一种高效计算各类基于方差灵敏度指标的方法

为同时计算各类基于方差的灵敏度指标,提出了基于空间分割和无迹变换(UT)的计算方法,其可以重复利用一组样本点近似计算出基于方差的全局灵敏度指标(Sobol指标)、基于方差的区域灵敏度指标以及基于方差的W指标。除此之外,还对基于方差的W指标进行了改进,改进的基于方差的W指标除包含原始指标所提供的信息外,还包含了输入变量取不同实现区间时对输出响应方差影响的变异性,可以更合理地反映调整输入变量的不同取值区间对输出离散程度的平均影响。数值算例以及工程算例的计算结果表明了本文方法在计算上的准确性以及改进的基于方差的W指标的合理性。 

An efficient method for estimating various variance-based sensitivity indices

In order to simultaneously estimate various variance-based sensitivity indices, a method is proposed by combining space-partition idea and unscented transformation (UT) method, which can estimate variance-based global sensitivity index (Sobol index), variance-based regional sensitivity index and variance-based W index by repeatedly using a set of UT samples. Besides, a modified variance-based W index is proposed, which can analyze the sensitivity of the model input variables comprehensively and reasonably. What's more, the modified variance-based W index includes both the original one and the variability of effect on the variance of model output when the model input variable is fixed in different intervals. Thus, the modified one more reasonably reflects the average impact on the variance of the model output when model input variable is fixed in different intervals. The results of numerical and engineering examples illustrate the accuracy and efficiency of the proposed method and the reasonability of the modified variance-based W index.