State consistence of data-driven reduced order models for parametric aeroelastic analysis

This paper investigates the state consistence of parametric data-driven reduced order models (ROMs) in a state-space form obtained by various system identification methods, including autoregressive exogenous (ARX) and subspace identification (N4SID), for aeroelastic analysis in varying flight conditions. The target flight envelop is first partitioned into discrete grid points, on each of which an aerodynamic ROM is constructed using system identification to capture the dependence of the generalized aerodynamic force on the generalized displacement of structural modes. High-fidelity aeroelastic modal perturbation simulations are used to generate the ROM training and verification data. Aerodynamic ROMs not on the grid point are obtained by interpolating those at neighboring grid points. Through a thorough analysis of the model coefficients and pole migration, it is found that only the ARX-based aerodynamic ROM preserves the state consistence, and hence, allowing direct interpolation of system matrices at the non-grid point and rapid aerodynamic ROM database development in the entire flight parameter space. In contrast, N4SID-based ROM destroys the state consistence and yields physically meaningless results when ROMs are interpolated. The origin of the difference in the state consistence caused by both methods is also discussed. The interpolated ARX aerodynamic ROMs coupled with the structural ROM for parametric aeroelastic analysis exhibit excellent agreement with the high fidelity full order model (mostly <5% relative error) and salient computational efficiency.