城市交通流中的若干非线性密度波方程

发布时间：2018-04-23 10:46

本文选题：交通流 + 跟驰模型　；参考：《宁波大学》2015年硕士论文

【摘要】：本文考虑交通中的一些重要因素,对微观跟驰模型以及宏观格子流体力学模型进行了建模,通过线性和非线性的理论方法,探讨模型的临界相变形态以及在小扰动情形下的交通密度波的演化。论文安排如下：一、考虑预期效应的跟驰模型在实际交通情况中,司机的驾驶行为会对交通产生一定的影响,根据该现象,基于葛红霞等人提出的双速度差跟驰模型,考虑司机的预期效应,我们提出预期双速度差跟驰模型。通过线性稳定性分析,得到中性稳定曲线和临界点,并在临界点附近,运用约化摄动法推导出TDGL和mKdV方程,并通过对热力学势求导得到共存曲线和亚稳态曲线。二、考虑急推效应的跟驰模型在日常交通中,由于很多人都有一些不好的驾驶习惯,例如在红灯前紧急刹车,绿灯时加速过大等,针对这种加减速过于剧烈的状况,我们提出急推效应跟驰模型。通过线性稳定性分析,得到中性稳定曲线和临界点,并在临界点附近,运用约化摄动法推导出TDGL不mKdV方程,并研究了这两种方程的联系。三、考虑预期效应的双车道格子流体力学模型基于Nagatani建立的双车道格子流体力学模型,考虑了预期效应,我们提出了新的格子流体力学模型。目前对单车道连续性模型,非线性分析的较多,而对双车道连续模型分析非常少见,大多数是对模型做数值模拟。在本文中,我们不仅对新模型进行线性分析得到中性稳定曲线,并且进行了非线性分析,得到TDGL方程和nKdV方程,并研究了这两种方程的联系。
[Abstract]:In this paper, considering some important factors in traffic, the micro car-following model and macroscopic lattice hydrodynamic model are modeled, and the linear and nonlinear theoretical methods are used. The critical phase transition morphology of the model and the evolution of the traffic density wave in the case of small disturbance are discussed. The arrangement of the thesis is as follows: first, in the actual traffic situation, the driver's driving behavior will have a certain impact on the traffic. According to this phenomenon, based on the two-speed differential car-following model proposed by GE Hongxia and others, Considering the expected effect of drivers, we propose a model of expected double speed difference following. By linear stability analysis, the neutral stable curves and critical points are obtained. The TDGL and mKdV equations are derived by using the reduced perturbation method near the critical points, and the coexistence curves and metastable curves are obtained by the derivation of thermodynamic potential. Second, in daily traffic, because many people have some bad driving habits, such as emergency braking in front of a red light, excessive acceleration at a green light, and so on, the acceleration and deceleration are too severe in daily traffic. We put forward the model of the rapid-push effect. The neutral stability curve and critical point are obtained by linear stability analysis, and the TDGL non- equation is derived by using the reductive perturbation method near the critical point, and the relationship between the two equations is studied. Third, a two-lane lattice hydrodynamic model with expected effects is proposed. A new lattice hydrodynamic model based on Nagatani is proposed, which takes into account the expected effect. At present, there are many nonlinear analysis for the single lane continuity model, but the analysis for the two-lane continuous model is very rare. Most of the models are numerically simulated. In this paper, we not only obtain the neutral stability curve by linear analysis of the new model, but also obtain the TDGL equation and nKdV equation by nonlinear analysis, and study the relationship between the two equations.
【学位授予单位】：宁波大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U491

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