短期交通量變化混沌特性之探索

Abstract

本研究旨在探索短期交通量變化是否存有混沌特性，並發展混沌預測方法。利用一系列的非線性系統幾何圖型與統計指標，以美國密尼蘇達州I-35州際高速公路一分鐘交通量之變化為測試對象，檢視其時間序列是否屬於隨機或混沌結構，再選出最重要之三項指標，分別為Lyapunov exponent 、Power spectra 、IFS clumpiness map，依此發展出檢測時間序列是否存有混沌特性之簡捷步驟，經利用已知之時間序列驗證本簡捷步驟之有效性後，再應用至其他地點一分鐘交通量之檢測，結果顯示短期交通量時間序列具有明顯之非線性跡象，且混沌時間序列可以成功解釋此種非線性結構。 此外，本研究利用狀態空間重構原理，以及不同之模糊推論方法，發展三種混沌時間序列預測模式。第一種預測模式(TC model)採時間限縮(Temporal Confined)概念，篩選「時間相近」之歷史軌道為模糊相等推論(Fuzzy Equal Inference)之依據。第二種預測模式(STC model)採時空限縮(Spatiotemporal Confined)概念，篩選「時間相近」及「空間相近」之歷史軌道為模糊相等推論之依據，第三種預測模式(SC model)採空間限縮(Spatial Confined)概念，篩選「空間相近」之歷史軌道為模糊比例推論(Fuzzy Proportion Inference)之依據。經以美國密尼蘇達州I-35州際高速公路一分鐘交通量之變化為對象，檢視三種混沌預測模式之預測能力，結果顯示本研究所發展之三種模式均有很好的預測準確度。

This research attempts to test for the presence of low-dimensional chaotic structure and to make predictions for traffic flow time series data. In order to test for chaos phenomena, we undertake a comprehensive comparison of promising plots and statistics between the observed freeway traffic flow data and their surrogates. The most crucial indexes are selected to develop the parsimony procedure. We also utilize some well-known time series data generators to validate the proposed procedure and further apply it to test for the chaoticity of traffic flows at different sites. Our results have shown strong evidence of chaoticity, rather than stochasticity, existent in the nature of freeway short-term (minute) traffic dynamics. In addition, this research develops three prediction models to forecast the chaotic traffic flow time-series data. The temporal confined (TC) model employs temporal similarity of flow trajectories to perform the prediction reasoning. The spatiotemporal confined (STC) model incorporates both spatial and temporal similarities into the prediction reasoning. The spatial confined (SC) model considers the spatial similarity to perform the reasoning. It is found that the three proposed models have demonstrated high prediction accuracy in capturing the short-term traffic flow dynamics.