基于偏导数的全局灵敏度指标的高效求解方法

在全局灵敏度分析领域，基于偏导数的全局灵敏度指标由于其优良的特性得到了广泛的关注。针对目前求解基于偏导数的全局灵敏度指标计算效率低的问题，提出了一种高效的求解方法。该方法利用乘法降维近似地将响应函数展开为连乘积的形式，从而将求解偏导数全局灵敏度的高维积分问题转化为一维积分的连乘积，在保证计算精度的前提下大大降低了求解基于偏导数的全局灵敏度指标的计算量。在求解特定点的偏导数时，采用了复数步长方法，提高了计算精度。最后，通过算例验证了所提方法的准确性和高效性。

Efficient algorithm for estimating derivative-based global sensitivity index

In the field of global sensitivity analysis, the derivative-based global sensitivity index attracts increasing attention because of its good properties. At present, the existing computing methods in estimating the derivative-based global sensitivity index have deficiencies of poor computational efficiency, thus, an efficient computational algorithm is developed in this article. In the proposed method, the multiplication dimension reduction is adopted to express the response function as the product-form. Then, the high-dimensional integration for estimating the derivative-based global sensitivity index can be transformed into the product of some one-dimensional integrations. Therefore, the proposed computational method can reduce the calculation cost for computing the derivative-based global sensitivity index dramatically, while the computational precision is kept. The complex step method is used to estimate the derivatives at specific points, and this method can improve the calculation precision. In the end, the test examples are adopted in order to demonstrate the accuracy and efficiency of the proposed method.