CN109472049B - Macroscopic population panic propagation dynamics model establishment method and dynamics model application - Google Patents

Macroscopic population panic propagation dynamics model establishment method and dynamics model application Download PDF

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CN109472049B
CN109472049B CN201811150760.5A CN201811150760A CN109472049B CN 109472049 B CN109472049 B CN 109472049B CN 201811150760 A CN201811150760 A CN 201811150760A CN 109472049 B CN109472049 B CN 109472049B
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赵荣泳
李翠玲
刘琼
胡钱珊
董大亨
田相克
马云龙
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Abstract

The invention relates to a macroscopic population panic propagation kinetic model establishing method and application of a kinetic model, which comprises the following steps: 1) dividing the evacuation space into a plurality of discretized unit grids, and constructing the panic entropy of each unit grid based on the information entropy theory; 2) constructing a panic entropy value gradient of each adjacent unit grid; 3) and constructing a macroscopic population panic propagation kinetic model based on the panic entropy and the panic entropy value gradient, wherein the macroscopic population panic propagation kinetic model reflects the speed direction and the size of the population and the panic entropy direction and the size. Compared with the prior art, the method has the advantages of realizing quantitative analysis of the panic propagation process, improving the simulation reliability and the like.

Description

Macroscopic population panic propagation dynamics model establishment method and dynamics model application
Technical Field
The invention relates to the technical field of crowd evacuation simulation, in particular to a macroscopic crowd panic propagation kinetic model establishing method and application of a kinetic model.
Background
The most catastrophic of the group's activities of evacuating people is the stepping of the people by panic, and stepping and overcrowding often results in a significant number of casualties. Therefore, researchers conduct a large number of evacuation simulation drills and hope to obtain the characteristics of panic transmission, however, the simulation drills are all used for organizing events in advance and cannot completely reflect the panic emotion of evacuated people in a disaster site, and the panic transmission has complexity, time-varying property and incapability of copying. Therefore, there is a need to establish a kinetic model describing the propagation of panic, and study the characteristics of the propagation of panic, thereby providing a method support for preventing overcrowding and pedaling. In addition, the classical social force model and the mental and behavioral panic fluctuation model proposed by Helbin D both provide a basic method for panic measurement. But to date, most researchers have mapped the degree of panic in microscopic models to changes in the speed of evacuating individuals; panic was studied in macroscopic models only by simulation experiments on animals and insects, and no quantitative analysis of the extent of panic was involved. However, macroscopic models are more convincing to the problem of large-scale crowd evacuation. Therefore, further research into the macroscopic model is required.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a macroscopic population panic propagation kinetic model establishing method and a kinetic model application.
The purpose of the invention can be realized by the following technical scheme:
a macroscopic population panic propagation dynamics model building method comprises the following steps:
1) dividing the evacuation space into a plurality of discretized unit grids, and constructing the panic entropy of each unit grid based on the information entropy theory;
2) constructing a panic entropy value gradient of each adjacent unit grid;
3) constructing a macroscopic population panic propagation kinetic model based on the panic entropy and the panic entropy value gradient, wherein the macroscopic population panic propagation kinetic model is specifically represented as follows:
Figure BDA0001817904250000021
Figure BDA0001817904250000022
Figure BDA0001817904250000023
Figure BDA0001817904250000024
wherein e isx，y(k +1) is the velocity gradientThe ratio, ξ, is a random coefficient between 0 and 1,
Figure BDA0001817904250000025
is the gradient of the panic entropy of the grid (x, y) and the adjacent grid (a, b) in time steps k, ∑ Grad(k) As a global panic entropy gradient value, vx，y(k) Is the velocity in the grid (x, y) with a time step of k, Ex，y(k) Is the panic entropy, σ, in the grid (x, y) at a time step of k1And σ2Is an adjustable constant, E1And E2Is the panic entropy feature point, dir (E)x，y(k+1))、||Ex，yAnd (k +1) | | is the panic entropy direction and the panic entropy magnitude in the whole evacuation space when the time step is k + 1.
Further, in each unit grid, the speed direction of the crowd to be evacuated is discretized into eight main directions which are equally spaced.
Further, the panic entropy is constructed taking into account the panic entropy direction in which people are evacuated in the grid (x, y)
Figure BDA0001817904250000026
And panic entropy magnitude
Figure BDA0001817904250000027
The panic entropy direction of the evacuated crowd is expressed as:
Figure BDA0001817904250000028
the panic entropy size of the evacuated population is expressed as:
Figure BDA0001817904250000029
where n is the total number of evacuated individuals per unit cell, ncIs the total number of evacuated individuals in each directional interval, mdIs the total number of evacuated individuals, V, in each discrete speed intervalmaxTo evacuate oneThe maximum speed of the body.
Further, the panic entropy gradient is represented as:
Figure BDA00018179042500000210
wherein E isa，b(k) Is the panic entropy in the grid (a, b) adjacent to grid (x, y) with time step k, a being x-1, x, x +1, b being y-1, y, y + 1.
Further, the overall panic entropy gradient value is expressed as:
Figure BDA0001817904250000031
the invention also provides a crowd evacuation simulation method based on the macroscopic crowd panic propagation dynamics model, which comprises the following steps:
a) setting an evacuation space and an initial position and an initial speed of an evacuation individual;
b) calculating the panic entropy of each grid and the moving direction of the crowd in the grid, and updating the position information of the evacuated people in real time;
c) and circularly utilizing the macroscopic population panic propagation dynamic model to calculate the evacuation population speed and the panic entropy value corresponding to each time step until the simulation is finished.
Further, in the step b), the moving direction is determined according to the speed gradient ratio of the crowd.
Further, the method further comprises:
d) and displaying the panic situation evolution process of the crowd in the panic propagation process in a 3D space.
Compared with the prior art, the method is based on a macroscopic crowd evacuation model, mainly researches the crowd panic factor in the evacuation process, proposes a panic entropy concept, calculates the crowd panic degree in real time, further proposes a panic propagation dynamic model, calculates the macroscopic crowd panic degree in real time after the crowd evacuation state parameter is initialized, obtains the crowd panic degree distribution at the next moment in a self-adaptive manner by utilizing the panic propagation characteristic, and dynamically analyzes the influence of the panic on crowd evacuation, and has the following beneficial effects:
(1) quantitative analysis of panic propagation and display of panic situation evolution
The invention provides an entropy gradient calculation formula of adjacent grids in panic propagation quantitative analysis based on a crowd evacuation Aw-Racle model of a two-dimensional space, and simultaneously calculates the integral entropy gradient value. The method comprises the steps of providing a crowd speed gradient ratio calculation formula by utilizing the ratio of discrete grid entropy gradient values to the whole entropy gradient values to obtain the maximum gradient ratio in the speed direction, quantitatively reflecting the crowd evacuation state at the moment of evacuating crowd k +1 by utilizing the speed gradient ratio, and providing a calculation formula of the size and the direction of panic entropy at the moment of k +1 based on the panic entropy gradient and the crowd speed at the moment of k, so that the quantitative analysis of the panic propagation process is realized, and the simulation reliability is improved.
Because the panic entropy value directly reflects the panic degree of the crowd, the method realizes the 3D display of the panic situation evolution process of the crowd in the panic propagation process, so that the simulation result is more practical and visual.
(2) Panic propagation dynamics simulation iteration method
Compared with the prior art, the method has the greatest advantage of realizing crowd panic propagation characteristic analysis by utilizing the dynamic propagation characteristic. The calculation of the panic entropy value cannot leave the speed of the crowd, so the speed formula at the moment k +1 is provided by utilizing the speed of the crowd at the moment k and combining the influence characteristics of the panic on the speed. In addition, in an iteration method of the panic entropy direction, firstly, a panic entropy value gradient at the moment k is proposed, because the panic entropy value directly reflects the panic degree of people, and the panic degree is related to the crowd density and the speed, when the panic entropy value gradient is maximum, the crowd density and the speed difference of two adjacent grids are maximum, the moving direction of people can be determined, and the panic entropy value in the evacuation space can be updated in real time through iterative calculation.
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FIG. 1 shows the overlapping of pedestrian flow speed and direction at a T-shaped intersection;
fig. 2 is a panic entropy of the evacuated individual velocity direction division and discretization grid, wherein (a) is a schematic direction diagram of velocity and (b) is a panic entropy diagram of the discretization grid;
fig. 3 is a simulation diagram of panic entropy 3D spatial distribution at time step 70;
fig. 4 is a simulation diagram of panic entropy 2D spatial distribution at time step 70;
FIG. 5 is a trend graph of density and panic entropy values as a function of time step during evacuation at T-shaped street intersections;
fig. 6 shows the relationship between the movement speed of the evacuated population and the panic entropy value.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
The invention provides a macroscopic population panic propagation dynamics model building method, which comprises the following steps: 1) dividing the evacuation space into a plurality of discretized unit grids, and constructing the panic entropy of each unit grid based on the information entropy theory; 2) constructing a panic entropy value gradient of each adjacent unit grid; 3) and constructing a macroscopic population panic propagation kinetic model based on the panic entropy and the panic entropy value gradient. Meanwhile, the crowd panic propagation is realized based on the macroscopic crowd panic propagation kinetic model, so that crowd evacuation simulation is realized.
First, crowd evacuation macro dynamics model
A.aw and m.rascle propose a two-dimensional space crowd evacuation model (hereinafter referred to as Aw-Rascle model) based on a one-dimensional flow model. The classical conservation of mass equation is determined by the conservation of partial differential equations, as shown in equation (1).
Figure BDA0001817904250000041
Where ρ and v are pedestrian density and velocity, respectively.
Figure BDA0001817904250000042
Is the partial derivative of the time t,
Figure BDA0001817904250000043
is the partial derivative of the distance x. Assuming that ρ and v are independent of each other, the pressure term P is given by the formula
Figure BDA0001817904250000044
Calculation of C0Is the expected response coefficient of the density. A partial differential equation for reflecting the relationship between ρ and v, as shown in equation (2).
Figure BDA0001817904250000051
Where P (ρ) is the pressure term and v is the horizontal velocity. The crowd one-dimensional dynamic Aw-Rascle model consists of two parts of hyperbolic partial equation (PDE) of formula (1) and formula (2). The one-dimensional Aw-Rascle model is converted into a two-dimensional Aw-Rascle model using formula (3), formula (4) and formula (5).
Figure BDA0001817904250000052
Figure BDA0001817904250000053
Figure BDA0001817904250000054
Where v is the horizontal velocity and u is the vertical velocity. The T-shaped street crowd evacuation dynamic model based on the crowd evacuation Aw-Rascle model increases the influence of vector bidirectional superposition, wherein the vertical direction is u, and the horizontal direction of the vector is v. s1And s2Are relaxation terms that balance speed and density. PhAnd PvRespectively, a horizontal pressure item and a vertical pressure item of an influence matrix considering the intersection area, which makes the pedestrian density distribution of the intersection moreThe addition is reasonable. In order to solve the problem of bidirectional flow superposition, an influence matrix M of a cross region is introducedimpAs shown in equation (6). C is the maximum influence coefficient, i and j are the grid coordinates of the evacuated individuals of the intersection region. Based on the one-dimensional model of crowd evacuation, a two-dimensional flow model of the T-shaped intersection as shown in FIG. 1 is constructed. Influence matrix M of intersection regionimpAs shown in equation (6).
Figure BDA0001817904250000055
Where i and j are the horizontal and vertical coordinates of the intersecting area,
Figure BDA0001817904250000056
is the influence factor at the (i, j) coordinates of the intersection region.
In addition, pedestrian flows enter the intersection area, and the influence of the road environment on the pedestrian flows is different. When people enter the intersection area for the first time, the influence of pedestrian flow close to the wall is different.
Figure BDA0001817904250000057
Is the influence matrix factor after the deviation of the speeds on the main road and the branch road. Macroscopic models of T-street panic crowd evacuation are shown in equations (7), (8) and (9).
Figure BDA0001817904250000058
Figure BDA0001817904250000059
Figure BDA00018179042500000510
Ph(ρ, v, u) and Pv(ρ, v, u) are the horizontal pressure term and the vertical pressure, respectively, after considering the influence matrix of the intersection regionAn item.
Figure BDA0001817904250000061
Figure BDA0001817904250000062
Figure BDA0001817904250000063
Is the influence factor after the velocity bias in the horizontal direction,
Figure BDA0001817904250000064
is the influence factor after the velocity bias in the vertical direction. β and γ are power factors for converting density to pressure.
Second, panic propagation kinetic model
(1) Initializing definition of panic entropy
The invention utilizes panic entropy to quantitatively analyze the relationship between individual behaviors and the confusion degree of the whole group. The panic entropy is a measure of the degree of panic in the evacuated population, i.e. the greater the degree of panic in the evacuated population, the greater the panic entropy value, the panic entropy is defined as follows:
let u be an arbitrary evacuated individual belonging to the set g ═ { u ═ u }1，u2…, the set represents a unit grid (x, y) with the grid center point coordinates (x, y) being the finite number of elements. Setting probability value
Figure BDA00018179042500000611
The panic entropy of a unit grid space (x, y) in the respective local region is defined as:
Figure BDA0001817904250000065
wherein u isiIndicating that the individual is evacuated,
Figure BDA0001817904250000066
representing the velocity distribution probability. As shown in FIG. 2, x is a horizontal coordinate value, y is a vertical coordinate value, the crowd in the unit grid is regarded as a whole, and the behavior characteristics of the evacuated individuals are represented by the magnitude and direction of the speed of the crowd in the unit grid. In fig. 2, the speed direction of each evacuated individual in each grid is divided into 8 directions,
panic entropy direction dir (E) for evacuating people in grid (x, y)x，y) And panic entropy size | | Ex，yThe formula of | is as follows:
Figure BDA0001817904250000067
Figure BDA0001817904250000068
where n is the total number of evacuated individuals in each discrete grid, ncIs the total number of evacuated individuals in each directional interval, mdIs the total number of evacuated individuals in each discrete speed interval. Thus, the initial value of panic entropy can be calculated by the distribution of the magnitude and direction of the crowd speed in the evacuation space.
At the zero time of the initial case, the speed of the sparse population in a certain e-direction (total of 8 directions) in the discrete grid (x, y) is:
Figure BDA0001817904250000069
gamma is a sector area between-22.5 deg. and +22.5 deg. with reference to the e direction,
Figure BDA00018179042500000610
is a velocity value in the gamma direction. And initializing the evacuation speed of each grid according to the initial speed distribution of the evacuated crowd.
(2) Establishment of panic propagation model
From the formula of panic entropy, the gradient of panic entropy values of the discrete grid (x, y) and the neighboring grid (a, b) at time step k can be obtained, as shown in formula (16).
Figure BDA0001817904250000071
The overall panic entropy gradient value is thus shown by equation (17):
∑Grad(k)＝∑a，b(Ex，y(k)-Ea，b)) (17)
the adjacent grids (a, b) are 8 grids corresponding to 8 directions around the discrete grid (x, y), wherein a is x-1, x, x +1 and b is y-1, y, y +1, and the position of the central point of the discrete space is (x, y). At time step k, the panic entropy of the discrete grid (x, y) is Ex，y(k) (ii) a The panic entropy of the discrete grid (a, b) is Ea，b(k)。
On the basis of a panic entropy gradient formula, a gradient ratio of the evacuation crowd speed, namely the ratio of the panic entropy gradient of the grid (x, y) to the grid (a, b) to the overall panic entropy gradient, is proposed. At time step k +1, the population velocity gradient ratio is as follows:
Figure BDA0001817904250000072
where ξ is a random coefficient between 0 and 1. And using a random coefficient xi in the gradient ratio to represent the randomness of the speed direction, obtaining the maximum gradient ratio in the speed direction and the direction corresponding to the maximum ratio, and determining the speed direction of the crowd by enabling the pedestrian in the direction to most probably enter the next grid.
The velocity magnitude of the population in the discretized grid (x, y) at time step k +1 is as follows:
Figure BDA0001817904250000073
wherein v isx，y(k) Is the velocity in the grid (x, y) with a time step of k, Ex，y(k) Is the panic entropy value in the grid (x, y) when the time step is k. Sigma1And σ2Is an adjustable constant, E1And E2Is a characteristic point of panic entropy. When the panic entropy of the crowd in the discrete grid is less than E1Panic has little effect on the speed of evacuating people. When the panic entropy of the population in the discrete grid is at E1And E2In between, panic factors promote crowd evacuation, increasing crowd evacuation speed and reducing evacuation time. When the panic entropy of the crowd in the discrete grid is larger than E2In time, the panic factor slows down the evacuation of people and is not beneficial to people to evacuate as soon as possible. The panic entropy direction and the panic entropy magnitude in the entire evacuation space at time step k +1 are given by formula (20) and formula (21).
Figure BDA0001817904250000074
Figure BDA0001817904250000081
Wherein a ═ x-1, x, x +1, and b ═ y-1, y, y + 1. The position of the central point of the discrete space is (x, y) and the velocity of the discrete grid (a, b) at a time step k is va，b(k) In that respect Therefore, the panic propagation kinetic model is composed of formula (18), formula (19), formula (20), and formula (21).
Assuming that the two grids are (x, y) and (a, b), respectively, at the moment k +1, the formula (18) can obtain that the number of people the crowd gushes from the grid (x, y) to the grid (a, b) is the largest, so that the direction is the direction of the panic entropy value at the moment, and the derivation process conforms to the dynamic propagation characteristic. By iterating the algorithm using equations (19), (20) and (21), real-time updating of the panic entropy values in the evacuation space can be achieved.
Third, crowd evacuation simulation
At each time step, the panic propagation model must compute panic entropy and update the population flow rate. In this embodiment, taking T-shaped streets as an example, the simulation execution process is as follows:
step 1: an evacuation space is arranged at the T-shaped street, and the width of two streets and the intersection of the two streets are arranged.
Step 2: the initial position and speed of the evacuated person are set. All evacuees are assumed to be randomly distributed in the space and to have an initial velocity.
And step 3: according to the initial speed of all the evacuated persons, the panic entropy of each grid and the moving direction of the crowd in the grid are calculated.
And 4, step 4: the speed and density (speed gradient ratio) of the evacuated crowd in each grid at the time step of k are calculated by using the formula (18), and the position information of the evacuated people is updated in real time.
And 5: and (3) performing formula iteration according to the formulas (19), (20) and (21) to update the panic entropy value in the evacuation space in real time.
Step 6: the time step is updated to k +1, and then the step 4 is returned to, and the process is cycled until the crowd density reaches the maximum value corresponding to the pedaling event.
Examples
By applying the modeling method for macroscopic population panic propagation dynamics, the T-junction trampling event occurring at the intersection of the street 204 and the street 223 is reproduced through simulation with the wheat and trampling event in 2015 as the background. The stepping event occurred at 06 hours (09 minutes at greenwich mean time 09), and at the t-junction on street 204 and on street 223, the hallowers went to the fifth floor around a post called jamaat bridge. On two opposite streets, a large number of people gather at the intersection of the t-junction, and the evacuated people behind, without knowledge of the congestion in front, continue to advance, resulting in a severe stepping event between pilgrims, which event results in the death of at least 2177 people.
According to the actual parameters of the trample event at the intersection of street 204 and street 223, 2000 evacuated persons were loaded on the street as initial conditions, the width of the exit on the right side wall was set to d, and the area marked with red in the map was the location of the actual crowd peak, as shown in fig. 4. Where street number 204 is the trunk, No. 223Streets are branches. Street number 204 has a width set to Wmain10m, street number 223 is set to a width of W branch9m, 204 streets have an analog length set to lmain500m and set the simulated length of street number 223 to lbranch300 m. Street 204 and street 223 have a width ratio of 1.1: 1. The high panic value of the crowd is mainly distributed at the intersection of the initial position and the T-junction. The concentration of people in the initialized location will result in an increase in panic entropy, and then as the people in street 204 and street 233 move to the intersection area, the crowd density in each grid will increase rapidly, resulting in a rapid increase in the degree of crowd panic, which is related to the crowd panic entropy as shown in fig. 5.
In addition, in the panic propagation model, the speed of movement of the population and the degree of panic of the population are mutually influenced. Different movement velocities may affect the panic entropy value of the population at the next time step, and the magnitude of the panic entropy value affects the movement velocity of the population after. Calculating the panic entropy value by using the known crowd evacuation speed vectors of the formula (13) and the formula (14), then calculating the evacuation crowd speed at the next time step by using a formula (19) of the panic propagation dynamic model, and calculating the panic entropy value at the moment by using a formula (20) and a formula (21). The process is cycled to obtain a graph of crowd evacuation speed versus panic entropy as shown in fig. 6. The dynamics of the propagation of panic and the relation between evacuated population density, velocity and panic entropy are evident from a combination of fig. 5 and 6.
And (4) obtaining the panic entropy distribution condition of the T-shaped street entrance evacuation crowd through program simulation of MATLAB R2013B. According to the simulation result, the high panic entropy value of the crowd is reflected by the fact that the high panic entropy value is mainly distributed at the initial position and the intersection of the T-shaped street. Initially, the panic entropy in the initialized location is larger due to the sudden concentration of people, while the panic entropy values in other locations of the street are lower. As the panic of the population propagates, the panic entropy of the entire street increases until the end of the simulation.
And loading the number and the initial speed value of the T-shaped street entrance evacuation population by using a panic propagation quantitative analysis formula, performing program simulation by using MATLAB R2013B to obtain the change condition of the panic entropy value of the T-shaped street entrance evacuation population, and displaying the change condition through a 3D space, wherein as shown in FIG. 3, the distribution of the panic entropy in the 3D space reaches higher panic degree when the simulation time step is 70.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (6)

1. A macroscopic population panic propagation dynamics model building method is characterized by comprising the following steps:
1) dividing an evacuation space into a plurality of discretization unit grids, constructing the panic entropy of each unit grid based on the information entropy theory, and discretizing the speed direction of the evacuated crowd into eight main directions with equal intervals in each unit grid;
2) constructing a panic entropy value gradient of each adjacent unit grid;
3) constructing a macroscopic population panic propagation kinetic model based on the panic entropy and the panic entropy value gradient, wherein the macroscopic population panic propagation kinetic model is specifically represented as follows:
Figure FDA0002865314160000011
Figure FDA0002865314160000012
Figure FDA0002865314160000013
Figure FDA0002865314160000014
wherein e isx，y(k +1) is the velocity gradient ratio, ξ is a random coefficient between 0 and 1,
Figure FDA0002865314160000015
is the gradient of the panic entropy of the grid (x, y) and the adjacent grid (a, b) in time steps k, ∑ Grad(k) As a global panic entropy gradient value, vx，y(k) Is the velocity in the grid (x, y) with a time step of k, Ex，y(k) Is the panic entropy, σ, in the grid (x, y) at a time step of k1And σ2Is an adjustable constant, E1And E2Is the panic entropy feature point, dir (E)x，y(k+1))、||Ex，y(k +1) | is the panic entropy direction and the panic entropy magnitude in the whole evacuation space when the time step is k + 1;
constructing the panic entropy taking into account the panic entropy direction of evacuating people in the grid (x, y)
Figure FDA0002865314160000016
And panic entropy magnitude
Figure FDA0002865314160000017
The panic entropy direction of the evacuated crowd is expressed as:
Figure FDA0002865314160000018
the panic entropy size of the evacuated population is expressed as:
Figure FDA0002865314160000019
where n is the total number of evacuated individuals per unit cell, ncIs the total number of evacuated individuals in each directional interval, mdIs each separatedTotal number of evacuated individuals in the dispersion speed interval, VmaxThe maximum speed for evacuating an individual.
2. The macroscopic population panic propagation dynamics model building method of claim 1, wherein said panic entropy gradient is represented as:
Figure FDA0002865314160000021
wherein E isa，b(k) Is the panic entropy in the grid (a, b) adjacent to grid (x, y) with time step k, a being x-1, x, x +1, b being y-1, y, y + 1.
3. The macroscopic population panic propagation dynamics model building method of claim 2, wherein said overall panic entropy gradient value is expressed as:
Figure FDA0002865314160000022
4. a crowd evacuation simulation method based on the macroscopic population panic propagation dynamics model according to claim 1, characterized in that it comprises the following steps:
a) setting an evacuation space and an initial position and an initial speed of an evacuation individual;
b) calculating the panic entropy of each grid and the moving direction of the crowd in the grid, and updating the position information of the evacuated people in real time;
c) and circularly utilizing the macroscopic population panic propagation dynamic model to calculate the evacuation population speed and the panic entropy value corresponding to each time step until the simulation is finished.
5. The crowd evacuation simulation method according to claim 4, wherein in the step b), the moving direction is determined according to a speed gradient ratio of the crowd.
6. The crowd evacuation simulation method of claim 4, further comprising:
d) and displaying the panic situation evolution process of the crowd in the panic propagation process in a 3D space.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106096115A (en) * 2016-06-06 2016-11-09 同济大学 A kind of crowd evacuation emulation method based on self-organizing sand ionization formula
CN106250677A (en) * 2016-07-21 2016-12-21 同济大学 Under hazardous condition based on kinesiology bead model, crowd panic propagates modeling method
CN106570811A (en) * 2016-11-15 2017-04-19 同济大学 Disaster filed situation change-based people flow evacuation method
CN106886764A (en) * 2017-02-22 2017-06-23 深圳市深网视界科技有限公司 A kind of panic degree computational methods and device based on deep learning

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE102011078801A1 (en) * 2010-12-22 2012-06-28 Siemens Aktiengesellschaft Activatable barrier system

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106096115A (en) * 2016-06-06 2016-11-09 同济大学 A kind of crowd evacuation emulation method based on self-organizing sand ionization formula
CN106250677A (en) * 2016-07-21 2016-12-21 同济大学 Under hazardous condition based on kinesiology bead model, crowd panic propagates modeling method
CN106570811A (en) * 2016-11-15 2017-04-19 同济大学 Disaster filed situation change-based people flow evacuation method
CN106886764A (en) * 2017-02-22 2017-06-23 深圳市深网视界科技有限公司 A kind of panic degree computational methods and device based on deep learning

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
"基于熵的火灾场景介观人群疏散模型";魏心泉 等;《系统工程理论与实践》;20151031;第35卷(第10期);第2473-2483页 *

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