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.