Periodical sparse low-rank matrix estimation algorithm for fault detection of rolling bearings.

Early bearing fault detection is crucial to avoid catastrophic accidents. However, the repetitive defect impulses indicating bearing fault are buried in heavy background noise. In the paper, a novel periodical sparse low-rank (PSLR) matrix estimation algorithm is proposed for extracting repetitive transients from noisy signal. Concretely, periodical group sparsity and low-lank property of fault transients in time-frequency domain are first revealed, and then an optimization problem is proposed for simultaneously promoting these two properties. Meanwhile, to further highlight the sparsity of fault features, the non-convex penalty functions are incorporated into the optimization problem. Then, for solving the proposed optimization problem, an iterative algorithm is derived based on alternating direction method of multipliers (ADMM) and majorization-minimization (MM), in which the traditional soft-thresholding operation is replaced by the proposed Gini-guided fault information thresholding (FIT) scheme to enhance fault transient extraction. Finally, simulated and real signals confirm the performance of proposed PSLR in extracting defect impulses from noisy vibration signal.