A simulation method and device for the evolution of population stability in high-risk areas

Abstract

The present invention relates to a method and device for simulating the evolution of stability of a crowd in a high-risk area. The method comprises the following steps: treating a crowd as a fluid, obtaining the equivalent pressure of crowd disturbance under the influence of random disturbance inside the crowd based on fluid dynamics; constructing a dynamic model of disturbance propagation inside the crowd based on the Aw-Rascle model and the equivalent pressure of crowd disturbance; constructing a criterion of crowd flow stability based on the dynamic model of disturbance propagation inside the crowd using the first Lyapunov method, simulating the evolution of stability of a crowd in a high-risk area, and displaying the simulation results. Compared with the prior art, the present invention has the advantages of high reliability and intuitiveness.

Description

Technical Field

[0001] The present invention relates to the technical field of large-scale crowd flow stability analysis, and in particular to a method and a device for simulating the evolution of crowd stability in a high-risk area. Background Art

[0002] Large-scale crowd flow scenes have problems such as large crowd movement range and large crowd flow fluctuations, so the safety supervision and guidance of crowd flow is more difficult and requires more manpower and material resources. The waiting halls of large high-speed railway stations are overcrowded all year round, and the study of crowd flow stability has theoretical significance and practical value. However, the existing research methods for macro crowd flow stability are still in their infancy. The research methods can be roughly divided into four categories: 1) Based on statistical analysis methods, through data collection and literature retrieval, statistical analysis of past crowd disaster events, exploration of crowd instability factors, and crowd management suggestions. 2) Based on machine vision methods. Using the theory of optical flow method, crowd movement characteristics are obtained, crowd behavior anomaly detection models are designed, and crowd stability is qualitatively judged based on abnormal behavior. 3) Based on control theory methods. Based on the idea of ​​control system feedback, the interaction group matrix is ​​used to qualitatively predict group behavior, and the system stability theory is used to determine whether the system structure is reasonable. 4) Based on mathematical deduction methods. Based on fluid dynamics and traffic flow theory, the conservation equation of macro crowd flow dynamics is established, and the system stability judgment theory is used to analyze crowd flow stability.

[0003] So far, there are still some deficiencies in the study of macro crowd stability evolution: 1) At present, the research on the stability determination of crowd movement is mostly at the stage of single density prediction, and there is still a lack of comprehensive models that comprehensively consider the typical movement characteristics of crowd density, velocity vector and acceleration vector. 2) As a dynamically changing system, there is still little research on the dynamic evolution characteristics of crowd flow stability over time, and there is still a lack of evolution process and visualization devices. 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 highly reliable and intuitive simulation method and simulation device for the stability evolution of population in high-risk areas.

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

[0006] A method for simulating the evolution of population stability in a high-risk area comprises the following steps:

[0007] Considering the crowd as a fluid, the equivalent pressure of the crowd disturbance under the influence of random disturbance inside the crowd is obtained based on fluid dynamics.

[0008] A crowd internal disturbance propagation dynamics model is constructed based on the Aw-Rascle model and the crowd disturbance equivalent pressure;

[0009] Based on the dynamic model of internal disturbance propagation in the crowd, the Lyapunov first method is used to construct the crowd flow stability criterion, and the stability evolution of the crowd in high-risk areas is simulated, and the simulation results are displayed.

[0010] Furthermore, the crowd disturbance equivalent pressure at the position (x, y) under the influence of random disturbance inside the crowd is expressed as follows:

[0011]

[0012] Among them, P ξ (x, y, t) represents equivalent pressure, ρ represents crowd density, γ represents pressure factor, ξ p represents the random disturbance intensity, (a, b) represents the location of the disturbance outbreak point, and t represents the duration of the disturbance outbreak.

[0013] Furthermore, the pressure factor γ satisfies 0.1<γ<1.2.

[0014] Furthermore, the dynamic model of disturbance propagation within the crowd is expressed as:

[0015]

[0016]

[0017]

[0018] Among them, V eh 、V el denote the equilibrium speeds in the horizontal and vertical directions, τ denotes the relaxation factor, and P ξh , P ξl denote the horizontal and vertical crowd disturbance pressure terms, v h 、v l are the horizontal and vertical velocities at the position (x, y), t represents the duration of the disturbance, and ρ represents the crowd density.

[0019] Furthermore, in the process of simulating the evolution of population stability in high-risk areas, the wavefront theory in fluid dynamics is used to represent the propagation of crowd disturbance.

[0020] Furthermore, the crowd flow stability criterion includes a horizontal crowd flow stability criterion and a vertical crowd flow stability criterion, and the horizontal crowd flow stability criterion is expressed as:

[0021]

[0022]

[0023] Among them, ρ represents the population density, γ represents the pressure factor, and ξ p represents the random disturbance intensity, (a, b) represents the location of the disturbance outbreak point, t represents the duration of the disturbance outbreak, τ represents the relaxation factor, and v h 、v l are the horizontal and vertical velocities at position (x, y).

[0024] Furthermore, the high-risk area includes the waiting hall of a large high-speed railway station.

[0025] The present invention also provides a device for simulating the evolution of population stability in high-risk areas, comprising:

[0026] The perturbation dynamics building block is used to obtain the equivalent perturbation pressure of the crowd under the influence of random perturbations within the crowd based on fluid dynamics;

[0027] A propagation dynamics model building module, used to build a crowd internal disturbance propagation dynamics model based on the Aw-Rascle model and the crowd disturbance equivalent pressure;

[0028] A simulation module, for constructing a crowd flow stability criterion based on the crowd internal disturbance propagation dynamics model using the Lyapunov first method, and simulating the stability evolution of the crowd in the high-risk area;

[0029] Visualization module, used to display simulation results.

[0030] Furthermore, in the simulation module, when simulating the stability evolution of the crowd in the high-risk area, the wave front theory in fluid dynamics is used to represent the propagation of crowd disturbance.

[0031] Furthermore, in the simulation module, the crowd flow stability criterion constructed includes a horizontal crowd flow stability criterion and a vertical crowd flow stability criterion, and the horizontal crowd flow stability criterion is expressed as:

[0032]

[0033]

[0034] Among them, ρ represents the population density, γ represents the pressure factor, and ξ p represents the random disturbance intensity, (a, b) represents the location of the disturbance outbreak point, t represents the duration of the disturbance outbreak, τ represents the relaxation factor, and v h 、v l are the horizontal and vertical velocities at position (x, y).

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] 1. The existing technology for determining the stability of crowd movement mostly stays at the stage of predicting a single density indicator. The present invention comprehensively considers factors such as crowd density, velocity vector, and acceleration vector, rather than a single density factor, and can more accurately analyze the stability of crowd flow under the propagation of internal disturbances in the crowd. The analysis results are highly reliable and are suitable for the evolution of crowd stability in high-risk areas such as waiting halls of large high-speed railway stations.

[0037] 2. As a dynamic system, the crowd movement system changes with time, and the crowd flow stability keeps changing. However, there is a lack of research on the dynamic evolution characteristics of crowd flow stability over time. The present invention designs a visualization module for the evolution process, which is convenient for displaying the crowd stability evolution process and has good intuitiveness.

[0038] 3. The present invention linearizes the nonlinear crowd flow model and uses Lyapunov's first method to analyze the stability of the crowd flow. It can accurately analyze the speed, horizontal pressure and vertical pressure of the crowd in the crowd flow, and show the evolution process of the stability of the crowd flow in the vertical and horizontal directions. The analysis results are comprehensive. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a schematic diagram of the simulation method flow of the present invention;

[0040] Figure 2 Schematic diagram of the crowd disturbance propagation wavefront;

[0041] Figure 3 This is a visualization diagram of crowd gathering risk distribution (step=400) in an embodiment of the present invention;

[0042] Figure 4 Schematic diagram of the stability evolution process based on the Lyapunov stability criterion in an embodiment of the present invention. DETAILED DESCRIPTION

[0043] 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.

[0044] The present embodiment provides a method for simulating the evolution of crowd stability in high-risk areas. The method regards the crowd as a fluid, and obtains the equivalent disturbance pressure of the crowd under the influence of random disturbances inside the crowd based on fluid dynamics; constructs a dynamic model of disturbance propagation inside the crowd based on the Aw-Rascle model and the equivalent disturbance pressure of the crowd; and constructs a crowd flow stability criterion based on the dynamic model of disturbance propagation inside the crowd using the Lyapunov first method to simulate the evolution of crowd stability in high-risk areas, and displays the simulation results.

[0045] like Figure 1 As shown, the method specifically comprises the following steps:

[0046] Step S1: Modeling the internal disturbance dynamics of the crowd

[0047] In many cases, due to sudden changes in some physical environment or sudden changes in pedestrian behavior, a certain point in the crowd movement area is disturbed, which will cause the crowd flow to gradually change from a stable and orderly state to a chaotic and unstable state. These key points are called disturbance points. According to the formation principle of crowd disturbance points, they are divided into: mutation disturbance points and release disturbance points. Among them, the mutation disturbance point is a sudden abnormal situation inside the pedestrian. The abnormality of pedestrians in public places is mainly manifested in abnormal posture, followed by abnormal expression and voice. Release disturbance points refer to external disturbance factors such as insufficient number of entrances and exits in crowded places, insufficient number of passages, evacuation passages and stairs in the place, which lead to restricted crowd flow. For the public places that have been used, in the study of crowd flow, the sudden abnormal behavior disturbance of pedestrians is more worthy of attention, and according to statistics, mutation crowd disturbance is more likely to cause serious crowd accidents.

[0048] The internal disturbance of the crowd is similar to white noise interference, and its randomness cannot be fully represented by deterministic variables, but can be represented by random processes. However, the numerical solution of random equations and the inherent mathematical complexity of stochastic calculus are challenging problems. In the context of probability density function (PDF), the Langevin equation is used to describe the speed of fluid particles subjected to turbulence, which is modeled as Brownian motion. The present invention is implemented based on Brownian motion.

[0049] When a crowd moves in a crowded state, a certain "pressure" will be generated among the crowd. The present invention regards the crowd as a fluid and establishes a crowd flow model based on fluid dynamics. Therefore, according to the characteristics of fluid dynamics, the equivalent pressure between the crowd can be established as shown in formula (1).

[0050] P=ρ γ ,0.1<γ<1.2 (1)

[0051] Here, γ represents the pressure factor.

[0052] Therefore, under the influence of random disturbances within the crowd, the equivalent pressure of the crowd flow at (x, y) is shown in formula (2).

[0053]

[0054] Among them, ξ p represents the random disturbance intensity, (a, b) represents the location of the disturbance outbreak point, and t represents the duration of the disturbance outbreak.

[0055] Step S2: Modeling the dynamics of disturbance propagation within the crowd

[0056] Based on the Aw-Rascle model, a dynamic model of disturbance propagation within a crowd is established, as shown in equations (3)-(5).

[0057]

[0058] Among them, V eh , V el They represent the equilibrium speed in the horizontal and vertical directions, respectively, which are represented by the steady-state relationship between speed and density (refer to the fundamental diagrams of crowd flow), τ is the relaxation factor, and P ξh , P ξl denote the pressure terms of horizontal and vertical crowd disturbances, respectively, i.e.

[0059]

[0060] Step S3: Crowd flow stability determination and simulation based on Lyapunov

[0061] The nonlinear crowd flow model is linearized, and the crowd flow stability analysis is performed using the Lyapunov first method. The crowd stability in the sense of Lyapunov is defined as follows:

[0062] Assume that the equilibrium flow rate of the large-scale macro crowd flow model is q e (x, y, t) = [ρ e (x,y,t),v he (x,t),v le (y, t)] T , the disturbance flow is q ξ (x, y, t). If the spatial gradient of the disturbance flow is bounded, then the crowd flow is ξ The propagation under (x, y, t) disturbance is stable, that is, and For any t>0, (x, y)∈M, where M is the study scenario of the entire crowd flow. In addition to the above, when and Equilibrium flow rate q e The propagation of (x, y, t) is asymptotically stable.

[0063] Based on the above definition of Lyapunov crowd stability, the present invention uses the wavefront theory in fluid dynamics to represent crowd disturbance propagation. 0 There is a sudden disturbance at the location, which makes it impossible for pedestrians around to maintain their original balance state. Assuming that Figure 2The crowd flow wavefront propagation curve is shown in Figure 1. If the crowd flow system is stable, the disturbed flow will not increase infinitely during its propagation, but will slowly converge and disappear, that is, the wavefront curve of the disturbed flow is bounded. However, if the crowd flow system is unstable, the disturbed flow wave may increase during the propagation process, and eventually form a shock wave or bottleneck in the crowd flow scene.

[0064] Assume that the internal disturbance occurs in equilibrium (ρ 0 , v h0 , v l0 ), then the initial solution of equations (3), (4), and (5) is ρ 0 =ρ e , v h0 =V eh (ρ e ), v l0 =V el (ρ e ). First, the solution of the equations near the wavefront WF is expanded in a power series.

[0065] ξ=(x,y)-(X,Y)(t) (8)

[0066] Among them, (X, Y)(t) refers to the position of the wavefront at time t. Since the wavefront WF is the boundary of the disturbance influence range under the population equilibrium state, the eigenvalue method is still valid near the wavefront WF, so the eigenvalue can be used to calculate the derivatives of X(t) and Y(t) respectively:

[0067]

[0068] We can get ρ(x, y, t), v h (x, t) and v l The power series expansion of (y, t) is shown in equations (11), (12) and (13).

[0069]

[0070] Keep the first two items 0 and 1 , and obtain equations as shown in (14)-(16).

[0071] u h 0 ρ 1 +ρ 0 v h 1 =0 (14)

[0072]

[0073] From formula (14), we can get Substituting it into equations (15) and (16), we obtain the Bernoulli equation as shown in equation (17).

[0074]

[0075] in,

[0076] Under disturbance conditions, the density of large-scale, high-density crowds generally increases sharply, and the speed decreases sharply, so the derivative of the speed is less than 0, that is,

[0077]

[0078] In the formula (19), “-” indicates the direction, and τ is the relaxation factor. a c (x, t) is named as the critical acceleration function, and its value is related to the random disturbance pressure inside the crowd. ξh Substitute a c (x, t) is solved to obtain equation (20).

[0079]

[0080] Similarly, a c Substituting the (x, t) value into formula (19), we can obtain the stability criterion of horizontal crowd flow as shown in formula (21).

[0081]

[0082] In crowd flow analysis, the speed and pressure of the crowd are divided into two directions: horizontal and vertical. The stability of the crowd flow in the vertical direction is derived in the same way as the horizontal direction. Similarly, the criterion for the stability of the crowd flow in the vertical direction can be obtained as shown in formula (22).

[0083]

[0084] Based on the above stability criteria, the stability of the crowd at each location under the disturbance of the crowd can be judged in real time in the simulation.

[0085] In order to verify the effectiveness of the above simulation method, this embodiment uses a waiting hall of a railway station as a scene for case verification.

[0086] Simulation scenario: The initial crowd is 10,000 people, evenly distributed in three waiting areas, and evacuated to eight emergency exits. When the simulation step length is 400, the crowd gathering risk distribution is as follows: Figure 3 shown.

[0087] choose Figure 3 A point in the typical high-risk area B (one of the crowd converging intersections) is used as the research scene. The crowd flow stability analysis method considering internal disturbances proposed in this invention is used to analyze the crowd flow stability. In this case analysis, the special restrictions on the crowd movement direction are not considered. The stability evolution process based on the Lyapunov stability criterion is as follows: Figure 4 shown.

[0088] If the above method is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0089] In another embodiment, a device for simulating the evolution of population stability in a high-risk area is provided, including: a disturbance dynamics construction module, used to obtain the disturbance equivalent pressure of the crowd under the influence of random disturbances inside the crowd based on fluid dynamics; a propagation dynamics model construction module, used to construct a disturbance propagation dynamics model inside the crowd based on the Aw-Rascle model and the crowd disturbance equivalent pressure; a simulation module, used to construct a crowd flow stability criterion based on the disturbance propagation dynamics model inside the crowd using the Lyapunov first method, and perform a simulation of the stability evolution of the crowd in the high-risk area; and a visualization module, used to display the simulation results.

[0090] 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 simulating the evolution of population stability in high-risk areas, characterized in that: The following steps are involved: Considering the crowd as a fluid, the equivalent pressure of the crowd disturbance under the influence of random disturbance inside the crowd is obtained based on fluid dynamics. A crowd internal disturbance propagation dynamics model is constructed based on the Aw-Rascle model and the crowd disturbance equivalent pressure; Based on the crowd internal disturbance propagation dynamics model, the Lyapunov first method is used to construct the crowd flow stability criterion, and the crowd stability evolution simulation in high-risk areas is carried out, and the simulation results are displayed; The crowd disturbance equivalent pressure at the position (x, y) under the influence of random disturbance inside the crowd is expressed as follows: Among them, P ξ (x, y, t) represents equivalent pressure, ρ represents crowd density, γ represents pressure factor, ξ p represents the random disturbance intensity, (a, b) represents the location of the disturbance outbreak point, and t represents the duration of the disturbance outbreak.

2. The method for simulating the evolution of population stability in high-risk areas according to claim 1, characterized in that: The pressure factor γ satisfies 0.1<γ<1.

2.

3. The method for simulating the evolution of population stability in high-risk areas according to claim 1, characterized in that: The dynamic model of disturbance propagation within the crowd is expressed as: Among them, V eh 、V el denote the equilibrium speeds in the horizontal and vertical directions, τ denotes the relaxation factor, and P ξg , P ξl denote the horizontal and vertical crowd disturbance pressure terms, v h 、v l are the horizontal and vertical velocities at the position (x, y), t represents the duration of the disturbance, and ρ represents the crowd density.

4. The method for simulating the evolution of population stability in high-risk areas according to claim 1, characterized in that: During the simulation of the stability evolution of the crowd in the high-risk area, the wavefront theory in fluid dynamics is used to represent the propagation of crowd disturbance.

5. The method for simulating the evolution of population stability in high-risk areas according to claim 1, characterized in that: The crowd flow stability criterion includes a horizontal crowd flow stability criterion and a vertical crowd flow stability criterion. The horizontal crowd flow stability criterion is expressed as: Among them, ρ represents the population density, γ represents the pressure factor, and ξ p represents the random disturbance intensity, (a, b) represents the location of the disturbance outbreak point, t represents the duration of the disturbance outbreak, τ represents the relaxation factor, and v h 、v l are the horizontal and vertical velocities at position (x,y).

6. The method for simulating the evolution of population stability in high-risk areas according to claim 1, characterized in that: The high-risk areas include waiting halls of large high-speed railway stations.

7. A device for simulating the evolution of population stability in high-risk areas, characterized in that: include: The perturbation dynamics building block is used to obtain the equivalent perturbation pressure of the crowd under the influence of random perturbations within the crowd based on fluid dynamics; A propagation dynamics model building module, used to build a crowd internal disturbance propagation dynamics model based on the Aw-Rascle model and the crowd disturbance equivalent pressure; A simulation module, for constructing a crowd flow stability criterion based on the crowd internal disturbance propagation dynamics model using the Lyapunov first method, and simulating the stability evolution of the crowd in the high-risk area; Visualization module, used to display simulation results; The crowd disturbance equivalent pressure at the position (x, y) under the influence of random disturbance inside the crowd is expressed as follows: Among them, P ξ (x, y, t) represents the equivalent pressure, ρ represents the crowd density, γ represents the pressure factor, ξ p represents the intensity of random disturbance, (a, b) represents the location of the disturbance outbreak point, and t represents the duration of the disturbance outbreak.

8. The device for simulating the evolution of population stability in high-risk areas according to claim 7, characterized in that: In the simulation module, when simulating the stability evolution of the crowd in the high-risk area, the wave front theory in fluid dynamics is used to represent the propagation of crowd disturbance.

9. The device for simulating the evolution of population stability in high-risk areas according to claim 7, characterized in that: In the simulation module, the crowd flow stability criterion constructed includes the horizontal crowd flow stability criterion and the vertical crowd flow stability criterion. The horizontal crowd flow stability criterion is expressed as: Among them, ρ represents the population density, γ represents the pressure factor, and ξ p represents the random disturbance intensity, (a, b) represents the location of the disturbance outbreak point, t represents the duration of the disturbance outbreak, τ represents the relaxation factor, and v h 、v l are the horizontal and vertical velocities at position (x,y).

Images