基于尖点突变理论的公共建筑中人群拥挤现象分析
|
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。
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.
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。
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.
引文
[1]Henderson L F. The statistics of crowd fluids[J]. Nature,1971,229:381-383
[2]Hughes R L. The flow of large crowds of pedestrians[J]. Mathematics and Computers in Simulation,2000,53:367-370
[3]Hughes R L. A continuum theory for the flow of pedestrians[J]. Transportation Research Part B,2002,36:507-535
[4]Hughes R L. The flow of human crowds[J]. Annual Review of Fluid Mechanics,2003,35: 169-182
[5]Colombo R M, Rosini M D. Pedestrian flows and non-classical shocks[J]. Mathematical Methods in the Applied Sciences,2005,28:1553-1567
[6]Helbing D, Johansson A, Al-Abideen H Z. Dynamics of crowd disasters:An empirical study[J]. Physical Review E,2007,75:046109
[7]Fang Z, Lo S M, Lu J A. On the relationship between crowd density and movement velocity[J]. Fire Safety Journal,2003,38:271-283
[8]Fang Z, Yuan J P, Wang Y C, et al. Survey of pedestrian movement and development of a crowd dynamics model[J]. Fire Safety Journal,2008,43(6):459-465
[9]Rosini M D. Nonclassical interactions portrait in a macroscopic pedestrian flow model[J]. Differential Equations,2009,246(1):408-427
[10]卢春霞.人群流动的波动性分析[J].中国安全科学学报,2006,16(2)：30-34
[11]周爱桃,景国勋,魏平儒等.L型房间单元人员疏散探讨[J].中国安全科学学报,2006,16(8)：28-31
[12]Yamamoto K, Kokubo S, Nishinari K. Simulation for pedestrian dynamics by real-coded cellular automata (RCA)[J]. Physica A,2007,379:654-660
[13]Kirchner A, Schadschneider A. Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics[J]. Physica A,2002,312:260-276
[14]Kirchnera A, Klupfel H, Nishinari K, et al. Simulation of competitive egress behavior: comparison with aircraft evacuation data[J]. Physica A,2003,324:689-697
[15]Zhao D L, Yang L Z, Li J. Exit dynamics of occupant evacuation in an emergency[J]. Physica A,2006,363:501-511
[16]Yuan W F, Tan K H. An evacuation model using cellular automata[J]. Physica A,2007,384: 549-566
[17]Yang L Z, Zhao D L, Li J, et al. Simulation of the kin behavior in building occupant evacuation based on Cellular automaton[J]. Building and Environment,2005,40:411-415
[18]Nishinari K, Sugawara K, Kazama T, et al. Modelling of self-driven particles:Foraging ants and pedestrians[J]. Physica A,2006,372:132-141
[19]Varas A, Cornejo M D, Mainemer D, et al. Cellular automaton model for evacuation process with obstacles[J]. Physica A,2007,382:631-642
[20]Song W G, Yu Y F, Wang B H, et al. Evacuation behaviors at exit in CA model with force essentials:A comparison with social force model[J]. Physica A,2006,371:658-666
[21]Yu Y F, Song W G Cellular automaton simulation of pedestrian counter flow considering the surrounding environment[J]. Physical Review E,2007,75:046112
[22]李伟.对包含障碍墙的建筑空间内的人群疏散效果的仿真研究[D].北京：北京化工大 学,2010
[23]Muramatsu M, Nagatani T. Jamming transition in two-dimensional Pedestrian traffic[J]. Physica A,2000:275281-291
[24]Takimoto K, Nagatani T. Spatio-temporal distribution of escape time in evacuation process [J]. Physica A,2003,320:611-621
[25]Song W G, Xu X, Wang B H, et al. Simulation of evacuation processes using a multi-grid model for pedestrian dynamics[J]. Physica A,2006,363:492-500
[26]Nagai R, Nagatani T, Isobe M, et al. Effect of exit configuration on evacuation of a room without visibility [J]. Physica A,2004,343:712-724
[27]Nagai R, Fukamachi M, Nagatani T. Evacuation of crawlers and walkers from corridor through an exit[J]. Physica A,2006,367:449-460
[28]Tajima Y, Nagatani T. Scaling behavior of crowd flow outside a hall[J]. Physica A,2001,292: 545-554
[29]Tajima Y, Nagatani T. Clogging transition of pedestrian flow in T-shaped channel[J]. Physica A,2002,303:239-250
[30]Weng W G, Shen S F, Yuan H Y, et al. A behavior-based model for pedestrian counter flow[J]. Physica A,2007,375:668-678
[31]Parisi D R, Dorso C O. Microscopic dynamics of pedestrian evacuation[J]. Physica A,2005, 354:606-618
[32]Helbing D, Molnar P. Social for model force pedestrian dynamics[J]. Physical Review E, 1995,51(5):4282-4286
[33]Helbing D, Farkas I, Vicsek T. Simulating dynamical features of escape panic[J]. Nature, 2000,407:487-490
[34]Zheng M H, Kushimori Y, Kumbura T. A model describing collective behaviors of pedestrians with various personalities in danger situations[A]. In:Wang L P, Rajapakse J C, Fukushima K, et al. Proceedings of the 9th international conference on neural information processing (ICONIP'02)[C]. Singapore:IEEE,2002,2083-2087
[35]Seyfried A, Steffen B, Lippert T. Basics of modelling the pedestrian flow[J]. Physica A,2006, 368:232-238
[36]Parisi D R, Dorso C O. Morphological and dynamical aspects of the room evacuation p rocess[J]. Physica A,2007,385:343-355
[37]Goldstone R L, Janssen M A. Computational models of collective behavior[J]. Trends in Cognitive Sciences,2005,9(9):424-430
[38]Braun A, Bodmann B E J, Musse S R. Simulating virtual crowds in emergency situations[A]. In:Singh G, Lau R W H, Chrysanthou Y, et al. Proceedings of the ACM symposium on Virtual reality software and technology (VRST'05)[C], New York:ACM Press,2005, 244-252
[39]Pelechano N, Allbeck J M, Badler N I. Controlling individual agents in high-density crowd simulation[A]. In:Metaxas D, Popovic J. Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation[C]. Switzerland: Eurographics Association,2007,99-108
[40]Henein C M, White T. Information in crowds:the swarm information model[A]. In:Yacoubi El S, Chopard B, Bandini S. Lecture notes in computer science[C]. Berlin, Heidelberg: Springer,2006,703-706
[41]Pan X S, Han C S, Dauber K, et al. A multi-agent based framework for the simulation of human and social behaviors during emergency evacuations[J]. AI & Society,2007,22: 113-132
[42]Toyama M C, Bazzan A L C, Da Silva R. An agent-based simulation of pedestrian dynamics: from lane formation to auditorium evacuation[A]. In:Stone P, Weiss G. Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems[C]. New York:ACM Press,2006,108-110
[43]Lo S M, Huang H C, Wang P, et al. A game theory based exit selection model for evacuation[J]. Fire Safety Journal,2006,41:364-369
[44]Hoogendoorn S, Bovy P H L. Simulation of pedestrian flows by optimal control and differential games[J]. Optimal Control Applications and Methods,2003,24:153-172
[45]Zhang L, Dai S G. Application of Markov model to environmental fate of phenanthrene in Lanzhou Reach of Yellow River[J]. Chemosphere,2007,67:1296-1299
[46]Lovas G G. Modeling and simulation of pedestrian traffic flow[J]. Transportation Research B, 1994,28(6):429-443
[47]Wakim C F, Capperon S, Oksman J. A Markovian model of pedestrian behavior[A], In: Proceedings of 2004 IEEE International Conference on Systems, Man and Cybernetics [C], Piscataway (New Jersey, USA):IEEE,2004,4028-4033
[48]Georgiadou P S, Papazoglou I A, Kiranoudisc C T, et al. Modeling emergency evacuation for major hazard industrial sites[J]. Reliability Engineering and System Safety,2007,92: 1388-1402
[49]杜丽娟.应急标识的疏散作用研究[D].北京：北京化工大学,2010
[50]Benthorn L, Frantzich H. Fire alarm in a public building:how do people evaluate information and choose an evacuation exit?[J]. Fire and Materials,1999,23:311-315
[51]Benthorn L, Frantzich H. Managing evacuating people from facilities during a fire emergency[J]. Facilities,1999,17(9/10):325-330
[52]Gamberini L, Cottone P, Spagnolli A, et al. Responding to a fire emergency in a virtual environment:different patterns of action for different situations[J]. Ergonomics,2003,46(8): 842-858
[53]Isobe M, Helbing D, Nagatani T. Experiment, theory, and simulation of the evacuation of a room without visibility[J]. Physical Review E,2004,69:066132
[54]Helbing D, Isobe M, Nagatani T, et al. Lattice gas simulation of experimentally studied evacuation dynamics[J]. Physical Review E,2003,67:067101
[55]Saloma C, Perez G J, Tapang G, et al. Self-organized queuing and scale-free behavior in real escape panic[J]. PNAS,2003,100(21):11947-11952
[56]Helbing D, Buzna L, Johansson A, et al. Self-organized pedestrian crowd dynamics: experiments, simulations, and design solutions[J]. Transportation Science,2005,39(1):1-24
[57]钟庭宽.化工厂突发事件条件下的群体疏散研究[D].北京：北京化工大学,2009
[58]Altshuler E, Ramos O, Nunez Y N, et al. Symmetry breaking in escaping ants[J]. The American Naturalist,2005,166(6):643-649
[59]Burd M. Ecological consequences of traffic organisation in ant societies[J]. Physica A,2006, 372:124-131
[60]Peters K, Johansson A, Dussutour A, et al. Analytical and numerical investigation of ant behavior under crowded conditions[J]. Advances in Complex Systems,2006,9(4):337-352
[61]刘俊卿.基于时间优化的多出口紧急疏散决策研究[D].北京：北京化工大学,2010
[62]Kenneth T W Y, Sai O C.A catastrophe model of construction conflict behavior[J]. Building and Environment,2006,41:438-447
[63]Sallam A. Power system transient stability assessment using catastrophe theory[J]. IEE Proc, 1989,136-C(2):108-114
[64]Solimaxun, M S and ThomPson J M T. Transient and steady state analysis of capasize phenomena[J]. Applied Ocean Research,1991,13(2):35-42
[65]Persaud B N, Hall F L. Catastrophe theory and patterns in 30-second freeway traffic data-implications for incident detection[J]. Transportation Research Part A,1989,23:103-113
[66]Acha-Daza J A, Hall F L. Application of catastrophe theory to traffic flow variables[J]. Transportation Research Part B,1994,28:235-250
[67]Xie Z K, Fan W C. An catastrophe mechanism and classification of discontinuity behavior in thermal science(Ⅱ)-cuap catastrophe[J]. Chinese Science Bulletin,2000,20:102-109
[68]厉励.多级电力系统暂态稳定性的快速计算突变理论模型[J].郑州工业大学学报,1999,1：19-22
[69]蒋军成.突变理论及其在安全工程中的一应用[J].南京化工大学学报,1999,21(1)：24-28
[70]黄光球,胡晓婷,刘通.基于突变理论的网络异常行为分析方法[J].微电子学与计算机,2006,23(7)：65-69
[71]刘聚涛,高俊峰,姜加虎等.基于突变理论的太湖蓝藻水华危险性分区评价[J].湖泊科学,2010,(04)：488-494
[72]周小平,钱七虎,张永兴等.基于突变理论的滑坡时间预测模型[J].工程力学,2011,(02)：165-174
[73]于鹏飞,董守华,杨小慧等.基于突变理论的煤层不连续性检测技术[J].煤田地质与勘探,2011,(01)：57-60
[74]郑东健,雷霆.基于突变理论的高拱坝失稳判据研究[J].岩土工程学报,2011,(01)：23-27
[75]DOGBE C. On the numerical solutions of second order macroscopic models of pedestrian flows[J]. Computers and Mathematics with Applications,2008,56(7):1884-1898
[76]Thompson P A, Marchant E W. Computer and fluid modelling of evacuation[J]. Safety Science,1995,18(4):277-289
[77]Fang Z M, Song W G, Zhang J, al et. Experiment and modeling of exit-selecting behaviors during a building evacuation[J]. Physica A,2010,389:815-824
[78]Jiang R, Wu Q S. Pedestrian behaviors in a lattice gas model with large maximum velocity[J]. Physica A,2007,373:683-693
[79]Liu X, Song W G, Zhang J. Extraction and quantitative analysis of microscopic evacuation characteristics based on digital image processing[J]. Physica A,2009,388:2717-2726
[80]Fiammetta V, Luca B. An interpretative model of the pedestrian fundamental relation[J]. Comptes Rendus Mecanique,2007,335:194-200
[81]Zhang H M. A mathematical theory of traffic hysteresis[J]. Transportation Research Part B, 1999,33:1-23
[82]Smith R A. Density, velocity and flow relationships for closely packed crowds[J]. Safety Science,1995,18:321-327
[2]Hughes R L. The flow of large crowds of pedestrians[J]. Mathematics and Computers in Simulation,2000,53:367-370
[3]Hughes R L. A continuum theory for the flow of pedestrians[J]. Transportation Research Part B,2002,36:507-535
[4]Hughes R L. The flow of human crowds[J]. Annual Review of Fluid Mechanics,2003,35: 169-182
[5]Colombo R M, Rosini M D. Pedestrian flows and non-classical shocks[J]. Mathematical Methods in the Applied Sciences,2005,28:1553-1567
[6]Helbing D, Johansson A, Al-Abideen H Z. Dynamics of crowd disasters:An empirical study[J]. Physical Review E,2007,75:046109
[7]Fang Z, Lo S M, Lu J A. On the relationship between crowd density and movement velocity[J]. Fire Safety Journal,2003,38:271-283
[8]Fang Z, Yuan J P, Wang Y C, et al. Survey of pedestrian movement and development of a crowd dynamics model[J]. Fire Safety Journal,2008,43(6):459-465
[9]Rosini M D. Nonclassical interactions portrait in a macroscopic pedestrian flow model[J]. Differential Equations,2009,246(1):408-427
[10]卢春霞.人群流动的波动性分析[J].中国安全科学学报,2006,16(2)：30-34
[11]周爱桃,景国勋,魏平儒等.L型房间单元人员疏散探讨[J].中国安全科学学报,2006,16(8)：28-31
[12]Yamamoto K, Kokubo S, Nishinari K. Simulation for pedestrian dynamics by real-coded cellular automata (RCA)[J]. Physica A,2007,379:654-660
[13]Kirchner A, Schadschneider A. Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics[J]. Physica A,2002,312:260-276
[14]Kirchnera A, Klupfel H, Nishinari K, et al. Simulation of competitive egress behavior: comparison with aircraft evacuation data[J]. Physica A,2003,324:689-697
[15]Zhao D L, Yang L Z, Li J. Exit dynamics of occupant evacuation in an emergency[J]. Physica A,2006,363:501-511
[16]Yuan W F, Tan K H. An evacuation model using cellular automata[J]. Physica A,2007,384: 549-566
[17]Yang L Z, Zhao D L, Li J, et al. Simulation of the kin behavior in building occupant evacuation based on Cellular automaton[J]. Building and Environment,2005,40:411-415
[18]Nishinari K, Sugawara K, Kazama T, et al. Modelling of self-driven particles:Foraging ants and pedestrians[J]. Physica A,2006,372:132-141
[19]Varas A, Cornejo M D, Mainemer D, et al. Cellular automaton model for evacuation process with obstacles[J]. Physica A,2007,382:631-642
[20]Song W G, Yu Y F, Wang B H, et al. Evacuation behaviors at exit in CA model with force essentials:A comparison with social force model[J]. Physica A,2006,371:658-666
[21]Yu Y F, Song W G Cellular automaton simulation of pedestrian counter flow considering the surrounding environment[J]. Physical Review E,2007,75:046112
[22]李伟.对包含障碍墙的建筑空间内的人群疏散效果的仿真研究[D].北京：北京化工大 学,2010
[23]Muramatsu M, Nagatani T. Jamming transition in two-dimensional Pedestrian traffic[J]. Physica A,2000:275281-291
[24]Takimoto K, Nagatani T. Spatio-temporal distribution of escape time in evacuation process [J]. Physica A,2003,320:611-621
[25]Song W G, Xu X, Wang B H, et al. Simulation of evacuation processes using a multi-grid model for pedestrian dynamics[J]. Physica A,2006,363:492-500
[26]Nagai R, Nagatani T, Isobe M, et al. Effect of exit configuration on evacuation of a room without visibility [J]. Physica A,2004,343:712-724
[27]Nagai R, Fukamachi M, Nagatani T. Evacuation of crawlers and walkers from corridor through an exit[J]. Physica A,2006,367:449-460
[28]Tajima Y, Nagatani T. Scaling behavior of crowd flow outside a hall[J]. Physica A,2001,292: 545-554
[29]Tajima Y, Nagatani T. Clogging transition of pedestrian flow in T-shaped channel[J]. Physica A,2002,303:239-250
[30]Weng W G, Shen S F, Yuan H Y, et al. A behavior-based model for pedestrian counter flow[J]. Physica A,2007,375:668-678
[31]Parisi D R, Dorso C O. Microscopic dynamics of pedestrian evacuation[J]. Physica A,2005, 354:606-618
[32]Helbing D, Molnar P. Social for model force pedestrian dynamics[J]. Physical Review E, 1995,51(5):4282-4286
[33]Helbing D, Farkas I, Vicsek T. Simulating dynamical features of escape panic[J]. Nature, 2000,407:487-490
[34]Zheng M H, Kushimori Y, Kumbura T. A model describing collective behaviors of pedestrians with various personalities in danger situations[A]. In:Wang L P, Rajapakse J C, Fukushima K, et al. Proceedings of the 9th international conference on neural information processing (ICONIP'02)[C]. Singapore:IEEE,2002,2083-2087
[35]Seyfried A, Steffen B, Lippert T. Basics of modelling the pedestrian flow[J]. Physica A,2006, 368:232-238
[36]Parisi D R, Dorso C O. Morphological and dynamical aspects of the room evacuation p rocess[J]. Physica A,2007,385:343-355
[37]Goldstone R L, Janssen M A. Computational models of collective behavior[J]. Trends in Cognitive Sciences,2005,9(9):424-430
[38]Braun A, Bodmann B E J, Musse S R. Simulating virtual crowds in emergency situations[A]. In:Singh G, Lau R W H, Chrysanthou Y, et al. Proceedings of the ACM symposium on Virtual reality software and technology (VRST'05)[C], New York:ACM Press,2005, 244-252
[39]Pelechano N, Allbeck J M, Badler N I. Controlling individual agents in high-density crowd simulation[A]. In:Metaxas D, Popovic J. Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation[C]. Switzerland: Eurographics Association,2007,99-108
[40]Henein C M, White T. Information in crowds:the swarm information model[A]. In:Yacoubi El S, Chopard B, Bandini S. Lecture notes in computer science[C]. Berlin, Heidelberg: Springer,2006,703-706
[41]Pan X S, Han C S, Dauber K, et al. A multi-agent based framework for the simulation of human and social behaviors during emergency evacuations[J]. AI & Society,2007,22: 113-132
[42]Toyama M C, Bazzan A L C, Da Silva R. An agent-based simulation of pedestrian dynamics: from lane formation to auditorium evacuation[A]. In:Stone P, Weiss G. Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems[C]. New York:ACM Press,2006,108-110
[43]Lo S M, Huang H C, Wang P, et al. A game theory based exit selection model for evacuation[J]. Fire Safety Journal,2006,41:364-369
[44]Hoogendoorn S, Bovy P H L. Simulation of pedestrian flows by optimal control and differential games[J]. Optimal Control Applications and Methods,2003,24:153-172
[45]Zhang L, Dai S G. Application of Markov model to environmental fate of phenanthrene in Lanzhou Reach of Yellow River[J]. Chemosphere,2007,67:1296-1299
[46]Lovas G G. Modeling and simulation of pedestrian traffic flow[J]. Transportation Research B, 1994,28(6):429-443
[47]Wakim C F, Capperon S, Oksman J. A Markovian model of pedestrian behavior[A], In: Proceedings of 2004 IEEE International Conference on Systems, Man and Cybernetics [C], Piscataway (New Jersey, USA):IEEE,2004,4028-4033
[48]Georgiadou P S, Papazoglou I A, Kiranoudisc C T, et al. Modeling emergency evacuation for major hazard industrial sites[J]. Reliability Engineering and System Safety,2007,92: 1388-1402
[49]杜丽娟.应急标识的疏散作用研究[D].北京：北京化工大学,2010
[50]Benthorn L, Frantzich H. Fire alarm in a public building:how do people evaluate information and choose an evacuation exit?[J]. Fire and Materials,1999,23:311-315
[51]Benthorn L, Frantzich H. Managing evacuating people from facilities during a fire emergency[J]. Facilities,1999,17(9/10):325-330
[52]Gamberini L, Cottone P, Spagnolli A, et al. Responding to a fire emergency in a virtual environment:different patterns of action for different situations[J]. Ergonomics,2003,46(8): 842-858
[53]Isobe M, Helbing D, Nagatani T. Experiment, theory, and simulation of the evacuation of a room without visibility[J]. Physical Review E,2004,69:066132
[54]Helbing D, Isobe M, Nagatani T, et al. Lattice gas simulation of experimentally studied evacuation dynamics[J]. Physical Review E,2003,67:067101
[55]Saloma C, Perez G J, Tapang G, et al. Self-organized queuing and scale-free behavior in real escape panic[J]. PNAS,2003,100(21):11947-11952
[56]Helbing D, Buzna L, Johansson A, et al. Self-organized pedestrian crowd dynamics: experiments, simulations, and design solutions[J]. Transportation Science,2005,39(1):1-24
[57]钟庭宽.化工厂突发事件条件下的群体疏散研究[D].北京：北京化工大学,2009
[58]Altshuler E, Ramos O, Nunez Y N, et al. Symmetry breaking in escaping ants[J]. The American Naturalist,2005,166(6):643-649
[59]Burd M. Ecological consequences of traffic organisation in ant societies[J]. Physica A,2006, 372:124-131
[60]Peters K, Johansson A, Dussutour A, et al. Analytical and numerical investigation of ant behavior under crowded conditions[J]. Advances in Complex Systems,2006,9(4):337-352
[61]刘俊卿.基于时间优化的多出口紧急疏散决策研究[D].北京：北京化工大学,2010
[62]Kenneth T W Y, Sai O C.A catastrophe model of construction conflict behavior[J]. Building and Environment,2006,41:438-447
[63]Sallam A. Power system transient stability assessment using catastrophe theory[J]. IEE Proc, 1989,136-C(2):108-114
[64]Solimaxun, M S and ThomPson J M T. Transient and steady state analysis of capasize phenomena[J]. Applied Ocean Research,1991,13(2):35-42
[65]Persaud B N, Hall F L. Catastrophe theory and patterns in 30-second freeway traffic data-implications for incident detection[J]. Transportation Research Part A,1989,23:103-113
[66]Acha-Daza J A, Hall F L. Application of catastrophe theory to traffic flow variables[J]. Transportation Research Part B,1994,28:235-250
[67]Xie Z K, Fan W C. An catastrophe mechanism and classification of discontinuity behavior in thermal science(Ⅱ)-cuap catastrophe[J]. Chinese Science Bulletin,2000,20:102-109
[68]厉励.多级电力系统暂态稳定性的快速计算突变理论模型[J].郑州工业大学学报,1999,1：19-22
[69]蒋军成.突变理论及其在安全工程中的一应用[J].南京化工大学学报,1999,21(1)：24-28
[70]黄光球,胡晓婷,刘通.基于突变理论的网络异常行为分析方法[J].微电子学与计算机,2006,23(7)：65-69
[71]刘聚涛,高俊峰,姜加虎等.基于突变理论的太湖蓝藻水华危险性分区评价[J].湖泊科学,2010,(04)：488-494
[72]周小平,钱七虎,张永兴等.基于突变理论的滑坡时间预测模型[J].工程力学,2011,(02)：165-174
[73]于鹏飞,董守华,杨小慧等.基于突变理论的煤层不连续性检测技术[J].煤田地质与勘探,2011,(01)：57-60
[74]郑东健,雷霆.基于突变理论的高拱坝失稳判据研究[J].岩土工程学报,2011,(01)：23-27
[75]DOGBE C. On the numerical solutions of second order macroscopic models of pedestrian flows[J]. Computers and Mathematics with Applications,2008,56(7):1884-1898
[76]Thompson P A, Marchant E W. Computer and fluid modelling of evacuation[J]. Safety Science,1995,18(4):277-289
[77]Fang Z M, Song W G, Zhang J, al et. Experiment and modeling of exit-selecting behaviors during a building evacuation[J]. Physica A,2010,389:815-824
[78]Jiang R, Wu Q S. Pedestrian behaviors in a lattice gas model with large maximum velocity[J]. Physica A,2007,373:683-693
[79]Liu X, Song W G, Zhang J. Extraction and quantitative analysis of microscopic evacuation characteristics based on digital image processing[J]. Physica A,2009,388:2717-2726
[80]Fiammetta V, Luca B. An interpretative model of the pedestrian fundamental relation[J]. Comptes Rendus Mecanique,2007,335:194-200
[81]Zhang H M. A mathematical theory of traffic hysteresis[J]. Transportation Research Part B, 1999,33:1-23
[82]Smith R A. Density, velocity and flow relationships for closely packed crowds[J]. Safety Science,1995,18:321-327