工程结构椭球凸集模型可靠度的二次型计算方法研究  

Study on quadratic calculation method for reliability of ellipsoidal convex set model of engineering structures

作　　者：冉志红 凌枫 董国华 谢璐源 林帆 RAN Zhihong;LING Feng;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》2024年第2期25-31,共7页Sichuan Building Science

基　　金：国家自然科学基金项目(51968074)。

摘　　要：工程结构概率可靠度在理论上已经建立了完整的计算体系,但在实际工程应用中却停留在近似或半经验阶段。对于既有工程结构的可靠度评估,由于测试数据有限,采用椭球凸集模型可靠度进行评估有很高的工程价值和广泛的应用前景。椭球凸集模型可靠度有很多种不同的定义,但无论何种定义,如果完全脱离概率可靠度与失效概率的基本假定,则很难与现在基于概率可靠度评估方法的主流实现有效的衔接。从多维正态联合概率密度出发,推导了斜椭球方程及其标准化方法,同时结合极限状态方程,给出了椭球凸集模型可靠度与概率可靠度之间的数学关系。算例表明,得出的特殊简化情况下的椭球凸集模型可靠度计算方法和几何解释,可进一步推动该类可靠度在工程中的应用。The probabilistic reliability of engineering structures has established a complete system in theory,but it only stays in the approximate or semi empirical stage in the practical engineering application.Based on the reliability evaluation of existing engineering structures,due to the limited test data,the reliability evaluation of ellipsoidal convex set model has high engineering value and wide application prospect.There are many different definitions of ellipsoidal convex set model reliability,but no matter what definition,if it is separated from the basic assumptions of probability reliability and failure probability,it is difficult to effectively connect with the mainstream of evaluation methods based on probability reliability.Based on the multidimensional normal joint probability density,the oblique ellipsoid equation and its standardization method were derived.At the same time,combined with the limit state equation,the mathematical relationship between the reliability of ellipsoid convex set model and probability reliability was given.The example shows that the reliability calculation method and geometric interpretation of ellipsoidal convex set model in special simplified case can be used as a theoretical support for engineering application.

关 键 词：结构可靠度 椭球凸集模型 工程结构可靠度 极限状态方程 

分 类 号：TU311.4[建筑科学—结构工程]