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ArticlesResearch on Emotion Simulation Method of Large-Scale Crowd Evacuation under Particle Model
  • Peng Mei1,*, GangYi Ding1, QianKun Jin1 and FuQuan Zhang2

Human-centric Computing and Information Sciences volume 11, Article number: 01 (2021)
Cite this article 8 Accesses
https://doi.org/10.22967/HCIS.2021.11.001

Abstract

Due to the high complexity of large-scale crowds’ movement and behavior, the relevant responsible person cannot guide people’s flow the first time and control the risks correctly when an emergency event occurs. At present, computer simulation tools for large-scale crowd movement behavior modeling have become an effective means of solving emergency events using computer science development. However, existing simulation methods have certain limitations and distortions. Therefore, this paper proposes a particle model. Based on the proposed model, the simulation method of the entangled emotional model (EEM) is used to deal with the gathering phenomenon and group collisions in the evacuation process. The model simulates the crowd’s kinship by forming multiple entangled pairs, which can form multiple motion clusters through the mechanism of emotion propagation and quantum entanglement for a large number of people. This paper explores the influence of the group characteristics of motion clusters on the evacuation process. It aims to simulate the evacuation process of large-scale crowds using computer simulation and improve evacuation efficiency.


Keywords

Crowd Simulation, Emergency Evacuation, Entangled Emotion Model (EEM), Quantum Entanglement


Introduction

The simulation uses the project model to convert the uncertainty specific to a concrete level into their impact on the target. The impact is expressed in the overall simulation project [1] and helps to calculate and predict large-scale crowds [2]. The simulation method is not only a technique, but a method for problem-solving. In simulations, various models and techniques can be used to model actual problems. The simulation system can evaluate various alternatives and confirm which measures are sufficient for solving particular problems [3]. Therefore, using simulation technology to build a large-scale crowd simulation framework has become one of the essential means for studying crowd behavior simulation [4]. Simulation technology has been effectively applied to the large-scale population field [5]. The simulation described in this article refers to dynamic crowd simulation. Simulation technology enables many complex scientific problems to be effectively solved, such as simultaneous simulation research of crowd [6], immersive experience of crowd movement [7], and virtual reality simulation system construction [8]. The simulation technology has been used to construct the dynamic model of crowd movement successfully [9]. Besides, data-based computer simulation technology has an essential
auxiliary role in solving the problem of large-scale crowds’ evacuation.
The movement of large-scale crowds is highly complex. Each individual represents an agent in the crowd, and all individuals have behavior autonomy. It should be noted that the behavior of a crowd composed of multiple agents does not represent a linear superposition of all agents’ behaviors. Namely, the crowds exhibit certain characteristics that a single-agent does not have. There is also an interactive relationship between the crowd and the surrounding physical environment during the crowds’ movement and environmental factors can affect the behavior of crowds. Also, the simulation system cannot quickly calculate the crowd behavior once the number of people becomes relatively large. Therefore, many methods have been proposed to optimize crowd movement simulation and understand and model people’s interaction with the environment.
Sanchez et al. [10] proposed a BDI (belief, desire, intention) software agent based on virtual reality training that can be used to simulate emergency crowd movement behavior. The BDI framework allows high-fidelity modeling of human behavior and simulates crowd evacuation. The influence of different environmental parameters has been verified by the framework. It mainly focuses on the key performance indicators of crowd evacuation rate and density. Sohn et al. [11] used a dedicated graphics acceleration algorithm to simulate complex environments quickly and realistically. Paris et al. [12] realized route navigation through the target and studied the problem of virtual pedestrian autonomous navigation in crowd simulation. The proposed method is based on subjects and predictions: each subject perceives the surrounding subjects and infers their trajectory. Narain et al. [13] proposed a variational constraint to simulate large-scale crowds’ behavior and accelerate conflict avoidance between agents in dense situations. Karamouzas et al. [14] avoided the agents’ collision with other agents or the environment according to the crowd’s density. Agents could choose a path with an appropriate density to ensure the crowd’s sufficient flow in path selection. Pellegrini et al. [15] proposed a target selection model (TSM) to guide movement behavior by specifying targets. The authors [16] proposed a method of forming local groups with different population densities using models for finding paths and avoiding squeezing. This method can adapt well to crowd movement in different scenes.
To solve specific problems in large-scale crowd simulation in a targeted manner, scientists have proposed various simulation models. The authors [17] treated each agent as an independent unit for processing and proposed motion planning in dynamic environments (DMP). This method regards buildings and people as obstacles in the process of travel. During the evacuation process, the crowd’s movement causes the dynamic calculation of this method to be extensive. Hughes [18] considered the crowd as a whole and expounded the characteristics of crowd movement from the perspective of fluid dynamics. Furthermore, it revealed the separation relationship between people and surrounding objects through free streamline calculations (FSC) to predict motion. This model weakens the collision between individuals and their independence and simplifies the research process. Narain et al. [19] proposed a unilateral incompressibility constraint (UIC) model to avoid conflicts through agents’ constraints to accelerate evacuation efficiency. The authors [20] studied large-scale crowd movement based on the CA method and evaluated crowd movement using the minimum and maximum flows. However, this method is limited to the homogeneity of the population and ignores individual differences. Li et al. [21] proposed the centralized information control (CIC) method to guide the crowds’ movement. The guidance could effectively alleviate congestion, but the implementation of guidance was weak. Alahi et al. [22] proposed the OD-prior (priors over origin and destination) method to limit pedestrian movement and used social affinity maps (SAM) to describe pedestrian behavior. This method reinforces individual differences, but it ignores the collective behavior of the crowd. The authors [23] proposed a simulation framework for crowd scheduling and path allocation. It evaluated the simulation method’s effectiveness based on the minimal travel time (MTT) and the preferred arrival time (PAT). Aros-Vera et al. [24] proposed a method to guide the crowd’s movement according to two consecutive security rings (TCSR). This method uses the crowd’s waiting time to arrange the order and speed if people should pass. The model makes each person’s evacuation time tend to the mean value, which is an idealized case. Ji et al. [25] proposed a multi-degree-of-freedom evacuation strategy to accelerate the evacuation process and simulated the evacuation process from the perspective of potential energy. Bode et al. [26] conducted an exploratory experiment of action delay during the evacuation process, explaining the impact of abnormal conditions on the evacuation. The authors [27] studied people’s evacuation in the Madrid Arena by using the location information sharing and avoided safety accidents through guidance. Wang et al. [28] also adopted the concept of information sharing. The paper uses the literature analysis method [29] to compare the output data predicted by the simulation model with the actual output data. The output data can be detected, and noise-reduced to make the data more in line with the real situation [30].
It is necessary to evacuate the crowd within the venue when an emergency happens. Many uncontrollable factors often affect the evacuation process because of the contingencies of events. In recent years, applications appearing in emergency response and disaster management have been paying more and more attention to the interaction ability of individuals within the crowd so that the manager can understand the situation of emergency entirely [24]. The authors [31] found that different crowd sizes, crowd internal structures, and relationships between smaller parts of crowds have significant impacts on crowd behavior. Liu et al. [32] proposed an agent interaction modeling method to associate multiple agents to achieve composite control. Lozano et al. [33] used simulation software to reproduce the crowd’s behaviors of agents in real-time by studying individual behavior in the crowd. Heigeas et al. [34] simulated the movement of individuals in a limited environment based on physical particle interactions and demonstrated the interaction between them. Moore et al. [35] pointed out that crowd density has a certain impact on crowd behavior. For instance, drunk individuals can increase the probability of violent behavior. Also, the “kinship” between individuals can promote the agents to move together as a cluster during the evacuation process. Liu et al. [36] studied the influence of family assembling behavior on the evacuation process. The authors [37] analyzed the impact of dynamic dependence between evacuees on the evacuation time. Namely, it was observed that when individuals with “kinship” were far apart, they would gradually come closer before they looked for each other. The occurrence of such behavior increases the difficulty of evacuation and a total length of the evacuation route. Xu et al. [38] studied the influence of detour behavior on the evacuation process, which motivated us to think about the evacuation behavior from the aspects of “kinship” seeking and gathering. At present, there are a few studies on individual affiliation leading to aggregation behavior. Therefore, it is of great significance to combine this research with crowd evacuation. This article explores the impact of related individuals by studying the movement of “kinship” during the emergency response process. The purpose is to provide plans and verification of plans for handling emergencies.
The rest of this paper is organized as follows. Section 2 introduces the occurrence mechanism and implementation method of particle model (PM), nervous psychological generation model (NPG), and entangled emotion model (EEM). Section 3 compares the output data of the EEM and other models for the simulation of the evacuation process. Section 4 discusses the advantages of the proposed method and presents future work directions.


Methodology

There must be individuals with “kinship” in the crowd and “kinship” results in forming a connection between two individuals, which is similar to quantum entanglement. This article defines “kinship” from a quantum perspective, and each individual, i.e., an agent, is regarded as a particle. A PM is proposed to describe an agent. Also, the EEM model is proposed to deal with the composition and movement of entangled pair (EP) and motion cluster (MC). The NPG model performs the generation and dissemination of information in the crowd.


Particle Model

As mentioned, this study defines an agent as a particle, and a large-scale crowd as a quantum system composed of multiple particles. The correlation between EPs is achieved through information sharing in the quantum system. Based on the calculation of a controllable quantum system, the simulation system speculates some attributes of another part of the crowd.

Fig. 1. An agent-particle model.


As shown in Fig. 1, the PM is divided into three parts. The central core area contains more than 90% of the particles’ information, and this area represents the kernel of an agent; this area is represented by blue particles in Fig. 1. The outer circular track carries information units in the quasi-electron state. These units store information that has just been received but has neither been processed nor extended to other particles yet. This part is represented by colored particles in Fig. 1. There are field structures like a particle at both sides of the model. The field structure is the source of the force that make EPs shorten the distance to each other, and it is also a detection and processing structure for particles to avoid collision with surrounding particles and obstacles. Particles rely on the channel of the field structure to spread emotions and receive information. The received information is free on the peripheral ring orbit, and this information is stored in the kernel after being processed. Particles can change their state by learning this information to adapt to the current environment better. It is the reverse process of information reception when a particle sends out the information.
Usually, two entangled particles form the entangled state |ψ〉 of zero spins, which is the superposition of two direct product states, which is expressed as Dirac:

(1)


where |↑〉 and |↓〉 indicate that the spin of the particles is up and down, respectively [39].
According to (1), quantum entanglement can be represented as a correlation between two particles. Define two particles with an entangled relationship to form an EP. The two particles need to find each other during the evacuation process and then go together. Assume that multiple EPs come together and form a MC with the particle field forces between them. Then, in the subsequent evacuation process, the movement of MC will affect other MCs.
The characteristic of quantum entanglement enhances the correlation between particles and realizes the rapid transmission of information. Authoritative information can be copied as desired, but it cannot be transmitted in time. Although entanglement cannot copy information, it can connect two points in space and time. Traditional information manipulation processes destroy entanglement, but quantum manipulations can re-establish relationships and use them for changeable purposes [40]. In this way, the quantum world method can be used to improve and optimize the traditional information processing methods in real-world applications [41]. Kitaev et al. [42] introduced the new theory of quantum computing in their research and study of classical computing theory and quantum mapping. This article can control the entire EP by operating on one particle of the EP. Quantum simulation uses a well-controlled quantum system to predict another quantum system under study [43].


Nervous Psychology Generating Model

Behavioral processes are a collective term for movements, reactions, and actions that occur outside the organism. Any behavior is produced under the guidance and regulation of psychology. Thus, the complexity of human psychology causes the complexity of human behavior. Psychology is expressed through behavior, i.e., the behavior is the externalization of human psychology. Fu et al. [44] introduced individual differences in which reflected the influence of individual personality, strength, and psychology on evacuation behavior. Due to different personalities and psychology during the evacuation, individuals move in an uncontrollable direction. Therefore, the purpose of the simulation purpose is to guide and intervene in the movement process of agents and clusters as much as possible to make the complex disorder phenomenon within the controllable range. Liu et al. [45] proposed a few approaches to deal with the spread of negative emotions in the crowd during the evacuation process. Fei [46] studied emotional communication in the social process and analyzed the principle of emotional diffusion. However, this work studies the mechanism of emotion generation and transmission using an emotional model to provide emergency strategy and plan verification for large-scale crowd evacuation.
When an emergency occurs, the agents, i.e., particles, start feeling nervous. The occurrence of nervousness is affected by many factors, including internal and external factors. The internal factors include personality, age, gender, and personal experience, which are defined as individual’s attributes that determine the individual’s moving speed, reaction speed, and the probability of generating nervousness. Among the mentioned internal factors, the average value of the former two can be obtained from the survey data of the population, and the latter can be obtained based on the most probabilities O(P) under different stress levels through multiple experiments. The external factors include the surrounding people’s performance and the distance from the exit and the incident location. They calculated the coefficient k of the crowd’s stress mental model. The value of k is adjusted according to the error between simulation and actual evacuation results. The NPG model promotes the generation of nervous psychology through internal induction and external promotion.
In the example shown in Fig. 2, in a square stadium, the incident is placed at the center point. Nervousness can be divided into five levels according to its urgency: flustered, intensive, vigilant, undisturbed, and undisciplined from low to high, and they are denoted by levels from five to one in Fig. 2, respectively. The crowd strolled aimlessly in the undisciplined state as shown in Fig. 2. People in the undisturbed state walk mostly at an average pace. In the vigilant state, the crowd walks faster than the average speed and walks towards the exit purposefully. When the crowd is in the intensive state, there will be some running towards the exit. In the clustered state, the crowd will move at high speed, and there can be many collisions. In this state, the agents do not have a clear decision on their destination. By taking the location of the incident as the origin of the reference coordinate system, the initial level of nervousness Lev(d) can be divided according to the straight-line distance. The maximum distance d_i can be defined as:

Fig. 2. The initial level of a nervous psychology evacuation site


(2)


where L denotes the side length of the approximate regular polygon of the site, and the approximate graphics of the site can be calculated during scene modeling; n is the number of sides of an approximate regular polygon. For the part of the site that exceeds the length of d_1, 〖Lev〗_ (d)=1 is defined directly, and,

(3)

(4)

In Eqs. (3) and (4), the condition of d_5≥5 m needs to be satisfied. If d_5<5 m after calculation, it is defined that d_5=5 m, and the value of d_i is adjusted corresponding to 〖Lev〗_ (d) as follows:

(5)

Each level of particles can have different motion attributes and propagation capabilities. According to the attributes of particle storage, the awareness of the emergency handling degree of the event as Er(x,y). The value of Er(x,y) is in the interval of [0,100]. The coordinates of an agent in the simulation system are denoted as coordinates (x,y) is the world coordinate system. According to the affected factors of the agent, it can be written that:

(6)

(7)

where D(x,y) denotes the location of the safety exit, N(x,y) denotes the location of the incident, Sel(x,y) is the current location of an agent, m is the number of the nervous agents within the scope of the agent’s perspective, O(P) represents the dominant internal factors causing agents to make decisions; Ch,A,S, and Exp represent the personality, age, gender, and personal experience, respectively; k is the coefficient of nervous people in different number. l_i is the distance mapping value of an agent far away from other agents. The larger Er(x,y) is, the higher the level of the corresponding nervous psychology model well be. According to (6), the value of Er(x,y) corresponds to one to five in Fig. 2, which corresponds to the five tension levels, i.e., clustered, intensive, vigilant, undisturbed, and undisciplined. When the value of Er(x,y) exceeds a value of 60, it is necessary to strengthen the observation and guidance of a particle.
Based on the particle model, particles transmit nervousness to their surrounding particles through the particle field. The spread of emotions is discrete, and particles are moving under the affection of emotions. The probability P(x,y) of agents being propagated by nervous emotions is determined according to the current degree of crowding 〖Cr〗_ρ and the duration of the EP with entanglement lost 〖Tr〗_t as follows:

(8)


where (x,y) are the world coordinates of an agent, α and β are the specific gravity coefficients, and α^2+β^2=1. When the crowding degree increases or the duration of the lost EP increases, the probability that the particle is propagated by nervousness will increase, too. The parameter variables α and β in (8) are called the entanglement parameters, and their entanglement is called the parametric entanglement (PaE), which will be explained in detail later.
When a single-particle agent feels nervous emotions, the model will use it as a center that can infect the surrounding agents with a certain probability to have nervous psychology gradually. When the nervousness is transmitted to another particle, the other particle agents corresponding to it will be instantly infected and realize the rapid transmission of information. The nervousness makes the EP data synchronized at a higher level of nervousness, which can be expressed as:

(9)


For instance, suppose that one particle has the EP value of Er(x,y)= 81.32 and another has EP value of Er(x,y)= 35.58, then their Er(x,y) will be synchronized to 81.32. Agent particles infected by receiving the information can then infect surrounding particles, which make them new centers.
As shown in Fig. 3, the NPG model divides particles’ nervous levels according to (6). Particles send and receive information following particle models. According to each particle’s attribute, the nervousness is spread using the formula’s probability (8). For each EP, the information is synchronized to a higher degree of nervousness. The simulation system defines Er(x,y)≥60 as a high degree of emergency treatment. The system will give priority monitoring and data processing to the particles in this state.
Fig. 3. Principles of nervous psychological generation model.



Entangled Emotional Model

This paper makes full use of the advantages of quantum modeling to simulate individual behavior and crowd behavior in the large-scale crowd simulation. This paper proposes the EEM to improve the simulation’s authenticity and the degree of association between agents.
The quantum entanglement is used from two aspects. This article regards a single agent as an independent quantum system, and it needs to be parameterized according to its inherent properties to complete its control and simulation. If a particle needs multiple parameters to determine its emotions together, the interrelated parameter variables constitute the first level of entanglement, i.e., the PaE. This entanglement level is achieved by the PM. For multiple agents, where each agent is regarded as a particle, if two agents have a kinship, including a blood relationship, friend relationship, and other relationships between them, then it is considered that they have an entangled relationship. The proposed model defines that interrelated particles constitute the second level of entanglement, i.e., the quantum entanglement (QuE). This entanglement level is achieved through the EEM. It should be mentioned that the PM is the foundation of the EEM.
In an isolated simple quantum system that mostly includes one agent, the kernel of the particle stores the agent’s inherent attributes, including gender, age, speed and personality. Simultaneously, there is a particular entangled relationship between these attributes, which is the first level of entangled, i.e., the PaE. The PaE accelerates the numerical change in the particle’s inherent property parameters through the entanglement of parameters, thereby affecting particles’ movement behavior. Based on (1), the Bell state can be defined by the quantum entanglement principle of quantum mechanics as follows:

(10)


Define R to be a unitary matrix, which is expressed as:

(11)


where a,b,c,and d denote arbitrary scalars on the unit plane of the complex plane. The solution of R satisfies the Yang–Baxter equation, which is given by:

(12)


where M(n×n) denotes the n-order square matrix of each row on the unit circle of the complex plane. When n=2, there are two parameters entangled. Due to the quantum state, it can be written:

(13)


Then,

(14)


If ф can be expressed as a direct product state, then ab=cd, and ф is not an entangled state. Therefore, if ab≠cd, ф is an entangled state. The parameters of the entangled state can be constructed according to (14). When n≥3, the construction method can be deduced for n=2.
In a complicated quantum system with multiple particles, particles interact with the surrounding particles and the environment through the field structure. The two particles of an EP that are close to each other gather together through the field force. Due to the existence of the field force, multiple groups of EPs have structural crossovers, and constitute MCs. Thus, an MC is a composite particle consisted of multiple particles, as shown in Fig. 4. Similar to the agent PM in Fig. 1, the core part gathers multiple entangled particle pairs. The periphery represents a free state of smart particles, which may be separated from the MC with the movement or added to the MC during the movement. The MCs also interact through field forces. The composite particle structure also includes non-EP particles in the kernel and free particles in the peripheral ring orbit. These particles, which are at a similar level of nervousness, spread and receive emotional information under the previous section’s NPG model. The particle group within the field force is determined by the center distance dis(x,y) between the particles, which is given by:

(15)


where (x_i,y_i ) represents the world coordinates of particle i in the EP set, and (x_j,y_j ) represents the world coordinate of particle j in the non-EP set. Then, U(P_mc ) can be defined as an EP and surrounding particles form the new MC set. The free-electron set of U(P_mc ) is defined as U(P_e ), which is given by:

(16)

(17)


where, P_a (x,y) is currently detected particle, and r is the radius of the particle model’s kernel.
Fig. 4. The multi-particle MC model


An MC moves with a relatively stable structure under the action of the particle field force. If the MC collides violently with other MCs or obstacles, its structure will change by the interference.
Each EP under a strong field force still maintains relative stability of the structure. As shown in Fig. 4, there are three EPs. Nevertheless, the cross structure of EPs produces relative displacement. The MC model shown in Fig. 4 defines the force f experienced by two particles of different EP in the nuclear region is as follows:

(18)


where rn represents the radius of particle, mn is the mass of particles, pf is the pressure of the particle field, and pn is the density of the particle. Since the properties of a single agent are the same, its mass is m_ . However, if the number of particles in two MCs increases to n1, and n2, then for the composed MC consisted of multiple particles, mn in (18) should be calculated as n1 mn, n2 mn. Although m1 and m2 are used in this part to distinguish the mass values of two particles in the two MCs, actually m1 = m2 = m Thus, the force F experienced between these two particles is expressed as:

(19)


Multiple EPs remain relatively stable in structure with the influence of the volume of space occupied by their particles and the particle field force. The component F^' of the external force F_E generated by n_1 particles in the field force direction cause the displacement of n_2 individual particles. It should be noted that the movement principle of n_1 particles are the same. The total force F_total of a particle in an MC represents is the sum of internal force F_I and external force F_E, which can be expressed as:

(20)

(21)

(22)


where θ denotes the angle between the displacement component of a single particle F^' and the internal force F_I, and θ_MC represents the angle between the overall force component 〖F^'〗_MC and the total force F_total.
The non-EP under the weak field force will selectively enter the peripheral ring orbit according to the force’s direction and magnitude. If it has entered the orbit, it will be in the free electrons state, which belongs to the set U(P_e ). The initial value of the selected probability is expressed as:

(23)


The values of P_stay and P_escape are affected by the external force F_E, and it can be written:

(24)


When P_escape is large enough, particles will even break away from the field force and no longer belong to the set U(P_mc ). Similarly, if the collided MC is closer to another MC and the independent particles are moving too fast, they may also break into the neighboring MC and become its new part. The change in the MC particle composition will further cause a difference in the overall movement characteristics, thus affecting the evacuation results of the large-scale crowds.
If two particles of the same EP are far apart when an emergency occurs, they will transmit information using the entanglement. The EP determines the movement direction based on the Fuzzy-Co (fuzzy coordinates) provided by particles.
As shown in Fig. 5, the system calculates the center distance (Dis) of the EP. In Fig. 5, (X_A0,Y_A0 ) and (X_B0,Y_B0 ) denotes the coordinates of the center points of particles A and B, respectively. Using (X_A0,Y_A0 ) and (X_B0,Y_B0 ) as the origins, the system delimits the fuzzy domain (FD) with r=0.093Dis as a radius. Fuzzy coordinates (X_A,Y_A ) and (X_B,Y_B ) are randomly generated in the FD. Particles A and B travel to their target points (X_B,Y_B ) and (X_A,Y_A ), respectively. (X_A,Y_A ) and (X_B,Y_B ) are updated every two seconds and release the cache of the previous target points directly. When Dis≤10, the EP particles are pulled closer by the particle field force to form part of the MC.
Fig. 5. The EP fuzzy coordinate generation principle.


Results

The proposed NPG and EEG models were verified by two experiments. The NPG model was used to describe the spread of tension in the crowd after an emergency, and the EEG model was used to describe the gathering and movement of crowds during evacuation.


NPG Simulation Experiment of Nervousness

The experimental site size was 70 m×70 m, and an exit of 7-m width was set in the middle of the four sides. There were 3,000 agents included in the experiments. The experiment was carried out on a computer with 64 g memory, an 8-core processor, and a 1080T graphics card. According to statistics, there are only 165 couples or relatives among 3,000 people. Then, the simulation system generates 165 pairs of EPs marked in green in Fig. 6.
At the zeroth minute after the event broke out, the system calculated the range of Lev(d)=5. The result was that there were three people under nervousness according to the NPG model. The system used this as the base of infection for simulation. These three people are shown in red color in Fig. 6. After 10 minutes of the experiment, a wide range of emotions appeared near the vital infection source. At the same time, the nervousness of the closer particles to the incident location was instantly transmitted to the other particle because of the entanglement between the particles of EP. Afterward, the distant particles continued to spread nervousness as a new source of infection. These EPs are indicated in orange in Fig. 6. After 15 minutes, nervousness also appeared around the EP particles that were far away from the incident. As shown in Fig. 6 that an apparent emotional infection was formed around them. After 25 minutes, the nervousness spread to most of the particles. The red color in Fig. 6 has become dominant, indicating that the situation became severe.

Fig. 6. Experimental results of nervous psychology spread.


Fig. 7. The change in the number of nervous people with time.


As shown in Fig. 7, the number of people infected with nervousness increased sharply over time. However, the upward trend did not show exponential growth, and it has almost a linear growth within a specific range of fluctuation. This was due to the difference in individual attributes; namely, each agent was susceptible to infection to a different degree, and the infectivity of the infection source to the other agents was also different. The growth rate of particles under nervousness would not be continuously accelerated by increasing infection sources, which represents the outstanding feature of the proposed PM. The experimental results reflect the difference in the ability of the particles to receive and diffuse information. Moreover, these experimental results illustrate the trend of the EEM model spreading nervous emotion between the EPs in the simulation.
To ensure the statistical significance of the algorithm results, the experiment included 10 simulations on 165 pairs of EPs in the same simulation environment with a site size of 70 m×70 m, and a 7-m exit. The number of people infected by tension in the venue was calculated every 5 minutes, and the obtained results are shown in Table 1.
When an emergency occurred, the initial number of nervous individuals in the crowd could be obtained according to the distribution of the crowd within the distance from the incident point, and its degree of freedom was four. According to the results of 10 simulation experiments, the significance level was p > 0.05. Therefore, there was no significant difference in the results of 10 simulations. The proposed method achieved good data stability, and the simulation results were reliable. The computational complexity of the NPG model was O(n log⁡n ). The number of iterations of the experimental test simulation system for 3,000 people in one minute was 12. The average memory occupancy rate was 28.4%. The model had good effectiveness in dealing with large-scale populations.
The experimental results show that, based on the EEM model, almost all agents can be affected by the nervousness within half an hour. During the crowd’s evacuation, there is a risk of crowding and trampling due to large-scale tension. Therefore, in response to this result, the system makes suggestions for an evacuation plan. The people in the area under study should be guided within 10–20 minutes in time under the evacuation base of 3,000 people; otherwise, evacuation will cause crowd riots in the site due to the spread of nervousness resulting in casualties.

Table 1. Data statistics of multiple experiments (unit: person)
Time (min) Experimental test
1 2 3 4 5 6 7 8 9 10
0 3 4 3 4 2 3 5 4 4 6
5 322 257 244 265 241 289 312 298 304 327
10 632 643 664 615 616 652 603 601 622 647
15 859 942 916 935 879 933 887 823 855 898
20 1,185 1,201 1,157 1,096 1,087 1,243 1,175 1,144 1,085 1,206
25 1,682 1,541 1,658 1,722 1,597 1,685 1,513 1,729 1,624 1,677


EEM Simulation Experiment of Crowd Evacuation Process

In this experiment, the EPs in the entangled state looked for each other and maintained the trend of getting closer. As mentioned before, the EEM model promotes the movement of EPs and the formation of MC based on the particle model. Thus, due to the spread of tension in the NPG model, EPs already in nervousness will speed up the search, while particles not in nervousness will be slower.
The first image from the left in Fig. 8(a) shows the crowd and EPs’ relative static positions at the time of the emergency. In the experiment, the EP kept looking for each other and gathering together, as shown in in Fig. 8(a). The second image from the left in Fig. 8(a) shows the entangled EP who just found each other in the crowd area represented by yellow in Fig. 8(a). The third image from the left in Fig. 8(a) shows that most of the EPs have found each other. They and their surrounding particles were infected with nervousness and formed MC, and the MC moved toward the same evacuation exit as a whole. After a while, the exit’s population density became more crowded due to the disordered influx of agents in nervousness, as shown in Fig. 8(a). The density map at the time points corresponding to those in Fig. 8(a) is shown in Fig. 8(b).
By comparing the evacuation process and the density map, it can be found that the particles that existed as EP caused crowd in the center area during the evacuation process because of the mutual search and formation of MC, causing the collision among them, as shown in the third image in Fig. 8(a). Correspondingly, as shown in the density map of Fig. 8(b), the density of the core area increased. The simulation system reflects this situation, which can help decision-makers make evacuation plans and provide scientific guidance to deploy on-site guidance.

Fig. 8. Simulation of the influence of kinship on the evacuation result obtained using the entangled emotion model during the evacuation process. (a) The overall movement of large-scale crowds. (b) The density change during the movement of large-scale crowds.


In the same site environment, 100 simulations were performed for a different number of people in the range of [300–3000] to test the applicability of the proposed EEM model. The results are shown in Fig. 9. The results prove that the proposed EEM model can satisfy linear regression well, which indicates that the proposed method has credibility in the simulation and prediction of assembly and evacuation results. The computational complexity of the EEM model is O(n^2 ). As shown in Fig. 9, the evacuation time increased linearly with the number of people evacuated. The average memory occupancy rate during the simulation was 47.2%.
The additional experiment was conducted for 3,000 people and the same hardware equipment using different algorithms in the same scenario as that used in the first experiment. The proposed EEM model was compared with other crowd evacuation algorithms regarding multiple indicators; start time (ST), preferred arrival time (PAT), minimum flow rate (MinFR), maximum flow rate (MaxFR), maximum density (MaxD), finish time (FT), and minimum travel time (MTT). In Table 2, ST denotes the system time at which the last particle responded to the event and performed evacuation; PAT is the average reference time within which the particle could reach the closest entrance without guidance; it should be noted that the final exit did not necessarily correspond to the most recent exit because the EPs needed to search for each other. MinFR and MaxFR represent the minimum and maximum numbers of people who passed through the exit per minute; MTT is the average value of the time needed for particles in the system to travel under the field force without taking the exit as the target.
Fig. 9. The results of 100 evacuation simulations with the number of people in the interval of [300–3000] using the EEM model.


Table 2. Data results of 3,000 people using different crowd evacuation algorithms with two 5 m exits in a venue accommodating 5,000 people
  ST PAT MinFR MaxFR MaxD FT MTT
CIC 1.764 s 7 min 13 s 46 125 6 26 min 18 s 1 min 21 s
SAM 1.525 s 8 min 22 s 44 147 3 24 min 23 s 2 min 53 s
TCSR 1.088 s 9 min 9 s 50 189 2 17 min 41 s 5 s
CA 2.092 s 15 min 30 s 17 128 3 29 min 50 s 32 s
FSC 2.235 s 11 min 55 s 13 255 5 19 min 45 s 2 s
DMP 3.006 s 13 min 41 s 39 164 6 21 min 36 s 4 min 05 s
EEM 0.569 s 12 min 20 s 35 177 2 28 min 32 s 5 min 56 s
As presented in Table 2, the EEM model has a shorter response time than the other algorithms. The MTT value of the EEM model represented a fair reflection of the social phenomenon of kinship groups looking for each other, but other models did not have this feature. According to the data statistics of the proposed model in Table 2, the significance level was p < 0.05, which indicates that there were differences between the EEM model and other models. Moreover, the EEM model had the smallest variance in the result data in multiple tests and achieved better stability in the simulation calculation process than the other methods.
The EEM model was used in multiple simulations at different numbers of people in a venue with different capacities. As shown in Table 3, the recorded data included group size (GZ), venue capacity (VC), MinFR, MaxFR, MaxD, and total evacuation duration (SumTime).
As presented in Table 3, the simulation results obtained using the EEM model were very close to the actual evacuation results. The results show that the proposed EEM model can simulate large-scale crowd evacuation and can effectively reflect the crowd gathering phenomenon in the evacuation process by adding kinship and emotional transmission factors. Moreover, it can more genuinely reflect the actual situation of evacuation. The results confirm the main effect of nervous emotions in large-scale crowd evacuation and illustrate the effectiveness of the EEM model.

Table 3. Comparison of the EEM’s simulation results for different numbers of people in a venue with different capacities with the actual evacuation results
  GZ VC MinFR MaxFR MaxD SumTime
EEM simulation system 1,000 8,000 2 142 2 8 min 18 s
3,000 8,000 5 161 2 16 min 43 s
6,000 8,000 14 155 3 48 min 23 s
1,000 10,000 2 133 2 9 min 30 s
3,000 10,000 4 169 2 19 min 54 s
6,000 10,000 9 161 2 48 min 38 s
Practical exercises 1,000 8,000 2 139 2 8 min 28 s
3,000 8,000 6 158 3 17 min 26 s
6,000 8,000 14 146 3 52 min 19 s
1,000 10,000 3 135 2 9 min 44 s
3,000 10,000 4 166 2 21 min 32 s
6,000 10,000 8 163 3 55 min 22 s

Fig. 10. Comparison of the results of the EEM and other crowd evacuation models with the actual evacuation results.


The results of seven evacuation models presented in Table 2 were compared with the actual evacuation drill results, and the comparison is shown in Fig. 10. The TCSR, SAM, DMP, and CIC models had noticeably uniform evacuation effects and could not fully reflect the situation changes. Although the PSC and CA models could change the evacuation curve due to crowds in some areas at the beginning or the middle of the evacuation, the fluctuation curve tended to be ideal. The proposed EEM model was more consistent with the actual evacuation effect. This can be because the EEM model defines each person’s unique attribute parameters according to the characteristics of that person, and the particle model describes people. Moreover, after an emergency occurs, the NPG model spreads tension through the particle model’s field force to affect the evacuation results of the crowd. Each particle can gather and move together in the form of MC, which represents large compound particles. This simulation principle effectively simulates the gathering phenomenon during the evacuation process. The whole simulation process considers the individual differences between people and pays attention to the group phenomenon. This allows the simulation results to meet expectations and composite the real evacuation situation effectively.


Results Summary

In the experiment, based on the original crowd agent model, the constraint conditions of the kinship relationship between agents were considered. By simulating the evacuation process of a crowd consisting of 3,000 people in an emergency, the NPG model stress psychology spread, and the EEM influence on the evacuation results were explored. The experimental results show that compared with the other simulation models, the simulation of evacuation effects by the proposed EEM model was more similar to the real situation. Thus, the proposed model can effectively provide guidance strategies for the evacuation process. The experiment used the method of controlling scalar, and the effectiveness of the model was proven by simulating venues with different capacities and people with different number. The main controlling parameters of the proposed method were verified according to the results of multiple experimental iterations. The comparison with the actual evacuation data shows that the proposed model is in good agreement with the actual scenario. However, introducing a single constraint condition into the proposed model cannot fully explain the degree of agreement with the actual results. Therefore, it is needed to conduct additional experiments to verify the conclusions drawn in this work.


Conclusion

This paper proposes the PM that simulates a single person or a crowd in the simulation system. Each agent representing a person is regarded as a particle. The inherent properties of the agent are stored in the particle kernel. The PaE structure is constructed using the parameters that together affect the particles’ emotions. This paper defines two entangled particles as an EP, which represents the QuE structure. It is assumed that after the emergency occurs, particles closer to the incident start generating nervousness. These particles use the NPG to transmit emotions to the surroundings particles through the particle field. Emotions can spread to distant places through the nature of EPs’ entanglement. The EEM is proposed to simulate EPs that are far apart and need to find each other, tending to gather and complete the evacuation process together. The EEM model prompts EPs and the closer particles to gather together by the particle field force. They form MCs with the particles at a similar emotional level. The MC represents a composite particle structure composed of multiple particles. The MC moves and completes the evacuation process as a whole. Compared with the other evacuation algorithms, the results of the EEM model coincide better with the actual evacuation results. The proposed method explores the crowd gathering effect by studying the spread of emotions and their impact on evacuation in emergencies. The aim is to evaluate the evacuation status of large-scale crowds by further studying the movement of local groups. The proposed model can reflect the crowd's density and the urgency of the situation in the site during the evacuation process. Thus, it can provide significant help in designing a reasonable evacuation plan.
The proposed method is developed primarily to study the impact of emotional factors and kinship on the evacuation results in the large-scale evacuation. Therefore, this model has certain limitations. In future work, other human attributes will be included in the experiment to study the comprehensive impact of crowd evacuation factors.


Acknowledgements

The authors want to thank Dr. Jeffrey Robens for his suggestion for manuscript structure, Guan Zheng for his guidance on the experimental codes, Wu Yufeng for his guidance on visualization, and Mr. Li Peng for his efforts to verify the real experimental scene. We thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript.


Author’s contributions

Peng Mei conducted data research and wrote most part of the manuscript. Gangyi Ding designed the experiment and wrote some parts of the manuscript. Qiankun Jin wrote some parts of the manuscript and revised the manuscript. Fuquan Zhang analyzed the data and wrote some parts of the manuscript.


Funding

None


Competing Interests

The authors declare that they have no competing interests.


Author information

author

Name: Peng Mei
Affiliation: Digital Performance and Simulation Laboratory, School of Computer Science and Technology, Beijing Institute of Technology
Biography: Peng Mei graduated from Software College of Hunan University in 2012, admitted to Beijing Institute of Technology in 2013 to studied digital performance and simulation technology under Professor Gangyi Ding. He Graduated in 2015 with a master's degree in engineering. In 2016, he was admitted to the school of computer science and technology of Beijing Institute of Technology, and mainly studied the interdisciplinary research of quantum technology modeling and simulation and creative generation.

author

Name: Gangyi Ding
Affiliation: Digital Performance and Simulation Laboratory, School of Computer Science and Technology, Beijing Institute of Technology
Biography: Gangyi Ding graduated from the Department of Peking University mechanics in June 1988 and from Beijing Institute of Technology in June 1993. He is a doctoral supervisor. In March 2002, he participated in establishing the national demonstration software institute as the vice president. From December 2008, he was the dean of the school of software to April 2018, and in September 2017, he was the librarian of the University. He is a member of the Party committee, academic committee, and academic degree committee of Beijing Institute of Technology. Meanwhile, he is the director of digital performance and simulation technology.

author

Name: Qiankun Jin
Affiliation: Digital Performance and Simulation Laboratory, School of Computer Science and Technology, Beijing Institute of Technology
Biography: Qiankun Jin received his Ph.D. in mechanics and Construction Engineering College at the China University of mining and technology in 1997. He received his postdoctoral degree in weapon science and technology from the mechanical and electrical College of Beijing Institute of Technology. in 1999. Mainly engaged in system simulation and visualization, quantum cognition, quantum simulation research, published nearly 20 articles.

author

Name: Fuquan Zhang
Affiliation: Fujian Provincial Key Laboratory of Information Processing and Intelligent Control, Minjiang University
Biography: Fuquan Zhang received a Ph.D. degree from the School of Computer Science & Technology, Beijing Institute of Technology, China, in 2019. Now he is a professor at Minjiang University, China. He is now a member of the National Computer Basic Education Research Association of the National Higher Education Institutions, also a member of the Online system of it, a member of the MOOC Alliance of the College of Education and Higher Education Teaching Guidance Committee, ACM SIGCSE, CCF member, CCF YOCSEF member, director of Fujian Artificial Intelligence Society. He has published about 70 research papers.


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Peng Mei1,*, GangYi Ding1, QianKun Jin1 and FuQuan Zhang2, Research on Emotion Simulation Method of Large-Scale Crowd Evacuation under Particle Model, Article number: 11:01 (2021) Cite this article 8 Accesses

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  • Recived11 July 2020
  • Accepted23 December 2020
  • Published29 January 2021
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Keywords
  • Crowd Simulation
  • Emergency Evacuation
  • Entangled Emotion Model (EEM)
  • Quantum Entanglement