Airfoil optimization using Design-by-Morphing with minimized design-space dimensionality

TL;DR

AirDbM reduces airfoil design-space dimensionality by selecting a compact set of $n=12$ baselines from the UIUC database and morphing between them with weights $w_i \in [-1,1]$, achieving reconstruction of the broader database with a mean absolute error around $\sim 10^{-3}$–$10^{-2}$ and $\approx 99\%$ of shapes meeting tight error targets. The method enables rapid, interpretable design exploration and improves optimization efficiency: in a two-objective airfoil optimization, the hypervolume front is surpassed earlier than in prior work with $n=25$ baselines, with new Pareto-optimal solutions at moderate stall tolerances. Additionally, an RL-based geometry-generation study shows AirDbM offering faster convergence and lower error compared to conventional parameterizations when guiding a PPO agent across $1{,}644$ target shapes. These results demonstrate that a carefully chosen, low-dimensional, geometry-aware baseline set can preserve diversity while enabling efficient ML-augmented design and higher-fidelity future extensions.

Abstract

Effective airfoil geometry optimization requires exploring a diverse range of designs using as few design variables as possible. This study introduces AirDbM, a Design-by-Morphing (DbM) approach specialized for airfoil optimization that systematically reduces design-space dimensionality. AirDbM selects an optimal set of 12 baseline airfoils from the UIUC airfoil database, which contains over 1,600 shapes, by sequentially adding the baseline that most increases the design capacity. With these baselines, AirDbM reconstructs 99 % of the database with a mean absolute error below 0.005, which matches the performance of a previous DbM approach that used more baselines. In multi-objective aerodynamic optimization, AirDbM demonstrates rapid convergence and achieves a Pareto front with a greater hypervolume than that of the previous larger-baseline study, where new Pareto-optimal solutions are discovered with enhanced lift-to-drag ratios at moderate stall tolerances. Furthermore, AirDbM demonstrates outstanding adaptability for reinforcement learning (RL) agents in generating airfoil geometry when compared to conventional airfoil parameterization methods, implying the broader potential of DbM in machine learning-driven design.

Figures (12)

• Figure 1: General flowchart of DbM to get a new design by morphing baseline shapes.
• Figure 2: Selig coordinate format for airfoil geometry of a unit chord length SeligUIUC.
• Figure 3: Comparison of original (black solid line) and reconstructed (red dashed line) airfoil geometries via Design-by-Morphing using the selected 12 baselines (see Table \ref{['tab:baseline_airfoils']}). The 10 airfoils displayed here are selected at equal rank intervals from best to worst reconstruction based on the Mean Absolute Error (MAE) similarity metric (see Equation \ref{['eq:similarity_5']}).
• Figure 4: Percentage of airfoils in the database that can be reconstructed via Design-by-Morphing with an Mean Absolute Error (MAE) below 0.005 for baseline set sizes from 2 to 12 (see Table \ref{['tab:baseline_airfoils']}).
• Figure 5: Reconstruction of Wortman FX 79-W-660A airfoil. Depicted are target (black solid line) versus reconstructed (red dashed line) airfoils for the present 12-baseline Design-by-Morphing (AirDbM), Hicks-Henne, class-shape transformation (CST), non-uniform rational B-spline (NURBS), and parametric section (PARSEC) methods.