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 the machine condition monitoring. The 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. Therefore, in this paper, a novel sparse low-rank 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 (ADMM) and forward-and-backward splitting (FBS) algorithm, are applied to obtain global optimal solution. In the iterative algorithm, a weighting strategy is designed for the singular value 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.