Modelling of physical systems with a Hopf bifurcation using mechanistic models and machine learning
This provides a more accurate and data-efficient modeling approach for engineers and physicists studying oscillatory systems like aeroelastic structures, though it is incremental as it builds on existing hybrid modeling concepts.
The authors tackled the problem of predicting limit cycle oscillations in physical systems with Hopf bifurcations by developing a hybrid approach that combines mechanistic normal-form models with machine learning to map to experimental data. The method demonstrated good accuracy and data efficiency in numerical tests on a Van der Pol oscillator and aeroelastic models, and was validated on wind tunnel data of an aeroelastic structure.
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.