扩展的输入变量对失效概率重要性测度及其积分算法  

Extended moment-independent importance measure and its integral solution

作　　者：胡吉祥[1] 吕震宙[1] 王迅[1] 

机构地区：[1]西北工业大学,西安710072

出　　处：《中国科学：物理学、力学、天文学》2014年第8期851-857,共7页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：航空科学基金(编号:2011ZA53015);国家自然科学基金(批准号:51175425);博士学科点专项科研基金(编号:20116102110003)

摘　　要：为了全面地分析输入变量对可靠性工程中所关心的结构或系统失效的影响,在继承了传统矩独立重要性测度的基础上提出了扩展的失效概率重要性测度指标.针对失效概率重要性测度计算量大的问题,本文结合能高效、准确求解概率密度函数的核密度估计法,建立了一种求解所提测度的积分法.文中算例表明,所提重要性测度包含了更加全面的输入变量对结构失效影响的信息,所建积分法破除了重要性测度计算的"维数诅咒",大大地减少了重要性测度指标的计算量.To fully analyze the effects of input variables on failure probability in reliability, an extended moment-independent importance measure based on the traditional moment-independent one is proposed. The computational cost of the moment-independent important measure is too high as direct Monte Carlo simulation is used. To overcome the difficulty, an integral solution is established by combining the highly efficient and exact Kernel density estimation. Results of several examples are used to demonstrate that the proposed importance measure can describe the effects of input variables on failure probability more fully and the established method can overcome the problem of ＂curse of dimensionality＂, which reduces the computational cost significantly.

关 键 词：失效概率 门限值 核密度估计 矩独立 

分 类 号：O213.2[理学—概率论与数理统计]