• 论文 •

### 一种平均矩独立重要性指标及其拒绝抽样方法

1. 中国运载火箭技术研究院, 北京 100076
• 收稿日期:2018-05-08 修回日期:2018-07-27 出版日期:2019-01-20 发布日期:2019-01-28
• 通讯作者: 张磊刚 E-mail:leigang_zhang@163.com
• 作者简介:程蕾,女,博士,工程师。主要研究方向:结构、机构可靠性设计;张磊刚,男,硕士,工程师。主要研究方向:结构可靠性设计。
• 基金资助:
军委装备发展部“十三五”装备预研领域基金（6140244010216HT15001）

### An average moment-independent importance index and its rejection sampling method

CHENG Lei, ZHANG Leigang, LEI Bao, LIANG Zudian, LIU Peng

1. China Academy of Launch Vehicle Technology, Beijing 100076, China
• Received:2018-05-08 Revised:2018-07-27 Online:2019-01-20 Published:2019-01-28
• Supported by:
Equipment Development Department the "13th Five-year" Equipment Research Field Foundation of China Central Military Commission (6140244010216HT15001)

Abstract: In the process of moment-independent importance analysis, importance index are always used to quantify the inverse allocation of structural system output uncertainty to input uncertainty.An assumption is given that the variance of a given factor can be reduced by future research, which leads to the development the moment-independent index function. The moment-independent importance index function provides an index for a given factor as a function of the amount of variance of that factor can be reduced. Meanwhile, by assuming the reduction amount of a particular factor variance as a random variable, the average moment-independent importance index is defined by taking average of the moment-independent importance index function. Estimating the average moment-independent importance index involves a large amount of computation using Sobol's method, and thus rejection sampling (RS) method is introduced here with the generated samples used in Sobol's method. Consequently, RS can use the samples generated during Sobol's method to accurately estimate the moment-independent importance index function and the average moment-independent importance index without any further model evaluation, which greatly reduces the computational cost. Numerical and engineering examples are demonstrated to show the effectiveness of the proposed measures and the accuracy and availability of the RS method.