CN108280251B - T-shaped intersection high risk area calibration method based on street width ratio - Google Patents

T-shaped intersection high risk area calibration method based on street width ratio Download PDF

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CN108280251B
CN108280251B CN201711385883.2A CN201711385883A CN108280251B CN 108280251 B CN108280251 B CN 108280251B CN 201711385883 A CN201711385883 A CN 201711385883A CN 108280251 B CN108280251 B CN 108280251B
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赵荣泳
汪栋
胡钱珊
李翠玲
董大亨
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Abstract

The invention relates to a T-shaped intersection high risk area calibration method based on a street width ratio, which comprises the following steps: 1) acquiring street parameters at a T-shaped intersection; 2) establishing an Aw-Rascle crowd dynamics model; 3) introducing an influence matrix of a cross junction area on the basis of the Aw-Rascle crowd dynamics model, and constructing a T-junction crowd evacuation dynamics model; 4) establishing a population initialization Gaussian distribution model based on the street parameters; 5) and after the population density is initialized based on the population initialization Gaussian distribution model, simulating by using the population evacuation dynamics model at the T-shaped intersection, and calibrating the population evacuation high-risk area. Compared with the prior art, the method has the advantages of accurately reflecting the density distribution condition of the actual street crowd, being clear and intuitive and the like.

Description

T-shaped intersection high risk area calibration method based on street width ratio
Technical Field
The invention relates to the technical field of road traffic safety, in particular to a T-junction high-risk area calibration method based on a street width ratio.
Background
High risk areas in the process of crowd evacuation at the T-shaped intersection are prone to crowding and trampling, and the high risk areas are very important in crowd evacuation guidance and management and control. At present, the high risk area of the T-shaped intersection is defined mainly by means of experience calibration and computer simulation and by means of measures such as traffic control, and a calibration method for evacuating the high risk area of the T-shaped intersection is not available. Because the confluence mechanism of the T-shaped intersection is very complicated, the intersection of the T-shaped intersection is easy to form a high risk area, and crowding and trampling events occur.
To date, the study of high risk areas by population evacuation at t-junctions has focused mainly on one-way pedestrian and experience level studies, with several disadvantages: 1) at present, a method for calibrating a high-risk area of a T-shaped intersection is not available; 2) a visual simulation method for the influence of the T-shaped intersection street width comparison on crowd evacuation is not available.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a T-junction high-risk area calibration method based on street width ratio.
The purpose of the invention can be realized by the following technical scheme:
a T-junction high risk area calibration method based on street width ratio comprises the following steps:
1) acquiring street parameters at a T-shaped intersection;
2) establishing an Aw-Rascle crowd dynamics model;
3) introducing an influence matrix of a cross junction area on the basis of the Aw-Rascle crowd dynamics model, and constructing a T-junction crowd evacuation dynamics model;
4) establishing a population initialization Gaussian distribution model based on the street parameters;
5) and after the population density is initialized based on the population initialization Gaussian distribution model, simulating by using the population evacuation dynamics model at the T-shaped intersection, and calibrating the population evacuation high-risk area.
The street parameters comprise the width of a main road street at the T-shaped intersection, the width of a branch road street, the length of the main road street and the length of the branch road street.
The Aw-Rascle population dynamics model is expressed as:
ρt+(ρv)x+(ρu)y＝0
(v+Ph)t+v(v+Ph)x+u(u+Ph)y＝s1
(v+Pv)t+v(v+Pv)x+u(u+Pv)y＝s2
where ρ represents the population density, v represents the horizontal velocity, u represents the vertical velocity, and PhRepresenting a pressure term in the horizontal direction, PvIndicating the vertical directionPressure term of(s)1And s2Indicating the relaxation term factor, subscript t indicating the partial derivative over time, subscript x indicating the partial derivative over distance x, and subscript y indicating the partial derivative over distance y.
The relaxation term factor s1And s2Are respectively:
Figure BDA0001516606160000021
Figure BDA0001516606160000022
where τ is the relaxation time, the velocity V (ρ) is the maximum velocity in the horizontal direction, and U (ρ) is the maximum velocity in the vertical direction.
The impact matrix of the intersection region is represented as:
Figure BDA0001516606160000023
wherein M isimpC is the maximum influence coefficient, i and j are respectively the abscissa and the ordinate of the evacuated individual in the intersection region, and E is a matrix with elements of 1.
The T-junction crowd evacuation dynamics model is expressed as:
ρt+(ρv)x+(ρu)y＝0
ρ(v+Ph(ρ,v,u))t+ρv(v+Ph(ρ,v,u))x
+ρu(u+Ph(ρ,v,u))y＝ρs1
ρ(v+Pv(ρ,v,u))t+ρv(v+Pv(ρ,v,u))x
+ρu(u+Pv(ρ,v,u))y＝ρs2
wherein, Ph(ρ, v, u) and Pv(ρ, v, u) are the horizontal pressure term and the vertical pressure term, respectively, after considering the influence matrix of the intersection regionThe pressure term of the direction.
The population initialization gaussian distribution model is expressed as:
Figure BDA0001516606160000024
wherein ρ (x, y,0) is the crowd density at coordinate (x, y,0) determined by the T-junction crowd evacuation dynamics model, DmaxTo set the maximum density, a and b are the horizontal and vertical coordinates of the vertical and horizontal density distribution center, respectively, obtained based on street parameters, and σ is the amount of relaxation.
And in the step 5), a visualized crowd density contour map is generated through simulation, and a crowd evacuation high risk area is marked out from the crowd density contour map.
The crowd evacuation high-risk area is that the crowd density is greater than the set density maximum value DmaxThe area of (a).
The influence of different street widths on crowd evacuation density is obtained through simulation of the T-shaped intersection crowd evacuation dynamics model under different street parameters.
Compared with the prior art, the invention has the following beneficial effects:
1. the density initialization Gaussian distribution function established by the invention has high-order characteristics and smooth curve, can better reflect the flow density and the actual speed of pedestrians, fully considers factors such as weather conditions, environmental conditions, pedestrian composition, building environment and the like, and better accords with the actual crowd evacuation situation at the T-shaped intersection, thereby having the great advantage of the invention.
2. The method can reflect the high-risk area and the density value of crowd evacuation, is clear and intuitive, can effectively define the boundary of the high-risk area and a non-high-risk area (non-influence area), provides technical basis for crowd evacuation guidance, and avoids state disordered development and out of control.
3. The prior art focuses on theoretical research on crowd evacuation, theoretically analyzes trend change in the crowd evacuation process, and clearly and definitely shows fewer simulation results. The invention utilizes the proposed T-shaped intersection crowd evacuation dynamics model to carry out accurate numerical simulation on crowd evacuation of the T-shaped intersection with different street width ratios, dynamically displays the whole crowd evacuation process by using accurate data, and automatically calibrates a high risk area with the density value larger than the maximum density value. The simulation result is displayed by mainly using a visual population density contour map for marking a high risk area, the influence of different street width ratios on population evacuation can be clearly and definitely analyzed, the width ratio for forming the minimum vortex (corresponding to local treading) is obtained, and theoretical support is provided for the planning of urban street width, large-scale activity evacuation plans and field commands in the construction industry.
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FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 shows the location of the trampling event of McJohn's republic of Ma in 2015
Fig. 3 is a t-junction density contour map with the parameters set to: mimp＝1,Rwid＝1.0,(P204,P223)＝(2,1)；
Fig. 4 is a t-junction density contour map with the parameters set to: mimp＝1,Rwid＝1.4,(P204,P223)＝(2,1)；
Fig. 5 is a t-junction density contour map with the parameters set to: mimp＝1,Rwid＝2.0,(P204,P223)＝(2,1)。
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
As shown in fig. 1, the present invention provides a method for calibrating a high risk area of a t-junction based on street width ratio, which comprises the following steps:
1) acquiring street parameters at the T-shaped intersection, wherein the street parameters comprise the width of a main road street at the T-shaped intersection, the width of a branch road street, the length of the main road street and the length of the branch road street;
2) establishing an Aw-Rascle crowd dynamics model;
3) introducing an influence matrix of a cross junction area on the basis of the Aw-Rascle crowd dynamics model, and constructing a T-junction crowd evacuation dynamics model;
4) establishing a population initialization Gaussian distribution model based on the street parameters;
5) after the population density is initialized based on the population initialization Gaussian distribution model, simulating by using the population evacuation dynamics model at the T-shaped intersection to calibrate a population evacuation high-risk area, wherein the population evacuation high-risk area is a region with the population density larger than a set density maximum value DmaxThe area of (a).
According to the method, the density is initialized by utilizing a higher-order smooth Gaussian distribution model, the actual street crowd density distribution condition is reflected, the high risk area and the density value of crowd evacuation can be reflected, and the method is clear and visual. The method effectively defines the boundary of the high-risk area and the non-high-risk area (non-influence area), provides a technical basis for crowd evacuation guidance, and avoids disordered development and out of control of the situation.
1. Establishment of Aw-Rascle crowd dynamics model
A.Aw and M.rascle provide a two-dimensional space crowd evacuation model (hereinafter referred to as Aw-Rascle model) based on a one-dimensional flow model. The classical conservation of mass equation is determined by the partial differential equation of conservation of mass:
ρt+(ρv)x＝0 (1)
where ρ and v represent population density and velocity, ρtIs the partial derivative of time, (ρ v)xIs the partial derivative of the distance x.
To reflect the anisotropy of the evacuated population with the anisotropy of the fluid motion, a "pressure" term is defined. Assuming ρ and v are independent, the fluid mechanics navier-stokes equation is introduced and the pressure term is changed to:
Figure BDA0001516606160000051
wherein C is0Representing the driver's expected coefficient of response to density. The relationship of ρ and v is reflected with a partial differential equation:
(v+P(ρ))t+v(v+P(ρ))x＝0 (2)
where P (ρ) represents the "pressure" term in the model, v represents the horizontal velocity, and u represents the vertical velocity, the model is applied to a two-dimensional space. The one-dimensional Aw-Racle population dynamics model is a model formed by two nonlinear hyperbolic Partial Differential Equations (PDE) in formula (1) and formula (2).
Converting a one-dimensional mass conservation partial differential equation into a two-dimensional partial differential equation shown as a formula (3), and converting a one-dimensional Aw-Rascle crowd dynamics model into a two-dimensional Aw-Rascle crowd dynamics model (consisting of the formulas (3), (4) and (5)):
ρt+(ρv)x+(ρu)y＝0 (3)
(v+Ph)t+v(v+Ph)x+u(u+Ph)y＝s1 (4)
(v+Pv)t+v(v+Pv)x+u(u+Pv)y＝s2 (5)
where ρ represents the population density, v represents the horizontal velocity, u represents the vertical velocity, and PhRepresenting a pressure term in the horizontal direction, PvRepresenting the pressure term, s, in the vertical direction1And s2Indicating the relaxation term factor, subscript t indicating the partial derivative over time, subscript x indicating the partial derivative over distance x, and subscript y indicating the partial derivative over distance y.
Relaxation term factor s1And s2The pedestrian adjusts the actual speed to the expected speed V (rho) and U (rho) according to the current density of the stream of people, which are respectively expressed as:
Figure BDA0001516606160000052
Figure BDA0001516606160000053
where τ is the relaxation time spent close to the desired speed, the speed V (ρ) is the maximum speed in the horizontal direction, and U (ρ) is the maximum speed in the vertical direction, i.e., the desired speed.
In the Aw-Rascle model, PhIs a function of P and v and can be expressed as Ph(ρ,v)，PvIs a function of rho and u and can be expressed as Pv(ρ, v). The initial conditions are that rho (x, y,0) is more than or equal to 0, and v (x,0) is more than or equal to | vf1| v is less than or equal to | and u (y,0) < | vf2||，vf1And vf2Is the maximum speed at which individuals are evacuated in both directions. The function is given by equation (8) and equation (9):
Figure BDA0001516606160000054
Figure BDA0001516606160000055
wherein, both beta and gamma are constants.
2. Establishment of T-shaped intersection crowd evacuation dynamic model
On the basis of the Aw-Rascle crowd evacuation model, the T-shaped intersection crowd evacuation dynamics model increases the influence of bidirectional superposition of vectors in the vertical direction u and the horizontal direction v in the T-shaped intersection area, so that the crowd density distribution at the intersection position is more reasonable. Influence matrix M for introducing intersection regionimpAnd the problem of bidirectional superposition is solved:
Figure BDA0001516606160000061
wherein M isimpC is the maximum influence coefficient, i and j are respectively the abscissa and the ordinate of the evacuated individual in the intersection region, and E is a matrix with elements of 1.
In the central intersection, the moving directions of the main road and the branch road crowd are horizontally and vertically overlapped, the main road is taken as a main reference direction by the model, and the central position of the intersection is determined by modifying a pressure item P. Taking into account the cross-port areaInfluencing the horizontal pressure term P after the matrixh(ρ, v, u) and the pressure term P in the vertical directionv(ρ, v, u) are respectively expressed as:
Figure BDA0001516606160000062
Figure BDA0001516606160000063
wherein, tau1、τ2Are different parameter impact matrices.
First, it is necessary to derive the x-axis component, obtain the y-axis component through the same process, and substitute equations (11) and (12) with equations (4) and (5) multiplied by ρ to obtain equations (13) and (14). Constructing a crowd evacuation dynamics model (consisting of formulas (3), (13) and (14)) of the T-junction area:
ρt+(ρv)x+(ρu)y＝0 (3)
Figure BDA0001516606160000064
Figure BDA0001516606160000065
3. establishment of population initialization Gaussian distribution model
Establishing a population initialization Gaussian distribution model as shown in the following formula:
Figure BDA0001516606160000066
wherein ρ (x, y,0) is the crowd density at coordinate (x, y,0) determined by the T-junction crowd evacuation dynamics model, DmaxTo set the maximum density, a and b are the horizontal and vertical coordinates of the vertical and horizontal density distribution center, respectively, obtained based on street parameters, and σ is the amount of relaxation. According to the research of scholars at home and abroad,in this embodiment, the maximum density value can be optionally set to Dmax＝7.0p/m2。
4. Numerical simulation and visual output of T-shaped intersection high risk area calibration method
The high risk area is marked by marking the crowd density greater than the set density maximum value DmaxThe area of (a). The model is applied to simulate the crowd evacuation of T-shaped intersections with different street width ratios, an accurate numerical simulation is obtained through the running of an MATLAB R2013B program, a visualized crowd density contour map is generated, critical values of the density can be visually captured and positioned, crowd evacuation high-risk areas with different street width ratios are marked, the influence of different street width ratios on the crowd evacuation density is analyzed, the evacuation process of the whole crowd is dynamically displayed, and the development trend of the crowd movement is judged.
The 2015-year event of barley trampling was studied in the above-described manner, and the trampling event occurring at the T-junction between street 204 and street 223 (intersection 204-223) was reproduced by simulation. Setting the width W of the main road 204 streetmai(main), width W of the Branch 223 streetbra(branch), trunk 204 street length lbraThe length of the branch 223 street is set to lmai。
According to the actual parameters of the treading events at the intersection of 204 street and 223 street, 2000 evacuated persons were set on the street as initial conditions, the width of the exit at the right side wall was set as d, and the position where the treading actually occurred was marked with a red pattern, as shown in fig. 2. The width of the street of the trunk 204 is set to Wbra10m, and the width of the street branch 223 is set to Wmai10m, the street length of the trunk 204 is set to lbraThe length of the trunk 223 street is set to l 50mmai30 m. The ratio of the width of main road street 204 to the width of branch road street 223 is 5: 3. the method comprises the steps of writing an MATLAB R2013B program for simulation, changing street width ratio, respectively obtaining crowd evacuation density contour maps with different width ratios through simulation, writing a program for calibrating high-risk areas, and enabling density values to be larger than Dmax＝7.0p/m2The area of (a) is indicated as shown in fig. 3-5. By analyzing 3 density contour plots,it can be concluded that: different street width ratios affect the area of the high risk area for the same environmental parameters. In this case, the width ratio of the main street 204 to the main street 223 is about 1.4, which can effectively reduce the formation of eddy current and better suppress the occurrence of trampling.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (6)

1. A T-junction high risk area calibration method based on street width ratio is characterized by comprising the following steps:
1) acquiring street parameters at the T-shaped intersection, wherein the street parameters comprise the width of a main road street at the T-shaped intersection, the width of a branch road street, the length of the main road street and the length of the branch road street;
2) establishing an Aw-Rascle crowd dynamics model:
ρt+(ρv)x+(ρu)y＝0
(v+Ph)t+v(v+Ph)x+u(u+Ph)y＝s1
(v+Pv)t+v(v+Pv)x+u(u+Pv)y＝s2
where ρ represents the population density, v represents the horizontal velocity, u represents the vertical velocity, and PhRepresenting a pressure term in the horizontal direction, PvRepresenting the pressure term, s, in the vertical direction1And s2Denotes the relaxation term factor, subscript t denotes the partial derivative over time, subscript x denotes the partial derivative over distance x, subscript y denotes the partial derivative over distance y;
3) introducing an influence matrix of a cross junction region on the basis of the Aw-Rascle crowd dynamics model, and constructing a T-junction crowd evacuation dynamics model:
the T-junction crowd evacuation dynamics model is expressed as:
ρt+(ρv)x+(ρu)y＝0
ρ(v+Ph(ρ,v,u))t+ρv(v+Ph(ρ,v,u))x+ρu(u+Ph(ρ,v,u))y＝ρs1
ρ(v+Pv(ρ,v,u))t+ρv(v+Pv(ρ,v,u))x+ρu(u+Pv(ρ,v,u))y＝ρs2
wherein, Ph(ρ, v, u) and Pv(ρ, v, u) are the horizontal and vertical pressure terms, respectively, after considering the influence matrix of the intersection region;
4) establishing a population initialization Gaussian distribution model based on the street parameters;
5) after the crowd density is initialized based on the crowd initialization Gaussian distribution model, the crowd evacuation dynamics model at the T-shaped intersection is used for simulating, a visualized crowd density contour map is generated through simulation, and a crowd evacuation high-risk area is marked out from the crowd density contour map.
2. The method for calibrating high-risk area of T-junction based on street width ratio as claimed in claim 1, wherein the relaxation factor s1And s2Are respectively:
Figure FDA0002839049640000011
Figure FDA0002839049640000021
where τ is the relaxation time, the velocity V (ρ) is the maximum velocity in the horizontal direction, and U (ρ) is the maximum velocity in the vertical direction.
3. The method for calibrating high-risk areas of a T-junction based on street width ratio as claimed in claim 1, wherein the influence matrix of the intersection area is represented as:
Figure FDA0002839049640000022
wherein M isimpC is the maximum influence coefficient, i and j are respectively the abscissa and the ordinate of the evacuated individual in the intersection region, and E is a matrix with elements of 1.
4. The method for calibrating high-risk areas of a T-junction based on street width ratio as claimed in claim 1, wherein the population initialized Gaussian distribution model is expressed as:
Figure FDA0002839049640000023
wherein ρ (x, y,0) is the crowd density at coordinate (x, y,0) determined by the T-junction crowd evacuation dynamics model, DmaxTo set the maximum density, a and b are the horizontal and vertical coordinates of the vertical and horizontal density distribution center, respectively, obtained based on street parameters, and σ is the amount of relaxation.
5. The method for calibrating high-risk areas of T-junctions based on street width ratio as claimed in claim 1, wherein the crowd evacuation high-risk areas have crowd density greater than a set density maximum value DmaxThe area of (a).
6. The method for calibrating high-risk areas of T-junctions according to claim 1, wherein the influence of different street width ratios on crowd evacuation density is obtained through simulation of T-junction crowd evacuation dynamics models under different street parameters.
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