一种基于改进MCMC算法的模型修正方法

彭珍瑞,郑捷,白钰,殷红

振动与冲击 ›› 2020, Vol. 39 ›› Issue (4) : 236-245.

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PDF(3478 KB)
振动与冲击 ›› 2020, Vol. 39 ›› Issue (4) : 236-245.
论文

一种基于改进MCMC算法的模型修正方法

  • 彭珍瑞,郑捷,白钰,殷红
作者信息 +

A model updating method based on an improved MCMC algorithm

  • PENG Zhenrui,ZHENG Jie,BAI Yu,YIN Hong
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文章历史 +

摘要

标准马尔可夫链蒙特卡罗(MCMC)算法不易收敛、拒绝率高,使其应用受到限制。在贝叶斯方法中引入最大熵值法来估计参数的后验概率密度函数最大值,进而将布谷鸟算法中新鸟巢更新的思想融入Metropolis-Hasting(MH)抽样算法得到改进的MH抽样算法,同时使用支持向量机(SVM)建立待修正参数与有限元模型输出之间的代理模型,以提高模型修正的计算效率。分别使用三自由度线性系统和平面桁架模型来验证本文方法的有效性,结果表明:修正后样本的马尔可夫链混合性能好,停滞概率低,修正后参数相对误差均小于2%。

Abstract

The standard Markov Chain Monte Carlo (MCMC) algorithm is not easy to converge and the rejection rate is high, which limits its application.The maximum entropy method was introduced into the Bayesian method to estimate the maximum value of the posterior probability density function of the parameters, and then the updating idea of new bird nest in the cuckoo algorithm was integrated into the Metropolis-Hasting (MH) sampling algorithm to obtain an improved MH sampling algorithm.Meanwhile, support vector machine (SVM) was used to establish the surrogate model between the parameters to be updated and the output of the finite element model to improve the computational efficiency of model updating.A linear system with three degrees of freedom (DOFs) and a plane truss model were used to verify the effectiveness of the proposed method.The results show that the Markov chain of the updated sample has better mixing performance, and low stagnation probability, and the relative error of the updated parameters is less than 2%.

关键词

模型修正 / 贝叶斯估计 / 支持向量机(SVM) / 马尔可夫链蒙特卡罗(MCMC)算法 / 布谷鸟算法

Key words

model updating / Bayesian estimates / support vector machine (SVM) / Markov Chain Monte Carlo(MCMC)algorithm / cuckoo algorithm

引用本文

导出引用
彭珍瑞,郑捷,白钰,殷红. 一种基于改进MCMC算法的模型修正方法[J]. 振动与冲击, 2020, 39(4): 236-245
PENG Zhenrui,ZHENG Jie,BAI Yu,YIN Hong. A model updating method based on an improved MCMC algorithm[J]. Journal of Vibration and Shock, 2020, 39(4): 236-245

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