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mandatorily validated at high fidelity, and the population is re-evaluated to prevent evolutionary selection based on outdated fitness values produced by earlier surrogate states.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.

Figures (14)

• Figure 1: Airfoil parametric space generated using a full factorial combination of three equidistant values within the limits of \ref{['tab:CST_domain']}. Left: The envelope of valid geometries. Right: The envelope of geometries discarded by the constraints. The black line indicates the mean surface, while the shaded blue and red regions denote the upper and lower surface boundaries, respectively.
• Figure 2: Computational grid for a representative airfoil geometry. The visualization highlights the unstructured domain discretization, the local refinement zones, and the inflation layers resolving the boundary layer at the leading and trailing edges.
• Figure 3: Surface pressure of the finest mesh versus the reference surface pressure, obtained from jespersen2016overflowReference.
• Figure 4: Schematic of the multi-fidelity evaluation workflow. The process accepts a geometric parameter vector $\boldsymbol{\Theta}$, evaluates the low-fidelity physics, and queries the Kriging surrogate. The active learning loop is triggered if the prediction uncertainty $CV$ exceeds the threshold $\kappa$, invoking the High-Fidelity solver for model refinement.
• Figure 5: Evolution of the optimization campaign and aerodynamic objectives. (a) Cost-function convergence ($J$) over 15 generations, with individuals labeled by generation method (LHS, exploration, exploitation, elitism); symbols show the best design in generations 1--4 () and the overall best individual (). (b) Scatter of cruise efficiency ($E^{\alpha=2^\circ}$) and (c) take-off lift ($C_L^{\alpha=10^\circ}$) over 15 generations, color-coded by $J$, with the overall best individual marked by a star.