Collaborative Double Difference Sparse Regularization and Convex Optimization for Bearing Fault Detection

The localized faults of bearings often produce a series of periodic impacts. However, how to extract these repetitive transients from the signals with strong noise interference is still a challenging problem. In this paper, a new method called collaborative double difference sparse regularization (CDDSR) is proposed for bearing fault detection. To be specific, the first and second-order difference matrices are integrated into sparse regularization term, and the differential sparsity and denoising effect of fault signal are enhanced by collaboration. According to the time domain impulse characteristics of fault signal, the sparsity of signal itself will also be considered. Based on the majorization-minimization (MM) algorithm, the objective optimization model can be solved quickly. Furthermore, the selection of regularization parameters is deeply studied, and an adaptive parameter selection strategy is given. The performance of CDDSR is verified through simulation analysis and two experimental cases, and the ability of CDDSR to extract fault features is further evaluated by quantitative index. Results demonstrate its superiority in eliminating noise interference and extracting periodic impulses in comparison to other state-of-the-art methods.