A space-filling sampling method for sample generation in aerodynamic modeling of flapping airfoil over complex motion state spaces

Accurate unsteady aerodynamic surrogate models are important for the aerodynamic analysis and model-based design of flapping-wing air vehicles (FWAVs). However, the construction of such models is often limited by the cost of generating high-quality unsteady aerodynamic samples. Traditional design of experiment (DoE) sampling methods have fundamental limitations in sampling cases involving strongly nonlinear time-varying kinematic equations for flapping airfoil. While DoE generates uniformly distributed samples in the kinematic parameter space, these samples undergo significant distribution distortion in the actual input feature space of the deep neural network (DNN) after being mapped through the parameterized harmonic kinematic model. Ultimately, the local prediction accuracy and generalization ability of the DNN model are affected by nonlinear kinematic mapping. A space-filling sampling method for sample generation in aerodynamic modeling of the flapping airfoil over complex motion state spaces is proposed to overcome the limitations. The proposed sampling method integrates two stages: an initial sample distribution optimization using a Genetic Algorithm, followed by a sample augmentation stage via active learning. This method is applied to the training-sample selection problem for a two-dimensional NACA0012 flapping airfoil within complex motion state spaces. The results indicate that space-filling sampling is particularly useful for reducing local prediction failures caused by nonlinear kinematic mapping, rather than merely increasing the average accuracy over already well-covered regions.