基于多项式混沌的全局敏感度分析

Global Sensitivity Analysis Based on Polynomial Chaos

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.

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.