Prognostics and Health Management of Engineering Systems

Prognostics and Health Management of Engineering Systems

Nam-Ho Kim Dawn An Joo-Ho Choi Prognostics and Health Management of Engineering Systems An Introduction 123

Nam-Ho Kim Mechanical and Aerospace Engineering University of Florida Gainesville, FL USA Joo-Ho Choi Aerospace & Mechanical Engineering Korea Aerospace University Goyang-City, Kyonggi-do Republic of Korea Dawn An Daegyeong Division/Aircraft System Technology Group Korea Institute of Industrial Technology Yeongcheon-si, Gyeongbuk-do Republic of Korea ISBN 978-3-319-44740-7 ISBN 978-3-319-44742-1 (ebook) DOI 10.1007/978-3-319-44742-1 Library of Congress Control Number: 2016948272 Springer International Publishing Switzerland 2017 This work is subject to copyright. All rights are reserved 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, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

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Preface A good maintenance strategy is essential to keep complex engineering systems safe. Historically, maintenance has evolved from post-failure repair to preventive maintenance to Condition-Based Maintenance (CBM). Preventive maintenance is an expensive and time-consuming process because it is carried out periodically regardless of the health state of systems. For modern complex systems with high reliability requirements, preventive maintenance has become a major expense of many industrial companies. CBM has recently received much attention as a cost-effective maintenance strategy, which is to perform maintenance only when needed. Prognostics and Health Management (PHM) is the key technology to accomplish CBM. PHM is a new engineering approach that enables real-time health assessment of a system under its actual operating conditions, as well as the prediction of its future state based on up-to-date information, by incorporating various disciplines including sensing technologies, physics of failure, machine learning, modern statistics, and reliability engineering. It enables engineers to turn data and health states into information that will improve our knowledge on the system and provide a strategy to maintain the system in its originally intended function. While PHM has roots from the aerospace industry, it is now explored in many applications including manufacturing, automotive, railway, energy and heavy industry. Since PHM is a relatively new research area, many researchers and students struggle to find a textbook that clearly explains basic algorithms and provides objective comparison between different algorithms. The objective of this book is to introduce the methods of predicting the future behavior of a system s health and the remaining useful life to determine an appropriate maintenance schedule. The uniqueness of this book lies not only in its introduction to various prognostics algorithms, but also in its explanations of their attributes and pros and cons in terms of model definition, model parameter estimation, and ability to handle noise and bias in data. Therefore, beginners in this field can select appropriate methods for their fields of application. vii

viii Preface This book is suitable for graduate students in mechanical, civil, aerospace, electrical and industrial engineering, and engineering mechanics, as well as researchers and maintenance engineers in the above fields. The textbook is organized into seven chapters. In Chap. 1, the basic ideas of PHM are introduced along with historical backgrounds, industrial applications, reviews of algorithms, and benefits and challenges of PHM. Before discussing individual prognostics algorithms in detail, Chap. 2 provides prognostics tutorials with a MATLAB code using simple examples. Even if simple polynomial models are used with the least-squares method, they contain most of important attributes of various prognostics algorithms. The tutorials include physics-based and data-driven prognostics algorithms to identify model parameters as well as to predict the remaining useful life. This chapter also introduces prognostics metrics to evaluate the performance of different algorithms as well as uncertainty due to noise in data. A key step in prognostics is to convert the measured data from health monitoring systems into knowledge on damage degradation. Many prognostics algorithms utilize Bayes theorem to update information on unknown model parameters using measured data. Chapter 3 introduces Bayesian inference with an explanation of uncertainty and conditional probability. For the purpose of prognostics, the chapter focuses on how to utilize prior information and likelihood functions from measured data in order to update the posterior probability density function (PDF) of model parameters. Depending on how information is updated, both recursive and total forms are discussed. The chapter ends with a method of generating samples from a posterior PDF. When a physical model that describes the behavior of damage is available, it is always better to use it for prognostics. Chapter 4 presents physics-based prognostics algorithms, such as nonlinear least squares, Bayesian method, and particle filter. The major step in physics-based prognostics is to identify model parameters using measured data and to predict the remaining useful life using them. The chapter focuses on how to improve the accuracy of a degradation model and how to incorporate uncertainty in the future. The chapter ends by discussing issues in physics-based prognostics, which includes model adequacy, correlation between parameters, and quality of degradation data. Even if physics-based approaches are powerful, many complex systems do not have a reliable physical model to describe the degradation of damage. Chapter 5 introduces data-driven approaches, which use information from observed data to identify the patterns of the degradation progress and predict the future state without using a physical model. As representative algorithms, the Gaussian process regression and neural network models are explained. Data-driven approaches share the same issues with physics-based approaches, such as model-form adequacy, estimation of optimal parameters, and quality of degradation data. In Chap. 6, these prognostics algorithms are applied to fatigue crack growth problems to understand the attributes of different algorithms. In the case of physics-based approaches, correlation between model parameters, initial conditions, and loading conditions play an important role in the performance of algorithms. In the case of data-driven approaches, the availability of training data and the level of

Preface ix noise are important. Chapter 7 presents several applications of prognostics in practical engineering systems, including wear in a revolute joint, fatigue crack growth in a panel, prognostics using accelerated life test data, and fatigue damage in bearings. MATLAB programs for different algorithms as well as measurement data used in the book are available on the companion website of the book http://www2.mae. ufl.edu/nkim/phm/. Each chapter contains a comprehensive set of exercise problems, some of which require MATLAB programs. We thank the students who took various courses at the University of Florida and Korea Aerospace University. We are grateful for their valuable suggestions, especially those regarding the example and exercise problems. Finally, special thanks to Ms. Ting Dong for her outstanding work to correcting many errors in the manuscript. Gainesville, USA Yeongcheon-si, Republic of Korea Goyang-City, Republic of Korea June 2016 Nam-Ho Kim Dawn An Joo-Ho Choi

Contents 1 Introduction.... 1 1.1 Prognostics and Health Management... 1 1.2 Historical Background... 5 1.3 PHM Applications... 8 1.4 Review of Prognostics Algorithms... 10 1.5 Benefits and Challenges for Prognostics... 14 1.5.1 Benefits in Life-Cycle Cost... 14 1.5.2 Benefits in System Design and Development... 15 1.5.3 Benefits in Production.... 16 1.5.4 Benefits in System Operation... 16 1.5.5 Benefits in Logistics Support and Maintenance.... 17 1.5.6 Challenges in Prognostics... 18 References.... 21 2 Tutorials for Prognostics.... 25 2.1 Introduction... 25 2.2 Prediction of Degradation Behavior... 28 2.2.1 Least Squares Method... 28 2.2.2 When a Degradation Model Is Available (Physics-Based Approaches)... 31 2.2.3 When a Degradation Model Is NOT Available (Data-Driven Approaches).... 38 2.3 RUL Prediction.... 44 2.3.1 RUL... 44 2.3.2 Prognostics Metrics... 49 2.4 Uncertainty... 53 2.5 Issues in Practical Prognostics... 68 2.6 Exercises... 69 References.... 70 xi

xii Contents 3 Bayesian Statistics for Prognostics... 73 3.1 Introduction to Bayesian Theory.... 73 3.2 Aleatory Uncertainty versus Epistemic Uncertainty... 76 3.2.1 Aleatory Uncertainty... 76 3.2.2 Epistemic Uncertainty... 78 3.2.3 Sampling Uncertainty in Coupon Tests... 80 3.3 Conditional Probability and Total Probability... 86 3.3.1 Conditional Probability... 86 3.3.2 Total Probability... 92 3.4 Bayes Theorem... 93 3.4.1 Bayes Theorem in Probability Form... 93 3.4.2 Bayes Theorem in Probability Density Form... 95 3.4.3 Bayes Theorem with Multiple Data... 99 3.4.4 Bayes Theorem for Parameter Estimation... 102 3.5 Bayesian Updating... 104 3.5.1 Recursive Bayesian Update... 104 3.5.2 Overall Bayesian Update.... 108 3.6 Bayesian Parameter Estimation... 110 3.7 Generating Samples from Posterior Distribution... 114 3.7.1 Inverse CDF Method.... 114 3.7.2 Grid Approximation Method: One Parameter... 116 3.7.3 Grid Approximation: Two Parameters.... 119 3.8 Exercises... 122 References.... 124 4 Physics-Based Prognostics.... 127 4.1 Introduction to Physics-Based Prognostics... 127 4.1.1 Demonstration Problem: Battery Degradation... 130 4.2 Nonlinear Least Squares (NLS)... 131 4.2.1 MATLAB Implementation of Battery Degradation Prognostics Using Nonlinear Least Squares... 133 4.3 Bayesian Method (BM)... 140 4.3.1 Markov Chain Monte Carlo (MCMC) Sampling Method... 140 4.3.2 MATLAB Implementation of Bayesian Method for Battery Prognostics... 147 4.4 Particle Filter (PF)... 152 4.4.1 SIR Process.... 154 4.4.2 MATLAB Implementation of Battery Prognostics.... 160 4.5 Practical Application of Physics-Based Prognostics... 165 4.5.1 Problem Definition... 165 4.5.2 Modifying the Codes for the Crack Growth Example... 167 4.5.3 Results... 170

Contents xiii 4.6 Issues in Physics-Based Prognostics... 172 4.6.1 Model Adequacy.... 173 4.6.2 Parameter Estimation.... 174 4.6.3 Quality of Degradation Data... 175 4.7 Exercise... 176 References.... 177 5 Data-Driven Prognostics... 179 5.1 Introduction to Data-Driven Prognostics... 179 5.2 Gaussian Process (GP) Regression... 181 5.2.1 Surrogate Model and Extrapolation... 181 5.2.2 Gaussian Process Simulation.... 183 5.2.3 GP Simulation.... 187 5.2.4 MATLAB Implementation of Battery Prognostics Using Gaussian Process... 201 5.3 Neural Network (NN).... 207 5.3.1 Feedforward Neural Network Model.... 208 5.3.2 MATLAB Implementation of Battery Prognostics Using Neural Network... 221 5.4 Practical Use of Data-Driven Approaches.... 226 5.4.1 Problem Definition... 226 5.4.2 MATLAB Codes for the Crack Growth Example... 228 5.4.3 Results... 230 5.5 Issues in Data-Driven Prognostics... 232 5.5.1 Model-Form Adequacy... 232 5.5.2 Optimal Parameters Estimation... 233 5.5.3 Quality of Degradation Data... 235 5.6 Exercise... 236 References.... 238 6 Study on Attributes of Prognostics Methods... 243 6.1 Introduction... 243 6.2 Problem Definition... 245 6.2.1 Paris Model for Fatigue Crack Growth... 245 6.2.2 Huang s Model for Fatigue Crack Growth... 247 6.2.3 Health Monitoring Data and Loading Conditions... 250 6.3 Physics-Based Prognostics... 252 6.3.1 Correlation in Model Parameters.... 253 6.3.2 Comparison of NLS, BM, and PF.... 263 6.4 Data-Driven Prognostics... 269 6.4.1 Comparison Between GP and NN.... 270 6.5 Comparison Between Physics-Based and Data-Driven Prognostics... 274 6.6 Results Summary... 275

xiv Contents 6.7 Exercise... 276 References.... 279 7 Applications of Prognostics.... 281 7.1 Introduction... 281 7.2 In Situ Monitoring and Prediction of Joint Wear... 282 7.2.1 Motivation and Background... 282 7.2.2 Wear Model and Wear Coefficient... 283 7.2.3 In Situ Measurement of Joint Wear for a Slider-Crank Mechanism... 285 7.2.4 Bayesian Inference for Predicting Progressive Joint Wear.... 288 7.2.5 Identification of Wear Coefficient and Prediction of Wear Volume... 292 7.2.6 Discussion and Conclusions... 296 7.3 Identification of Correlated Damage Parameters Under Noise and Bias Using Bayesian Inference... 298 7.3.1 Motivation and Background... 298 7.3.2 Damage Growth and Measurement Uncertainty Models... 299 7.3.3 Bayesian Inference for Characterization of Damage Properties... 301 7.3.4 Conclusions.... 309 7.4 Usage of Accelerated Test Data for Predicting Remaining Useful Life at Field Operating Conditions... 309 7.4.1 Motivation and Background... 310 7.4.2 Problem Definition... 311 7.4.3 Utilizing Accelerated Life Test Data... 312 7.4.4 Conclusions.... 321 7.5 Bearing Prognostics Method Based on Entropy Decrease at Specific Frequencies... 321 7.5.1 Motivation and Background... 321 7.5.2 Degradation Feature Extraction... 324 7.5.3 Prognostics... 331 7.5.4 Discussions on Generality of the Proposed Method... 336 7.5.5 Conclusions and Future Works... 338 7.6 Other Applications... 339 References.... 342 Index... 345