Derivative-based global sensitivity measure using radial basis function

Global sensitivity analysis (GSA) is always used to measure the contribution of input variables on the variation of model output. In the fields of GSA, derivative-based global sensitivity measure (DGSM) has gained much attention because of its high efficiency in the identification of insignificant input variables. The commonly used approach to estimate DGSM is the Morris method, which requires a large number of model evaluations to compute the gradient of model output. Therefore, it leads to a great challenge in the computational costs, particularly for expensive problems. To alleviate the intensive computation, an estimator based on Gaussian radial basis function (RBF) metamodel is proposed to compute DGSM. With the aid of RBF, the DGSM can be formulated in an explicit expression of one-dimensional Gaussian integrals. For the case of uniformly and normally distributed variables, the analytical expressions of the integral can be derived while for other cases with general distribution, the numerical approach with the quasi-Monte Carlo method is developed to approximate the integrals. The performance of the proposed method is validated by five numerical examples, which illustrate the proposed RBF-based estimator has the capability to yield desirable accuracy and convergence with a limited number of model evaluations.