揭示物理系统的准周期性--以信号交叉口为例
Uncovering Quasi-periodic Nature of Physical Systems: A Case Study of Signalized Intersections
摘要：
提出了一种分析拟周期驱动动力系统的新方法。它旨在开发一个完整的数据驱动框架，用于对这种未知的动态进行建模。为了实现这一点，我们表征库普曼本征频率的准周期驱动器的系统的产生频率。利用再生核希尔伯特空间（RKHS）理论和遍历论的结果计算了Koopman算子的真本征频率.我们还展示了准周期驱动动力学分解成两个组成部分，i）准周期驱动源的产生频率和ii）驱动的非线性动力学。所提出的框架的一个独特的方面是，它适用于分析系统的周期性成分是非主导的，甚至不存在。作为一个案例研究，我们分析了一个系统的九个交通信号交叉口。所提出的框架准确地重建信号交叉口的实测队列长度，并作出稳定的长期预测。
英文摘要：
This paper presents a novel approach to analyze quasiperiodically driven dynamical systems. It aims to develop a complete data-driven framework for modeling such unknown dynamics. To achieve this, we characterize Koopman eigenfrequencies as generating frequencies of the quasiperiodic driver of the system. We compute true eigenfrequencies of Koopman operators by applying the theory of Reproducing Kernel Hibert Space (RKHS) and results from ergodic theory. We also demonstrate the decomposition of quasiperiodically driven dynamics into two components, i) the quasiperiodic driving source with generating frequencies and ii) the driven nonlinear dynamics. A unique aspect of the proposed framework is that it applies to the analysis of systems where the periodic component is either non-dominant or even absent. As a case study, we analyze a system of nine traffic signalized intersections. The proposed framework accurately reconstructs the measured queue lengths of the signalized intersections and makes stable long-term predictions.
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