European Workshop on Structural Health Monitoring: Special Collection of 2020 Papers - Volume 2 (Lecture Notes in Civil Engineering, 128) 3030649075, 9783030649074

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Lecture Notes in Civil Engineering

Piervincenzo Rizzo Alberto Milazzo   Editors

European Workshop on Structural Health Monitoring Special Collection of 2020 Papers Volume 2

Lecture Notes in Civil Engineering Volume 128

Series Editors Marco di Prisco, Politecnico di Milano, Milano, Italy Sheng-Hong Chen, School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan, China Ioannis Vayas, Institute of Steel Structures, National Technical University of Athens, Athens, Greece Sanjay Kumar Shukla, School of Engineering, Edith Cowan University, Joondalup, WA, Australia Anuj Sharma, Iowa State University, Ames, IA, USA Nagesh Kumar, Department of Civil Engineering, Indian Institute of Science Bangalore, Bengaluru, Karnataka, India Chien Ming Wang, School of Civil Engineering, The University of Queensland, Brisbane, QLD, Australia

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Piervincenzo Rizzo Alberto Milazzo •

Editors

European Workshop on Structural Health Monitoring Special Collection of 2020 Papers - Volume 2

123

Editors Piervincenzo Rizzo Department of Civil and Environmental Engineering University of Pittsburgh Pittsburgh, PA, USA

Alberto Milazzo Department of Engineering Università degli Studi di Palermo Palermo, Italy

ISSN 2366-2557 ISSN 2366-2565 (electronic) Lecture Notes in Civil Engineering ISBN 978-3-030-64907-4 ISBN 978-3-030-64908-1 (eBook) https://doi.org/10.1007/978-3-030-64908-1 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Structural health monitoring (SHM) is the scientific process of identifying damage or ascertaining the static and dynamic characteristics of given structures using remote sensors or a noninvasive network of sensors embedded or bonded to those structures of interest. SHM evolves the maintenance paradigm from “time-based” nondestructive evaluation (NDE) in which a structure is inspected periodically, to continuous monitoring. The European Workshop on SHM (EWSHM) is an International event that started in 2002. Ever since, it has been organized every two years in a different European country, in an alternating fashion with respect to the International Workshop on SHM (IWSHM) held at Stanford University every odd-numbered year and paired to the Asia-Pacific SHM meetings. The 2020 event has been jointly organized by the University of Palermo (Italy) and the University of Pittsburgh (USA) and should have been hosted by the Faculty of Engineering of the University of Palermo, in the beautiful island of Sicily. Over 600 abstracts from 52 countries were accepted for the workshop. Regrettably, the Covid-19 pandemic has forced the organizers and the scientific committee members to postpone the event to the year 2022 to the same great location. The authors of the accepted abstracts have been encouraged to submit a full paper to be included in this special collection. About 170 papers have been accepted after a rigorous peer-review process, and are presented here. The variety and quality of the papers are a testament of the very stimulating event that the EWSHM 2020 would have been. Overall, this EWSHM Special Collection includes the latest developments in key technology fields of sensor development, network design, signal processing, modeling, diagnostics, and prognostics with applications to aerospace, civil, and mechanical engineering. The proceedings are organized in thirty-two sections, split into two volumes, Volume 1 (ISBN 978-3-030-64593-9) including sections 1–15 and Volume 2 (ISBN 978-3-030-64907-4) including sections 16–32. The first 31 sections are the special sessions organized by true experts in their respective fields, whereas the last

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section contains the papers of those abstracts that were not submitted to any of the following special sessions:

1

Title Seismic structural health monitoring for civil structures

2

SHM in wind turbine technology

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Nonlinear ultrasonic guided wave methods for SHM Real-time monitoring of built infrastructure

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5 6

Nonlinear SHM methods for high sensitivity Toward the next generation of performance indicators supported by SHM

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Standardization and guidelines on SHM and NDT: needs and ongoing activities

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Wireless sensing systems for structural health monitoring

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Integrated approaches for SHM: models, data and experiments Diagnostics and prognostics of composite structures toward a condition-based maintenance framework Vehicle-based indirect SHM for infrastructure

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Guided waves in structures for SHM

Organizers M. P. Limongelli (Politecnico di Milano, Italy) M. Celebi (Earthquake Science Center, USGS, USA) W. Ostachowicz (Polish Academy of Sciences, Poland) N. Yelve (Fr.C. Rodrigues Institute of Technology, Mumbai, India) V. Pakrashi and B. Bhowmik (University College Dublin, Ireland) E. Chatzi (Swiss Federal Institute of Technology, Switzerland) C. Lissenden (Pennsylvania State University) H. Sousa (HS Consulting Ltd/BRISA Group, Portugal) A. Mandic (University of Zagreb, Croatia) A. Strauss (Univ. of Natural Resources and Life Sciences, Austria) S. Kessler (Helmut Schmidt University / University of the Federal Armed Forces Hamburg, Germany) A. Strauss (Boku University) H. Wenzel (WENZEL Consulting Engineers GmbH) H. Fu (Loughborough University, UK) Z. Sharif Khodaei (Imperial College, UK) A. Cicirello (University of Oxford, UK) D. Zarouchas (Delft University of Technology, The Netherlands) T. Loutas (Patras University, Greece) H. Y. Noh (Stanford University, USA) A. Malekjafarian (University College Dublin) C.-W. Kim (Kyoto University) Y. Yang (National Taiwan University) W. Ostachowicz (Polish Academy of Sciences, Poland) A. Pau (Sapienza University of Rome, Italy (continued)

Preface

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(continued) 13

Smart multifunctional materials and systems for SHM of large structures

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Human performance monitoring

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Structural health monitoring of cultural heritage structures New opportunities for structural health monitoring and artificial intelligence

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Acoustic emission for structural health monitoring of civil infrastructure Space-borne health monitoring for civil infrastructure

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Autonomous machine learning-enhanced SHM for aerostructures

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Electromagnetic surface and subsurface sensing methods for SHM Ultrasonic NDTs for the SHM of train wheel-axle and rail

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New trends and challenges of SHM in civil engineering

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Infrared thermography for structural health monitoring Fiber optics sensors

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Robust statistical and probabilistic methods for structural health monitoring

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Optical and computer-vision techniques for SHM and NDT

A. D’Alessandro, F. Ubertini (University of Perugia–Italy) S. Laflamme (Iowa State University– USA) K. Loh (Univ. of California, San Diego, USA) E. García-Macías, F. Ubertini (Univ. of Perugia, Italy) Y-B. Lin (National Center for Research on Earthquake Engineering, Taiwan) T.-K. Lin (National Chiao Tung University, Hsinchu, Taiwan) D. Ozevin (University of Illinois at Chicago, USA) G. Giardina (University of Bath, UK) P. Milillo (NASA Jet Propulsion Laboratory, USA) A. Kundu and R. Pullin (Cardiff School of Engineering, Cardiff University, UK) W. Ostachowicz (Polish Academy of Sciences, Poland) T. Yu (University of Massachusetts Lowell, USA) D. Cerniglia, N. Montinaro (Univ. di Palermo, Italy) G. Epasto (Università di Messina, Italy) A. Formisano (University of Naples “Federico II,” Italy), F. Clementi (Polytechnic University of Marche, Italy), N. Cavalagli (University of Perugia, Italy), and G. Milani (Politecnico di Milano, Italy) G. Pitarresi (University of Palermo, Italy) B. Glisic (Princeton University, USA) D. Zonta (University of Trento, Italy) F. Kopsaftopoulos (Rensselaer Polytechnic Institute, USA) S. Fassois (University of Patras, Greece) J. Sakellariou (University of Patras, Greece) A. Sabato (Univ. of Massachusetts, Lowell, USA) (continued)

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(continued) 27

Carbon nanotube and graphene-based sensors for SHM applications

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Damage identification under changing environment and operational conditions

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Multifunctional materials and composites Structural health monitoring of high-speed rail and Maglev systems Defect imaging algorithms based on guided waves for BVIDs detection: a Round Robin test on a large-scale aeronautical composite structures

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A. Güemes (Univ. Politecnica de Madrid, Spain) Z. Su (The Hong Kong Polytechnic University, HK) D. Li (Shantou University, China) M. Cao (Hohai University, China) P. Kraemer (University of Siegen, Germany) O. I. Okoli, V. O. Eze, M. A. Shohag (FAMU-FSU, Tallahassee, USA) Yi-Q. Ni (The Hong Kong Polytechnic University, Hong Kong) A. Marzani, L. De Marchi (University of Bologna, Italy)

The organization of the workshop and the success of this volume would not have been possible without the contributions of many people who have assisted or provided guidance during the last two years. As such, we acknowledge the contribution of the members of the local organizing committee: Ivano Benedetti, Ph.D., University of Palermo, Italy Guido Borino, Ph.D., Università degli Studi di Palermo, Italy Donatella Cerniglia, Ph.D., Università degli Studi di Palermo, Italy Fabrizio Micari, Ph.D., Università degli Studi di Palermo, Italy Giuseppe Pitarresi, Ph.D., University of Palermo, Italy and the members of the International Scientific Board: G. Akhras, Canada C. Boller, Germany P. Cawley, UK F. Cegla, UK F.-K. Chang, USA B. Chapuis, France E. Chatzi, Switzerland A. Cunha, Portugal A. Cusano, Italy Z. Fan, Singapore S. Fassois, Greece C.-P. Fritzen, Germany M. Giordano, Italy V. Giurgiutiu, USA B. Glisic, USA

M. Gresil, UK A. Güemes, Spain L. Jankowski, Poland I. Kressel, Israel J. Kullaa, Finland V. Le Cam, France M. P. Limongelli, Italy N. Mechbal, France L. Mevel, France Y.-Q. Ni, Hong Kong W. Ostachowicz, Poland C. Papadimitriou, Greece S. Pierce, UK N. Rajic, Australia J. Rodellar, Spain

Preface

M. Salvia, France D. Saravanos, Greece H. Sohn, Korea W. Staszewski, Poland Z. Su, Hong Kong

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N. Takeda, Japan M. Tur, Israel T. Uhl, Poland S. Yuan, China D. Zonta, Italy

Last but not least, we would like to express our sincere gratitude to Collage S.p.A. and in particular Mrs. Antonella Giuggioli, Mrs. Cinzia Gentile, and Mrs. Giusy Ventura for coordinating the effort with the logistics before the Covid-19 pandemic forced us to postpone the event to the year 2022. We believe you will find this volume scientifically stimulating and we trust you will consider submitting your latest work to the EWSHM 2022 scheduled to be held in Palermo (Italy) in the first week of July 2022. Sincerely, November 2020

Piervincenzo Rizzo Alberto Milazzo EWSHM 2020 Chairs Fabrizio Ricci Francesco Lanza di Scalea EWSHM 2020 Co-chairs

Organization

Program Chairs Piervincenzo Rizzo Alberto Milazzo

Department of Civil and Environmental Engineering, University of Pittsburgh, USA Department of Engineering, Università degli Studi di Palermo, Italy

Program Co-chairs Fabrizio Ricci Francesco Lanza di Scalea

Department of Engineering, Università di Napoli Federico II, Italy Department of Structural Engineering, University of California, San Diego, USA

Program Committee Ivano Benedetti Donatella Cerniglia Francesco Lanza di Scalea Fabrizio Micari Alberto Milazzo Giuseppe Pitarresi

Department of Engineering, Università degli Studi di Palermo, Italy Department of Engineering, Università degli Studi di Palermo, Italy Department of Structural Engineering, University of California, San Diego, USA Department of Engineering, Università degli Studi di Palermo, Italy Department of Engineering, Università degli Studi di Palermo, Italy Department of Engineering, Università degli Studi di Palermo, Italy

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Fabrizio Ricci Piervincenzo Rizzo

Organization

Department of Engineering, Università di Napoli Federico II, Italy Department of Civil and Environmental Engineering, University of Pittsburgh, USA

Contents

New Opportunities for Structural Health Monitoring and Artificial Intelligence Structural Geometric Morphology Monitoring for Bridges Using Holographic Visual Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shuai Shao, Guojun Deng, and Zhixiang Zhou

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Generative Adversarial Neural Networks for Guided Wave Signal Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mateusz Heesch, Ziemowit Dworakowski, and Krzysztof Mendrok

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Concrete Surface Crack Segmentation Based on Deep Learning . . . . . . Shun-Hsiang Hsu, Ting-Wei Chang, and Chia-Ming Chang Deep-Learning-Based Bridge Condition Assessment by Probability Density Distribution Reconstruction of Girder Vertical Deflection and Cable Tension Using Unsupervised Image Transformation Model . . . Yang Xu, Yadi Tian, Yufeng Zhang, and Hui Li

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Summary of Current Practice in Vibration Monitoring of Utility Tunnels and Shafts in the UK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Clive Chin-Kang Shen and Ursula Lawrence

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Gaussian Process Based Grey-Box Modelling for SHM of Structures Under Fluctuating Environmental Conditions . . . . . . . . . . . . . . . . . . . . Sikai Zhang, Timothy J. Rogers, and Elizabeth J. Cross

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Applying Neural Networks for Multi-site Damage Detection in Fuselage Lap Joints of Cargo Aircraft . . . . . . . . . . . . . . . . . . . . . . . . Andrey Bautin and Yury Svirskiy

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Deep Learning Based Identification of Elastic Properties Using Ultrasonic Guided Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Karthik Gopalakrishnan, Mahindra Rautela, and Yiming Deng

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A Methodology for Diagnosis of Damage by Machine Learning Algorithm on Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Abhijeet Kumar, Anirban Guha, and Sauvik Banerjee

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Acoustic Emission for Structural Health Monitoring of Civil Infrastructure Joint Optimization of the Number of Clusters and Their Parameters in Acoustic Emission Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Martin Mbarga Nkogo, Emmanuel Ramasso, Patrice Le Moal, Gilles Bourbon, Benoit Verdin, and Gaël Chevallier Space-Borne Health Monitoring for Civil Infrastructure Remote Sensing and In-Situ Measurements for the Structural Monitoring of Historical Monuments: The Consoli Palace of Gubbio, Italy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Nicola Cavalagli, Alban Kita, Elisabetta Farneti, Salvatore Falco, Francesco Trillo, Mario Costantini, Gianfranco Fornaro, Diego Reale, Simona Verde, and Filippo Ubertini Investigation on the Use of SAR Data at the Building Scale . . . . . . . . . 129 Simone Castelli, Luca Rota, Andrea Belleri, Alessandra Marini, and Paolo Riva Sentinel-1 Data for Monitoring a Pre-failure Event of Tailings Dam . . . 140 Lorenzo Ammirati, Nicola Mondillo, Domenico Calcaterra, and Diego Di Martire Ground Deformation Monitoring of a Strategic Building Affected by Slow-Moving Landslide in Cuenca (Ecuador) . . . . . . . . . . . . . . . . . . 149 Chester Sellers, Ricardo Rodas, Nadia Paulina Carrasco, Rita De Stefano, Diego Di Martire, and Massimo Ramondini Autonomous Machine Learning-Enhanced SHM for Aerostructures Imbalanced Classification of Fatigue Crack for Aluminum Plates Using Lamb Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Ziwei Fang, Jingjing He, and Jie Liu Multiple Model Filtering for Failure Identification in Large Space Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Giovanni B. Palmerini, Federica Angeletti, and Paolo Iannelli

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Electromagnetic Surface and Subsurface Sensing Methods for SHM Guided Electromagnetic Waves for Damage Localization in a Structural Health Monitoring Framework . . . . . . . . . . . . . . . . . . . 185 Jochen Moll, Duy Hai Nguyen, and Viktor Krozer Ultrasonic NDTs for the SHM of Train Wheel-Axle and Rail Laser Ultrasonics Inspection of Train Wheel - Evaluation of Optimized Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Gabriella Epasto, Nicola Montinaro, Donatella Cerniglia, and Eugenio Guglielmino New Trends and Challenges of SHM in Civil Engineering A New Concept Regarding the Modeling of Steel Cantilever Beams with Branched Cracks: A Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Gilbert-Rainer Gillich, Cristian Tufisi, Dorian Nedelcu, Zeno-Iosif Praisach, and Codruta Oana Hamat A State-of-the-Art Review of Nature-Inspired Systems for Smart Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Henrieke Fritz and Kay Smarsly Hardness vs Strength for Structural Steels: First Results from Experimental Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Antonio Formisano and Antonio Davino Performance-Based Design of Structural Health Monitoring Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 Daniel Tonelli, Carlo Cappello, and Daniele Zonta Vibration Testing and System Identification of a Monumental Building in Sabbioneta, Italy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 Alfredo Calì, Carmelo Gentile, and Antonella Saisi Structural Health Monitoring Based on Artificial Intelligence Algorithm and Acoustic Emission Analysis . . . . . . . . . . . . . . . . . . . . . . 258 Carmelo Scuro, Renato Sante Olivito, Francesco Lamonaca, and Domenico Luca Carnì Guided Wave Based-Occupancy Grid Robotic Mapping . . . . . . . . . . . . 267 Morteza Tabatabaeipour, Oksana Trushkevych, Gordon Dobie, Rachel S. Edwards, Charles Macleod, and Stephen G. Pierce SHM of Vibrating Stay-Cables by Microwave Remote Sensing . . . . . . . 276 Alessandro Cabboi, Carmelo Gentile, and Giacomo Zonno

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Contents

Infrared Thermography for Structural Health Monitoring Prediction of Refractory Lining Thickness in an Electric Furnace Using Thermography as a Non-destructive Testing Technique . . . . . . . . 289 Luis Carlos Bonilla, Juan Carlos Forero, Hugo Perez, Jose Ricardo, Bernardo Rueda, Oscar Zurita, Miguel David Mendez Bohorquez, and Juan M. Mantilla Assesment of Thermography as a Non-destructive Testing Technique to Structural Health Monitoring of an Electric Furnace . . . . . . . . . . . . 299 Luis Carlos Bonilla, Juan Carlos Forero, Hugo Perez, Jose Ricardo, Bernardo Rueda, Oscar Zurita, Carlos Alberto Barrera Soto, Miguel David Mendez Bohorquez, and Juan M. Mantilla Infrared Thermography to Study Damage During Static and Cyclic Loading of Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 Rosa De Finis, Davide Palumbo, and Umberto Galietti Study of Damage Behavior of T-Joint Components by Means of Different Non-destructive Techniques . . . . . . . . . . . . . . . . . . . . . . . . . 319 Davide Palumbo, Rosa De Finis, Andrea Saponaro, Riccardo Nobile, Francesco Panella, and Umberto Galietti Fiber Optics Sensors Smart Composite Rebars Based on DFOS Technology as Nervous System of Hybrid Footbridge Deck: A Case Study . . . . . . . . . . . . . . . . . 331 Rafał Sieńko, Łukasz Bednarski, and Tomasz Howiacki Shape Sensing with Inverse Finite Element Method on a Composite Plate Under Compression Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 Daniele Oboe, Luca Colombo, Claudio Sbarufatti, and Marco Giglio Dynamic Distributed Fibre Optic Sensing for Environmental and Operational Aircraft Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 Patricia Díaz-Maroto Fernández, Santiago Guerrero Vázquez, Jaime García Alonso, Alejandro Sánchez Sánchez, Carlos de Miguel, Manuel Iglesias Vallejo, and Daniel Iñesta González Strategies for Embedding Optical Fiber Sensors in Additive Manufacturing Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 Francesco Falcetelli, Raffaella Di Sante, and Enrico Troiani Simultaneous Measurement of Torque and Position of a Motor Operated Valve Actuator Using a Fiber Bragg Grating Sensor Embedded into the Surface of the Worm Shaft . . . . . . . . . . . . . . . . . . . 372 Tao Li, Yun Tu, Xinhai Yu, Jian Zhang, Ya-Li Wang, Shan-Tung Tu, Shijian Chen, and Chongke Qi

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Impact Area Estimation in CFRP Panels by Cross-Correlation Driven Features and Distributed Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 Monica Ciminello, Salvatore Ameduri, and Fulvio Romano Optical Fiber-Based Crack Monitoring on Engineered Barrier of Radioactive Waste Repository . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392 Michio Imai, Hiroshi Fujihara, Toshikazu Waki, Yoshikazu Hironaka, Motoyuki Mizunari, Yasuaki Yamano, Toshiyuki Sasaki, and Yasuhiro Suyama Robust Statistical and Probabilistic Methods for Structural Health Monitoring Damage Detection on an Operating Wind Turbine Blade via a Single Vibration Sensor: A Feasibility Study . . . . . . . . . . . . . . . . . . . . . . . . . . 405 A. I. Panagiotopoulos, D. Tcherniak, and S. D. Fassois New Modes of Inference for Probabilistic SHM . . . . . . . . . . . . . . . . . . . 415 Lawrence A. Bull, Paul Gardner, Timothy J. Rogers, Elizabeth J. Cross, Nikolaos Dervilis, and Keith Worden Early Damage Detection for Partially Observed Structures with an Autoregressive Spectrum and Distance-Based Methodology . . . 427 Alireza Entezami and Stefano Mariani MCMC-Based Probabilistic Damage Characterization for Plate Structures Using Responses at Vibration Nodes . . . . . . . . . . . 438 Tianxiang Huang, Chengrui Wan, and Kai-Uwe Schröder Seismic Performance Monitoring and Identification of Steel Storage Pallet Racks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 Nadia Baldassino, Martina Bernardi, Claudio Bernuzzi, Arturo di Gioia, and Marco Simoncelli Active-Sensing Structural Health Monitoring via Statistical Learning: An Experimental Study Under Varying Damage and Loading States . . . . Ahmad Amer, Shabbir Ahmed, and Fotis Kopsaftopoulos

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Fast Computation of the Autogram for the Detection of Transient Faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 Alessandro Paolo Daga, Alessandro Fasana, Luigi Garibaldi, Stefano Marchesiello, and Ali Moshrefzadeh On the On–Board Random Vibration–Based Detection of Hollow Worn Wheels in Operating Railway Vehicles . . . . . . . . . . . . . . . . . . . . . 480 N. Kaliorakis, I. A. Iliopoulos, G. Vlachospyros, J. S. Sakellariou, S. D. Fassois, A. Deloukas, G. Leoutsakos, E. Chronopoulos, C. Mamaloukakis, and K. Katsiana

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Optical and Computer-Vision Techniques for SHM and NDT Experimental Investigation on the Bond Behavior of FRCM-Concrete Interface via Digital Image Correlation . . . . . . . . . . . . . . . . . . . . . . . . . 493 Dario De Domenico, Antonino Quattrocchi, Santi Urso, Damiano Alizzio, Roberto Montanini, Giuseppe Ricciardi, and Antonino Recupero Visual Bridge Damage Measurement Using Drone-Captured Image Quality Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 Junwon Seo, Euiseok Jeong, and James Wacker Carbon Nanotube and Graphene-Based Sensors for SHM Applications Cast Method Effect of Carbon Nanofiber Aggregates on Structural Health Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517 Bhagirath Joshi, Xiaonan Shan, Jiaji Wang, Yagiz Oz, and Y. L. Mo Self-sensing of CNT-Doped GFRP Panels During Impact and Compression After Impact Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527 Claudio Sbarufatti, Bhavik Patel, Xoan F. Sánchez-Romate, Diego Scaccabarozzi, Simone Cinquemani, Alberto Jiménez-Suárez, and Alejandro Ureña Damage Identification Under Changing Environment and Operational Conditions A Scalable Temperature Compensation Method for Guided Wave Based Structural Health Monitoring of Anisotropic CFRP Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539 Nan Yue and M. H. Aliabadi Prognostic Health Monitoring for Downhole Drilling Tools . . . . . . . . . . 550 Mauro Caresta and Adam Bowler System Identification of Beam-Like Structures Using Residual Indicators Derived from Stochastic Subspace Analysis . . . . . . . . . . . . . . 559 Riccardo Cirella, Angelo Aloisio, and Rocco Alaggio Rebar Local Corrosion Monitoring of RC Structures Based on Fractal Characteristics of Piezoelectric Guided Waves . . . . . . . . . . . . . . . . . . . . 569 Shi Yan, Xuenan Wang, Yaoyao Chen, and Yuanyuan Yao Electromechanical Impedance Data Fusion for Damage Detection . . . . . 580 Tomasz Wandowski and Pawel Malinowski

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Multifunctional Materials and Composite Online Inspection System Based on Resin Flow Monitoring by Distributed Optical Fiber Sensors Immersed Inside Aeronautical RTM Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593 Carlos Miguel Giraldo and José Sánchez del Río Sáez Embedded Perovskite-Mechanoluminescent Sensor for Applications in Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603 Lucas Braga Carani, Md Abu Shohag, Vincent Obiozo Eze, G. Ryan Adams, and Okenwa Okoli In-Situ SEM Investigation of the Fatigue Behavior of Additive Manufactured Titanium Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612 Xinyan Wang, Yang Zhao, Limin Wei, and Xuefei Guan Enhanced Photoresponse of Inorganic Cesium Lead Halide Perovskite for Ultrasensitive Photodetector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622 Vincent Obiozo Eze, Geoffrey Ryan Adams, Bryana Beckford, Md Abu Shohag, and Okenwa I. Okoli Fatigue Reliability Assessment of Pipeline Weldments Subject to Minimal Detectable Flaws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632 Xiaochang Duan, Xinyan Wang, and Xuefei Guan Structural Health Monitoring of High-speed Rail and Maglev Systems Image Detection of Foreign Body Intrusion in Railway Perimeter Based on Dual Recognition Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645 Yumeng Sun, Zhengyu Xie, Yong Qin, Li Chuan, and Zhiyu Wu Defect Imaging Algorithms Based on Guided Waves for BVIDs Detection: a Round Robin test on a Large-Scale Aeronautical Composite Structures The Delay Multiply and Sum Algorithm for Lamb Waves Based Structural Health Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657 Michelangelo Maria Malatesta, Denis Bogomolov, Marco Messina, Dennis D’Ippolito, Nicola Testoni, Luca De Marchi, and Alessandro Marzani General Session Monitoring Local Impedance Changes with Solitary Waves . . . . . . . . . 669 Hoda Jalali, Amir Nasrollahi, and Piervincenzo Rizzo

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Influence of Temperature on Additive Manufacturing Polymer Structure with Embedded Fibre Bragg Grating Sensors . . . . . . . . . . . . 679 Magdalena Mieloszyk, Katarzyna Majewska, and Artur Andrearczyk Methods for Degradation Assessment of Fibre Reinforced Polymer Structure Exposed to the Simultaneous Influence of Temperature and Humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687 Katarzyna Majewska, Magdalena Mieloszyk, and Wieslaw Ostachowicz Analytical Modeling of Vibrations in a Damaged Beam Using Green-Volterra Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699 Damien Bouvier, Nazih Mechbal, and Marc Rébillat Damage Localisation by Residual Energy from Multiple-Input Finite Impulse Response Prognosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711 Benedikt Hofmeister, Clemens Jonscher, Clemens Hübler, and Raimund Rolfes Towards an Industrial Deployment of PZT Based SHM Processes: A Dedicated Metamodel for Lamb Wave Propagation . . . . . . . . . . . . . . 720 Hadrien Postorino, Marc Rebillat, Eric Monteiro, and Nazih Mechbal Damage Detection in Tensegrity Using Interacting Particle-Ensemble Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732 Neha Aswal, Subhamoy Sen, and Laurent Mevel Monitoring of Lithium-Ion Cells with Elastic Guided Waves . . . . . . . . . 742 Tobias Gaul, Uwe Lieske, Kristian Nikolowski, Peter Marcinkowski, Mareike Wolter, and Lars Schubert Does the Precision Value Influence the Fusion Performance? A Method-Based Experimental Study . . . . . . . . . . . . . . . . . . . . . . . . . . 754 Sandra Rothe and Dirk Söffker Automatic Fault Detection and Classification in Lift Door Systems Using Vibration Signal Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765 Angel Torres Perez, Stefan Kaczmarczyk, and Rory Smith Numerical Modelling of Stochastic Fatigue Damage Accumulation in Thick Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 776 Richard Loendersloot, M. Ehsani, N. Sepehry, and M. Shamshirsaz Optimal Finite Difference Schemes for Multiple Damage Identification in Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 788 Daniele Cinque, Jose Viriato Araújo dos Santos, Stefano Gabriele, Sonia Marfia, and Hernani Lopes Path Identification of a Moving Load Based on Multiobjective Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 799 Michał Gawlicki and Łukasz Jankowski

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Damage Study Using Series and Parallel Electrode in Electromechanical Impedance Method . . . . . . . . . . . . . . . . . . . . . . . . 808 Shishir Kumar Singh, Wiesław M. Ostachowicz, and Paweł H. Malinowski Damage Identification in Beams by Post-processing Modal Displacements and Rotations with Haar Wavelet . . . . . . . . . . . . . . . . . . 817 J. V. Araújo dos Santos, H. Lopes, and A. Katunin Nonlinear Frequency Mixing in GFRP Laminate with a Breathing Delamination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825 Akhilendra S. Gangwar, Yamnesh Agrawal, and Dhanashri M. Joglekar Data-Driven Damage Detection Based on Moving-Loads Responses - The Luiz I Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837 Filipe Cavadas, Bruno J. Afonso Costa, Joaquim A. Figueiras, Mário Pimentel, and Carlos Félix Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847

New Opportunities for Structural Health Monitoring and Artificial Intelligence

Structural Geometric Morphology Monitoring for Bridges Using Holographic Visual Sensor Shuai Shao1,2,3 , Guojun Deng2,3 , and Zhixiang Zhou1(B) 1 College of Civil and Transportation Engineering, Shenzhen University, Shenzhen, China

[email protected], [email protected] 2 College of Civil Engineering, Chongqing Jiaotong University, Chongqing, China

[email protected] 3 State Key Laboratory of Mountain Bridge and Tunnel Engineering, Chongqing, China

Abstract. Full-field noncontact structural geometry morphology monitoring can be used to achieve a breakthrough in the fields of structural safety monitoring and digital twins owing to its advantages of economy, credibility, high frequency, and holography. Moreover, such type of monitoring can improve the precision and efficiency of the structural health monitoring technology and theory of large-scale structures. This study validated the performance of a proposed holographic visual sensor and algorithms in computer vision-based, full-field, noncontact displacement and vibration measurement. On the basis of the temporal and spatial characteristics of the measured series data, denoising, and the disturbance-rejection algorithm, the microscopy algorithm of subpixel motion and the extracting algorithm of motion information were respectively constructed for weak high-order displacement components and the holographic measurement of high-quality geometric morphology. Moreover, an intelligent perception method optimized for holographic-geometric and operational-modal shapes were used to extract morphological features from a series of holographic transient responses under excitation. Experimental results showed that the holographic visual sensor and the proposed algorithms can extract an accurate holographic displacement signal and factually and sensitively accomplish vibration measurement while accurately reflecting the actual change in structural properties under various damage/action conditions. The accuracy and efficiency of the system in the structural geometry monitoring for dense full-field displacement measurement and smooth operational modal shape photogrammetry were confirmed in the experiments. The proposed method could serve as a foundation for further research on digital twins for large-scale structures, structural condition assessment, and intelligent damage identification methods. Keywords: Structural geometry morphology monitoring · Holographic visual sensor · Dense full-field displacement measurement · Operational modal shapes photogrammetry · System identification · Digital twins

1 Introduction Structural geometric deformation monitoring is a key component of health monitoring in the field of bridge engineering and a critical index of structural behavior evaluation © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 3–13, 2021. https://doi.org/10.1007/978-3-030-64908-1_1

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for bridges [1–5]. To a certain extent, anomalous changes in structural geometry provide an embodiment to present the safety status of bridges; moreover, different degrees of structural damage or defects during long-term service are embodied in such anomalous changes [3–5]. However, existing structure health monitoring (SHM) systems with poor economic efficiency only produce a limited number of structural geometric deformations on discrete monitoring points, and it is much less likely to acquire holographic-geometric morphology, which accurately represents the global and local safety status of the bridge structure [3, 6–9]. In consideration of the above research, the philosophy of full-field structural geometry monitoring is combined with structural holographic technology. Structural holographic technology is derived from holography and front-projected holographic displays [8–11]. On the basis of computer vision-based measurement and noncontact geometric morphology monitoring technologies [11–14], a visual sensor is comprehensively adopted to acquire original segmental dynamic and static video monitoring data to the largest possible extent. Such data contain all the structural information (i.e., geometric parameters, mechanical behavior responses, structural performance parameters, structural state parameters, load effects, and environmental activity) that is available to digital twins [3, 15]. In these data, the optical and phase information of various points on the structural surface are truthfully and accurately recorded. In principle, three-dimensional space images of original structures can be dynamically reproduced without mutual interference. Hence, the dynamic interaction between real structures and virtual digital models is achieved. Furthermore, the proposed method overcomes the problem of response data discretization, which is caused by restrictions over the quantity of sensors, on observation points. In addition, information on the global and local damages of structures can be presented truthfully and continuously by the proposed holographic visual sensor [16]. This study aims to address the lack of sufficient data that support structural health monitoring, damage identification, and digital twins for large-scale structures. Such issue is common in traditional single-point measurement methods. An emerging holographic visual sensor and algorithms have been proposed for full-field noncontact displacement and vibration measurements the basis of computer vision technology, with improved efficiency and reduced cost. The sensor and the algorithms can be applied to the full-field geometry monitoring of engineering structures.

2 Experiment of Structural Geometric Morphology Monitoring 2.1 Holographic Visual Sensor The holographic visual sensor [3, 16] can arrange dense and continuous pixellevel/subpixel-level virtual measuring points on the surface of the tested object space; therefore, actual physical characteristics of structural geometry and deformation can be collectively obtained, as presented in Fig. 1.

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Cannon 5Dsr camera Sony AX700 high-definition camera

Autocruise platform

Data storage and analysis processor External connection fixation base

Fig. 1. Holographic visual sensor: (a) main components of sensor; (b) holography geometric morphology of the structure.

In terms of full-field structural geometry monitoring, virtual measuring point positions and color information are primarily selected as the measurement features for digital transformation of corresponding dynamic and static images, as shown in Fig. 2 and Eq. (1). Notably, each pixel in image or video information is an information zone f (i, j).

f1,1 f1,2

f 2,1 f 2,2

f M,1 f M,2

f1,N

f 2,N

f M,N

f i, j f x, y

x, y

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N

Fig. 2. Matrix representation of pattern information digitalization.

f (x, y) = g(x, y) · h(x, y) · QL

(1)

where, x and y refers to planar coordinates of the information zone f (i, j) after image function discretization; g(·) is an incidence function that embodies the external features of an image, such as illumination intensity and environmental factors; h(·) represents a reflection function, standing for reflection characteristics on the structural surface and internal characteristics of the image; and, QL is spatial position information contained in multi-time-history, multi-angle and multi-field-of-vision series data of dynamic/static images [16]. Normalized cross correlation analysis (NCC analysis) is made to figure out correlations among various information zones f (i, j) in neighboring series data before and after the structure. Equation (2) defines the coefficients of NCC analysis, and Fig. 3 shows the matching schematic diagram.

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Template Image The Feature Points set of Structural Holography Morphology

Current Search Area

H ij ,h x, y, z

Previous Frame Matching Position

/

H ij ,h x, y, z

Matching Template

H ij ,v x, y, z

/

H ij ,v x, y, z

Fig. 3. Matching schematic diagram. M  N        f x,y (i, j) − E S i,j  · f T (i, j) − E f T (i, j) 

δ(i, j) = 

i=1 j=1 N  M  

N  M  2   2 · f x,y (i, j) − E S i,j f T (i, j) − E f T (i, j)



i=1 j=1

(2)

i=1 j=1

where, δ(i, j) is the Normalized Cross Correlation coefficients, f x,y (i, j) is the source image, f T (i, j) is the template, S i,j is the region under the template, E f T (i, j) is the   mean of the template, E S i,j is the mean of in the region under the template, (i, j) represents coordinates of the original image function f (x, y) that denotes the information zone f (i, j) [16]. Using spatial and temporal differential analysis of H ij (x, y, z) and H ij  (x, y, z) (Eqs. (3), (4)), full-field structural geometry monitoring is conducted. As shown in the following figure, structural geometry of the test bridge is acquired by a holographic visual sensor in the field of vision, and the feature point set of structural holography geometry and holography feature contours are built up. On this basis, geometric parameters of the structure can be further extracted. Subsequently, such parameters can be utilized to dynamically update a model of digital twins and optimize and correct such a model in accordance with real-time structural response under loads. x =

n  m     (x, y, z) Hij,h (x, y, z) − Hij,h

(3)

i=1 j=1

y =

n  m     (x, y, z) Hij,v (x, y, z) − Hij,v

(4)

i=1 j=1

where, m and n represent space serial numbers of the structure’s holographic probability edge feature points; x, y and z are space coordinates of feature points; H ij (x, y, z) refers to the measured horizontal/vertical structural responses in the holography geometric morphology in a field of vision at a moment/period; and, H ij  (x, y, z) stands for the measured horizontal/vertical structural responses of the holography geometric morphology function in a normal state [16].

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2.2 Experimental Setup and Procedure The scale test model of 24 m-span self-anchored suspension (SAS) bridge (see Fig. 4) is selected as the test model here, because the structure itself has abundant feature points and its performance and mechanical behavior have been also explored by the group at the earlier research work.

Fig. 4. The diagram of test bridge (total length of bridge is 24 m, Units: mm).

Figure 5 shows the field arrangement of holography geometric morphology monitoring for test bridge.

Measuring Position of Holographic Visual Sensor Drawbar

Test Loading Vehicle

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Fig. 5. The Experiment site layout: (a) specific arrangement of sensors; (b) measuring points of dial gauges and accelerometers.

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The holographic visual sensor is used to full-field non-contact displacement and vibration measurement, as shown in Fig. 6.

Current View

The Spatial and Temporal Series Data

Obtain Bridge Dynamic and Static Morphology Monitoring Data

Cannon 5Ds R Obtain Static Morphology Series Data

a. Personal Computer & Control Software of Holographic Visual Sensor

Control & Data Analysis

Sony AX700 Obtain Dynamic Morphology Series Data

Control & Testing Parameters Setting

b. Details of Holographic Visual Sensor

Accelerometer DH5902N Data Acquisition and Analysis System

Dial Gauge

d. Details of Test Loading Vehicle

c. Details of the Conventional Contact Sensors

Fig. 6. The details of full-field non-contact displacement and vibration measurements.

2.3 The Spatial and Temporal Series Data The spatial and temporal series data for structural geometric morphology monitoring that are collected by the holographic visual sensor are listed in Fig. 7.

Structural Geometric Morphology Monitoring for Bridges View 6

View 5

View 4

View 3

View 2

View 1

View 5

View 4

View 3

View 2

View 1

Time

View 6

9

Space

Fig. 7. The spatial and temporal series data for structural geometric morphology monitoring.

3 Test Results and Analysis 3.1 Analysis of Dense Full-Field Displacement Measurement Results Through the intelligent sensing system of a holographic vision sensor, denoising, and the disturbance-rejection algorithm, the microscopy algorithm of subpixel motion and the extracting algorithm of motion information were constructed respectively. The dense full-field displacement and time curves under different test conditions are depicted in Fig. 8.

2 1 0 -1 -2 0

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Holographic Visual Sensor Dial Gauge 30 35 40 45

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0

5

Holographic Visual Sensor Dial Gauge 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Time (Sec)

Fig. 8. Comparison of displacement responses: (a) single-point excitation; (b) running vehicle excitation.

Figure 9 demonstrates that holographic full-field displacement signals can be accurately and simultaneously measured, thus proving the accuracy and feasibility of the proposed approach. On the basis of the full-view area, the full-field displacement signal of each section can be obtained using the proposed holographic visual sensor and the algorithms of structural geometry morphology monitoring under different working conditions.

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Fig. 9. Dense full-field displacement [16].

3.2 Analysis of Operational Modal Shapes Photogrammetry Results

1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0

3

Dislacement (mm)

Acceleration (m/s2)

After the displacement time-history curve of the test bridge is obtained by using the intelligent sensing system of the holographic vision sensor, the frequency spectrum of the displacement time-history curve and the acceleration time-history curve are analyzed; furthermore, the modal parameters of the structure under different working conditions are identified in accordance with the power spectrum of the vertical load response, as presented in Figs. 10 and 11.

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f1=2.170 f1=2.154 f2=3.442

f3=5.029

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Fig. 10. Comparison between the measured frequencies of single-point excitation: (a) acceleration signal; (b) displacement response; (c) the power spectral density (PSD).

Structural Geometric Morphology Monitoring for Bridges 10.0

Dislacement (mm)

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7.5 5.0 2.5 0.0 -2.5 -5.0 -7.5 -10.0

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f4=6.274

1.4x10-5 1.2x10-5 1.0x10-5 8.0x10-6

f1=2.100

6.0x10-6

f2=3.650

f1=2.112

f =4.822 4.0x10 f3=4.700 3 2.0x10-6 f1=3.735 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 -6

Frequency (Hz)

Fig. 11. Comparison between the measured frequencies of running vehicle excitation: (a) acceleration signal; (b) displacement response; (c) the power spectral density.

The sensor test results in this study are consistent with the data curve shape. For the power spectrum of vertical load response, the two measured results are in good agreement in the low frequency range. Full-field structural geometry monitoring can be performed using a holographic vision sensor to obtain more data compared with what traditional acceleration sensors can. Additionally, image and video data are valid for the retention and extraction of high-order modal displacement components. For this reason, highfrequency information is acquired for the structure, and a smooth and continuous modal shape can be obtained. This condition is beneficial for structural damage identification. In Fig. 12, the first two mode shapes are compared using accelerometers and a vision sensor; the results indicate that the vision sensor can achieve smooth mode shapes, whereas the resolution of the mode shapes from accelerometers is limited by the sensor number. 1st Mode Shape

1.0

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Fig. 12. Comparison of mode shapes between vision sensor and accelerometer.

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4 Conclusion Aiming to develop a scale test model of a 24 m-span self-anchored suspension bridge, this study performs holographic-geometric morphology monitoring tests under multi damage/operating conditions. The following conclusions can be drawn: First, in consideration of spatial and temporal series data, which are collected from holographic visual sensor-based bridge morphology monitoring, a holographic deformation sample dataset is constructed; moreover, a holographic morphology monitoring method is established for mapping between data sampling and structural geometry by virtue of hierarchical thinking. Hopefully, the SHM technique has improved in terms of cost-effectiveness, efficiency and directness. Second, bridge image stitching defects are incurred during the early phase of the study when noncontact measurement is performed to acquire structural holographic deformations. These defects are modified in this study. In addition to full-bridge holographicgeometric morphology data and holographic displacement time-history curves that are fundamentally coincident with the measured values of the conventional contact sensor, the curve variation trends of the test bridge are almost entirely consistent with each other under different working conditions. Specifically, RMSE is less than 0.5, whereas the error rate is within 5%. Moreover, their accuracy also meets the requirement of engineering practice. Third, in consideration of bridge performance and safety evaluation, the proposed holographic visual sensor, together with the corresponding structural morphology monitoring method, can be considered an efficient, continuous, and convenient preliminary holographic displacement monitoring technique.

References 1. Feng, D.M., Feng, M.Q.: Computer vision for SHM of civil infrastructure: from dynamic response measurement to damage detection-a review. Eng. Struct. 156, 105–117 (2018) 2. Editorial Department of China Journal of Highway and Transport: Review on China’s bridge engineering research: 2014. China J. Highw. Transp. 27(5), 1–96 (2014) 3. Shao, S., Zhou, Z.X., Deng, G.J., Wang, S.R.: Experiment of structural morphology monitoring for bridges based on non-contact remote intelligent perception method. China J. Highw. Transp. 32(11), 91–102 (2019) 4. Sun, L.M., Shang, Z.Q., Xia, Y.: Development and prospect of bridge structural health monitoring in the context of big data. China J. Highw. Transp. 32(11), 1–20 (2019) 5. Ye, X.W., Dong, C.Z.: Review of computer vision-based structural displacement monitoring. China J. Highw. Transp. 32(11), 20–39 (2019) 6. Bao, Y.Q., Li, H., Ou, J.P.: Emerging data technology in structural health monitoring: compressive sensing technology. J. Civ. Struct. Health Monit. 4(2), 77–90 (2012) 7. Bao, Y.Q., Yu, Y., Li, H., Mao, X.Q., Jiao, W.F., Zou, Z.L., Ou, J.P.: Compressive sensing based lost data recovery of fast-moving wireless sensing for structural health monitoring. Struct. Control Health Monit. 22(3), 433–448 (2015) 8. Javh, J., Slaviˇc, J., Boltežar, M.: The subpixel resolution of optical-flow-based modal analysis. Mech. Syst. Signal Process. 88, 89–99 (2017) 9. Guo, J., Zhu, C.A.: Dynamic displacement measurement of large-scale structures based on the Lucas-Kanade template tracking algorithm. Mech. Syst. Signal Process. 66, 425–436 (2016)

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10. Yang, Y.C., Dorn, C., Mancini, T., Talken, Z., Kenyon, G., Farrar, C., Mascareñas, D.: Blind identification of full-field vibration modes from video measurements with phase-based video motion magnification. Mech. Syst. Signal Process. 85, 567–590 (2017) 11. Xu, Y., Brownjohn, J., Kong, D.L.: A non-contact vision-based system for multipoint displacement monitoring in a cable-stayed footbridge. Struct. Control Health Monit. 25(5), 21–55 (2018) 12. Cha, Y.J., Chen, J.G., Büyüköztürk, O.: Output-only computer vision based damage detection using phase-based optical flow and unscented Kalman filters. Eng. Struct. 132, 300–313 (2017) 13. Feng, D.M., Feng, M.Q.: Model updating of railway bridge using in situ dynamic displacement measurement under trainloads. J. Bridge Eng. 20, 04015019 (2015) 14. Cha, Y.J., Trocha, P., Büyüköztürk, O.: Field measurement-based system identification and dynamic response prediction of a unique MIT building. Sensors 16, 1016 (2016) 15. Mei, Q.P., Gül, M., Boay, M.: Indirect health monitoring of bridges using Mel-frequency cepstral coefficients and principal component analysis. Mech. Syst. Signal Process. 119, 523–546 (2019) 16. Shao, S., Zhou, Z.X., Deng, G.J., Du, P., Jian, C.Y., Yu, Z.Y.: Experiment of structural geometric morphology monitoring for bridges using holographic visual sensor. Sensors 20, 1187 (2020)

Generative Adversarial Neural Networks for Guided Wave Signal Synthesis Mateusz Heesch(B) , Ziemowit Dworakowski, and Krzysztof Mendrok AGH, University of Science and Technology, Al. A. Mickiewicza 30, 30-059 Krakow, Poland [email protected]

Abstract. Interpretation of the data acquired from guided-wave-based measurements often utilizes machine learning. However, creating effective machine learning models generally requires a significant amount of data - which in the case of guided waves are costly and time-consuming to acquire. This limitation significantly reduces the application perspective of many advanced machine learning algorithms, most notably deep learning. The problem of data scarcity has been partially addressed in the field of computer vision via the usage of generative adversarial neural networks. These generate synthetic data samples, matching the real data distribution. Aside from images, generative adversarial networks have also been applied to synthesize audio data - with recent advances going as far as successfully synthesizing human speech. These developments suggest that they may be applicable for generating guided waves data - as fundamentally the problem is in many ways similar to that presented by audio waves. This work explores the capabilities of generative adversarial neural networks in the area of guided-wave signal synthesis. The used database was acquired in a series of pitch-catch experiments in which various sensor locations were utilized, and is significantly extended both in terms of sensor locations and data available from each sensor pair. Lastly, the resultant synthesized data is evaluated by qualitative signal comparison. Keywords: SHM · Guided waves · Generative Adversarial Networks Deep learning · Artificial Intelligence

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·

Introduction

Properly monitoring structures has always been an important topic in engineering, whether aimed at assessing the state of the structure, estimating the remaining lifespan, or detecting its structural faults early. One of many researched methods of achieving these goals are SHM systems based on guided waves - which function on the basis of analyzing the propagation of high frequency vibration on predefined paths on the structure. While they offer numerous advantages [7], such as relatively low cost and mass of transducers, or the ability to monitor large structures with few transducers, their shortcoming is the complexity of the c The Author(s), under exclusive license to Springer Nature Switzerland AG 2021  P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 14–23, 2021. https://doi.org/10.1007/978-3-030-64908-1_2

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output signal analysis. This results in attempts to create complex machine learning models to tackle that problem. However, these usually require large amounts of data to train on - data that is generally difficult or costly to acquire. Another field that struggles with this is deep learning, which drew a lot of research attention as the computational hardware advances have spread and allowed for experimentation with considerably deeper and more complicated models. As these models grow, so does their need for adequate data to be trained and tuned on. This is not a particularly big problem to overcome in case of common image recognition tasks, for which not only are there well established and abundant public data sets, but also additional data is often not difficult to acquire. However, when it comes to applying these techniques to more niche areas, the problems of data availability and acquisition become apparent very quickly. One way of combating this issue is data augmentation - generating new data samples by transforming original data. It is usually achieved by passing it through series of transformations - like blurring or adding noise - to acquire a larger data set. However, new viable techniques surface in that area as well. Generative Adversarial Networks (GANs) [3], which are deep neural networks trained specifically to mimic the data from its training distribution, via a contest-like training. In it, a Generator network competes with a Discriminator network, iteratively improving the ability of the Generator to create believable data. Since their conception, there has been a significant amount of research on how to improve them and apply them to various problems [4]. Their use has spread from images to other types of data, e.g. to synthesizing sounds and speech [1], which indicates that they may also apply to guided waves, as these tasks are in many ways similar. GANs have been successfully used as a data augmentation tool to improve the model performance in a myriad of areas - from card fraud detection [2], through kidney CT scan segmentation [9], to machine fault detection [10]. Motivated by the success of GANs in multiple areas, and the relative lack of existing GAN applications in the field of guided waves, this article proposes a GW-GAN (Guided Waves - Generative Adversarial Network) model. It is based on a state-of-the-art style based architecture for image synthesis StyleGAN2 [5,6] as its style vectors can be later leveraged to control the output of the Generator. This opens up more potential uses and future research directions. The model was trained on the OpenGuidedWaves data set [8] to ensure adequate quality and quantity of data. The rest of this paper starts with a brief explanation of the generativeadversarial network concept, moving onto style-based GAN, and the changes made to original StyleGAN2 architecture to facilitate the generation of guided wave signals. Next, the results of training are shown and described, closing with discussion and conclusions.

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Model Preparation Generative-Adversarial Networks

Generative-adversarial networks are a type of a generative model, which in essence means that their task is to generate new data. The way in which it is achieved is creating a “generator” network, which is fed random noise as its input. Naturally, the network needs to be trained, as with random initialization it is just going to return noise as well - albeit one that is different from the input. To give the generator a training direction - as the goal is to generate data within some boundaries, and not random noise - a second network is incorporated into the training process, this one called a discriminator. The task of the discriminator is to distinguish the data produced by the generator, from the examples supplied to the training - the real data. Both generator and discriminator are trained in an alternating fashion, leading to an extended “tug of war” contest. The networks attempt to best each other, with the generator getting increasingly better at generating believable “fake” examples, and the discriminator getting better at pinpointing these “fakes”. 2.2

Style-Based GAN

StyleGAN [5,6] architecture departs from the GAN staple of having the input to the network be a random latent vector. Instead, the first convolutional layer is fed a constant vector, which has its values unfrozen during the training stage to find an optimal initialization. The random latent vector is moved out to the side and applied to the network differently. First, it passes through a “mapping network” which is a multi-layer perceptron that transforms the random input into a set of features (or styles). As this part of the network is also subject to training together with the rest of the generator, the mapping network can find a way to “describe” the signal using these features. In later stages, finding the relationships between this style vector and the signals produced by the generator allows for a large level of control over what the generator produces. The styles themselves are applied to the network on multiple scales (or levels) - more specifically to each convolutional block. The convolutional blocks consist of 2 convolutional layers with weight demodulation as a weaker alternative of instance normalization, preceded by an upsampling operation (except for the first block). Outputs of each scale (postupsampling) are added together via skip-connections, resulting in the output signal being a sum of these (appropriately upsampled) multi-scale signals. This allows for retaining the benefits of progressive-growing GAN training strategy [3], while simplifying the training process and avoiding some of the drawbacks of progressive-growing [6]. The discriminator is a simple residual convolutional network with 2 convolution layers and average-pooling downsampling per block, together with a dense layer head for classification purposes, as seen in Fig. 1

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Fig. 1. Proposed GW-GAN discriminator architecture

2.3

GW-GAN

The architecture of the proposed GW-GAN is largely similar to that of StyleGAN2 [6], with most of the changes centered around accommodating the switch from three-dimensional signal (RGB images) to that of a “catch” guided wave signal which is one-dimensional. These include: 1. Changing relevant activations as the desired output is no longer strictly in positive values 2. Switching over to 1d convolutions 3. Reducing input noise magnitude

Fig. 2. Final GW-GAN generator architecture

The first two of these are self explanatory, however, the necessity for the third change has been made apparent as the initial tests with full magnitude resulted in a Generator whose output was too strongly dictated by the noise vector. Aside from the aforementioned changes, the numbers of convolution blocks in the generator and discriminator have been decreased, and the up/downsampling ratio has been increased from 2 to 4, cutting down on some of the unnecessary depth of the model, and resulting in around 2.5 million total trainable parameters. The resulting generator architecture can be seen in Fig. 2.

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Data and Training

The data used for training has been obtained from OpenGuidedWaves database [8], containing series of “pitch-catch” measurements on a square composite board with 12 sensors, and a total of 28 damage positions. The exact data used for training was all baseline data, and damage positions from 1 to 24, at 240 kHz excitation frequency. For in-depth information on the data set and its acquisition, the reader is referred to OpenGuidedWaves data set documentation. The signals have been trimmed to 2e13 samples to match the output size of the generator network. The training has followed procedures applied to original styleGAN2, with the same losses and optimizer parameters, the only difference being expanding the batch size to 48 samples. The model was trained on a single Nvidia GeForce 1080ti GPU for around 120 h.

3

Results

After completing training, the generator network was used to generate synthetic data via two distinct methods: 1. standard generation from random latent vector 2. generation via directly manipulating the style vectors The first method is straightforward and generates examples in the same way as during training - by feeding a random vector into the mapping network to generate styles, which are then used by the generator. In the second method, the style vectors are manipulated directly, skipping the mapping network and allowing for some level of control over the result. 3.1

Base Results

The generator was capable of producing a diverse set of signals (both in terms of modes, and magnitude), as can be seen in Fig. 3, pointing to successful training and lack of mode collapse (generator “collapsing” into only producing a single type of output regardless of its input). Admittedly, most of the signals it produces when using styles supplied by the mapping network are very close to those present in training data, however, there is some variation between them, as it did not completely overfit the data.

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Fig. 3. Examples of signals synthesized from random noise

As can be seen in Fig. 4, when it produces a signal that is close to one of the training examples, the signal is reproduced fairly accurately. However, it does have visible shortcomings. For example, it has some amount of both low, and high frequency noise that is not present in the original signals (as per Fig. 5 and Fig. 6). Short-term Fourier transforms of the signals show that in the main frequency band the signals behave similarly, with bigger differences appearing in later portions of the signals. Additionally, some of the generated signals have noticeable artefacts in the early parts of the signal, Fig. 7 being a good example of these.

Fig. 4. Comparison of similar synthesized and real signals in time domain

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Fig. 5. Comparison of similar synthesized and real signals in frequency domain

Fig. 6. Comparison of short-term Fourier transforms of similar signals

Fig. 7. Example of artefacts in early portions of synthetic signal

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Style Space Exploration

The way style-based GANs are meant to be used is directly manipulating the style vectors to acquire specific results. Full control of the result via style space is not addressed in this paper - however, as a proof of concept, it presents a simple linear traversal between 2 sets of styles provided by mapping network, which can be seen in Fig. 8. These traversals can produce signals which are not present in the training data.

Fig. 8. Example of linear style-space traversal between two (1st and 5th) styles from mapping network

4

Discussion

As presented in Sect. 3, the generator of GW-GAN appears to produce believable samples, which certainly marks a success on the road to generate guided wave signals using generative-adversarial models. However, the results also show that this road is not likely to be a short or easy one. For one, the generated signals are visibly noisy and at this stage would certainly require additional post-processing before being used for anything. Admittedly this is not a big hurdle, as knowing the approximate frequency bands in which the signals should appear allows for easy application of band-pass filtering. It is however something that needs to be addressed. Additionally, there is also the issue of minor artefacts mostly present in early portions of the signal. Removing these to move the synthetic signals closer to the real ones is certainly a research direction worth exploring. One alternative to post-processing would be investigating and potentially revising the exact effects of multi-scale style and

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noise application, as this may be the root cause of the added noise - after all the original architecture was designed and tailored towards images, in case of which the presence of noise is much less apparent. The other problem stems from the fact that while the synthetic signals that aren’t close to the examples in training data seem plausible based on visual inspection, their legitimacy has yet to be validated. The initial batches of synthesized signals suggest that the generator may have learned the underlying physical properties of the monitored object, and the way the guided waves propagate through it, however, a definite proof is necessary for it to be a reliable data-generation tool. Lastly, provided that the uncertainty from the previous paragraph is addressed with a positive outcome, proper control for the style-space has to be formulated to enable complete data generation. Correctly mapping the stylespace will enable generating data for any combination of transducer and damage positions (though likely less accurate the further they are from combinations recorded in training data), potentially increasing the amount of available data by as much as few orders of magnitude, while retaining its reliability. As far as the efficiency of generation goes, aside from training, the process is very fast due to entire signals being generated at once, not recursively. This leads to a generation time of 24.2 ms +– 375 µs per signal on a single Nvidia GeForce 1060ti GPU.

5

Conclusions

The GW-GAN architecture has been a successful implementation of style-based GAN framework for 1d signals and generates satisfying results after being trained to generate guided wave signals based on OpenGuidedWaves data set [8]. The initial results are imperfect as they contain additional noise and artefacts, pointing to the need for post-processing to bring them closer to real signals. Manipulating the style space allows for generating signals which were not present in the training data set. Future research directions are: verifying whether these new signals could be valid guided wave measurements, post-processing or rethinking multi-scale generator approach for 1d signals, and formulating control over the style space to allow for targeted signal generation.

References 1. Donahue, C., McAuley, J.J., Puckette, M.S.: Synthesizing audio with generative adversarial networks. CoRR abs/1802.04208 (2018). http://arxiv.org/abs/1802. 04208 2. Fiore, U., Santis, A., Perla, F., Zanetti, P., Palmieri, F.: Using generative adversarial networks for improving classification effectiveness in credit card fraud detection. Inf. Sci. 479, December 2017 3. Goodfellow, I.J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y.: Generative adversarial nets. In: Proceedings of the 27th International Conference on Neural Information Processing Systems - Volume 2, pp. 2672–2680. NIPS’2014, MIT Press, Cambridge, MA, USA (2014)

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4. Gui, J., Sun, Z., Wen, Y., Tao, D., Ye, J.: A review on generative adversarial networks: algorithms, theory, and applications (2020) 5. Karras, T., Laine, S., Aila, T.: A style-based generator architecture for generative adversarial networks (2018) 6. Karras, T., Laine, S., Aittala, M., Hellsten, J., Lehtinen, J., Aila, T.: Analyzing and improving the image quality of stylegan (2019) 7. Mitra, M., Gopalakrishnan, S.: Guided wave based structural health monitoring: a review. Smart Mater. Struct. 25(05), 053001 (2016) 8. Moll, J., Kathol, J., Fritzen, C.P., Moix-Bonet, M., Rennoch, M., Koerdt, M., Herrmann, A.S., Sause, M.G., Bach, M.: Open guided waves: online platform for ultrasonic guided wave measurements. Struct. Health Monit. 18(5–6), 1903–1914 (2019). https://doi.org/10.1177/1475921718817169 9. Sandfort, V., Yan, K., Pickhardt, P.J., Summers, R.M.: Data augmentation using generative adversarial networks (cyclegan) to improve generalizability in CT segmentation tasks. Sci. Rep. 9(1), 1–9 (2019) 10. Shao, S., Wang, P., Yan, R.: Generative adversarial networks for data augmentation in machine fault diagnosis. Comput. Ind. 106, 85–93 (2019)

Concrete Surface Crack Segmentation Based on Deep Learning Shun-Hsiang Hsu, Ting-Wei Chang, and Chia-Ming Chang(B) Department of Civil Engineering, National Taiwan University, Taipei, Taiwan [email protected], [email protected], [email protected]

Abstract. Structural health monitoring becomes popular and important in the field of structural engineering because this technology can elongate the structural life cycle as well as protect structures from natural hazards. In the past, structural health monitoring mostly relied on the contact sensors to acquire structural responses and then diagnosed structures from these measurements. Therefore, this study presents a deep learning-based method which can detect and segment the concrete cracks through the noncontact measurements, e.g., images. This method implements deep learning with computer vision to identify crack existence and to further perform segmentation. First, the training data are prepared by collecting images of concrete surfaces with/without cracks, and two state-of-the-art models such as DeepLabv3+ and Mask R-CNN are established along with the transfer learning methods and trained by real crack images. Then, the trained models can extract crack features and yield a mask (i.e. probability map). The cracks are identified and segmented in images from the predicted mask. Finally, the pixel-wise result is processed to determine the geometric properties of cracks such as lengths and widths. Three experiments are designed to examine these two models, and performance of these two models are evaluated with the mean intersection-over-union (mIoU) ratings. Moreover, a comprehensive comparison between Mask R-CNN and DeepLabv3+ is carried out. To sum up, cracks on the concrete surface can be successfully identified, and the near optimal selection of segmentation models under different scenarios is discussed and provided in this study. Keywords: Concrete crack identification · Image segmentation · Deep learning · Segmentation model selection · Mean intersection over union

1 Introduction 1.1 Background In recent years, the autonomous inspection and maintenance of built infrastructure and buildings has drawn great attention from civil engineering researchers. Structural health monitoring (SHM) plays an important role in elongating the structural service life and assuring users’ safety [1]. Although periodically monitoring should better achieve the goal, this approach is time-consuming or labor-intensive to collect such amount of data. In practice, the locations of surface cracks in each photo are still determined by humans © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 24–34, 2021. https://doi.org/10.1007/978-3-030-64908-1_3

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that may result in substantial labor cost and inevitable mistakes in small crack identification. Instead, various automatic approach had been proposed such as the deployment or utilization of additional sensors. Among all sorts of sensors, noncontact imaging measurements have advantages of broad monitoring areas and visualization of possible damage. Moreover, an advanced deep learning model can not only extract high-level features from an image but also recognize complex appearance of targets. These relevant approaches had shown dominant performance in different tasks such as image segmentation [2]. Similarly, the idea with these state-of-the-art techniques can be implemented to identify concrete surface cracks [3]. However, because of the rapid development in deep learning, most studies were focused on illustrating crack detection using a single deep learning models, while limited studies aimed at comparing applicability among various deep learning models. As a result, this paper mainly centers on the implementation and comparison of Mask R-CNN [4] and DeepLabv3+ [5] models for concrete surface crack segmentation. 1.2 Concrete Crack Segmentation To analyze the influence of cracks on structural safety, dimensional information such as widths and lengths of cracks is indispensable. In other words, pixel-level result is needed to yield this kind of information. As a result, studies focusing on image segmentation as well as the extended research on crack detection were reviewed. First, Fig. 1 shows that image segmentation can be subdivided into semantic segmentation and instance segmentation [6]. The main difference between these two methods is to classify each pixel without and with discriminating different object instances. Nevertheless, crack instances rarely overlap, and thus semantic segmentation can be exploited to separate crack instances. Consequently, both kinds of segmentations should be implemented and compared to understand the applicability of concrete surface cracks.

Fig. 1. Demonstration of semantic segmentation and instance segmentation

After the review of associated studies, two state-of-the-art models, i.e., DeepLabv3+ and Mask R-CNN, are selected to perform crack segmentation. DeepLabv3+ features semantic segmentation and executes atrous convolution that can enlarge receptive fields

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under the end-to-end training. In addition, Mask R-CNN is designed for instance segmentation and built on the basis of object detection. A branch for mask prediction is subsequently added to segment object in each detection. In comparison to DeepLabv3+ , Mask R-CNN combines classification loss and bounding-box loss with mask loss. Finally, because only common object categories such as persons are included in open datasets, an additional dataset comprised of crack images is required to achieve crack segmentation. Thus, transfer learning is adopted to the dataset. For example, Song et al. [7] proposed a tunnel crack identification and analysis system based on DeepLabv3. The segmentation model was trained by 8,702 images and validated by 7,016 images. To achieve good performance and real-time applicability, many experiments and adjustments were carried out to optimize the model. The final result had 46.5% intersection-over-union (IoU) on the validation set. The calculation of IoU refers to IoU =

x∪y x∩y

(1)

where x is the area of prediction; y is the area of ground truth. In addition, Kalfarisi et al. [8] integrated crack identification with assessment and visualization to form a unified framework. This study directly applied Mask R-CNN to crack identification, the model was trained with transfer learning by 1,250 images, of which 250 were mainly for validation. The testing result of the model showed outstanding performance and the best IoU was 37%. Although the two models had been tested and implemented, limited studies discussed and compared performance between these two models for crack segmentation. Moreover, direct comparison on IoU in these two studies may not be adequate due to different datasets used in model training. Therefore, this study implements both models for crack segmentation and evaluates the models with the same dataset. The most suitable model can be then determined for concrete surface cracks. Also, the geometric properties in accordance with predicted masks can be estimated, and autonomous inspection can eventually be executed.

2 Deep Learning-Based Method for Crack Segmentation 2.1 Overview Figure 2 illustrates the flowchart of the proposed method for crack segmentation for concrete surface inspection. To begin with model implementation, a dataset should be prepared to train the model and to recognize the appearance of cracks on concrete surfaces. Performance is then evaluated by a validation dataset, and the best model will be deployed for crack identification. Moreover, on-site test images will be examined by the model to obtain predicted mask (i.e. results of segmentation). The result should be visualized on the original image. Finally, geometric properties can be further acquired by analyzing segmentation of cracks. 2.2 Model Implementation To recognize the appearance of various objects, the convolutional neural network (CNN) had been developed with its dominant ability to extract significant features from raw

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Fig. 2. Flowchart that demonstrates crack detection through deep learning model(s)

images. In a model, the function to extract features is defined as backbone. Because of the heavy computational cost and hyperparameters uncertainties, researchers may not be able to reproduce others’ results. Thus, the backbone with being trained weights can be utilized for those categories of objects varied from the original image tasks. Then, transfer learning can be applied to satisfy different objectives. Two kinds of backbones used in the implementation are introduced. One of the backbones is ResNet101 [9], a short name for the residual network, is well-known for avoiding gradient vanishing and can learn significant features. Moreover, the number standing for the depth of layers is 101 layers in the backbone. DeepLabv3+ is implemented in this study based on ResNet101. The other backbone is ResNet101-FPN which combines feature pyramid networks (FPN) with ResNet101 [10]. FPN contributes to fusing feature maps in different levels of resolutions. This backbone is employed to build Mask R-CNN, because for the detection algorithm, features of small objects may miss after convolutional computation. With the help of FPN, detection performance can be enhanced and is beneficial to crack segmentation. In summary, the backbone of DeepLabv3+ is ResNet101 and the pre-trained weight is downloaded from Pytorch [11], while the backbone of Mask R-CNN is ResNet101 combined with FPN with the pre-trained weight originated from FAIR [12]. To specify other parameters in each model, the default values in the original papers [4, 5] are adopted to meet the objectiveness. 2.3 Analysis of Geometric Properties After the inference, the predicted mask reflects the position of cracks on the pixel coordinates of images. Subsequently, post-processing of segmentation is required to acquire the widths and lengths of cracks, which are the most crucial information for structural safety evaluation. Because the geometry of cracks is arbitrary polygon, the definition

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of widths and lengths should be clarified. The analysis procedure of geometric properties is shown in Fig. 3. For the calculation of widths and lengths, the centerline of a crack polygon should be found. With the position of the centerline, the width equals the aggregate of the shortest distance between nodes on the centerline and points on the polygon border. Moreover, in despite of different branch lines in the centerline, the crack length refers to the one with maximum length. Consequently, the width and length can be obtained and presented as pixel units. Note that this study does not include any projection methods, and the collected images are obtained in parallel to the concrete surface.

Fig. 3. Illustration of geometrical properties analysis

3 Training and Validation 3.1 Training and Validation Dataset To train the deep learning models, this study prepares a dataset composed of concrete crack images. A part of these images named “public” are collected from open sources [13], and the rest named “private” are self-acquired. As can be seen in Table 1, totally 265 images used in the training include 140 RGB images from public dataset and 125 grayscale images from private dataset. The corresponding resolution of these images is also listed. The private dataset is derived from the inspection photos of two built tunnels, and thus this private dataset can be classified into two groups: 97 images (namely private_1) and 28 images (namely private_2). The dataset is further divided into a training set and validation set. Because the validation set varies among experiments, more details will be elaborated in the next section. Moreover, the data augmentation such as horizontal flips and random rotations will be applied to the training set because the number of all datasets is much smaller than that of open datasets. After the augmentation, the size of training data is increased by 8 times.

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Table 1. Details of the training dataset Source of dataset

Size Resolution (width, height)

Public

140 (448, 448)

Private

125 (400, 400), (512,512)

3.2 Experimental Setup To validate and compare performance of Mask R-CNN and DeepLabv3+ , three experiments are designed. Each experiment uses different combinations of data sources. In the beginning of the first experiment, the training and validation sets are only composed by the public dataset, and the rest dataset is viewed as a test set. Because the appearance of cracks is distinct from different data sources, the test set having different sources from the training set can be utilized to measure the generality of the model. Next, one of the private datasets is joined to the public dataset, and the combined set is used to train and validate models. Similarly, the test set originates from the other private dataset which is not considered during the training. In addition, the last experiment incorporates all the dataset in this study, and thus no more data belong with a test set. The detailed number of the splitting ratio of training set to validation set in each experiment are presented in Table 2. Finally, the model is trained with the hyperparameters shown in Table 3. As can be seen, the batch size and epoch are fixed while the optimizer and learning rate adopt decay policy. The weight decay aims at restraining the sum of weights of deep learning models that can prevent overfitting. The polynomial decay helps the model converge to a local optimum for learning rate. Table 2. Experiments from various datasets Exp.

Training set (Size)

Validation set (Size)

Test set (Size)

1

public only (110)

public only (30)

all private 125

2

public+ private_1 (187)

public + private_1 (30 + 20)

private_2 (28)

3

All (207)

public + private_1 + private_2 (30 + 20 + 8)

None

4 Results and Discussions To evaluate performance of segmentation, the mean intersection-over-union (mIoU) rating is selected, and IoU of each category is also listed. The highest value in evaluation

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S.-H. Hsu et al. Table 3. Hyperparameters used in training Hyperparameters DeepLabv3+ Mask R-CNN Batch size

8

4

Epoch

200

100

Optimizer

stochastic gradient descent (momentum = 0.9, weight_decay = 1e − 4)

Learning rate

2e − 4 (poly decay)

by the validation and test sets is shown in Table 4. After epochs of each experiment, the training and validation losses are illustrated in Fig. 4. As can be seen in Fig. 4(a), the top indicates the training mask loss of Mask R-CNN, and the bottom plot shows changes of mIoU calculated by the validation set. The loss drops smoothly meaning that the model successfully learns the features of cracks in the training set. Despite the increased amount of data, the loss curves in different experiments are almost identical. As a result, the validation is required to acquire the performance of the model from a more objective perspective. In the bottom, the mIoU curve of Experiment 3 is higher than the others, while the mIoU curve of Experiment 1 is much lower than the others. Thus, when different sources of data are included, the model is still capable of crack identification and even performs better. Moreover, although the training loss tends to be diminished, the mIoU becomes saturated with a slight decline occurring in the end of training. In short, for Mask R-CNN, the size of data hinders its performance and if the dataset is small, roughly 70 epochs are enough to train the model. Table 4. The result of three experiments Exp.

1 2 3

Model

Validation (Test) IoU (crack)

IoU (background)

mIoU

Mask R-CNN

0.2451(0.0667)

0.9627(0.9749)

0.6039(0.5208)

DeepLabv3+

0.3910(0.0115)

0.9772(0.9757)

0.684(0.4936)

Mask R-CNN

0.3169(0.0719)

0.9701(0.9735)

0.6435(0.5403)

DeepLabv3

0.3870(0.0155)

0.9760(0.9669)

0.6815(0.4912)

Mask R-CNN

0.3278(−)

0.9728(−)

0.6503(−)

DeepLabv3

0.3924(−)

0.9708(−)

0.6816(−)

The loss and mIoU curves of DeepLabv3+ are shown in Fig. 4(b). Being different from instance segmentation, semantic segmentation models output the mask of the whole image. The total loss is only calculated by subtraction between a predicted mask and the ground truth. In this context, a merely small difference in the changes of loss and mIoU

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Fig. 4. Training log of Mask R-CNN and DeepLabv3+ in each experiment. Note that x-axis represents the number of training epochs while y-axis represents their values.

between experiments is found. Thus, the loss and mIoU curves are drawn in separated figures. The result shows that performance does not improve when the amount of data used increase. Moreover, after total 200 epochs training, both loss and mIoU become convergent. As a result, DeepLabv3+ needs more training epochs than Mask R-CNN, and training with more data is not helpful for improving performance. In comparison of the mIoU curves, the curves of DeepLabv3+ are higher and can be found in Table 4. In contrast, Mask R-CNN outperforms DeepLabv3+ on the test set; therefore, Mask R-CNN may extract a more general representation of cracks. Although the validation IoU of cracks is comparable with the results in other recent studies [7, 8], the test IoU is seriously low. This outcome indicates that it is not feasible for the model

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to identify cracks on different concrete surfaces. However, the model can have much more accurate prediction on a different case by an additional small dataset to fine-tune the model. To discuss performance on different datasets, the mask predictions by Mask R-CNN and DeepLabv+ in Experiment 3 are shown in Fig. 5. As can be seen, Mask R-CNN can better learn with the data labeled with smooth borders, while DeepLabv3+ performs better on the data with pixel-wise labels, which are accompanied by rough borders. Because the private and public datasets are labeled with the polygon and pixel-wise labeled, respectively, the mIoU of DeepLabv+ drops a little after adding private datasets.

Fig. 5. Comparison of predictions between Mask R-CNN and DeepLabv3+ The first row is from private_2, while the second is from private_1. The last two rows are selected from the public dataset.

In conclusion, Mask RCNN has comparable performance with DeepLabv3+ and according to the test result, Mask R-CNN learns more robust features of cracks than DeepLabv3+ . For a different label policy, Mask R-CNN is considered to be suitable for polygon-based labels, while DeepLabv3+ has better performance on the dataset with

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pixel-wise labels. Because Mask R-CNN aims at achieving instance segmentation, discontinuous and fragmented cracks should cause different instances that can confuse the model. By contrast, DeepLabv3+ is trained by the whole images, and thus polygon-based labeling policy may include too much unnecessary noise beyond the actual borders of cracks. As a result, the selection of a segmentation model depends on the characteristics of a dataset. The ensemble of the two models can also be an option to tackle different conditions.

5 Conclusion In this study, the comparison between Mask R-CNN and DeepLabv3+ segmentation models was presented for concrete surface crack identification. Three experiments were designed to evaluate performance of these two models with different combinations of datasets. With the increase in the amount of data, only Mask R-CNN improved performance, while DeepLabv3+ remained almost the same. The test result also indicated that both Mask R-CNN and DeepLabv3+ cannot identify cracks in the image from a dataset which is not included in the training. Moreover, different types of labels were able to influence performance of models. Due to the definition difference between instance segmentation and semantic segmentation, Mask R-CNN preferred polygon-based labels, while DeepLabv3+ preferred pixel-wise labels. To sum up, performance of deep learning models still relied on the characteristics of datasets. As a result, the characteristics were considered as a key factor to select the most appropriate model.

References 1. Feng, D., Feng, M.Q.: Computer vision for SHM of civil infrastructure: from dynamic response measurement to damage detection–a review. Eng. Struct. 156, 105–117 (2018) 2. Guo, Y., Liu, Y., Georgiou, T., Lew, M.S.: A review of semantic segmentation using deep neural networks. Int. J. Multimedia Inf. Retrieval 7(2), 87–93 (2018) 3. Dung, C.V.: Autonomous concrete crack detection using deep fully convolutional neural network. Autom. Constr. 99, 52–58 (2019) 4. He, K., Gkioxari, G., Dollár, P., Girshick, R.: Mask r-cnn. In: Proceedings of the IEEE International Conference on Computer Vision (2017) 5. Chen, L.-C., Zhu, Y., Papandreou, G., Schroff, F., Adam, H.: Encoder-decoder with atrous separable convolution for semantic image segmentation. In: Proceedings of the European Conference on Computer Vision (ECCV) (2018) 6. Lin, T.-Y., Maire, M., Belongie, S., Hays, J., Perona, P., Ramanan, D., Dollár, P., Zitnick, C.L.: Microsoft coco: common objects in context. European conference on computer vision, Zurich, Switzerland (2014) 7. Song, Q., Wu, Y., Xin, X., Yang, L., Yang, M., Chen, H., Liu, C., Hu, M., Chai, X., Li, J.: Real-time tunnel crack analysis system via deep learning. IEEE Access 7, 64186–64197 (2019) 8. Kalfarisi, R., Wu, Z.Y., Soh, K.: Crack detection and segmentation using deep learning with 3D reality mesh model for quantitative assessment and integrated visualization. J. Comput. Civil Eng. 34(3), 04020010 (2020)

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9. He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, Nevada (2016) 10. Lin, T.-Y., Dollár, P., Girshick, R., He, K., Hariharan, B., Belongie, S.: Feature pyramid networks for object detection. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2017) 11. Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L.: Pytorch: an imperative style, high-performance deep learning library. In: Advances in Neural Information Processing Systems (2019) 12. Wu, Y., Kirillov, A., Massa, F., Lo, W.-Y., Girshick, R.: Detectron2 (2019). https://github. com/facebookresearch/detectron2 13. Liu, Y., Yao, J., Lu, X., Xie, R., Li, L.: DeepCrack: a deep hierarchical feature learning architecture for crack segmentation. Neurocomputing 338, 139–153 (2019)

Deep-Learning-Based Bridge Condition Assessment by Probability Density Distribution Reconstruction of Girder Vertical Deflection and Cable Tension Using Unsupervised Image Transformation Model Yang Xu1,2,3(B) , Yadi Tian1,2,3 , Yufeng Zhang4 , and Hui Li1,2,3 1 Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of

Industry and Information Technology, Harbin Institute of Technology, Harbin 150090, China [email protected] 2 Key Lab of Structures Dynamics Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China 3 School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China 4 State Key Laboratory of Safety and Health for Inservice Long Span Bridges, Nanjing 211112, China

Abstract. This study proposes a deep-learning-based condition assessment approach by reconstructing marginal probability density distributions of girder vertical deflection (GVD) and cable tension (CT) using unsupervised image transformation (UNIT) model for a real cable-stayed bridge. 27 and 139 sensors of GVD and CT are distributed along the full bridge, and both the sampling frequencies are 2 Hz. First, vehicle-induced components of GVD and CT are extracted by data pre-processing while the temperature-induced components are removed, a time window of 3 h with a sliding length of 10 min is used to obtain original GVD and CT segments, and the corresponding margin probability density distributions (PDFs) are calculated by kernel density estimation. The training and test sets consist of 2986 and 6236 PDFs, respectively. The proposed UNIT model consists of a series of variational autoencoders (VAEs) and generative adversarial networks (GANs). Both the PDFs of GVD and CT are used as inputs. Then, the proposed UNIT model is updated by solving the mini-max problem of training GANs, in which VAEs act as generative models. Finally, the Wasserstein distance between the predicted and ground-truth PDFs of CT acts as the indicator of bridge condition change. Results show that specific modes of PDF variations induced by SHM system upgrade, cable damage, data anomaly, and traffic jam can be recognized to assess bridge condition. Keywords: Bridge condition assessment · Unsupervised image transformation model · Girder vertical deflection · Cable tension · Probability density distribution · Wasserstein distance

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 35–45, 2021. https://doi.org/10.1007/978-3-030-64908-1_4

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1 Introduction Recently, machine learning (ML) based structural health monitoring has attracted considerable attentions in the structural health monitoring (SHM) community. Worden and Manson extracted the transmissibility of monitoring data as the input feature, then used multi-layer perceptron (MLP) and support vector machine (SVM) for damage localization and degree evaluation [1]. Their results pointed out that acquiring data under different damage states was of great significance to the damage evaluation. Ding et al. modeled correlations between modal frequencies and environmental factors using neural networks (NN) [2], in which feature extraction was performed based on prior experiences, and thus might not be suitable under other real-world application scenarios. Posenato et al. used moving principal component analysis to recognize structural anomalous behaviors, which was only demonstrated by the FEM simulation data [3]. Lin and Cai compared the traditional neural networks (TNN) and time-delay neural networks (TDNN) in detecting stiffness reduction of truss bridge [4], which used vertical displacements of joints and cross-sectional areas as inputs and outputs, respectively. Their results showed that TDNN performed much better than TNN, especially facing incomplete structural health monitoring data. Abdeljaber et al. used one-dimensional convolutional neural networks to conduct vibration-based damage detection and localization [5]. Nazarian et al. studied the relationship between the deck strain and cable tension by structural analysis and could detect the reduction of cable tension larger than 30% [6]. For a cable-stayed bridge, the relationship between girder vertical displacement (GVD) and cable tension (CT) can reflect the structural condition and should be properly evaluated. Thus, correlation variations between these two types of structural responses can be used as the indicator for condition assessment of a cable-stayed bridge. This study proposes a deep-learning-based method to model correlation variations between probability density distributions (PDFs) of GVD and CT using unsupervised image transformation (UNIT) model, and further utilizes the Wasserstein distance (W-distance) between predicted and ground-truth PDFs of CT to represent the change degree of bridge condition. This paper is organized as follows. Section 2 introduces the methodology of UNIT model and W-distance. Section 3 describe implementation details. Section 4 shows the corresponding training and test results and discusses specific modes of structural condition changes. Section 5 concludes the paper.

2 Methodology The probability distribution function (PDF) variation between vehicle-induced GVD and CT is modeled by unsupervised image transformation (UNIT) model, which consists of a series of variational auto-encoders (VAEs) and generative adversarial networks (GANs). Both the PDFs of GVD and CT are used as inputs of the established UNIT model as

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    (i) (i) (i) (i) (i) (i) (i) (i) X1 = X1,1 , X1,2 , . . . , X1,m ∈ Rl×m , X2 = X2,1 , X2,2 , . . . , X2,n ∈ Rl×n T T   (i) (i) 1 2 l 1 2 l X1,ja = x1,ja , x1,ja , . . . , x1,ja ∈ Rl×1 , X2,jb = x2,jb , x2,jb , . . . , x2,jb ∈ Rl×1 (1) (i)

(i)

where X1 and X2 represent the PDF matrixes of the i-th GVD and CT segments, (i) (i) and x2,jb denote the i-th PDF of the ja-th and jb-th GVD and CT respectively; x1,ja sensors, respectively; subscripts m and n denote the total number of GVD and CT sensors, and l is the number of discretization intervals in each PDF. Figure 1 shows the network topology of the established UNIT model. The UNIT model was originally proposed to transfer images in one domain to another domain in an unsupervised manner [7]. The proposed UNIT model is constructed using variational autoencoders [8] (VAEs, noted by E 1 -G1 and E 2 -G2 ) and generative adversarial networks [9] (GANs, noted by G1 -D1 and G2 -D2 ). It is composed of six subnetworks, i.e., GVD encoder E 1 , CT encoder E 2 , GVD generator G1 , CT generator G2 , GVD adversarial discriminator D1 , and CT adversarial discriminator D2 .

Fig. 1. Network topology of the established UNIT model

Combining the GVD encoder E 1 and GVD generator G1 , a VAE for GVD is built by mapping the input GVD (X1 ) to a latent variable (Z) by E 1 and reconstructing it by (i) (i) decoding the latent variable (Z) by G1 . In this study, inputs X1 and X2 are obtained with one-to-one correspondence in the time domain, and identical vehicle loads and structural condition are embedded inside. Therefore, it can be assumed that a pair of GVD and CT PDFs can be mapped into a shared-latent space. That is, Z = E1 (X1 ) = E2 (X2 ). Considering X1 = G1 (Z) and X2 = G2 (Z), X1 and X2 can then be transferred mutually as X1 = G1 (Z)=G1 (E2 (X2 )),X2 = G2 (Z)=G2 (E1 (X1 )). Therefore, GVD and CT are supposed to be reconstructed by translating CT and GVD in another way. Thus, the assumption of shared-latent space also implies the cycle-consistence assumption [10], and the transferred components of GVD and CT can be noted as X1 = G1 [E2 (X2 )]=G1 [E2 (G2 [E1 (X1 )])], X2 = G2 [E1 (X1 )]=G2 [E1 (G1 [E2 (X2 )])] (2) The shared latent space assumption is achieved by sharing weights. Specifically, weights of the last two layers in E 1 and E 2 and the first two layers of G1 and G2 are shared during the training process.

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The UNIT model uses a synthetical loss function, which includes in total six components of VAE1 , VAE2 , GAN1 , GAN2 , cycle-consistencies CC1 and CC2 as L=

min

max LVAE1 (E1 , G1 ) + LGAN1 (E2 , G1 , D1 ) + LCC1 (E1 , G1 , E2 , G2 )

E1 ,E2 ,G1 ,G2 D1 ,D2

+LVAE2 (E2 , G2 ) + LGAN2 (E1 , G2 , D2 ) + LCC2 (E2 , G2 , E1 , G1 ) (3) The VAE losses are LVAE1 (E1 , G1 )=λ1 KL(q1 (Z|X1 )||pη (Z))−λ2 EZ∼q1 (Z|X1 ) [log pG1 (X1 |Z)] LVAE2 (E2 , G2 )=λ1 KL(q2 (Z|X2 )||pη (Z))−λ2 EZ∼q2 (Z|X2 ) [log pG2 (X2 |Z)]

(4)

where hyper-parameters λ1 and λ2 control the ratios of KL-divergence and expected reconstruction errors. The KL-divergence term penalizes the deviation of the approximated posterior distribution of latent space from the prior one. The GAN losses are LGAN1 (G1 , D1 )=λ0 EX1 ∼PX1 [log D1 (X1 )] + λ0 EZ∼q2 (Z|X2 ) [log(1 − D1 (G1 (Z)))] LGAN2 (G2 , D2 )=λ0 EX2 ∼PX2 [log D2 (X2 )] + λ0 EZ∼q1 (Z|X1 ) [log(1 − D2 (G2 (Z)))] (5) where hyper-parameter λ0 controls the ratio of GAN losses in the whole function. The cycle-consistency losses are LCC1 (E1 , G1 , E2 , G2 )=λ3 KL(q1 (Z|X1 )||pη (Z))+ λ3 KL(q2 (Z|X11→2 )||pη (Z))−λ4 EZ∼q2 (Z|X1→2 ) [log pG1 (X1 |Z)] 1

LCC2 (E2 , G2 , E1 , G1 )=λ3 KL(q2 (Z|X2 )||pη (Z))+ λ3 KL(q1 (Z|X12→1 )||pη (Z))−λ4 EZ∼q1 (Z|X2→1 ) [log pG2 (X2 |Z)]

(6)

2

where the first two KL-divergence terms penalize the approximated latent variable distribution deviating from the prior one in the cycle-reconstruction process, and the third term represents the expected reconstruction error. Hyper-parameters λ3 and λ4 control the ratios of KL-divergence and reconstruction errors. Adversarial training is performed on GAN1 (G1 -D1 ) and GAN2 (G2 -D2 ). G1 can generate GVD from the reconstruction stream of G1 (E1 (X1 )) and the translation stream of G1 (E2 (X2 )). Since G1 (E1 (X1 )) can be trained in a supervised manner by VAE1 , only the translated component G1 (E2 (X2 )) applies the adversarial training with D1 . Similarly, D2 is trained to discriminate the translated PDF of CT G2 (E1 (X1 )). First, the discriminator losses need to be maximized to update D1 and D2 . Second, the VAE and cycle-consistency losses need to be minimized. Both two processes are iteratively performed until the total loss converges. After the proposed UNIT model is trained, it can be used to transform PDFs between GVD and CT. To evaluate the similarity between predicted and ground-truth PDFs, the Wasserstein distance (W-distance, also noted as earth mover’s distance EMD) is used as the indicator of bridge condition changes [11]. EMD denotes the minimum cost to move the predicted PDF to the ground-truth one, which is analogous to the energy required to move a pile

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of earth from one shape to another shape. The predicted and ground-truth PDFs P and Q are discretized to u and v intervals. Positions of interval center and values of probability density are noted as p and w. The distance from pi to qj is dij , and the value gap from wpi to wqj is fij . The W-distance can be calculated as P=



       p1 , wp1 , . . . , pu , wpu , Q = q1 , wq1 , . . . , qv , wqv

⎛  u v ⎞ u

v





EMD = min⎝ dij fij fij ⎠, fij = wpi , fij = wqj , i = 1 · · · u, j = 1 · · · v (7) i=1 j=1

i=1 j=1

j

i

3 Implementation Details 3.1 Sensor Locations The investigated cable-stayed bridge has a main span of 648 m and two side spans of 63 + 257 m. There are 168 cables in total. CTs are measured by anchorage load cells, and GVDs are measured by hydraulic pressure transmitters. Figure 2 shows locations of 27 GVD and 139 CT sensors. A sampling frequency of 2 Hz is adopted, and a time window of 3 h with a sliding length of 10 min is used to generate GVD and CT segments. The monitoring period lasts from 2006 to 2015, data from 2016-2017 are used for training and the rest data is for test. The training and test sets include 2986 and 6236 segments, respectively.

(a) Locations of GVD sensors (denoted by black dots)

(b) Location of CT sensors (red dots and green triangles represent upriver and downriver) Fig. 2. Locations of GVD and CT sensors

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3.2 Data Pre-processing Raw monitoring data of GVD and CT consist of temperature and vehicle-induced effects. The temperature effect is removed by detrending, and the detrending result is shown in Fig. 3 using CT for example.

(a) Raw data and the temperature effect

(b) the vehicle-induced effect after detrending

Fig. 3. Extraction of the vehicle-induced component for CT

After detrending, the vehicle-induced components of each GVD and CT sensor are regularized in the range of [−1,1] by     (j)  (t) (t) αja = α˜ ja max(α˜ ja , j = 1 · · · k), ja = 1 · · · m     (j)  (t) (t) βjb (8) max(β˜jb , j = 1 · · · k), jb = 1 · · · n = β˜jb (t) (t) (t) (t) where α˜ ja and β˜jb are the detrended GVD and CT data at time t, αja and βjb are the corresponding data after regularization, k denotes the number of data samples in a time window, m and n denote the number of GVD and CT sensors. To reduce the effect of measurement noises, data deviating from the base line less than 0.3 σ are removed in Fig. 4(a). Then, the probability density distribution of the rest data samples is obtained by kernel density estimation in Fig. 4(b).

3.3 Hyper-Parameter Setting λ0 = 10, λ1 = λ3 = 0.1, λ2 = λ4 = 100. E 1 includes 4 convolutional layers, 4 residual layers and 2 shared layers. G1 includes 2 shared layers, 4 convolutional layers and 4 residual layers. D1 includes 6 convolutional layers. E 2 , G2 , D2 are the same as E 1 , G1 , D1 .

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(a) removing noises in CT data

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(b) PDF of a 3-hour CT segment

Fig. 4. Illustration of PDF generation using CT for example

4 Results and Discussions 4.1 SHM System Upgrade Figure 5 displays the EMD of predicted and ground-truth PDFs for a typical short cable. It reveals that the EMD become larger since 2011. We are informed by the bridge management authority that the SHM system was upgraded at that time.

Fig. 5. EMD changes of a typical cable induced by SHM system upgrade

4.2 Cable Damage Next, we focus on the data before SHM system upgrade from 2006-2009. Figure 6 displays the results of a damaged cable SA12_1, in which the red vertical line represents the boundary of training and test sets. Figure 6(a) shows that the EMD has changed since 2008/12. B and C are selected as test samples in normal and abnormal conditions, respectively. Figure 6(b) (c) and Fig. 6d show the raw data (blue line), data to compute PDF (red line), and predicted and ground-truth PDFs at B and C. 4.3 Data Anomaly Figure 7 detects data anomaly of SA11_1. Figure 7(a) shows the EMD of SA11_1 changed since 2008/12. Figure 7(b) (c) and Fig. 7(d) show that sensor anomaly exists at C.

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(a) EMD changes

(b) time history data of B before cable damage

(c) time history data of C after cable damage

(d) comparisons of predicted and ground-truth PDFs in B and C

Fig. 6. Results of SA12_1 detecting cable damage

4.4 Traffic Jam Figure 8 displays the results of NA08_1 detecting traffic jam. Figure 8(a) shows the EMD changes, and it indicates that EMDs at A and B are much larger than the general level. Figure 8(b) and Fig. 8(c) show that traffic jams happened at that time.

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(a) EMD changes

(b) time history data of B without data anomaly

(c) time history data of C with data anomaly

(d) comparisons of predicted and ground-truth PDFs in B and C

Fig. 7. Results of SA11_1 detecting sensor anomaly

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(a) EMD changes

(b) time history data of A with traffic jam

(c) time history data of B with traffic jam

(d) comparisons of predicted and ground-truth PDFs in A and B

Fig. 8. Results of NA08_1 detecting traffic jam

5 Conclusions This study proposes a deep-learning-based bridge condition assessment approach by modeling marginal probability density distributions of girder vertical deflection (GVD) and cable tension (CT) by the unsupervised image transformation (UNIT) model. Results show that the Wasserstein distance between the predicted and ground-truth PDFs of CT can act as the indicator of bridge condition changes. Specific modes of PDF variation

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induced by SHM system upgrade, cable damage, data anomaly, and traffic jam are successfully identified. Acknowledgements. Financial support for this study was provided by the National Natural Science Foundation of China [Grant No. 51921006, 51638007, U1711265 and 52008138], National Key R&D Program of China [Grant No. 2019YFC1511102 and 2018YFC0705605], China Postdoctoral Science Foundation [Grant No. BX20190102 and 2019M661286], Heilongjiang Postdoctoral Funding [Grant No. LBH-TZ2016 and LBH-Z19064], Open Funding of State Key Laboratory of Safety and Health for In-service Long Bridges [Grant No. 2020SJKHIT001], and CCCC Science and Technology R&D Project [Grant No. 2018-ZJKJ-02].

References 1. Worden, K., Manson, G.: The application of machine learning to structural health monitoring. Philos. Trans. 2007(365), 515 (1851) 2. Ding, Y.L., Deng, Y., Li, A.Q.: Study on correlations of modal frequencies and environmental factors for a suspension bridge based on improved neural networks. Sci. China-Technol. Sci. 53(9), 2501–2509 (2010) 3. Posenato, D., et al.: Model-free data interpretation for continuous monitoring of complex structures. Adv. Eng. Inform. 22(1), 135–144 (2008) 4. Niu, L., Cai, Q.: Structural health monitoring and damage detection using neural networks technique. In: 2013 Third International Conference on Intelligent System Design and Engineering Applications (Isdea), pp. 1302–1304 (2013) 5. Abdeljaber, O., et al.: Real-time vibration-based structural damage detection using onedimensional convolutional neural networks. J. Sound Vib. 388, 154–170 (2017) 6. Nazarian, E., et al.: Detection of tension loss in cables of cable-stayed bridges by distributed monitoring of bridge deck strains. J. Struct. Eng. 142(6), 04016018 (2016) 7. Liu, M., Breuel, T.M., Kautz, J.: Unsupervised image-to-image translation networks. arXiv: Computer Vision and Pattern Recognition (2017) 8. Kingma, D.P., Welling, M.: Auto-encoding variational bayes. arXiv: Machine Learning (2013) 9. Goodfellow, I., et al.: Generative adversarial nets. In: Advances in Neural Information Processing Systems (2014) 10. Zhu, J.-Y., et al.: Unpaired image-to-image translation using cycle-consistent adversarial networks. In: Proceedings of the IEEE International Conference on Computer Vision (2017) 11. Rubner, Y., Tomasi, C., Guibas, L.J.: The earth mover”s distance as a metric for image retrieval. Int. J. Comput. Vis. 40(2), 99–121 (2000) 12. Li, S., et al.: Condition assessment of cables by pattern recognition of vehicle-induced cable tension ratio. Eng. Struct. 155, 1–15 (2018)

Summary of Current Practice in Vibration Monitoring of Utility Tunnels and Shafts in the UK Clive Chin-Kang Shen1(B) and Ursula Lawrence2 1 Arcadis, formerly Capital Real Estate and Infrastructure, London, UK

[email protected] 2 Capita Real Estate and Infrastructure, East Grinstead, UK

Abstract. The development of urbanzation areas requires more land and space in the already congested space. Increasingly new structures are having to be constructed in proximity to existing underground infrastructure. In the UK, this infrastructure is of varying ages and the new construction poses a potential threat to the serviceability or integrity of existing structures in respect of their original SLS and ULS design capacities. One of the concerns is construction vibration. Activities such as piling, demolition and compaction will generate vibrations at various frequencies. Due to the complexity of vibration propagation related to the structure damage, there is a lack of reliable data on the threshold of vibration-induced damage in structures both in countries where national standards already exist and in the UK. This paper will summarize the currently available UK guidance, BS 5228-2, BS 7385-2, and CIRIA TN142, build up a systematic assessment approach, and present real monitoring data collected from construction sites. These monitoring data are normally enormous and recorded in real time, hence opened the opportunities for artificial intelligence data transmission and alert notification. The assessment approach suggested to adopt the 3 Tiers system similar to the better developed building response to ground movements assessment proposed by Burland (1995) and Mair (1996). The first tier will screen out any structures monitored to have less than a threshold of vibration because damage to these structures is highly unlikely. The second tier will look at individual sources of vibration frequency, if applicable, and their respective limits will be assigned according to available case histories. The third tier will apply if monitored vibrations at a particular structure exceeds the limits set out in the second tier. A detailed inspection and specific structure assessment will be required to ensure the integrity of such a structure. The artificial intelligence driven monitoring can apply this criterion accordingly. Keywords: Vibration monitoring · Structure health · Tunnel · Underground shaft · Artificial intelligence

1 Introduction The increasing trend of urbanization has seen great demands for residential or office developments over existing underground infrastructures in congested urban areas. How © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 46–54, 2021. https://doi.org/10.1007/978-3-030-64908-1_5

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to evaluate construction impacts in order to minimize disruption to the infrastructure services becomes an increasingly important issue. One of the construction impacts is ground vibration. It can be generated by demolition of derelict structures, ground compaction, pile driving, or other earthworks activities. Due to the complexity of vibration propagation, related to the associated structure damage, there is a lack of reliable data on the thresholds of vibration-induced damage. Only guidelines are available in the UK and these are listed as below in Table 1. Table 1. Current guidance of construction vibration control in the UK Guidance

Subject

1 BS 5228–2

Vibration

2 BS 7385–2

Damage Levels

3 CIRIA TN142 Piling Vibrations

BRE Digest 251 (Head and Jardine, 1992) has published a classification based on visible damage to walls due to ground vibration as listed in Table 2 below. Noted that crack width is one factor in the assessment of damage category, but it should not be used on its own as direct measure of it. Table 2. Ground vibration induced damage to the wall by crack observation

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2 Vibration Measurement Caused by Piling and Other Construction The sources of ground vibration can be broadly classified into three categories, transient vibration, continuous vibration, and occasional vibration. • Transient vibrations are produced by rapid-impact driven piling techniques such as precast piles, sheet piles or driven cast-in-place piles. Also building demolition which includes pile removal. • Continuous vibrations are produced by vibratory driven piles when a steady-state vibration is generated when using vibro-drivers, vibroflots or resonant drivers. A less regular but continuous form of vibration can also result from rapid impact piling where the vibrations do not fully die away between blows. • Occasional vibrations are produced from the driving of casing or chiselling through obstructions from bored and augered piling techniques. Also includes breaking down/trimming of pile heads. For all construction induced ground vibration, including piling, the vibration is measured by peak particle velocity (ppv), which is also known as simulated resultant peak particle velocity. It is defined as the vector sum of the peak velocities in the three mutually perpendicular directions, irrespective of the time at which these three peak values occurred.  2 2 2 + vymax + vzmax ppv = vxmax The simulated resultant treats the three maximum components as though they occurred at the same instant and is sometimes referred to as Square Root Sum of Squares (SRSS). A similar strategy to the well-established building damage assessment due to underground construction has been adopted here to develop the greenfield structure impact assessment due to ground vibration. The assessment is based on the records of peak particle velocity, ppv (mm/sec) and vibration frequency (Hz) if available, measured at the foundation level. The effects of piling energy and attenuation, ground settlements and movements caused by vibration, piling methods and mitigation actions, and existing structure reinforcement details and conditions are not taken into account in this assessment strategy.

3 Phase 1 Assessment Structure damage is unlikely to occur at the level of ppv less than 2 mm/sec measured at the substructure, e.g. the outer face of structural foundations or the tunnel extrados. At ppv values of between 2 and 8 mm/sec, there is the increasing possibility of plaster cracking for above ground structures. At ppv values between 8 and 50 mm/sec, damage is an increasingly high risk (Part 2 of BS 5228 limits light framed structures to 15 to 20 mm/sec and heavy reinforced structures to 50 mm/sec). Ppv values of above

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50 mm/sec, some form of damage is likely and might include adverse effects on the load-bearing units. For underground infrastructures, production of a contoured plan of ppv values of 8 mm/sec, 12 mm/sec, and 50 mm/sec may be useful to visualise and identify those structures which suffer greater than 8 mm/sec vibration. These structures will then advance into Phase 2 assessment as described in the next section.

4 Phase 2 Assessment Two types of vibration sources are classified in this assessment phase 2, one for occasional vibration which is based on the experience gained from blasting technology; the other is for transient and continuous vibration which is more applicable to most piling and demolition/construction works induced vibrations. Here the discussions will be only focused on the latter which is the transient and continuous case due to the limit of article length. Some organisations have provided guidance for construction related vibration monitoring in the UK. They are presented below and a recommended conclusion to cover most available guidelines will be presented in the end of this section. The German Standards Institution (Deutsche Industrie-Norm, Berlin) DIN 4150 (1986) in Part 3 as quoted by Head and Jardine (1992) deals with transient and continuous vibrations in structures and provides a guideline shown as the Table 1 below. The Swiss Standard SN 640 312 (1978) which is also quoted in BRE Digest 353 and Head and Jardine (1992), is entitled ‘Effects of Vibrations on Structures’. It provides guide values of limiting peak particle velocities and is shown as the Table 2 below. BS 5228: Part 2 has also provided an additional section to discuss the assessment of vulnerability of ground-related structures and services in its section B.4. It does not specify the predominant frequency range of ground vibration, instead giving generic threshold guidelines. It doesn’t provide the threshold limits specifically for shaft structures, however guidelines are provided for retaining walls and underground service tunnels. The threshold guidelines for retaining wall structures in Section B.4.2 recommend that a ppv limit of 10 mm/sec at the toe and 40 mm/sec at the crest should generally be adopted, with a reduction factor of 1.5 to 2.5 for continuous vibrations according to individual structure circumstances. Section B.4.4 of BS 5228: Part 2 provides the threshold guidelines for underground service tunnels, with a remark that the guidelines are only used in the absence of specific criteria from the undertakers. A maximum ppv threshold of 15 mm/sec is recommended for continuous vibrations. This limit is not applicable for service tunnels that are in a state of incipient failure. These tunnels could exhibit the following features: such as poorly formed joints, hard spots, badly prepared trench bases, distortion due to settlement or heave, or unstable surrounding ground caused by previous or existing leaks. Summary guidelines based on the consideration of above various recommended guidelines are presented in Table 3 below, and suggested to be used for future practice in phase 2 assessments. Ground vibration monitoring ppv levels exceeding these guidelines listed in Table 3 are recommended to advance to Phase 3 assessment.

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Table 3. Guidelines for continuous foundation vibration (after DIN4150, 1986 and as given in BRE Digest 353) Type of structure

Vibration velocity, vp in mm/sec Foundation

Plane of floor of uppermost full storey

At a frequency (Hz) of

Frequency mixture

99%

Non critical

99.9%

99.2%

0. Amplitude compensation factor α at (c) 50 kHz (d) 250 kHz. Phase compensation factor β at (c) 50 kHz (d) 250 kHz.

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Fig. 5. The stiffened panel with 8 surface mounted DuraAct transducers

Figure 4 shows the direction dependence of amplitude ratio α and arrival time ratio β for temperature deviation δT from −40 ◦ C to 40 ◦ C. The compensation factors in the orientation that is not present in Fig. 1 are obtained using linear interpolation with the adjacent available orientations. It is evident that α and β values vary in different directions, which is as expected considering the anisotropic lay up and direction dependence of wave amplitude and velocity shown in Fig. 2. Direction dependence of thermal effects on wave features in an-isotropic composite laminates might be further investigated with numerical simulations, but is out of the scope of this work.

5

Experimental Implementation and Validation

Figure 5 shows the stiffened CFRP composite panel with 8 surface mounted DuraAct sensors. The dimension of panel is 500 mm × 250 mm × 2.5 mm. A 500 mm long stiffener with omega (Ω) cross-section is attached at the centre panel. A weight was dropped at the foot of the stiffener to create a 30 J impact, introducing barely visible impact damage. Signals were recorded from the two panels in an environmental chamber from 20◦ C to 45◦ C at every 5◦ C before the impact. Previously obtained compensation factors from Flat panel (shown in Fig. 4) in the respective directions were used to compensate the signal change due to change in temperature condition.

Fig. 6. Temperature compensation of the signal recorded in path A2S3 from the stiffened panel. Signal S0 was recorded at T0 = 20◦ C. Signal S1 was recorded at T1 = 40◦ C. The figure above plots the two signals and the figure below plots the compensated signal S0 , αST0 (βt), with S1 . (a) Response to 50 kHz 5-cycle toneburst excitation. (b) Response to 250 kHz 3-cycle toneburst excitation.

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Fig. 7. Damage localisation for the stiffened panel using A0 mode guided wave response to 50 kHz toneburst excitation at various temperature conditions.The purple circle marks the actual damage location, the cross marks the predicted damage location.

Figure 6 shows the signals from path A2S3 on the same side of the stiffener. Despite being prone to superposition of the reflected wave from the edge of the panel and the edge of the stiffener, the shape of the signals remain similar to those in the simple panels and the first arrival of the two wave modes can still be clearly spotted. Even though the first wavepacket overlaps with multiple boundary reflected wavepackets, the phase difference between the two signals is well compensated for the first two wave packets of the signal length at both 50 kHz and 250 kHz. The amplitude difference is almost entirely eliminated for signal at 50 kHz and is compensated at the beginning of the signal at 250kHz.

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Figure 7 presents the delay-and-sum damage imaging results using all signal path. Path network diagrams are shown on the top left of Fig. 7. The localisation results for the signals corresponding to the pristine and damaged states at 20◦ C are shown for reference to the results obtained with pristine and damaged signals at different temperatures. The damage state signal at 30◦ C, 35◦ C, 40◦ C and 45◦ C are used with pristine state signal at 20◦ C as baseline. Without temperature compensation, the localisation results deteriorate as the damaged state temperature deviates from the baseline temperature for both panels. When temperature compensation is implemented, the localisation result can be restored to nearly the unimpaired result provided that the current temperature is less than 20◦ C higher than the baseline temperature.

6

Conclusion

In this work a physical based temperature baseline reconstruction approach for guided wave structural health monitoring in anisotropic composite structures is presented. The effects of temperature on signal amplitude and arrival time are investigated and quantified as dimensionless amplitude and arrival time factors. Both factors show significant dependence on signal path orientation. As a result, these factors are expressed as functions of this orientation as well as temperature difference, allowing this technique to be conveniently applied to baseline reconstruction in anisotropic structures. In addition, by deriving dimension independent compensation factors, those derived for simple structures can be easily applied to other structures of larger size and increased complexity, provided the structures are composed of the same material and installed with the same type of sensors. The derived compensation factors are shown to be effective in compensating the temperature effect of signals in a stiffened panel. Using baseline signals recorded at 20◦ C and the corresponding compensation factors, consistent localisation of a barely visible impact damage was achieved at current temperatures up to 20◦ C higher than the baseline temperature.

References 1. Michaels, J.E., Michaels, T.E.: Guided wave signal processing and image fusion for in situ damage localization in plates. Wave Motion 44(6), 482–492 (2007) 2. Zhao, X., et al.: Active health monitoring of an aircraft wing with embedded piezoelectric sensor/actuator network: I. defect detection, localization and growth monitoring. Smart Mater. Struct. 16(4), 1208–1217 (2007) 3. Flynn, E.B., Todd, M.D., Wilcox, P.D., Drinkwater, B.W., Croxford, A.J.: Maximum-likelihood estimation of damage location in guided-wave structural health monitoring. Proc. R. Soc. A: Math. Phys. Eng. Sci. 467(2133), 2575–2596 (2011) 4. Flynn, E.B., Todd, M.D., Croxford, A.J., Drinkwater, B.W., Wilcox, P.D.: Enhanced detection through low-order stochastic modeling for guided-wave structural health monitoring. Struct. Health Monit. 11(2), 149–160 (2012)

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5. Sharif-Khodaei, Z., Aliabadi, M.H.: Assessment of delay-and-sum algorithms for damage detection in aluminium and composite plates. Smart Mater. Struct. 23(7), 075007 (2014) 6. Sharif-Khodaei, Z., Aliabadi, M.H.: Lamb-wave based damage detection in anisotropic composite plates. Key Eng. Mater. 627, 1–4 (2014) 7. Konstantinidis, G., Drinkwater, B.W., Wilcox, P.D.: The temperature stability of guided wave structural health monitoring systems. Smart Mater. Struct. 15(4), 967 (2006) 8. Lu, Y., Michaels, J.E.: A methodology for structural health monitoring with diffuse ultrasonic waves in the presence of temperature variations. Ultrasonics 43(9), 717– 731 (2005) 9. Croxford, A.J., Moll, J., Wilcox, P.D., Michaels, J.E.: Efficient temperature compensation strategies for guided wave structural health monitoring. Ultrasonics 50(4), 517–528 (2010) 10. Harley, J.B., Moura, J.M.F.: Scale transform signal processing for optimal ultrasonic temperature compensation. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(10), 2226–2236 (2012) 11. Dworakowski, Z., Ambrozinski, L., Stepinski, T.: Multi-stage temperature compensation method for lamb wave measurements. J. Sound Vib. 382, 328–339 (2016) 12. Liu, G., Xiao, Y., Zhang, H., Ren, G.: Baseline signal reconstruction for temperature compensation in lamb wave-based damage detection. Sensors 16(8), 1273 (2016) 13. di Scalea, F.L., Salamone, S.: Temperature effects in ultrasonic lamb wave structural health monitoring systems. J. Acoust. Soc. Am. 124(1), 161–174 (2008) 14. Roy, S., Lonkar, K., Janapati, V., Chang, F.-K.: A novel physics-based temperature compensation model for structural health monitoring using ultrasonic guided waves. Struct. Health Monit. 13(3), 321–342 (2014) 15. Fendzi, C., Rebillat, M., Mechbal, N., Guskov, M., Coffignal, G.: A data-driven temperature compensation approach for structural health monitoring using lamb waves. Struct. Health Monit. 15(5), 525–540 (2016) 16. Croxford, A.J., Wilcox, P.D., Drinkwater, B.W., Konstantinidis, G.: Strategies for guided-wave structural health monitoring. Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci. 463, 2961–2981 (2007). The Royal Society 17. Gresil, M., Giurgiutiu, V.: Prediction of attenuated guided waves propagation in carbon fiber composites using rayleigh damping model. J. Intell. Mater. Syst. Struct. 26(16), 2151–2169 (2015) 18. Schubert, K.J., Herrmann, A.S.: On the influence of moisture absorption on lamb wave propagation and measurements in viscoelastic CFRP using surface applied piezoelectric sensors. Compos. Struct. 94(12), 3635–3643 (2012) 19. Williams, W.B., Michaels, T.E., Michaels, J.E.: Characterization of guided wave velocity and attenuation in anisotropic materials from wavefield measurements. In: AIP Conference Proceedings, vol. 1706, p. 030002. AIP Publishing (2016) 20. Yue, N., Khodaei, Z.S., Aliabadi, F.M.H.: An innovative secondary bonding of sensors to composite structures for SHM application. In: Advances in Fracture and Damage Mechanics XVII. Key Engineering Materials, vol. 774, pp. 516–522. Trans Tech Publications Ltd. (2018). https://doi.org/10.4028/www.scientific.net/KEM. 774.516 21. Michaels, J.E., Lee, S.J., Croxford, A.J., Wilcox, P.D.: Chirp excitation of ultrasonic guided waves. Ultrasonics 53(1), 265–270 (2013)

Prognostic Health Monitoring for Downhole Drilling Tools Mauro Caresta(B) and Adam Bowler Schlumberger Cambridge Research, Cambridge CB3 0EL, UK {mcaresta,abowler}@slb.com

Abstract. In recent years there has been a substantial increase in the rate-ofpenetration in drilling operations with the aim of reducing costs and reaching the reservoir in shorter times. This improvement comes as a result of the greater capabilities of land rigs which are now able to push larger amounts of energy into the drilling system. Consequently, the stress on downhole tools has increased and fatigue failures are becoming more common. Typical failures include cracks in the weaker spots of the downhole tools. In this work we demonstrate that downhole vibration measurements can be used for prognostic health monitoring and to track the structural integrity of the tools. We show evidence that a fundamental downhole frequency mode drops 30% during drilling operations as a crack propagates in the tool. A structural model of the drilling tool is presented, illustrating the relationship between the natural frequency and the localized crack stiffness. By monitoring this frequency shift in real-time, catastrophic and costly failures can be avoided. Keywords: Prognostic heath monitoring · Drilling · Crack propagation

1 Introduction In recent years there has been a substantial increase in the rate-of-penetration (ROP) in drilling operations for oil and gas, with the aim of reducing costs and reaching the reservoir in shorter times. This is particularly evident in United States (US) shale gas operations where the ROP has more than doubled in the past 5 years. Typical wells in this market are characterized by horizontal sections of 10,000 feet or more. This has resulted in the stress on the drilling tools increasing and fatigue failures becoming more common in the weakest points of the bottom hole assembly (BHA). Figure 1 shows a typical torsional fatigue crack on a drill collar port hole and a dramatic twist-off of a steering unit which led to a lost-in-hole (LIH) event. These result in considerable amounts of non-productive time, charges for fishing operations and loss of reputation to the client [1]. Many of the failures occur when the steering tool is located below a positive displacement motor (known in the industry as a mud motor), which is used to increase the rotational speed of the drill-bit. This configuration has the peculiarity of uncoupling the torsional dynamics of the portions of the drillstring above and below the motor. This is due to the power section of the mud motor generating the rotational speed of the driveshaft and everything attached to it, while providing a rigid axial connection by means of a © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 550–558, 2021. https://doi.org/10.1007/978-3-030-64908-1_51

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Fig. 1. Cracks in steering tools.

thrust bearing necessary for the weight transfer to the drill-bit. The torsional uncoupling generates two resonant systems. The first is on the long length scale of the drillstring above the motor which can be 4–6 km long and with a torsional resonance typically in the order of 1 Hz. The second is on the shorter length scales of the BHA. One example is in the collars below the motor which can be 15-20 m long and with fundamental torsional resonance in the order of 100–200 Hz, which are the focus of this paper. In the oil industry these resonances are called High Frequency Torsional Oscillations (HFTO) because they are well above the drillstring torsional harmonics. The excitation of HFTO is very detrimental for the fatigue life of the tool due to the high number of torque cycles with respect to a typical low frequency excitation. It is suggested that a prognostic health monitoring (PHM) of the tools is possible by monitoring for changes in the frequency of HFTO.

2 Torsional Resonances in a BHA A drillstring is a long sequence of pipes connected from the drill-bit to a surface top drive which rotates the whole string to transmit the torque and the weight to the drill-bit in order to cut the rock. The bottom of the string, called the bottom hole assembly (BHA), has specialized tools for steering, measurements and telemetry. In horizontal wells, a mud motor is often placed above the steering tool in the BHA to increase the rotational speed of the drill-bit. As explained above, the focus of this work is on the torsional vibrations of the BHA below the motor, which is torsionally uncoupled from the long section above it. Torsional vibrations have been long studied in the industry, especially focusing in low frequency stick-slip dynamics [2] and more recently in high frequency vibrations [3–5]. The excitation mechanism of the HFTO is beyond the scope of this work, but it is here enough to say that these modes are well excited during the drilling operations especially when drilling hard rock. The torque generated to cut the rock has enough bandwidth to excite the natural modes of the BHA. Torsional resonances, mode shapes and transfer functions can be predicted using a modified version of the Dynamic Stiffness Method [6]. The BHA can be modelled using classic beam theory and as a combination of pipes with variable cross-sectional area. The equation of motion for the

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torsional vibrations of each pipe i is given by Eq. 1 1 δ2 u δ2 u − =0 δx 2 c2 δt 2

(1)

where the index i has been omitted, u is angular position, x is the distance, t is the time and c is the torsional wave speed in pipe i given by c = (G/ρ)0.5, where G is the shear modulus and ρ is the material density. The solution to Eq. 1 can be written in terms of two propagating waves and is given by Eq. 2 u(x, t) = A1 ekx+ jt + A2 e−kx+ jt

(2)

where k is the torsional wave number given by k = ω/c, ω is the angular frequency, and A1 and A2 are coefficients. The pipes can be joined together applying the continuity conditions of torque and angular displacement at the connections. The boundary conditions are free at both top and bottom ends. All the continuity and boundary conditions can be arranged in the matrix form DX = 0 where X is the vector of the unknown coefficients couples (A1 , A2 ) and D is the dynamic stiffness matrix (DSM). The vanishing of the determinant of the DSM gives the natural frequencies of the system. The steady-state response under harmonic torque excitation can be calculated using a direct method in which the force is considered as part of the boundary conditions. The vector with the unknown amplitudes can be found by inverting the DSM and multiplying by the force vector F, for any frequency, as given by Eq. 3: X = D−1 F

(3)

The advantage of this method respect to the Finite Element Method (FEM) is that the DSM is formally exact and computationally much more efficient since element discretization is not needed. Structural damping can be added using a complex Young’s Modulus E(1 + jη) where E is the Young’s Modulus and η is the structural loss factor. The schematic cross-section side view of a 6.75-inch diameter BHA below the mud motor investigated in this paper is shown in Fig. 2, where the horizontal and vertical axes have different scales for illustration purposes. The BHA is made of 10 cylindrical pipe sections with different cross-sectional areas, each made of steel. More details are not given for reasons of confidentiality. The drill-bit is on the left-hand side and the narrowest section is the mud motor’s transmission shaft. Everything beyond 6 m is hidden inside the motor housing and the long section on the right-hand side is the motor’s rotor. The point mobility for a unit torque impulse at the drill-bit was calculated with the DSM and is shown in Fig. 3. The lowest three natural modes are evident from the peaks in the mobility. Figure 4 and Fig. 5 show the mode shapes scaled to unit amplitude. The modes at 63 Hz (Fig. 4) and at 235 Hz are mostly localized in the rotor and in reality will be more damped due to the motor’s elastomer. Consequently, they generally do not appear in downhole measurements. The mobility was calculated assuming a loss factor η = 0.001. The main frequency observed during drilling is the one at 211 Hz (Fig. 5) which involves the motion of the whole BHA. The mode shape of the torque is also shown in Fig. 6.

Prognostic Health Monitoring for Downhole Drilling Tools Drill-bit

Drill collars

Transmission shaft

Rotor

Fig. 2. Schematic of the 6.75-in. diameter BHA.

Fig. 3. Mobility of the 6.75-in. diameter BHA.

Fig. 4. Mode shape at 63 Hz of the 6.75-in. diameter BHA.

Fig. 5. Mode shape at 211 Hz of the 6.75-in. diameter BHA

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Fig. 6. Torque mode shape at 211 Hz of the 6.75-in. diameter BHA

3 Steering Unit Twist-off The steering tool records high frequency acceleration data in 65 ms bursts sampled at 32.5 kHz for post-job monitoring and investigation purposes. These intermittent recordings are triggered whenever the tool experiences large shock events. The acceleration in the radial direction (perpendicular to the tool’s rotational axis) typically shows an HFTO signature by cross coupling between torsion and bending inside the tool. During one particular drilling operation which resulted in the dramatic twist off shown in Fig. 1, a total of 462 waveforms were recorded corresponding to 30 s recording time (but taken during around 1 day of drilling). The absolute values of the acceleration and the rootmean-square (RMS) of the waveforms are against equivalent time in Fig. 7, showing some missing data around 18 s. The spectrogram of the waveforms is shown in Fig. 8. The striking feature is the 211 Hz resonance dropping by 30% down to 150 Hz. The 211 Hz resonance is the second natural mode of the BHA as predicted by the model in the previous section. The change of the HFTO frequency versus the drilling time in days is shown in Fig. 9, which suggests that the major shifts in frequency happened at three specific events rather than gradually over time.

Fig. 7. Waveforms recorded.

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Fig. 8. Spectrogram of the radial acceleration.

Fig. 9. HFTO shift vs drilling time.

4 Crack Model The shift in the fundamental frequency can be explained by the presence of a progressively opening crack, which locally reduces the stiffness of the BHA. The change of natural modes in response to a localized damage in a structure has often been used for PHM in other industries such as civil engineering and aeronautics [8, 9] but to the authors’ knowledge there have not been cases reported in the drilling industry. A crack is typically modelled as a localized spring with variable stiffness K, which is related to the crack size. A large value for the stiffness, in this case larger than K = 108 Nm/rad can be considered as a perfectly rigid connection, while on the other hand, K = 0 means the two parts are completely disconnected. The torsional model described before can be modified by adding a localized spring at the location of the bias unit crack, which was around 0.6 m from the drill-bit end, to study how the natural modes changes with K. Results in Fig. 10 show how the three lowest frequencies evident in the mobility of Fig. 3 shift as K get smaller.

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Fig. 10. Natural modes shift as function of K.

The graph shows that as the value of K decreases (the crack size increases) the dominant frequency at 211 Hz shifts towards a lower frequency. For the frequency to shift down to 150 Hz, as seen in the field data, the stiffness must drop around two orders of magnitude. It is also interesting to see a mode veering as K approaches 105 Nm/rad; when the frequency is approaching the value of the first mode originally at 62 Hz, then veering happens [7]. As another example, the crack in the port hole shown on the left of Fig. 1 occurred in a 4.75-in. diameter BHA. The length of the BHA below the motor was similar to the previous case. The spectrogram of the acceleration data is shown in Fig. 11. The HFTO shifted around 10% during the run.

Fig. 11. Spectrogram of the radial acceleration for the 4.75-inch diameter BHA.

The same modelling approach can be applied to the 4.75-in. diameter BHA configuration. Similarly to the previous case, the first mode at 169 Hz is localized in the rotor. The second mode at 232 Hz is more evenly distributed and is the mode excited and measured during the run (Fig. 12). The frequency shift is predicted and shown in

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Fig. 13 for a crack located at the position of the port hole in Fig. 1, which was around 4 m from the drill-bit end.

Fig. 12. Mode shape at 232 Hz of the 4.75” BHA.

Fig. 13. Frequencies shift for the 4.75” BHA.

5 Prognostic Health Monitoring The field data and analysis in this paper suggests that a prognostic health monitoring is possible by tracking the value of the dominant resonance of the BHA, to detect in real-time changes in the structural integrity of the tools. As shown from the field data, the HFTO shift was a clear indication of an opening crack, and knowledge of that in real-time could have prevented a costly Lost-In-Hole incident. A simple algorithm using the accelerometer data can be implemented in the processor of the downhole tool and the measurement can be sent to the surface in the telemetry to flag to the driller any change larger than a predefined noise threshold. The exact relationship between the stiffness K and the crack size is interesting but it is not necessary for monitoring purposes. Furthermore, the range of possible cracks shapes is large, and a simplified crack model would not add values to the application of the health monitoring.

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6 Conclusions In this work it has been shown that a crack on a drilling tool can lead to the shift of the resonance frequency of the BHA. This is particularly true for tools attached below the motor, which have clear and distinct fundamental torsional frequencies in the region of 100–200 Hz. The frequency shift could be tracked and monitored in real-time to offer a simple and valid prognostic on the structural integrity of the tool and avoid catastrophic failures.

References 1. Zhang, Z., et al.: Continuous High Frequency Measurement Improves Understanding of High Frequency Torsional Oscillation in North America Land Drilling, SPE-187173-PA (2017) 2. Halsey, G.W., et al.: Drillstring Torsional Vibrations: Comparison Between Theory and Experiment on a Full-Scale Research Drilling Rig, SPE-15564-MS (1986) 3. Oueslati, H., et al.: New Insights Into Drilling Dynamics Through High-Frequency Vibration Measurement and Modeling, SPE-166212-MS (2013) 4. Warren, T.M., Oster, J.H.: Torsional Resonance of Drill Collars with PDC Bits in Hard Rocks, Paper SPE 49204 (1998) 5. Bowler, A., et al.: Continuous High-Frequency Measurements of the Drilling Process Provide New Insights Into Drilling-System Response and Transitions Between Vibration Modes, SPE170713-PA (2016) 6. Caresta, M., et al.: Design modifications to a submarine propulsion system for reduction of hull radiated noise. J. Ship Res. 55, 149–162 (2011) 7. Pierre, C.: Mode localization and eigenvalue loci veering phenomena in disordered structures. J. Sound Vibr. 126, 485–502 (1988) 8. Doebling, S.W., et al.: A summary review of vibration-based damage identification method. Shock Vibr. Dig. 30, 91–105 (1998) 9. Salawu, O.S.: Detection of structural damage through changes in frequency: a review. Eng. Struct. 19, 718–723 (1997)

System Identification of Beam-Like Structures Using Residual Indicators Derived from Stochastic Subspace Analysis Riccardo Cirella(B) , Angelo Aloisio, and Rocco Alaggio Dipartimento di Ingegneria Civile Edile-Architettura ed Ambientale, Universit` a degli Studi dell’Aquila, Piazzale Pontieri, Monteluco di Roio, 67100 L’Aquila, Italy [email protected]

Abstract. In this paper, the parameters of numerical models of beamlike structures are estimated from scalar indicators derived from ambient vibration measurements. Parameters are estimated through an optimization process, in which indicators are taken as objective function. This approach is developed for an indicator, chosen from literature, derived from the reference-based covariance-driven stochastic subspace analysis. The reliability of the parametric identification is further estimated: the method proposed is numerically tested and then applied to a laboratory steel beam. Both simulated and measured vibration data are used to validate the practicability and accuracy of the approach. Keywords: System identification Model-driven identification

1

· Operational modal analysis ·

Introduction

System identification consists in building mathematical models of dynamical systems and updating them on data observed from systems themselves [1]. This process is based on three main elements: the acquisition of system experimental data, the realization of the numerical representation of the investigated system, and the choice of a proper loss function, which expresses the discrepancy between measured data and the simulated response from the mathematical model. Identification can therefore be considered as an optimization problem in which the minimization of the objective function C(x) : D ⊂ Rz → R leads to the identification of the system parameters x ˆ ∈ Rz , with z representing the number of parameters to be identified. x ˆ = arg min C(x) x∈Rz

(1)

The choice of the objective function is conditioned by the data to be measured: when performing vibration tests on structures such as civil engineering ones, data c The Author(s), under exclusive license to Springer Nature Switzerland AG 2021  P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 559–568, 2021. https://doi.org/10.1007/978-3-030-64908-1_52

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collection is subjected to important constraints since often tests have to be performed under environmental excitation [2,3]. This is the reason why algorithms working with output-only measurements, such as the stochastic system identification (SSI), became very popular. Within the framework of the SSI, one of the steps involves the decomposition of the dynamic response into subspaces [4]. Focusing on this concept, it can be noted that the discrepancy between two different responses, one derived from data relating to the actual structural behavior and that simulated with numerical model, is measurable as a defect of orthogonality between the relative subspaces. In the last decades, this approach has been deepened in the general context of structural health monitoring (SHM) [5–8], for the investigation of structural damage detection, through the introduction of sub-space based damage indicators [9–12]. As they are defined, damage indicators are well suited to be used as objective function in an identification procedure. In this work, damage indicator from [13] is chosen as objective function to be minimized and its performance is numerically tested. The method is then validated through experimental tests on a real suspended steel beam. Typical nomenclature of the SHM literature is assumed, referring to the actual structural behavior as referenc state and to the simulated responses as the reference states.

2

Subspace-Based Damage Indicators for Vibrating Structures

State-space representation of output-only measured vibration data corresponds to the following discrete time model, known as discrete-time stochastic statespace model xk+1 = Axk + vk (2) yk = Cxk + wk with the states xk ∈ Rn , the outputs yk ∈ Rr , the state transition matrix A ∈ Rn×n and the observation matrix C ∈ Rr×n , where r is the number of sensors and n is the system order. The process noise vk is an unmeasured Gaussian white noise sequence with zero mean and constant covariance matrix def Q = E(vk vkT ) = Qδ(k − k  ), where E (·) denotes the expectation operator and wk is the measurement noise. In [12,14] a residual function was proposed to detect changes in the system eigenstructure from measurements yk without actually identifying the eigenstructure in the possibly damaged state. The considered residual is associated with a covariance-driven output-only subspace identification algorithm. Let G = E(xk+1 ykT ) be the cross-covariance between the states and the outputs, T ) = CAi−1 G be the theoretical output covariances, and Λi = E(yk yk−i

System Identification of Beam-Like Structures

⎡

Λ1 Λ2 .. .

⎢ def ⎢ Hp+1,q = ⎢ ⎣ Λp+1

⎤ Λ 2 . . . Λq Λ3 . . . Λq+1 ⎥ ⎥ def .. . . .. ⎥ = Hank(Λi ) . . . ⎦ Λp+2 . . . Λp+q

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(3)

the theoretic block Hankel matrix. Using measured data (yk )k=1,...,n , a consistent ˆ p+1,q is obtained from the empirical output covariances estimate H n 1  T Λˆi = yk yk−1 N

(4)

ˆ p+1,q = Hank(Λˆi ) H

(5)

k=1

The residual function, originally proposed by [12,14], compares the undamaged system, called also reference state, with the damaged or current one. The considered residual matrix can be written as ˆ p+1,q Rc = Sˆ0T H

(6)

ˆ p+1,q in the referwhere SˆT is the left null space of the block Hankel matrix H ˆ p+1,q is the covariance block Hankel matrix in the current one; ence state and H subscript c stays for conventional. In practice, the excitation covariance Q may change between different measurement sessions of the system due to different environmental factors, while the excitation is still assumed to be stationary during one measurement. A change in the excitation covariance Q leads to a change in the cross-covariance between states and outputs G and thus in the Hankel matrix. Some researchers [13,15] proposed a new residual, which is robust to changing excitation. Let ˆ p+1,q . U1 be the matrix of the left singular vectors obtained from an SVD of H As U1 is a matrix with orthonormal columns, it can be regarded as independent of the excitation Q, which qualifies its use for a residual function that is robust to changes in the excitation covariance. Then, the residual matrix can be written as (7) Rr = Sˆ0T U1T where subscript r stays for robust. A subspace-based damage indicator may be defined as an arbitrary scalar function of the residual matrix. Id = f (R)

(8)

where Id is a damage indicator, f (.) an arbitrary scalar function and R the residual matrix. In the current paper, the damage test presented by Yan et al. [13] is implemented, built on the robust residuals (Eq. (7)): Iy,r = norm(Rr ) where norm picks the maximum singular value of the matrix Rr .

(9)

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Setup Description

In order to validate the method and illustrating the performance of the chosen indicator in guessing the actual values of the parameters involved, numerical and experimental test have been performed: in both the tests, the optimization procedure is applied for the identification of the Young modulus E and the mass density ρ of a suspended steel beam. Both parameters have been discreetly varied within a range of feasible values: this allows to graphically represent the trend of the objective function and verify the possible presence of local minima. The structure considered in both numerical and experimental tests is a 2.5 m long steel IPE120 beam, with welded rectangular end plates of 200 mm × 100 mm × 5 mm. The beam is held up by two steel supports using springs. The structure corresponds to an actual experimental setup at the Dynamic Laboratory of the DICEAA, Universit` a degli Studi dell’Aquila, Italy (Fig. 1).

Fig. 1. (a) Experimental setup, (b) Experimental setup with added mass.

The data acquisition system is composed of seven vertical velocimeters, placed over the beam at equidistant positions and aligned along its longitudinal axis. The input signal is a white noise in the frequency band 0–1000 Hz applied by means of an electrodynamic shaker at the left end of the beam. In order to perform the analyses required for the identification process, an in-plane finite element model of the beam described above has been considered (Fig. 2). The beam has been divided in 8 beam finite elements [16], basing on the disposition of the velocimeters on the real structure. The input signal is simulated with a white noise vertical displacement, assigned to node 1. The output signals obtained from the model are the 7 vertical velocities of the nodes in positions corresponding to that of the 7 velocimeters placed over the experimental beam.

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Fig. 2. Schematic representation of the FE model of the steel beam.

A constant value of 1% is taken for damping ratio for all modes involved in the analysis. Basing on laboratory experience, this value is adoptable for this kind of structure; moreover, this assumption is confirmed by results of the modal identification, described in Sect. 5.

4

Numerical Test

In order to perform the numerical test, the FE model presented in Sect. 3 has ˆ to the Young been considered. After assigning to the model a chosen value E modulus and ρˆ to the mass density, its dynamic response has been simulated: this response is considered as the reference state in the identification procedure. The damaged states are produced by varying E and ρ in a discrete range of values; the objective function is then estimated comparing the damaged states to the reference. The test was repeated several times varying the noise, in order to have a demonstration that robust indicators are indifferent to changes in noise amplitude.

Fig. 3. Variation of the mean value of the objective function over the selected range of values for parameters E and ρ: numerical test. On the left, the trend of the objective function, on the right, the contour plot. The red cross indicates the identified point of minimum.

Figure 3 shows that the indicator presents a trend in which minima are arranged along a straight line, whose direction is that given by constant ratio between E and ρ. From the contour plot it can be seen that, in the valley, the objective function presents an absolute minimum, right in correspondence of the ˆ in the best point, the mean value of indicator is close to zero. chosen pair (ˆ ρ, E):

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Experimental Test

The same methodology tested in the numerical case has been applied to identify the Modulus E and the mass density ρ of the experimental steel beam described in Sect. 3. In the optimization process, experimental data are used as reference state, while simulated data refers to the states produced using attempt parameters. ˆ and ρˆ are then compared with the pair Eexp The identified parameters E and ρexp , which are respectively the conventional value of the Young modulus adopted for the steel and the measured mass density of the beam (Table 1). Table 1. Beam parameters, frequencies and damping ratios of the first three flexural modes from modal identification, with their 2σ uncertainty bounds. Eexp ·105 ρexp ·10−5 fexp,1 (N/mm3 )

fexp,2

fexp,3

ξexp,1

ξexp,2

ξexp,3

(MPa)

(Hz)

(Hz)

(Hz)

(%)

(%)

(%)

2.10

7.95

127.3 ± 0.005 337.6 ± 0.010 625.7 ± 0.007 1.28 ± 0.37 1.08 ± 0.49 0.126 ± 0.11

As a preliminary action, vibration data acquired during the experimental tests has been processed according to the SSI-COV driven algorithm, detecting the natural frequencies, the damping ratios, and the mode shapes of the steel beam. In the frequency band 0–1000 Hz, the first three modes are rigid body ones, followed by the three flexural in-plane described in Table 1 and Fig. 4.

(a) 1st mode 127.3 Hz

(b) 2nd mode 337.6 Hz

(c) 3rd mode 625.7 Hz

Fig. 4. First three flexural in-plane mode shapes of the steel beam in the frequency range (0–1000 Hz). Full line: mode shapes, dashed line: estimated standard deviation x200.

5.1

Parametric Identification Results

Results from parametric identification (Fig. 5) show objective functions with trends similar to that obtained in numerical tests. However, unlike in the numerical case, a clear absolute minimum can’t be found.

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Fig. 5. Experimental test. Variation of the objective function over the selected range of values for parameters E and ρ: 3d graph (left) and relative contour plot (right).

Fig. 6. Experimental test: mean value of the robust indicator along the valley and its σ bounds.

This fact can be addressed to practical problems generally relating to an experimental campaign, such as the uncertainty due to experimental measures, noise presence or other reasons, like the bias of the model or the computational uncertainty due to the chosen discretization of the parameters state D (Fig. 6). Taking into account the sensitivity of the dynamics with respect to a mass variation [17], an auxiliary case is considered, in order to further constrain the solution: an additional mass of 1.4 kg/m is distributed along the beam (Fig. 3). To ensure good results, the value of the masses is chosen in a way that they produce frequency shift of about 4% [18]. The addition of the mass produces a difference in the response of the dynamic system and a consequent variation of the trend of the curves described by the objective functions: in particular, it changes the slope of the straight line that identifies the alignment of the points of minimum (Fig. 7). Since the physical parameters to be identified do not change during the process (the total mass density is the sum of that to be identified and of a known term), the point of minimum of the objective functions has to be the same for both cases. Therefore, it is logical to think that the pair to be identified is close to that given by the point of intersection between the two straight lines obtained (Fig. 7b).

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Fig. 7. (a) Results from experimental test with added mass. (b) Intersection between the lines of minima identified in the case without mass (Fig. 5) and in that with mass added (Fig. 7): the cross defines the couple of parameters identified, the circle indicates the pair (ρexp , Eexp ). In the figure, the conventional variation interval for the Young modulus of the steel is shown. Table 2. Experimental case: identified parameters and discrepancies with measured values. ˆ Ind E (MPa)

Iˆd ρˆ 3 (N/mm )

Eexp (MPa)

ρexp (N/mm3 )

ΔE Δρ (%) (%)

Iy,r 2.19 · 105 7.62 · 10−5 0.109 2.10 · 105 7.925 · 10−5 4.19 −3.81

ˆ ρˆ) obtained from this process for Table 2 shows the pair of minimum (E, both the indicators adopted and makes a comparison with the experimental one. Table 3 compares experimental modal parameters and that obtained from numerical model in which identified parameters has been applied. Despite this discrepancy, a very small difference between the numerical and experimental frequencies and between the relative modal shapes is noted (Tables 3 and 4, Fig. 8). It’s worth noticing that, while modal shapes and frequencies are almost perfectly matching, the index could be further minimized, working on the inaccuracies: this suggests that objective function based on indicators could contain more information about the system dynamics than ones based on modal properties only. Table 3. Numerical frequencies obtained after the identification procedure and comparison with the experimental ones. Ind f1 (Hz)

fexp,1 Δf1 (Hz) (%)

f2 (Hz)

fexp,2 Δf2 (Hz) (%)

f3 (Hz)

fexp,3 Δf3 (Hz) (%)

Iy,r 126.6 127.3 −0.55 336.1 337.6 −0.44 625.4 625.7 −4.8 · 10−6

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(a) 1st mode 126.6 Hz

(b) 2nd mode 336.1 Hz

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(c) 3rd mode 625.4 Hz

Fig. 8. Mode shapes obtained from the finite element model updated using Iy,r as objective function. The dotted line indicates the experimental shape. Table 4. MAC matrix, calculated between numerical and experimental modes: Iy,r indicator. MAC

Inum

IInum

IIInum

Iexp 0.9969 4.048e−04 0.2889 8.896e−08 IIexp 3.014e−04 0.9980 4.384e−04 0.9945 IIIexp 0.2509

6

Conclusions

This paper presented a technique for the parametric identification of a dynamical system, assuming a residual indicator as objective function in a optimization algorithm. In the first step, the proposed method has been assessed with numerical tests on a finite-element beam model, evaluating its efficiency as objective function. Secondly, the method has been validated through an experimental test, carried out to identify the mass density and the elastic modulus of a real steel beam. Results have shown that the proposed method seems to be more sensitive to the variation of dynamic system properties than techniques which uses objective functions based only on modal parameters.

References 1. Ljung, L.: System Identification: Theory for the User. Prentice-Hall Inc., Upper Saddle River (1986) 2. Reynders, E., Pintelon, R., De Roeck, G.: Uncertainty bounds on modal parameters obtained from stochastic subspace identification. Mech. Syst. Signal Process. 22(4), 948–969 (2008) 3. Aloisio, A., Capanna, I., Cirella, R., Alaggio, R., Di Fabio, F., Fragiacomo, M.: Identification and model update of the dynamic properties of the san silvestro belfry in l’aquila and estimation of bell’s dynamic actions. Appl. Sci. 10(12), 4289 (2020) 4. Peeters, B., De Roeck, G.: Reference-based stochastic subspace identification for output-only modal analysis. Mech. Syst. Signal Process. 13(6), 855–878 (1999)

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5. Farrar, C.R., Worden, K.: An introduction to structural health monitoring. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 365(1851), 303–315 (2007) 6. Aloisio, A., Di Battista, L., Alaggio, R., Fragiacomo, M.: Sensitivity analysis of subspace-based damage indicators under changes in ambient excitation covariance, severity and location of damage. Eng. Struct. 208, 110235 (2020) 7. Aloisio, A., Battista, L.D., Alaggio, R., Antonacci, E., Fragiacomo, M.: Assessment of structural interventions using Bayesian updating and subspace-based fault detection methods: the case study of S. Maria di Collemaggio basilica, L’aquila, Italy. Struct. Infrastruct. Eng. 1–15 (2020) 8. Antonacci, E., Aloisio, A., Galeota, D., Alaggio, R.: The S. Maria di Collemaggio basilica: from vulnerability assessment to first results of SHM. J. Architect. Eng. 26(3), 05020007 (2020) 9. Balm`es, E., Basseville, M., Bourquin, F., Mevel, L., Nasser, H., Treyss`ede, F.: Merging sensor data from multiple temperature scenarios for vibration monitoring of civil structures. Struct. Health Monit. 7(2), 129–142 (2008) 10. Basseville, M., Benveniste, A., Goursat, M., Mevel, L.: Subspace-based algorithms for structural identification, damage detection, and sensor data fusion. EURASIP J. Adv. Signal Process. 2007(1), 069136 (2006) 11. D¨ ohler, M., Mevel, L.: Subspace-based fault detection robust to changes in the noise covariances. Automatica 49(9), 2734–2743 (2013) 12. Basseville, M., Abdelghani, M., Benveniste, A.: Subspace-based fault detection algorithms for vibration monitoring. Automatica 36(1), 101–109 (2000) 13. Yan, A.-M., Golinval, J.-C.: Null subspace-based damage detection of structures using vibration measurements. Mech. Syst. Signal Process. 20(3), 611–626 (2006) 14. Basseville, M., Mevel, L., Goursat, M.: Statistical model-based damage detection and localization: subspace-based residuals and damage-to-noise sensitivity ratios. J. Sound Vibr. 275(3–5), 769–794 (2004) 15. D¨ ohler, M., Mevel, L., Hille, F.: Subspace-based damage detection under changes in the ambient excitation statistics. Mech. Syst. Signal Process. 45(1), 207–224 (2014) 16. Bathe, K.-J., Wilson, E.L.: Numerical Methods in Finite Element Analysis. Prentice-Hall, Upper Saddle River (1976) 17. Parloo, E., Cauberghe, B., Benedettini, F., Alaggio, R., Guillaume, P.: Sensitivitybased operational mode shape normalisation: application to a bridge. Mech. Syst. Signal Process. 19(1), 43–55 (2005) 18. Parloo, E.: Application of Frequency-Domain System Identification Techniques in the Field of Operational Modal Analysis. Vrije Universiteit Brussel, Brussels (2003)

Rebar Local Corrosion Monitoring of RC Structures Based on Fractal Characteristics of Piezoelectric Guided Waves Shi Yan(B)

, Xuenan Wang, Yaoyao Chen, and Yuanyuan Yao

School of Civil Engineering, Shenyang Jianzhu University, Shenyang 110168, LN, China [email protected], {wxn1705,cyy6893, yaoyuanyuan}@stu.sjzu.edu.cn

Abstract. In offshore reinforced concrete (RC) structures, how to monitor early occurrences and developments of rebar corrosion is of great significance. However, the rebar corrosion in RC structures is localized and developed along interfaces, having great challenges to evaluations of rebar corrosion levels. In this paper, the theoretical analysis, numerical calculation, and experiment validation are used to study the rebar local corrosion monitoring and evaluation of RC structures with piezoelectric ultrasonic guided waves (UGWs). A reasonable selection of the UGW excitation and reception method and corresponding experimental setup are studied. Frequency dispersion curves of the selected UGWs under different corrosion conditions are obtained by analyzing the wave dispersion and multimodal characteristics. Based on energy values and fractal dimension characteristic values of echo signals for different corrosion levels, a rebar corrosion evaluation index is proposed, and a corresponding evaluation algorithm is established. The effectiveness of the proposed algorithm is verified by a rebar corrosion monitoring test based on the accelerated corrosion and guided wave technologies. A fitting relationship between corrosion levels (length and thickness) and basic characteristics of sensing signals is established. A corrosion evaluation method is established based on the corrosion index and algorithm. The results show that rebar corrosions have a sensitive effect on the energy and fractal characteristics of longitudinal UGWs. The larger corrosion length and the thicker corrosion layer result in the smaller energy value of echo signal and the smaller fractal characteristic value, and the larger corrosion index value. Keywords: Reinforced concrete (RC) · Rebar corrosion · Corrosion monitoring · Piezoelectric ultrasonic guided waves (UGWs) · Fractal characteristics · Corrosion index

1 Introduction Rebar corrosion effect in RC structures is the key source for the most important durability problem, and these phenomena often occur in coastal zones and metropolitan traffic roads spraying deicing salts. Professor Mehta [1] suggests that steel rust is the most important © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 569–579, 2021. https://doi.org/10.1007/978-3-030-64908-1_53

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factor lowering RC structure durability, accounting for about 40% of all rebars corrosion damages. Therefore, the rebar corrosion monitoring is of great importance. However, the direct monitoring of rebar corrosion damages in RC structures is difficult and complicated due to rebars being wrapped in concrete. If the rebar corrosion damage cannot be found early, the developed damages may cause serious casualties and economic losses. Therefore, it is especially important to early identify the rebar corrosion damage in RC structures, and take effective measurements to lower the rebar corrosion induced influences. Nowadays, non-destructive (NDT) detection methods such as ultrasonic detection, vortex detection, and sound emission, etc., are commonly used for damage detections in RC structures [2]. However, these NDT technologies usually need scanning the damaged structure point by point, which are time-consuming, laborious, and cumbersome with low identification efficiency during the detection process. The UGW-based rebar corrosion detection technology has many advantages, such as high detection efficiency, quick and convenient, and wide range of detection, etc., being proved to be effective, economical, and convenient [3, 4]. Because the propagation of UGWs has the typical characteristics of multi-modes and frequency dispersion, it is important to reasonably select UGW’s appropriate frequencies and modes to make the UGWs easily detecting and signal processing in tests. The UGW dispersion curves are usually used as an important reference for the UGW parameter selection. Therefore, a frequency dispersion equation for the UGWs propagating in the rebar of RC structures should be firstly established and numerically solved, and then the UGW parameters can be appropriately determined. The original ultrasonic wave propagation equation was established by the famous scientist Lamb [5] in the process of solving the wave equation in the plate structure, using free boundary conditions to solve the equation. The proposed wave was named the Lamb wave which is widely used in scientific research and engineering application. Based on the Lamb wave, Chree [6] obtained the frequency dispersion characteristics and laws of the guided wave propagating in an infinite cylindrical tube. Ghosh [7] deduced the elastic solution of wave propagation in a hollow circular tube. On this basis, Love [8], Cooper [9] and other experts studied the propagation law of guided waves in the hollow cylinder under different circumstances. Gazis [10] used the elasticity theory to study the propagation mechanism of the guided wave in the three-dimensional direction of the hollow cylindrical structure and deduce the general solution of the simple harmonic in an infinite long cylindrical structure. Silk and Bainton [11] classified the guided waves in the cylinder into three modes, which are the axisymmetric longitudinal mode L(0, m), torsional mode T(0, m) and bending mode F(n, m). Lowe [12] deduced the frequency dispersion equation of guided waves in layered cylinder and solved it. The corrosion monitoring method of RC structures based on the UGW technology has been proved to be effective. The method of numerical analysis [13, 14] and experimental validation [15] is usually used to investigate the issue of rebar corrosion monitoring. The concept of information dimension originated from the entropy of information, which was put forward by American engineer Shannon [16] in the theory of information, which can quantify the quantitative degree of information. The algorithm of information dimension is based on Hausdorff’s dimensional method. Zhang [17] summarized and analyzed Hausdorff’s definition in his book. Chen [18] explained the measurement

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method of each dimension. Cao [19] and others proposed a non-destructive assessment of RC structures based on the fractal theory. Hadjileontiadis and Douka [20] detected cracks in plate structures based on the fractal dimension. Li [21] successfully evaluated the cracks in beams with a uniform cross-section by the fractal dimension-based damage detection method. Based on the theory of UGWs and fractal, this paper presents a method to describe the propagation characteristics of guided waves in RC structures, which lays a foundation for the detection of uneven corrosion damage of rebars by using UGW technology. Therefore, in this paper, taking a RC structure as the research objective, the frequency dispersion equation of guided waves in the RC structure is established and solved by numerical analysis. Then, the MATLAB software is used to analyze and draw the group velocity and phase velocity dispersion curves. A rebar corrosion detection experiment is performed to validate the efficiency of the proposed detection algorithm based on the Hausdorff dimensions.

2 Guided Waves and Frequency Dispersion Curves The basic principle of piezoelectric effect is to use piezoceramics (such as Lead Zirconite Titanate, PZT) as transducers by sticking on the surface of a rebar in pairs, using a group of PZT actuators at the excitation points to generate UGWs, and utilizing the other group of PZT sensors at the reception positions to receive the UGWs returning after reflection and refraction by boundaries or damages. By comparing the characteristics of the sensing signals such as the changes of the signal’s energy, mode, and time delay, etc., the tiny damages which are difficult to identify by the naked eyes within the test piece can be detected.

Fig. 1. Frequency dispersion curves of bare rebar. (a) Phase velocity. (b) Group velocity.

A UGW propagation within rebars will accompany with the frequency dispersion phenomenon which can be described by frequency dispersion curves. Under the condition of given material and geometric parameters, the MATLAB software is used to compile a corresponding program, and the transcendental frequency dispersion equation

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is solved according to the iterative method. All solution data are saved and used to plot the phase velocity and group velocity dispersion curves for the given rebars in the RC structure. According to the frequency dispersion equation, the dispersion curves of the rebar are drawn, and the characteristic values of guided wave propagation are characterized from the dispersion curves. The dispersion characteristics of UGWs are analyzed through the dispersion curves, and different dispersion modes are obtained to select the required modes and frequencies. The propagation velocity of UGW in rebar of the RC specimen can be found through the dispersion mode, shown in Fig. 1.

3 Experimental Validation 3.1 Selection of Actuators and Sensors The aim of the experiment is to validate the efficiency of the proposed rebar corrosion detection method. Considering the feasibility in actual application, the excitation and reception points for PZT transducers are placed at the same end in the test. To reduce the boundary reflection influence on sensing signals, 20 mm from the excitation point (the PZT center) to the end of rebar is reserved. Meanwhile, 20 mm between the reception point and the reinforced concrete interface (end) is also reserved. The return echo at the end and concrete interface due to impedance changes can be received simultaneously. The setup and specific placement locations for PZT transducers are shown in Fig. 2.

Fig. 2. The schematic of the corrosion detection experiment based on UGWs.

To generate a UGW with the pure L mode, four PZT actuators are placed in a ring array. Two symmetrical PZT sensors are also applied at the reception point to ensure the sensing signal with an enough amplitude to be caught. A set of the compression type of PZT-5 is used as transducers to make the UGW conveniently passing through the interface section into the concrete cover. The information of PZT transducer parameter is shown in Table 1.

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Table 1. PZT transducer parameters. Model

Type

Actuator number

Sensor number

Size/mm

PZT-5

Compression

6

2

12 × 6 × 1

In addition, a rebar corrosion detection system of RC structure is also established based on the UGW propagation technology. The established system setup includes the tested RC specimens, a function generator, a signal amplifier, a digital oscilloscope and a computer, shown in Fig. 2. 3.2 Accelerated Corrosion and Damage Detection Experiments The experiments are divided into two parts of the accelerated corrosion and damage detection. Accelerated Corrosion Experiment. The accelerated corrosion experiment aims at quickly creating a rebar corrosion level to meet the corrosion monitoring requirement. To ensure experimental results to be closer to actual project, the specimens in the experiment are designed with the parameter of the concrete cover thickness of 25 mm and the concrete covering length of 1.2 m.

(a) Longitudinal profile

(b) 1-1 profile

Fig. 3. The schematic of accelerated corrosion. (a) Longitudinal profile. (b) Cross-sectional 1-1 profile.

To speed up the test and shorten the test period, the accelerated corrosion method is adopted to simulate the corrosion of rebar. The electrolytic cell principle is used for the accelerated corrosion. An electrode is needed which can control the corroded length as the cathode. The setup of the experiment includes corroded concrete specimens, a copper mesh, copper strips, cotton wool, plastic film, and a DC regular power supply. The absorbent cotton is soaked in saline water. Saline water in the wet cotton penetrates the concrete through the cracks in the concrete and connects the steel bar in the concrete with the copper electrode outside the concrete to form a closed loop to control the corrosion

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length, shown in Fig. 3. In this test, the voltage is controlled by parallel connection method so that all three specimens are in the same degree of corrosion. Four specimens are designed and tested in this experiment, which are three specimens with different corrosion lengths of 300 mm, 600 mm, and 900 mm, named D300, D600, and D900, respectively, and one standard specimen without corrosion, named H1200, as a baseline for comparison. The same parameters for the four specimens are completed except the corrosion length, shown in Fig. 4.

Fig. 4. The specimens in the accelerated corrosion experiment.

Corrosion Monitoring Experiment. During the accelerated corrosion experiment, the rebar corrosion monitoring experiment based on UGW technology is performed. Since the electrodes made in the experiment are difficult to remove, the accelerated corrosion test is temporarily paused, and the corrosion monitoring experiment is performed to collect the sampling point for every two days. Therefore, the sampling time are the start day, 2 days, 4 days, and 6 days, respectively. After 6 days, the specimens are supposed to be severely damaged based on the observation. During the corrosion monitoring experiment, the five-peak pulse signals are used to detect the corrosion damage of the specimens based on the guided wave method. Finally, all the collected signal data are used for the subsequent analysis, then an algorithm of rebar corrosion monitoring based on UGWs is proposed.

4 Algorithm of Rebar Corrosion Monitoring Based on UGWs 4.1 Signal Processing After the accelerated corrosion experiment and rebar corrosion monitoring experiment, the collected sensing signals are ready for data processing. The typical specimen failure patterns show the concrete cracks and peeling in the three specimens which are visible to the naked eye after a 6-day accelerated corrosion test (Fig. 5). It has been determined that these concrete cracks or peeling are developed along a longitudinal direction in

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concrete because of the bulk-expansion after the rebar corrosion. Therefore, it can be presumed that serious interface separation damages in the range of corrosion length have been caused inside the concrete, resulting in the change of sensing signals of PZT-based UGWs. D600 specimen is the most representative in the local corrosion experiment. Therefore, the sensing signal is selected to process and analyze. The sensing signal for D600 specimen at the start day (healthy state) is shown in Fig. 6(a) and that after 2 days is shown in Fig. 6(b). Meanwhile, the sensing signals after 4 days and 6 days are shown in Fig. 7. Compared with the healthy state, the energy (amplitude) ratio of the far-end echo to the head wave for the corroded specimens decreased at the first stage and then increased at the last stage. This is consistent with the corrosion process of reinforced concrete.

Fig. 5. Concrete cover damages due to rebar corrosion expansion. (a) The concrete cover peeling. (b) The concrete cracks.

Fig. 6. The experimental sensing signals for D600 specimen. (a) In the healthy state. (b) In the damaged state.

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Fig. 7. The experimental sensing signals for D600 specimen after different time. (a) After 4 days. (b) After 6 days.

4.2 Fractal Dimension Method The sensing signals contain plenty of nonlinear difficultly identified rebar corrosion information which can be solved by a fractal dimension method. The concept of information dimension comes from information entropy, which was put forward by Shannon [16]. The algorithm of information dimension is based on Hausdorff dimension. P is set to represent the probability that the fractal set element belongs to covering U, then the information dimension Di can be described in Eq. (1). N 

Di = lim

ε→0

Pi ln P

i=1

(1)

ln ε

in which, ε is the selected diameter of the small ball. The information dimension can be used to characterize the sensing signal, but it is extremely complicated and difficult to calculate the information dimension in practical application. Therefore, box dimensions are used instead of good Hausdorff dimensions to describe information metrics in Eq. (2). log( d = − lim

t→0

N 

|Xi + 1 − Xi |/t)

i=1

log t

log( =−

N 

|Xi + 1 − Xi |/t)

i=1

log t

(2)

where t is the sampling time interval; X i is the signal voltage in time domain; N is the total number of sampling points. The results of signal processing using the fractal dimension are shown in Table 1. Since the entropy is conserved from the concept of information entropy, this theorem is also applied to fractal dimension; therefore, the characteristic values of the obtained fractal dimension can be dealt with. Adding the characteristic values of damage echo and far end echo in each corresponding position in Table 2, the final data is shown in Table 3. The sum of fractal dimension characteristic values of each specimen under different corrosion days is almost the same, and the error is within 10%, which is in accordance

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Table 2. Echo characteristic values. Specimens 2 days

4 days

6 days

Damage Far end Damage Far end Damage Far end D900

1.2745

1.3163 1.2634

1.2994 1.2923

1.2820

D600

1.2487

1.4018 1.2512

1.3375 1.2735

1.2822

D300

1.2129

1.4404 1.2781

1.3788 1.2857

1.3022

Table 3. Total end echo characteristic values. Specimens 2 days 4 days 6 days D900

2.5908 2.5628 2.5743

D600

2.6505 2.5887 2.5557

D300

2.6533 2.6569 2.5879

with the theory. The proportion of the characteristic value of the end echo signal and the damage echo signal to the total value was plotted. After the same days accelerated corrosion, the radius loss level of rebar in each specimen can be the same. It indicates from Faraday formula that the rebar damage radius is proportional to electric current and time. Therefore, the relationship between the proportion of the characteristic value and the damage radius level of rebar can be obtained, shown in Fig. 8. Therefore, the Eq. 3 can be derived from Fig. 8 to describe the damage index K. K = −

4r R

Pr − 0.58  2 − + 2r R2

r 4

(3)

where Pr is the proportion of far-end echo fractal dimension feature value; r is the change of radius of rebar; R is the original rebar radius. By the calculation, K should

Fig. 8. Proportion of the characteristic value and the damage radius of rebar.

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be in the range of (0.13, 0.56). From Eq. (3), the corrosion thickness of rebar in RC structures based on UGW technology can be proximately evaluated.

5 Conclusions After the theoretical derivation and experimental verification, the fractal dimension method can be used to establish a rebar corrosion monitoring index for RC structure based on UGW technology. The proportion of fractal dimension characteristic value of far end echo decreases gradually with the increase of corrosion degree, and finally stabilizes around 50% after the corrosion interface separation between concrete and rebar. The larger the percentage of corrosion length in the entire rebar, the more stable the rate of change of the far end echo proportion will be. Acknowledgments. This work was partially funded by National Key R&D Program of China with grant 2018YFC0705602 and No. 2017YFC1503106.

References 1. Metha, P.K.: Concrete durability: fifty year’s progress. In: 2nd international Conference on Durability of Concrete,ACISPI26-1, pp. 1–33 (1991) 2. Luo, G., Shi, Y.K.: Non-destructive testing method of steel corrosion in reinforced concrete components. Fujian Architect. Constr. 4, 55–57 (2002) 3. Miller, T.H., Kundu, T., Huang, J.Q., Grill, J.Y.: A new guided wave-based technique for corrosion monitoring in reinforced concrete. J. Struct. Health Monit. 12(1), 35–47 (2012) 4. Mitra, M., Gopalakrishnan, S.: Guided wave based structural health monitoring: a review. Smart Mater. Struct. 25(5), 053001 (2016) 5. Lamb, H.: On waves in an elastic plate. Proc. R. Soc. 93(468), 114–128 (1917) 6. Chree, C.: Longitudinal vibrations of a circular bar. Q. J. Math. 21(83), 287–295 (1886) 7. Ghosh, J.: Longitudinal Mathematical Society: Vibrations of a hollow cylinder. Bull. Calcutta 24(14), 32–40 (1923) 8. Love, A.E.H.: A treatise on the mathematical theory of elasticity. J.Nat.9(1), 1385 (1994). Dover Publications, New York 9. Cooper, R.M., Naghdi, P.M.: Propagation of nonaxially symmetric waves in elastic cylindrical shells. Acoust. Soc. Am. 29, 1365–1373 (1957) 10. Gazis, D.C.: Exact analysis of the plane- strain vibrations of thick-walled hollow cylinders. Acoust. Soc. Am. 30(8), 786–794 (1958) 11. Silk, M.G., Bainton, K.P.: Propagation in metal tubing of ultrasonic wave modes equivalent to Lamb waves. Ultrasonics 17(1), 11–19 (1979) 12. Lowe, M.J.S.: Matrix techniques for modeling ultrasonic waves in multilayered media. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42(4), 525–542 (1995) 13. Zheng, Z.P., Lei, Y.: Effects of concrete on propagation characteristics of guided wave in steel bar embedded in concrete. Shock Vibr. 2014, 1–4 (2014) 14. Zheng, Z.P., Lei, Y., Xue, X.: Numerical simulation of monitoring corrosion in reinforced concrete based on ultrasonic guided waves. Sci. World J. 2014, 1–9 (2014) 15. Liang, M.T., Su, P.J.: Detection of the corrosion damage of rebar in concrete using impact-echo method. Cement Concr. Res. 31, 1427–1436 (2001)

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16. Shannon, C.E., Weaver, W., Wiener, N.: The Mathematical Theory of Communication. University of Illinois Press, Urbana (1949) 17. Zhang, J.Z.: Fractal. Tsinghua University Press, Beijing (1995) 18. Chen, J.A.: Definition and measurement of fractal dimension. Electron. Sci. Technol. 4, 44–46 (1999) 19. Cao, M., Ren, Q., Qiao, P.: Nondestructive assessment of reinforced concrete structures based on fractal damage characteristic factors. J. Eng. Mech. 132(9), 924–931 (2006) 20. Hadjileontiadis, L.J., Douka, E.: Crack detection in plates using fractal dimension. Eng. Struct. 29(7), 1612–1625 (2007) 21. Li, H., Huang, X., Ou, J., et al.: Fractal dimension-based damage detection method for beams with a uniform cross-section. Comput. Aided Civ. Infrastruct. Eng. 26(3), 190–206 (2011)

Electromechanical Impedance Data Fusion for Damage Detection Tomasz Wandowski(B)

and Pawel Malinowski

Polish Academy of Sciences, Institute of Fluid–Flow Machinery, Fiszera 14 Street, 80–231 Gdansk, Poland {tomaszw,pmalinowski}@imp.gda.pl

Abstract. In this paper results of application of electromechanical impedance (EMI) method for damage assessment in composite panel is presented. Artificial damage simulated by additional mass and real impact damage are investigated. Large number of measurements is analyzed and possibility of utilization of machine learning approach for clustering the damage cases is validated. Clustering is based on principal components obtained based on conductance spectra. Machine learning methods based on K-nearest neighbor, neural networks and Kmeans are utilized. Moreover, popular damage indices RMSD and CCD were also utilized. Keywords: Electromechanical impedance · Composite materials · K-nearest neighbor · Multilayer perceptron · K-means

1 Introduction Electromechanical impedance (EMI) method is very popular in the field of structural health monitoring (SHM). This method is based on measurements of electrical impedance of piezoelectric transducer mounted on the assessed structure. Due to electromechanical coupling of the transducer and structure, the mechanical resonances are registered in electrical impedance. Due to this fact any changes in resonant frequencies caused by damage are seen in the impedance spectra of transducer. EMI method have been utilized for damage assessment of metallic [1], polymer composite [2] and concrete [3] structures. The main advantages of this method are: utilization of the piezoelectric transducer as actuator and sensor and low cost of realization. Unfortunately EMI is local method and its sensitivity to damage is strongly reduced in fiber reinforced polymer composite materials or concrete due to high damping of material and low voltage of excitation signal utilized. In this paper authors investigated application of EMI method for detection of discontinuities in the form of additional mass and impact damage in carbon fiber reinforced polymer (CFRP) panel. Moreover, authors investigated the possibility of utilization of machine learning methods for classification of obtained results.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 580–590, 2021. https://doi.org/10.1007/978-3-030-64908-1_54

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2 Measurement Set-Up Measurement set-up consisted of HIOKI IM3570 impedance analyzer, woven CFRP panel with dimensions 500 mm × 200 mm × 5 mm and notebook. CFRP sample was equipped in piezoelectric transducer Noliac NCE51 in the form of disc with diameter 10 mm and 0.5 mm thickness. Transducer was bonded in the middle of the sample surface. During the EMI measurements CFRP sample was hanged on the two strings bonded to the sample edges. In this paper only the conductance spectra were analyzed. Measurements were performed for the case of referential state of panel, panel with additional mass as artificial damage (two magnets, each with mass 60 g, attached on both panel surfaces) and impact damage (impact energy 24 J). Additional mass was utilized due to possibility of simple change its location without damaging the specimen. Measurements in the case of magnets were performed for different distances of the magnets from the piezoelectric transducer (Mag 1 – Mag 10 where distance changes from 30 mm to 225 mm, see Table 1). In the case of impact damage two cases were investigated: one impact at distance 143 mm (the same location where magnets in case 6 were located) and case with additional impact at distance 235 mm (near edge). Different number of conductance spectra were gathered for each case (see Table 1). The aim of this research was to utilize machine learning for damage classification problem. Table 1. Set of conductance measurements. Case

Distance from transducer

Description

No. of measurements

Ref

-

referential case

600

Mag 1

30 mm up

magnets

300

Mag 2

52 mm up

magnets

600

Mag 3

75 mm up

magnets

300

Mag 4

98 mm up

magnets

400

Mag 5

121 mm up

magnets

300

Mag 6

143 mm up

magnets

300

Mag 7

166 mm up

magnets

300

Mag 8

189 mm up

magnets

300

Mag 9

212 mm up

magnets

300

Mag 10

225 mm up

magnets

300

Imp 1

143 mm up

impact at mag 6 position

100

Imp 2

235 mm up

additional impact near edge

300 SUM: 4400

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The EMI measurements were performed for frequency band 1 kHz–10 kHz with step of 20 Hz. The EMI method is vulnerable to temperature change therefore the measurements were performed in air conditioned laboratory in the temperature 23 ± 1 ºC.

3 Conductance Spectra In the case of EMI method different parameters are measured in the function of frequency (spectra) but very often real parts of impedance or admittance (resistance and conductance respectively) are measured for the purpose of damage detection. In this paper conductance spectra were registered and analyzed. In the Fig. 1 exemplary of conductance spectra for the referential case (bottom plot - black), the case of impact 2 (plot in the middle - red) and impact 1 (plot on the top blue) are presented. Different number of spectra were plotted in each investigated case (respectively 600, 300 and 100) what causes the data spread visible in Fig. 1. All cases are described in Table 1.

Fig. 1. Conductance spectra for CFRP panel with impact damage.

In order to analyze the changes of conductance spectra due to impact damage spectra for each cases were averaged (over all spectra in the case). It results in one signal for each case. Example of averaged conductance spectra for referential case and impact cases were presented in Fig. 2. It could be observed that impact damage caused vertical shift of conductance spectra. There is almost no frequency shift (horizontal) for resonance peaks in the conductance spectra. Conductance spectra were also averaged for the case of magnets located at different distances. Examples of averaged conductance spectra for referential case and cases of magnets 1, 4, 6 and 10 were presented in Fig. 3. It could be noticed that the magnets (additional mass) have larger influence on changes in the conductance spectra than investigated impact cases. Amplitudes of resonant peaks and its frequency were changed.

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Moreover vertical shifts of spectra were also noticed. In the next step, for all conductance spectra damage indices RMSD and CCD were calculated. They are based on statistical signal parameters and are very popular in EMI-based damage detection [4]. Is should be emphasized that RMSD and CCD indices were normalized to unity using their maximum value for the whole data set.

Fig. 2. Averaged conductance spectra for the case of impact damage.

Fig. 3. Averaged spectra for the case of ad-ditional mass (magnets).

Analyzing results for RMSD and CCD presented respectively in Fig. 4 and Fig. 5 it could be noticed that results are divided in three group: Ref – referential without any discontinuity, Mag 1–10 – magnets with different distances from piezoelectric transducer in increasing manner (10 distances) and Imp 1–2 – for impact damage 1 and 2.

Fig. 4. Normalized RMSD damage index for the whole data set.

Smallest RMSD values (Fig. 4) were achieved for referential cases. Higher RMSD values were obtained for magnet cases and much higher for impact damage. However, some referential cases give higher RMSD value than for some of the data for magnets. Impact damage case Imp 1 gives higher RMSD values than Imp 2 case, although in the latter additional impact was applied. In the case of CCD index (Fig. 5) the referential

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Fig. 5. Normalized CCD damage index for the whole data set.

cases give the smallest values of CCD. Values of CCD for impacts are higher than for referential cases. Values of CCD for magnets for all distances are much larger that values for impacts and referential cases. However, decreasing value of CCD index can be seen with increasing distance of magnets from the transducer. Damage indices RMSD and CCD are very popular but it seem that their values are not strictly correlated with damage size and type. Therefore authors of this paper decided to analyse other approach based on principal component analysis.

4 Principal component analysis. Principal component analysis (PCA) is a method utilized for reduction of data dimensionality based on linear data transformation to subspace with smaller number of dimensions. It is commonly utilized in data compression problems. PCA is utilized for searching the directions of maximum variance in multidimensional space. In this purpose covariance matrix is calculated for data set. Next the eigenvectors of covariance matrix are calculated and are sorted based on eigenvalues in descending order. Principal components are vectors related to eigenvalues. In our case PCA is applied for conductance spectra for all investigated cases (Table 1). Whole data set consisted of 4400 spectra where each spectrum has a length of 451 data points. In the case of conductance spectra the 99.96% of the variance is explained by the first principal component (PC 1). In this paper the focus was put on two principal components for conductance spectra representation in new subspace. After a check of PC values it was noticed that the use of PC 2 and PC 3 components allows to cluster of conductance spectra for different cases (Fig. 6). Analyzing principal components distribution in Fig. 6 clusters containing certain cases can be noticed. First cluster includes following cases: Ref, Imp 1 and Imp2, next cluster includes cases of Mag 9 and 10. Large cluster including cases of Mag 4–Mag 8 can be distinguished. Moreover, cluster that includes Mag 2–Mag 3 cases and cluster including only the Mag 1 case is seen. It seem that separation of magnets cases from referential cases (distance between data points in Fig. 6) depends on the distance of magnet from piezoelectric transducer. Magnet Mag 1 is located at closest distance from

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Fig. 6. Conductance spectra transformed to PC2-PC3 plane (raw data – not normalized).

transducer and located faraway from referential cases in the PC2-PC3 plane. Similar case is for magnets 2–3. Data points for magnets 9–10 located far away from the transducer are seen close to referential case in Fig. 6. Next step was related to machine learning approach for conductance spectra representation in new subspace defined by PC 2 and PC 3.

5 Machine Learning (ML) Machine learning process could be divided to supervised, unsupervised and learning by amplification. Supervised approach is based on learning process that uses labelled training data. In unsupervised learning the structure of data is unknown. In the learning by amplification the controller is utilized which gives the awards if the system correctly recognize the response/solution. In this paper supervised learning based on K-nearest neighbor (KNN) and multilayer perceptron (MLP) neural network, and unsupervised learning based on K-means were utilized. The KNN is very simple algorithm that stores learning cases and classifies new cases based on similarity measure. Based on selected distance measure (Euclidean distance in our case) KNN algorithm search the k nearest data points located near the classified data point. Next the label is selected based on the majority vote. The MLP is group of neural network composed of multiple layers containing perceptrons. The aim of neural network is to learn function of representation of output vector based on input vector. Learning is related to choose and tune the weights related to neurons based on learning algorithm. K-means is data clustering algorithm that divide data to clusters based on nearest mean for calculated centroids. More information about mentioned algorithms could be found e.g. in [5].

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The aim of applied ML algorithms is clustering of conductance spectra for different investigated cases. Part related to ML was performed in Python language with the use Scikit-learn library. It should be underlined that data normalization (values from range 0– 1) for PC 2 and PC 3 was performed before further processing. In the first step decisions related to selection data clusters and labels related to these clusters based on PC 2 and PC 3 results presented in Fig. 6 were taken. Then full data set (4400 values of PC 2 and PC 3) was divided to training data and testing data subsets (70% and 30% respectively). Next mentioned ML algorithms were tested for investigated data set.

6 Results First step was related to determine possible number of clusters that could be isolated in results presented in Fig. 6. Three cases of data clustering were proposed. In first case four classes/clusters were selected: Ref, Mag 1–10, Imp 1 and Imp 2. Second case includes six classes: Ref, Mag 1, Mag 2–3, Mag 4–8, Mag 9–10, Imp 1–2. Third case includes seven classes: Ref, Mag 1, Mag 2–3, Mag 4–8, Mag 9–10, Imp 1 and Imp 2. Then results in the form of principal components PC2 and PC 3 were processed by KNN algorithm using Euclidean metric and neighbor number k = 100. This number was based on the smallest number of conductance spectra measurements in one turn. For example in case of referential measurements (Ref in Table 1) six measurement turns (100 measurements in each) were registered what gives 600 signals. Smaller number of k does not affect the results of clustering. Values o k over 150 affects the clustering results in case of our data. Results for first case (four classes) for KNN algorithm were presented in Fig. 7. Additionally, results for testing data set (30% of data sets) were plotted there as well. It could be noticed that KNN algorithm was able to cluster correctly the learning and testing data. Results for KNN algorithm in the case of six classes were presented in Fig. 8. In this case algorithm was also able to cluster correctly the learning and testing data.

Fig. 7. Decision regions for KNN (4 classes). Fig. 8. Decision regions for KNN (6 classes).

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Finally, results for KNN algorithm for seven classes were presented in Fig. 9. In this case KNN algorithm is able to separate the referential data from damage cases. Moreover, it is possible to separate referential case from four groups of results for the case of magnets located at different distances from actuator. Results for magnets 1 are located far away from the referential case results in Fig. 9, while the magnet is located at the shortest distance from the piezoelectric transducer (30 mm). Far away are also located results for Mag 2–3 in Fig. 9 which are placed farther from the transducer (distances: 52 mm and 75 mm). Next group of results (Mag 4–8) are located closer to the referential case in Fig. 9 because magnets are located at larger distances from the transducer (distances: 98–189 mm). Much closer to referential case is located group of results for magnets Mag 9–10 (Fig. 9) which are located at distance 212–225 mm from the actuator. This shows certain correlation of distance of magnets from actuator and distance between clusters. The KNN algorithm is also able to distinguish both impact cases. However, results for both impact cases in Fig. 9 are located very close to each other and to the referential case. So they are almost treated as referential case. This could cause problems in separation of new data registered under varying conditions (e.g. at different temperatures). Due to fact that KNN algorithm was able to classified correctly data for seven classes similar analysis was performed for the MLP algorithm. In this case neural network includes 8 hidden layer (each with 9 hidden units). Output layer contains 7 units for seven classes which were labeled in the range: 0–6. The Relu activation function was utilized. This architecture was chosen based on trial-error analysis. The results for MLP algorithm was presented in Fig. 10. In this case clustering regions looks different than for KNN (Fig. 9) but algorithm also works correctly. In this case test data were also marked in this plot what shows that classification works correctly.

Fig. 9. Decision regions for KNN (7 classes). Fig. 10. Decision regions for MLP (7 classes).

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In previous cases supervised learning process with labeled data was utilized. In next step unsupervised learning was tested based on K-means algorithm. First result, for K-means algorithm in the case of six clusters (classes) were presented in Fig. 11. This result does not allow to separate impact cases from referential data points. Magnets are separated and grouped in five clusters/classes. In next step number of clusters in K-means algorithm was increased to seven. The aim of this test was to check if it is possible to separate impact cases from referential cases. Results for this case were presented in Fig. 12. More classes does not solve the problem of separation of impact and referential cases. Additional cluster of results for magnets was created by the algorithm. In the next step the number of clusters was increased to eights and results were presented in Fig. 13.

Fig. 11. K-means clustering (k = 6).

Fig. 12. K-means clustering (k = 7).

Increased number of clusters to eights also does not cause the correct separation of results for impact damage and referential cases. Again, the algorithm assigned more classes to magnet cases. In the case of unsupervised learning (not labeled data), in real conditions we do not know how many damage cases we have. Continuous damage growth will be related to many states depending on damage size. Therefore, analyzing the clusters of principal components in Fig. 11-Fig. 13 it looks that smaller number of clusters should be utilized in the real case. This will allow to achieve the safety margin between clusters. Results for K-means algorithm for five classes were presented in Fig. 14. In this case K-means algorithm is able to cluster the results for following classes: Ref + Imp 1–2, Mag 1, Mag 2–3, Mag 4–8 and Mag 9–10.

Electromechanical Impedance Data Fusion for Damage Detection

Fig. 13. K-means clustering (k = 8).

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Fig. 14. K-means clustering (k = 5).

7 Summary Results showed that the values of RMSD and CCD indices are not strictly correlated with damage size and type. Therefore clustering based on principal components was proposed as different approach. It was shown that simple KNN clustering algorithm gives good results in separation of different investigated cases. Similar results were achieved by the MLP network. It was possible to distinguish cases for referential state, magnet and impact damage. Moreover, two impact cases were separated from each other and four groups of magnet locations. However, impact cases data points are located close to the referential state data points and this could cause problems under varying conditions (e.g. temperature). In the case of unsupervised learning based on K-nearest neighbor, the clustering is only possible for five classes. Four groups of magnet distance are separated but impact cases are not separated from referential case. More classes than five have not solved the problem of separation of impact cases from the referential cases. Further research will be related to investigation of distance of additional mass from the transducer and its influence on separation of clusters from the referential case. Moreover, influence of temperature will be investigated. Acknowledgements. Authors would like to gratefully acknowledge the support given by the National Science Centre, Poland under grant agreement no. UMO-2016/22/E/ST8/00068 in the frame of SONATA BIS project. Some of the Calculations were carried out with the software provided by the Academic Computer Centre in Gda´nsk (TASK).

References 1. Zhu, H., Luo, H., Ai, D., Wang, C.: Mechanical impedance-based technique for steel structural corrosion damage detection. Measurement 88, 353–359 (2016) 2. Mohammadabadi, A., Dugnani, R.: Design and evaluation of a novel low acoustic impedancebased PZT transducer for detecting the near-surface defects. Int. J. Eng. Technol. Innov. 9(3), 196–211 (2019)

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3. Perera, R., Sun, R., Sevillano, E., Ruiz, A.: A multi-objective electromechanical impedance technique to identify debonding in RC beams flexural strengthened with FRP. Procedia Eng. 199, 2232–2237 (2017) 4. Na, W.S., Baek, J.: A review of the piezoelectric electromechanical impedance based structural health monitoring technique for engineering structures. Sensors 18, 1307 (2018) 5. Raschka, S.: Python Machine Learning. Packt Publishing Ltd., Birmingham (2019)

Multifunctional Materials and Composite

Online Inspection System Based on Resin Flow Monitoring by Distributed Optical Fiber Sensors Immersed Inside Aeronautical RTM Process Carlos Miguel Giraldo1(B) and José Sánchez del Río Sáez2,3(B) 1 Airbus Operations, S.L, Paseo John Lennon S/N, Getafe, 28906 Madrid, Spain

[email protected] 2 Physics Department, Universidad Carlos III de Madrid, 28911 Leganés, Spain

[email protected], [email protected] 3 ICAI, Mechanical Engineering Department, Comillas Pontifical University, Str. Alberto

Aguilera, 23, 28015 Madrid, Spain

Abstract. RTM (Resin Transfer Molding) is a well-known closed-mold injection process widely used in manufacturing aeronautical composite parts in low and medium volume production. Resin viscosity and temperature, pressure gradient between ports and inlet and outlet positions in the mold are some of the key parameters of such process as well as fabric material properties, and more in particular, fabric permeability. This last parameter plays an essential role in the infusion process by affecting the advance of the resin flow and it has high influence on possible sources of voids and defects the same as on porosity. This paper describes the technology and feasibility of the Rayleigh distributed optical fiber technique to visually inspect the resin flow inside the mold in two RTM trials. In both of them, resin flow was monitored by studying the variation of the optical fiber backscattering as resin was impregnating the fabrics and also by recording it with a video camera. Results obtained in both trials were analyzed and compared one each other. This online inspection technique presented in this work might be used for detecting irregularities in the resin flow such as either too low/fast speed or non- impregnated areas and moreover, it opens the possibility of modifying intime injection parameters in RTM processes which will allow correcting possible defects before the part is finished. Keywords: OFDR · Distributed optical fiber sensing · RTM process · Online monitoring

1 Introduction RTM [1] is a well-known closed-mold injection process widely used to manufacture composite parts in low and medium volume production. In a typical RTM process the reinforcement is placed into the cavity of a mold, subsequently the mold is closed and resin is injected under relatively low pressure. Once resin is cured, the finished component can be demolded and its internal quality is conventionally checked by physical-chemical © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 593–602, 2021. https://doi.org/10.1007/978-3-030-64908-1_55

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analysis and non-destructive inspections. Parameters such as resin viscosity, temperature and pressure are very relevant during the RTM process and they are monitored in the manufacturing cycle [2, 3]. Resin and preform properties and their compatibilities between them have also demonstrated a very strong influence on the final quality of the parts. Furthermore, it is the fabric permeability that plays an essential role in the infusion process and although it could be in principle measured in advance, there are many issues in practice that can modify and make this parameter unpredictable, therefore affecting the advance of the resin flow and as a result contributing to the presence of internal defects such as porosity or lack of resin in certain parts of the laminate. This paper is focused on the capability of Rayleigh optical fiber backscattering sensing to detect and monitor the resin flow inside the mold during the RTM manufacturing process [4].

2 Distributed Optical Fiber Sensing Technology The Rayleigh backscattering in optical fibers is caused by the elastic interaction of the photons with the random fluctuations of the core refraction index profile along the fiber length. This scattering that varies from segment to segment in the fiber is highly repeatable and can be considered as a unique static property for a given fiber. Therefore, changes in the local period of the Rayleigh scattering caused by an external stimulus produce changes in the local reflected spectrum [5, 6, 7]. The measurement system used in this work was a LUNA ODiSI-B system and is based on the swept-wavelength coherent interferometry (SWI) (see scheme Fig. 1). It interrogates the fiber and measures the Rayleigh backscattering (amplitude and phase) as a function of the position in the optical fiber [8]. On one hand, the SWI collects the backscattered optical power in the spectral frequency domain. On the other hand, the detectors collect the light backscattered from the fiber under test as the laser spectral frequency is tuned through a range of frequencies. Backscattered power data is processed by using the Fourier Transform to generate the backscattered optical power as a function of the time delay that in turn, it can be converted into a distance function. When a physical parameter such as temperature or strain changes in the sensing fiber, a measurable change on the backscattered light along the optical fiber is produced. Making use of cross correlation, the backscattered light of the sensing fiber under test in the two states is compared and as a result the physical state of the fiber at the time of measurement is determined. The two backscattered profiles are correlated (segment to segment) to determine the spectral shift of the backscattering along the length of the sensing fiber. The shift is analogous to the spectral shift produced in a Bragg grating: λ/λ = KT .T + Kε .ε

(1)

where default values for most germane-silicate core fibers are KT = 6.45 × 10−6 °C−1 and Kε = 0.780.

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Fig. 1. Scheme of swept-wavelength coherent interferometry

3 Impregnation Process The velocity and pressure fields in liquid composite molding processes are commonly inferred modelling the fluid advancement as a flow through a porous medium, according to the well-known Darcy’s law, which, under the hypothesis of single scale porosity and permeability it is written as follows (see Eq. 2): vs = (−K/μ)∇P

(2)

Being vs the fluid superficial velocity (accounting for the volume porosity φ), K the permeability tensor, μ the resin viscosity and ∇P the pressure gradient. For incompressible media, the continuity equation imposes that: ∇2P = 0

(3)

and consequently fill time can be obtained by integrating Darcy’s law, resulting in: tRTM = ϕμX2 /2K∇P

(4)

where X, ϕ, μ, K and ∇ P represent the instantaneous flow front position, porosity, viscosity, permeability and driving pressure. Equation (4) shows that fill time is inversely proportional to the driving pressure and directly proportional to the flow front position.

4 Experimental Set-Ups Two resin infusion (RI) trials were prepared and tested with the purpose of evaluating the capability of distributed optical fiber sensing technology for the detection and monitoring of the resin flow during the impregnation of dry reinforcement materials with resin (see Fig. 2a and Fig. 2b). Table 1 collects the main features of both tests.

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Process

Tool

RI RI

Preform

Resin

Impregnation conditions & Times

Monitoring technologies

Single side 4 layers (CFRP G0926- Hexcel)

Derakane 8084 (Ashland),

Vacuum, RT 24 min

3 segments OF, video camera

Single side 4 layers (CFRP G0926Hexcel)

RTM6

Vacuum, Resin 80 ºC, Tool 100 ºC 52 s

3 segments OF, Olympus borescope

The preform was composed of four rectangular composite unidirectional carbon fiber fabric layers of 250 × 290 mm2 and was placed on 500 × 300 mm2 aluminum tool. The optical fiber used to monitor the resin flow consisted of a single mode optical fiber, coated by polyimide and 145 μ diameter. The fiber was inside the preform, between the third and fourth layer, entering in of the panel up to form three segments, aligned to the flow direction. The ingressegress of the optical fiber through the vacuum bag was done by compatible silicone 3 mm diameter tubes. At the edge of the longest sides of the rectangular preform, two distribution resin channels were positioned for inlet/outlet purposes, connected to the resin tank and the vacuum pump respectively. The complete pack was covered and sealed by a vacuum bag.

Fig. 2. a) Set-up for the first injection trial, b) set-up for the second infusion trial

In the first impregnation trial, the set up was laid out on a table and a video camera was located over the test panel in order to record the resin flow during the infusion process. For the second experimental set up, the tool was introduced into an oven at 100 ºC. A distribution media was placed on the top of the upper fabric. The video was recorded by an Olympus 6 mm diameter borescope specially designed for high temperature applications and connected externally to an Olympus PEN camera by using a special adapter. The Fig. 3a and Fig. 3b shows the details of the set-ups.

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Fig. 3. a) Complete set up for the first and, b) second infusion trials

Previously to the infusions, the optical fiber system and the video camera were set up and 10 Hz acquisition rate established. The optical fiber system acquired the fiber baselines in both setups, each one showing the three consecutives fiber segments (see Fig. 4 and Fig. 5 for the first and the second trials respectively) inside the panel. In both figures X-axis displays distance in meters and Y-axis the flow indicator which is directly related to temperature and strain shifts.

Fig. 4. Distributed optical fiber baseline before the first infusion trial: flow indicator vs fiber length

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Fig. 5. Distributed optical fiber baseline before the second infusion trial: flow indicator vs fiber length

5 Results Results obtained from the impregnation trials were given by the fiber optic acquisition system and the video camera. The fiber optic results for each of the infusion trials are divided into three plots (see Fig. 6a–c for the first trial and Fig. 8a–c for the second one and in both cases, for each segment). The optical fiber lengths outside the preform were not considered for the analysis since they remained invariable throughout the complete impregnation process. They correspond to the horizontal upper areas in Fig. 5 and Fig. 6. Images of the impregnation process were extracted from the camera video recordings at selected times for the first trial (see Fig. 7) and for the second trial (see Fig. 9).

6 Discussion The distributed optical fiber curves show the variation of the backscattering over the time. These curves remain unalterable when the preform is dry and without any contact with the resin. Once the impregnation process starts, the resin goes into the preform and the curves change up to theoretically the point of the fiber where the resin contact with it, remaining the fiber length unchanged where the perform continue being dry. In order to know the advance of the resin flow over the time, a comparison of the three segments of the optical fiber with respect to the baseline acquired before the injection was done. Distances measured along the X-axis between the beginning of the fiber for each segment and the position where the baseline and successive curves separate, determine the resin flow for this particular time. This analysis was extended to the three segments and to the two impregnation trials. The detection process was done by the visual observation of the curves. However, one of the aims for a future implementation

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would entail the development of a specific algorithm to calculate automatically the resin flow advance in base of predicting the change of slopes in such curves. Once the analysis of the data collected with the fibers were concluded, the advance of the resin flow through the preform (in units of distance) versus the injection time were plot for both injection trials (see Fig. 10). In parallel to the analysis of the curves obtained with the optical fibers, video recordings of the two impregnations were analyzed. A set of images at selected times were extracted from both injections. Since the fiber system and camera were synchronized, resin flow measurements from fiber and camera were plot together (see Fig. 10). Despite results were acceptable for both impregnations, the first one demonstrated higher correlation. The reason for explaining this issue could be related to the effect of the different temperature conditions present in both tests and this can be used to reinforce the idea of the necessity of developing a special algorithm to process and determine the differences between fiber baseline and successive curves.

Fig. 6. OF results first impregnation; a) Segment 1, b) Segment 2, c) Segment 3

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Fig. 7. Real images first impregnation at selected times

Fig. 8. OF results of the second impregnation trial; a) Segment 1, b) Segment 2, c) Segment 3

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Fig. 9. Real images second impregnation trial at selected times

Fig. 10. a) First impregnation test: resin flow front advance versus time, b) Second impregnation test: resin flow front advance versus time

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7 Conclusions The capability of Rayleigh optical fiber backscattering sensing technique to detect and monitor the resin flow in impregnation tests was explored. Two experimental set-ups were prepared including in each one three optical fiber segments sensitive to the advance of the resin flow front. The first test was done at room temperature and the second one at temperatures more representative to the ones used in a RTM process. Both tests included a video camera record to visualize the flow and compare it with optical fiber results. The correlation results have been successful but they manifest the need of developing a special algorithm to process the differences between fiber baseline and subsequent curves in order determine with more accuracy the advance of the resin flow. Acknowledgments. Authors acknowledge IMDEA Materials for allowing the use their materials and the facility and Olympus for lending us the high temperature IR camera.

References 1. Torres, M.: Parameters’ monitoring and in-situ instrumentation for resin transfer moulding: a review. Compos. Part A Appl. Sci. Manuf. (2019). https://doi.org/10.1016/j.compositesa.2019. 105500 2. Lee, S.H., Yang, M., Song, Y.S., Kim, S.Y., Youn, J.R.: Three-dimensional flow simulation of resin transfer molding utilizing multilayered fiber preform. J. Appl. Polym. Sci. (2009). https:// doi.org/10.1002/app.30698 3. Vilà, J., González, C., Llorca, J.: Fabric compaction and infiltration during vacuum-assisted resin infusion with and without distribution medium. J. Compos. Mater. (2017). https://doi. org/10.1177/0021998316649783 4. Sánchez, D.M., Gresil, M., Soutis, C.: Monitoring manufacturing of composites using embedded distributed optical fibre sensors. In: System Reliability for Verification and Implementation – Proceedings of 10th International Workshop on Structural Health Monitoring, IWSHM 2015 (2015) 5. Miguel Giraldo, C., Zúñiga Sagredo, J., Sánchez Gómez, J., Corredera, P.: Demonstration and methodology of structural monitoring of stringer runs out composite areas by embedded optical fiber sensors and connectors integrated during production in a composite plant. Sensors (Basel) (2017). https://doi.org/10.3390/s17071683 6. Liehr, S., Nother, N., Krebber, K.: Incoherent optical frequency domain reflectometry and distributed strain detection in polymer optical fibers, Meas. Sci. Technol. 21, 017001 (2009) 7. Soller, B.J., Gifford, D.K., Wolfe, M.S., Froggatt, M.E.: High resolution optical frequency domain reflectometry for characterization of components and assemblies. Opt. Express. (2005). https://doi.org/10.1364/opex.13.000666 8. Kreger, S.T., Sang, A.K., Gifford, D.K., Froggatt, M.E.: Distributed strain and temperature sensing in plastic optical fiber using Rayleigh scatter. In: Fiber Optical Sensors Appl. VI, (2009). https://doi.org/10.1117/12.821353

Embedded Perovskite-Mechanoluminescent Sensor for Applications in Composite Materials Lucas Braga Carani1 , Md Abu Shohag2 , Vincent Obiozo Eze1 , G. Ryan Adams1 , and Okenwa Okoli1(B) 1 High-Performance Materials Institute, FAMU-FSU College of Engineering,

2525 Pottsdamer St., Tallahassee, FL 32310, USA [email protected] 2 Department of Engineering and Technology, University of North Alabama, Florence, AL 35632, USA

Abstract. There is a growing need to automatically detect and monitor functional changes such as fatigue, wear, damage, or age in the structural components. It is even more attractive if the sensors are embedded in the structure for in-situ structural health monitoring (SHM). In this work, we developed Mechanoluminescence-based sensors for damage sensing and SHM. A flexible, sensitive, and self-powered pressure sensor was developed by integrating a mechanoluminescent device with a light-absorbing layer of the perovskite material. Understanding the behavior of the device as an embedded sensor is necessary for its application in continuous in-situ SHM of multifunctional composite materials. We showed a successful encapsulation process and the embedment of this sensing device into a glass fiber composite. Further investigations were performed to confirm the capability of the embedded sensor to detect the damages in the structures. The embedded sensor could be an effective method for real-time in-situ SHM. Keywords: Structural health monitoring · Mechanoluminescence · Sensor · Perovskite · Composite material

1 Introduction The last decades have seen a growing use of composite materials in industrial fields such as aeronautics, astronautics or automotive, due to their weight savings, and structural benefits, such as improved strength, stiffness, fatigue and impact resistance [1]. In these strategical sectors, the composite structures will be frequently exposed to harsh environmental conditions that can compromise the structural integrity of the material [2–5]. Consequently, there is a great interest in monitoring the conditions of these structures. Structural health monitoring (SHM) system refers to the method of implementing a damage detection and characterization strategy for engineering structures. The SHM process involves the observation and evaluation of a structure over time using data collected often from an array of sensors to determine the conditions of the structure [6]. A lot of effort © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 603–611, 2021. https://doi.org/10.1007/978-3-030-64908-1_56

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has been done in the development of efficient and reliable tools for real-time monitoring the health of the structures for prolonged service. Mechanoluminescence-based sensors have been developed for damage sensing in multifunctional composite materials [7–13]. Mechanoluminescence (ML) is the non-thermal emission of light as a response to mechanical stimuli on a solid material [14]. ML can be triggered by simple rubbing, applied pressure, crushing, impact load, or even the action of the wind [8, 11]. These materials can have many applications in stress sensing, dynamic pressure mapping, light sources, or the detection of electric and magnetic fields [14, 15]. In addition, ML materials are useful in determining crack propagation or stress distribution in different situations [6, 8, 10–12]. Embedding ML-based sensors into composites structures could be an effective way for real-time, continuous SHM. Researchers at the High-Performance Materials Institute developed the in-situ triboluminescent optical fiber (ITOF) sensor. The sensor consists of polymer optical fiber coated with manganese-doped zinc sulfide (ZnS:Mn). The sensor converts the energy from impacts and cracks propagation into the ML signal, which is then transmitted by the optical fiber for SHM. ITOF sensors were used for SHM applications of composite and concrete structures [4, 10–17]. Shohag et al. demonstrated a highly sensitive, flexible thin-film ML pressure sensor by integrating ZnS:Cu embedded in polydimethylsiloxane (PDMS) and a perovskite light-absorbing layer [7]. Organic-inorganic perovskites offer large light absorption coefficient, high and balanced charge carrier mobility, long carrier diffusion length, and other properties that make them attractive light-absorbing materials for photodetectors [16–18]. Understanding the behavior of this novel device under embedment in a composite system is imperative for future applications in composite structures. The performance of perovskite devices is known to be highly susceptible to deterioration upon exposure to ambient atmospheric conditions [19]; thus, for long operating lifetime sensor devices, it is necessary to develop an encapsulation to protect the perovskite layer from rapid degradation. Additionally, encapsulation is necessary for embedding the sensor to composite. Without any form of encapsulation, the perovskite film cannot withstand the embedment process, degrading with direct contact of a resin matrix [20, 21]. In this work, we showed a successful encapsulation process using a well-known commercial encapsulant, ethylene-vinyl acetate (EVA), and the embedment of this sensing device with a simplified architecture into a glass fiber composite material. The investigation of the embedment process of the integrated flexible pressure sensor in a composite material will open a new opportunity for in-situ sensing research in a mechanoluminescent sensor system for SHM.

2 Photodiode-Type Photodetector Device Architecture The perovskite photodiode was fabricated in a simplified structure as shown in Fig. 1, consisting of ITO-PET/tin oxide (SnO2 )/perovskite/Au. SnO2 was used as an alternative for the low-temperature electron transport layer (ETL) since ITO-coated PET films have a maximum operating temperature of 120 °C [22]. The Au electrode was deposited directly on the perovskite layer, avoiding the use of a hole transport layer (HTL), and consequently, reducing the cost and manufacturing time of the process [23–25]. In this

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structure, electron-hole pairs are generated in the perovskite layer when the incident photons are absorbed and dissociated into electrons and holes at the SnO2 /perovskite interfaces. The electrons are collected and transport in the SnO2 layer, while the holes transport in the perovskite layer and are collected by the Au electrode, generating an electrical signal output. Gold Perovskite SnO2 PET/ITO ZnS:Cu-PDMS

Fig. 1. Schematics of the sensor device.

3 Device Fabrication First, PET/ITO substrates were cut and patterned by etching with hydrochloric acid and cleaned sequentially with Hellmanex detergent, nano pure water, acetone, and isopropanol in a sonication bath. The PET substrates were treated with oxygen plasma for 5 min. The SnO2 ETL was prepared by spin-coating a 0.1 M solution of SnCl2 .2H2 O (Sigma-Aldrich) in ethanol at 3000 rpm for 30 s. The samples were then transferred to ambient conditions and annealed at 120 °C for 80 min. The substrates were returned to the glovebox in N2 environment. The light-absorbing MAPb(Br0.1 I0.9 )3 perovskite films were prepared using a one-step deposition method and anti-solvent bath method. The precursor solution was prepared by mixing 190 mg of CH3 NH3 I (Sigma-Aldrich), 46 mg of PbBr2 (Alfa Aesar), 413 mg of PbI2 (Acros Organics) into a solution of 0.5 ml NMethyl-2-pyrrolidone (NMP, Sigma-Aldrich) and 0.1 ml γ-butyrolactone (GBL, SigmaAldrich). The prepared solution was left stirring on a hot plate at 70 °C overnight. The solution was then filtered using 0.2 μm filters to remove possible particles. Before deposition, the solution was heated on a hot plate at 70 °C for 30 min. The perovskite solution was spin-coated at 900 rpm for 3 s followed by 4500 rpm for 30 s. The substrates were dipped into Diethyl Ether (DEE, Sigma-Aldrich) bath for 2 min and then annealed at 70 °C for 5 min followed by 130 °C for 15 min. 100 nm Au electrodes were deposited on top of the perovskite via thermal evaporation. ZnS:Cu (Phosphor Technology), PDMS base, and curing agent were mixed to a 20:10:1 weight ratio, respectively, using a planetary centrifugal mixer. The ZnS:Cu-PDMS blend was coated on the opposite side of perovskite film. The thin film was heated at 100 °C for 10 min to complete cure. Figure 2 shows pictures of the device.

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(b)

10 mm

(c)

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Fig. 2. (a) Top, (b) back, and (c) side view of the device.

4 Results and Discussion 4.1 Device Mechanism During deformation and self-recovery of ZnS:Cu/PDMS, green ML emission is observed and attributed to deformation of the ZnS:Cu and frictional interactions between the ZnS:Cu and the PDMS, caused by the trapping of drifting charge carriers in the piezoelectric field, and electrons movements to the material conduction band [26–28]. Figure 3a shows the UV-vis absorption spectrum of the MAPb(Br0.1 I0.9 )3 film on the PET substrate. The optical band gap (Eg ) of the MAPb(Br0.1 I0.9 )3 perovskite is 1.64 eV, calculated from the Tauc plot, which is lower than the ML light emission energy from ZnS:Cu (2.28 eV) [29]. Therefore, the perovskite material can fully absorb ML emission from ZnS:Cu. The light emitted by ZnS:Cu/PDMS layer due to the applied pressure or strain is sufficient to excite the perovskite layer, generating free electrons and holes pairs in the material, which are then transported to the cathode (ITO) and anode (Au), respectively. The device performance is intrinsically related to the quality of the perovskite film. Figure 3b shows the SEM image of the high-quality uniform perovskite film, confirming full coverage of the substrate surface and lack of pinholes, which is fundamental for the device photovoltaic performance.

Fig. 3. (a) UV-vis absorption spectrum and (b) SEM image of the MAPb(Br0.1 I0.9 )3 perovskite film.

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4.2 Encapsulation and Embedment Process The device was assembled in the following order: first, a slightly larger PET substrate was placed beneath the ML-perovskite device; then, an EVA sheet was placed on the top layer and used as an encapsulant. The package was further sealed using polyimide tape and laminated under vacuum using a heat gun for 3 min and then put in a vacuum oven at 100 °C for 30 min. Figure 4 shows the schematics of the encapsulated device. EVA Encapsulant Polyimide Tape Gold Electrode Perovskite SnO2 PET/ITO ZnS:Cu-PDMS PET

Fig. 4. Schematic of the encapsulated device.

For the embedment process, glass fiber woven reinforcement was chosen for two primary reasons: i) the transparency of the final composite allows for tracking the conditions of the device after the manufacturing process; ii) the non-conductive nature of glass fiber prevents short circuits or electric interference between the fibers and the device. Figure 5 depicts the sensor embedment process in glass fiber composite.

Fig. 5. Schematics of sensor embedment in glass fiber composite.

The sensing device was placed in the middle of 4 plies of glass fiber cloth woven, as shown in Fig. 6. Vinyl ester resin was used for the Vacuum Assisted Resin Transfer Molding (VARTM) infusion. VARTM is a common out-of-autoclave manufacturing technique that is utilized for automotive and ship engineering, and in wind turbine blades [30]. The process has a relatively low-cost method and can be used to fabricate high-quality composite parts.

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Sensor

Copper Leadss

Fig. 6. Embedded sensor in glass fiber reinforced composite panel.

4.3 Sensor Response with Applied Pressure Tapping Tests Figure 7a shows the schematic of the experiment setup for the sensor response due to the applied pressure by finger pressure on the ML-perovskite sensor. The pressure was applied to the sensor several times, which demonstrated clear signals in each time. The results can be seen in Fig. 7b, where I represents the change in current, and I0 represents the baseline current. The tests were performed in ambient conditions (21 °C, 71% RH) and with no bias voltage. It was also observed signal peaks in the opposite direction, right after the actual signals. Further investigation is necessary to understand the mechanism responsible for the occurrence of these signals.

Fig. 7. a) Schematics of the experiment. b) Sensor response due to applied pressure by an index finger.

To confirm that the ML material is indeed responsible for the light collected by the perovskite layer, a perovskite photodetector was embedded without a ML layer. All other processes were kept the same. Figure 8a shows the schematics of the sensor without ML

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material and Fig. 8b shows the response signals from the sensor with ML material and without ML material. Without the ML material, no light emission was occurred due to the mechanical impact on the composite. Therefore, no evident signals were observed. It is possible to affirm that the light harvested by the perovskite comes from the ML layer. (a)

(b)

Gold Perrovskite SnO2 T/ITO PET PD DMS

Fig. 8. (a) Schematics of the sensor device without ML material. (b) Comparison between response signals from the sensor with ML material (red) and without ML material (blue).

Impact Hammer Tests For a more consistent experiment procedure, an automated impact hammer equipment was used (AS-1220, Alta Solutions). In total, 12 impacts with different magnitudes were executed to the composite panel, with a 2 s interval between the impacts. Figure 9 shows the impact hammer test result. The impact pressure applied varied from 100 kPa to 200 kPa, and the sensor generated distinct signals for most impacts, which demonstrates that the sensor can be used for SHM of composite structures. The tests were conducted in ambient conditions (21 °C, 75% RH).

Fig. 9. Hammer impact test results.

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5 Conclusion This article demonstrated a successful method of encapsulation and embedment of the ML-perovskite flexible damage sensor in glass fiber composite. The encapsulation method showed that the device could withstand the embedment process into a glass fiber composite manufacturing. The sensor demonstrated distinct response signals due to pressure applied to the ML layer, and it was proved that the ML layer was fundamental for the operation of the sensor. The ML-perovskite sensor can be embedded in a composite material for real-time SHM purposes. This opens an excellent opportunity for the development of low-cost damage sensors for in-situ SHM of multifunctional composite materials.

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In-Situ SEM Investigation of the Fatigue Behavior of Additive Manufactured Titanium Alloys Xinyan Wang1 , Yang Zhao2 , Limin Wei3 , and Xuefei Guan1(B) 1 Graduate School of China Academy of Engineering Physics, Beijing 100193, China

[email protected] 2 National Key Laboratory for Remanufacturing, Beijing 100072, China 3 Institute of Systems Engineering, China Academy of Engineering Physics,

Mianyang 621999, China

Abstract. Additive manufacturing of large-scale metal components has a great potential to be applied in the field of equipment manufacturing, repairing, and remanufacturing. The wire and arc additive manufacturing (WAAM) technology has become the preferred additive manufacturing technology for the production of large parts due to its higher deposition rate and better flexibility. The WAAM procedure may lead to a significant periodicity and inhomogeneity in material deposition layers, affecting mechanical properties of materials. The in-situ fatigue testing of Ti-6Al-4V specimens made by WAAM is performed to study fatigue performance based on in-situ observations with scanning electron microscope (SEM). The crack initiation and growth behaviors can be monitored during the fatigue testing of the specimens. The microstructure effect on crack growth rate and path are observed. The uncertainty of fatigue crack growth rate due to these factors is quantified using the experimental data with Paris’ model. Keywords: Wire and arc additive manufacturing · Fatigue crack propagation · Titanium alloy · In-situ SEM fatigue testing · Microstructure

1 Introduction Additive manufacturing (AM) is an emerging technology of joining materials based on layer-by-layer accumulation process [1, 2]. AM technology provides an effective method to fabricate structural parts with complex shapes more flexibly and easily, and reduces the production time and cost comparing with traditional manufacturing process [3]. Additive manufacturing of metal components has demonstrated its great potential in the field of equipment manufacturing, repairing, and remanufacturing. Among current mainstream AM technologies, the wire and arc additive manufacturing (WAAM) has the highest deposition rate due to its unique heat source and raw material form [4, 5]. By feeding the metal wires of the raw materials into an arc, the materials can be melted onto a substrate or the previously deposited layer much faster than powder based AM processes using laser or electron beam as heat sources [6, 7]. In addition, some metals © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 612–621, 2021. https://doi.org/10.1007/978-3-030-64908-1_57

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with higher reflection properties make it difficult to apply the laser-based AM methods [8, 9]. Therefore, WAAM has become the preferred AM technology for the production of large parts with a wider variety of raw materials. The Ti-6Al-4V alloy is a typical α + β dual-phase titanium alloy with high specific strength, low density, excellent fracture toughness and good corrosion resistance. It has been widely used in the aerospace industry [10, 11], for example, the manufacture of aircraft landing gear components and shell. The manufacturing of titanium alloy can be cumbersome using traditional metallurgical and machining processes [12, 13]. The inherent properties of titanium alloys, such as low thermal conductivity and high chemical activity, may result in premature tool failure [14]. In particular, the remanufacturing and repairing of few individual titanium alloy parts and components in a short time using traditional process can cost much higher than the original ones. WAAM technology can greatly alleviate the difficulties, and provides a low-cost alternative means in those cases. The WAAM procedure may lead to a significant periodicity and heterogeneity in material deposition layers [15], which in turn can affect mechanical properties of materials. Therefore, understanding the mechanical properties of Ti-6Al-4V material made by WAAM, particularly the fatigue and fracture behaviors, is highly necessary when the resulting parts and components are used in safety critical applications [16, 17]. The mechanical properties of Ti-6Al-4V material made by AM have been reported in several studies [1, 3]. It is shown that the static properties of AM materials can meet the minimum specification required by standard AMS 4985C [18] through adopting suitable manufacturing parameters or post-processing the materials. A recent work [19] demonstrated that the fatigue life of most of WAAM deposited Ti-6Al-4V specimens with fully lamellar microstructure exceeds the forged specimen. In addition to the low-cycle fatigue, the fatigue crack growth is also an important property for critical applications [20]. Zhang et al. [21] observed that the crack growth rate (FCGR) and path between WAAM deposited Ti-6Al-4V and wrought alloys are different due to their microstructure characteristics. The wrought alloy with equiaxed structure developed a smooth and straight crack path, whereas the WAAM material with lamellar structure generated a tortuous crack path and a lower crack growth rate. In Ref. [22], the FCGR of wrought, WAAM deposited, and cast Ti-6Al-4V alloys were investigated, and results show that the wrought alloys has the highest crack growth rates and the cast ones has the lowest rates. For WAAM deposited material, the crack propagating across the layers has a slightly greater FCGR than that propagating along the layers. Xie et al. [23] reported that the FCGR of vertical samples (crack growth direction paralleled to layer build direction) is 5% higher than that of the horizontal samples (crack growth direction paralleled to the welding torch movement direction). The grain boundary and thinner lamellae structure are more resistant to the crack propagation in horizontal sample, and the fatigue crack in vertical sample spreads through the colony and the basket weave with the lowest growth resistance. The anisotropic fatigue crack behavior of WAAM deposited Ti-6Al-4V are influenced by the microstructure and grain boundary. For small cracks whose lengths are comparable to the grain sizes, the microstructure and grain features can have a much more significant influence on the crack growth behaviors, which have seldomly been reported for titanium alloys made by WAAM.

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The objective of the study is to investigate small crack fatigue behaviors of Ti6Al-4V made by WAAM. The fatigue mechanical characterization of the crack is an important part of structural health monitoring system. To achieve that, in-situ SEM fatigue tests of WAAM deposited Ti-6Al-4V material are performed. The crack growth behaviors in one grain or across grain boundaries are monitored, and the microstructure effect on crack growth rate and path is discussed. The uncertainty modeling of fatigue crack growth rate is performed utilizing the experimental data. The remainder of the paper is organized as follows. First, the experimental tests of the WAAM Ti-6Al-4V specimens are presented. Next, the fatigue behaviors based on the in-situ SEM are discussed. Following that, the fatigue crack growth data and resulting FCGR parameters are established, and conclusions are made based on the current results.

2 Experimental Procedures 2.1 Material and Specimens A titanium alloy block made of Ti-6Al-4V is manufactured by WAAM technology with the Cold Metal Transfer (CMT) arc welding process. The AM equipment are Fronius TPS 4000 CMT welder and ABB 1410 robot with a controlling software, as shown in Fig. 1(a). The welding wire material are 1.2 mm-diameter Ti-6Al-4V wires. The substrate is forged Ti-6Al-4V plate with the geometric dimensions of 300 mm × 230 mm × 20 mm.

5mm

(a)

Building direction

(b)

Fig. 1. (a) WAAM experimental setup, and (b) material deposition path

The deposition path adopted in this paper is direct back-and-forth deposition strategy, as illustrated in Fig. 1(b). The Ti-6Al-4V wires are fed into the welding machine. The welding machine, driven by the six-axis robot, is used to gradually form the metal parts according to the designed path. At each pass, a 5 mm thickness of layer is formed. The manufacturing process is shielded by argon. The process parameters for fabrication are shown in Table 1. Table 1. The process parameters for manufacturing component Parameters

Current (A)

Wire feed speed (mm/min)

Travel speed (mm/min)

Shielding gas rate (L/min)

Value

150

2

4

15

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3

8.5

2.5

0.2

0.09

The resulting Ti-6Al-4V material fabricated by WAAM is shown in Fig. 2. The specimens are extracted from the top layer of the material block using Electron Discharge Machining (EDM), as indicated in the red polygons in Fig. 2(a). The geometry of Ti6Al-4V specimen used in in-situ fatigue testing is shown in Fig. 2(b). The specimens have a dog-bone shape with a 2.5 mm × 1 mm middle cross section. An ellipse-shaped notch with a depth of 0.09 mm and a width of 0.2 mm is prepared. The notch located at the center of the gauge section is fabricated for creating local stress concentration for crack initiation.

(8) 20

(a)

(b)

45

Fig. 2. (a) The geometry of Ti-6Al-4V specimen, and (b) the cutting position of specimens.

To study the microstructure of the material and microstructure effect on crack propagation under SEM, the specimens are polished using standard mechanical polishing method and etched with a mixed solution of HF:HNO3 :H2 O at a ratio of 1:2:17. The sample for in-situ SEM fatigue testing is shown in Fig. 3. The prepared specimens are placed for a period of time to release residual stress before performing the fatigue tests.

Fig. 3. The Ti-6Al-4V specimen for fatigue testing.

2.2 Experimental Setup The studies of in-situ SEM for fatigue crack propagation behaviors can be found in several researches, including, but not limited to, Refs. [24–26]. The in-situ SEM fatigue testing is performed to monitor the fatigue cracks initiation and growth behaviors and the crack growth processes can be analyzed utilizing the captured SEM images accurately. In-situ fatigue testing is carried out with an electro hydraulic servo system at room temperature and in-situ observation of cracks is performed in the vacuum chamber of the SEM. The in-situ fatigue testing system is shown in Fig. 4. The experimental load is sinusoidal cyclic load with loading frequency of 5 Hz. The maximum force is 1 kN with a load ratio of 0.1. SEM is utilized to record the processes of crack initiation and propagation behaviors at different cycles. The fatigue testing rig is stopped at mean load

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for observing the crack tip clearly and acquiring SEM images. The microstructure effect on the crack propagation and crack growth rate can be subsequently studied using the resulting SEM images.

Fig. 4. The SEM chamber of the in-situ fatigue testing system.

3 Fatigue Crack Growth of WAAM Deposited Ti-6Al-4V 3.1 Microstructure Properties Microstructure is one of the main factors affecting the mechanical properties of WAAM deposited components. During the WAAM, the deposited material is subjected to the processes of repeated rapid heating and cooling thermal cycles. The microstructure is different between lower deposited layers and upper layer owing to different thermal conditions. Existing studies [19, 23, 27] have reported that the microstructure of WAAM deposited Ti-6Al-4V material is characterized by the coarse columnar prior-β grains growing from the substrate to throughout the deposited layers. The microstructure of the experimental material extracted from the upper deposited layer is shown in Fig. 5. The α phase nucleates at the prior β grain boundaries, and the grain boundaries, α (αGB ), are formed. The α plates grow and form the colonies. The colony is a lamellar microstructure, which consists of parallel α plates separated by the retained β matrix. At higher cooling rates, the α phase nucleates within the remaining β in a basket weave morphology.

GB

Colony Colony

Basket weave

Fig. 5. Microstructure of the Ti-6Al-4V material manufactured by WAAM.

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3.2 Fatigue Crack Growth Behavior Figure 6 shows the process of the fatigue crack propagation from the in-situ SEM images where multi-site cracks are initiated at the root of notch. With the increasing of the loading cycles, only one initial crack continues to propagate at the center of the notch due to local stress concentration and becomes main crack. As the number of loading cycles progresses, many slip bands are formed in front of the crack tip, as shown in Fig. 6(b). The direction of the slip lines is 45° inclined from the notch direction. The slip system accelerates the occurrence and propagation of cracks. Some secondary cracks initiate from the slip lines and assist the propagation of the main crack. The main crack propagates in a local zigzag pattern and the crack path is roughly perpendicular to the loading direction, as shown in Fig. 6(c).

One crack becomes dominated

Zigzag manner of crack path

Second cracks Multi-site initiation (a) 11410 cycle

Slip lines (b) 17551 cycle

(c) 20852 cycle

Fig. 6. The fatigue crack growth behaviors of a tested specimen.

The crack length a and the corresponding number of loading cycles N can be acquired utilizing the SEM images. The crack growth rates (da/dN) vs. the crack length (a) are calculated using the 3-point average of the a − N data, and results are as shown in Fig. 7. The remaining life prediction of the structural parts is necessary for making a reasonable maintenance plan and ensuring the safety operation of the equipment [28, 29]. To achieve that, a linear elastic fracture mechanics (LEFM)-based crack growth model can be adopted [30, 31]. The fatigue crack growth data obtained in this study indicates that the crack should be considered as a small crack whose length is comparable to microstructural features. To incorporate small crack effects, the modified Paris’ equation for small cracks can be used, for example, modified ones reported in Refs. [32–34]. To simplify the prediction, the Paris’ equation for long cracks is employed for demonstration purposes [35], da = C(K)m , dN

(1)

where a is the crack length, N is the number of loading cycles, K is the range of stress intensity factor, C and m are material parameters. The stress intensity factor range of the specimen can be calculated according to Ref. [36] √  K = σ π a F(a/b), (2) 0.752 + 2.02(a/b) + 0.37(1−sin π2ba )3 , F(a/b) = π2ba tan π2ba • cos π a 2b

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Several cracks grow

8 6

Crack propagates in colony microstructure

Zigzag path

10-4

(a)

Crack grows across grain (c) boundary

(b)

4 2 0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

a(mm) Fig. 7. The crack growth rate vs. the crack size.

where b is the width of the center of the specimen and b = 2.5 mm, the σ is the applied stress range. The crack growth rate data, da/dN vs. K, of the specimen are presented in Fig. 8. The fatigue crack growth parameters of the Paris’ equation are statistically identified from experimental data. The matrix of (lnC, m) are  mean and covariance  3.5725, −1.2164 μ = (−23.3903, 4.5940) and  = , respectively. The mean and −1.2164, 0.4174 95% bound prediction results are shown in Fig. 8 in solid and dash lines, respectively.

Fig. 8. The fatigue crack growth rate vs. the stress intensity factor range.

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4 Conclusion The paper investigates the fatigue crack growth behaviors of WAAM deposited Ti-6Al4V alloy using in-situ SEM fatigue testing. The crack growth processes and paths are observed from SEM imaging. The microstructure properties and the microstructure effect on crack growth behaviors are studied, and the crack growth parameters are obtained using Paris’ equation with the acquired experimental data. Based on the current study, the following conclusions can be made. (1) The microstructure of upper deposited Ti6Al-4V alloy layer is composed of grain boundary α (αGB ), colony primary α and basket weave in the coarse columnar prior-β grain. (2) The microstructure affects the initiation and growth of the crack. The persistent slip system promotes the main crack initiation and the crack growth. The main crack grows in zigzag pattern locally and maintains a roughly overall straight path perpendicular to the loading direction. It is observed that the branching of secondary cracks slows down the overall FCGR, and the grain boundaries also hinder the crack propagation. (3) A fatigue crack growth rate model is established for the remaining life prediction of the structural parts manufactured by this material. Acknowledgement. The work in this study was supported by National Natural Science Foundation of China, Nos. 51975546, U1930403. The support is greatly acknowledged.

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Enhanced Photoresponse of Inorganic Cesium Lead Halide Perovskite for Ultrasensitive Photodetector Vincent Obiozo Eze1 , Geoffrey Ryan Adams1 , Bryana Beckford1 , Md Abu Shohag2 , and Okenwa I. Okoli1(B) 1 High-Performance Materials Institute, FAMU-FSU College of Engineering, 2525, Pottsdamer

Street, Tallahassee, FL 32310, USA [email protected] 2 Department of Engineering and Technology, University of North Alabama, Florence, AL 35632, USA

Abstract. We report on a simple way to enhance the photoresponse and efficiency of inorganic cesium lead halide (CsPbIBr2 ) perovskite for use as a light-absorbing layer in photodetectors integrated with a mechanoluminescent (ML) or triboluminescence (TL) materials for pressure sensing applications. Herein, we proposed to integrate a thermal and moisture stable inorganic cesium lead halide-based CsPbIBr2 perovskite with the TL materials to develop a novel pressure sensor for real-time and in-situ structural health monitoring (SHM) of aerospace vehicles’ fuselage, automobiles and structures. However, the inorganic CsPbIBr2 perovskite layer fabricated using a one-step spin-coating method is usually composed of small grain size with a large number of grain boundaries and compositional defects. Therefore, we employed a metal doping approach to enhance the CsPbIBr2 perovskite film quality. By introducing a small amount of silver iodide (AgI), the photoresponse, responsivity, and response time of the detector were enhanced. This work offers a promising approach for developing an integrated ML pressure sensor with high-quality polycrystalline perovskite for SHM. Keywords: Inorganic perovskite · Additive · Photodetector · Structural health monitoring · Sensor · Composite

1 Introduction The Triboluminescence (TL) phenomenon, which is equally known as mechanoluminescence (ML), has been proposed for use as sensor systems for monitoring and detecting damage in both aerospace and civil structures [1–3]. TL materials emit light when they are scratched, stressed, or fractured. There is a plethora of TL materials, including both organic and inorganic materials. Among all the TL materials, the zinc-sulfide manganese (ZnS:Mn) and zinc sulfide copper (ZnS:Cu) have been actively studied for their efficient triboluminescent production [4, 5]. The mechanism behind luminescence is derived from © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 622–631, 2021. https://doi.org/10.1007/978-3-030-64908-1_58

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mechanical excitation upon accruing crystal defects during new surface creation [3, 6, 7]. To date, non-destructive testing techniques such as emission and ultrasonic testing; thermography, ultrasonic pulse velocity (UPV), and ground penetrating radar (GPR); X-ray, gamma-ray and neutron ray methods have been widely deployed for damage detection and monitoring [8–10]. However, these techniques cannot provide in situ distributed sensing. The lack of in-situ prevents real-time monitoring of the structural states of engineering structures, which inevitably add to the cost of the downtime required for the periodic non-destructive inspections. Okoli and his coworkers have previously developed the in-situ triboluminescent optical fiber (ITOF) sensors for applications of composite sensor integration for real-time distributed damage monitoring [11]. The ITOF sensor exhibited impressive characteristics of an excellent damage sensor by providing a real-time damage detection in composite without generating any false signal. However, the ITOF data acquisition process is complicated and expensive. It requires an expensive photomultiplier tube (PMT) to boost the number of photons generated by the ITOF sensor upon impact and convert it into electrical signals. To address this issue and eliminate the use of the expensive and less-rugged PMT devices, we recently proposed a self-powered sensor that integrates the physical principles of ML and polycrystalline perovskite photodetector (PD) for structural health monitoring (SHM) applications [12]. The perovskite PD can capture all the light emitted from the excitation of TL, even at low impact energy. It has determined capabilities to detect external pressure events as low as 11 kPa [12, 13]. Recently, we investigated the organic-inorganic triple cation lead-halide perovskites for self-powered PDs. The PDs had a vertical n-i-p (where n, i, p refer to the electron transporting layer (ETL), intrinsic layer and hole transporting layer (HTL), respectively) device structure that showed high responsivity, impressive detectivity, and high on/off ratio and rapid response speed [14, 15]. Despite the significant advances in the electronic and photoresponse performance, the intrinsic poor thermal and moisture stability issues of the organic-inorganic perovskites hinder their practical applications [16]. All inorganic cesium lead halide (CsPbIx Br3-x , x = 0–3) perovskites have been shown to be potential candidates for the fabrication of PDs due to their superb moisture and thermal stability, as well as the high carrier mobility of all CsPbIx Br3-x perovskite [17–21]. In this work, we fabricated a CsPbIBr2 perovskite film using a one-step spincoating together with an additive assisted solution approach for a self-powered PD [21]. Among all the inorganic CsPbIx Br3-x perovskite system, the CsPbIx Br3-x (where x = 1, CsPbIBr2 ) is the most favorable material for optoelectronic device applications (e.g., solar cells and PDs) due to its stable α-phase and suitable bandgap of about 2.05 eV) [21]. Nevertheless, achieving high-quality CsPbIBr2 perovskite films using a simple spin-coating method is challenging. In order to address this fundamental issue, a small amount of silver iodide (AgI) additive was added into the CsPbIBr2 perovskite precursor to form a 1% doped-AgI-CsPbIBr2 (CsI(PbBr2 )0.99 (AgI)0.01 ) composition [21]. The 1% doped-AgI-CsPbIBr2 perovskite displays numerous advantages of uniform coverage, phase pure, enlarge grain size, higher crystallinity, fewer defects perovskite films. A self-powered PD based on 1% doped-AgI-CsPbIBr2 perovskite was constructed. The device exhibited a higher photocurrent, lower dark current, higher on/off ratio, improved

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photoresponsivity, and faster response speed, which is higher than the pristine CsPbIBr2 perovskite device.

2 Device Fabrication The fluorine-doped tin oxide (FTO) coated glass substrates were patterned by etching with hydrochloric acid (HCl) and zinc (Zn) powder and consecutively cleaned with Hellemanex, nano-pure water, acetone, and isopropanol. The substrates were then treated with an oxygen plasma cleaner for 5 min. The electron transport layer (ETL) (compact TiO2 (c-TiO2 )) was prepared as reported elsewhere [22] and spin-coated at 3000 rpm for 30 s and dried at 125 °C for 10 min. A chemical bath treatment using TiCl4 (0.04 M) at 70 °C for 30 min was further performed on the c-TiO2 layer. The c-TiO2 films were then annealed at 500 °C for 30 min [22, 23]. A one-step solution process method was used to prepare the inorganic CsPbIBr2 perovskite layer. First, the CsPbIBr2 precursor solutions were prepared in a nitrogen-filled glovebox by mixing CsI (1 M) and PbBr2 (1 M) in DMSO (1 ml). Next, the perovskite precursor solution containing the AgI additive was prepared by introducing a 1% mass percentage of AgI with respect to PbBr2 into the solution [21]. The solutions were stirred for 12 h at 70 °C. Subsequently, the perovskite films were prepared by dripping the solution on top of the c-TiO2 layer and spin-coated at 1500 rpm for 45 s to obtain a thickness of about 250 nm. Lastly, the perovskite films were thermally annealed at 70 °C for 2 min, followed by 280 °C for 10 min. The HTL was prepared by spin-coating a solution of Spiro-OMeTAD on top of the perovskite film at a spin speed of 2000 rpm for 60 s. The obtained Spiro-OMeTAD thickness was ~230 nm. The Spiro-OMeTAD solution was prepared by mixing 17.5 μl of Li-TFSI solution (520 mg of Li-TSFI in 1 ml of acetonitrile), 28.8 μl of 4-tert-butyl pyridine with 90 mg of Spiro-OMeTAD in 1 ml of chlorobenzene solution. The final devices were finalized by the thermal evaporation of gold (Au) electrode with a thickness of 100 nm at 3.4 × 10−4 Pa. The devices have an active area of 0.06 cm2 .

3 Results and Discussion The preparation method of the 1% doped-AgI-CsPbIBr2 perovskite film using a onestep spin-coating process is shown in Fig. 1a. The 1% doped-AgI-CsPbIBr2 perovskite precursor solution was prepared by partial substitution of PbBr2 with 1% AgI (mass percent) [21]. The precursor solution was one-step deposited on top of the FTO/c-TiO2 layer to form the 1% doped-AgI-CsPbIBr2 perovskite film. See the preparation procedures in the experimental section. Based on the experimental results, it is apparent that the additive AgI induced a uniform perovskite morphology with larger grain size, as depicted in Fig. 1a. This observation will be discussed in detail hereafter. The surface morphological features of the corresponding perovskite films were studied using a high-resolution field emission scanning electron microscope (FESEM), JEOL 7401F. Figure 2a, b show SEM images of the CsPbIBr2 and 1% doped-AgI-CsPbIBr2 perovskite films. It can be seen that the CsPbIBr2 perovskite film exhibited a non-uniform morphology with pinholes on its surface. Zhu et al. have previously suggested that the formation of pinholes may be due to the enormously slow crystallization of CsPbIBr2 , where

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CsPbIBr2 species will crystallize from the precursor film containing plenty of DMSO molecules and then shrink to leave isolated voids behind [24]. Interestingly, the 1% doped-AgI-CsPbIBr2 perovskite film showed obvious changes on the surface (Fig. 2b). A dense and even morphology with larger grain sizes and fewer grain boundaries can be observed. It is expected that the improved surface coverage can alleviate the crystal defects, trap density, charge recombination and enhance the charge transport in the 1% doped-AgI-CsPbIBr2 device [22, 23, 25–28]. The perovskite films crystal structure were examined using powder X-ray Diffraction (Scintag Pad-V XRD Powder Diffractometer, graphite monochromated Cu Kα radiation). Figure 2c presents the XRD results of the CsPbIBr2 and 1% doped-AgI-CsPbIBr2 perovskite films. The diffraction peaks around 14.93 and 30.16° can be assigned to the lattice plane (100) and (200) of the α-phase perovskite [21, 29], respectively. In comparison, the diffraction peak intensities of the (100) and (200) crystal planes were stronger for the 1% doped-AgI-CsPbIBr2 perovskite film, indicating better crystallinity with fewer grain defects. These features are expected to be beneficial in enhancing the electronic properties and photoresponse of the 1% doped-AgI-CsPbIBr2 perovskite PD. The UV-vis absorption spectra of CsPbIBr2 and 1% doped-AgI-CsPbIBr2 perovskite films is presented in Fig. 2d. It can be seen that the 1% doped-AgI-CsPbIBr2 perovskite film showed improved absorption, which is probably related to its higher crystallinity and/or improved surface morphology [21]. The improved optical absorption obtained by the 1% doped-AgI-CsPbIBr2 perovskite film can influence the PDs to achieve higher photoresponse.

Fig. 1. Schematic fabrication procedures of CsPbIBr2 and 1% doped-AgI-CsPbIBr2 perovskite films.

To assess the influence of the 1% doped-AgI-CsPbIBr2 perovskite on the currentvoltage characteristics, a self-powered PD based on the 1% doped-AgI-CsPbIBr2 perovskite was fabricated as shown in Fig. 3a. The results of the device based on 1% doped-AgI-CsPbIBr2 perovskite film was compared with the device constructed using the pristine CsPbIBr2 perovskite film. Figure 3b shows the energy diagram of the selfpowered PD, with its energy values extracted from literature [30, 31]. Typically, when perovskite absorbs photon energies larger than its bandgap, the layer can generate quasifree carriers and electron-hole pairs that swiftly dissociate at the TiO2 /perovskite and

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Fig. 2. SEM images of (a) CsPbIBr2 and (b) 1% doped-AgI-CsPbIBr2 perovskite films. (c) XRD results of CsPbIBr2 and 1% doped-AgI-CsPbIBr2 perovskite films. (d) UV-vis absorption spectra of CsPbIBr2 and 1% doped-AgI-CsPbIBr2 perovskite films. The scale bar is 1 μm.

perovskite/Spiro-OMeTAD interfaces (see Fig. 3b). As shown in Fig. 3b, the electrons in the perovskite light-absorbing layer is injected into the conduction band of the perovskite upon illumination from the ML materials ZnS:Mn or ZnS:Cu with sufficient photon energy of 2.12 eV or ~2.28 eV, respectively, which is further transported into the c-TiO2 layer. The holes are collected by the hole transporting material (HTM), spiroOMeTAD, and transported to the contact electrode Au to form a complete circuit. In principle, ML materials are capable of emitting light upon impact due to a change of energy state in the material [12, 32]. The light emitted by the ML material is captured by the perovskite light-absorbing layer and is converted into an electrical signal, which is further analyzed by the processing terminal. Generally, if the perovskite film possesses high-quality features such as fewer crystal defects, uniform, and pinhole-free morphology with smaller grain boundaries and so on, a higher photocurrent and lower dark current can be achieved in vertical structure PD at 0 V The J–V plots of the CsPbIBr2 and 1% doped-AgI-CsPbIBr2 PDs measured in the dark and under LED white light illumination (100 mW/cm2) is presented in Fig. 3c. The 1% doped-AgI-CsPbIBr2 perovskite device yielded a lower dark current density of 9.71 × 10−6 A/cm−2 under 0 V in comparison to the CsPbIBr2 device that achieved a dark current density 4.44 × 10−5 A/cm2 . Also, the light on/off ratios were determined to be 1.68 × 103 and 1.21 × 102 for 1% dopedAgI-CsPbIBr2 and CsPbIBr2 perovskite PDs, respectively. The lower dark current and higher on/off ratio displayed by the 1% doped-AgI-CsPbIBr2 perovskite-based PD can

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be ascribed to the better perovskite film quality [21]. The responsivity (R) spectra and detectivity (D*) curves of CsPbIBr2 and 1% doped-AgI-CsPbIBr2 based perovskite PDs were calculated and provided in Fig. 3c. R is the measure of electrical output per watt of incident radiant power, which can be expressed using Eq. 1 [33].

Fig. 3. Schematic diagram of the device structure. (b) Energy level diagram (c) J–V curves of devices in the dark and under white light illumination (100 mW/cm2 ). (d) R and D* of the CsPbIBr2 and 1% doped-AgI-CsPbIBr2 perovskite PDs, respectively under 0 V bias.

R = Jph /Pin = EQE ∗ λe/hc

(1)

where λ is the incident-light wavelength, h is the Planck constant, c is the speed of light. The D* represents the device’s capability of detecting low-level light signals and is calculated using Eq. 2 [33, 34]. D* = R/(2qJdark )1/2

(2)

Equation 2 provides an approximate expression of the specific detectivity when shot noise is the dominant noise in the system. Consequently, the calculation provides an upper approximation of the actual specific detectivity. The R of 0.43 A/W was achieved, and D* of 2.46 × 1011 Jones for 1% doped-AgI-CsPbIBr2 perovskite PD is higher than the control device (see Fig. 3d). The higher R and D* values shown by the device proves that the 1% doped-AgI-CsPbIBr2 perovskite film was of high crystalline quality with fewer defects resulting in efficient photon absorption, charge generation, and transport to the electrode [21]. Furthermore, another vital parameter for PDs is the response speed which reveals the capability of the PD to follow a fast-varying optical signal. Fast and reproducible responses to light illumination are indispensable for high-performance PDs

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for application in smart systems, image sensing, structural health monitoring, and optical communication [1, 21, 32, 35–39]. The response time of the CsPbIBr2 and 1% dopedAgI-CsPbIBr2 perovskite PDs were measured using a 470 nm pulse light source from a LED and driven by a function generator with square waves at a frequency of 500 Hz under ambient condition [21]. The CsPbIBr2 and 1% doped-AgI-CsPbIBr2 perovskite devices revealed stable and reproducible transient responses (see Fig. 4a), signifying that both CsPbIBr2 and 1% doped-AgI-CsPbIBr2 are excellent materials for the fabrication of PDs. The rise (τrise ) and fall (τfall ) time of both devices, which were the time taken for the PD to reach 90% and drop to 10% of steady-state values, respectively were investigated (see Fig. 4b). The 1% doped-AgI-CsPbIBr2 perovskite device displays a τrise and τfall of 22.4 μs and 25.7 μs [21], respectively, which is much faster than CsPbIBr2 perovskite PD shown in Fig. 4c.

Fig. 4. (a) Turn on-off cycles of CsPbIBr2 and 1% doped-AgI-CsPbIBr2 PD under a 470 nm pulse light from a LED at a frequency of 500 Hz and (b) The matching rise and decay time of the 1% doped-AgI-CsPbIBr2 perovskite PD

4 Conclusions In summary, we enhanced the photoresponse and electronic properties of CsPbIBr2 perovskite prepared using one-step spin-coating process. 1% AgI additive was introduced into the perovskite precursor solution to produce a high-quality CsPbIBr2 perovskite film. As a result, the 1% doped-AgI-CsPbIBr2 perovskite film composition exhibited uniform surface morphology, a pure phase, micro-sized grains, higher crystallinity, fewer

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defects in contrast with pristine CsPbIBr2 perovskite film. The 1% doped-AgI-CsPbIBr2 perovskite was integrated into a simple architecture of FTO/c-TiO2 /1% doped-AgICsPbIBr2 /Spiro-OMeTAD/Au to fabricate a self-powered PD. The device showed a lower dark current density of 9.71 × 10−6 A/cm−2 at 0 V bias, a peak R of 0.43 A/W, a peak D* of 2.46 × 1011 Jones, and a rapid response time of 22.4 μs, which are much higher than PD based on CsPbIBr2 perovskite. It is believed that the possible mechanism to the improved performance of the self-powered 1% doped-AgI-CsPbIBr2 perovskite PD stem from the improved surface morphology and reduced crystal defects in the perovskite film. This work shows the possible integration of inorganic CsPbIBr2 perovskites with ML materials for developing efficient pressure sensors for structural health monitoring.

References 1. Olawale, D.O., Sullivan, G., Dickens, T., Tsalickis, S., Okoli, O.I., Sobanjo, J.O., et al.: Development of a triboluminescence-based sensor system for concrete structures. Struct. Health Monit. 11(2), 139–147 (2012) 2. Sage, I., Bourhill, G.: Triboluminescent materials for structural damage monitoring© British Crown Copyright 2000/DERA: published with the permission of the Controller of Her Britannic Majesty’s Stationery Office. J. Mater. Chem. 11(2), 231–245 (2001) 3. Walton, A.J.: Triboluminescence. Adv. Phys. 26(6), 887–948 (1977) 4. Monette, Z., Kasar, A.K., Menezes, P.L.: Advances in triboluminescence and mechanoluminescence. J. Mater. Sci. Mater. Electron. 1–16 (1977) 5. Womack, F.N., Goedeke, S.M., Bergeron, N.P., Hollerman, W.A., Allison, S.W.: Measurement of triboluminescence and proton half brightness dose for ZnS: Mn. IEEE Trans. Nucl. Sci. 51(4), 1737–1741 (2004) 6. Chandra, B., Baghel, R., Chandra, V.: Mechanoluminescence glow curve of ZnS: Mn. Chalcogenide Lett. 7(1), 1–9 (2010) 7. Dickens, T., Armbrister, C., Olawale, D., Okoli, O.: Characterization of triboluminescent enhanced discontinuous glass–fiber composite beams for micro-damage detection and fracture assessment. J. Lumin. 163, 1–7 (2015) 8. Chang, P.C., Flatau, A., Liu, S.: Health monitoring of civil infrastructure. Struct. Health Monit. 2(3), 257–267 (2003) 9. Chong, K.P., Carino, N.J., Washer, G.: Health monitoring of civil infrastructures. Smart Mater. Struct. 12(3), 483 (2003) 10. Xu, C.-N., Watanabe, T., Akiyama, M., Zheng, X.: Preparation and characteristics of highly triboluminescent ZnS film. Mater. Res. Bull. 34(10–11), 1491–1500 (1999) 11. Shohag, M.A.S., Okoli, O.I.: Nonparasitic behavior of embedded triboluminescent sensor in multifunctional composites. Compos. Part A Appl. Sci. Manuf. 116, 114–125 (2019) 12. Shohag, M.A., Eze, V.O., Braga Carani, L., Okoli, O.I.: Fully-integrated mechanoluminescent devices with nanometer-thick perovskite film as self-powered flexible sensor for dynamic pressure sensing. ACS Appl. Nano Mater. 3(7), 6749–6756 (2020) 13. Shohag, M.A., Adams, G.R., Eze, V.O., Ichite, T., Carani, L.B., Okoli, O.: Mechanoluminescent-perovskite pressure sensor for structural health monitoring. Struct. Health Monit. (2019). https://doi.org/10.12783/shm2019/32233 14. Adams, G.R., Eze, V.O., Carani, L.B., Pino, A., Jolowsky, C., Okoli, O.I.: Synergistic effect of the anti-solvent bath method and improved annealing conditions for high-quality triple cation perovskite thin films. RSC Adv. 10(31), 18139–18146 (2020)

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15. Adams, G.R., Eze, V.O., Shohag, M.A.S., Simpson, R., Parker, H., Okoli, O.I.: Fabrication of rapid response self-powered photodetector using solution-processed triple cation lead-halide perovskite. Eng. Res. Express 2(1), 015043 (2020) 16. Meng, L., You, J., Yang, Y.: Addressing the stability issue of perovskite solar cells for commercial applications. Nat. Commun. 9(1), 1–4 (2018) 17. Li, C., Han, C., Zhang, Y., Zang, Z., Wang, M., Tang, X., et al.: Enhanced photoresponse of self-powered perovskite photodetector based on ZnO nanoparticles decorated CsPbBr3 films. Solar Energy Mater. Solar Cells 172, 341–346 (2017) 18. Li, Y., Shi, Z.-F., Li, S., Lei, L.-Z., Ji, H.-F., Wu, D., et al.: High-performance perovskite photodetectors based on solution-processed all-inorganic CsPbBr3 thin films. J. Mater. Chem. C 5(33), 8355–8360 (2017) 19. Liu, H., Zhang, X., Zhang, L., Yin, Z., Wang, D., Meng, J., et al.: A high-performance photodetector based on an inorganic perovskite–ZnO heterostructure. J. Mater. Chem. C 5(25), 6115–6122 (2017) 20. Yantara, N., Bhaumik, S., Yan, F., Sabba, D., Dewi, H.A., Mathews, N., et al.: Inorganic halide perovskites for efficient light-emitting diodes. J. Phys. Chem. Lett. 6(21), 4360–4364 (2015) 21. Eze, V.O., Adams, G.R., Braga Carani, L., Simpson, R.J., Okoli, O.I.: Enhanced inorganic CsPbIBr2 perovskite film for a sensitive and rapid response self-powered photodetector. J. Phys. Chem. C 124, 20643–20653 (2020) 22. Eze, V.O., Lei, B., Mori, T.: Air-assisted flow and two-step spin-coating for highly efficient CH3 NH3 PbI3 perovskite solar cells. Jpn. J. Appl. Phys. 55(2S), 02BF8 (2016) 23. Eze, V.O., Mori, T.: Enhanced photovoltaic performance of planar perovskite solar cells fabricated in ambient air by solvent annealing treatment method. Jpn. J. Appl. Phys. 55(12), 122301 (2016) 24. Zhu, W., Zhang, Q., Chen, D., Zhang, Z., Lin, Z., Chang, J., et al.: Intermolecular exchange boosts efficiency of air-stable, carbon-based all-inorganic planar CsPbIBr2 perovskite solar cells to over 9%. Adv. Energy Mater. 8(30), 1802080 (2018) 25. Eze, V.O., Seike, Y., Mori, T.: Efficient planar perovskite solar cells using solution-processed amorphous WOx/fullerene C60 as electron extraction layers. Org. Electron. 46, 253–262 (2017) 26. Lei, B., Eze, V.O., Mori, T.: High-performance CH3 NH3 PbI3 perovskite solar cells fabricated under ambient conditions with high relative humidity. Jpn. J. Appl. Phys. 54(10), 100305 (2015) 27. Lei, B., Eze, V.O., Mori, T.: Effect of morphology control of light absorbing layer on CH3 NH3 PbI3 perovskite solar cells. J. Nanosci. Nanotechnol. 16(4), 3176–3182 (2016) 28. Wang, K., Lin, Z., Ma, J., Liu, Z., Zhou, L., Du, J., et al.: High-performance simple-structured planar heterojunction perovskite solar cells achieved by precursor optimization. ACS Omega 2(9), 6250–6258 (2017) 29. Chen, L., Wan, L., Li, X., Zhang, W., Fu, S., Wang, Y., et al.: Inverted all-inorganic CsPbI2 Br perovskite solar cells with promoted efficiency and stability by nickel incorporation. Chem. Mater. 31(21), 9032–9039 (2019) 30. Gholipour, S., Correa-Baena, J.P., Domanski, K., Matsui, T., Steier, L., Giordano, F., et al.: Highly efficient and stable perovskite solar cells based on a low-cost carbon cloth. Adv. Energy Mater. 6(20), 1601116 (2016) 31. Zhu, W., Zhang, Z., Chai, W., Zhang, Q., Chen, D., Lin, Z., et al.: Band alignment engineering towards high efficiency carbon-based inorganic planar CsPbIBr2 perovskite solar cells. Chemsuschem 12(10), 2318–2325 (2019) 32. Yan, J., Uddin, M.J., Olawale, D.O., Dickens, T.J., Okoli, O.O.: 3D sensing using solid-state wire-shaped photovoltaic sensor in TL-based structural health monitoring. In: Triboluminescence, pp. 351–377. Springer (2016)

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Fatigue Reliability Assessment of Pipeline Weldments Subject to Minimal Detectable Flaws Xiaochang Duan, Xinyan Wang, and Xuefei Guan(B) Graduate School of China Academy of Engineering Physics, Beijing 100193, China [email protected]

Abstract. The study presents a probabilistic modeling of the fatigue crack growth prediction of the pipeline steel weldments in nuclear power plants in the context of an integrated structural health monitoring setting. Fatigue testing of the crack growth in the fusion line region of the steel weldments is made using compacttension specimens. In particular, the uncertainty of the crack growth due to different crack plane orientations is investigated in details. A total of six orientations of the specimens are manufactured and tested according to the ASTM standards to obtain the fatigue crack growth data. The Bayesian method is used to identify the probability density function of the parameters of the Paris’ fatigue crack growth model. Using the concept of damage tolerance, the reliability model of the pipeline weldments given the minimal detectable internal flaws of the ultrasonic nondestructive evaluations can be established. The time-dependent reliability of the pipeline weldments is obtained using the efficient first-order reliability method. Results indicate the uncertainty of the orientations of the flaws plays an important role in the overall reliability of the pipeline weldments. Keywords: Reliability assessment · Pipeline weldments · First-order reliability method · Fatigue life prediction

1 Introduction The welding fusion zone is a critical location susceptible to fatigue damage due to the inevitable welding defects, such as inclusions, cracks, and pores [1–3]. For high reliability-demanding applications, such as pipelines of power plants and underground gas lines, the weldment must be carefully inspected and evaluated for safe and continuous service [4]. Existing means of damage detection including Lamb-wave based methods, phased-array ultrasound, and X-ray inspection. In particular, Lamb-wave based flaw quantification in conjunction with life and reliability assessment provides new opportunities in life management and extensions [5, 6]. It is therefore highly necessary to characterize the crack propagation behavior of the weld seam under cyclic loading. In particular, a fatigue crack growth model and its corresponding reliability prediction method can be greatly beneficial to establish the structural health monitoring systems [7–10] and service maintenance planning [11, 12]. The welded zone is highly homogenous due to the fused materials and residual stress caused by the welding process [13]. Tang [14] studied the fatigue crack growth behavior © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 632–641, 2021. https://doi.org/10.1007/978-3-030-64908-1_59

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of the base metal, weld metal, and heat affected zone materials in stainless steel welded area. The results show that the fatigue crack growth rate of the weld sample is the largest, followed by the heat affected zone sample and the base metal samples. Tagawa [15] reported experimental investigation of the fatigue properties of cast aluminum welded joints prepared by friction stir welding and gas shielded arc welding, and compared the properties with that of the substrate material. The authors found that when the crack tip reaches the weld metal, the fatigue crack growth rate of the specimen accelerates. Basak [16] investigated the fatigue performance of DP600 steel joints based on the load control fatigue test, and found that the crack growth rate of the welded metal is greater than the base for the near-threshold region of the stress intensity factor. Gaur [17] compared the low cycle fatigue lives of different welding filler materials considering the mean stress and load ratio effects. Due to the nonuniform material properties of the welded zone, the resulting fatigue life shows a larger dispersion around the mean life. It is therefore necessary to quantify the uncertainties for fatigue life prediction and reliability assessment of the weldment [18–23]. Despite many studies have been reported on the probabilistic models of the welded zone, the uncertainty of the fatigue crack growth due to the different orientation of the cracks in the weldment is rarely seen. This study is focused on the reliability assessment of the pipeline weldment subject to fatigue crack growth. In particular, the overall uncertainty incorporating the orientation of the crack in the welded zone is quantified for reliability assessment considering the minimal detectable flaws using ultrasonic non-destructive evaluations. The remainder of the study is organized as follows. First the experimental testing considering the effect of crack orientation is presented. A total of six specimens oriented differently in the carbon steel weldment are prepared, and fatigue testing is performed to obtain the fatigue crack growth data. Next, the probability distributions of the fatigue crack growth parameters are obtained using Paris’ model. Following that, the reliability assessment of the weldment is performed using the first-order reliability method considering the minimal detectable size, and conclusions are drawn.

2 Experiment 2.1 Materials and Specimen Preparation A welded block with the base metal of Q235 carbon steel is made using actual welding parameters according to the RCC-M standard [24]. The welding wires are ER70S-3 alloy with 1.6 mm diameter, and its chemical composition is shown in Table 1. Tungsten Inert Gas Welding (TIG) is used for the preparation of welding materials. The resulting weldment after mechanical grinding and cutting is shown in Fig. 1. The compact tensile specimens (CT) are prepared according to the ASTM E647 standard. The thickness of the sample is 4.5 mm and the length of the notch is 5 mm. A total of six specimens with different orientations are manufactured from the weldment, as shown in Fig. 2. 2.2 Fatigue Crack Growth Testing and Data The fatigue crack growth tests are carried out on the MTS Land Mark 379.10 fatigue testing machine, following the ASTM E647-15 standard, as shown in Fig. 3. The fatigue

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Table 1. The chemical composition of base material and welding material (mass fraction, %) Materials C

P

S

ER70S-3 0.025 0.42 1.91 19.10 12.58 2.57 /

/

Q235

Si

Mn

0.024 0.4

Cr

1.46 18.47

Ni

Mo

8.04 /

0.03 1.46

Welding seam Base material

Base material

Fig. 1. The welding material after grading and cutting

6 5 4 3 2 1

Fig. 2. The sample sampling method of compact tensile specimens

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load is a 10 Hz sinusoidal load with a stress ratio of 0.05 and a maximum value of 4 KN. The crack opening displacement meter (COD gauge) is used to obtain crack length by compliance method. To eliminate the influence of the notch on the crack propagation, a pre-crack with a length of 1 mm is generated using the K-drop method.

Fig. 3. The fatigue crack growth testing machine

Figure 4 presents the crack length a vs. the number of cyclic loads N. It is observed from Fig. 4 that the specimens no. 1, 2, and 3 have slower fatigue crack growth rate compared with that of specimens no. 4, 5, and 6. By correlating the rates with the crack orientation in Fig. 2, it can be found that the cracks of specimens nos. 1–3 grow perpendicular to the welding seam, and the cracks of specimens nos. 4–6 grow parallel with the welding seam. The difference is attributed to the inhomogeneity of the welded zone.

Fig. 4. Fatigue crack growth results under constant amplitude load

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3 Fatigue Crack Growth Model The conventional Paris’ equation is adopted here to describe the crack growth rate [25], as shown in Eq. (1) da = C(K)m , (1) dN where C and m are fitting parameters. The stress intensity factor range K for CT specimen is given by   2+β  2 3 4 √ K = P 3/2 0.886 + 4.64β − 13.32β + 14.72β − 5.6β (1−β) B W , (2) β = a/W , β ≥ 0.2 where β is the ratio of the crack length to the thickness of the test piece, P is the amplitude of the cycle force, and B is the width of the specimen. The equivalent logarithmic linear model can be written as   da = lg C + m lg(K). (3) lg dN Equation (3) is used to fit the parameters of the fatigue testing data of the six specimens, and the results are shown in Table 2. A linear dependence between the two parameters can be found as shown in Fig. 5. Table 2. Summary table of parameter fitting results Specimen number Mean of (lgC, m) 1

[−13.7032, 3.2384]

2

[−15.9213, 3.9636]

3

[−13.4344, 3.1615]

4

[−12.4906, 2.9073]

5

[−12.2721, 2.8208]

6

[−13.4855, 3.1767]

Using the regression results in Table 2, the parameter of (lgC, m) can be described using a bivariate normal distribution:    T

1 1 lg C + 13.5515 lg C + 13.5512 −1 p(lg C, m) = exp − · · , √ m − 3.2114 m − 3.2114 2 2π || (4) where the covariance matrix  is =



1.6839 −0.5234 . −0.5234 0.163

(5)

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Fig. 5. Linear regression results of 6 groups (lgC, m)

4 Reliability Assessment Subject to Minimal Detectable Size The critical crack length ac is set as 10 mm for illustration purposes. In realistic applications, a proper fracture toughness K c can be used to calculate the ac when available. The limit state function can be formulated using the failure criterion. The reliability assessment is made using the first-order reliability method (FORM) [26, 27]. The FORM provides a fast asymptotic approximation of the limit state function at the most probable point, and the minimal distance between the most probable point to the origin of the standard normal space is the so-called reliability index [28]. Figure 6 illustrates the basic numerical steps of the FORM calculation, where g is the limit state function, x i is the ith random variable, μ is the mean of the variable, σ is the standard deviation of the variable, and β HL is the reliability index. The probability of failure can be obtained by Eq. (6) where (•) is the cumulative density function of the standard normal variable. pf = (−βHL ).

(6)

The minimal detectable flaw size required in MIL-HDBK-1783B [29] is used in this study to represent the reliability of the ultrasonic non-destructive evaluation. For manual or semi-auto inspections, the 90/95 flaw size is the 0.9 mm in diameter. Using the transformation method in Ref. [30, 31] it can be converted to a 0.6 mm elliptical crack with a shape ratio of 0.4. For demonstration purposes, the boundary and geometry factors of the stress intensity factor due to the pipe diameter, thickness, and eccentric position of the crack with respect to the thickness dimension are not considered. The stress intensity factor of the embedded elliptical crack is ⎧ 1 √  ⎪ ⎨ KI = σ π a sin2 ϕ+ a22 cos2 ϕ 4  c , (7) 1 π   2 −a 2 ⎪ c 2 ϕ 2 dϕ ⎩ = 2 1 − sin 0 c2 where a and c are the minor and major radii of the ellipse, respectively, and the angle ϕ is defined as shown in Fig. 7. To obtain a conservative result, a/c = 0.4 and ϕ = π /2 are

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Fig. 6. Flow chart of FORM

used in Eq. (7). The reliability assessment is performed using the FORM with an initial crack size a0 = 0.6 mm and a critical crack size of 10 mm given the constant amplitude load of 300 MPa. The reliability assessment result in terms of probabilities of failure (PoF) is shown in Fig. 8. If the inspection and maintenance of the structure requires a failure probability of 10−5 , the corresponding fatigue life is about 3.15 × 104 cycles.

Fig. 7. Schematic diagram of embedded elliptical cracks

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Fig. 8. Probability of failure estimated using FORM

5 Conclusion The reliability assessment of the Q235 carbon steel pipeline weldment subject to fatigue crack growth was reported in this study. In particular, this study focused on incorporation the uncertainty from crack orientation in the welded zone. A total of six compact tension specimens with different orientations are prepared using a carbon steel weldment fabricated with a realistic welding configuration. The fatigue crack growth testing data were obtained using constant load fatigue testing, and the Paris’ model parameters are statistically identified. Reliability assessment using the Paris’ model with the resulting parameters was performed. It is observed that the orientation of the crack in the welded zone can greatly influence the crack growth rate. The fatigue life of the crack perpendicular to welding seam is about twice of that parallel to the welding seam. The uncertainty from the orientation cannot be overlooked in fatigue reliability assessment. Acknowledgement. The work in this study was supported by National Natural Science Foundation of China, Nos. 51975546, U1930403. The support is greatly acknowledged.

References 1. Qiao, Q., Cheng, G., Li, Y., et al.: Corrosion failure analyses of an elbow and an elbow-to-pipe weld in a natural gas gathering pipeline. Eng. Fail. Anal. 82, 599–616 (2017) 2. Shalaby, H.M.: Failure investigation of 321 stainless steel pipe to flange weld joint. Eng. Fail. Anal. 80, 290–298 (2017) 3. Jaske, C.E.: Fatigue-strength-reduction factors for welds in pressure vessels and piping. J. Press. Vessel Technol. 122(3), 297–304 (2000) 4. Jia, X., An, J., Jing, J.: Transient characteristics of main feedwater line rupture accident for AP1000 nuclear power plant. Atomic Energy Sci. Technol. 50(8), 1422–1427 (2016) 5. Frangopol, D., Kim, S.: Prognosis and life-cycle assessment based on SHM information. In: Sensor Technologies for Civil Infrastructures, pp. 145–171. Elsevier (2014)

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6. He, J., Guan, X., Peng, T., et al.: A multi-feature integration method for fatigue crack detection and crack length estimation in riveted lap joints using Lamb waves. Smart Mater. Struct. 22(10), 105007 (2013) 7. Kulkarni, S., Achenbach, J.D.: Structural health monitoring and damage prognosis in fatigue. Struct. Health Monit. 7(1), 37–49 (2008) 8. Friswell, M.I., Penny, J.E.: Crack modeling for structural health monitoring. Struct. health Monit. 1(2), 139–148 (2002) 9. Vanniamparambil, P.A., Bartoli, I., Hazeli, K., et al.: An integrated structural health monitoring approach for crack growth monitoring. J. Intell. Mater. Syst. Struct. 23(14), 1563–1573 (2012) 10. Ling, Y., Mahadevan, S.: Integration of structural health monitoring and fatigue damage prognosis. Mech. Syst. Sig. Process. 28, 89–104 (2012) 11. Bang, D.J., Ince, A., Noban, M.: Modeling approach for a unified crack growth model in short and long fatigue crack regimes. Int. J. Fatigue 128, 105182 (2019) 12. Wang, X.G., Ran, H.R., Jiang, C., et al.: An energy dissipation-based fatigue crack growth model. Int. J. Fatigue 114, 167–176 (2018) 13. Xie, X., Jiang, W., Luo, Y., et al.: A model to predict the relaxation of weld residual stress by cyclic load: experimental and finite element modeling. Int. J. Fatigue 95, 293–301 (2017) 14. Tang, L., Qian, C., Ince, A., et al.: Fatigue crack growth behavior of the MIG welded joint of 06Cr19Ni10 stainless steel. Materials 11(8), 1336 (2018) 15. Tagawa, T., Tahara, K., Abe, E., et al.: Fatigue properties of cast aluminium joints by FSW and MIG welding. Weld. Int. 28(1), 21–29 (2014) 16. Basak, S., Pal, T.K., Shome, M.: High-cycle fatigue behavior of MIG brazed galvanized DP600 steel sheet joint—Effect of process parameters. Int. J. Adv. Manuf. Technol. 82(5–8), 1197–1211 (2015) 17. Gaur, V., Enoki, M., Okada, T., et al.: A study on fatigue behavior of MIG-welded Al-Mg alloy with different filler-wire materials under mean stress. Int. J. Fatigue 107, 119–129 (2018) 18. D’Angelo, L., Nussbaumer, A.: Estimation of fatigue S-N curves of welded joints using advanced probabilistic approach. Int. J. Fatigue 97, 98–113 (2017) 19. Guan, X., Jha, R., Liu, Y.: Model selection, updating, and averaging for probabilistic fatigue damage prognosis. Struct. Saf. 33(3), 242–249 (2011) 20. Yang, J., He, J., Guan, X., et al.: A probabilistic crack size quantification method using in-situ Lamb wave test and Bayesian updating. Mech. Syst. Sig. Process. 78, 118–133 (2016) 21. He, J., Huo, H., Guan, X., et al.: A Lamb wave quantification model for inclined cracks with experimental validation. Chin. J. Aeronaut. (2020). https://doi.org/10.1016/j.cja.2020.02.010 22. Du, Y.-M., Ma, Y.-H., Wei, Y.-F., et al.: Maximum entropy approach to reliability. Phys. Rev. E 101(1), 012106 (2020) 23. He, J., Chen, J., Guan, X.: Lifetime distribution selection for complete and censored multilevel testing data and its influence on probability of failure estimates. Struct. Multidiscip. Optimiz. 62(1), 1–17 (2020) 24. Triay, M., Meister, E., Lefever, B., et al.: RCC-M code: recent evolutions and perspectives. In: Pressure Vessels and Piping Conference. American Society of Mechanical Engineers (2019) 25. Paris, P., Erdogan, F.: A critical analysis of crack propagation laws (1963) 26. Maier, H.R., Lence, B.J., Tolson, B.A., et al.: First-order reliability method for estimating reliability, vulnerability, and resilience. Water Resour. Res. 37(3), 779–790 (2001) 27. Xiang, Y., Liu, Y.: Application of inverse first-order reliability method for probabilistic fatigue life prediction. Probab. Eng. Mech. 26(2), 148–156 (2011) 28. Mazzoleni, M., Barontini, S., Ranzi, R., et al.: Innovative probabilistic methodology for evaluating the reliability of discrete levee reaches owing to piping. J. Hydrol. Eng. 20(5), 04014067 (2015) 29. U.S. Air Force, MIL-HDBK-1783B CHANGE 2: Engine Structural Integrity Program (ENSIP). Air Force Sustainment Center, Oklahoma City (2004)

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30. Guan, X., Zhang, J., Zhou, S., et al.: Probabilistic modeling and sizing of embedded flaws in ultrasonic non-destructive inspections for fatigue damage prognostics and structural integrity assessment. NDT & E Int. 61, 1–9 (2014) 31. Guan, X., He, J., Rasselkorde, E.M., et al.: Probabilistic fatigue life prediction and structural reliability evaluation of turbine rotors integrating an automated ultrasonic inspection system. J. Nondestr. Eval. 33(1), 51–61 (2014)

Structural Health Monitoring of High-speed Rail and Maglev Systems

Image Detection of Foreign Body Intrusion in Railway Perimeter Based on Dual Recognition Method Yumeng Sun, Zhengyu Xie(B) , Yong Qin, Li Chuan, and Zhiyu Wu Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing, People’s Republic of China [email protected]

Abstract. In order to ensure the safety of railway operation, it is urgent to strengthen the detection and protection of railway perimeter safety. This paper proposes a method for detecting foreign body intrusion in railway perimeter based on double recognition. The Gaussian Mixture Model (GMM) is used to process the video image of the railway scene, and the foreign objects are pre-screened, and the foreign object existence frames are extracted, and then the YOLOv3 algorithm is used to perform secondary detection and recognition on the foreign object existence frames. This method can improve the accuracy of target recognition, reduce the false alarm rate and false alarm rate of foreign object invasion in railway scenes, and occupy less on-site computing resources, which is suitable for on-site requirements. The results show that, compared with the GMM, the false negative rate of the algorithm in this paper is lower, and the algorithm is more suitable for railway site requirements than the deep learning algorithm. Keywords: Railway perimeter · GMM · YOLOv3 · Object detection

1 Research Background By the end of 2019, China’s railway operating mileage had reached 139,000 km, of which 35,000 km were high-speed railways, ranking first in the world. How to ensure its safe operation has become an important problem we need to solve urgently. The intelligent detection technology of railway perimeter safety is helpful to prevent and reduce the occurrence of railway intrusion and destruction and to ensure the safe operation of China’s rail transit. Railway video monitoring is an important detection method to study foreign body invasion in railway perimeter. At present, most of the detection methods commonly used by researchers are in addition to moving target detection methods. With the development of artificial intelligence, deep learning algorithms are also widely applied in railway scenes. Common detection methods for moving objects include frame difference method, background subtraction method and optical flow method, R-CNN and YOLO algorithms for deep learning. Among them, gaussian mixture algorithm is widely applied in the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 645–654, 2021. https://doi.org/10.1007/978-3-030-64908-1_60

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field due to its good detection effect, easy implementation and high accuracy. Shen et al. proposed a moving human body tracking method based on optimized Gaussian Mixture Model, but the calculation process of this method is tedious and the real-time performance is poor. Huang Jinhai proposed the research on moving target detection algorithm for traffic video, which is susceptible to the influence of light and needs to constantly adjust the threshold. In 2014, Girshick et al. proposed R-CNN detection algorithm, which uses Selective Search algorithm to Search potential targets in candidate regions. This algorithm has high detection accuracy, but it takes too long to run and its performance is difficult to optimize. Girshick proposed Fast R-CNN on the basis of R-CNN, and Shared computing improved its speed, but still failed to achieve the purpose of real-time detection. Redmon et al. proposed that the YOLO algorithm regards target detection as a regression problem, realizing the output of results more quickly and accurately.

2 Model Introduction Railway monitoring front in a more open environment, affected by the illumination, such as fog, rain and snow weather is larger, and the scene more interference factors such as catenary, utility poles and gravel, so according to the scene image characteristics and the current application of railway more algorithm characteristics, this paper proposes a compound algorithm, the hybrid algorithm in dual recognition way, railway perimeter foreign intrusion detection, overall architecture as shown in Fig. 1.

Fig. 1. Railway perimeter intrusion detection overall architecture.

2.1 Primary Foreign Extraction Considering only the calculation accuracy, deep learning method is better than other methods. But obviously, it requires a lot of computing resources. For railway application scenarios, it is difficult to calculate and analyze hundreds of thousands of videos simultaneously with deep learning algorithm. Therefore, considering the limitation of field computing resources, this paper adopts gaussian mixture model to propose the initial extracting of target foreign bodies, and the flow chart is shown in Fig. 2.

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Input video Median filtering processing Gaussian mixture modeling Object detection Update Parameters Output foreign body frame Fig. 2. The flow chart of primary foreign extraction.

Gaussian mixture background modeling core idea is to use a different K gaussian function to describe the video value of each pixel in the image sequence, and then to K gaussian function according to the priority sorting, B before using a gaussian function represents the actual background model, then by matching the number of gaussian function compared with B to determine the pixel is a background or foreground. Build a Model. Assuming that each pixel is described by K gaussian functions, and the weight of the Kth gaussian model is ϕ(k), then at time t, the gaussian model of background pixel X(t) can be described as: P(Xt ) = Of which, N (Xt , μk , k ) =

K k=1

ϕk ∗ τ (Xt , μk , k )

1 D 2

(2π) |k |

1

1 2

e− 2 (x−μk )

T

−1 k

(x−μk )

, k = σk2 I .

(1)

After the background pixels are described using the above model, each pixel in the background is described by a gaussian sequence, where each gaussian has a weight ϕ(k). The value of K is generally between 3 and 5. The larger the value of K, the stronger the algorithm’s ability to deal with fluctuations, the better the anti-noise performance, and the more stable the background modeling effect will be. However, as the value of K increases, the algorithm complexity will also increase, and the speed of background modeling will also slow down.

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Object Detection. The gaussian sequence should be arranged in descending order according to the weight ratio ϕ(k)/σ. In this way, the gaussian function whose sum of the first B weights is greater than the threshold value T is used to describe the actual background model. B. Mathematical description: ⎞ ⎛ b  ϕj > T ⎠ (2) B = arg min⎝ b

j=1

For the pixel value X(N) at a new time N, the sequence of gaussian models representing the background model is traversed in order. When the first gaussian model satisfying the formula (3) is the Kth, and k is less than B, the point is considered to be the foreground, otherwise the background. |XN − μk | ≤ 2.5σk

(3)

Update Parameters. For the matching gaussian model, that is, the first gaussian model satisfying formula 3, the following parameter updates are made. ⎧  ⎨ σk = (1 − α)ϕk + αρ  μ = (1 − ρ)μk + ρXt ⎩ 2k σk = (1 − ρ)σk2 + ρ(Xt − μk )T (Xt − μk )   Of which, α is the learning rate, ρ = ατ Xt , μk , k . The following figure shows the gaussian modeling binary images at three different moments (Fig. 3).

Fig. 3. The gaussian modeling binary images at three different moments.

2.2 Secondary Recognition The frame obtained from the initial screening of foreign body was sent to the deep learning algorithm for secondary detection and the type of foreign body was identified. The high precision advantage of deep learning algorithm can be used to improve the accuracy of recognition. The flow chart is shown in Fig. 4.

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Input foreign body frame YOLOv3 Output detection image

Fig. 4. The flow chart of the secondary recognition.

The YOLO algorithm has been updated to YOLOv3. YOLOv3 algorithm is improved on the basis of YOLOv2, and Darknet53 network structure is proposed based on the idea of resnet101, which significantly improves the detection accuracy. The most prominent feature of the YOLO algorithm is that it can predict the border and category information of the image directly through a phase, which greatly improves the detection speed and can reach the rate of 45 frames on Titan X GPU. The following figure is the framework diagram of YOLOv3 model detection and the framework is from YOLOv3 (Fig. 5).

Fig. 5. The framework of YOLOv3 detection.

Detection Process. YOLO algorithm by moving the image is divided into a grid S * S cell, each grid cell is responsible for the predicted B a bounding boxes and bounding boxes of confidence, and C categories, and define a Bounding box to predict (x, y, w, h) four information, is the center of the Bounding box respectively horizontal ordinate and width, network with all categories of output connection layer, finally so full connection layer dimensions for the S * S * (5 × B + C), For the Pascal VOC data set, S is 7 and B is 2, since it contains 20 kinds of detectors and C is 20. The flow chart of YOLO detection is shown in Fig. 6.

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Fig. 6. The detection flow chart of YOLO.

2.3 Double Recognition Algorithm Detection First, a railway perimeter video stream was input, and the video frame was extracted and saved. The noise points in the non-target range were filtered out through the median filter for the image of frame N, and holes were filled and the contour of the invading target was highlighted through expansion processing. Then the number of objects detected in frame N is included in the list L to determine whether the detected frame is a multiple of 15. If the remainder of N divided by 15 is 0, then the main element in the list L is determined, that is, whether the number of objects present in each frame is 0. If the main element in the list L is not 0, the corresponding frame i of Max {n} is output. Finally, YOLOv3 model is started to detect frame i twice and output the final detection result graph. The flow chart of the dual recognition algorithm is shown in Fig. 7.

3 The Experimental Contrast The mixed gaussian algorithm was used to process the railway scene video images, the foreign bodies were initially screened, and the frames of foreign bodies were extracted. Then the YOLOv3 algorithm was used to detect and identify the frames of foreign bodies. This method can improve the accuracy of target identification and reduce the missing rate and false alarm rate of foreign body invasion in railway scene. The results show that the missing report rate is lower than that of gaussian mixture algorithm, and the algorithm is more suitable for railway field demand than deep learning algorithm. Figure 8 is the original image of the railway scene in sunny days, Fig. 9 is the GMM algorithm detection image of the railway scene in sunny days, and Fig. 10 is the dualrecognition algorithm detection image of the railway scene in sunny days. Figure 11 is the original snow railway scene, Fig. 12 is the GMM algorithm detection diagram of snow railway scene, and Fig. 13 is the dual-recognition algorithm detection diagram of snow railway scene. As can be seen from the figure, the algorithm presented in this paper has a good detection effect on both sunny and snowy days.

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Input video Extract frame N Save frame N N=N+1 Initial screening of foreign body based on GMM The number of foreign bodies n is included in the list L the remainder of N divided by 15 is 0

The main element in L is 0

Output the frame corresponding to Max {n} Secondary detection based on YOLOv3 Output the final detection picture Fig. 7. Detection flow chart of the paper.

Fig. 8. Original picture of sunny railway scene.

Table 1 shows the comparison diagram of accuracy between the algorithm in this paper and the GMM algorithm. According to the detection results of the first 37 frames, the algorithm in this paper is stable with the accuracy more than 60%. The GMM algorithm has high volatility and low detection accuracy. Table 2 is a summary table of the advantages and disadvantages of the proposed algorithm, GMM algorithm and YOLOv3 algorithm.

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Fig. 9. GMM detection of railway scene in sunny days.

Fig. 10. Dual recognition algorithm detection for railway scene in sunny days.

Fig. 11. Original picture of snow railway scene.

Fig. 12. GMM detection of railway scene in snow days.

Fig. 13. Dual recognition algorithm detection for railway scene in snow days.

Based on the dual recognition algorithm, the mixed gaussian algorithm is used to process the railway scene video image, the foreign bodies are initially screened, and the frames of foreign bodies are extracted. Then the YOLOv3 algorithm is used to detect and identify the frames of foreign bodies. This method can improve the accuracy of target identification and reduce the missing rate and false alarm rate of foreign body

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Table 1. The accuracy of this algorithm is compared with that of GMM algorithm.

Chart Title 120.00% 100.00% 80.00% 60.00% 40.00% 20.00% 0.00% 1

3

5

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9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 Series1

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invasion in railway scene. The results show that the missing report rate is lower than that of gaussian mixture algorithm, and the algorithm is more suitable for railway field demand than deep learning algorithm. Table 2. Summary of advantages and disadvantages Object detection algorithm

Advantages

Disadvantages

GMM

Be sensitive to moving targets

1. Fast detection speed, 1. High false alarm and high real-time false alarm 2. Low processor 2. Influenced by light, performance climate and other requirements conditions greatly

YOLOv3

Fast detection speed, high real-time

1. Recognize the 1. High processor object’s category performance position information requirements 2. Low false alarm and false alarm

The paper

Effective filtering of redundant information

1. Improve the efficiency of effective information processing 2. Save computer resources for a long time

1. Real-time is not as good as GMM algorithm

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4 Conclusion Through experiments, it is found that gaussian mixture method has higher processing speed and lower requirement for processor performance. As for YOLO target detection algorithm, it has a good detection effect, low false alarm and missing alarm, and can accurately identify the category and location information of objects. However, it has a high requirement for processor performance, and cannot process multiple images at the same time. The dual recognition algorithm proposed in this paper firstly uses gaussian mixture algorithm to process video images of railway scenes, and then YOLOv3 algorithm is used to detect and identify foreign bodies. This method can improve the accuracy of target identification and reduce the missing rate and false alarm rate of foreign body invasion in railway scene.

References 1. Jain, R.: On the analysis of accumulative difference pictures from image sequences of real world scenes. IEEE Trans. Pattern Anal. Mach. Intell. 1(2), 206–214 (1979) 2. Gloyer, B.: Video-based freeway-monitoring system using recursive vehicle tracking. In: Proceedings of SPIE - The International Society for Optical Engineering, vol. 2421, pp. 173–180 (1995) 3. Kim, K.: Real-time foreground-background segmentation using codebook mode. Real-Time Imaging 11(3), 172–185 (2005) 4. Shen, S.: A moving human body tracking method based onoptimized Gaussian Mixture Model. J. Nanjing Nor Univ. (Eng. Technol. Ed.) 19(01), 51–57 (2019) 5. Huang, J.: Research on moving target detection algorithm for traffic video. Mod. Electron. Tech. (01), 62–65(2019) 6. Girshick, R.B.: Rich feature hierarchies for accurate object detection and semantic segmentation. In: Computer Vision and Pattern Recognition, pp. 580–587. IEEE (2014) 7. Girshick, R.: Fast R-CNN. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 1440–1448. IEEE (2015) 8. Redmon, J.: You only look once: unified, real-time object detection. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 779–788. IEEE (2016) 9. Redmon, J.: YOLOv3: an incremental improvement [EB/OL], 25 April 2019. https://arxiv.org/ PDF/1804.02767.pdf

Defect Imaging Algorithms Based on Guided Waves for BVIDs Detection: a Round Robin test on a Large-Scale Aeronautical Composite Structures

The Delay Multiply and Sum Algorithm for Lamb Waves Based Structural Health Monitoring Michelangelo Maria Malatesta1(B) , Denis Bogomolov1 , Marco Messina1 , Dennis D’Ippolito1 , Nicola Testoni1 , Luca De Marchi3 , and Alessandro Marzani2 1

2 3

ARCES, University of Bologna, Viale Carlo Pepoli 3/2, 40123 Bologna, Italy [email protected] DICAM, University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy DEI, University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy

Abstract. Ultrasonic guide waves (GWs) have increasingly been adopted in Structural Health Monitoring (SHM) of plate-like structures because of their versatility. To operate, SHM based on GWs generally adopt arrays of piezoelectric transducers and imaging techniques for damage detection, localization and quantification. Among the different ultrasonic imaging techniques, Delay-and-Sum (DAS) beamforming applied to Lamb waves is one of the most exploited methods due to the low noise sensitivity and the advantageous trade-off between the image resolution and the number of required sensors. However, DAS shows a limited imaging resolution and contrast which is emphasized as the number of sensors decrease. To tackle these limitations, the scientific literature offers an alternative nonlinear beamforming algorithm called Delay-Multiply-and-Sum (DMAS), which has been successfully applied in RADAR systems and medical ultrasound beamforming. In this work, the DMAS algorithm is applied on guided waves signals to map damages in a composite plate. To the best of author’s knowledge, the DMAS has never been adopted before in the SHM context. In particular, the freely available Guided Waves dataset Open Guided Waves (http://openguidedwaves.de/) that collects piezoelectric actuated and received guided waves signals travelling through a quasi-isotropic composite plate in different damage conditions has been exploited. The DMAS performance has been investigated and compared with the conventional DAS, showing improved imaging resolution and defect localization capabilities. Keywords: DMAS waves · Air-craft

1

· DAS · SHM · Lamb waves · SHM · Ultrasonic

Introduction

Nowadays, Guided Waves (GWs) are rising as one of the most encouraging Non Destructive Evaluation (NDE) method for Structural Health Monitoring (SHM), c The Author(s), under exclusive license to Springer Nature Switzerland AG 2021  P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 657–666, 2021. https://doi.org/10.1007/978-3-030-64908-1_61

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especially in the aerospace and automotive industry [4]. In particular, guided Lamb waves in thin plate–like structures have been intensively studied since the 1980’s, demonstrating to be suitable for the quantitative identification and characterization of damages, delaminations and cracks in both isotropic and non– isotropic materials [19]. Generally, active–passive [20] networks of piezoelectric transducers are exploited for these purposes, even though literature presents also GWs passive-only networks for impact detection and localization [5,7]. Among the different active-passive approaches, recent studies focused on the development of GW systems based on imaging reconstruction, such as Delay and Sum (DAS) beamforming [18] or tomographic techniques [21]. Unfortunately, conventional tomographic approach resolution is strictly related to the number of transducers, which can become prohibitive if high precision damage localization is required. On the other hand, DAS beamforming achieves higher resolution and less sensitivity to noise, being suitable for the localization of damages, such as bonded masses, notches, and stiffeners [6,15]. Like all beamforming algorithms, DAS implementation is based on a source-receiver dependence. Usually, in the actuation phase, one element of the transducers array is excited for every transmission event. Then, in the receiving phase, all the elements of the array are exploited to acquire the signal and a low–resolution image is generated for every transmission event. In particular, by taking into account the mutual position of the pairs actuator-receivers and the wave velocity in the material, it is possible to compute a unique time delay between each pair of sensors and a scatterer point in order to compensate the differences of arrival times. Once the signals are aligned by this delay procedure, the image is computed by spatial interpolation. Finally, all the images are summed together in order to achieve higher quality in terms of spatial resolution, contrast and penetration depth [2]. However, DAS beamforming shows a reduced off-axis interference rejection and a limited imaging resolution, especially when a small number of sensors is required. To tackle these limitations, literature offers an alternative nonlinear beamforming algorithm called Delay-Multiply-and-Sum (DMAS), which has been successfully applied in RADAR systems and medical ultrasound [10]. The DMAS beamforming can be considered as an improved version of the classic DAS algorithm, in which a nonlinear multiply operation is performed among combinatorially coupled signals before summation. In such a way, it is possible to achieve better performance in terms of contrast resolution, object definition and dynamic range [10]. Nevertheless, to the best of author’s knowledge, DMAS algorithm has never been applied to SHM application contexts. In this paper, an implementation of the DMAS beamforming in a SHM use case is presented. In particular, to test and validate the proposed algorithm in terms of reliability and robustness, a freely available online GWs dataset [14] has been used. The online benchmark measurements consist in a series of pitch-catch acquisitions in a carbon fiber plate sensorized by piezoelectric transducers. The large amount of baseline data, different damage positions and the controlled environment provided by the climate chamber in which the carbon plate was inserted during the experimental campaign, allow the proposed methodology to

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be validated in well known operational conditions. Then, the DMAS approach has been directly compared with the common DAS algorithm, demonstrating that the DMAS provides higher contrast and resolution for SHM application as well. The paper is divided into four sections. First, the theoretical background about the DAS and DMAS beamforming algorithms is provided in Sect. 2. The DMAS validation and characterization with respect to the DAS approach is carried on in Sect. 3. Finally, Sect. 4 summarizes the main findings of the paper and provides recommendation for future investigations.

2

Beamforming Algorithms

The term Beamforming refers to the process of adjusting the phasing of signals in an array of transducers in order to provide the desired directionality properties [16]. In particular, by changing the phasing between the piezoelectric transducers, the received waves can be focused in a specific direction of interest. Depending on the application context, which imposes constraints on the number of transducers, their configuration and positioning, different beamforming approaches can be adopted. For instance, the Total Focusing Method (TFM) emulates a wave converging at the image point by means of the combination of signals from multiple transmitters-receivers, known as the Full Matrix Capture (FMC). The Synthetic Aperture Focusing Technique (SAFT) exploits the same principle but in this case, only one element of the piezoelectric array is used both for transmitting and receiving the signal for every transmission event. The Plane Wave Imaging (PWI) algorithm and the Virtual Source Aperture instead, use plane waves and spherical waves respectively [1]. By means of some adjustments, DAS and DMAS beamforming can be applied to each of the previous cases [3,9,17]. 2.1

Delay and Sum

Consider a piezoelectric array of N + 1 elements, with one actuator and N receivers. Thus, there are Np = N (N − 1) possible transmit-receiver combinations. Following the Michaels et al. [13] formulation, if we consider the i –th transducer pair with the actuator located at (xa , y a ) and the receiver located at (xr , y r ), the propagation time of the GW traveling from the actuator to a generic scatterer point located at (x, y), and then from there to the receiver is defined as:  a  (xi − x)2 + (yia − y)2 + (xri − x)2 + (yir − y)2 xy ti = (1) cg where cg is the group velocity. Each signal si (t) referred to the i –th pair actuatorreceiver, is shifted by txy i and then summed, obtaining the focusing of the beam in the (x, y) location:

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sDAS (t, x, y) =

Np  i=1

si (t − txy i )

(2)

By simply interpolating the sDAS signal in the (x, y) domain, the Damage Index DIDAS for the specific (x, y) point is calculated. Finally, the DIDAS (x, y) is extracted by repeating such a procedure for each possible scatterer point of the plate. Depending on the specific application, other signal processing steps might be necessary. In particular, the DAS algorithm is strongly dependant on the group velocity estimation of the GWs. In isotropic materials, a calibration might be sufficient, while in non-isotropic structures, a more precise and accurate velocity estimation and compensation is necessary. Moreover, temperature changes, acquisition noise, multi-modal and dispersive behaviour of the GWs must be taken into account in order to improve the image reconstruction [11]. 2.2

Delay Multiply and Sum

In the Delay Multiply and Sum approach, after the re-alignment, the signals are combinatorially coupled and multiplied. Consider two transducer pairs which share the same actuator but different receivers. The actuator is located at (xa , y a ) and the two receivers are located at (xri , y ri ) and (xrj , y rj ) respectively. It is xy possible to define the propagation times txy i and tj as in Eq. (1) for the GWs referred to the i–th and j–th pairs passing through a generic scatterer point (x, y) on the plate. Thus, the DMAS beamformed signal for the (x, y) point is computed as: sDM AS (t, x, y) =

N −1 

N 

i=1 j=i+1

xy si (t − txy i )sj (t − tj )

(3)

xy where si (t − txy j ) and sj (t − tk ) are the delayed signals from the i–th and j– th transducers pair respectively. Once the sDM AS (t, x, y) is obtained for each spatial point (x, y), the DIDM AS is computed by means of the same procedure of the DAS technique. By exploiting the multiplication operation, the algorithm is more robust against outliers and noise, at the cost of a higher computational effort. In fact, by multiplying two noisy weak signals, a weaker signal will result as output. On the other hand, if an outlier occurs in one of the input signals, the uncorrelated samples will be lowered. Moreover, the contrast resolution, and thus the capability to clearly identify the damaged zone, is enhanced with respect to traditional DAS.

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Experimental Validation Setup

In order to validate the DMAS beamforming algorithm in a SHM scenario, data from the online platform Open Guided Waves described in Moll et al. [14] has been exploited. The specimen is a Carbon-Fiber-Reinforced Polymer (CFRP) plate based on prepreg material Hexply M21/34%/UD134/T700/300 with dimensions 500 mm × 500 mm × 2 mm and layup [45/0/−45/90/−45/0/45/90]S . The plate was sensorized with 12 DuraAct lead-zirconate-titanate (PZT) circular disk transducers of 0.2 mm in thickness and 5 mm in diameter placed as depicted in Fig. 2 (white circles). The carbon plate was placed in a climate chamber at a controlled constant temperature of 23◦ and 50% RH. Data has been acquired in pitch-catch configuration, exploiting a ±100 V, 5 cycles, Hann-filtered sine wave as excitation signal. In order to mimic a damaged condition, a reversible defect model where an aluminum disk is mounted on the surface of the CFRP plate by a tacky tape was used. The entire dataset is composed by a total of 60 baseline measurements and 28 different damage position measurements. Each measurement was performed multiple times with different excitation frequencies, from 30 to 240 kHz. The 60 kHz excitation dataset has been used in this work. 3.2

Processing

The entire algorithm which has been exploited is schematically depicted in Fig. 1. At first, a pre-processing procedure has been carried on. Usually, imaging techniques such as DAS or DMAS require the knowledge of the GWs group velocity and their dispersion curves in order to accurately estimate the propagation time given a specific wave path. Nevertheless, due to the quasi-isotropic behaviour of the material, the wave velocity has been considered in first approximation as constant. Moreover, in order to reduce the dispersion effects and noise, a bandpass filter centred at 60 kHz, from 40 to 80 kHz, has been applied to signals. Then, the signals have been subtracted with their relative baseline acquired in pristine conditions, in order to highlight the mismatch when damage occurs. Finally, the

Fig. 1. Algorithm chain

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Hilbert transform has been performed in order to obtain envelope-detected differenced signals. In fact, because of the dispersive and multimodal behaviour of the material, during the addition phase of the beamforming algorithm, signals might be affected by phase cancellation even if the signal envelopes are in alignment. Thus, by the envelope detection, phase cancellations due to dispersion will no longer occur [12]. After the pre–processing phase, the beamforming techniques described in Sect. 2 are performed, providing as output the normalized DIDAS (x, y) and DIDM AS (x, y) matrices, which represent the health conditions of the plate in spatial coordinates. As a final step, DAS and DMAS are directly compared by means of the Contrast to Noise Ratio (CNR), which was used as a metric to assess the damage image quality. The CNR can be defined as: μD − μB (4) σB where μD is the spatial average computed in the damaged imaged area, μB and σB are the spatial average and standard deviation of the undamaged imaged area, respectively. In order to compute the CNR metric, a circular region centered at the actual reversible defect model with radius 4 cm has been considered as damaged area. The complementary region has been considered as undamaged. CN R =

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Results

Some examples of the beamforming outputs are presented in Fig. 2. In particular, the images for three damage positions are shown to present how the DAS and DMAS outputs differ. These results lead to some considerations. At first, it can be observed that DMAS improves the damage reconstruction in comparison with the DAS output by reducing the color gradient and noise which is achieved by focusing the images peak. In fact, an increase of 18%, 22% and 14% of the CNR for D1, D9 and D21 respectively is achieved. It’s worthy to notice that in the case of the damage D1 (Fig. 2(a, b)), the images show a well localized damaged zone, shifted on the left of the actual damage position. This error is probably due to the constant group velocity assumed in the algorithm. Nevertheless, this aspect does not affect the considerations about the comparison between the DAS and DMAS beamforming algorithms. Moreover, in the case of D9 (Fig. 2(c, d)), although the damage region is wider and less focused with respect to the other cases presented, the DMAS approach results more efficient with a CNR gain of 22%. The analysis has been carried on the entire dataset in order to validate the algorithm for as many damage positions as possible. The results are shown in Fig. 3(a) where the CNR values for each damage position are plotted for both DAS and DMAS cases. Moreover, the percentage increment of the DMAS approach in comparison with DAS is presented in Fig. 3(b). Attention may be drawn to the fact that the DMAS algorithm provides a better CNR for each damage condition, with a mean increment of 14.5% and a peak of 27%. The results achieved prove the suitability of the DMAS algorithm in the GWs based SHM application, by enhancing the image reconstruction in terms

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Fig. 2. DAS (left column: a, c, e) and DMAS (right column: b, d, f) image output

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Fig. 3. Comparison between DAS and DMAS CNR in terms of absolute value (a) and percentage increment of DMAS CNR with respect to DAS (b)

of contrast and resolution with respect to DAS approach. Future works will investigate the behaviour of this approach in a more complex SHM scenario, such as the open dataset described in Marzani et al. [8], which provides GWs propagating on a composite panel of a full scale aeronautical structure in non controlled environmental conditions. In this case, temperature and humidity variations, the complexity of the non-isotropic structure and different operation conditions will be a challenging tasks to address in order to extend the DMAS capabilities and robustness.

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Conclusion

In this work, the suitability of the Delay Multiply and Sum beamforming algorithm for SHM purposes has been evaluated. For such a purpose, a SHM online available guided waves dataset has been exploited. The dataset is composed by piezo pitch-catch measurements in a carbon fiber plate, where damages were induced by attaching small aluminium disks on its surface. The controlled environmental conditions such as the quasi-isotropic behaviour of the material reduce the complexity of the use case in which no specific temperature, humidity, dispersion or velocity compensations were needed for the DAS and DMAS comparison purposes. Thus, it has been demonstrated the improvement of the DMAS beamforming imaging method with respect to the common DAS technique in terms of resolution and contrast, by achieving a better Contrast-to-noise ratio in each examined damage condition. In particular, the average Contrast-to-noise ratio improvement was estimated at 14.5% with a peak value of 27%.

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References 1. Budyn, N.: On the use of the geometric median in delay-and-sum ultrasonic array imaging. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 67, 2155–2163 (2020) 2. Demi, L.: Practical guide to ultrasound beam forming: beam pattern and image reconstruction analysis. Appl. Sci. 8(9), 1544 (2018) 3. Fyleris, T., Jasi¯ unien˙e, E.: Comparative analysis of plane-wave imaging and the total focusing method in the reconstruction of complex geometrical surfaces. Surf. Topogr.: Metrol. Prop. 7(3), 035011 (2019) 4. Gorgin, R., Luo, Y., Wu, Z.: Environmental and operational conditions effects on lamb wave based structural health monitoring systems: a review. Ultrasonics, 106114 (2020) 5. Kundu, T., Das, S., Jata, K.V.: Detection of the point of impact on a stiffened plate by the acoustic emission technique. Smart Mater. Struct. 18(3), 035006 (2009) 6. Lu, G., Li, Y., Wang, T., Xiao, H., Huo, L., Song, G.: A multi-delay-and-sum imaging algorithm for damage detection using piezoceramic transducers. J. Intell. Mater. Syst. Struct. 28(9), 1150–1159 (2017) 7. Malatesta, M.M., Testoni, N., Marzani, A., De Marchi, L.: Guided waves direction of arrival estimation based on calibrated multiresolution wavelet analysis. In: International Conference on Applications in Electronics Pervading Industry, Environment and Society, pp. 363–369. Springer (2019) 8. Marzani, A., Testoni, N., De Marchi, L., Messina, M., Monaco, E., Apicella, A.: An open database for benchmarking guided waves structural health monitoring algorithms on a composite full-scale outer wing demonstrator. Struct. Health Monit. 19, 1475921719889029 (2019) 9. Matrone, G., Savoia, A.S., Caliano, G., Magenes, G.: Ultrasound plane-wave imaging with delay multiply and sum beamforming and coherent compounding. In: 2016 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 3223–3226. IEEE (2016) 10. Matrone, G., Savoia, A.S., Caliano, G., Magenes, G.: The delay multiply and sum beamforming algorithm in ultrasound B-mode medical imaging. IEEE Trans. Med. Imaging 34(4), 940–949 (2014) 11. Michaels, J.E.: Detection, localization and characterization of damage in plates with an in situ array of spatially distributed ultrasonic sensors. Smart Mater. Struct. 17(3), 035035 (2008) 12. Michaels, J.E., Michaels, T.E.: Enhanced differential methods for guided wave phased array imaging using spatially distributed piezoelectric transducers. In: AIP Conference Proceedings, vol. 820, pp. 837–844. American Institute of Physics (2006) 13. Michaels, J.E., Michaels, T.E.: Guided wave signal processing and image fusion for in situ damage localization in plates. Wave Motion 44(6), 482–492 (2007) 14. Moll, J., et al.: Open guided waves: online platform for ultrasonic guided wave measurements. Struct. Health Monit. 18(5–6), 1903–1914 (2019) 15. Muller, A., Robertson-Welsh, B., Gaydecki, P., Gresil, M., Soutis, C.: Structural health monitoring using lamb wave reflections and total focusing method for image reconstruction. Appl. Compos. Mater. 24(2), 553–573 (2017) 16. Olson, S.E., DeSimio, M.P., Derriso, M.M.: Beam forming of lamb waves for structural health monitoring. J. Vib. Acoust. 129(6), 730–738 (2007). https://doi.org/ 10.1115/1.2731404

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17. Opretzka, J., Vogt, M., Ermert, H.: A model-based synthetic aperture focusing technique for high-frequency ultrasound imaging. In: 8th European Conference on Synthetic Aperture Radar, pp. 1–4. VDE (2010) 18. Sharif-Khodaei, Z., Aliabadi, M.: Assessment of delay-and-sum algorithms for damage detection in aluminium and composite plates. Smart Mater. Struct. 23(7), 075007 (2014) 19. Su, Z., Ye, L., Lu, Y.: Guided lamb waves for identification of damage in composite structures: a review. J. Sound Vib. 295(3–5), 753–780 (2006) 20. Ursu, I., Giurgiutiu, V., Toader, A.: Towards spacecraft applications of structural health monitoring. INCAS Bull. 4(4), 111–124 (2012) 21. Yan, F., Royer Jr., R.L., Rose, J.L.: Ultrasonic guided wave imaging techniques in structural health monitoring. J. Intell. Mater. Syst. Struct. 21(3), 377–384 (2010)

General Session

Monitoring Local Impedance Changes with Solitary Waves Hoda Jalali1(B) , Amir Nasrollahi2 , and Piervincenzo Rizzo1 1 Laboratory for Nondestructive Evaluation and Structural Health Monitoring Studies, Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA [email protected] 2 Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA

Abstract. Structural health monitoring methods based on the generation and detection of highly nonlinear solitary waves have emerged as a cost-effective technique for a variety of structures and materials. Outlier analysis is a statistic tool able to identify anomalies in data that diverge from a set of baseline data. In this paper the use of outlier analysis in terms of discordancy test and Mahalanobis squared distance was explored to enhance the damage detection capability based on the propagation and detection of highly nonlinear solitary waves. An experiment was performed to demonstrate the procedure. A thick steel plate was monitored with a solitary wave transducer placed above the plate, and damage was simulated in terms of a foreign object attached to the bottom of the plate. Three different masses located at an increasing distance from the transducer were considered. A few features were extracted from the experimental time waveforms, and then fed to a univariate and a multivariate analysis that compared the testing data to a set of baseline data. The experimental results show that the outlier analysis significantly enhances the ability to detect damage. Keywords: Highly nonlinear solitary waves · Outlier analysis, mechanical impedance · Damage detection

1 Introduction Nondestructive evaluation (NDE) based on solitary waves has emerged as a simple and low-cost method for monitoring structures. This method relies on the propagation of highly nonlinear solitary waves (HNSWs) in arrays of closely packed particles [1–3]. In this method, an incident solitary wave (ISW) is generated in the granular chain by the impact of the first particle in the chain. Solitary wave propagates along the chain of particles interacting via nonlinear contact forces. At the interface between the chain and the structure of interest, most of the acoustic energy carried by the ISW is reflected back, creating one or two reflected solitary waves, referred to as the primary and the secondary reflected solitary waves (PSW and SSW).

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 669–678, 2021. https://doi.org/10.1007/978-3-030-64908-1_62

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Researcher have reported that the amplitude and the arrival time of the reflected solitary waves depend on the mechanical and geometric properties of the adjacent structure/material [4–11]. For example, the amplitude and the arrival time of the reflected solitary waves, interacting with thin plates, depend on the plate thickness, the particles size, and the distance from the plate boundaries [12]. Solitary waves are also shown to be effective to detect subsurface voids [11] and delamination in composites [7, 13, 14]. Solitarywave based NDE applications include but are not limited to assessing the quality of adhesive joints [6], orthopedic and dental implants [8, 15], measurement of internal pressure in tennis balls [16] and measurement of axial stress [17]. This paper investigates the application of solitary wave-based NDE for detecting localized corrosion in plates. This study follows the recent numerical and experimental study by the authors [18], where both the numerical and experimental results demonstrate that solitary wave features are affected by the progression of localized corrosion in the plate. This paper is organized as follows: Sect. 2 presents the experimental setup. Section 3 presents the numerical modeling used study the interaction of solitary waves with pristine and corroded plates. The experimental and numerical results are presented and discussed in Sect. 4. Finally, Sect. 5 ends the paper with some concluding remarks.

2 Experimental Setup In this study, accelerated corrosion test based on electrochemical corrosion process was used to induce corrosion in a steel plate. As shown in Fig. 1a, the steel plate was half immersed in a 3.5% NaCl solution, and a copper sheet was immersed in the solution. A voltage of 10 V was applied between the two plates using a DC power supply. The steel and the copper plates were connected to the positive and the negative pole of the power supply, respectively. To increase the corrosion rate, an oxygen diffuser was also placed in the NaCl solution. (a)

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The steel plate was 609.6 mm × 609.6 mm × 6.35 mm in size. The lower face of the steel plate was (shown in Fig. 2b) was first covered with corrosion resistant

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tape. Then, three square-shaped tape cores were removed to expose the steel to the NaCl solution locally and induce localized corrosion. The locations of these areas are labeled with letters A, B, and C in Fig. 2b. Two solitary wave transducers and one pulseecho ultrasonic transducer (model Olympus DHC713) were used to monitor localized corrosion above the areas B, C, and A, respectively. A third solitary wave transducer was positioned on a protected part of the plate, labeled with the letter D in Fig. 2b.

Fig. 2. Numerical model of the interaction between the granular chain and the plate. (a) The coupled discrete element (DE) and finite element (FE) models integrated at the contact point of the granular chain and the plate. (b) Schematic of the DE model. (c) A zoom-in of the mesh refinement pattern in a square of 20 mm × 20 mm in the middle of the plate. (e) The nodes and the degrees of freedom of each plate element.

Figure 2c presents the scheme of HNSW transducers. As shown in this figure, each HNSW transducer consisted of eight particels. The particles were made of stainless steel and were 19.05 mm in diameter. All the particles except the top one (striker) were made of non-ferromagnetic stainless-steel. The striker (ferromagnetic particle) was lifted and released from a height of 5 mm using a commercial electromagnet. The solitary wave force profiles were recorded using a sensor disk positioned in the middle of the chain. The sensor disk was made of a lead zirconate titanate PZT wafer, embedded between two 19.05 mm × 6.05 mm cylindical disks. The experiment continued for about 350 h, and the corroding areas were monitored on average every hour. Each measurement set included one ultrasonic recording at area A and ten solitary wave recordings at areas B, C, and D.

3 Numerical Modeling The interaction of solitary with a thin plate in the pristine and the corroded conditions was studied using a coupled DE/FE model in MATLAB® . The two models were integrated at the contact point between the last particle of the chain and the plate, as shown in Fig. 2a.

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The DE model simulates the chain of particles as a series of N point masses connected by nonlinear springs and dashpots (Fig. 2b). The nonlinear springs were defined based 3/2 on the Hertzian contact law: F = Aδ+ . Here, F represents the contact force, A presents the stiffness coefficient, and δ presents the deformation of the diameter connecting the centers of adjacent particles. The subscript + denotes the operator max (δ, 0) to indicate the absence of interaction force between two particles when they are separated from each other. The equation of motion of each particle in the chain is as follows:  3/2  3/2 m¨ui = Ai−1,i ui−1 − ui + − Ai+1,i ui − ui+1 +       +γi−1,i u˙ i−1 − u˙ i ui−1 − ui + − γi+1,i u˙ i − u˙ i+1 ui − ui+1 + + mg (1) where m is the mass of the particle, g is the gravitational acceleration, and ui and u˙ i represent the displacement and the velocity of the ith particle, respectively. As shown in Fig. 2b, uN +1 represents the displacement of the plate at the contact point. The coefficient Ai,i+1 is the contact stiffness between the ith and the i + 1th particles: ⎧ √ Eb 2R ⎪ i = 1 : N − 1, ⎪ 2 ⎨

3 1−νb   √ Ai,i+1 = (2) 1−νp2 1−νb2 4 R ⎪ ⎪ + i = N . ⎩ 3 Eb Ep According to Eq. (2), the stiffness constant is a function particles radius R, the Poisson’s ratio ν, and the elastic modulus E of the particles and the plate. The subscripts b and p indicate the properties associated with the beads and the plate, respectively. The coefficient γi,i+1 represents dissipation in the chain (for i = 1:N−1) and at the chainplate interface (for i = N). The dissipation coefficients in the chain and at the chain-plate interface were equal to 4.5 N.s/m and 34.05 N.s/m (as reported in [6]), respectively. In this study, 9216 elements were used in the plate FE model (96 elements along each edge). According to Fig. 2a, finer mesh was used close to the interaction point of the plate and the granular chain, and the elements size gradually increased along edges. Figure 2c shows a zoom-in view of the mesh pattern in a square of 20 mm × 20 mm at the interaction area. A preliminary convergence test was conducted to determine the mesh pattern so that further mesh refinement does not result in a significant change of the properties of solitary waves and the plate deformations. The FE model was based on the Reissner-Mindlin plate theory. As shown in Fig. 2d, each element consisted of four nodes, and each node had three degrees of freedom: transverse deflection w, rotation about the x-axis θ x , and rotation about the y-axis θ y . The element stiffness matrix ke of each element is defined as [19]: ke = ∫ A

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The first and second terms in Eq. (3) represent the bending and shear stiffness, respectively. Also, the parameters h, ρp , and κ represent the plate thickness, density, and the shear correction factor equal to 5/6 respectively. The strain matrices BI and BO depend on the element shape functions and their derivatives and the material matrix c and cs depend on the mechanical properties of the plate [19].

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A second modeling approach was also implemented in ABAQUS/Standard in which only one quarter of the geometry was modeled due to symmetry in the problem geometry. Symmetry boundary conditions were applied to the nodes on the two planes of symmetry. In this model, the first eight particles in the chain were modeled as eight mass points of mass m/4. The last particle in the chain and the plate were modeled as deformable solid parts meshed using 3D 8-noded linear isoparametric (C3D8) elements. The interaction between particles was simulated using nonlinear axial connectors, defined such to resemble the Hertzian contact law and the energy dissipation in the chain considering one quarter of the geometry. The interaction between the last particle and the plate was modeled using the hard contact and frictionless tangential contact behaviors. The effect of gravity was considered by applying concentrated forces of w = mg/4 on the point masses and proper body forces on the plate and the 3D particle. In both numerical models, simply supported boundary conditions were applied along the plate external edges. The mechanical properties of the plate and particles were as E = 200 GPa, ν = 0.3, and ρ = 7 800 kg/m3 . The localized corrosion defect was modeled as square-shape defect of size 25.4 mm × 25.4 mm at the middle of the plate by changing the plate thickness from a baseline value of 6.35 mm to smaller values. In each model, a solitary wave was generated by applying an impact velocity of V imp = 0.31 m/s to the first mass point in the chain, then the solitary wave force profiles were obtained by averaging the interaction forces between the sensor particle and its adjacent particles [1, 13].

4 Results and Discussion The recorded solitary wave signals at each monitoring area were analyzed and solitary wave features including time of flight (ToF) and amplitude ratio were extracted. ToF and amplitude ratio were defined as the time difference between the ISW and the PSW peaks, and the ratio of the PSW amplitude to the ISW amplitude, respectively. Figures 3 presents ToF and amplitude ratio at areas B, C, and D as the corrosion propagates in the plate. Each point represents the average of the ten recordings at a given instant. According to Figs. 3a and 3b show, ToF increased about 10% with the progression of corrosion in corroding areas B and C. On the other hand, Fig. 3c shows that ToF was relatively constant throughout the experiment at the pristine area D. In addition, Figs. 3d and 3e show a 30% decrease of amplitude ratio as localized corrosion propagates in corroding areas B and C. In contrast, as shown in Fig. 3f, amplitude ratio was mostly constant at the pristine area D. In fact, amplitude ratio is significantly affected by the presence of localized corrosion defects in areas B and C, whereas it does not show variation in area D, which was protected from corrosion. The effect of localized corrosion on the solitary wave features can be explained with the analytical Zener model [20], which describes the impact of one sphere on a large thin uniform plate. This model assumes that part of the kinetic energy of the impact is dispersed by the propagation of flexural elastic waves in the plate. Thus, the impact is not perfectly elastic, and the coefficient of restitution e, defined as the ratio of the reflected to the incident velocity, is between zero and one. Zener [20] described the impact by coupling the equations of motion of the plate and the sphere. It is shown that as the plate thickness reduces, energy dissipation at the chain-plate interface increases. Therefore,

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the amplitude ratio decreases as the plate thickness reduces, resulting in weaker reflected solitary waves. It is also shown that the contact time between the last particle in the chain and the plate increases as the plate thickness decreases [12]. It means that ToF is longer in solitary waves interacting with thinner plates. Furthermore, a unique characteristic of HNSWs is that their propagation velocity V is proportional to F 1/6 m , where F m is the maximum dynamic force between particles [2]. It implies that weaker pulses propagate slower. Considering the effect of plate thickness on amplitude ratio, it can be concluded that the plate thickness reduction results in slower reflected solitary waves in the chain and therefore higher ToFs. Overall, the analytical model suggests that ToF increases as the plate thickness decreases. This effect was also as confirmed experimentally and numerically elsewhere [12]. The analytical model, discussed above, delve with plates of uniform thickness. However, it can be argued that localized corrosion increases energy dissipation and contact time at the chain-plate interface locally, yielding to a local decrease in amplitude ratio (as observed in Figs. 3d and 3e) and increase in ToF (as observed in Figs. 3a and 3b). To explore additional wave features that may enhance the sensitivity of the proposed approach, the area under the PSW and the auto-correlation technique were also considered. The former quantifies the restituted acoustic energy at the chain-plate interface. Figure 4 shows that this feature decreases in the transducers located on the corroding regions (Figs. 4a and 4b) and it remains constant at area D (Fig. 4c). Overall, the PSW area variation with respect to the progression of corrosion were similar to what observed in Figs. 3a and 3b. The autocorrelation technique was also implemented to find repeating patterns in the solitary wave signals. This method calculates the correlation of a signal with a delayed

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copy of itself as a function of a time delay, τ . The autocorrelation Rxx (τ ) of a given signal, x(t), is defined as: Rxx (τ ) = E[x(t)x(t + τ )]

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was computed. Here, mx and σ x present the mean and the variance of the signal, respectively. The autocorrelation coefficient is representative of the similarity between the original and the delayed signals. The coefficient is equal to 1 at τ = 0, implying maximum correlation (maximum similarity of the signal with itself). In addition, there is another peak in the autocorrelation coefficient at a time delay τ equal to solitary wave ToF. Therefore, the correlation method can be used for calculating the time of flight in solitary waves. Furthermore, the autocorrelation coefficient at τ = ToF is a representative of amplitude ratio. Figure 5 presents ToF and amplitude ratio calculate by the correlation method. The results show similar trends with respect to the results obtained from the peak to peak method, displayed in Fig. 3. It can be concluded that the autocorrelation method is an effective and promising technique for analyzing HNSWs. Compared to the results shown in Fig. 3, the autocorrelation data are less sparse. Therefore, implementing this technique can improve the capability of solitary waves to detect defects such as localized corrosion. The numerical results are presented in Fig. 6. According to Fig. 6a, the MATLAB model suggests the increase of ToF from 319 µs to 355 µs as the corrosion depth varies from 0 to 80% of the plate thickness. The ABAQUS model results also suggest an increase in ToF from 326 µs to 379 µs for the same corrosion depth range. The numerical ToFs are in excellent agreement with the experimental results presented in Figs. 3a,3b,5a, and 5b. Both the models show a nonlinear trend in ToF as a function of corrosion depth. In fact, it is shown that the sensitivity of ToF to localized corrosion increases as the relative depth of localized corrosion is higher than 0.5. In addition, Fig. 6b shows that amplitude ratio decreases from 0.74 to 0.57 and 0.84 to 0.76 as the relative corrosion depth increases in the ABAQUS and the MATLAB

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models, respectively. The amplitude ratios obtained from the ABAQUS model is closer to the experimental data (presented in Figs. 3d and 3e), since the 3D modeling of the impact between the last particle and the plate, allows capturing energy dissipation during the impact. The amplitude ratio of the MATLAB model can be fitted to the experimental results by modifying the dissipation coefficient at the chain-plate interface. Figure 7 shows the ultrasonic time of flight measured by the pulse-echo transducer located above area A. The estimated values of the remaining plate thickness on the right axis in Fig. 7. The graphs show an overall linear trend of the corrosion with respect to the time of the experiment. According to the estimate from the ultrasonic transducer, after 300 h the plate under probe was about 4.2 mm. At the end of the experiments, this area

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Fig. 7. Ultrasonic travel time in the corrosion area A (on the left axis) and the relative local plate thickness (on the right axis).

5 Conclusions In summary, application of solitary wave-based NDE to detect localized corrosion in steel plates was investigated experimentally and numerically. In the experimental study, three HNSW transducers and one ultrasonic transducer were used to monitor localized corrosion in a corroding plate. The experimental results provide evidence that solitary wave features, including time of flight and amplitude ratio, are affected by the presence of localized defects in the plate. Moreover, some new parameters, including correlation coefficient and area under PSW, were shown as useful parameters in analyzing solitary wave-based NDE. In numerical study, the interaction of solitary waves with a steel plate in pristine and corroded conditions was simulated using a coupled DE/FE model. The numerical results are in good agreement with the experimental findings, and they indicate that time of flight and amplitude ratio are strongly affected when the localized corrosion depth is higher than 50% of the plate thickness. Acknowledgement. The work was supported by the U.S. National Science Foundation, grant number 1809932, and the American Society for Nondestructive Testing through the 2019 Fellowship Research Award granted to the first author.

References 1. Daraio, C., Nesterenko, V., Herbold, E., Jin, S.: Strongly nonlinear waves in a chain of Teflon beads. Phys. Rev. E 72(1), 016603 (2005) 2. Job, S., Melo, F., Sokolow, A., Sen, S.: Solitary wave trains in granular chains: experiments, theory and simulations. Granul. Matt. 10(1), 13–20 (2007) 3. Coste, C., Falcon, E., Fauve, S.: Solitary waves in a chain of beads under Hertz contact. Phys. Rev. E 56(5), 6104 (1997) 4. Job, S., Melo, F., Sokolow, A., Sen, S.: How hertzian solitary waves interact with boundaries in a 1D granular medium. Phys. Rev. Lett. 94(17), 178002 (2005)

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5. Yang, J., Silvestro, C., Khatri, D., De Nardo, L., Daraio, C.: Interaction of highly nonlinear solitary waves with linear elastic media. Phys. Rev. E 83(4), 046606 (2011) 6. Ni, X., Rizzo, P.: Highly nonlinear solitary waves for the inspection of adhesive joints. Exp. Mech. 52(9), 1493–1501 (2012) 7. Kim, E., Restuccia, F., Yang, J., Daraio, C.: Solitary wave-based delamination detection in composite plates using a combined granular crystal sensor and actuator. Smart Mater. Struct. 24(12), 125004 (2015) 8. Yang, J., Silvestro, C., Sangiorgio, S.N., Borkowski, S.L., Ebramzadeh, E., De Nardo, L., Daraio, C.: Nondestructive evaluation of orthopaedic implant stability in THA using highly nonlinear solitary waves. Smart Mater. Struct. 21(1), 012002 (2011) 9. Nasrollahi, A., Deng, W., Rizzo, P., Vuotto, A., Vandenbossche, J.: Nondestructive testing of concrete using highly nonlinear solitary waves. Nondestruct. Test. Eval. 32(4), 381–399 (2017) 10. Rizzo, P., Nasrollahi, A., Deng, W., Vandenbossche, J.: Detecting the presence of high waterto-cement ratio in concrete surfaces using highly nonlinear solitary waves. Appl. Sci. 6(4), 104 (2016) 11. Schiffer, A., Alkhaja, A.I., Yang, J., Esfahani, E.N., Kim, T.Y.: Interaction of highly nonlinear solitary waves with elastic solids containing a spherical void. Int. J. Solids Struct. 118, 204–212 (2017) 12. Yang, J., Khatri, D., Anzel, P., Daraio, C.: Interaction of highly nonlinear solitary waves with thin plates. Int. J. Solids Struct. 49(13), 1463–1471 (2012) 13. Schiffer, A., Kim, T.-Y.: Modelling of the interaction between nonlinear solitary waves and composite beams. Int. J. Mech. Sci. 151, 181–191 (2019) 14. Singhal, T., Kim, E., Kim, T.-Y., Yang, J.: Weak bond detection in composites using highly nonlinear solitary waves. Smart Mater. Struct. 26(5), 055011 (2017) 15. Berhanu, B., Rizzo, P., Ochs, M.: Highly nonlinear solitary waves for the assessment of dental implant mobility. J. Appl. Mech. 80(1), 011028 (2013) 16. Nasrollahi, A., Rizzo, P., Orak, M.S.: Numerical and experimental study on the dynamic interaction between highly nonlinear solitary waves and pressurized balls. J. Appl. Mech. 85(3), 031007 (2018) 17. Nasrollahi, A., Rizzo, P.: Axial stress determination using highly nonlinear solitary waves. J. Acoust. Soc. Am. 144(4), 2201–2212 (2018) 18. Jalali, H., Rizzo, P.: Highly nonlinear solitary waves for the detection of localized corrosion. Smart Mat. Struct. (2020) 19. Liu, G.-R., Quek, S.S.: The finite element method: a practical course. Elsevier (2013) 20. Zener, C.: The intrinsic inelasticity of large plates. Phys. Rev. 59(8), 669–673 (1941)

Influence of Temperature on Additive Manufacturing Polymer Structure with Embedded Fibre Bragg Grating Sensors Magdalena Mieloszyk(B) , Katarzyna Majewska, and Artur Andrearczyk Institute of Fluid Flow Machinery, Polish Academy of Sciences, Gdansk, Poland [email protected]

Abstract. Additive manufacturing (AM) is a common name for a group of techniques that are applied for constructing three-dimensional objects in a layer-by-layer process. The main advantages of such methods are variety of materials (polymers, metals, ceramics) and possibility of manufacturing elements with complex shapes. Therefore, such techniques have been already adopted for rapid prototyping results in shortening delay between design concept and final product. One of the AM methods is multi-jet printing, which offers high accuracy of printed polymeric elements, that can be applied in many industrial branches, e.g. energetic. Safety requirements related to exploitation of structures results in development of structural health monitoring (SHM) methods based on fibre optic sensors. One of the sensor types are fibre Bragg grating (FBG) sensors. Their advantages (small dimensions, multiplexing capabilities) allow them to be embedded into AM structure during manufacturing process. The goal of the paper is to analyse temperature influence on FBG sensors embedded into an AM polymeric material. The analyses will be concerned on both spectrum reflected from the sensor and strain determined using on Bragg wavelength change.

Keywords: Polymer Temperature

1

· Additive manufacturing · Fibre Bragg grating ·

Introduction

Additive manufacturing (AM) techniques are recently applied in many industrial branches (e.g. automotive [1], energetic [2]). Such techniques replace traditional manufacturing methods and allow producing elements fast and with less amount of waste. A wide variety of AM techniques allow them to be applied to fabricate three-dimensional (3D) elements from a variety of materials (e.g. metal, polymer, ceramics) in a layer-by-layer process [3]. Polymers are one of the AM materials that are widely applied in rapid prototyping. It allows shortening the delay between the design concept and the final c The Author(s), under exclusive license to Springer Nature Switzerland AG 2021  P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 679–686, 2021. https://doi.org/10.1007/978-3-030-64908-1_63

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product due to possibility of relatively cheap verification of several proposed solutions. Polymeric elements can be manufactured using multi-jet printing (MJP) technique that has been adapted at the Institute of Fluid Flow Machinery, Polish Academy of Sciences (IMP PAN) for manufacturing of microturbine components [4]. During the printing process two materials are used: photocurable plastic resin (polymer) and casting wax material (supporting material). Applicability of AM polymeric elements in industry and increasing demand of safety results in development of structural health monitoring (SHM) methods. Fibre Bragg grating sensors (FBG) were chosen due to their advantages (e.g. small size and low weight, multiplexing capability, high resistance to corrosion and absence of electric current in measurement array), that allow them to be embedded into elements made of different material types with limited influence on material durability [5]. The paper is organised as follows. Firstly polymeric element manufactured using MJP technique will be presented together with the measurement set up, then experimental and numerical results related to strain determined for different temperature values will be shown. Finally, some conclusions are drawn.

2

Sample and Set-Up

The analysed object is AM polymeric sample manufactured using MJP technology by 3D printer (ProJet HD 3500 Max). The sample was made from UVcurable polymeric resin – M3 crystal. The sample external dimensions are as follows: total length of 165 mm, width 20 mm, and thickness of 4.2 mm. In the middle of the sample, a fibre optic (diameter 250 µm) with an FBG sensor (10 mm gauge length) was embedded. The fiber was acrylate coated, whereas the coating around the measured grating length was removed. The sample photograph, with marked (light orange) FBG sensor location, is presented in Fig. 1.

Fig. 1. Sample photograph.

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The spectra of the FBG sensor were measured using FBG interrogator FS4200 from Fiber Sensing, while Bragg wavelength measurements in a purpose of strain calculations were performed using interrogator si425-500 (Micron Optics) with a measurement frequency equal to 1 Hz. The experimental investigation was performed in environmental chamber MyDiscovery DM600C (Angelantoni Test Technologies Srl, Italy) that allowed to conduct research in a range of temperatures from −75 ◦ C to 180 ◦ C under different levels of RH ranging from 10% up to 98%. The analyses were related to a temperature range of −30 ◦ C to 30 ◦ C (with a 5 ◦ C step and stabilization time of 0.5 h) under stable relative humidity 20%. The program scheme is presented in Fig. 2.

Fig. 2. Environmental chamber program.

During the experimental investigation, the sample was kept on a shelf to allow it to expand in all directions. The temperature in the chamber (in the sample surroundings) was measured using an FBG temperature probe. For each case, the measurements were performed twice. For analyses of the influence of environmental parameters on the polymeric material the averaged values from two measurements were applied. The polymeric sample behaviour under temperature influence was modelled R . The numerically by finite element method (FEM) using software ABAQUS model (Fig. 3) contains 344 (8-node solid) elements. The boundary condition was the same like for the experimental investigation. The material parameters are collected in Table 1. The majority of them were given by the manufacturer, while the coefficient of thermal expansion was determined experimentally for temperature equal to 20 ◦ C and relative humidity equal to 20%.

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Fig. 3. Numerical model of the analysed sample. Table 1. Material parameters using during numerical calculations. Parameter

Value

Thermal conductivity

0.3 W/m◦ C

Density

1020 kg/m3

Young’s modulus

1.5 MPa

Poisson’s ratio

0.3

Coefficient of thermal expansion 8.4 10−5 1/◦ C Heat capacity

3

1100 J/kg◦ C

Results

The analyses were concerned on changes in spectra reflected from the FBG sensor and strain values in the polymeric sample related to temperature influence. 3.1

Spectra

A comparison of FBG sensor spectra is presented in Fig. 4. It is observed that neither the embedding process nor the temperature treatment results in changes in the spectrum shape. The shift toward higher wavelengths (E) is most probably caused by the increase in the temperature owing to the UV lamp working and the solidification of the liquid polymer. On the other side, the shift toward smaller wavelengths (Eend ) is probably an effect of the structural material change due to negative temperature influence.

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Fig. 4. FBG sensor spectra: F – free, E – after the embedding process, Eend – after the end of the experimental test.

3.2

Strain

For both numerical and experimental calculations as a base conditions 20% relative humidity and 20 ◦ C were assumed. Strain values determined from the experimental investigation were determined using the following relationship ε S = εc − ε f

(1)

where εc is a total strain related to FBG sensor embedded into the sample. εf is a strain values determined experimentally for FBG sensor material. It is calculated using the relationship εf = αΔT

(2)

where α is a coefficient of thermal expansion for the fibre optic material and T is temperature. For the strain calculations the temperature values are equal to those measured by the temperature probe. A comparison of strain values determined experimentally and numerically for polymer material is presented in Fig. 5. Both curves have similar shapes related to the assumed temperature curve – see Fig. 2. The main difference is related to the assumed temperature amplitude decreasing process realised experimentally (slower to achieve equal temperature inside the whole element) and numerically (default ramp function). It results in elongation of the numerical temperature treatment process in comparison to the experimental one. In a purpose of better visibility, the strain values for 13 chosen temperatures related to steps in the chamber program (Fig. 2) are presented in Fig. 6. It shows good agreement between strains determined numerically and experimentally. The main differences are observed for temperatures close to 0 ◦ C. In a purpose of comparison of experimental and numerical results, a percentage error was determined according to the following formula    εS − ε n   100%  (3) E= εS 

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Fig. 5. Comparison of strain curves determined: (a) experimentally, (b) numerically.

Fig. 6. Comparison of strain values determined numerically and experimentally for chosen temperature values.

where εn means strain value determined from numerical calculation for embedded FBG sensor location and εS are strain values determined according to Eq. 1. The strain values (numerical and experimental) and the error for all temperatures are presented in Table 2. The highest error values are observed for temperatures from −5 ◦ C to 5 ◦ C. It can be related to changes in the material properties due to temperature values close to 0 ◦ C. The mean error value for all measurement steps is equal to 5.3%. The differences in strain values determined experimentally and numerically can be also an effect of AM material structure changes due to its exposition on sub-zero temperatures. A comparison of microstructures for the sample just after manufacturing and the temperature treatment is presented in Fig. 7. The solidification process resulted in amorphous structure in each layer. The intact sample surface has characteristic lines related to the manufacturing process (Fig. 7(a)). Exposition on temperatures below 0 ◦ C results in structural changes in the sample material. A partial crystallisation can be observed on the sample surface (Fig. 7(b)). The crystallised and amorphous parts are divided by a boundary – denoted by an arrow.

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Table 2. Comparison of experimental and numerical results for chosen temperature values. Temperature Experiment Numerical model Error 10−3 [m/m] 10−3 [m/m] [%] [◦ C] −30

−4.038

−4.200

4.0

−25

−3.721

−3.781

1.6

−20

−3.400

−3.360

1.2

−15

−3.049

−2.940

3.6

−10

−2.677

−2.520

5.9

−5

−2.273

−2.100

7.6

0

−1.869

−1.680

10.1

5

−1.433

−1.260

12.1

10

−0.875

−0.840

4.1

15

−0.458

−0.420

6.7

20

0

0

–

25

0.404

0.420

3.8

30

0.791

0.840

6.1

Fig. 7. Sample surface microstructure after: (a) AM, (b) temperature treatment.

4

Conclusion

The present study is related to the influence of temperature on AM polymeric sample with embedded FBG sensor. The analyses concern both changes in spectrum reflected from FBG sensor as well as strain values determined from the embedded sensor. It was shown that neither the manufacturing process nor the temperature treatment influenced the spectrum shape. The strain values for

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temperature treatment were determined numerically and experimentally based on the same thermal program. A good agreement was shown between those two results – the mean error value is equal to 5.3%. Additionally, a microstructure of the sample just after the manufacturing process and after the temperature treatment were compared. It showed that the sub-zero temperatures result in changes in the microstructure from amorphous to partially crystallised. Such differences can also influence on the mechanical properties of the polymeric material and can be visible in strain values not only determined for the sample directly affected by sub-zero temperatures but also for operational temperatures. Acknowledgements. This research was supported by the project ‘Polymeric structures with embedded FBG sensors’ that has received funding from the National Science Centre (NCN) under grant agreement number 2018/31/D/ST8/00463. ABAQUS calculations were carried out at the Academic Computer Centre in Gda´ nsk (Poland). The opinions expressed in this manuscript do not necessarily reflect those of the sponsors.

References 1. Lee, J.-Y., An, J., Chua, C.K.: Fundamentals and applications of 3D printing for novel materials. Appl. Mater. Today 7, 120–133 (2017) 2. Mofidian, M., Bardaweel, H.: A dual-purpose vibration isolator energy harvester: experiment and model. Mech. Syst. Signal Process. 118(1), 360–376 (2019) 3. Gibson, I., Rosen, D., Stucker, B.: Additive Manufacturing Technologies: 3D Printing, Rapid Prototyping and Direct Digital Manufacturing. Springer, New York (2015) 4. Andrearczyk, A., Baginski, P., Klonowicz, P.: Numerical and experimental investigations of a turbocharger with a compressor wheel made of additively manufactured plastic. Int. J. Mech. Sci. 178, 10 (2020). Article ID 105613 5. Mieloszyk, M., Ostachowicz, W.: Moisture contamination detection in adhesive bond using embedded FBG sensors. Mech. Syst. Signal Process. 84(Part A), 1–14 (2017)

Methods for Degradation Assessment of Fibre Reinforced Polymer Structure Exposed to the Simultaneous Influence of Temperature and Humidity Katarzyna Majewska(B) , Magdalena Mieloszyk, and Wieslaw Ostachowicz Institute of Fluid Flow Machinery, Polish Academy of Sciences, Gdansk, Poland [email protected]

Abstract. Fibre reinforced polymers are commonly used in many industrial branches. The continuous technical progress in the applied science and technology requires more and more advanced materials. The structural damage can occur due to many factors which are difficult to predict in advance. Safety and reliability requirements results in development of a variety of structural health monitoring (SHM) systems and non-destructive testing (NDT) techniques. In the paper the comparative studies of two nondestructive testing (NDT) methods (infrared thermography and THz spectroscopy) are presented. NDT techniques that can be applied for evaluation of internal structure of composite materials are infrared thermography (pulse and/ or vibrothermography) and THz spectroscopy. Both methods can be used for identification of material structural disintegrations. Infrared thermography allows to observe changes of temperature field distribution, while THz spectroscopy allows to observe changes of absorption coefficient, refractive index or scattering of THz waves propagating throughout analysed material. The goal of the paper is to study the sensitivity and applicability limitations of proposed methods with application to fibre reinforced polymers under simultaneous temperature (form negative to elevate) and relative humidity influence. Keywords: Composite · Degradation · Aging process Temperature · IRT · THz spectroscopy

1

· Humidity ·

Introduction

Composites have a lot of advantages like low cost, light weight, high strength and stiffness to weight ratios etc., as a result, they are applied in different industrial branches (aerospace, renewable energy, marine etc). In recent times there is a demand for larger, and more complex composite components (such as wind turbine blades, aircraft parts). This increase in the complexity of components c The Author(s), under exclusive license to Springer Nature Switzerland AG 2021  P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 687–698, 2021. https://doi.org/10.1007/978-3-030-64908-1_64

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leads to difficulties in manufacturing and maintenance. Any structural damage appears in two ways: by external impacts or by internal failure introduced during the manufacturing process. To detect structural failures non-destructive testing (NDT) is applied. The infrared thermography (IRT) is a technique for investigating the internal structure of composites. The method allows the creation of an image presenting the power of radiation emitted from the surface of the analysed structure. In the active methods, external thermal excitation is applied to the structure. Optical excitation methods allow non-contact excitation and allow to avoid modifications of temperature field of the structure due to the contact of exciting transducer (ultrasound based methods). Active methods can be divided into two groups based on the form of thermal excitation implemented: pulse or continuous [10]. In the case of pulse method choice of proper thermal pulse parameters is a key issue [9]. IRT allows to easily visualize changes in temperature distribution and to observe any discontinuity in the material. IRT is used for damage detection in metallic [8] and composites structures. It has been proven to be an effective method to detect cracks or delaminations [7] as well as water ingress or embedded fibre optics [2] in composite materials. The THz technique can be used for inspecting the internal structure of a nonconducted component, like glass fibre reinforced polymer (GFRP). The THz technique uses electromagnetic waves in the frequency range from 0.1 THz to 10 THz. All THz based damage detection methods are related to changes in one of the parameters: refractive index, absorption coefficient or wave scattering [4]. In the reflection based technique, the emitter and receiver are on the same side of the sample. Small electromagnetic pulses are reflected off the sample, some part of the signal gets reflected at each interface between media having a different refractive index, while the remaining propagates through the sample. In case of multilayer samples (e.g. GFRP) the sequence of pulses shifted in time reflected from particular interfaces are registered. It enables the precise analysis of the internal structure (the time-of-flight imaging). The THz technique has a unique capacity for examining composite materials and identification of defects like gaps [6], delaminations [3], or thermal damage [5].

2

Experimental Investigation – Sample and Set-Up

The measurements were performed on rectangular glass fibre reinforced polymer (GFRP) sample. The dimensions of a sample were L = 250 mm, W = 50 mm, H = 1.5 mm – details in Fig. 1. The sample was manufactured using infusion method R for bidirectional material (glass SGlass ) and epoxy resin. In the middle of the beam, the burning area was introduced using air heating gun (300 s/480 ◦ C.) The idea of the measurement was to study the sensitivity, applicability and limitations of proposed methods for burning areas introduced into composite structures and under simultaneous temperature (form negative to elevate) and relative humidity influence. Two methods were proposed, IRT and THz spectroscopy, which can be successfully applied to the composite material for observation of its structure.

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Fig. 1. Sample with infrared thermography and THz spectrometer set-ups.

The IRT experimental set-up is presented in Fig. 1 (right, upper corner). Measurements were conducted using signal generator, amplifier, ultrasound exciter, camera Flir SC-5600 (working frequency 50 Hz), support frame with pneumatic control and PC computer. Signal form generator after amplification drives the ultrasound exciter. The signal was modulated with sine waveform with the frequency equal to 4 kHz and peak-to-peak amplitude equal to 8 Vpp. Generated vibrations change the temperature field of the sample in the places with any discontinuities. The camera registered the changing local temperature field in 1500 frames, lasting 30 s. For the THz experimental investigation the equipment (TPS Spectra 300 THz R ) in reflection mode was Pulsed Imaging and Spectroscopy from TerraView used (Fig. 1 (right, bottom corner)). The measuring heads were arranged in an angle of 22◦ between them. The measurement step was equal 0.2 mm in both directions (xy plane) and THz signals were registered with tenfold averaging. As the THz waves are sensitive on ambient moisture all measurements were performed with air dryer that removes moisture from the heads area and air condition that drying and stabilise laboratory temperature on an assumed level equal to 20 ◦ C.

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The sample structural degradation processes analyses were divided into three stages. The first one (SR ) was the reference state for the sample after its preparation. The second one (ST ) was after temperature treatment. In the case, the sample was put into a climate chamber (MyDiscovery DM600C) for 100 thermal cycles with a temperature range of −20 ◦ C to 20 ◦ C under stable relative humidity 75%. The last stage (SD ) was performed after 216 h of the drying process.

3

Results

For both proposed methods after every stage (SR , ST , SD ) the studies were performed. The analyses were focused on the area marked as grey rectangle in Fig. 1. 3.1

Infrared Thermography Analyses

The first set of figures (Figs. 2, 3 and 4) presents the pure thermogram achieved in selected time [s] (0, 1, 5, 10, 15, 20, 25, 30) for the sample stages SR , ST , SD , respectively. It is easy to track how the discontinuity reveals in time and how the sample structure differs among stages due to the temperature and humidity influence. For the deeper analyses, the standard post-processing techniques were proposed (based on the thermal field). The first spatial derivative (DT ) and the norm of the first spatial derivative (DT ) of the were calculated using the relationships [1]  2  2 ∂T ∂T ∂T & DT (x, y, t) = + (1) DT (x, y, t) = ∂x∂y ∂x ∂y where T is temperature and x, y are the coordinates in a sample plane. The results are presented in two sets of figures Figs. 5, 6 and 7 for the DT and Figs. 8, 9 and 10 for the DT , respectively. After the analyses, the change in the sample structure and characteristic pattern of the burning area can be observed. As it was not possible for pure thermograms. However, it is well visible that results achieved for stages SR and SD are similar. For stage ST influence of remaining moisture in the material due to temperature and humidity sample treatment is visible.

Degradation Assessment of GFRP

Fig. 2. IRT analysis: SR .

Fig. 3. IRT analysis: ST .

Fig. 4. IRT analysis: SD .

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Fig. 5. IRT analysis: SR – spatial derivative.

Fig. 6. IRT analysis: ST – spatial derivative.

Fig. 7. IRT analysis: SD – spatial derivative.

Degradation Assessment of GFRP

Fig. 8. IRT analysis: SR – norm of spatial derivative.

Fig. 9. IRT analysis: ST – norm of spatial derivative.

Fig. 10. IRT analysis: SD – norm of spatial derivative.

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THz Spectroscopy Analyses

A comparison of C-scan and B-scans for each stage is presented in Fig. 11.

Fig. 11. Images of the sample in: (a)–(c) SR , (d)–(f) ST , (g)–(i) SD .

C-scans are determined for the sample surface. In each of them, the damaged area is well visible. The sample exposition on temperature cycles results in increasing of differentiation between the burned area and the rest of the sample. As the burned area has the ellipsoidal size the B-scans were performed along its main axis (x, y directions). The damaged region appearance (parallel glass fibre strips along the y-axis) results in differences among B-scans in the x and the y direction. In the first group, the air/ material boundary in the burned area is presented as a jagged line as it is crossing separated glass fibre strips (bundles). On the contrary, the boundary in B-scans (the second group) is smooth, as it is laying on one strip located in the middle of the burned area. It is possible to observe the progressive degradation process of the GFRP material comparing

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B-scans for the consecutive stages. However, there is a lack of strong difference in the burned region among the stages. In the purpose of analyses of the structural degradation process, series of C-scans were determined for all stages. The images presented in Figs. 12, 13 and 14 were determined from the sample surface in the material thickness direction. The C-scans for the SR (Fig. 12) show that the burning process resulted in degradation not only of the sample surface but also the material hidden below. It caused that the temperature treatment influenced the internal part of the GFRP sample close to the burned region. It resulted in highlighting of the burned area in C-scans presented in Fig. 13. The moisture occurrence caused smoothing of the boundary between intact and burned parts of the sample, as THz waves are sensitive to water occurrence. Drying process highlighted the damaged area character – separated glass fibre bundles (Fig. 14).

Fig. 12. C-scans for SR with a step of 0.23 ps.

In a purpose of determination of the differences of temperature treatment influences on intact (denoted as M) and burned (denoted as B) GFRP material the following analyses was performed using the formulas n

M=

n

m

1  M A(xM i , yj ) nm i=1 j=1

&

B=

m

1  B A(xB i , yj ) nm i=1 j=1

(2)

M B B where A(xM i , yj ), A(xi , yj ) are the THz wave amplitude reflected from a point lying on the intact material or the burned material, respectively.

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Fig. 13. C-scans for the sample after the temperature treatment with a step of 0.23 ps.

Fig. 14. C-scans for the sample after drying process with a step of 0.23 ps.

Additionally, a damage index was introduced I = B/M. The results of the calculations are presented in Table 1. As it is well visible the M values for stages SR and SD are similar. The observed difference is probably an effect of the residual moisture occurrence in the material. On contrary to this, the degradation process of the burned area is developing. Probably the polymeric matrix that was not destroyed during the burning process was influenced by temperature treatment and humidity.

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Table 1. A comparison of parameters calculated for three stages of the sample. Stage M [a.u.] B [a.u.] I [-]

4

SR

0.0601

0.0505

0.8399

ST

0.0842

0.0739

0.8776

SD

0.0690

0.0764

1.1084

Conclusions

The comparative study was undertaken for the detection of burning area (heat induced damage) in a composite beam using two techniques, IRT and THz spectroscopy. As a result for qualitative assessment of the burning area in composite structures under the simultaneous influence of temperature and humidity proposed techniques can be successfully applied. Both methods allow observing and visualizing the internal structure and the character of introduced damage. Acknowledgement. The authors are grateful to Aditya Choure (from Dresden International University) and Rohan Soman for manufacturing the sample and preparation it for the research. The research was supported by the project: The influence of temperature and moisture interaction effect on anisotropic structures: from theory to experimental investigation (2016/23/B/ST8/03088) granted by the National Science Centre in Poland. The opinions expressed in the work do not necessarily reflect those of the sponsors.

References 1. Chrysafi, A.P., Athanasopoulos, N., Siakavellas, N.J.: Damage detection on composite materials with active thermography and digital image processing. Int. J. Therm. Sci. 116, 242–253 (2017) 2. Majewska, K., Mieloszyk, M., Ostachowicz, W.: Active thermography as a tool for internal composite structure observation and evaluation. Int. J. Struct. Integr. 9(6), 779–792 (2018) 3. Mieloszyk, M., Jurek, M., Majewska, K., Ostachowicz, W.: Terahertz time domain spectroscopy and imaging application for analysis of sandwich panel with embedded fibre Bragg grating sensors and piezoelectric transducers. Opt. Lasers Eng. 134, 106226 (2020) 4. Park, J.W., Im, K.H., Yang, I.Y., Kim, S.K., Kang, S.J., Cho, Y.T., Jung, J.A., Hsu, D.K.: THz radiation NDE of composite materials for wind turbine applications. Int. J. Precis. Eng. Manuf. 15(6), 1247–1254 (2014) 5. Radzienski, M., Mieloszyk, M., Rahani, E.K., Kundu, T., Ostachowicz, W.: Heat induced damage detection in composite materials by terahertz radiation. In: Proceedings of SPIE, p. 94381P (2015) 6. Stoik, C.D., Bohn, M.J., Blackshire, J.: Nondestructive evaluation of aircraft composites using transmissive terahertz time domain spectroscopy. Opt. Express 16, 17039–17051 (2008)

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7. Swiderski, W.: Nondestructive testing of composite materials used in military applications by eddy current thermography method. In: Proceedings of SPIE, p. 998705 (2016) 8. Tomic, L.D., Jovanovic, D.B., Karkalic, R.M., Damnjanovic, V.M., Kovzcevic, B.V., Filipovic, D.D., Radakovic, S.S.: Application of pulsed flash thermography method for specific defect estimation in aluminum. Therm. Sci. 19(5), 1845–1854 (2015) 9. Vollmer, M., Mollmann, K.P.: Infrared Thermal Imaging: Fundamentals, Research and Applications. Wiley, Hoboken (2010) 10. Yang, R., He, Y.: Optically and non-optically excited thermography for composites: a review. Infrared Phys. Technol. 75, 26–50 (2016)

Analytical Modeling of Vibrations in a Damaged Beam Using Green-Volterra Formalism Damien Bouvier(B) , Nazih Mechbal , and Marc R´ebillat Arts et Metiers Institute of Technology, CNRS, CNAM, PIMM, HESAM Univesit´e, 75013 Paris, France [email protected]

Abstract. Structural Health Monitoring of aeronautic composite structures through Lamb waves can advantageously exploit the fact that Lamb wave damage interaction is nonlinear. However, one difficulty in this context is to be able to distinguish between nonlinearities due to the propagation (i.e. material or geometrical nonlinearities) and those due to the damage itself that are of main interest here. This work proposes to use the Green-Volterra formalism to build up a model for Lamb Wave propagation and damage interaction that is complex enough to represent both types of nonlinearities, and simple enough to be used for simulation and estimation purposes. This approach is presented for the low frequency S0 mode nonlinear propagation in a damaged beam. An analytical model of the nonlinear wave propagation is first derived, where the damage is represented with a polynomial stiffness characteristic acting via boundary conditions. This model is then used to derive the Green-Volterra series describing the nonlinear input-output relationship of the system. A modal decomposition of the Green-Volterra series is also provided. Simulations are presented, and the proposed approach is successfully compared to state-of-the-art methods based on finite-elements models. Keywords: Lamb waves · Nonlinear damage · Nonlinear propagation in composite materials · Green-Volterra model

1

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Structural Health Monitoring (SHM) combines advanced sensor technology with intelligent algorithms to interrogate the structural “health” condition. Generally, a SHM process entails establishing: (1) the existence of damage, (2) the damage locations, (3) the types of damage, and (4) the damage severity [1]. On the basis of the assumption that in many cases damage causes a structure to exhibit nonlinear dynamical response and that the damage monitoring process can be significantly enhanced if one takes advantage of these nonlinear effects [2], we aim here at providing a framework with a richer representation of nonlinear damages and nonlinear Lamb waves propagation in composite aeronautic complex c The Author(s), under exclusive license to Springer Nature Switzerland AG 2021  P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 699–710, 2021. https://doi.org/10.1007/978-3-030-64908-1_65

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structures. Such approaches in that direction have already been achieved [3,4] but were not general enough in terms of damage models and did not include nonlinear Lamb wave propagation thus motivating the present study. In order to model nonlinearities, this paper relies on the Volterra formalism. Volterra series is a model representation that describes the output signal of a system as an homogeneous series with respect to the input [5]. This approach, similar to Taylor series approximations for functions, has been shown to be an universal approximator for any nonlinear dynamical system with fading memory [6]. To correctly take into account the spatial dependency of the problem under study, this paper uses the Green-Volterra series [7,8], which are an extension of the Volterra formalism incorporating the notion of Green’s function. Furthermore, we use the method presented in [8] which allow to easily compute the Green-Volterra kernels for an inhomogeneous nonlinear partial differential equation where the nonlinearities are in a polynomial form. In this paper, we thus use the Green-Volterra formalism to find analytical solutions for the S0 mode nonlinear propagation and nonlinear damage interaction in a damaged beam. Firstly, the wave propagation model used for the damaged beam is presented, where the damage is represented with a polynomial stiffness characteristic acting via boundary conditions. This model is then used to derive the Green-Volterra series describing the input-output relationship of the system. A modal decomposition of the Green-Volterra series is then given. Simulations are presented, and the proposed approach is successfully compared to a state-of-the-art method based on finite elements.

2

Modelisation of the Damaged Beam

2.1

Assumptions

In this paper, we consider a beam of length L and section S, with fixed boundary conditions at both ends1 and a damage localized at x = d (see Fig. 1). The material is homogeneous, isotrope and dissipative, with Young modulus E, volumic mass ρ and damping factor γ; physical nonlinearity in the propagation is also taken into account, with  and β respectively the quadratic and cubic nonlinearity coefficients [9]. In order to represent the damage, we will consider that the beam is divided into two sub-beams linked by a nonlinear spring (see Fig. 2), which is characterized by a polynomial stiffness relation, i.e. K [x] =

+∞ 

Kn xn ,

(1)

n=1

with K [x] the force applied by the spring at its extremities in response to an elongation x. We will respectively note Ωl = [0, d[ and Ωr = ]d, L] the left-part and right-part domains. 1

The presented approach is also valid for other types of boundary conditions, but for sake of clarity and concision we restrict here the presentation to this case only.

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Fig. 1. Damaged beam under study.

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Constitutive Equations

We consider that the beam is excited by an external force f (x, t). Then, given the previous assumptions, the longitudinal vibration u (x, t) follows the wave equation   ρS ∂t2 u (x, t) + γ ∂t u (x, t) − ES 1 −  ∂x u (x, t) + β (∂x u (x, t))2 ∂x2 u (x, t) = f (x, t)

for x ∈ Ωl ∪ Ωr . Furthermore, the fixed extremities at x = 0 and x = L give the boundary conditions u (0, t) = 0,

u (L, t) = 0,

and the damage imposes at x = d− and x = d+        ES ∂x u d− , t = K u d+ , t − u d− , t ,        −ES ∂x u d+ , t = −K u d+ , t − u d− , t . The constitutive equations of the damaged beam model are thus given by  ⎧ ⎪ 1 −  ∂x u (x, t) + β (∂x u (x, t))2 ∂x2 u (x, t) ⎪ ⎪ for x ∈ Ωl ∪ Ωr ⎪ ⎪ 1 γ 1 ⎪ ⎪ ⎪ − 2 ∂t2 u (x, t) − ∂t u (x, t) = f (x, t) ⎪ ⎨ cL F0 F0 Σ : u (0, t) = 0 ⎪ ⎪ ⎪ ⎪ ⎪ u (L,t) = 0  ⎪ ⎪ ∂ u d− , t = ∂x u d+ , t = ⎪ ⎪ ∂x u(d, t)  ⎩ x + F0 ∂x u (d, t) = K u d , t − u d− , t

(2)

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 with cL = Eρ the longitudinal wave celerity, and F0 = ES a factor homogeneous to a force. The vibration u is thus solution of a non-homogeneous differential equations system made up of one nonlinear propagation equation on Ωl ∪ Ωr , two homogeneous Dirichlet boundary conditions at x = 0 and x = L, one homogeneous Cauchy boundary conditions at x = d and one inhomogeneous Robin boundary conditions at x = d. The following section will present an analytical solution of this problem using the Green-Volterra formalism.

3 3.1

Analytical Solution via Green-Volterra Series Volterra and Green-Volterra Series

The Volterra series [5], which have been used for many decades to model a variety of nonlinear dynamical systems, rely on the assumption that the output signal can be described as an homogeneous series, i.e. that u=

+∞ 

un

(3)

n=1

where each order un is homogeneous of order n w.r.t. the input force f , i.e. un ∝ f n . This idea allows to extend the idea of linear filter to each order of nonlinearity via the introduction of Volterra kernels. One important property of Volterra series is that it can approximate any nonlinear dynamical system with fading memory [6]. An extension of the Volterra formalism, the Green-Volterra series, has been introduced in [7,8] to model problems that were also space-dependent. In this model, each homogeneous order of the output vibration un is written as a convolution between a space-time Green-Volterra kernel gn and multiple product of delayed versions of the input force f , i.e. un (x, t) =



L

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(4)

Furthermore, it has been shown in [8] how to compute the kernels gn from an inhomogeneous differential equation where the nonlinearities are in a polynomial form, and that it is only needed to find the Green kernel corresponding to the linear part of the differential operator (and respecting the boundary conditions of the problem). In the following, we will use this approach to derive analytical solutions for the problem stated in Eq. (2).

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Problem Reformulation

Incorporating (3) into the model (2), and sorting terms by their homogeneity order gives the sub-model that each order un must follow, i.e.

Σn :

⎧ 1 2 γ 2 ⎪ ⎪ ⎪ ∂x un (x, t) − c2 ∂t un (x, t) − F ∂t un (x, t) = gn (x, t) for x ∈ Ωl ∪ Ωr ⎪ ⎪ 0 L ⎪ ⎨ u (0, t) = 0 n

un (L,t) = 0 ⎪ ⎪  ⎪ ⎪ ∂ u d− , t = ∂x un d+ , t = ∂x un (d, ⎪ ⎪  t) ⎩ x n + F0 ∂x un (d, t) − K1 un d , t + K1 un d− , t = rn (t)

(5)

with the “input force” gn given by ⎧ 1 ⎪ ⎪ f (x, t) for n = 1, ⎪ ⎪ 0 ⎨ F 2 ∂x um1 (x, t) ∂x um2 (x, t)  gn (x, t) = m1 +m2 =n ⎪ ⎪ for n ≥ 2.  ⎪ ⎪ ⎩ −β ∂x um1 (x, t) ∂x um2 (x, t) ∂x2 um3 (x, t) m1 +m2 +m3 =n

and the “residual force” rn at damage given by ⎧ 0 for n = 1, ⎪ ⎪   ⎨ n j

rn (t) = Kj for n ≥ 2. umk (d+ , t) − umk (d− , t) ⎪ ⎪ k=1 m∈Nj ⎩ j=2 m1 +···+mj =n

From (5) and the expression of gn and rn , we can remark that each order un is solution of a linear differential problem with mixed boundary conditions, where the “input force” and part of the boundary condition are function of lower orders um with m < n. This means that, in order to find analytical solutions for un , it is only needed to solve once the linear differential problem (5). Furthermore, this allows a numerical simulation of our problem, where orders un will be computed iteratively. In order to facilitate the resolution of Eq. (5), we will take the expression in the Laplace domain: ⎧ 2 for x ∈ Ωl ∪ Ωr ⎪ ⎪ ∂x Un (x, s) − σ(s)Un (x, s) = Gn (x, s) ⎪ ⎪ ⎨ Un (0, s) = 0 Σn : Un (L,s) = 0  ⎪ ⎪ ∂ U d− , s = ∂x Un d+ , s = ∂x Un (d, ⎪ ⎪  s) ⎩ x n + F0 ∂x Un (d, s) − K1 Un d , s + K1 Un d− , s = Rn (s)

with σ(s)2 =

(6)

s2 γs − , 2 cL F0

and where spatio-frequency signals Un , Gn and Rn are the Laplace transform of spatio-temporal signal un , gn and rn .

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Analytical Solution

Let δ = L − d be the length of the right-part beam, and Q (s) =

1     . K1 sinh σ(s)L + F0 σ(s) cosh σ(s)δ cosh σ(s)d 

(7)

Then, the solution of (6) is given by, ∀s = 0, Un (x, s) =

2σ(s) Q(s) +

F0 2Q(s)

Fn (ξ, s) 0



cosh σ(s)(L − |x − ξ|)



 d



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cosh σ(s)δ



+



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K1

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sinh σ(s) x cosh σ(s) δ





− cosh σ(s)(L − x − ξ)



sinh σ(s)(d − |x − ξ|)



 dξ



− sinh σ(s)(d − x − ξ)

 dξ



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Rn (s)

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2σ(s) Q(s) +



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Fn (ξ, s) 0



cosh σ(s)d



−

 L





cosh σ(s)(L − |x − ξ|)

d

 Fn (ξ, s)



sinh σ(s) (L − x) cosh σ(s) d Q(s)





− cosh σ(s)(L − x − ξ)



sinh σ(s)(δ − |x − ξ|)



 dξ



− sinh σ(s)(δ − x − ξ)

 dξ

 R (s)

(9) for x ∈ Ωr . The static part, i.e. for s = 0, is given by K1 L Un (x, 0) = K1 L + F0

L 0

  ξx Fn (ξ, 0) 1[0,x] (ξ) ξ + 1[x,L] (ξ) x − dξ L   d Fn (ξ, 0) 1[0,x] (ξ) ξ + 1[x,d] (ξ) x

F0 + K1 L + F0 0 x Rn (0) + F0 + K1 L

(10)

for x ∈ Ωl , and K1 L Un (x, 0) = K1 L + F0

L 0

F0 + K1 L + F0

  ξx Fn (ξ, 0) 1[0,x] (ξ) ξ + 1[x,L] (ξ) x − dξ L   L Fn (ξ, 0) L − 1[d,x] (ξ) x − 1[x,L] (ξ) ξ dξ d

(L − x) − Rn (0) F0 + K1 L for x ∈ Ωr .

(11)

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Equations (8) and (9) share the same first term, which is, to a factor, the vibration of an healthy beam of length L fixed at both its boundaries. For the left part (respectively the right part), the second term is, also to a factor, the vibration of an healthy beam of length d (resp. L − d) with boundary condition fixed-free (resp. free-fixed). In both parts, the third and last term corresponds to the vibration induced by the inhomogeneous mixed boundary condition due to the damage. The same remarks can be made for the static solutions (10) and (11). Direct numerical simulation of Eqs. (8–11) requires: – that damping be present; if not, discretization of the frequency domain will cause leaking effects that disables the possibility to simulate transient response. – to compute the spatial integral, which will introduce numerical approximations. To alleviate those requirements, the next section presents a modal decomposition that can be used to solve (6).

4 4.1

Modal Decomposition Determination of Modal Shapes

We search for an orthonormal family of modes φp such that, ∀p ∈ N∗ , it respects ⎧  φp (x) + λ2 φp (x) = 0 for x ∈ Ωl ∪ Ωr ⎪ ⎪ ⎪ ⎪ ⎨ φp (0) = 0 Φ : φp (L) = 0 (12) ⎪  −  + ⎪ (d ) = φ (d ) φ ⎪ ⎪ ⎩ p  − p F0 φp (d ) − K1 φp (d+ ) + K1 φp (d− ) = 0 Depending whether the damage is positioned on an anti-node or not, the mode φp can be of one of two form. General Case: In this case, the damage is not positioned on an anti-node, i.e. φp (d) = 0, and therefore the modal shape φp has a discontinuity at x = d. Its shape is given by ⎧ for x ∈ Ωl , ⎨ A sin (λp x)   (13) φp (x) = cos (λd) ⎩ −A sin λp (L − x) for x ∈ Ω, cos (λδ) where the wavenumber λp is solution of the transcendental equation 0=

F0 sinc (λp d) sinc (λp δ) + . + K1 cos (λp d) cos (λp δ)

(14)

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Fig. 3. The first six modal shapes for a damaged beam (with L = 1 m, Fo = 2.1 · 107 N, d = 0.7 m and K1 = 0.7 · 109 N/m); the fifth one is a particular case, where the damage position corresponds to the fourth anti-node.

If we want the modal shape to have an unit norm, then the amplitude must be   2 2 cos (λp δ)   .   (15) A= 2 2 d cos (λp δ) 1 − sinc (2λp d) + δ cos (λd) 1 − sinc (2λp δ) Particular Case: In this case, the damage is exactly on an anti-node, i.e. φp (d) = 0, and the modal shape is continuous. This type of modal shape is quite rare, (q + 1/2) π (p + 1/2) π = . and appears only if there exists (p, q) ∈ N2 such that d δ Its shape is then given by   (p + 1/2) π x . (16) φp (x) = A sin d  2 For the modal shape to have an unit norm, the amplitude must be A = . L Figure 3 shows the first modal shapes for a beam with L = 1 m, Fo = 2.1 · 107 N, d = 0.7 m, K1 = 0.7 · 109 N/m. All modes are quite similar in shape to those of an healthy beam with fixed boundary conditions at both its extremities, except for the discontinuity at the damage position; the fifth mode, which is a particular case where the damage position corresponds exactly to the fourth anti-node, is equal to the corresponding healthy mode.

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Modal Solution

Once the modal decomposition for the damaged beam is computed, it is possible to solve (6) if the assumption that the solution Un can be decomposed on a modal basis is made. Because problem (6) contains one inhomogeneous boundary condition (i.e. F0 ∂x Un (d, s) − K1 Un (d+ , s) + K1 Un (d− , s) = Rn (s)), we also need to add a particular solution that takes it into account. Therefore the modal solution of problem (6) is given by Un (x, s) = h (x) Rn (s) +

+∞ 

φp (x) Un,p (s) ,

(17)

p=1

where h is a spatial shape with null second derivative that respects condition F0 ∂x h (d) − K1 h (d+ ) + K1 h (d− ) = 1, given by ⎧ x ⎪ for x ∈ Ωl , ⎨ F0 + K1 L h (x) = (18) (L − x) ⎪ ⎩− for x ∈ Ωr , F0 + K1 L and Un,p is the spectral response of the p-th mode of Un , given by the equation s2 Un,p (s)+

γs

γs Un,p (s)+λ2 c2L Un,p (s) = −c2L Gn , φp  (s)+h, φp  Rn (s)−Rn (s) , ρS ρS

(19) or equivalently the ordinary differential equation  γ  γ u˙ n,p (t)+λ2 c2L un,p (t) = −c2L gn , φp (t)+h, φp r˙n (t)− r¨n (t) , ρS ρS (20) where the notation a, b corresponds to the spatial scalar product between a and L b, i.e. a, b = 0 a(x)b(x)d x. The modal solution of (6) can thus be numerically simulated, for each order n, as follows: u ¨n,p (t)+

1. compute terms gn and rn from previous orders um , m < n; for n = 1, we have g1 (x, t) = f (x, t) and rn (t) = 0; 2. numerically solve (20) using a discretization method (Euler method, bilinear transform, first-order hold, etc.); 3. compute the solution using (17).

5

Simulation and Comparison with State-of-the-Art

In this section, we will compare numerical simulations of the two solutions of the damaged beam problem (2) (given in Sects. 3.3 and 4.2) with SDTools Matlab Toolbox [10], a state-of-the-art analysis and simulation toolbox for vibration which uses finite-elements method.

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Simulation Parameters

The base model is a steel beam of length L = 1 m, with a square section of surface 3 S = 1 cm2 , a Young modulus of E = 210.0 GPa, a density of ρ = 7850.0, kg/m , −1 −1 3 and a damping factor of γ = 5.0 · 10 kgm s . For the simulation, the propagation is supposed linear, i.e.  = 0 and β = 0. The damage is taken as a cubic spring, i.e. with a characteristic relation given by (21) K [x] = K1 x + K3 x3 , 3

3

where K1 = 0.7e · 109 N/m and K3 = 5.0 · 1027 N/m . It is placed at d = 0.7 m. The input force is taken as sine burst excitation, located at x0 = 0.3 m. It is comprised of three cycles at f0 = 100 kHz multiplied by a Hann window of unit amplitude, sampled at fs = 5 MHz. Output vibration is simulated for a duration of 1 ms. For both simulation methods presented in this paper, only the N = 15 first orders of the series are simulated. The analytical solution simulation uses a zero-padding of 50000 points to avoid leaking effects due to windowing. The modal solution simulation uses a number of 100 modes and a first-order hold as discretization method. 5.2

Simulation Results

Figure 4 shows the results for the three simulation. We can see that obtained results are qualitatively similar for all three simulations, with small differences in the damping of the vibrations. The damage acts as a nonlinear semi-reflecting barrier, which creates harmonic distortion (visible in the output spectra). Furthermore, we can quantitatively compare simulations by computing the RMS value of their difference, which gives: – a value of −14 dB between the analytical approach and the result given by SDTools; – a value of −13 dB between the modal approach and the result given by SDTools; – a value of −16 dB between the modal and analytical approach. Therefore, the simulations using both proposed approaches and through SDTools obtain qualitatively and quantitatively similar results, thus validating the approaches.

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6

Conclusion

In this study, we have shown how the Green-Volterra formalism can be used to find analytical solutions for the S0 mode nonlinear propagation and nonlinear damage interaction in a damaged beam. Furthermore, those solutions can be

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decomposed onto an appropriate modal basis for simulation purposes. Finally, we have shown through a simulation example that both proposed approach for simulations gave qualitatively and quantitatively similar results with a state-ofthe-art finite element method. Future research will focus on using the obtained analytical model to derive SHM tools for damage classification or quantification, as well as extending the proposed approach to other types of vibration, e.g. transverse A0 mode or other Lamb wave modes. Acknowledgements. This work has received funding from the European Union’s Horizon 2020 research and innovation program under the REMAP project (grant agreement number 769288).

References 1. Rytter, A.: Vibrational based inspection of civil engineering structures. Ph.D. thesis, Denmark (1993) 2. Worden, K., Farrar, C.R., Haywood, J., Todd, M.: A review of nonlinear dynamics applications to structural health monitoring. Struct. Control Health Monit. 15(4), 540–567 (2008) 3. R´ebillat, M., Hajrya, R., Mechbal, N.: Nonlinear structural damage detection based on cascade of Hammerstein models. Mech. Syst. Signal Process. 48(1–2), 247–259 (2014) 4. Ghrib, M., R´ebillat, M., des Roches, G.V., Mechbal, N.: Automatic damage type classification and severity quantification using signal based and nonlinear model based damage sensitive features. J. Process Control 83, 136–146 (2018) 5. Rugh, W.J.: Nonlinear System Theory. Johns Hopkins University Press, Baltimore (1981) 6. Boyd, S., Chua, L.O.: Fading memory and the problem of approximating nonlinear operators with Volterra series. IEEE Trans. Circ. Syst. 32(11), 1150–1161 (1985) 7. Li, H.X., Qi, C., Yu, Y.: A spatio-temporal Volterra modeling approach for a class of distributed industrial processes. J. Process Control 19(7), 1126–1142 (2009) 8. Roze, D., H´elie, T.: Introducing a Green-Volterra series formalism to solve weakly nonlinear boundary problems: application to Kirchhoff’s string. J. Sound Vib. 333(7), 2073–2086 (2014) 9. Broda, D., Staszewski, W., Martowicz, A., Uhl, T., Silberschmidt, V.: Modelling of nonlinear crack-wave interactions for damage detection based on ultrasound—A review. J. Sound Vib. 333(4), 1097–1118 (2014) 10. Balm`es, E.: SDTools, vibration software and consulting (2020). https://www. sdtools.com/

Damage Localisation by Residual Energy from Multiple-Input Finite Impulse Response Prognosis Benedikt Hofmeister(B) , Clemens Jonscher , Clemens H¨ ubler , and Raimund Rolfes Institut f¨ ur Statik und Dynamik, Leibniz University Hannover, Hanover, Germany [email protected]

Abstract. We present a method for damage detection and localisation based on multiple-input finite impulse responses. A validation is carried out using measurement data obtained for a girder mast structure. The damage localisation using output-only vibration measurement data of beam-like structures has been a research topic for a long time and many methods have been developed to tackle the problem. However, the identification of finite impulse response filters with multiple inputs has not yet been covered in great detail in the context of these SHM methods. To localise structural damage, first the healthy structure is dynamically excited and finite impulse filters are derived using acceleration sensor data. In this process, we use multiple adjacent sensors as an input to derive the impulse response on a local level in the girder mast structure. The derived filters are applied to obtain an estimation of the transient response for healthy as well as damaged states. Residual signal energies between measured and predicted data are calculated, which increase locally when structural damages occur, enabling the localisation. The outlined damage localisation method, which solely relies on finite impulse responses as an output-only model of the structure, yields promising results in experimental validation. Keywords: Damage localisation · Structural dynamics · Finite impulse response · Vibration estimation · Residual energy

1

Introduction

A central challenge in structural health monitoring is the detection and localisation of damages from sensor data. Particularly interesting approaches to this problem are output-only methods, which only rely on sensor data to detect changes in the structure. These methods can thus be applied with neither detailed knowledge about the mechanical parameters of the structure to be monitored nor any information about the exciting forces. In order to obtain a mathematical solution for this problem, complex mechanical interactions are often simplified and linear c The Author(s), under exclusive license to Springer Nature Switzerland AG 2021  P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 711–719, 2021. https://doi.org/10.1007/978-3-030-64908-1_66

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time invariant models are employed. This means that the monitored structure is assumed to operate in a linear elastic regime, which is reasonable for many civil engineering structures under nominal operating conditions. Structural changes are detected by comparing the ‘healthy’ behaviour, which is known from a reference measurement, to the observed behaviour when monitoring the structure. Using the monitoring measurement data, the damage localisation is carried out by extraction of damage sensitive features. Many authors proposed localisation methods in the past decades, using a variety of damage sensitive features and considering diverse environmental and operating conditions. Some of these localisation methods are based on global parameter estimation approaches, for example: – – – – –

Approaches based on the flexibility matrix [2] Localisation using modal parameters [6] Finite element model updating [3] Power of difference processes obtained using state estimators [9] Models based on vector autoregression methods [7].

Many authors successfully applied localisation approaches, which use transmissibility functions to describe the dynamic behaviour on a local level [5,8]. This approach, however, has some drawbacks, as discussed by Chesn´e and Deraemaeker [1]. Transmissibility functions are very sensitive to changes in the location of excitation sources. Another limitation is a mathematical restriction in the identification of multiple-input transmissibility functions, which is only possible, if multiple uncorrelated excitation sources are present [4]. Thus, usually only the single-input topology is used, i.e. the transmissibility from one sensor to another sensor is identified. The multiple-input finite input responses proposed in this paper overcome these limitations. By considering more than one sensor as an input, the selectivity increases, which enables the use of basic energy residuals to localise structural damages.

2

Theory

The method presented in this paper is based on the concept of transfer functions in a discrete time setting. Transfer functions provide a mapping from a transient signal x(z) to another transient signal y(z). This can be expressed graphically as a signal flow, where the transfer function T (z) acts as a digital filter.

x(z)

T (z)

y(z)

The finite impulse response filter corresponding to the transfer function shown above can be expressed as y[i] =

M  j=0

b[j] x[i − j],

(1)

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where M is the filter order and the coefficient vector b is comprised of M + 1 elements. The indices i and j denote the time step and the filter coefficients, respectively. This formulation implies that the finite impulse response filter ignores all samples outside the range [i − M, i]. In contrast, the transmissibility function corresponding to the same filter is y(s) = T (s)x(s),

(2)

where s is the Laplace variable, T (s) is the transmissibility function, x(s) is the spectrum of the measured signal and y(s) is the spectrum of the estimated spectrum. The transmissibility can in practice be computed from the frequency response of the system [8]. Finite impulse response and transmissibility functions express the same concept in this regard, i.e. providing a mathematical description of the transmission path between two measurement points. The difference is that the former is formulated in time domain and the latter in frequency domain. Since time-domain models are notoriously hard to interpret, an examination of the spectrum of identified filters is advisable. A single-input filter topology relies on the information of only one sensor to infer the vibrational state of the structure, making it inaccurate in practice. Using multiple inputs thus generally improves the quality of the prognosis obtained using transfer functions. The derivation of multiple-input transmissibility functions in the frequency domain has numerical restrictions though, since the frequency response matrices need to be invertible [4]. These restrictions do not apply to the time-domain identification presented in the following. We extend the finite impulse response filter topology to consider N input signals N  M  bk [j] xk [i − j], (3) y[i] = k=1 j=0

where k is the index corresponding to the input signal. To obtain finite impulse responses, we first formulate the convolution using matrix algebra Xkij = xk [i − j],

(4)

where Xk is the shift matrix of the signal xk (z). As a next step, an overdetermined system of equations can be established ⎛ ⎞ b1 ⎟   ⎜ ⎜ b2 ⎟ X1 X2 . . . XN · ⎜ . ⎟ = y, (5) ⎝ .. ⎠ bN and its approximate solution yields the coefficient vectors bk . For slender structures, it is straightforward to pick the adjacent sensors to estimate a measurement position in between. Figure 1 illustrates this concept for a simple beam structure using a biaxial sensor setup.

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1[

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Fig. 1. Schematic diagram of a beam structure with three measurement locations. The time series y[i] is estimated using the coefficient vectors b1 through b4 and the signals x1 through x4 obtained at adjacent measurement locations. Signals measured in the x-direction and y-direction are marked red and blue, respectively.

The impulse responses identified using Eq. 5 contain the structural dynamics on a local level and for the full spectrum. When structural changes due to damage, environmental or operating conditions occur, the vibration prognosis will thus no longer reflect the actual structural behaviour. We use residual energies to detect such changes with respect to the ‘healthy’ state. The residual  is therefore defined as the difference between the estimated vibration and the measured one N  M  bk [j] xk [i − j]. (6) [i] = y[i] − k=1 j=0

We calculate the residual energy E by accumulating the residuals for the whole time series to obtain a damage sensitive feature  2 E= ([i]) . (7) i

In this work, we focus on the damage sensitive feature itself, so we resort to simply using the maximum energy to localise the damage. We also assume that structural changes only occur due to damage, since the data was obtained from a laboratory structure. The effects of environmental and operating conditions are therefore not subject of this work. The reliability and accuracy of the proposed localisation approach can definitely be improved by application of more advanced classifiers in this regard.

3

Results

In this section, we present an experimental validation of the proposed damage localisation method. First, we introduce the structure, the damage mechanism and the measurement setup. Second, the coefficients of the finite impulse responses are derived and discussed. In a third step, we discuss the results obtained by means of residual energies.

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Experimental Setup

The experimental structure is a girder mast, which is situated in a laboratory workshop. It consists of three equal sections which are bolted together. The segments have a length of 3 m, resulting in a total height of 9 m. Each segment has three legs and consists of seven bracing levels as well as short connecting sections at the ends. A photograph of the structure is shown in Fig. 2. Ten measurement levels are each instrumented with biaxial IEPE accelerometers in the horizontal plane. The locations of the measurement levels are indicated in Fig. 3 as well as the position of a shaker mounted near the base of the mast. A white noise signal band-limited to 300 Hz is generated by a computer and fed into the shaker amplifier using a digital to analogue converter module. The measured sampling rate is 2560 Hz and all time series have a length of 600 s. On three levels of the structure, a reversible damage mechanism enables the disconnection of one of the bracings, which changes the structural stiffness locally. The corresponding positions are depicted in Fig. 3. Two time series were measured in the ‘healthy’ state, when all bracings were intact. For the third time series, the damage DAM1 was activated. The damage was then repaired and another time series was recorded in the repaired state.

z

y Fig. 2. Girder mast structure in the laboratory. Acceleration sensors are arranged in a biaxial setup along one of the three legs.

x

Fig. 3. Schematic figure of the measurement levels (ML), damage locations (DAM), and shaker position as well as definition of the global coordinate system.

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The same procedure was followed for DAM2 and DAM3, resulting in eight time series in total. Though the damage mechanism is mechanically reversible, the structural responses are not fully recovered every time. 3.2

Impulse Response Coefficients

Amplitude

We use the same scheme as shown in Fig. 1 to localise the structural damage. There are two sensors at each measurement level, so two residuals are calculated for each measurement level. The 16 sensors in measurement levels ML2 through ML9 each have four contributing filters, the measurement levels ML1 and ML10 have two thereof. Using Eq. 5, the filter coefficients are determined by computing approximate solutions. In total, 72 finite impulse responses of the order 2000 were derived to obtain the prognosis model for the local dynamics of the structure. As an example, the finite impulse response coefficients contributing to the prognosis of sensor 5y are shown in Fig. 4. The corresponding spectra of the contributing filters are shown in Fig. 5. As one might suspect for a sensor measuring the y-direction, contributions of the y-direction are in general higher than those of the x-direction. Yet, for some frequencies there are significant contributions from the x-direction, hence the orthogonal direction should not be omitted.

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Fig. 4. The first 400 coefficients of the finite impulse responses contributing to the prognosis of sensor 5y. These correspond to sensors from measurement levels ML4 and ML6 in both x and y-direction

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Fig. 5. Spectra of the four finite impulse response filters for the adjacent sensors contributing to the prognosis of sensor 5y. The lack of dynamic excitation 300 Hz leads to high noise in the identification.

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Residual Energies and Localisation

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To localise the structural damage, the residuals for the different damage states are calculated. We derive the finite impulse responses using the ‘healthy’ or ‘repaired’ time series measured directly before we introduced the damage. Thus, the filters were calculated three times, i.e. once for each of the three damage states. The damage was introduced to weaken only the x-direction of the structure, therefore residuals were expected to be highest in the x-direction for the damaged cases. To obtain an understanding of the stability of the residual energies, we analyse two separate time series for the ‘healthy’ state. The results are shown in Fig. 6. For the graphical presentation of the residuals, the two measured directions are evaluated separately. From these results we conclude that the variability of the residual energies is negligibly small from one measurement to the next.

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Fig. 6. Comparison of the two ‘healthy’ time series before introducing any damage. Residual energies are shown for x-direction (left panel) and y-direction (right panel).

Residuals are not zero in the healthy state because of effects, which are not adequately modelled using finite impulse responses. These include inaccurately derived filters, measurement noise, nonlinear dynamics, etc. Residuals for measurement level 1 are further elevated, because there is only one adjacent measurement level, which means that there are only two inputs for the impulse responses. Additionally, the measured acceleration signal is clipped at measurement levels 1 and 2. The clipping is due to an excessive amplitude of the shaker excitation and introduces a nonlinear effect into the time series. At measurement level 10, the residuals are not elevated, since it is near the free end of the structure. The three damage states were analysed in the same fashion. The results are presented in Fig. 7. The measurement levels, where the damage occurred, exhibit the highest residuals in x-direction. Damage 1 corresponds to measurement level 3, damage 2 to level 6 and damage 3 to level 9, as indicated by Fig. 3. As is typical for damage sensitive features, residual energies react to the structural damage at all positions. This ‘leakage’ is associated with changes in the global behaviour of the structure, which are overlaid with the local changes. These global changes lead to a misprediction of the structural dynamics by the impulse response filters, which in turn leads to an elevated residual energy. To a lesser extent, the residuals in y-direction also increase, even though the damage occurred in x-direction.

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Fig. 7. Comparison of the ‘healthy’ and ‘damaged’ time series for damage locations DAM1–3. Residual energies are shown for x-direction (left panel) and y-direction (right panel). The damage location is indicated by a red ellipse.

4

Discussion and Outlook

An advantage of the proposed method is its simplicity and the low number of parameters that have to be adjusted to obtain acceptable finite impulse responses. Energy residuals can be computed in real-time even on low-end computers, because the convolution can be implemented very efficiently using vector processing. This enables online monitoring and damage localisation. However, output-only methods are only capable of giving a first indication about the damage location and their usefulness is highly dependent on the density of the sensor network. Moreover, the interpretation of energy residuals is not trivial for real structures, due to the ‘leakage’ of global behaviour changes to residuals at positions far away from the damage location. This problem is common to most localisation techniques based on residual energies. To some extend, sophisticated classifiers can overcome this limitation and increase the selectivity. To pinpoint and also quantify damages indicated by output-only methods during online monitoring, model-based techniques are probably the best option. Changing environmental and operating conditions, like temperature changes and excitation spectra different from white noise, have to be considered as well. To this end, further experiments focusing on distributed dynamic excitation due to wind interaction are going to be carried out. Investigations on the sensitivity to changing locations and types of excitation sources are also planned.

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Acknowledgments. We greatly acknowledge the financial support of the Federal Ministry for Economic Affairs and Energy of Germany (research project Deutsche Forschungsplattform f¨ ur Windenergie, FKZ 0325936E).

References 1. Chesn´e, S., Deraemaeker, A.: Damage localization using transmissibility functions: a critical review. Mech. Syst. Signal Process. 38, 569–584 (2013) 2. Duan, Z., Yan, G., Ou, J., Spencer, B.: Damage localization in ambient vibration by constructing proportional flexibility matrix. J. Sound Vib. 284(1), 455–466 (2005) 3. Hofmeister, B., Bruns, M., Rolfes, R.: Finite element model updating using deterministic optimisation: a global pattern search approach. Eng. Struct. 195, 373–381 (2019) 4. Maia, N., Silva, J., Ribeiro, A.: The transmissibility concept in multi-degree-offreedom systems. Mech. Syst. Signal Process. 15(1), 129–137 (2001) 5. Manson, G., Worden, K., Allman, D.: Experimental validation of a structural health monitoring methodology: Part III. Damage location on an aircraft wing. J. Sound Vib. 259(2), 365–385 (2003) 6. Perera, R., Ruiz, A., Manzano, C.: An evolutionary multiobjective framework for structural damage localization and quantification. Eng. Struct. 29(10), 2540–2550 (2007) 7. Tsiapoki, S., H¨ ackell, M.W., Grießmann, T., Rolfes, R.: Damage and ice detection on wind turbine rotor blades using a three-tier modular structural health monitoring framework. Struct. Health Monit. 17(5), 1289–1312 (2018) 8. Weijtjens, W., Sitter, G.D., Devriendt, C., Guillaume, P.: Operational modal parameter estimation of MIMO systems using transmissibility functions. Automatica 50(2), 559–564 (2014) 9. Wernitz, S., Pache, D., Grießmann, T., Rolfes, R.: Damage localization with SP2E under changing conditions. In: Structural Health Monitoring 2019 (2019)

Towards an Industrial Deployment of PZT Based SHM Processes: A Dedicated Metamodel for Lamb Wave Propagation Hadrien Postorino(B) , Marc Rebillat, Eric Monteiro, and Nazih Mechbal Laboratoire PIMM, Arts et Metiers Institute of Technology, CNRS, CNAM, HESAM Universite, 151 boulevard de l’Hopital, 75013 Paris, France [email protected]

Abstract. Numerical simulations of Structural Health Monitoring processes based on wave propagation can be very costly in terms of computation time, especially for complex aeronautic composite structures, and therefore strongly limits the deployment of industrial applications. Metamodels build a relatively simple relationship between inputs and outputs from a set of data and thus can overcome that difficulty. A metamodel based on radial basis functions interpolation is build in order to predict a Lamb Wave measurement on a damaged composite plate equipped by a network of 3 piezoelectric elements. The input parameters describe the position of the damage. This surrogate model is used to predict the measured signals for new damage configurations with a limited computational cost. Moreover, this metamodel is used in a reverse way to solve the inverse problem. A swarm particle optimisation algorithm tries to find the position of a damage from a set of simulated signals. This approach allows us to identify correctly the damage localisation for an unknown configuration, providing therefore a new method for damage localization.

Keywords: SHM problem

1

· Lamb waves propagation · Metamodel · Inverse

Introduction

In the past decades, composite materials have become omnipresent in the aeronautical, automotive, space and nautical industries [6]. They outperform metallic materials in terms of mechanical and chemical resistance. They allow for the design of lightweight structures with unique mechanical and geometric characteristics. They offer the possibility of reducing the weight of aircraft and increasing their lifespan. However composite structures are also subject to damages caused by fatigue, defect during manufacturing or impact incidents. These damages can typically take the form of cracks, holes, delimitation or discontinuity. Nondestructive testing still plays a major role in the industry to ensure the integrity c The Author(s), under exclusive license to Springer Nature Switzerland AG 2021  P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 720–731, 2021. https://doi.org/10.1007/978-3-030-64908-1_67

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of a structure but needs the interruption of service of the plane for regular human visual inspections. Thus, the creation of smart structures able to monitor and autonomously determine their structural health has become an important subject of research and innovation over the last decades [4]. These new control and monitoring methods are called Structural Health Monitoring (SHM). SHM has the main objective to determine the structural health in real time. It will then be possible to adapt the maintenance strategy to the actual state of the structure, allowing to optimize the costs and to guarantee more safety. SHM systems should ideally meet the following requirements [13] : low cost, continuous evaluation, sensitive to small and different types of damage, insensitive to operating conditions, noise and environmental changes. In order to evaluate the maturation of SHM techniques, four levels are distinguished: (i) Damage Detection, (ii) Damage localisation, (iii) Damage quantification and (iv) Damage characterization. The most advanced techniques in SHM reach level 2 with satisfaction. On the other hand, level 3 and 4 are still active research subjects. These techniques can be grouped into three categories: vibration monitoring, deformation monitoring and wave propagation monitoring. This paper will focus on Lamb wave propagation monitoring. Lamb waves have the particularity to propagate in plates with low attenuation. When the wave propagates through a damage, it is modified by the damage. By studying and analyzing the wave propagation in the structure, it is then possible to determine the structural state of the structure. The generation and measurement of Lamb waves is done using a network of Piezoelectric Transducer (PZT) distributed over the entire structure under study. These PZT act alternately in actuator mode and in sensor mode. The data is then collected and processed to determine the state of the structure. For this purpose, the recorded signals of unknown state are compared with the previously recorded signals of a healthy state. Different values, called Damage Index, allow the comparison of the signals. The SHM has been subject to a significant amount of works over the past several decades [4]. Applications already exist in civil engineering for the monitoring of buildings, civil structures, roads and railways. In the aeronautics industry, the industrial deployment of research advances has been slow to take place. Various explanations can be given, but one of the main issue is the difficulty to evaluate correctly the performance of SHM systems. The evaluation of SHM systems passed by the computation quantity of interest such as the Probability Of Detection or Probability Of Localisation [14]. This involves to collect a huge amount of data on structures with a lot of damage configurations in order to make statistical evaluation. A fully experimental approach is thus difficult and costly: Moriot [12] robustly evaluated their SHM processes based on experimental data with a plate equipped by piezoelectric transducers. An evaluation based on numerical data appears to be more feasible. However, to simulate SHM processes is not a trivial task because of the complexity of the aeronautic structures and the large diversity of damage. Numerical simulations

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can be costly in terms of computational time, but are necessary in order to evaluate the processes and determine their effectiveness. The creation of a metamodel (or surrogate model) able to predict the effect of a damage on a structure would considerably reduce the computation time and allow to test SHM processes on a large number of damage configurations. Building a metamodel means looking for a relatively simple relationship between inputs and outputs. Many methods of metamodelisation exists for a very large variety of applications. In the context of Lamb waves SHM, Borate et al. [3] recently used Proper Orthognal Decomposition and Artificial Neural Network in order to predict the position of a damage in a numerical plate and in a beam based on the measurement of the displacement and acceleration. An inverse use of the metamodel is also possible in order to find back the parameters that lead to a result of a simulation. The use of metamodels to solve an inverse problem has been implemented by Zhang [15] to find the characteristics of a damage from the measurement of eigenfrequencies. This numerical and experimental study shows that the use of a metamodel combined with a genetic algorithm obtains better results than a neural network to identify the parameters of a damage. Joy [9] has also shown that the use of a metamodel for inverse problem resolution is more efficient than a direct neural network. In this paper, a numerical model of a simple aeronautic structure with one damage is proposed. The parameters describing the position (xdam , ydam ) of the dommage are used to generate a database with different damage configuration. Then a metamodel based on Radial Basis Function (RBF) interpolation is build in order to strongly reduce the computation time of the simulations for new damage positions. This surrogate model can be used to predict and generate a high quantity of data. It is then used to solve the inverse problem and find the position of a damage from SHM measurements. That lead to a new strategy for damage localisation.

2

Numerical Model

The finite element simulation is computed with the SDT software developed by SDTools [2]. The structure under study is a 300 × 300 × 2.4 mm plate in a composite material for the aeronautic industry. The plate has 8 plis [0/45/0/45/45/0/45/0]. The mechanical properties can be seen in the Table 1. The plate is modeled by shell elements with a linear elastic orthotropic behavior. The damage is modeled by a reduction by half of all theYoung and Shear moduli for all layers on a circle with 10 mm diameter. The damping introduced in the model is proportional to the stiffness matrix with a coefficient β = 1.5e−8. Free mechanical boundary conditions are chosen. In order to monitor its structural health, the plate is equipped by 3 PZT with a diameter of 25 mm. Each PZT can be used as actuator or sensor. The excitation signal is a burst with 5 cycles at 150 kHz for the central frequency (Fig. 1). The plate is meshed by a regular grid. The excitation frequency is fixed at 150 kHz, which corresponds, according to the dispersion curves, to a wavelength λ ≈ 20 mm for this material. The dispersion

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curve for lamb wave can be seen Fig. 2. The mesh size must be less than 10% of the wavelength, that is to say less than 2 mm. Table 1. Mechanical properties of the composite material Name E1

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Fig. 2. Dispersion curve for the material under study

Metamodel

A metamodel can be seen as a black box which for any input vector x associates a prediction Yˆ , such as Yˆ = M(x). The application M is computed during a training phase from a set of previously computed input and output. Let p be the number of inputs parameters and q the number of outputs. The set of n inputs and outputs can be assembled respectively in a matrix X and Y . The terms Xji and Yji correspond to the value taken by the j -th parameter during the i-th simulation. The two matrices X, Y contain the data used to train the metamodel. The data (Xi , Yi ) associated to the i -th simulation are called a Snapshot or sampling point. The snapshots are computed beforehand from a numerical model, or measured from experimental data but can also be a mix of numerical and experimental data within the framework of a hybrid model [5].

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⎛

X11 ⎜ .. ⎜ . ⎜ 1 X=⎜ ⎜Xi ⎜ .. ⎝ . Xp1

⎞ ⎞ ⎛ 1 Y1 · · · Y1n · · · X1n ⎜ .. .. .. ⎟ . ⎟ ⎜ . · · · .. ⎟  . . ⎟ ⎟ ⎟ ⎜ x · · · x · · · x dam1 dami damn n⎟ ⎜ 1 · · · Xin ⎟ ⎟ = ydam1 · · · ydami · · · ydamn and Y = ⎜Yi · · · Yi ⎟ ⎜ .. .. .. ⎟ . ⎟ ⎝ . · · · .. ⎠ . . ⎠ · · · Xpn Yq1 · · · Yqn

A surrogate model is build in order to predict a Lamb wave SHM control process (Fig. 3) based on the numerical model of the structure previously described. One damage is included on the structure. Two parameters (xdam , ydam ) describing the damage position are considered. So the inputs are X = (xdam , ydam ) with xdam the horizontal position of the damage and ydam the vertical position of the damage. The Y output is the measured signal on a sensor for one actuator. Each way of actuator/sensor are considered independently: it is necessary to build one metamodel for each way of actuator/sensor.

Fig. 3. Input/output of the metamodel for actuator i to sensor j

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Fig. 4. DOE for plate structure

Sampling

The construction of a metamodel requires beforehand the computation of a database X, Y resulting from numerical simulations or experimental data. The choice of input variables X for the training is not trivial because it strongly influences the precision and the speed of the metamodel. This choice of parameters X is called Design Of Experiment, or Sampling within the framework of metamodels. Many DOE exist: random sampling, Latin hypercube Sampling [11], full grid sampling, scattered grid sampling, etc. In this work, the sampling strategy is based on a randomly perturbed regular grid [1] and can be seen Fig. 4. 196 damage configurations are computed with 3 different actuators. The database regroups therefore a total of 588 simulations.

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Signal Compression

The choice of the data representation is significant to obtain an efficient metamodel but also to facilitate its training. The data representation must be both parsimonious and, ideally, also have a physical meaning. The question is in which format express the output matrix Y of the metamodel. The Singular Value Decomposition (SVD) offers the possibility to compress data sparsingly and easily. The SVD gives a matrix where each column correspond to a basis vector. The basis is truncated according to the following criteria:

nr λi

i=1 ≥ 98% (1) ns i=1 λi where ns is the number of snapshots, nr the number of modes in the reduced basis and {λi }n1 are the sorted eigenvalues [7]. For this criteria, the reduced basis counts 16 vectors (Fig. 5). The output signals are projected on this basis.

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Different metamodeling methods have been tested and evaluated. The method that got the best results is the Radial Basis Function interpolation (RBF). RBF were deployed by Hardy [8] for the interpolation of multi-variate scattered data. Radial basis functions have the particularity to decrease monotonically with distance from a central point. In that section, it is considered that the metamodel is build only for one output (q = 1). For multiple outputs metamodels, each input is treated independently. The RBF model computes a linear combination of radial basis function ϕ centered on each Xi sampling point. Each center Xi is associated with a weight ωi such that: ∀x ∈ Rp , Yˆ (x) =

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The coefficients ωi can be computed by applying the interpolation condition : ∀i ∈ [1 : n], Yi =

n 

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(3)

j=1

resulting a linear system of equations: Y = ϕω

(4)

where Y is the vector of values of the function at the sampling points, ω is the vector of weights of the radial basis function, and the matrix ϕ is also known as the Gram matrix: ⎞ ⎛ ϕ( X1 − X1 ) · · · ϕ( Xn − X1 ) ⎟ ⎜ .. .. .. ϕ=⎝ (5) ⎠ . . . ϕ( X1 − Xn )) · · · ϕ( Xn − Xn ) The weights ω are then computing by inverting the matrix ϕ or using a QR decomposition for large matrices. The main parameters for RBF metamodels are the choice of the kernel function and the value of the kernel width defined by σ. In the presented results, an Inverse MultiQuadric kernel function ϕ(r, σ) = √ 1 r 1+ σ

is used with a width of 0.06. 3.4

Metamodel Evaluation

Amoung the 196 snapshots from the simulations, 75% are used for training and 25% are kept for validation. The error between the predicted signal Yˆ and the validation signal Yˆ is computed with a FFT based implementation of the maximum of the correlation. This error is also a Damage Index used for damage detection. ⎞

⎛ IFFT FFT(Yˆ )FFT(Y ) ⎠  (6) Error = 1 − max ⎝ EYˆ EY Here the FFT is the Fast Fourrier Transform, IFFT the Inverse Fast Fourier Transform, E the mean value, Yˆ the predicted signal and Y the reference signal. The results obtained by this surrogate model are presented in the Figs. 6, 7, 8 and 9. Figures 6 and 7 compare the predicted and simulated signals with minimum and maximum error respectively at the sensor 2 with the actuator 1. There is a good match between the signals, indicating that the metamodel correctly predicts the effect of a damage. The Fig. 9 shows the evolution of the error with the distance to the nearest training point.

A Dedicated Metamodel for Lamb Wave Propagation Based SHM Error min=0.003 X=0.1458 Y=0.13008

0.05 0.04

Error max = 0.475 X=0.3157 Y=0.92462

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Fig. 7. Comparison of predicted/ simulated signal with maximum error for actuator 1 to sensor 2

Inverse Problem Resolution

Metamodels allow to predict very quickly the results of a long simulation. Thus, a surrogate models can be used to predict signals on a large number of damage configurations. An inverse use of the metamodel is possible in order to find back the parameters that lead to a result of a simulation with the help of an optimisation algorithm. The surrogate model is used to find the (xdam , ydam ) position of a damage from a set of simulated signals. The signals come from the validation database, they have not been used to train the metamodel. A swarm particle minimization algorithm [10] tries to minimize the global error. The global error here is the sum of the cross correlation based error (Eq. 6) for 0.5 0.45 0.4 0.35

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Fig. 8. Error histogram for actuator 1 to sensor 2

Fig. 9. Error versus distance to the nearest training point for the metamodel for actuator 1 to sensor 2

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Fig. 12. Histogram of the error distance

Fig. 13. Damage position y estimation

each actuator/sensor configuration between the signals predicted by the metamodel and the signals to be found (Eq. 7). Global Error =

3 3  

Errori,j

(7)

i=1 i=j,j=1

where Errori,j is the error between the predicted and simulated signal at the sensor j with the actuator i. The optimisation process can be seen Fig. 14. This method has been tested on 30 points that don’t belong to the training set. The results are shown in Figs. 10, 11, 12 and 13. In the Fig. 10, the predicted position appears in red while the actual damage position is displayed in blue. The optimisation algorithm reached the convergence for all the test points. This method gives promising results but some points remain far from the actual position of

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the damage (points 1, 2, 8, 14 and 31). The reasons for these discrepancies are being investigated.

Fig. 14. Block Diagram for the inverse problem resolution with particle swarm optimisation

5

Conclusion

The previously described surrogate model allows to quickly predict the effect of a damage on the structure. It could be used to predict a large amount of data in order to evaluate statistically the SHM algorithms or to generate a database for other machine learning approach in SHM. The resolution of inverse problem based on a surrogate model gives promising results for damage localisation and must be tested with noisy and experimental data. Other parameters - such as the size, the severity, the thickness - need to be integrated into the damage model in order to gain realism. Moreother, the damage model used in this work is probably not the most realistic. It will be necessary to study other damage models and fit numerical results with measurements carried out on a real plate. The inverse

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problem method should be extend to a metamodel with more parameters such as size, severity or shape of the dommage. That could lead to an efficient strategy to monitor structural health. Acknowledgement. This work was supported by the French Government via the program Fonds Unique Interminist´eriel (project Monarque).

References 1. Bachoc, F.: Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes. http://arxiv.org/abs/1301.4321 2. Balmes, E., Deraemaeker, A.: Modeling structures with piezoelectric materials. Theory and SDT tutorial. SDTools, Paris, France, September 2013–2020. http:// www.sdtools.com/help/piezo.pdf 3. Borate, P., Wang, G., Wang, Y.: Data-driven structural health monitoring approach using guided lamb wave responses. 33(4), 04020033. https://doi.org/10. 1061/(ASCE)AS.1943-5525.0001145 4. Cawley, P.: Structural health monitoring: closing the gap between research and industrial deployment. 17(5), 1225–1244. https://doi.org/10.1177/1475921717750047, http://journals.sagepub.com/doi/10.1177/1475921717750047 5. Chinesta, F., Cueto, E., Abisset-Chavanne, E., Duval, J.L., Khaldi, F.E.: Virtual, digital and hybrid twins: a new paradigm in data-based engineering and engineered data . https://doi.org/10.1007/s11831-018-9301-4 6. Giurgiutiu, V.: Structural Health Monitoring of Aerospace Composites. Elsevier, Amsterdam (2015) 7. Guo, M., Hesthaven, J.S.: Data-driven reduced order modeling for time-dependent problems. 345, 75–99. https://doi.org/10.1016/j.cma.2018.10.029, http://www. sciencedirect.com/science/article/pii/S0045782518305334 8. Hardy, R.L.: Multiquadric equations of topography and other irregular surfaces. 76(8), 1905–1915. https://doi.org/10.1029/JB076i008p01905, http://doi. wiley.com/10.1029/JB076i008p01905 9. Joy, E.J., Menon, A.S., Biju, N.: Implementation of Kriging surrogate models for delamination detection in composite structures. 27(6), 096369351802700. https:// doi.org/10.1177/096369351802700604, http://journals.sagepub.com/doi/10.1177/ 096369351802700604 10. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of ICNN 1995 - International Conference on Neural Networks. vol. 4, pp. 1942–1948 (1995) 11. Kleijnen, J.P.: Kriging metamodeling in simulation: a review. 192(3), 707– 716. https://doi.org/10.1016/j.ejor.2007.10.013, https://linkinghub.elsevier.com/ retrieve/pii/S0377221707010090 12. Moriot, J., Quaegebeur, N., Le Duff, A., Masson, P.: A model-based approach for statistical assessment of detection and localization performance of guided wave-based imaging techniques. 17(6), 1460–1472. https://doi.org/10.1177/ 1475921717744679, http://journals.sagepub.com/doi/10.1177/1475921717744679 13. Ostachowicz, W., Soman, R., Malinowski, P.: Optimization of sensor placement for structural health monitoring: a review. 18(3), 963–988. https://doi.org/10.1177/ 1475921719825601, http://journals.sagepub.com/doi/10.1177/1475921719825601

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14. Schubert Kabban, C.M., Greenwell, B.M., DeSimio, M.P., Derriso, M.M.: The probability of detection for structural health monitoring systems: repeated measures data. 14(3), 252–264. https://doi.org/10.1177/1475921714566530, https:// doi.org/10.1177/1475921714566530 15. Zhang, Z., Pan, J., Luo, W., Ramakrishnan, K.R., Singh, H.K.: Vibration-based delamination detection in curved composite plates. 119, 261–274. https://doi. org/10.1016/j.compositesa.2019.02.002, https://linkinghub.elsevier.com/retrieve/ pii/S1359835X19300430

Damage Detection in Tensegrity Using Interacting Particle-Ensemble Kalman Filter Neha Aswal1(B) , Subhamoy Sen1 , and Laurent Mevel2 1

Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, India [email protected], [email protected] 2 Univ. Gustave Eiffel, Inria, Cosys-SII, I4S, Campus de Beaulieu, Bouguenais, France [email protected] Abstract. Tensegrity structures form a special class of truss with dedicated cables and bars, that take tension and compression, respectively. To ensure equilibrium, the tensegrity members are required to be prestressed. Over prolonged usage, the cables may lose their prestress while bars may buckle, affecting the structural stiffness as well as its dynamic properties. The stiffness of tensegrities also vary with the load even in the absence of damage. This can potentially mask the effect of damage leading to a false impression of tensegrity health. This poses a major challenge in tensegrity health monitoring especially when the load is stochastic and unknown. Present study develops a vibration based output-only time-domain approach for monitoring the health of any tensegrity in the presence of uncertainties due to ambient force and measurement noise. An Interacting Particle Ensemble Kalman Filter (IPEnKF) has been used that can efficiently monitor tensegrity health from contaminated response data. IPEnKF combines a bank of Ensemble Kalman Filters to estimate response states while running within a Particle Filter envelop that estimates a set of location based health parameters. Further to make damage detection cheaper, strain responses are used as measurements. The efficiency of the proposed methodology has been demonstrated using numerical experiments performed on a simplex tensegrity. Keywords: Tensegrity · Structural Health Monitoring Particle Ensemble Kalman Filter · Damage detection

1

· Interacting

Introduction

Coined by Buckminster Fuller, the term tensegrity is a combination of the words - tension and integrity. As the name suggests, these structures derive their integrity from the prestress present in their members. From being introduced as a simple yet elegant piece of art by Snelson to being utilised in various complex and state of the art engineering structures like masts, stadium roofs, bridges, space c The Author(s), under exclusive license to Springer Nature Switzerland AG 2021  P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 732–741, 2021. https://doi.org/10.1007/978-3-030-64908-1_68

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and aerospace structures, tensegrity has come a long way in less than a century. Tensegrities are light-weight and help creating large column-free spaces. Many researchers have developed various design methodologies for complex tensegrities that are statically stable and can be constructed into reality. Tensegrities are selfstiffening structures. They can modify their stiffnesses through morphing their shape in order to carry any external load. Consequently, the vibrational response of the structure [1] gets affected by the external loading. It should therefore be noted that, stiffness alteration due to member prestress modification induced by force variability does not imply a damage in the structure. Hence, to identify a possible structural anomaly in tensegrity, it is important to have an Structural Health Monitoring (SHM) approach that takes the inherent nature of tensegrity [2] into account, yet very less literature is available on this. Bhalla et al. [3] successfully assessed the damage existing in tensegrity using dynamic strain measurements. Sychterz and Smith [4] compared three methods to detect damage in tensegrity, namely, frequency analysis, error-domain model falsification (EDMF) using node position measurement and moving-window principal component analysis (MWPCA) using strain measurements. It was observed that the natural frequencies and the mode shapes cannot be used to detect and localize the damage in a tensegrity. The complexities involved with tensegrity mode shapes do not support damage identification. EDMF tends to become costly when tracking positions at submillimeter resolution and the results are sensitive to the amount of ambient uncertainty. MWPCA has an advantage as it uses inexpensive strain gauges and is efficient with noisy signal with high signal to noise ratio (SNR) but fails at low SNR levels. Evidently, most of the works pertaining to tensegrity health monitoring is defined for deterministic scenarios. Nevertheless, for a real one, uncertainties arise during modelling error, ambient forcing and noise in the measurement which cannot be accounted for in a deterministic approach. In order to propose a practical SHM approach aimed to monitor real life tensegrities, it is necessary to incorporate the effects of uncertainties originating from unavoidable model inaccuracies, sensor noises and unknown external disturbances. Bayesian filtering has proved its efficiency in detecting damage in structures in presence of uncertainties. Bayesian filtering approaches define the structural dynamics using a set of unobserved variables-termed as “states”. The state dynamics and their impact on the measured responses are further defined using two separate probabilistic models, namely, process and measurement models/equations which individually account for uncertainties arising from ambient forcing and sensor noises. The inherent self-stiffening property of tensegrities [2] can be modelled by considering the geometric non-linearity in the dynamic model. This physical space dynamic model subjected to a stochastic input forcing is further transformed into a discrete time state space model to facilitate the estimation of the system states. A set of location based health parameters, θ k , to monitor the tensegrity health in terms of stiffness deterioration, is further added to the state definition as parameter states alongside the regular system states.

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Evidently, the process equation is non-linear. In addition, the mapping of the mentioned health parameters to the corresponding measured responses is also non-linear. Handling these non-linearities simultaneously poses a major challenge in tensegrity SHM. Using an interacting filtering technique can be a reliable option [5] for such system health estimation problems. This paper attempts to employ an Interacting Particle Ensemble Kalman Filtering (IPEnKF) strategy to estimate health of tensegrity in presence of process and measurement uncertainties. The major benefit with this approach is that the computational efficiency can easily be enhanced by exploiting the flexibility of parallelization of the complete computation, allowing to target a prompt detection of damage.

2

Geometric Non-linear Finite Element Model

Non-linearity in a structure may arise due to geometric (large deformations, etc.), material (plasticity, etc.) or boundary (contact) non-linearity. Geometric nonlinearity is only considered in this study since strain-displacement relation, in a tensegrity, is prominently non-linear. Since tensegrity can typically be classified as a special case of truss, its finite element model (FEM) can be considered with a typical bar element defined with natural discretization [6] (Fig. 1).

Fig. 1. LCS and GCS for bar element type

The transformation from global coordinate system (GCS) to local coordinate system (LCS) is performed using the transformation matrix, T as, qlk = Tqk

(1)

 0 0 0 cosθx cosθy cosθz , qlk = {q1l q2l }Tk and 0 0 0 cosθx cosθy cosθz qk = {q1 q2 q3 q4 q5 q6 }Tk . Subscript k denotes the time step at which the stiffness is being defined. The deformation at any point in the element can 

with, T =

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further be defined using its nodal displacements and shape functions N1 and N2 as, (2) u∗k = [N1 N2 ]qlk where N1 = (1 − r)/2 and N2 = (1 + r)/2 are the shape functions defined in the natural coordinate system with r being the natural variable defined within the range −1 ≤ r ≤ 1. The strain field can further be obtained by differentiating the displacement field including second order expansion as, (e)

εk =

1 ∂u∗k + ∂x 2



∂u∗k ∂x

2 (3)

which leads to the following expansion including the linear and non-linear parts of the strain as, (4) εk = {BL qlk }linear + {BN L (qlk )qlk }non−linear     T ∂N1 /∂x  ∂N1 ∂N2  1 ∂N2 and BN L (qlk ) = 12 qlk are linear where BL = ∂N ∂x ∂x ∂x ∂x ∂N2 /∂x and non-linear strain-displacement matrices, respectively. Employing the principle of virtual work, the element stiffness matrix can be obtained by equating the work done by the internal forces to the virtual work done by the external forces.  (e) (e) (e) εk σk dV = δqTk Fk (5) (e)

V (e)

(e)

with σk being the member stress that can be obtained from the constitutive (e) (e) relation as σk = E(e) εk with E(e) being the constitutive matrix. With this, Eq. (5) can be expanded as,  (e) δqk T TT BTk E(e) Bk Tδqk dV = δqTk Fk (6) V (e)

with Bk = BL + BN L (qlk ). Imposing the non-trivial solution condition, δqk = 0 (e) (e) and further comparing with Fk = Kk δqk , the element stiffness matrix in the natural coordinate system can be obtained as,  1 l(e) (e) dr (7) TT BTk Bk T Kk = E(e) A(e) 2 −1 assuming a uniform cross section A(e) over the entire length l(e) of the element e. The Gauss-Quadrature method has further been applied to find the numerical integration for the above integral (ng = 1). Assembling all the element stiffness matrices and applying the natural boundary conditions, one can get the global stiffness matrix Kk . Similarly, the mass matrix M can be obtained by following the consistent mass matrix assumption.

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Non-linear Response from Newmark-Beta

Due to its superior accuracy, Newmark-beta is one of the popular methods to find the response of the non-linear systems. The method solves an incremental equilibrium equation (see Eq. (8)) to find non-linear structural response variables, ¨ k , q˙ k and qk , of the following governing differential equation, i.e., q MΔ¨ qk + Ck (qk )Δq˙ k + Kk (qk )Δqk = ΔPk

(8)

¨ k(n×1) , q˙ k(n×1) and qk(n×1) are the acceleration, velocity and displacement where, q responses, respectively and the Δ operator signifies the corresponding increment over each time step. M(n×n) is the time invariant global mass and Ck(n×n) and Kk(n×n) are the time dependent damping and stiffness matrices of the structure, respectively. The time dependence of Kk originates from its dependence on the displacement response qk . With Rayleigh damping assumption, Ck being a function of Kk is also time dependent. Pk(n×1) is the external force acting on the structure. Clearly, the above dynamics is an implicit equation which requires an iterative solution at each step. However, in the context of tensegrity SHM, the same equation can be redefined using an explicit formulation with Newmark-beta explicit integration scheme without losing much on the precision yet achieving promptness in detection. Newmark-beta is a well established method and for the sake of brevity, it is not discussed here. Details of this method can be found in [7]. The method shows an unconditional stability for γ = 0.5 and β = 0.25 (average constant acceleration assumption), hence these values are utilised in this study.

3

State Space Formulation for System Dynamics

Bayesian filtering employs a process equation to define the system dynamics in terms of dynamics of a set of unobserved variable, named as states. To estimate the time varying nature of the system due to damage, a set of location based health parameters, θ k , are additionally defined as parameter states. These health parameters monitor the residual elasticity after damage within a range of [0, 1] in which 0 and 1 mean complete and no damage, respectively. While the system states are estimated using a bank of EnKF (Ensemble Kalman Filter), the parameter states are estimated through an envelop PF (Particle Filter). Within EnKF, the system dynamics is defined with displacement, velocity and ¨ k }T . The preacceleration responses in the state vector, i.e. Xk = {qk q˙ k q viously detailed non-linear FEM of tensegrity is further employed to propagate these system states in time. Prior to this, the tensegrity stiffness needs to be recalibrated considering the current nodal displacement that causes a change in the prestress. Integrated using the Guass-Quadrature method, Eq. (7) is discretized to find the discrete elemental stiffness matrix with Bk−1 re-calibrated as Bk using the current nodal displacements qk−1 . All the elemental stiffness matrices are further assembled to obtained the global stiffness matrix Kk . Next, the system states are forwarded in time using the Newmark-beta integration scheme.

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Xk = f (Xk−1 , Kk , M, dt, Pk ) + vk

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(9)

where f denotes the intrinsic calculations involved in Newark-beta integration scheme. dt denotes the time step for which the simulation is performed. Pk is the stochastic ambient force acting on the structure modelled as a white Gaussian 1 noise (WGN) of distribution N(0, QP k ) . The process noise vk accounts for the unavoidable inaccuracies in the prediction model f (•) and can be modelled as WGN of distribution N(0, Qk ). Next, the unobserved response states are mapped to the corresponding strain fields in several members using the non-linear strain measurement mapping equation. The dependence of the strain-displacement matrix Bk on the displacement qk can be demonstrated using the notation B(Xk ) since qk is a subset of Xk . The measurement equation can then be obtained from Eq. (4) by incorporating the partial measurement information and the sensor noises as, yk = HB(Xk )TXk + wk

(10)

where H is the selection matrix that defines which of the member strains are measured. wk accounts for measurement noises arising from the sensors modeled using WGN model of distribution N(0, Rk ).

4

System Estimation Using IPEnKF Algorithm

The system states are estimated using an IPEnKF algorithm which is a modification of the Interacting Particle-Kalman Filter (IPKF) algorithm [8]. With IPEnKF, the response states are estimated using a nested EnKF instead of KF to enable handling the non-linear systems, while an enveloping PF estimates the parameter θ k . All of the filtering steps are briefly described in the following. The details can be found in the article [8]. 4.1

Envelop Parameter Filter - PF

In order to avoid an explicit analytical integration over the entire parameter space, θ k , a particle approximation of this integration is approached with PF that propagates the parametric uncertainty through a cloud of Np independent N particles Ξ k = [ξ 1k , ξ 2k , · · · , ξ k p ]. At each time step, the particle distribution gets updated depending on their likelihood against measured data and thus no assumption is needed on their distribution apriori. Within the envelop PF, the particle representations of parameter estimates evolve assuming a Gaussian perturbation around the current estimate ξ jk−1 as, ξ jk = αξ jk−1 + N(δξ k ; σ ξk )

1

A + BN(μ; σ) means A + Bz where z follows N(μ; σ).

(11)

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where a Gaussian blurring is performed on ξ jk−1 with a shift δξ k = (1 − α)ξ¯k−1 and a spread of σ ξk 1 . α is a hyper-parameter that controls the turbulence in the estimation. 4.2

Nested State Filter - EnKF

In the nested EnKF, Ne sets of state ensembles for each j th parameter particle are propagated through the system state propagation model (see Eq. (9)). However, since the tensegrities are functions of nodal displacements, stiffness matrix has to be modified based on the current estimate of nodal displacement responses i,j th particle qi,j k−1|k−1 which is a subset of the state estimate Xk−1|k−1 pertinent to j th and i ensemble. Equation (7) can be employed and can be expressed as, j i,j Ki,j k|k−1 = m(ξ k−1 , Xk−1|k−1 )

(12)

where m(•) is the stiffness calibration function detailed in Eq. (7). With the i,j modified stiffness matrix Ki,j k|k−1 and a realization for the ambient forcing, Pk , drawn from a known statistic (N(0, QP k ) as mentioned in Sect. 3), the prior state are propagated to the next time step as Xi,j estimates Xi,j k−1|k−1 k|k−1 , i,j i,j i,j i,j Xi,j k|k−1 = f (Xk−1|k−1 , Kk|k−1 , M, dt, Pk ) + vk

(13)

The measurement function described in Eq. (10) is further employed to map i,j each of the ensembles to the corresponding measurement prediction, yk|k−1

from which innovation, i,j k|k−1 , for each ensemble, can be obtained from the corresponding real measurement yk . Next, the ensemble mean estimates for the j ) are obtained propagated states (Xjk|k−1 ) and predicted measurements (yk|k−1 as means of corresponding entities for all ensembles. Cross-covariance between state and measurement prediction Ckj,XY and the measurement prediction covariance Ckj,Y Y can further be computed following [9]. The innovation error covariance, Sjk and EnKF gain, Gjk , are then obtained as Sjk = Ckj,YY + Rk and Gjk = Ckj,XY (Sjk )−1 . With this gain, the state ensembles are updated as, i,j j i,j Xi,j k|k = Xk|k−1 + Gk k|k−1

4.3

(14)

Particle Approximation

Likelihood of each particle, i.e. L(ξ jk ), is further calculated based on the innovation mean jk|k−1 and co-variance, Sjk , of all the ensemble simulations running within it. The normalized weight for each j th particle is further updated as, w (ξ j )L(ξ jk ) w (ξ jk ) = N k−1j j j=1 w (ξ k−1 )L(ξ k )

(15)

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−1  jT −1 j with L(ξ jk ) = (2π)n |Sk | e−0.5¯ Sk ¯ . The particle approximations for the parameters and states are then estimated as: xk|k =

N

j=1

5

w (ξ jk )xjk|k ;

and θ k|k =

N

j=1

w (ξ jk )ξ jk

(16)

Numerical Experiment

The proposed SHM approach has been tested on a simplex tensegrity. Simplex tensegrity (see Fig. 2) is a type of cylindrical tensegrity with 3 bars and 9 cables. For dynamic analysis, it is fixed at its bottom nodes (1–3) while ambient Gaussian force is applied in x-dir on the fourth node (see Fig. 2). 90% damage is induced in element 11 (bar) of the simplex. Nine strain gauges are attached on all the unrestricted members, i.e, elements 4–12, from where the measurements are collected. The initial statically stable coordinates (see Fig. 2) are obtained from [10]. The stable form of the simplex is further excited with an ambient WGN forcing of variance 104 N throughout the simulation. Damage is initiated 0.5 s after the start of the simulation. The response from strain gauges is sampled at a fixed sampling frequency 100 Hz for 5 s and further contaminated with a WGN of 1% SNR. The initial distribution type for the parameter particles (damage indices) is set to be Gaussian, with their mean set as 1 assuming an undamaged condition and a standard deviation of 0.02. 2500 filter particles are selected for PF while 75

Fig. 2. Simplex tensegrity configuration

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ensembles are chosen for EnKF. A better precision may however be expected with a higher number of particles or ensembles in exchange of a higher computational cost. Figure 3 compares the effect of various SNR (1%, 2% and 5%) on the proposed approach for simplex. It can be observed that the damage percentage estimated is fairly precise and prompt for all the SNR levels, but the promptness of detection is rather poor for 5% SNR. This, however, can be improved at higher computational cost. The method is observed to perform poorly for 10% SNR levels which demarcates the limitation of the approach.

Fig. 3. Measurement noise sensitivity of proposed approach for simplex tensegrity

6

Conclusion

A novel interacting filtering based damage detection technique has been proposed for tensegrity structures. EnKF is coupled with PF for simultaneous estimate of system states along with identification of a set of location based health parameters that monitor the stiffness deterioration. The health assessment is performed using ambient vibration response without knowing the input forces explicitly. The proposed method is found to be prompt and precise in detecting damages in a simplex tensegrity. The sensitivity of the proposed method under different SNR levels (1%, 2%, 5% and 10%) has been investigated and limiting SNR level (10%) is also identified. Funding. This study was funded by Science & Engineering Research Board (SERB), New Delhi, India, through grant file no. ECR/2018/001464.

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References 1. Ashwear, N., Eriksson, A.: Natural frequencies describe the pre-stress in tensegrity structures. Comput. Struct. 138, 162–171 (2014) 2. Sabouni-Zawadzka, A., Gilewski, W., et al.: Inherent properties of smart tensegrity structures. Appl. Sci. 8(5), 787 (2018) 3. Bhalla, S., Panigrahi, R., Gupta, A.: Damage assessment of tensegrity structures using piezo transducers. Meccanica 48(6), 1465–1478 (2013) 4. Sychterz, A.C., Smith, I.F.: Using dynamic measurements to detect and locate ruptured cables on a tensegrity structure. Eng. Struct. 173, 631–642 (2018) 5. Ghanem, R., Ferro, G.: Health monitoring for strongly non-linear systems using the ensemble Kalman filter. Struct. Control Health Monit.: Official J. Int. Assoc. Struct. Control Monit. Eur. Assoc. Control Struct. 13(1), 245–259 (2006) 6. Kebiche, K., Kazi-Aoual, M., Motro, R.: Geometrical non-linear analysis of tensegrity systems. Eng. Struct. 21(9), 864–876 (1999) 7. Chopra, A.K.: Dynamics of Structures, a Primer, vol. 2. Earthquake Engineering Research (1995) 8. Sen, S., Crini`ere, A., Mevel, L., C´erou, F., Dumoulin, J.: Seismic-induced damage detection through parallel force and parameter estimation using an improved interacting particle-Kalman filter. Mech. Syst. Sig. Process. 110, 231–247 (2018) 9. Evensen, G.: The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dyn. 53(4), 343–367 (2003) 10. Attig, M., Abdelghani, M., Kahla, N.B.: Output-only modal identification of tensegrity structures. Eng. Struct. Technol. 8(2), 52–64 (2016)

Monitoring of Lithium-Ion Cells with Elastic Guided Waves Tobias Gaul(B) , Uwe Lieske, Kristian Nikolowski, Peter Marcinkowski, Mareike Wolter, and Lars Schubert Fraunhofer IKTS, Fraunhofer Institute for Ceramic Technologies and Systems, Dresden, Germany [email protected]

Abstract. The application of lithium-ion batteries is widely spread nowadays. They can be found especially in consumer electronics such as mobile phones and notebooks, as well as in the rapidly growing field of electric cars. Highly available power and energy density of a lithium-ion battery over its lifetime are crucial for their effective operation. A replacement of the battery is recommended if the capacity is reduced by aging to below 80% of the initial capacity. For the estimation of the remaining cell-life, a precise estimation of the state of charge (SoC) and state of health (SoH) is necessary. This cannot be assured by common battery management systems, which only rely on current counting and cell voltage measurements. This work presents the potential to determine the SoC and SoH of lithium-ion cells with elastic guided waves. As the propagation of guided waves is dependent on the density and elastic modulus of a media, a correlation between the state of charge and the measured amplitude and phase of the wave can be shown, as the porosity of the anode will change during charge and discharge. Experimental studies in a pitch-catch arrangement of piezoelectric transducers were conducted on a representative pouch cell. The attached transducer network allows the examination of multiple travel paths through the battery. Keywords: Lithium-ion battery · Ultrasonic guided waves · State of charge · State of health

1 Introduction The application of lithium-ion batteries (LIBs) is nowadays widespread. They can be found especially in consumer electronics such as mobile phones and notebooks, as well as in the rapidly growing field of electric cars. Highly available power and energy density of a lithium-ion battery over its lifetime are crucial for their effective operation. However, their complex physicochemical nature should be more investigated, especially in the field of batteries’ degradation. Degradation of the battery may occur over time and with use over several cycles and it can significantly reduce the battery’s lifetime, which may have serious, dangerous effects for the user, e.g. while driving the electric vehicle. The main problems are the decrease in the LIB capacity and the decrease in power. The first is related to the amount of energy that can be stored in the LIB, the latter with © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 742–753, 2021. https://doi.org/10.1007/978-3-030-64908-1_69

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the power that LIB can provide. In the process of LIB aging, these two problems may occur simultaneously [1]. Many processes influence the aging of the LIB, e.g. the loss of lithium inventory – a decrease in the amount of cyclable lithium in the LIB. In such a case, those lithium ions cannot intercalate into the electrodes, which then decreases the LIB’s capacity. On the contrary, loss of active material refers to the degradation of electrodes and results in the reduction of domains, where lithium can intercalate. This, however, results in a decrease in capacity and power. Among these issues, another one is the deposition of lithium metal on anodes, usually in the form of dendrites. The monitoring of such processes which leads to battery degradation is still an issue in current research. Different techniques, such as impedance spectroscopy [2] and in situ neutron diffraction [3] were applied to identify this degradation with external measurement systems. The previously mentioned techniques contributed a lot in understanding the aging behavior of a LIB, however, such techniques cannot be practically implemented and, in most cases, can only be performed on small-scale, non-standard cells. Therefore the use of non-destructive testing methods to characterize the state of modern lithiumion batteries is addressed by different research groups. Especially methods based on ultrasonic waves have the potential to determine the charge state and monitor the health state of a battery over the entire lifetime [4–8]. This method shows the potential to work as an onboard system. Also, the latest research indicates that the capacity loss of a battery can be reduced by homogenization of the lithium-ion concentration with the use of elastic waves [9]. One of the first works on this new research area was published by Sood et al. [10]. Monitoring is performed using a separate ultrasonic pulser and receiver that are attached to the external surfaces of a lithium-ion cell. Compressional waves were excited to verify the degradation of lithium-ion batteries due to gas evolution. Real-time data from the ultrasonic transducer and receiver are used to non-destructively evaluate the internal condition of vital interfaces inside the cell. Also, the results were verified with radiographic images of degraded cells. With a comparable transducer arrangement, Hsieh et al. [7] investigated the charge and health state in commercially available lithium-ion and alkaline batteries. The behaviour of the transmitted and reflected bulk-wave signal were related to the state of charge and aging processes within the cells. The results demonstrate strong correlations between the state of charge (SoC) and the density distribution within a cell, as determined by the acoustic measurements. Furthermore, it was shown that the proposed analysis technique will work regardless of the battery’s chemistry and form factor. Furthermore, a 1D computational model was introduced to reproduce different effects. Due to the assumptions made in the model, only general effects like changes in the wave velocity could be observed. The work conducted by Gold et al. [6] also presented a method of SoC estimation based on ultrasound transmission but used a pulser-receiver setup. They extended this method by showing, that ultrasonic signals in the lithium-ion battery are sensitive to changes in porosity of graphite anode during cycling. Those changes in porosity of anode are caused by the lithiation of graphite, which varying level has a big impact and is correlated with the SoC of the battery. Gold et al. explained this correlation with Biot’s

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theory for the propagation of waves in fluid-saturated porous media. These observations allowed them for direct measurement of lithiation of graphite. In comparison to the previous authors, Ladpli et al. used guided elastic waves instead of ultrasonic waves to determine the state of charge and state of health (SoH) of a lithiumion battery. Piezoelectric transducers were attached on the surface of a battery and cycling under constant ambient condition were utilized [11]. Ladpli et al. proved a strong correlation between changes in the time-of-flight and the signal amplitude resulting from shifts in the guided wave signals and the electrochemical charge-discharge cycling and aging. With the use of differential voltage and differential time-of-flight analysis, they were able to detect intercalation staging and phase transitioning in the LIB. Besides, an analytical model of the battery was generated and the nominal magnitude and range of experimental time-of-flight during cycling are validated [12]. The work presented in this paper will follow the approach of Ladpli et al. and guided elastic waves are used for examination of the LIB.

2 Vibrometer Measurements 2.1 Measurement Set-Up The experiments were performed on a commercially available lithium polymer battery. Compared to LIB, this type uses a polymer electrode instead of a liquid electrode. The negative electrode is made of graphite, while the positive electrode consists of lithium cobalt oxide. The battery type used has a capacity of 10.000 mAh in mint condition and dimensions of 150 mm × 50 mm × 10 mm. The guided elastic waves were excited by a piezoelectric transducer P-876.SP1 of PI Ceramic. The transducer is attached by honey and pressed on the surface with low force clamps to avoid damages in the interior of the battery. The experimental setup can be seen in Fig. 1.

Fig. 1. Picture of measurement set-up with the laser vibrometer

For driving the piezoelectric transducers the MAS 2 (multi-channel acoustic system) hardware platform, developed at the Fraunhofer IKTS, was used. As excitation, a

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16 cycled Hanning windowed sinc function with a cut-off frequency of 140 kHz was generated. The peak-to-peak amplitude of the actuation signal is equal to 150 V. A PSV500-3D scanning laser-doppler vibrometer was used for sensing the guided waves on the surface of the battery. The 3D laser-doppler vibrometer allows the decomposition of three individual measured oscillation directions into three normal ones on the surface of the battery. A line-scan in the direct propagation direction of the wave was carried out, while the point distance between each individual measurement point equaled approx. 1 mm, resulting in a total of 123 points. Each point was sampled with 6.25 MHz and averaged 42 times. During the charge and discharge cycle, a measurement every 12 min was carried out. At a constant current of 1.3 A, the full charge lasted 8 h, resulting in a total of 39 measurements. 2.2 Results of Laser Vibrometer Measurements With the use of the 3D vibrometer, a wide frequency range can be evaluated for many different propagation paths with little instrumentation effort. It is therefore suitable for determining sensitive frequencies and optimal distances for further laboratory measurements. The vibrometer is used to determine the frequency-dependent wave velocity and attenuation rate of the first arriving wave package as a function of the charge state here.

Fig. 2. Dispersion diagram of the group velocity as a function of the state of charge calculated from the measured data

For this purpose, the two time-domain signal parameters maximum signal amplitude (SA) and time-of-flight (ToF) of the wave packet were extracted. The SA is the maximum amplitude of the Hilbert envelope of the received signal and the ToF is the time of this maximum of the Hilbert envelope. To obtain frequency-dependent signal parameters, the broadband received signal is bandpass filtered in steps of 5 kHz between 40 kHz and 150 kHz. Therefore, the signal parameters were extracted separately for each frequency step. In a single frequency step, the group velocity of the calculated signal is the slope of the arrival time over travel distance. The attenuation rate is the slope of the logarithmic maximum signal amplitude over travel distance. The results for the group velocity can be taken from Fig. 2, which shows the group velocity color-coded as a function of the

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excitation frequency and state of charge. It can be seen that it exists a clear dependency between the SoC and the group velocity of the propagating wave. With regard to the state of charge, there are four regions to differentiate. Below 60 kHz, there is a constant decrease in wave velocity with an ongoing state of charge. This decrease flattens with increasing frequency. Between 60 and 80 kHz, there is an intense change in wave velocity when the battery is at low and full capacity. Between 80 and 100 kHz, the wave velocity decreases as the battery capacity increases. Beyond 100 kHz, there is a constant increase in wave speed as the state of charge increases. Other researchers [6, 12] reported the same observation from similar experiments but used pouch cells of different thicknesses for the experiments. In Fig. 3 the result for the attenuation rate is plotted. The figure shows the attenuation rate color-coded as a function of the excitation frequency and the SoC. It can be seen that there exists a clear dependency between SoC and the attenuation rate, or the amplitude of the propagating wave, respectively. In general, the attenuation rate increases with increasing frequency, which leads to a shorter usable propagation path. With respect to the SoC, there are three regions to differentiate. Above 120 kHz an increasing capacity leads to an increasing attenuation rate. Therefore the amplitude will decrease with increasing SoC. Between 60 and 120 kHz, there is a flat decrease in attenuation rate with an increasing SoC, which results in increased signal amplitude with an ongoing charge process. This range is in good agreement with the observation of [4] and [7]. For frequencies below 60 kHz, the span of the attenuation rate between the charged and uncharged state is rather small and will result in a low shift in signal amplitude over the charging process. In addition, the attenuation rate in the uncharged state is lower compared to the charged state. Therefore the signal amplitude will decrease with increasing state of charge. As to the best knowledge of the authors, no comparable work could be found in the literature so far. Other authors mostly work with a fixed frequency and did not consider a wide frequency range.

Fig. 3. Frequency-dependent attenuation rate calculated from the measurement data depending on the state of charge

Laser-vibrometry was used to show the complex behaviour of the battery in terms of frequency dependence and state of charge. Apart from this, the elastic parameters of the

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battery components at different charge states, it is not well-reviewed in literature, which complicates the analytical calculation of the wave propagation. A set of parameters was determined by Jocker [13] and condensed by Ladpli [12] and seems to be promising for further investigation.

3 Battery Measurements 3.1 Measurement Set-Up for Pitch-Catch Measurements The experiments were conducted with the same Lithium polymer battery used for the laser vibrometer measurements. Instead of a line of measurement points, four piezoelectric transducers P-876.SP1 of PI Ceramic were used for generation and excitation of guided elastic waves. They were attached by honey and pressed on the surface with low force clamps to avoid damages in the inner of the battery. The experimental setup can be seen in Fig. 4. During the measurements, the environmental conditions kept constant with a temperature of 25 °C and a humidity of 50% in a climate chamber. For driving the piezoelectric transducers and receiving the signals the MAS 2 hardware platform was used. As excitation, a four cycled Hanning windowed tone burst at frequencies of 50, 75, and 110 kHz was used. The peak-to-peak amplitude of the actuation signals differs from frequency between 67.5 V and 90 V. Each signal path was sampled with 5 MHz and every point was averaged 64 times. During the charge and discharge cycle, a measurement every 5 min was carried out. At a constant current of 2 A, the full charge lasted 5 h, resulting in a total of 60 measurements per cycle.

Fig. 4. Experimental setup in a climate chamber of Fraunhofer IKTS (left) and the arrangement of the four piezoelectric transducers on the battery (right)

3.2 State of Charge To illustrate the behaviour of guided waves during charging and discharging of the battery, Fig. 5 represents three signals of the transducer pair T3–T1 at different charge

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states during the charging phase. It can be seen that the signal amplitude of the received wave packages increases with an increasing state of charge. On the other hand, the wave package becomes more compact, resulting in a decreasing ToF while the SoC increases. For further analysis, the time-domain signal parameters maximum signal amplitude (SA) and time-of-flight (ToF) of the wave packet were extracted. To show the general behaviour of guided waves during the charge and discharge process only the most sensitive path for each frequency is considered for further analysis in this paper.

Fig. 5. Time-domain signals for transducer pair T3 (actuator) and T1 (sensor) at an excitation frequency of 75 kHz at different SoC level

A signal path is supposed to be sensitive when the change in signal amplitude and time-of-flight is clearly visible within the data between charged and discharged state of the battery. This is acceptable when the change in ToF is ten times higher than the sampling rate (2000 ns) and the amplitude change is fifty times higher than the resolution of the measurement system (35 mV). Table 1 shows the absolute difference in SA and ToF for all transducer pairs. It can be seen that different configuration have their most sensitive change at different frequencies. Only the most sensitive frequency for a specific pair is used for further analysis, as marked in Table 1. Table 1. Calculated differences of signal amplitude and time of flight between the charged and discharged state at different transducer pairs and frequencies

50 kHz 75 kHz 110 kHz

Path T2 – T1 ΔSA ΔToF 58,3 mV 8,0 μs 69,5 mV 1,6 μs 29,9 mV 3,2 μs

Path T3 – T1 ΔSA ΔToF 157,5 mV 1,4 μs 241,8 mV 5,8 μs 285,9 mV 3,4 μs

Path T3 – T2 Δ SA ΔToF 24,9 mV 5,4 μs 81,4 mV 6,0 μs 103,1 mV 7,0 μs

The results of the time-domain signal parameters for the whole charge and discharge process at three different transducer configurations T2–T1, T3–T1 and T3–T2 (compare

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Fig. 4) at the most sensitive frequency are given in Fig. 6. The results are plotted over the SoC where the actual battery capacity is normalized to the maximum charge capacity. For the transmissions paths T3–T1 and T3–T2, there is a constant increase in SA and in ToF above 30% SoC in the charge phase and a constant decrease in the discharge phase. This is in accordance with other results from Hsieh et al. [7] where it was shown that during discharge the acoustic absorption is generally increasing and therefore the amplitude decreases. In contrary, the acoustic absorption is generally decreasing during charge, and therefore the amplitude increases. Below 30% SoC the SA and ToF remain static or begin to shift in the opposite direction. In this range, the cell voltage drops below 3.5 V in the discharge phase and shows fast-changing values in the charge phase. Similar effects were observed by Ladpli et al. [11] in comparable measurements. In these ranges, it is hypothesized that an occurring phase transformation in the cathode leads to a strong change in the density and the modulus of the cathode [7]. When the cell is charged, the acoustic intensities decrease slightly as the phase transformation is reversed and then followed by a steady increase in the intensities with increasing SoC. However, measuring directly under the actuator (transmission path T2-T1) shows an inverse behaviour of the signal amplitude which was also present in the laser-vibrometer measurements and cannot be fully explained yet. (a)

Path T2 (Actuator) – T1 (Sensor), Frequency: 50 kHz

(c)

Path T3 (Actuator) – T2 (Sensor), Frequency: 110 kHz

(b)

(d)

Path T3 (Actuator) – T1 (Sensor), Frequency: 75 kHz

Hysteresis for Path T2 (Actuator) – T1 (Sensor)

Fig. 6. Evolution of signal parameters ToF and SA with respect to the change in SoC for different transducer pairs (a)–(c) and hysteresis of signal parameters for transducer pair T2–T1 (d)

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Another effect that can be recognized is a hysteresis between the charge and discharge cycle for both parameters ToF and SA. As an example Fig. 6(d) shows the hysteresis effect for transducer pair T2 - T1 at 50 kHz in detail, whereas the parameter of the charge cycle sare plotted in solid lines and the for the discharge cycle in dashed lines. Again, especially below 30% SoC where the cell voltage drops below 3.5 V, the hysteresis effects are beyond measuring inaccuracy. Hysteresis effects are reported before for both mechanical [14] and electrical [15] properties of lithium-ion cells. Roscher et al. compared the open-circuit voltage (OCV) and the SoC for the charge and discharge process [15]. They showed that the OCV after certain discharge steps is significantly lower than the OCV after charging and both curves enclose a hysteresis. The hysteresis was reduced with increasing current rate and it was stated out that interparticle charge transfer, resulting from strong inhomogeneities among the particles’ lithium contents, is a reasonable explanation for a shrinking OCV hysteresis with increasing current application. Sethuraman et al. reported from compressive stress due to binder swelling and electrochemical intercalation of lithium ions during charge and discharge process [14]. During deintercalation, the stress is reduced but showed also a hysteresis effect. In addition, there appears to be an approximate correlation between the rate of stress rise and the staging behavior of the lithiated graphite. The previous authors also reported hysteresis effects and explained it with the different intercalation processes of lithium ions during charge and discharge within the anode. As the wave propagation of guided waves is also influenced by pre-stress within the material hysteresis effects will appear in a comparable manner. 3.3 State of Health As the results of the previous section were only presented for one charge/discharge cycle, a health state of the battery cannot be deduced. Therefore more cycles with the same measurement setup where performed. A total number of 17 charge/discharge cycles were carried out and a notable capacity loss of 0.8% was determined. The capacity loss is defined as the ratio of maximum capacity at the beginning of the measurements to the current cycle hereby. In Fig. 7, the results are plotted comparable to Fig. 6 over the state of charge where the actual battery capacity is normalized to the maximum charge capacity. In addition, all measured cycles for the considered transducer paths added as color-coded lines, whereas a dark colour denotes cycles close to the beginning and a light colour denotes cycles close to the end of the experiments. A dependency between the aging of the battery and the used signal parameters can be observed from the presented image. For the parameter ToF, the values shifts globally towards higher values (wave speed decreases) for all considered transducer paths with progressing battery aging. Therefore, the elastic modulus of the battery materials degrades with ongoing aging. Especially for both paths with frequencies below 100 kHz, the most prominent shift in ToF is between an SoC of 30% and 80%. It appears that with ongoing cycling the shift in ToF decreases. It must be noted, that this cannot be claimed for sure due to the relatively small amount of charge and discharge cycles does not allow for a general conclusion at the present point of investigation. In comparison to ToF, the signal amplitude behaves differently for the different signal paths and frequencies. Path T2–T1 shows a decreasing amplitude with

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Amplitude Actuator: T2 Sensor: T1 Frequency: 50 kHz

Time of Flight Actuator: T2 Sensor: T1 Frequency: 50 kHz

Amplitude Actuator: T3 Sensor: T1 Frequency: 75 kHz

Time of Flight Actuator: T3 Sensor: T1 Frequency: 75 kHz

Fig. 7. Evolution of signal parameters ToF and SA with respect to the change in SoH for different transducer pairs

increasing cycles while path T3–T1 shows an increasing amplitude. As for the behavior of ToF, the most prominent shifts occur between an SoC of 30% and 80%. Changes in the amplitude are rather small, especially in the uncharged state. This was also pointed out by Hsieh [7] as the scarcity and excess of lithium ions near the end of charge or discharge could also cause the abrupt stiffness change. To visualise the cycle-dependent behaviour more detailed the signal parameters for the path T3–T1 were extracted at two different states of charge for every measured cycle and are shown in Fig. 8. To avoid hysteresis effects, only data from the charge cycle were used. Even for a small amount of battery lifetime cycles, an existent correlation between the extracted guided wave signal parameters and the decrease in the maximum capacity can be shown. While the battery wears off, ToF increases non-monotonic for both paths and the signal amplitude shows a position-dependent behaviour where it linearly decreases on transducer path T2–T1 and linearly increases on transducer path T3–T1. Furthermore, the slope of the parameters is not independent of the state of charge.

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Comparative measurements should always be collected at the same state of charge. To estimate the current state of health of a battery, signal parameters will be compared with a pre-collected set of baselines for this type of cell, allowing to evaluate the remaining capacity or the passed through charge/discharge cycles.

Fig. 8. Evolution of signal parameters SA and ToF versus cycles at a constant charge state of 80% of maximum capacity (dashed line) and constant charge state of 100% of maximum capacity (solid line)

4 Conclusion The presented work shows the potential to determine the SoC and SoH of lithium-ion cells using elastic guided waves. For this purpose, extensive measurements with laservibrometer and conventional surface-mounted piezoelectric transducers were performed on a commercially available Lithium polymer battery. Several signal parameters (maximum amplitude, time-of-flight) were used to show the correlation between the battery state and the guided wave behaviour. Using laser-vibrometry, a complex frequency-dependent behaviour for the wave velocity and the wave amplitude was discovered. Depending on the frequency, the sensitivity of the signal parameters regarding the change of the SoC is different. Also, an evaluation of the signal parameter for a certain frequency showed that the SoC can be predicted using guided elastic waves. Measurements with multiple piezoelectric transducers proved that all path combinations are able to detect the SoC and SoH in the battery. Therefore, the paper showed a clear dependence between amplitude and phase with SoC. However, the different pathways between the transducers have varying sensitivities at different frequencies. In the paper, only the most sensitive pathways were shown. Furthermore, the influence of SoH of the battery to the evaluated signal parameters was shown. With an increasing number of cycles, explicit shifts in amplitude and time of flight to a reference state were observed. These shifts were even present for a small amount of battery life cycles. Therefore, the determination of SoC only by absolute values of the signal parameters is not possible due to the change with increasing battery life. The ongoing work will focus on the development of a monitoring strategy where SoC and SoH can be predicted simultaneously.

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References 1. Woody, M., Arbabzadeh, M., Lewis, G.M., Keoleian, G.A., Stefanopoulou, A.: Strategies to limit degradation and maximize li-ion battery service lifetime -critical review and guidance for stakeholders. J. Energy Storage 28, 101231 (2020) 2. Tröltzsch, U., Kanoun, O., Tränkler, H.-R.: Characterizing aging effects of lithium ion batteries by impedance spectroscopy. Electrochimica Acta 51, 1664–1672 (2005) 3. Sharma, N., et al.: Structural changes in a commercial lithium-ion battery during electrochemical cycling: an in situ neutron diffraction study. J. Power Sources 195, 8258–8266 (2010) 4. Chang, J.-J., Zeng, X.-F., Wan, T.-L.: Real-time measurement of lithium-ion batteries’ stateof-charge based on air-coupled ultrasound. AIP Adv. 9, 085116 (2019) 5. Davies, G., et al.: State of charge and state of health estimation using electrochemical acoustic time of flight analysis. J. Electrochem. Soc., 2746–2755 (2017) 6. Gold, L., et al.: Probing lithium-ion batteries’ state-of-charge using ultrasonic transmission concept and laboratory testing. J. Power Sources, 536–544 (2017) 7. Hsieh, A.G., et al.: Electrochemical-acoustic time of flight: in operando correlation of physical dynamics with battery charge and health. Energy Environ. Sci., 1569–1577 (2015) 8. Wu, Y., Wang, Y., Yung, W.K.C., Pecht, M.: Ultrasonic health monitoring of lithium-ion batteries. Electronic 8, 751 (2019) 9. Huang, A., Liu, H., Manor, O., Liu, P., James, F.: Enabling rapid charging lithium metal batteries via surface acoustic wave-driven electrolyte flow. In: Advanced Materials (2020) 10. Sood, B., Michael, O., Michael, P.: Health monitoring of lithium-ion batteries. In: IEEE Symposium (2013) 11. Ladpli, P., Kopsaftopoulos, F., Nardari, R., Chang, F.-K.: Battery charge and health state monitoring via ultrasonic guided-wave-based methods using built-in piezoelectric transducers. In: SPIE Smart Structures and Materials+Nondestructive Evaluation and Health Monitoring (2017) 12. Ladpli, P., Kopsaftopoulos, F., Chang, F.-K.: Estimating state of charge and health of lithiumion batteries with guided waves using built-in piezoelectric sensors/actuators. J. Power Sources, 342–354 (2018) 13. Jocker, J., Smeulders, D.: Ultrasonic measurements on poroelastic slabs: determination of reflection and transmission coefficients and processing for Biot input parameters. Ultrasonics 49, 319–330 (2009) 14. Sethuraman, V.A., Van Winkle, N., Abraham, D.P., Bower, A.F., Guduru, P.R.: Real-time stress measurements in lithium-ion battery negative-electrodes. J. Power Sources 206, 334–342 (2012) 15. Roscher, M.A., Bohlen, O., Vetter, J.: OCV hysteresis in li-ion batteries including two-phase transition materials. Int. J. Electrochem., 1–6 (2011)

Does the Precision Value Influence the Fusion Performance? A Method-Based Experimental Study Sandra Rothe(B)

and Dirk S¨ offker

Chair of Dynamics and Control, University of Duisburg-Essen, 47057 Duisburg, Germany [email protected] Abstract. Considering technically complex systems, the evaluation of situations or conditions is a challenging task. To ensure a high accuracy assignments from different classifiers can be fused. To define requirements for a good fusion performance and to evaluate the potential for higher accuracy, in this paper the idea of a fictional classifier is introduced. The precision values of one classifier denoted as fictional classifier are varied to demonstrate the influence on fused accuracy. From the results of this contribution some important challenges can be solved: Can the performance of one individual classifier improve the overall accuracy? Can the performance of the fused results be improved by changing performance measures of the fictional classifier? This allows the establishment of a supervised strategy to adapt precision values to get better fusion results. For illustrating the effectsfour benchmark examples are used. The introduced methods are applied to fault diagnosis of hot rolling mills. The results show that using a fictional classifier the overall accuracy can be outperformed depending on data sets. Keywords: Classifier fusion · Ensemble selection Combination Rule · Fictional classifier.

1

· Bayesian

Introduction

The overall system reliability of complex or safety critical systems is of increasing importance. For evaluating situations, conditions, or states, classification approaches are widely used in several application fields, such as fault diagnosis, image recognition, or object detection. Instead of developing individual classifiers to perform with a high reliability, the results of more than one classifier can be combined using information fusion methods to combine the individual advantages of different classifiers to improve the overall reliability. By using different classifier outputs, the methods on classifier level can be applied. Once the features are selected and the classifiers are tuned, classifier fusion methods only use the classifier outputs. The advantage of combining different classifier outputs is the independency from changes in the system behavior, so that using one individual classifier not trained with data related to the new situation can c The Author(s), under exclusive license to Springer Nature Switzerland AG 2021  P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 754–764, 2021. https://doi.org/10.1007/978-3-030-64908-1_70

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lead to a wrong decision whereas another classifier possibly not well trained, but performing better in new situations. The goal is to combine the individual advantages to improve the overall performance. From the literature several contributions [1–4], focusing to the improvement of the performance of the decision support system are known. In the application field of fault diagnosis, the improvement of feature selection or classification approaches is still challenging (like in [2]). In [3] classification results are combined using the Bayesian belief method (or Bayesian Combination Rule (BCR)), which is a fusion method on measurement level based on conditional probability. Another example using BCR for bearing fault diagnosis is given in [4]. In both contributions the performance of a single classifier is outperformed using the proposed fusion algorithm. To optimize the fusion performance, optimization techniques can be used to find optimal parameter within the fusion method (see [5,6]). From the literature it can be concluded, that fusion methods are widely used in several application fields and optimization techniques. The applied fusion methods can improve the accuracy of a decision support system, but as shown in several literature as well as in this contribution, an improvement using fusion methods is not always possible. Instead of using optimization of fusion methods, ensemble selection methods are designed to avoid the combination of classifiers with low accuracy or high dependency in comparison to other classifiers. The Static Classifier Ensemble (SCE) is set by a global selection of best classifiers based on validation data sets. The ensemble of classifiers is not changing during the classification of unknown data. Optimization algorithms are also used to get the optimal static classifier ensemble. In [7] the fusion algorithm as well as the classifier ensemble including the features are optimized to maximize the number of correct classified samples and to minimize the number of selected features and classifiers. For application of prognostics, also ensemble learning algorithms can be used to combine predictions from multiple sources [8]. The results show, that a reduced number of selected features and classifiers in combination with a simple fusion method (sum rule) can result in comparable accuracy values than a complex fusion algorithm. In general, no conclusive statement of the best fusion or selection method can be given, independent from the statistical base of the individual fusion approaches. From applications [1,4,9] it can be concluded that the results are strongly affected by application data, but not especially from the fusion method applied. To examine the effects from data structure to resulting accuracy using different data sets in this contribution one classifier from the classifier ensemble is denoted as fictional classifier. The idea is to change precision values for one of the classifiers in order to evaluate options to improve overall fusion accuracy. Using this fictional classifier the influence of the precision values on the overall fusion performance becomes visible. The goal is to get the optimal precision values to see, if they are generalizable for different ensembles or data sets. Inspired by this idea also a training-based fusion algorithm is applied, where the optimal values in training are used in test.

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The organization of this paper is as follows. In Sect. 1, the recent applications and developments of fusion methods and ensemble selection strategies are described. In Sect. 2, the new idea of the fictional classifier and the training-based fusion algorithm are presented. Section 3 shows the simulation results using four benchmark data sets with distinction between two classes. The experimental results distinguishing between four classes are discussed in Sect. 4. Section 5 summarizes the results.

2

Concept of Fictional Classifier

The concept of a fictional classifier (FC) is introduced based on the idea that the precision value has a significant influence on the fusion performance. In case of using BCR for a two class problem, the precision value is the value used for calculating the belief values. Therefore the influence on fused accuracy by changing the precision values should be analyzed, validation is used to show possible improvements. All classifiers of the static classifier ensemble classify the validation data, but one is set as fictional classifier. Classification assignments stay the same, but precision values, which are used to calculate the belief value, are now considered as variable. In the case of two considered classes the probability matrix of FC will be   p1 1 − p2 , (1) P FC = 1 − p1 p2 with p1 and p2 as variable precision values of class 1 and class 2 respectively. Using different values for p1 and p2 , the influence of the precision values of one classifier on the overall accuracy of fused results can be shown. Using NSGA-II [10], the values of p1 and p2 as decision variables leading to the maximum reachable fused accuracy (objective) can be determined. In each step, the decision variables are changed according to an evolutionary algorithm. Depending on the resulting accuracy, the new generation is generated. In most cases, especially for considering two classes, there is more than one precision value set leading to the same fused accuracy. Based on the concept of fictional classifier, the idea is extended to a trainingbased fusion algorithm. In training, the precision values of the FC are optimized and selected by calculating the mean value and finding the nearest neighbor. Using this parameter set, unknown data samples (test data) can be fused.

3

Application to Benchmark Data

Benchmark data from the UCR Archive [11] are used to analyze the dependencies between precision values of FC and accuracy of fused results. Therefore four data sets with two classes are chosen: Coffee (28 samples), ECG200 (100 samples), GunPoint (150 samples), and Yoga (3000 samples). The data sets have to be classified to use classifier fusion. Using WEKA [12], 11 different classification

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approaches are applied with each data set using default parameters. The results of the individual classification are published in [9]. For the four data sets, different individual classifiers are better or worse, so that no classifier can be denoted as best. Therefore a combination of this classifiers using fusion methods as well as using an FC can be realized. Different static classifier ensembles are used to examine the results for various combinations of classifiers with different performances. The selection of ensembles is based on the accuracy of individual classifiers. The ensembles are denoted by a number and a B for best, W for worst, and M for medium. An ensemble denoted as 2B + 2W means the two best and two worst classifiers are used in this ensemble. For each ensemble, each classifier in this ensemble is set as FC, which is denoted by the second number (e.g. 2B 2). In total nine different ensembles are considered. The data sets are divided into three training and test data sets using 3-fold cross-validation. The simulation results for the data sets are shown in Figs. 1, 2, 3 and 4. In the first row the results from training and in the second row from test are shown. The figure on top left shows the suitable parameter ranges achieving maximum accuracy of fused results for each classifier ensemble with varying classifier set as FC. The corresponding maximum accuracy achievable as well as the maximum individual accuracy of the ensemble and the accuracy of fused results not using one classifier as FC are shown in the figure top right. On bottom left the selected parameter sets are shown, which lead to an accuracy of fused results (shown in figure on bottom right) combining FC with selected parameters and the other classifiers of this ensemble. The results of training phase for data set Coffee shows that the range of precision values leading to the maximum achievable accuracy is different for different classifier ensembles (see Fig. 1). In the case of 2B, 5B, and ALL the range for p1 and p2 varies between 0% and 100%. This means, for all parameter sets in between this values, the accuracy is the same. In case 2 W and 5W (combining the worst classifiers) the range for suitable precision values is smaller and the resulting accuracy is higher than the accuracy achievable without FC and the maximum individual accuracy (top right). Not always a smaller range of precision values lead to a higher achievable accuracy (5M, 1B + 1W, and 3M). The specific value ranges of p1 and p2 also varies for different classifiers set as FC. For example in case of combining one best and one worst classifier (1B + 1W), the range is smaller for the second classifier (best classifier) set as FC. The selected values both for p1 and p2 are nearly the same and vary around 50–60% (bottom left). Combining the five worst classifiers (5W) the selected parameters show the most deviation for different data sets. Also the deviation of accuracy (bottom right) leads to the dependency of results from the considered training and test data sets. The maximum achievable accuracy in training phase can not be reached in test. In all cases the fusion with FC can not outperform the best individual classifier, but compared to the fusion without FC the accuracy is the same or higher.

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Fig. 1. Simulation results of data set Coffee.

The simulation results of data set ECG200 (Fig. 2) lead to similar conclusions, although there is a higher dependency of precision value ranges and achievable accuracy on different classifiers set as FC (top left and top right). In Fig. 2 it can be seen, that the selected parameter values (bottom left) vary more significantly compared to data set Coffee, especially by fusing the ensembles 5M and ALL. Otherwise the deviation of accuracy (bottom right) is less. Again the highest achievable accuracy from training can not be reached in the test. In most cases the accuracy is less than the best individual and also sometimes less than the fusion without FC. The improvement of achievable accuracy using the data set GunPoint is higher than for the other data sets (see Fig. 3). In most cases the accuracy of fused results using FC is higher than the best individual fusion accuracy. Also the range of precision values leading to this higher accuracy is lower than for the data sets Coffee and ECG200 (top left). From the figure bottom left it can be seen that the selected values of p1 and p2 differ from each other. This can not be clearly detected from the other data sets, which leads to the conclusion, that for this data set the classifiers show different behaviors for each class and a different precision value for each class leads to better results in the accuracy. Using the selected parameter sets for the FC, the accuracy of the fused results can be improved in some cases (3M, 5W, 5M), but can not outperform the individual best like in training. For data set Yoga a very specific range of precision values is resulting in the maximum achievable accuracy (Fig. 4), but the absolute values are varying for the different ensembles. A higher accuracy than the accuracy of fusion with-

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Fig. 2. Simulation results of data set ECG200.

out FC can be obtained, but again the best individual performance can not be improved (top right). Nevertheless, the results from training can be achieved also in test using the selected parameter (bottom left) and again the fusion results using an FC are better than the results of using normal BCR. Additionally the deviation of results is very small. This data set contains more samples, than the others, which can be the reason for different results. To proof this, more data sets with high and low number of samples should be analyzed. Lessons Learned. Summarizing the analysis using 3-fold cross-validated fusion based on benchmark data sets, some conclusions can be drawn to generalize the (numerical) results: – Resuming all example combinations it can be concluded that in general a higher accuracy can be obtained using the FC compared to the accuracy of fusion without FC. The best individual performance can not be outperformed. – The best individual performance for one data set does not always result from the same classifier, so that in case of data changes, which are not trained, the fusion performance using an FC is more reliable than without using FC. – It can be detected that no common value of p1 and p2 can be concluded for all ensembles or data sets. The precision values are very different for specific ensembles, data sets, and in some cases also for different classifiers set as FC. – Using the selected precision values to new data, fusion results can be improved.

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Fig. 3. Simulation results of data set GunPoint.

– In case of a higher data sample number (example: Yoga), the results are more specific, the training and test results are nearly the same, but for lower number of data samples (example: Coffee) the variation of precision values as well as achievable accuracy is very high. – Using varying precision values, the data sets with improvement potential using ensembles and classifiers set as FC can be stated. – Combining classifiers with low accuracy, the improvement potential affected by the precision values is higher.

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How can this result be used? – There is no best classifier. This is a known result denoted as ‘No Free Lunch Theorem’ [13]. – Knowing the specific conditions for classification it makes sense to search for the best individual classifier. – Not knowing specific conditions, fusion is useful while providing more robust (with respect to new and untrained situations) results. – Using fusion, it is useful to evaluate the improvement potentials by varying the precision values and determine the best ensemble and classifier as FC. – If no improvement is possible, common fusion method (like the Bayesian Combination Rule) can be used. – If an improvement is possible, the precision values as well as the ensemble selection and classifier set as FC from training can be used for fusion of new samples. – If only classifiers with worse performance are available, a fusion with FC should always be considered. The evaluation using the introduced fictional classifier can help to analyze the improvement potentials and assists by deciding if under which conditions a fusion of results is useful.

4

Application to Experimental Data

The idea of fictional classifier is applied to real industrial data from hot rolling mills (HRM). First results using FC regarding the distinction of four classes are

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shown. Deviations in strip travel lead to influences on product quality and cause down times. The events can be classified as CLASS 1: Stable rolling with strip in stand, CLASS 2: Stable rolling without strip in stand, CLASS 3: Fault cobble, and CLASS 4: Fault shearing tale. In [14] five different time-frequency-based analysis methods are applied to the detection of cobble as a fault in rolling process: continuous and discrete wavelet transform (CWT/DWT), empirical mode decomposition (EMD), short-time Fourier transform (STFT), and Wigner-Ville distribution (WVD). The data set HRM contains 80 samples (20 per class) filtered using the mentioned methods and classified using two different classification approaches: support vector machine (SVM) and cross-correlation (CC). This leads to six different filter-classification combinations: CWT-SVM, DWTSVM, EMD-CC, EMD-SVM, STFT-SVM, and WVD-SVM. In the following 3-fold cross-validation is used to generalize the results. In case of four classes, 12 parameters (pij ) in the probability matrix ⎤ ⎡ ... p14 p11 ⎥ ⎢ p21 ... p24 ⎥, (2) P FC = ⎢ ⎦ ⎣ p31 ... p34 3 3 1 − i=1 pi1 . . . 1 − i=1 pi4 are optimized. This means, that not only the precision values (i = j) are variable, but also the probability the classifier assigns class i, but the real class is j (i = j). In Fig. 5 the accuracies of best individual classifier, fusion without and with FC of training and test process are shown. Compared to the results of benchmark data with two classes, the training results show different behavior. Here an improvement using fusion is always possible. Using the FC, the accuracy is higher or less than without FC depending on the ensembles. There are also two cases (2W 2 and 1B+1W), in which the results using FC are significantly worse compared to the best individual accuracy and the fusion without FC, especially when the worst classifier in the ensemble is set as FC. In test the accuracy using fusion with FC is not improved compared to fusion without FC in most cases. In general the results using fusion (with or without FC) can not outperform the best individual classifier. Obviously the values calculated/optimized during training can not be applied for test data. Lessons Learned. Compared to the results from benchmark data, the experimental results lead to similar conclusions with some restrictions. – In training the accuracy can be improved using the optimized parameters for specific ensembles and classifiers set as FC. – The improvement potential is different for all considered cases. – Considering a four class problem, the in training optimized parameters can not be directly transferred to unknown samples. Using the fictional classifier the improvement potentials also for a four class problem can be shown. In this case the optimized 12 parameters are too specific to select them for unknown samples.

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5

Summary and Conclusions

Several contributions have shown, that the fusion of results have the potential to improve the performance of decision making. In this contribution a fictional classifier is introduced to analyze the dependency of precision values of one classifier to the overall fused accuracy to get requirements for a good fusion performance. Four benchmark data sets with two classes and one experimental data set with four classes are considered and fused in different ensembles. To ensure generalizability all results are 3-fold cross-validated. From the results it can be concluded, that varying the precision values an improvement of fused accuracy can be obtained. The related precision values vary for every case, so no general information about precision values can be given, just for each data set and ensemble individually. In general and by the nature of the problem no overall suggestion for the requirements for good fusion performance can be established. To overcome this problem it can be shown that the precision values influence the performance. Furthermore the potential to improve the fusion performance using a fictional classifier can be shown. For benchmark data the knowledge about precision values can be used to fuse results of further unknown samples to improve the reliability of the fusion. This is not valid for the experimental data with four classes. If this is a significant result for data sets with more than two classes or is only dependent on the specific data set has to be analyzed in further works. In general, the evaluation using the introduced concept of a fictional classifier can help to analyze the improvement potentials. It can assist by deciding if a fusion of results will be successful or the individual classifier should be preferred. For future work, also other influencing factors can be analyzed to discuss the effects on the overall performance and to state the requirements for improvement using fusion methods.

References 1. Bilski, P.: Analysis of the classifier fusion efficiency in the diagnostics of the accelerometer. Measurement 67, 116–125 (2015)

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2. Islam, M.M.M., Kim, J.-M.: Reliable multiple combined fault diagnosis of bearings using heterogeneous feature models and multiclass support vector machines. Reliabil. Eng. Syst. Saf. 184, 55–66 (2019) 3. Qu, J., Zhang, Z., Gong, T.: A novel intelligent method for mechanical fault diagnosis based on dual-tree complex wavelet packet transform and multiple classifier fusion. Neurocomputing 171, 837–853 (2016) 4. Xia, M., Kong, F., Hu, F.: An approach for bearing fault diagnosis based on PCA and multiple classifier fusion. In: 6th IEEE Joint International Information Technology and Artificial Intelligence Conference, vol. 1, pp. 321–325 (2011) 5. Nanni, L., Lumini, A.: A genetic encoding approach for learning methods for combining classifiers. Expert Syst. Appl. 36(4), 7510–7514 (2009) 6. Nguyen, T.T., Pham, X.C., Liew, A.W.C., Pedrycz, W.: Aggregation of classifiers: a justifiable information granularity approach. IEEE Trans. Cybern. 99, 1–10 (2018) 7. Nguyen, T.T., Liew, A.W.C., Pham, X.C., Nguyen, M.P.: Optimization of ensemble classifier system based on multiple objectives genetic algorithm. In: International Conference on Machine Learning and Cybernetics, Lanzhou, pp. 46–51 (2014) 8. Li, Z., Wu, D., Hu, C., Terpenny, J.: An ensemble learning-based prognostic approach with degradation-dependent weights for remaining useful life prediction. Reliabil. Eng. Syst. Saf. 184, 110–122 (2019) 9. Rothe, S., S¨ offker, D.: Comparison of different information fusion methods using ensemble selection considering benchmark data. In: 19th International Conference on Information Fusion (FUSION), Heidelberg, pp. 73–78 (2016) 10. Song, L.: A NSGA-II program in Matlab v1.4. http://www.mathworks.com/ matlabcentral/fileexchange/31166-ngpm-a-nsga-ii-program-in-matlab-v1-4. Accessed Feb 2014 11. Chen, Y., Keogh, E., Hu, B., Begum, N., Bagnall, A., Mueen, A., Batista, G.: The UCR time series classification archive. http://www.cs.ucr.edu/eamonn/time series data/. Accessed Feb 2014 12. Hall, M., Frank, E., Holmes, G., Pfahringer, B., Reutemann, P., Witten, I.H.: The WEKA data mining software: an update. SIGKDD Explor. 11(1) (2009) 13. Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1, 67–82 (1997) 14. Rother, A., Jelali, M., S¨ offker, D.: A brief review and a first application of timefrequency-based analysis methods with application to strip rolling mills. J. Process Control 35, 65–79 (2015)

Automatic Fault Detection and Classification in Lift Door Systems Using Vibration Signal Features Angel Torres Perez, Stefan Kaczmarczyk(B) , and Rory Smith University of Northampton, University Drive, Northampton NN1 5PH, UK {Angel.TorresPerez,stefan.kaczmarczyk}@northampton.ac.uk

Abstract. The Internet of Things (IoT) is shaping the concept of the modern intelligent built environment. The latest developments in IoT have led to secure, energy efficient systems enabling low-cost real-time analytics. In the Vertical Transportation (VT) technologies developed by the lift industry real-time analytics are facilitating predictive maintenance which in turn decreases operational and downtime costs. Data driven predictive maintenance does not always reach an optimal performance because the quality and quantity of the data matters. Fault classification and the estimation of the remaining useful life (RUL) requires a deep understanding of failure modes and component degradation. In lift systems, most of the malfunctions are due to faults developed by the automatic power operated door systems. The most widespread Structural Health Monitoring (SHM) sensor technology used in monitoring the door mechanisms are acoustic and vibration sensors. In this paper, an automatic fault detection system using Artificial Neural Networks (ANN) is implemented using vibration signal features. Obtained results reveal that the fault classification performance is high (>70%) under low noise environmental conditions. Keywords: Internet of Things · Intelligent built environment · Predictive maintenance · Remaining useful life · Vibration signal features · Artificial Neural Networks

1 Introduction Engineering systems are designed using relevant failure criteria so that they can operate under specific loads and conditions. However, the actual behaviour of a system is not fully known until it is in service [1]. Due to unpredicted loads, the system may fail and will no longer operate satisfactorily. The more real-time information a manufacturer has about the status of customers’ equipment, the better the equipment could be maintained. Ideally, real time analytics allow the maintenance service team the detection of potential problems early enough to prevent them from even happening. Real time predictive maintenance in lift systems utilises a wealth of sensor data and advanced analytical methods to predict failures well before immediate action is taken. This maintenance approach is usually taken © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 765–775, 2021. https://doi.org/10.1007/978-3-030-64908-1_71

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when high costs are incurred due to downtimes or maintenance. Real time analytics enable the estimation of the RUL of assets with increasing accuracy. Most relevant lift manufacturers such as ThyssenKrupp AG are implementing Industry 4.0 solutions enabling predictive maintenance solutions such as MAX [2]. Most of the service calls of elevators are related to the door mechanism [3]. On average, the number of opening and closing cycles of a door elevator per year is estimated to be above 100000. All these operating cycles produce a lot of wear and tear on the equipment that opens and closes the doors, especially if it is not properly maintained. A detailed study of call-back data over a three-year period in four different cities in the US has also confirmed that the door operator is the most frequent fault in lift systems [4]. Fault classification applies a data mining technique [5] for the prediction of different fault classes. It is an example of supervised learning and it requires categorical labels. Fault classification involves two steps. The first step is the learning/training step in which a classifier is built to describe a predetermined set of faults using labelled data. The second step evaluates the model for classification of unknown data such as test data for estimating the classifier accuracy. There are many classification algorithms like decision trees, K nearest neighbour, naive Bayesian classifier, support vector machines (SVM) and artificial neural networks (ANN) [6]. In this study the fault classifier is based on ANN [7]. An artificial neural network (ANN) is a computational model based on the structure and functions of biological neural networks. An ANN consists of nodes in different layers; input layer, intermediate hidden layer(s) and the output layer. The connections between nodes of adjacent layers have “weights” associated with them. Learning of neural network is performed by adjusting the weight of connection. ANN can be classified in two types: feed-forward network and recurrent networks depending on the way they channel information. The feed-forward neural network is the network in which connections between units do not form cycle whereas in recurrent neural network connection form cycles [7]. The main advantages associated with neural network are the ability to identify highly complex non-linear relationships between input and output variables without the need to understand the nature of the physical process, inferring unseen relationships on unseen data and their tolerance to noisy data [8]. ANN parallelism increases the speed of the network. However, there are drawbacks: ANN training is costly, time consuming, it plays an important role in classification accuracy and it is difficult for humans to interpret the symbolic meaning behind the learned weights and of “hidden units” in the network. There are many algorithms used for training of neural network [9, 10].

2 Door Mechanism The lift (elevator) door system comprises landing (hoistway) doors and car doors. Most elevators intended for passengers have fully automated power-operated doors. The standard arrangement for automatic power operation involves a ‘master’ operator, a selfcontained electric motor driven unit mounted on the car top. There are several different types of door configurations depending on the number of panels, typically doors range from a single panel to four panels. A review of door classification and door components is discussed in [3]. The study involves automated power-operated doors, with an electronically controlled door operator as shown in Fig. 1.

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Fig. 1. Automated power-operated elevator door with an electronically controlled door operator

Most relevant faults in these mechanisms are: • • • • • • • •

Motors with defective bearings (shaft bearings defective). Incorrect belt tensions. Worn-out door sill. Worn-out door rollers (door rollers defective). Sluggishness of door guide (door panel guide dirty). Door lock out of alignment (door interlock error). Worn-out door cam. Worn-out door ropes (door rope frayed).

3 Defects Classification Using Vibration Measurements The complexity and cost of the automatic fault classifier was the main constraint in this research. In terms of cost, only one high specification vibration sensor could be placed in the door mechanism. The best location to place the vibration sensor was the top centre of the door operator case. This location was identified after conducting modal analysis tests with impact hammer excitation. The structure was excited with the hammer near the locations were the defective components are fitted in. The vibration signals were recorded with an acquisition platform of 24 bits and a sampling rate of 96 ksamples/s. The piezoelectric accelerometer was a B&K 4382 connected to a (0–40 dB) gain charge amplifier.

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After placing the vibration sensor in the door mechanism, several tests were systematically conducted using door operational cycles. A door operational cycle consists of the following phases: silence (doors closed), doors transient open (variable speed), doors opening (constant speed), reverse motor direction, doors closing (constant speed), doors transient close (variable speed), silence (doors closed). The different phases after pre-processing the raw vibration signal are shown in Fig. 2. The timing of these phases could be estimated, or obtained directly from the lift controller records.

Fig. 2. Phase separation of the door vibration signal. Motor fault.

Various door operation cycles were conducted with and without different types of defects. After these tests, it was concluded from the vibration spectrogram that not all defective parts could be easily detected with a monitoring system mounted on the carrier of the cabin door. Table 1 summarises the defects that could be detected with this vibration sensor.

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Table 1. Fault detection using the spectrogram Defect (Fault)

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Good

1–2 kHz

Incorrect belt tensions

Poor

1–1.2 kHz

Worn-out door cam

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1–6 kHz

Worn-out door rollers

Good

630 Hz–10 kHz

Rough-running door guide

Satisfactory

2–10 kHz

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Poor

–

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4 ANN Training Process The vibration sensor recording of each door operational cycle was stored in order to build an ANN training dataset. The number of vibration recordings for each class of defect are shown in Table 2. It should be noted that there are defect classes that have not been taken into consideration in this research. Table 2. Vibration recordings (Dataset) CLASS

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Different belt tensions Door rope torn

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Loosened motor chain

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Each vibration record was divided according to the door operational phases and it was labelled with a type of defect or target class. The raw vibration signals that were obtained with 24 bit resolution and a sampling frequency of 44.1 kHz were pre-processed by removing the average value and then they were normalised by dividing by the standard

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deviation. The spectra of the ‘silence’ frames of the signals were also subtracted from the whole signal in order to remove the stationary noise. After pre-processing, spectrograms and cepstrograms of the input signal were chosen as the extracted signal features, respectively. The spectrogram was obtained using a Hanning window of 256 samples and applying an overlap of 25%. The cepstrogram was later obtained from the spectrogram and both signal features were stored in files forming a training dataset. Only the first 64 coefficients were used in the cepstrogram. A block diagram of the feature extraction process is shown in Fig. 3.

Fig. 3. Training dataset and ANN training process

A pattern recognition network was trained using the following operational phases of the door mechanism: doors transient open (variable speed, TOPEN), doors opening (constant speed, OPEN), doors closing (constant speed, CLOSE), doors transient close (variable speed, TCLOSE). The network used was is a feedforward ANN that has been trained to classify inputs according to the target classes. The input size dimension of the network has been fixed. This network was trained by framing the cepstrogram of the signals. The chosen input size dimension corresponds to approximately 1.6 s of the audio or vibration signals which was assumed long enough to detect the fault. The input size dimension of each ANN training sample corresponds to 200 time samples by 64 cepstrum coefficients (200 × 64 = 12800 points). The signal shown in Fig. 4 graphically demonstrates this concept. The records contained in red or green rectangles in Fig. 4 are approximately 1.6 s long each and they have a matrix dimension of 200 × 64 points in the cepstrograms, respectively. The overlap between these rectangular frames is 10% or 160 ms. The spectrogram and the cepstrogram of each vibration file were framed and then stored depending on each operational phase leading to the total number of frames shown in Table 3.

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Fig. 4. Framing the spectrogram and the cepstrogram of the door vibration signal for training the ANN. Class 1 - No fault. Table 3. Spectrogram and Cepstrogram frames on each phase in the training dataset Number of frames per operation phase Spectrogram (size 200 × 129) and Cepstrogram (size 200 × 64) CLASS

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No defect

2

Worn-out door cam

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Door interlock bent

4

Worn-out door rollers

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OPEN

CLOSE

TCLOSE

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261

306

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59

78

66

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27

70

82

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6

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77

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The ANN was chosen according to the diagram presented in Fig. 5. The input size dimension is 12800 points and the output size dimension is 8 (the number of fault classes). The total number of neurons in the hidden layer was selected following a rule of thumb which is by selecting this number as about half of the input size dimension (or 6500 neurons). The larger this number is, the longer the training process will last.

Fig. 5. ANN architecture.

The ANN was trained, tested and validated using the MATLAB Neural Pattern Recognition tool (or nprtool).

5 Results For training, testing and validation of the ANN, the original training dataset was split into 70% of the samples for training the ANN, 15% of the samples for validation and the remaining 15% for testing. The training results are shown in the training confusion matrix. These results reflect the classification percentage of the ANN when all the inputs belong to the training dataset. A good classifier should show a very high overall accuracy in the training confusion matrix. The test and validation datasets contain samples that do not belong to the training dataset. These two datasets are useful for giving an estimate of the real fault classification performance. The classification results for each door operational phase are presented in the test confusion matrices shown in Fig. 6. In the confusion matrix plot, the rows correspond to the predicted class (Output Class) and the columns correspond to the true class (Target Class). The diagonal cells correspond to observations that are correctly classified. The offdiagonal cells correspond to incorrectly classified observations. Both the number of observations and the percentage of the total number of observations are shown in each cell. The column on the far right of the plot shows the percentages of all the examples predicted to belong to each class that are correctly and incorrectly classified. These metrics are often referred to as the precision (or positive predictive value) and false discovery rate, respectively. The row at the bottom of the plot shows the percentages of all the examples belonging to each class that are correctly and incorrectly classified. These metrics are often called the recall (or true positive rate) and false negative rate, respectively. The cell in the bottom right of the plot shows the overall accuracy. The test confusion matrix is a real indicator of the ANN real classification performance. For example, in the TOPEN test confusion matrix in Fig. 6, the bottom row

Automatic Fault Detection and Classification in Lift Door Systems

Fig. 6. Fault classification results using the vibration signal over the phases

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shows the percentages of all the samples that are correctly classified. For target class 1 (no error) the correctly classified percentage is 58.3% and incorrectly is 41.7%. This percentages are easily calculated considering that for target class 1, the output classes of the test confusion matrix where 7 for class 1, 2 for class 2 and 3 for class 5. The correctly classified percentage is 7/(7 + 2 + 3) = 58.3%.

6 Conclusions From the test confusion matrix results shown in Fig. 6, it could be concluded that training an ANN with the information in the OPEN and CLOSE phases has led to an overall classification accuracy in the test confusion matrix above 70% (77.8% and 70.4% respectively). The classification accuracy of the ANN using the information in the phases TOPEN and TCLOSE was poor ( 60 mV·s). A clear explanation could not be found. However, the conversion from the time-dependent output data to the scalar valued QoIs can be tricky to automate. Specific settings may have caused the deviations, but they do not affect the overall quality of the fit of the meta model.

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40

V [mV]

V [mV]

20 0

Area: 15.90 mV·µs

-20 0

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t = 64.09 µs t = 93.81 µs A = 14.20 mV A = 13.57 mV

20 10 0

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Fig. 3. Time response of PZT3 and PZT7. PZT2 is assigned as actuator.

log10 (|Yα |)

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250

a: PCE coefficient spectrum

300

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b: True versus predicted QoI

Fig. 4. Spectrum diagram and PCE value versus true value of the energy based QoI, using a sparse base of 14 coefficients, obtained using LARS.

The First and Ttotal Sobol’ indices (Eqs. (5) and (6)) of the delamination meta models for PZT3 and PZT7 are shown in Fig. 5. Each group of four bars with changing gray-scale colour shows the sensitivity of the four random variables for each of the six QoI. The optimum degree p and q-norm were used, based on the lowest LOO error. The number of delaminations is, according to the expectations, an important parameter. However, it is not the most important variable in all cases, especially not for the total Sobol’ index. The importance of the x-location appears to be low: it does not matter at which location the propagating wave interacts with the delamination. The x-location can therefore be eliminated as a random variable, largely reducing the number of simulations needed to construct a sufficiently accurate meta model. Secondly, there are distinct differences between the indices of PZT2 and PZT7, hence the waves traveling along one surface and those traveling through the material. Further analysis, with other PZTs acting as actuator, are needed to explain this observation.

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ToF2 Enrgy CWT

d: Total Sobol’ PZT7

Fig. 5. First and total Sobol’ indices for the four random variables and six quantities of interest calculated from the response of PZT3 and PZT7. Amplitudes: ‘Amp1’ and ‘Amp2’; Time of Flight ‘ToF1’ and ‘ToF2’, signal energy: ‘Enrgy’; and time-frequency based energy area: ‘CWT’

6

Conclusions and Future Work

The main conclusion of the current work is that PCE can be used to create meta models of damage accumulation in a structure. With these, the effect of presence of cracks in the structure on the response measured by installed PWAS can be analysed. The global sensitivity aids in reducing the model, which is an important step in the further development. This is a first step in the direction of a RUL estimation. The next steps involve a better understanding of the relation between the QoI and the effect of the micro-cracks – which analysis is currently ongoing – and delaminations on the propagating waves. Only then, further extensions, such as the inclusion of crack propagation Random Variables and the use of 3D models can be developed.

References 1. Bakhtiari-Nejad, F., Sepehry, N., Shamshirsaz, M.: Polynomial chaos expansion sensitivity analysis for electromechanical impedance of plate. In: International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 50206. American Society of Mechanical Engineers (2016)

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2. Berveiller, M., Sudret, B., Lemaire, M.: Stochastic finite element: a non intrusive approach by regression. Eur. J. Comput. Mech. 15(1–3), 81–92 (2006) 3. Boller, C.: Structural Health Monitoring – its association and use. In: New Trends in Structural Health Monitoring. CISM – International Centre for Mechanical Sciences, vol. 542. Springer (2013) 4. Giurgiutiu, V.: SHM of fatigue degradation and other in-service damage of aerospace composites. In: Giurgiutiu, V. (ed.) Structural Health Monitoring of Aerospace Composites, pp. 395–434. Academic Press, Oxford (2016) 5. Just, G., Koch, I., Brod, M., Jansen, E., Gude, M., Rolfes, R.: Influence of reversed fatigue loading on damage evolution of cross-ply carbon fibre composites. Materials 12(7), 1153 (2019) 6. Keshtgar, A., Sauerbrunn, C.M., Modarres, M.: Structural reliability prediction using acousticemission-based modeling of fatigue crack growth. Appl. Sci. 8(1225), 1–15 (2018) 7. Konakli, K., Sudret, B.: Global sensitivity analysis using low-rank tensor approximations. Reliab. Eng. Syst. Saf. 156, 64–83 (2016) 8. Konakli, K., Sudret, B.: Polynomial meta-models with canonical low-rank approximations: numerical insights and comparison to sparse polynomial chaos expansions. J. Comput. Phys. 321, 1144–1169 (2016) 9. Lahuearta, F.: Identification of typical failures in composite rotor blades and structural health monitoring. Technical report project SLOWIND, Knowledge center WMC (2016) 10. Liu, Z., Lesselier, D., Sudret, B., Wiart, J.: Surrogate modeling based on resampled polynomial chaos expansions. Reliab. Eng. Syst. Saf. 202, 107008 (2020) 11. Loendersloot, R., Buethe, I., Michaelides, P., Bonet, M.M., Lampeas, G.: Damage identification in composite panels - methodology and visualisation. In: Smart Intelligent Aircraft Structures (SARISTU): Proceedings of the Final Project Conference, pp. 579–604. Springer (2015) 12. Loendersloot, R., Venterink, M., Krause, A., Lahuerta, F.: Acousto-ultrasonic damage monitoring in a thick composite beam for wind turbine applications. In: 9th European Workshop on Structural Health Monitoring, EWSHM 2018 (2018) 13. Moix-Bonet, M., Eckstein, B., Loendersloot, R., Wierach, P.: Identification of barely visible impact damages on a stiffened composite panel wit a probabilitybased approach. In: Proceedings of the International Workshop on Structural Health Monitoring, Stanford, USA (accepted for oral presentation). DEStech Inc. (2015) 14. Moix-Bonet, M., Wierach, P., Loendersloot, R., Bach, M.: Damage assessment in composite structures based on acousto ultrasonics - evaluation of performance. In: Smart Intelligent Aircraft Structures (SARISTU): Proceedings of the Final Project Conference, pp. 617–629. Springer (2015) 15. Ono, K., Mizutani, Y., Takemoto, M.: Analysis of acoustic emission from impact and fracture of CFRP laminates. J. Acoust. Emission 25, 179–186 (2007) 16. Puti´c, S., Uskokovi´c, P., Aleksi´c, R.: Analysis of fatigue and crack growth in carbonfiber epoxy matrix composite laminates. Strength Mater. 35, 500–507 (2003) 17. Sepehry, N., Shamshirsaz, M., Bakhtiari-Nejad, F.: Low-cost simulation using model order reduction in structural health monitoring: application of balanced proper orthogonal decomposition. Struct. Control Health Monit. 24(11), 10 (2017) 18. Su, Z., Ye, L.: Identification of Damage Using Lamb Waves - From Fundamentals to Applications. Lecture Notes in Applied and Computational Mechanics, vol. 48. Springer (2009)

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19. Su, Z., Ye, L., Bu, X.: A damage identification technique for CF/EP compositelaminates using distributed piezoelectric transducers. Compos. Struct. 57, 465–471 (2002) 20. Su, Z., Ye, L., Lu, Y.: Guided lamb waves for identification of damage in composite structures: a review. J. Sound Vibr. 295(3–5), 753–780 (2006) 21. Sudret, B.: Polynomial chaos expansions and stochastic finite element methods. In: Risk and Reliability in Geotechnical Engineering, pp. 265–300. CRC Press (2015) 22. Worden, K., Farrar, C., Manson, G., Park, G.: The fundamental axioms of structural health monitoring. Proc. Roy. Soc. A 463, 1639–1664 (2007)

Optimal Finite Difference Schemes for Multiple Damage Identification in Beams Daniele Cinque1(B) , Jose Viriato Araújo dos Santos2 , Stefano Gabriele3 , Sonia Marfia1 , and Hernani Lopes4 1 Department of Engineering, Roma Tre University, Rome, Italy

[email protected] 2 Universidade de Lisboa, IDMEC, Instituto Superior Técnico, Lisbon, Portugal 3 Department of Architecture, Roma Tre University, Rome, Italy 4 Instituto Politécnico do Porto, DEM, ISEP, Porto, Portugal

Abstract. This paper presents an experimental and numerical study on multiple damage localization in a beam. The modal rotations of an aluminum beam were measured with shearography and post-processed to obtain the modal curvatures. The modal curvatures, which are computed by finite differences, are used as damage indicators. In most approaches available in the literature, the modal curvatures are defined from the modal displacements, requiring the computation of the second order derivate. In the present approach, since the modal rotations are available, the curvatures are obtained by computing only the first order derivative, reducing the propagation of measurement errors. Optimal samplings for both the forward and the central finite difference schemes, the latter with three and five points formulas, are derived. The results of applying these three finite difference formulas are compared, showing that both central finite differences allow for a better representation of the experimental modal curvature. Therefore, the perturbations on the modal curvatures are better identified, thus clearly indicating the damage presence. Keywords: Multiple damage · Beam · Modal rotations · Shearography · Finite differences · Optimal sampling

1 Introduction Structural damage detection has always been a problem of great interest in engineering. The possibility of identifying where a structural problem is located and characterising it is indeed a question of major relevance in order to guarantee the safety of structures. The spread of different damage detection methods through the twentieth century led to the need for a classification that was presented by Rytter [1] at the beginning of the nineties. The standard by which different methods are classified is based on the information about the damage that each method is able to provide: Level 1 - Identification of the presence of the damage; Level 2 - Localisation of the damage to the structure; Level 3 - Quantification of the severity of the damage; Level 4 - Estimation of the remaining

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 788–798, 2021. https://doi.org/10.1007/978-3-030-64908-1_73

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lifetime of the structure. The main purpose of the present paper is to show an efficient technique capable of identifying single and multiple damage in beams with respect to the first two levels of Rytter’s classification. The work involved an experimental campaign and a subsequent numerical analysis of the measured data. During the experimental part, Electronic Speckle Pattern Shearing Interferometry (ESPSI), known in the literature as shearography, was used to measure the rotation fields of the mode shapes of three damaged beams. Each one of the beams has a specific damage intensity. According to Pandey et al. [2], the curvature of the mode shapes, also referred to as modal curvature, represents the best eigenparameter to detect the damage location. Indeed, since the curvature of a beam, ∂ 2 w/∂x2 , is related to its bending stiffness, EI, the alteration of its section properties (e.g. section’s area) produced by the damage will significantly affect its curvature. From an experimental point of view, only the displacement and the rotation fields of the mode shapes, which are also referred to as modal displacements and modal rotations, are available. Therefore, to obtain the curvature field, one has to numerically differentiate the experimental data, with the risk of propagating both the noise present in the experimental data and the error of the numerical method. The advantage of using shearography is that this is a full-field optical technique that allows a direct measurement of the modal rotations of the structure. As a result, just one numerical differentiation is needed to obtain the modal curvatures and therefore, propagation of both the numerical error and the noise during the derivation process is minimised. The experimental modal rotations were numerically differentiated by using various Finite Difference Methods (FDMs), with the purpose of analysing which approach would lead to the most accurate evaluation of the modal curvatures. Thus, the search for the best modal curvatures was conducted through the analysis of the total error that each FDMs generated. With the purpose of minimising the total error and consequently avoiding its propagation through the differentiation process, the optimal spatial sampling technique was used. A comprehensive description of this technique can be found in the work of Mininni et al. [4].

2 Methodology 2.1 Measurement of Modal Rotations with Shearography The experiment involved analysing the dynamic behaviour of damaged beams by using shearography. In order to study both single and multiple damage scenarios, the experiment considered three different damage scenarios relative to three different damaged beams. The first four bending modal rotations of the beams in a free-free condition were measured. Each scenario involved an aluminium beam (400 mm × 40 mm × 2.85 mm) that was intentionally damaged by introducing slots with a milling machine. The three damaged scenarios consisted of one single damage scenario and two multiple damage scenarios. The experiment also considered an undamaged scenario that serves as a baseline for a comparative analysis. The dimensions of the aluminium beam and the location and width of the two slots are displayed in Fig. 1, while the three damage scenarios with the identification of the characteristics of the slots are presented in Table 1 and Table 2.

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Slot 2

Slot 1

As can be noticed in both tables, the presence of a slot results in the reduction of thickness and thus in a reduction of bending stiffness. The location of the slots was chosen according to the maximum curvatures of the first four mode shapes for the free-free condition of the beam, in order to maximize the effect of the slots on the mode shapes.

Fig. 1. Dimensions of the beam and the slots in mm.

Table 1. Characteristics of slot 1 in the different damage scenarios. Damage scenario

SLOT 1 Location [mm]

Depth [mm]

Width [mm]

1

200

0.2

10

2

200

0.2

10

7

20

3

200

0.85

10

28

63

Reduction of thickness [%] 7

Reduction of bending stiffness [%] 20

Table 2. Characteristics of slot 2 in the different damage scenarios. Damage scenario

SLOT 2 Location [mm]

1

–

2

64.5

3

64.5

Depth [mm]

–

Width [mm]

Reduction of thickness [%]

Reduction of bending stiffness [%]

–

–

–

0.2

10

7

20

0.85

10

28

63

Since shearography measures the modal rotations of the beam through an optical analysis of the deformation of its surface, the beam must be analysed while being excited by an external stimulus capable of deforming the surface according to its modal shapes. Therefore, in order to correctly excite the beam, natural frequencies must be previously measured. With this purpose, experimental modal analysis was performed on the beams, allowing the measurement of the natural frequencies of the different beams. This analysis

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requires a type of equipment that measures the external stimulus as input and the response of the structure as output, in order to evaluate the Frequencies Response Functions (FRFs). An impact hammer (model 086C01 from PCB Piezotronics) was used to excite the beam. The force sensor incorporated in the hammer’s striking surface allows to capture the impulsive force produced during the impact. The structure response was measured by a microphone (model 46AE from GRAS). This enabled us to measure the sound pressure levels caused by the vibration of the excited beam that propagate through air. According to Elwali et al. [5], acoustic modal analysis is based on the assumption that emitted sound pressure levels vary linearly with vibration amplitudes at a certain frequency. The microphone measures the frequencies of the excited beam directly, with the great advantage (in respect to other methods of acquisition such as modal analysis conducted with the use of accelerometers) of not adding mass to the structure. Once the input and output signals are sampled and post-processed by the signal analyser (model OR34 from OROS), the relation between response and force, i.e. the FRF, can be evaluated. The natural frequencies are obtained from this FRF. The results presented in Table 3 indicate a reduction of the natural frequencies as the severity of the damage increases. Table 3. Natural frequencies of the beam analysed in the different damage scenarios. Frequency order

Undamaged beam [Hz]

Damage scenario 1 [Hz]

Damage scenario 2 [Hz]

Damage scenario 3 [Hz]

1st

92.00

91.25

91.25

87.00

2nd

254.25

254.00

253.00

248.50

3rd

499.50

496.50

493.00

465.00

4th

827.75

826.75

820.50

793.00

After the estimation of the natural frequencies, we proceeded by setting-up the shearography tests, showed in Fig. 2. The beams are analysed in free-free boundary conditions. These conditions were obtained by suspending the beams from a frame with two flexible wires that were glued to each extremity. To increase the stability of the beams during their excitation and avoid rigid body motions, two pieces of soft foam were placed close to the opposite side of the measurement surfaces. We also placed two loudspeakers close to the surfaces, in order to excite the beams at their natural frequencies. Shearography is fundamentally based on the speckle pattern effect, which is generated on the surface of objects by a highly coherent light with which this surface is illuminated. With this purpose, a laser source of 1.3 W with a wavelength of 532 nm from Coherent model Verdi was used. To perform the measurements, two of these waves of light must be superimposed, resulting in the interference pattern that appears as a granular image characterised by the presence of random bright and dark spots. We let the laser beam pass through a calibrated lens in order to spread the well-collimated light source and get a more homogeneous illumination of the object. A 4-megapixel camera allowed us to capture a digital image of the surface with a spatial resolution of 2,300 × 225 pixels,

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Dual signal generator Loudspeaker

Acoustic-optic modulator Soft foam

Suspended beam

Spatial filter Calibrated lens Piezolectric system controller

Shearography system

Fig. 2. Experimental setup for the shearography test.

respectively, in the horizontal and vertical directions. This spatial resolution corresponds to a sampling interval of 0.17 mm. The shearography system that was used in the present work uses a stroboscopic laser illumination combined with the temporal phase modulation technique [6]. The synchronization between the illumination and the vibration excitation, obtained by using an acoustic-optic modulator, model ADM-70 from InterAction Corp, freezes in time the speckle pattern [7]. With this technique the phase distributions before and after the acoustic excitation can be measured and the relative phase change can be evaluated by simple subtraction. The graphical representation of φ takes the name of phase map and it appears as a phase fringe pattern. There is noise in the phase map that must be filtered in order to smooth the phase fringe pattern. Then, a subsequent unwrapping process is needed to eliminate the discontinuity in the filtered phase map. In the present work, the sine/cosine average filter technique, presented by Aebischer and Waldner [8] and the Goldstein unwrapping method, which is discussed in the work of Ghiglia et al. [9], were applied. According to Mininni et al. [4], all these steps are part of the image processing, which is a numerical technique required to make the modal rotation fields as clean and clear as possible. The post-processed phase map is finally used to evaluate the modal rotations of the beams. Indeed, it can be demonstrated that there is a relation between the first derivative of the out-of-plane displacement, ∂w(x, y)/∂x, and the relative phase change, φ, as Eq. (1) shows. φ(x, y) ≈

4π δx ∂w(x, y) λ ∂x

(1)

In the above expression, λ represents the wavelength of the laser (532 nm) and δx is the shearing amount in the direction (5 mm). The shearing value given by the Michelson

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interferometer can be adjusted in order to control the sensitivity of the measurements of the modal amplitude. It can be noticed that by taking into consideration the hypothesis of small deformations, Eq. (1) describes the relation between the modal rotation and the phase map. Hence, the unwrapped two-dimensional phase map can be used to solve Eq. (1) in order to obtain the modal rotations (Fig. 3).

Fig. 3. Results of shearography for damage scenario 3: a) Phase map; b) Filtered phase map; c) Modal rotations.

2.2 Computation of Modal Curvatures with Finite Differences In order to evaluate the modal curvatures of a beam, the Finite Difference Method (FDM) was implemented. All the finite difference formulas that were evaluated in this section, can be found in the book of Abramowitz and Stegun [10]. In this book, one can find the Forward Finite Difference formula with two points (FFD2) and two central Finite Difference (CFD) formulas: the three points formula (CFD3) and the five-points formula (CFD5). These three formulas give us three distinct ways to compute the modal curvatures, as the first derivative of rotations: θ (x + h) − θ (x) d θ (x) ≈ dx h

(2)

d θ (x) θ (x + h) − θ (x − h) ≈ dx 2h

(3)

d θ (x) 2θ (x − 2h) − 16θ (x − h) + 16θ (x + h) − 2θ (x + 2h) ≈ dx 24h

(4)

Equations (2), (3) and (4) lead to three distinct error values, which are dependent on the spatial sampling h. Indeed, as the number of points used to evaluate the first order derivative gets higher, the numerical error gets lower. The three approximated mean errors are displayed in Eqs. (5), (6) and (7).   h  d 2 θ (x)  (5) Em,FFD2 =   2  dx2    h2  d 3 θ (x)  Em,CFD3 =  (6)  6  dx3 

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Em,CFD5

  h4  d 5 θ (x)  =   30  dx5 

(7)

By observing the mean errors, it is obvious that as the spatial sampling decreases, the approximated modal curvature becomes more precise. This is in accordance with the definition of derivative of a function as the limit of the difference quotient as h approaches zero. However, in practice, when a lower value of the spatial sampling is considered, a larger error will occur in the evaluation of the modal curvature. This behaviour is due to the round-off error, which is generated by several disturbances present in the measurements, such as the varying background illumination, electronic noise, speckle decorrelation, digitization and environmental noise. The summation of all these factors creates a noisy measurement. According to Moreno-García et al. [3, 11] this error is defined as follows: θ (x) = θ˜ (x) ± Er (x)

(8)

In Eq. (8), θ indicates the measured values of the modal rotation obtained with the experiment, while θ˜ indicates the value of the modal rotation that one should obtain ˜ making the hypothesis that the data is noise-free. According to Mininni et al. [4], θ(x) can be evaluated by smoothing the experimental measures in order to get a set of noisefree values. Therefore, the round-off error can be estimated for each value of the modal rotation with Eq. (9).  ∈  ˜  (9) Er (x) = θ(x) 2 In the above expression,  is the measurement accuracy, which is computed as the mean difference between the measured modal rotations and the smoothed modal rotations. The smoothing was carried out by using a cubic spline interpolation of the measured modal rotation. In this process, we considered several splines, each one leading to different values of the measurement accuracy. The values of the measurement accuracy obtained from the four mode shapes considered show an oscillation of the average value between 0.0001 m/m and 0.0003 m/m. In order to avoid an overestimation of the round-off error, a value of 0.0001 m/m was considered in the evaluation of the modal curvature of each mode shape. The round-off error for each finite difference method is simply obtained by substituting Eq. (8) in the finite difference formulas. For the FFD2, CFD3 and CFD5 formulas, the mean value of the round-off error is given, respectively, by Eqs. (10), (11) and (12).  2 ∈  ˜  θ(x) h2  2 ∈  ˜  Er,CFD3 = θ(x) 2h 2  36 ∈   Er,CFD5 = θ˜ (x) 24h 2 Er,FFD2 =

(10) (11) (12)

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The total mean error is obtained by the summation of the error of the method and the round-off error. By considering the mean total error of a finite difference method, it can be noticed that there is a value of the spatial sampling that minimizes the error. This value, highlighted in Fig. 4 as hopt , is commonly referred to as optimal spatial sampling. If the modal curvatures are evaluated by using either a lower or a higher value than the optimal spatial sampling, they will have considerable errors. The two distinct cases are generally known as oversampling and undersampling. Table 4 presents the optimal spatial sampling for each modal curvature and for each finite difference method studied. According to the results showed by Mininni et al. [4], it can be observed that the values of the optimal spatial sampling decrease as the mode shape of the beam becomes more complex, while the values of the total mean error increases.

Fig. 4. Optimal spatial sampling of the FFD2, CFD3 and CFD5 formulas estimated for the first modal curvature.

Table 4. Optimal spatial sampling values and total mean error of the FFD2, CFD3 and CFD5 formulas. Mode shape

hopt,FFD2 [mm]

hopt,CFD3 [mm]

hopt,CFD5 [mm]

Etot,FFD2 [mm−1 ]

Etot,CFD3 [mm−1 ]

Etot,CFD5 [mm−1 ]

Mode 1

1.7219

5.1656

20.8348

0.0813

0.0098

0.0031

Mode 2

0.8609

2.9272

12.2254

0.1336

0.0149

0.0046

Mode 3

0.5166

2.0663

8.4372

0.1827

0.0194

0.0059

Mode 4

0.5166

1.7219

6.7153

0.2446

0.0261

0.0080

3 Damage Identification After the evaluation of the optimal spatial sampling, hopt , the modal curvatures of the damage scenarios were calculated by applying the three numerical methods and the respective optimal spatial sampling values previously obtained. In order to check the accuracy of the results, the numerical modal curvatures are displayed together with their analytical counterparts. Since the purpose is to localize the damage by analysing

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the modal curvature, a mode-by-mode analysis was carried out. Indeed, some modal curvatures take on the value zero in some points of the beam, with the consequence that the damage cannot be detected at those locations (e.g. Fig. 5d, Fig. 5e and Fig. 5f). Moreover, it can be noticed how the difficulty of detecting the damage varies accordingly to its intensity. Indeed, damage scenario 1, consisting of a small slot, shows a perturbation due to the damage that is comparable to the disturbances due to the total error (e.g. Fig. 6).

Fig. 5. Damage scenario 3: Third modal curvature estimated with a) FFD2; b) CFD3; c) CFD5; Second modal curvature estimated with d) FFD2; e) CFD3; f) CFD5.

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Fig. 6. Damage scenario 1: First modal curvature estimated with a) FFD2; b) CFD3; c) CFD5.

4 Conclusions In conclusion, the FFD2 formula gave the worst evaluation of the modal curvatures, while the CFD formulas gave the best results. Among the CFD formulas, the smoothest results were achieved by using the CFD5 formula. However, it can be noticed that the damage is not detected as well as when the modal curvatures were evaluated with the CFD3 formula. Indeed, since the CFD5 formula is characterised by a larger optimal spatial sampling, the evaluated modal curvatures appear smoother as well as the perturbation due to the damage. In order to detect the damage, it is therefore recommended to use the CFD3 formula, which shows a less smooth modal curvature. Furthermore, when large damage is considered, which is the case of damage scenarios 2 and 3, all three formulas will show the perturbation due to the damage. However, in this last case it is advisable not to use the CFD5 formula, which will lead to an unnecessary smoothed modal curvature, from which the damaged area can hardly be detected.

References 1. Rytter, A.: Vibrational Based Inspection of Civil Engineering Structures, p. 193 (1993) 2. Pandey, A., Biswas, M., Samman, M.: Damage detection from mode changes in curvature. J. Sound Vib. 145, 321–332 (1991) 3. Moreno-García, P., Araújo dos Santos, J.V., Lopes, H.: A new technique to optimize the use of mode shape derivatives to localize damage in laminated composite plates. Compos. Struct. 108(1), 548–554 (2014) 4. Mininni, M., Gabriele, S., Lopes, H., Araújo dos Santos, J.V.: Damage identification in beams using speckle shearography and an optimal spatial sampling. Mech. Syst. Signal Process. 79, 47–64 (2016) 5. Elwali, W., Satakopan, H., Shauche, V., Allemang, R., Phillips, A.: Modal parameter estimation using acoustic modal analysis (2010)

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6. Araújo dos Santos, J.V., Lopes, H.: Application of speckle interferometry to damage identification, pp. 299–330 (2012) 7. Yang, L., Xie, X.: Digital Shearography: New Developments and Applications. SPIE Press, Bellingham (2016) 8. Aebischer, H.A., Waldner, S.: Simple and effective method for filtering speckleinterferometric phase fringe patterns. Opt. Commun. 162(4), 205–210 (1999) 9. Ghiglia, D., Pritt, M.: Two-dimensional phase unwrapping: theory, algorithms, and software (1998) 10. Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (1964) 11. Moreno-García, P., Lopes, H., Araújo dos Santos, J.V.: Application of higher order finite differences to damage localization in laminated composite plates. Compos. Struct. 156, 385– 392 (2016)

Path Identification of a Moving Load Based on Multiobjective Optimization Michał Gawlicki and Łukasz Jankowski(B) Institute of Fundamental Technological Research (IPPT PAN), Polish Academy of Sciences, Warsaw, Poland [email protected]

Abstract. This contribution presents and tests experimentally a nonparametric approach for indirect identification of 2D paths of moving loads, based on the recorded mechanical response of the loaded structure. This is an inverse problem of load identification. The method to be proposed is based on multicriterial optimization with two complementary criteria. The first criterion is purely mechanical, and it quantifies the misfit between the recorded mechanical response of the structure and its predicted response under a given trajectory. The second criterion is geometric: it represents the heuristic knowledge about the expected geometric regularity characteristics of the load paths (such as related to linear and angular velocity), and in fact it can be considered to be a regularizing criterion. A multicriterial genetic search is used to determine and advance the Pareto front, which helps to strike the balance between the response fit and the geometric regularity of the path. The proposed approach is tested in an experimental laboratory setup of a plate loaded by a line-follower robot and instrumented with a limited number of strain gauges. Keywords: Moving load · Trajectory identification · Inverse problem · Structural health monitoring · Multicriterial optimization

1 Introduction Structural health monitoring (SHM) is a rapidly developing field of research with a clear and well-defined application context [1]. The objectives of SHM systems can be generally divided into two main groups: identification of structural damages [2, 3] and identification of structural loads and excitations [4, 5]. This contribution belongs to the second group, as it is devoted to the problem of indirect identification of a moving load based on the recorded mechanical responses of the structure subjected to the load. More specifically, the goal is to determine only the path of the moving load, irrespective of its magnitude (which can be a subject to identification and/or processing at the later stages). In general, such a problem is an inverse problem of load or input identification. These inverse problem have been intensively studied, and thorough reviews can be found in references [6–8]. As their typical feature, load identification problems are characterized by © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 799–807, 2021. https://doi.org/10.1007/978-3-030-64908-1_74

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1) a very large number of the structural degrees of freedom in which the moving load can act and should be ultimately identified, and 2) a relatively limited number of sensors that can be used to measure the response of the structure and provide the information for identification. Any naïve solution, to be found directly based on the minimization of the response misfit, is not well-defined, which stems from the fact that the number of unknowns to be identified is much larger than the number of equations used for this purpose. The solution formulated this way is thus nonunique. To guarantee its uniqueness, typical approaches impose restrictions on the generality of the load that is identified, which in case of moving loads amounts primarily to the assumption that the movement path (and thus the degrees of freedom on the way) is known. In effect, the problem is most often reduced to the case of a single vehicle moving at a constant speed through a one dimensional bridge [9–12], which lefts unknown and subject to identification only the magnitude of the load (or the vehicle mass). This work follows the opposite approach. The goal is to ignore the exact magnitude of the load and to identify its temporal path. The problem was already studied [13] in the context of one-dimensional beams using l1 -based promotion of sparsity [14, 15], and it has been possible to perform a qualitative path identification of a load moving on a beam, including its temporal features such as accelerations, stops, decelerations, etc. However, path identification becomes particularly interesting in case of loads freely moving over two-dimensional structures such as plates. Related investigations can be also found in references [16] and [17]. Therefore, the aim of this work is to perform a qualitative identification of the path of a single load that moves and excites a plate structure. To ensure the uniqueness of the solution, it is noticed that paths of such loads are expected to demonstrate certain geometric regularity features. Informally, in many contexts they are expected to be relatively smooth. Such a requirement occurs also in vision-based target-tracking algorithms [18], and it can be promoted by using a multiobjective optimization approach to balance between the mechanical response-based criterion and the criterion of geometric regularity. This amounts to an inclusion of an apriorical information into the identification procedure with the aim of providing for missing information (limited number of sensors) and errors (related to modeling and measurement inaccuracies). In the following, the experimental laboratory setup is described in Sect. 2, including the actual path of the moving load. Section 3 outlines the identification approach. Finally, Sect. 4 presents preliminary identification results.

2 Laboratory Test Stand 2.1 Plate The experimental laboratory setup is a plate made of steel and pointwise supported in the middle and near the edges. The plate is 1 m × 1 m × 0.5 mm in dimensions. It is shown in Fig. 1.

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Fig. 1. The experimental steel plate on the supporting structure. The line-follower robot is shown in the bottom left part of the plate. The outermost square path is used in the identification process.

The moving load is vertical and is implemented in the form of the gravity of a moving line-follower robot (0.3 kg). The speed of the robot is constant and about 10 cm/s. In the experiment, it followed the square closed-loop path as indicated by thick black marks on the upper face of the plate. At the bottom face, the plate was instrumented with 8 strain gauges with the response recorded at 50 Hz. 2.2 The Actual Path of the Moving Load The line-follower robot follows the outermost square path marked with a thick black line in Fig. 1. The path is followed two times, that is the robot accomplished approximately two loops around the plate. The corresponding recorded responses of the strain sensors (located at the bottom face of the plate) are plotted in Fig. 2. It can be noticed that the response has a quasi-static character, which results from a relatively low speed of the line-follower robot. In effect, in computing the response of the plate, no timedeconvolution has to be considered, which significantly decreases the computational cost of identification.

3 The Inverse Problem The standard approach to inverse problems in structural engineering is to minimize the misfit between the measured and modeled response of the structure (or certain characteristics of the response). This amounts to the task of minimization of the response residuum. This is also the basic objective function used in this research. However, as discussed in Introduction, formulations directly based on such an objective function only are characterized by two typical problems:

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Fig. 2. Signals of the eight strain sensors in response to the line-follower robot following the square path twice. The quasi-static character of the response is evident.

1) The solution is nonunique in result of insufficient number of sensors. In practical applications there are usually much more degrees of freedom potentially exposed to load than sensors used to measure the response. In effect, the inverse problem is not well-defined underdetermined and there are infinitely many exact solutions. 2) Ill-conditioning of the problem, which manifests itself in a large sensitivity of the identified load to the measurement data, and especially to the measurement errors, even if small. As in typical formulation there is usually an infinite number of exact solutions that minimize the response residuum, it is reasonable to further sort such exact or near-exact solutions based on additional knowledge. In case of path identification, there are two such criteria, which are both intuitively obvious and expected: 1) The load is sparse. This is sometimes formulated in terms of the l1-norm of the solution [8, 11, 12]. Here, the so-called l 0 -norm of the solution is restricted to one, which amounts to the assumption that there is only a single load and a single load path that needs to be identified. 2) A reasonable path of a moving load is expected to behave somewhat predictably in geometric terms. In other words, it might be assumed to satisfy certain geometric regularity conditions. The geometric regularity is quantified here and expressed in the form of an additional objective function. Such a function complements the response-based objective function and effectively regularizes the geometry of the load path. Both functions can be optimized concurrently using a multiobjective optimization approach. The resulting Pareto front identifies the paths that represent the changing importance of the two objectives and allows the balanced load path to be found.

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3.1 Response Residuum The recorded responses of the strain sensors, as shown in Fig. 2, do not demonstrate any clear transient dynamic features. Consequently, it is assumed that the problem is quasi-static, which allows the computationally costly operation of deconvolution to be avoided. The response of the sensors can be thus modeled time point by time point by the following static equation: ε(t) = Bf (t),

(1)

where the response is a vector of the eight measurements of the strain sensors in time point t, the load is represented in the form of the vector f (t) of nonnegative load magnitudes in a number of potentially loaded plate points (the 10 × 10 grid shown in Fig. 1), and the compliance matrix B represents the relation between the strain responses and potentially loaded plate points. Such a formulation, together with the assumption of sparsity outlined above, allows the response of the sensors to be modeled directly in terms of the load location and magnitude as ε(x(t)), where x(t) is the location of the moving load in time t. Given such a response model, the first objective function quantifies the misfit between the measured response of the sensors and the modeled response, and it is defined as:  2   (2) F1 (x) = ln ∫T0 ε(x(t)) − ε M (t) , where εM (t) is the senor response measured in time t. 3.2 Path Regularity The regularity of the path x(t) is quantified by the second objective function. Here the regularity is defined in geometric terms by means of the linear speed and angular velocity of the moving load. Formally, it is proposed to associate the geometric regularity with a stable linear speed and limited angular velocity, in the form of the following weighted sum:     2 2 ∫T0 ˙x − ∫T0 ˙xdt dt (˙x1 x¨ 2 − x˙ 2 x¨ 1 ) T , (3) F2 (f ) = α ∫0 ln 1 + 2 dt + β  ∫T0 ˙xdt δ + x˙ 2 + x˙ 2 1

2

where the explicit dependence on time has been omitted for notational clarity. In Eq. (3), the first term quantifies the angular velocity, the second term quantifies the stability of the linear speed, and δ is a small number that ensures the denominator of the first term is nonzero for temporary stable paths. The magnitudes of the weighting coefficients can be selected based on the F 1 -optimal path. 3.3 The Optimization Procedure The optimization aims at a concurrent minimization of two objective functions, F 1 defined in Eq. (2) and F 2 defined in Eq. (3). This a multiobjective optimization problem that needs to be solved using specialized techniques. The result of optimization is

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the Pareto front of best, that is non-dominated solutions, which allows to balance the influence of the objective functions on the resulting path of the moving load: from fully conforming to the noisy measurements (but irregular geometrically) to fully regular geometrically (but having not much in common with the measurements). A specialized multiobjective genetic algorithm is used, and the initial population contains the F 1 -best load path. In successive generations, this naïve path is modified by the typical binary operations of mutation, cross-over and selection. Notice that the objective functions defined in Eqs. (2), (3) are computationally relatively costly and thus before application they are discretized to consider a discretized representation of the load path, which allows the computational time to be significantly reduced.

4 Preliminary Identification Results The outermost square path has been followed twice by the robot, see Fig. 1. The corresponding measurements of the strain sensors are shown in Fig. 2. The response and the load have a quasi-static character, so that the measurements are downsampled to one measurement each 2 s, which allows the robot to advance about 20 cm along the path in-between the measurement time instances. The total number of the time steps is 34, which corresponds to 66 s. Figure 3 shows the Pareto front obtained after 10000 generations together with the entire population of size 300 individuals. Each individual corresponds to a load path and is represented by a point in the F 1 –F 2 space. All the individuals are located on the Pareto front, and they are marked with green dots. The mechanical criterion F 1 was computed using the responses of only three sensors out of the eight considered (No. 1, 5 and 7). Figure 4 illustrates six specific load paths that correspond to the individuals labelled “A” to “F” in Fig. 3 and marked with larger yellow dots. The path “A” is the F 1 -best path, that is the path that minimizes the residuum norm. The path “F” is the F 2 -best path that was found during the 10000 iterations. It is the most regular path out of all paths generated and considered. It can be noticed how the relative importance of the criteria F 1 and F 2 change along the Pareto front from the path “A” to the path “F”. The proposed criterion of geometric regularity indeed has a regularizing effect on the identified paths.

Fig. 3. The population of 300 individuals obtained in 10000 generations, shown in the F 1 –F 2 space. The individuals on the Pareto front are marked green. Six selected individuals on the Pareto front are explicitly marked and correspond to the load paths shown in Fig. 4.

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Fig. 4. The load paths that correspond to the six individuals labelled “A” to “F” in Fig. 3. The paths have been sampled every 2 s, which corresponds to 20 cm of the robot path. The blue path in-between the sampling points is a 3rd -order spline interpolation. The changing importance of the criterion of regularity can be clearly observed along the Pareto front.

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5 Conclusion and Future Research A multiobjective identification of two-dimensional moving load paths is presented and tested using a lab-sized plate structure. The proposed approach is based on concurrent minimization of two objective functions. One of them is based on the measured mechanical response of the loaded formulation employs two objective functions: one is response-based and quantifies the response misfit between the measurements and the modeled response. The second function is designed to quantify the path regularity as expressed in purely geometric terms of linear speed and angular velocity. The lab setup is a 1 m × 1 m thin steel plate subjected to a moving excitation in the form of a line-follower robot. There are several interesting direction for future research, such as identification of multiple load paths, reformulation into the Bayesian context [19, 20], the problem of proper placement of the available sensors [21], reformulation into a local substructural monitoring problem [22] of moving loads, as well as incorporation into the online context of semi-active control systems to limit the response of the loaded structure [23, 24]. Acknowledgments. The authors gratefully acknowledge the support of the National Science Centre, Poland, granted under the grant agreement 2018/31/B/ST8/03152.

References 1. Annamdas, V.G.M., Bhalla, S., Soh, C.K.: Applications of structural health monitoring technology in Asia. Struct. Health Monit. 16(3), 324–346 (2017) 2. An, Y., Chatzi, E., Sim, S., Laflamme, S., Błachowski, B., Ou, J.: Recent progress and future trends on damage identification methods for bridge structures. Struct. Control Health Monit. 26(10), e2416 (2019) 3. Miskiewicz, M., Pyrzowski, L., Wilde, K.: Structural health monitoring system for suspension footbridge. In: Proceedings of the 2017 Baltic Geodetic Congress (Geomatics), Gda´nsk, Poland, Article No. 8071495, pp. 321–325 (2017) 4. Yu, L., Chan, T.H.T.: Moving force identification from bridge dynamic responses. Struct. Eng. Mech. 21(3), 369–374 (2005) 5. Jankowski, Ł.: Off-line identification of dynamic loads. Struct. Control Health Monit. 37(6), 609–623 (2009) 6. Zhu, X.Q., Law, S.S.: Recent developments in inverse problems of vehicle–bridge interaction dynamics. J. Civ. Struct. Health Monit. 6(1), 107–128 (2016) 7. Yu, L., Chan, T.H.T.: Recent research on identification of moving loads on bridges. J. Sound Vib. 305(1–2), 3–21 (2007) 8. Klinkov, M., Fritzen, C.P.: An updated comparison of the force reconstruction methods. Key Eng. Mater. 347, 461–466 (2007) 9. Zhu, X.Q., Law, S.S.: Practical aspects in moving load identification. J. Sound Vib. 258(1), 123–146 (2002) 10. Zhang, Q., Jankowski, Ł., Duan, Z.: Simultaneous identification of moving masses and structural damage. Struct. Multidiscipl. Optim. 42(6), 907–922 (2010) 11. Wu, S.Q., Law, S.S.: Statistical moving load identification including uncertainty. Probab. Eng. Mech. 29, 70–78 (2012)

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12. Zhang, Q., Jankowski, Ł., Duan, Z.: Simultaneous identification of moving vehicles and bridge damages considering road rough surface. Math. Probl. Eng. 2013, 963424 (2013) 13. Gawlicki, M., Jankowski, Ł.: Identification of moving loads using the l1 norm minimization. AIP Conf. Proc. 1922, 100007 (2018) 14. Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006) 15. Baraniuk, R.G.: Compressive sensing. IEEE Signal Process. Mag. 24(4), 118–121 (2007) 16. Pan, C.D., Yu, L., Liu, H.L., Chen, Z.P., Luo, W.F.: Moving force identification based on redundant concatenated dictionary and weighted l1-norm regularization. Mech. Syst. Signal Process. 98, 32–49 (2018) 17. Bao, Y., Li, H., Chen, Z., Zhang, F., Guo, A.: Sparse l1 optimization-based identification approach for the distribution of moving heavy vehicle loads on cable-stayed bridges. Struct. Control Health Monit. 23(1), 144–155 (2016) 18. Milan, A., Schindler, K., Roth, S.: Multi-target tracking by discrete-continuous energy minimization. IEEE Trans. Pattern Anal. Mach. Intell. 38(10), 2054–2068 (2016) 19. Samagassi, S., Jacquelin, E., Khamlichi, A., Sylla, M.: Bayesian sparse regularization for multiple force identification and location in time domain. Inverse Probl. Sci. Eng. 27(9), 1221–1262 (2019) 20. Hou, J., An, Y., Wang, S., Wang, Z., Jankowski, Ł., Ou, J.: Structural damage localization and quantification based on additional virtual masses and Bayesian theory. J. Eng. Mech. 144(10), 04018097 (2018) ´ 21. Błachowski, B., Swiercz, A., Ostrowski, M., Tauzowski, P., Olaszek, P., Jankowski, Ł.: Convex relaxation for efficient sensor layout optimization in large-scale structures subjected to moving loads. Comput. Aided Civil Infrastruc. Eng. 35(10), 1085–1100 (2020) 22. Hou, J., Jankowski, Ł., Ou, J.: Frequency-domain substructure isolation for local damage. Adva. Struct. Eng. 18, 137–154 (2015) 23. Pisarski, D., My´sli´nski, A.: Online adaptive algorithm for optimal control of structures subjected to travelling loads. Optimal Control Appl. Methods 38(6), 1168–1186 (2017) 24. Popławski, B., Mikułowski, G., Mróz, A., Jankowski, Ł.: Decentralized semi-active damping of free structural vibrations by means of structural nodes with an on/off ability to transmit moments. Mech. Syst. Signal Process. 100, 926–939 (2018)

Damage Study Using Series and Parallel Electrode in Electromechanical Impedance Method Shishir Kumar Singh(B) , Wiesław M. Ostachowicz, and Paweł H. Malinowski Institute of Fluid Flow Machinery, Polish Academy of Sciences, Fiszera 14, 80-231 Gdansk, Poland [email protected]

Abstract. Electromechanical Impedance (EMI) method employs high frequencies range in assessing the local structural damage, using various damage metrics. These dam-age metrics are used as a tool to separate quantitatively EMI spectra into classes of the damage presence level and location in the structure. This paper describes the EMI based damage quantification using two piezoelectric transducers on the steel beam structure. The series and parallel combinations were studied and compared with the output of single sensors. The theoretical approach for simulating the serial and parallel connections was proposed and tested. The performance comparison was done in the selected frequency range: 600–800 kHz. The advantage of using the parallel connection was shown on the considered example of the steel beam with and additional mass. The mass was successfully detected and the time needed for measurements was reduced. It was also shown that the simplified model of parallel connection gives the comparison result to the real connection of the two transducers. Keywords: Electromechanical impedance · Piezo-actuator · Series combination · Parallel combination · Damage index

1 Introduction The civil, aerospace and mechanical structures are prone to corrosion, fatigue, wear and delamination-like structural defects. Electromechanical impedance (EMI) method is considered as sensitive to incipient damage and useful for monitoring cracks, delamination, etc. EMI method employs high frequencies range for assessing the local structural health of the structure [1, 2]. The piezoelectric transducers are used in an EMI method for the data acquisition and act as sensor and actuator. The electrical impedance (Z) of the bonded transducer is equal to the applied voltage (V) divided by the current (I) passing through it, and it is a function of frequency (ω) [2, 3]: Z(ω) =

1 V = I G + jB

where: G – conductance B – susceptance. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 808–816, 2021. https://doi.org/10.1007/978-3-030-64908-1_75

(1)

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The EMI method effectiveness depends on the selection of effective frequency spectrum which is hard to determine for the incipient damages in the structure. There is no theoretical methodology to determine the effective frequency range of the transducer from the experimental data and trial and error method is the most popular in determination of the robust frequency range [4, 5]. The suitable frequency band for damage detection can be very narrow, which encourage novel piezo arrangement-based damage quantification strategies. The robust damage detection leads to multiple sensors application and different modified approaches in EMI damage detection methodology. Yang and Divsholi proposed use of RMSD in the sub-frequency intervals in the large frequency range to study the location and severity of the damage [6]. Zuo developed a modified EMI technique for crack detection that involves fusing information from multiple sensors using a new damage-sensitive feature to examine the degree and position of crack damage in a pipeline [7]. Venu presented a semi-analytical multiple PZT–structure interaction model which considers the mass influence of the multiple PZT transducers. This model considers both the extensional and longitudinal actuations of all the PZT transducers which were previously neglected by the other researchers [8]. Adhikari proposed a modified dual piezo configuration which sensitivity increases with increasing number of actuators connected in parallel due to an increase in the output current. The proposed integration enables an early detection of damage, its propagation and improved severity measurement for reinforced concrete structures [9]. The approach studied in this paper involve two sensors used simultaneously.

2 Theory and Methodology Root mean square deviation (RMSD) and mean absolute percentage deviation (MAPD) are the most popular damage location detection index employed in EMI techniques [10, 11]. The Eq. 2 and Eq. 3 are used to quantify damage with respect to a healthy state of the structure using the resistance (R):    n   i=1 Ri − Ro 2 i  (2) RMSD = n  o 2 i=1 Ri i=n 100  Ri − Roi MAPD = Ro n i

(3)

i=1

where symbol n is used for number of frequency spectrum samples, symbol 0 is used for healthy state, Ri is the single sample of the spectrum for damage state. In this study we focus on the connection of the transducers (both parallel and serial). The damage sensitivity of this approach is studied using experimental and theoretical signals. The theoretical signals are obtained from the experimental ones by defining the equivalent resistance of the series (Rs ) and the parallel (Rp ) combination of piezoelectric transducers using Eq. 4 and 5: Rs = R1 + R2

(4)

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Rp = (R1 × R2)/(R1 + R2)

(5)

where R1 and R2 are the resistance of the piezo 1 and piezo 2 coupled to the structural element. This is a theoretical model in the frequency range for the sensitivity analysis using individual piezoelectric transducers. The experimental data of steel beam were acquired in the 1 kHz–4 MHz frequency range and the statistical indices (RMSD, MAPD) were applied in smaller frequency band.

3 Experimental Setup This paper demonstrates the cases of series and parallel combination of piezoelectric transducers (p1 and p2) for the damage identification. The data for the EMI variables are measured in the 1 kHz–4 MHz frequency with 200 Hz steps. The EMI experimental study was performed on a steel beam (35.6 × 3 × 0.3 cm3 ) with attached piezo-actuators p1 and p2 (Fig. 1). The study investigates the change of EMI responses to the simulated mass (m) at the distance of 3 cm from the p1 transducer. The temperature in the room during the experiments was approximately 20 °C. The IM3570 Impedance Analyzer was used to measure the EMI signatures at the piezo-actuator terminals using breadboard and connecting wires.

Fig. 1. Schematic diagram of p1 and p2 transducers connections with steel beam using breadboard.

4 Results and Discussions The sensors connections and respective measurements were assigned with following symbols (Fig. 2): p1 and p2 – single sensors, p12s – series combination, p12p – parallel combination, p12rp – reverse parallel combination, and p12rs reverse series combination.

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Fig. 2. Diagram of sensor connection using breadboard for the damage detection in the steel beam.

Fig. 3. The G spectrum plot of the p1, p2, p12p, p12s, p12rp, p12rs combinations in the healthy state.

The raw data plot of G and R EMI the healthy state spectrum of the p1, p2, p12p, p12s, p12rs and p12rp are given in Fig. 3 and Fig. 4 respectively. The symbol H is used to denote the healthy state measurement. The behavior of the p12p and p12rp combinations are similar in nature as well as behavior of p12s and p12rs. However, there are small differences in peaks of data. Good deviation of healthy and damage state data was found in resistance in the 600–800 kHz frequency band and hence this range is the suitable to demonstrate the proposed approach for damage detection. Figure 5 shows the plot for R data for all considered connections in the frequency range of 600–800 kHz.

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Fig. 4. The R spectrum plot of the p1, p2, p12p, p12s, p12rp, p12rs combinations in the healthy state.

Fig. 5. The damage and healthy state R plot for the p1, p2, p12p, p12s, p12rp and p12rs combinations in the 600–800 kHz frequency range.

The calculation of the damage indexes was made using Eq. 2 and Eq. 3 for the RMSD and MAPD indices, respectively. The Fig. 6 shows the comparative study of these connections using these indices for healthy and damage state. The largest observed differences are for the p12p for both the RMSD and MAPD, since there was a clear shift of the spectra as shown in Fig. 5. The raw measurements were noised and contained a trend so the calculation were also done for the detrend and filtered data (DF) and compared with the previous results (Fig. 6). The filtering was conducted using the Savitzky-Golay filter [12], while the detrending was made by removing the frequency dependence from the curves [13]. The healthy bar was calculated using the two healthy state measurements for the raw and the DF case. The p2 shows more damage sensitivity in comparison to p1 using raw data based damage index which contradicts our assumptions. In p12p combination, both raw and DF indices show significant damage sensitivity in comparison

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to a healthy state for the damage introduced in the steel beam structure. The p1, p2 and p12s raw and DF data based indices shows the sensitivity for the mass. However, the p12rp and p12rs cases do not have this sensitivity.

Fig. 6. The a) RMSD, b) and MAPD damage indices quantification of the R variable in different combinations of connection for raw and detrended and filtered (DF) spectra.

The filtered and detrended data for the experimental (exp) resistance value is compared to the theoretical (theor) studying the behavior of the above combinations of the piezo-actuators. The piezo p1 and p2 parallel and series connections combination were studied using theoretical Eqs. 4 and 5 and compared with the experimental data for the same combinations. The results shown in the Fig. 7 and Fig. 8 represent the healthy state data. The theoretical and experimental data show similarity in shape, but there is a significant vertical shift.

Fig. 7. The comparison for the parallel resistance combination of the p1 and p2 (p12p) at 20 °C.

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Fig. 8. The comparison for the series resistance combination of the p1 and p2 (p12s) at 20 °C.

The performance of p12p dominates over the individual and series combination of piezoactuators performance (Fig. 6) so it was chosen to be studied here. The Fig. 9 shows a comparison study of healthy and damage state of the theoretical and experimental data for the p12p connection. It can be seen from the Fig. 9 that both the theoretical and experimental data behaves similarly. In both cases the damage was detected since the damage case values are above the healthy case values. Obviously there are differences in the absolute values but they do not cause any misinterpretation of the results. Hence, the p12p connection based damage indices are suitable for detection of the added mass. The results show that it is enough to connect two sensors in parallel and conduct the measurement instead of measuring two sensors individually. Moreover, the theoretical approach for simulating parallel connection is also enough to detect the mass.

Fig. 9. The a) RMSD b) and MAPD damage indices of the theoretical and experimental data for R variable in the 600 kHz–800 kHz frequency range.

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5 Conclusions This paper successfully demonstrates the advantage of the parallel combination of the EMI-based damage detection. This methodology enhanced the scope of study from individual connections of the actuators to fusion based damage detection. This paper studies fusion of resistance using two sensors. This approach allows for time consumption reduction using the proposed connection. This method shows sensitivity for mass detection. However, it should note that the mass was within the sensitivity range of both transducers. Acknowledgements. The authors acknowledge the funding support provided by National Science Center, Poland under SONATA BIS project entitled: Study of piezoelectric sensors placement and their interaction with structural elements (2016/22/E/ST8/00068). Calculations were carried out at the Academic Computer Centre in Gda´nsk (TASK).

References 1. Farrar, C.R., Park, G., Allen, D.W., Todd, M.D.: Sensor network paradigms for structural health monitoring. Structural Control Health Monit. 13(1), 210–225 (2006). https://doi.org/ 10.1002/stc.125 2. Liang, C., Sun, F., Rogers, C.A.: Electro-mechanical impedance modeling of active material systems. Smart Mater. Struct. 5(2), 171–186 (1996). https://doi.org/10.1088/0964-1726/5/ 2/006 3. Huynh, T.C., Dang, N.L., Kim, J.T.: Advances and challenges in impedance-based structural health monitoring. Structural Monitoring and Maintenance 4(4), 301–329 (2017). https://doi. org/10.12989/smm.2017.4.4.301 4. Baptista, F.G., Filho, J.V.: Optimal frequency range selection for PZT transducers in impedance-based SHM systems. IEEE Sens. J. 10(8), 1297–1303 (2010). https://doi.org/ 10.1109/JSEN.2010.2044037 5. Peairs, D.M., Tarazaga, P.A., Inman, D.J.: Frequency range selection for impedance-based structural health monitoring. J. Vibr. Acoust. 129(6), 701–719 (2007) 6. Yang, Y., Sabet Divsholi, B.: Sub-frequency interval approach in electromechanical impedance technique for concrete structure health monitoring. Sensors (Basel, Switzerland) 10, 11644–61 (2010). https://doi.org/10.3390/s101211644 7. Zuo, C., Feng, X., Zhang, Y., Lu, L., Zhou, J.: Crack detection in pipelines using multiple electromechanical impedance sensors. Smart Materials Struct. 26 (2017). https://doi.org/10. 1088/1361-665x/aa7ef3 8. Adhikari, S., Bhalla, S.: Modified dual piezo configuration for improved structural health monitoring using electro-mechanical impedance (EMI) technique. Exp. Techniques. 43 (2018). https://doi.org/10.1007/s40799-018-0249-y 9. Annamdas, V.G.M., Soh, C.K.: Multiple piezoceramic transducers (PZT): structure interaction model. In: Proceedings of the SPIE 6174, Smart Structures and Materials 2006: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems, 61743G, 11 April 2006. https://doi.org/10.1117/12.657888 10. Giurgiutiu, V., Rogers, C.A.: Recent Advancements in the Electro-Mechanical (ElM) Impedance Method for Structural Health Monitoring and NDE, 3329 (1998) 11. Zagrai, A.N., Giurgiutiu, V.: Electro-mechanical impedance method for crack detection in thin plates. J. Intell. Mater. Syst. Struct. 12, 709–718 (2001)

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12. Press, W.H., Saul, A.T.: Savitzky-Golay Smoothing Filters. Comput. Phys. 4(6), 669 (1990). https://doi.org/10.1063/1.4822961 13. Skarbek, L., Wandowski, T., Opoka, S., Malinowski, P., Ostachowicz, W.: Electromechanical impedance technique and scanning vibrometry for structure characterization. In: Proceedings of 6th European Workshop on Structural Health Monitoring, vol. 1, pp. 179–185 (2012)

Damage Identification in Beams by Post-processing Modal Displacements and Rotations with Haar Wavelet J. V. Araújo dos Santos1(B) , H. Lopes2 , and A. Katunin3 1 IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

[email protected] 2 DEM-ISEP, Instituto Politécnico do Porto, Porto, Portugal 3 Department of Fundamentals of Machinery Design, Faculty of Mechanical Engineering,

Silesian University of Technology, Gliwice, Poland

Abstract. A study on the post-processing of modal displacements and modal rotations with the Haar wavelet is presented in this paper. A free-free aluminum beam is chosen as a structure to be analyzed and its modal displacements and rotations in both undamaged and multiple damaged states are computed with the finite element method. Three sets of damage indicators are proposed: (1) wavelet transform of damaged modal displacements or modal rotations, (2) wavelet transform of differences in modal displacements or modal rotations, and (3) ratio of wavelet transform of differences in modal displacements or modal rotations to wavelet transform of undamaged modal displacements or modal rotations. The study shows that post-processing modal displacements with the Haar wavelet leads to poor damage identifications. On the other hand, if one applies the same type of wavelet to modal rotations, the damage indicators (2) and (3) clearly pinpoints the location of the damage. Although the set of damage indicators (1) and (2) are prone to the boundary effect, where high values of wavelets coefficients are present, the third set of damage indicators does not present this problem. Furthermore, for large values of damage, this damage indicators shows the presence of damage in all scales of the wavelet scalogram. The present study clearly shows that by post-processing modal rotations with the simplest wavelet one can obtain reliable identifications of multiple damage. Keywords: Multiple damage identification · Beam · Finite element method · Modal displacement and modal rotation · Wavelet transform · Boundary effect

1 Introduction Structural damage identification usually encompasses the acquisition of measurement and computational data, such as modal displacements (mode shapes), that need to be post-processed to obtain dynamic characteristics sensitive to damage. Some of these characteristics are the modal curvatures (second order derivative of modal displacements) [1] or even higher order derivatives, such as third and fourth order derivatives of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 817–824, 2021. https://doi.org/10.1007/978-3-030-64908-1_76

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modal displacements [2]. An alternative to the use of modal displacements, is the use of modal rotations, which can be measured by shearography [3–5]. One of the objectives of this study is to define if one should post-process displacements or rotations in order to obtain the best damage identifications. Among various post-processing techniques applied for the enhancement of damage detectability, it seems that one of the most promising approaches is to apply a wavelet transform to modal data. Moreover, recent studies by the authors [6] show that the continuous wavelet transform (CWT) provides a superior enhancement of damage detection and identification, as well as reduction of the boundary effect, which is typically found when one applies wavelet transforms. The wavelet transforms for the enhancement of damage detectability based on modal data has been used by numerous researchers. For example, Rucka and Wilde [7] used CWT for detection of structural damage in beams and plates, while Solís et al. [8, 9] used this transform for damage detection in beams based on an approach which requires reference data. In this paper, the modal displacements and modal rotations of a free-free aluminum beam in undamaged and damaged states are computed with the finite element method. The damage states studied are multiple damage cases, simulated by decreasing the thickness of the beam at certain points. Quantities based on these modal displacements and modal rotations are post-processed with the Harr wavelet, leading to the definition of three sets of damage indicators: (1) wavelet transform of damaged modal displacements or modal rotations, (2) wavelet transform of the difference in modal displacements or nodal rotations, and (3) ratio of wavelet transform of differences in modal displacements or modal rotations to wavelet transform of undamaged modal displacements or modal rotations. A comparison among these indicators clearly shows that with the third set of damage indicators one does not notice the appearance of the boundary effect. This is clearer if one uses the third damage indicator with modal rotations, instead of the third damage indicator with modal displacements.

2 Analyzed Structure, Post-processing Method and Damage Indicators 2.1 Finite Element Analysis A free-free aluminum beam with the length 400 mm, the width 40 mm and the thickness 3 mm was chosen as the structure to be analyzed (Fig. 1). The aluminum has a Young’s modulus of 67.8 GPa and a specific mass of 2700 kg/m3 . A discretization of the beam in 2263 finite elements of equal length was created in order to carry out a modal analysis. This analysis gives the values of natural frequencies and modal displacement and modal rotations. The large number of finite elements used is necessary to simulate the type of full-field measurements one gets using interferometric techniques, such as shearography. An Euler-Bernoulli finite element, which has two nodes, each with displacement and rotation degrees of freedom, was used (Fig. 2). The formulation of this finite element can be found in reference [10]. Three damage scenarios were studied, as described in Table 1. As depicted in Fig. 1, the first slot, with the width 5 mm, is located at 284 mm from the left edge, whereas the second has the width of 3 mm and is located at mid-span.

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Fig. 1. Geometry of the aluminum beam, and location of the two slots.

Fig. 2. Two nodes Euler-Bernoulli finite element with two displacements, w1 and w2 , and two rotations, θ1 and θ2 . Table 1. Thickness reduction of the slots. Scenario Slot 1 Slot 2 1

0.409 0.100

2

0.409 0.200

3

0.409 0.300

2.2 Continuous Wavelet Transform The continuous wavelet transform (CWT) is an integral transform given by the following equation:    ∞ 1 x−b Wf (a, b) = √ dx, (1) f (x)ψ ∗ a a −∞ where a signal f (x) is multiplied by the complex conjugate of the wavelet kernel ψ ∗ (·). This kernel depends on the scaling and translation parameters, a and b, respectively. By carrying out scaling and translation operations, a family of elementary wavelet functions is generated according to:   x−b 1 ∗ . (2) ψa,b (x) = √ ψ a a Besides other properties, a CWT has the property of linearity, so that the following equality holds: W (f1 + f2 )(a, b) = Wf1 (a, b) + Wf2 (a, b),

(3)

where f1 and f2 are two distinct signals. According to this property, it is possible to show that   W f˜ − f (a, b) = W f˜ (a, b) − Wf (a, b) (4)

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where f˜ is, in the context of this work, the signal related to the damaged structure and f is the baseline signal, which is related to the undamaged structure. This means that the wavelet coefficients of the difference of two signals are equal to the difference of the wavelet coefficients of two signals. The wavelet used in this work is the Haar wavelet, which was chosen due to its mathematical simplicity and effectiveness in damage identification. The scaling function of this wavelet can be represented by the following relation: ⎧ ⎨ 1 for 0 ≤ x < 1, ϕ(x) = (5) ⎩ 0 otherwise, while the wavelet function is given by another piecewise relation: ⎧ ⎪ 1 for 0 ≤ x < 1/2, ⎪ ⎪ ⎪ ⎪ ⎨ ψ(x) = −1 for 1/2 ≤ x < 1, ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ 0 otherwise,

(6)

Both functions fulfill the two-ale relations given below: ϕ(x) =

K 

pk ϕ(2x − k),

(7)

qk ϕ(2x − k),

(8)

k=1

ψ(x) =

K  k=1

where {pk } and {qk } are the sequences of interscale coefficients for the scaling and wavelet functions, respectively. 2.3 Damage Indicators Three sets of damage indicators, based on post-processing of modal displacements or modal rotations, are proposed and studied in this paper. The first set only uses data acquired in the damaged state, such that one may write: ˜ b) W w(a, ˜ b) or W θ(a,

(9)

where the tildes over w and θ denote that the modal characteristics are those of the damaged structure. The second set of damage indicators corresponds to the post-processing of differences in modal displacements or differences in modal rotations:   W (w˜ − w)(a, b) or W θ˜ − θ (a, b) (10) Finally, a third set of damage indicators is proposed. These indicators involve the computation of the ratio of wavelet transform of differences in modal displacements

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or modal rotations to wavelet transform of undamaged modal displacements or modal rotations:   ˜ − θ (a, b) W θ W (w˜ − w)(a, b) or (11) Ww(a, b) W θ (a, b)

3 Results and Discussion Figure 3 presents the modal displacement and modal rotation corresponding to the first natural frequency and damage scenario one. Although one observes a very small perturbation in the modal rotation, the modal displacement is completely smooth. Furthermore, the perturbation is present only at the position where there is the largest reduction in thickness, indicating that it is not possible to localize both slots. This clearly shows that there is a need for post-processing the dynamic characteristics in order to achieve the identification of multiple damage.

(a)

(b)

Fig. 3. Plots of the modal displacement (a) and modal rotation (b) of damage scenario one.

3.1 Identification with Modal Displacements and Modal Rotations In order to study which dynamic characteristics are the best one regarding damage identification ability, a post-processing of the data of the third damage scenario was carried out. The three sets of damage indicators described by Eqs. (9), (10), and (11) were computed and the corresponding scalograms are shown in Fig. 4. This figure clearly shows that the identification of the slots is not achieved by post-processing the modal displacement with the three damage indicators. Indeed, there is only possible to observe an incipient damage signature of the second slot using the ratio of wavelet transform of differences in displacements to wavelet transform of undamaged displacements (Fig. 4(c)). From the observation of Fig. 4 it is also possible to conclude that the use of the damage indicators based only on the damaged data (Fig. 4(a) and (d)) leads to large values of the wavelet coefficients at the right and left edges of the beam. This shows that the first and second sets of damage indicators (Eqs. (9) and (10)) are very prone to the boundary effect. It is worth noting that the application of the third damage indicator leads to the identification of both slots in all scales when using the modal rotations (Fig. 4(f)).

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(a)

(b)

(c)

(d)

(e)

(f)

Fig. 4. Scalograms of three distinct damage indicators [(a)–(d), (b)–(e), and (c)–(f)] for the postprocessing of the modal displacements [(a), (b), and (c)] and the modal rotations [(d), (e), and (f)] of damage scenario three.

3.2 Identification of Small Damage In view of the discussion and conclusions in the previous section, the damage identification of the two slots was only carried out with the second and third damage indicators, which were just applied to the modal rotations. As can be seen in Fig. 5(a), the slot at mid-span is not identified with the damage indicator based on the post-processing of differences (second damage indicator, described in Eq. (10)). Furthermore, with this indicator the boundary effect appears at the left edge of the beam, for both damage scenarios (Figs. 5(a) and (c)). Another interesting feature that can be seen in Figs. 5(a) and (c) is that the slots are not visible in lower scales, namely scales lower than 15, if one applies the second damage indicator. According to Figs. 5(b) and (d), the opposite is true when the third damage indicator is used, i.e. the slots are either identified in all scales or, which is the case for the slot in the mid-span, in lower scales. In particular, the damage signature of this slot vanishes for scales above 40 (damage scenario one) and 80 (damage scenario two). One also observes, in Figs. 4(f) and 5(b) and (d), that the areas in the scalogram relative to the second slot, which has a width of 5 mm, are wider than those located at the position of the slot with 3 mm. This shows that it is possible to obtain information about the extent of the damage.

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(a)

(b)

(c)

(d)

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Fig. 5. Scalograms of damage indicators two and three [(a)–(c), and (b)–(d)] for the postprocessing of the modal rotations of damage scenarios one and two [(a)–(b), and (c)–(d)].

4 Conclusions The present study, consisting of the analysis of a free-free aluminum beam with multiple damage, shows that the post-processing of modal displacements with the Haar wavelet leads to poor damage identifications. However, if one uses modal rotations, the multiple damage can be identified, in particular with the computation of the ratio of wavelet transform of differences in modal rotations to wavelet transform of undamaged modal rotations. Although the identification of slots corresponding to small damage (thickness reduction lower than 6.6%) is only possible at some wavelet scales, the cases where the damage is larger, the application of the third damage indicator leads to the identification of both slots in all scales. It is also found that this damage indicator leads to results that are not affected by the boundary effect, which is commonly found in post-processing of data with wavelets. Acknowledgments. The first and second authors would like to thank the financial support by FCT, through IDMEC, under LAETA, project UIDB/50022/2020, whereas the third author acknowledges the Polish National Agency for Academic Exchange for the scholarship within the Bekker programme (PPN/BEK/2019/1/00048).

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References 1. Pandey, A., Biswas, M., Samman, M.: Damage detection from changes in curvature mode shapes. J. Sound Vib. 145, 321–332 (1991) 2. Moreno-García, P., dos Santos, J.V.A., Lopes, H.: A new technique to optimize the use of mode shape derivatives to localize damage in laminated composite plates. Compos. Struct. 108, 548–554 (2014) 3. Reis Lopes, H.M., dos Santos, J.V.A., Mota Soares, C.M., Miranda Guedes, R.J., Pires Vaz, M.A.: A numerical-experimental method for damage location based on rotation fields spatial differentiation. Comput. Struct. 89(19–20), 1754–1770 (2011) 4. Mininni, M., Gabriele, S., Lopes, H., dos Santos, J.V.A.: Damage identification in beams using speckle shearography and an optimal spatial sampling. Mech. Syst. Sig. Process. 79, 47–64 (2016) 5. Katunin, A., Lopes, H., dos Santos, J.V.A.: Identification of multiple damage using modal rotation obtained with shearography and undecimated wavelet transform. Mech. Syst. Sig. Process. 116, 725–740 (2019) 6. Katunin, A., dos Santos, J.V.A., Lopes, H.: Application of wavelet analysis to differences in modal rotations for damage identification. In: IOP Conference Series: Materials Science and Engineering, vol. 561, p. 012024 (2019) 7. Rucka, M., Wilde, K.: Application of continuous wavelet transform in vibration based damage detection method for beams and plates. J. Sound Vibr. 297(3–5), 536–550 (2006) 8. Solís, M., Algaba, M., Galvín, P.: Continuous wavelet analysis of mode shapes differences for damage detection. Mech. Syst. Sig. Process. 40(2), 645–666 (2013) 9. Solís, M., Benjumea, A.J., Algaba, M., Galvín, P.: Analysis of stationary roving mass effect for damage detection in beams using wavelet analysis of mode shapes. J. Phys: Conf. Ser. 628, 012014 (2015) 10. Rao, S.S.: Mechanical Vibrations – Fifth Edition in SI Units. Prentice Hall, Upper Saddle River (2011)

Nonlinear Frequency Mixing in GFRP Laminate with a Breathing Delamination Akhilendra S. Gangwar, Yamnesh Agrawal, and Dhanashri M. Joglekar(B) Indian Institute of Technology Roorkee, Roorkee 247667, India [email protected]

Abstract. In view of diversified applications in aerospace, civil, and mechanical engineering, Lamb wave based NDE of composite laminates has been of continued interest. In particular, the techniques based on the nonlinear wave damage interactions have attracted significant attention in the recent past. A delamination defect with contacting interfaces (referred to as a breathing delamination) is a potential source of nonlinearity because of the bilinear stiffness characteristics instigating through an intermittent contact. Past investigations have dealt predominantly with a single frequency excitation leading to the generation of higher harmonics that can be utilized as a viable damage indicator. In this work, we investigate numerically the nonlinear interactions of a dual frequency Lamb wave signal with breathing delamination in a composite plate. To this end, an eight layer GFRP laminate is considered in the analysis. Explicit dynamic simulations are performed using commercial finite element software ANSYS. It is demonstrated that the nonlinear wave-damage interactions lead to frequency side-bands in the response spectrum occurring at the algebraic combinations of the two constituent frequencies. A modulation parameter is introduced for quantifying the strength of the combination harmonics relative to the fundamental harmonics. Further, a thorough parametric study is performed for assessing the impact of ply orientations and inter-laminar position of the delamination on the proposed modulation parameter. This investigation can find its potential use in devising damage localization strategies for laminated composites based on the nonlinear wave-damage interactions. Keywords: Breathing delamination · Dual frequency excitation · Combination harmonics · Finite element analysis · Ply orientation

1

Introduction

Composite plates are widely used in industries ranging from civil to aerospace owing to its attractive properties [7]. On the downside, a very crucial defect in the form of delamination is developed which leads to catastrophic failure of structures [6,17,22]. Because of higher inter-laminar stresses, delamination is inadvertently produced in composite plates at the interfaces between any adjacent plies. To overcome these aspects, regular inspection is necessary. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2021  P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 825–836, 2021. https://doi.org/10.1007/978-3-030-64908-1_77

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Non-Destructive Evaluation (NDE) techniques has become a subject of considerable research interest to assure the safety without destroying the structures during inspection. From the perspective of NDE of composite plates, Lamb waves based damage detection techniques has been a topic of interest in the past few years. Linear Lamb wave methods use the time domain wave signals characteristics such as reflection, mode conversion, attenuation, etc. for detection and characterization of the delamination but not suited for evaluation of the incipient and small damages [4,9,10,16,19–21]. Nonlinear Lamb wave detection methods are sensitive to detect such damages relative to the linear one. Nonlinear interaction of Lamb wave with delamination in composite plates results in frequency shifts and nonlinear harmonics generation [11,13,18,24]. In recent past, researchers have been focusing on nonlinear harmonics generation in the frequency domain from which the size and location of delamination in composite plates can be studied [2,3,26]. A recently introduced nonlinear method named Vibro-Acoustic Modulation (VAM) method has been appertained to composite structures for the evaluation of incipient and small damages [5,25,27,28]. VAM is based on a high-frequency ultrasonic wave combined with a low-frequency vibration. In practice, implementation of VAM would be difficult with such combination frequencies owing to the spatial constraints. Therefore, researchers have propounded certain modifications such as cross-modulations and nonlinear frequency mixing. When two high frequency signals encounter a damage, mixing of the frequencies occur that are comparable in magnitude [13–15]. The basis and methodology for utilising nonlinear interaction of Lamb waves frequency mixing for damage detection is discussed. In this work, authors have focussed on the nonlinear interactions of a dual frequency Lamb wave signal with 8-layered GFRP composite plates with different ply orientations and interlaminar location of delamination employing numerical models [1,8,10]. The numerical analysis were conducted on [0]8 , [0,45,−45,90]s , [0,45,90,−45]s , [90,45,−45,0]s , [90,−45,0,45]s , [45,−45,0,90]s , and [45, 90,−45,0]s composite laminates in order to examine the effect of ply orientations and interlaminar position of delamination on the nonlinear harmonics. The numerical analysis was conducted on these composite laminates with different stacking sequence with the variation of 45◦ in order to examine the effect of ply layups on the nonlinear harmonics. The nonlinearity arising from the opening and closing of the sub-laminates in the delaminated region generates contact acoustic nonlinearity (CAN). These harmonics are found to be dependent on the ply orientations and interlaminar location of delamination. Based on the numerical results, a thorough parametric study is conducted for assessing the impact on the nonlinearity due to the presence of delamination. The remaining part of the paper has been compiled into three sections. FE modelling along with contact pair are presented in Sect. 2. In Sect. 3, results have been discussed thoroughly and Sect. 4 is devoted to summarize the conclusions.

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Finite Element Simulation Structural Modelling

A two-dimensional structure of E-glass fiber reinforced laminated composites has been modelled in the thickness direction using ANSYS 19.0. The 2D model of 450 × 4 mm2 dimension, consist of 8 laminas each having orthogonal elastic properties and the thickness of each lamina is 0.5 mm as shown in Fig. 1. The material properties for the 0◦ ply orientation lamina is shown in Table 1. The elastic properties for the different ply orientation lamina can easily be calculated from the properties of 0◦ ply angle.

Fig. 1. Schematic 2D representation of [0]8 laminate.

Table 1. Material properties of GFRP laminated composite plate Material E11 (GP a) E22 (GP a) G13 (GP a) G23 (GP a) υ13 υ23 GFRP

44.68

6.90

2.54

2.5459

ρ (kg/m3 )

0.28 0.355 1990

In these simulations, PLANE82 element with plane strain conditions are applied to the model. After meshing of all the 8 plies, merging of nodes at surfaces of different layers present at same location is imperative as it ensures the physical and chemical bonding between the layers. To create delamination of any size in between any two layers, nodes at those surfaces should remain unmerged. A0 wave mode signal is excited by giving in-plane transient force of a tone burst signal with Gaussian window in the opposite direction at the top and bottom nodes at the actuation points, as shown in Fig. 1. The excitation force file for a total time of 0.5 ms with the time step of 100 ns is generated using MATLAB. The excitation time of 0.1 ms is kept constant rather than the number of cycles for the same spectral leakage of both excitation frequencies. Figure 2 shows time and the frequency domain of the excitation pulse of mix frequency signal of 70 & 100 kHz.

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Normalised amplitude

Normalised force

1.2 0.8 0.4 0.0 -0.4 -0.8 -1.2 0.0

0.1

0.2

0.3

0.4

0.5

1.0 0.8 0.6 0.4 0.2 0.0

0

Time (ms)

(a)

100

200

300

400

500

Frequency (kHz)

(b)

Fig. 2. The dual-frequency tone-burst excitation input signal in (a) time domain, (b) frequency domain.

2.2

Mesh Size and Time Step Calculation

Mesh size is a crucial factor in any numerical simulations. Mesh size of the structure should be small enough to be at least 20 nodal distance per wavelength to get a reasonable accuracy. The interrogation frequencies used in the simulations are 70 & 100 kHz and some additional frequencies are also expected to generate as a result of CAN. The smallest wavelength in the waveguide during the simulation would be deciding factor for the mesh size. Group velocities and their corresponding wavelengths were obtained using Semi-Analytical Finite Element (SAFE) approach. The wavelength of laminates with different ply orientations must also be considered. A 300 kHz A0 wave signal in the 0.5 mm laminate with 90◦ ply orientation would have minimum wavelength of 4.5 mm. Thus the nodal distance should be less than 0.225 mm. Since PLANE82 element has mid-side nodes, so the element size should be less than 0.45 mm. In all numerical simulations in this study, authors have used very fine discretized mesh with element size of 0.25 mm. The time step is a key parameter in FE simulation in order to get a desired accuracy. Group velocities for the respective frequencies are already known using SAFE and thus optimum time step can be easily calculated using Courant–Friedrichs–Lewy condition. Time step obtained from the aforementioned condition is 0.1 µs. 2.3

Modelling of Contact Pair

To model the contact pair in these simulations, authors have used the hard contact conditions as it minimizes the penetration of the slave surface into the master surface. Without contact pair or hard contact conditions, nodes on delamination faces would penetrate into each other without having any physical impact as if both sub-laminates do not exist for each other. In the sublaminate region,

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when both delamination faces interact with each other, the local stiffness of surfaces must change to avoid penetration. ANSYS provides many algorithms in finite element modelling, namely augmented Lagrange method, penalty method and direct method for the purpose of creating contact pair. In present work, Augmented Lagrange (AL) method was used as it offers better penetration control, better satisfaction on governing equations and takes less computational time. These algorithms are based on methods of changing normal penalty stiffness and penetration tolerance with a series of iterations by updating those penalties. 2D surface contact elements such as CONTA172 and TARGET169 were assigned to delamination faces as contact and target surfaces. The governing equations for contact pressure in terms of normal contact stiffness updation, contact gap size and behaviour of contact surface is elaborated in [25]. In this problem, no friction forces were assumed to be present between the delamination faces. 2.4

Formulation of Nonlinearity Index (NLI)

When an incident wave propagates through the delamination region, it results in a nonlinear contact interaction of both sub-laminates, that would lead to the generation of some additional frequency components. Thus, a mathematical formulation of contact nonlinearity is imperative for the nonlinear contact analysis owing to delamination detection and characterization. Many researchers in the past have developed their formulation for CAN. Shen [23] used wave energy ratio method where the energy of individual harmonics is proportional to its respective amplitude in the frequency domain. Formulation used by Shen [23] is given in Eq. 1, where Ai is the amplitude of the ith harmonics in Fast Fourier Transform (FFT) response of the signal.  A2 + A3 + A4 + · · · N LI = . (1) A1 In this analysis, there will also be the sidebands along with the higher harmonics in the output response and it would be better to formulate CAN caused by higher harmonics and sidebands separately. Joglekar [12] defined two types of nonlinearity parameter i.e., Rh (for higher harmonics) and Rm (for sidebands). Formulation for Rh and Rm is given in Eq. 2. Rh =

A2f1 + A2f2 Af1 + Af2

Rm =

Af2 −f1 + Af2 +f1 Af1 + Af2

(2)

A combined parameter Rt is also formulated that can signify the total nonlinearity and it would simply be the algebraic sum of Rh and Rm as given in Eq. 3. (3) Rt = Rh + Rm

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Results and Discussion

In the non-destructive evaluation of structures, different properties of delamination detection can be found out from the nonlinearity trends that are obtained from the numerical simulations. The aforementioned finite element framework was used to study the nonlinear interactions of dual mixed frequency signal with delamination defect. For this purpose, seven types of composite laminates of [0]8 , [0,45,−45,90]s , [0,45,90,−45]s , [90,45,−45,0]s , [90,−45,0,45]s , [45,−45,0,90]s , and [45, 90,−45,0]s with each having 8 plies which are symmetric about the mid plane, are investigated and all these laminates can be referred as P1 to P7 respectively for any future references. All the plies of the P1 have ply angle of 0◦ and the remaining 6 laminates (P2 to P7) have the two plies with angles each of 0◦ , 45◦ , −45◦ and 90◦ . Further, the 12 mm delamination was modelled in between any interlaminar location with aforementioned ply orientations. 3.1

Effect of Dual Frequency Excitation Signal on Delamination

0.30

Normalised amplitude

0.15 0.00 0.30

f2-f1 0

0.30

0

0.30

f2

150

2f2 200

f1+f2

2f1

100

250

300

350

150

2 -3rd 2f2 200

250

300

350 rd

3 -4th

f2-f1 f1 0

f1+f2

nd

50

50

f2 100

2f1

f1+f2 150

2f2 200

250

300

350 th

4 -5th

0.15 0.00

f2 100

f1

0.15 0.00

50 f2-f1

0.15 0.00

f1

1st-2nd

2f1

f1 0

50

f2 100

150

200

250

300

350

Frequency (kHz) Fig. 3. FFT response of various inter-laminar location of delamination with ply orientation [0,45,−45,90]s .

When a wave pass through delamination, both sub-laminates interact with each other. The nonlinear interaction of sub-laminates result in the generation of some additional frequency components besides the interrogation frequencies. In case of single frequency excitation, the additional frequency components in the FFT response lie at the integral multiples of the fundamental tone. When dual frequency signal is excited in the composite plate having delamination, it would

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Table 2. Group velocities of sub-layer formed in different laminates at 70 and 100 kHz Thickness (mm) Ply orientations 70 kHz Vg (m/s) 100 kHz Vg (m/s) 0.5

[0]

703.20

805.18

0.5

[90]

464.80

544.23

0.5

[45]

556.51

641.99

1

[0,0]

901.64

996.63

1

[0,45]

771.52

868.20

1

[90,45]

659.72

753.9

1

[90,−45]

659.72

753.9

1

[45,−45]

684.40

780.17

1.5

[0,0,0]

1008.53

1083.64

1.5

[0,45,−45]

912.94

994.67

1.5

[0,45,90]

846.08

939.49

1.5

[90,45,−45]

772.11

867.22

1.5

[90,−45,0]

846.08

939.49

1.5

[45,−45,0]

909.29

994.67

1.5

[45,90,−45]

781.26

876.04

2

[0,0,0,0]

1070.96

1125.45

2

[0,45,−45,90]

935.96

1012.66

2

[0,45,90,−45]

963.72

1039.67

2

[90,45,−45,0]

932.49

1012.66

2

[90,−45,0,45]

945.53

1023.42

2

[45,−45,0,90]

933.03

1015.27

2

[45,90,−45,0]

963.72

1039.67

generate some peculiar combination frequency components along with the higher harmonics of each tone. These peculiar combination frequencies are the algebraic combinations of the input frequencies. In this study, dual frequency excitation signal with the central frequency of 70 & 100 kHz has been used and the nonlinear interaction of the wave signal generates higher harmonics at 140 & 200 kHz and the combination frequencies at 30 & 170 kHz. The relative strength of higher harmonics and combination frequencies is dependent on various factors. However, strength of combination frequencies are observed to be comparatively higher. Figure 3 shows the FFT response of out-of-plane displacement for the composite plate having ply orientation [0, 45, −45, 90]s for different inter-laminar location of delamination. It has been further observed that the nonlinearity has been decreasing as the inter-laminar location of delamination shifts towards midthickness location.

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Effect of Ply Orientation on Group Velocity

To analyse the effect of ply orientation, three cases of ply orientation angle has been considered i.e., 0◦ , 45◦ & 90◦ . Group velocities of the wave signal in the plate depends on laminate thickness, ply orientations and the sequencing of ply orientations of laminate having multiple plies. The prominent factor for the variation of the group velocities are ply thickness. It was observed that a wave signal in the composite plate have comparatively higher group velocity for the thicker laminate. Table 2 shows the group velocities for the different combinations of ply orientation and thickness for the wave signal with 70 and 100 kHz. It is clearly evident that the thicker laminates have higher group velocity irrespective of other factors (ply orientation and its sequence). There is a variation of approximate 100 to 200 m/s for every 0.5 mm increment in laminate thickness for the same ply orientation. Apart from the laminate thickness of the composite, ply orientation plays a key role in the determination of group velocities. It was observed that the 0◦ ply orientation angle has higher group velocity and it is decreasing as ply orientation angle increases to 90◦ . For single ply laminate, 0◦ , 45◦ and 90◦ ply orientation has group velocity of 703.2, 556.5 and 464.8 m/s respectively for the 70 kHz signal and the same trend is also observed in the case of 100 kHz signal. The trend in group velocities for multiple plies laminate with different ply orientation can also be predicted. The laminate with the plies having maximum number of 0◦ ply orientation would have higher group velocity. If the number of 0◦ plies are same, then next ply orientation angle is checked which has higher group velocity following 0◦ ply angle. From the Table 2, it is evident that for two plies laminate, [0, 0] has the highest group velocities and [0,45], [45,−45], [90,45] would follow the same order. In a similar way, comparison of group velocities for multiple plies with different orientation angle can be easily made. The sequence of ply orientations in a laminate also has minor impact in the determination of its group velocities. From Table 2, it can be observed that the laminate which has plies of angle 0◦ , 45◦ , −45◦ , 90◦ has very small diffrences in group velocity. The contribution of each ply towards the overall group velocity of the laminate is same but the group velocity would be different due to different sequencing pattern. However, the group velocity variation because of sequencing pattern is comparatively very small. 3.3

Effect of Ply Orientation on Nonlinearity

When the wave passes through the leading edge of the delamination, it splits into two wave signals. The group velocities in both sub-laminates would be dependent on its thickness and ply orientations. If the inter-laminar location of delamination is asymmetric about mid plane (i.e., delamination location is not at the mid plane), there would be some difference in group velocities of sub-laminates primarily due to the difference in laminate thickness. At the leading edge of delamination, the out-of-plane displacement for both waves in the sub-laminates region would be in the same phase but due to difference in their

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833

Normalised displacement

respective group velocities, it starts gaining some phase difference as the wave move along the delamination region. Figure 4 shows the displacement response of top and bottom sub-laminates at the leading and trailing edge of the delamination for 100 kHz signal. At the leading edge, both sub-laminates move in the same phase without hindering the movement of each other but at the trailing edge, both wave signal are almost in the opposite phase leading to some level of wave distortion. The FFT response of the distorted signal would also give some additional frequency components as discussed earlier in Sect. 3.1. The strength of other harmonics are dependent on the degree of wave signal distortion in the delamination region. So, it can be inferred that a higher difference in the group velocities of wave in the sub-laminates will give rise to higher nonlinearity. 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 0.00 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 0.00

bottom sub-laminate top sub-laminate

0.04

0.08

Trailing edge

0.12

bottom sub-laminate top sub-laminate

0.04

0.08

0.16

0.20

Leading edge

0.12

0.16

0.20

Time (ms) Fig. 4. Displacement response of top and bottom sub-laminate at leading and trailing edge of delamination.

To study the nonlinearity variation due to ply orientation, the simulation cases for same delamination location with different ply orientations was considered. For delamination between 1–2 layer, the top and bottom sub-laminate would have one and seven plies respectively. The group velocity of bottom laminate would be higher owing to its higher thickness irrespective of their ply angles. The difference in their group velocities would be more if the top sub-laminate have 90◦ ply orientation angle because it has the least group velocity. So, the nonlinearity in 90◦ ply orientation in top sub-laminate would be comparatively higher among other ply orientation cases. P4 and P5 has 90◦ ply angle at top sublaminate and both have higher nonlinearity, as evident from Fig. 5. P1, P2 and P3 have the lowest nonlinearity because they have 0◦ ply orientation in their top sub-laminate. Similar analogy can also be used to compare nonlinearity among

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Nonlinearity index

0.4

[04]s [0,45,-45,90]s [0,45,90,-45]s [90,45,-45,0]s [90,45,0,-45]s [45,-45,0,90]s [45,0,-45,90]s

0.3

0.2

0.1

0.0 1-2

2-3

3-4

4-5

Interlaminar location Fig. 5. Nonlinearity index with interlaminar location of delamination for different ply orientations.

the delamination located at 2–3 and 3–4 layer. For the 2–3 delamination layer, nonlinearity would be higher for cases in which top sub-laminates have [90, 45] ply orientation. P4 and P5 has higher nonlinearity as its top sub-laminate have plies with 45◦ and 90◦ orientation. Although, the group velocities of top sublaminates in case of P4 and P5 are equal but they have different nonlinearity because of the sequence of the ply orientation in both top and bottom sublaminates. For 3–4 delmination layer, top laminate of P4 [90,45,−45] has lowest group velocity and highest nonlinearity among all seven cases.

4

Summary and Conclusions

This paper carried out a numerical analysis based on FE simulation to investigate the effect of ply orientations and interlaminar location on amplitude of higher harmonics and combination frequencies generated due to mix frequency wave signal. It is concluded that nonlinear interaction of dual frequency excitation signal with the delamination generates some peculiar combination frequencies along with the higher harmonics of each tone. Group velocities of a laminate depends on laminate thickness and the combination pattern of ply orientation. It was observed that group velocities increase with ply thickness. It was further observed that there was a variation in group velocity which further depends on ply orientation. It can also be concluded that the higher difference in the group velocities of wave in the delamination region will give rise to higher nonlinearity. Moreover, this study also suggest that the strength of nonlinear harmonics depends on the interlaminar location and ply orientations of laminates.

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Acknowledgements. The authors gratefully acknowledge the financial aid provided by the Science and Engineering Research Board (SERB) under the Department of Science and Technology (DST), Government of India under the Grant No.: ECR/2017/001171.

References 1. Amaro, A., Santos, J., Cirne, J.: NDT of COMPOSITES: comparative study of different non-destructive testing techniques in the characterisation and quantification of the damage effects in carbonepoxy laminates. Insight Non Destr. Test. Condition Monit. 46(9), 559–565 (2004) 2. Bovsunovsky, A., Surace, C.: Non-linearities in the vibrations of elastic structures with a closing crack: a state of the art review. Mech. Syst. Signal Process. 62, 129–148 (2015) 3. Broda, D., Staszewski, W., Martowicz, A., Uhl, T., Silberschmidt, V.: Modelling of nonlinear crack-wave interactions for damage detection based on ultrasound–a review. J. Sound Vibr. 333(4), 1097–1118 (2014) 4. Della, C.N., Shu, D., Zhao, Y.: Vibration of composite beams with two overlapping delaminations. Acta Mech. Sin. 21(1), 47–55 (2005) 5. Donskoy, D., Sutin, A., Ekimov, A.: Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing. NDT & E Int. 34(4), 231–238 (2001) 6. Feng, B., Ribeiro, A.L., Ramos, H.G.: Interaction of lamb waves with the edges of a delamination in CFRP composites and a reference-free localization method for delamination. Measurement 122, 424–431 (2018) 7. Giurgiutiu, V.: Structural Health Monitoring of Aerospace Composites. Academic Press, Cambridge (2015) 8. Gros, X., Takahashi, K.: Non-destructive evaluation of the effect of ply orientation on the impact resistance of thermoplastic toughened thermoset resin polymeric matrix composite. Int. Conf. Adv. Mater. 4, 8–14 (1998) 9. Guo, N., Cawley, P.: The interaction of lamb waves with delaminations in composite laminates. J. Acoust. Soc. Am. 94(4), 2240–2246 (1993) 10. Gupta, S., Rajagopal, P.: Effect of ply orientation and through-thickness position of delamination on the reflection of fundamental symmetric s0 lamb mode in gfrp composite plate structures. Ultrasonics 90, 109–119 (2018) 11. Jhang, K.Y.: Nonlinear ultrasonic techniques for nondestructive assessment of micro damage in material: a review. Int. J. Precis. Eng. Manuf. 10(1), 123–135 (2009) 12. Joglekar, D.: Analysis of nonlinear frequency mixing in timoshenko beams with a breathing crack using wavelet spectral finite element method. J. Sound Vibr., 115532 (2020) 13. Joglekar, D., Mitra, M.: Analysis of nonlinear frequency mixing in 1D waveguides with a breathing crack using the spectral finite element method. Smart Mater. Struct. 24(11), 115004 (2015) 14. Joglekar, D., Mitra, M.: Nonlinear analysis of flexural wave propagation through 1D waveguides with a breathing crack. J. Sound Vibr. 344, 242–257 (2015) 15. Joglekar, D., Mitra, M.: Time domain analysis of nonlinear frequency mixing in a slender beam for localizing a breathing crack. Smart Mater. Struct. 26(2), 025009 (2016)

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16. Mitra, M., Gopalakrishnan, S.: Wavelet based spectral finite element modelling and detection of de-lamination in composite beams. Proc. Roy. Soc. A Math. Phys. Eng. Sci. 462(2070), 1721–1740 (2006) 17. Munian, R.K., Mahapatra, D.R., Gopalakrishnan, S.: Lamb wave interaction with composite delamination. Compos. Struct. 206, 484–498 (2018) 18. Pieczonka, L., Klepka, A., Staszewski, W.J., Uhl, T.: Nonlinear acoustic imaging of structural damages in laminated composites (2014) 19. Ramadas, C., Balasubramaniam, K., Joshi, M., Krishnamurthy, C.: Interaction of the primary anti-symmetric lamb mode (AO) with symmetric delaminations: numerical and experimental studies. Smart Mater. Struct. 18(8), 085011 (2009) 20. Ramadas, C., Balasubramaniam, K., Joshi, M., Krishnamurthy, C.: Interaction of guided lamb waves with an asymmetrically located delamination in a laminated composite plate. Smart Mater. Struct. 19(6), 065009 (2010) 21. Ramadas, C., Padiyar, J., Balasubramaniam, K., Joshi, M.: Propagation of the fundamental symmetric lamb mode in a symmetrically delaminated composite laminate. Int. J. Veh. Struct. Syst. (IJVSS) 4(3) (2012) 22. Schaal, C., Samajder, H., Baid, H., Mal, A.: Rayleigh to lamb wave conversion at a delamination-like crack. J. Sound Vibr. 353, 150–163 (2015) 23. Shen, Y.: Numerical investigation of nonlinear interactions between multimodal guided waves and delamination in composite structures. In: Health Monitoring of Structural and Biological Systems 2017, vol. 10170, p. 101701Z. International Society for Optics and Photonics (2017) 24. Soleimanpour, R., Ng, C.T.: Locating delaminations in laminated composite beams using nonlinear guided waves. Eng. Struct. 131, 207–219 (2017) 25. Yelve, N.P., Mitra, M., Mujumdar, P.: Detection of stiffener disbonding in a stiffened aluminium panel using nonlinear lamb wave. Appl. Acoust. 89, 267–272 (2015) 26. Yelve, N.P., Mitra, M., Mujumdar, P.: Detection of delamination in composite laminates using lamb wave based nonlinear method. Compos. Struct. 159, 257– 266 (2017) 27. Yelve, N.P., Mitra, M., Mujumdar, P., Ramadas, C.: A hybrid method based upon nonlinear lamb wave response for locating a delamination in composite laminates. Ultrasonics 70, 12–17 (2016) 28. Zaitsev, V.Y., Matveev, L.A., Matveyev, A.: Elastic-wave modulation approach to crack detection: comparison of conventional modulation and higher-order interactions. NDT & E Int. 44(1), 21–31 (2011)

Data-Driven Damage Detection Based on Moving-Loads Responses - The Luiz I Bridge Filipe Cavadas1(B) , Bruno J. Afonso Costa1 , Joaquim A. Figueiras1 , Mário Pimentel1 , and Carlos Félix2 1 CONSTRUCT-LABEST, Faculty of Engineering (FEUP), University of Porto, Porto, Portugal

[email protected] 2 CONSTRUCT-LABEST, Engineering School (ISEP), Polytechnic Institute of Porto, Porto,

Portugal

Abstract. In the last decades, structural health monitoring (SHM), and, in particular, early damage detection methodologies, have emerged as an important tool to assist in the maintenance and management of infrastructures. In this context, this work presents a methodology for damage detection in full-scale bridges based on moving-loads responses. The Luiz I bridge, an outstanding centenary steel double-deck arch bridge, was selected as a case study. The methodology consists in building time-series of vehicle-influence lines of the strains observed in the selected cross-sections and processing data by using moving principal component analysis (MPCA). Firstly, the effectiveness of the approach is assessed on numerically-simulated data, to show, on the one hand, the stability of the approach under undamaged conditions, and, on the other, the ability of the approach to highlight changes in the structural condition. Finally, the methodology is applied on field data collected for a 3-months period. Keywords: Structural health monitoring (SHM) · Damage detection · Moving principal component analysis (MPCA) · Bridges · Moving-loads

1 Introduction Bridges are susceptible to structural damage due to many factors, such as ageing, operating loads, fatigue, corrosion, etc. Undetected damage may lead to the failure of the structure, which may be very costly, both in human lives and in economic terms. Therefore, ensuring the integrity and safety of structures is paramount. In this context, over the last decades, structural health monitoring (SHM) of bridges, and in particular the development of damage detection methodologies, have attracted a huge attention from both the infrastructure owners and the scientific community. Following previous studies, based either on numerically-simulated [1] or on experimental [2] data of a reduced-scale laboratorial model, this paper addresses the application of a methodology for early damage detection in full-scale bridges, based on moving-loads data of in-service traffic. This methodology involves, in a first stage, building time-series © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 837–846, 2021. https://doi.org/10.1007/978-3-030-64908-1_78

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of moving-loads responses and, in a second stage, processing data using moving principal component analysis (MPCA) to detect changes in the structural behaviour and, thus, identifying the occurrence of damage. With the purpose of demonstrating the applicability of the approach to full-scale bridges, the Luiz I Bridge, located in Porto, was selected as a case study. This structure, an outstanding centenary steel double-deck arch bridge, was rehabilitated and strengthened in 2005 in order to allow the integration of its upper deck in the Porto metro light rail network. In this context, a very comprehensive monitoring system was implemented in the bridge, which has been used to continuously monitor its structural response under environmental actions, namely the temperature variation [3]. For the work presented herein, a set of sensors was selected to monitor the railway traffic of the upper deck. The responses of in-service metro compositions were collected in a continuous basis using a dedicated B-WIM system to characterize the traffic loads [4]. The use of this data, in the form of vehicle influence-lines, for the damage detection is explored in this work. In order to evaluate its performance, first, the approach is tested on numerically simulated data of the structural response of the upper-deck, for the in-service traffic of the metro of Porto. The objectives are, on the one hand, to verify the stability of the approach under undamaged conditions, and, on the other, to assess the ability of the approach for early detection of damage. Finally, the results given by this approach using field measurements collected for a 3-months monitoring period are presented.

2 The Luiz I Bridge 2.1 Brief Description of the Bridge Luiz I Bridge spans the Douro River, connecting the cities of Porto and Vila Nova de Gaia, in the north of Portugal (Fig. 1). This Porto’s iconic double-deck bridge, designed by the Belgian engineer Théophile Seyrig, was inaugurated in 1886, and it was at that time the longest steel arch in the world [5]. The bridge is constituted by a steel double-hinged arch, with a span length of 172 m and a height of 45.1 m, supporting simultaneously two decks at different levels over the river crossing. The upper deck, which is the focus of this work, comprises two continuous truss girders, 4.65 m apart, supported by the arch crown, seven piers and the abutments, materializing a total of 13 spans (Fig. 1). The connections between the upper deck and the piers located over the river banks are accomplished by bearing devices that enable both longitudinal-translations and–rotations, whereas the piers supported by the arch are rigidly connected at both ends. Diagonal and transverse beams at the chords’ levels, in the verticals alignment, laterally brace the truss girders. The loads of the metro vehicles are transferred from the rails to the crossbeams, which deliver the corresponding forces to the girders’ upper chords at the nodes of each vertical alignment. Integrated in the Porto Metro Network, the metro vehicles cross the upper deck in the upstream track in the Gaia-Porto direction, whereas Porto-Gaia crossings, take place in the downstream track. One or two coupled vehicles may constitute the metro compositions. The dimensions of one vehicle as well as the axle loads corresponding to its tare weight are depicted in Fig. 2.

Data-Driven Damage Detection Based on Moving-Loads Responses

Gaia

P1

P2

M1

M2

M3

M4

P3

P4

P5

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Porto

Fig. 1. Luiz I Bridge (Gaia, on the left, and Porto, on the right).

Fig. 2. Scheme of a metro vehicle.

2.2 Monitoring System The monitoring system installed on the bridge (along with the major strengthening and rehabilitation works carried out in 2005) consists in a fibre optic network comprising 15 optical channels containing multiple FBG sensors connected in series [3]. This monitoring system has been used for long-term continuous observation of the bridge behaviour due to changes in the surrounding environment, namely temperature variations, as well as shifts induced by slow deterioration phenomena. For this purpose, the sensors signals have been acquired every 5 min. Recently, with the objective of taking the maximum advantage of the measurement system installed in the bridge, two additional applications have emerged. First, a B-WIM system to characterize the metro traffic on the upper deck was implemented [4]. Second, a structural health monitoring approach using in-service vehicle influence-line data of metro vehicles as described in this work has been developed. For both purposes, two spans of the upper deck instrumented with sensors allocated to four channels were selected, for which the data acquisition rate was set at 50 Hz. The selected spans of the upper-deck are indicated by the red rectangle in Fig. 1 and comprise 19 instrumented bar cross-sections distributed as depicted in Fig. 3. Except for the cross-section denoted as S12, located at mid-span of the upstream lower chord at the 11th span, both the lower and upper chords, as well as the diagonals, were instrumented in the downstream girder. The cross-sections of two crossbeams (S25–S30) are also included in the selected monitoring system.

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Fig. 3. Monitoring system: scheme of the side view of the upper deck depicting the location of the instrumented cross-sections (top); and scheme of the instrumented cross-sections (bottom).

3 Approach for Damage Detection Based on Moving-Loads 3.1 General Remarks This work shows the applicability of a data-driven methodology for early damage detection in a full-scale bridge, using the moving principal component analysis (MPCA) on moving-loads responses. The method presented herein lays on the identification of changes in the pattern of the strain responses for 1-vehicle compositions of the light metro of Porto, crossing the upper deck of the Luiz I Bridge on the downstream track (from Porto to Gaia). For that purpose, the vehicle influence-lines of strains for selected cross-sections are assembled in time-series and subsequently processed by using the MPCA. Figure 4 depicts a set of vehicle influence-lines for the strains in selected crosssections collected during a 3-months monitoring period of the Luiz I Bridge. Although during this period a set of about 1500 vehicle influence-lines have been collected, in order to facilitate the interpretation, this figure depicts only 50 influence-lines equally distributed along the whole period of observation. The colour scheme varies between different shades of blue, green and red for, respectively, the first, intermediate and last crossings. It should be noted, in addition, that Fig. 4 does not include the whole vehicle influence-line. Only the measurements regarding the span in which the cross-section is located, as well as the adjacent spans, are taken into account. Therefore, for S11 and S14 the selected portion of the vehicle influence-line comprises, respectively, spans 9 to 12 and 10 to 12. The vertical dashed lines correspond to the pier alignments. As noticeable in Fig. 4, for each cross-section, although the pattern of the vehicle influence-lines collected during the monitoring period is similar, the results exhibit some variability. Note that these results are obtained under regular traffic of metro vehicle compositions on the bridge. Therefore, although all the vehicle influence-lines concern to 1-vehicle compositions, in which the geometry of the vehicle is always the same, the loading conditions may vary as regards either the total load of the vehicle or the relation between the loads in each bogie. In addition, deviations between the estimates of the

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position of the vehicle (to obtain the vehicle influence-line) and its actual location must be also taken into account. Finally, although the acquired signals are smoothed [4] the effects of noise may affect the accuracy of the measurements. Therefore, the adoption of methodologies that allow to swiftly distinguish, on the vehicle influence-lines that are continuously collected, abnormal behaviour of the bridge from the variability of its response related with the normal operation, as described above, are needed. In this context, as referred earlier, the vehicle influence-lines collected within this work have been assembled in time-series and subsequently processed using the MPCA.

Fig. 4. Field data of 50 vehicle influence-lines of the flanges’ strains for selected cross-sections (S11, on the left, and S14, on the right), for a set of 1-vehicle compositions, collected during a 3-months monitoring period of the Luiz I Bridge.

3.2 Moving Principal Component Analysis The key idea of principal component analysis (PCA) is to reduce a large number of interdependent variables to a much smaller number of uncorrelated variables while retaining as much as possible of the variation present in the original dataset, which is achieved by transforming the original variables into a new set of uncorrelated variables, the principal components (PCs) [6]. Consider a dataset matrix X ∈ n×p , containing n observations for p variables. The row i is a p-dimensional vector representing the ith observation, whereas the column j is a n-dimensional vector representing the jth variable. The dataset matrix can be written as a linear combination of a set of orthogonal vectors as follows: [X ] = [Z][U ]T

(1)

where Z ∈ n×p is the scores matrix and U ∈ p×p is the loadings matrix. The scores correspond to the coordinates of the original data in the  new coordinate system defined by the orthogonal vectors Uj = U1,j , U2,j , . . . , Up,j . Posenato et al. [7] proposed the moving principal component analysis (MPCA), as an extension of the application of PCA for damage detection, with the objective of reducing the influence of old measurements, which leads to additional time to detect changes. This approach consists in the calculation of the principal components of the data comprised in a window of constant size moving along the entire dataset. The analysis of the evolution,

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in terms of eigenvalues and eigenvectors, of the covariance matrix of the dataset gives a good indication of the damage initiation. If the group of sensors considered in the analysis are correlated and if the structural conditions have not changed, the main eigenvalues, and corresponding eigenvectors, remain stable with time. However, when something occurs in the structure, the measurements collected by some sensors may vary with respect to others, which leads to changes in the eigenvectors.

4 Results 4.1 General Remarks The results of the application of the methodology for early damage detection introduced above, using the moving-loads responses of the upper deck of the Luiz I Bridge for the in-service traffic of the metro of Porto, are presented herein. Firstly, the approach is tested on numerically simulated data. The objectives are, on the one hand, to verify the stability of the approach under undamaged conditions, and, on the other, to assess the ability of the approach for early detection of damage. Then, the methodology is applied on field data collected for a 3-months period, comprising about 1500 vehicle-influence lines of the strains observed in the selected cross-sections. In order to define the thresholds for detecting anomalous behaviour in the monitoring phase, in this work, it was considered a training period comprising 100 vehicle influencelines. The thresholds are given by μi ± k · σi , in which μi and σi are, respectively, the mean and the standard deviation computed in the training phase, of the control parameters i (the MPCA coordinates). It was considered k = 4, in order to, on the one hand, enable the detection of damage as quick as possible, and, on the other, prevent false-positive indication of damage. Still, an anomaly is flagged only when 10 consecutive points exceed the thresholds. The window size, moving along the entire dataset, was assumed to include one single vehicle-influence line. 4.2 Numerically-Simulated Data This section shows the applicability of the methodology by using numerically simulated data of the structural response of the upper-deck, for the in-service traffic of the metro of Porto. Therefore, the characteristics of the numerically simulated data analysed herein should be as similar as possible with those of the field measurements. Thus, the factors that lead to the variability of the field results (mentioned in Sect. 3.1) were taken into account within the numerical simulation of data. Figure 5 shows the numerical estimates for a set of 50 vehicle influence-lines of the flanges’ strains for selected cross-sections, for a set of 1-vehicle compositions crossings in the downstream track (from Porto to Gaia), for the baseline scenario (undamaged). The estimates try to reproduce the field-data variability, namely varying conditions as regards the vehicles loads, the vehicle positions, and noise. Detailed information about the simulation of the structural response of the bridge as well as the simulation of the aforementioned varying conditions may be found in [8]. The colour scheme varies between different shades of blue, green and red for, respectively, the first, intermediate

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and last crossings. Similarly to Fig. 4, these plots include only the numerical estimates regarding the span in which the cross-section is located as well as the adjacent spans. Although these results do not reproduce exactly the experimental vehicle influence-lines shown in Fig. 4, the pattern of the results is analogous. In this context, the performance of the proposed approach for early damage detection applied on such numerically simulated data may give good indications as regards its ability to be applied to field measurements.

Fig. 5. Numerical estimates for a set of 50 vehicle influence-lines of the flanges’ strains for selected cross-sections (S11, on the left, and S14, on the right), for a set of 1-vehicle compositions, reproducing variability of the vehicles loads, the vehicle positions, and noise.

Fig. 6. MPCA coordinates related with the vehicle influence-lines for the flange’s strains of S14, for the numerically-simulated data under undamaged conditions.

The first objective of using numerically-simulated data was to verify the stability of the approach, i.e., to evaluate the possibility of occurrence of false-positive identification of damage. Therefore, the first scenario under analysis consisted in a time-series comprising a set of 500 vehicle influence-lines for the undamaged condition only (as those depicted in Fig. 5), in which the structure is under normal operating conditions. As an example, Fig. 6 depicts the evolution of the MPCA coordinate related with the strains estimated at the flange of cross-section S14. As a result of the variability of the vehicle parameters, the control values vary along the time-series. Still, the thresholds defined in the training period (comprising 100 vehicle influence-lines) are never exceeded, and, thus, there is no false-positive indication of damage. The second objective was to assess the ability of the approach for early detection of damage. For this purpose, a damage scenario regarding a malfunction of the support bearings installed over pillar P4 was analysed. Under normal operating conditions,

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the longitudinal displacements are free. To simulate a restraint for the longitudinal displacement, for the sake of simplicity, a linear spring with a stiffness of 19600 kN/m in each support bearing was added to the baseline finite element model of the bridge. The analysis of the effects of this restraint on the structural responses has shown noticeable changes in the strains estimated at the instrumented cross-sections, as explained in detail in [8]. However, as depicted in Fig. 7, which shows a set of vehicle influence lines for both the undamaged and damaged conditions, as a result of the variability of the characteristics of the in-service vehicles, these changes, although slightly perceptible, become less clear.

Fig. 7. Numerical estimates for a set of 50 vehicle influence-lines (35 and 15 in, respectively, undamaged and damaged conditions) of the flanges’ strains for selected cross-sections (S11, on the left, and S14, on the right), for a set of 1-vehicle compositions, reproducing variability of the vehicles loads, the vehicle positions, and noise.

Fig. 8. MPCA coordinates related with the vehicle influence-lines for the flange’s strains of S14, for the numerically-simulated data under undamaged and damaged conditions.

The second scenario analysed in this work consisted, thus, in a time-series in which the first part (with 350 vehicle influence-lines) corresponds to the baseline condition, and, the second part, to the damaged condition corresponding to the restraint for the longitudinal displacements at pillar P4 mentioned above (with 150 vehicle influencelines). Although, due to the variability of the loading, the effects on the strain estimates of the restraint for the longitudinal displacement become less clear, in the evolution of the principal component coordinates, depicted in Fig. 8, the structural change is clearly highlighted.

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4.3 Field Data This section presents the results of the application of the damage detection approach on field data collected for a 3-months period. It comprises 1500 vehicle-influence lines of the strains in the cross-sections identified above and shown in Fig. 4. As shown in Fig. 9, the control values resulting from the application of MPCA occasionally exceed the threshold bounds (computed for a training period of 100 vehicle influence-lines), which may indicate changes in the structural condition of the Luiz I Bridge. Even though, the structural changes do not seem consistent in that the control values do not remain permanently beyond the thresholds. In addition, the visual inspection of the vehicle-influence lines along the monitoring period has shown that the variability is different over the different cross-sections (for instance, for S14 and S16, the variability is larger [8]). Therefore, further and deeper analyses of the field measurements are needed in order to identify and explain the observed behaviour. One possible explanation might be the role of environmental effects, most notably the temperature variations, leading to seasonal variations on the structural response to moving vehicles. This is an important aspect that still requires further research and most notably, additional data over an extended period comprising both winter and summer periods to evaluate if this variability can be explained by the method. Still, the monitoring of the control values of the data-processing algorithms, as well as the shape of the vehicle influence-lines, must be continued in order to assess whether these fluctuations are only circumstantial – as a result of transitional changes in the structural condition – or if evolve clearly beyond the thresholds.

Fig. 9. MPCA coordinates related with the vehicle influence-lines for the flange’s strains of S16, for field data.

5 Conclusions This work addresses the application of a methodology based on moving-loads data, for early damage detection. The Luiz I Bridge was selected as a case study. The methodology consists in assembling the vehicle influence-lines of strains for selected cross-sections, for the light metro crossings on the upper deck. Then, data are processed by using the MPCA in order to detect changes in the structural responses. The effectiveness of the approach was firstly demonstrated on numerically simulated data. On the one hand, the stability of the approach under undamaged conditions was

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clearly shown. On the other, it was demonstrated the ability of the approach for detecting changes in the structural condition of the bridge, namely restraints for the longitudinal displacements of the support bearings. Finally, the methodology was applied on field data collected for a 3-months period, comprising about 1500 vehicle-influence lines. Although the control parameters resulting from the application of the methodology occasionally exceed the thresholds defined in the training period, the results do not remain stable over time. One possible explanation might be the role of environmental effects, most notably the temperature variations, leading to seasonal variations on the structural response to moving vehicles. Therefore, it is necessary to continue monitoring the structure and carry out further analyses to explain the structural behaviour of the bridge. Acknowledgments. This work was financially supported by: Base Funding – UIDB/04708/2020 and Programmatic Funding – UIDP/04708/2020 of the CONSTRUCT – Instituto de I&D em Estruturas e Construções – funded by national funds through the FCT/MCTES (PIDDAC); and by the project POCI-01-0145-FEDER-031355 – “S4Bridges – A smart approach for the maintenance of existing bridges” funded by FEDER funds through COMPETE2020 – Programa Operacional Competitividade e Internacionalização (POCI) and by national funds (PIDDAC) through FCT/MCTES. The authors also gratefully acknowledge the infrastructure owner, Metro do Porto, S.A.

References 1. Cavadas, F., Smith, I.F.C., Figueiras, J.: Damage detection using data-driven methods applied to moving-load responses. Mech. Syst. Sig. Process. 39(1–2), 409–425 (2013) 2. Cavadas, F., Figueiras, J.: Deteção de dano em pontes apoiada em linhas de influência de cargas móveis. In: 55.º Congresso Brasileiro do Concreto (CBC 2013). IBRACON. Gramado, Rio Grande do Sul, Brasil (2013) 3. Costa, B.J.A.: Structural identification of old steel bridges - monitoring and rehabilitation assessment. Ph.D. thesis, Faculty of Engineering, University of Porto, Porto (2012) 4. Cavadas, F., Costa, B., Figueiras, J.: Implementation of a B-WIM system in a centenary steel truss bridge. In Multi-Span Large Bridges (MSLB 2015), Porto, Portugal (2015) 5. Figueiras, J., Félix, C., Costa, B.A.: Testing and monitoring of a centenary arch bridge. Struct. Infrastruct. Eng. 1(1), 63–73 (2005) 6. Jolliffe, I.T.: Principal Component Analysis. Springer Series in Statistics, 2nd edn. Springer, New York (2002). ISBN 0-387-95442-2 7. Posenato, D., Lanata, F., Inaudi, D., Smith, I.F.C.: Model-free data interpretation for continuous monitoring of complex structures. Adv. Eng. Inform. 22(1), 135–144 (2008) 8. Cavadas, F.: Structural health monitoring of bridges: physics-based assessment and data-driven damage identification. Ph.D. thesis, Faculty of Engineering, University Porto, Porto (2016)

Author Index

A Adams, Geoffrey Ryan, 603, 622 Afonso Costa, Bruno J., 837 Agrawal, Yamnesh, 825 Ahmed, Shabbir, 456 Alaggio, Rocco, 559 Aliabadi, M. H., 539 Alizzio, Damiano, 493 Aloisio, Angelo, 559 Ameduri, Salvatore, 382 Amer, Ahmad, 456 Ammirati, Lorenzo, 140 Andrearczyk, Artur, 679 Angeletti, Federica, 171 Aswal, Neha, 732 B Baldassino, Nadia, 447 Banerjee, Sauvik, 91 Bautin, Andrey, 67 Beckford, Bryana, 622 Bednarski, Łukasz, 331 Belleri, Andrea, 129 Bernardi, Martina, 447 Bernuzzi, Claudio, 447 Bogomolov, Denis, 657 Bohorquez, Miguel David Mendez, 289, 299 Bonilla, Luis Carlos, 289, 299 Bourbon, Gilles, 109 Bouvier, Damien, 699 Bowler, Adam, 550 Braga Carani, Lucas, 603 Bull, Lawrence A., 415

C Cabboi, Alessandro, 276 Calcaterra, Domenico, 140 Calì, Alfredo, 248 Cappello, Carlo, 238 Caresta, Mauro, 550 Carnì, Domenico Luca, 258 Carrasco, Nadia Paulina, 149 Castelli, Simone, 129 Cavadas, Filipe, 837 Cavalagli, Nicola, 119 Cerniglia, Donatella, 195 Chang, Chia-Ming, 24 Chang, Ting-Wei, 24 Chen, Shijian, 372 Chen, Yaoyao, 569 Chevallier, Gaël, 109 Chronopoulos, E., 480 Chuan, Li, 645 Ciminello, Monica, 382 Cinque, Daniele, 788 Cinquemani, Simone, 527 Cirella, Riccardo, 559 Colombo, Luca, 342 Costantini, Mario, 119 Cross, Elizabeth J., 55, 415 D D’Ippolito, Dennis, 657 Daga, Alessandro Paolo, 469 Davino, Antonio, 227 De Domenico, Dario, 493 De Finis, Rosa, 309, 319

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 P. Rizzo and A. Milazzo (Eds.): EWSHM 2020, LNCE 128, pp. 847–850, 2021. https://doi.org/10.1007/978-3-030-64908-1

848 De Marchi, Luca, 657 de Miguel, Carlos, 352 De Stefano, Rita, 149 Deloukas, A., 480 Deng, Guojun, 3 Deng, Yiming, 77 Dervilis, Nikolaos, 415 di Gioia, Arturo, 447 Di Martire, Diego, 140, 149 Di Sante, Raffaella, 362 Díaz-Maroto Fernández, Patricia, 352 Dobie, Gordon, 267 dos Santos, Jose Viriato Araújo, 788, 817 Duan, Xiaochang, 632 Dworakowski, Ziemowit, 14 E Edwards, Rachel S., 267 Ehsani, M., 776 Entezami, Alireza, 427 Epasto, Gabriella, 195 Eze, Vincent Obiozo, 622 F Falcetelli, Francesco, 362 Falco, Salvatore, 119 Fang, Ziwei, 161 Farneti, Elisabetta, 119 Fasana, Alessandro, 469 Fassois, S. D., 405, 480 Félix, Carlos, 837 Figueiras, Joaquim A., 837 Forero, Juan Carlos, 289, 299 Formisano, Antonio, 227 Fornaro, Gianfranco, 119 Fritz, Henrieke, 217 Fujihara, Hiroshi, 392 G Gabriele, Stefano, 788 Galietti, Umberto, 309, 319 Gangwar, Akhilendra S., 825 García Alonso, Jaime, 352 Gardner, Paul, 415 Garibaldi, Luigi, 469 Gaul, Tobias, 742 Gawlicki, Michał, 799 Gentile, Carmelo, 248, 276 Giglio, Marco, 342 Gillich, Gilbert-Rainer, 207 Giraldo, Carlos Miguel, 593

Author Index Gopalakrishnan, Karthik, 77 Guan, Xuefei, 612, 632 Guerrero Vázquez, Santiago, 352 Guglielmino, Eugenio, 195 Guha, Anirban, 91 H Hamat, Codruta Oana, 207 He, Jingjing, 161 Heesch, Mateusz, 14 Hironaka, Yoshikazu, 392 Hofmeister, Benedikt, 711 Howiacki, Tomasz, 331 Hsu, Shun-Hsiang, 24 Huang, Tianxiang, 438 Hübler, Clemens, 711 I Iannelli, Paolo, 171 Iglesias Vallejo, Manuel, 352 Iliopoulos, I. A., 480 Imai, Michio, 392 Iñesta González, Daniel, 352 J Jalali, Hoda, 669 Jankowski, Łukasz, 799 Jeong, Euiseok, 503 Jiménez-Suárez, Alberto, 527 Joglekar, Dhanashri M., 825 Jonscher, Clemens, 711 Joshi, Bhagirath, 517 K Kaczmarczyk, Stefan, 765 Kaliorakis, N., 480 Katsiana, K., 480 Katunin, A., 817 Kita, Alban, 119 Kopsaftopoulos, Fotis, 456 Krozer, Viktor, 185 Kumar, Abhijeet, 91 L Lamonaca, Francesco, 258 Lawrence, Ursula, 46 Le Moal, Patrice, 109 Leoutsakos, G., 480 Li, Hui, 35 Li, Tao, 372 Lieske, Uwe, 742

Author Index Liu, Jie, 161 Loendersloot, Richard, 776 Lopes, Hernani, 788, 817 M Macleod, Charles, 267 Majewska, Katarzyna, 679, 687 Malatesta, Michelangelo Maria, 657 Malinowski, Paweł H., 580, 808 Mamaloukakis, C., 480 Mantilla, Juan M., 289, 299 Marchesiello, Stefano, 469 Marcinkowski, Peter, 742 Marfia, Sonia, 788 Mariani, Stefano, 427 Marini, Alessandra, 129 Marzani, Alessandro, 657 Mbarga Nkogo, Martin, 109 Mechbal, Nazih, 699, 720 Mendrok, Krzysztof, 14 Messina, Marco, 657 Mevel, Laurent, 732 Mieloszyk, Magdalena, 679, 687 Mizunari, Motoyuki, 392 Mo, Y. L., 517 Moll, Jochen, 185 Mondillo, Nicola, 140 Montanini, Roberto, 493 Monteiro, Eric, 720 Montinaro, Nicola, 195 Moshrefzadeh, Ali, 469 N Nasrollahi, Amir, 669 Nedelcu, Dorian, 207 Nguyen, Duy Hai, 185 Nikolowski, Kristian, 742 Nobile, Riccardo, 319 O Obiozo Eze, Vincent, 603 Oboe, Daniele, 342 Okoli, Okenwa I., 603, 622 Olivito, Renato Sante, 258 Ostachowicz, Wiesław M., 687, 808 Oz, Yagiz, 517 P Palmerini, Giovanni B., 171 Palumbo, Davide, 309, 319 Panagiotopoulos, A. I., 405 Panella, Francesco, 319 Patel, Bhavik, 527 Perez, Hugo, 289, 299

849 Pierce, Stephen G., 267 Pimentel, Mário, 837 Postorino, Hadrien, 720 Praisach, Zeno-Iosif, 207 Q Qi, Chongke, 372 Qin, Yong, 645 Quattrocchi, Antonino, 493 R Ramasso, Emmanuel, 109 Ramondini, Massimo, 149 Rautela, Mahindra, 77 Reale, Diego, 119 Rébillat, Marc, 699, 720 Recupero, Antonino, 493 Ricardo, Jose, 289, 299 Ricciardi, Giuseppe, 493 Riva, Paolo, 129 Rizzo, Piervincenzo, 669 Rodas, Ricardo, 149 Rogers, Timothy J., 55, 415 Rolfes, Raimund, 711 Romano, Fulvio, 382 Rota, Luca, 129 Rothe, Sandra, 754 Rueda, Bernardo, 289, 299 S Saisi, Antonella, 248 Sakellariou, J. S., 480 Sánchez del Río Sáez, José, 593 Sánchez Sánchez, Alejandro, 352 Sánchez-Romate, Xoan F., 527 Saponaro, Andrea, 319 Sasaki, Toshiyuki, 392 Sbarufatti, Claudio, 342, 527 Scaccabarozzi, Diego, 527 Schröder, Kai-Uwe, 438 Schubert, Lars, 742 Scuro, Carmelo, 258 Sellers, Chester, 149 Sen, Subhamoy, 732 Seo, Junwon, 503 Sepehry, N., 776 Shamshirsaz, M., 776 Shan, Xiaonan, 517 Shao, Shuai, 3 Shen, Clive Chin-Kang, 46 Shohag, Md Abu, 603, 622 Sieńko, Rafał, 331 Simoncelli, Marco, 447 Singh, Shishir Kumar, 808

850 Smarsly, Kay, 217 Smith, Rory, 765 Söffker, Dirk, 754 Soto, Carlos Alberto Barrera, 299 Sun, Yumeng, 645 Suyama, Yasuhiro, 392 Svirskiy, Yury, 67

T Tabatabaeipour, Morteza, 267 Tcherniak, D., 405 Testoni, Nicola, 657 Tian, Yadi, 35 Tonelli, Daniel, 238 Torres Perez, Angel, 765 Trillo, Francesco, 119 Troiani, Enrico, 362 Trushkevych, Oksana, 267 Tu, Shan-Tung, 372 Tu, Yun, 372 Tufisi, Cristian, 207 U Ubertini, Filippo, 119 Ureña, Alejandro, 527 Urso, Santi, 493

V Verde, Simona, 119 Verdin, Benoit, 109 Vlachospyros, G., 480

Author Index W Wacker, James, 503 Waki, Toshikazu, 392 Wan, Chengrui, 438 Wandowski, Tomasz, 580 Wang, Jiaji, 517 Wang, Xinyan, 612, 632 Wang, Xuenan, 569 Wang, Ya-Li, 372 Wei, Limin, 612 Wolter, Mareike, 742 Worden, Keith, 415 Wu, Zhiyu, 645 X Xie, Zhengyu, 645 Xu, Yang, 35 Y Yamano, Yasuaki, 392 Yan, Shi, 569 Yao, Yuanyuan, 569 Yu, Xinhai, 372 Yue, Nan, 539 Z Zhang, Jian, 372 Zhang, Sikai, 55 Zhang, Yufeng, 35 Zhao, Yang, 612 Zhou, Zhixiang, 3 Zonno, Giacomo, 276 Zonta, Daniele, 238 Zurita, Oscar, 289, 299