A method and device for simulating the propagation of pedestrian turning disturbances in a crowded place

Abstract

The application relates to a simulation method and a simulation device for pedestrian turning disturbance propagation in a crowded place, the simulation method comprising the following steps: based on fluid dynamics theory, a crowd internal disturbance propagation dynamics model considering pedestrian turning disturbance is constructed; based on the crowd internal disturbance propagation dynamics model, a pedestrian turning disturbance point is set, simulation of pedestrian turning disturbance propagation in a crowded place is carried out, and simulation results are displayed; wherein the crowd internal disturbance propagation dynamics model comprises a crowd flow pressure term, and the crowd flow pressure term is constructed based on a pressure coefficient considering the turning behavior of pedestrians. Compared with the prior art, the application considers the propagation law of the turning behavior disturbance of pedestrians in time and space, and more objectively represents the generation mechanism of the disturbance after the turning behavior occurs through modeling and numerical value, so that the simulation reliability is high.

Description

Technical Field

[0001] This invention relates to the field of crowd flow stability analysis technology, and in particular to a simulation method and simulation device for the propagation of pedestrian U-turn disturbances in densely populated areas. Background Technology

[0002] In recent years, with the continuous improvement of public activity venues and the emergence of numerous large-scale public events, large crowds have gathered. The precursor to dangerous incidents in densely populated places is often a state of chaos and disorder among the crowd. To prevent stampedes and other safety accidents caused by crowd chaos and overcrowding, this study analyzes the specific content of interfering factors and the inherent relationships between them to identify the root causes. Based on the analysis results, control measures are proposed to reduce the likelihood of stampedes. This is of great significance for the safety management of densely populated places.

[0003] In most cases, abnormal U-turns by pedestrians disrupt a specific point in the crowd's movement, causing the crowd flow to gradually shift from a stable, orderly state to a chaotic and unstable one. These key points are called disturbance points. Due to human intelligence, we can clearly perceive and recognize significant changes in the behavior of surrounding individuals and react accordingly. When moving forward in crowded conditions, once a disturbance occurs among the crowd, it spreads like ripples in a pond, affecting the subsequent movement of the crowd. Disturbances arising from abnormal U-turns are a common phenomenon affecting crowd flow.

[0004] Currently, there are still some shortcomings in research on pedestrian U-turn behavior:

[0005] 1) In many cases, pedestrians turning around can cause disturbances to a certain point in the movement area of ​​the crowd, which can lead to the crowd flow gradually changing from a stable and orderly state to a chaotic and unstable state. There are few studies on constructing specific disturbance models based on this kind of abstract behavior.

[0006] 2) During the movement of a crowd, there is a certain degree of "pressure" within the crowd, which is one of the important characteristics of crowd movement. Currently, there is a lack of quantitative discussion and dynamic analysis of the pressure of turning around behavior.

[0007] 3) Although existing research on pedestrian U-turn behavior recognition in densely populated areas has a few methods, there is still a lack of visualization of U-turn behavior disturbance propagation and stability analysis. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a simulation method and device for the propagation of pedestrian U-turn disturbances in densely populated places, which considers the propagation law of pedestrian U-turn behavior disturbances in time and space and represents the generation mechanism of disturbances after U-turn behavior occurs more objectively through modeling and numericalization.

[0009] The objective of this invention can be achieved through the following technical solutions:

[0010] A simulation method for pedestrian U-turn disturbance propagation in densely populated areas includes the following steps:

[0011] Based on fluid dynamics theory, a dynamic model of the propagation of disturbances within a crowd that takes into account pedestrian U-turn disturbances is constructed.

[0012] Based on the dynamic model of disturbance propagation within the crowd, a pedestrian U-turn disturbance point is set, and a simulation of pedestrian U-turn disturbance propagation in densely populated areas is conducted, with simulation results displayed.

[0013] The crowd internal disturbance propagation dynamics model includes a crowd flow pressure term, which is constructed based on a pressure coefficient that takes into account pedestrian U-turn behavior.

[0014] Furthermore, the dynamics model of disturbance propagation within the crowd is constructed based on the AR traffic flow model.

[0015] Furthermore, the pressure coefficient considering pedestrian U-turn behavior is expressed as:

[0016]

[0017] Where γ represents the pressure coefficient, p represents the pedestrian pressure when there is a pedestrian turning around, and F represents the pedestrian's center of mass force.

[0018] Furthermore, the calculation formula for pedestrian pressure p when pedestrians turn around differs depending on the location within the crowd. Specifically:

[0019] For pedestrian i who makes a U-turn, the pedestrian pressure p i Represented as:

[0020]

[0021] For pedestrian i-1 behind, the pedestrian pressure p i-1 Represented as:

[0022]

[0023] For pedestrian i+1 ahead, the pedestrian pressure p i+1 Represented as:

[0024]

[0025] Where, subscript b represents rear pressure, subscript f represents front pressure, p0 represents the front or rear pressure when pedestrian i has not made a U-turn, and t sLet t represent the time when pedestrian i makes a U-turn. e This indicates the time when pedestrian i finishes turning around.

[0026] Furthermore, the crowd flow pressure term is expressed as P = f(ρ, γ, ξ), where ρ represents the crowd density, γ represents the pressure coefficient, and ξ represents the disturbance intensity.

[0027] Furthermore, the disturbance intensity is constructed based on a random walk model.

[0028] Furthermore, the simulation results are specifically shown as follows:

[0029] Contour maps are used to depict pedestrian pressure at different locations.

[0030] The present invention also provides a computer-readable storage medium including one or more programs executable by one or more processors of an electronic device, the one or more programs including instructions for performing the pedestrian U-turn disturbance propagation simulation method as described above in densely populated areas.

[0031] The present invention also provides a simulation device for the propagation of pedestrian U-turn disturbance in densely populated areas, comprising:

[0032] The model building module, based on fluid dynamics theory, constructs a dynamic model of the propagation of disturbances within a crowd that takes into account the disturbance caused by pedestrians turning around;

[0033] The simulation module, based on the dynamic model of disturbance propagation within the crowd, sets the pedestrian U-turn disturbance point and performs simulation of pedestrian U-turn disturbance propagation in densely populated areas;

[0034] The visualization module is used to display simulation results;

[0035] The crowd internal disturbance propagation dynamics model includes a crowd flow pressure term, which is constructed based on a pressure coefficient that takes into account pedestrian U-turn behavior.

[0036] Furthermore, when displaying simulation results, the visualization module uses contour maps to describe pedestrian pressure at different locations.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] (1) Pedestrians possess numerous characteristics, including psychological, physiological, and kinematic features, all of which reflect the pedestrian's state in relation to the abnormal U-turn behavior itself. This invention focuses on extracting and analyzing the more reliable stress characteristics of U-turn behavior, and on this basis, conducts quantitative discussion and dynamic analysis.

[0039] (2) This invention establishes the behavior-disturbance process, and performs quantitative analysis on the extracted features and the propagation process of the disturbance. Through modeling and numericalization, it can more objectively represent the generation mechanism of the disturbance after the turning behavior occurs, obtain a more accurate pressure coefficient, and thus improve the reliability of the simulation.

[0040] (3) After the U-turn occurs, the process of disturbance propagation within the crowd should be considered in depth. The impact mechanism of local disturbance on the overall crowd flow should be considered in depth, and a dynamic model of disturbance propagation within the crowd should be established. This model can more intuitively show the process of "pressure" caused by U-turn in dense crowds propagating within the crowd, and provide better guidance and suggestions for crowd management based on this. Attached Figure Description

[0041] Figure 1 This is a schematic flowchart of the method of the present invention;

[0042] Figure 2 This is a schematic diagram of the pedestrian U-turn pressure characteristics of the present invention, wherein (2a) is the pressure change of pedestrian i, (2b) is the pressure change of pedestrian i-1, and (2c) is the pressure change of pedestrian i+1;

[0043] Figure 3 This is a schematic diagram of a pedestrian making a U-turn according to the present invention;

[0044] Figure 4 This is a schematic diagram illustrating the propagation of the turning behavior disturbance in this invention. Detailed Implementation

[0045] 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.

[0046] Example 1

[0047] like Figure 1 As shown, this embodiment provides a simulation method for the propagation of pedestrian U-turn disturbances in densely populated areas, including the following steps: S1, based on fluid dynamics theory, constructing a dynamic model of the propagation of disturbances within a crowd that considers pedestrian U-turn disturbances; S2, based on the dynamic model of the propagation of disturbances within a crowd, setting pedestrian U-turn disturbance points, and conducting simulations of the propagation of pedestrian U-turn disturbances in densely populated areas; S3, displaying the simulation results; wherein, the dynamic model of the propagation of disturbances within a crowd includes a crowd flow pressure term, which is constructed based on a pressure coefficient considering pedestrian U-turn behavior. This method considers the activity characteristics of pedestrian U-turn disturbances, quantifies and dynamically analyzes the pressure during the propagation of disturbances in densely populated areas, and more reliably simulates the propagation dynamics of pedestrian U-turn behavior disturbances, thereby providing a basis for crowd safety management.

[0048] The dynamic model of internal disturbance propagation in the crowd constructed in this embodiment includes a crowd flow pressure term and considers the disturbance intensity to improve the simulation accuracy.

[0049] 1. Dynamics model of disturbance propagation within a crowd

[0050] (1) Construct the disturbance intensity of the population under the influence of random disturbances within the population.

[0051] Random walk models were originally individual mobility models. Because individual behavior involves free will and arbitrariness, the movement itself also possesses a degree of randomness. Brownian motion is the simplest type of random walk, and its probability density function (PDF) is:

[0052]

[0053] Where μ = <ΔX> and σ 2 =<ΔX 2 > represents the mean and variance of the random walk displacements.

[0054] Since disturbances within a crowd are similar to white noise interference and cannot be fully represented by deterministic variables, they also exhibit randomness. Therefore, a random walk model can be used to describe the disturbance motion. Applying equation (1) to a real disturbance motion scenario, the first moment is zero and σ 2 =1. A stochastic process represents displacement along the x-axis. Assuming the initial position is x0, the Brownian motion transition equation, i.e., the probability density function, is:

[0055]

[0056] When an abnormal pedestrian U-turn is detected, the point is determined to be the disturbance point (a, b), with an initial disturbance amount ξ0. The disturbance is random, and the disturbance intensity reflects the disturbance decay law within the crowd, exhibiting an exponential power decay function characteristic. That is, the disturbance intensity of the crowd at the disturbance point is the greatest, and the surrounding crowd decays exponentially in the form of e. Therefore, the disturbance intensity of the crowd at (x, y) under the influence of random disturbance within the crowd is as shown in equation (3):

[0057]

[0058] Where ξ represents the disturbance intensity, and t represents the duration of the disturbance.

[0059] (2) Obtain the pressure coefficient.

[0060] The study takes the scenario of pedestrians making a U-turn as an example. Figure 3As shown, assuming the movement of pedestrians is on a one-dimensional plane, and the pedestrians are labeled as i-1, i, i+1, when the middle pedestrian i turns around, it will affect the pedestrians in front and behind it. This means that the turning around behavior has caused a disturbance and has been propagated.

[0061] For pedestrian i, when the U-turn occurs, its velocity gradually decreases to zero in the forward direction and then reverses, while pedestrian i-1 behind it still has a forward momentum. Therefore, the pressure p behind pedestrian i is... back There will be a sudden increase, followed by a sustained period of high pressure. Pedestrian i+1 ahead will continue moving forward due to limited visibility, thus increasing the pressure p ahead. front It becomes zero.

[0062] according to Figure 2 The diagram illustrates the pressure characteristics of pedestrians making U-turns, showing the following dynamic model for pedestrian U-turns:

[0063] like Figure 2 As shown in (2a), for pedestrian i:

[0064]

[0065] Where, p i p represents the total pressure exerted on pedestrian i. i,f p represents the forward pressure on pedestrian i. i,b p0 represents the pressure exerted on pedestrian i from behind, p0 represents the pressure exerted on pedestrian i from the front or back when pedestrian i has not fallen, and t represents the pressure exerted on pedestrian i from the front or back. s t represents the moment when pedestrian i falls. e This indicates the moment when pedestrian i's fall ends.

[0066] By superimposing the forces acting on the pedestrian's front and rear, it can be seen that when a U-turn occurs, the total pressure on pedestrian i will be at t. s The time drops sharply, then rises rapidly in an exponential manner, at t e After a certain time, it reaches a relatively stable high value.

[0067] like Figure 2 As shown in (2b), for pedestrian i-1 behind:

[0068]

[0069] Where, p i-1 p represents the total pressure exerted on pedestrian i-1 behind. i-1,f p represents the forward pressure exerted by pedestrian i-1 behind. i-1,b p0 represents the rear pressure on pedestrian i-1, p0 represents the frontal or rear pressure on pedestrian i before falling, and t represents the pressure on pedestrian i before falling. s t represents the moment when pedestrian i falls. e This indicates the moment when pedestrian i's fall ends.

[0070] The combined forces acting on the pedestrian from the front and back will eventually result in a total pressure on pedestrian i-1 that is greater than the initial pressure.

[0071] like Figure 2 As shown in (2c), for pedestrian i+1 in front:

[0072]

[0073] Where, p i+1 p represents the total pressure exerted on pedestrian i+1 ahead. i+1,f p represents the forward pressure of pedestrian i+1 ahead. i+1,b p0 represents the pressure exerted from the front or rear by pedestrian i+1, and p0 represents the pressure exerted by pedestrian i before or after the fall. s t represents the moment when pedestrian i falls. e This indicates the moment when pedestrian i's fall ends.

[0074] The combined forces acting on the front and rear of the pedestrian cause the total pressure on pedestrian i+1 to decrease first and then stabilize.

[0075] The stress coefficient γ, which considers pedestrian U-turn behavior, is expressed as follows:

[0076]

[0077] The pressure coefficient γ is the ratio of pedestrian pressure p to pedestrian's center of mass force F. Pressure represents the external force exerted on a pedestrian per unit area, while center of mass force is the internal force driving the pedestrian's movement. When p > F, the compression experienced by the pedestrian exceeds their controllable force, making unsafe incidents more likely. Based on research on pedestrian U-turn behavior, the value range of γ is (1, 1.7).

[0078] (3) Construction of dynamic model of disturbance propagation within the crowd

[0079] The dynamic model of crowd disturbance propagation in this embodiment is based on the AR traffic flow model in fluid dynamics theory. The AR traffic flow model includes a crowd flow pressure term, and the crowd flow pressure term with disturbance behavior is shown in equation (8):

[0080] P=f(ρ,γ,ξ) (8)

[0081] Where ρ is the crowd density, γ represents the pressure coefficient, and ξ represents the disturbance intensity. The two-dimensional pressure terms of the crowd flow under U-turn behavior are given by equations (9) and (10):

[0082]

[0083]

[0084] Among them, P h and P l Let ξ0 represent the horizontal and vertical pressure terms, respectively, and (a,b) represent the initial disturbance.

[0085] Finally, the dynamic model of the propagation of disturbances within a crowd considering pedestrian U-turn behavior is expressed as follows:

[0086]

[0087]

[0088]

[0089] Where v and u represent the horizontal and vertical velocities, respectively, V eh and V el Let represent the equilibrium velocities in the horizontal and vertical directions, respectively, and τ be the relaxation factor. The constructed dynamic model of perturbation propagation within a crowd provides a more intuitive view of the propagation process of "pressure" caused by turning behavior within a dense crowd, and based on this, better guidance and suggestions can be provided for crowd control.

[0090] 2. Based on the aforementioned dynamic model of disturbance propagation within the crowd, a simulation of pedestrian U-turn disturbance propagation in densely populated areas is conducted, and the simulation results are presented. Specifically, contour maps are used to depict pedestrian pressure at different locations, allowing for a visual understanding of the propagation characteristics.

[0091] In this embodiment, based on literature summaries, a pressure of 6200N for 15 seconds will cause suffocation due to overcrowding. The pressure threshold decreases over time. Using the simulation method of this invention, in this embodiment of a densely populated crowd, the effective contact area between pedestrians is assumed to be 0.15m². 2 p max =4.13*10 4 N / m 2 .like Figure 4 As shown, TB (turn back) is used as the identifier. In the figure, v represents the overall flow velocity and direction of the crowd. The entire coordinate system describes a simulated scene area of ​​4.5*4.5 meters, assuming a U-turn occurs at the coordinate (3.5, 3) within this scene. The distribution of contour lines and the grayscale values ​​in the grayscale bar on the right side of the figure clearly show the propagation of the disturbance in all directions and the pressure relationships within the crowd.

[0092] The experimental results show that for a given U-turn, at the time [t] of the abnormal U-turn behavior... s ,t e At any given moment within a certain distance range, the pressure value at the center of the disturbance is at its maximum.

[0093] If the above methods are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0094] Example 2

[0095] This embodiment provides a simulation device for the propagation of pedestrian U-turn disturbances in densely populated areas, including a model building module, a simulation module, and a visualization module. The model building module, based on fluid dynamics theory, constructs a dynamic model of the propagation of disturbances within a crowd that considers pedestrian U-turns. The simulation module, based on the dynamic model of the propagation of disturbances within the crowd, sets pedestrian U-turn disturbance points and simulates the propagation of disturbances in densely populated areas. The visualization module displays the simulation results. The dynamic model of the propagation of disturbances within the crowd includes a crowd flow pressure term, which is constructed based on a pressure coefficient considering pedestrian U-turn behavior. When displaying the simulation results, the visualization module uses contour maps to describe the pedestrian pressure at different locations. The rest is the same as in Embodiment 1.

[0096] 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 simulation method for the propagation of pedestrian U-turn disturbance in densely populated areas, characterized in that, Includes the following steps: Based on fluid dynamics theory, a dynamic model of the propagation of disturbances within a crowd that takes into account pedestrian U-turn disturbances is constructed. Based on the dynamic model of disturbance propagation within the crowd, a pedestrian U-turn disturbance point is set, and a simulation of pedestrian U-turn disturbance propagation in densely populated areas is conducted, with simulation results displayed. The crowd internal disturbance propagation dynamics model includes a crowd flow pressure term, which is constructed based on a pressure coefficient that takes into account pedestrian U-turn behavior. The pressure coefficient considering pedestrian U-turn behavior is expressed as follows: in, γ Indicates the pressure coefficient. p This indicates pedestrian pressure when a pedestrian makes a U-turn. F Indicates the pedestrian's center of mass; The pedestrian pressure when pedestrians turn around occurs at different locations within the crowd. p The calculation formulas are different, specifically: For pedestrians who make a U-turn i Its pedestrian pressure Represented as: For pedestrians behind i -1, its pedestrian pressure p i-1 Represented as: For the pedestrians ahead i +1, its pedestrian pressure p i+1 Represented as: Among them, subscript b Indicates pressure from behind, subscript f Indicates pressure ahead. p 0 represents pedestrians i Frontal or rearal pressure when no U-turn occurs t s pedestrian i The moment the U-turn occurred, t e pedestrian i The moment the U-turn ended.

2. The method for simulating the propagation of pedestrian U-turn disturbance in densely populated areas according to claim 1, characterized in that, The dynamics model of disturbance propagation within the crowd is constructed based on the AR traffic flow model.

3. The simulation method for pedestrian U-turn disturbance propagation in densely populated areas according to claim 1, characterized in that, The crowd flow pressure term is expressed as: ,in, ρ Indicates population density. γ Indicates the pressure coefficient. ξ Indicates the intensity of the disturbance.

4. The method for simulating the propagation of pedestrian U-turn disturbance in densely populated areas according to claim 3, characterized in that, The disturbance intensity is constructed based on a random walk model.

5. The simulation method for pedestrian U-turn disturbance propagation in densely populated areas according to claim 1, characterized in that, The simulation results shown are as follows: Contour maps are used to depict pedestrian pressure at different locations.

6. A computer-readable storage medium, characterized in that, It includes one or more programs that are executed by one or more processors of an electronic device, the one or more programs including instructions for performing the pedestrian U-turn disturbance propagation simulation method for densely populated areas as described in any one of claims 1-5.

7. A simulation device for the propagation of pedestrian U-turn disturbance in densely populated areas, characterized in that, include: The model building module, based on fluid dynamics theory, constructs a dynamic model of the propagation of disturbances within a crowd that takes into account the disturbance caused by pedestrians turning around; The simulation module, based on the dynamic model of disturbance propagation within the crowd, sets the pedestrian U-turn disturbance point and performs simulation of pedestrian U-turn disturbance propagation in densely populated areas; The visualization module is used to display simulation results; The crowd internal disturbance propagation dynamics model includes a crowd flow pressure term, which is constructed based on a pressure coefficient that takes into account pedestrian U-turn behavior. The pressure coefficient considering pedestrian U-turn behavior is expressed as follows: in, γ Indicates the pressure coefficient. p This indicates pedestrian pressure when a pedestrian makes a U-turn. F Indicates the pedestrian's center of mass; The pedestrian pressure when pedestrians turn around occurs at different locations within the crowd. p The calculation formulas are different, specifically: For pedestrians who make a U-turn i Its pedestrian pressure Represented as: For pedestrians behind i -1, its pedestrian pressure p i-1 Represented as: For the pedestrians ahead i +1, its pedestrian pressure p i+1 Represented as: Among them, subscript b Indicates pressure from behind, subscript f Indicates pressure ahead. p 0 represents pedestrians i Frontal or rearal pressure when no U-turn occurs t s pedestrian i The moment the U-turn occurred, t e pedestrian i The moment the U-turn ended.

8. The pedestrian U-turn disturbance propagation simulation device in densely populated areas according to claim 7, characterized in that, When displaying simulation results, the visualization module uses contour maps to describe pedestrian pressure at different locations.

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