Written by global leaders and pioneers in the field, this book is a must-have read for researchers, practicing engineers and university faculty working in SHM. Structural Health Monitoring: A Machine Learning Perspective is the first comprehensive book on the general problem of structural health monitoring. The authors, renowned experts in the field, consider structural health monitoring in a new manner by casting the problem in the context of a machine learning/statistical pattern recognition paradigm, first explaining the paradigm in general terms then explaining the process in detail with further insight provided via numerical and experimental studies of laboratory test specimens and in-situ structures. This paradigm provides a comprehensive framework for developing SHM solutions. Structural Health Monitoring: A Machine Learning Perspective makes extensive use of the authors' detailed surveys of the technical literature, the experience they have gained from teaching numerous courses on this subject, and the results of performing numerous analytical and experimental structural health monitoring studies. Considers structural health monitoring in a new manner by casting the problem in the context of a machine learning/statistical pattern recognition paradigm Emphasises an integrated approach to the development of structural health monitoring solutions by coupling the measurement hardware portion of the problem directly with the data interrogation algorithms Benefits from extensive use of the authors' detailed surveys of 800 papers in the technical literature and the experience they have gained from teaching numerous short courses on this subject.

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. Support Vector Machines

11.5.3. Kernels

11.6. Case Study II: Support Vector Clasification

11.7. Support Vector Regression

11.8. Case Study III: Support Vector Regression

11.9. Feature Selection for Classification using Genetic Algorithms

11.9.1. Feature Selection using Engineering udgement

11.9.2. Genetic Feature Selection

11.9.3. Issues of Network Generalisation

11.9.4. Discussion and Conclusions

11.10. Discussion and Conclusions

12. DATA NORMALISATION 1

12.1. Introduction 1

12.2. An Example Where Data Normalisation was Neglected 3

12.3. Sources of Environmental and Operational Variability 4

12.4. Sensor System Design 8

12.5. Modelling Operational and Environmental Variability 10

12.6. Look-up Tables 14

12.7. Machine Learning Approaches to Data Normalisation 22

12.7.1. Auto-associative Neural Networks 23

12.7.2. Factor Analysis 23

12.7.3. Mahalanobis Squared Distance 24

12.7.4. Singular Value Decomposition 25

12.7.5. Application to the 4-Storey Structure Data 26

12.8. Intelligent Feature Selection 30

12.9. Cointegration 33

12.10. Summary 33

12.11. References

13. Fundamental Axioms of Structural Health Monitoring

13.1 Introduction 1

13.2 Axiom I: All Materials Have Inherent Flaws or Defects 3

13.3 Axiom II: Damage Assessment Requires a Comparison Between Two System States. 4

13.4 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. 8

13.5 AXIOM IVa: Sensors cannot measure damage. Feature extraction and statistical classification are necessary to convert sensor data into damage information. 10

13.6 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. 11

13.7 AXIOM V: The length and time scales associated with damage initiation and evolution dictate the required properties of the SHM sensing system.

13.8 AXIOM VI: There is a trade-off between the sensitivity to damage of an algorithm and its noise rejection capability. 14

13.9 AXIOM VII: The size of damage that can be detected from changes in system dynamics is inversely proportional to the frequency range of excitation. 16

13.10 Axiom VIII: Damage increases the complexity of a structure 20

13.11 Summary 25

13.12 Bibliography 25

DAMAGE PROGNOSIS 1

14.1 Introduction 1

14.2 Motivation for Damage Prognosis 2

14.3 The Current State of Damage Prognosis 3

14.4 Defining the Damage Prognosis Problem 4

14.5 The Damage Prognosis Process 6

14.6 Emerging Technologies Impacting the Damage Prognosis Process. 8

14.7 A Prognosis Case Study: Crack Propagation in a Titanium Plate 9

14.7.1 The Computational Model 10

14.7.2 Monte Carlo Simulation 13

14.7.3 Issues 16

14.8 Damage Prognosis of UAV Structural Components 17

14.9 Concluding Comments on Damage Prognosis 18

14.10 Cradle-to-Grave System State Awareness 19

14.11 References 20

Appendix A. SIGNAL PROCESSING FOR SHM

A.1. Deterministic and Random Signals

A.1.1. Basic Definitions

A.1.2. Transducers, Sensors and Calibration

A.1.3. Classification of Deterministic Signals

A.1.4. Classification of Random Signals

A.2. Fourier Analysis and Spectra

A.2.1. Fourier Series

A.2.2. The Square Wave Revisited

A.2.3. A First Look at Spectra

A.2.4. The Exponential Form of the Fourier Series

A.3. The Fourier Transform

A.3.1. Basic Transform Theory

A.3.2. An Interesting Function that isn’t a Function

A.3.3. The Fourier Transform of a Periodic Function

A.3.4. The Fourier Transform of a Pulse/Impulse

A.3.5. The Convolution Theorem

A.3.6. Parseval’s Theorem

A.3.7. The Effect of a Finite Time Window

A.3.8. The Effect of Differentiation and Integration

A.4. Frequency Response Functions and the Impulse Response

A.4.1. Basic Definitions

A.4.2. Harmonic Probing

A.5. The Discrete Fourier Transform

A.5.1. Basic Definitions

A.5.2. More About Sampling

A.5.3. The Fast Fourier Transform

A.5.4. The DFT of a Sinusoid

A.6. Practical Matters: Windows and Averaging

A.6.1. Windows

A.6.2. The Harris Test

A.6.3. Averaging and Power Spectral Density

A.7. Correlations and Spectra

A.8. FRF Estimation and Coherence

A.8.1. FRF Estimation I

A.8.2. The Coherence Function

A.8.3. FRF Estimators II

A.9. Wavelets

A.9.1. Introduction and Continuous Wavelets

A.9.2. Discrete and Orthogonal Wavelets

A.10. Filters

A.10.1. Introduction to Filters

A.10.2. A Digital Low-Pass Filter

A.10.3. A High-Pass Filter

A.10.4. A Simple Classification of Filters

A.10.5. Filter Design

A.10.6. The Bilinear Transformation

A.10.7. An Example of Digital Filter Design

A.10.8. Combining Filters

A.10.9. General Butterworth Filters

A.11. System Identification

A.11.1. Introduction

A.11.2. Discrete-Time Models in the Frequency Domain

A.11.3. Least-Squares Parameter Estimation

A.11.4. Parameter Uncertainty

A.11.5. A Case Study

Appendix B. ESSENTIAL LINEAR STRUCTURAL DYNAMICS

B.1. Continuous-Time Systems: The Time Domain

B.2. Continuous-Time Systems: The Frequency Domain

B.3. The Impulse Response

B.4. Discrete-Time Systems: Time-Domain

B.5. Multi Degree-of-Freedom (MDOF) Systems

B.6. Modal Analysis

B.6.1. Free, Undamped Motion

B.6.2. Free, Damped Motion

B.6.3. Forced, Damped Motion