ORCID
https://orcid.org/0000-0001-7708-7974
Keywords
Data-driven dynamical systems, Traffic flow, Self-similarity, Extreme value theory, Koopman operator, Gray-box model
Abstract
The dissertation demonstrates the applicability of the data-driven dynamical systems (DDS) approach at both macroscopic and microscopic scales to extract mathematical structures from observed traffic data. Firstly, a novel DDS model is developed to capture the evolution of queue lengths in a signalized arterial corridor, dividing the dynamics into quasiperiodic and chaotic components. The proposed model effectively captures nonlinear dynamics from time series data. The Reproducing Kernel Hilbert Space (RKHS) method is employed to estimate mathematically guaranteed Koopman eigenvalues and functions of the system, providing valuable insights into the periodic and chaotic behaviors of the system. Secondly, to further characterize the periodic nature of the dynamics, the study performs a power spectral density analysis, which reveals a 1/f structure, indicating the presence of self-similar fractals in the time series. This self-similarity is also identified in the time domain through detrended fluctuation analysis, suggesting a link between quasi-periodicity and fractal behavior. Thirdly, the dissertation aims to understand the characteristics of the nonperiodic component of the dynamics by analyzing the distribution of residuals in the time series computed after removing the periodic and trend components. The analysis reveals that the residuals follow an extreme value distribution, highlighting an implicit relationship between chaos and extreme events. Finally, the study explores microscopic traffic flow modeling by introducing a data-driven car-following model that employs the Dynamic Mode Decomposition (DMD) technique to capture vehicular interactions at a microscopic level. Additionally, it explores appropriate observable functions for car-following behavior, deepening the understanding of traffic flow at the individual vehicle level. Through these contributions, the dissertation provides a foundation for integrating dynamical systems theory into traffic modeling, aiming to enhance interpretability in data-driven modeling.
Completion Date
2024
Semester
Fall
Committee Chair
Agarwal, Shaurya
Degree
Doctor of Philosophy (Ph.D.)
College
College of Engineering and Computer Science
Department
Department of Civil, Environmental and Construction Engineering
Degree Program
Civil Engineering
Format
Identifier
DP0029021
Language
English
Release Date
12-15-2024
Access Status
Dissertation
Campus Location
Orlando (Main) Campus
STARS Citation
Mustavee, Shakib, "Bridging Data and Theory: A Gray-Box Approach to Traffic Flow Dynamics" (2024). Graduate Thesis and Dissertation post-2024. 56.
https://stars.library.ucf.edu/etd2024/56
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