基于特征值分解的工程结构凸集模型可靠度计算理论  

Reliability calculation theory of engineering structure convex set model based on eigenvalue decomposition

作　　者：冉志红 杨子富 董国华 谢璐源 林帆 RAN Zhihong;YANG Zifu;DONG Guohua;XIE Luyuan;LIN Fan(School of Architecture and Planning,Yunnan University,Kunming 650091,China)

机构地区：[1]云南大学建筑与规划学院,云南昆明650091

出　　处：《四川建筑科学研究》2023年第6期24-33,45,共11页Sichuan Building Science

基　　金：国家自然科学基金项目(51968074)。

摘　　要：在工程结构可靠度研究中,对于结构抗力和作用效应具有相关性的情况,采用概率可靠度计算比较繁琐。从多维正态联合概率密度出发,推导了按某个分位点做截集得到的斜椭球方程,该方程为二次型,通过求取系数矩阵的特征值和特征向量,进而求得了斜椭球的几何参数。在概率可靠度定义的基础上,定义了凸集模型的非概率可靠度,同时给出了非概率可靠度与概率可靠度的关系。在结构抗力和作用效应分析的基础上,推导了二维具有相关性的情况下非概率可靠度的解析表达式以及多维不具有相关性情况下非概率可靠度的解析表达式。In the study of engineering structure reliability,the calculation of probability reliability is cumbersome for the correlation between structural resistance and action effect.Based on the multi-dimensional normal joint probability density,the oblique ellipsoid equation obtained by making a cut set according to a quantile was deduced.The equation was quadratic.The geometric parameters of the oblique ellipsoid were obtained by calculating the eigenvalues and eigenvectors of the coefficient matrix.Based on the definition of probabilistic reliability,the nonprobabilistic reliability of convex set model was defined,and the relationship between non-probabilistic reliability and probabilistic reliability was given.Based on the analysis of structural resistance and action effect,the analytical expression of non-probabilistic reliability in the case of two-dimensional correlation was deduced,and the analytical expression of non-probabilistic reliability in the case of multi-dimensional non-correlation was also deduced.

关 键 词：椭球凸集模型 工程结构可靠度 极限状态方程 

分 类 号：TU312[建筑科学—结构工程] TP114.3[自动化与计算机技术—控制理论与控制工程]