Multi-fidelity Methods in Aerodynamic Robust Optimization

Abstract

In order to design robust and reliable aerospace systems it is necessary to properly quantify the effect of uncertainties on the systems’ behavior. Performing a robust optimization with the highest fidelity method is desired albeit not feasible because of the prohibited computational cost associated with the many simulations needed in the optimization iterations to compute statistics of the system’s performance. Here we describe a multi-fidelity method to enable high-fidelity robust optimization. Our multi-fidelity method uses a polynomial chaos expansion constructed from the combination of a low-fidelity model and a model correction to approximate the high-fidelity statistics and the gradients of the statistics used in each optimization iteration. The model correction accounts for the difference between the high-fidelity (Computational Fluid Dynamics RANS) model and the low-fidelity (CFD Euler) model. A key feature of the multi-fidelity method is its incorporation of analytic gradients (adjoints) from the CFD to obtain the gradients of the statistics. The application of the multi-fidelity method to the robust optimization of an RAE2822 airfoil subject to uncertain flow conditions shows that 60% to 90% computational savings can be achieved when compared to the high-fidelity optimization.