Compare the Efficiencies of Kriging and RBF Approximation Methods

Design Optimization is research area which was carried out a lot in the world, with many applications in the specifications of mechanical engineering, aerospace engineering, civil engineering. This area can help the engineering designs to be improved and optimized. Executing the global optimization codes is a time-consuming activity in engineering designs, hence the researchers should utilize the approximation methods (or interpolation methods). In this article, the authors will do research about comparing the efficiencies of 2 approximation methods (interpolation methods) Kriging and Radial Basis Function (RBF). The 2 approximation methods (interpolation methods) will be compared in some aspects, such as the accuracy of the methods, the robustness of the methods, the computational cost of the methods. The methods will be applied to approximate several complicated mathematical functions. For the used correlation function and radial basis function in this article, and for the used correlation parameter and width factor in this article, it is investigated that Kriging is more accurate and robust than RBF in finding the approximations (interpolations), Kriging can produce the approximations (interpolations) which are closer to the exact solutions, Kriging can make the approximations (interpolations) with less errors than RBF, Kriging also takes less computational cost than RBF, Kriging is less time-consuming than RBF. In summary, in this circumstance, Kriging is better than RBF.