基本变量区域重要性测度及其稀疏网格解

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

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.

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 effcient 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 effciency of the regional importance analysis considerably in case of acceptable accuracy.