Bearing fault prognostics using Rényi entropy based features and Gaussian process models

Abstract Bearings are considered to be the most frequent cause for failures in rotational machinery. Hence efficient means to anticipate the remaining useful life (RUL) on-line, by processing the available sensory records, is of substantial practical relevance. Many of the data-driven approaches rely on conjecture that evolution of condition monitoring (CM) indices is related with the aggravation of the condition and, indirectly, with the remaining useful life of a bearing. Problems with trending may be threefold: (i) most of the operational life show no significant trend until the time very close to failure; this is usually accompanied by rapidly growing values of CM indices which is not easy to forecast, (ii) the evolution of CM indices is not necessarily monotonous, (iii) variable and immeasurable fluctuations in operating may fool the trend. Motivated by these issues we propose an approach for bearing fault prognostics that employs Renyi entropy based features. It exploits the idea that progressing fault implicates raising dissimilarity in the distribution of energies across the vibrational spectral band sensitive to the bearing faults. The innovative way of predicting RUL relies on a posterior distribution following Bayes׳ rule using Gaussian process (GP) models׳ output as a likelihood distribution. The proposed approach was evaluated on the dataset provided for the IEEE PHM 2012 Prognostic Data Challenge.

[1]  Ricardo López-Ruiz,et al.  A Statistical Measure of Complexity , 1995, ArXiv.

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

[3]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[4]  J Kocijan,et al.  Application of Gaussian processes for black-box modelling of biosystems. , 2007, ISA transactions.

[5]  E.L. Owen,et al.  Assessment of the Reliability of Motors in Utility Applications - Updated , 1986, IEEE Transactions on Energy Conversion.

[6]  Lei Guo,et al.  Robust bearing performance degradation assessment method based on improved wavelet packet–support vector data description , 2009 .

[7]  Pavle Boškoski,et al.  Fault detection of mechanical drives under variable operating conditions based on wavelet packet Rényi entropy signatures , 2012 .

[8]  Osvaldo A. Rosso,et al.  Generalized statistical complexity measures: Geometrical and analytical properties , 2006 .

[9]  Iain Murray Introduction To Gaussian Processes , 2008 .

[10]  Young,et al.  Inferring statistical complexity. , 1989, Physical review letters.

[11]  Ruoyu Li,et al.  Fault features extraction for bearing prognostics , 2012, J. Intell. Manuf..

[12]  PF Albrecht,et al.  Assessment of the Reliability of Motors in Utility Applications , 1987, IEEE Transactions on Energy Conversion.

[13]  T. A. Harris,et al.  Fatigue Failure Progression in Ball Bearings , 2001 .

[14]  Robert B. Randall,et al.  A Stochastic Model for Simulation and Diagnostics of Rolling Element Bearings With Localized Faults , 2003 .

[15]  Robert B. Randall,et al.  THE RELATIONSHIP BETWEEN SPECTRAL CORRELATION AND ENVELOPE ANALYSIS IN THE DIAGNOSTICS OF BEARING FAULTS AND OTHER CYCLOSTATIONARY MACHINE SIGNALS , 2001 .

[16]  Evandro Agazzi,et al.  What is Complexity , 2002 .

[17]  Deniz Erdogmus,et al.  Renyi's Entropy, Divergence and Their Nonparametric Estimators , 2010, Information Theoretic Learning.

[18]  Đani Juričić,et al.  Rényi Entropy Based Statistical Complexity Analysis for Gear Fault Prognostics under Variable Load , 2012 .

[19]  Peter Tavner,et al.  Survey of commercially available condition monitoring systems for wind turbines. , 2014 .

[20]  Paolo Pennacchi,et al.  The relationship between kurtosis- and envelope-based indexes for the diagnostic of rolling element bearings , 2014 .

[21]  J. D. Gorman,et al.  Alpha-Divergence for Classification, Indexing and Retrieval (Revised 2) , 2002 .

[22]  Steven Y. Liang,et al.  Damage mechanics approach for bearing lifetime prognostics , 2002 .

[23]  Steven Y. Liang,et al.  STOCHASTIC PROGNOSTICS FOR ROLLING ELEMENT BEARINGS , 2000 .

[24]  Bojan Likar,et al.  Predictive control of a gas-liquid separation plant based on a Gaussian process model , 2007, Comput. Chem. Eng..

[25]  S. Janjarasjitta,et al.  Bearing condition diagnosis and prognosis using applied nonlinear dynamical analysis of machine vibration signal , 2008 .

[26]  N. Tandon,et al.  A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings , 1999 .

[27]  Dong Wang,et al.  Robust health evaluation of gearbox subject to tooth failure with wavelet decomposition , 2009 .

[28]  Blanco,et al.  Time-frequency analysis of electroencephalogram series. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[29]  Noureddine Zerhouni,et al.  Feature Evaluation for Effective Bearing Prognostics , 2013, Qual. Reliab. Eng. Int..

[30]  S. Mallat A wavelet tour of signal processing , 1998 .

[31]  W. Wang Autoregressive model-based diagnostics for gears and bearings , 2008 .

[32]  Michèle Basseville,et al.  Divergence measures for statistical data processing , 2010 .

[33]  K. Loparo,et al.  Online tracking of bearing wear using wavelet packet decomposition and probabilistic modeling : A method for bearing prognostics , 2007 .

[34]  J. Antoni Cyclostationarity by examples , 2009 .

[35]  O. A. Rosso,et al.  EEG analysis using wavelet-based information tools , 2006, Journal of Neuroscience Methods.

[36]  Angelo Plastino,et al.  Distances in Probability Space and the Statistical Complexity Setup , 2011, Entropy.

[37]  Alejandra Figliola,et al.  Time-frequency analysis of electroencephalogram series. III. Wavelet packets and information cost function , 1998 .

[38]  S. Marble,et al.  Validating Prognostic Algorithms: A Case Study Using Comprehensive Bearing Fault Data , 2007, 2007 IEEE Aerospace Conference.

[39]  Darko Vrečko,et al.  Multi-criteria analyses of wastewater treatment bio-processes under an uncertainty and a multiplicity of steady states. , 2012, Water research.

[40]  Jus Kocijan,et al.  Prognosis of gear health using Gaussian process model , 2011, 2011 IEEE EUROCON - International Conference on Computer as a Tool.

[41]  P. Laguna,et al.  Signal Processing , 2002, Yearbook of Medical Informatics.

[42]  Michael R. Chernick,et al.  Wavelet Methods for Time Series Analysis , 2001, Technometrics.