Denosing Algorithm Based on Local Laplace Model in Wavelet Domain and Its Application in Mechanical Fault Diagnosis

Abstract

A denoising algorithm based on local Laplace model in wavelet domain is proposed,and it is successfully applied in mechanical fault diagnosis.Magnitude-phase compounding information of complex wavelet transform is used to position singular points of signal on each level for its good sensitivity to singular points of signal.And then the coefficients of real wavelet transform are separated into two sorts by the certain neighborhood width and the positions of singular points on each level,the two sorts include effective coefficients and ineffective coefficients.And ineffective coefficients out of neighborhoods of singular points are directly set zero,while local statistical distribution of efficient coefficients in neighborhood is assumed to Laplace model.And on the basis of prior distribution,maximum a posteriori(MAP) estimator is used to restore the wavelet coefficients to signal from the noisy observations.New wavelet coefficients are used for the reconstruction to the denoising signal.This algorithm is analyzed and certificated by simulation and automotive main reducer gear fault diagnosis example respectively.Analysis results show that this algorithm has good noise reduction effect,and can efficiently reduce the noise of gear fault signal in main reducer.