Uncertainties in the friction moment of rolling bearings based on the Bayesian theory and robust theory

Abstract

A method combining median estimation with Huber M estimation based on robust theory is proposed to establish prior distributions for Bayesian methods, and the posterior distribution is induced according to Bayesian methods. Uncertainties in the friction moment according to the posterior distribution of the Bayesian method, which consist of the mean, confidence level and wave range of the friction moment, are used to assess the friction performance of rolling bearings. The results show that the method combining median estimation with Huber M estimation can precisely determine the confidence level of test data and reduce the effect of the artificial confidence level. The wave range and mean value of uncertainties can more effectively describe the performance characteristics of a rolling bearing than can classical methods. Thus, robust data obtained via the fusion method reduce the effect of discrete test data. The extraction of robust data from test data to constitute the prior distribution is proposed to solve established problems of the prior distribution of the Bayesian method; the method combining median estimation with Huber M estimation provides a method for establishing the prior distribution of the Bayesian method and represents a valuable application of the boundary value of the Huber M estimate in modern statistics. The proposed method provides a robust estimation technique for unknown distributions and the significance level of test data in modern statistics and provides a means for determining the confidence level in statistics. The method provides a theoretical basis for assessing the friction performance of rolling bearings.