基于鞍点逼近法的基本随机变量重要性测度算法  

Saddlepoint Approximation Method for Importance Measure of Basic Random Variable

作　　者：李贵杰[1] 吕震宙[1] 吕媛波[1] 

机构地区：[1]西北工业大学航空学院,西安710072

出　　处：《力学季刊》2011年第4期605-611,共7页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(10572117;50875213);新世纪优秀人才支持计划(NCET-05-0868);航空基础基金(2007ZA53012);863计划课题(2007AA04Z401)

摘　　要：利用鞍点逼近法可以直接逼近单个线性响应功能函数概率分布的特点,提出了基于鞍点逼近的基本随机变量重要性测度分析方法。在所提方法中,首先将非线性响应功能函数进行线性化,再利用鞍点逼近方法近似得到响应功能函数的概率密度函数及其在变量某个实现值下响应功能函数的条件概率密度函数,进而根据基本随机变量重要性测度的定义计算出相应变量对响应功能函数分布影响的重要程度。最后给出了该方法的实现步骤和原理,并通过算例验证了该方法的合理性和可行性。By using saddlepoint approximation property of directly estimating probability distribution of linear response performance function, saddlepoint approximation based method is presented for basic ran- dom variable importance measure analysis of basic random variable effect on distribution of the response performance function. The response performance function is firstly linearized; the saddlepoint approximation is employed to estimate the probability density function（PDF） of response performance function and its conditional PDF under a certain realization of the basic random variable, on which the important meas- ure definition is used for calculating the effect of the basic random variable on the distribution of the response performance function. The concept and the implementation of the presented method are described, and several examples are given for demonstrating the rationality and the feasibility of the presented method.

关 键 词：灵敏度分析 矩独立 重要性测度 灵敏度指标 鞍点逼近 

分 类 号：TB114.3[理学—概率论与数理统计]