基于非均匀格子气模型的人群疏散动力学模拟
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摘要
突发事件下的人群疏散运动是一个非常复杂的过程。由于疏散实验具有一定的人员伤亡风险,很难进行实验,从而导致实际疏散的数据缺失。所以计算机仿真模拟目前是研究突发事件下人群疏散的最主要方法。社会力模型(SF)和元胞自动机模型(CA)是两种比较成熟的用于模拟人群疏散运动的连续模型和离散模型。社会力模型中个体间的相互作用两两进行评价,对于Ⅳ个个体,计算量为O(N2)。对于很大的N,意味着计算负担过大,计算成本昂贵。相比于社会力模型,元胞自动机模型的计算量为O(N),这极大的提高了大规模人群疏散模拟的可行性。另一方面,人群疏散运动中,个体之间的相互作用力是一个基本的要素,对于合理模拟人群疏散起到关键作用。在元胞自动机模型中,通常忽略了这一基本要素。针对以上问题,本文的主要研究内容和取得的成果如下：
(1)基于元胞自动机模型和移动格子气模型,建立了模拟突发事件下人群疏散动力学的非均匀格子气模型。该模型的更新规则中包含出口信息因子D,它是影响人群疏散过程的关键参数。D随局部人群密度的变化而发生改变,从而体现了非均匀更新。个体之间的相互作用力通过个体之间距离的非线性函数来描述。他们之间的排斥力随他们之间距离的减小而急剧增大。引入了受伤临界力的概念,并分析了它对疏散过程的影响。数值算例表明,非均匀格子气模型可以再现人群疏散的基本特征,如堵塞和拱形现象。该模型是元胞自动机模型和移动格子气模型的扩展,具有更宽的适用范围。
(2)在非均匀格子气模型中引入高程因素,建立了扩展的非均匀格子气模型。高程因素用来描述元胞格子在疏散空间里的位置高度,并通过二维平面来描述三维空间状态。通过模型模拟和实验,研究了人员从阶梯教室疏散的疏散特征。为了研究火灾下的人群疏散过程,将火灾场与格子气模型进行同步耦合,建立了火灾与人员交互作用的人群疏散仿真模型。借助软件FDS,采用大涡模拟的方法模拟了阶梯教室火灾的发展与烟气蔓延过程。模型中假设个体可能移动方向与周围环境温度相关。个体疏散速度与能见度有关,利用多格子方法来体现速度的变化。分析表明基于扩展的非均匀格子气模型模拟所得结果与实验所得结果有很好的一致性。高程因素对疏散有引导作用,而火灾场明显的改变了行人的疏散路线,造成了频繁的局部拥挤,对疏散过程有明显的阻碍作用。
(3)基于格子气模型思想,引入高程因素,建立了模拟地铁站人员疏散的扩展非均匀格子气模型。该模型考虑紧急情况下人员的移动特征,引入多格子方法,根据人员实时步长确定人员移动速度。考虑了人员初始分布对疏散过程的影响,同时分析了紧急疏散出口对疏散的作用。地铁站火灾情况下人员疏散的分析结果表明,适度地使用紧急疏散出口能提高疏散效率,高程因素的引入也促进了疏散进程。
Evacuation under emergency is a complex process. Due to the limits of undertaking such dangerous experiments and the absence of data from real evacuation, computer simulation is the main approach for studying emergency evacuation at present. Two kinds of models, i.e. continuous models (the social force model) or discrete models (the cellular automata model) are widely used for simulating pedestrian evacuation. In a social force model, for N pedestrians, the requirement of solving a couple of differential equations for each pedestrian implying that the calculation load is the order O(N2), which is a heavy computation burden for large N. It means that the computational cost is very expensive in general. By contrast, a cellular automata model can greatly improve the computational efficiency in simulating large-scale pedestrian evacuation since the calculation amount is the order O(N). The interaction between pedestrians which is a fundamental element plays a key role for simulating pedestrian evacuation.But in a cellular automata model, the interaction between pedestrians is neglected.
Aiming at the problems mentioned above, the main contents and achievements in this paper are listed as follows:
(1) Based on the cellular automata method (CA model) and the mobile lattice gas model (MLG model), we have developed a heterogeneous lattice gas model for simulating pedestrian evacuation processes under emergency. A local population density concept is introduced first. The update rule in the new model depends on the local population density and the exit crowded degree. The drift D which is one of the key parameters influencing the evacuation process is allowed to change according to the local population density of the pedestrians. Interactions including attraction, repulsion and friction between every two pedestrians and those between a pedestrian and the building wall are described by a nonlinear function of the corresponding distance, and the repulsion forces increase sharply as the distances get small. A critical force of injury is introduced into the model, and its effects on the evacuation process are investigated. The model proposed has the heterogeneous features as compared to the MLG model or the basic CA model. Numerical examples show that the model proposed can capture the basic features of pedestrian evacuation, such as clogging and arching phenomena.
(2) An extended heterogeneous lattice gas (E-HLG) model is developed by introducing an altitude factor into the heterogeneous lattice gas model (HLG model). The altitude factor is used to describe the position height of lattice sites. Evacuation features from a terrace classroom are investigated through both simulations using the model and experiments. To study evacuation processes under fire emergency, an agent-based fire and pedestrian interaction model (FPI model) is proposed. It is supposed that the possible moving directions of a pedestrian depend on the environmental temperature field which is simulated by the software FDS. The walking speed reduction due to the visibility worsening in the FPI model is described by a multi-grid method. It is found that simulation results based on the extended HLG model are in good agreement with the experiments. The altitude factor plays a guidance role to the evacuation, and the fire notably delays the evacuation due to both the harmfulness of the high temperature field and the change of evacuation routes which results in frequent local jamming and clogging.
(3) An extended heterogeneous lattice gas model is developed by introducing an altitude factor into the heterogeneous lattice gas model for simulating pedestrian evacuation form subway station. Taking into account the mobile characteristics of pedestrians, the multi-grid method is introduced into the model. The walk speed is determined by the real-time moving step sizes of themselves. The influences of the initial distribution of pedestrians on evacuation process are investigated. The role of emergency exits to evacuation is analyzed. Evacuation processes of pedestrians with exit preference and under fire emergency are simulated by using the model mentioned above. Numerical examples show that moderate use of emergency exits can improve the evacuation efficiency and the altitude factor contributes to evacuation process.
(1)基于元胞自动机模型和移动格子气模型,建立了模拟突发事件下人群疏散动力学的非均匀格子气模型。该模型的更新规则中包含出口信息因子D,它是影响人群疏散过程的关键参数。D随局部人群密度的变化而发生改变,从而体现了非均匀更新。个体之间的相互作用力通过个体之间距离的非线性函数来描述。他们之间的排斥力随他们之间距离的减小而急剧增大。引入了受伤临界力的概念,并分析了它对疏散过程的影响。数值算例表明,非均匀格子气模型可以再现人群疏散的基本特征,如堵塞和拱形现象。该模型是元胞自动机模型和移动格子气模型的扩展,具有更宽的适用范围。
(2)在非均匀格子气模型中引入高程因素,建立了扩展的非均匀格子气模型。高程因素用来描述元胞格子在疏散空间里的位置高度,并通过二维平面来描述三维空间状态。通过模型模拟和实验,研究了人员从阶梯教室疏散的疏散特征。为了研究火灾下的人群疏散过程,将火灾场与格子气模型进行同步耦合,建立了火灾与人员交互作用的人群疏散仿真模型。借助软件FDS,采用大涡模拟的方法模拟了阶梯教室火灾的发展与烟气蔓延过程。模型中假设个体可能移动方向与周围环境温度相关。个体疏散速度与能见度有关,利用多格子方法来体现速度的变化。分析表明基于扩展的非均匀格子气模型模拟所得结果与实验所得结果有很好的一致性。高程因素对疏散有引导作用,而火灾场明显的改变了行人的疏散路线,造成了频繁的局部拥挤,对疏散过程有明显的阻碍作用。
(3)基于格子气模型思想,引入高程因素,建立了模拟地铁站人员疏散的扩展非均匀格子气模型。该模型考虑紧急情况下人员的移动特征,引入多格子方法,根据人员实时步长确定人员移动速度。考虑了人员初始分布对疏散过程的影响,同时分析了紧急疏散出口对疏散的作用。地铁站火灾情况下人员疏散的分析结果表明,适度地使用紧急疏散出口能提高疏散效率,高程因素的引入也促进了疏散进程。
Evacuation under emergency is a complex process. Due to the limits of undertaking such dangerous experiments and the absence of data from real evacuation, computer simulation is the main approach for studying emergency evacuation at present. Two kinds of models, i.e. continuous models (the social force model) or discrete models (the cellular automata model) are widely used for simulating pedestrian evacuation. In a social force model, for N pedestrians, the requirement of solving a couple of differential equations for each pedestrian implying that the calculation load is the order O(N2), which is a heavy computation burden for large N. It means that the computational cost is very expensive in general. By contrast, a cellular automata model can greatly improve the computational efficiency in simulating large-scale pedestrian evacuation since the calculation amount is the order O(N). The interaction between pedestrians which is a fundamental element plays a key role for simulating pedestrian evacuation.But in a cellular automata model, the interaction between pedestrians is neglected.
Aiming at the problems mentioned above, the main contents and achievements in this paper are listed as follows:
(1) Based on the cellular automata method (CA model) and the mobile lattice gas model (MLG model), we have developed a heterogeneous lattice gas model for simulating pedestrian evacuation processes under emergency. A local population density concept is introduced first. The update rule in the new model depends on the local population density and the exit crowded degree. The drift D which is one of the key parameters influencing the evacuation process is allowed to change according to the local population density of the pedestrians. Interactions including attraction, repulsion and friction between every two pedestrians and those between a pedestrian and the building wall are described by a nonlinear function of the corresponding distance, and the repulsion forces increase sharply as the distances get small. A critical force of injury is introduced into the model, and its effects on the evacuation process are investigated. The model proposed has the heterogeneous features as compared to the MLG model or the basic CA model. Numerical examples show that the model proposed can capture the basic features of pedestrian evacuation, such as clogging and arching phenomena.
(2) An extended heterogeneous lattice gas (E-HLG) model is developed by introducing an altitude factor into the heterogeneous lattice gas model (HLG model). The altitude factor is used to describe the position height of lattice sites. Evacuation features from a terrace classroom are investigated through both simulations using the model and experiments. To study evacuation processes under fire emergency, an agent-based fire and pedestrian interaction model (FPI model) is proposed. It is supposed that the possible moving directions of a pedestrian depend on the environmental temperature field which is simulated by the software FDS. The walking speed reduction due to the visibility worsening in the FPI model is described by a multi-grid method. It is found that simulation results based on the extended HLG model are in good agreement with the experiments. The altitude factor plays a guidance role to the evacuation, and the fire notably delays the evacuation due to both the harmfulness of the high temperature field and the change of evacuation routes which results in frequent local jamming and clogging.
(3) An extended heterogeneous lattice gas model is developed by introducing an altitude factor into the heterogeneous lattice gas model for simulating pedestrian evacuation form subway station. Taking into account the mobile characteristics of pedestrians, the multi-grid method is introduced into the model. The walk speed is determined by the real-time moving step sizes of themselves. The influences of the initial distribution of pedestrians on evacuation process are investigated. The role of emergency exits to evacuation is analyzed. Evacuation processes of pedestrians with exit preference and under fire emergency are simulated by using the model mentioned above. Numerical examples show that moderate use of emergency exits can improve the evacuation efficiency and the altitude factor contributes to evacuation process.
引文
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