Parametrized Global Linearization Models for Flutter Prediction

We present a data-driven flutter analysis and prediction method based on the Koopman theory. The Koopman formalism represents nonlinear dynamics in a higher-dimensional linear space via the so-called lifting of coordinates. The resulting linear model is valid over an wide region, and sometimes globally, in the state space, and thus provide a potent tool to extend the classical linearized stability analysis for flutter to a global stability analysis procedure. In this paper we first present how a nonlinear aeroelastic system is represented using a bilinear model, with an input-affine term for the flutter parameter. Next, the eigenvalues and eigenvectors of the bilinear model are rigorously connected to those of the nonlinear dynamics, in both cases of fixed point (i.e., equilibrium point) and limit cycle (i.e., flutter). Finally, the presented methods are demonstrated on a 2D academic example and a more realistic panel flutter problem and, in particular, show how the pre-flutter data can be used to predict the flutter point in a model-free data-driven manner.