Bearing fault diagnosis via generalized logarithm sparse regularization

Bearing fault is the most common causes of rotating machinery failure. Therefore, accurate bearing fault identification technique is of tremendous significance. Vibration monitoring has been used widely and the key is to reconstruct the fault shock components from monitoring signals with noise. Sparse representation is proved to be a promising method to extract the repetitive transient component from noisy signals. However, common sparse representation methods suffer from the shortcomings of insufficient reconstruction accuracy or the underestimation of amplitude. To overcome these drawbacks, we proposed a new non-convex penalty called generalized logarithm(G-log) penalty, which enhances the sparsity and reduces noise disturbance. Although the proposed penalty is not convex itself, the cost function of sparse representation is preserved to be convex by parameter setting, hence the convex optimization algorithms are capable of being applied to obtain the global minimum. In addition, the k-sparsity method is used to decide the regularization parameter adaptively. Simulation and experiments verify that the proposed G-log method performs well in bearing fault diagnosis and generates more reconstruction accuracy compared to other sparse representation methods.