A recursive sparse representation strategy for bearing fault diagnosis

Partial faults of bearings trigger periodic vibration features, but the interference makes fault diagnosis more difficult. A recursive sparse representation (RSR) algorithm is proposed to solve the fault diagnosis of bearings from sparse representation in the time and frequency domains. The tunable Q-factor wavelet transform (TQWT) filtering strategy is used to adaptively obtain the best wavelet with the signal vibration features. The optimal wavelet data is used as a fragment of each basic atom to obtain an optimal atomic complete dictionary (OACD) by Toeplitz's complementary zero expansion. The sparse representation based on the OACD obtains sparse coefficients with time domain features. The sparse group lasso (SGL) based on Majorize-Minimization (MM) optimization solves the sparse coefficients and extracts the primary vibration information in the frequency domain. Simulation experiments, signal experiments, and a comparative analysis of spectral kurtosis (SK) prove that RSR can effectively extract the vibration characteristics of faulty bearings.