CAJ | 학술논문

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。
침대공정중보편존재적수궤변량분포삼수불학정성적문제，위판단분포삼수불학정성대모형수출특정치（이실효개솔위례）적영향，건립료분석분포삼수대모형수출통계특정치영향적전국령민도지표，병침대전통방법구해분포삼수기우실효개솔적전국령민도지표수삼중추양，계산량대적문제，제출일충고효구해방법，해방법위량중추양，쾌속득출분포삼수적전국령민도지표。소제방법이중심겁한정리위의거，통과재대양본조건하심조합괄적고계량，건립수출통계특정량화중간고계량이급중간고계량화전국령민도지표지간적대수관계，근사전국령민도지표。유우고계량적량호수렴성，타가재보증여전통몽특잡락방법계산결과동등정도적조건하，대폭도감소대모형적계산차수，제고료효솔。최후，산례험증소제방법적준학성화고효성。
For the engineering structure involving 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 .