计算近似失效概率的最大熵密度函数法

A METHOD OF MAXIMUM ENTROPY DENSITY FUNCTION FOR CALCULATION OF APPROXIMATE FAILUREPROBABILITY

本文应用最大熵密度函数作为结构功能函数Ｚ的近似密度函数来计算结构的失效概率。最大熵密度函数以Ｚ的期望和高阶中心矩为约束条件加以拟合。文中着重研究了应用最优化方法和数值求积法确定最大熵密度函数的拉格朗日系数的方法，并给出了一个算例。算例表明，最大熵密度函数法的结果与其它三种方法非常接近。本文方法特别适用于基本随机变量为非正态分布的情况。

The maximum entropy density function os taken as an approximate density function of Z,the state function of a structure,to calculate the failure probability of strtucture. The maximum entropy density function is fitted with the restriction of expectation and high de- gree central moments of Z.The method to determine the Lagrange coefficients of the maximum entropy density function is analyzed emphatically by means of optimization method and numerical integration,and a calculation example is given in this paper.THe calculation example shows that the result computed by the maximum entropy density method is close to the results very well obtained by other three methods,The method presented in this paper is especially efficient for the case with elemental random variables of abnormal distribution.