Frobenius and nuclear hybrid norm penalized robust principal component analysis for transient impulsive feature detection of rolling bearings

Transient impulsive feature detection is of vital importance in fault diagnosis of rolling bearing. However, the transient impulsive feature of rolling bearing is always heavily buried in the noise contaminated signal, which makes it difficult to be detected. Robust principal component analysis (PRCA) is an effective approach to exploit the underlying structure from the corrupted observation, where the decomposed low-rank matrix (LRM) and the sparse matrix can represent the useful diagnostic information and the unwanted background noise respectively. In this study, a Frobenius and nuclear hybrid norm penalized RPCA (FNHN-RPCA) is served as a specific RPCA solver on account of it has a great ability to approach to the rank of the LRM and make the execution procedure efficiently To make the recorded signal suitable for the input criterion of the RPCA solver, a fault information matrix (FIM) construction method is proposed to arrange the recorded signal into a matrix form. After the RPCA solver is conducted on it, a reversed recovery operation is also proposed to rearrange the two dimensional LRM into a one-dimensional signal form. To confirm all recorded data is processed by the RPCA solver, both the forward and backward FIMs are constructed and a synthesis of the recovered signals from both the forward and backward FIMs is served as the final transient impulsive feature enhanced signal. The diagnostic results on simulated and experimental case studies verify that the presented technique is suitable for transient impulsive feature detection of rolling bearings even when the test bearing works in a low speed operating condition or the operating environment is in the presence of random impact interference.