小样本下结构系统可靠度分析方法的研究  

RESEARCH ON METHOD FOR STRUCTURAL SYSTEM RELIABILITY ANALYSIS WITH SMALL SAMPLES

作　　者：冯健[1] 蒋友宝[2] 孟少平[1] 许玮[1] 

机构地区：[1]东南大学混凝土及预应力混凝土结构教育部重点实验室,江苏南京210096 [2]长沙理工大学桥梁与结构工程学院,湖南长沙410076

出　　处：《工程力学》2007年第9期37-42,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(50478075);江苏省自然科学基金项目(BK2003061)

摘　　要：结构随机变量的空间分为可靠空间和失效空间。采用Monte Carlo法中的自适应抽样技巧可以较高效率地抽取出失效空间中的样本点。然后统计出可靠空间和失效空间的分布参数。最终采用判别分析的思想重构出结构的功能函数。由此提出一种小样本下结构系统可靠度分析的新方法。该方法仅以样本点的状态即可靠或失效来重构功能函数,具有广泛性。数值算例表明该方法在样本数量不多的情况下仍具有较高的精度。The whole structural space of random variables can be divided into reliable space and failure space. Based on the adaptive sampling skill in the Monte Carlo method, the sampling point in failure space can be selected efficiently. Therefore, the distributed parameters of reliable space and failure space can be determined. Then the performance function is restructured by means of Mahalanobis distance analysis method. Consequently, a new method is proposed to analyze structural reliability with small samples. It is of universality since it only uses the state of sampling point, the reliable or the failure. Numerical simulation experiments show that the new method is of higher precision with small samples.

关 键 词：结构工程 可靠度 状态空间 自适应 抽样 回归分析 

分 类 号：TU311.2[建筑科学—结构工程]