基于多项式混沌的全局敏感度分析

计算物理 ›› 2016, Vol. 33 ›› Issue (1): 1-14.

• 研究论文 • 下一篇

基于多项式混沌的全局敏感度分析

胡军, 张树道

北京应用物理与计算数学研究所, 北京 100094

收稿日期:2014-10-24 修回日期:2015-05-29 出版日期:2016-01-25 发布日期:2016-01-25
作者简介:胡军(1978-),男,博士,副研究员,主要从事流体力学稳定性和数值模拟不确定度量化研究,E-mail:hu_jun@iapcm.ac.cn
基金资助:
国家自然科学基金（11172049，11472060，11101045）和中国工程物理研究院科学技术发展基金（2015B0201037，2013A0101004）资助项目

Global Sensitivity Analysis Based on Polynomial Chaos

HU Jun, ZHANG Shudao

Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

Received:2014-10-24 Revised:2015-05-29 Online:2016-01-25 Published:2016-01-25

摘要/Abstract

摘要： 回顾基于多项式混沌和方差分解的全局敏感度分析方法，针对高维数随机空间和高阶多项式混沌展开面临的“维数灾难”问题，采用回归法、稀疏网格积分及基于l₁优化的稀疏重构技术（即压缩感知技术）来减少非嵌入式多项式混沌方法所需的样本配置点数目.针对几个典型响应面模型（包括Ishigami函数、Sobol函数、Corner peak函数和Morris函数）进行Sobol全局敏感度指标计算，展示多项式混沌方法在基于方差分解的全局敏感度分析中的有效性.

关键词: 多项式混沌, 全局敏感度, 维数灾难, 稀疏重构

Abstract: Global sensitivity analysis method based on polynomial chaos and variance decomposition is reviewed comprehensively. In order to alleviate "curse of dimensionality" coming from high-dimensional random spaces or high-order polynomial chaos expansions, several approaches such as least square regression, sparse grid quadrature and sparse recovery based on l₁ minimization (i. e. compressive sensing) are used to reduce sample size of collocation points that needed by non-intrusive polynomial chaos method. With computation of Sobol global sensitivity indices for several benchmark response models including Ishigami function, Sobol function, Corner peak function and Morris function, effective implementations of polynomial chaos method for variance-based global sensitivity analysis are exhibited.

Key words: polynomial chaos, global sensitivity, curse of dimensionality, sparse recovery

中图分类号:

O213

胡军, 张树道. 基于多项式混沌的全局敏感度分析[J]. 计算物理, 2016, 33(1): 1-14.

HU Jun, ZHANG Shudao. Global Sensitivity Analysis Based on Polynomial Chaos[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(1): 1-14.

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基于多项式混沌的全局敏感度分析

Global Sensitivity Analysis Based on Polynomial Chaos

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