Sparse Time–Frequency Representation via Greedy Method for Diagnosing Bearing Fault Under Variable Speed Conditions

Time-frequency analysis (TFA) is an effective tool for addressing the issue of bearing fault diagnosis under variable speed conditions. As a class of improved TFA methods, sparse time-frequency representation (STFR) enhances the detection capability for fault features through the pathway of sparse optimization. However, the existing STFR approaches necessitate the use of regularization, making the optimization results highly dependent on the selection of regularization parameters, and thus the optimization performance is difficult to guarantee. To overcome this drawback, a new STFR method using a sparsity adaptive matching pursuit by restricting atom distribution (SAMP-RAD) is proposed. This method resolves the optimization problem of STFR with an improved greedy algorithm, thereby freeing it from the issue of regularization parameter selection. Building upon orthogonal matching pursuit (OMP), SAMP-RAD introduces constraints on atom distribution to enhance noise suppression capabilities and achieves sparsity adaptation by limiting the maximum number of searches for feasible atoms. To accurately evaluate the performance of STFR methods, a new quantitative indicator is also introduced. The effectiveness of SAMP-RAD in overcoming parameter dependency while further enhancing TFA performance is verified with simulated and experimental bearing fault signals under variable speed conditions. Further comparison with other state-of-art methods validates the superiority of the proposed method.