Abstract: Unsteady aerodynamic modeling provides the foundation for flight-quality analysis and flight-control design of high angle-of-attack aircraft. Symbolic, white-box models can explicitly represent unsteady aerodynamic mechanisms and thus mitigate the poor interpretability and limited trustworthiness characteristic of conventional black-box neural-network models, offering greater potential for engineering adoption. To enable efficient, high-fidelity construction of white-box reduced-order aerodynamic models, this paper proposes a frequency-domain unsteady aerodynamic modeling approach 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.

Key words: Unsteady Aerodynamics, Machine Learning, Sparse Identification, CFD, Reduced-Order Model