基于Lagrange坐标的交通流方程的建立与仿真

发布时间：2018-01-18 23:57

本文关键词： 交通流 Lagrange坐标连续方程多值元胞自动机　出处：《兰州交通大学》2016年硕士论文　论文类型：学位论文

【摘要】：交通运输紧密联系着居民的生活、社会的发展和国家的进步。由于交通拥堵和交通事故频发不但引起众多的社会和环境问题,还阻碍社会经济的健康发展。所以要解决交通问题,不但需要利用现有的交通设施资源,还需要通过运用科学的方法研究交通流,对交通进行合理的规划、布置和控制,更重要的是理论联系实际,应用于实际当中交通项目的建设管理。所以,探索科学的交通理论、发展先进的交通科技来指导现实生活中交通设施资源的建设,对促进国民经济的发展尤为重要。交通流理论用分析法描述现实中的交通情况,能够真实的反应交通现象和本质,进而提出有效的道路规划设计和运营管理方案,以及道路交通事故的预防和解决措施。当前,很多关于交通流的研讨都是基于Euler坐标的。Euler方法的研究是在固定的空间位置来观测物体的运动,观察在不同时间经过该点的各个质点的变化量随时间的变化。所以,Euler方法在研究单个质点的运动变化规律上有局限性。本文运用Lagrange形式的研究方法,通过观测单个质点上各物理量随时间的变化,能够准确的描述单个物体的运动界面,而且还能跟踪质点的运动轨迹,最后把全部质点的运动轨迹作平均,通过总结进而获得整个交通流的运动规律。之后采用元胞自动机模型对Lagrange坐标下的交通流进行仿真,根据实际情况,建立Lagrange坐标下的多值元胞自动机模型,对模型进行模拟仿真,分析仿真结果。首先,对交通流流体力学理论进行概述,详细介绍交通流基本参数以及三参数之间的关系,然后介绍交通波的基本原理,并对交通波进行简单分析。其次,分别对Lagrange坐标法和Euler坐标法,以及两种方法之间的转换方法进行了介绍。建立Lagrange形式的交通流基本关系式,在此基础上对LWR方程在Euler坐标下的连续方程进行离散化,运用质量守恒定律,将Euler坐标转化成Lagrange坐标下的量,建立Lagrange坐标下的交通流连续方程,再运用Godunov方法求解这个双曲线方程。发现LWR模型的Lagrange形式与一维微观模型是等价的。再次,对多值元胞自动机模型包括BCA模型、Lagrange形式的多值元胞自动机模型以及GBCA模型的演化方程式进行介绍。重点对Lagrange形式的多值元胞自动机模型的演化方程进行推理,得到任意速度条件下、多车道条件下的演化方程式。最后,对Lagrange形式的多值元胞自动机模型进行建模和仿真。模型采用周期性边界,对车辆的更新规则和位置跟踪方法进行定义。主要包括三方面的仿真:任意速度条件下、多车道条件下和信号引导条件下的Lagrange形式的演化模型进行仿真,并对仿真得到的运行图和基本图作对比分析。从各种条件下的仿真结果基本图可以看出,仿真后的密度、流量、速度三参数的关系与第三章建立的连续方程中Lagrange形式的交通流参数之间的关系一致,并且与宏观交通流三参数之间的关系相对应。本文的研究能为实际中解决交通问题、以及道路交通流的时空分布特征提供理论支持。将理论应用于实践,能够帮助发展更加先进的交通研究技术,进而提高交通工作的效率,促进道路畅通,方便居民出行以及促进绿色交通的发展。
[Abstract]:Transportation is closely related to people's life, social development and national progress. Due to traffic congestion and traffic accidents not only caused many social and environmental problems, but also hinder the healthy development of society and economy. So to solve the traffic problems, not only need to use the existing transportation facilities and resources, but also through the use of scientific methods to study traffic flow needs, reasonable planning and layout of traffic control, more important is the theory and practice, applied to the actual traffic project construction management. Therefore, the scientific exploration of traffic theory, construction and development of advanced transportation technology to guide traffic facilities and resources in real life, is very important to promote the development of the national economy by using the analysis method to describe the traffic situation. The reality of the traffic flow theory, able to respond to traffic phenomena and the nature of reality, and puts forward the effective design of road planning Operation and management scheme, and the prevention of road traffic accidents and measures. At present, a lot of traffic flow of the research is to study the.Euler method based on Euler coordinate is in the space fixed position to observe the movement of objects, observed at different time after the change of the amount of each particle changes with time. So the Euler method, there are limitations in the movement rule of single particle. This paper uses research methods in the form of Lagrange, the amount of the physical observation of a single particle with the change of time, can describe a single object moving interface accurately, but also to track the motion of the particle trajectory, the trajectory of the particle average for all through the summary, and then get the movement rule of the traffic flow. After using the cellular automaton model of Lagrange coordinates of the traffic flow simulation, according to the actual situation, The establishment of the value of the cellular automaton model coordinates Lagrange, simulation model, simulation results and analysis. First, the traffic flow theory of fluid mechanics are summarized in detail, the relationship between traffic flow parameters and three basic parameters, and then introduces the basic principle of traffic wave, and a simple analysis of the traffic wave. Secondly, separately on the Lagrange coordinate and Euler coordinate method, conversion method and two methods are introduced. The establishment of Lagrange forms of traffic flow basic relations, on the basis of the LWR equation in the Euler coordinates of the continuous equation is discretized by using the law of conservation of mass, Euler coordinates into coordinates Lagrange the amount of Lagrange, set up under the coordinate of the traffic flow continuity equation, then use the Godunov method to solve the hyperbolic equation. That is equivalent to the Lagrange form and the microscopic model one-dimensional LWR model . again, the multi value cellular automaton models including BCA model, Lagrange forms of multi value cellular automaton model and GBCA model of the evolution equation are introduced. Focusing on the Lagrange form multi value evolution equation of cellular automaton model for reasoning, get any speed conditions, evolution equation of multi Lane conditions. Finally, on the Lagrange form multi value cellular automaton model for modeling and simulation. The model with periodic boundary conditions, define the update rules of vehicle and position tracking method. Mainly includes three aspects: Simulation of arbitrary velocity under the condition of multi Lane conditions and signals that guide the evolution model of Lagrange form under the condition of simulation operation, map and basic map and the simulation are analyzed. From the simulation result under the condition of different basic map can, after the simulation of density, flow, speed of three. Consistent relationship between traffic flow parameters Lagrange continuity equation relationship with the third chapter to establish the number of, and corresponding relationship between the macroscopic traffic flow parameters. This study can actually solve the traffic problem, and the temporal and spatial distribution of traffic flow and provide theoretical support. The theory is applied to practice, can transportation research to help in the development of more advanced technology, so as to improve the efficiency of transportation work, promote the smooth road, convenient for residents to travel and promote the development of green transportation.

【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：U491

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