A new rolling bearing fault diagnosis approach based on multiscale permutation entropy (MPE), Laplacian score (LS), and support vector machines (SVMs) is proposed in this paper. Permutation entropy (PE) was recently proposed and defined to measure the randomicity and detect dynamical changes of time series. However, for the complexity of mechanical systems, the randomicity and dynamic changes of the vibration signal will exist in different scales. Thus, the definition of MPE is introduced and employed to extract the nonlinear fault characteristics from the bearing vibration signal in different scales. Besides, the SVM is utilized to accomplish the fault feature classification to fulfill diagnostic procedure automatically. Meanwhile, in order to avoid a high dimension of features, the Laplacian score (LS) is used to refine the feature vector by ranking the features according to their importance and correlations with the main fault information. Finally, the rolling bearing fault diagnosis method based on MPE, LS, and SVM is proposed and applied to the experimental data. The experimental data analysis results indicate that the proposed method could identify the fault categories effectively. 1. Introduction The vibration signals of mechanical systems, especially for ones with fault, often show mutation, nonlinearity, and nonstationarity because of the strike, velocity chopping, structure transmutation, loading, and friction. Hence, it is very crucial for mechanical fault diagnosis to extract the fault feature information from the nonlinear and nonstationary signal. A primary method for dealing with the nonlinear and nonstationary signal is time-frequency analysis [1], which has been applied to the mechanical fault diagnosis field widely for its ability to provide local information both in time and frequency domains of vibration signals [2]. However, the time-frequency analysis method, such as wavelet transform or Hilbert-Huang transform [3, 4], which decomposes the vibration signal into several stationary monocomponent signals, cannot reflect the subtle dynamic changes of vibration signal effectively and, therefore, inevitably will have some limitations [5]. With the development of nonlinear dynamic theories, especially in recent years, a number of nonlinear parameters and methods, such as chaos theory, fractal dimension, and information entropy, have been applied to machine condition monitoring and fault diagnosis. For instance, Logan and Mathew elaborated the application of the correlation dimension to vibration fault diagnosis of rolling element bearing
References
[1]
D. Yu, J. Cheng, and Y. Yang, “Application of EMD method and Hilbert spectrum to the fault diagnosis of roller bearings,” Mechanical Systems and Signal Processing, vol. 19, no. 2, pp. 259–270, 2005.
[2]
E. Sejdi？, I. Djurovi？, and J. Jiang, “Time-frequency feature representation using energy concentration: an overview of recent advances,” Digital Signal Processing, vol. 19, no. 1, pp. 153–183, 2009.
[3]
N. E. Huang, Z. Shen, S. R. Long et al., “The empirical mode decomposition and the Hubert spectrum for nonlinear and non-stationary time series analysis,” Proceedings of the Royal Society A, vol. 454, no. 1971, pp. 903–995, 1998.
[4]
Z. Wu and N. E. Huang, “A study of the characteristics of white noise using the empirical mode decomposition method,” Proceedings of the Royal Society A, vol. 460, no. 2046, pp. 1597–1611, 2004.
[5]
R. Yan and R. X. Gao, “Approximate entropy as a diagnostic tool for machine health monitoring,” Mechanical Systems and Signal Processing, vol. 21, no. 2, pp. 824–839, 2007.
[6]
D. Logan and J. Mathew, “Using the correlation dimension for vibration fault diagnosis of rolling element bearings—I. Basic concepts,” Mechanical Systems and Signal Processing, vol. 10, no. 3, pp. 241–250, 1996.
[7]
J. D. Jiang, J. Chen, and L. S. Qu, “The application of correlation dimension in gearbox condition monitoring,” Journal of Sound and Vibration, vol. 223, no. 4, pp. 529–541, 1999.
[8]
L. Zhang, G. Xiong, H. Liu, H. Zou, and W. Guo, “Bearing fault diagnosis using multi-scale entropy and adaptive neuro-fuzzy inference,” Expert Systems with Applications, vol. 37, no. 8, pp. 6077–6085, 2010.
[9]
J. S. Richman and J. R. Moorman, “Physiological time-series analysis using approximate and sample entropy,” American Journal of Physiology—Heart and Circulatory Physiology, vol. 278, no. 6, pp. H2039–H2049, 2000.
[10]
Y.-H. Pan, Y.-H. Wang, S.-F. Liang, and K.-T. Lee, “Fast computation of sample entropy and approximate entropy in biomedicine,” Computer Methods and Programs in Biomedicine, vol. 104, no. 3, pp. 382–396, 2011.
[11]
M. Costa, A. L. Goldberger, and C.-K. Peng, “Multiscale entropy analysis of complex physiologic time series,” Physical Review Letters, vol. 89, no. 6, Article ID 068102, 4 pages, 2002.
[12]
M. Costa, A. L. Goldberger, and C. K. Peng, “Multiscale entropy analysis of biological signals,” Physical Review E, vol. 71, Article ID 021906, 2005.
[13]
W. Aziz and M. Arif, “Multiscale permutation entropy of physiological time series,” in Proceedings of the 9th International Multitopic Conference (INMIC '05), December 2005.
[14]
C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Physical Review Letters, vol. 88, no. 17, Article ID 174102, 4 pages, 2002.
[15]
C. Bandt, G. Keller, and B. Pompe, “Entropy of interval maps via permutations,” Nonlinearity, vol. 15, no. 5, pp. 1595–1602, 2002.
[16]
R. Yan, Y. Liu, and R. X. Gao, “Permutation entropy: a nonlinear statistical measure for status characterization of rotary machines,” Mechanical Systems and Signal Processing, vol. 29, pp. 474–484, 2012.
[17]
N. Nicolaou and J. Georgiou, “Detection of epileptic electroencephalogram based on Permutation Entropy and Support Vector Machines,” Expert Systems with Applications, vol. 39, no. 1, pp. 202–209, 2012.
[18]
X. He, D. Cai, and P. Niyogi, “Laplacian score for feature selection,” in Advances in Neural Information Processing System, MIT Press, Cambridge, Mass, USA, 2005.
[19]
Y. Yang, D. Yu, and J. Cheng, “A fault diagnosis approach for roller bearing based on IMF envelope spectrum and SVM,” Measurement, vol. 40, no. 9-10, pp. 943–950, 2007.
[20]
P. Konar and P. Chattopadhyay, “Bearing fault detection of induction motor using wavelet and Support Vector Machines (SVMs),” Applied Soft Computing Journal, vol. 11, no. 6, pp. 4203–4211, 2011.
[21]
J. Cheng, D. Yu, J. Tang, and Y. Yang, “Application of SVM and SVD technique based on EMD to the fault diagnosis of the rotating machinery,” Shock and Vibration, vol. 16, no. 1, pp. 89–98, 2009.
[22]
Y. Cao, W.-W. Tung, J. B. Gao, V. A. Protopopescu, and L. M. Hively, “Detecting dynamical changes in time series using the permutation entropy,” Physical Review E, vol. 70, no. 4, Article ID 046217, 7 pages, 2004.
[23]
Y. Lei, Z. He, and Y. Zi, “A new approach to intelligent fault diagnosis of rotating machinery,” Expert Systems with Applications, vol. 35, no. 4, pp. 1593–1600, 2008.
[24]
P. K. Kankar, S. C. Sharma, and S. P. Harsha, “Fault diagnosis of ball bearings using machine learning methods,” Expert Systems with Applications, vol. 38, no. 3, pp. 1876–1886, 2011.
[25]
P. Qin, Y. Shen, J. Zhu, and H. Xu, “Dynamic analysis of hydrodynamic bearing-rotor system based on neural network,” International Journal of Engineering Science, vol. 43, no. 5-6, pp. 520–531, 2005.
[26]
Y. Yang, D. Yu, and J. Cheng, “A roller bearing fault diagnosis method based on EMD energy entropy and ANN,” Journal of Sound and Vibration, vol. 294, no. 1-2, pp. 269–277, 2006.
[27]
S.-W. Fei and X.-B. Zhang, “Fault diagnosis of power transformer based on support vector machine with genetic algorithm,” Expert Systems with Applications, vol. 36, no. 8, pp. 11352–11357, 2009.
