Non-convex group sparse regularization method for local fault detection of spiral bevel gear

Local fault is a common failure mode in spiral bevel gear transmission system. However, the periodical impulses indicating faults are usually submerged in background noise and interferences. This paper provides a non-convex group sparse regularization method for local fault diagnosis of spiral bevel gears via ℓ_p regularization. The periodical sparsity within and across groups (SWAG) property of the fault impulses is introduced as prior to construct penalty term. The non-convex ℓ_p sparse regularization is utilized to constraint SWAG to further highlight the sparsity. Additionally, a weight factor with ℓ₂-norm of the periodic impulse groups is constructed to suppress underestimation of high-amplitude components in reconstructed fault features. To solve the optimization problem, an iterative algorithm is deducted using the majorization-minimization framework. Finally, simulated and experimental signals are analyzed to confirm the effectiveness of the proposed method. The results demonstrate that the proposed method can effectively extract and enhance pitting fault features. The proposed method outperforms the comparative methods in terms of extracting and enhancing fault features.