结构物理参数识别的贝叶斯估计马尔可夫蒙特卡罗方法

李小华;谢礼立;公茂盛

振动与冲击 ›› 2010, Vol. 29 ›› Issue (4) : 59-63.

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振动与冲击 ›› 2010, Vol. 29 ›› Issue (4) : 59-63.
论文

结构物理参数识别的贝叶斯估计马尔可夫蒙特卡罗方法

  • 李小华;谢礼立;公茂盛
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STRUCTURAL PHYSICAL PARAMETER IDENTIFICATION USING BAYESIAN ESTIMATION WITH MARKOV CHAIN MONTE CARLO METHODS

  • Li Xiaohua;Xie Lili;Gong Maosheng
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摘要



从结构动力特征方程出发,以结构主模态参数为观测量,推得结构物理参数线性回归模型。对该模型应用贝叶斯估计理论得到物理参数后验联合分布,再结合马尔可夫蒙特卡罗抽样方法给出各个物理参数的边缘概率分布和最优估计值,而提出了基于结构主模态参数的结构物理参数识别贝叶斯估计马尔可夫蒙特卡罗方法。对五层剪切型结构的数值研究表明,此方法能够利用少数主模态参数给出结构质量和刚度参数的概率分布和最优识别值,而且在主模态参数较准确时识别误差很小。




Abstract

The linear regression models of the physical parameters of structures whose variables are the modal parameters of dominant modes are inferred from the dynamic characteristic equations of structure. Based on these models, Bayesian statistics theory is used to obtain the posterior joint probability density function (PDF) of structural physical parameters, from which the marginal PDF and optimal estimate of the physical parameters are obtained with the Markov Chain Monte Carlo (MCMC) methods. The theoretical analysis and numerical simulation of 5DOF shear building show that the approach presented can not only give the optimal estimate and associated plausibility of the physical parameters using modal data of few primary modes but also get high identification accuracy with relatively exact modal parameters used.

关键词

物理参数识别 / 贝叶斯估计 / 马尔可夫蒙特卡罗方法 / 模态参数

Key words

physical parameter identification / Bayesian estimation / Markov Chain Monte Carlo methods / modal parameters

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导出引用
李小华;谢礼立;公茂盛. 结构物理参数识别的贝叶斯估计马尔可夫蒙特卡罗方法[J]. 振动与冲击, 2010, 29(4): 59-63
Li Xiaohua;Xie Lili;Gong Maosheng. STRUCTURAL PHYSICAL PARAMETER IDENTIFICATION USING BAYESIAN ESTIMATION WITH MARKOV CHAIN MONTE CARLO METHODS[J]. Journal of Vibration and Shock, 2010, 29(4): 59-63

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