Abstract
This study applied a Kriging model to optimization of a constrained aerodynamic design problem. The objective function and all constraint functions are considered statistically independent to avoid treating the complicated multivariate normal distribution in the constrained optimization problem. In the Kriging model of objective functions, expected improvements (EI) is calculated and in the Kriging model of constraint function, the probabilities of satisfying the constraints are calculated. Based on these values, an efficient exploration of the global optimum is performed. Two data mining techniques are used to investigate the information of design space such as the relationship between objective function and design variables: Functional Analysis of Variance (ANOVA), and Self-Organizing Map (SOM). ANOVA shows information quantitatively, while SOM shows it qualitatively. Based on the information, elimination of design variables with little effect on objective function is performed. The present method is applied to two-dimensional (2D) transonic airfoil design. The results showed the validity of the present method.
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