一种基于Bayes方法的随机模型修正方法  

Stochastic model updating based on Bayesian method

作　　者：马天政[1] 吕昊[1] 张义民[1] 

机构地区：[1]东北大学机械工程与自动化学院,辽宁沈阳110819

出　　处：《工程设计学报》2016年第3期206-211,共6页Chinese Journal of Engineering Design

基　　金：国家自然科学基金重点资助项目(51135003);国家自然科学基金资助项目(U1234208);国家重点基础研究发展计划(973计划)项目(2014CB046303);中央高校基本科研业务费资助项目(02090022115014);"高档数控机床与基础制造装备"科技重大专项课题(2013ZX04011011)

摘　　要：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.A new method for stochastic model updating was proposed to estimate the statistical information 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（maximum 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.

关 键 词：随机模型修正 Kriging代理模型 BAYES方法 MCMC抽样 

分 类 号：O327[理学—一般力学与力学基础] TU311[理学—力学]