This paper contributes towards the development of a reduced-order modelling methodology for nonlinear, unsteady aerodynamic loads for the active control of transonic aeroelastic flutter. To this end, a 1-DOF torsional NACA0012 airfoil is chosen as the test configuration. The aim is to develop the reduced-order model in nonlinear state-space form to be used in active control scenarios. Hence, a nonlinear coupled differential equation that captures the shock dynamics. The underlying hypothesis of this work is that, once these aerodynamic effects are included in the low-order model, the nonlinear trend in the flutter stability boundary, specifically in the transonic regime, will be predicted purely based on first principles, without the need for numerical or experimental corrections. In this work, we observe that the aeroelastic system could become prematurely unstable as soon as the aerodynamic flow field undergoes a Hopf bifurcation. For low amplitude airfoil pitching below a certain threshold, the aerostructural system is seen to exhibit a coupled oscillator behaviour that has an exact linear analytical formulation. The analytical formulation thus produces an accurate prediction whilst being orders of magnitude faster than the numerical simulation. @en

This paper aims to explore the advantages offered by machine learning (ML) for dimensionality reduction of nonlinear transonic aerodynamics. Three ML techniques are evaluated in terms of their ability to generate interpretable low-dimensional manifolds of the transient pressure distributions over a NACA4412 airfoil equipped with a flap. These ML techniques are Kernel Principle Component Analysis (kPCA), Locally Linear Embedding (LLE), and t-distributed Stochastic Neighbourhood Embedding (t-SNE). Initial investigations are also carried out to evaluate the performance of Artificial Neural Networks (ANNs). Three transient aerodynamic test cases are evaluated. First, a static aerodynamic transient analysis. Second, pitching and heaving airfoils in terms of prescribed sinusoidal displacements. Lastly, the airfoil geometry is adapted to include a flap under sinusoidal actuation. The snapshots forming the ground truth are obtained from unsteady CFD simulations. The preliminary results of this study reveal that patterns exist in low-dimensional nonlinear manifolds. Furthermore, unsupervised learning techniques are seen to outperform supervised neural networks in terms of both training cost and reconstruction accuracy. Promising reconstruction capabilities are observed with unsupervised learning.@en