Research on multi-source sparse optimization method and its application on gearbox compound fault detection

In general, gearbox is prone to occur compound fault frequently because of its harsh working environment, its fault vibration signal often contains polymorphic-oscillatory components and is corrupted by heavy background noise, which brings great difficulty to diagnose fault. Sparse decomposition is often utilized to extract weak fault feature among heavy background noise. In order to solve the problems of traditional sparse decomposition method, such as lacking signal fidelity, causing local optimal solution by using the non-convex objective function, and presenting poor universality, a multi-source sparse optimization objective function with convexity is constructed based on the generalized mini-max concave penalty function. By using forward–backward splitting algorithm combination with Laplace wavelet dictionary, Morlet wavelet dictionary and DFT dictionary, the sparse coefficients corresponding to polymorphic-oscillatory components can be computed efficiently and each oscillatory component can be extracted accurately. Finally, simulation and experimental signal validate that the proposed method can decompose fault signal according to oscillatory property and diagnose gearbox compound fault without the prior knowledge of specific fault numbers.