Study On Entropy-based Crowd Evacuation Model Considering Crowd Disorder

With the development of social economy and urbanization,the phenomenon of crowd gathering in transportation hubs,large venues,commercial centers,hospitals,schools and other places has become very common.Considering the risks and hazards brought by emergencies,the study of crowd evacuation has become a very important issue in the field of public safety management.Constructing crowd evacuation model to describe the process of crowd evacuation is the main method to analyze the influencing factors of crowd evacuation and predict the dynamic of crowd evacuation.Studies have shown that the degree of crowd disorder is a key factor affecting the efficiency and safety of crowd evacuation.However,most crowd evacuation models ignore the influence of crowd disorder degree on individual behavior and evacuation process,resulting in a certain gap between the simulation results and the actual evacuation process,which brings a certain impact on the scientific formulation of public safety management measures.Therefore,it is of great significance to study the heterogeneous panic evacuation model considering the degree of crowd disorder.How to quantitatively characterize the degree of crowd disorder is the first and key issue when it is introduced into the crowd evacuation model.Although the information entropy of the probability distribution of pedestrian speed is used to measure the degree of crowd disorder,it is also used to quantify the level of crowd panic,resulting in the confusion of crowd disorder and panic emotion.In addition,the internal correlation and influencing mechanism between typical evacuation behavior of heterogeneous people and crowd disorder have not been analyzed and need to be explored.In particular,small social groups in heterogeneous populations are often regarded as a whole to reflect the gathering behavior of small groups in existing studies,but the behavior of searching for each other when the members of small groups are separated is ignored.The detour and reentry caused by searching behavior have a direct effect on the degree of crowd disorder and the process of crowd evacuation.Aiming at the above problems,this paper considers the degree of crowd disorder and the individual’s perception of the disorder,and combines panic emotion,social small group behavior and guidance behavior of heterogeneous people to carry out a series of entropy-based crowd evacuation models:(1)In view of the problem that crowd chaos is ignored and confused with panic in current studies,this article explicitly uses the entropy to express the degree of crowd chaos,and introduces information entropy and Boltzmann entropy respectively to quantitatively describe the degree of crowd chaos in an individual’s field of vision.At the same time,considering the influence of crowd disorder on panic emotion,the degree of visible crowd disorder is taken as one of the influencing factors of individual panic emotion,combined with physical,psychological and environmental factors such as exit distance,abnormal speed,speed gap and loneliness,to quantify individual panic emotion.Based on Boids theory and Agent-based simulation framework,the"Entropy-based Panic Crowd Evacuation Model"is constructed.By introducing panic as speed update smoothing index,the direct influence of panic on individual moving speed and indirect influence of crowd confusion perception on individual behavior are demonstrated.Experiments show that,compared with information entropy,Boltzmann entropy can reflect crowd disorder and crowd density at the same time,so it is more suitable to describe an individual’s perception of the chaos degree of the surrounding crowd.By comparison,it is found that crowd chaos will aggravate panic.Under the combined effect of crowd chaos and panic,the time of crowd evacuation will increase,even by more than 10%when the visual field radius is10 meters and the crowd density is greater than 0.1 person/m~2.If the influence of crowd chaos is ignored,the simulation results of crowd evacuation may be better than the actual evacuation process.(2)For heterogeneous evacuation crowd composed of individuals,social groups in pairs,and guiders who are familiar with the environment and can lead others,we propose an"Entropy-based Combined Behavior Model of Heterogeneous Crowd".Based on the aggregation and separation rules of the Boids model and agent-based simulation framework,behavior rules of escape,aggregation,obstacle avoidance,family seeking,and guidance are designed to reflect the behavior characteristics of heterogeneous evacuees.At the same time,Boltzmann entropy is introduced into this model.On the one hand,dynamic adjustment of individual perception range is realized based on entropy value,which reflects the interference of crowd chaos on individual perception ability,namely entropy increase effect.On the other hand,an entropy-based velocity correction strategy is designed to describe the unilateral preference of individuals when moving,and reflect the entropy-reducing effect of the strategy on evacuation dynamics.Experiments show that the unilateral preference based on entropy is more conducive to crowd evacuation than the unilateral preference based on density and the right preference.Family seeking behavior of social small group has a negative impact on evacuation efficiency and orderliness.Guiders can effectively reduce the seeking behavior of small groups,and the higher the proportion of small groups,the more significant the positive effect of guidance behavior.(3)In order to further analyze the influence of social small groups’seeking behavior on crowd evacuation dynamics,the"Entropy-based Crowd Evacuation Model considering Obstacles and Paired Social Groups"is established on the basis of"Entropy-based Combined Behavior Model of Heterogeneous Crowd"to simulate the evacuation process of heterogeneous crowd composed of paired small groups and individuals in obstacle scenario.By introducing the memory mechanism of social small groups’partner position,the seeking behavior rule of paired small groups is improved.And the the visual field algorithm considering shielding effect of obstacles is designed.Boltzmann entropy is used to measure individuals’perception of visible crowd disorder,and as a velocity updating coefficient to reflect the influence of crowd disorder on individual behavior.The simulation results show that compared with the individual velocity update without entropy,the entropy-based velocity update can reflect the entropy increase effect of crowd chaos on evacuation process.The areas with high incidence of seeking behavior include those far away from the exit,near obstacles,narrow bottleneck areas and the outside of the exit arch.In addition,the model is also used to analyze the crowd dynamics of different obstacle spatial distribution structures.The experiment shows that the"reverse L"type obstacle structure has the optimal distance to the exit,while the"L"type and"I"type obstacle structure should be as far away from the exit as possible.(4)Aiming at the heterogeneous panic evacuation crowd containing larger multi-person social groups and guiders,this paper constructs the"Evacuation Model for Multi-person Social Groups based on Entropy and Panic propagation"on the basis of the above models,to simulate the rational and irrational evacuation behavior of social groups,and the guide behavior of guiders on individuals and social groups.In order to quantify the level of panic more accurately,a calculation method of panic considering the accumulation and propagation of emotion is proposed,and the panic value and entropy value are simultaneously used in speed update.Through simulation experiments,the influence of social groups and guiders on evacuation efficiency and crowd dynamics under the effect of panic and disorder perception is analyzed.It is found that the irrational seeking behavior ignoring pedestrian information in visual field is more likely to lead to the increase of panic level and confusion degree of local population.The number of social groups has a greater impact on evacuation time and panic than the size of social groups.In order to reduce the disorder of the crowd,when the proportion of guides is less than 5%,they should be distributed in the area near the exit.When the proportion of guides is more than 5%,they should be distributed in the area far away from the exit.Taking crowd disorder as the starting point,this paper conducts in-depth discussion on crowd disorder and panic as well as social small groups behavior and guiding behaviors of heterogeneous crowd.Four entropy-based crowd evacuation models are proposed and corresponding simulation analysis is carried out.To some extent,the research results of this paper fill the deficiencies existing in the current crowd evacuation problem.And the simulation analysis conclusions can provide a certain reference basis for the management measures of crowd evacuation.The entropy-based crowd evacuation models constructed in this paper can provide a powerful analysis tool and rich theoretical support for the follow-up research of crowd evacuation.