Sparse and low-rank decomposition of the time-frequency representation for bearing fault diagnosis under variable speed conditions

Ran Wang; Haitao Fang; Longjing Yu; Liang Yu; Jin Chen

doi:10.1016/j.isatra.2021.11.030

Sparse and low-rank decomposition of the time-frequency representation for bearing fault diagnosis under variable speed conditions

ISA Trans. 2022 Sep;128(Pt B):579-598. doi: 10.1016/j.isatra.2021.11.030. Epub 2021 Dec 10.

Authors

Ran Wang¹, Haitao Fang¹, Longjing Yu¹, Liang Yu², Jin Chen³

Affiliations

¹ College of Logistics Engineering, Shanghai Maritime University, Shanghai, 201306, China.
² Institute of Vibration, Shock and Noise, State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, 200240, China. Electronic address: liang.yu@sjtu.edu.cn.
³ Institute of Vibration, Shock and Noise, State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, 200240, China.

PMID: 34952690
DOI: 10.1016/j.isatra.2021.11.030

Abstract

Rolling element bearings typically operate with fluctuating speed, leading to nonstationary vibrations. Moreover, bearings vibration signals are frequently hidden by strong distributions, making it difficult to detect clear bearing fault characteristics for diagnosis. Under this circumstance, the key issue is effectively extracting the transient features from the background interference and highlighting the time-varying fault characteristics. To address this issue, a sparse and low-rank decomposition approach is proposed. In this study, the sparsity of the variable defective characteristics and low-rank of background interference is revealed and exploited for bearing fault detection. Firstly, the time-frequency representation (TFR) of the envelope of measured signal is generated by the time-frequency transform. Then, a sparse and low-rank decomposition model is established based on robust principal component analysis (RPCA) to denoise the measured time-frequency representation and gain the sparse component. Finally, a time-frequency reassignment strategy is utilized to further enhance the capability of detecting the faulty characteristics in the decomposed sparse TFR. The synthetic and actual signals are evaluated to illustrate the reliability and efficacy of the proposed technique. The superiority is also validated by comparisons with STFT, synchrosqueezing transform (SST), ridge extraction method, and scaling-basis chirplet transform (SBCT).

Keywords: Bearing fault diagnosis; Robust principal component analysis; Sparse and low-rank decomposition; Variable speed conditions; time–frequency representation.