Sparsity-based fractional spline wavelet denoising via overlapping group shrinkage with non-convex regularization and convex optimization for bearing fault diagnosis

Vibration monitoring has become a relatively common method for the fault diagnosis of rolling bearings in recent years. Vibration-based fault diagnosis technologies essentially rely upon accurate fault signature extraction from noisy vibration signals. To this end, this paper presents a sparsity-assisted denoising method using the fractional spline wavelet transform (FrSWT) and overlapping group shrinkage (OGS) with non-convex regularization and convex optimization (OGSNCRCO) to diagnose bearing faults. The FrSWT is used to promote sparsity of the wavelet coefficients for bearing fault signals. The OGSNCRCO balances data consistency and sparsity by using non-convex regularization and convex optimization, and is applied to shrink the wavelet coefficients of noisy signals in the fractional spline wavelet domain to extract bearing fault signals. Simulations and experiments validate the efficiency of the proposed method for fault diagnosis of rolling bearings. The results of analysis suggest that the proposed method is superior to other state-of-art techniques also commonly used for extracting fault signatures of rolling bearings, including the L1-norm denoising method (FrSWT with L1-norm regularization) and spectral kurtosis method.