Using scientific machine learning for experimental bifurcation analysis of dynamic systems

Abstract

Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and reality through measurement data. Our exploratory study focuses on training universal differential equation (UDE) models for physical nonlinear dynamical systems with limit cycles: an aerofoil undergoing flutter oscillations and an electrodynamic nonlinear oscillator. We consider examples where training data is generated by numerical simulations, whereas we also employ the proposed modelling concept to physical experiments allowing us to investigate problems with a wide range of complexity. To collect the training data, the method of controlbased continuation is used as it captures not just the stable but also the unstable limit cycles of the observed system. This feature makes it possible to extract more information about the observed system than the standard, open-loop approach would allow. We use both neural networks and Gaussian processes as universal approximators alongside the mechanistic models to give

Complex nonlinear dynamics and vibration suppression of conceptual airfoil models: A state-of-the-art overview

“…At the same time, they also investigated the transonic flutter boundaries of a NACA 64A010 airfoil to illustrate the performance of the proposed technique. Beregi et al 192 carried out a study that focuses on discovering universal differential equation (UDE) models for a nonlinear aeroelastic airfoil section. Both neural networks and Gaussian processes were considered as universal approximators against the mechanistic models from the first principles.…”