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

With advances in computational aerodynamics, automated shape optimization has become a viable component of modern design workflows. Compared to traditional cycles dominated by wind-tunnel testing and empirical iteration, CFD-driven optimization enables systematic exploration with fewer simplifying assumptions. However, its practical deployment is constrained by the high dimensionality typical of aerodynamic design spaces and the cost of repeated high-fidelity evaluations. These constraints motivate the development of surrogate-based global optimization frameworks that manage fidelity adaptively, combining low-cost models with targeted high-fidelity corrections. In recent years, surrogate modeling has been increasingly adopted, with surrogate models trained on an initial set of simulations providing inexpensive predictions across the design space, facilitating the use of global, derivative-free optimizers.

In aerodynamic design, shape optimization has historically relied on gradient-based methods coupled with adjoint equations. Although computationally efficient in terms of design-variable scaling, these approaches typically require a tight integration between the flow solver and the optimizer, often leading to problem-specific implementations and limiting portability in industrial settings. To overcome these limitations, the field has increasingly adopted surrogate modeling. By reducing reliance on repeated CFD simulations, significant gains in evaluation speed are offered, albeit often at the expense of fidelity relative to high-fidelity solvers.

The core innovations of this paper include:

1) Proposing an optimization-embedded active multi-fidelity strategy applied to multi-condition airfoil shape optimization.

2) Combining active learning and genetic algorithms to dynamically allocate high-fidelity simulations based on uncertainty triggers.

3) Introducing condition-wise decoupling of multi-fidelity models, allowing independent optimization for each flight condition, ensuring consistent multi-point performance.

These innovations present significant advantages in uncertainty quantification and dynamic model refinement, especially in the dynamic allocation of high-fidelity calls.

The methodology of this paper includes the following key steps:

• �� Use low-fidelity XFOIL evaluations to provide inexpensive features.
• �� Adaptively allocate sparse RANS simulations when predictive uncertainty exceeds a threshold.
• �� Mandatorily validate elite candidates at high fidelity, re-evaluating the population to prevent evolutionary selection based on outdated fitness values.
• �� Dynamically trigger high-fidelity evaluations based on uncertainty quantification, ensuring that expensive simulations are invoked only when necessary.
• �� Introduce condition-wise decoupling of multi-fidelity models, allowing independent optimization for each flight condition.

The experimental design includes a two-point problem under conditions of Re=6×10^6: cruise at α=2° (maximize E=L/D) and take-off at α=10° (maximize CL), using a 12-parameter CST representation. Independent multi-fidelity surrogates per flight condition enable decoupled refinement, ensuring consistent multi-point performance. Experimental results demonstrate that the optimized design improves cruise efficiency by 41.05% and take-off lift by 20.75%. Throughout the optimization campaign, only 14.78% of individuals (cruise) and 9.5% (take-off) require RANS evaluations, indicating a substantial reduction in high-fidelity usage.

Experimental results demonstrate that under conditions of Re=6×10^6, the optimized design improves cruise efficiency by 41.05% and take-off lift by 20.75%. Throughout the optimization campaign, only 14.78% of individuals (cruise) and 9.5% (take-off) require RANS evaluations, indicating a substantial reduction in high-fidelity usage. Independent multi-fidelity surrogates per flight condition enable decoupled refinement, ensuring consistent multi-point performance. These results validate the effectiveness of the method in reducing high-fidelity CFD costs while maintaining RANS-level accuracy.

The method has broad applications in aerospace design, particularly in scenarios requiring multi-condition optimization. By reducing high-fidelity CFD costs while maintaining RANS-level accuracy, the method offers new possibilities for future aerospace design. Application scenarios include airfoil design, aircraft performance optimization, and other aerospace engineering problems requiring optimization across multiple operating conditions.

Despite the method's excellent performance in reducing high-fidelity usage, the correlation between low- and high-fidelity models may locally deteriorate in large, weakly constrained design spaces, leading to reduced model reliability. Additionally, the current framework may require further adjustments and optimizations when handling extreme flight conditions. Future research directions include further optimizing the dynamic adaptability of multi-fidelity surrogate models, exploring applications under more complex flight conditions, and integrating other machine learning techniques to enhance model prediction accuracy and computational efficiency.