An efficient robust aerodynamic design optimization method based on a multi-level hierarchical Kriging model and multi-fidelity expected improvement

Robust aerodynamic design optimization (RADO) is developed to obtain aircraft designs with insensitive aerodynamic performance. The uncertainties in manufacturing, operating conditions, or freestream turbulence intensity are quantified and involved in the objective and constraint functions of RADO. The iterative uncertainty quantification (UQ) based on high-fidelity simulations for each design generated in the optimization greatly increases the computation cost, which is the main challenge of RADO. To alleviate this problem, an efficient robust RADO method based on a multi-level hierarchical Kriging (MHK) model and multi-fidelity expected improvement (MFEI) is proposed. A regularized multi-fidelity framework is established for RADO and a progressive multi-round multi-fidelity strategy is further developed to reduce the cost. The MHK surrogate is utilized for global optimization and UQ, which is constructed with very few high-fidelity simulations by taking advantage of cheap simulations of multiple lower fidelities. The MFEI can adaptively infill samples of arbitrary fidelity during the optimization to accelerate the convergence. The proposed RADO method is verified by drag minimization of RAE 2822 airfoil under operational uncertainties and then demonstrated by robust designs of a natural-laminal-flow airfoil NLF0416 at high lift under environmental uncertainty and ONERA M6 wing in transonic viscous flow under operational and geometric uncertainties. The results confirm that the proposed method significantly improves optimization efficiency and obtains robust aerodynamic design within an affordable computational budget. In contrast to the deterministic optimum, the robust configurations can retain a good performance when uncertainties exist.