An adaptive sampling strategy for Kriging metamodel based on Delaunay triangulation and TOPSIS

Metamodels have been widely used in engineering design and optimization. Sampling method plays an important role in the constructing of metamodels. This paper proposes an adaptive sampling strategy for Kriging metamodel based on Delaunay triangulation and TOPSIS (KMDT). In the proposed KMDT, Delaunay triangulation is employed to partition the design space according to current sample points. The area of each partitioned triangle is used to indicate the degree of dispersion of sample points, and the prediction error of Kriging metamodel at each triangle's centroid is used to represent the local error of each triangle region. By calculating the weight of the area and prediction error for each triangle region using the entropy method and TOPSIS, the degree of dispersion of sample points and local errors of metamodel are taken into consideration to make a trade-off between global exploration and local exploitation during the sequential sampling process. As a demonstration, the proposed approach is compared to other three sampling methods using several numerical cases and the modeling of the aerodynamic coefficient for a three-dimensional aircraft. The result reveals that the proposed approach provides more accurate metamodel at the same simulation cost, which is very important in metamodel-based engineering design problems.