A Nonconvex Periodic Group Sparse Regularization for Fault Diagnosis of Spiral Bevel Gear

Spiral bevel gear is one of the most important components in transmission systems. However, due to the harsh working environments, faults will generate on spiral bevel gears. And the fault features are usually submerged in the heavy noise, making it hard to perform accurate fault diagnosis. To solve this issue, a nonconvex periodic group sparse regularization is proposed for fault diagnosis of spiral bevel gears. The sparsity within and across groups is used as the prior of the fault impulses. And the minimax-concave penalty (MCP) is employed to constraint SWAG. Besides, we weighted the regularizer based on the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{2}$</tex> norm of the periodic groups to promote the ability of fault feature extraction. The majorization-minimization (MM) algorithm is used to get the solution of the proposed method. Finally, numerical simulations are carried out to validate the effectiveness of the proposed method.