考虑结构极限状态随机性的多维易损性分析

本文同时考虑结构在地震激励下响应的随机性和极限状态的随机性,将概率-凸集混合模型应用于结构的多维易损性分析。以最大层间位移、最大层加速度作为反映结构性能和非结构性能的两种工程需求参数,并视为符合对数正态分布的随机变量,两种需求参数的阈值被视为非概率凸集变量,分别建立阈值的椭球模型和区间模型,建立同时包含凸集变量和概率变量的二维联合性能极限状态方程;根据凸集模型和概率模型之间的相容性,提出一种混合模型下基于克里金模型的蒙特卡洛法用于求解超越概率的上、下界,得到反映超越概率区间的易损性曲线。研究表明:区间模型建立的易损性曲线较为保守;在罕遇地震作用下,不考虑阈值随机性会会低估结构的抗震能力。

Multidimensional fragility analysis considering the randomness of structural limit state

In this paper,the stochasticity of the response of the structure and the randomness of the limit state under earthquake are considered and the seismic-convex set model is applied to the fragility analysis of structure.The maximum inter-layer displacement and the maximum layer acceleration are used as two engineering demand parameters reflecting structural performance and non-structural performance,and both are treated as random variables that conform to the lognormal distribution.The thresholds of the two demand parameters are treated as convex variables.The threshold ellipsoid model and interval model are established respectively,and a two-dimensional joint limit state equation with both convex set variables and probability variables is established.According to the compatibility between the convex set model and the probabilistic model,a Monte Carlo method based on Kriging model is proposed to calculate the upper and lower bounds of the failure probability,and the fragility curve that reflects the upper and lower bounds of the failure probability is obtained.The research shows that the fragility curve established by the interval model is conservative.Without considering threshold randomness will underestimate the seismic capacity of the structure.