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基本变量区域重要性测度及其稀疏网格解

李璐祎 吕震宙

李璐祎, 吕震宙. 基本变量区域重要性测度及其稀疏网格解[J]. 力学学报, 2013, 45(4): 568-579. doi: 10.6052/0459-1879-12-260
引用本文: 李璐祎, 吕震宙. 基本变量区域重要性测度及其稀疏网格解[J]. 力学学报, 2013, 45(4): 568-579. doi: 10.6052/0459-1879-12-260
Li Luyi, Lü Zhenzhou. REGIONAL IMPORTANCE MEASURE OF THE BASIC VARIABLE AND ITS SPARSE GRID SOLUTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(4): 568-579. doi: 10.6052/0459-1879-12-260
Citation: Li Luyi, Lü Zhenzhou. REGIONAL IMPORTANCE MEASURE OF THE BASIC VARIABLE AND ITS SPARSE GRID SOLUTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(4): 568-579. 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
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

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

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: 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.

     

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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

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