Sparsity-enhanced signal decomposition via generalized minimax-concave penalty for gearbox fault diagnosis

Vibration signals arising from faulty gearboxes are often a mixture of the meshing component and the periodic transient component, and simultaneously contaminated by noise. Sparsity-assisted signal decomposition is an effective technique to decompose a signal into morphologically distinct components based on sparse representation and optimization. In this paper, we propose a sparsity-enhanced signal decomposition method which uses the generalized minimax-concave (GMC) penalty as a nonconvex regularizer to enhance sparsity in the sparse approximation compared to classical sparsity-assisted signal decomposition methods, and thus to improve the decomposition accuracy for gearbox fault diagnosis. Even though the GMC penalty itself is nonconvex, it maintains the convexity of the GMC regularized cost function to be minimized. Hence, similar to the classical L1-norm regularization methods, the global optimal solution can be guaranteed via convex optimization. Moreover, we present and validate a straight-forward way to choose transforms and set parameters for the proposed method. Through simulation studies, it is demonstrated that the proposed sparsity-enhanced signal decomposition method can effectively decompose the simulated faulty gearbox signal into the meshing component and the periodic transient component. Comparisons with the classical L1-norm regularized signal decomposition method and spectral kurtosis show that the proposed method can accurately preserve the amplitude of the periodic transient component and provide a more accurate estimation result. Experiment and engineering case studies further verify that the proposed method can accurately estimate the periodic transient component from vibration signals, which demonstrate that the proposed method is a promising tool for gearbox fault diagnosis.