Modelling of physical systems with a Hopf bifurcation using mechanistic models and machine learning

We propose a new hybrid modelling approach that combines a mechanistic model with a machine-learnt model to predict the limit cycle oscillations of physical systems with a Hopf bifurcation. The mechanistic model is an ordinary differential equation normal-form model capturing the bifurcation structure of the system. A data-driven mapping from this model to the experimental observations is then identified based on experimental data using machine learning techniques. The proposed method is first demonstrated numerically on a Van der Pol oscillator and a three-degree-of-freedom aeroelastic model. It is then applied to model the behaviour of a physical aeroelastic structure exhibiting limit cycle oscillations during wind tunnel tests. The method is shown to be general, data-efficient and to offer good accuracy without any prior knowledge about the system other than its bifurcation structure.

Automated summary

We present a novel hybrid modelling approach that integrates a mechanistic model and a machine-learnt model for predicting limit cycle oscillations in physical systems with a Hopf bifurcation. The mechanistic model, in the form of an ordinary differential equation, captures the bifurcation structure of the system. Through machine learning techniques, a data-driven mapping is established between this model and experimental observations. The efficacy of the proposed method is demonstrated through numerical simulations on Van der Pol oscillator and a three-degree-of-freedom aeroelastic model, as well as its application to a physical aeroelastic structure in wind tunnel tests. The method is shown to be general, data-efficient, and accurate even without prior knowledge of the system other than its bifurcation structure.