An efficient multi-fidelity Kriging surrogate model-based method for global sensitivity analysis

Global sensitivity analysis (GSA), particularly for Sobol index, is a powerful tool to quantify the variation of model response sourced from the uncertainty of input variables over the entire design space. However, GSA requires a large number of model evaluations to achieve satisfactory accuracy, which will lead to a great challenge in computational efforts when the model is expensive to be evaluated. To address this issue, an efficient method based on multi-fidelity Kriging (Cokriging) surrogate model is proposed. To this end, high dimensional model representation of Cokriging predictor is preformed to derive the analytical expressions of total and partial variances. Then, the sensitivity analysis is transformed into the computation of several one-dimensional integrals, which is beneficial to reduce the computational burden. Four examples are employed to validate the performance of the proposed method. The results demonstrate that Cokriging estimator is an efficient approach to yield promising accuracy and reduce computational costs in the sensitivity analysis.