藤 Copula 函数与 MC 方法在桥梁地震易损性分析中的联合应用

考虑到地震作用下桥梁各个构件间的相互影响, 构件间相关性的模拟对系统易损性的分析尤为重要。针对传统蒙特卡洛(Monte Carlo, MC)方法计算桥梁系统地震易损性的不足及藤 Copula 函数可将高维 Copula 分解为若干二元 Copula 以简化计算的优点, 引入藤 Copula 函数替代 MC 方法中构件间联合概率分布函数。文章基于某异形桥塔斜拉桥工程实例, 考虑了结构不确定性参数, 采用拉丁超立方技术对其分层抽样建立了桥梁-地震动样本; 通过增量动力分析(incremental dynamic analysis, IDA)建立构件概率地震需求模型, 得到了样本值的均值与回归残差; 使用藤 Copula 函数拟合回归残差之间的相关关系, 并采用 MC 抽样技术结合抗震模型即可对桥梁整体进行易损性评估。结果表明, 引入藤 Copula 函数的 MC 方法能准确模拟构件间的相关关系, 验证了所构建模型的可行性和优越性。

Considering the interaction of various components of the bridge under the action of earthquake, the simulation of the correlation between components is particularly important for the analysis of system vulnerability. In response to the shortcomings of the traditional Monte Carlo (MC) method in calculating the seismic vulnerability of bridge systems, and the advantages of the Vine Copula function in decomposing high-dimensional Copula function into several binary Copulas to simplify the calculation, the Vine Copula function is introduced to replace the joint probability distribution function between components in the MC method. Based on an engineering example of a cable-stayed bridge with special-shaped pylon considering structural uncertainty parameters, the bridge-ground motion samples are established by stratified sampling with Latin hypercube technology. A probabilistic seismic demand model (PSDM) for components is established through incremental dynamic analysis (IDA), and the mean and regression residuals of the sample values are obtained. The correlation between the regression residuals is fitted using the Vine Copula function, and the vulnerability assessment of the bridge is performed by using MC sampling technology combined with seismic modeling. The analysis results show that the MC method incorporating the Vine Copula function can accurately