基于贝叶斯方法与稳健理论的滚动轴承摩擦力矩不确定度建立方法

Uncertainties establishment method of friction moment on rolling bearing based on Bayesian theory and robust theory

基于贝叶斯方法与稳健化理论,提出一种未知分布时间序列不确定度的建立方法。该方法以中位数估计与Huber M估计融合方法分析时间序列数据的稳健性,构建贝叶斯先验分布,并与实验数据建立贝叶斯后验分布,创建以贝叶斯后验分布建立时间序列数据的不确定度。在显著性水平为0~0.1,通过对滚动轴承摩擦力矩分析,中位数估计与Huber M估计相融合方法确定了滚动轴承摩擦力矩稳健数据的边界值、显著性水平,构建了贝叶斯先验分布。以贝叶斯后验分布构建滚动轴承摩擦力矩不确定度。与经典统计学得到的不确定度比较,在相同置信水平下,该方法缩短了评估区间,提高了评估精度0~50%。该融合方法以稳健数据构建先验分布,提供一种贝叶斯方法先验分布建立方法;采用中位数估计与Huber M估计融合方法确定了数据显著性水平和边界值的确定,减小置信水平与稳健数据边界值主观确定的误差;为未知分布时间序列的不确定度建立提供了一种理论。

A method on basis of Bayesian theory and robust theory was proposed to solve uncertainties of time series data on unknown distribution. The method combining with median and Huber M estimate was used to analyze robust property of time series data and establish prior distribution on Bayesian theory. Uncertainties were established by inferring from prior distribution and distribution function on time series data. At the significance level 0—0. 1 range, for studies of friction torque of rolling bearing,the method determined boundaries value and confidence level of friction torque,and established prior distribution on Bayesian theory. Compared with classic statistics, the method distinctly increased evaluation accuracy 0—50% under the same confidence level. Application significance of the method lied in taking robust data to establish prior distribution,and provide a establishment method of prior distribution on Bayesian theory;adopting the median and Huber M estimate method to determine confidence level and boundary value could reduce errors of subjective factors, and provide a theory to establish uncertainties on unknown distribution.