Abstract: Generally, it is a difficulty to extract weak periodical impulses from the bearing non-stationary vibration signals that are often corrupted by heavy background noise, especially at the early stage of bearing faulty development. In this paper, a novel fault feature extraction methodology is proposed based on non-convex penalty regularization sparse low-rank matrix (NPRSLM) for taper roller bearing. The proposed NPRSLM model neither relies on the priori knowledge of the analyzed signal, nor requires a large number of sample signals to form a training dictionary before diagnosis, thus it avoids a series of redundant dictionary problems such as physical model matching problem and poor universality. The core idea is that the proposed method considers the observed signal and fault impulses as the one-dimensional matrix (or vector), and the fault impulses can be obtained by solving the anti-problem of the sparse regularization. Specifically, on the modeling system, the non-convex function is introduced to replace the conventional minimization L1-norm fused lasso low-rank matrix (ML1-FLLM) so as to reconstruct a novel non-convex regularization model. Meanwhile, the solution of the proposed NPRSLM model is derived by ADMM technique, and strictly convex property, boundary condition problem and convergence of the proposed model are also provided. The simulation and practical rolling bearing experiments indicate that the proposed method not only successfully extract weak periodical impulses from observed signal corrupted by heavy background noise, but also the energy attenuation problem and impulse loss problem are improved when the conventional ML1-FLLM process the weak fault vibration signals.

Key words: alternating direction method of multipliers, incipient fault, non-convex regularization, sparse low-rank matrix, taper roller bearings