A Metamodeling Method Using Dynamic Kriging and Sequential Sampling

Abstract

In engineering design, metamodeling has been widely applied to design problems by building a surrogate model for compute-intensive engineering models. Among metamodeling methods, the Kriging method has gained significant interest for developing the surrogate model. However, in traditional Kriging methods, the optimization methods applied to correlation parameter estimation do not provide a global optimum and the mean structure is fixed polynomials basis functions. In this paper, a new method, the so-called Dynamic Kriging (DKG) method is proposed to fit the true model more accurately. In this DKG method, a pattern search algorithm is applied to find the global optimum for the correlation parameter estimation, and the 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. In addition, a sequential sampling technique based on the prediction interval of the surrogate model is used and integrated with the DKG method. Numerical examples show that the DKG method shows significantly more accurate results compared with traditional Kriging methods and other metamodeling methods.