基于黄金分割二分法鞍点线抽样的可靠性分析

Reliability Analysis Based on Saddlepoint Approximation-line Sampling Method of Golden Section Dichotomy

为解决非正态变量空间中复杂多变的隐式非线性功能函数的可靠性问题,融合鞍点估计与线抽样法的优点,结合二分法的特点与黄金分割法的求解效率,提出基于黄金分割二分法的鞍点线抽样法.在标准化变量空间中,沿重要线抽样方向,利用黄金分割点的二分法快速找到各样本点对应于功能函数的零点,从而可按照鞍点估计的思想将结构的失效概率转化为一系列线性功能函数失效概率的算术平均值.研究表明:基于黄金分割二分法的鞍点线抽样法在求解非正态变量空间中复杂多变的隐式非线性功能函数的结构可靠性时不仅精度高,而且速度快.

To solve the structural reliability of the implicit nonlinear performance function（PF） that is complicated and changeable in the non-normal variable space,the advantages of the saddle-point approximation（SA） and line sampling（LS） were merged,and the merits of dichotomy and the solution efficiency of the golden section method were combined to propose the saddle-point approximation-line sampling（SA-LS） method based on the dichotomy of the golden section point.According to SA,it is quick to find the zero-point in PF corresponding to each sample along the important LS direction by the above dichotomy so that the structural failure probability can be transformed into the arithmetical mean of a series linear PF failure probability.This research shows that the SA-LS method based on the dichotomy of the golden section point is of high precision and fast velocity when it is used to analyze the structural reliability for implicit nonlinear PF,which are complicated,changeable and of non-normal variables.