基于凸集模型的结构地震多维易损性分析

Structure seismic multidimensional fragility analysis based on convex set model

将凸集模型应用于结构的地震多维易损性分析。建立钢筋混凝土框架结构模型,选择最大层间位移角和最大层加速度两种参数建立多维性能极限状态方程。通过平均信息熵理论,获得两种参数的区间估计。考虑椭球模型和区间模型两种形式的凸集模型,在标准空间内通过拉丁超立方抽样生成样本点,通过矩阵变换将其映射到凸集空间内,建立结构地震响应的凸集模型。将凸集变量样本点代入极限状态方程,进行了易损性分析。采用概率模型进行对比计算,研究表明,与概率模型相比,当PGA较小时,凸集模型的破坏概率较大,而PGA较大时,凸集模型的破坏概率较小;椭球模型和凸集模型的分析结果差距较小,在各个PGA下破坏概率差值仅为0.05~0.1,因此可以不考虑凸集类型不同对易损性分析结果的差异。

The convex set model is applied to the multi-dimensional seismic fragility analysis.An RC frame structure model is established,the maximum layer displacement angle and maximum layer acceleration are selected to establish the multi-dimensional performance limit state equation.Based on the average information entropy theory,the interval estimation of the two parameters is obtained.Considering the ellipsoid model and the interval model,the sample points are generated by Latin hypercube sampling in the standard space,and they are then mapped into the convex set space by matrix transformation to establish a convex set model.The convex set variable sample points are substituted into the limit state equation,and the fragility analysis is performed.The probabilistic models is used for comparison calculations.The research shows that compared with the probability model,when PGA is small,the probability of failure of the convex set model is large,and when PGA is large,the damage probability of the convex set model is small;The difference between the analysis results of the ellipsoid model and the convex set model is small,and the difference between the failure probability under each PGA is only 0.05~0.1.So the difference of different convex set types can be ignored.