Ensemble learning of multi-kernel Kriging surrogate models using regional discrepancy and space-filling criteria-based hybrid sampling method

Kriging surrogate model has been widely used to simulate expensive models in engineering application. Ensemble of multi-kernel Kriging surrogate models can integrate the information of different kernel functions and enhance the predictive robustness. The performance of the ensemble Kriging model is dependent on the collection of samples. However, the traditional sampling methods primarily concentrate on the accuracy of individual-kernel Kriging, disregarding the difference among different kernel functions. To deal with the issue of sample selection in the context of ensemble Kriging, a regional discrepancy and space-filling criteria-based hybrid sampling (RSHS) method is proposed in this paper. According to the bias-variance decomposition, the expected leave-one-out cross validation error is introduced to compute the weight of each Kriging component. Considering the disagreement of different kernel-based Kriging models, the combination of regional correlation and regional predictive error is derived to measure the regional discrepancy for pursuing local accuracy. The space-filling criterion is also employed to ensure the even coverage across the entire space for global exploration. Therefore, the hybrid sampling criterion is developed to select sample point sequentially by maximizing the regional discrepancy with subject to the constraint of space-filling criterion. The performance of the proposed method is validated by six benchmark examples and an engineering application of airfoil shape model. The results demonstrate the RSHS sampling method can provide promising accuracy and robustness for ensemble Kriging metamodeling.