高速公路動態交通時間狀態特性之分析、預測與應用

Abstract

研究動態交通（Traffic dynamics）的時間狀態特性（Temporal features）與預測短期交通的變化，對尋求解決各項交通問題以及改善先進交通管理系統（Advanced traffic management systems, ATMS）等相關領域效能，均扮演相當重要的關鍵角色。然而傳統一維空間時間序列分析方法，對交通動態隨時間狀態演進的特徵，無法充分掌握其訊息；復以過去許多研究著手進行預測之前，未能審慎考量交通特性暨影響預測準確性的因素，均顯示出過去研究不足之處急待解決。

綜觀過去對交通時間序列的分析，不外乎著重於線性型態的研究，當然，也有為數不少相當有貢獻的研究係著重於探討車輛軌跡在時間-空間上的交互作用；然而這些研究的資料仍僅限於使用模擬模型所產生，其實驗結果缺乏實證交通資料的驗證。因此，本研究利用Takens法則，以多維空間方法進行分析，佐以最大里亞帕諾夫指數（the largest Lyapunov exponent）以及吸引子維度（Correlation dimension），在多維空間中仔細觀察交通流量、速率及佔有率，隨時間演進之軌跡，並藉此發展出一套檢驗動態交通在時間狀態特性的準則。

此外，在本研究中，採用輻狀基底函數類神經網路（Radial Basis Function Neural Network, RBFNN）以及即時回饋學習演算法（Real-time recurrent learning algorithm, RTRL），探討在不同量測尺度、時間稽延、空間維度以及不同時段的情況下，對短期動態交通預測的影響程度；同時在不同預測方法中，利用一階自我迴歸隨機時間序列（First-order autoregressive stochastic time series）與確定性一階微分方程式（Deterministic first-order differential-delay equation），成對比較了[線性-即時回饋學習演算法]與[簡單非線性法-即時回饋學習演算法]在預測能力方面的差異特性。

最後，經由中山高速公路實測資料，進行時間狀態特性的實證研究與短期交通預測的敏感度分析，其結果顯示：隨著量測尺度、歷史資料、觀察時段不同，交通流量、速率及佔有率在多維空間中呈現不同非線性時間形態；而藉由流量-速率-佔有率，三者成對觀察中發現透過時間順序的遞進，多維空間不啻提供更多有效訊息。另外，使用輻狀基底函數類神經網路以及即時回饋學習演算法在短期交通預測方面，具有令人滿意的結果；但是預測準確度也同時會受到量測尺度、時間稽延以及不同時段的影響。本研究的實證成果可做為未來發展交通管理的架構參考，特別是在動態的交通控制方面。

The characterization of the dynamics of traffic states remains fundamental to seeking for the solutions of diverse traffic problems while short-term prediction of dynamic traffic states remains critical in the field of advanced traffic management systems (ATMS) and related areas. However, the scarcity of information provided by conventional one-dimensional traffic time-series data and the hasty prediction without deliberately taking into account the characteristics of traffic dynamics as well as affected factors may have shed light on the lack which need to be solved urgently.

Conventional analysis of traffic time series may play a part in the investigation of traffic patterns characterized by linear statistics. A certain number of studies working at the vehicle trajectories or their interactions within a time-space domain have significant contributions. Nevertheless, most of the results simulated by formulated models are not easy to be calibrated by real data. To gain more insights in traffic dynamics in the temporal domain, this paper explored traffic patterns in higher-dimensional state spaces, where we attempted to map the one-dimensional traffic series into appropriate multidimensional space by Takens’ algorithm. After such a state space reconstruction, we then made use of the largest Lyapunov exponent to depict the rate of expansion or contraction of traffic state trajectories in the reconstructed spaces. The correlation dimension was further estimated to examine if the traffic state trajectories exhibited chaotic-like or stochastic-like motions. In accordance with the above procedures, a novel filtering approach was proposed to inspect the characteristics of real-world temporal traffic flow dynamics.

In addition, a radial basis function neural network (RBFNN) and a real-time recurrent learning algorithm (RTRL) were proposed to learn about whether or not the dynamics of short-term traffic states characterized in different time intervals, collected in diverse time lags, dimensions and times of day have significant influence on the performance of the proposed model relative to the published forecasting methods. Furthermore, we also dabble in comparing pair predictability of linear method-RTRL algorithms and simple nonlinear method-RTRL algorithms individually using a first-order autoregressive stochastic time series AR(1) and a deterministic first-order differential-delay equation.

Finally, an empirical study and a sensitivity analysis were conducted. Wherein, 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 was processed in the empirical study and the same traffic data was fulfilled in the sensitivity analysis with various time intervals, time lags and times of day. The numerical results revealed that different nonlinear traffic patterns could emerge depending on the observed time-scale, history data and time-of-day. In addition, with consideration of sequential order and spatiotemporal features, more information about traffic dynamical evolution was extracted. On the other hand, the performances of RBFNN and RTRL algorithms in predicting short-term traffic dynamics are satisfactorily accepted. Furthermore, it is found that the dynamics of short-term traffic states characterized in different time intervals, collected in diverse time lags and times of day may have significant effects on the prediction accuracy of the proposed algorithms. The above findings may support that the proposed methods in this study can be used to develop traffic management schemes which are practically applicable in dynamic control.