Derivative-Enhanced Variable Fidelity Surrogate Modeling for Aerodynamic Functions

Abstract

In this paper a derivative-enhanced variable-fidelity surrogate model approach is developed based on a cokriging formulation. In this approach the absolute values of a high-fidelity function as well as the trends obtained by low-fidelity function values are utilized to develop an accurate surrogate model. Derivative information of arbitrary fidelity levels can be also utilized to develop a more accurate surrogate model. The efficiencies of the developed approaches are investigated by analytic function-fitting, aerodynamic data modeling and two-dimensional airfoil-drag-minimization problems. In the aerodynamic problems low-fidelity levels are defined by a different physical model or coarser computational mesh. The numerical examples show that the developed surrogate-model approach is shown to be useful for efficient aerodynamic data modeling and accurate uncertainty analysis with low computational cost. An efficient aerodynamic shape optimization is also realized with the variable fidelity Kriging model. Faster reduction of an aerodynamic objective function is achieved by utilizing the derivative-enhanced variable-fidelity-model approach in which low-fidelity information as well as adjoint-derivative information are simultaneously utilized to construct a surrogate model.