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

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).