Sparse Low-Rank Matrix Estimation With Nonconvex Enhancement for Fault Diagnosis of Rolling Bearings

The diagnosis of bearing early fault is significant and fundamental in machine condition monitoring. An accurate and effective diagnosis is of great importance to avoid further serious accidents. However, existing sparse low-rank (SLR) methods for bearing fault diagnosis suffer from underestimation of amplitude and inaccurate approximation of singular values (SVs). Therefore, in this article, a novel SLR matrix estimation method with nonconvex enhancement (SLRNE) is proposed, extracting the fault transients from observed noisy signal. Specifically, fault transients have both sparse and low-rank properties in time-frequency domain. Based on this, a SLR optimization model is proposed to simultaneously promote the above two properties via truncated nuclear norm (TNN) and generalized minimax concave (GMC) penalty function. The two nonconvex functions aim to promote low-rank property and sparsity, respectively. Then, based on derived convexity conditions of the optimization problem, convex optimization algorithm, alternating direction method of multipliers (ADMMs), and forward-and-backward splitting (FBS) algorithm are applied to obtain a global optimal solution. In the iterative algorithm, a weighting strategy is designed for the SV threshold operator to enhance the effect of fault feature extraction. Simulated and experimental signals verify the effectiveness of SLRNE and contrast experiments verify its superiority.

Automated summary

The diagnosis of early bearing faults is crucial for machine condition monitoring. The existing sparse low-rank (SLR) methods have limitations in accurately estimating amplitude and approximating singular values (SVs). To address this, a novel SLR matrix estimation method with nonconvex enhancement (SLRNE) is proposed in this article. The method extracts fault transients from observed noisy signals, leveraging their sparse and low-rank properties in the time-frequency domain. Simulated and experimental signals confirm the effectiveness of SLRNE, and contrast experiments demonstrate its superiority.