行人流数值模拟的若干新方法

发布时间：2018-05-02 05:49

  本文选题：行人流数值方法 + 元胞模型　； 参考：《上海大学》2015年博士论文

【摘要】：行人流数值模拟的基本目标是通过建模和模拟的方法重现行人在各种场景下的运动状态,研究各种典型现象背后蕴含的机理。本文提出了几种新的行人流数值模拟方法,并将其应用到行人流的若干典型问题中。文中回顾了行人流研究历史,对几种典型行人流模型的基本方法与建模思路做了系统阐述。在此基础上,做了如下工作:一.提出了一种基于背景场的多向行人流相互作用元胞模型,并将该模型应用于行人对流和正交流问题的研究。为了反映更加真实的行人间相互作用,在背景场模型的基础上建立了多向行人流的相互作用模型。该模型的特点在于:将一组行人的动态场作为另一组行人的参考依据,借此体现行人跟随-避让的基本选择。同时,假设两组行人的冲突强度与运动方向的夹角有关,以便灵活处理多种情况下的多向行人流问题。在行人个体方面,还假设行人间存在有条件的换位行为。此外,改进了动态场耗散性,使其更加符合行人避免冲突的心理。在将该模型应用至对流问题后,通过数值试验分析讨论了动态场强度、行人流平均密度以及动态场耗散-衰减作用等模型参数对行人流成行现象的各方面影响,包括成行现象中的行人队列数、非同向行人间的换位次数以及成行现象的发生概率等。从而获知,动态场强度对成行现象的影响可分为两个密度区间,只有在高密度区间其影响才是显著的;而动态场的耗散与衰减都直接影响行人队列的稳固程度,并间接影响成行概率与行人间的换位次数。在数值试验中还发现,平均个人换位次数这一参数可以用来区分成行与不稳定成行现象。针对正交流,相互作用模型重现了其对应的拟定常态,数值结果反映出行人绕路和路径穿越等一系列行为。特别是,当行人流密度持续增加时,交互区外的部分行人会沿着已有路径通过交互区,而不是开辟新的路径。二.将社会力思想引入元胞自动机模型,设计了两种复合模型。利用两者的基本图,研究了行人的疏散问题与瓶颈对流问题。设计了两种将社会力与元胞模型相结合的复合模型,即基本复合模型与S-RCA模型。基本复合模型建立在静态场上,为了更加真实地反映行人运动的特征,引入了最小运动步数、行人视野以及元胞效费比的概念。假设行人的移动概率与所受社会力的分量有关。而S-RCA模型则利用了RCA模型的原理,使得行人能够以任意速度向任意方向移动。将行人的驱动力表示为行人周围行人流等效密度的函数,真实反映了不同情况下的行人心理预期。此外,S-RCA模型的还将行人的受力限制在试验范围内,减小了模型的计算时间的耗费。基本模型的基本图测算表明,在一些参数条件下结果与观测数据相吻合,说明了模型的合理性。另外,基本图还反映出视野范围和跟随行为对行人运动效率的影响具有两面性。S-RCA模型的基本图与Helbing等实测得到的基本图相近,同时数值结果揭示了行人视野和行人间距与行人运动效率的关系:行人视野只有在低密度区间内才对提高运动效率有利,而适当的间距有助于提高行人流整体的移动速度,过小或过大则起反作用。这些结论都与现实中的行人运动常识相符。在将S-RCA模型应用于瓶颈疏散问题的过程中,数值试验结果表明,行人视野对行人疏散效率的影响与瓶颈宽度有关;行人间距对行人疏散效率的影响则具有两面性。试验所得的瓶颈处流量与Nagai等[163]试验结果基本吻合,该结果还同时验证了设施内行人流初始密度对瓶颈处流量存在的影响。在对行人个体疏散时间的讨论上,试验测得了几种经典情况下疏散时间的空间分布。结果表明疏散时间分布与瓶颈宽度、行人视野和排斥力强度等因素密切相关。接着,重点讨论了有相对排斥力因子的S-RCA模型在瓶颈对流问题中的应用。模拟结果显示,瓶颈对流时的行人流运动可归结为死锁、振荡流与双向流三种典型现象的混合,而且这三种现象的发生概率与瓶颈宽度、行人间排斥力(行人间距)以及相对排斥力因子的大小有关。三.将松弛-WENO格式引入行人流流体力学模型的数值模拟,论证了流体力学模型下的对流成行现象对初始-边界条件的敏感性。行人流反应型动态用户最优模型的对流项通过程函方程与密度隐式相关,判断特征速度常采用估计的方法。通过将松弛-WENO格式引入行人流流体力学模型的数值模拟。这种方法将守恒方程改写为具有线性对流项与非线性刚性项的松弛系统,便于在WENO这样的高阶格式内对流通量直接采取迎风离散,简化了数值格式。利用此格式模拟了不同初始-边界条件下的行人对流问题。数值试验表明,在流体力学模型中,行人对流问题对初始-边界条件有敏感性,此结果拓展了此领域已有的研究结论。在一种初始-边界条件下,行人流的入流直接影响行人的相对速度并间接影响行人队列的形成。而在另一种初始-边界条件下,衡量行人间相互作用强度的参数只有在较低密度区间内才对行人成行有直接影响。最后,在总结本文工作的基础上提出了在未来工作中的重点研究方向和亟待解决的问题。
[Abstract]:The basic goal of the numerical simulation of pedestrian flow is to reproduce the motion state of pedestrians in various scenes by modeling and simulation, and to study the mechanism behind the typical phenomena. In this paper, several new numerical simulation methods of pedestrian flow are proposed and applied to the typical problems of pedestrian flow. The study of pedestrian flow is reviewed in this paper. In history, the basic methods and modeling ideas of several typical pedestrian flow models are systematically expounded. On this basis, the following work is done: firstly, a multidirectional pedestrian interaction model based on the background field is proposed, and the model is applied to the study of pedestrian convection and positive communication. The interaction model is built on the basis of the background field model. The characteristic of this model is that the dynamic field of a group of pedestrians is used as the reference basis of another group of pedestrians, thus the basic choice of pedestrian following and avoidance is embodied. At the same time, it is assumed that the conflict intensity of the two groups of pedestrians is related to the angle of the direction of movement. In addition, it improves the dynamic field dissipation and makes it more consistent with the psychology of pedestrians avoiding conflict. After applying the model to the problem of convection, the dynamic field intensity is discussed and discussed through numerical experiments. The model parameters such as the average density of the flow of human flow and the dissipation and attenuation of dynamic field influence all aspects of the pedestrian flow, including the number of pedestrians, the number of transposition between non identical pedestrians and the probability of the occurrence of rows, and the effect of the dynamic field intensity on the row phenomenon can be divided into two density intervals. It is only in the high density interval that the effect is significant, and the dissipation and attenuation of the dynamic field directly affect the stability of the pedestrian queue and indirectly affect the number of transposition between the pedestrian probability and the pedestrians. The interaction model reproduces the corresponding normal state, and the numerical results reflect a series of behaviors such as the travel and path crossing. Especially, when the traffic density continues to increase, some pedestrians outside the interactive zone pass through the interactive zone along the existing path, but not the new path. Two. The idea of social force is introduced into the cell. Two kinds of composite models are designed. Using the basic diagram of the two, the problem of pedestrian evacuation and bottleneck convection is studied. Two complex models, the basic compound model and the S-RCA model, are designed to combine the social force with the cellular model. The basic compound model is built on the static field to reflect the pedestrian more truly. The concept of the minimum movement step number, pedestrian vision and cellular efficiency ratio is introduced. Assuming that the pedestrian moving probability is related to the component of the social force, the S-RCA model makes use of the principle of RCA model so that pedestrians can move to any direction at any speed. The driving force of pedestrians is expressed as pedestrian flow around pedestrians. The function of the equivalent density reflects the psychological expectation of pedestrians in different circumstances. In addition, the S-RCA model also limits the force of pedestrians to the test range, which reduces the time cost of the model. The basic model calculation shows that the result of the model is consistent with the observation data under some parameters, indicating the rationality of the model. In addition, the basic map also reflects the effect of field of vision and following behavior on the efficiency of pedestrian movement. The basic map of the two sides.S-RCA model is similar to that obtained by Helbing. At the same time, the numerical results reveal the relationship between pedestrian vision and pedestrian space and the efficiency of pedestrian movement: the pedestrian vision is only in the low density interval. It is beneficial to improve the movement efficiency, and the appropriate spacing helps to improve the movement speed of the pedestrian flow as a whole, and it is counterproductive. These conclusions are consistent with the common sense of the pedestrian movement in the reality. In the process of applying the S-RCA model to the problem of bottleneck evacuation, the numerical results show that the pedestrian vision has a shadow on the efficiency of pedestrian evacuation. The effect of the pedestrian spacing on the pedestrian evacuation efficiency is two sides. The flow rate of the bottleneck is basically consistent with the results of the [163] test, such as Nagai. The results also verify the effect of the initial density of the pedestrian flow on the flow rate at the bottleneck. The spatial distribution of the evacuation time is measured in several classic cases. The results show that the evacuation time distribution is closely related to the bottleneck width, the pedestrian vision and the strength of the rejection. Then, the application of the S-RCA model with relative rejection factor in the bottleneck convection problem is discussed. The simulation results show that the pedestrian flow in the bottleneck convection is carried out. The motion can be attributed to the mixing of deadlock, oscillating flow and two-way flow, and the probability of the three phenomena is related to the size of the bottleneck width, the interpedestrian repulsion (pedestrian spacing) and the relative repulsive force factor. Three. The relaxation -WENO scheme is introduced into the numerical simulation of the hydrodynamic model of the pedestrian flow, and the hydrodynamic model is demonstrated. The convection term is sensitive to the initial boundary condition. The convection term equation of a pedestrian flow response type dynamic user optimal model is related to the density implicit equation. The estimation method is often used to judge the characteristic velocity. By introducing the relaxation -WENO scheme to the numerical simulation of the hydrodynamic model of the pedestrian flow, the conservation equation is applied to the conservation equation. It is rewritten as a relaxation system with linear convective term and nonlinear rigid term. It is convenient to direct the flow of flow directly in the high order form such as WENO, and simplify the numerical scheme. This scheme is used to simulate the problem of pedestrian convection under different initial boundary conditions. The numerical experiment shows that the problem of pedestrian convection in the fluid mechanics model is the problem of pedestrian convection. In an initial boundary condition, the influx of pedestrian flow directly affects the relative velocity of pedestrians and indirectly affects the formation of pedestrian queues under an initial boundary condition. In another initial boundary condition, the parameters of the inter pedestrian interaction intensity are only low. In the density interval, the pedestrian has a direct impact on the pedestrians. Finally, on the basis of the summary of this work, the key research direction and the problems to be solved in the future work are put forward.

【学位授予单位】：上海大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：U491
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本文编号：1832613