An effective gradient and geometry enhanced sequential sampling approach for Kriging modeling

Surrogates have been widely used for replacing computationally costly computer simulations. To improve the prediction accuracy with less sampling cost, sequential sampling is often used to seek targeted training samples for surrogate modeling. Previous methods often integrate gradient information to improve the sampling effect, but the increase of prediction accuracy is still limited for complicated problems. It is intractable how to better exploit the useful gradient information to sample potential highly nonlinear regions. In this paper, an effective gradient and geometry enhanced Kriging sequential sampling approach is proposed to handle this problem. First, a novel improvement function, which combines the approximate gradient and prediction variance, is constructed to measure the improvement of a candidate sampling point. Second, the design domain is partitioned into multiple Voronoi subdomains according to design points, and an adaptive and efficient cross-validation-based criterion is introduced to determine the candidate sampling regions and reduce the optimization cost. Finally, the improvement function is maximized in the selected Voronoi subdomains to sample a new point, which can effectively achieve great accuracy improvement in the nonlinear area. The proposed approach is tested on several highly nonlinear functions and an application-related example, and the experimental results confirm its effectiveness.