【作者】 孙家惠；

【导师】 郑小平；

【作者基本信息】 北京化工大学 ， 管理科学与工程， 2011， 硕士

【摘要】 根据公布的公共建筑内人群事故的数据显示,人群事故中最易发生的便是踩踏事故,而人群拥挤是导致踩踏事故发生的最直接及最根本的原因。因此,对公共建筑内的人群疏散的研究应包括对大型人群的运动机理的研究。当前对大型人群运动的研究主要是基于偏微分方程模型进行研究的。偏微分方程模型是基于人群连续运动的物理规律建立的,对初始条件有很强的依赖性。此外,应用偏微分方程模型不能反映现实中拥挤人群的一些行为特征,如人群疏散中表现出来的非连续的“跳跃”现象。针对当前研究存在的缺陷,本文试图应用突变理论研究大型人群的运动机理。本文基于人群运动速率同密度的非线性关系,将人群运动的三参数关系模型同尖点突变模型结合,建立了拥挤人群的尖点突变模型。通过拥挤人群的尖点突变模型分析了一维空间中人群拥挤现象的形成机理,并推导出人群运动发生突变的临界密度和临界速率。研究结果表明：(1)基于复杂系统的突变模型不但能描述人群状态的非连续性现象,而且更能针对性地求出人群状态突变的临界密度和临界速率；(2)突变模型没有初始条件的限制,并且不涉及时间和地点。因此相比于偏微分方程模型,突变模型的适用性更加广泛,尤其是复杂系统的研究中；(3)突变模型在实践中可以通过对变量的监测和调整,实现拥挤人群状态的预测和控制。本文的研究成果将有助于公共建筑内的安全管理人员合理有效的组织管理大型人群的疏散,也有助于建筑设计人员对公共建筑空间的布局设计。更多还原

【Abstract】 Published data on crowd accidents in public buildings show that most crowd accidents are trampling. The direct and basic reason of trampling is crowd jam. Therefore studying the crowd evacuation in modern complex buildings should involve the study of the movement of a large number of people and the mechanism of crowd jam.Current researches on the movement of a large crowd are based on the partial differential equation (PDE) model. The partial differential equation model is established based on the physical movement of the continuous crowd states. It has a strong dependence on the initial conditions. In addition, some characteristics of large crowd like the phenomena of discontinuous jumping in reality are hard to explain by partial differential equations (PDEs). For the defects in the current study, this study attempts to study the movement mechanism of crowd jam applied the catastrophe theory.In this paper, a cusp-catastrophe model is presented based on the non-linear relationship between the crowd density and movement velocity. The model combines the three-parameter model of crowd flow and cusp-catastrophe mathematical model. The paper studies the movement mechanism of crowd jam in a 1-D space. The critical density and the critical velocity of a crowd flow can be calculated through the catastrophe model. Results of the analysis indicate that (1) the catastrophe model based on complex systems cannot only describe the phenomena of non-continuity in crowds, but also obtain the critical density and the critical velocity; (2) the catastrophe model does not require initial conditions, besides the problem solving process does not involve the time and location. This means the applicability of the catastrophe model can be used more broadly than PDE model, especially the study of complex systems; (3) the catastrophe model can forecast and control the jamming state by monitoring and adjusting the variables in practice. The model supports the decision of the management of emergency evacuation.The results of the research can help safety managers evacuate the large crowd in public buildings reasonably and effectively. The results are also useful to the layout of the public building space.更多还原