论文标题
使用深度学习的模型识别MIMO WIENER型Koopman模型用于数据驱动模型
Identification of MIMO Wiener-type Koopman Models for Data-Driven Model Reduction using Deep Learning
论文作者
论文摘要
我们使用Koopman理论来为多输入多输出（MIMO）输入型动力学系统开发数据驱动的非线性模型还原和识别策略。尽管目前的文献集中在线性和双线性Koopman模型上，但我们得出并使用Wiener型Koopman公式。我们讨论维纳结构特别适合减少模型，并且可以自然源自库普曼理论。此外，Wiener块结构统一了线性动力学块的数学简单性和双线性动力学的准确性。我们提出了一种结合自动编码器和线性动力学的Koopman深学习策略，该策略生成了Mimo Wiener类型的低阶替代模型。在三个案例研究中，我们将框架应用于具有输入多重性，化学反应器和高纯度蒸馏柱的系统的识别和减少。我们将确定的Wiener模型的预测性能与线性和双线性Koopman模型进行了比较。我们观察到低阶Wiener型Koopman型号的最高精度和最强的模型还原能力，使它们有望控制。
We use Koopman theory to develop a data-driven nonlinear model reduction and identification strategy for multiple-input multiple-output (MIMO) input-affine dynamical systems. While the present literature has focused on linear and bilinear Koopman models, we derive and use a Wiener-type Koopman formulation. We discuss that the Wiener structure is particularly suitable for model reduction, and can be naturally derived from Koopman theory. Moreover, the Wiener block-structure unifies the mathematical simplicity of linear dynamical blocks and the accuracy of bilinear dynamics. We present a Koopman deep-learning strategy combining autoencoders and linear dynamics that generates low-order surrogate models of MIMO Wiener type. In three case studies, we apply our framework for identification and reduction of a system with input multiplicity, a chemical reactor and a high-purity distillation column. We compare the prediction performance of the identified Wiener models to linear and bilinear Koopman models. We observe the highest accuracy and strongest model reduction capabilities of low-order Wiener-type Koopman models, making them promising for control.
