Wavelet leaders multifractal features based fault diagnosis of rotating mechanism

Abstract A novel method based on wavelet leaders multifractal features for rolling element bearing fault diagnosis is proposed. The multifractal features, combined with scaling exponents, multifractal spectrum, and log cumulants, are utilized to classify various fault types and severities of rolling element bearing, and the classification performance of each type features and their combinations are evaluated by using SVMs. Eight wavelet packet energy features are introduced to train the SVMs together with multifractal features. Experiments on 11 fault data sets indicate that a promising classification performance is achieved. Meanwhile, the experimental results demonstrate that the classification performance of the SVMs trained with eight wavelet packet energy features in tandem with multifractal features outperforms that of the SVMs trained only with wavelet packet energy features, time domain features, or multifractal features, and it is also superior to that of wavelet packet energy features in tandem with time domain features, or multifractal features combined with time domain features. The feature selection method based on distance evaluation technique is exploited to select the most relevant features and discard the redundant features, and therefore the reliability of the diagnosis performance is further improved.

[1]  Oscar Castillo,et al.  A hybrid fuzzy‐fractal approach for time series analysis and plant monitoring , 2002, Int. J. Intell. Syst..

[2]  Qiao Hu,et al.  Fault diagnosis of rotating machinery based on improved wavelet package transform and SVMs ensemble , 2007 .

[3]  Paulo Gonçalves,et al.  Multifractal analysis of ECG for intrapartum diagnosis of fetal asphyxia , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[4]  Junyan Yang,et al.  Intelligent fault diagnosis of rolling element bearing based on SVMs and fractal dimension , 2007 .

[5]  P. Purkait,et al.  Impulse fault classification in transformers by fractal analysis , 2003 .

[6]  A. Arneodo,et al.  Wavelet transform of multifractals. , 1988, Physical review letters.

[7]  Emmanuel Bacry,et al.  Wavelet based fractal analysis of DNA sequences , 1996 .

[8]  Chih-Jen Lin,et al.  A comparison of methods for multiclass support vector machines , 2002, IEEE Trans. Neural Networks.

[9]  Patrice Abry,et al.  Wavelet Leader multifractal analysis for texture classification , 2009, 2009 16th IEEE International Conference on Image Processing (ICIP).

[10]  P. Tse,et al.  Singularity analysis of the vibration signals by means of wavelet modulus maximal method , 2007 .

[11]  Ibrahim Esat,et al.  ARTIFICIAL NEURAL NETWORK BASED FAULT DIAGNOSTICS OF ROTATING MACHINERY USING WAVELET TRANSFORMS AS A PREPROCESSOR , 1997 .

[12]  Jianping Xuan,et al.  Application of a modified fuzzy ARTMAP with feature-weight learning for the fault diagnosis of bearing , 2009, Expert Syst. Appl..

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

[14]  Patrice Abry,et al.  Multifractality Tests Using Bootstrapped Wavelet Leaders , 2007, IEEE Transactions on Signal Processing.

[15]  Jin Chen,et al.  Weak fault feature extraction of rolling bearing based on cyclic Wiener filter and envelope spectrum , 2011 .

[16]  E. Bacry,et al.  The Multifractal Formalism Revisited with Wavelets , 1994 .

[17]  S. J. Loutridis,et al.  Self-Similarity in Vibration Time Series: Application to Gear Fault Diagnostics , 2008 .

[18]  Junyan Yang,et al.  Application Research of Support Vector Machines in Condition Trend Prediction of Mechanical Equipment , 2005, ISNN.

[19]  Wensheng Su,et al.  Rolling element bearing faults diagnosis based on optimal Morlet wavelet filter and autocorrelation enhancement , 2010 .

[20]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[21]  B. Samanta,et al.  Gear fault detection using artificial neural networks and support vector machines with genetic algorithms , 2004 .

[22]  Alain Arneodo,et al.  Wavelet Based Multifractal Formalism: Applications to DNA Sequences, Satellite Images of the Cloud Structure, and Stock Market Data , 2002 .

[23]  E. Serrano,et al.  Wavelet Leaders: A new method to estimate the multifractal singularity spectra , 2009 .

[24]  Jensen,et al.  Direct determination of the f( alpha ) singularity spectrum and its application to fully developed turbulence. , 1989, Physical review. A, General physics.

[25]  Patrice Abry,et al.  Wavelet leaders and bootstrap for multifractal analysis of images , 2009, Signal Process..

[26]  Patrice Abry,et al.  Comprehensive multifractal analysis of turbulent velocity using the wavelet leaders , 2008 .

[27]  Stéphane Jaffard,et al.  Multifractal formalism for functions part I: results valid for all functions , 1997 .

[28]  Patrice Abry,et al.  Wavelet leader based multifractal analysis , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[29]  Bing Li,et al.  Feature extraction for rolling element bearing fault diagnosis utilizing generalized S transform and two-dimensional non-negative matrix factorization , 2011 .

[30]  Youren Wang,et al.  A novel approach of analog circuit fault diagnosis using support vector machines classifier , 2011 .

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

[32]  Rong-Juin Shyu,et al.  A New Fault Diagnosis Method of Rotating Machinery , 2008 .

[33]  Patrice Abry,et al.  Log Wavelet Leaders Cumulant Based Multifractal Analysis of EVI fMRI Time Series: Evidence of Scaling in Ongoing and Evoked Brain Activity , 2008, IEEE Journal of Selected Topics in Signal Processing.

[34]  P. Abry,et al.  Bootstrap for Empirical Multifractal Analysis , 2007, IEEE Signal Processing Magazine.

[35]  E. Bacry,et al.  Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[36]  Kang Yuzhe,et al.  Fault Pattern Recognition of Turbine-Generator Set Based on Wavelet Network and Fractal Theory , 2007, 2007 8th International Conference on Electronic Measurement and Instruments.

[37]  Yong Xu,et al.  A new texture descriptor using multifractal analysis in multi-orientation wavelet pyramid , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[38]  E. P. de Moura,et al.  Applications of detrended-fluctuation analysis to gearbox fault diagnosis , 2009 .

[39]  S. Jaffard,et al.  Methodology for multifractal analysis of heart rate variability: From LF/HF ratio to wavelet leaders , 2010, 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology.

[40]  Bernhard E. Boser,et al.  A training algorithm for optimal margin classifiers , 1992, COLT '92.

[41]  E. Bacry,et al.  Singularity spectrum of fractal signals from wavelet analysis: Exact results , 1993 .

[42]  Nacim Betrouni,et al.  Fractal and multifractal analysis: A review , 2009, Medical Image Anal..

[43]  Qiao Hu,et al.  Fault diagnosis of rotating machinery based on multiple ANFIS combination with GAs , 2007 .

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

[45]  Eduardo Serrano,et al.  About the Effectiveness of Different Methods for the Estimation of the Multifractal Spectrum of Natural Series , 2010, Int. J. Bifurc. Chaos.

[46]  Reinaldo R. Rosa,et al.  Multiscale analysis from turbulent time series with wavelet transform , 2001 .