Experimental Data-Driven Volterra Modeling of Flapping-Wing Aerodynamics

Within the field of robotic birds, it is essential to develop efficient models capable of meeting the requirements of real-time control systems, thereby enabling semi-autonomous or autonomous flight. High-fidelity computational fluid dynamics simulations are generally unsuitable for online applications because of their computational cost, while traditional theoretical models are often unable to adequately capture the complex aerodynamic phenomena involved. Reduced-order data-driven modeling techniques offer a promising alternative. This work investigates the use of first-order Volterra models for predicting the aerodynamic forces generated by a flapping wing from measurable kinematic variables. The analysis is carried out using a publicly available experimental dataset obtained from a dynamically scaled robotic wing at Re = 1000. A single-input model and three two-input configurations were identified for both the normal and chordwise aerodynamic force components using ridge-regularized least squares. Candidate inputs were selected through mutual-information analysis, while model hyperparameters were determined through five-fold cross-validation. The wing-normal velocity was selected as the primary input, while pitching velocity, normal acceleration and angle of attack were evaluated as candidate second inputs, with pitching velocity yielding the best overall performance among the considered configurations. On the independent test set, the single-input models yielded mean RRMSE values of 26.64% and 37.53% for the normal and chordwise force components respectively. Including pitching velocity reduced these values to 21.60% and 25.25%, corresponding to improvements of 5.04 and 12.28 percentage points. These findings show that, even when truncated at the first order, a Volterra-series based model with appropriately selected inputs can make a useful prediction of the aerodynamic loads generated by a flapping wing, motivating further development toward higher-order models and model-based flight-control applications.