An Improved Sparse Regularization Method for Weak Fault Diagnosis of Rotating Machinery Based Upon Acceleration Signals

The periodical impulses caused by the localized fault are the important feature information for fault diagnosis of rotating machinery. However, it is a challenge to extract weak and sensitive fault characteristics information from non-stationary vibration signals that are often corrupted by heavy background noise, especially at the early stage of faulty development. In this paper, a novel fault diagnosis methodology is proposed based on the alternating direction method of multipliers (ADMMs) and the improved non-convex regularization algorithm (I-NCRA) for the weak fault diagnosis of rotating machinery. The proposed I-NCRA model is based on the formulation of a convex optimization problem, which consists of a signal-fidelity function and two parameterized non-convex penalty terms, and it not relies on the priori knowledge to form a training dictionary. Due to the improved non-convex penalty function induces sparsity more strongly than the L1-norm, the traditional drawbacks such as the strict convexity problem of objective function and the convergence problem of traditional non-convex regularization approach (e.g., Lp-Norm (0 <; p <; 1) and reweighted L2-/L1-norm) can be addressed. Furthermore, the solution of the I-NCRA model is derived by ADMM technique; meanwhile, the strict convexity and convergence of the proposed objective cost model are also provided. Last, the diagnostic results of simulation experiment, practical rolling bearing, and gearbox experiments indicate that the proposed method is superior to the L1-norm fused lasso algorithm and the traditional spectral kurtogram method in weak fault feature extraction.