论文标题
使用机械模型和机器学习对实体系统建模
Modelling of physical systems with a Hopf bifurcation using mechanistic models and machine learning
论文作者
论文摘要
我们提出了一种新的混合建模方法，该方法将机械模型与机器学习模型相结合，以预测具有HOPF分叉的物理系统的极限周期振荡。机械模型是一种普通的微分方程法线形式模型，可捕获系统的分叉结构。然后，根据实验数据，使用机器学习技术来识别从该模型到实验观察结果的数据驱动映射。首先在范德尔振荡器和三级自动弹性弹性模型上进行数值证明。然后将其应用于在风隧道测试期间表现出极限周期振荡的物理弹性结构的行为。该方法被证明是一般，数据效率的，并且可以提供良好的准确性，而没有任何对系统除分叉结构以外的其他知识。
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.
