A Novel High-Dimensional Gradient-Based Robust Optimization Framework Applied to Adjoint-Based CFD Applications

High Aspect Ratio Wings (HARW) is a promizing technology of next-generation aircraft. They offer greater aerodynamic efficiency, lowering fuel consumption and carbon emissions. However, the aeroelastic deformation inherent to HARW are not yet well established notably in the early design stage, introducing an epistemic mismatch between the idealized numerical simulations and real-world behaviours. This discrepancy may compromise aerodynamic performance and slows the design process, requiring additional fine-tuning and adjustments. Gradient-based aerodynamic shape optimization, using Computational Fluid Dynamics (CFD) and the Adjoint process, is efficient but susceptible to unknown inertia and structural information in the early design stage. To mitigate this, robust optimization offers a lead by incorporating uncertainty quantification into the optimization process, ensuring more reliable and resilient designs. Nevertheless, it suffers from high computational costs for high-dimensional problems, both for optimisation and for uncertainty propagation. Dimension reduction and uncertainty propagation techniques address these problems well. This paper investigates the practicability of robust high-dimensional aerodynamic shape optimization under uncertain parameters, using the Gradient-Based Polynomial Chaos Expansion to propagate the randomness and the Active Subspace technique to reduce dimension of the uncertain space and/or the optimization space. We apply the method to the DLR-F25 Wing-Body configuration considering uncertainty on the twist parameters and optimization variables are wing twist and airfoil shapes at different wing stations.