A Robust Error Pursuing Sequential Sampling Approach for Global Metamodeling Based on Voronoi Diagram and Cross Validation

Abstract

Surrogate models are widely used in simulationbased engineering design and optimization to save the computing cost. The choice of sampling approach has a great impact on the metamodel accuracy. This article presents a robust errorpursuing sequential sampling approach called crossvalidation (CV)Voronoi for global metamodeling. During the sampling process, CVVoronoi uses Voronoi diagram to partition the design space into a set of Voronoi cells according to existing points. The error behavior of each cell is estimated by leaveoneout (LOO) crossvalidation approach. Large prediction error indicates that the constructed metamodel in this Voronoi cell has not been fitted well and, thus, new points should be sampled in this cell. In order to rapidly improve the metamodel accuracy, the proposed approach samples a Voronoi cell with the largest error value, which is marked as a sensitive region. The sampling approach exploits locally by the identification of sensitive region and explores globally with the shift of sensitive region. Comparative results with several sequential sampling approaches have demonstrated that the proposed approach is simple, robust, and achieves the desired metamodel accuracy with fewer samples, that is needed in simulationbased engineering design problems.