Sparsity enforced time–frequency decomposition in the Bayesian framework for bearing fault feature extraction under time-varying conditions

Fault characteristic extraction of rolling bearings is essential for fault diagnosis. Rolling bearings are usually operated at changing speeds, and the nonstationary signals of the bearings are covered by the heavy background noise, making the extraction task of fault features very difficult. To address this issue, a robust fault characteristic extraction approach based on the time–frequency analysis under variable speed conditions is proposed in this paper. Firstly, the sparse property of the time-variant fault characteristics and low-rankness of background noise are explored and utilized in the time–frequency representation (TFR). Then, the sparse and the low-rank components are integrated into a hierarchical Bayesian model, and a random error term is considered to make the Bayesian model more robust. The Gibbs sampler is applied to extract the desired sparsity-enhanced component of the TFR in the Bayesian framework. Eventually, the time–frequency reassignment technique is adopted further to optimize the time–frequency resolution of the sparse component. Two simulated scenarios and a real-data experiment are used to evaluate the suggested approach's performance. It turns out that the proposed approach is robust to noise and can extract the bearing time-varying fault features effectively.