Modelling of physical systems with a Hopf bifurcation using mechanistic models and machine learning. (15th May 2023)

• Record Type: Journal Article
• Authors: Lee, K.H.; Barton, D.A.W.; Renson, L.
• Is Part Of: Mechanical systems and signal processing. Volume 191(2023)
• Publication Date: 2023-05-15
• Subjects: Hopf bifurcation -- Machine learning -- Hybrid mechanistic/machine-learnt model -- Aeroelastic system -- Limit cycle oscillations; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2023.110173
• Languages: English
• ISSNs: 0888-3270

Abstract

Abstract: 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.