Evacuation Simulation Study Of Macro Crowd

With the development of the material society and the renewal of the Internet of Things,more and more people are pouring into big cities.The population density has increased,which has brought serious hidden dangers to urban safety.For example,the promotion of large-scale shopping mall activities,the holding of various concerts and sports events will attract a large number of people.Once an unexpected situation occurs,a small disturbance will cause serious stamping accidents,resulting in casualties and property losses.Therefore,how to conduct efficient and rapid evacuation of intensive people has become a problem to be studied.By introducing a mathematical model of pedestrian dynamics in the control system,the process of crowd evacuation and the disturbance of external disturbances to the system can be more realistically depicted,so that a scientific emergency evacuation strategy can be formulated to effectively and reasonably control and guide dense populations.The accident occurred and the safety of pedestrians was guaranteed.Therefore,controlling the crowd to carry out rapid and efficient evacuation is of great significance both in theory and in the actual evacuation process.The innovation of this paper is as follows:First,considering the behavioral characteristics of the panic crowd movement in the unexpected situation,combined with the LWR model and the Underwood model,the LWR-Underwood mathematical model of the macro population was established.Comparing the LWR-Greenshields model,it is verified that the LWR-Underwood model has a faster moving speed and is in line with the evacuation of the crowd in a panic state.Second,based on the existing classical pedestrian flow theory research,a method of panic crowd evacuation based on discrete optimal control is designed for LWR-Underwood mathematical model.Compared with the boundary control method,the simulation shows that the discrete optimal control can better control the evacuation speed of the crowd,and ensure that the crowd can better control the population density at the exit and reduce the occurrence of stamping accidents.Last but not least,the one-dimensional corridor is expanded into a two-dimensional plane,and a two-dimensional mathematical model of crowd evacuation is established.This model is based on the law of conservation of mass and momentum,which satisfies the distribution in time and space.A method based on distributed feedback control is designed and the stability of the evacuation system is verified by Lyapunov function.Compared with the boundary control method,the simulation shows that distributed feedback control can achieve faster evacuation of the crowd.