Optimization-Embedded Active Multi-Fidelity Surrogate Learning for Multi-Condition Airfoil Shape Optimization

Abstract: Active multi-fidelity surrogate modeling is developed for multi-condition airfoil shape optimization to reduce high-fidelity CFD cost while retaining RANS-level accuracy. The framework couples a low-fidelity-informed Gaussian process regression transfer model with uncertainty-triggered sampling and a synchronized elitism rule embedded in a hybrid genetic algorithm. Low-fidelity XFOIL evaluations provide inexpensive features, while sparse RANS simulations are adaptively allocated when predictive uncertainty exceeds a threshold; elite candidates are mandatorily validated at high fidelity, and the population is re-evaluated to prevent evolutionary selection based on outdated fitness values produced by earlier surrogate states. The method is demonstrated for a two-point problem at $Re=6\times10^6$ with cruise at $α=2^\circ$ (maximize $E=L/D$) and take-off at $α=10^\circ$ (maximize $C_L$) using a 12-parameter CST representation. Independent multi-fidelity surrogates per flight condition enable decoupled refinement. The optimized design improves cruise efficiency by 41.05% and take-off lift by 20.75% relative to the best first-generation individual. Over the full campaign, only 14.78% (cruise) and 9.5% (take-off) of evaluated individuals require RANS, indicating a substantial reduction in high-fidelity usage while maintaining consistent multi-point performance.