VIBRATION ANALYSIS for OCEAN TURBINE RELIABILITY MODELS by Randall David Wald
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VIBRATION ANALYSIS FOR OCEAN TURBINE RELIABILITY MODELS by Randall David Wald A Dissertation Submitted to the Faculty of The College of Engineering and Computer Science in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Florida Atlantic University Boca Raton, FL December 2012 Copyright by Randall David Wald 2012 ii ACKNOWLEDGEMENTS I would like to recognize the assistance and guidance provided by my advi- sor, Dr. Taghi M. Khoshgoftaar, towards the completion of my doctoral studies at Florida Atlantic University. His years of research experience and invaluable advice and support were an essential part of my studies. I would also like to thank Dr. Howard Hanson, Dr. Martin K. Solomon, and Dr. Bassem Alhalabi for serving on my dissertation committee. I am also grateful to the Southeast National Marine Renewable Energy Center (SNMREC) for supporting and funding this research. In addition, I would like to acknowledge my colleagues in the Data Mining and Machine Learning Laboratory, Janell Duhaney, Dr. John C. Sloan, and Dr. Amri Napolitano, who I have been fortunate enough to collaborate with on this research. Finally, I wish to thank the researchers and staff in the Department of Ocean and Mechanical Energy at the Dania Beach campus for their collaboration and assistance with the SNMREC ocean turbine project. iv ABSTRACT Author: Randall David Wald Title: Vibration Analysis for Ocean Turbine Reliability Models Institution: Florida Atlantic University Dissertation Advisor: Dr. Taghi M. Khoshgoftaar Degree: Doctor of Philosophy Year: 2012 Submerged turbines which harvest energy from ocean currents are an impor- tant potential energy resource, but their harsh and remote environment demands an automated system for machine condition monitoring and prognostic health monitor- ing (MCM/PHM). For building MCM/PHM models, vibration sensor data is among both the most useful (because it can show abnormal behavior which has yet to cause damage) and the most challenging (because due to its waveform nature, frequency bands must be extracted from the signal). To perform the necessary analysis of the vibration signals, which may arrive rapidly in the form of data streams, we develop three new wavelet-based transforms (the Streaming Wavelet Transform, Short-Time Wavelet Packet Decomposition, and Streaming Wavelet Packet Decomposition) and propose modifications to the existing Short-Time Wavelet Transform. We also prepare post-processing techniques to resolve additional problems such as interpreting wavelet data in a fully-streaming format, au- tomatically choosing the appropriate transformation depth without performing classi- fication, and building models which can perform state identification correctly even as v the turbine’s environment changes. Collectively, these new approaches solve problems not currently dealt with by existing algorithms and offer important improvements. The proposed algorithms allow for data to be processed in a fully-streaming manner. These algorithms also create and select frequency-band features which focus on the areas of the signal most important to MCM/PHM, producing only the information necessary for building models (or removing all unnecessary information) so models can run on less powerful hardware. Finally, we demonstrate models which can work in multiple environmental conditions. To evaluate these algorithms, along with the Short-Time Fourier Transform which is often neglected in the context of MCM/PHM, we perform six case studies on data from two different physical machines, a fan and a dynamometer model of the ocean turbine. Our results show that many of the transforms give similar results in terms of performance, but their different properties as to time complexity, ability to operate in a fully streaming fashion, and number of generated features may make some more appropriate than others in particular applications, such as when streaming data or hardware limitations are extremely important (e.g., ocean turbine MCM/PHM). vi DEDICATION To my parents, Harlan and Karen Wald, for always supporting me and pushing me to achieve my goals. VIBRATION ANALYSIS FOR OCEAN TURBINE RELIABILITY MODELS List of Tables .............................. xi List of Figures . xiii 1 Introduction .............................. 1 1.1 Motivation.................................3 1.2 Contributions...............................8 1.3 Organization...............................9 2 Background ............................... 12 2.1 Prognostic Health Monitoring...................... 12 2.1.1 Designing an MCM/PHM system................ 13 2.1.2 Combining MCM/PHM algorithms............... 14 2.1.3 Applying MCM/PHM to machine maintenance........ 17 2.2 Vibration Analysis............................ 19 2.2.1 Fourier Transforms........................ 20 2.2.2 Wavelet Transforms........................ 21 2.2.3 Comparing Fourier and Wavelet Approaches.......... 23 2.2.4 Streaming Data.......................... 25 3 Methodology .............................. 27 3.1 Classification............................... 27 vii 3.1.1 C4.5................................ 28 3.1.2 Random Forest.......................... 30 3.1.3 Naïve Bayes............................ 31 3.1.4 k-Nearest Neighbor........................ 32 3.1.5 Logistic Regression........................ 32 3.1.6 Support Vector Machines..................... 32 3.1.7 Multi-Layer Perception...................... 33 3.1.8 RIPPER.............................. 34 3.1.9 Radial Basis Function Neural Networks............. 34 3.2 Feature Selection............................. 35 3.2.1 Chi Squared............................ 35 3.2.2 Information Gain......................... 36 3.2.3 Signal to Noise.......................... 37 3.3 Performance Evaluation......................... 38 3.3.1 Performance Metrics....................... 38 3.3.2 Training and Test Datasets................... 39 3.4 Fourier Transforms............................ 40 3.4.1 Short Time Fourier Transforms................. 41 4 Wavelet Transforms .......................... 45 4.1 Continuous Wavelet Transforms..................... 46 4.2 Discrete Wavelet Transforms....................... 48 4.2.1 Short-Time Wavelet Transform................. 51 4.2.2 Streaming Wavelet Transform.................. 54 4.3 Wavelet Packet Decomposition...................... 57 4.3.1 Short-Time Wavelet Packet Decomposition........... 59 4.3.2 Streaming Wavelet Packet Decomposition........... 62 viii 5 Post-Processing ............................. 69 5.1 Scale Detection.............................. 69 5.2 Data windowing.............................. 73 5.3 Automatic Depth Selection........................ 75 5.4 Baseline-Differencing........................... 77 6 Datasets ................................. 80 6.1 Fan Experiments............................. 80 6.2 Fan Transformation Parameters..................... 81 6.2.1 Short-Time Fourier Transform.................. 82 6.2.2 Streaming Wavelet Transform.................. 82 6.2.3 Short-Time Wavelet Packet Decomposition........... 84 6.2.4 Streaming Wavelet Packet Decomposition........... 85 6.3 Dynamometer Data............................ 86 6.4 Dynamometer Transformation Parameters............... 88 7 Case Studies .............................. 89 7.1 Case Study One.............................. 90 7.1.1 Parameter optimization..................... 90 7.1.2 Classification........................... 91 7.1.3 Experimental procedure..................... 91 7.1.4 Results............................... 92 7.2 Case Study Two.............................. 95 7.2.1 Classification........................... 95 7.2.2 Results............................... 96 7.3 Case Study Three............................. 98 7.3.1 Classification........................... 99 ix 7.3.2 Results............................... 99 7.4 Case Study Four............................. 104 7.4.1 Classifiers and Feature Selection................. 104 7.4.2 Results............................... 106 7.5 Case Study Five.............................. 107 7.5.1 Feature Ranking for Depth Selection.............. 108 7.5.2 Classification........................... 110 7.5.3 Results............................... 110 7.6 Case Study Six.............................. 112 7.6.1 Classification........................... 112 7.6.2 Results............................... 113 8 Conclusions and Future Work . 125 8.1 Conclusions................................ 126 8.2 Future Work................................ 130 Bibliography .............................. 132 x LIST OF TABLES 7.1 CS1: Fan Experiment One........................ 92 7.2 CS2: Fan Experiment Two........................ 93 7.3 CS2.................................... 97 7.4 CS3: STFT with NB........................... 99 7.5 CS3: STFT with 5NN.......................... 100 7.6 CS3: STFT with C4.5.......................... 100 7.7 CS3: STWPD with NB.......................... 101 7.8 CS3: STWPD with 5NN......................... 102 7.9 CS3: STWPD with C4.5......................... 102 7.10 CS4: STWPD............................... 105 7.11 CS4: SWPD................................ 105 7.12 CS5: Largest Selected Features..................... 108 7.13 CS5: Fan Experiment One, Distribution of Features.......... 109 7.14 CS5: Fan Experiment Two, Distribution of Features.......... 110 7.15 CS5: Classification Performance..................... 111 7.16 CS6: Dyn Experiment One, Test on 656, No Baselining........ 115 7.17 CS6: Dyn Experiment One, Test on 656, Baseline-Differencing.... 116