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2

R

SSE

MSE

MRSE

RMSE

MAE

MARE

VAF

E

Fig. 11.18 Evaluation metrics for 30 runs-based LL problem

to reach the optimum solution of the two kernel parameters (γ, α) of LSSVR. In this study, 75% of the observed or produced data for LL and PG prediction are used in the training phase and the remaining 25% is used in the testing phase. As evaluation metrics, 9 different evaluation metrics and various statistical graphs are used, and the following principal conclusions are deducted; • In the solution of engineering design problems, the hybrid models are obtained by integrating the LSSVR method with the HS, ABC and PSO algorithms, and it is seen that the evaluation criteria obtained with this novel solution models are mighty compatible with the literature.

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2

229

R

SSE

MSE

MRSE

RMSE

MAE

MARE

VAF

E

Fig. 11.19 Evaluation metrics for 30 runs-based PG problem

• The hybridization of LSSVR with metaheuristic optimization algorithms has transformed the time-consuming nested loops in modeling into meaningful loops, provided the solution of the model to be understood and added robustness to the solution model. • The top-performing hybrid solution models for the LL design problem are LSSVR-ABC and LSSVR-PSO, which achieved metric values of RMSE = 0.050581, MAE = 0.032534, and R2 = 0.995639.

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(a)

(b)

Fig. 11.20 Taylor diagram; a LL problem, b PG problem

(a)

(b)

Fig. 11.21 Violin graph; a LL problem, b PG problem

• Comparable to the LL design problem, LSSVR-ABC, and LSSVR-PSO hybrid solution models demonstrate outstanding performance in resolving the PG design problem. This is supported by their metric values of RMSE = 0.011021, MAE = 0.0074940.032534, and R2 = 0.997648, respectively. Moreover, the five main limitations of this study can be stated as follows; (i) the use of 73 years of actual data in the estimation of lake-water levels, which is a researched topic in water resources engineering, (ii) using 1200 synthetic data for pile group design, one of the researched topics in geotechnical engineering, (iii) the use of correlation and autocorrelation analysis for input selection, (iv) the usage of three different optimization techniques such as HS, ABC and PSO in the hybridization of LSSVR, (v) the use of visual comparison criteria in addition to 9 different evaluation metrics.

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Comparison of Multilayer Perceptron and Other Methods for Prediction of Sustainable Optimum Design of Reinforced Concrete Columns Yaren Aydın, Gebrail Bekda¸s, Sinan Melih Nigdeli, Ümit I¸sıkda˘g, and Zong Woo Geem

Abstract Machine learning has become a popular science in recent years, as it produces concrete and fast solutions to solve many problems. The rapidly increasing world population and the developments in technology have caused large greenhouse gas emissions. The harmful effects of carbon dioxide emissions from cement in concrete on climate change and global warming are quite remarkable. In this study, the most commonly used machine learning (ML) models in the literature were used for CO2 minimization of reinforced concrete columns. Harmony search was employed to find the optimum dataset for machine learning. The performances of these algorithms were compared and the best algorithm was tried to be found. As a result of all, it is observed that Multilayer Perceptron (MLP) has higher performance than other algorithms. The R2 of the MLP is 0.999. According to this result, it was observed that MLP is the most successful ML model in the design of eco-friendly reinforced concrete columns. Keywords Machine learning · Reinforced concrete · CO2 emission · Columns · Harmony search Y. Aydın · G. Bekda¸s (B) · S. M. Nigdeli Department of Civil Engineering, Istanbul University - Cerrahpa¸sa, 34320 Avcılar, Istanbul, Turkey e-mail: [email protected] Y. Aydın e-mail: [email protected] S. M. Nigdeli e-mail: [email protected] Ü. I¸sıkda˘g Department of Informatics, Mimar Sinan Fine Arts University, 34427 Si¸ ¸ sli, Istanbul, Turkey e-mail: [email protected] Z. W. Geem College of IT Convergence, Gachon University, Seongnam 1342, South Korea e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Bekda¸s and S. M. Nigdeli (eds.), Hybrid Metaheuristics in Structural Engineering, Studies in Systems, Decision and Control 480, https://doi.org/10.1007/978-3-031-34728-3_12

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1 Introduction As a result of the unplanned and uncontrolled use of resources in the world, resources are consumed rapidly and irregularly. This creates the problem of not being able to leave a livable environment to future generations. Developing technology for people to have more comfortable living conditions brings more energy consumption [1]. As a result of the rapidly increasing production in the world after the industrial revolution, rapid growth and development have occurred in countries that have adapted to the industrialization process. Especially in the twentieth century, the increase in both quantity and quality of needs has led to the emergence of new inventions and technological developments. As a result of this process, the natural environment and resources have started to be polluted; nature has started to have difficulty coping with this pollution [2]. In addition to the increase in the world population, the increase in the standard of living in developing countries has led to a significant increase in total world energy production in the recent period. Climate change is the statistical or systematic change in the average behavior of precipitation, temperature, wind, and pressure over a certain period. Human impacts affect global climate elements and this is interpreted as climate change [3]. Between 2015 and 2022, the temperature reached the highest levels due to the continuous increase in the number of greenhouse gases and heat accumulation [4]. Extreme heat waves and droughts adversely affected many people [5]. Since the industrial revolution until today, greenhouse gases released into the atmosphere have been increasing with various human activities such as the burning of fossil fuels and industrial development. Due to this increase, the temperature increase in the earth and the lower layers of the atmosphere is called global warming [6]. In the 5th assessment report of the IPCC (Intergovernmental Panel on Climate Change) [7], it was reported that carbon dioxide (CO2 ), methane (CH4 ), and N2 O concentrations in the atmosphere have increased unprecedentedly in the last 800,000 years. Carbon dioxide (CO2 ), methane (CH4 ), and nitrous oxide (N2 O) are greenhouse gases (GHGs). Increases in the level of greenhouse gases lead to higher amounts of solar radiation being absorbed which causes climate change [8]. In terms of the greenhouse effect, it has been reported that the effect of CO2 on a rapid increase in Earth’s average surface temperature and climatic change is 60% [7]. Methane is the second largest greenhouse gas causing climate change. Extraction and processing of fossil fuels, collection, and disposal of municipal solid wastes, wastewater plants produce methane gas [9]. Nitrous oxide (N2 O) is one of the greenhouse gases that cause global climate change and also damages the ozone layer [10]. Table 1 represents the greenhouse gases and their contributions. From the table, it can be seen that carbon dioxide has the highest impact and is highly man-made than others. So, efforts should be made to minimize carbon dioxide emissions. The concentration of carbon dioxide in the atmosphere is monitored by the number of particles per million units (ppm). The value of 300 ppm was never exceeded in the world until 1950. In 2013, CO2 levels surpassed 400 ppm for the first time in

Comparison of Multilayer Perceptron and Other Methods for Prediction … Table 1 Greenhouse gases and their contributions [11]

Greenhouse gases

237

Greenhouse effect (%)

Natural (%)

Man-made (%)

Water vapor

95.000

94.999

0.001

Carbon dioxide (CO2 )

3.618

3.502

0.117

Methane (CH4 )

0.360

0.294

0.066

Nitrous oxide (N2 O)

0.950

0.903

0.047

Misc. gases

0.072

Total

1

0.025 99.72

0.047 0.28

recorded history. The rapid increase in the record amount of carbon dioxide in the atmosphere after the 1950s has made the impact of the industrial revolutions even more evident [12]. Carbon dioxide is a tasteless, colorless, odorless, non-combustible, and weakly acidic gas with the chemical formula CO2 . It is heavier than air. The amount of carbon dioxide in the atmosphere is 0.03%. Carbon dioxide production is made from natural underground outlets and chemical methods in factories. Carbon dioxide can be liquefied and solidified at high pressure and temperatures [13, 14]. The increase in world energy consumption leads to an increase in CO2 emissions and global warming [15]. The International Energy Agency [16] reports that the current trend in energy supply and use is unsustainable from economic, environmental, and social perspectives and that energy-related carbon dioxide CO2 emissions will more than double by 2050 unless decisive and lasting measures are taken, and that increasing oil demand will raise security concerns in oil-supplying countries [17]. The increase in CO2 emission increases environmental pollution and causes deterioration of climatic and environmental natural balance with global warming. Because the cost of environmental degradation in the long term causes an unsustainable situation in economic and social terms, causing the destruction and even depletion of natural resources. The damage to natural resources limits the livable environmental conditions of both present and future generations. Therefore, CO2 emissions of countries are a major cause of concern in terms of global warming [18]. Intense carbon emission prevents the sun’s rays from reflecting back to the earth and causes an increase in temperature. Considering this situation, climate and environmental problems are increasing day by day [19]. One of the activities carried out to raise awareness about the increase in carbon dioxide concentration in the atmosphere in the last century is the calculation and reduction of carbon footprint. Carbon footprint is the gas emission represented directly or indirectly in the production and consumption activities of individuals or organizations. it is measured by calculating carbon dioxide emissions [20]. In addition to the reasons mentioned above, the construction sector is also a sector that causes environmental problems. Mankind has been using concrete as a material in buildings for a very long time. Concrete is the most consumed material after water

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in the world because it is easy to shape, though to environmental influences, low-cost, and practical to use and produce [21, 22]. Concrete is obtained by mixing cement homogeneously with sand, gravel, and water [23]. As in every field, changes have occurred in concrete over the years. To overcome the disadvantages of concrete such as low tensile strength and brittleness, concrete is often used in combination with steel reinforcements. By eliminating the disadvantages of concrete, which is a cheap material, and steel, which is an expensive material, a composite material, reinforced concrete (RC), has emerged with adherence and a usable material has been obtained. In reinforced concrete, steel reinforcement resists tensile effects and ensures the ductile behavior of the material. Concrete with high compressive strength prevents buckling around the reinforcement and protects the material [23]. Cement is the raw material for concrete, the most widely used man-made material on earth. Since the cement is used in concrete, the use of cement has also become widespread and has become an important issue. The use of cement increases the emission of carbon dioxide (CO2 ) into the atmosphere. Cement in concrete is an important source of carbon dioxide (CO2 ) emissions [24]. For this reason, studies to be carried out to reduce carbon emissions in the cement sector are important for a livable world. Since the amount of carbon dioxide emission is higher in the cement sector, the environmental impact is greater [25]. Table 2 presents that China takes first place in cement production. India follows China. Cement is the source of carbon dioxide emission approximately 8% of the carbon dioxide emission [24]. In reinforced concrete (RC) structures, reinforced concrete columns are one of the most important structural systems under earthquake loads. Columns in reinforced concrete structures are vertical bearing elements. It enables the structure to survive Table 2 Cement production by selected countries (in metric tonnes) [26, 27] Countries

2018

2019

2020

2021

2022

China

2,200,000

2,200,000

2,400,000

2,500,000

2,100,000

Brazil

53,000

55,000

61,000

65,000

65,000

China

2,200,000

2,200,000

2,400,000

2,500,000

2,100,000

USA

87,000

89,000

89,000

92,000

95,000

Egypt

81,200

76,000

42,000

40,000

51,000

India

300,000

320,000

295,000

330,000

370,000

Indonesia

75,200

74,000

65,000

66,000

64,000

Iran

58,000

60,000

68,000

62,000

62,000

Japan

55,300

54,000

51,000

52,000

50,000

Korea, Republic of

57,500

55,000

48,000

48,000

50,000

Russia

53,700

57,000

56,000

56,000

62,000

Turkey

72,500

51,000

72,000

76,000

85,000

Vietnam

90,200

95,000

98,000

100,000

120,000

Other countries (rounded)

870,000

900,000

760,000

810,000

850,000

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both under vertical loads such as building weight and under horizontal effects such as earthquakes. It is one of the most critical elements in terms of building safety. Reinforced concrete columns have high axial strength, stiffness, and a high damping ratio. Columns are the elements that ensure the safe transfer of vertical loads to the ground and the carrying of horizontal loads, especially in buildings without reinforced concrete shear walls or cross members. Any problem that may occur in the design and/or manufacturing of the columns may jeopardize the safety of the structure by itself [28]. There are square, rectangular, and circular types of columns. The seismic resistance of the circular column may be better than the rectangular column. A rectangular or square section is easier to construct than a circle [29]. From Fig. 1, the geometry of an RC rectangular column where the section width and height, and the lateral and longitudinal reinforcements can be seen. b is the section width, h is the section height and L is the total length of the column. The increasing threat of global warming and climate change in the world has led researchers to CO2 minimization in civil engineering applications. Paya-Zaforteza et al. [30] used a metaheuristic algorithm for minimizing the CO2 of a reinforced concrete building frame. The methodology they used proved that an environmentally friendly way can be followed in RC structural design. Yepes et al. [31] applied optimization designs for minimizing CO2 emissions of reinforced concrete retaining walls. The analyzes have shown that the reduction in cost and CO2 emissions are in parallel. Camp and Huq [32] used hybrid optimization for designing reinforced concrete frames with minimum cost or CO2 emission. With the algorithm used, they produced both economical and environmentally friendly designs

Fig. 1 Geometry of RC column

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by reducing construction costs and CO2 emissions. Purnell [33] stated that CO2 emission can be reduced by adjusting the normal mix design parameters of concrete and that reinforced concrete beams contain significantly lower carbon than steel or wood composite beams. De Medeiros and Kripka [34] adopted an optimization algorithm to optimize the financial cost and environmental costs (CO2 emissions, energy consumption, etc.) of reinforced concrete columns. The results show that with the minimization of financial costs, there is a decrease in environmental costs. Destrée and Pease [35] compared a type of steel fiber-reinforced concrete with conventional concrete flooring systems. The results showed that the steel fiber-reinforced concrete type reduced CO2 emissions by 40.5%. Yepes et al. [36] optimized the cost and CO2 emissions of precast–prestressed concrete road bridges. The analysis showed that optimal cost can cause reduce CO2 . Yeo and Potra [37] carried out optimization approaches with the view to allow decision makers to sustainable and economic design of reinforced concrete structures. The optimized CO2 footprint design resulted in 5 to 10% fewer emissions than the cost-optimized design. Kaveh and Ardalani [38] utilized an optimization algorithm to minimize the amount of CO2 emissions of RC frames. The results show that the CO2 emission of reinforced concrete frames can be reduced by slightly increasing the cost. Wang et al. [39] explored the concrete manufacturing process’s potential effect on global warming. According to the results, while under different functional units, the environmental performance of composite and cast-in-situ floors varies. Zhu et al. [40] suggested that variations in the span of RC slabs affect environmental sustainability. The study showed that composite slabs are commonly preferred in engineering for eco-friendly sustainability. Paik and Na [41], dealt with CO2 emissions by using a different slab system instead of a normal reinforced concrete slab. The result showed that the void slab system has 34% less emission than the ordinary RC slab. Kayabekir et al. [42] applied a multi-objective harmony search optimization method for analyzing the eco-friendly and cost-effective design of reinforced concrete cantilever retaining walls. Their approach performed well to find both economic and ecological results. Arama et al. [43] introduced parametric modeling of military pile walls based on CO2 and cost optimization by the optimization algorithm. As a result of the analyses, both cost and CO2 emission were minimized. Cakiroglu et al. [44] optimized the CO2 emission of concrete-filled steel tubular columns. The results showed that concretes of the lower concrete class are more economical and environmentally friendly. Cakiroglu et al. [45] compared different concrete classes according to minimum CO2 emissions from a metaheuristic algorithm. In their study, it was observed that high compressive strength concretes increase CO2 emissions. Bekda¸s et al. [46] used a methodology to minimize the CO2 emission of reinforced concrete beams. As a result of their work, using recycled members provides a sustainable design. Yücel et al. [47] studied to reduce the carbon emission and total cost of reinforced concrete beams. As a result of their study, it was seen that the use of C25 and C30 concrete is more advantageous both environmentally and economically. Bekda¸s et al. [48] applied an optimization process to generate an eco-friendly and cost-effective structural model for a posttensioned axial symmetric reinforced concrete cylindrical wall. It was found that increasing the number of post-tensioning loads in the optimum design reduces CO2

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emissions. Aydın et al. [49] proposed optimization and machine learning pipeline for the prediction of an eco-friendly design. The results showed that the machine learning algorithms are effective in CO2 minimization. In the field of civil engineering, machine learning has been frequently used in sub-fields such as structures, geotechnics, hydraulics, construction management, and transportation. Structural engineering includes the framing of structures, their analysis, and the design of these structures to withstand the stresses, loads, and pressures of their environment and remain safe throughout their use. In 1989, Adeli and Yeh [50] used artificial neural networks (ANN) to design steel beams, which is one of the first applications of machine learning in structural engineering. Other applications of structural engineering are structure health monitoring, predicting failure mode and shear capacity of ultra-high performance concrete beams, evaluating flexural strength of concrete, predicting concrete compressive strength, estimation of optimum tuned mass damper parameters, and simulation of structural dynamics [51–55]. Due to the inherent complexity of soils and geotechnical materials, the use of machine learning to solve geotechnical estimation problems has become widespread. Machine learning applications in geotechnical engineering are CPT data interpretation, assessment of pile drivability, prediction of undrained shear strength, and estimation of deflections soil classification [56–60]. Hydraulics is generally concerned with the control and management of water resources. Machine learning applications are flow velocity prediction in alluvial channels, hydraulic fracturing pressure prediction, anomaly detection in dam behavior, predict the discharge coefficient of curved labyrinth overflows, and prediction of flood risks [61–65]. To follow a correct process in construction, parameters such as time and finance must be accurately estimated. Applications of ML in the field of construction management delay risk prediction, assessment of defect risk, predicting preliminary factory construction cost, predicting the occurrence of construction disputes, and prediction of accident construction [66–70]. In the transportation field; traffic prediction, detection of cracks in road pavement, arrival time forecasting, forecasting transportation demand, and freight vehicle travel time prediction [71–75] are the applications of ML. The increasing threat of global warming and climate change in the world has led researchers to CO2 minimization. This study is aimed to provide CO2 minimization in optimum design of RC columns by using machine learning methods. In this chapter, it is mentioned that machine learning algorithms, a sub-branch of artificial intelligence, can be utilized for sustainable and environmentally friendly reinforced concrete column design. Section 2 provides detailed information about the materials used in this study and which methods will be used for these materials. In this study, analyses were performed for CO2 minimization using machine learning methods.

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2 Material and Methods The environmentally friendly structural design in this study consists of two stages. The first stage is to generate the data set through optimization algorithms. The second stage is a machine learning application in which bending moment (M) and axial force (N) are inputs and column section width (b), column section height (h) and section reinforcement area (As ) are outputs and predicted.

2.1 Generating a Dataset via Optimization Algorithm The dataset used in this study is generated via an optimization algorithm. The Harmony Search algorithm [76] is employed by MATLAB [77] for the optimal RC rectangular column dimensions and the total area of longitudinal reinforcement (As ) for a given bending moment and axial force to minimize CO2 emissions to ensure a sustainable structural design of reinforced concrete columns. The Harmony Search (HS) algorithm developed by Geem [76] was inspired by jazz musicians improvising to find better melodies. HS algorithm based on the principle of finding the best harmonic has been applied to many civil engineering optimization problems such as reinforced concrete structures [42, 43, 78–92], structural control [93–112], steel structures [113–115], and others [116–118]. Figure 2 shows the flowchart of HS. The aim is to minimize CO2 emissions. The objective function of this optimization problem is given in Eq. (1): min f (C O 2 ) = CC,C O 2 ∗ VS + C S,C O 2 ∗ W S

(1)

The descriptions of the constants used in Eq. 1 are given in Table 3. For each design variable in the optimal design problem, a valid range of values is defined. From these values, the search space for the design variables of the algorithm is created. Then the number of solution vectors of the memory matrix (HMS), the memory matrix consideration ratio (HMCR), the itch adjustment rate (PAR), and the maximum number of iterations are determined. Then, the matrix called harmony memory (HM) (Eq. 2) is filled with randomly generated variable values, and the corresponding objective function values are calculated. Here m corresponds to the number of design variables and the number of rows of the HMS. In the harmony memory matrix, the solution vectors are evaluated according to the objective functions. ⎡ ⎢ ⎢ HM = ⎢ ⎣

b1 h 1 A1s M 1 N 1 f (x 1 ) b2 h 2 A2s M 2 N 2 f (x 2 ) .. .. .. .. .. .. . . . . . . m m m ) bm h m Am M N f (x s

⎤ ⎥ ⎥ ⎥ ⎦

(2)

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Fig. 2 Flowchart of HS algorithm [119]

Table 3 Descriptions of the constants

Constants

Descriptions

CC,CO2

Carbon dioxide emission per unit volume

VC

The total volume of concrete

CS,CO2

Steel carbon dioxide emission per unit weight

Ws

Total weight of steel

In Eq. 2, M, N, b, h, and As are the bending moment, axial force, column width, column height, and the total area of the longitudinal reinforcement in the i-th solution candidate, respectively. Then, a new harmonic memory (HM) matrix is developed. In the harmonic search method, the generation of a new solution vector is controlled by the two main parameters of this method (HMCR and PAR) as shown in Eq. 3. HMCR is a probability value that directs the algorithm to select a value for a design variable either from the harmonic memory or from the set of all values. The aim here is to perform a more detailed search by providing transitions around a current solution. This phenomenon in the harmony search method is based on two is known as the adjustment between values (PAR). k is the randomly chosen existing solution (Eq. 3). k value in Eq. 3 is found in Eq. 4.

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Table 4 Details of the dataset Data Type

Variables

Min

Max

Mean

Standard deviation

Inputs Bending moment

float64a

100.003

399.806

237.550

81.593

Axial force

float64

1000.298

399.929

2387.248

831.938

Outputs Cross section width

float64

250

266.841

250.551

2.372

Cross section height

float64

310.392

1000

646.801

202.609

Total reinforcement area

float64

2127.295

7016.328

3615.801

1010.983

a float64:

64-bit double precision values [120]

{ X i,new =

) ( X i,min + rand() ( X i,max − X i,min ) i f H MC R > r1 X i,k + P A R X i,max − X i,min i f H MC R ≤ r1 k = ceil(rand ∗ H M S)

(3) (4)

In the last step, the new solution candidate is compared with the worst solution candidate in HM. The process of creating a new solution candidate is repeated until a predetermined stopping condition is met.

2.2 Data Description The data for his study is generated via the HS algorithm as mentioned in 2.1. By using the HS algorithm, b, h, and As values minimizing the total CO2 emission were obtained for each combination of M and N. Thus, a dataset of 4429 configurations has been generated via HS. Descriptive statistics of features and outputs of the dataset are shown in Table 4. Figure 3 is the histogram of the dataset. and M, N, h, and As variables (normal-like) are distributed. Moreover, b has a value of about 250 mm. Using the Seaborn [121] library of Python [122] programming language, the correlation matrix in Fig. 4 was generated. A value close to 0 indicates that there is no connection between these two variables. It can be seen that the lowest correlation between them were b and As .

2.3 Machine Learning Artificial intelligence is the technology of developing machines that are created entirely by artificial means without making use of any living organism and that can show human-like behaviors and movements [123]. Machine learning (ML), which

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Fig. 3 Histogram plot of the dataset Fig. 4 Correlation matrix

is a sub-unit of artificial intelligence, measures learning algorithms and the performance of these algorithms. It constitutes the scientific field of study that enables computer algorithms to learn like them based on the way people think [124]. Machine learning focuses on learning relationships from data using efficient computational algorithms. The convergence of mathematics and computer science stems from the unique computational challenges of building statistical models from massive datasets

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that can contain billions or trillions of data points [125]. ML can model complex systems quickly [126]. There are various methods used in the literature to apply machine learning. Suitable methods should be selected according to the variety and amount of data. Machine learning algorithms have 4 basic categories for their intended use [127]. In supervised learning, the dependent variable is predicted using one or more independent variables. Unsupervised machine learning algorithms are used when the data used for training is not labeled or classified. Semi-supervised learning algorithms use small amounts of labeled and large amounts of unlabeled data for training. Reinforcement learning aims to train a function that generates output depending on the feedback received from the environment using data [128]. As machine learning algorithms gain experience, their accuracy and efficiency improve. This enables algorithm developers to get better results and make low-error predictions for the future. Types of ML are shown in Fig. 5. In this study, supervised learning was used since the dependent variables were continuous. Regression was also used since the prediction was aimed. Regression is widely used in prediction [130]. The dataset used in this study has three outputs. Python [122] programming language, Anaconda3 [131] open-source distribution, and Spyder 5.2.2 are used. Scikit-learn library [132] is used for the ML process. The machine learning models used for an eco-friendly reinforced concrete design are described below.

Fig. 5 ML algorithms [129]

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2.3.1

247

Featured Machine Learning Models

Foundational: Simple linear regression is a model structure that examines the relationship between independent and dependent variables [133]. In decision tree regression, the numerical outcomes of the dependent variables are predicted by using a tree-based structure [134, 135]. The elastic net method is used to perform model selection and parameter estimation simultaneously in linear or logistic regression models [136]. KNN regression method is a regression method based on the average of k nearest neighbors [137]. The support Vector Regression method is aiming to find the function with the lowest generalization error [138]. Multilayer Perceptron (MLP): As a result of the failure of single-layer sensors in solving nonlinear problems, the concept of multilayer sensors has emerged. In multilayer perceptrons, the input layer consists of an input layer, a hidden layer, and an output layer. All layers are interconnected. There are transitions between the layers called backpropagation and forward propagation. In the backpropagation phase, the output and error values of the artificial neural network are calculated. To minimize the error value found in the backpropagation phase, the weight values of the connection between the layers are updated [139]. Figure 6 shows MLP architecture. Ensemble: Random forest (RF) is a supervised learning algorithm that can be used in classification and regression problems. RF is an ensemble learning method that combines the predictions of separately trained trees and makes new predictions by averaging these predictions [141]. Gradient boosting uses a sequential approach instead of building parallel trees to obtain predictions. Thus, in the gradient boosting method, all decision trees improve

Fig. 6 Multilayer Perceptron (MLP) [140]

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the error by predicting the error of the previous decision tree [142]. Histogram-based gradient boosting is a technique for training faster than gradient boosting for large datasets [143]. In the voting method, the class predictions made by a large number of different classifiers are subjected to voting, and the class with the most votes is presented as the class prediction of the community. The simplest voting scheme is plurality voting. According to this voting scheme, each base-level classifier casts one vote for its prediction. The sample is categorized into the class with the most votes [144]. Stacking consists of two levels of modeling. The first of these (often called submodels) are models based on a single algorithm and the second is a model responsible for combining the results provided by the sub-models to obtain a final prediction [145]. Stacking is based on accepting the predictions of different types of classifiers as inputs for the meta-classifier and producing a higher-performing prediction from these predictions [146]. Voting and Stacking can be scheme seen in Fig. 7. Extreme Gradient Boosting (XGBoost) is a machine learning technique based on gradient boosting and decision tree algorithms. XGBoost algorithm can be used very effectively in a large amount of data analyses since it has computational simplicity compared to other ML methods [149]. CategoryBoosting (CatBoost) is a gradientboosting application that uses binary decision trees as basic determinants [150]. Adaptive Boosting (AdaBoost), one of the most widely used boosting algorithms, is preferred more than other models thanks to its features such as having a higher prediction rate than other algorithms, using memory at a lower level than other algorithms, and being applicable [151].

(a) Fig. 7 The flowchart of a Voting and b Stacking method [147, 148]

(b)

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Fig. 8 Illustration of the multioutput regressor [157]

2.3.2

Multitarget Regression (MOR)

In this study, multioutput regression, also known as multi-target, multivariate, or multi-response regression in the literature, is used to estimate multiple real-valued output/target variables simultaneously [152–154]. Many studies have proved that multi-output regression methods generally provide better forecasting performance compared to single-output methods and preserve the relationship between outputs since the compound dependencies between outputs in single regression are ignored in multi-output methods [155, 156]. Figure 8 is the illustration of the multioutput regressor.

2.4 K Fold Cross Validation When separating the data set for the training and testing phase of learning algorithms, it can be separated in various ways. The important thing here is not to use the same data set for training and testing because after a while the algorithm may memorize the data set and accurate performance measurement may not be possible. In the k-fold cross-validation technique, the entire data set is divided into k subsets consisting of equal or nearly equal amounts of data. During the creation of the subsets, the data are randomized. Each of the subsets is run in turn as a test set, with the k-1 number of subsets being used as the training data set during each run. The model to be tested is run k times and the entire dataset is tested once. The advantage of the k-fold cross-validation technique is that all data is used once for training and testing purposes [158]. Since the most preferred k value in the literature is 10, 10 is taken in the study.

250 Table 5 Performance metrics for regression

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Constants

Descriptions

Coefficient of determination

R2 = 1 −

Root Mean Squared Error

RMSE =

Mean Absolute Error

M AE =

Mean Squared Error

MSE =

∑n (yi −xi )2 ∑i=1 n 2 i=1 (yi −x i )

/

∑n i=1

∑n

(yi −xi )2 n

i=1 |yi −x i |

∑n

n

i=1

(yi −xi )2 n

2.5 Performance Criterion Performance metrics are used to measure and compare the predictions made. Different methods are used to measure the suitability of the prediction methods to the data and the efficiency of the algorithms. Performance metrics that are widely used in the literature will be used in this thesis. In this study, 4 basic performance metrics used; determination coefficient (R2 ), root mean squared error (RMSE), mean absolute error (MAE) and mean squared error (MSE) performance criteria were used to evaluate the performance of the models in our study. The coefficient of determination (R2 ) expresses the part of the changes in the dependent variable that can be explained by the independent variable. R2 can take values between 0 and 1 [159]. The model is successful when the measured value of R2 is close to 1. Root Mean Squared Error (RMSE) takes into account the effect of error squares and is widely used to compare different estimation methods [160]. Mean Absolute Error (MAE) is the mean of the absolute value of each difference between the actual value and the predicted value [161]. Mean Squared Error (MSE) is the average squared difference between observed and predicted values [162]. The calculation of these metrics is shown in Table 5. n represents the number of predictions; yi , xi and x i represents the actual value for the ith observation, the predicted value for the ith observation, and the average of predicted values, respectively. Figure 9 gives a summary of the ML process in this study.

3 Results and Discussion As a result, the highest result was achieved with Multilayer Perceptron (MLP). The column data set created with the Harmony Search algorithm was converted into “.csv” format and prepared for use in the development environment. The data set was divided into 70% training and 30% test data, and the k-fold cross-validation method was used to minimize deviations and errors arising from the distribution of the data set as training and test data. For Multilayer Perceptron (MLP) model was scaled before being fed with the data and reinstated after the prediction.

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Fig. 9 A summary of the applied methodology

After training the algorithms, their performances were measured on the test data set. The determination coefficient (R2 ), root mean squared error (RMSE), mean absolute error (MAE), and mean squared error (MSE) were taken into account. The obtained values are shown in Table 6 and discussed in this section. The most successful model parameters are shown among the models where the R2 value approaches 1 and the MSE value approaches 0. Different numbers of hidden layers and the number of processing elements in the hidden layer were selected for MLP. When examining the performance metrics of the Foundational methods, it is seen that Decision Tree has a high R2 and less RMSE, MAE, and MSE values but it is not good as MLP. ElasticNet has the least R2 , so it is the most unsuccessful foundational method in predicting. Among the Ensemble methods, Random Forest and CatBoost have high R2 (99.8%) values and fewer error values. AdaBoost has an R2 value of 0.964 but it is not performing well as other Ensemble methods. The highest R2 (99.9%)) and least RMSE, MAE, and MSE values belong to MLP. In various combinations of the Voting method, the increase in the R2 value with the addition of MLP compared to the other foundational methods shows again that MLP has the best performance among the foundational methods. In the Voting method, the highest performances are observed in combinations where boosting algorithms

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and MLP combinations are used together. The highest success in the combinations in Voting was achieved with MLP via a different number of combinations. In the Stacking method, the use of random forest and histogram gradient boosting as the final estimator gave very close results. In this method, combinations using them together have higher performance. However, the highest success in the combinations in Stacking was achieved with MLP. Table 6 Results of the ML algorithms Model

R2

NRMSE

NAME

NMSE

Foundational DecisionTreeRegressor

0.996

LinearRegression

0.550 245.971

202.094 170,863.191

ElasticNet

0.546 243.435

204.567 166,992.324

29.915

14.465

2505.221

KNeighborsRegressor

0.617 154.277

104.274

SVR

0.016 406.631

286.463 371,551.833

54,986.445

MLP* mlp1 hidden layer sizes (10,10)*

0.991

0.086

0.058

0.008

mlp2 hidden layer sizes (10,20)

0.993

0.078

0.051

0.006

mlp3 hidden layer sizes (10,10,15)

0.993

0.078

0.053

0.006

mlp4 hidden layer sizes (30,40,50)

0.995

0.064

0.043

0.004

mlp5 hidden layer sizes (10,20,30,40,50,60)

0.994

0.059

0.043

0.004

mlp6 hidden layer sizes (30,40,50)

0.995

0.066

0.043

0.004

mlp7 hidden layer sizes (10,20,30,40)

0.993

0.074

0.046

0.005

mlp8 hidden layer sizes (10,20,30,40,50)

0.994

0.069

0.042

0.004

mlp9 hidden layer sizes (100,100)

0.995

0.064

0.041

0.004

mlp10 hidden layer sizes (10,10)**

0.998

0.026

0.012

0.001

mlp11 hidden layer sizes (10,20)

0.999

0.026

0.012

0.0008

mlp12 hidden layer sizes (10,10,15)

0.998

0.027

0.012

0.0009

mlp13 hidden layer sizes (30,40,50

0.998

0.025

0.011

0.0007

mlp14 hidden layer sizes (10,20,30,40,50,60) 0.999

0.024

0.011

0.0008

mlp15 hidden layer sizes (30,40,50)

0.999

0.026

0.012

0.0008

mlp16 hidden layer sizes (10,20,30,40)

0.999

0.026

0.011

0.0009

mlp17 hidden layer sizes (10,20,30,40,50)

0.999

0.025

0.011

0.001

mlp18 hidden layer sizes (100,100)

0.999

0.027

0.011

0.0008

0.998

17.777

10.162

Ensemble RandomForestRegressor

840.449

HistGradientBoostingRegressor

0.997

20.212

12.456

1090.250

GradientBoostingRegressor

0.995

33.965

22.829

3406.932 (continued)

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Table 6 (continued) AdaBoostRegressor

0.964 106.479

88.300

CatBoostRegressor

0.998

15.207

10.012

30,811.579 622.920

XGBoostRegressor

0.997

14.492

14.034

1572.969

0.994

39.426

31.835

4288.886

Voting Combinations ab,cb,xgb ab,dtr,cb

0.994

39.932

32.055

4362.423

hgbr,rfr,gbr

0.998

19.921

12.868

1211.681

cb,xgb,knr

0.956

53.600

37.371

7064.303

mlp1,rfr,gbr

0.997

0.046

0.028

0.002

mlp2,rfr,gbr

0.997

0.045

0.026

0.002

mlp1,hgbr,gbr,mlp2

0.996

0.053

0.032

0.003

mlp1,hgbr,gbr,mlp18

0.997

0.0391

0.023

0.001

gbr,hgbr,rfr,mlp3

0.998

0.040

0.023

0.001

gbr, dtr,rfr,mlp4

0.998

0.038

0.021

0.001

lm,dtr,knr,svr

0.738 177.226

137.481

74,641.302

lm,dtr,ent,knr

0.790 148.851

120.047

59,889.432

lm,svr,rfr,hgbr

0.852 150.574

117.956

56,440.011

102.064

43,174.734

dtr,lm,hgbr,ent

0.886 123.958

dtr,rfr,hgbr,gbr

0.998

19.608

12.668

1155.584

ent, rfr,hgbr,gbr

0.968

62.278

53.828

12,587.107 5089.051

knr, rfr,hgbr,gbr

0.975

45.830

31.108

mlp1,dtr,rfr,mlp4

0.997

0.046

0.028

0.002

svr,lm,hgbr,rfr

0.852 151.568

118.307

56,129.966

lm,knr,svr,rfr

0.788 178.366

137.091

75,001.233

gbr,hgbr,rfr,ent

0.969

66.271

53.565

12,658.159

ab,cb,xgb,gbr

0.995

35.337

27.246

3353.604

gbr,cb,xgb,knr

0.975

44.725

30.351

5025.545

lm,cb,xgb,knr

0.910

91.406

71.826

21,844.489

gbr,hgbr,rfr,mlp3,mlp16

0.998

0.040

0.023

0.001

gbr, dtr,rfr,mlp4

0.998

0.038

0.021

0.001

gbr,dtr,rfr,mlp4,mlp15

0.998

0.032

0.016

0.001

148.981

86,171.159

ent,dtr,lm„knr, svr

0.722 186.811

ab,cb,xgb,gbr,knr

0.979

51.8133714

38.458

6770.1621

ab,cb,xgb,gbr,dtr

0.996

29.9054851

23.133

2629.4288

gbr,cb,xgb,knr,lm

0.941

75.4987471

59.041

mlp4,dtr,rfr,mlp18,hgbr

0.998

0.032

0.017

15,238.650 0.002 (continued)

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Table 6 (continued) mlp4,dtr,rfr,mlp14,hgbr

0.998

0.031

0.017

0.001

2547.112

Stacking Final Estimator = Gradient Boosting Regressor lm, dtr,ent,knr,svr

0.996

30.292

18.912

hgbr,gbr,rfr

0.998

17.952

11.102

881.042

gbr,hgbr,rfr,ent,lm,dtr,knr,svr

0.998

18.445

11.616

895.697 1550.0595

ab,xgb,ent

0.997

23.872

15.855

ab,cb,xgb

0.998

15.282

10.602

691.734

cb,xgb,dtr

0.998

15.633

10.740

689.732

mlp1,hgbr,gbr,mlp2

0.996

0.053

0.032

0.002

0.998

0.034

0.015

0.001

gbr,rfr,mlp4,mlp17 mlp1, hgbr, gbr,rfr,mlp4,mlp15

Final Estimator = Hist Gradient Boosting Regressor lm, dtr,ent,knr,svr

0.996

30.388

17.929

2840.752

hgbr,gbr,rfr

0.997

19.249

11.326

1028.443

gbr,hgbr,rfr,ent,lm,dtr,knr,svr

0.997

18.023

11.443

1021.252

ab,xgb,ent

0.997

24.457

15.418

1551.257

ab,cb,xgb

0.998

16.760

10.821

697.945 746.261

cb,xgb,dtr

0.998

16.540

10.533

mlp1, hgbr, gbr,dtr,rfr,mlp4,mlp17

0.998

0.030

0.014

0.001

mlp1, hgbr, gbr,rfr,mlp4,mlp17

0.998

0.036

0.015

0.001

Final Estimator = Random Forest Regressor lm, dtr,ent,knr,svr

0.996

30.151

18.697

2897.098

hgbr,gbr,rfr

0.998

18.106

11.824

939.706

gbr,hgbr,rfr,ent,lm,dtr,knr,svr

0.998

17.582

10.921

912.215

ab,xgb,ent

0.997

24.259

15.829

1663.914

ab,cb,xgb

0.998

16.421

10.817

706.292

cb,xgb,dtrr

0.998

16.380

10.326

718.070

mlp1,hgbr, gbr,rfr,mlp4,mlp15

0.998

0.026

0.011

0.001

Additional Hyperparameters: *MLPRegressor, activation = ‘tanh’,solver = ‘adam’, random_state = 0 **activation = relu, solver = ‘lbfgs’, random_state = 0

Finally, the success of machine learning algorithms in estimating the parameters of the eco-friendly reinforced concrete column was compared and it was seen that good performances can be obtained. Promising results have been obtained for the use of the algorithms used in the study for sustainable design.

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4 Conclusion In recent years, where carbon emission has been observed to be in a continuously increasing trend, the damages to national economies, climates, and human health should now be evaluated on a global scale. In this study, it is pointed to reduce the increasing CO2 emission due to various reasons such as technology and industrialization. This study was carried out since the CO2 emissions released to the environment in the production of reinforced concrete columns are very high due to the cement in the content of concrete. In this study, it is shown that machine learning techniques can be used to achieve CO2 minimization. A dataset of labeled data and different regression algorithms (Linear Regression, Decision Tree, K Neighbors, Elastic Net, Support Vector, Multilayer Perceptron, Gradient Boosting, Random Forest, Histogram Gradient Boosting, Adaptive Boosting, Category Boosting, Extreme Gradient Boosting, Stacking, Voting) were used in the study and the performance of the algorithms were compared using determination coefficient (R2 ), mean squared error (MSE), root mean squared error (RMSE) and mean absolute error (MAE). The dataset was generated with the HS algorithm and consists of 2 inputs, 3 outputs, and 4,429 rows. In the regression algorithms, bending moment (M) and axial force (N) are inputs; the outputs are column section width (b), column section height (h), and the reinforcement area of the section (As ). Multioutput Regressor was applied. The k-fold cross-validation method was used to prevent the algorithms from memorizing the training dataset and obtaining incorrect results. The results show that Multilayer Perceptron variations have the best accuracy performance among the applied algorithms with the highest R2 and the lowest RMSE, RMAE, and RMSE. Finally, the performance of machine learning algorithms in predicting CO2 emissions was compared and it was seen that good performances can be obtained. Promising results have been obtained for the use of the algorithms used in the study for sustainable design.

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Artificial Intelligence and Deep Learning in Civil Engineering Ayla Ocak, Sinan Melih Nigdeli, Gebrail Bekda¸s, and Ümit I¸sıkda˘g

Abstract Artificial intelligence is a variety of software developed that imitates the human brain to perform the tasks that the human brain can do. Aiming to minimize human intervention, this software has a wide range of content that deals with many problems such as perception, problem-solving, information transfer, planning, natural language processing, and so on. As a purpose-oriented method that can be used in many disciplines, it is preferred with high success rates, especially in the solution of engineering problems. Its sub-branches include machine learning, in which machines are trained to extract information from the available data. Machine learning and deep learning methods, which express more specific learning, make it possible to create a powerful predictive model. In this study, deep learning methods, which are a sub-branch of artificial intelligence and artificial intelligence, and the studies in which these methods are used in civil engineering are explained. Keywords Artificial ˙Intelligence · Machine Learning · Deep Learning

1 Introduction The advancement of science and technology brought about the industrial revolution and mechanization with new inventions in the eighteenth and nineteenth centuries and caused a decrease in human intervention in production and technology. This transition to mechanization has created a universal mechanical language among all A. Ocak · S. M. Nigdeli · G. Bekda¸s (B) Department of Civil Engineering, Istanbul University - Cerrahpa¸sa, 34320 Avcılar, Istanbul, Turkey e-mail: [email protected] S. M. Nigdeli e-mail: [email protected] Ü. I¸sıkda˘g Department of Informatics, Mimar Sinan Fine Arts University, 34427 Si¸ ¸ sli, Istanbul, Turkey e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Bekda¸s and S. M. Nigdeli (eds.), Hybrid Metaheuristics in Structural Engineering, Studies in Systems, Decision and Control 480, https://doi.org/10.1007/978-3-031-34728-3_13

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people. In the middle of the eighteenth century, the source of communication called “shared technical vocabulary” was the beginning of an unpredictable change [1]. The fact that the work that can be produced by human hands can be done with the help of machines has also made it easier to reach the needed resources by increasing production. However, the idea that machines are devices that act systematically and that the human brain cannot do the things it can do even though it imitates human behavior paved the way for a second technological revolution. This idea of mechanization pushed the limits of human production and led to the development of a machine that imitated the capabilities of the human brain. Progress in science and technology has made it possible to transfer the abilities of the human brain to perception, problem-solving, learning, and similar abilities to various software called artificial intelligence. In other words, “intelligent machines” were produced as a continuation of the industrial revolution. Afterward, artificial intelligence software was divided into sub-branches and various artificial intelligence techniques were developed.

2 Artificial Intelligence (AI) Artificial intelligence is a new technology that is characterized as a kind of intelligent machine that has emerged with the features of human intelligence such as learning, perception, decision-making, problem-solving, and similar features of human brain imitation. In one of his studies, John McCarthy defined artificial intelligence as “the science and engineering of making intelligent computer programs” alongside intelligent machines [2, 3]. In other words, it consists of simulated human brain experiments to make machines smart [3]. In the mid-twentieth century, English mathematician and computer scientist Alan Mathison Turing said, “Can machines think? He laid the foundation of artificial intelligence with the Turing test he developed to answer the question [4]. This test investigates the communication between a man and a woman in two different rooms with a typewriter called a teletype, as in today’s electronic chat rooms. Accordingly, while the interrogator initially communicates with a human, then a machine replaces the person in front of him. The decision of the interrogator, whether there is a machine or a human being on the other party, gives the result of whether the machine is intelligent [5]. This imitation game created by Turing is described as the first step of artificial intelligence. Considering the living things in nature, there is an instinctive behavior and learned behavior common to both humans and animals. While instinctive behavior is observed in the reflex of sucking the breast milk of a newborn creature, this symbolizes a learned behavior for a child who experiences burner from a fire and understands that he should not approach it. In the behavior mechanism based on artificial intelligence technology, there is a learned behavior and the ability to make inferences. As it can be understood from this situation, to develop a non-instinctive learned behavior mechanism, some knowledge must be added to the repertoire of artificial intelligence. The breadth of this knowledge reinforces the inference power

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of artificial intelligence, just as it increases a person’s ability to distinguish between right and wrong in line with their experiences. For this purpose, the process of transferring various data to the machine regarding the abilities to be gained from artificial intelligence has had an important place in the development of artificial intelligence technology and has been a pioneer in the development of a new branch of science. This branch of science is called “Data Science” and researchers interested in this science are called “Data Scientists”. It refers to the studies carried out to reveal general knowledge from the existing data based on data science [6]. Obtaining the knowledge used in artificial intelligence with data science has made these technology fields an inseparable duo. Investigating features such as the comprehensibility, distribution, and frequency of the data has led to the creation of more accurate artificial intelligence technology. For example, the presence of unusual daily weather in data consisting of a long-term weather report may reduce the success level of weather forecasts made by artificial intelligence. Data science comes into play at this point, allowing artificial intelligence to make a more accurate prediction by detecting the extreme value in the data and removing it from the flow. Although data science and artificial intelligence technologies have similar points, data science focuses more on data analysis, data processing, and statistics, while artificial intelligence focuses on data modeling, inference, and prediction from data. Artificial intelligence is actively used in many fields such as computer science, medicine, engineering, mathematics, biochemistry, physics and astronomy, pharmacology, social sciences, business administration, management and accounting, economics, and psychology in today’s world. With artificial intelligence, it has been possible to explore different types of fields such as facial recognition, mastering a game, estimation of landslide danger, cancer diagnosis from scans, predicting the future effects of epidemics, earthquake, and location detection, human behavior prediction from digital records, social network analysis and political orientation prediction [7–14]. When the studies in the field of engineering are examined, it is seen that areas such as the estimation of the compressive strength of the rocks, the evaluation of land pollution and soil quality, the estimation of wind-based energy production, the estimation of long-term braking events to reduce emissions in the automotive sector, the stability estimation of debris breakwater structures, the paint structure quality estimation are investigated [15–20]. In the field of civil engineering, artificial intelligence, and its sub-branches have been frequently used in subjects such as structural control and monitoring of building behavior, as well as prediction model production studies for soil and material properties. In soil studies on construction, modeling of hydraulic conductivity of sandy soils, classification of different types of soils, liquefaction prediction of fine-grained soils, and estimation of shear strength of soil have been investigated and successful prediction models have been produced [21–24]. In the field of building materials, mechanical properties of sand concrete, thermo-mechanical properties of recycled aggregate concrete, compressive strength of concrete, compressive strength of construction demolition waste geopolymers, the effect of cement-based materials on compressive strength, performance evaluation of slag-based concrete at high temperatures, concrete-filled steel pipes has been done on the estimation of areas such as the

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load bearing capacity of the columns [25–31]. In the field of hydraulics, artificial intelligence methods have been applied to determine the fragility of concrete-lined rockfill dams under seismic loads, flow variables of sharply curved channels, the flow velocity of open channel junction, and discharge coefficient of side weirs [32– 35]. In the fields of structural engineering and building management, building design and performance evaluation, nominal shear capacity of a reinforced concrete wall, shear strength of reinforced concrete beams, the seismic failure mode of reinforced concrete shear walls, the fatigue life of bridge decks, cost of engineering services in the construction industry, structural health monitoring for damage and detection investigation topics were examined with artificial intelligence methods [36–42]. In the field of structural mechanics, studies are carried out in the design and evaluation of structural control systems. With artificial intelligence, the production of performance estimation models related to the structure was provided for the evaluation of the effectiveness of the tuned mass dampers (TMDs) used in bridges to prevent wind-induced vibrations, the estimation of the fatigue performance of the metallic damper under cyclical loading, the estimation of the optimally tuned mass damper parameters, the evaluation of the reaction of structures exposed to fire and similar extreme conditions [43–46]. Artificial intelligence is a comprehensive method that includes many methods. While the application examples of artificial intelligence technologies, which are also expressed as smart machines, are seen in the programming of robots, the machine learning method is used to give the machine the ability to make inferences by training with a certain data set. In addition to these methods, there are also sub-fields such as expert systems, data mining, machine perception, natural language processing, planning, and optimization [47]. The sub-branches of artificial intelligence and the fields associated with artificial intelligence are shown in Fig. 1. Machine learning is a sub-branch of artificial intelligence developed in the 1980s, consisting of learning algorithms [48]. Its basic logic is to train and test the machine with a data set and demonstrate its ability to make inferences from new data with what it has learned. The aim here is to expose the machine to information, just as a person working at a convenience store constantly learns about product prices while receiving payment so that the cashier can predict a product at an approximate rate, as well as the machine. As an example of this; in a data set consisting of various information

Fig. 1 Artificial intelligence and sub-branches associated with artificial intelligence [47]

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such as age, height, weight, and similar information of a group of people and the results of the analysis, the characteristics and test results given for each individual represent the inputs of the data set. In this data, the column in which each candidate’s cancer patient status is expressed or not indicates the unit of the data set, which is called output. When the machine in your hand is taught the inputs in this data and the outputs about whether it is sick or not, it becomes possible with the machine learning method at a high level of success for the machine to decide whether the next person is sick or not. There are supervised, unsupervised, semi-supervised, and reinforcement learning options. A deep learning method has been developed by training machine learning with more specific and intensive data. Deep learning, a sub-branch of machine learning, is a machine learning method that aims to make sense of high-precision data.

2.1 Deep Learning Deep learning is an artificial intelligence method, which consists of neural networks resembling neurons in the human brain, focused on working like the human brain and using large amounts of data. It directs people to think like the human brain by using different sources such as text, sound, pictures, and so on as data. In today’s world, digital assistants on smartphones and computers are used in many areas such as voice search on the internet, face recognition systems used in phones and security units, creating subtitles for various video applications, and personalized internet advertisements according to people’s product preferences. In the defense industry and security sector, it plays an important role in preventing accidents and detecting dangerous elements with its aspects such as identifying objects that threaten security and providing driver support in the limited visibility of vehicles in traffic. In 2006, an unsupervised learning method, which can be used to create feature layers without labeled data, was introduced [49]. Figure 2 gives a schematic representation of artificial intelligence, machine learning, and deep learning over the years. Deep learning is a method that resembles artificial neural networks consisting of layers. In other words, they are multilayer neural networks. In this method, unlike machine learning, the inputs used do not have tags. For example; in a 4-feature dataset consisting of crown and sepal lengths and widths of three different iris flower species, the 5th column includes the iris flower species. When this data set is modeled with machine learning, the machine trained with 4 features learns the type of iris flower against the features in each row and produces a prediction model for deciding the type of iris flower according to these features. Thus, the machine can determine the type of iris flower by reading the properties of new data. In deep learning, unlike machine learning, the data given as input to the machine is defined as a node, not a feature. In this method is added as many nodes (4 for this example) as the column with the number of features in the layer with the inputs. Each node is multiplied with a random weight coefficient close to 0, and outputs are obtained through the transfer function and activation functions. Starting from the first row in the data set, if the

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Fig. 2 Artificial Intelligence, Machine Learning, and Deep Learning chronological display

estimated iris flower type output and the actual value are not the same, the error is calculated and feedback is sent to the network. As a result, the weight coefficients are updated. All rows of the data set are used for this task, and the weighting coefficients of the attributes in the data reach a correct value. Figure 3 shows the artificial neuron model and Fig. 4 shows the layers for iris data. Backpropagation is one of the methods used in deep learning. In the deep learning system, the weight coefficients to multiply each feature in the data set are determined randomly. The margin of error of the determined weights in the prediction model is important. Backpropagation is used to minimize this margin of error. There are varieties of deep learning such as Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs). Convolutional Neural Networks

Fig. 3 Artificial neuron model [50]

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Fig. 4 Iris dataset deep learning layers

are a type of deep learning used in image processing that enables classification and discrimination by capturing the features of images. In this method, images are used as input. The pixels in which each image is reduced to small squares are learned with layers and visual classification of objects is provided. The machine, which has learned the features of the visuals it has divided into classes, can guess what the new visual is when it encounters a new visual. Recurrent Neural Networks is an artificial intelligence deep learning technology that provides successful results in predicting the next step used for time series problems. The Recurrent Neural Networks method is frequently used in price determination and natural language processing of systems that are constantly changing depending on time, such as the stock market. In deep learning, while the features given as input are independent, in Recurrent Neural Networks, a relationship is established between the inputs, and this relationship is remembered in the training by memorizing. The deep learning method is a technology used in many fields such as computer science, medicine, physics, mathematics, materials science, biochemistry, genetics, social sciences, and so on.

2.2 Deep Learning in Civil Engineering Deep learning applications have attracted attention in civil engineering as well as in other fields of science. The development of deep learning has been on the rise in the twenty-first century because it requires large amounts of data due to its structure and faster processors facilitating implementation. In the field of civil engineering, many data sources such as observation reports obtained from buildings, displacement records caused by various vibrations in buildings, flow-energy data obtained from water structures such as hydroelectric power plants and dams, information reports where construction management costs are stored, damage assessment data of structures have prepared the ground for deep learning applications. A large amount of

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data sources in the construction industry has increased the use of deep learning in this industry. It is frequently used especially in building damage detection, material quality, and monitoring of building health.

2.2.1

Deep Learning Studies in Geotechnics

Deep learning technology started to be used intensively after 2006, and its application to civil engineering studies gained frequency after ten years. Applications of deep learning techniques in the department of geotechnical have been seen in subjects such as bearing capacity of foundations, settlement of soil, soil permeability, slope safety, slope stability, and soil classification [51–59]. A summary table of the studies in the field of geotechnical is given in Table 1.

2.2.2

Deep Learning Studies in Construction Materials

Deep learning is an artificial intelligence method that allows the processing of visual data. Thanks to this feature, image data from picture videos can be easily used as training data. In civil engineering, it is known that the damage and determination of the materials used in the construction process of the buildings for various reasons are important for the health of the building. Construction materials are an area that needs to be kept under control due to reasons such as cracks and deterioration that may occur during and after application, reducing the quality of the material and reducing the strength level. The application of deep learning techniques in the field of construction materials ensures that negative factors such as time and cost are avoided in the detection of material defects. When the studies in this field are examined, deep learning methods are applied for many subjects such as the detection of concrete defects, concrete compressive strength, corrosion, concrete slump and workability, detection of surface cracks, changes in the mechanical properties of concrete under high temperature, and so on. In Table 2, some of the studies on the construction material are summarized.

2.2.3

Deep Learning Studies in Construction Management

Energy consumption of buildings is a parameter that should be considered in reducing environmental impacts such as carbon emissions. In today’s world, for the design of sustainable structures, both the construction materials and the energy embedded in the structure must be well controlled. Deep learning methods are an artificial intelligence technology preferred for the control of energy consumption and the detection of negative situations. In addition to the energy monitoring advantages of models created with deep learning methods in construction management, it acts as a very good detector for the detection of dangerous worker behaviors and vehicle usage in terms of construction safety. In deep learning studies in the field of construction

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Table 1 Deep learning studies in geotechnics Study summary

Authors

Estimating the carrying capacity of shallow foundations with deep Bagi´nska, M., & neural networks (DNNs) when data is scarce has been investigated, Srokosz, P. E and it has been observed that different numbers of neurons and layers are more effective in the prediction performance of the model than the number of layers [51] The deep learning method has been used to estimate the shaft Lu, S. L., Zhang, N., resistance of cast in situ piles in reclaimed soils, it has been verified to Shen, S., Zhou, A., & Li, H. Z be efficient in determining the shaft resistance in offshore areas [52] Traditional methods and deep learning methods were compared for slope stability analysis, and an accuracy and calculation efficiency exceeding 99% was obtained [53]

Azmoon, B., Biniyaz, A., & Liu, Z

In the tunneling process, two models were developed with deep learning for the determination of the parameters affecting the settlement of the surface and the prediction of collapse against these parameters, it was determined that the models predicted collapse at a very good level [54]

Lee, H. K., Song, M. K., & Lee, S. S

The use of machine learning and deep learning methods to predict settlement in the ground as a result of tunneling and the applicability of the prediction model were examined [55]

Tang, L., & Na, S

A deep learning method was applied to estimate the permeability of consolidated silty clay [56]

Liu, Y., Chen, S. J., Sagoe-Crentsil, K., & Duan, W

To avoid slope shifts, the deep learning method was applied to the simulated model by changing various features, and a high-precision model was produced that predicts the safety factors [57]

Pandey, V. H. R., Kainthola, A., Sharma, V., Srivastav, A., Jayal, T., & Singh, T. N

For the evaluation of the soil taken from the excavation sites, a model Zhan, L. T., Guo, Q. has been developed that can classify soils with an accuracy of close to M., Chen, Y. M., Wang, 90%, using deep learning and cone penetration testing [58] S. Y., Feng, T., Bian, Y., … & Yin, Z. Y In land reclamation studies, deep learning algorithms were used to predict the settlement of the ground, and the created model successfully predicted the settlement of the airport fill [59]

Chen, X. X., Yang, J., He, G. F., & Huang, L. C

management, subjects such as monitoring building health, monitoring of construction workers, detection of unsafe behavior, price estimation of basic construction costs, and the efficiency of construction equipment are covered. Some examples of the content of the studies carried out are shown in Table 3.

2.2.4

Deep Learning Studies in Mechanics

Structures can be damaged by various dynamic effects such as wind and earthquakes. Various analysis methods are used to determine the damage of such vibrations in

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Table 2 Deep learning studies in construction materials Study summary

Authors

A good image-based approach is provided by detecting the defects of the concrete in the tunnels utilizing robotic controllers trained with deep learning [60]

Protopapadakis, E., & Doulamis, N

The data of concrete block walls consisting of recycled fine and coarse aggregate, water-cement ratio, and fly ash ratio were used in deep learning, and more successful results were obtained in estimating the compressive strength of concrete compared to the classical neural network [61]

Deng, F., He, Y., Zhou, S., Yu, Y., Cheng, H., & Wu, X

In the detection of corrosion, a prediction model was created Atha, D. J., & Jahanshahi, M. R using different convolutional neural networks based on texture and color analysis, and the proposed methods were compared [62] By applying deep learning with image data, a model was developed that takes into account the slump flow value and funnel flow time of self-compacting concrete and predicts its workability [63]

Ding, Z., & An, X

In the estimation of the compressive strength of concrete, the model was trained with a deep convolutional neural network (DCNN) using images obtained from various digital images and video recordings, and it was determined that the method was an advantageous option [64]

Shin, H. K., Ahn, Y. H., Lee, S. H., & Kim, H. Y

In the detection of concrete surface cracks, a deep Yamane, T., & Chun, P. J learning-based high-sensitivity crack detection model has been developed in which the factors that negatively affect detection such as mold marks, shadows, dirt, and tie rod holes can be removed [65] Convolution-based deep learning method was used to predict the change in the mechanical response of fiber-reinforced concrete at high temperatures, such as fire, and a successful prediction model was developed [66]

Chen, H., Yang, J., & Chen, X

By applying different temperatures to the concrete samples produced in the laboratory, deep learning techniques were applied to the data set including the strengths, and the methods were compared to the strength of the concrete damaged by fire [67]

Hacıefendio˘glu, K. E. M. A. L., Akbulut, Y. E., Nayır, S. A. F. A., Ba¸sa˘ga, H. B., & Altunı¸sık, A. C

For the detection of concrete defects, an image processing Gonthina, M., Chamata, R., method with a convolutional neural network was used, and the Duppalapudi, J., & Lute, V quantities of cracks, damage, and similar situations were determined with the trained model [68] A self-healing mortar has been produced, and a model has been developed that evaluates the ability to heal cracks with a deep learning method with an accuracy of up to 99% [69]

Jin, X., Haider, M. Z., Cui, Y., Jang, J. G., Kim, Y. J., Fang, G., & Hu, J. W

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Table 3 Deep learning studies in construction management Study summary

Authors

In the security and control of tunnels, a deep learning system has been Makantasis, K., established with the images obtained from the camera images, and a flaw Protopapadakis, E., detector that makes fast predictions has been obtained [70] Doulamis, A., Doulamis, N., & Loupos, C In building energy consumption, a prediction model was produced with deep learning and machine learning-based algorithms that take into account outdoor weather conditions, the deep learning model was more successful in the prediction performance comparison [71]

Amasyali, K., & El-Gohary, N

An extreme deep learning approach has been proposed for the detection of building energy consumption, and the performance of the approach has been compared with various machine learning-based methods [72]

Li, C., Ding, Z., Zhao, D., Yi, J., & Zhang, G

To ensure safe working control of construction workers, a deep learning method was applied using images obtained from far-field surveillance records, and the helmet uses the status of the workers was determined with high sensitivity [73]

Fang, Q., Li, H., Luo, X., Ding, L., Luo, H., Rose, T. M., & An, W

For the action definition of excavation excavators, the model was trained Kim, J., & Chi, S from around 72 thousand excavation field images with convolutional neural network (CNN) and double-layer long-short-term memory algorithms, and 80–94% accurate action definition was obtained from case studies [74] A model that infers construction practice constraints from construction regulations was trained with a hybrid deep learning method, and the performance of the model in inferring construction procedures was successful [75]

Zhong, B., Xing, X., Luo, H., Zhou, Q., Li, H., Rose, T., & Fang, W

For structural health monitoring, deep learning was applied with a visual Zhang, Y., Sun, X., dataset consisting of images of tight and loose bolts, and a high-precision Loh, K. J., Su, W., prediction model was developed that predicts bolt damage in an Xue, Z., & Zhao, X image-based structure [76] Using the generic data set, a good detector was obtained from the construction site videos from the models trained with deep learning and machine learning techniques, and it was found that both methods gave successful results [77]

Neuhausen, M., Pawlowski, D., & König, M

Deep learning was applied with image processing data to detect unsafe behaviors in the construction site and to take precautions, it was recommended that construction companies use the model created to prevent accidents [78]

Fang, W., Love, P. E., Ding, L., Xu, S., Kong, T., & Li, H

A convolutional neural network model has been developed to detect changes in iron prices in the construction industry, and the accuracy of the model has been tested with events affecting iron prices [79]

Feng, C. and Chiang, Y

Deep learning was provided with the images of the railway bridge Park, S. M., Lee, J. obtained by web browsing for the detection of the building components H., & Kang, L. S in the construction area, it was observed that the shooting angle of the images greatly affected the estimation sensitivity in object detection [80] (continued)

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Table 3 (continued) Study summary

Authors

Using deep learning to measure equipment efficiency, the model was trained with kinematic and noise data, and an accuracy exceeding 99% was obtained in estimating excavator performance [81]

Mahamedi, E., Rogage, K., Doukari, O., & Kassem, M

the structure. However, factors such as time and cost extend the determination of properties such as seismic fragility of the structure over a long period. Another structural problem is that the constructed structures have a limited lifespan. Among the main reasons for this is the fatigue share created by environmental and dynamic effects in the structure. Problems such as the inability to exhibit the same rigidity on all floors over time in a structure subject to seismic excitation and the formation of soft stories further reduce the life of the structure. The efficiency of deep learning methods has proven to be an artificial intelligence suitable for use in this field. Determining structural damage after various disasters only with visual data and video images shows that deep learning can be adapted to structural mechanics problems. In the field of structural mechanics, deep learning techniques are applied in many areas such as fragility level detection, vibration-induced damage detection, determination of soft-story structures, and fatigue life of structures. In Table 4, some of the studies carried out with deep learning techniques in mechanics are summarized.

2.2.5

Deep Learning Studies in Transportation

Transportation branch researches the issues of establishing the necessary infrastructure in civil engineering, land, air, and water transportation, designing and constructing transportation facilities, and operating them in a safe, economical, and environmentally friendly manner. Deep learning techniques can be easily applied in the field of transportation, such as damage detection of transportation resources, detection of negative effects of dynamic vibrations on highway and railway lines, and monitoring of transportation structures. Similar to the use of image processing technology in construction materials, deep learning methods give successful results in determining the damage to pavement surfaces as a result of various factors on highways. Some of the deep learning studies in the field of transportation are summarized in Table 5.

2.2.6

Deep Learning Studies in Hydraulics

Hydraulics branch provides the most appropriate project design and safe construction facility by examining natural disasters such as water structures, drinking water and waste water channels, port facilities, abutment structures, hydroelectric power plants, floods, and tsunamis. It carries out the construction of dams and similar water structures with observation stations that collect precipitation data to keep various

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Table 4 Deep learning studies in mechanics Study summary

Authors

A damage detection model was developed using a deep neural network with dynamic responses of beam-like structures, and it was found that deep neural network technology gave positive results in damage detection [82]

Lin, Y. Z., & Ma, H. W

Parameters calculated from the finite element model of a real bridge are used in deep learning training for the detection and calibration of a reinforced concrete bridge against aging [83]

Darsono, D., & Torbol, M

Low-level sensor data has been used in deep learning for structural damage detection, and it has been observed from the data that there are features that increase the success of the method and damage locations [84]

Lin, Y. Z., Nie, Z. H., & Ma, H. W

For the prediction of the fatigue life of the structures, the deep learning model trained with acceleration data was tested with loading experiments on a beam suitable for the laboratory environment [85]

Gulgec, N. S., Takáˇc, M., & Pakzad, S. N

To reduce the damage of wind-induced vibrations to the structure, an aerodynamic mitigating shape optimization model was created with a deep reinforcement learning method [86]

Li, S., Snaiki, R., & Wu, T

A convolutional neural network method trained with image data was used to detect soft-skinned structures to reduce seismic risk, and parameter sensitivity limits were determined by comparing them with the latest technology convolutional neural network techniques [87]

Chen, P. Y., Wu, Z. Y., & Taciroglu, E

A method that uses seismic fragility analysis to examine the response of various disasters and vibrations due to aging in bridges, as an aid in increasing the prediction success of deep learning, is proposed and its accuracy is supported by examples [88]

Wang, M., Zhang, H., Dai, H., & Shen, L

To determine the fragility level created by the wind load on the transmission tower, Li, H., a prediction model was developed using the structural health monitoring data of the Zhang, W. tower, and it was observed that the model could detect the fragility effectively [89] & Fu, X To detect the vibration-induced damage caused by dynamic traffic loads on a bridge Sajedi, S., & Liang, with a high-resolution trident instrument, damage data were generated from the X vehicle transition simulation with real vehicle data, and a high estimation success was obtained as a result of training with deep learning techniques [90] Three deep learning methods were used for the time-history response prediction of vibrations arising from the movements of vehicles in bridge traffic, the fastest prediction model was observed in a deep feed-forward neural network (DFNN), while the best prediction performance was found in convolutional neural network (CNN) [91]

Li, H., Wang, T., Yang, J. P., & Wu, G

water sources under control. Hydraulic engineering plays an important role in the calculations and design of hydroelectric power plants to obtain clean energy from water in the most efficient way. In addition, by examining the characteristics of water under coastal engineering, safe construction of port structures and issues such as tsunamis, and flood are the subjects of his research. Looking at the research areas,

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Table 5 Deep learning studies in transportation Study summary

Authors

For the estimation of pavement friction level affecting road safety, training with pavement texture data was applied using a convolutional neural network (CNN), and it was determined that deep learning techniques were suitable for road speed and pavement friction [92]

Yang, G., Li, Q. J., Zhan, Y., Fei, Y., & Zhang, A

For the prediction of vehicle-body vibrations on high-speed railway lines, the model produced using an integrated deep-learning method has successfully predicted vehicle-body vibrations at frequencies below a certain value [93]

Ma, S., Gao, L., Liu, X., & Lin, J

In the detection of asphalt pavement cracks that threaten highway safety, deep learning methods with 3D pixel-based image processing data have been applied, and it has been observed that the applied methods show good results in detecting thin cracks [94]

Fei, Y., Wang, K. C., Zhang, A., Chen, C., Li, J. Q., Liu, Y., … & Li, B

The deep learning method was used for moisture content determination Zhang, J., Yang, X., Li, W., Zhang, S., & Jia, Y in asphalt pavements, and it was determined by experimental results that the produced prediction model significantly detected moisture damage [95] A model trained with drone images was created for various road damage detection using a pre-trained convolutional neural network (CNN) with a two-layer optimizer [96]

Samma, H., Suandi, S. A., Ismail, N. A., Sulaiman, S., & Ping, L. L

In subway tunnels, a model was created for the detection of water leaks Qiu, D., Liang, H., by using the hybrid supervised deep learning method with the image Wang, Z., Tong, Y., & data obtained from mobile vision systems, and the hybrid deep learning Wan, S method was more successful than other deep learning methods [97] To detect and classify highway cracks, pre-trained convolutional neural network (CNN) deep learning methods were used to produce a prediction model with visual data, and it was observed that the proposed method successfully tested highway cracks in a short time [98]

Elghaish, F., Talebi, S., Abdellatef, E., Matarneh, S. T., Hosseini, M. R., Wu, S., & Nguyen, T. Q

A deep learning technique has been proposed for the detection of pavement deterioration on asphalt surfaces, and it has been determined that the model trained with the pavement deterioration dataset can make inferences with an accuracy exceeding 80% and in a good time [99]

Wen, T., Ding, S., Lang, H., Lu, J. J., Yuan, Y., Peng, Y., … & Wang, A

For the structural health monitoring of bridges, in the detection of Ye, X., Wu, P., Liu, A., abnormal data caused by heavy rain and similar extreme events, image Zhan, X., Wang, Z., & processing and convolutional neural network (CNN)-based deep Zhao, Y learning was performed, and the accuracy of the technique was evaluated with long span suspension bridge data [100] To realize the designs to reduce the vibration created by subway trains while they are in motion, a vibration evaluation model has been developed by using a deep learning method to identify train-induced vibrations and detect vibrations created by subway transitions [101]

Liu, W., Liang, R., Zhang, H., Wu, Z., & Jiang, B

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the applicability of deep learning techniques is examined by various studies. Channels built for the transmission of clean water and removal of harmful wastewater are damaged by precipitation and seismic dynamic effects over time. Detection of leaks and damages in water pipes, which adversely affect human health, is a difficult and costly process to control, especially in underground networks. In addition to the water channels, the cracks in the dam structures also threaten the living conditions in the region. Deep learning techniques have yielded successful results in the detection of leaks and damage to water structures, taking into account the data consisting of water pressure, flow rate, and similar properties. In the research, it has been understood that deep learning methods have a high potential in crack detection with visual monitoring data and flood and leak prediction with the flow characteristics of water and the change in precipitation amount. Some of the results obtained from a few studies are given in Table 6.

2.2.7

Deep Learning Studies in Structures

Structures is a branch of civil engineering that deals with the construction and design of buildings, bridges, towers, silos, and similar structures with steel, reinforced concrete, wood, metal, and similar materials, and examines the reactions of structures to various static and dynamic effects. It works on the economical design of buildings with sufficient strength, and a safe carrier system, suitable for the seismicity of the region and the ground structure. The task of the structural engineers starts with the necessary static analysis during the design phase and continues with the correct application, the protection, and monitoring of the health of the building, which is affected by various dynamic and environmental factors after the application. Applying deep learning techniques to solve such structural problems facilitates the task of structural engineers and leads the way in the establishment of an autonomous system. It is applied in many areas such as deep learning techniques, structural stress and damage detection, design optimization, and cable force adjustment in the building department. Summary information on the content of some studies conducted in Table 7 is presented.

3 Summary and Conclusions In this study, artificial intelligence technology was examined in general, and deep learning techniques, which is a branch of artificial intelligence, and its current applications in civil engineering were mentioned. In the literature research, it has been supported by the studies that deep learning techniques, especially the issues such as structural damage detection, and road and construction safety related to the image processing area, can be easily estimated through recorded images and videos. It has been determined that the deep learning method has a successful performance in the detection of ordinary situations such as floods and floods and leaks in sewer systems

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Table 6 Deep learning studies in hydraulics Study summary

Authors

To detect the faults in the sewer pipes, a model created using deep learning Cheng, J. C., & techniques with closed-circuit television images has been trained, and a Wang, M system that provides high-sensitivity detection has been produced [102] It has been observed that unmeasured watershed attributes improve Ojha, R., & hydrological predictions in the deep-learning estimation of flood quantities Tripathi, S [103] To ensure the cyber security of water distribution systems, a detection Taormina, R., & model has been created by the deep learning method, and the trained model Galelli, S has successfully predicted all cyber attacks that threaten the security of hydraulic distribution networks [104] In the water distribution system, deep learning and artificial intelligence algorithms were used to predict water demand for short periods, such as 15 min, and the model created by deep learning was found to perform better in 15-min and 24-h water demand forecasting [105]

Guo, G., Liu, S., Wu, Y., Li, J., Zhou, R., & Zhu, X

The convolutional neural network (CNN) model, which best predicts eight algal species, has been determined for the monitoring and classification of algae that negatively affect drinking water lines, and it has been presented with experimental results that it is an effective model [106]

Park, J., Lee, H., Park, C. Y., Hasan, S., Heo, T. Y., & Lee, W. H

A deep learning technique was applied to detect leaks in water distribution Cody, R. A., pipes using acoustic monitoring data, and the model succeeded in detecting Tolson, B. A., & 0.25 L per second leaks with an accuracy of up to 97% [107] Orchard, J A model was prepared by applying hybrid deep learning training with Dong, S., Yu, T., channel network sensor data, and it was verified by performing a real flood Farahmand, H., & event prediction test that the trained model was suitable for flood Mostafavi, A forecasting and taking precautions for flood warnings [108] The convolutional neural network (CNN) method was used to predict the long-term temporal flood range and depth of the structures, and it was observed that the model was successful and could obtain predictions within seconds [109]

Wang, H. W., Lin, G. F., Hsu, C. T., Wu, S. J., & Tfwala, S. S

To predict the deformation of mortar masonry dams against time-varying factors such as temperature and aging, a deep learning model has been constructed and it has been verified that it provides high-precision dam deformation prediction [110]

Su, Y., Zheng, Z., Lin, C., Lin, Y., He, Q., Zhang, T., & Huang, S

For the detection of damage such as corrosion, scaling, and tearing in buried sewer pipes, a prediction model has been produced with various deep learning and artificial intelligence algorithms, and a real-time damage estimation platform has been proposed [111]

Wang, N., Fang, H., Xue, B., Wu, R., Fang, R., Hu, Q., & Lv, Y

for the hydraulics branch, which is one of the civil engineering fields. Based on the studies in the field of construction management, it is seen that deep learning is an appropriate method for determining the conditions such as monitoring the health of the structure, controlling the work and worker safety during the construction phase, and evaluating the performance of construction equipment. In addition, it has been determined by studies that construction materials are very effective in determining strength, cracks, and damage. The use of artificial intelligence technologies

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Table 7 Deep learning studies in structures Study summary

Authors

A design optimization based on deep learning neural networks that improve flooring design to reduce the negative environmental impacts of floors such as carbon emissions and embedded energy has been developed and tested with a case study [112]

Ferreiro-Cabello, J., Fraile-Garcia, E., de Pison Ascacibar, E. M., & Martinez-de-Pison, F. J

Using deep learning technologies, a model has been produced that predicts fragmentation, component condition, and damage level and type in the detection of structural damage by image processing [113]

Gao, Y., & Mosalam, K. M

Deep learning techniques have been used to determine the load Chen, G., Li, T., Chen, conditions and damage conditions that cause plastic deformation of the Q., Ren, S., Wang, C., shell structures [114] & Li, S By creating a deep learning model with various building images, it has Yu, Q., Wang, C., been tried to determine the structures with soft stories that may cause McKenna, F., Yu, S. X., destruction [115] Taciroglu, E., Cetiner, B., & Law, K. H With a model trained with deep learning techniques, the total stress of steel components was tried to be estimated, and a proposal was presented for stress detection, which is difficult to obtain with conventional sensors [116]

Wang, W., Shi, P., Chu, H., Deng, L., & Yan, B

A multi-layer perceptron deep learning method was used to adjust the cable strength of cable-suspended bridges with long spans, and a fast and high-precision model was produced [117]

Shan, D., Zhang, X., Gu, X. & Li, Q

A deep learning method has been used for structural health and a successful prediction model has been developed that detects facade defects [118]

Guo, J., Wang, Q., & Li, Y

By using multilayer perceptron, long-short-term memory network, 1D convolutional neural network, and convolutional neural network deep learning techniques, the suitability of these techniques in detecting multiple damage situations was investigated and a table was created [119]

Dang, H. V., Raza, M., Nguyen, T. V., Bui-Tien, T., & Nguyen, H. X

Derogar, S., Ince, C., Column connections of reinforced concrete slabs were modeled with Yatbaz, H. Y., & Ever, various artificial intelligence, machine learning, artificial neural networks, and deep learning methods using drilling-shear experiment E data, and the puncture shear strength could be estimated with sufficient accuracy [120] In the structural stress distribution, a model that performs stress analysis of loaded steel plates is used convolutional neural networks (CNNs) are constructed, and finite element simulation is used to compare the performance of the model [121]

Bolandi, H., Li, X., Salem, T., Boddeti, V. N., & Lajnef, N

In earthquakes and similar extreme events, a prediction model was Bai, Y., Zha, B., Sezen, created for the unmanned detection of damage to the structure by using H., & Yilmaz, A image processing and deep learning methods, and remarkable results were obtained [122]

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in the classification of the soil and determination of the bearing capacity, such as soil surveys, which is among the first processes for the construction of a construction, brings speed and accuracy to the project. Situations for the areas of structure and structure mechanics expressing the subsequent processes of the construction, having the most suitable carrier system, and protection against earthquake, wind, and similar dynamic effects after construction are important. Deep learning seems to be a good predictor and damage estimator in civil engineering problems such as structural damage, fatigue life under dynamic effects, and detection of load states that trigger structural deformation. Looking at the studies in the field of transportation, crack detection that threatens road safety, strength estimation of coating materials, and similar areas have been the areas where deep learning is frequently used. In light of all the studies, it is understood that deep learning techniques are in a structure that can be used easily at every stage of construction and produce the necessary forecasting models for the optimum level of efficiency to be obtained from construction materials, as well as a good damage assessment expert and the determination of the elements that threaten the structure safety. It can be said that it is a suitable method for use in a long process, both at the beginning of the construction and after the construction, until deciding on the life of the structure.

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Deep Learning-Based Framework for Reconstruction and Optimisation of Building Information Models Containing Parametric Rules Vincent J. L. Gan

Abstract The building information model (BIM) is maturing as a new paradigm for storing information and exchanging knowledge about a building. BIM models precisely show existing structural elements which can be conveniently extracted to support condition monitoring, quality assessment and design optimisation of engineering structures. However, current practice does not fully address the integration of 3D modelling and computational intelligence to support the automatic reconstruction and optimisation of BIM models. To resolve this challenge, this paper presents a framework for deep learning-based reconstruction and optimisation of BIM, with a case study to demonstrate its application for the parametric design optimisation of high-rise buildings. The proposed framework involves the development and application of deep neural network for automated reconstruction of content-rich building models subject to certain design rules. After obtaining the geometric details about a building, the performance of the generated 3D models is assessed towards identifying the optimum solution. In this study, attempts have been made to optimise the wind flow of a high-rise residential building, as the wind plays an important role in designing a high-rise. The findings provide a deeper understanding and interesting insights into 3D reconstruction and optimisation of BIM subject to parametric design rules. Keywords Building information model · Machine learning · Geometric modelling · Computational optimisation · High-rise building

V. J. L. Gan (B) Department of the Built Environment, National University of Singapore, Singapore 117566, Singapore e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. Bekda¸s and S. M. Nigdeli (eds.), Hybrid Metaheuristics in Structural Engineering, Studies in Systems, Decision and Control 480, https://doi.org/10.1007/978-3-031-34728-3_14

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1 Introduction Due to rapid urbanisation, the design and construction of new buildings have reached an unprecedented level in densely populated metropolises. Buildings nowadays have more complex built forms [1], and understanding the impact of time-varying ambient environment helps optimise building geometries and provide positive attributes to maintain the buildings. For example, adaptive designs that can utilise naturallyoccurring wind force to create a better-built environment increasingly interests many researchers [2]. In light of this, evolutionary algorithms or generative modelling techniques were leveraged to generate different spatial-geometric configurations, whereas a simulation-based approach served to evaluate the fitness of each candidate solution [3, 4]. The research suggests a persistent need to develop new strategies to accurately reconstruct and optimise the building geometries to improve the built environment. Eleftheriadis, Duffour [5] and Choi, Lee [6] proposed multiobjective computational optimisation models to forecast and optimise the building’s structural layout and element details to lower cost and carbon footprint. Instead of generating a single optimum, the ultimate target of multi-objective optimisation was to search for a Pareto Front, which contains a set of non-dominated solutions where multiple objective functions are balanced and equally good [7]. The new optimum searching method, including Multi-Objective Particle Swarm Optimisation (MOPSO) [8], pattern search PSO with Hooke-Jeeves algorithms [9], etc., were proposed to support the exploration of the Pareto Front. However, traditional heuristic-based optimisation methods face challenges which are gaining attention as the industry is adopting artificial intelligence in computational optimisation. Emerging digital technologies (such as computational intelligence) are pervasive across the virtual design and construction of new facilities. Building information modelling (BIM) is a cutting-edge technology that allows the digital representation of physical assets in virtual simulation models [10]. It enables the virtual reconstruction of the detailed building geometry, followed by assessing and optimising buildings in the physical world to meet clients’ requirements [11]. Based upon this digital framework, BIM has been increasingly used to digitally represent and improve the performance of modern buildings [12]. Figure 1 displays the process taking laser scanning to collect point clouds of real-world structures, followed by using computational intelligence to process the point cloud for automated reconstruction of BIM. The 3D digital model accurately represents the as-built conditions, allowing architects, engineers and construction professionals to depict building conditions and plan more effectively for future projects. Researchers [13, 14] critically reviewed stateof-the-art approaches with BIM for building optimisation. Among these, Liu, Meng [15] presented a design optimisation method with a BIM environment to extract the project-based initial information to facilitate the evaluation of design candidates. The proven design can be put into simulating different design strategies and realising the optimal solution. Ramaji and Memari [16] presented an information interoperability standard to underpin BIM applications in the design and construction of residential buildings.

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Fig. 1 Automated 3D reconstruction of as-built BIM

With the adoption of BIM, robust simulation-based optimisation methods were proposed to forecast and optimise the building performance. Based upon parameterisation, it is paramount to establish ways to generate BIM models for integrated simulation and performance assessment for different candidate designs. For instance, a study [17] on coupling BIM and genetic algorithms (GA) to optimise modular highrise housing was performed. The design variables, including building shape, structural form, and member size, were parameterised to generate BIM models [18, 19] automatically. The structural components were defined as a set of numerical parameters which manipulate the building geometry [18]. Integrating predefined parametric relationships and design rules among structural components can be used for reconstructing and optimising the BIM model [19]. To save computing resources, numerical simulation was undertaken to evaluate the performance of alternative solutions [20]. For example, Gan et al. [18] and Solnosky, Memari [21] proposed a structural BIM optimisation, with the aid of finite element analysis and hybrid metaheuristic algorithms (e.g. optimality criteria GA), to explore, simulate and identify the optimal design solution. BIM was leveraged in the construction planning of buildings, including cost estimation [22], site logistics planning and control [23], and offsite manufacturing [24, 25]. Design BIM models provide geometrical and semantics such as resources and manufacturers, which empower the precise prefabrication of building components. However, these new approaches still show disadvantages in computational time and optimality of final solutions because of potential iterations of simulation-based assessment in the optimisation process. Yet, possibilities to incorporate BIM and computational intelligence, especially for reconstructing and optimising building design subject to wind effects, are largely unexplored. In addition, buildings constructed nowadays have complex shapes and geometry. Understanding the impact of building geometries and the surrounding environment (such as wind) is essential yet lacking; therefore, a comprehensive study on deep learning-based BIM reconstruction and optimisation is still much needed. This paper presents a deep learning-assisted framework to underpin the reconstruction and optimisation of BIM subject to specific parametric design rules, with a case study to demonstrate its application for high-rise building optimisation. The proposed new framework involves geometric modelling and 3D reconstruction of structural elements in the design space. After obtaining the geometric details about a building, a deep learning algorithm is developed and deployed to assess the 3D model

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and its resulting performance. In this research, attempts have been made to optimise the geometry and layour high-rise modular buildings. The suggested approach combines computational simulation with neural network computing to quantitatively analyse the wind flow of high-rise buildings. To examine the flow characteristics of high-rise buildings in different forms, numerical simulation is used to create the training dataset for a strong neural network model in accurate forecasting and optimisation. Details about the methdology and results are provided in the following sub-sections.

2 Methodology This section articulates the deep learning-assisted framework for reconstruction and computational optimisation of BIM. BIM is considered a single information hub containing all the necessary spatial, geometric, and material information extracted to optimise building performance. Provided BIM 3D objects, the architect assembles customised floor plans using a parametric object library containing different standard units. It is advised to undergo an optimisation process for the distribution of the BIM objects to optimise the building’s overall performance subject to certain geometrical constraints. Building design optimisation is implemented, which involves establishing the optimal architectural layout plan for optimising the wind environment, as it plays an essential role in constructing and optimising building models. To save the computing resource, deep learning was leveraged in this study for automatic performance assessment of airflow patterns associated with building spatial-geometric features. A deep neural network (DNN) model was developed to learn from different outdoor flow conditions and building spatial-geometric features to interpolate the complex relationship between building physical characteristics and airflow. We will accomplish this via supervised training, which iteratively tunes the deep learning algorithms between data-driven prediction and high-resolution physics-based computation. In general, this study contributes to a new method by synthesising BIM with deep learning to optimise the building performance subject to wind effects. A diverse set of realistic designs was created first with BIM, followed by DNN prediction with its supervised learning capacity on the problem structure to identify the optimum. The proposed new approach will leverage the strength of deep learning and BIM to enhance the automatic generation and optimisation of 3D building models. The optimisation methods are described in the following sections.

2.1 Optimal Design Formulation As shown in Fig. 2, the developed approach couples automated computer-generated design and machine learning data-driven prediction to iteratively analyse, predict

Deep Learning-Based Framework for Reconstruction and Optimisation …

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Fig. 2 Computer-generated parametric BIM model

and optimise the design performance in the physical world. The proposed method starts by creating design BIM models using metaheuristic algorithms, which generate building layout plans containing the distribution of BIM objects, building geometry, and site constraints. This is followed by evaluating the performance of the developed models using a deep neural network (DNN) to identify the optimal design option. As there is a growing academic interest in improving building design, the DNN in the study considers the wind effects on buildings. To illustrate the proposed approach for automatic generation and optimisation of BIM, this study considers building structures with standardised units, such as residential units, which usually could meet the structural performance requirements while giving a higher degree of design freedom for architectural layout planning. As such, this study considers typical buildings composed of modular/standardised units and space dimensions from a parametric object library. A structural system with one or several concrete cores is used, in which the core provides overall stability, whereas the modular/standardised units are clustered around the core(s). The modular/standardised units are subject to compression force in these structural systems. Since proper design formulation is crucial to the quality of the final design, the proposed method first identifies the parametric design variables and constraints. The computer-generated design of buildings includes defining one or more spatial variables to characterise the layout plan for the entire building. The focus of the design problem is on seeking the optimal layout configuration to maximise the building performance subject to regulatory and code-stipulated performance requirements, as follows: ⎤ϕ ⎡ I ∑ K J J ∑ ∑ ∑ j j τ =⎣ Zi + Ck ⎦ wher e Z i → (m i , n i , ai , bi , θi ) (1) i=1 j=1

k=1

j=1

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V. J. L. Gan j

Z i ∈ A(SC)

i = 1, 2, . . . I ; j = 1, 2, . . . J.

A

( L ∑

(2)

) ≤ Ca

(3)

mi H ≤ Car ni

(4)

Fwl

l=1 L Car