本文關鍵詞： 交通流 Lagrange坐標 連續(xù)方程 多值元胞自動機　出處：《蘭州交通大學》2016年碩士論文　論文類型：學位論文

【摘要】：交通運輸緊密聯(lián)系著居民的生活、社會的發(fā)展和國家的進步。由于交通擁堵和交通事故頻發(fā)不但引起眾多的社會和環(huán)境問題,還阻礙社會經濟的健康發(fā)展。所以要解決交通問題,不但需要利用現(xiàn)有的交通設施資源,還需要通過運用科學的方法研究交通流,對交通進行合理的規(guī)劃、布置和控制,更重要的是理論聯(lián)系實際,應用于實際當中交通項目的建設管理。所以,探索科學的交通理論、發(fā)展先進的交通科技來指導現(xiàn)實生活中交通設施資源的建設,對促進國民經濟的發(fā)展尤為重要。交通流理論用分析法描述現(xiàn)實中的交通情況,能夠真實的反應交通現(xiàn)象和本質,進而提出有效的道路規(guī)劃設計和運營管理方案,以及道路交通事故的預防和解決措施。當前,很多關于交通流的研討都是基于Euler坐標的。Euler方法的研究是在固定的空間位置來觀測物體的運動,觀察在不同時間經過該點的各個質點的變化量隨時間的變化。所以,Euler方法在研究單個質點的運動變化規(guī)律上有局限性。本文運用Lagrange形式的研究方法,通過觀測單個質點上各物理量隨時間的變化,能夠準確的描述單個物體的運動界面,而且還能跟蹤質點的運動軌跡,最后把全部質點的運動軌跡作平均,通過總結進而獲得整個交通流的運動規(guī)律。之后采用元胞自動機模型對Lagrange坐標下的交通流進行仿真,根據實際情況,建立Lagrange坐標下的多值元胞自動機模型,對模型進行模擬仿真,分析仿真結果。首先,對交通流流體力學理論進行概述,詳細介紹交通流基本參數以及三參數之間的關系,然后介紹交通波的基本原理,并對交通波進行簡單分析。其次,分別對Lagrange坐標法和Euler坐標法,以及兩種方法之間的轉換方法進行了介紹。建立Lagrange形式的交通流基本關系式,在此基礎上對LWR方程在Euler坐標下的連續(xù)方程進行離散化,運用質量守恒定律,將Euler坐標轉化成Lagrange坐標下的量,建立Lagrange坐標下的交通流連續(xù)方程,再運用Godunov方法求解這個雙曲線方程。發(fā)現(xiàn)LWR模型的Lagrange形式與一維微觀模型是等價的。再次,對多值元胞自動機模型包括BCA模型、Lagrange形式的多值元胞自動機模型以及GBCA模型的演化方程式進行介紹。重點對Lagrange形式的多值元胞自動機模型的演化方程進行推理,得到任意速度條件下、多車道條件下的演化方程式。最后,對Lagrange形式的多值元胞自動機模型進行建模和仿真。模型采用周期性邊界,對車輛的更新規(guī)則和位置跟蹤方法進行定義。主要包括三方面的仿真:任意速度條件下、多車道條件下和信號引導條件下的Lagrange形式的演化模型進行仿真,并對仿真得到的運行圖和基本圖作對比分析。從各種條件下的仿真結果基本圖可以看出,仿真后的密度、流量、速度三參數的關系與第三章建立的連續(xù)方程中Lagrange形式的交通流參數之間的關系一致,并且與宏觀交通流三參數之間的關系相對應。本文的研究能為實際中解決交通問題、以及道路交通流的時空分布特征提供理論支持。將理論應用于實踐,能夠幫助發(fā)展更加先進的交通研究技術,進而提高交通工作的效率,促進道路暢通,方便居民出行以及促進綠色交通的發(fā)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.

【學位授予單位】：蘭州交通大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：U491

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本文編號：1441698