Fast sparse morphological decomposition with controllable sparsity for high-speed bearing fault diagnosis

Sparse representation has been widely applied in mechanical fault diagnosis. However, fault diagnosis of high-speed bearings requires high precision and real-time performance. To meet these requirements, this paper proposes a fast sparse morphological decomposition method with controllable sparsity for high-speed bearing fault diagnosis. A circulant dictionary with predetermined sparsity is proposed to quickly identify prominent shift-invariant components containing impulses. Subsequently, the index of the maximum difference mean ratio is designed to adaptively control the sparsity of the Fourier dictionary and eliminate interference from discrete frequency components. Inspired by morphological component analysis, a fast sparse decomposition model with controllable sparsity is constructed in this paper and its solution is provided. In particular, the algorithm has the characteristics of low complexity and fast calculation speed. Through simulations and high-speed bearing diagnosis cases, the effectiveness of the proposed method has been verified, and the results indicate that the proposed method offers superior performance in comparison to methods of classical morphological component decomposition and spectral kurtosis.