基于格子流体力学模型的交通流建模及仿真研究

发布时间：2018-06-17 16:30

本文选题：交通流 + 智能交通系统　；参考：《北京交通大学》2015年博士论文

【摘要】：道路交通流的运行状态直接影响整个城市交通系统的稳定性,一旦城市交通系统失稳将给社会环境带来各种不利因素,如交通堵塞、环境污染、资源浪费、事故频发等。本文利用格子流体力学理论研究了封闭系统和开放系统中的宏观交通流建模问题。一方面,在封闭系统中借助智能交通系统理念,分别构建了单车道、双车道格子流体力学模型,并对模型进行线性和非线性分析,通过数值仿真验证理论分析结果,进一步在亚稳态区域研究不同扰动在交通流中的演化情况；另一方面,城市交通系统本身就是开放的复杂巨系统,而其中交通瓶颈是阻碍交通系统运行状态的集中点,也是引起城市交通病的症结所在。本文将新建的道路交通模型应用到不同类型的交通瓶颈中,重现了实测观察到的交通流拥挤模式,分析不同交通拥挤模式演化机理及形成条件。具体来讲,本文研究工作包括如下几个方面： (1)首先在封闭系统中,借助智能交通系统,充分考虑前面多个格子的密度信息对当前格子的影响,建立基于密度差格子流体力学合作驾驶模型。采用线性稳定性理论和摄动理论对新建模型进行分析,前者可以得到模型的线性稳定性条件,后者推导出了描述拥挤区域密度波的mKdV方程,同时求得了关于密度的扭矩-反扭矩解。通过数值仿真发现合作驾驶能够提高交通流的稳定性。其次,把单车道密度差格子流体力学模型扩展到双车道,建立双车道格子流体力学模型。与合作驾驶模型一样,通过上述两种理论方法和数值模拟对该模型中的交通流特性进行了理论分析和仿真研究。结果表明：在双车道系统中考虑密度差的作用同样可以提高交通流的稳定性。 (2)进一步依据Kerner三相交通流理论中描述的同步流特征,单纯的密度并不能完全反映拥挤区域的交通流状况,因此本文考虑下游多个格子的流量信息建立合作驾驶模型。通过对所构建的新模型进行理论分析得到解析的线性稳定性条件,通过非线性分析方法对模型进行分析,推导出了其mKdV方程并求得解析解。在上述分析的基础上,本文采用敏感系数-密度的相空间图阐述了流量差信息在改善交通流稳定性方面的作用。并通过数值模拟得出在ITS系统中合作驾驶的最优作用范围。此外,通过延伸研究将流量差作用引入到双车道封闭系统中,建立了考虑流量差的双车道格子流体力学模型。不仅从理论上对模型进行了线性和非线性研究,还对亚稳态区域扰动随时间的演化情况进行了仿真研究,同样得到了有意义的结论。 (3)基于本文所构建的双车道密度差模型,在封闭系统中采用摄动方法推导模型的KdV方程,此方程中通过逆散射变换求得准确的孤子解。在开放边界条件下对模型进行数值模拟,得到随着时间的推移保持其形状不变且向上游传播的孤子。此外,本文通过在开放系统下游设置格子的密度以随机扰动的方式进行波动研究实测阻塞交通流模式。通过调整系统初始密度,系统复现了各种实测交通流拥挤模式,并给出了这些拥堵模式的相基本图。实测的拥挤模式主要包括：运动局部阻塞、引发的时走时停交通波、震荡拥挤流和均匀拥挤流。此外,通过数值模拟,给出了相基本图中所有交通流模式的时空演化图。 (4)为克服密度差双车道格子流体力学模型中会出现车辆倒退的现象,本文采用改进的换道规则和流量转移函数,建立了新的双车道格子流体力学模型。新模型不同于以前的双车道模型,左右两个车道的守恒方程各自独立且通过换道相互关联。首先,结合该模型,论文设计了确定型的入匝道和两种随机型入匝道。新模型应用于随机型匝道系统时除了能够预测第四章中的四种拥挤模式外,还能预测同步流(HST)拥挤模式和固定的局部集簇(PLC)。其次,设计入匝道与出匝道的组合匝道系统。新模型在组合交通瓶颈中依然能够预测MLC、PLC、TSC、 OCT和HCT拥挤模式,且在同样的初始条件下,组合匝道中交通流的阻塞程度远远小于入匝道瓶颈系统中的阻塞程度。
[Abstract]:The running state of the road traffic flow directly affects the stability of the whole urban traffic system. Once the instability of the urban traffic system will bring all kinds of unfavorable factors to the social environment, such as traffic jam, environmental pollution, waste of resources, frequent accidents and so on. This paper uses the lattice fluid mechanics theory to study the macroscopic intersection in the closed system and the open system. On the one hand, in the closed system, with the help of the idea of intelligent traffic system, a single lane, two lane lattice hydrodynamics model is constructed respectively, and the linear and nonlinear analysis of the model is carried out. The theoretical analysis results are verified by numerical simulation, and the evolution of different disturbances in the traffic flow is further studied in the metastable region. On the other hand, the urban traffic system itself is an open and complex giant system, and the traffic bottleneck is the central point that hinders the running state of the traffic system. It is also the crux of the urban traffic disease. In this paper, the new road traffic model is applied to different types of traffic bottlenecks, and the observed traffic congestion is reproduced. The evolution mechanism and formation conditions of different traffic congestion modes are analyzed. Specifically, the research work in this paper includes the following aspects:
(1) first of all, in the closed system, with the help of the intelligent traffic system, the density difference lattice fluid dynamics cooperative driving model based on the density difference lattice fluid dynamics is fully considered. The linear stability theory and perturbation theory are used to analyze the new model. The former can obtain the linear stability condition of the model. The latter derives the mKdV equation describing the density wave in the crowded area and obtains the torque reverse torque solution about the density. Through the numerical simulation, it is found that cooperative driving can improve the stability of the traffic flow. Secondly, the single lane density difference lattice fluid mechanics model is extended to the double lane, and the two lane lattice hydrodynamics model is established. As a driving model, the traffic flow characteristics in the model are analyzed and simulated through the two theoretical methods and numerical simulations. The results show that the stability of traffic flow can be improved by considering the effect of density difference in the dual lane system.
(2) according to the characteristics of the synchronous flow described in the Kerner three phase traffic flow theory, the simple density does not fully reflect the traffic flow situation in the crowded area. Therefore, this paper considers the traffic information of the downstream multiple lattices to establish the cooperative driving model. By theoretical analysis of the new model, the analytic linear stability bar is obtained. By analyzing the model by nonlinear analysis method, the mKdV equation is derived and the analytical solution is derived. On the basis of the above analysis, the function of the flow difference information in improving the stability of traffic flow is explained by the phase space diagram of the sensitive coefficient density, and the best cooperative driving in the ITS system is obtained by numerical simulation. In addition, by introducing the flow difference into a double lane closed system by extending the flow difference, a two lane lattice hydrodynamics model, which considers the flow difference, is established. Not only is the linear and nonlinear study of the model, but also the simulation of the evolution of the metastable regional disturbance is also studied. To a meaningful conclusion.
(3) based on the two lane density difference model constructed in this paper, the KdV equation of the model is derived by the perturbation method in the closed system. In this equation, the exact soliton solution is obtained by the inverse scattering transformation. The model is numerically simulated under the open boundary condition, and the soliton propagating to the upstream is maintained with the passage of time. In addition, in this paper, the traffic flow pattern is measured by random disturbance in the way of setting the density of the lattices in the downstream of the open system. By adjusting the initial density of the system, a variety of traffic flow congestion models are reproduced, and the phase basic diagrams of these congestion modes are given. The measured congestion mode mainly includes: Movement In the case of local congestion, traffic waves are stopped at the time of departure, and the congestion and congestion flow are concussion. In addition, the spatio-temporal evolution of all traffic flow patterns in the phase basic diagram is given by numerical simulation.
(4) in order to overcome the phenomenon that the vehicle falls back in the density difference double lane lattice fluid mechanics model, a new double lane lattice fluid mechanics model is established by using the improved channel change rule and the flow transfer function. The new model is different from the previous two lane model, and the conservation equations of the left and right two lanes are independent and through the channel change phase. First, combining the model, the paper designs the deterministic ramp and two random ramps. The new model can predict the HST congestion mode and the fixed local cluster (PLC) in addition to the prediction of four congestion modes in the fourth chapter. Secondly, the ramp and the ramp are designed. Combined ramp system. The new model can still predict MLC, PLC, TSC, OCT and HCT congestion in combined traffic bottlenecks. Under the same initial conditions, the congestion of the traffic flow in the combined ramp is far less than the degree of congestion in the bottleneck system of the ramp.
【学位授予单位】：北京交通大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：U491.112

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