公共场所交叉通道的人群汇流动力学建模与稳定性分析

作为人群聚集公共场所不可或缺的行人流动功能布局之一，交叉通道是人群运动学汇流和心理学恐慌传播的网络节点，其人群汇流区域存在紊流、扰动和密度波动现象，极易失稳引发踩踏事件，亟待理清人群汇流与恐慌演化机理。本项目拟建立常见交叉通道人群汇流模型和恐慌传播模型，研究人群稳定性分析与验证方法。1）分析人群汇流情景特征，根据行人数量和场景规模选择宏观AR模型或微观社会力模型，构造汇流冲击矩阵，建立人群汇流动力学模型；2）分析人群逃生恐慌心理特征，扩展恐慌熵定义，构建恐慌传播动力学模型；3）分析突发外部扰动和内部扰动特征，建立交叉通道人群汇流加速度-临界密度时滞模型，得到基于李雅普诺夫的人群汇流稳定性判据，进而构建机器视觉并行卷积神经网络模型，提出交叉通道人群汇流稳定性的理论与实测互补式验证方法。本研究为人群聚集公共场所行人流动通道功能布局的规划设计和人群稳定流动的管控措施提供理论和方法支持。

As one of the indispensable function layout of pedestrian flow in the crowd gathering public places, cross passages are the common network nodes of crowd kinematics merging and psychology panic propagation. There are turbulences, disturbances and density fluctuations in the crowd merging area, which is very easy to cause stampede events. It is urgent to clarify the mechanisms of crowd merging and panic evolution. This project plans to build the crowd merging model and panic propagation model in a cross passage, and proposes the crowd stability analysis and verification method. 1) This project analyzes the characteristics of crowd merging scenarioes, selects macroscopic AR model or microscopic social force model according to the number of pedestrians and the scale of the cross passage layout, constructs merging impact matrix, and establishes crowd merging dynamics model; 2) This project analyzes the psychological characteristics of crowd panic, expands the definition of panic entropy, and builds panic propagation dynamic model; 3) This project analyzes the characteristics of external and internal disturbances, and establishes the crowd acceleration-critical density delay model in a cross passage, the criterion of crowd convergence stability based on Lyapunov is obtained, and then the parallel convolution neural network model of machine vision is constructed. This paper presents a complementary verification method combined with theoretical analysis and measurement for the stability of pedestrian merging in cross passages. This study provides theoretical and methodological support for the planning and design of the functional layout of pedestrian flow passage in public crowd-gathering places and the control measures to keep the pedestrian flow stable.