分布参数不确定情况下全局灵敏度及高效求解方法  

Global Sensitivity Measure for Uncertainty Distribution Parameters and Effective Solution for Obtaining It

作　　者：任博[1] 吕震宙[1] 王攀[1] 张磊刚[1] 

机构地区：[1]西北工业大学航空学院,陕西西安710072

出　　处：《西北工业大学学报》2013年第4期540-546,共7页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(51175425);航空科学基金(2011ZA53015)资助

摘　　要：针对工程中普遍存在的随机变量分布参数不确定性的问题,为判断分布参数不确定性对模型输出特征值(以失效概率为例)的影响,建立了分析分布参数对模型输出统计特征值影响的全局灵敏度指标,并针对传统方法求解分布参数基于失效概率的全局灵敏度指标需三重抽样,计算量大的问题,提出一种高效求解方法,该方法为两重抽样,快速得出分布参数的全局灵敏度指标。所提方法以中心极限定理为依据,通过在大样本条件下寻找合适的估计量,建立输出统计特征量和中间估计量以及中间估计量和全局灵敏度指标之间的代数关系,近似全局灵敏度指标。由于估计量的良好收敛性,它可在保证与传统蒙特卡洛方法计算结果同等精度的条件下,大幅度减少对模型的计算次数,提高了效率。最后,算例验证所提方法的准确性和高效性。For the engineering structure involvisg uncertain distribution parameters, a global sensitivity measure based on failure probability is established. To get the effect of uncertain distribution parameters on the failure prob- ability, traditional Monte Carlo method generally needs a ＂triple-loop＂ crude and time consuming sampling proce- dure to compute the established global sensitivity. To overcome the disadvantage of MC method, we propose an im- proved sampling method for global sensitivity measure of failure probability, in which the triple-loop is simplified in- to a ＂double-loop＂ and the computing efficiency is greatly improved. The main idea of the proposed method, which is explained in section 1 and 2 of the full paper, consists of： （ 1 ） generating samples, （2） searching suitable estima- tors and establishing the relationship between failure probability based global sensitivity measure and the estimators, （3） obtaining the global sensitivity measure. Compared with the traditional MC method, the proposed method is more efficient for the same acceptable precision, due to the fast convergence of the estimators. Calculated results of 1 numerical and 2 engineering examples, presented in section 3, and their analysis demonstrate preliminarily the reasonability of the proposed sensitivity measure and the efficiency of the proposed method.

关 键 词：计算效率 概率密度函数 失效概率 Sobol指标 分布参数不确定性 

分 类 号：TB114.3[理学—概率论与数理统计]