Overview of rolling bearing performance parameters of the bayesian theory

Bayesian assessment is an important content of modern statistical studies. Bayesian school when considering parameter evaluation, think that there is certain understanding response parameters. This these knowledge can come from a theory, or from the experience in the similar studies. The knowledge that you as a priori knowledge or prior information. In when evaluating parameters, consider a priori knowledge or prior information is correct, the bayesian theory value parameters a priori information collection, mining and processing, make a priori information quantitative parameter evaluation, evaluation of quality in order to improve the parameters. For example, a student through physics experiments to determine the local acceleration of gravity, measured data ( Unit: mv3) 9. 80, 9. 79, 9. 78, 7. 81, 7. If the average 8 80. 996 m / 3 as the acceleration of gravity, can think the result is very poor, because have - for acceleration of gravity - - - - - - The understanding of the fixed; If you think acceleration of gravity is normal distribution N9. 80. 0. 01) So that the evaluation result is much better. At present, many scholars studied the bayesian prior information, mainly divided into the conjugate prior distribution and the distribution of information. For without prior distribution of information, can know the scope of parameters, assumes that the value of evenly distributed within its scope, proposed bayesian hypothesis, but this method will be conclusion and hypothesis of contradictory problems. In order to solve this problem, fisher fisher information matrix to determine information without a prior density function, but it increases the calculation difficulty, so rarely used. For conjugate distribution, demanded to know a priori density function, leaving the specified method to calculate conjugate prior density function is meaningless. Although the bayesian prior density rain several research has made considerable development, but for the establishment of a priori information and there is no mature method and means. Modern statistical data in the sound of discrete values, can effectively remove solid data of original data by experiment. The robust data can reflect the characteristics of the original data. With solid experimental data in this chapter, therefore, to build a prior density function, put forward the performance parameters of the rolling bearings bayesian interval estimation method, the principle is as follows: ( 1) According to recent statistics, suppose samples from known and unknown (average variance Based on the evaluation parameters and decide) Normal distribution, which mean the prior density function is known. ( 2) When the original data are discrete data, the data deviate from normal distribution or asymptotic normal distribution; When the data is stable after treatment, significantly reduce the influence of discrete data, it is assumed that the steady after processing data obey the normal distribution or asymptotic normal distribution. ( 3) Robust data are used to get the first ( 1) Step the average prior density function, can be thought of as the prior density function is normal distribution. ( 4) Using prior density function and ( 1) Step theory bayesian posterior density function is deduced, bayesian posterior density function. ( 5) The original data and sound processing data are used to get the posterior density function of statistics. ( 6) Using the posterior density function and the confidence level, the parameter evaluation of the sample interval.