Sparse representation based on generalized smooth logarithm regularization for bearing fault diagnosis

Abstract

Bearings in rotating machinery are prone to performance degradation and failures under complex working environments. The key issue of this work is to accurately extract the bearing fault induced transient signal from the noise signals. One of the effective methods to extract such transient components from noisy signals is sparse representation. However, commonly used sparse representation methods have the shortcomings of the underestimation of amplitude and insufficient estimation accuracy. To address these problems, we propose a generalized smoothing logarithmic (GSL) regularization based sparse representation method, which uses the Moreau envelope to perform generalized smoothing on the traditional logarithmic penalty function. Then the tunable Q-factor wavelet transform (TQWT) is adopted to construct sparse dictionaries for bearing faults since it is tight frame and matrix-free, which can ameliorate the computation speed of the proposed method. Simulation and experiments verify that the proposed GSL method is effective and applicable for bearing fault diagnosis.