Cyclic correlation density decomposition based on a sparse and low-rank model for weak fault feature extraction of rolling bearings

The weak fault feature extraction of rolling element bearings is of critical interest for fault diagnosis. The initial fault is always very weak and buried in high background noise, making it extremely hard to extract the fault feature. Thus, it is essential to correctly extract the weak fault feature of the rolling bearings. A weak fault feature extraction approach using Cyclic correlation density decomposition based on the sparse and low-rank model is proposed in this article. According to the cyclic statistical properties of the fault-bearing signal, the Fast Spectral Correlation (Fast-SC) algorithm is employed to obtain the Cyclic Spectral Density (CSD). It is founded that the CSD of periodic impulse exhibits a high degree of sparsity. Then, the sparsity is exploited into the sparse and low-rank decomposition model to extract the fault features. The CSD is decomposed into two components with the Robust Principal Component Analysis (RPCA) algorithm. The sparse component corresponds to the periodic fault impulse, while the low-rank component represents interference. It is noteworthy that the decomposed sparse component exhibits high resolution and high sparsity, which means the bearing fault features can be revealed clearly and accurately. Finally, the rolling bearing fault feature is detected effectively by the Enhanced Envelope Spectrum (EES). Both simulation fault signal and experimental data are analyzed to verify the proposed method's performance. A Frequency Component Indicator (FCI) and a Relative Indicator Gain (RIG) are constructed to quantify the comparison of the extraction results. The RIG of the proposed method relative to the envelope spectrum is more than 10 dB in the simulated bearing signal with a low SNR of-10 dB, and more than 6 dB in the experimental case. These results validate that the proposed method can extract weak fault features more effectively than some existing methods.