Fuzzy model identification based on mixture distribution analysis for bearings remaining useful life estimation using small training data set

Abstract The research work presented in this paper proposes a data-driven modeling method for bearings remaining useful life estimation based on Takagi-Sugeno (T-S) fuzzy inference system (FIS). This method allows identifying the parameters of a classic T-S FIS, starting with a small quantity of data. In this work, we used the vibration signals data from a small number of bearings over an entire period of run-to-failure. The FIS model inputs are features extracted from the vibration signals data observed periodically on the training bearings. The number of rules and the input parameters of each rule of the FIS model are identified using the subtractive clustering method. Furthermore, we propose to use the maximum likelihood method of mixture distribution analysis to calculate the parameters of clusters on the time axis and the probability corresponding to rules on degradation stages. Based on this result, we identified the output parameters of each rule using a weighted least square estimation. We then benchmarked the proposed method with some existing methods from the literature, through numerical experiments conducted on available datasets to highlight its effectiveness.

[1]  J. Wolfe.  PATTERN CLUSTERING BY MULTIVARIATE MIXTURE ANALYSIS. , 1970, Multivariate behavioral research.

[2]  David,et al.  A comparative experimental study on the use of acoustic emission and vibration analysis for bearing defect identification and estimation of defect size , 2006 .

[3]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[4]  J. Lawless.  Statistical Models and Methods for Lifetime Data , 2002 .

[5]  Stephen L. Chiu,et al.  Fuzzy Model Identification Based on Cluster Estimation , 1994, J. Intell. Fuzzy Syst..

[6]  Joseph Mathew,et al.  USING THE CORRELATION DIMENSION FOR VIBRATION FAULT DIAGNOSIS OF ROLLING ELEMENT BEARINGS—II. SELECTION OF EXPERIMENTAL PARAMETERS , 1996 .

[7]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[8]  Takashi Hiyama,et al.  Predicting remaining useful life of rotating machinery based artificial neural network , 2010, Comput. Math. Appl..

[9]  Hai Qiu,et al.  Wavelet filter-based weak signature detection method and its application on rolling element bearing prognostics , 2006 .

[10]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[11]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  A. Savitzky,et al.  Smoothing and Differentiation of Data by Simplified Least Squares Procedures. , 1964 .

[13]  Joseph Mathew,et al.  USING THE CORRELATION DIMENSION FOR VIBRATION FAULT DIAGNOSIS OF ROLLING ELEMENT BEARINGS—I. BASIC CONCEPTS , 1996 .

[14]  Buyung Kosasih,et al.  An application of nonlinear feature extraction - A case study for low speed slewing bearing condition monitoring and prognosis , 2013, 2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics.

[15]  Robert Babuska,et al.  Constructing fuzzy models by product space clustering , 1997 .

[16]  Jyh-Shing Roger Jang,et al.  ANFIS: adaptive-network-based fuzzy inference system , 1993, IEEE Trans. Syst. Man Cybern..

[17]  Yaguo Lei,et al.  A New Method Based on Stochastic Process Models for Machine Remaining Useful Life Prediction , 2016, IEEE Transactions on Instrumentation and Measurement.

[18]  Y N Pan,et al.  Spectral entropy: A complementary index for rolling element bearing performance degradation assessment , 2009 .

[19]  Wahyu Caesarendra,et al.  A Review of Feature Extraction Methods in Vibration-Based Condition Monitoring and Its Application for Degradation Trend Estimation of Low-Speed Slew Bearing , 2017 .

[20]  Enrico Zio,et al.  Combining Relevance Vector Machines and exponential regression for bearing residual life estimation , 2012 .

[21]  A. P,et al.  Mechanical Vibrations , 1948, Nature.

[22]  Dimiter Driankov,et al.  Fuzzy model identification - selected approaches , 1997 .

[23]  Nikola K. Kasabov,et al.  HyFIS: adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems , 1999, Neural Networks.

[24]  Infineon,et al.  On the Suitability of the Weibull Distribution for the Approximation of Machine Failures , 2003 .

[25]  Daming Lin,et al.  A review on machinery diagnostics and prognostics implementing condition-based maintenance , 2006 .

[26]  H.A. Toliyat,et al.  Condition Monitoring and Fault Diagnosis of Electrical Motors—A Review , 2005, IEEE Transactions on Energy Conversion.

[27]  Buyung Kosasih,et al.  Application of the largest Lyapunov exponent algorithm for feature extraction in low speed slew bearing condition monitoring , 2015 .

[28]  Robert X. Gao,et al.  Mechanical Systems and Signal Processing Approximate Entropy as a Diagnostic Tool for Machine Health Monitoring , 2006 .

[29]  Joseph Mathew,et al.  Rotating machinery prognostics. State of the art, challenges and opportunities , 2009 .

[30]  Brigitte Chebel-Morello,et al.  PRONOSTIA : An experimental platform for bearings accelerated degradation tests. , 2012 .

[31]  Noureddine Zerhouni,et al.  A Data-Driven Failure Prognostics Method Based on Mixture of Gaussians Hidden Markov Models , 2012, IEEE Transactions on Reliability.

[32]  Multiple Model Approaches To Nonlinear Modelling And Control , 2020 .

[33]  See-Kiong Ng,et al.  ARPOP: An Appetitive Reward-Based Pseudo-Outer-Product Neural Fuzzy Inference System Inspired From the Operant Conditioning of Feeding Behavior in Aplysia , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[34]  Michio Sugeno,et al.  An introductory survey of fuzzy control , 1985, Inf. Sci..