Generalized gaussian noise distribution enabled sparse representation model for bearing fault diagnosis

Sparse representation (SR) theory gets great development in recent years for bearing fault diagnosis. Many scholars focus on constructing proper regularization terms, while few of them notice that the noise assumption is also quite important. Because in the actual engineering signal, the noise does not necessarily obey a single Gaussian distribution, while it is usually assumed so in the traditional SR model. Therefore in this paper, we propose a new SR model, which fits the noise in signal with a generalized Gaussian distribution (0 ≤q ≤2) and also assumes the coefficient obeys a hyper-Laplacian distribution (0 ≤ p ≤ 1). Thus this new SR model is marked as a generalized Gaussian noise distribution enabled the sparse representation model (GGSR). It has a flexible form because the parameters q and p can be adjusted to fit the true noise and coefficient distributions. Then the solving algorithm of the model is also developed based on the ADMM algorithm. Finally, the denoising performance of GGSR is verified by a series of simulation and engineering experiments. It shows that the GGSR model is effective in extracting impulses from the noisy signal.