Synthesis versus analysis priors via generalized minimax-concave penalty for sparsity-assisted machinery fault diagnosis

Sparse priors for signals play a key role in sparse signal modeling, and sparsity-assisted signal processing techniques have been studied widely for machinery fault diagnosis. In this paper, synthesis and analysis priors are introduced for sparse regularization problems via the generalized minimax-concave (GMC) penalty to improve the performance of signal denoising or signal decomposition for the purpose of machinery fault diagnosis. Firstly, the GMC-synthesis and GMC-analysis methods are proposed simultaneously for sparse regularization. Secondly, the gap between GMC-synthesis and GMC-analysis is explored systematically via theoretical and numerical analysis, especially via comparing the performance of GMC-synthesis and GMC-analysis for machinery fault diagnosis, including bearing fault diagnosis and gearbox fault diagnosis. Thirdly, a majorization-minimization-like (MM-like) algorithm is proposed to solve the optimization problem of GMC-synthesis and GMC-analysis. Furthermore, the early stop criterion and the adaptive strategy for regularization parameter selection is also provided in this paper. The results of the numerical simulation, experiment verification, and practical applications show that GMC-synthesis performs better for fault feature extraction than GMC-analysis and the other methods, including ℓ ₁ -synthesis, ℓ ₁ -analysis, and spectral kurtosis.