Crowd stability evolution method and system based on crowd energy and medium

Abstract

The invention relates to a crowd stability evolution method and system based on crowd energy and a medium, and the method comprises the following steps: dividing a channel region into a plurality of grids, taking pedestrians in the grid region as a crowd, obtaining the horizontal average speed, the vertical average speed and the pedestrian density of the crowd, and calculating the crowd stability. Establishing a crowd internal disturbance propagation dynamical model in the channel area; constructing a crowd energy equation according to the crowd internal disturbance propagation dynamical model, and calculating a crowd energy derivative; and qualitatively judging the stability of the crowd according to the positive and negative of the energy derivative of the crowd to obtain the stability evolution trend of the crowd. Compared with the prior art, the method does not excessively depend on a computer vision technology, avoids environmental interference, and deeply explains the influence of internal disturbance of crowds on stability.

Description

Technical Field

[0001] The present invention relates to the field of crowd flow, and in particular to a crowd stability evolution method, system and medium based on crowd energy. Background Art

[0002] Stable crowd flow is an important guarantee for the safety of people in large-scale events. The mobile crowd in large-scale events is a typical complex system, and its stability reflects the ability of the crowd to return to a normal and stable state of motion under disturbance conditions. Judging the stability of the crowd in public places is crucial to maintaining the stable flow of the crowd and preventing stampedes due to emergencies during crowd movement. When passengers suddenly accelerate in the passage area of ​​the waiting hall of a high-speed railway station, it may cause panic among the surrounding people, thereby affecting the stability of the entire crowd. Existing research methods are mostly based on computer vision and control theory. For example, Chinese patent CN110866453 B discloses a real-time crowd stability state recognition method and device based on a convolutional neural network, the method comprising the following steps: obtaining an input image, taking the input image as the input of a multi-column convolutional neural network model, and obtaining the number of people in a given grid area; performing image correction on the input image to obtain the actual area of ​​the given grid area; obtaining the crowd density value of the given grid area based on the crowd number and the actual area; and identifying the crowd stability state of each given grid area based on the crowd density value; wherein the multi-column convolutional neural network model comprises a plurality of parallel convolutional neural networks with the same structure, the convolution kernel size of each convolutional neural network is different, and the output of each convolutional neural network is mapped by a 1×1 filter to generate a two-dimensional density map matrix to obtain the number of people in the given grid area.

[0003] At present, there are several shortcomings in the research on crowd stability: 1) Computer vision methods have high cost and complex calculations for deploying monitoring equipment in complex scenes; 2) Control theory methods do not consider the evolution of internal disturbances and cannot deeply explain the impact of internal disturbances of the crowd on stability. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a method, system and medium for evolving the stability of a population based on a population energy function, so as to achieve the deduction of the stability change trend of a population.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] The channel area is divided into several grids, and the pedestrians in the grid area are regarded as a crowd. The horizontal average speed, vertical average speed and pedestrian density of the crowd are obtained, and the dynamic model of the internal disturbance propagation of the crowd in the channel area is established.

[0007] Constructing a crowd energy equation based on the crowd internal disturbance propagation dynamics model and calculating the crowd energy derivative;

[0008] The stability of the crowd is qualitatively judged by the positive or negative nature of the crowd energy derivative, and the stability evolution trend of the crowd is analyzed.

[0009] Furthermore, the plane coordinates of the pedestrians in the grid area as follows:

[0010]

[0011] In the formula, (x i ,y i ) is the plane coordinate of pedestrian i, m i is the mass of pedestrian i, and N is the number of pedestrians in the observation grid at a certain moment.

[0012] Furthermore, the horizontal average speed of the crowd is calculated as follows:

[0013]

[0014] Where V grid_x is the average speed of the crowd, is the horizontal position coordinate of the pedestrian at time t2, is the horizontal position coordinate of the pedestrian at time t1;

[0015] The vertical average speed of the crowd is calculated as follows:

[0016]

[0017] Where V grid_y is the average vertical velocity of the crowd, is the vertical position coordinate of the pedestrian at time t2, is the vertical position coordinate of the pedestrian at time t1;

[0018] The calculation formula of the pedestrian density of the crowd is as follows:

[0019]

[0020] In the formula, ρ grid is the pedestrian density, L is the length of the grid area, and W is the width of the grid area.

[0021] Furthermore, the dynamic model of disturbance propagation within the crowd is as follows:

[0022]

[0023] In the formula, ρ represents the crowd density, v x is the horizontal speed of pedestrians in the moving crowd, vy is the vertical speed of pedestrians in the moving crowd, V x is the equilibrium speed of pedestrians in horizontal direction, V y is the equilibrium speed of the pedestrian in the vertical direction, and τ is the relaxation time coefficient.

[0024] Furthermore, the pedestrians are compared to fluids, and according to the Bernoulli equation, the crowd energy equation is constructed as follows:

[0025]

[0026] In the formula, p grid For the crowd pressure, V grid is the average speed of the crowd, P x is the horizontal pressure, P y is the vertical pressure, h is the average height of the crowd, ρ grid is the crowd density, and g is the acceleration due to gravity.

[0027] Furthermore, the crowd energy equation is differentiated with respect to time t to obtain the crowd energy derivative as follows:

[0028]

[0029] In the formula, is the crowd energy derivative.

[0030] Furthermore, the crowd pressure p grid The calculation formula is as follows:

[0031]

[0032] Where P x is the horizontal pressure of the crowd, P y is the vertical pressure of the crowd.

[0033] Furthermore, the stability evolution trend of the population is visualized.

[0034] According to another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, a crowd stability evolution method based on crowd energy can be implemented.

[0035] According to another aspect of the present invention, a panic crowd stability evolution system based on crowd energy function is provided, comprising:

[0036] The crowd dynamics model building module is used to build a crowd internal disturbance propagation dynamics model in the channel area based on the crowd's horizontal average speed, vertical average speed and pedestrian density;

[0037] A crowd energy derivative calculation module, used to construct a crowd energy equation according to the crowd internal disturbance propagation dynamics model and calculate the crowd energy derivative;

[0038] The crowd stability determination module is used to determine the stability of the crowd according to the positive or negative qualitative property of the crowd energy derivative, and obtain the stability evolution trend of the crowd.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] 1. The present invention establishes a crowd dynamics model, constructs a crowd energy function, and deduces the stability change trend of the panic crowd by calculating the energy derivative. It does not rely too much on computer vision technology, reduces the interference caused by ambient light and occlusion, and improves the accuracy of deduction.

[0041] 2. The present invention regards the crowd as an ideal fluid with stable flow and constructs a crowd dynamics model based on the fluid mechanics model. It can deeply explore the evolution characteristics of crowd flow stability and deeply explain the impact of internal disturbances of the crowd on stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A schematic flow chart of a panic crowd stability evolution method based on crowd energy function proposed by the present invention;

[0043] Figure 2 This is a schematic diagram of a rectangular passage in front of shops in the waiting hall of Shanghai Hongqiao Railway Station in Example 1;

[0044] Figure 3 This is a distribution diagram of the energy derivative values ​​of the crowd at t=1.30s in Example 1. In the diagram, the ellipse represents a pedestrian running at an accelerated speed, the arrow represents the direction in which the pedestrian is running at an accelerated speed, and the color legend represents the energy derivative value of the crowd;

[0045] Figure 4 The energy derivative value distribution diagram of the crowd at t = 2.41s in Example 1, in which the ellipse represents the pedestrians running faster, the arrow indicates the direction of the pedestrians running faster, and the color legend indicates the energy derivative value of the crowd;

[0046] Figure 5 This is a distribution diagram of the energy derivative values ​​of the crowd at t=2.83s in Example 1. In the figure, the ellipse represents the pedestrians running at an accelerated speed, the arrow indicates the direction in which the pedestrians are running at an accelerated speed, and the color legend indicates the energy derivative values ​​of the crowd. DETAILED DESCRIPTION

[0047] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0048] Example 1

[0049] This embodiment selects the rectangular passage in front of the shops in the waiting hall of Shanghai Hongqiao Railway Station as the experimental scene. Figure 2 The passages in this area are narrow and the pedestrian flow is large. Pedestrians may fall down due to being pushed by others or may suddenly accelerate due to time pressure, which can easily cause confusion and short-term congestion, and stampede accidents are very likely to occur.

[0050] This embodiment provides a panic crowd stability evolution method based on crowd energy function, such as Figure 1 As shown, the following steps are included:

[0051] S1. Divide the channel area into several grids, regard the pedestrians in the grid area as a crowd, obtain the horizontal average speed, vertical average speed and pedestrian density of the crowd, and establish a crowd dynamics model in the channel area.

[0052] A rectangular area of ​​20m×4m is selected as the experimental scene. The passage area is divided into several grids. All pedestrians in the grid area are regarded as a whole. At a certain time t, the plane coordinates of the pedestrians in the grid area are as follows:

[0053]

[0054] In the formula, (x i ,y i ) is the plane coordinate of pedestrian i, m i is the mass of pedestrian i, and N is the number of pedestrians in the observation grid at a certain moment.

[0055] The formula for calculating the horizontal average speed of a crowd is as follows:

[0056]

[0057] Where V grid_x is the average speed of the crowd, is the horizontal position coordinate of the pedestrian at time t2, is the horizontal position coordinate of the pedestrian at time t1;

[0058] The vertical average speed of the crowd is calculated as follows:

[0059]

[0060] Where V grid_y is the average vertical velocity of the crowd, is the vertical position coordinate of the pedestrian at time t2, is the vertical position coordinate of the pedestrian at time t1;

[0061] The calculation formula for the pedestrian density of a crowd is as follows:

[0062]

[0063] In the formula, ρ grid is the pedestrian density, L is the length of the grid area, and W is the width of the grid area.

[0064] Taking pedestrians running at an accelerated speed as an example, COMSOL Multiphysics fluid simulation is used to simulate the pedestrians' running at an accelerated speed. In the simulation, pedestrians run at an accelerated speed from right to left in a direction parallel to the x-axis.

[0065] The dynamic model of disturbance propagation within the crowd is constructed as follows:

[0066]

[0067] In the formula, ρ represents the crowd density, v x is the horizontal speed of pedestrians in the moving crowd, v y is the vertical speed of pedestrians in the moving crowd, V x is the equilibrium speed of pedestrians in horizontal direction, V y is the equilibrium speed of the pedestrian in the vertical direction, and τ is the relaxation time coefficient.

[0068] Furthermore, since the crowd is not a continuous fluid medium, the crowd in the grid is used to replace the individual pedestrians, and V grid_x 、V grid_y Replace v respectively x 、v y , as follows:

[0069]

[0070] In the formula, ρ grid is the pedestrian density.

[0071] S2. Construct the crowd energy equation based on the crowd dynamics model and calculate the crowd energy derivative.

[0072] Comparing pedestrians to fluids, according to the Bernoulli equation, the crowd energy equation is constructed as follows:

[0073]

[0074] In the formula, p grid For the crowd pressure, V grid is the average speed of the crowd, P x is the horizontal pressure, P y is the vertical pressure, h is the average height of the crowd, ρ grid is the crowd density, and g is the acceleration due to gravity.

[0075] The energy derivative of the crowd obtained by differentiating the energy equation at time t is as follows:

[0076]

[0077] In the formula, is the crowd energy derivative.

[0078] Crowd pressure grid The calculation formula is as follows:

[0079]

[0080] Where P x is the horizontal pressure of the crowd, P y is the vertical pressure of the crowd.

[0081] The crowd state variables sta include crowd pressure p grid 、Crowd average speed V grid and the average height of the crowd h.

[0082] The crowd energy derivative is organized as:

[0083]

[0084] In the formula, f sta is a function containing crowd state parameters sta, f unsta is a function that does not include the crowd state parameter sta.

[0085] S3. The stability of the crowd is judged qualitatively by the positive or negative derivative of the crowd energy, and the stability evolution trend of the crowd is obtained.

[0086] In this embodiment, taking the area around point A (14, 2.5) as an example, the change of the energy derivative value of the crowd under the disturbance of panic behavior of accelerated running is obtained.

[0087] From the analysis, we can know that the function E(p grid ,V grid ,h) is naturally positive definite when p grid Range, V grid The non-zero states p in the range and h range grid 、V grid and h, so that f unsta Always greater than f sta ,Right now is always less than 0, then the equilibrium state at the origin is uniformly asymptotically stable.

[0088] When f unsta Greater than or equal to f sta But f unsta Not equal to fsta ,Right now Always less than or equal to 0 and If it is not always equal to 0, then it can be used Take the negative semidefinite instead Take the negative condition.

[0089] In addition, when ||p grid ,V grid ,h||→∞ satisfies E(p grid ,V grid ,h)→∞, then the equilibrium state at the origin is uniformly asymptotically stable over a large range; when there exists f unsta Less than f sta , that is, existence Greater than 0, then If it is positive definite in the neighborhood, then the origin is unstable.

[0090] The timing starts from the moment the pedestrians start to accelerate and run. The distribution diagram of the energy derivative value of the crowd at time t = 1.30s is as follows Figure 3 As shown, at this time, area A is in front of the right side of the accelerating pedestrian. The average energy derivative value of this area is greater than 1.0, which is positive definite, and the crowd is extremely unstable.

[0091] The distribution diagram of the energy derivative value of the crowd under the disturbance of pedestrian acceleration at time t = 2.41s is as follows Figure 4 As shown in the figure, area A is located to the right rear of the accelerating pedestrian. At this time, the average energy derivative value of area A decreases to about 0.03, which is positive definite. Although the crowd is still unstable at this time, its stability is enhanced compared to the time t=1.30s.

[0092] The distribution diagram of the energy derivative value of the crowd under the disturbance of pedestrian acceleration at time t = 2.83s is as follows: Figure 5 As shown in the figure, the distance between area A and the accelerating pedestrian is relatively short. Figure 4 increases, and the average energy derivative value in area A is Figure 3 and Figure 4 Decreases, the value is about -0.5, which is negative definite, and the population is in a stable state.

[0093] S4. Visualize the stability evolution trend of the population.

[0094] The stability evolution trend composed of the stable state of the crowd at time t=1.30s, the stable state of the crowd at time t=2.41s and the stable state of the crowd at time t=2.83s is visualized to obtain the stability evolution trend of the crowd more intuitively.

[0095] Example 2

[0096] This embodiment provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, a crowd stability evolution method based on crowd energy can be implemented.

[0097] The rest is the same as in Example 1.

[0098] Example 3

[0099] This embodiment provides a panic crowd stability evolution system based on crowd energy function, including:

[0100] The crowd dynamics model building module is used to build a crowd dynamics model in the channel area based on the horizontal average speed, vertical average speed and pedestrian density of the crowd;

[0101] A crowd energy derivative calculation module, used to construct a crowd energy equation according to the crowd dynamics model and calculate the crowd energy derivative;

[0102] The crowd stability determination module is used to determine the stability of the crowd according to the positive or negative qualitative characteristics of the crowd energy derivative, and to analyze and obtain the stability evolution trend of the crowd.

[0103] The rest is the same as in Example 1.

[0104] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for evolving crowd stability based on crowd energy, characterized in that: The following steps are involved: The channel area is divided into several grids, and the pedestrians in the grid area are regarded as a crowd. The horizontal average speed, vertical average speed and pedestrian density of the crowd are obtained, and the dynamic model of the internal disturbance propagation of the crowd in the channel area is established. Constructing a crowd energy equation based on the crowd internal disturbance propagation dynamics model and calculating the crowd energy derivative; The stability of the crowd is qualitatively judged by the positive or negative nature of the crowd energy derivative, and the stability evolution trend of the crowd is obtained.

2. The method for evolving crowd stability based on crowd energy according to claim 1, characterized in that: The plane coordinates of the pedestrians in the grid area as follows: In the formula, (x i ,y i ) is the plane coordinate of pedestrian i, m i is the mass of pedestrian i, and N is the number of pedestrians in the observation grid at a certain moment.

3. The crowd stability evolution method based on crowd energy according to claim 1, characterized in that: The horizontal average speed of the crowd is calculated as follows: Where V grid_x is the average speed of the crowd, is the horizontal position coordinate of the pedestrian at time y2, is the horizontal position coordinate of the pedestrian at time t1; The vertical average speed of the crowd is calculated as follows: Where V drid_y is the average vertical velocity of the crowd, is the vertical position coordinate of the pedestrian at time t2, is the vertical position coordinate of the pedestrian at time t1; The calculation formula of the pedestrian density of the crowd is as follows: In the formula, ρ grid is the pedestrian density, L is the length of the grid area, and W is the width of the grid area.

4. The method for evolving crowd stability based on crowd energy according to claim 1, characterized in that: The dynamic model of disturbance propagation within the crowd is as follows: In the formula, ρ represents the crowd density, v x is the horizontal speed of pedestrians in the moving crowd, v y is the vertical speed of pedestrians in the moving crowd, V x is the equilibrium speed of pedestrians in horizontal direction, V y is the equilibrium speed of the pedestrian in the vertical direction, and τ is the relaxation time coefficient.

5. The method for evolving crowd stability based on crowd energy according to claim 1, characterized in that: Comparing the pedestrians to fluids, according to the Bernoulli equation, the crowd energy equation is constructed as follows: In the formula, p grid For the crowd pressure, V grid is the average speed of the crowd, P x is the horizontal pressure, P y is the vertical pressure, h is the average height of the crowd, ρ gyid is the crowd density, and g is the acceleration due to gravity.

6. The method for evolving crowd stability based on crowd energy according to claim 5, characterized in that: The crowd energy derivative obtained by differentiating the crowd energy equation with respect to time t is as follows: In the formula, is the crowd energy derivative.

7. The method for evolving crowd stability based on crowd energy according to claim 5, characterized in that: The population pressure p grid The calculation formula is as follows: Where P x is the horizontal pressure of the crowd, P y is the vertical pressure of the crowd.

8. The method for evolving crowd stability based on crowd energy according to claim 1, characterized in that: The stability evolution trend of the population is visualized.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for evolving crowd stability based on crowd energy as claimed in any one of claims 1 to 8 can be implemented.

10. A crowd stability evolution system based on crowd energy, characterized in that: include: The crowd dynamics model building module is used to build a crowd internal disturbance propagation dynamics model in the channel area based on the crowd's horizontal average speed, vertical average speed and pedestrian density; A crowd energy derivative calculation module, used to construct a crowd energy equation according to the crowd internal disturbance propagation dynamics model and calculate the crowd energy derivative; The crowd stability determination module is used to determine the stability of the crowd according to the positive or negative qualitative property of the crowd energy derivative, and obtain the stability evolution trend of the crowd.

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