三相混行交通流临界相变高阶模型与实证研究

In order to resolve the disputes between the classical theories based on the fundamental diagram of traffic flow and the three-phase traffic theory, a variety of express highways which have the characteristics of mixed traffic flow and critical phase transition has been chosen for the research in this paper. Through collecting the vehicle data by means of video captures, manual observations and electronic tracking, we established a high-order mathematical model for this traffic flow critical phase transition, with the intention of resolving the divergence of the two theories at critical phenomenon and model of phase transition in a microcosmic aspect. With the aid of the high-order mathematical model, considering the classical simulation models of the two theories and the phase changing process of 'Z' phase and double 'Z' phase, we established a new cellular automata simulation model (CA Model). Setting the reasonable parameters of the mixed traffic flow, this CA model could simulate the free flow, the synchronized flow, as well as the wide moving jam, which might eliminate the disputes of the two theories and amend the shortcomings of them and improve it further. Finally, in order to make up the deficiency and the limitations of the passive observations, we have done a plenty of controllable traffic flow experiments by selecting randomly the expressway sections, the urban roads and some traffic testing areas. By comparison with the results of the feedback data, we expect to prove the correctness and reasonableness of the simulation model and the mathematical model, to provide technical support for further enhancing the road capacity and increasing the stability and the security of road traffic.

本课题从解决传统交通流基本图理论与三相交通流理论的分歧点入手，选取多条具有混行交通流临界相变特征的路段，运用视频采集、人工观测与电子追踪相结合的方法进行数据采集，构建个体车辆交通流临界高阶数学模型，从微观角度逐一解析两种理论在临界现象与相变模式方面存在的争议。依托高阶数学模型，考虑两种理论经典仿真模型及Z字与双Z字相变过程，建立新的元胞自动机仿真模型，通过合理设置混行车流的相关参数，模拟从自由流相、同步流相到宽堵塞运动相三者之间的动态演化过程，旨在消除两种理论争议点的基础上，补充和完善两种临界相变理论的不足。选取特定高速路段、城市路段与交通试验场，进行可控性交通流实验，以弥补被动观测存在的欠缺，根据数据反馈结果对比，验证仿真模型的合理性，确保数学模型的科学性和可靠性，为进一步提高道路通行能力，增加道路交通稳定性与安全性提供技术支持。

三相交通流作为一种典型的自驱远离平衡态系统，对其理论的研究可以加深人们对社会生活中一类伴有复杂的、相互作用的多体系统远离平衡态演化规律的认识，对促进统计物理学、流体力学、非线性动力学、应用数学、交通工程学等多学科交叉研究和发展，不仅具有重要的工程应用价值，还具有深远的科学意义。本项目对三相混行交通流模型及相变机理进行了深入的研究和探讨，从解决传统交通流基本图理论与三相交通流理论的分歧点入手，选取了多个基本图理论及三相交通流理论模型进行比较分析，按计划完成了研究内容，并取得了预期的成果。首先，我们通过构建高阶微分方程建立了一系列的基本图理论模型及三相交通流理论模型。然后，我们以建立的基本图及三相交通流理论模型为基础，通过数值模拟研究了基本图理论以及三相交通流理论下的交通临界特征，并重点分析了个体车辆的六种典型交通临界模式。最后，我们通过实地调研连霍高速公路区段、兰州市城市道路、临合高速公路区段，获得了仿真实验所需的交通流数据，依据获得的数据对仿真模型中的各参数进行了标定，并运用计算机模拟出了自由流相、同步流相到宽堵塞运动相三者之间的动态演化过程。