An adaptive generalized logarithm sparse regularization method and its application in rolling bearing fault diagnosis

The generalized logarithm sparse regularization method (G-log) for fault diagnosis of rotating devices can effectively reconstruct repetitive transient shocks from noise-disturbed signals, but its reconstruction accuracy frequently becomes inferior due to unsuitable regularization parameters. Moreover, conventional sparse regularization methods perform nothing on the input signals to guarantee that the impulse characteristics remain constant during the entire iteration process, which exacerbates the influence of noise on the reconstruction accuracy. To overcome these challenges, an adaptive generalized logarithm sparse regularization method (AG-log) based on the second-order cyclostationary indicator (ICS2) and the improved maximum correlation Pearson correlation coefficient deconvolution (IMCPCCD) method is proposed in this paper. Firstly, the optimal threshold parameter k for each iteration of AG-log is determined based on the ICS2 criterion to ensure the optimal reconstruction accuracy, while the optimal combination of iteration numbers N and k is established. Secondly, the original signal and the IMCPCCD filtered signal are alternately used as the input signal of AG-log according to the parity of the iterative steps to reduce the interference of noise. Finally, the application on simulated and two engineering case signals demonstrates that AG-log has better reconstruction accuracy compared with conventional nonconvex sparse regularization methods.