The key properties of REB fault impulse response truncated matrix for revealing the causes of SPCP-based separation problems

Abstract Accurate separation of rolling element bearings (REBs) fault impulse responses allows precise monitoring of fault conditions to improve mechanical system reliability. Stable principal component pursuit (SPCP) is a very effective method in image, video, and sound signal separation. However, two problems occur when directly using SPCP to separate REB fault impulse responses: (1) separation accuracy is not as expected in the presence of strong noise; (2) separation of fault impulse responses that are subject to amplitude fluctuations is worse. In this paper, we reveal the key low-dimensional properties that cause the above two problems: the reason for (1) is that the low-rank constraint in SPCP cannot accurately model the truncated matrix space of REBs fault impulse response: Rank-1 is the precise expression; the reason for (2) is the presence of Rank-Sparsity Coherence in the REB fault impulse response. Rank-1 and Rank-Sparsity Coherence can provide theoretical references for the separation of fault impulse responses of REBs, gears and so on.