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

TL;DR

This paper introduces a hybrid modeling approach combining mechanistic and machine learning models to accurately predict limit cycle oscillations in physical systems with Hopf bifurcations, demonstrated on numerical and real-world aeroelastic data.

Contribution

It presents a novel hybrid modeling method that leverages mechanistic bifurcation models and machine learning to predict complex oscillatory behavior without extensive prior knowledge.

Findings

Effective in modeling limit cycle oscillations

Data-efficient with high accuracy

Applicable to physical aeroelastic systems

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.