斜拉桥系统地震易损性评估的Pair Copula技术

大跨度斜拉桥作为高次超静定结构，通常包含主塔、斜拉索、主梁、辅助墩及连接墩等较多构件，由于地震作用下各构件相互影响，准确模拟构件地震响应之间的相关性对斜拉桥整体系统的易损性评估十分关键。因Pair Copula能较好地模拟构件两两之间的相关性，理论上可将Pair Copula分层迭代模拟斜拉桥整体系统，进而提出基于Pair Copula迭代模型的斜拉桥系统地震易损性评估方法。基于结构不确定性参数及地震动不确定性，采用拉丁超立方抽样技术建立桥梁-地震动概率地震响应分析样本；通过非线性动力时程及相关性分析，量化构件地震响应之间的相关性；采用极大似然估计拟合Pair Copula模型，基于AIC及BIC准则对其进行优选；通过Pair Copula分层迭代，建立斜拉桥整体模型并对其进行地震易损性评估。工程实例表明，基于Pair Copula分层迭代技术能准确模拟多构件之间的相关性，假定构件地震响应完全不相关，会显著高估斜拉桥整体系统的地震易损性。

PAIR COPULA TECHNIQUE OF SEISMIC VULNERABILITY ASSESSMENT OF CABLE-STAYED BRIDGE SYSTEM

As a high-order statically indeterminate structure, long-span cable-stayed bridges usually consist of many components such as main towers, stay cables, main beams, auxiliary piers, and connecting piers. Due to the mutual influence between components under earthquakes, the accurate simulations of the correlations among component seismic responses are critical to the vulnerability assessment of the overall system of a cable-stayed bridge. Pair Copula can simulate the correlation between two components. It is theoretically feasible to use Pair Copula in a hierarchically iterated way to simulate the whole system of a cable-stayed bridge. Therefore, a new seismic vulnerability assessment method of a cable-stayed bridge system is proposed based on Pair Copula iterative model. Based on structural uncertainty parameters and ground motion uncertainty, Latin hypercube sampling technique is used to establish bridge-ground motion probabilistic seismic response analysis samples. The correlations among the seismic responses of components are quantified through nonlinear dynamic time history and correlation analysis. Pair Copula models are fitted with maximum likelihood estimation and optimized based on AIC and BIC criteria. Through the hierarchical iteration of Pair Copulas, the overall model of a cable-stayed bridge is established, and its seismic vulnerability is evaluated. The engineering example shows that the correlation among multiple components can be accurately simulated based on the technology of hierarchical iteration of Pair Copula. With the assumption that the seismic responses of components are completely unrelated, the seismic vulnerability of a whole cable-stayed bridge system will be significantly overestimated.