Summary  7

Streszczenie  9

Acknowledgements  11

1. Introduction  12

1.1. SHM and similar research fields  12

1.2. Effects of varying environmental and operational conditions on SHM  13

1.3. Why cointegration has been applied to SHM  16

1.4. A review of cointegration-based approaches for SHM  20

1.5. Motivation and scope of this monograph  24

2. Stationarity and nonstationarity  27

2.1. Definitions and basic concepts  27

2.2. Time series and stationarity  29

2.3. Unit root tests  32

2.4. The Dickey-Fuller (DF) and augmented Dickey-Fuller (ADF) tests  35

3. Cointegration method  39

3.1. Introduction to cointegration  39

3.2. Cointegration and common trends  40

3.3. Testing for cointegration  42

3.4. Johansen’s cointegration procedure  43

3.5. Testing for stationarity  45

3.6. Example using the Weierstrass–Mandelbrot cosine fractal function  46

3.7. Summary and discussion  49

4. Lag length selection in cointegration analysis used for SHM  52

4.1. Background  52

4.2. Conventional selection methods from econometrics  53

4.2.1. Methods based on the information criteria  53

4.2.2. Methods based on the likelihood ratio test  54

4.2.3. Methods based on the sequential modified likelihood ratio test  55

4.2.4. Sample size and lag length selection  56

4.3. Optimal lag length selection based on stationarity analysis used for structural damage detection  57

4.4. Summary and conclusions  59

5. Cointegration-based approach to SHM applications  60

5.1. Damage detection scenarios  60

5.1.1. Using geometrical features of cointegration residuals  61

5.1.2. Using wavelet variance characteristics of cointegration residuals  61

5.1.2.1. Fractal-based signal processing using wavelets  61

5.1.2.2. Wavelet-based fractal analysis of cointegration residuals  63

5.1.3. Using stationary statistical characteristics of cointegration residuals  63

5.2. Case study 1: Structural damage detection in aluminium plates using lamb waves under temperature variations  64

5.2.1. Lamb wave data contaminated by temperature  64

5.2.2. Lag length selection results  66

5.2.3. Damage detection results using cointegration residuals  67

5.2.4. Damage detection results using wavelet variance characteristics of cointegration residuals  70

5.2.5. Damage detection results using stationary statistical characteristics of cointegration residuals  76

5.3. Case study 2: Impact damage detection in composite plates using nonlinear acoustics under load changes  77

5.3.1. Principle of nonlinear vibro-acoustic wave modulation technique  77

5.3.2. Vibro-acoustic data for different frequencies of modal excitations  78

5.3.3. Lag length selection results  80

5.3.4. Damage detection results using stationary statistical characteristics of cointegration residuals  81

5.4. Summary and conclusions  84

6. Cointegration-based approach to condition monitoring of wind turbines  86

6.1. Introduction  86

6.2. Condition monitoring and fault diagnosis of wind turbines using SCADA data  87

6.2.1. Review of previous work  88

6.2.2. Discussion  90

6.3. Cointegration-based approach to condition monitoring of wind turbines  91

6.4. Experimental wind turbine data  93

6.5. Case study 1: Using various process parameters of the wind turbine  99

6.5.1. Optimal cointegrating vectors  99

6.5.2. Condition monitoring and fault detection using cointegration residuals  100

6.5.3. Discussion  104

6.6. Case study 2: Using only the temperature data of gearbox and generator  105

6.7. Summary and conclusions  109

7. Summary and conclusions  110

7.1. Summary  110

7.2. Conclusions  112

References  114