摘要
提出了一种基于响应面法的二阶可靠度分析的新算法。在U空间中确定基本随机变量,通过空间变换和相关矩阵分解,在X空间中计算试验点的功能函数;通过迭代算法构造响应面,并在此基础上进行FORM/SORM计算。以三个具有不同类型功能函数的问题为例,通过与蒙特卡洛模拟结果的比较,验证了该算法的准确性和高效性。结果表明:该算法可直接利用已有的SORM公式,有效的解决了具有相关非正态分布变量的二阶可靠度分析问题。分析过程中,功能函数的确定性计算和可靠度分析相互独立。因此,该算法即适用于功能函数具有解析表达式的简单问题,也适用于功能函数需要迭代求解或数值分析的复杂问题。
A new algorithm of second-order reliability analysis is presented based on response surface method. Independent standard normal random variables in U-space are chosen as basic variables and transformed into correlated non- normal variables in original X- space. The response surface is constructed using an iterative algorithm on which the probability of failure is calculated using FORM and SORM. The accuracy and the efficiency of the proposed algorithm are illustrated for three examples with different type of performance functions and compared with Monte-Carlo simulations. The results show that the proposed algorithm makes the procedure easy to use the existing SORM formulas directly and perform the reliability analysis involving correlated non- normal variables. The deterministic computations of the performance functions and the probabilistic analyses are conducted separately in the algorithm which makes the proposed method could be used for not only the simple problems with analytical performance functions but also the complicated applications where iterative methods or numerical procedures are always needed to evaluate the performance functions.
出处
《科技通报》
北大核心
2015年第9期8-14,共7页
Bulletin of Science and Technology
基金
浙江省交通厅科技项目(2012H28)
国家自然科学基金项目(41202216)
浙江省教育厅科研项目(Y200909163)
作者简介
吕庆,副教授,E-mail：lvqing@zju.edu.cn.
