Adaptive redundant multiwavelet denoising with improved neighboring coefficients for gearbox fault detection

Abstract Gearbox fault detection under strong background noise is a challenging task. It is feasible to make the fault feature distinct through multiwavelet denoising. In addition to the advantage of multi-resolution analysis, multiwavelet with several scaling functions and wavelet functions can detect the different fault features effectively. However, the fixed basis functions not related to the given signal may lower the accuracy of fault detection. Moreover, the multiwavelet transform may result in Gibbs phenomena in the step of reconstruction. Furthermore, both traditional term-by-term threshold and neighboring coefficients do not consider the direct spatial dependency of wavelet coefficients at adjacent scale. To overcome these deficiencies, adaptive redundant multiwavelet (ARM) denoising with improved neighboring coefficients (NeighCoeff) is proposed. Based on symmetric multiwavelet lifting scheme (SMLS), taking kurtosis—partial envelope spectrum entropy as the evaluation objective and genetic algorithms as the optimization method, ARM is proposed. Considering the intra-scale and inter-scale dependency of wavelet coefficients, the improved NeighCoeff method is developed and incorporated into ARM. The proposed method is applied to both the simulated signal and the practical gearbox vibration signal under different conditions. The results show its effectiveness and reliance for gearbox fault detection.

[1]  Xiang-Gen Xia,et al.  Why and how prefiltering for discrete multiwavelet transforms , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[2]  Gilbert Strang,et al.  Finite element multiwavelets , 1994 .

[3]  Li Zhen,et al.  Customized wavelet denoising using intra- and inter-scale dependency for bearing fault detection , 2008 .

[4]  George C. Donovan,et al.  Construction of Orthogonal Wavelets Using Fractal Interpolation Functions , 1996 .

[5]  Yuesheng Xu,et al.  Gearbox fault diagnosis using empirical mode decomposition and Hilbert spectrum , 2006 .

[6]  Yu Yang,et al.  The envelope order spectrum based on generalized demodulation time–frequency analysis and its application to gear fault diagnosis , 2010 .

[7]  J. Antoni.  The spectral kurtosis: a useful tool for characterising non-stationary signals , 2006 .

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

[9]  Yanyang Zi,et al.  Multiwavelet denoising with improved neighboring coefficients for application on rolling bearing fault diagnosis , 2011 .

[10]  Y. Zi,et al.  Gear fault detection using customized multiwavelet lifting schemes , 2010 .

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

[12]  J. N. Kapur,et al.  Entropy optimization principles with applications , 1992 .

[13]  Jiang Xiuchen.  A Multi-wavelet Based Algorithm for Extracting Diversiform Partial Discharge Signals , 2007 .

[14]  Peter W. Tse,et al.  Development of an advanced noise reduction method for vibration analysis based on singular value decomposition , 2003 .

[15]  Shahriar Gharibzadeh,et al.  Microarray image enhancement by denoising using decimated and undecimated multiwavelet transforms , 2010, Signal Image Video Process..

[16]  Zhengjia He,et al.  Fault feature enhancement of gearbox in combined machining center by using adaptive cascade stochastic resonance , 2011 .

[17]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[18]  Guo Yan,et al.  Engineering signal processing based on bistable stochastic resonance , 2007 .

[19]  Yanyang Zi,et al.  Multiwavelet construction via an adaptive symmetric lifting scheme and its applications for rotating machinery fault diagnosis , 2009 .

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

[21]  J. Antoni.  Fast computation of the kurtogram for the detection of transient faults , 2007 .

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

[23]  Amir Averbuch,et al.  Multiwavelet Frames in Signal Space Originated From Hermite Splines , 2007, IEEE Transactions on Signal Processing.

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

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

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