Metamodeling Method Using Dynamic Kriging for Design Optimization

Abstract

Metamodeling has been widely used for design optimization by building surrogate models for computationally intensive engineering application problems. Among all the metamodeling methods, the kriging method has gained significant interest for its accuracy. However, in traditional kriging methods, the mean structure is constructed using a fixed set of polynomial basis functions, and the optimization methods used to obtain the optimal correlation parameter may not yield an accurate optimum. In this paper, a new method called the dynamic kriging method is proposed to fit the true model more accurately. In this dynamic kriging method, an optimal mean structure is obtained using the basis functions that are selected by a genetic algorithm from the candidate basis functions based on a new accuracy criterion, and a generalized pattern search algorithm is used to find an accurate optimum for the correlation parameter. The dynamic kriging method generates a more accurate surrogate model than other metamodeling methods. In addition, the dynamic kriging method is applied to the simulation-based design optimization with multiple efficiency strategies. An engineering example shows that the optimal design obtained by using the surrogate models from the dynamic kriging method can achieve the same accuracy as the one obtained by using the sensitivity-based optimization method.