Borgonovo moment independent global sensitivity analysis by Gaussian radial basis function meta-model

Moment independent sensitivity index is widely concerned and used since it can reflect the influence of model input uncertainty on the entire distribution of model output instead of a specific moment. In this paper, a novel analytical expression to estimate the Borgonovo moment independent sensitivity index is derived by use of the Gaussian radial basis function and the Edgeworth expansion. Firstly, the analytical expressions of the unconditional and conditional first four-order moments are established by the training points and the widths of the Gaussian radial basis function. Secondly, the Edgeworth expansion is used to express the unconditional and conditional probability density functions of model output by the unconditional and conditional first four-order moments, respectively. Finally, the index can be readily computed by measuring the shifts between the obtained unconditional and conditional probability density functions of model output, where this process doesn't need any extra calls of model evaluation. The computational cost of the proposed method is independent of the dimensionality of model inputs and it only depends on the training points and the widths which are involved in the Gaussian radial basis function meta-model. Results of several case studies demonstrate the effectiveness of the proposed method.