Efficient Bilevel Surrogate Approach for Optimization Under Uncertainty of Shock Control Bumps

The assessment of uncertainties is essential in aerodynamic shape optimization problems to come up with configurations that are more robust against operational and geometrical uncertainties. However, exploring the stochastic design space significantly increases the computational cost. The aim of this paper is to develop a framework for efficient optimization under uncertainty by means of a bilevel surrogate approach and to apply it to the robust design of a retrofitted shock control bump over an airfoil. The framework combines a surrogate-based optimizer with an efficient surrogate-based approach for uncertainty quantification. The optimizer efficiently finds the global optimum of a given quantile of the quantity of interest through the combination of adaptive sampling and a moving trust region. At each iteration of the optimization, the surrogate-based uncertainty quantification uses an active infill criterion to accurately quantify the quantile requiring a reduced number of samples. Two different quantiles of the drag are chosen for the design of the shock control bump: the 95% to increase the robustness at off-design conditions, and the 50% for a configuration that is preferred for day-to-day operations. In both cases, the optimum bumps are more robust, compared to the one obtained through classical deterministic optimization