An Efficient Bi-Level Surrogate Approach for Optimizing Shock Control Bumps under Uncertainty

The assessment of uncertainties is essential in aerodynamic shape optimization problems in order to come up with configurations that are more robust. The influence of aleatory fluctuations in flight conditions and manufacturing tolerances is of primary concern when designing shock control bumps, as their effectiveness is highly sensitive to the shock wave location. However, exploring the stochastic design space for the global robust optimum increases the computational cost, especially when dealing with nonconvex design spaces and multiple local optima. The aim of this paper is to develop a framework for efficient aerodynamic shape optimization under uncertainty by means of a bi-level 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 optimization algorithm with an efficient surrogate-based approach for uncertainty quantification. The surrogate-based optimizer efficiently finds the global optimum of a given quantile of the drag coefficient. It outperforms traditional evolutionary algorithms by effectively balancing exploration and exploitation 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 in order to accurately quantify the quantile of the drag at a reduced number of function evaluations. Two different quantiles of the drag are chosen, the 95% to increase the robustness at off-design conditions, and the 50% for a configuration that is best for day to day operations. In both cases, the optimum configurations lead to an airfoil that is more robust to geometrical and operational uncertainties, compared to the configuration obtained through classical deterministic optimization.