结构抗震可靠度分析的特征函数卷积方法  

Convolution of characteristic functions for structural seismic reliability analysis

作　　者：张付泰 徐军 兰昱璁[1] ZHANG Futai;XU Jun;LAN Yucong(College of Civil Engineering,Hunan University,Changsha 410082,China;State Key Laboratory of Bridge Engineering Safety and Resilience,Hunan University,Changsha 410082,China)

机构地区：[1]湖南大学土木工程学院,长沙410082 [2]湖南大学桥梁工程安全与韧性全国重点实验室,长沙410082

出　　处：《东南大学学报(自然科学版)》2025年第1期59-65,共7页Journal of Southeast University:Natural Science Edition

基　　金：国家自然科学基金资助项目(52278178)。

摘　　要：为提高极值分布尾部的计算精度,提出了一种结构抗震可靠度分析新方法,该方法通过特征函数卷积技术实现了精度的提升。首先,利用带权重的高斯混合分布来表征极值分布,并推导了极值分布特征函数的解析表达式;结合数值计算得到的特征函数曲线,运用卷积技术高效地确定了特征函数解析表达式中所有参数,包括权重系数、均值和标准差。将这些参数回代入极值分布表达式,即可获得极值分布及其累积分布函数,进而可方便地计算结构抗震可靠度。通过数值算例,验证了所提方法在重构极值分布中的有效性;进一步与Mellin变换和广义分布重构方法进行了对比,凸显了所提方法在极值分布尾部计算精度上的优势。To enhance the accuracy of extreme value distribution tail estimation,a novel method for structural seismic reliability analysis is proposed,employing characteristic function convolution techniques to achieve improved precision.The approach starts by expressing the extreme value distribution as a weighted Gaussian mixture distribution and derives an analytical expression for its characteristic function.By applying convolu-tion techniques to the numerical characteristic function,the method efficiently estimates all parameters in the analytical expression,including weight coefficients,means,and standard deviations.These parameters are then used to reconstruct the extreme value distribution and its cumulative distribution function,allowing for the calculation of structural seismic reliability.A numerical example validates the effectiveness of the method in reconstructing extreme value distributions.Comparisons with the Mellin transform and generalized distribu-tion reconstruction methods demonstrate the superior accuracy of the proposed method in extreme value distri-bution tail estimation.

关 键 词：结构抗震可靠度 卷积 特征函数 极值分布 自适应 

分 类 号：TU311.3[建筑科学—结构工程]