基于RPCA低秩稀疏分解的循环频率检测方法

The accurate detection of cyclic frequency under strong noise interference is of great significance for cyclostationary signal processing. This paper proposes a new method of low-rank sparse decomposition technology based on Robust Principal Component Analysis (RPCA) applied to cyclic spectral density (CSD) matrix under low signal-to-noise ratio (SNR) to detect cyclic frequency. Firstly, RPCA is used to decompose the cyclic spectral density matrix into a low noise matrix representing noise interference and a sparse matrix representing cyclostationary characteristics. Subsequently, the sparse matrix is used to construct the detection function to realize the automatic detection of the cyclic frequency. The simulation results prove the superiority of the method in terms of detection probability under strong noise interference, and can provide the detection order for different signal-to-noise ratio conditions according to the receiver operating characteristic (ROC) curve of the detection of each order of cycle frequency harmonics. reference. In order to further verify the effectiveness of this method in application, this method is applied to the early fault diagnosis of rolling bearings. The analysis results on the accelerated fatigue life test data of rolling bearings prove that the method can accurately detect the characteristic frequency of the bearing fault from the low SNR vibration signal in the early stage of bearing failure, and realize the early fault diagnosis of the bearing.