Feature enhancement via balanced non-convex regularization for rotary machine fault diagnosis

Feature detection from compound vibration signal is a fundamental task for rotary machine fault diagnosis. Dual synthesis sparse decomposition (DSSD) based on convex regularization is an effective framework for signal decomposition and feature detection. However, the decomposed components via convex regularization are often underestimated, which is unfavorable to feature detection. Therefore, this paper describes and analyzes a novel dual enhanced sparse decomposition (DESD) framework based on the balanced decomposition model and non-convex regularization. The balanced model bridges the synthesis-based and analysis-based model, and balances the fidelity, sparsity, and smoothness of the solution. Besides, the non-convex minimax-concave (MC) penalty is used as the regularization terms in the framework to better estimate the signal values than convex regularization. The proposed framework is formulated as a minimization problem involving a data fidelity term, two balanced regularization terms and two synthesis non-convex regularization terms on wavelet-domain sparsity. Then, the proposed framework is solved by a variable splitting strategy and alternating direction method of multiplier (ADMM). Moreover, adaptive selection rules for the regularization parameters are investigated in detail through the comprehensive numerical studies. Numerical simulations and experimental signal analysis validate that the proposed method has better performance than the DSSD method with convex regularization on the feature enhancement and detection.