EFFICIENT OPTIMIZATION DESIGN METHOD USING KRIGING MODEL Shinkyu Jeong 1 , Mitsuhiro Murayama 2 and Kazuomi Yamamoto 3 Information Technology Center, Institute of Space Technology and Aeronautics Japan Aerospace Exploration Agency, Chofu, Tokyo, 182-8522, Japan Abstract The Kriging-based genetic algorithm is applied to aerodynamic design problems. The Kriging model, one of the response surface models, represents a relationship between the objective function (output) and design variables (input) using stochastic process. The kriging model drastically reduces the computational time required for objective function evaluation in the optimization (optimum searching) process. ‘Expected improvement (EI)’ 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. In this paper, 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. 1. Introduction With the growth in computing power of current computers and the advance in technique of computational fluid dynamics (CFD), CFD becomes one of the inevitable tools in the aerodynamic optimization design nowadays. However, in the process of the optimization design, the number of objective function evaluations using high fidelity CFD analysis solver is severely limited by time and cost, even with the current supercomputer. One alternative is to construct a simple approximate model of the complicated CFD analysis solver. The approximate model expresses the relationship between the objective function (output) and the design variables (input) with simple equation. This model requires very little time to evaluate the objective function. It makes possible to save a lot of computation time and to explore more wide design space. The most widely used approximation model is polynomial-based model [1, 2], due to its simplicity and ease of use. However, this model is not suitable for representing multi-modalities and non-linearity that often appear in the aerodynamic problem. Recently, the Kriging model [3, 4], developed in the field of spatial statistics and geostatistics, has gained popularity in this field. This model predicts the value of the unknown point using stochastic processes. Sample points are interpolated with the Gaussian random function to estimate the trend of the stochastic processes. The model has a sufficient flexibility to represent the nonlinear and multimodal functions at the expense of computation time. However, the computation time to construct the Kriging model is still short compared to that of the direct CFD analysis. In this study, the genetic algorithms (GAs) are adopted as searching algorithm. GAs are based on the mechanism of natural selection and natural genes. GAs are very attractive to the engineering problems where discontinuities and multi-modalities may exist, because GAs do not utilize derivative information. Another merit of GAs is that they search the optimum point from a population of points, not a single point. This feature is very promising to multi-objective problems. However, GAs require many objective function evaluations, which may be impractical if we rely solely on the time-consuming high fidelity CFD analysis solver. The time consuming CFD analysis solver in the objective function evaluation process of GA is replaced with the Kriging model. However, it is possible to miss the global optimum in the searching space if we rely only on the prediction value of the Kriging model, because the model includes uncertainty at the prediction point. For the robust exploration of the global optimum point, both the prediction value and its uncertainty should be considered at the same time. This concept is expressed in the criterion ‘expected improvement (EI)’. EI indicates the probability of a point being optimum in the design space. 1. Invited researcher 2. Scientist, AIAA member 3. Senior researcher, AIAA member American Institute of Aeronautics and Astronautics 1