Dynamical Bayesian Significance Testing for Information on Performance Variation of Rolling Bearing for Space Applications

Abstract

A dynamical Bayesian significance testing method is proposed to examine information on performance variation of rolling bearings for space applications under the condition of an unknown probability distribution and trend in advance. Sub-series of time series of rolling bearing performance are obtained via a regularly sampling, probability density functions of sub-series are acquired with bootstrap and maximum entropy theory, a referenced sequence from sub-series is found by minimum variance principle, posterior probability density function is established according to Bayesian theory, and mutation probability is defined in the light of fuzzy set theory. At the given significance level, dynamical Bayesian significance testing for information on performance variation of rolling bearings is put into effect with the help of mutation probability. Experimental investigation presents that the method proposed can effectively detect variation information of rolling bearing performance with unknown probability distributions and trends.Keywords: rolling bearing, space applications, Bayesian significance testing, information analysis, performance variation IntroducationWith the devolopment of the fields of aeronautics and astronautics, bullet trains, and alternative energy, research of rolling bearing performance has attracted much attention, with many new findings (Randall & Antoni, 2011;Oguma, 2011;Xia, 2012;Mukhopadhyay & Bhattacharya, 2011;Sinha et al., 2010). At present, studies of rolling bearing performance mainly rely on a known probability distribution and trend in advance. For example, the probability distribution of performance is considered as a normal distribution, a Weibull distribution, or a Poisson distribution; and the trend of performance is regarded as a given potential function and kernel function and wavelet basis function, and a piecewise linearized function. However, many performance indexes are required for rolling bearings, different performance indexes for different applications (Shimizu, 2012;Siegel David et al., 2012;Yasufuku et al., 2010;Soylemezoglu et al., 2010;Arakere et al., 2010). So far, failure probability distributions and degradation trends of much performance, such as friction torque, vibration, and running accuracy, still are unknown. Particularly, degradation of rolling bearing performance belongs to a non-stationary stochastic process characterized by nonlinear dynamics, which goes through three phases, early degradation phase, gradual degradation phase, and rapid degradation phase, along with a change in failure probability distributions and trends of performance (Xia, 2012a(Xia, & 2012bSinou, 2009;Ahmad et al., 2009;Xia & Chen, 2013). Thus, the rolling bearing performance analysis theory relied on prior information of probability distributions and trends encounters serious challenges, resulting in this hard problem to solve. For this end, under the condition of unknown probability distributions and trends in advance, a method for dynamical Bayesian significance testing is p...