基于贝叶斯理论嵌套抽样的结构物理参数识别研究  

Structural physical parameter identification based on Bayesian theory and nested sampling

作　　者：王坤阳 公茂盛[1] 左占宣[1] WANG Kunyang;GONG Maosheng;ZUO Zhanxuan(CEA Key Lab of Earthquake Engineering and Engineering Vibration,Institute of Engineering Mechanics,China Earthquake Administration(CEA),Harbin 150080,China)

机构地区：[1]中国地震局工程力学研究所,中国地震局地震工程与工程振动重点实验室,哈尔滨150080

出　　处：《振动与冲击》2022年第7期74-80,共7页Journal of Vibration and Shock

基　　金：国家重点研发计划课题(2017YFC1500601);国家自然科学基金项目(51678541,51708523);国家科技重点研发计划课题省级资助项目(GX18C005);黑龙江省头雁计划。

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。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。采用该方法分别对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,并与试验现象进行了对比。结果表明,该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,同时也验证了该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。In identification of structural physical parameters based on Bayesian estimation,the traditional Markov chain Monte Carlo(MCMC) sampling often has problems of low sampling efficiency and non-convergence when solving the high-dimensional joint probability density function problem.Here,the nested sampling method was used to replace the traditional MCMC sampling,and solve the high-dimensional posterior joint probability density function problem in structural physical parameter identification.Firstly,starting from time histories of structural acceleration response,the posterior joint probability density function was established,and then the prior distribution and likelihood function of structural parameters were redefined to realize structural physical parameters identification based on nested sampling.Using the proposed method,the numerical model of a 10-story shear structure and the shaking table test model of a 3-story RC frame structure were identified to obtain structural stiffness and damping ratio,respectively.These obtained parameters were compared with those measured in tests.The results showed that the proposed method can solve the high-dimensional posterior joint probability density function problem in Bayesian formula,and effectively identify structural physical parameters;the applicability and reliability of the proposed method in real structural physical parameter identification and structural damage identification are also verified.

关 键 词：结构物理参数识别 贝叶斯估计 嵌套抽样 振动台试验 结构损伤识别 

分 类 号：TU311.3[建筑科学—结构工程]