Machine fault diagnois and condition prognois using adaptive neuro fuzzy inference system and classification and regression trees

Thesis for the Degree of Doctor of Philosophy Machine Fault Diagnosis and Condition Prognosis using Adaptive Neuro-Fuzzy Inference System and Classification and Regression Trees by Van

Thesis for the Degree of Doctor of Philosophy

Machine Fault Diagnosis and Condition

Prognosis using Adaptive Neuro-Fuzzy Inference System and Classification and Regression Trees

by Van Tung Tran Department of Mechanical Engineering

The Graduate School Pukyong National University

February 2009

Machine Fault Diagnosis and Condition

Prognosis using Adaptive Neuro-Fuzzy Inference System and Classification and Regression Trees

기계 결함진단 및 예지를 위한 ANFIS 와 CART

Advisor: Prof Bo-Suk Yang

by Van Tung Tran

A thesis submitted in partial fulfillment of the requirements

for the degree of

Doctor of Philosophy

in the Department of Mechanical Engineering, The Graduate School,

Pukyong National University

February 2009

Contents

List of Figures v

List of Tables viii

List of Symbols ix

Abstract

I Introduction 1

1 Background 1

2 Motivation of This Research 6

3 Research Objectives 6

4 Tools and Approaches 7

5 Scientific Contribution of This Research 7

6 Organization of Thesis 8

References 9

II The State-of-The-Art of Machine Fault Diagnosis and Prognosis 11

1.Machine Fault Diagnosis 11

1.1 Model-based approaches 11

1.2 Knowledge-based approaches 13

1.3 Pattern recognition-based approaches 15

2 Machine Fault Prognosis 19

2.1 Statistical approaches 20

2.2 Model-based approaches 21

2.3 Data-driven based approaches 22

References 22

III Background Knowledge 36

1 Feature-Based Diagnosis and Prognosis: a Review 36

1.1 Feature extraction techniques 37

1.2 Feature selection techniques 39

2 Feature Representation 40

2.1 Features in time domain 40

2.1.1 Cumulants 40

2.1.2 Upper and lower bound histogram 44

2.1.3 Entropy estimation and error 45

2.1.4 Auto-regression coefficients 45

2.2 Feature in frequency domain 46

2.2.1 Fourier transform 46

2.2.2 Spectral analysis 47

2.2.3 Frequency parameter indices 48

3 Classification and Regression Trees (CART) 49

3.1 Introduction 49

3.2 Tree growing 50

3.2.1 Classification tree 50

3.2.2 Regression tree 52

3.3 Tree pruning 54

3.3.1 Classification tree 54

3.3.2 Regression tree 55

3.4 Cross-validation for selecting the best tree 56

4 Adaptive Neuro-Fuzzy Inference System (ANFIS) 57

4.1 Architecture of ANFIS 57

4.2 Learning algorithm of ANFIS 60

5 Conclusions 61

References 61

IV CART and ANFIS Based Fault Diagnosis for Induction Motors 67

1 Introduction 67

2 Induction Motor Faults 67

2.1 Bearing faults 70

2.2 Stator or armature faults 72

2.3 Broken rotor bar and end ring faults 74

2.4 Eccentricity related faults 75

3 The Proposed Fault Diagnosis System for Induction Motors 77

3.1 Experiment and data acquisition 79

3.2 Feature calculation 81

3.3 Feature selection and classification 83

4 Conclusion 90

References 91

V Machine Condition Prognosis 94

1 Introduction 94

2 Prediction Strategies 97

2.1 Recursive prediction strategy 97

2.2 DirRec prediction strategy 98

2.3 Direct prediction strategy 98

3 Time Delay Estimation 99

4 Determining Embedding Dimension 100

4.1 Cao’s method 100

4.2 False nearest neighbor method (FNN) 101

5 Proposed System for Machine Condition Prognosis 103

6 Experiment 105

7 Case Studies of Machine Condition Prognosis 108

7.1 Case study 1: CART and OS prediction 108

7.2 Case study 2: parallel CART and MS direct prediction 115

7.2.1 Parallel structure of CART 115

7.2.2 Results and discussions 116

7.3 Case study 3: ANFIS and MS direct prediction 124

8 Conclusions 130

References 132

VI Conclusions and Future Works 134

1 Conclusions 134

2 Future Works 135

Acknowledgements

List of Figures

Fig 1.1 System costs depending on type of maintenance strategy 3

Fig 1.2 Architecture of a CBM system 4

Fig 3.1 Histogram for bearing signal with different condition 44

Fig 3.2 Classification tree 51

Fig 3.3 Regression tree 53

Fig 3.4 Schematic of ANFIS architecture 58

Fig 4.1 View of a squirrel cage induction motor 68

Fig 4.2 Four types of rolling-element bearing misalignment 70

Fig 4.3 Bearing sizes marked 71

Fig 4.4 Proposed system for fault diagnosis 78

Fig 4.5 Test rig for experiment 79

Fig 4.6 Faults on the induction motors 80

Fig 4.7 Vibration and current signals of each fault condition 81

Fig 4.8 Decision tree of features obtained from vibration signal 84

Fig 4.9 Decision tree of features obtained from current signal 84

Fig 4.10 Topology of ANFIS architecture for vibration signals 85

Fig 4.11 The network RMS error convergence curve 86

Fig 4.12 Bell shaped membership functions for vibration signals 87

Fig 5.1 Hierarchy of prognostic approaches 96

Fig 5.2 Proposed system for machine fault prognosis 104

Fig 5.3 Low methane compressor: wet screw type 105

Fig 5.4 The entire of peak acceleration data of low methane compressor

106

Fig 5.5 The entire of envelope acceleration data of low methane compressor

107

Fig 5.6 The faults of main bearings of compressor 108

Fig 5.7 Training and validating results of peak acceleration data (the first 300 points) 109

Fig 5.8 Predicted results of peak acceleration data 110

Fig 5.9 Peak acceleration of low methane compressor 110

Fig 5.10 The values of E1 and E2 of peak acceleration data of low methane compressor 111

Fig 5.11 Training and validating results of peak acceleration data 112

Fig 5.12 Predicted results of peak acceleration data 112

Fig 5.13 Data trending of envelope acceleration of low methane compressor 113

Fig 5.14 The values of E1 and E2 of envelope acceleration data 114

Fig 5.15 Training and validating results of envelope acceleration data

114

Fig 5.16 Predicted results of envelope acceleration data 115

Fig 5.17 Architecture and input values for sub-model of parallel-structure of CART 116

Fig 5.18 Time delay estimation 117

Fig.5.19 The relationship between FNN percentage and embedding

dimension 118

Fig 5.20 Training and validating results of peak acceleration data 120

Fig 5.21 Training and validating results of envelop acceleration data 121

Fig 5.22 Predicted results of peak acceleration data 123

Fig 5.23 Predicted results of envelop acceleration data 124

Fig 5.24 Training and validating results of the ANFIS model for peak acceleration data 126

Fig 5.25 Training and validating results of the ANFIS model for envelope

acceleration data 126

Fig 5.26 RMSE convergent curve 127

Fig 5.27 The changes of MFs after learning 128

Fig 5.28 Predicted results of ANFIS model for peak acceleration data

129

Fig 5.29 Predicted results of the ANFIS model for envelope acceleration data 130

Fig 6.1 The general hybrid system 136