Emergency evacuation method based on dynamic coupling of cellular automaton and social force model

Abstract

This invention discloses an emergency evacuation method based on the dynamic coupling of cellular automata and social force models. The method first obtains the coordinates of pedestrians within the evacuation space and constructs a Voronoi diagram. Next, it calculates the area of ​​Voronoi cells with physical boundary constraints and introduces a pedestrian radius *r* correction term for lower bound constraints. It then calculates the local density within the evacuation space and introduces an exponential smoothing method to correct the local density. Finally, it designs the weight function of the SFM model; calculates the weights of the CA model based on the SFM model weights; and weights the SFM acceleration and the CA expected velocity correction term to obtain the final acceleration of each individual. Based on the final acceleration, it updates the individual's velocity and position. This invention can better reflect the realism of the microscopic behavior of evacuated individuals and achieve higher evacuation efficiency.

Description

Technical Field

[0001] This invention belongs to the field of safety and emergency management technology, specifically relating to an emergency evacuation method based on the dynamic coupling of cellular automata and social force models. Background Technology

[0002] With the acceleration of urbanization, large public buildings, transportation hubs, commercial complexes, and other densely populated places are increasing, drawing widespread attention to public safety. In emergencies such as fires, earthquakes, and terrorist attacks, efficient and safe evacuation is the last line of defense for protecting lives. Statistics show that in many major mass casualty incidents in recent years, inefficient evacuation has often been the main cause of increased casualties. Therefore, studying the dynamics of crowd evacuation and designing accurate and efficient evacuation simulation models and methods has significant theoretical and practical value for building safety design and emergency response plan development.

[0003] Crowd evacuation simulation models have evolved from macroscopic fluid models to microscopic individual models. Currently, the mainstream microscopic models include two main paradigms: cellular automata (CA) models and social force models (SFM). CA models discretize space into a grid, with individuals updating according to local rules. They offer advantages such as high computational efficiency and ease of implementation, but the individual behavior rules are relatively simple, making it difficult to realistically reproduce the complex dynamics of crowds at high densities. SFM models, based on Newtonian mechanics, describe individual motion as the combined action of multiple forces, realistically reproducing complex behaviors such as self-organization and arched blockages. However, they have high computational complexity and are inefficient for large-scale simulations. Summary of the Invention

[0004] To address the aforementioned problems and overcome the inherent contradiction between computational efficiency and behavioral realism in single evacuation models, as well as the issues of abrupt switching and poor adaptability in traditional models, this invention proposes an emergency evacuation method based on dynamic coupling of cellular automata and social force models, utilizing a local density adaptive mechanism and a nonlinear weighted function design. First, based on the gridded partitioning of the evacuation space, this invention proposes a method for calculating crowd density in each partition based on a Voronoi diagram, avoiding the inter-frame fluctuations in traditional density calculations. Second, this invention designs a nonlinear Sigmoid function with local density as input, dynamically allocating coupling weights between the CA rule and SFM force experienced by pedestrians, achieving adaptive coupling between low-density, high-density, and medium-density transition zones. Finally, this invention provides a mechanism for updating the speed and position of crowd evacuation, achieving speed vector synthesis based on coupling weights, ensuring the continuity of individual trajectories. Compared to traditional cellular automata and social force models, this invention can better reflect the micro-behavioral realism of evacuated crowds and achieve higher evacuation efficiency.

[0005] The above objectives are achieved through the following technical solutions:

[0006] An emergency evacuation method based on the dynamic coupling of cellular automata and social force models includes the following steps:

[0007] S1. Obtain the coordinates of pedestrians within the evacuation area;

[0008] S2. Using the pedestrian coordinates obtained in step S1 as generators, construct Thiessen polygons, i.e., Voronoi diagrams;

[0009] S3. Using the space to be evacuated as the physical boundary constraint, calculate the area of ​​the Voronoi cell with physical boundary constraints, and introduce a pedestrian radius r correction term to impose a lower limit constraint on the area of ​​the Voronoi cell.

[0010] S4. Calculate the local density in the space to be evacuated based on physical boundary constraints and pedestrian radius correction, and introduce the out-of-boundary exponential smoothing method to correct the local density.

[0011] S5. Using the local density corrected in step S4 as input, introduce the Sigmoid nonlinear function to design the weight function of the SFM model; calculate the weight of the CA model based on the weight of the SFM model.

[0012] S6. The CA model provides an individual with a desired motion direction and velocity based on local rules. The SFM acceleration and the CA desired velocity correction term are weighted and synthesized to obtain the individual's... final acceleration ;

[0013] S7. Obtain the final acceleration based on step S6. The velocity of an individual is updated using the Euler integral method; then, based on the updated velocity, the position of the individual is updated again using the Euler integral method.

[0014] The advantages of this invention compared to the prior art are:

[0015] (1) In view of the problem that traditional density calculation methods have large inter-frame fluctuations in small areas, this invention proposes a population density calculation method based on Voronoi diagram for each partition based on the gridded partition of sparse space. This method effectively avoids the inter-frame fluctuation problem of traditional density calculation and improves stability.

[0016] (2) To address the problem of poor adaptability of evacuation models caused by traditional hard switching or simple linear transition methods, this invention designs a nonlinear Sigmoid function with local density as input, dynamically allocates the coupling weights of CA rules and SFM forces on pedestrians, and realizes adaptive coupling in low-density areas, high-density areas and medium-density transition areas.

[0017] (3) To address the problem of poor continuity of evacuation trajectories, this invention designs a velocity vector synthesis method based on coupling weights, and provides the velocity and position update process of evacuation, thereby improving the efficiency of evacuation. Attached Figure Description

[0018] Figure 1 Flowchart of the method of this invention.

[0019] Figure 2 Scenario 1: Plan of distribution when 150 people are to be evacuated.

[0020] Figure 3 Comparison of evacuation results using different methods in Scenario 1.

[0021] Figure 4 Scenario 2: Plan of distribution when the number of evacuees is 450.

[0022] Figure 5 Comparison of evacuation results using different methods in scenario 2. Detailed Implementation

[0023] The present invention will be further described below with reference to the accompanying drawings and specific examples.

[0024] like Figure 1 As shown, with the acceleration of urbanization, large public buildings, transportation hubs, commercial complexes, and other densely populated places are increasing, and the safety of people is receiving widespread attention. In emergencies such as fires, earthquakes, and terrorist attacks, efficient and safe evacuation is the last line of defense for protecting lives. In this scenario, this invention provides an emergency evacuation method based on the dynamic coupling of cellular automata and social force models. This method can improve evacuation efficiency, and the specific implementation steps are as follows:

[0025] Step 1: Obtain the pedestrian's coordinates.

[0026] Let the two-dimensional space for crowd evacuation be... There are n pedestrians in the space. For any i-th individual (i=1,2,…,n), its real-time two-dimensional coordinates at any time t are... for: in, , , , represent the x and y coordinates of individual i at time t.

[0027] Step 2: Construct the Voronoi diagram.

[0028] Using the crowd coordinates obtained in step one as generators, Thiessen polygons, i.e., Voronoi diagrams, are constructed to represent the simulation space. Divide into m mutually disjoint Voronoi units, the Voronoi unit corresponding to the i-th individual. Defined as: in, Voronoi unit represents the Euclidean distance in two-dimensional space, indicating the straight-line distance from any point p in space to individuals i and j. It is the set of all points in the simulation space whose distance to individual i is no greater than the distance to any other individual j. That is, the cell is the "exclusive space" of individual i, and the cell boundary is the perpendicular bisector between adjacent individuals.

[0029] Step 3: Calculate the area of ​​each unit.

[0030] Calculation of cell area under physical boundary constraints.

[0031] Area calculation of Voronoi cells with boundary constraints. Real-world evacuation scenarios involve spaces with physical boundaries, such as corridors and walls. These physical boundaries truncate the convex polygons of the Voronoi cells. In this case, the cell is enclosed by the perpendicular bisectors of adjacent cells and the physical boundary. Therefore, area calculations need to be corrected based on boundary constraints. Let the physical boundary of the space be... For the Voronoi unit of the i-th individual, if it is adjacent to the physical boundary If they intersect, then they will As an edge of a unit, the vertex set consists of the intersection of the perpendicular bisector and the intersection of the perpendicular bisector with the physical boundary. The area is calculated using the following formula: Where s is the total number of vertices of a Voronoi element under physical boundary constraints. Let x be the x-coordinate of the m-th Voronoi element vertex under physical boundary constraints. Let be the ordinate of the m-th Voronoi element vertex under physical boundary constraints. Let x be the x-coordinate of the (m+1)th Voronoi element vertex under physical boundary constraints. Let y be the ordinate of the (m+1)th Voronoi element vertex under physical boundary constraints.

[0032] Pedestrian radius constraint correction.

[0033] In the simulation, actual pedestrians have a physical radius r. To prevent the Voronoi element area from approaching zero due to excessively close spacing between individuals, a pedestrian radius r correction term is introduced to impose a lower limit constraint on the element area. The corrected element area is: Where max() represents the maximum value function; r represents the pedestrian radius, which is generally taken as r=0.2m, that is, the pedestrian occupies a circular space with a diameter of 0.4m; To ensure that the area of ​​each individual Voronoi unit is not less than its actual occupied space, the circular footprint of each pedestrian is taken into account, thus avoiding distortion in density calculation.

[0034] Step 4: Calculate the local density.

[0035] This invention considers physical boundary constraints and pedestrian radius constraints, and finally gives the local density formula: in, Let be the local density at time t.

[0036] To avoid drastic fluctuations in Voronoi cell area caused by small changes in individual cell positions within the simulation step, which could lead to abrupt changes in density, this invention introduces an exponential smoothing method for local density correction. The final corrected local density is as follows: in, This represents the local density after correction at time t; This represents the corrected local density from the previous time step. This represents the smoothing factor, with a value of 0.7.

[0037] Step 5: Calculate the coupling weights.

[0038] SFM weight calculation.

[0039] Building upon the local density in the fourth step, this invention uses the local density as input, introduces a Sigmoid nonlinear function, and designs the weight function of the SFM model. : in: This represents the SFM weight value of the i-th person at time t. Indicates the density of the transition center. This represents the transition slope parameter, with a value of 0.8; This represents the upper limit of the SFM weight, with a value of 0.95; This represents the lower limit of the SFM weight, with a value of 0.15.

[0040] CA weight calculation. Since the sum of the weights of the CA model and the SFM model should be 1, the weight function of the CA model is: in, To set the maximum expected speed for an individual; Indicates the desired direction of CA. According to Newton's second law, SFM acceleration. for: in, Represents an individual The net force acting on it; For the virtual quality of an individual, it is usually taken as To ensure numerical stability;

[0041] Based on dynamic coupling weights and The SFM acceleration and the CA expected velocity correction term are weighted and synthesized to obtain the individual. final acceleration : in: and These are the coupling weights for SFM and CA, respectively. For the individual's current speed, For the simulation step size, the second term This represents a corrected acceleration, which adjusts the individual's current velocity. Tends towards CA expected speed .

[0042] Step 7: Speed ​​update and location update.

[0043] Speed ​​update. Obtain the final acceleration. Then, the velocity of the individual is updated using Euler's integral method: in, For the current moment speed, For the next moment The speed.

[0044] Position update. Based on the updated velocity, update the individual's position again using Euler's integral: in, For the current moment Location coordinates, For the next moment The location coordinates.

[0045] Simulation experiment:

[0046] To verify the effectiveness of the emergency evacuation method proposed in this invention, which is based on the dynamic coupling of cellular automata and social force models, crowd evacuation simulation experiments were designed under different scenarios. The simulation scenario was a 15m × 10m area with one exit, 1.5m wide, located in the middle of the right side of the space. Scenario 1: 150 pedestrians, local density approximately 1 person / m². Scenario 2: 450 pedestrians, local density approximately 3 people / m². In all scenarios, the initial positions of pedestrians were randomly distributed, the maximum expected speed of pedestrians was uniformly set to 1.5m / s, the simulation time step was 0.1s, the CA mesh size was 0.4m × 0.4m, and the pedestrian mass was 70kg. Based on the above evacuation environments, evacuation simulation experiments were conducted using a cellular automata model, a social force model, and the method of this invention.

[0047] Results Analysis: Based on Figure 3 It can be seen that in Scenario 1 (total evacuation number of 150 people, low-density scenario), all three methods can complete the evacuation, ultimately evacuating 150 people. The cellular automata model requires 45.8s, the social force model requires 62.3s, and the method of this invention requires 40.2s. The results show that in Scenario 1, the method of this invention requires the least evacuation time, i.e., has the highest evacuation efficiency. Compared with the cellular automata model and the social force model, the evacuation efficiency of the method of this invention is improved by 12.23% and 35.47%, respectively.

[0048] Figure 4 For evacuation scenarios with high population density, Figure 5 The corresponding evacuation results are given. According to... Figure 5 As can be seen, in high-density scenario 2, all three methods were able to complete the evacuation, with a final evacuation number of 450 people. The cellular automata model required 82.5 s, the social force model required 95.2 s, and the method of this invention required 78.3 s. The results show that in scenario 1, the method of this invention requires the least evacuation time, i.e., has the highest evacuation efficiency. In high-density crowd evacuation scenarios, compared with the cellular automata model and the social force model, the evacuation efficiency of the method of this invention is improved by 5.09% and 17.75%, respectively.

Claims

1. An emergency evacuation method based on dynamic coupling of cellular automaton and social force model, characterized in that, The method includes the following steps: S1. Obtain the coordinates of pedestrians within the evacuation area; S2. Using the pedestrian coordinates obtained in step S1 as generators, construct Thiessen polygons, i.e., Voronoi diagrams; S3. Using the space to be evacuated as the physical boundary constraint, calculate the area of ​​the Voronoi cell with physical boundary constraints, and introduce a pedestrian radius r correction term to impose a lower limit constraint on the area of ​​the Voronoi cell. S4. Calculate the local density in the space to be evacuated based on physical boundary constraints and pedestrian radius correction, and introduce the out-of-boundary exponential smoothing method to correct the local density. S5. Using the local density corrected in step S4 as input, introduce the Sigmoid nonlinear function to design the weight function of the SFM model; calculate the weight of the CA model based on the weight of the SFM model. S6. The CA model provides an individual with a desired direction and speed of motion based on local rules, which is weighted with the SFM acceleration and the CA desired velocity modifier to obtain the individual's final acceleration ;​ S7. Final acceleration is obtained based on step S6 The velocity of the individual is updated using Euler integration method; and based on the updated velocity, the position of the individual is updated again using Euler integration method.

2. The emergency evacuation method based on dynamic coupling of cellular automaton and social force model according to claim 1, characterized in that, The specific method for step S1 is as follows: Let the two-dimensional space for crowd evacuation be... There are n pedestrians in the space. For any i-th individual (i=1,2,…,n), its real-time two-dimensional coordinates at any time t are... for: in, , , , represent the x and y coordinates of individual i at time t.

3. The emergency evacuation method based on dynamic coupling of cellular automaton and social force model according to claim 2, characterized in that, The specific method for step S2 is as follows: Using the pedestrian coordinates obtained in step S1 as generators, Thiessen polygons, i.e., Voronoi diagrams, are constructed to represent the simulation space. Divide into m mutually disjoint Voronoi units, the Voronoi unit corresponding to the i-th individual. Defined as: in, Voronoi unit represents the Euclidean distance in two-dimensional space, indicating the straight-line distance from any point p in space to individuals i and j. It is the set of all points in the simulation space whose distance to individual i is no greater than the distance to any other individual j. That is, the cell is the "exclusive space" of individual i, and the cell boundary is the perpendicular bisector between adjacent individuals.

4. The emergency evacuation method based on the dynamic coupling of cellular automata and social force model according to claim 1, characterized in that, The specific method for step S3 is as follows: S3.

1. Calculating the area of ​​a Voronoi cell with boundary constraints: In a space with physical boundaries, a Voronoi cell is enclosed by the perpendicular bisectors of adjacent cells and the physical boundary. Area calculation requires correction based on boundary constraints. Let the physical boundary of the space be... Let m represent the m-th Voronoi cell vertex under physical boundary constraints. For the i-th individual's Voronoi cell, if it is confined to the physical boundary... If they intersect, then... As an edge of a cell, the vertex set consists of the intersection of the perpendicular bisector and the intersection of the perpendicular bisector with the physical boundary. The area of ​​the Voronoi cell of the i-th individual is... The calculation formula is as follows: Where s is the total number of vertices of a Voronoi cell under physical boundary constraints. Let x be the x-coordinate of the m-th Voronoi element vertex under physical boundary constraints. Let be the ordinate of the m-th Voronoi element vertex under physical boundary constraints. Let x be the x-coordinate of the (m+1)th Voronoi element vertex under physical boundary constraints. Let y be the ordinate of the (m+1)th Voronoi element vertex under physical boundary constraints; S3.

2. Introduce a pedestrian radius r correction term to impose a lower limit constraint on the Voronoi cell area calculated in step S3.

1. The corrected cell area... for: Where max() represents the maximum value function; r represents the pedestrian radius, which is generally taken as r=0.2m, that is, the pedestrian occupies a circular space with a diameter of 0.4m; To ensure that the area of ​​each individual Voronoi unit is not less than its actual occupied space, the circular footprint of each pedestrian is taken into account, thus avoiding distortion in density calculation.

5. The emergency evacuation method based on the dynamic coupling of cellular automata and social force model according to claim 4, characterized in that, The specific method for step S4 is as follows: Calculate the local density within the evacuation space based on physical boundary constraints and pedestrian radius correction: in, Let be the local density of the individual at time t; By introducing the out-of-bounds exponential smoothing method for local density correction, the final corrected local density is: in, This represents the local density of an individual after correction at time t; This represents the corrected local density from the previous time step. This represents the smoothing factor, with a value of 0.

7.

6. The emergency evacuation method based on dynamic coupling of cellular automaton and social force model according to claim 5, characterized in that, The specific method for step S5 is as follows: S5.

1. Using the corrected local density as input, introduce the Sigmoid nonlinear function and design the weight function of the SFM model. : in: This represents the SFM weight value of the i-th person at time t. Indicates the density of the transition center. This represents the transition slope parameter, with a value of 0.8; This represents the upper limit of the SFM weight, with a value of 0.95; This represents the lower limit of the SFM weights, with a value of 0.

15. S5.

2. Since the sum of the weights of the CA model and the SFM model should be 1, the weight function of the CA model is: wherein: represents the CA weight value of the ith individual at time t.

7. The emergency evacuation method based on the dynamic coupling of cellular automata and social force model according to claim 6, characterized in that, The specific method for step S6 is as follows: The CA model provides an individual with a desired direction and speed of motion based on local rules, the CA desired velocity vector : wherein, to set the maximum desired velocity of the individual; represents the desired direction of the CA, according to Newton's second law, SFM acceleration is: in, Represents an individual The net force acting on it; For the virtual quality of an individual, it is usually taken as To ensure numerical stability; Based on dynamic coupling weights and The SFM acceleration and the CA expected velocity correction term are weighted and synthesized to obtain the individual. final acceleration : in: and These are the coupling weights for SFM and CA, respectively. For the individual's current speed, For the simulation step size, the second term This represents a corrected acceleration, which adjusts the individual's current velocity. Tends towards CA expected speed .

8. The emergency evacuation method based on the dynamic coupling of cellular automata and social force model according to claim 7, characterized in that, The specific method for step S7 is as follows: The final acceleration is obtained Then, the velocity of the individual is updated using Euler's integral method: in, For the current moment speed, For the next moment speed; Based on the updated velocity, update the individual's position again using Euler's integral: in, For the current moment Location coordinates, For the next moment The location coordinates.

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