Randomness complexity as a family feature of rolling bearings’ degradation

Randomness complexity is a kind of features which is widely used to describe bearings’ degradation. However, different randomness complexities present different properties. It is necessary to figure out different randomness complexities’ properties. In this paper, we are going to make comparisons of seven commonly used randomness complexities namely approximate entropy, sample entropy, fuzzy entropy, Shannon entropy, permutation entropy, Lempel-Ziv complexity and C0 complexity by simulation signals with three different aspects and two run-to-failure bearing’s data. By comparisons, we have found that there are a kind of similarity between them and we have proposed a trend similarity index to expound this similarity. Based on the comparisons, we can infer that randomness complexities are a family feature of rolling bearings’ degradation. Among the seven discussed complexities, sample entropy has the best performance, and it can be a good representative of the complexity features. In this paper, the difference between complexity features and other features when monitoring bearings’ degradation have been discussed. The research will provide a reference for rolling bearings’ multi-features dimensionality reduction by attribute selection method.

[1]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[2]  Abraham Lempel,et al.  On the Complexity of Finite Sequences , 1976, IEEE Trans. Inf. Theory.

[3]  Thomas M. Cover,et al.  Some equivalences between Shannon entropy and Kolmogorov complexity , 1978, IEEE Trans. Inf. Theory.

[4]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[5]  J. Guyader,et al.  Routes To Chaos In Ball Bearings , 1993 .

[6]  A. Shiryayev On Tables of Random Numbers , 1993 .

[7]  P E Rapp,et al.  Complexity measures in molecular psychiatry. , 1996, Molecular psychiatry.

[8]  Fang Chen,et al.  A New Measurement of Complexity for Studying EEG Mutual Information , 1998, ICONIP.

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

[10]  Tanya Schmah,et al.  DYNAMICAL ANALYSIS IN CLINICAL PRACTICE , 2000 .

[11]  O. Prakash,et al.  EFFECT OF RADIAL INTERNAL CLEARANCE OF A BALL BEARING ON THE DYNAMICS OF A BALANCED HORIZONTAL ROTOR , 2000 .

[12]  J. Richman,et al.  Physiological time-series analysis using approximate entropy and sample entropy. , 2000, American journal of physiology. Heart and circulatory physiology.

[13]  Thomas R. Kurfess,et al.  Rolling element bearing diagnostics in run-to-failure lifetime testing , 2001 .

[14]  B. Pompe,et al.  Permutation entropy: a natural complexity measure for time series. , 2002, Physical review letters.

[15]  Robert X. Gao,et al.  Complexity as a measure for machine health evaluation , 2004, IEEE Transactions on Instrumentation and Measurement.

[16]  Madalena Costa,et al.  Multiscale entropy analysis of biological signals. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Yang Yu,et al.  A roller bearing fault diagnosis method based on EMD energy entropy and ANN , 2006 .

[18]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

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

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

[21]  Wangxin Yu,et al.  Characterization of Surface EMG Signal Based on Fuzzy Entropy , 2007, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

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

[23]  Bin Zhang,et al.  Rolling element bearing feature extraction and anomaly detection based on vibration monitoring , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[24]  Jie Sun,et al.  Convergence of C0 Complexity , 2009, Int. J. Bifurc. Chaos.

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

[26]  Bin Zhang,et al.  A Probabilistic Fault Detection Approach: Application to Bearing Fault Detection , 2011, IEEE Transactions on Industrial Electronics.

[27]  Robert B. Randall,et al.  Rolling element bearing diagnostics—A tutorial , 2011 .

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

[29]  Ruqiang Yan,et al.  Permutation entropy: A nonlinear statistical measure for status characterization of rotary machines , 2012 .

[30]  Lin Liang,et al.  Quantitative diagnosis of a spall-like fault of a rolling element bearing by empirical mode decomposition and the approximate entropy method , 2013 .

[31]  Jinde Zheng,et al.  A rolling bearing fault diagnosis approach based on LCD and fuzzy entropy , 2013 .

[32]  E. Jantunen,et al.  A descriptive model of wear evolution in rolling bearings , 2014 .

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

[34]  Idriss El-Thalji,et al.  A summary of fault modelling and predictive health monitoring of rolling element bearings , 2015 .

[35]  Noureddine Zerhouni,et al.  Enabling Health Monitoring Approach Based on Vibration Data for Accurate Prognostics , 2015, IEEE Transactions on Industrial Electronics.

[36]  Đani Juričić,et al.  Bearing fault prognostics using Rényi entropy based features and Gaussian process models , 2015 .

[37]  Ming Liang,et al.  Spectral kurtosis for fault detection, diagnosis and prognostics of rotating machines: A review with applications , 2016 .

[38]  Meng Sun,et al.  A New Feature Extraction Method Based on EEMD and Multi-Scale Fuzzy Entropy for Motor Bearing , 2016, Entropy.

[39]  Bing Wang,et al.  Rolling bearing performance degradation condition recognition based on mathematical morphological fractal dimension and fuzzy C-means , 2017 .

[40]  Peng Chen,et al.  An Automatic Filtering Method Based on an Improved Genetic Algorithm—With Application to Rolling Bearing Fault Signal Extraction , 2017, IEEE Sensors Journal.

[41]  Bing Wang,et al.  The application of a general mathematical morphological particle as a novel indicator for the performance degradation assessment of a bearing , 2017 .

[42]  Bernardo Spagnolo,et al.  Nonlinear Relaxation Phenomena in Metastable Condensed Matter Systems , 2016, Entropy.

[43]  Wu Deng,et al.  A Novel Fault Diagnosis Method Based on Integrating Empirical Wavelet Transform and Fuzzy Entropy for Motor Bearing , 2018, IEEE Access.

[44]  Shulin Liu,et al.  Numerical analysis of the dynamic behavior of a rotor-bearing-brush seal system with bristle interference , 2019, Journal of Mechanical Science and Technology.