Structural Health Monitoring

Charles R Farrar, Los Alamos National Laboratory, New Mexico, USA is currently the director of The Engineering Institute at LANL. His research interests focus on developing integrated hardware and software solutions to structural health monitoring problems and the development of damage prognosis technology. The results of this research have been documented in 50 refereed journal articles, 14 book chapters, more than 100 conference papers, 31 Los Alamos Reports and numerous keynote lectures at international conferences. In 2000 he founded the Los Alamos Dynamics Summer School. His has recently received the inaugural Los Alamos Fellows Prize for Technical Leadership and the inaugural Lifetime Achievement Award in Structural Health Monitoring. He is currently working with engineering faculty at University of California, San Diego to develop the Los Alamos/UCSD Engineering Institute and Education Initiative with a research focus on Damage Prognosis. He is associate editor for the Int. Journal of Structural Health Monitoring and Earthquake Engineering and Structural Dynamics. Keith Worden, University of Sheffield, UK is Head of the Dynamics Research Group in the Department of Mechanical Engineering at the University of Sheffield. His research interests lie in the applications of advanced signal processing and machine learning methods to structural dynamics. He has authored over 400 research publications including two co-authored books on nonlinear structural dynamics and nonlinear system identification, two book chapters and over 130 refereed journal papers. He serves on the editorial boards of 2 international journals: Journal of Sound and Vibration and Mechanical Systems and Signal Processing. He was awarded "2004 Person of the Year" (jointly with W.J. Staszewski) awarded by Structural Health Monitoring journal for outstanding contribution in the field.

• Preface xviiAcknowledgements xix1 Introduction 11.1 How Engineers and Scientists Study Damage 21.2 Motivation for Developing SHM Technology 31.3 Definition of Damage 41.4 A Statistical Pattern Recognition Paradigm for SHM 71.4.1 Operational Evaluation 101.4.2 Data Acquisition 101.4.3 Data Normalisation 101.4.4 Data Cleansing 111.4.5 Data Compression 111.4.6 Data Fusion 111.4.7 Feature Extraction 121.4.8 Statistical Modelling for Feature Discrimination 121.5 Local versus Global Damage Detection 131.6 Fundamental Axioms of Structural Health Monitoring 141.7 The Approach Taken in This Book 15References 152 Historical Overview 172.1 Rotating Machinery Applications 172.1.1 Operational Evaluation for Rotating Machinery 182.1.2 Data Acquisition for Rotating Machinery 182.1.3 Feature Extraction for Rotating Machinery 192.1.4 Statistical Modelling for Damage Detection in Rotating Machinery 202.1.5 Concluding Comments about Condition Monitoring of Rotating Machinery 212.2 Offshore Oil Platforms 212.2.1 Operational Evaluation for Offshore Platforms 212.2.2 Data Acquisition for Offshore Platforms 242.2.3 Feature Extraction for Offshore Platforms 242.2.4 Statistical Modelling for Offshore Platforms 252.2.5 Lessons Learned from Offshore Oil Platform Structural Health Monitoring Studies 252.3 Aerospace Structures 252.3.1 Operational Evaluation for Aerospace Structures 282.3.2 Data Acquisition for Aerospace Structures 292.3.3 Feature Extraction and Statistical Modelling for Aerospace Structures 312.3.4 Statistical Models Used for Aerospace SHM Applications 322.3.5 Concluding Comments about Aerospace SHM Applications 322.4 Civil Engineering Infrastructure 322.4.1 Operational Evaluation for Bridge Structures 342.4.2 Data Acquisition for Bridge Structures 342.4.3 Features Based on Modal Properties 352.4.4 Statistical Classification of Features for Civil Engineering Infrastructure 362.4.5 Applications to Bridge Structures 362.5 Summary 37References 383 Operational Evaluation 453.1 Economic and Life-Safety Justifications for Structural Health Monitoring 453.2 Defining the Damage to Be Detected 463.3 The Operational and Environmental Conditions 473.4 Data Acquisition Limitations 473.5 Operational Evaluation Example: Bridge Monitoring 483.6 Operational Evaluation Example: Wind Turbines 513.7 Concluding Comment on Operational Evaluation 52References 524 Sensing and Data Acquisition 534.1 Introduction 534.2 Sensing and Data Acquisition Strategies for SHM 534.2.1 Strategy I 544.2.2 Strategy II 544.3 Conceptual Challenges for Sensing and Data Acquisition Systems 554.4 What Types of Data Should Be Acquired? 564.4.1 Dynamic Input and Response Quantities 574.4.2 Other Damage-Sensitive Physical Quantities 594.4.3 Environmental Quantities 594.4.4 Operational Quantities 604.5 Current SHM Sensing Systems 604.5.1 Wired Systems 604.5.2 Wireless Systems 614.6 Sensor Network Paradigms 634.6.1 Sensor Arrays Directly Connected to Central Processing Hardware 644.6.2 Decentralised Processing with Hopping Connection 654.6.3 Decentralised Processing with Hybrid Connection 664.7 Future Sensing Network Paradigms 674.8 Defining the Sensor System Properties 684.8.1 Required Sensitivity and Range 704.8.2 Required Bandwidth and Frequency Resolution 714.8.3 Sensor Number and Locations 714.8.4 Sensor Calibration, Stability and Reliability 724.9 Define the Data Sampling Parameters 734.10 Define the Data Acquisition System 744.11 Active versus Passive Sensing 754.12 Multiscale Sensing 754.13 Powering the Sensing System 774.14 Signal Conditioning 774.15 Sensor and Actuator Optimisation 784.16 Sensor Fusion 794.17 Summary of Sensing and Data Acquisition Issues for Structural Health Monitoring 82References 835 Case Studies 875.1 The I-40 Bridge 875.1.1 Preliminary Testing and Data Acquisition 895.1.2 Undamaged Ambient Vibration Tests 905.1.3 Forced Vibration Tests 915.2 The Concrete Column 925.2.1 Quasi-Static Loading 955.2.2 Dynamic Excitation 955.2.3 Data Acquisition 955.3 The 8-DOF System 985.3.1 Physical Parameters 1005.3.2 Data Acquisition 1005.4 Simulated Building Structure 1005.4.1 Experimental Procedure and Data Acquisition 1015.4.2 Measured Data 1025.5 The Alamosa Canyon Bridge 1045.5.1 Experimental Procedures and Data Acquisition 1045.5.2 Environmental Measurements 1075.5.3 Vibration Tests Performed to Study Variability of Modal Properties 1085.6 The Gnat Aircraft 1085.6.1 Simulating Damage with a Modified Inspection Panel 1095.6.2 Simulating Damage by Panel Removal 112References 1166 Introduction to Probability and Statistics 1196.1 Introduction 1196.2 Probability: Basic Definitions 1206.3 Random Variables and Distributions 1226.4 Expected Values 1256.5 The Gaussian Distribution (and Others) 1306.6 Multivariate Statistics 1326.7 The Multivariate Gaussian Distribution 1336.8 Conditional Probability and the Bayes Theorem 1346.9 Confidence Limits and Cumulative Distribution Functions 1376.10 Outlier Analysis 1406.10.1 Outliers in Univariate Data 1406.10.2 Outliers in Multivariate Data 1416.10.3 Calculation of Critical Values of Discordancy or Thresholds 1416.11 Density Estimation 1426.12 Extreme Value Statistics 1486.12.1 Introduction 1486.12.2 Basic Theory 1486.12.3 Determination of Limit Distributions 1516.13 Dimension Reduction – Principal Component Analysis 1556.13.1 Simple Projection 1566.13.2 Principal Component Analysis (PCA) 1566.14 Conclusions 158References 1597 Damage-Sensitive Features 1617.1 Common Waveforms and Spectral Functions Used in the Feature Extraction Process 1637.1.1 Waveform Comparisons 1647.1.2 Autocorrelation and Cross-Correlation Functions 1657.1.3 The Power Spectral and Cross-Spectral Density Functions 1667.1.4 The Impulse Response Function and the Frequency Response Function 1687.1.5 The Coherence Function 1697.1.6 Some Remarks Regarding Waveforms and Spectra 1707.2 Basic Signal Statistics 1717.3 Transient Signals: Temporal Moments 1787.4 Transient Signals: Decay Measures 1817.5 Acoustic Emission Features 1837.6 Features Used with Guided-Wave Approaches to SHM 1857.6.1 Preprocessing 1867.6.2 Baseline Comparisons 1867.6.3 Damage Localisation 1887.7 Features Used with Impedance Measurements 1887.8 Basic Modal Properties 1917.8.1 Resonance Frequencies 1927.8.2 Inverse versus Forward Modelling Approaches to Feature Extraction 1947.8.3 Resonance Frequencies: The Forward Approach 1957.8.4 Resonance Frequencies: Sensitivity Issues 1957.8.5 Mode Shapes 1977.8.6 Load-Dependent Ritz Vectors 2037.9 Features Derived from Basic Modal Properties 2067.9.1 Mode Shape Curvature 2077.9.2 Modal Strain Energy 2107.9.3 Modal Flexibility 2157.10 Model Updating Approaches 2187.10.1 Objective Functions and Constraints 2207.10.2 Direct Solution for the Modal Force Error 2217.10.3 Optimal Matrix Update Methods 2227.10.4 Sensitivity-Based Update Methods 2267.10.5 Eigenstructure Assignment Method 2307.10.6 Hybrid Matrix Update Methods 2317.10.7 Concluding Comment on Model Updating Approaches 2317.11 Time Series Models 2327.12 Feature Selection 2347.12.1 Sensitivity Analysis 2347.12.2 Information Content 2387.12.3 Assessment of Robustness 2397.12.4 Optimisation Procedures 2397.13 Metrics 2397.14 Concluding Comments 240References 2408 Features Based on Deviations from Linear Response 2458.1 Types of Damage that Can Produce a Nonlinear System Response 2458.2 Motivation for Exploring Nonlinear System Identification Methods for SHM 2488.2.1 Coherence Function 2508.2.2 Linearity and Reciprocity Checks 2518.2.3 Harmonic Distortion 2568.2.4 Frequency Response Function Distortions 2618.2.5 Probability Density Function 2648.2.6 Correlation Tests 2668.2.7 The Holder Exponent 2668.2.8 Linear Time Series Prediction Errors 2718.2.9 Nonlinear Time Series Models 2738.2.10 Hilbert Transform 2778.2.11 Nonlinear Acoustics Methods 2798.3 Applications of Nonlinear Dynamical Systems Theory 2808.3.1 Modelling a Cracked Beam as a Bilinear System 2818.3.2 Chaotic Interrogation of a Damaged Beam 2828.3.3 Local Attractor Variance 2848.3.4 Detection of Damage Using the Local Attractor Variance 2868.4 Nonlinear System Identification Approaches 2888.4.1 Restoring Force Surface Model 2888.5 Concluding Comments Regarding Feature Extraction Based on Nonlinear System Response 291References 2929 Machine Learning and Statistical Pattern Recognition 2959.1 Introduction 2959.2 Intelligent Damage Detection 2959.3 Data Processing and Fusion for Damage Identification 2989.4 Statistical Pattern Recognition: Hypothesis Testing 3009.5 Statistical Pattern Recognition: General Frameworks 3039.6 Discriminant Functions and Decision Boundaries 3069.7 Decision Trees 3089.8 Training – Maximum Likelihood 3099.9 Nearest Neighbour Classification 3129.10 Case Study: An Acoustic Emission Experiment 3129.10.1 Analysis and Classification of the AE Data 3149.11 Summary 320References 32010 Unsupervised Learning – Novelty Detection 32110.1 Introduction 32110.2 A Gaussian-Distributed Normal Condition – Outlier Analysis 32210.3 A Non-Gaussian Normal Condition – A Neural Network Approach 32510.4 Nonparametric Density Estimation – A Case Study 32910.4.1 The Experimental Structure and Data Capture 33110.4.2 Preprocessing of Data and Features 33210.4.3 Novelty Detection 33310.5 Statistical Process Control 33810.5.1 Feature Extraction Based on Autoregressive Modelling 33910.5.2 The X-Bar Control Chart: An Experimental Case Study 34010.6 Other Control Charts and Multivariate SPC 34310.6.1 The S Control Chart 34410.6.2 The CUSUM Chart 34410.6.3 The EWMA Chart 34510.6.4 The Hotelling or Shewhart T2 Chart 34610.6.5 The Multivariate CUSUM Chart 34710.6.6 The Multivariate EWMA Chart 34710.7 Thresholds for Novelty Detection 34810.7.1 Extreme Value Statistics 34810.7.2 Type I and Type II Errors: The ROC Curve 35410.8 Summary 359References 35911 Supervised Learning – Classification and Regression 36111.1 Introduction 36111.2 Artificial Neural Networks 36111.2.1 Biological Motivation 36111.2.2 The Parallel Processing Paradigm 36411.2.3 The Artificial Neuron 36511.2.4 The Perceptron 36611.2.5 The Multilayer Perceptron 36711.3 A Neural Network Case Study: A Classification Problem 37211.4 Other Neural Network Structures 37411.4.1 Feedforward Networks 37411.4.2 Recurrent Networks 37511.4.3 Cellular Networks 37511.5 Statistical Learning Theory and Kernel Methods 37511.5.1 Structural Risk Minimisation 37511.5.2 Support Vector Machines 37711.5.3 Kernels 38111.6 Case Study II: Support Vector Classification 38211.7 Support Vector Regression 38411.8 Case Study III: Support Vector Regression 38611.9 Feature Selection for Classification Using Genetic Algorithms 38911.9.1 Feature Selection Using Engineering Judgement 39011.9.2 Genetic Feature Selection 39011.9.3 Issues of Network Generalisation 39511.9.4 Discussion and Conclusions 39711.10 Discussion and Conclusions 398References 40012 Data Normalisation 40312.1 Introduction 40312.2 An Example Where Data Normalisation Was Neglected 40512.3 Sources of Environmental and Operational Variability 40612.4 Sensor System Design 40912.5 Modelling Operational and Environmental Variability 41112.6 Look-Up Tables 41412.7 Machine Learning Approaches to Data Normalisation 42112.7.1 Auto-Associative Neural Networks 42212.7.2 Factor Analysis 42312.7.3 Mahalanobis Squared-Distance (MSD) 42412.7.4 Singular Value Decomposition 42412.7.5 Application to the Simulated Building Structure Data 42512.8 Intelligent Feature Selection: A Projection Method 42912.9 Cointegration 43112.9.1 Theory 43212.9.2 Illustration 43312.10 Summary 436References 43613 Fundamental Axioms of Structural Health Monitoring 43913.1 Introduction 43913.2 Axiom I. All Materials Have Inherent Flaws or Defects 44013.3 Axiom II. Damage Assessment Requires a Comparison between Two System States 44113.4 Axiom III. Identifying the Existence and Location of Damage Can Be Done in an Unsupervised Learning Mode, but Identifying the Type of Damage Present and the Damage Severity Can Generally Only Be Done in a Supervised Learning Mode 44413.5 Axiom IVa. Sensors Cannot Measure Damage. Feature Extraction through Signal Processing and Statistical Classification Are Necessary to Convert Sensor Data into Damage Information 44613.6 Axiom IVb. Without Intelligent Feature Extraction, the More Sensitive a Measurement is to Damage, the More Sensitive it is to Changing Operational and Environmental Conditions 44713.7 Axiom V. The Length and Time Scales Associated with Damage Initiation and Evolution Dictate the Required Properties of the SHM Sensing System 44813.8 Axiom VI. There is a Trade-off between the Sensitivity to Damage of an Algorithm and Its Noise Rejection Capability 44913.9 Axiom VII. The Size of Damage that Can Be Detected from Changes in System Dynamics is Inversely Proportional to the Frequency Range of Excitation 45113.10 Axiom VIII. Damage Increases the Complexity of a Structure 45413.11 Summary 458References 45914 Damage Prognosis 46114.1 Introduction 46114.2 Motivation for Damage Prognosis 46214.3 The Current State of Damage Prognosis 46314.4 Defining the Damage Prognosis Problem 46414.5 The Damage Prognosis Process 46514.6 Emerging Technologies Impacting the Damage Prognosis Process 46714.6.1 Damage Sensing Systems 46714.6.2 Prediction Modelling for Future Loading Estimates 46714.6.3 Model Verification and Validation 46714.6.4 Reliability Analysis for Damage Prognosis Decision Making 46714.7 A Prognosis Case Study: Crack Propagation in a Titanium Plate 46814.7.1 The Computational Model 46914.7.2 Monte Carlo Simulation 47114.7.3 Issues 47114.8 Damage Prognosis of UAV Structural Components 47414.9 Concluding Comments on Damage Prognosis 47514.10 Cradle-to-Grave System State Awareness 476References 476Appendix A Signal Processing for SHM 479A.1 Deterministic and Random Signals 479A.1.1 Basic Definitions 479A.1.2 Transducers, Sensors and Calibration 480A.1.3 Classification of Deterministic Signals 481A.1.4 Classification of Random Signals 485A.2 Fourier Analysis and Spectra 489A.2.1 Fourier Series 489A.2.2 The Square Wave Revisited 493A.2.3 A First Look at Spectra 495A.2.4 The Exponential Form of the Fourier Series 496A.3 The Fourier Transform 497A.3.1 Basic Transform Theory 497A.3.2 An Interesting Function that is not a Function 499A.3.3 The Fourier Transform of a Periodic Function 501A.3.4 The Fourier Transform of a Pulse/Impulse 502A.3.5 The Convolution Theorem 504A.3.6 Parseval’s Theorem 506A.3.7 The Effect of a Finite Time Window 506A.3.8 The Effect of Differentiation and Integration 509A.4 Frequency Response Functions and the Impulse Response 510A.4.1 Basic Definitions 510A.4.2 Harmonic Probing 511A.5 The Discrete Fourier Transform 512A.5.1 Basic Definitions 512A.5.2 More About Sampling 516A.5.3 The Fast Fourier Transform 519A.5.4 The DFT of a Sinusoid 524A.6 Practical Matters: Windows and Averaging 525A.6.1 Windows 525A.6.2 The Harris Test 527A.6.3 Averaging and Power Spectral Density 528A.7 Correlations and Spectra 532A.8 FRF Estimation and Coherence 535A.8.1 FRF Estimation I 535A.8.2 The Coherence Function 536A.8.3 FRF Estimators II 538A.9 Wavelets 540A.9.1 Introduction and Continuous Wavelets 540A.9.2 Discrete and Orthogonal Wavelets 549A.10 Filters 564A.10.1 Introduction to Filters 564A.10.2 A Digital Low-Pass Filter 566A.10.3 A High-Pass Filter 569A.10.4 A Simple Classification of Filters 570A.10.5 Filter Design 571A.10.6 The Bilinear Transformation 573A.10.7 An Example of Digital Filter Design 576A.10.8 Combining Filters 578A.10.9 General Butterworth Filters 579A.11 System Identification 583A.11.1 Introduction 583A.11.2 Discrete-Time Models in the Frequency Domain 586A.11.3 Least-Squares Parameter Estimation 587A.11.4 Parameter Uncertainty 589A.11.5 A Case Study 590A.12 Summary 591References 592Appendix B EssentialLinear StructuralDynamics 593B.1 Continuous-Time Systems: The Time Domain 593B.2 Continuous-Time Systems: The Frequency Domain 600B.3 The Impulse Response 603B.4 Discrete-Time Models: Time Domain 605B.5 Multi-Degree-of-Freedom (MDOF) Systems 607B.6 Modal Analysis 613B.6.1 Free, Undamped Motion 613B.6.2 Free, Damped Motion 617B.6.3 Forced, Damped Motion 618References 621Index 623

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