Sparse identification modeling method for unsteady aerodynamics of aircraft

To enable efficient, high-fidelity construction of white-box reduced-order aerodynamic models, a frequency-domain unsteady aerodynamic modeling approach is proposed based on Sparse Identification of Nonlinear Dynamics (SINDy). The proposed method uses simulation data of harmonic aircraft motions at representative amplitudes and frequencies, constructs a candidate function library guided by classical algebraic aerodynamic model architectures, and applies sparse regression to select optimal terms and identify parameters-thereby automatically yielding sparse, highly interpretable reduced-order aerodynamic models. Leveraging both classical algebraic model structures and Theodorsen's unsteady aerodynamic theory, we formulate a globally sampled unified model (SINDyA) and a parameter-varying local model (SINDyB). The approach is validated on two canonical problems-transonic pitch oscillations of the NACA64A010 airfoil and of the CHN-T1 aircraft-using lift and pitching-moment coefficients as modeling targets. Results indicate that the identified models require only a small number of dominant terms to capture the key nonlinear and hysteretic features of the unsteady aerodynamics; the SINDyB model, which performs local interpolation of coefficients, achieves higher prediction accuracy. Because the pitching-moment coefficient exhibits stronger nonlinearity, its prediction proves markedly more challenging than that of lift. The models predict aerodynamic responses accurately under small-amplitude excitations, while performance degrades for large-amplitude, high-frequency cases. These findings demonstrate the promise of symbolic machine-learning methods for constructing high-accuracy, interpretable unsteady aerodynamic models and highlight their potential for engineering application.