方差全局灵敏度求解的空间分割结合无迹变换方法

为有效计算基于方差的全局灵敏度指标尤其是非线性程度较高的响应函数的,将积分空间的可加性以及无迹变换结合起来,利用函数在子空间内非线性程度会降低以及无迹变换方法在概率空间内对低非线性函数性质具有强捕捉能力的特点,提出计算基于方差的全局灵敏度指标的高效方法。该方法只需产生一组无迹变换样本就可以近似求得各阶灵敏度指标,并且该近似解随空间分割个数的增加而收敛于真值。通过非线性程度较高的验证算例及工程算例验证了所提方法在处理非线性功能函数上的高效性和准确性。

An efficient method for variance-based global sensitivity analysis by combination of space-partition and unscented transformation

In order to efficiently and accurately estimate the variance based sensitivity indices, especially for highly nonlinear response functions, a method is proposed by combining the additive property of integration region and unscented transformation (UT). Because the nonlinearity of response function is reduced in the local sub-space, in which the UT can explore the probability space very efficiently, the proposed method can estimate the variance based sensitivity indices effectively. Moreover, the proposed method can estimate all the indices by using the same set of UT samples, and the approximate solution converges to the actual value with the increased number of divided sub-space. The results of the nonlinear test examples and engineering example illustrate the efficiency and accuracy of our proposed method.