A crowd stability evolution method and system based on crowd energy and a medium

Abstract

The present application relates to a kind of crowd stability evolution method, system and medium based on crowd energy, the method comprises the following steps: the passage area is divided into several grids, the pedestrian in grid area is regarded as a crowd, the horizontal average speed, vertical average speed and pedestrian density of crowd are obtained, and the crowd internal disturbance propagation dynamics model in passage area is established;According to the crowd internal disturbance propagation dynamics model, the crowd energy equation is constructed, and the crowd energy derivative is calculated;The stability of crowd is judged by the positive and negative nature of the crowd energy derivative, and the stability evolution trend of crowd is obtained.Compared with prior art, the present application does not rely on computer vision technology too much, avoids environmental interference, and deeply explains the influence of crowd internal disturbance on stability.

Description

Technical Field

[0001] This invention relates to the field of population mobility, and in particular to a method, system, and medium for population stability evolution based on population energy. Background Technology

[0002] Stable crowd flow is crucial for the safety of people at large-scale events. Crowds moving through large events constitute typical complex systems, and their stability reflects their ability to return to a normal, stable state of motion under disturbance conditions. Assessing crowd stability in public places is essential for maintaining stable crowd flow and preventing stampedes caused by sudden events during crowd movement. When passengers suddenly accelerate and run in the passageway area of ​​a high-speed rail station waiting hall, it may cause panic among the surrounding crowd, thus 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 method and apparatus for real-time crowd stability state recognition based on convolutional neural networks. The method includes the following steps: acquiring an input image, using the input image as input to a multi-column convolutional neural network model to obtain the number of people in a given grid region; performing image correction on the input image to obtain the actual area of ​​the given grid region; obtaining the crowd density value of the given grid region based on the number of people and the actual area; and identifying the crowd stability state of each given grid region based on the crowd density value. The multi-column convolutional neural network model includes multiple parallel convolutional neural networks with identical structures. The kernel size of each convolutional neural network is different, and the output of each convolutional neural network is mapped through a 1×1 filter to generate a two-dimensional density map matrix to obtain the number of people in the given grid region.

[0003] Currently, there are several shortcomings in the research on crowd stability: 1) Computer vision methods are costly and computationally complex to deploy monitoring equipment in complex scenarios; 2) Control theory methods do not consider the evolution of internal disturbances and cannot deeply explain the impact of internal disturbances on stability. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology by providing a population stability evolution method, system and medium based on the population energy function, so as to realize the deduction of the stability change trend of the population.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] The passage area is divided into several grids, and pedestrians within each grid area are considered as a crowd. The average horizontal velocity, average vertical velocity, and pedestrian density of the crowd are obtained, and a dynamic model of disturbance propagation within the crowd in the passage area is established.

[0007] Based on the dynamics model of disturbance propagation within the crowd, a crowd energy equation is constructed, and the crowd energy derivative is calculated.

[0008] The stability of the population is qualitatively determined by the positive or negative sign of the population energy derivative, and the evolution trend of population stability is analyzed.

[0009] Furthermore, the planar coordinates of pedestrians within the grid area as follows:

[0010]

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

[0012] Furthermore, the formula for calculating the horizontal average speed of the crowd is as follows:

[0013]

[0014] In the formula, V grid_x The average speed at the population level Let t2 be the horizontal coordinates of the pedestrian. Here are the horizontal coordinates of the pedestrian at time t1;

[0015] The formula for calculating the vertical average velocity of the crowd is as follows:

[0016]

[0017] In the formula, V grid_y The vertical average velocity of the crowd Let t2 be the vertical position coordinates of the pedestrian. The coordinates of the pedestrian's vertical position at time t1;

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

[0019]

[0020] In the formula, ρ grid Let L be the pedestrian density, L be the length of the grid area, and W be 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 population density, and v x v is the horizontal velocity of a pedestrian in a moving crowd.y V is the vertical velocity of a pedestrian in a moving crowd. x V is the pedestrian's equilibrium speed in the horizontal direction. y Let τ be the pedestrian's equilibrium velocity in the vertical direction, and τ be the relaxation time coefficient.

[0024] Furthermore, considering the pedestrians as a fluid, the crowd energy equation can be constructed based on Bernoulli's equation as follows:

[0025]

[0026] In the formula, p grid To alleviate population pressure, V grid P represents the average speed of the crowd. x For horizontal pressure, P y The vertical pressure is given by h, where h is the average height of the crowd, and ρ is the vertical pressure. grid Where is the population density and g is the gravitational acceleration.

[0027] Furthermore, differentiating the crowd energy equation with respect to time t yields the crowd energy derivative as follows:

[0028]

[0029] In the formula, The energy derivative of the population.

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

[0031]

[0032] In the formula, P x For the horizontal pressure of the crowd, P y The pressure in the vertical direction 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, which, when executed by a processor, enables a population stability evolution method based on population energy.

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

[0036] The crowd dynamics model building module is used to establish a dynamic model of the propagation of disturbances within the crowd in the passage area based on the average horizontal velocity, average vertical velocity, and pedestrian density of the crowd.

[0037] The crowd energy derivative calculation module is used to construct the crowd energy equation based on the crowd internal disturbance propagation dynamics model and calculate the crowd energy derivative.

[0038] The population stability determination module is used to qualitatively determine the stability of the population based on the positive or negative sign of the population energy derivative, and to obtain the population stability evolution trend.

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

[0040] 1. This invention establishes a crowd dynamics model, constructs a crowd energy function, and infers the stability change trend of panicked crowds by calculating the energy derivative. It does not rely excessively on computer vision technology, reduces interference from ambient light and occlusion, and improves the accuracy of the inference.

[0041] 2. This invention treats the crowd as an ideal fluid in a stable flow and constructs a crowd dynamics model based on a fluid dynamics model. This allows for in-depth exploration of the evolution characteristics of crowd flow stability and a thorough explanation of the impact of internal disturbances on stability. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating a method for the evolution of panic crowd stability based on a crowd energy function proposed in this invention.

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

[0044] Figure 3 The figure shows the energy derivative distribution of the crowd at t=1.30s in Example 1. The ellipse in the figure represents pedestrians running at an acceleration, the arrow indicates the direction of the pedestrians' acceleration, and the color legend represents the energy derivative value of the crowd.

[0045] Figure 4 The figure shows the distribution of energy derivative values ​​of the crowd at t = 2.41s in Example 1. The ellipse in the figure represents pedestrians running at an acceleration, the arrow indicates the direction of the pedestrians' acceleration, and the color legend represents the energy derivative values ​​of the crowd.

[0046] Figure 5 The figure shows the energy derivative distribution of the crowd at t=2.83s in Example 1. The ellipse represents a pedestrian running at an acceleration, the arrow indicates the direction of the pedestrian's acceleration, and the color legend represents the energy derivative value of the crowd. Detailed Implementation

[0047] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0048] Example 1

[0049] This embodiment selects the rectangular passageway in front of the shops in the waiting hall of Shanghai Hongqiao Railway Station as the experimental scenario, such as... Figure 2 As shown in the image, the passageways in this area are narrow and there is a large flow of pedestrians. Pedestrians may fall due to being pushed from behind or suddenly accelerate due to time constraints, which can easily cause chaos and temporary congestion, and greatly increase the risk of stampedes.

[0050] This embodiment provides a method for the evolution of panic crowd stability based on a crowd energy function, such as... Figure 1 As shown, it includes the following steps:

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

[0052] A rectangular area of ​​20m × 4m was selected as the experimental scenario. The passage area was divided into several grids. All pedestrians within a grid area were considered as a whole. At a certain time t, the planar coordinates of the pedestrians within the grid area were determined. as follows:

[0053]

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

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

[0056]

[0057] In the formula, V grid_x The average speed at the population level Let t2 be the horizontal coordinates of the pedestrian. Here are the horizontal coordinates of the pedestrian at time t1;

[0058] The formula for calculating the vertical average velocity of the crowd is as follows:

[0059]

[0060] In the formula, V grid_y The vertical average velocity of the crowd Let t2 be the vertical position coordinates of the pedestrian. The coordinates of the pedestrian's vertical position at time t1;

[0061] The formula for calculating pedestrian density in a crowd is as follows:

[0062]

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

[0064] Taking a pedestrian accelerating while running as an example, COMSOL Multiphysics fluid simulation is used to simulate the pedestrian's accelerating running behavior. In the simulation, the pedestrian accelerates 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 population density, and v x v is the horizontal velocity of a pedestrian in a moving crowd. y V is the vertical velocity of a pedestrian in a moving crowd. x V is the pedestrian's equilibrium speed in the horizontal direction. y Let τ be the pedestrian's equilibrium velocity in the vertical direction, and τ be the relaxation time coefficient.

[0068] Furthermore, since the crowd is not a continuous fluid medium, the crowd within the grid is replaced by individual pedestrians, which can be represented by V. grid_x V grid_y Replacing v respectively x v y As shown in the following formula:

[0069]

[0070] In the formula, ρ grid Pedestrian density.

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

[0072] If we consider pedestrians as a fluid, and based on Bernoulli's equation, we can construct the following energy equation for the crowd:

[0073]

[0074] In the formula, p grid To alleviate population pressure, V grid P represents the average speed of the crowd. x For horizontal pressure, P y The vertical pressure is given by h, where h is the average height of the crowd, and ρ is the vertical pressure. grid Where is the population density and g is the gravitational acceleration.

[0075] Taking the derivative of the energy equation with respect to time t, we obtain the energy derivative of the crowd as follows:

[0076]

[0077] In the formula, The energy derivative of the population.

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

[0079]

[0080] In the formula, P x For the horizontal pressure of the crowd, P y The pressure in the vertical direction of the crowd.

[0081] Population state variables sta include population stress p grid Average speed of the crowd V grid And the average height of the crowd, h.

[0082] The energy derivative of the population is summarized as follows:

[0083]

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

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

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

[0087] Analysis shows that the function E(p) grid V grid ,h) is naturally positive definite, when p grid Range of values, V grid The range of values ​​and the non-zero state p in the range of h. grid V grid and h, such that f unsta Always greater than f sta ,Right now If the value is always less than 0, then the equilibrium state at the origin is consistently 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 half-definite value as a substitute The condition for taking a negative definite value.

[0089] Furthermore, when ||p grid V grid When h||→∞, E(p) is satisfied. grid V grid If f(h)→∞, then the equilibrium state at the origin is asymptotically stable over a large range; when there exists f unsta Less than f sta That is, it exists If it is greater than 0, then If the neighborhood is positive definite, then the origin is an unstable state.

[0090] Timing begins when the pedestrians start to accelerate, and the energy derivative distribution of the crowd at time t = 1.30s is shown in the following figure. Figure 3 As shown, at this time, region A is located to the right front of the accelerating pedestrian. The average energy derivative value of this region is greater than 1.0, which is positive definite, and the crowd has great instability.

[0091] The distribution of the energy derivative values ​​of the crowd under the disturbance of pedestrians accelerating while running at time t = 2.41s is shown in the figure below. Figure 4 As shown in the figure, region A is located to the right rear of the accelerating pedestrian. At this time, the average energy derivative of region 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 of the energy derivative values ​​of the crowd under the disturbance of pedestrians accelerating while running at time t = 2.83s is shown in the figure below. Figure 5 As shown in the figure, area A is relatively far from the accelerating pedestrian. Figure 4 The average energy derivative of region A increases, at which point it is relatively higher. Figure 3 and Figure 4 The value decreases to approximately -0.5, which is negative constant, indicating that the population is in a stable state.

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

[0094] The stability evolution trend, consisting of the stable states of the population at time t = 1.30s, time t = 2.41s, and time t = 2.83s, is visualized to obtain a more intuitive understanding of the population's stability evolution trend.

[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, it can realize a population stability evolution method based on population energy.

[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 a crowd energy function, including:

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

[0101] The crowd energy derivative calculation module is used to construct the crowd energy equation based on the crowd dynamics model and calculate the crowd energy derivative.

[0102] The population stability determination module is used to qualitatively determine the stability of the population based on the positive or negative sign of the population energy derivative, and to analyze the population stability evolution trend.

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

[0104] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A population stability evolution method based on population energy, characterized in that, Includes the following steps: The passage area is divided into several grids, and pedestrians within each grid area are considered as a crowd. The average horizontal velocity, average vertical velocity, and pedestrian density of the crowd are obtained, and a dynamic model of disturbance propagation within the crowd in the passage area is established. Based on the aforementioned dynamic model of disturbance propagation within the crowd, a crowd energy equation is constructed, and the crowd energy derivative is calculated. The dynamic model of disturbance propagation within the crowd is as follows: In the formula, Indicates population density. The horizontal speed of pedestrians in a moving crowd. The vertical speed of pedestrians in a moving crowd. The horizontal equilibrium speed of the pedestrian. The equilibrium speed of the pedestrian in the vertical direction. The relaxation time coefficient is... If we consider pedestrians as a fluid, and based on Bernoulli's equation, we can construct the following energy equation for the crowd: In the formula, For the pressure of the population, The average speed of the crowd The average height of the population For population density, It is the acceleration due to gravity. The pressure on the population The calculation formula is as follows: In the formula, For the horizontal pressure of the population, The pressure in the vertical direction of the crowd; The stability of the population is qualitatively determined by the positive or negative sign of the population energy derivative, thus obtaining the population stability evolution trend.

2. The population stability evolution method based on population energy according to claim 1, characterized in that, The planar coordinates of pedestrians within the grid area as follows: In the formula, For pedestrians plane coordinates, For pedestrians quality The number of pedestrians observed within a grid at a given moment.

3. The population stability evolution method based on population energy according to claim 1, characterized in that, The formula for calculating the average horizontal velocity of the population is as follows: In the formula, The average speed at the population level for The horizontal coordinates of the pedestrian at any given time. for The horizontal coordinates of the pedestrian at any given time; The formula for calculating the vertical average velocity of the crowd is as follows: In the formula, The vertical average velocity of the crowd for Vertical coordinates of the pedestrian at any given time for Vertical coordinates of the pedestrian at any given time; The formula for calculating the pedestrian density of the crowd is as follows: In the formula, For pedestrian density, The length of the grid region. This represents the width of the grid area.

4. The population stability evolution method based on population energy according to claim 1, characterized in that, The population energy equation is applied to time. The derivative of the crowd energy is obtained by taking the derivative as follows: In the formula, The energy derivative of the population.

5. The population stability evolution method based on population energy according to claim 1, characterized in that, The stability evolution trend of the population is visualized.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, enables the implementation of the population stability evolution method based on population energy as described in any one of claims 1 to 5.

7. A population stability evolution system based on population energy, characterized in that, include: The crowd dynamics model building module is used to establish a dynamic model of the propagation of disturbances within the crowd in the passage area based on the average horizontal velocity, average vertical velocity, and pedestrian density of the crowd. The crowd energy derivative calculation module is used to construct a crowd energy equation based on the crowd internal disturbance propagation dynamics model, and calculate the crowd energy derivative. The crowd internal disturbance propagation dynamics model is as follows: In the formula, Indicates population density. The horizontal speed of pedestrians in a moving crowd. The vertical speed of pedestrians in a moving crowd. The horizontal equilibrium speed of the pedestrian. The equilibrium speed of the pedestrian in the vertical direction. The relaxation time coefficient is... If we consider pedestrians as a fluid, and based on Bernoulli's equation, we can construct the following energy equation for the crowd: In the formula, For the pressure of the population, The average speed of the crowd The average height of the population For population density, It is the acceleration due to gravity. The pressure on the population The calculation formula is as follows: In the formula, For the horizontal pressure of the population, The pressure in the vertical direction of the crowd; The population stability determination module is used to qualitatively determine the stability of the population based on the positive or negative sign of the population energy derivative, and to obtain the population stability evolution trend.

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