Maximum correlation Pearson correlation coefficient deconvolution and its application in fault diagnosis of rolling bearings

Blind deconvolution (BD) has been proved to be an effective tool for recovering periodic impulses from strong background noise signals is widely used for fault diagnosis of bearings and gears. However, the existing BD focus more on improving the quantity and amplitude-frequency characteristics of interested periodic impulses without considering their phase-frequency characteristics and impulse waveform characteristics (attenuation coefficient and oscillation frequency), which results in severe distortion of the reconstructed signal. In this scenario, a new BD method, named maximum correlation Pearson correlation coefficient deconvolution (MCPCCD), is presented in this paper. Firstly, a new objective function is constructed which include two terms: correlation Pearson correlation coefficient (CPC) and signal fidelity term (SFT). CPC is a new norm with strong sensitivity to interested impulse signals, while SFT is a dimensionless error measure similar to RMSE. Then, the optimal FIR filter is obtained by maximizing the objective function of the reconstructed signal. Meanwhile, a new preprocessing step is designed to reduce the requirement of MCPCCD for periodic prior. Finally, the application on simulated and two experimental signals indicates that MCPCCD significantly outperforms the traditional BD method in recovering the periodic impulses.