基于马尔可夫链蒙特卡洛的地震易损性函数贝叶斯更新方法

BAYESIAN UPDATING OF SEISMIC FRAGILITY FUNCTIONS BASED ON MARKOV CHAIN MONTE CARLO

  • 摘要: 地震易损性函数是度量结构概率抗震性能的重要工具,其准确性会影响震灾风险评估和减灾对策。贝叶斯理论依据震害或试验等观测数据能提高易损性函数的精度。然而,当前计算易损性函数参数后验估计的数值方法缺乏具体的步骤和明确的参数设置。本文系统阐述了采用马尔科夫链蒙特卡洛模拟计算参数的后验估计,实现地震易损性函数贝叶斯更新的方法。首先介绍了地震易损性函数及其参数;其次,阐述了易损性函数贝叶斯更新理论,包括先验分布、似然函数和后验分布;然后给出采用马尔可夫链蒙特卡洛模拟,计算易损性函数参数贝叶斯后验估计的具体步骤及采样策略;最后利用足尺振动台试验观测数据,阐述了使用该方法修正多层钢框架结构易损性函数的实施过程,并分析了易损性函数参数的更新效果。结果表明:采用马尔可夫链蒙特卡洛计算贝叶斯后验估计来修正易损性函数的两个参数是有效的,中位值的更新效果显著,本例最高达35%,而对数标准差的更新效果不明显。观测数据中超过某个极限状态的证据越多,对该状态易损性函数贝叶斯更新后验估计的置信度越高。本文的研究能为融合多源数据的结构抗震性能评估提供参考。

     

    Abstract: Seismic fragility function is an important tool for measuring the probabilistic seismic performance of structures, and its accuracy affects earthquake risk assessment and disaster reduction strategies. Bayesian method can improve the accuracy of fragility functions by incorporating observed data such as post-earthquake damage investigation or large-scale experiments. However, the current numerical methods for posterior estimation of the fragility function parameters lack specific steps and clear parameter settings. To this end, Bayesian updating method for seismic fragility functions based on Markov Chain Monte Carlo is systematically presented. Firstly, seismic fragility function and its parameters were introduced; Secondly, Bayesian updating method for fragility functions, including the prior distribution, likelihood function, and posterior distribution were elaborated. Thirdly, the specific steps and sampling strategies for calculating the Bayesian posterior estimation of the fragility function parameters using Markov Chain Monte Carlo simulation were given. Finally, the implementation process with this method to update the fragility function of a multi-story steel frame structure based on the observed data from a full-scale shaking table test were presented, including the analyses of the updating effect of the fragility function parameters. The results show that calculating the Bayesian posterior estimation with Markov Chain Monte Carlo to correct the two parameters of the fragility function is effective, and the updating effect of the median value is significant, with the highest reaching 35% in this example. However, the updating effect of the logarithmic standard deviation is not obvious. The more evidence in the observed data that exceed a certain limit state, the higher the confidence level of the posterior estimated fragility function for that state in Bayesian updating. This research can provide a reference for the assessment of structural seismic performance by integrating multiple sources of data.

     

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