Hierarchical hyper-Laplacian prior for weak fault feature enhancement

Sparsity-assisted methods are one of the most effective fault feature extraction methods which have been widely studied recently. However, no one has explained or discussed the choice of a suitable sparse prior from the perspective of the probability theory. In this paper, we define a hierarchical hyper-Laplacian prior induced model (HHLP) through maximizing the posterior probability for bearing fault diagnosis. In the proposed model, we conclude that the hyper-Laplacian prior can better model coefficients of fault feature than the Laplacian prior. Furthermore, we introduce a hierarchical hyper-Laplacian prior which embeds the physical characteristics to discriminate the harmonic interference. The main insight of this paper is that we provide a new way to model the sparse prior from the perspective of maximizing the posterior probability. Numerical simulations and an experimental application are performed to demonstrate performance of HHLP. Meanwhile, comparisons with the kurtosis based weighted sparse model, the generalized minimax-concave regularization inducing model, and the spectral kurtosis also verify the effectiveness of HHLP.