Fast Sparsity-Assisted Signal Decomposition With Nonconvex Enhancement for Bearing Fault Diagnosis

Sparsity-assisted signal decomposition (SASD) based on morphological component analysis (MCA) for bearing fault diagnosis has been studied in-depth. However, existing algorithms often use different combinations of representation dictionaries and priors, leading to difficult dictionary choice and high computational complexity. This article aims to develop a fast sparsity-assisted algorithm to decompose a vibration signal into discrete frequency and impulse components for bearing fault diagnosis. We introduce the morphological discrimination of discrete frequency and impulse components in time and frequency domains, respectively, for the first time. To use this morphological discrimination, we establish a fast SASD based on MCA with nonconvex enhancement. We further prove the necessary and sufficient condition to guarantee the convexity and use the majorization minimization algorithm to derive a fast solver. The proposed algorithm not only has low computational complexity, but also avoids choosing multiple dictionaries as well as underestimation of impulse features. Furthermore, an adaptive parameter selection algorithm to set parameters of our algorithm is designed for real applications. The effectiveness of fast SASD and its adaptive variant is verified by both simulation studies and bearing diagnosis cases. The source codes will be released at https://github.com/ZhaoZhibin/Fast_SASD.