基于贝叶斯理论嵌套抽样的结构物理参数识别研究

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (7) : 74-80.

论文

王坤阳，公茂盛，左占宣

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Structural physical parameter identification based on Bayesian theory and nested sampling

WANG Kunyang, GONG Maosheng, ZUO Zhanxuan

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摘要

基于贝叶斯估计的结构物理参数识别中，传统马尔可夫蒙特卡洛抽样（MCMC）在解决高维密度函数问题时往往存在抽样效率低、不收敛等问题。本文采用嵌套抽样方法代替传统的马尔可夫蒙特卡洛抽样，解决了结构物理参数识别中高维后验联合概率密度函数问题。首先从结构加速度时程响应时程出发，建立了后验联合概率密度函数，然后重新定义了结构参数先验分布与似然函数，实现了基于嵌套抽样的结构物理参数识别。采用所提方法分别对10层剪切结构数值模型与3层RC框架结构振动台试验模型进行识别，得到了结构刚度及阻尼比等参数，并与实验现象进行了对比。结果表明，所提方法可以解决贝叶斯公式高维后验联合概率密度函数问题，且能高效识别结构物理参数，同时也验证了方法在真实结构物理参数识别与结构损伤识别中的适用性与可靠性。

Abstract

In the identification of structural parameters based on Bayesian estimation, the most widely used Markov Chain Monte Carlo (MCMC) sampling often encounters the problems such as low sampling efficiency and non-convergence, especially in solving high-dimensional joint posterior function. The Nested sampling is proposed and modified to solve the high-dimensional joint posterior function problem instead of MCMC sampling in the structural parameter identification in this paper. The joint posterior function is derived from the structural acceleration response time-history firstly, and then the prior and likelihood are re-constructed to realize the sampling and identity the structural parameter. The parameters of a 10-story shear numerical building and a 3-story shaking table test structural model are identified by using the Nested sampling method, and the physical parameters such as stiffness and damping ratio obtained. The results show that the proposed method can be used to solve the high dimensional joint posterior function problem and identify the structural parameters efficiently and reliably. It is also shown that the proposed method can be used in parameter identification and damage detection for real engineering structure.

导出引用

王坤阳，公茂盛，左占宣. 基于贝叶斯理论嵌套抽样的结构物理参数识别研究[J]. 振动与冲击, 2022, 41(7): 74-80

WANG Kunyang, GONG Maosheng, ZUO Zhanxuan. Structural physical parameter identification based on Bayesian theory and nested sampling[J]. Journal of Vibration and Shock, 2022, 41(7): 74-80

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