Using scientific machine learning for experimental bifurcation analysis of dynamic systems
Using scientific machine learning for experimental bifurcation analysis of dynamic systems
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DOI：
10.1016/j.ymssp.2022.109649
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发表时间：
2021-10
期刊：
影响因子：
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通讯作者：
S. Beregi;D. Barton;D. Rezgui;S. Neild
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文献类型：
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作者：
S. Beregi;D. Barton;D. Rezgui;S. Neild
使用机器可学习结构增强机械常微分方程 (ODE) 模型是一种新颖的方法，可以通过测量数据创建高精度、低维的工程系统模型，将专家知识和现实结合起来。我们的探索性研究重点是训练具有极限环的物理非线性动力系统的通用微分方程 (UDE) 模型：经历颤振的机翼和电动非线性振荡器。我们考虑通过数值模拟生成训练数据的示例，同时我们还将所提出的建模概念应用于物理实验，使我们能够研究各种复杂性的问题。为了收集训练数据，使用基于控制的连续方法，因为它不仅捕获观察系统的稳定极限环，而且捕获不稳定极限环。与开环方法（通过参数扫描而不使用控制来调查稳态响应）相比，此功能可以提取更多有关观察系统的信息。我们使用神经网络和高斯过程作为通用逼近器以及机械模型，对 UDE 建模方法的准确性和鲁棒性进行严格评估。我们还强调了在训练过程中可能遇到的潜在问题，表明当前建模框架的局限性。
Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is a novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and reality through measurement data. Our exploratory study focuses on training universal differential equation (UDE) models for physical nonlinear dynamical systems with limit cycles: an aerofoil undergoing flutter oscillations and an electrodynamic nonlinear oscillator. We consider examples where training data is generated by numerical simulations, whereas we also employ the proposed modelling concept to physical experiments allowing us to investigate problems with a wide range of complexity. To collect the training data, the method of control-based continuation is used as it captures not just the stable but also the unstable limit cycles of the observed system. This feature makes it possible to extract more information about the observed system than the open-loop approach (surveying the steady state response by parameter sweeps without using control) would allow. We use both neural networks and Gaussian processes as universal approximators alongside the mechanistic models to give a critical assessment of the accuracy and robustness of the UDE modelling approach. We also highlight the potential issues one may run into during the training procedure indicating the limits of the current modelling framework.