A Metamodeling Method Using Dynamic Kriging and Sequential Sampling

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