Evaluation Of Statistical Moments For Bayesian Updated System And Its Application

Point Estimate Method(PEM),one of approaches of the stochastic system analysis,is a simple and effective method for its briefness and efficiency.The precision and efficiency in the process of calculation are two indexes which evaluate the strength and weakness of Point Estimate Method(PEM).By the means of theoretical derivation,numerical analysis and simulation,this paper will do some research on efficient Bayes updating of system and efficient evaluation of statistical moments.Firstly,the predictive distribution is an important component in Bayesian updating.Even though there are many methods for predictive distribution,some disadvantages still exists.This paper proposes a new method for obtaining the predictive distribution,which is very easy to implement.Firstly,a series of samples from the posterior PDF is obtained based on the prior PDF of the parameter and observing samples of random variable,in which MCMC method is exploited.Then the samples of predictive distribution can be obtained by the Rosenblatt transformation,and the predictive distribution of random variable can be approximated by the generalized unified probability plot,which different assumptions distribution can be compared.Without calculating the explicit solution of the posterior PDF and with the merits of obtaining the approximate explicit solution of predictive distribution,the proposed method is of wide applicability,high efficiency and easy implementation.Lastly,the accuracy and rationality of this method are verified by examples.Secondly,it considers the Bayesian updated system as a new random system in the process of calculating statistical moments which can work out with two ways: Four Order Moments Methods based on Taylor and Point Estimate Method based on dimension-reduction,although there is a certain correlation between Bayesian updated system and former system.In order to develop evaluation statistical moments of the Bayesian updated system,this paper uses two methods: the first one is based on Taylor,and the second one is based on adaptive estimation of statistical moments.Then the two methods are used to calculate statistical moments of response function through some examples.Finally,the effectiveness and rationality are verified by the comparison of two methods.Finally,focusing on two actual service projects:double column suspension cable tower structure and space grid structure,this paper conducts two analysis: finite element analysis of ANSYS and Matlab numerical analysis.Then,a simple and reasonable distribution model for the prediction distribution of the basic random variable is established by using the Rosenblatt transform and the generalized unified probability plot.Lastly,it can get statistical moments of response function by using two proposed methods:the first one is evaluation statistical moments of Bayesian updated system based on adaptive dimension-reduction and the second one is evaluation statistical moments of Bayesian updated system based on Taylor.The calculating results verify that the two proposed methods are effective,practical and reasonable.At the same time,these two methods enriches the theoretical system of reliability analysis and can be used as reference methods of reliability analysis in the future.