Abstract: Gearbox is prone to compound fault because of its harsh working environment. The fault vibration signal of gearbox often contains multiple components and is corrupted by heavy background noise, which brings great difficulties to gearbox fault diagnosis. Weak fault features corrupted by heavy background noise can be effectively extracted through sparse decomposition. In order to solve the problems of traditional sparse decomposition method, such as the lack of signal fidelity, the local optimal solution caused by the non-convex objective function, and the poor universality of the model, a multi-source sparse optimization objective function with convexity is constructed based on the generalized minimax concave penalty function. Then the sparse coefficients of bearing transient components, gear transient components and harmonic components are calculated respectively based on Laplace wavelet dictionary, Morlet wavelet dictionary and DFT dictionary using forward backward splitting algorithm. Finally, each component can be extracted based on these sparse coefficients. The analysis of simulation signal and experimental signal verify that the proposed model can realize the accurate decomposition of compound fault signal and compound fault diagnosis of gearbox without the prior knowledge of specific number of faults.

Key words: gearbox, compound fault diagnosis, sparse decomposition, convex optimization