Stair evacuation simulation method based on potential field and slope perception

Abstract

This invention discloses a staircase evacuation simulation method based on potential field and slope perception, relating to the field of pedestrian evacuation simulation modeling. The method includes: acquiring the geometric parameters of the staircase to be simulated and the pedestrian motion parameters, constructing a two-dimensional regular grid map; constructing a local passage cost field and solving the equation to generate a globally optimal navigation function, determining the topology-aware potential field; generating the negative gradient field of the topology-aware potential field to obtain the desired motion direction; correcting the pedestrian's initial expected speed on flat ground; generating an environment-driven speed; combining social obstacle avoidance speed with weighted fusion to obtain the final composite speed of the pedestrian; updating the spatial position of the pedestrian in the two-dimensional regular grid map based on the final running speed and a preset simulation step size, until all pedestrians have evacuated to the exit, completing the staircase evacuation process simulation. It achieves accurate simulation of path planning and slope-dependent speed decay in parallel double-flight staircase evacuation, and is applicable to the assessment of vertical evacuation capacity in multi-story and high-rise buildings.

Description

Technical Field

[0001] This invention relates to the field of pedestrian evacuation simulation modeling, and more specifically to a staircase evacuation simulation method based on potential field and slope perception. Background Technology

[0002] Staircase evacuation in multi-story and high-rise buildings is a core element for the safe evacuation of people in emergencies such as fires and earthquakes. Among them, parallel double-flight staircases are the most common type of vertical evacuation channel, and their passage efficiency directly determines the overall evacuation time and the risk of casualties.

[0003] Existing evacuation simulation models have significant shortcomings when dealing with staircase scenarios. On the one hand, the classic social force model and its first-order meshed improvement model perform well in planar evacuation, but when applied to parallel double-flight staircases, the complex topology of the staircase, consisting of two opposing flight paths and an intermediate platform, makes path planning methods based on local vision or static shortest distances prone to falling into local minima. This leads to unreasonable backtracking or even stagnation of pedestrian simulation trajectories at the junction of flight paths and platforms, failing to stably guide pedestrians to complete continuous movement from any floor to the exit along the actual feasible space. On the other hand, most models directly project the three-dimensional staircase passage space into a two-dimensional planar mesh for uniform processing, losing the slope information determined by the step height and step width. Pedestrian movement speed depends only on flat ground walking parameters, failing to reflect the real modulation effect of slope on step frequency, stride length, and physiological exertion. The simulation results differ somewhat from the empirical data on staircase speed reduction in fire protection engineering manuals.

[0004] For group evacuation scenarios, existing models have shortcomings in depicting the macroscopic passage characteristics at stairwell bottlenecks. Due to the lack of effective modeling of individual speed decay caused by slope, after multiple pedestrians rush into the stairwell, the model often passes through the stair section at an almost constant high speed, causing the instantaneous flow peak at the monitoring section to far exceed the real physical limit, and failing to reproduce the forced constraint effect of the stairwell as a geometric bottleneck on macroscopic passage capacity. At the same time, typical dynamic characteristics such as the self-organized following behavior of pedestrians due to speed differences and the natural formation process of queues are also difficult to reasonably represent within the confined stairwell space.

[0005] Furthermore, while some existing studies have attempted to reduce the overall speed of stair flights by fixing a conversion factor or using a potential field method for path guidance, they have failed to couple topology-aware global path planning with a speed adjustment mechanism based on real-time slope perception. This results in defects such as speed distortion or local pathfinding errors in the model. In particular, for the special geometric configuration of parallel double-flight staircases where stair flights and platforms alternate, there is a lack of a simulation framework that can guarantee global path optimization and dynamically respond to terrain changes.

[0006] Therefore, how to design a staircase evacuation simulation method based on potential field and slope perception, which can accurately simulate the vertical evacuation process of multi-story and high-rise buildings and reliably assess the passage capacity, is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0007] In view of this, the present invention provides a staircase evacuation simulation method based on potential field and slope perception, which aims to solve the problems that existing evacuation simulation models are prone to getting trapped in local minima in parallel double-flight staircase scenarios, and that the loss of slope information due to two-dimensional simplification leads to distorted speed characterization. This method can achieve accurate simulation of pedestrian path selection and adaptive speed adjustment during vertical evacuation, and provide simulation support for staircase geometric design optimization and traffic capacity verification.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A staircase evacuation simulation method based on potential field and slope perception includes the following steps: S1. Obtain the geometric parameters of the staircase to be simulated and the pedestrian motion parameters, and discretize the three-dimensional staircase passage space into a two-dimensional regular grid map containing obstacle markers; S2. Construct a local passage cost field based on the two-dimensional regular grid map, and use a fast travel algorithm to solve the process function equation to generate the globally optimal navigation function from any grid cell to the exit, and determine the topology sensing potential field; S3. Generate a corresponding negative gradient field based on the topological sensing potential field, extract the negative gradient direction of the grid cell where the current pedestrian is located as the expected motion direction, and correct the pedestrian's initial expected speed on flat ground through the slope sensing speed adjustment mechanism to obtain the corrected expected motion rate. S4. Vector synthesis of the desired motion direction and desired motion rate to generate environmental driving speed; S5. Combine the social obstacle avoidance speed with the environmental driving speed and perform a weighted fusion to obtain the final composite speed of the pedestrian. S6. Based on the final running speed and the preset simulation step size, update the spatial position of pedestrians in the two-dimensional regular grid map, and iteratively execute steps S3 to S5 until all pedestrians are evacuated to the exit, thus completing the simulation of the stair evacuation process.

[0010] Preferably, in step S2, constructing the local access cost field includes: Define grid cells Local traffic costs :

[0011] The first term on the right side of the equation is the basic cost of free movement; It is a repulsive potential of an obstacle, used to push pedestrians away from the obstacle;

[0012] in, For grid cells Euclidean distance to the nearest obstacle mesh cell, The repulsion strength coefficient of the obstacle. This is the decay factor of the repulsive potential with distance.

[0013] Preferably, in step S2, generating the globally optimal navigation function includes: Based on local access cost field Solve the equation:

[0014] in, Represents the gradient operator; The navigation function represents the function used to navigate from the grid cell. The minimum cumulative cost to reach the target exit; The fast travel algorithm is used to numerically solve the equation on a discrete grid to obtain the globally optimal navigation function as the topology sensing potential field.

[0015] Preferably, in step S3, the desired direction of motion is expressed as:

[0016] in, For pedestrian i in the current grid cell The unit vector of the expected direction of motion at that location. Represents the gradient operator. For navigation functions.

[0017] Preferably, in step S3, correcting the pedestrian's initial expected speed on flat ground through the slope-sensing speed adjustment mechanism includes: Based on the stair slope angle of the current pedestrian grid cell Calculate the speed adjustment factor The corrected expected motion rate is obtained. :

[0018]

[0019] Where k is a calibration coefficient reflecting pedestrian slope sensitivity. For pedestrians The initial expected velocity on flat ground.

[0020] Preferably, the method for determining the local terrain slope angle θ includes: If the current grid cell belongs to the stair flight region, then the slope angle is calculated based on the riser height h and riser width w. ; If the current grid cell belongs to the stair landing area, then θ=0.

[0021] Preferably, in S4, the environmental driving speed Represented as:

[0022] in, The corrected desired motion rate, The desired direction of motion.

[0023] Preferably, in S5, the final synthesis speed of the pedestrian... Represented as:

[0024] in, To improve the speed of social obstacle avoidance, The speed is driven by the environment, and α is a weighting coefficient. The higher the local population density, the larger the value of α.

[0025] Preferably, the social obstacle avoidance speed is determined. include: According to pedestrians Basic acceleration ,quality and the pressure gradient generated by nearby pedestrian groups Calculate the social obstacle avoidance acceleration along the direction of decreasing pressure. ; Based on preset simulation step size The aforementioned social obstacle avoidance acceleration By performing discrete integration, the increment of social obstacle avoidance speed is obtained.

[0026] Based on the aforementioned social obstacle avoidance speed increment Determine the social obstacle avoidance direction vector with obstacle avoidance intensity, and correlate the social obstacle avoidance direction vector with the pedestrian... Expected motion rate Vector synthesis is performed to obtain pedestrians. Social obstacle avoidance speed at the current time step .

[0027] Preferably, in step S6, updating the spatial position of the pedestrian in the two-dimensional regular grid map includes: The position of pedestrian i is updated using the first-order Euler integral algorithm:

[0028] in, and Let be the spatial position vectors of pedestrian i at the current time t and the next time t+Δt, respectively, where Δt is the preset simulation step size.

[0029] As can be seen from the above technical solution, compared with the prior art, the technical solution of the present invention has the following beneficial effects: 1. For complex vertical evacuation spaces such as parallel double-flight staircases with reverse stair sections and intermediate platforms, this method effectively overcomes the shortcomings of traditional path planning methods based on local responses, which are prone to falling into local minima, by constructing a local passage cost field that incorporates obstacle repulsion effects and solving the equation to generate a globally optimal navigation function. In multi-story building staircase evacuation simulation scenarios, this method can stably guide pedestrian path selection within the stairwell, thereby achieving effective connection between floor evacuation paths and the final exit path. Therefore, for pedestrians on any floor, as long as they travel through the stairwell to the final exit, continuous path planning and evacuation simulation can be completed.

[0030] 2. This method introduces a slope-sensing speed adjustment mechanism, which corrects the initial expected speed on flat ground in real time based on the slope angle of the staircase in the grid cell where the pedestrian is located. In the simulation application of staircase evacuation in multi-story buildings, it can accurately depict the spontaneous deceleration behavior of pedestrians in the stair section area due to gravity and physiological consumption, so that the attenuation ratio of the stair section movement speed and the speed on flat ground conforms to the empirical range of fire safety engineering, making up for the physical deficiency of the traditional model in the height dimension.

[0031] 3. In the simulation application of crowd evacuation in stairwells of high-rise buildings, this method can naturally present the effect of staircases as geometric bottlenecks on the forced reduction of micro velocity, thereby flattening the input peak flow into a steady-state passage platform. The peak value of the output specific flow converges to the empirical range of the maximum specific flow of downward staircases given in the fire protection engineering manual, providing certain simulation calculation support for the assessment of the passage capacity of vertical evacuation facilities. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0033] Figure 1 A flowchart of a staircase evacuation simulation method based on potential field and slope perception provided in an embodiment of the present invention; Figure 2This is a schematic diagram of the three-dimensional structure and two-dimensional projection of a parallel double-flight staircase provided in an embodiment of the present invention. Figure 3 This is a schematic diagram of a three-story building simulation scene provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of a parallel double-flight staircase in a three-story building simulation scenario provided in an embodiment of the present invention; Figure 5 A schematic diagram of the single-person trajectory averaged by multiple rounds of experiments for the baseline model and potential field model provided in the embodiments of the present invention; Figure 6 This is a schematic diagram of the Euclidean distance from a pedestrian to a target point provided in an embodiment of the present invention; Figure 7 A schematic diagram illustrating the path expansion of the potential field model and the improved model provided in the embodiments of the present invention; Figure 8 This is a schematic diagram illustrating the variation of the normalized rate with the stair slope provided in an embodiment of the present invention. Figure 9 The embodiments of the present invention provide a schematic diagram of the specific flow rate evolution process of the potential field model; Figure 10 The embodiment of this invention provides a schematic diagram of the specific flow evolution process of the improved model. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] like Figure 1 As shown, this embodiment provides a staircase evacuation simulation method based on potential field and slope perception, including the following steps: S1. Obtain the geometric parameters of the staircase to be simulated and the pedestrian motion parameters, and discretize the three-dimensional staircase passage space into a two-dimensional regular grid map containing obstacle markers; S2. Construct a local passage cost field based on the two-dimensional regular grid map, and use a fast travel algorithm to solve the process function equation to generate the globally optimal navigation function from any grid cell to the exit, and determine the topology sensing potential field; S3. Generate a corresponding negative gradient field based on the topological sensing potential field, extract the negative gradient direction of the grid cell where the current pedestrian is located as the expected motion direction, and correct the pedestrian's initial expected speed on flat ground through the slope sensing speed adjustment mechanism to obtain the corrected expected motion rate. S4. Vector synthesis of the desired motion direction and desired motion rate to generate environmental driving speed; S5. Combine the social obstacle avoidance speed with the environmental driving speed and perform a weighted fusion to obtain the final composite speed of the pedestrian. S6. Based on the final running speed and the preset simulation step size, update the spatial position of pedestrians in the two-dimensional regular grid map, and iteratively execute steps S3 to S5 until all pedestrians are evacuated to the exit, thus completing the simulation of the stair evacuation process.

[0036] This method addresses the local minimum problem of path planning in parallel double-flight staircase evacuation simulation. It guides pedestrians to move along the globally optimal direction by constructing a topology-aware potential field. Simultaneously, it introduces a slope-aware speed adjustment mechanism to dynamically correct the pedestrian's expected speed based on the slope angle determined by the height and width of the stair treads. This method can realistically reproduce the speed decay behavior of pedestrians on stair sections with different slopes, as well as the flow-limiting effect of the staircase as a geometric bottleneck on the macroscopic passage capacity. It is applicable to the passage capacity assessment and geometric parameter optimization of vertical evacuation facilities in multi-story and high-rise buildings.

[0037] The following provides a further explanation of each step and related features in the above method; In this embodiment, S1, the geometric parameters of the staircase to be simulated and the pedestrian motion parameters are obtained, and the three-dimensional staircase passage space is discretized into a two-dimensional regular grid map containing obstacle markers. like Figure 2 The parallel double-flight staircase shown in the figure has a 3D structure and a 2D projection. The staircase to be simulated in this step can be composed of a floor platform, a first flight of stairs, an intermediate rest platform, and a second flight of stairs connected in sequence. After obtaining geometric parameters such as step height, step width, clear width of the flight of stairs, platform width, and number of steps per flight, the 3D staircase passage space is projected horizontally and discretized into a 2D regular grid map at a fixed resolution. In the grid map, the grid cell sets corresponding to the floor platform, the first flight of stairs, the intermediate rest platform, and the second flight of stairs are marked respectively. The grid cells of the first flight of stairs and the second flight of stairs calculate the local terrain slope angle based on the actual step height-to-width ratio, while the slope angle of the floor platform and the rest platform is set to 0. At the same time, obstacle markers can be added according to the staircase boundary and wall position to distinguish between walkable areas and impassable areas of boundary walls, thereby transforming the evacuation path space indicated in the attached figure into a gridded computational domain with geometric attributes and slope information.

[0038] In this embodiment S2, a local passage cost field is constructed based on the two-dimensional regular grid map, and a fast travel algorithm is used to solve the process function equation to generate the globally optimal navigation function from any grid cell to the exit, thereby determining the topology sensing potential field. First, a gridded computational domain is formed based on a two-dimensional regular grid map. This includes dividing all grid cells into two categories: passable cells and obstacle cells, according to the obstacle markers of each grid cell. Passable cells allow pedestrians to occupy or pass through, while obstacle cells prohibit pedestrians from entering. The two-dimensional gridded computational domain thus formed provides a discretized spatial basis for the subsequent construction of the local access cost field and the solution of the equation. Furthermore, constructing a local access cost field includes: Define grid cells Local traffic costs :

[0039] The first term on the right side of the equation is the basic cost of free movement; It is a repulsive potential of an obstacle, used to push pedestrians away from the obstacle;

[0040] in, For grid cells Euclidean distance to the nearest obstacle mesh cell, The repulsion strength coefficient of the obstacle. This is the decay factor of the repulsive potential with distance.

[0041] Furthermore, generating the globally optimal navigation function includes: Based on local access cost field Solve the equation:

[0042] in, Represents the gradient operator; The navigation function represents the function used to navigate from the grid cell. The minimum cumulative cost to reach the target exit; the navigation function here is the topological sensing potential field, used to guide pedestrians along the minimum cost path; The fast travel algorithm is used to numerically solve the equation on a discrete grid to obtain the globally optimal navigation function as the topology sensing potential field. The topologically aware potential field obtained by solving the local passage cost field and the fast travel algorithm can ensure that pedestrians move along the global minimum cost path in the non-convex passage space composed of stair sections and platforms. This avoids the local minimum trap that occurs at corners and turns in traditional methods. Moreover, the potential field calculation only requires one preprocessing, which does not increase the burden on the simulation runtime.

[0043] In this embodiment S3, a corresponding negative gradient field is generated based on the topological sensing potential field, and the negative gradient direction of the grid cell where the current pedestrian is located is extracted as the expected motion direction; and the pedestrian's initial expected speed on flat ground is corrected through the slope sensing speed adjustment mechanism to obtain the corrected expected motion speed. The desired direction of motion is expressed as:

[0044] in, For pedestrian i in the current grid cell The unit vector of the expected direction of motion at that location. This represents the gradient operator.

[0045] Furthermore, the slope-sensing speed adjustment mechanism corrects the pedestrian's initial expected speed on flat ground by including: Based on the stair slope angle of the current pedestrian grid cell Calculate the speed adjustment factor The corrected expected motion rate is obtained. :

[0046]

[0047] Where k is a calibration coefficient reflecting pedestrian slope sensitivity. For pedestrians The initial expected velocity on flat ground.

[0048] Furthermore, methods for determining the local terrain slope angle θ include: If the current grid cell belongs to the stair flight region, then the slope angle is calculated based on the riser height h and riser width w. ; If the current grid cell belongs to the stair landing area, then θ = 0; By combining the desired motion direction determined by the negative gradient of the potential field with the slope-sensing speed adjustment mechanism, the model achieves collaborative decision-making where the direction is guided by the topology and the speed is modulated by the terrain. This allows pedestrians to maintain a normal walking speed on the platform and automatically reduce it to a reasonable range on the stair section. This linear correction law can be applied to stairs with different combinations of step height and width.

[0049] In embodiment S4, the desired motion direction and desired motion rate are vector-synthesized to generate the environmental driving speed; wherein, the environmental driving speed Represented as:

[0050] in, The corrected desired motion rate, The desired direction of motion.

[0051] In embodiment S5, the social obstacle avoidance speed is combined with the environmental driving speed and weighted fusion to obtain the final composite speed of the pedestrian; wherein, the final composite speed of the pedestrian Represented as:

[0052] in, To improve the speed of social obstacle avoidance, The speed is driven by the environment, and α is a weighting coefficient. The higher the local population density, the larger the value of α.

[0053] Furthermore, determine the social obstacle avoidance speed. include: According to pedestrians Basic acceleration ,quality and the pressure gradient generated by nearby pedestrian groups Calculate social obstacle avoidance acceleration :

[0054] The pressure gradient generated by the nearby pedestrian group This is used to quantify the unevenness of the crowd distribution around pedestrian i. It calculates the density distribution of pedestrians within a preset radius centered on pedestrian i, and then calculates the corresponding pressure gradient based on the spatial variation of this density distribution. Based on preset simulation step size Discrete integral of the social obstacle avoidance acceleration is performed to obtain the social obstacle avoidance velocity increment. ; Based on the aforementioned social obstacle avoidance speed Determine the social obstacle avoidance direction vector with obstacle avoidance intensity, and correlate the social obstacle avoidance direction vector with the pedestrian... Expected motion rate Vector synthesis is performed to obtain pedestrians. Social obstacle avoidance speed at the current time step ; By introducing the pressure gradient of neighboring pedestrian groups to quantify the uneven distribution of local crowds, and using this to drive the calculation of social obstacle avoidance acceleration, the social obstacle avoidance velocity increment and social obstacle avoidance direction vector are obtained through discrete integration. Finally, these are combined with the desired motion rate to obtain the social obstacle avoidance velocity. Social obstacle avoidance speed is used to reflect the local avoidance tendency of pedestrians under the influence of pressure from nearby crowds, and is used together with environmental guidance speed to determine the final movement speed.

[0055] In this embodiment, S6, based on the final running speed and the preset simulation step size, updates the spatial position of pedestrians in the two-dimensional regular grid map, iteratively executing steps S3 to S5 until all pedestrians are evacuated to the exit, completing the stair evacuation process simulation; wherein, updating the spatial position of pedestrians in the two-dimensional regular grid map includes: The position of pedestrian i is updated using the first-order Euler integral algorithm:

[0056] in, and are the spatial position vectors of pedestrian i at the current time t and the next time t+Δt, respectively, where Δt is the preset simulation step size; This step iteratively updates pedestrian positions using first-order Euler integrals and repeats direction calculation, velocity correction, and pedestrian obstacle avoidance at each time step until all pedestrians reach the exit. This method can effectively reproduce the evacuation time variation pattern under different stair geometry dimensions, providing a reliable simulation tool for stair design optimization and traffic capacity assessment of multi-story and high-rise buildings.

[0057] In addition, to verify the effectiveness and physical rationality of the methods described in S1 to S6 of this embodiment in a real staircase evacuation scenario, multiple sets of numerical experiments were set up using a parallel double-flight staircase in a typical three-story building as the object. These experiments tested the ability of the topological sensing potential field to overcome local minima, the accuracy of the slope sensing speed adjustment mechanism in restoring pedestrian speed decay, and the reproduction effect of the improved model on the bottleneck effect and self-organization characteristics during the group descent. The specific simulation scenarios, parameter configurations, and experimental results are as follows. like Figure 3 As shown, a three-story building is used as the main scene. Each floor has several rooms and corridors. A parallel double-flight staircase is connected by a floor platform. The exit is located on the first floor outdoors. Each experiment selects different observation ranges and personnel configurations according to the analysis objectives. Individual motion parameters remain consistent in all experiments. Spatial parameters remain unchanged unless otherwise specified. The pedestrian subjects in this embodiment are all young people. The key parameter settings are shown in Table 1. Table 1

[0058] like Figure 4 As shown, the tread width, tread height, clear stair width, and platform width are all taken from common architectural design parameters to ensure the representativeness of the scenario; the pedestrian's expected speed is set to... An adult's walking speed is between 1.2 and 1.7. Inside, Set to 0.013, slope-aware speed adjustment factor The calculated value is 0.65, which is highly consistent with current fire safety engineering standards. The stairwell evacuation speed is approximately 60% to 67% of the speed on flat ground, based on empirical values.

[0059] In this embodiment, three numerical models were designed for numerical experiments, as shown in Table 2. Table 2

[0060] 1) Experiment I; Experiment I conducts a numerical simulation experiment in a single-person scenario based on a baseline model and a potential field model. The focus is on verifying the adaptability of the topologically aware potential field and its effectiveness in overcoming the local minima defect of the baseline model. The observation range of the scenario in this experiment is a parallel double-flight staircase connecting floors 2 and 1; the initial position of the person is the starting point of the first staircase. Figure 5 As shown in the single-person trajectory graph, which is the average of multiple rounds of experiments using the baseline model and the potential field model, the trajectory of the baseline model infinitely zigzags between two very close positions, approaching a state of stagnation. This indicates that the baseline model cannot break through the local minimum trap of the current environment. The trajectory of the potential field model, on the other hand, has no zigzags or stagnations and is highly consistent with the passage space. This shows that the topology-aware potential field can fundamentally solve the local minimum problem in the passage domain of parallel double-flight staircases, assisting pedestrians in achieving movement consistent with the passage space. Moreover, the potential field output is stable and has good scene adaptability. To verify that the effectiveness of the potential field model is not limited to specific staircase geometry, this embodiment conducts a series of single-person numerical experiments for different geometric configurations; the results are as follows. Figure 6 As shown, under all operating conditions, when pedestrians start from the entrance of the first staircase, the Euclidean distance to the target point initially increases slightly under spatial constraints, then decreases continuously as they enter the second staircase and converges to zero. This indicates that the model can achieve effective path planning under different geometric conditions. Furthermore, the experimental results show that the smaller the total dimension of the staircase depth direction, i.e., the sum of the horizontal projection length of the staircase and the width of the platform, the shorter the evacuation time. Considering only the interaction between people and the environment, the horizontal projection length of the staircase and the width of the platform together determine the horizontal passage depth of the staircase, directly affecting the potential field path planning results, and thus significantly affecting the pedestrian evacuation time.

[0061] 2) Experiment II; Experiment II is a numerical simulation experiment in a single-person scenario based on the potential field model and the improved model. It mainly verifies the physical effectiveness and rationality of the slope-sensing speed adjustment in the improved model. The observation range and personnel configuration of this experiment are the same as those in Experiment I. like Figure 7As shown, to intuitively present the movement characteristics of pedestrians during the evacuation process in three-dimensional space, this embodiment uses a path unfolding diagram projected onto a one-dimensional cumulative travel distance axis for visualization analysis. In the potential field model, the pedestrian's expected movement speed does not change significantly with the distance traveled, only the vertical height decreases, indicating that the pedestrian only completes the action of going downstairs and does not characterize the impact of the slope on the pedestrian. The improved model reflects that the pedestrian's expected movement speed and vertical height change synchronously with the terrain slope, indicating that the pedestrian can effectively identify the slope and dynamically adjust the speed. In addition, in the improved model, the pedestrian's expected movement speed is negatively correlated with the slope: it remains at 1.3 m / s in flat areas and drops to 0.85 m / s in stairwell areas. This speed reduction phenomenon is consistent with the modeling logic of the slope-sensing speed adjustment mechanism in this embodiment. There is a slight offset between the speed inflection point and the slope change position in the figure. This is due to the discretization of the simulation space, which makes the continuous geometric shape approximated by grid cells. The slope transition boundary is difficult to accurately characterize, resulting in a positional deviation of the speed adjustment. This is a normal numerical error caused by the grid resolution and does not affect the rationality of the conclusion. Although the experimental scenario in this embodiment is set with a specific stair slope, in order to verify the universality of the speed adjustment mechanism, such as Figure 8 As shown, the normalized walking speed varies with the slope of the stairs in an indoor public building within the range of the speed adjustment mechanism. It can be seen that the model prediction curve falls completely within the error range of the Fujiyama experiment, indicating that the speed adjustment mechanism can accurately reflect the attenuation of speed due to the slope. In addition, the interpolation experimental value is close to the set scene slope of 26.57° in this embodiment, proving the physical authenticity of the model under specific parameters. The slope of a staircase is determined by both the riser height and the riser width. Different combinations of riser dimensions have different effects on the movement speed of pedestrians on the stairs. To explore how the slope affects evacuation time by adjusting the movement speed of pedestrians, this embodiment designed several sets of comparative numerical experiments: the total dimension of the staircase in the depth direction was fixed. Under the premise of keeping the total depth dimension unchanged, the riser height, riser width and number of steps per run were adjusted synchronously to characterize different slope conditions. The parameter settings, expected movement speed of the stair section and evacuation time for each condition are shown in Table 3. Table 3

[0062] Experimental results show that different combinations of step height and step width correspond to different slopes, which have varying degrees of attenuation on pedestrian movement speed, thus having a differentiated impact on individual evacuation time. Since the length of the flat path and the length of the staircase path traversed by pedestrians are consistent in all conditions, the path length factor can be eliminated, and the slope becomes the only variable affecting evacuation time. The results show that the greater the slope, the lower the expected movement speed of pedestrians on the staircase, and the longer the final evacuation time, with a positive correlation between the two.

[0063] 3) Experiment III; Experiment III conducted a numerical simulation experiment on a scenario with 35 people based on the potential field model and the improved model, focusing on the dynamic characteristics of a single stream of people descending a parallel double-flight staircase in a non-converging state. According to the definition of specific flow rate in the SFPE Fire Protection Engineering Manual:

[0064] Its equivalent observation expression can be derived as follows:

[0065] In the formula, The number of people passing through the monitoring section per unit time. To measure the clear width of the stair flight, a virtual monitoring section was set up at the entrance of the first stair flight on each floor, and statistics were collected over a fixed time window. Number of people passing within ,calculate And thus obtain This experiment uses 5 seconds as a fixed time window. In the following text, the entrances of the first flight of stairs from the 3rd to the 2nd floor are referred to as monitoring section A, and the entrances of the first flight of stairs from the 2nd to the 1st floor are referred to as monitoring section B. The observation range of the scene in this experiment is monitoring sections A and B. The personnel configuration is 35 people, and their initial positions are distributed in the rooms and corridors on the 3rd floor. The specific flow evolution process of monitoring sections A and B is shown in Table 4 below.

[0066] The experimental results showed that for both the potential field model and the improved model, the total number of people passing through monitoring section B was 35, the data layer was completely closed, and all 35 people successfully passed through 3-2 floors of stairs, confirming the effectiveness of the constructed topological sensing potential field and providing basic support for subsequent analysis. However, there was a difference in flow rate between the two models. In the potential field model, the speed of pedestrians after entering the stairs remained unchanged, and the instantaneous flow rate was higher at some times, such as 14 people passing through at 25 seconds. In the improved model, the slope effect was taken into account, and the speed of pedestrians after entering the stairs decreased. Only 3 people passed through at 25 seconds, and the overall flow rate was lower than that of the potential field model, which is more consistent with the speed decay and macroscopic delay characteristics of real evacuation. like Figure 9 The evolution process of specific flux in the potential field model, and Figure 10The evolution of the specific flow rate in the improved model shows that in the potential field model without considering the speed reduction of stairs, the flow rate curve at monitoring section B is almost a translation of section A delayed by 10 seconds, with a peak value as high as 1.87. This indicates that people pass through the stairs at an approximately constant speed, and the density and flow rate are not dissipated, which violates the dynamics of real pedestrians and proves the necessity of introducing a speed reduction mechanism. After the improved model introduces slope-sensing speed adjustment, the shape of the flow rate curve at section B is different from that at section A. The input peak value of 1.87 is significantly flattened after being constrained by the stairs, and stabilizes at around 1.07 in the 35–40s range, forming a flat-topped platform. This difference proves that the stairs, as a geometric bottleneck, limit the macroscopic passage capacity by forcibly reducing speed.

[0067] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0068] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A staircase evacuation simulation method based on potential field and slope perception, characterized in that, Includes the following steps: S1. Obtain the geometric parameters of the staircase to be simulated and the pedestrian motion parameters, and discretize the three-dimensional staircase passage space into a two-dimensional regular grid map containing obstacle markers; S2. Construct a local passage cost field based on the two-dimensional regular grid map, and use a fast travel algorithm to solve the process function equation to generate the globally optimal navigation function from any grid cell to the exit, and determine the topology sensing potential field; S3. Generate a corresponding negative gradient field based on the topological sensing potential field, and extract the negative gradient direction of the grid cell where the current pedestrian is located as the desired motion direction; The slope-sensing speed adjustment mechanism is used to correct the pedestrian's initial expected speed on flat ground, resulting in the corrected expected movement speed. S4. Vector synthesis of the desired motion direction and desired motion rate to generate environmental driving speed; S5. Combine the social obstacle avoidance speed with the environmental driving speed and perform a weighted fusion to obtain the final composite speed of the pedestrian. S6. Based on the final running speed and the preset simulation step size, update the spatial position of pedestrians in the two-dimensional regular grid map, and iteratively execute steps S3 to S5 until all pedestrians are evacuated to the exit, thus completing the simulation of the stair evacuation process.

2. The staircase evacuation simulation method based on potential field and slope perception according to claim 1, characterized in that, In S2, constructing the local access cost field includes: Define grid cells Local traffic costs : The first term on the right side of the equation is the basic cost of free movement; It is a repulsive potential of an obstacle, used to push pedestrians away from the obstacle; in, For grid cells Euclidean distance to the nearest obstacle mesh cell, The repulsion strength coefficient of the obstacle. This is the decay factor of the repulsive potential with distance.

3. The staircase evacuation simulation method based on potential field and slope perception according to claim 1, characterized in that, In step S2, generating the globally optimal navigation function includes: Based on local access cost field Solve the equation: in, Represents the gradient operator; The navigation function represents the function used to navigate from the grid cell. The minimum cumulative cost to reach the target exit; The fast travel algorithm is used to numerically solve the equation on a discrete grid to obtain the globally optimal navigation function as the topology sensing potential field.

4. The staircase evacuation simulation method based on potential field and slope perception according to claim 1, characterized in that, In S3, the desired direction of motion is expressed as: in, For pedestrian i in the current grid cell The unit vector of the expected direction of motion at that location. Represents the gradient operator, For navigation functions.

5. The staircase evacuation simulation method based on potential field and slope perception according to claim 1, characterized in that, In step S3, the slope-sensing speed adjustment mechanism corrects the pedestrian's initial expected speed on flat ground, including: Based on the stair slope angle of the current pedestrian grid cell Calculate the speed adjustment factor The corrected expected motion rate is obtained. : Where k is a calibration coefficient reflecting pedestrian slope sensitivity. For pedestrians The initial expected velocity on flat ground.

6. The staircase evacuation simulation method based on potential field and slope perception according to claim 5, characterized in that, The method for determining the local terrain slope angle θ includes: If the current grid cell belongs to the stair flight region, then the slope angle is calculated based on the stair tread height h and tread width w. ; If the current grid cell belongs to the stair landing area, then θ=0.

7. The staircase evacuation simulation method based on potential field and slope perception according to claim 1, characterized in that, In S4, the environmental driving speed Represented as: in, The corrected desired motion rate, The desired direction of motion.

8. The staircase evacuation simulation method based on potential field and slope perception according to claim 1, characterized in that, In S5, the final composite velocity of the pedestrian Represented as: in, To improve the speed of social obstacle avoidance, The speed is driven by the environment, and α is a weighting coefficient. The higher the local population density, the larger the value of α.

9. The staircase evacuation simulation method based on potential field and slope perception according to claim 1, characterized in that, Determine the social obstacle avoidance speed include: According to pedestrians Basic acceleration ,quality and the pressure gradient generated by nearby pedestrian groups Calculate the social obstacle avoidance acceleration along the direction of decreasing pressure. ; Based on preset simulation step size The aforementioned social obstacle avoidance acceleration By performing discrete integration, the increment of social obstacle avoidance speed is obtained. ; Based on the aforementioned social obstacle avoidance speed increment Determine the social obstacle avoidance direction vector with obstacle avoidance intensity, and correlate the social obstacle avoidance direction vector with the pedestrian... Expected motion rate Vector synthesis is performed to obtain pedestrians. The speed of social obstacle avoidance at the current time step .

10. The staircase evacuation simulation method based on potential field and slope perception according to claim 1, characterized in that, In step S6, updating the spatial position of the pedestrian in the two-dimensional regular grid map includes: The position of pedestrian i is updated using the first-order Euler integral algorithm: in, and Let be the spatial position vectors of pedestrian i at the current time t and the next time t+Δt, respectively, where Δt is the preset simulation step size.

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