Learning Aircraft Spin Dynamics from Measurement Data Using Hankel DMDc with Error in Variables

Aircraft spin, a nonlinear phenomenon dominated by unsteady aerodynamics, is difficult to predict. This article proposes a novel approach using Hankel Dynamic Mode Decomposition with Control (HDMDc) to identify an aircraft plant model for spin motion directly from measurement data. A key challenge in real-world data-driven modeling is addressing noise in both input and output measurements, often termed errors in variables (EIV). The standard HDMDc does not account for the distinct noise characteristics of different sensors. To overcome this, modifications are proposed to the standard HDMDc algorithm using EIV approaches: total least squares and bias-eliminating least squares. The proposed algorithms are validated first with a simple nonlinear dynamical system exhibiting limit cycle oscillation. Further, the methodology is applied to the simulated steady spin of the T-2 aircraft and the oscillatory spin motion of the F-18 aircraft. It is demonstrated that models identified using HDMDc with the EIV approach predicted spin trajectories with high goodness-of-fit values, even for unseen control inputs and initial conditions that differed from the training data. Specifically, the predicted trajectories had a FIT% close to 90% in most cases, with the worst-case FIT% being 38%. In contrast, the standard HDMDc algorithm’s predicted trajectory was not even visually close to the actual system trajectory, highlighting the significant improvement of the modified approach.