Customized wavelet denoising using intra- and inter-scale dependency for bearing fault detection

Bearing fault detection is a challenging task, especially at the incipient stage. Wavelet denoising is widely recognized as an effective tool for signal processing and feature extraction. The wavelet denoising method by incorporating neighboring coefficients (NeighCoeff), which is proposed by Cai and Silverman, gives the better results than the traditional term-by-term approaches. However, this method only exploits intra-scale dependency of wavelet coefficients. It does not consider the inter-scale dependency of wavelet coefficients. In this paper, customized wavelet denoising using intra- and inter-scale dependency of wavelet coefficients is proposed for bearing fault detection. By designing the prediction operator and update operator, a customized wavelet based on the lifting scheme is constructed directly to match the transient properties of a given signal. The NeighCoeff denoising algorithm is improved by taking into account the intra- and inter-scale dependency of wavelet coefficients. The results of the application to bearing fault detection show that the proposed method is very effective.

[1]  B.K.N. Rao,et al.  Handbook of Condition Monitoring , 1996 .

[2]  N. R. Iyer,et al.  DETECTION OF ROLLER BEARING DEFECTS USING EXPERT SYSTEM AND FUZZY LOGIC , 1996 .

[3]  Wim Sweldens,et al.  The lifting scheme: a construction of second generation wavelets , 1998 .

[4]  Eero P. Simoncelli.  Bayesian Denoising of Visual Images in the Wavelet Domain , 1999 .

[5]  Mohd Jailani Mohd Nor,et al.  Statistical analysis of sound and vibration signals for monitoring rolling element bearing condition , 1998 .

[6]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

[7]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[8]  Wim Sweldens,et al.  Building your own wavelets at home , 2000 .

[9]  C. Sujatha,et al.  Using neural networks for the diagnosis of localized defects in ball bearings , 1997 .

[10]  T. D. Bui,et al.  Multiwavelets denoising using neighboring coefficients , 2003, IEEE Signal Processing Letters.

[11]  W. Sweldens.  The Lifting Scheme: A Custom - Design Construction of Biorthogonal Wavelets "Industrial Mathematics , 1996 .

[12]  B. Vidakovic,et al.  Bayesian Inference in Wavelet-Based Models , 1999 .

[13]  Dennis M. Healy,et al.  Wavelet transform domain filters: a spatially selective noise filtration technique , 1994, IEEE Trans. Image Process..

[14]  Peter W. Tse,et al.  Wavelet Analysis and Envelope Detection For Rolling Element Bearing Fault Diagnosis—Their Effectiveness and Flexibilities , 2001 .

[15]  Jun Ma,et al.  Wavelet decomposition of vibrations for detection of bearing-localized defects , 1997 .

[16]  Robert D. Nowak,et al.  Wavelet-based statistical signal processing using hidden Markov models , 1998, IEEE Trans. Signal Process..

[17]  Jiang Hongkai,et al.  A sliding window feature extraction method for rotating machinery based on the lifting scheme , 2007 .

[18]  Chen Peng,et al.  Gearbox fault diagnosis using adaptive redundant Lifting Scheme , 2006 .

[19]  Qiao Sun,et al.  SINGULARITY ANALYSIS USING CONTINUOUS WAVELET TRANSFORM FOR BEARING FAULT DIAGNOSIS , 2002 .

[20]  D. W. Thomas,et al.  Adaptive noise cancelling and condition monitoring , 1981 .

[21]  P. D. McFadden,et al.  Vibration monitoring of rolling element bearings by the high-frequency resonance technique — a review , 1984 .

[22]  Pierre Moulin,et al.  Information-theoretic analysis of interscale and intrascale dependencies between image wavelet coefficients , 2001, IEEE Trans. Image Process..

[23]  Jing Lin,et al.  Feature Extraction Based on Morlet Wavelet and its Application for Mechanical Fault Diagnosis , 2000 .

[24]  Michel Barlaud,et al.  Design of signal-adapted multidimensional lifting scheme for lossy coding , 2004, IEEE Transactions on Image Processing.

[25]  Kikuo Nezu,et al.  Design of mixture de-noising for detecting faulty bearing signals , 2005 .