Research on Generalized Smooth Logarithm Regularization Sparse Decomposition Method and Its Application in Compound Fault Diagnosis of Gearbox

Gearbox is prone to failure due to their complex working conditions and harsh working environment, and the vibration signal often contains multiple components and is accompanied by strong background noise, which brings great difficulties to gearbox fault diagnosis. The sparse decomposition method can effectively extract transient feature components under strong background noise.In view of the problems of traditional sparse decomposition methods that low computational efficiency, underestimation of amplitude,and insufficient estimation accuracy, a generalized smoothing logarithmic regularization sparse decomposition method based on Tunable Q-factor wavelet transform（TQWT） as a sparse representation dictionary is proposed. This method studies the TQWT that satisfies the tight frame condition to construct a sparse representation dictionary, and then proposes a generalized smooth logarithmic regularization method based on the Moreau envelope smoothing idea, which can accurately reconstruct the transient components of the gearbox fault and maintain the amplitude and finally uses the forward-backward splitting（FBS） algorithm to accurately solve the sparse representation model. The simulation signal and the experimental signal verify the effectiveness of the proposed method in the gearbox compound fault diagnosis.