CN109145365B - Regional crowd motion state prediction method based on micro-macro conversion model - Google Patents

Regional crowd motion state prediction method based on micro-macro conversion model Download PDF

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CN109145365B
CN109145365B CN201810732013.6A CN201810732013A CN109145365B CN 109145365 B CN109145365 B CN 109145365B CN 201810732013 A CN201810732013 A CN 201810732013A CN 109145365 B CN109145365 B CN 109145365B
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赵荣泳
董大亨
胡钱珊
李翠玲
汪栋
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Abstract

The invention relates to a regional crowd motion state prediction method based on a micro-macro conversion model, which comprises the following steps: 1) establishing a micro-macro conversion model for realizing the conversion from micro panic to macro pressure item; 2) acquiring crowd flowing video information parameters; 3) and predicting the motion state of regional crowd based on the micro-macro conversion model and the crowd flow video information parameters, and displaying a prediction result. Compared with the prior art, the invention constructs a micro-macro conversion model, makes up the deficiency of the crowd evacuation modeling method to a certain extent, and provides a new idea for researching the crowd evacuation problem.

Description

Regional crowd motion state prediction method based on micro-macro conversion model
Technical Field
The invention relates to the technical field of crowd evacuation simulation, in particular to a regional crowd motion state prediction method based on a micro-macro conversion model.
Background
In recent years, with the frequent occurrence of various fire accidents and emergencies, the simulation of safe evacuation of emergencies in public places with crowd gathering has been increasingly emphasized. The simulation of crowd evacuation behavior in a real scene has important social significance, and can help emergency departments to formulate corresponding emergency plans, guide the design of scenes, avoid disasters and reduce casualties of people. The computer simulation technology is used for carrying out scene modeling, path optimization and crowd movement behavior modeling, so that the cost can be minimized while the optimal evacuation drilling effect is achieved. Therefore, computer simulation is the most important method for studying crowd evacuation in an emergency.
For the research work of crowd evacuation, two modeling methods are mainly used at present. The first is a macroscopic model and the second is a microscopic model. Specifically, the macro model focuses on considering the population as a whole, and can be generally used for simulating the motion of a large-scale population in real time while ignoring the behavior of an individual; the microscopic model is modeled from the perspective of individuals and focuses on the reproduction of individual behaviors and cognitive processes thereof, but the complexity of the model depends heavily on the number of individuals in a scene.
So far, for a regional crowd movement state prediction method based on a micro-macro conversion model, the shortcomings of lack of individual panic measurement and quantitative influence relationship on a macro crowd evacuation pressure item exist, and the conversion result is not accurate enough.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a regional crowd motion state prediction method based on a micro-macro conversion model.
The purpose of the invention can be realized by the following technical scheme:
a regional crowd motion state prediction method based on a micro-macro conversion model comprises the following steps:
1) establishing a micro-macro conversion model for realizing the conversion from micro panic to macro pressure item;
2) acquiring crowd flowing video information parameters;
3) and predicting the motion state of regional crowd based on the micro-macro conversion model and the crowd flow video information parameters, and displaying a prediction result.
Further, the micro-macro conversion model establishing step includes:
101) establishing a Gaussian distance weight function;
102) constructing a pressure term based on the Gaussian distance weight function;
103) and mapping the micro panic into the pressure item to obtain a micro-macro conversion model.
Further, the gaussian distance weight function is:
Figure BDA0001721131040000021
Figure BDA0001721131040000022
in the formula (I), the compound is shown in the specification,
Figure BDA0001721131040000023
is the position at time t
Figure BDA0001721131040000024
The population density, i.e. the gaussian distance weight function,
Figure BDA0001721131040000025
is the position of the pedestrian j and R is the measurement parameter.
Further, the pressure term includes a horizontal pressure term
Figure BDA0001721131040000026
And vertical pressure term
Figure BDA0001721131040000027
The formula is as follows:
Figure BDA0001721131040000028
Figure BDA0001721131040000029
Figure BDA00017211310400000210
Figure BDA00017211310400000211
in the formula (I), the compound is shown in the specification,
Figure BDA00017211310400000212
is a position
Figure BDA00017211310400000213
The density of the population at the site of the patient,
Figure BDA00017211310400000214
is the position at time t
Figure BDA00017211310400000215
At the value of the velocity in the horizontal direction,
Figure BDA00017211310400000216
is a position
Figure BDA00017211310400000217
At the average speed value in the horizontal direction,
Figure BDA00017211310400000218
is the position at time t
Figure BDA00017211310400000219
At the value of the velocity in the vertical direction,
Figure BDA00017211310400000220
is a position
Figure BDA00017211310400000221
Is perpendicular toThe value of the directional average velocity,<>trepresenting the value at time t.
Further, said mapping of microscopic panic to said pressure term is in particular:
131) obtaining a local discrete expression of the panic degree P:
Figure BDA00017211310400000222
Figure BDA00017211310400000223
in the formula, ppanic_hIs the horizontal component of the panic level P, Ppanic_vIs the vertical component of the panic level P, ρ is the crowd density,
Figure BDA0001721131040000031
is the position at time t
Figure BDA0001721131040000032
At the value of the velocity in the horizontal direction,
Figure BDA0001721131040000033
is a position
Figure BDA0001721131040000034
At the average speed value in the horizontal direction,
Figure BDA0001721131040000035
is the position at time t
Figure BDA0001721131040000036
At the value of the velocity in the vertical direction,
Figure BDA0001721131040000037
is a position
Figure BDA0001721131040000038
Is averaged in the vertical directionVelocity values, n is the number of panic groups, β and γ are weighting factors that convert density into pressure terms,
Figure BDA0001721131040000039
(ii) is an influence factor in the horizontal direction and the vertical direction, (i, j) represents a position coordinate;
132) and (3) taking the panic degree P as a pressure item of the macro model to realize the mapping from micro panic to macro pressure item:
ρ(v+Ppanic_h)t+ρv(v+Ppanic_h)x+ρu(u+Ppanic_h)y＝ρs1
ρ(v+Ppanic_v)t+ρv(v+Ppanic_v)x+ρu(u+Ppanic_v)y＝ρs2
in the formula, v and u respectively represent the crowd velocity in the horizontal and vertical directions in the macro model, and s1、s2Indicating the relaxation term factor, subscript t indicating the partial derivative over time, subscript x indicating the partial derivative over distance x, and subscript y indicating the partial derivative over distance y.
Further, the crowd quality loss of the micro-macro conversion model is evaluated through double integral coordinate transformation under polar coordinates.
Further, the prediction results comprise a crowd Mesh 3D map, a crowd density contour map and a thermodynamic distribution map.
Compared with the prior art, the invention has the following beneficial effects:
1. a micro-macro conversion model is constructed on the basis of the traditional micro-macro model.
As for the research method of crowd evacuation, at present, only a micro method and a macro method exist. According to the invention, a micro-macro conversion model is constructed according to a social force model (a micro model) and an Aw-Rascle model (a macro model), so that the deficiency of a crowd evacuation modeling method is made up to a certain extent, and a new thought is provided for researching the crowd evacuation problem. By utilizing the micro-macro conversion model, the motion state of the crowd can be rapidly obtained on the basis of certain crowd flowing video information parameters, and the panic degree of the micro model can be researched by using the pressure item in the macro model.
2. Simulating a micro-macro conversion model
The prior art focuses on theoretical research on crowd evacuation, theoretically analyzes trend change in the crowd evacuation process, and clearly and definitely shows fewer simulation results. The invention utilizes the proposed micro-macro conversion model, uses MATLAB R2017a to write a program, and can obtain more detailed crowd flowing movement information through a crowd Mesh 3D graph, a crowd density contour map and a thermal distribution map under the conditions of the same geographic information configuration and initialization parameter setting. Compared with the original micro-macro model, the micro-macro model has more accurate data output and better accords with the real actual situation.
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FIG. 1 is a schematic structural view of the present invention;
FIG. 2 is a schematic view of a micro-macro conversion model of the present invention;
FIG. 3 shows the location of a trampling event of McJohn's republic of McJohn 2015;
FIG. 4 is a Mesh 3D diagram of the crowd status;
FIG. 5 is a contour plot of population density;
figure 6 is a population density thermodynamic diagram.
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.
As shown in fig. 1, the present invention provides a regional population motion state prediction method based on a micro-macro conversion model, which comprises the following steps: 1) establishing a micro-macro conversion model for realizing the conversion from micro panic to macro pressure item; 2) acquiring crowd flowing video information parameters; 3) and predicting the motion state of regional crowds based on the micro-macro conversion model and the crowd flow video information parameters, and displaying a prediction result comprising a crowd Mesh 3D graph, a crowd density contour map, a thermal distribution map and the like. The invention establishes a micro-macro conversion model, and can rapidly acquire the motion state of the crowd on the basis of certain crowd flowing video information parameters.
Specifically, the establishing step of the micro-macro conversion model comprises the following steps:
the method comprises the following steps: a gaussian distance weighting function is established.
On the panic metric problem of the macroscopic model, the gradual change mechanism of the Aw-Rascle model is caused by a pressure term P (rho); in the microscopic model, the model dynamics is force analysis according to newton's second law for a single pedestrian. In order to continue to reflect the panic level of the population by macroscopic improvement of Aw-Rscle. Abstracting f in the micro model on the basis of the panic propagation model of the social force model (micro model)ijAnd fiwRelation of resultant force to P (ρ), fijRepresenting the interpersonal interaction force, fiwRepresenting the force between a person and a wall. Considering that P (P) in the macroscopic model is a positive function in the horizontal and vertical velocities u and v, the evacuated population is vulnerable to panic among the population at risk of being pedalled, it is desirable to accelerate the passage through the danger zone, which may lead to the occurrence of a pedalling accident, and the expected velocity of the population increases with the increase of panic.
The position at the time t can be obtained based on the social force model and the analysis of D.Helbin on the 2007 Mecca pilgrimage Meyer and Mecca Meyer and Meyer and Meyer Me
Figure BDA0001721131040000051
The population density of (A) is shown in formula (1).
Figure BDA0001721131040000052
Figure BDA0001721131040000053
Wherein the content of the first and second substances,
Figure BDA0001721131040000054
is the position at time t
Figure BDA0001721131040000055
The density of the population at the site of the patient,
Figure BDA0001721131040000056
r is a measurement parameter for the position of the pedestrian j. The larger R, the larger the effective measurement radius. Can calculate the area A located at the radius RR＝πR2The weight of the inner adjacent pedestrian is 63%. It can be demonstrated that the average of the local density values obtained by the equations (1) and (2) is consistent with the actual average density value. Furthermore, for R → ∞, all the local density measurements are the same value, which corresponds exactly to the total number of pedestrians NRDivided by their area AR＝πR2The latter corresponds to the average ("global") density.
Step two: construction of horizontal "pressure" terms
The local density is shown in formula (3).
Figure BDA0001721131040000057
Where d is the calculation factor introduced and,
Figure BDA0001721131040000058
for time t and position
Figure BDA0001721131040000059
Average population density in a circular region with a circle center and a radius of R.
When R → ∞, the density values will get closer and closer to the true values. Because:
Figure BDA00017211310400000510
Figure BDA00017211310400000511
wherein
Figure BDA00017211310400000512
Is the introduced calculation factor.
The definition of the regional population horizontal velocity is shown in equation (6).
Figure BDA00017211310400000513
Wherein
Figure BDA00017211310400000514
Is the horizontal velocity of the pedestrian j.
The expression of the horizontal direction flow is shown in (7).
Figure BDA00017211310400000515
Since the key factors in the population depend on the local situation, when the local density reaches more than 10 persons per square meter, one influencing mechanism reflecting the physical phenomenon is a "pressure" term, and the horizontal direction "pressure" term is shown in formula (8):
Figure BDA0001721131040000061
wherein the content of the first and second substances,
Figure BDA0001721131040000062
Figure BDA0001721131040000063
the horizontal direction average speed value of regional population is as follows:
Figure BDA0001721131040000064
similarly, a vertical "pressure" term can be obtained:
Figure BDA0001721131040000065
Figure BDA0001721131040000066
in "sloshing" conditions, where density and mechanical stress are difficult to withstand, people attempt to escape from the crowd and begin to push each other to gain space. This condition is sometimes referred to as "crowd panic" and is characterized by an additional energy input in the compressed region, as opposed to a common fluid or granular medium. This results in particularly severe displacements in extremely dense populations, which are practically impossible to control even with a large amount of safety effort.
Step three: realizing the conversion of micro panic to macro pressure item
In combination with the correction of the "pressure" term in panic in the AW-Rascle model, a local discrete expression of the panic level P can be deduced from the pressure term definition:
Figure BDA0001721131040000067
wherein p ispanic_hIs the horizontal component of the panic level P, Ppanic_vIs the vertical component of the panic level P, ρ is the crowd density,
Figure BDA0001721131040000068
is the position at time t
Figure BDA0001721131040000069
At the value of the velocity in the horizontal direction,
Figure BDA00017211310400000610
is a position
Figure BDA00017211310400000611
At the average speed value in the horizontal direction,
Figure BDA00017211310400000612
is the position at time t
Figure BDA00017211310400000613
At the value of the velocity in the vertical direction,
Figure BDA00017211310400000614
is a position
Figure BDA00017211310400000615
The average velocity value in the vertical direction, n is the number of panic people, beta and gamma are weight factors for converting the density into the pressure term,
Figure BDA00017211310400000616
the influence factors in the horizontal direction and the vertical direction (i, j) represent position coordinates. The degree of panic is just the magnitude of the ratio of the difference between the desired speed and the current actual speed to the current speed.
Non-linear hyperbolic Partial Differential Equation (PDE) without taking into account panic as in equations (13) and (14)
ρ(v+Pv)t+ρv(v+Pv)x+ρu(u+Pv)y＝ρs2 (13)
ρ(v+Pu)t+ρv(v+Pu)x+ρu(u+Pu)y＝ρs1 (14)
Wherein s is1、s2Indicating the relaxation term factor, subscript t indicating the partial derivative over time, subscript x indicating the partial derivative over distance x, and subscript y indicating the partial derivative over distance y.
P in the formula (12)panic_vAnd ppanic_uSubstituting equations (13) and (14) maps the "panic level" of the microscopic individuals. As shown in equations (15) and (16).
ρ(v+Ppanic_v(ρ,v,u))t+ρv(v+Ppanic_v(ρ,v,u))x+ρu(u+Ppanic_v(ρ,v,u))y＝ρs1 (15)
ρ(v+Ppanic_u(ρ,v,u))t+ρv(v+Ppanic_u(ρ,v,u))x+ρu(u+Ppanic_u(ρ,v,u))y＝ρs2 (16)
Where v and u represent the horizontal and vertical velocities of the population, respectively, a macroscopic model of pedestrian dynamics, i.e., a micro-to-macroscopic conversion model, can be obtained from equations (13) and (14) that maps panic, as shown in fig. 2.
According to the micro-macro conversion model, the motion state of the crowd in the drawing area can be rapidly predicted on the basis of obtaining certain crowd flowing video information parameters.
Since the helling model is a gaussian distributed circular area integral. Extracting a data source and converting the data source into an Aw-Rascle macroscopic square, wherein the mass loss of people in double integration exists in the two models, and the double integration coordinate transformation under the polar coordinate is carried out on a square area by an integral formula (4) and a microscopic-macroscopic conversion model shown in the figure 2:
Figure BDA0001721131040000071
therefore, the crowd quality accuracy error of model conversion is 26.8%. This data loss rate is acceptable in micro-macro model conversion. The original initialization process of the crowd flowing state is replaced by analyzing the moving condition of the crowd flowing in a certain time window. The discretized initial pedestrian state can be obtained, so that an iterative macro model calculation process is carried out, the change state of the regional crowd flow parameters after a certain time is redrawn, and the condition of the panic degree of the flowing crowd in the trampling region is reflected through the change and the density degree of the 'P' item.
Examples
The T-junction crowd evacuation dynamics model was used to study the trampling event in 2015, and the position of the trampling event was shown in FIG. 3 by reproducing the trampling event at the T-junction between 204 street and 223 street (204-223 junction) through simulation. At 06 hours (09 minutes at 09 Greenwich mean time) in 2015, the stepping event occurred at the T-shaped intersection at 204 and 223 streets. The initial population is distributed primarily on the 204 streets and moves forward in sequence to presenting a pilgrim. The bus on the 223 street downloads a batch of passengers, when the part of people enters the intersection of the 223 and 204 streets, the people in two directions collide with each other, the people fall down due to collision and trample, however, the people behind the bus cannot know the jam condition in the front and continuously move forward, and large-area trampling events among the pilgrims are caused.
2000 evacuated persons were set on the street as initial conditions according to the actual parameters of the treading events at the intersection of 204 street and 223 street. Based on the micro-macro conversion model provided by the invention, an MATLAB program is compiled, and a visual simulation result is calculated and obtained: the Mesh 3D map of the crowd status, as shown in fig. 4, can more finely understand the distribution of crowd density in the whole and local geographic information. The simulation can also obtain a contour map of the crowd evacuation density at the T-junction, as shown in FIG. 5. The crowd density rho of the high risk area of the trampling accident can be obtained through the crowd density contour mapmax. The pedestrian density thermodynamic diagram obtained by simulation can judge the distribution condition of the crowd according to the difference of the color depth in the diagram, as shown in fig. 6.
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 regional crowd motion state prediction method based on a micro-macro conversion model is characterized by comprising the following steps:
1) establishing a micro-macro conversion model for realizing the conversion from micro panic to macro pressure item;
2) acquiring crowd flowing video information parameters;
3) predicting the motion state of regional crowd based on the micro-macro conversion model and the crowd flow video information parameters, and displaying a prediction result;
the mapping of microscopic panic to the pressure item is specifically:
131) obtaining a local discrete expression of the panic degree P:
Figure FDA0002953965460000011
Figure FDA0002953965460000012
in the formula, ppanic_hIs the horizontal component of the panic level P, Ppanic_vIs the vertical component of the panic level P, ρ is the crowd density,
Figure FDA0002953965460000013
is the position at time t
Figure FDA0002953965460000014
At the value of the velocity in the horizontal direction,
Figure FDA0002953965460000015
is a position
Figure FDA0002953965460000016
At the average speed value in the horizontal direction,
Figure FDA0002953965460000017
is the position at time t
Figure FDA0002953965460000018
At the value of the velocity in the vertical direction,
Figure FDA0002953965460000019
is a position
Figure FDA00029539654600000110
The average velocity value in the vertical direction, n is the number of panic people, beta and gamma are weight factors for converting the density into the pressure term,
Figure FDA00029539654600000111
(ii) is an influence factor in the horizontal direction and the vertical direction, (i, j) represents a position coordinate;
132) and (3) taking the panic degree P as a pressure item of the macro model to realize the mapping from micro panic to macro pressure item:
ρ(v+Ppanic_h)t+ρv(v+Ppanic_h)x+ρu(u+Ppanic_h)y＝ρs1
ρ(v+Ppanic_v)t+ρv(v+Ppanic_v)x+ρu(u+Ppanic_v)y＝ρs2
in the formula, v and u respectively represent the crowd velocity in the horizontal and vertical directions in the macro model, and s1、s2Indicating the relaxation term factor, subscript t indicating the partial derivative over time, subscript x indicating the partial derivative over distance x, and subscript y indicating the partial derivative over distance y.
2. The micro-macro conversion model-based regional population motion state prediction method according to claim 1, wherein the micro-macro conversion model establishing step comprises:
101) establishing a Gaussian distance weight function;
102) constructing a pressure term based on the Gaussian distance weight function;
103) and mapping the micro panic into the pressure item to obtain a micro-macro conversion model.
3. The micro-macro conversion model-based regional population motion state prediction method of claim 2, wherein the gaussian distance weight function is:
Figure FDA0002953965460000021
Figure FDA0002953965460000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002953965460000023
is the position at time t
Figure FDA0002953965460000024
The population density, i.e. the gaussian distance weight function,
Figure FDA0002953965460000025
is the position of the pedestrian j and R is the measurement parameter.
4. The micro-macro transition model-based regional population motion state prediction method of claim 2, wherein the pressure term comprises a horizontal pressure term
Figure FDA0002953965460000026
And vertical pressure term
Figure FDA0002953965460000027
The formula is as follows:
Figure FDA0002953965460000028
Figure FDA0002953965460000029
Figure FDA00029539654600000210
Figure FDA00029539654600000211
in the formula (I), the compound is shown in the specification,
Figure FDA00029539654600000212
is a position
Figure FDA00029539654600000213
The density of the population at the site of the patient,
Figure FDA00029539654600000214
is the position at time t
Figure FDA00029539654600000215
At the value of the velocity in the horizontal direction,
Figure FDA00029539654600000216
is a position
Figure FDA00029539654600000217
At the average speed value in the horizontal direction,
Figure FDA00029539654600000218
is the position at time t
Figure FDA00029539654600000219
At the value of the velocity in the vertical direction,
Figure FDA00029539654600000220
is a position
Figure FDA00029539654600000221
At the average speed value in the vertical direction,<>trepresenting the value at time t.
5. The micro-macro conversion model-based regional population motion state prediction method of claim 1, wherein the population quality loss of the micro-macro conversion model is evaluated through double integral coordinate transformation under polar coordinates.
6. The micro-macro conversion model-based regional population motion state prediction method according to claim 1, wherein the prediction results comprise a population Mesh 3D map, a population density contour map and a thermodynamic distribution map.
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