Discovering Interpretable Dynamic Stall Models from Surface Pressure Data

Dynamic stall is a non-linear aerodynamic phenomenon that arises when there is sufficient unsteadiness at angles of attack close to stall. This can lead to significant fluctuations in aerodynamic loads due to the delay of massive flow separation, causing structural integrity and performance issues. Accurately modelling these unsteady loads is essential for preliminary design and control aimed to mitigate these effects. Current modelling approaches lie on a Pareto front, with increased model accuracy leading to loss in both generalizability and interpretability. Machine learning shows promise in pushing this boundary, but models often lack interpretability. This study aims to outline a framework for learning interpretable, reduced-order dynamic stall models from noisy, unsteady surface pressure measurements. Experiments were conducted on ramp-hold-return pitching motions across a wide range of mean angle of attack, ramp amplitudes and ramp rates - providing unsteady, surface pressure data in pre-stall, stall and post-stall flow regimes for model training. The modelling approach employed a conditional autoencoder structure to compress the high-dimensional surface pressure data to a latent space that is conditioned on the angle of attack. By simultaneously learning the compression with a Neural ODE model on the data trajectories in the latent space, the model discovered an interpretable, low-dimensional representation of the data. A conical manifold structure was presented that highlighted the bifurcation of the system dynamics about the static stall point. The neural ODE model, consisting of two state variables, showed good agreement with unseen test cases ranging from attached flow, to severe dynamic stall. Some disagreement was shown when operating largely in the separated flow regime, which suggested some disagreement between the model fixed points and steady state data. The flow maps of the neural ODE were inspected as a function of angle of attack and demonstrated interpretable behaviour that mirrored the nonlinear dynamics of pitching airfoils. This study highlights future work to replace the neural ODE with symbolic models for better interpretability, and highlights the sensitivity of the output to the training data, namely how it is essential for the model fixed points to align with the steady-state data in the latent space.