Fault diagnosis for rolling bearings under unknown time-varying speed conditions with sparse representation

•The sparse time frequency analysis method is proposed for bearing fault diagnosis.•The sparsity of the time-frequency fault feature is revealed.•The applied basis operator can derive the fault characteristic frequency directly.•The time and frequency resolutions are enhanced effectively.•The proposed method also denoise the signal effectively. In practice, bearings often run at a time-varying speed, which induces non-stationary vibration signals. How to extract the fault characteristic frequency (FCF) effectively under unknown variable speed conditions is a challenging work. This paper proposes a sparse time frequency method for fault diagnosis with no speed information demanded. Firstly, the Hilbert Transform is used to demodulate the vibration signal. Then the iterated soft-thresholding algorithm is applied to solve the l1 norm regularized linear least squares cost function. The sparsity of the FCF is expounded in detail, and how to choose the basis to map the vibration signal into the sparse space is also detailed. With the appropriate basis, the solution is exactly the optimized sparse TFR, which can enhance both time and frequency resolutions greatly, and meanwhile denoise the signal effectively. This method does not produce the confusing components when the bearing is in the healthy condition, while indicates the FCF when the bearing is defective. To show the robustness of the effectiveness, the proposed method is verified with simulated and experimental signals under various time-varying operating conditions. All the signals are also processed with the STFT, Fourier-based Synchrosqueezing Transform and ridge extraction method for comparison.