交通時間序列在多維空間中的特性

Features of Traffic Time-series on Multi-dimensional Spaces

傳統一維空間時間序列分析方法，對交通動態隨時間演進的特徵，無法充分掌握其訊息，本研究透過映射將一維時間序列資料，以多維空間方法進行分析，佐以最大里亞帕諾夫指數，在多維空間中仔細觀察交通流量、速率及占有率，隨時間演進之運動軌跡收斂或發散，並在空間中量測吸引子維度以確認其形態，同時藉由流量--速率--占有率，三者成對觀察中發現透過時間順序的遞進，多維空間方法不啻提供更多有效訊息。經以中山高速公路路面感應器實測資料進行分析發現，隨著量測尺度、歷史資料、觀察時段不同，交通流量、速率及占有率在多維空間中呈現不同非線性形態。

Investigation of traffic dynamics via advanced techniques for characterizing time-varying traffic data in multiple dimensions may provide more insights on dynamic traffic phenomena. Considering the scarcity of information provided by conventional one-dimensional traffic time-series data, this paper presents a novel analytical approach to explore the dynamics of traffic phenomena in multi-dimensional state spaces. Using four proposed parameters, including time delay, embedding dimension, the largest Lyapunov exponent, and attractor dimension, the proposed methodology reconstructs the traffic state space via mapping one-dimensional traffic time-series data into appropriate multidimensional spaces. Therein, the largest Lyapunov exponent is used to characterize the rate of expansion or contraction of traffic trajectories in the reconstructed spaces, and the attractor dimension is estimated to examine if the traffic trajectories exhibit deterministic-like features or not. An empirical study on flow, speed, and occupancy time-series data as well as the speed-flow, speed-occupancy, and flow-occupancy paired data collected from dual-loop detectors on a freeway of Taiwan is conducted. The results reveal that different nonlinear traffic features could emerge, depending on the observed time-scale, history data, and time-of-day. In addition, with consideration of sequential order, more information about traffic dynamical evolution is extracted.