一种基于鞍点近似的高效二阶可靠性分析方法

摘要

Firstorder reliability method(FORM)is in vain to solve the nonlinear limit state function for accuracy although it have high efficiency. While second order reliability method(SORM)ownsconsiderable precision of calculation but low efficiency,so it's difficult to be widely used in engineering practice.For this reason,this paper proposes a reliability analysis method with two order accuracy and relative high efficient than SORM. Before that the reasons for the low efficiency of traditional reliability analysis are researched firstly in it.First of all,the method approximates the limit state functions with a series of quadratic polynomial. Then the cumulative generating function of approximate limit state function is calculated. Finally the saddle point approximation is used to calculate the failure probability easily.At the end of the article,a numerical example is present to prove the effectiveness of the method.%一次可靠性分析方法虽然效率高但在解决非线性状态极限函数问题时精度低,二次可靠性分析方法计算精度高但是效率较低,工程实际中很难普遍使用.为此,在分析传统二阶可靠性分析方法精度损失原因的基础上提出了一种具有较高精度且相对二阶可靠性分析方法高效的可靠性分析方法.所提方法首先用一系列的二次多项式组合近似表示极限状态函数.进而通过变换求出近似极限状态函数的累积量母函数,使用鞍点近似求得失效概率.最后用一个数值案例证明方法的有效性.