基本变量区域重要性测度及其稀疏网格解

李璐祎; 吕震宙

doi:10.6052/0459-1879-12-260

基本变量区域重要性测度及其稀疏网格解

doi: 10.6052/0459-1879-12-260

李璐祎,
吕震宙^,

西北工业大学航空学院, 西安 710072

基金项目: 国家自然科学基金(51175425);航空基金(2011ZA53015);西北工业大学博士论文创新基金(CX201205); 教育部学术新人奖和西北工业大学顶尖博士研究生奖励基金(DJ201301)资助项目.

详细信息

通讯作者:
吕震宙,教授,主要研究方向:航空航天可靠性工程.E-mail:zhenzhoulu@nwpu.edu.cn

中图分类号: TB114.3
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- 被引次数: 0
出版历程
- 收稿日期: 2012-09-25
- 修回日期: 2013-05-03
- 刊出日期: 2013-07-18

REGIONAL IMPORTANCE MEASURE OF THE BASIC VARIABLE AND ITS SPARSE GRID SOLUTION

Li Luyi,
Lü Zhenzhou^,

School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

Funds: The project was supported by the National Natural Science Foundation of China (51175425), the Aviation Science Foundation (2011ZA53015), the Doctorate Foundation of Northwestern Polytechnical University (CX201205), the Ministry of Education Fund for Doctoral Students Newcomer Awards of China and the Excellent Doctorate Foundation of Northwestern Polytechnical University (DJ201301).

摘要

摘要: 为了提高现有基本变量对样本均值贡献的区域重要性测度指标的稳定性和收敛性, 提出了一个新的衡量基本变量内部各个区域对输出均值影响的重要性测度指标.并将其进一步扩展提出了一个衡量基本变量内部各个区域对输出总方差分解式中一阶方差影响的区域重要性测度指标.分析了所提指标的性质, 并探讨了它们与现有基本变量对样本均值贡献区域重要性测度指标和对样本方差贡献的区域重要性测度指标之间的关系. 另外, 针对所提指标的特点, 还建立了其求解高效的稀疏网格积分法.算例结果表明, 所提新的基本变量对输出均值贡献的区域重要性测度指标不仅继承了现有指标的优点, 而且比现有指标具有更高的收敛性和稳定性.所提基本变量对一阶方差贡献的区域重要性指标能够在基本变量对样本方差贡献区域重要性测度的基础上, 进一步提供基本变量内部各个区域对总方差的一阶分量的影响信息.而所建稀疏网格积分法可以在保证计算精度的同时大幅度提高基本变量区域重要性分析的效率.
- 基本变量 /
- 区域重要性 /
- 条件均值 /
- 一阶方差 /
- 主贡献 /
- 稀疏网格积分
Abstract: To improve the stability and convergence of the existing contribution to sample mean (CSM) regional importance measure (RIM), a new RIM is proposed to estimate the contribution to the mean of the model output by the different regions of basic variable, and it is named as improved contribution to sample mean (ICSM). An extended version of the ICSM, which is named as contribution to first order variance (CFOV), is developed to analyze the effect of the different regions of the basic variable on its corresponding first order variance in the variance decomposition. The properties of the two proposed RIMs are analyzed and their relationships with the existing CSM and contribution to sample variance (CSV) RIM are derived. Furthermore, based on the characteristics of the proposed RIMs, their highly efficient sparse grid integration (SGI) solutions are also established. Several numerical and engineering examples show that the newly defined ICSM can act as effectively as the CSM, but the convergence and stability of ICSM is better than those of CSM. The proposed CFOV can provide more detailed information than the existing CSV, which can effectively instruct the engineer on how to achieve a targeted reduction of the main effect of each basic variable. The established SGI-based method can improve the efficiency of the regional importance analysis considerably in case of acceptable accuracy.
- basic variable /
- regional importance /
- conditional mean /
- first order variance /
- main effect /
- sparse grid integration

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