Multi-fidelity robust aerodynamic design optimization under mixed uncertainty

The objective of this paper is to present a robust optimization algorithm for computationally efficient airfoil design under mixed (inherent and epistemic) uncertainty using a multi-fidelity approach. This algorithm exploits stochastic expansions derived from the Non-Intrusive Polynomial Chaos (NIPC) technique to create surrogate models utilized in the optimization process. A combined NIPC expansion approach is used, where both the design and the mixed uncertain parameters are the independent variables of the surrogate model. To reduce the computational cost, the high-fidelity Computational Fluid Dynamics (CFD) model is replaced by a suitably corrected low-fidelity one, the latter being evaluated using the same CFD solver but with a coarser mesh. The model correction is implemented to the low-fidelity CFD solutions utilized for the construction of stochastic surrogate by using multi-point Output Space Mapping (OSM) technique. The proposed algorithm is applied to the design of NACA 4-digit airfoils with four deterministic design variables (the airfoil shape parameters and the angle of attack), one aleatory uncertain variable (the Mach number) and one epistemic variable (β, a geometry parameter) to demonstrate robust optimization under mixed uncertainties. In terms of computational cost, the proposed technique outperforms the conventional approach that exclusively uses the high-fidelity model to create the surrogates. The design cost reduces to only 34 equivalent high-fidelity model evaluations versus 168 obtained with the conventional method.