Efficient optimization design method using kriging model

The kriging-based genetic algorithm is applied to aerodynamic design problems. The kriging model is a response surface model that represents a relationship between objective function (output) and design variables (input) using a stochastic process. The kriging model drastically reduces the computational time required for objective function evaluation in the optimization (optimum searching) process. Expected improvement is used as a criterion to select additional sample points. This makes it possible not only to improve the accuracy of the response surface, but also to explore the global optimum efficiently. The functional analysis of variance (ANOVA) is conducted to evaluate the influence of each design variable and their interactions to the objective function. Based on the result of the functional ANOVA, designers can reduce the number of design variables by eliminating those that have small effect on the objective function. The present method is applied to a two-dimensional airfoil design and the prediction of flap's position in a multi-element airfoil, where the lift-to-drag ratio (L/D) is maximized.