Robust Sparse Threshold Optimization for Impulsive Blind Deconvolution

Abstract

The impulsive blind deconvolution (IBD) has gained great popularity due to its widespread success on many fault feature detection problems. One favorable strategy for IBD is to exploit the intrinsic sparse structure of impulsive sources to design sparsity-inducing threshold operators. After profoundly investigating popular sparse threshold operators, we found that convex threshold is robust but has an underestimation pathology problem. On the contrary, nonconvex threshold is unbiased but has a threshold sensitivity problem. To retain the robustness and unbiasedness simultaneously, a robust convolutional sparse learning model based on a firm threshold operator is proposed in this article. The highlight of the proposed model is to adopt a small attenuation transition region for antinoise robustness and meanwhile enable unbiased amplitude distribution for perfect impulsive feature preservation. Moreover, a computationally efficient solver based on an alternating direction method of multiplier (ADMM) framework is developed to rapidly obtain satisfactory impulsive features. The algorithmic convergence, computation complexity, and deconvolutional performance are comprehensively evaluated through a set of numerical experiments. Finally, the proposed method is applied to the impulsive source recovery of bearing faults. All comparative results corroborate that the advocated approach achieves a significant accuracy improvement over state-of-the-art IBD methods.