Structural Health Monitoring: A Machine Learning Perspective

1 INTRODUCTION 1.1 How Engineers and Scientist Study Damage 1.2 Motivation for Developing SHM Technology 4 1.3 Definition of Damage 6 1.4 A Statistical Pattern Recognition Paradigm for SHM 9 1.4.1 Operational Evaluation 12 1.4.2 Data Acquisition 13 1.4.3 Data Normalisation 13 1.4.4 Data Cleansing 14 1.4.5 Data Compression 14 1.4.6 Data Fusion 14 1.4.7 Feature Extraction 14 1.4.8 Statistical Modelling for Feature Discrimination 15 1.5 Local versus global damage detection 16 1.6 Fundamental axioms of structural health monitoring 17 1.7 The approach taken in this book 18 1.8 References 19 2 HISTORICAL Overview1 2.1 Rotating Machinery Applications 2.1.1 Operational Evaluation for Rotating Machinery 2.1.2 Data Acquisition for Rotating Machinery 2.1.3 Feature Extraction for Rotating Machinery 2.1.4 Statistical modeling for damage detection in rotating machinery 2.1.5 Concluding comments about condition monitoring of rotating machinery 2.2 Offshore Oil Platforms 2.2.1 Operational Evaluation for Offshore Platforms 2.2.2 Data Acquisition for Offshore Platforms 2.2.3 Feature Extraction for Offshore Platforms 2.2.4 Statistical Modeling for Offshore Platforms 2.2.5 Lessons Learned from Offshore Oil Platform Structural Health Monitoring Studies 2.3 Aerospace Structures 2.3.1 Operational Evaluation for Aerospace Structures 2.3.2 Data Acquisition for Aerospace Structures 2.3.3 Feature Extraction and Statistical Modeling for Aerospace Structures 2.3.4 Statistical Model used for Aerospace SHM Applications 2.3.5 Concluding Comments about Aerospace SHM Applications 2.4 Civil Engineering Infrastructure 2.4.1 Operational Evaluation for Bridge Structures 2.4.2 Data Acquisition for Bridge Studies 2.4.3 Features Based on Modal Properties 2.4.4 Statistical Classification of Features for Civil Engineering Infrastructure 2.4.5 Applications to Bridge Structures 2.5 Summary 2.6 References 3 Operational Evaluation 2 3.1 Economic and Life Safety Justifications for Structural Health Monitoring 2 3.2 Defining the Damage to be Detected 3 3.3 The Operational and Environmental Conditions 4 3.4 Data Acquisition Limitations 5 3.5 Operational Evaluation Example: Bridge Monitoring 6 3.6 Operational Evaluation Example: Wind Turbines 7 3.7 Concluding Comment on Operational Evaluation 9 3.8 References 9 4. SENSING AND DATA ACQUISITION ISSUES 1 4.1 Introduction 1 4.2 Sensing and Data Acquisition Strategies for SHM 2 4.2.1 Strategy I 2 4.2.2 Strategy II 3 4.3 Conceptual Challenges for Sensing and Data Acquisition Systems 4 4.4 What Types of Data Should be Acquired? 5 4.4.1 Dynamic Input and Response Quantities 5 4.4.2 Other Damage-Sensitive Physical Quantities 8 4.4.3 Environmental Quantities 8 4.4.4 Operational Quantities 8 4.5 Current SHM Sensing Systems 9 4.5.1 Wired Systems 9 4.5.2 Wireless Systems 11 4.6 Sensor Network Paradigms 14 4.6.1 Sensor Arrays directly Connected to Central Processing Hardware 14 4.6.2 Decentralised Processing with Hopping Connection 15 4.6.3 Decentralised Processing with Hybrid Connection 15 4.7 Future Sensing Network Paradigms 17 4.8 Defining the Sensor System Properties 21 4.8.1 Required Sensitivity and Range 21 4.8.2 Required Bandwidth and Frequency Resolution 21 4.8.3 Sensor Number and Locations 22 4.8.4 Sensor Calibration, Stability and Reliability 22 4.9 Define the Data Sampling Parameters 25 4.10 Define the Data Acquisition System 25 4.11 Active versus Passive Sensing 26 4.12 Multi-Scale Sensing 28 4.13 Powering the Sensing System 28 4.14 Signal Conditioning 29 4.15 Sensor and Actuator Optimisation 30 4.16 Sensor Fusion 31 4.17 Summary of Sensing and Data Acquisition Issues for Structural Health Monitoring 34 4.18 References 35 5. case studies 1 5.1 The I-40 Bridge. 1 5.1.1 Preliminary Testing and Data Acquisition 4 5.1.2. Undamaged Ambient Vibration Tests 5 5.1.3. Forced Vibration Tests 7 5.2 The Concrete Column 8 5.2.1 Quasi-Static Loading 10 5.2.2 Dynamic Excitation 11 5.2.3 Data Acquisition 11 5.3 The 8 DOF System 14 5.3.1 Physical Parameters 17 5.3.2 Data Acquisition 18 5.4 Simulated Building Structure 18 5.4.1 Experimental Procedure and Data Acquisition 20 5.4.2 Measured Data 21 5.5 The Alamosa Canyon Bridge 22 5.5.1 Experimental Procedures and Data Acquisition 25 5.5.2 Environmental Measurements 26 5.5.3 Vibration Tests Performed to Study Variability of Modal Properties 27 5.6. The Gnat Aircraft 28 5.5.2 Simulating Damage with a Modified Inspection Panel 29 5.6.2 Simulating Damage by Panel Removal 35 5.7 References 39 6. INTRODUCTION TO PROBABILITY AND STATISTICS 6.1. Introduction 6.2. Probability: Basic Definitions 6.3. Random Variables and Distributions 6.4. Expected Values 6.5. The Gaussian Distribution (and Others) 6.6. Multivariate Statistics 6.7. The Multivariate Gaussian Distribution 6.8. Conditional Probability and Bayes Theorem 6.9. Confidence Limits and Cumulative Distribution Functions 6.10. Outlier Analysis 6.11. Density Estimation 6.12. Extreme Value Statistics 6.12.1. Introduction 6.12.2. Basic Theory 6.12.3. Determination of Limit Distributions 6.13. Dimension Reduction -- Principal Component Analysis 6.13.1. Simple Projection 6.13.2. Principal Component Analysis (PCA) 7 Damage-Sensitive FEATUREs 2 7.1 Common Waveforms and Spectral Functions used in the Feature Extraction Process 5 7.1.1 Waveform Comparisons 5 7.1.2 Autocorrelation and Cross-correlation Functions 6 7.1.3 The Power-spectral and Cross-spectral Density functions 8 7.1.4 The Impulse Response Function and the Frequency Response Function 11 7.1.5 The Coherence Function 13 7.1.6 Some Remarks Regarding Waveforms and Spectra 14 7.2 Basic Signal Statistics 15 7.3 Transient Signals: Temporal Moments 23 7.4 Transient Signals: Decay Measures 27 7.5 Acoustic Emission Features 30 7.6 Features used with Guided-Wave Approaches to SHM 31 7.6.1 Preprocessing 32 7.6.2 Baseline Comparisons 33 7.6.3 Damage Localisation 35 7.7 Features used with Impedance Measurements 36 7.8 Basic Modal Properties 39 7.8.1 Resonance Frequencies 40 7.8.2 Inverse versus Forward Modelling Approaches to Feature Extraction 42 7.8.3 Resonance Frequencies: The Forward Approach 43 7.8.4 Resonance Frequencies: Sensitivity Issues 43 7.8.5 Mode Shapes 45 7.8.6 Load-Dependent Ritz Vectors 56 7.9 Features Derived from Basic Modal Properties 59 7.9.1 Mode Shape Curvature 59 7.9.2 Modal Strain Energy 63 7.9.3 Modal Flexibility 69 7.10 Model Updating Approaches 73 7.10.1 Objective Functions and Constraints 74 7.10.2 Direct Solution for the Modal Force Error 76 7.10.3 Optimal Matrix Update Methods 80 7.10.4 Sensitivity-Based Update Methods 83 7.10.5 Eigenstructure Assignment Method 87 7.10.6 Hybrid Matrix Update Methods 88 7.10.7 Concluding Comment on Model Updating Approaches 88 7.11 Time Series Models 90 7.12 Feature Selection 92 7.12.1 Sensitivity Analysis 93 7.12.2 Information Content 98 7.12.3 Assessment of Robustness 99 7.12.4 Optimisation Procedures 99 7.13 Metrics 100 7.14 Concluding Comments 100 7.15 References 101 8 FEATURES BASED ON DEVIATION FROM LINEAR RESPONSE 1 8.1 Types of Damage that can Produce Nonlinear System Response 2 8.2 Motivation for Exploring Nonlinear System Identification Methods for SHM 8.2.1 Coherence Function 7 8.2.2 Linearity and Reciprocity Checks 11 8.2.3 Harmonic Distortion 18 8.2.4 Frequency Response Function Distortions 22 8.2.5 Probability Density Function 26 8.2.6 Correlation Tests 27 8.2.7 The Holder Exponent 29 8.2.8 Linear Time Series Prediction Errors 34 8.2.9 Nonlinear Time Series Models 36 8.2.10 Hilbert Transform 40 8.2.11 Nonlinear Acoustics Methods 43 8.3 Applications of Nonlinear Dynamical Systems Theory 44 8.3.1 Modelling a Cracked Beam as a Bilinear System 46 8.3.2 Chaotic Interrogation of a Damaged Beam. 50 8.3.3 Local Attractor Variance 51 8.3.4 Detection of Damage Using the Local Attractor Variance 52 8.4 Nonlinear System Identification Approaches 55 8.4.1 Restoring Force Surface Model 55 8.5 Concluding Comments Regarding Feature Extraction Based on Nonlinear System Response 59 8.6 REFERENCES 60 9. MACHINE LEARNING AND STATISTICAL PATTERN RECOGNITION 9.1.Introduction 9.2.Intelligent Damage Detection 9.3.Data Processing and Fusion for Damage Identification 9.4. Statistical Pattern Recognition: Hypothesis Testing 9.5. Statistical Pattern Recognition: General Frameworks 9.6. Discriminant Functions and Decision Boundaries 9.7. Decision Trees 9.8. Training -- Maximum Likelihood 9.9. Nearest Neighbour Classification 9.10. Case Study: An Acoustic Emission Experiment 9.10.1. Analysis and Classification of the AE Data 9.11. Summary 10. UNSUPERVISED LEARNING -- NOVELTY DETECTION 10.1. Introduction 10.2. A Gaussian Distributed Normal Condition -- Outlier Analysis 10.3. A Non-Gaussian Normal Condition -- A Neural Network Approach 10.4. Nonparametric Density Estimation -- A Case Study 10.4.1. The Experimental Structure and Data Capture 10.4.2. Pre-Processing of Data and Features 10.4.3. Novelty Detection 10.5. Statistical Process Control 10.5.1. Feature Extraction Based on Auto-Regressive Modelling 10.5.2. The X-bar Control Chart: An Experimental Case Study 10.6. Other Control Charts and Multivariate SPC 10.6.1. The S Control Chart 10.6.2. The CUSUM Chart 10.6.3. The EWMA Chart 10.6.4. The Hotelling or Shewhart T^2 Chart 10.6.5. The Multivariate CUSUM Chart 10.7. Thresholds for Novelty Detection 10.7.1. Extreme Value Statistics 10.7.2. Type I and Type II Errors: The ROC Curve 10.8. Summary 11. SUPERVISED LEARNING -- CLASSIFICATION AND EGRESSION 11.1. Introduction 11.2. Artificial Neural Networks 11.2.1. Biological Motivation 11.2.2. The Parallel Processing Paradigm 11.2.3. The Artificial Neuron 11.2.4. The Perceptron 11.2.5. The Multi-Layer Perceptron 11.3. A Neural Network Case Study: A Classification Problem 11.4. Other Neural Network Structures 11.4.1. Feedforward Networks 11.4.2. Recurrent Networks 11.4.3. Cellular Networks 11.5. Statistical Learning Theory and Kernel Methods 11.5.1. Structural Risk Minimisation 11.5.2. 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