  This paper compares the performance of two unsteady aerodynamic reduced-order
models (ROMs), namely linear Volterra series and the autoregressive with
exogenous input (ARX) model, on modeling dynamically linear aerodynamic
behaviors. The difference between these two methods is that the latter model
has an autoregressive term while the former model has only the input-related
term. The first system is a plunging cylinder in a low-Reynolds number flow,
where the flow stable (Re < 47). Although the training data can be fitted well
with both methods, the linear Volterra method requires a higher model order
than the ARX model for the same accuracy. Comparison of the frequency response
indicates that the ARX model approximates the frequency response more closely,
while the frequency response at high Reynolds number is over-fitted by Volterra
series. The second aerodynamic system is a flow over a pitching NACA0012
airfoil, including subsonic and transonic states. The convergence of the model
with respect to delay orders, at different Mach numbers and mean angles of
attack, is studied in detail. As the Mach number or the mean angle of attack
increases, the required delay order will increase. But the ARX model still
models this system with a small number of terms at the same level of accuracy.
All results indicate that the ARX model outperforms the linear Volterra series
in most of cases, especially when the flow is close to the unstable state.
