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 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 Background Motivation of This Research Research Objectives Tools and Approaches Scientific Contribution of This Research Organization of Thesis References II The State-of-The-Art of Machine Fault Diagnosis and Prognosis 11 Machine Fault Diagnosis 11 1.1 Model-based approaches 11 1.2 Knowledge-based approaches 13 1.3 Pattern recognition-based approaches 15 Machine Fault Prognosis 19 2.1 Statistical approaches .20 2.2 Model-based approaches 21 2.3 Data-driven based approaches .22 References 22 i III Background Knowledge 36 Feature-Based Diagnosis and Prognosis: a Review 36 1.1 Feature extraction techniques 37 1.2 Feature selection techniques 39 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 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 Adaptive Neuro-Fuzzy Inference System (ANFIS) 57 4.1 Architecture of ANFIS 57 4.2 Learning algorithm of ANFIS 60 Conclusions 61 ii References 61 IV CART and ANFIS Based Fault Diagnosis for Induction Motors 67 Introduction 67 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 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 Conclusion 90 References 91 V Machine Condition Prognosis 94 Introduction 94 Prediction Strategies 97 2.1 Recursive prediction strategy .97 2.2 DirRec prediction strategy .98 2.3 Direct prediction strategy .98 Time Delay Estimation 99 Determining Embedding Dimension 100 4.1 Cao’s method .100 4.2 False nearest neighbor method (FNN) 101 Proposed System for Machine Condition Prognosis 103 Experiment 105 iii 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 Conclusions 130 References 132 VI Conclusions and Future Works 134 Conclusions 134 Future Works 135 Acknowledgements iv List of Figures Fig 1.1 System costs depending on type of maintenance strategy 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 v 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 vi 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 vii