基于自适应嵌套抽样和贝叶斯理论的桥梁有限元模型修正  

Finite Element Model Updating for Bridges Based on Adaptive Nested Sampling and Bayesian Theory

作　　者：徐希堃 洪彧[1] 许靖业 周志达 蒲黔辉[1] 文旭光 XU Xikun;HONG Yu;XU Jingye;ZHOU Zhida;PU Qianhui;WEN Xuguang(School of Civil Engineering,Southwest Jiaotong University,Chengdu 610031,China;Guangxi Key Laboratory of Inter-national Join for China-ASEAN Comprehensive Transportation,Nanning University,Nanning 530000,China)

机构地区：[1]西南交通大学土木工程学院,四川成都610031 [2]南宁学院广西中国-东盟综合交通国际联合重点实验室,广西南宁530000

出　　处：《西南交通大学学报》2025年第2期503-512,共10页Journal of Southwest Jiaotong University

基　　金：广西科技计划(AA21077011);中央高校基本科研业务费专项资金(2682022CX003)。

摘　　要：在基于有限元模型的桥梁健康监测中,贝叶斯模型修正技术通常被用于量化有限元模型中重要参数的不确定性,以解决模型修正中由于测量误差、建模误差、计算误差等造成的非唯一解问题.为解决由于大量调用有限元模拟运算,导致修正效率低下的问题,基于自适应嵌套抽样(ANS)算法,提出一种贝叶斯模型修正方法.该方法利用模态参数构建概率目标函数,并采用ANS算法对其进行逼近,ANS保留了嵌套抽样(NS)的性质,通过逐层缩小抽样范围,使得样本最终逼近最优参数;通过逐层近似,将高维积分问题转化为简单的一维积分问题,简化了证据值和后验概率密度值的计算过程;在此基础上,ANS算法在迭代过程中通过自适应地调整样本数量,减少对有限元模型的调用;最后,对一座人行桁架桥进行了贝叶斯有限元模型修正试验.结果表明:在相同算法参数设置下,ANS算法相比传统NS算法降低了约84%的有限元模拟调用次数,节省了约86%计算时间,并能获得同等精度的不确定性修正结果.In bridge health monitoring based on finite element models,Bayesian model updating techniques are commonly used to quantify the uncertainties of important parameters in the finite element models,so as to address the issue of non-uniqueness in model updating caused by measurement errors,modeling errors,computational errors,etc.To resolve the problem of low efficiency in model updating due to the large number of finite element simulations required,a Bayesian model updating method based on an adaptive nested sampling(ANS)algorithm was proposed.The method used the modal parameters to construct the probability objective function and adopted the ANS algorithm to approximate it.ANS retained the nature of nested sampling(NS),which made the samples ultimately approximate the optimal parameters by narrowing the sampling range layer by layer,and it simplified the computation process of the evidence value and the a posteriori probability density value by transforming the high-dimensional integration problem into a simple one-dimensional integration problem through layer-by-layer approximation.On this basis,the ANS algorithm could also reduce the call of the finite element model by adaptively adjusting the number of samples during the iteration process.Finally,a pedestrian truss bridge was used as a case study for Bayesian finite element model updating experiments.The results demonstrate that under the same algorithm parameter settings,the ANS algorithm reduces the number of finite element simulation calls by approximately 84%compared to the traditional NS algorithm.This leads to approximately 86%computational time savings while obtaining uncertainty updating results with equal accuracy.

关 键 词：有限元模型 贝叶斯模型修正 不确定性量化 嵌套抽样算法 自适应算法 

分 类 号：U441[建筑科学—桥梁与隧道工程]