基于偏导数的Sobol总测度指标的上下限分析

中国机械工程

基于偏导数的Sobol总测度指标的上下限分析

宋述芳1;周桐2;吕震宙1

1.西北工业大学,西安,710072
2.香港理工大学,香港,999077

出版日期:2016-07-10 发布日期:2016-07-12
基金资助:
国家自然科学基金资助项目(NSFC51308459)；中央高校基本科研业务费专项资金资助项目(310201401JCQ01014，3102015BJ(Ⅱ)CG009)

Analyses for Lower and Upper Bounds of Sobol Total Sensitivity Index Based on Derivative

Song Shufang1;Zhou Tong2;Lü Zhenzhou1

1.Northwestern Polytechnical University，Xi'an,710072
2.Hongkong Polytechnical University,Hongkong,999077

Online:2016-07-10 Published:2016-07-12
Supported by:

摘要/Abstract

摘要： 以Sobol'主测度指标Si作为总测度指标Stoti的下限，建立并推导了基于偏导数的测度指标作为Stoti的新上限。基于泛函和Euler-Lagrange等式，进行了不同变量分布形式下（均匀、正态、指数、Beta、三角分布等），Sobol'总测度指标Stoti的基于偏导数的上限分析，并给出了新上限详细的推导过程和具体的计算公式。通过简单数值和工程算例，验证了新上限的精度及效率，为更准确地界定总测度指标Stoti的取值区间提供了参考。

关键词: 总测度指标, 主测度指标, 基于偏导数的测度指标, Euler-Lagrange等式

Abstract: A main sensitivity index Si was set as the lower bound of Stoti and the new upper bound of Stoti was built based on the derivative. On the basis of functional analysis and Euler-Lagrange equation, the new upper bound of Stoti based derivative was analyzed for different variable distribution types, such as uniform, normal, exponential, triangular, Beta distribution etc. The derived process and formulas were presented in detail. Several numerical and engineering examples were used to verify the precision and efficiency of the presented bounds, which may provide the accurate bounds of Stoti.

Key words: total global sensitivity index, main global sensitivity index, derivative based global sensitivity index, Euler-Lagrange equation

中图分类号:

TP302.7

宋述芳, 周桐, 吕震宙 . 基于偏导数的Sobol总测度指标的上下限分析[J]. 中国机械工程.

Song Shufang, Zhou Tong, Lü Zhenzhou. Analyses for Lower and Upper Bounds of Sobol Total Sensitivity Index Based on Derivative[J]. China Mechanical Engineering.

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