Kriging Surrogate Model Enhanced by Coordinate Transformation of Design Space Based on Eigenvalue Decomposition

Nobuo Namura, Koji Shimoyama, Shigeru Obayashi

Abstract: The Kriging surrogate model, which is frequently employed to apply evolutionary computation to real-world problems, with coordinate transformation of design space is proposed to improve the approximation accuracy of objective functions with correlated design variables. Eigenvalue decomposition is used to extract significant trends in the objective function from its gradients and identify suitable coordinates. Comparing with the ordinary Kriging model, the proposed method shows higher accuracy in the approximation of two-dimensional test functions and reduces the computational cost to achieve the global optimization. In the application to an airfoil design problem with spline curves as correlated design variables, the proposed method achieves better performances not only in the approximation accuracy but also the ability to explore the optimal solution.