一种基于Bayes方法的随机模型修正方法

摘要

A new method for stochastic model updating was proposed to estimate the statistical in-formation of the structural parameters.According to the principle of Bayesian method,the parameters'mean value and variance to be estimated were regarded as random variables and the likelihood functions were constructed by using kernel density estimation method.The posterior distribution of the parameters were calculated by utilizing the population-based MCMC simulation method and then the parameters'mean value and variance could be obtained based on MAP (max-imum a posterior)principle.A surrogate model based on Kriging method was established,which greatly saved the computational cost.Numerical example demonstrated the effectiveness of the method.%提出了一种随机模型的修正方法用以估计结构参数的统计特性.基于Bayes方法的参数估计原理,将需要修正的结构参数的均值和方差看作符合一定先验概率分布的随机变量,根据核密度估计原理构建得到似然函数,进而使用基于差分进化的MCMC方法估计参数的后验概率密度,并根据最大后验概率密度准则估计结构参数的均值和方差.同时使用Kriging方法建立了结构输入和输出之间的代理模型,保证计算精度的同时极大地节约了计算时间.数值算例验证了本方法的可行性.