Uncovering Quasi-periodic Nature of Physical Systems: A Case Study of Signalized Intersections

TL;DR

This paper introduces a data-driven framework for analyzing quasiperiodic dynamical systems, effectively decomposing complex signals and accurately predicting traffic flow at signalized intersections.

Contribution

It develops a novel Koopman operator-based method using RKHS and ergodic theory to analyze systems with weak or absent periodic components.

Findings

Successfully decomposes traffic signals into driving and driven components

Accurately reconstructs queue lengths at intersections

Provides stable long-term predictions of traffic dynamics

Abstract

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.