多链MCMC有限元模型修正收敛判定方法研究  

Convergence Determination Method for Multi-chain MCMC Finite Element Model Modification

作　　者：刘纲[1,2] 谭帅帅 邹春蓉[3] 陈奇 LIU Gang;TAN Shuaishuai;ZOU Chunrong;CHEN Qi(Key Laboratory of New Technology for Construction of Cities in Mountain Area,Chongqing University,Chongqing 400045,China;School of Civil Engineering,Chongqing University,Chongqing 400045,China;China Railway Southwest Research Institute Co.,Ltd.,Chengdu 611731,China)

机构地区：[1]重庆大学山地城镇建设与新技术教育部重点实验室,重庆400045 [2]重庆大学土木工程学院,重庆400045 [3]中铁西南科学研究院有限公司,四川成都611731

出　　处：《湖南大学学报（自然科学版）》2024年第11期85-93,共9页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(52078084)。

摘　　要：针对多链MCMC算法主要依靠设置较多迭代步以生成足量后验样本的问题,提出了算法收敛及所需后验样本数量的自动判定方法.在MCMC算法迭代初期引入最优竞争策略,通过定向差分代替原有随机差分,从而使多链样本快速向目标方向移动以提升计算效率;将当前迭代步多链带宽与预设精度指标相比较,自动判定由定向差分向随机差分的转换时机;基于抽样分布定理,采用一段区间内的样本构造t分布判定指标,对多链MCMC算法是否收敛进行自动判断,并在样本量满足统计要求后自动终止算法,以大幅减少算法平稳期的计算工作量.数值算例及实桥修正结果表明:在相同的计算精度下,所提判定方法可使多链MCMC算法燃烧期计算效率提高30%,考虑预设步长的情况下整个迭代过程可提速约50%,为基于贝叶斯的有限元模型修正在大型土木工程中的应用提供了方法支撑.An automatic determination method for the convergence and required posterior samples is proposed to address the problem that the multi-chain MCMC algorithm mainly relies on setting a large number of iteration steps to generate a sufficient number of posterior samples.The optimal competition strategy was introduced at the beginning of the MCMC algorithm iteration,replacing the random difference by the directional difference,so that the samples could be moved to the target direction quickly to accelerate the computational efficiency.Based on the sampling distribution theorem,a t-distribution determination index was constructed using samples within a period of time to automatically determine whether the multi-chain MCMC converged and automatically terminated the algorithm after the sample size meets the statistical requirements,so as to reduce the computational workload of the smooth period.The numerical examples and the results of the real bridge correction show that the proposed determination method can improve the computational efficiency of the multi-chain MCMC algorithm by 30%with the same calculation accuracy,and the entire iteration process can be accelerated by about 50%considering the preset step size,which provides a method to support the application of Bayesian-based finite element model correction in large civil engineering.

关 键 词：建筑结构 有限元模型修正 贝叶斯估计 马尔可夫链 判别指标 

分 类 号：TU311[建筑科学—结构工程]