A general sequential Monte Carlo method based optimal wavelet filter : A Bayesian approach for extracting bearing fault features

A general sequential Monte Carlo method, particularly a general particle filter, attracts much attention in prognostics recently because it is able to on-line estimate posterior probability density functions of the state functions used in a state space model without making restrictive assumptions. In this paper, the general particle filter is introduced to optimize a wavelet filter for extracting bearing fault features. The major innovation of this paper is that a joint posterior probability density function of wavelet parameters is represented by a set of random particles with their associated weights, which is seldom reported. Once the joint posterior probability density function of wavelet parameters is derived, the approximately optimal center frequency and bandwidth can be determined and be used to perform an optimal wavelet filtering for extracting bearing fault features. Two case studies are investigated to illustrate the effectiveness of the proposed method. The results show that the proposed method provides a Bayesian approach to extract bearing fault features. Additionally, the proposed method can be generalized by using different wavelet functions and metrics and be applied more widely to any other situation in which the optimal wavelet filtering is required.