Sparse Time–Frequency Representation for the Transient Signal Based on Low-Rank and Sparse Decomposition

Rolling element bearings are important parts of rotating machinery, and they are also one of the most fault-prone parts in rotating machinery. Therefore, many new algorithms have been proposed to solve the vibration-based diagnosis problem of rolling bearings. The measured vibration signal is typically composed of a periodic transient signal severely contaminated by loud background noise when the faults occur. In this paper, a transient signal extraction algorithm is proposed which depends on spectrum matrix decomposition. The sparse time–frequency representation of the periodic transient signals is exploited, and, further, a low-rank and sparse model is established to extract transient signals from strong noise. First, the low-dimensional representation matrix of the measured signal is generated by the synchrosqueezing transform based on short-time Fourier transform. It is found that the low-rank of the transient signal will be approximately preserved in the transformed domain. Then, semi-soft go decomposition is used to decompose the spectrum matrix into a low-rank matrix and a sparse matrix. Finally, the transient signal can be recovered through the inverse transformation of the decomposed low-rank matrix. The proposed method is a data-driven approach, and it does not require prior training. The performance of the algorithm is investigated on both synthetic and real vibration signals, and the results demonstrate that the algorithm is effective and robust.