Rolling bearing bayesian interval performance evaluation

Rolling bearing performance of bayesian interval evaluation: 1. Rolling bearing point estimation performance in rolling bearing performance point estimation, hypothesis estimated parameters for the day, an estimator of unknown parameters theta can remember to theta ( X1, X2,。 ,Xn) ( 8 - 1) Corresponds to a rolling bearing performance of the experimental value ( X1, X2,。 ,Xn) , there is a point estimates, remember to theta ( X1，X2,. ,Xn) ( 8 - 2) A point estimator can give a definite quantity, if the performance of a rolling bearing is the experimental data, according to the point estimator can get a rolling bearing performance data point estimates of the parameters. Give only a data, however, is not enough, because of the rolling bearing performance experimental data is only the sample approximation, then the point estimation is the performance parameters of the rolling bearing approximation. Therefore, there should be an estimate of the range and accuracy. To make up for the point estimation in this respect, the interval estimation of rolling bearing performance parameters can be used. 2. Rolling bearing performance interval estimation hypothesis for rolling bearing performance of distribution function F ( X; θ) Estimator, theta to stay, XI, X2,. , Xn is overall a sample, if there are two statistics: theta. 1 = 1 (theta X1, X2,。 。 。 Xn) ( 8 - 3) θ2 =θ2 ( X1, X2,。 。 。 Xn) ( 8 - 4) For a given significance level a ( 0 < < 1) , the performance parameters of the rolling bearing interval estimation: P ( @ < 0 < @) = 1 - 一个( 8 - 5) Type ( 8 - 5) For the parameter theta confidence level of 1 - A interval estimation. In bayesian assessment, the posterior density function occupies very important position. Usually, the first by a prior density function and experimental data to calculate the posterior density function, and then according to the posterior density function is obtained by bayesian assessments interval parameter theta. In view of the bayesian prior density function this - it is difficult to determine - - - - - - Problems, using the sound data in this chapter to establish bayesian prior density function, the distribution law of according to the prior density function and experimental data and the bayesian posterior density function, according to the bayesian posterior density function and the parameter interval estimation under a certain confidence level.