Within the performance-based earthquake engineering (PBEE) framework, the fragility model plays a pivotal role. Such a model represents the probability that the engineering demand parameter (EDP) exceeds a certain safety threshold given a set of selected intensity measures (IMs) that characterize the earthquake load. The-state-of-the art methods for fragility computation rely on full non-linear time-history analyses. Within this perimeter, there are two main approaches: the first relies on the selection and scaling of recorded ground motions; the second, based on random vibration theory, characterizes the seismic input with a parametric stochastic ground motion model (SGMM). The latter case has the great advantage that the problem of seismic risk analysis is framed as a forward uncertainty quantification problem. However, running classical full-scale Monte Carlo simulations is intractable because of the prohibitive computational cost of typical finite element models. Therefore, it is of great interest to define fragility models that link an EDP of interest with the SGMM parameters -- which are regarded as IMs in this context. The computation of such fragility models is a challenge on its own and, despite few recent studies, there is still an important research gap in this domain. This study tackles this computational challenge by using stochastic polynomial chaos expansions to represent the statistical dependence of EDP on IMs. More precisely, this surrogate model estimates the full conditional probability distribution of EDP conditioned on IMs. We compare the proposed approach with some state-of-the-art methods in two case studies. The numerical results show that the new method prevails its competitors in estimating both the conditional distribution and the fragility functions.

翻译：在基于性能的抗震工程（PBEE）框架中，易损性模型起着关键作用。该模型表征了在给定一组表征地震荷载的选定强度指标（IMs）条件下，工程需求参数（EDP）超过特定安全阈值的概率。当前主流的易损性计算方法依赖于完整的非线性时程分析。在此框架内主要有两种方法：第一种依赖于记录地震动的选取与调幅；第二种基于随机振动理论，采用参数化随机地震动模型（SGMM）刻画地震输入。后者的显著优势在于将地震风险分析问题转化为正向不确定性量化问题。然而，由于典型有限元模型的计算成本过高，传统全尺度蒙特卡洛模拟难以实现。因此，建立将目标EDP与SGMM参数（在此上下文中视为IMs）相关联的易损性模型具有重要价值。此类易损性模型的计算本身即是一项挑战，尽管已有少量近期研究，该领域仍存在重大研究空白。本研究通过采用随机多项式混沌展开来表征EDP对IMs的统计依赖性，以应对这一计算挑战。更准确地说，该代理模型估算了给定IMs条件下EDP的完整条件概率分布。我们通过两个案例研究将所提方法与若干主流方法进行了比较。数值结果表明，新方法在估计条件分布和易损性函数方面均优于其竞争对手。