A bayesian framework of computing and updating wavelet parameter distributions for identifying early bearing faults

Rolling element bearings are widely used in machines to support rotation shafts. Bearing failures may result in machine breakdown. In order to prevent bearing failures, early bearing faults are required to be identified. Wavelet analysis has proven to be an effective method for extracting early bearing fault features. Proper selection of wavelet parameters is crucial to wavelet analysis. In this paper, a Bayesian framework is proposed to compute and update wavelet parameter distributions. First, a smoothness index is used as the objective function because it has specific upper and lower bounds. Second, a general sequential Monte Carlo method is introduced to analytically derive the joint posterior probability density function of wavelet parameters. Last, approximately optimal wavelet parameters are inferred from the joint posterior probability density function. Simulated and real case studies are investigated to demonstrate that the proposed framework is effective in extracting early bearing fault features.