非正态变量可靠性分析的鞍点线抽样方法

结合鞍点概率分布估计和传统线抽样方法的优点，提出了非正态变量可靠性分析的鞍点线抽样方法。传统的线抽样方法对非正态变量问题进行可靠性分析时需将非正态变量等价转换为标准正态变量，非正态变量向标准正态变量的非线性转换将增加响应功能函数的非线性程度，进而加大了转换后响应函数失效概率估计的难度。所提鞍点线抽样方法则无需将非正态变量转化为标准正态变量，它利用鞍点概率分布估计方法可以直接估计非正态变量空间中线性响应函数概率分布的特点，并利用线抽样方法可以将非线性功能函数的失效概率转化为一系列线性功能函数失效概率平均值进行估计的优点，实现了非正态变量空间非线性功能函数失效概率的高精度估计。鞍点线抽样方法使用前需将变量进行标准化变换，这种变换是线性的，通过对变量的标准化变换可以消除变量的量纲，从而使得标准化变量空间概率分布更具规律性。理论推导可以证明：鞍点线抽样方法在基本变量服从正态分布时将退化为传统的线抽样方法。算例验证结果表明：针对非线性功能函数的可靠性问题，鞍点线抽样方法比传统的直接鞍点估计具有更高的精度。

LINE SAMPLING METHOD BASED ON SADDLEPOINT APPROXIMATION FOR RELIABILITY ANALYSIS WITH NON-NORMAL RANDOM VARIABLES

For reliability analysis of non-linear limit state function with non-normal random variables,a novel line sampling method based on saddlepoint approximation (LS_SA) is presented.For the structural reliability problem with non-normal variables,traditional line sampling reliability analysis method requires the transformation from the original non-normal variable space into the equivalent standard normal space.This transformation is nonlinear,which tends to increase the nonlinearity of the performance function and difficulty of estimating the failure probability.The presented LS_SA method does not require this nonlinear transformation.By use of SA to estimate the probability distribution directly for the linear performance function with non-normal variables,and the traditional LS method expressing the failure probability of nonlinear performance function as the arithmetic average of a set of failure probabilities of the linear performance functions,the presented method can realize the high precision estimation of the failure probability of non-linear limit state function with non-normal variables.Before employing LS_SA method,the linear standardized transformation is needed to eliminate the dimensions of variables.The theoretical derivation verifies that the LS_SA method degenerates into traditional LS method when all the random variables are normally distributed.The results of the illustrations show that the presented method has higher precision than the direct SA for non-linear performance function reliability problem.