CN102938208A - On-line traffic bottleneck predictive control method based on field programmable gate array (FPGA) and improved Payne-Whitham model - Google Patents

Abstract

The invention discloses an on-line traffic bottleneck control method based on a field programmable gate array (FPGA) and an improved Payne-Whitham model and aims to solve the technical problem that existing methods can not perform on-line predictive regulating and controlling for traffic bottlenecks in actual expressways or blocked roads. According to the on-line traffic bottleneck predictive control method, the Payne-Whitham model is improved, a variable information display board is integrated into the Payne-Whitham model, a whole predictive analysis is performed for the expressways or the blocked roads through the improved Payne-Whitham model based on the FPGA platform, the road bottleneck is found out according to defined state variables, then control schemes of junction control and the variable information display board are provided, the control schemes can be taken into prediction models according to priority levels, a reasonable control scheme can be found out, the on-line control for the traffic bottleneck can be achieved, and thereby the traffic bottleneck in the expressways or the blocked roads can be effectively controlled.

Description

Online traffic bottlenecks forecast Control Algorithm based on FPGA and improvement Payne-Whitham model

Technical field

The present invention relates to a kind of FPGA control method, particularly a kind of online traffic bottlenecks forecast Control Algorithm based on FPGA and improvement Payne-Whitham macroscopic traffic flow.

Background technology

The major issue that traffic congestion has become the common focus of paying close attention in countries in the world and has been badly in need of solving, the traffic bottlenecks problem is one of main problem of the restriction magnitude of traffic flow, because the restriction of hardware facility or the impact of emergency situations, so that some highway sections become the bottleneck of whole road, as not regulating and control, then can accelerate the flow accumulation of bottleneck road, traffic is worsened, get congestion, even cause whole transportation network paralysis.

At present, the mode of freeway traffic regulation and control only has the variable information display board to carry out speed restriction and the circle mouth is controlled two kinds, in order effectively to relieve traffic congestion, improve the service efficiency of highway, often uses the information display board as the means of transport information issue and control; Usually, information display board and variable speed-limit sign are as the important information issue of intelligent transportation system, carry out Long-distance Control by Surveillance center's computing machine by communication network, transmission also shows various graph text informations, in time issue different road surfaces situation and all kinds of transport information of different sections of highway to the driver, carry out the publicity of traffic law, traffic knowledge, reach and reduce the impact that the highway reappearance is blocked, reduced the non-reappearance accident of highway, improve traffic safety; Of document " Hai Yilatibala carries; the Expressway Information display board arranges Discussion on Technology; the land bridge visual field; in October, 2010; 139-140 ", the mechanism that arranges of information display board system is: (1) sensor information collection and disposal system, (2) information display board information provide, (3) communication system, (4) central control system; The setting of information display board should be from the angle of whole traffic navigation system Construction, takes into full account the related of leading and control, takes the comprehensive benefit of surface road and overpass into consideration, formulates the leading scheme of globality, rationality, high efficiency; The information display board adopts different forms according to the different of the place that arranges and purpose; A kind of being mounted on the main line carries out that main line is induced and outlet is induced, and shows the traffic in highway section, the place ahead such as unimpeded, crowded, delay etc. with character style, thereby makes the driver can turn to surface road, avoids crowded the district; Another kind is installed near the ring road entrance, and the queue length of ring road porch and crowded prediction case are reported to the driver, also can be shown to the traffic conditions on the contiguous main line driver on the ring road entrance, thereby induce for they provide reasonably; In addition, in the situation that the road congestion risk is very high, can control the input of circle mouth, even force some vehicles to roll highway away from road circle mouth, to avoid the generation of blocking up; Yet, these schemes, with the super expressway entrance induce, the road main line is induced, the road way outlet is only induced and demarcated according to information requirement, there is not the organic phase combination, particularly the demonstration information of information display board is not according to macro traffic model prediction output automatic setting, be difficult to from the angle of the overall situation bottleneck road be carried out traffic control, the highway section that the result of regulation and control regulates and control often is unimpeded, but the traffic jam phenomenon occurs in non-regulation and control highway section.

In order to analyse in depth traffic system, a large amount of scholar's research traffic flow model wherein adopt the both macro and micro model analysis traffic characteristics person of hydromechanical viewpoint foundation in the majority both at home and abroad; In macroscopic traffic flow, traffic flow is regarded as the compressible continuous fluid medium that is comprised of a large amount of vehicles, and the average behavior of research vehicle collective, the individual character of single unit vehicle do not highlight; Macroscopic traffic flow is studied the equation that they satisfy with average density ρ, average velocity v and the flow q portrayal traffic flow of vehicle; Macromodel can be portrayed the collective behavior of traffic flow better, thereby for designing effective traffic control strategy, simulation and estimating that the traffic engineering problems such as effect of road geometry modification provide foundation; Aspect numerical evaluation, simulation Macro-traffic Flow required time study with institute that number of vehicles has nothing to do in the traffic system, with research road, numerical method choose and the discrete steps of middle space x, time t relevant.So macroscopic traffic flow is suitable for processing the traffic flow problem of the traffic system that a large amount of vehicles form; This class model is used for discussing the traffic behavior of blocked road by Most scholars in the world.

Find through retrieval, number of patent application 200810117959.8, open day on January 14th, 2009, record " a kind of control method and device at the traffic bottlenecks place ", the method is by arranging buffer zone, the rule of travelling of vehicle in the restriction buffer zone, vehicle number in the control buffer zone comes vehicle flowrate is controlled, have certain effect, but the method fails to point out how to detect traffic bottlenecks, in the real road, traffic bottlenecks are not what fix, each highway section may become traffic bottlenecks, and therefore, the method has limitation; Document " Ceng Guangxiang. the analysis of road traffic bottleneck, control and simulation; 2010; Guangxi University's Master's thesis " take the LWR model as the basis, analyzed the disturbance of the one-way traffic bottleneck generation of road minimizing generation, and propose based on this in pedestrian traffic, to improve the method for traffic bottlenecks, and the harm that the road traffic bottleneck causes or economic loss are larger, and the document is not analyzed its solution;

In highway or blocked road, can only control to regulate traffic by variable information display board or circle mouth, and each highway section all might become traffic bottlenecks, present research mostly just produces the analysis of reason to traffic bottlenecks or only is how to solve specific road section traffic bottlenecks problem, just emulation is carried out in the traffic highway section, bottleneck forecasting and traffic control are not combined real-time monitoring is carried out in the traffic highway section, and mostly operate in computing machine and with upper mounting plate, bulky, these researchs exist and to be difficult to the technical matters of in the highway of reality or blocked road traffic bottlenecks being carried out on-line prediction and regulation and control.

Summary of the invention

Be difficult to the technological deficiency of in the highway of reality or blocked road, traffic bottlenecks being carried out the on-line prediction regulation and control in order to overcome existing method, the invention provides a kind of online traffic bottlenecks control method based on FPGA and improvement Payne-Whitham model, the method is improved the Payne-Whitham model, the variable information display board is dissolved in the Payne-Whitham model, by improved Payne-Whitham model highway or blocked road integral body are carried out forecast analysis based on the FPGA platform, state variable according to definition finds the road bottleneck, and then provide the control program of circle mouth control and variable information display board, and these control programs are according to priority brought into forecast model, find rational control program, thereby traffic bottlenecks are carried out On-line Control, can effectively solve existing scheme and be difficult to the technical matters of in the highway of reality or blocked road, traffic bottlenecks being carried out the on-line prediction regulation and control.

The technical solution adopted for the present invention to solve the technical problems: the online traffic bottlenecks forecast Control Algorithm based on FPGA and improvement Payne-Whitham model is characterized in may further comprise the steps:

Step 1, according to the Payne-Whitham model:

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\frac{V_e\left(\mathrm{\ρ}\right)-v}{T}-\frac{c^2\left(\mathrm{\ρ}\right)}{\mathrm{\ρ}}\frac{\∂\mathrm{\ρ}}{\∂x}\end{array}\right.$

In the formula, t is the time, and x is the distance with emulation road starting point, ρ is traffic flow density and is the function of x, t, ρ=ρ (x, t), v is vehicle average velocity and is the function of x, t, v=v (x, t), π [r (x, t), s (x, t)] be because the rate of change of the density function that the vehicle flowrate that the circle mouth enters or rolls away from causes, r (x, t)=r ₀(x, t)-r _qThe vehicle flowrate that (x, t) entered by the circle mouth for the t moment, x highway section, s (x, t)=s ₀(x, t)+s _qThe vehicle flowrate that (x, t) rolled away from by the circle mouth for the t moment, x highway section, r ₀(x, t), s ₀(x, t) for to sail the normal vehicle flowrate that rolls away from into by the circle mouth, r _q(x, t) is circle mouth control No entry flow reduction amount that the expressway causes, s _qThe flow increment that (x, t) forces outgoing vehicles to cause for the control of circle mouth, V _e(ρ) be equivalent speed and with free stream velocity v _fRelevant with the traffic flow density p, T is constant, and c (ρ) can be taken as different forms, and full application form symbol definition is identical;

Variable display board display speed is incorporated the Payne-Whitham model, with variable display board display speed v _IndReplace the free stream velocity v in the equivalent speed _f, the Payne-Whitham model that is improved is as follows:

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\frac{V_e(\mathrm{\ρ},v_{\mathrm{ind}})-v}{T}-\frac{c^2\left(\mathrm{\ρ}\right)}{\mathrm{\ρ}}\frac{\∂\mathrm{\ρ}}{\∂x}\end{array}\right.$

Step 2, definition two new state variable η (x, t), σ (x, t) work as state variable When being tending towards infinite, that represent traffic density is tending towards saturated traffic density, produces traffic congestion, works as state variable

When being tending towards infinite, representing vehicle average velocity and go to zero, produce traffic congestion;

In the formula, ρ _JamTraffic flow density when occurring blocking for traffic;

Step 3, a. represent differential term and omit higher order term with difference scheme according to the improved Payne-Whitham model that step 1 obtains, obtain:

$\frac{\∂\mathrm{\ρ}}{\∂t}=\frac{\mathrm{\ρ}(x,t+\mathrm{\ξ})-\mathrm{\ρ}(x,t)}{\mathrm{\ξ}}+o\left(\mathrm{\ξ}\right)=\frac{{\mathrm{\ρ}}_i^{n+1}-{\mathrm{\ρ}}_i^n}{\mathrm{\ξ}}$

$\frac{\∂\mathrm{\ρ}}{\∂x}=\frac{\mathrm{\ρ}(x+h,t)-\mathrm{\ρ}(x,t)}{h}+o\left(h\right)=\frac{{\mathrm{\ρ}}_{i+1}^n-{\mathrm{\ρ}}_i^n}{h}$

$\frac{\∂v}{\∂t}=\frac{v(x,t+\mathrm{\ξ})-v(x,t)}{\mathrm{\ξ}}+o\left(\mathrm{\ξ}\right)=\frac{v_i^{n+1}-v_i^n}{\mathrm{\ξ}}$

$\frac{\∂v}{\∂x}=\frac{v(x+h,t)-v(x,t)}{h}+o\left(h\right)=\frac{v_{i+1}^n-v_i^n}{h}$

In the formula: ξ is the differential of t, and h is the differential of x, and o (ξ) is that the high-order of ξ is infinitely small, and o (h) is that the high-order of h is infinitely small, and road is divided into a plurality of highway sections, and each road section length is h, and the sampling period is ξ,

Be i highway section in the average density of [n ξ, (n+1) ξ] interior vehicle,

Be that i highway section is at the average velocity of [n ξ, (n+1) ξ] vehicle; The difference form of the Payne-Whitham model that is improved is:

$\left\{\begin{array}{c}{\mathrm{\ρ}}_i^{n+1}=\mathrm{\ξ\π}(r_i^n,s_i^n)-\frac{\mathrm{\ξ}}{h}[v_i^n({\mathrm{\ρ}}_{i+1}^n-{\mathrm{\ρ}}_i^n)+{\mathrm{\ρ}}_i^n(v_{i+1}^n-v_i^n)]+{\mathrm{\ρ}}_i^n\\ v_i^{n+1}=v_i^n+\mathrm{\ξ}\{\frac{V_e[{\mathrm{\ρ}}_i^n,v_{\mathrm{ind}}(i,n)]-v_i^n}{T}-\frac{c^2\left({\mathrm{\ρ}}_i^n\right)({\mathrm{\ρ}}_{i+1}^n-{\mathrm{\ρ}}_i^n)}{{\mathrm{\ρ}}_i^{n}h}-\frac{v_i^n(v_{i+1}^n-v_i^n)}{h}\}\end{array}\right.$

In the formula: Represent the vehicle flowrate that i highway section entered by the circle mouth at [n ξ, (n+1) ξ], Represent the vehicle flowrate that i highway section rolled away from by the circle mouth at [n ξ, (n+1) ξ], v _IndI highway section of (i, n) expression variable display board display speed in [n ξ, (n+1) ξ];

B. set up the equivalent speed model: $V_e[{\mathrm{\ρ}}_i^n,v_{\mathrm{ind}}(i,n)]=\frac{v_{\mathrm{ind}}(i,n)(1-{\mathrm{\ρ}}_i^n/{\mathrm{\ρ}}_{\mathrm{jam}})}{1+E{({\mathrm{\ρ}}_i^n/{\mathrm{\ρ}}_{\mathrm{jam}})}^4},$

E is constant in the formula;

C. in FPGA, write based on the PREDICTIVE CONTROL module of improving the Payne-Whitham model, as shown in Figure 1, comprise data reception module, control program is selected and the data allocations module, computing module 1-computing module N, synchronization module, data outputting module, road is divided into N highway section, the corresponding computing module in each highway section, the forecasting traffic flow computing module of computing module 1-computing module N for using the floating point arithmetic device to combine according to the Difference Method of aforementioned partial differential equations among the figure, the data flow of PREDICTIVE CONTROL module is: traffic flow data (the traffic flow density in each highway section that data reception module reception host computer transmits, vehicle average velocity), then passing to control program selects and the data allocations module, control program is selected and the data allocations module is determined traffic bottlenecks according to these data, and formulation regulation and control scheme, then with enable signal, control program and traffic flow data are passed to each computing module, each computing module receives behind the enable signal simultaneously to be predicted and the result is deposited in register traffic flow density and vehicle average velocity, modules is passed to synchronization module to calculating end signal separately after calculating and finishing, synchronization module is finished at all computing modules and is calculated predicting the outcome of rear transmitted signal informing case selection and data allocations module reception traffic flow data, proceed prediction, at predicted time T _cIn, if traffic bottlenecks are removed, then adopt this scheme that actual traffic is regulated and control, if can not remove, control program select and the data allocations module according to traffic flow data and last time regulation and control scheme formulate new regulation and control scheme, and traffic flow data and regulation and control scheme are passed to each computing module, re-start prediction, repeatedly predict and adjust regulation and control scheme after select a suitable regulation and control scheme output that traffic bottlenecks are regulated and control, and the highway section of having regulated and control is in time T _cIn no longer regulate and control, then continue traffic is predicted, seek new traffic bottlenecks, and control;

Determine traffic bottlenecks in the described step 3 and to its method of controlling be: find the solution || η (x, t) || _∞=η _m(x _m, t _m), work as η _mGreater than given threshold value η _MThe time, highway section x is described _mAt t _mConstantly will become traffic bottlenecks, then at t _m-T ₀The moment is to the x of vehicle heading _mFront and back enter, go out the circle mouth and the variable information display board carries out speed limit (highway section, bottleneck road the place ahead Speed Reduction, highway section, rear Speed improving), restriction enters bottleneck road even bottleneck road is rolled in pressure away from; Or find the solution ‖ σ (x, t) || _∞=σ _m(x _m, t _m), work as σ _mGreater than given threshold value σ _MThe time, highway section x is described _mAt t _mConstantly will become traffic bottlenecks, then at t _m-T ₁The moment is to the x of vehicle heading _mFront and back go out, enter the circle mouth and the variable information display board carries out speed limit (highway section, bottleneck road the place ahead Speed Reduction, highway section, rear Speed improving), restriction enters bottleneck road even bottleneck road is rolled in pressure away from;

T in the formula ₀, T ₁For time of applying in advance control so that || η (x, t) || _∞=η _m(x _m, t _m)≤η _M, ‖ σ (x, t) || _∞=σ _m(x _m, t _m)≤σ _M, η _M, σ _MBe respectively the positive number that makes according to roading density maximum saturation, friction;

The priority principle of control is: 1. at first adjust highway section speed by the variable information display board, the car speed that enters bottleneck road is reduced, the car speed that rolls bottleneck road away from improves, 2. in the time of only can not reaching the control index by variable information display board adjustment highway section speed, then enter the bottleneck road flow by circle mouth restriction and adjust highway section speed with the variable information display board and control simultaneously, 3. adjust highway section speed and control simultaneously can not reach control and require the time when enter bottleneck road flow and variable information display board by circle mouth restriction, be controlled at interrupting time by the circle mouth and force part highway section vehicle to roll road away from, simultaneously circle mouth restriction is entered the bottleneck road vehicle flowrate and the variable information display board is adjusted highway section speed to reach the control index request.

The invention has the beneficial effects as follows: the present invention is by improving the equivalent speed in the Payne-Whitham model, variable information display board display speed is dissolved in the equivalent speed, by improved Payne-Whitham model highway or blocked road integral body are carried out forecast analysis based on the FPGA platform, state variable according to definition finds the road bottleneck, and then provide the control program of circle mouth control and variable information display board, and these control programs are according to priority brought into forecast model, guaranteeing that regulation and control scheme is practical, and then solve existing method and be difficult to the technical matters of in the highway of reality or blocked road, traffic bottlenecks being carried out the on-line prediction regulation and control.

Description of drawings

Fig. 1 is the FPGA realization block diagram that the present invention is based on FPGA and improve the online traffic bottlenecks forecast Control Algorithm of Payne-Whitham model;

Fig. 2 is the control method process flow diagram that the present invention is based on FPGA and improve the online traffic bottlenecks forecast Control Algorithm of Payne-Whitham model.

Embodiment

Describe the present invention in detail with reference to accompanying drawing 1,2.

Control method process flow diagram of the present invention as shown in Figure 2, in the situation that there are not traffic bottlenecks to produce, control program is that variable display board shows the free stream velocity that road allows, the control of circle mouth does not limit input and output, by traffic flow density, vehicle average velocity, variable display board display speed and circle mouth control program traffic flow density and the vehicle average velocity prediction a period of time T to each highway section _c(T _cGet T ₀, T ₁Between large value), and judge whether to occur traffic bottlenecks, if traffic bottlenecks do not occur, then use current control program to regulate and control, then adjust variable display board display speed and circle mouth control program according to aforementioned priority principle if there is bottleneck, and continue prediction a period of time T _cIf traffic bottlenecks can not be removed, then continue to adjust control program, until find a kind of control program can the transport solution bottleneck problem, and adopt this scheme that traffic bottlenecks are controlled, its method detailed is as follows:

1. according to the Payne-Whitham model:

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\frac{V_e\left(\mathrm{\ρ}\right)-v}{T}-\frac{c^2\left(\mathrm{\ρ}\right)}{\mathrm{\ρ}}\frac{\∂\mathrm{\ρ}}{\∂x}\end{array}\right.$

In the formula, t is the time, and x is the distance with emulation road starting point, ρ is traffic flow density and is the function of x, t, ρ=ρ (x, t), v is vehicle average velocity and is the function of x, t, v=v (x, t), π [r (x, t), s (x, t)] be because the rate of change of the density function that the vehicle flowrate that the circle mouth enters or rolls away from causes, r (x, t)=r ₀(x, t)-r _qThe vehicle flowrate that (x, t) entered by the circle mouth for the t moment, x highway section, s (x, t)=s ₀(x, t)+s _qThe vehicle flowrate that (x, t) rolled away from by the circle mouth for the t moment, x highway section, r ₀(x, t), s ₀(x, t) for to sail the normal vehicle flowrate that rolls away from into by the circle mouth, r _q(x, t) is circle mouth control No entry flow reduction amount that the expressway causes, s _qThe flow increment that (x, t) forces outgoing vehicles to cause for the control of circle mouth, V _e(ρ) be equivalent speed and with free stream velocity v _fRelevant with the traffic flow density p, T is constant, and c (ρ) can be taken as different forms, and full application form symbol definition is identical;

Variable display board display speed is incorporated the Payne-Whitham model, with variable display board display speed v _IndReplace the free stream velocity v in the equivalent speed _f, the Payne-Whitham model that is improved is as follows:

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\frac{V_e(\mathrm{\ρ},v_{\mathrm{ind}})-v}{T}-\frac{c^2\left(\mathrm{\ρ}\right)}{\mathrm{\ρ}}\frac{\∂\mathrm{\ρ}}{\∂x}\end{array}\right.$

2. define two new state variable η (x, t), σ (x, t), work as state variable

When being tending towards infinite, that represent traffic density is tending towards saturated traffic density, produces traffic congestion, works as state variable

When being tending towards infinite, representing vehicle average velocity and go to zero, produce traffic congestion;

In the formula, ρ _JamTraffic flow density when occurring blocking for traffic;

3. according to the improved Payne-Whitham model that obtains in 1, represent differential term and omit higher order term with difference scheme, obtain:

$\frac{\∂\mathrm{\ρ}}{\∂t}=\frac{\mathrm{\ρ}(x,t+\mathrm{\ξ})-\mathrm{\ρ}(x,t)}{\mathrm{\ξ}}+o\left(\mathrm{\ξ}\right)=\frac{{\mathrm{\ρ}}_i^{n+1}-{\mathrm{\ρ}}_i^n}{\mathrm{\ξ}}$

$\frac{\∂\mathrm{\ρ}}{\∂x}=\frac{\mathrm{\ρ}(x+h,t)-\mathrm{\ρ}(x,t)}{h}+o\left(h\right)=\frac{{\mathrm{\ρ}}_{i+1}^n-{\mathrm{\ρ}}_i^n}{h}$

$\frac{\∂v}{\∂t}=\frac{v(x,t+\mathrm{\ξ})-v(x,t)}{\mathrm{\ξ}}+o\left(\mathrm{\ξ}\right)=\frac{v_i^{n+1}-v_i^n}{\mathrm{\ξ}}$

$\frac{\∂v}{\∂x}=\frac{v(x+h,t)-v(x,t)}{h}+o\left(h\right)=\frac{v_{i+1}^n-v_i^n}{h}$

In the formula: ξ is the differential of t, and h is the differential of x, and o (ξ) is that the high-order of ξ is infinitely small, and o (h) is that the high-order of h is infinitely small, and road is divided into a plurality of highway sections, and each road section length is h, and the sampling period is ξ,

Be i highway section in the average density of [n ξ, (n+1) ξ] interior vehicle,

Be that i highway section is at the average velocity of [n ξ, (n+1) ξ] vehicle; The difference form of the Payne-Whitham model that is improved is:

$\left\{\begin{array}{c}{\mathrm{\ρ}}_i^{n+1}=\mathrm{\ξ\π}(r_i^n,s_i^n)-\frac{\mathrm{\ξ}}{h}[v_i^n({\mathrm{\ρ}}_{i+1}^n-{\mathrm{\ρ}}_i^n)+{\mathrm{\ρ}}_i^n(v_{i+1}^n-v_i^n)]+{\mathrm{\ρ}}_i^n\\ v_i^{n+1}=v_i^n+\mathrm{\ξ}\{\frac{V_e[{\mathrm{\ρ}}_i^n,v_{\mathrm{ind}}(i,n)]-v_i^n}{T}-\frac{c^2\left({\mathrm{\ρ}}_i^n\right)({\mathrm{\ρ}}_{i+1}^n-{\mathrm{\ρ}}_i^n)}{{\mathrm{\ρ}}_i^{n}h}-\frac{v_i^n(v_{i+1}^n-v_i^n)}{h}\}\end{array}\right.$

In the formula: Represent the vehicle flowrate that i highway section entered by the circle mouth at [n ξ, (n+1) ξ],

Represent the vehicle flowrate that i highway section rolled away from by the circle mouth at [n ξ, (n+1) ξ], v _IndI highway section of (i, n) expression variable display board display speed in [n ξ, (n+1) ξ];

4. set up the equivalent speed model: $V_e[{\mathrm{\ρ}}_i^n,v_{\mathrm{ind}}(i,n)]=\frac{v_{\mathrm{ind}}(i,n)(1-{\mathrm{\ρ}}_i^n/{\mathrm{\ρ}}_{\mathrm{jam}})}{1+E{({\mathrm{\ρ}}_i^n/{\mathrm{\ρ}}_{\mathrm{jam}})}^4},$

E is constant in the formula;

5. in FPGA, write based on the PREDICTIVE CONTROL module of improving the Payne-Whitham model, the traffic flow situation is predicted, find traffic bottlenecks, traffic bottlenecks are controlled, in the present embodiment, the FPGA chip is selected the EP4CE115F29C8 chip of altera corp, communicate by letter by wireless GPRS with other road information acquisition module (host computer), road is divided into 40 highway sections, as shown in Figure 1, comprise data reception module, control program is selected and the data allocations module, N gets 40 among the computing module 1-computing module 40(embodiment), synchronization module, data outputting module, the forecasting traffic flow computing module of computing module 1-computing module 40 for using the floating point arithmetic device to combine according to the Difference Method of aforementioned partial differential equations, the data flow of PREDICTIVE CONTROL module is: traffic flow data (the traffic flow density in each highway section that data reception module reception host computer transmits, vehicle average velocity), then passing to control program selects and the data allocations module, control program is selected and the data allocations module is determined traffic bottlenecks according to these data, and formulation regulation and control scheme, then with enable signal, control program and traffic flow data are passed to each computing module, each computing module receives behind the enable signal simultaneously to be predicted and the result is deposited in register traffic flow density and vehicle average velocity, modules is passed to synchronization module to calculating end signal separately after calculating and finishing, synchronization module is finished at all computing modules and is calculated predicting the outcome of rear transmitted signal informing case selection and data allocations module reception traffic flow data, proceed prediction, at predicted time T _cIn, if traffic bottlenecks are removed, then adopt this scheme that actual traffic is regulated and control, if can not remove, control program select and the data allocations module according to traffic flow data and last time regulation and control scheme formulate new regulation and control scheme, and traffic flow data and regulation and control scheme are passed to each computing module, re-start prediction, repeatedly predict and adjust regulation and control scheme after select a suitable regulation and control scheme output that traffic bottlenecks are regulated and control, and the highway section of having regulated and control is in time T _cIn no longer regulate and control, then continue traffic is predicted, seek new traffic bottlenecks, and control;

6. seek traffic bottlenecks in above-mentioned 5 and to the method that bottleneck is regulated and control be: find the solution || η (x, t) || _∞=η _m(x _m, t _m), work as η _mGreater than given threshold value η _MThe time, highway section x is described _mAt t _mConstantly will become traffic bottlenecks, then at t _m-T ₀The moment is to the x of vehicle heading _mFront and back enter, go out the circle mouth and the variable information display board carries out speed limit (highway section, bottleneck road the place ahead Speed Reduction, highway section, rear Speed improving), restriction enters bottleneck road even bottleneck road is rolled in pressure away from; Or find the solution ‖ σ (x, t) || _∞=σ _m(x _m, t _m), work as σ _mGreater than given threshold value σ _MThe time, highway section x is described _mAt t _mConstantly will become traffic bottlenecks, then at t _m-T ₁The moment is to the x of vehicle heading _mFront and back go out, enter the circle mouth and the variable information display board carries out speed limit (highway section, bottleneck road the place ahead Speed Reduction, highway section, rear Speed improving), restriction enters bottleneck road even bottleneck road is rolled in pressure away from;

T in the formula ₀, T ₁For time of applying in advance control so that || η (x, t) || _∞=η _m(x _m, t _m)≤η _M, ‖ σ (x, t) || _∞=σ _m(x _m, t _m)≤σ _M, η _M, σ _MBe respectively the positive number that makes according to roading density maximum saturation, friction;

The priority principle of control is: 1. at first adjust highway section speed by the variable information display board, the car speed that enters bottleneck road is reduced, the car speed that rolls bottleneck road away from improves, 2. in the time of only can not reaching the control index by variable information display board adjustment highway section speed, then enter the bottleneck road flow by circle mouth restriction and adjust highway section speed with the variable information display board and control simultaneously, 3. adjust highway section speed and control simultaneously can not reach control and require the time when enter bottleneck road flow and variable information display board by circle mouth restriction, be controlled at interrupting time by the circle mouth and force part highway section vehicle to roll road away from, simultaneously circle mouth restriction is entered the bottleneck road vehicle flowrate and the variable information display board is adjusted highway section speed to reach the control index request.

Claims (1)

1. one kind based on FPGA and improve the online traffic bottlenecks forecast Control Algorithm of Payne-Whitham model, it is characterized in that may further comprise the steps:

Step 1, according to the Payne-Whitham model:

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\frac{V_e\left(\mathrm{\ρ}\right)-v}{T}-\frac{c^2\left(\mathrm{\ρ}\right)}{\mathrm{\ρ}}\frac{\∂\mathrm{\ρ}}{\∂x}\end{array}\right.$

In the formula, t is the time, and x is the distance with emulation road starting point, ρ is traffic flow density and is the function of x, t, ρ=ρ (x, t), v is vehicle average velocity and is the function of x, t, v=v (x, t), π [r (x, t), s (x, t)] be because the rate of change of the density function that the vehicle flowrate that the circle mouth enters or rolls away from causes, r (x, t)=r ₀(x, t)-r _qThe vehicle flowrate that (x, t) entered by the circle mouth for the t moment, x highway section, s (x, t)=s ₀(x, t)+s _qThe vehicle flowrate that (x, t) rolled away from by the circle mouth for the t moment, x highway section, r ₀(x, t), s ₀(x, t) for to sail the normal vehicle flowrate that rolls away from into by the circle mouth, r _q(x, t) is circle mouth control No entry flow reduction amount that the expressway causes, s _qThe flow increment that (x, t) forces outgoing vehicles to cause for the control of circle mouth, V _e(ρ) be equivalent speed and with free stream velocity v _fRelevant with the traffic flow density p, T is constant, and c (ρ) can be taken as different forms, and full application form symbol definition is identical;

Variable display board display speed is incorporated the Payne-Whitham model, with variable display board display speed v _IndReplace the free stream velocity v in the equivalent speed _f, the Payne-Whitham model that is improved is as follows:

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\frac{V_e(\mathrm{\ρ},v_{\mathrm{ind}})-v}{T}-\frac{c^2\left(\mathrm{\ρ}\right)}{\mathrm{\ρ}}\frac{\∂\mathrm{\ρ}}{\∂x}\end{array}\right.$

Step 2, definition two new state variable η (x, t), σ (x, t) work as state variable

When being tending towards infinite, that represent traffic density is tending towards saturated traffic density, produces traffic congestion, works as state variable

When being tending towards infinite, representing vehicle average velocity and go to zero, produce traffic congestion;

In the formula, ρ _JamTraffic flow density when occurring blocking for traffic;

Step 3, a. represent differential term and omit higher order term with difference scheme according to the improved Payne-Whitham model that step 1 obtains, obtain:

$\frac{\∂\mathrm{\ρ}}{\∂t}=\frac{\mathrm{\ρ}(x,t+\mathrm{\ξ})-\mathrm{\ρ}(x,t)}{\mathrm{\ξ}}+o\left(\mathrm{\ξ}\right)=\frac{{\mathrm{\ρ}}_i^{n+1}-{\mathrm{\ρ}}_i^n}{\mathrm{\ξ}}$

$\frac{\∂\mathrm{\ρ}}{\∂x}=\frac{\mathrm{\ρ}(x+h,t)-\mathrm{\ρ}(x,t)}{h}+o\left(h\right)=\frac{{\mathrm{\ρ}}_{i+1}^n-{\mathrm{\ρ}}_i^n}{h}$

$\frac{\∂v}{\∂t}=\frac{v(x,t+\mathrm{\ξ})-v(x,t)}{\mathrm{\ξ}}+o\left(\mathrm{\ξ}\right)=\frac{v_i^{n+1}-v_i^n}{\mathrm{\ξ}}$

$\frac{\∂v}{\∂x}=\frac{v(x+h,t)-v(x,t)}{h}+o\left(h\right)=\frac{v_{i+1}^n-v_i^n}{h}$

In the formula: ξ is the differential of t, and h is the differential of x, and o (ξ) is that the high-order of ξ is infinitely small, and o (h) is that the high-order of h is infinitely small, and road is divided into a plurality of highway sections, and each road section length is h, and the sampling period is ξ,

Be i highway section in the average density of [n ξ, (n+1) ξ] interior vehicle,

Be that i highway section is at the average velocity of [n ξ, (n+1) ξ] vehicle; The difference form of the Payne-Whitham model that is improved is:

$\left\{\begin{array}{c}{\mathrm{\ρ}}_i^{n+1}=\mathrm{\ξ\π}(r_i^n,s_i^n)-\frac{\mathrm{\ξ}}{h}[v_i^n({\mathrm{\ρ}}_{i+1}^n-{\mathrm{\ρ}}_i^n)+{\mathrm{\ρ}}_i^n(v_{i+1}^n-v_i^n)]+{\mathrm{\ρ}}_i^n\\ v_i^{n+1}=v_i^n+\mathrm{\ξ}\{\frac{V_e[{\mathrm{\ρ}}_i^n,v_{\mathrm{ind}}(i,n)]-v_i^n}{T}-\frac{c^2\left({\mathrm{\ρ}}_i^n\right)({\mathrm{\ρ}}_{i+1}^n-{\mathrm{\ρ}}_i^n)}{{\mathrm{\ρ}}_i^{n}h}-\frac{v_i^n(v_{i+1}^n-v_i^n)}{h}\}\end{array}\right.$

In the formula:

Represent the vehicle flowrate that i highway section entered by the circle mouth at [n ξ, (n+1) ξ],

Represent the vehicle flowrate that i highway section rolled away from by the circle mouth at [n ξ, (n+1) ξ], v _IndI highway section of (i, n) expression variable display board display speed in [n ξ, (n+1) ξ];

B. set up the equivalent speed model: $V_e[{\mathrm{\ρ}}_i^n,v_{\mathrm{ind}}(i,n)]=\frac{v_{\mathrm{ind}}(i,n)(1-{\mathrm{\ρ}}_i^n/{\mathrm{\ρ}}_{\mathrm{jam}})}{1+E{({\mathrm{\ρ}}_i^n/{\mathrm{\ρ}}_{\mathrm{jam}})}^4},$

E is constant in the formula;

C. in FPGA, write based on the PREDICTIVE CONTROL module of improving the Payne-Whitham model, comprise data reception module, control program is selected and the data allocations module, computing module 1-computing module N, synchronization module, data outputting module, road is divided into N highway section, the corresponding computing module in each highway section, the forecasting traffic flow computing module of computing module 1-computing module N for using the floating point arithmetic device to combine according to the Difference Method of aforementioned partial differential equations, the data flow of PREDICTIVE CONTROL module is: traffic flow data (the traffic flow density in each highway section that data reception module reception host computer transmits, vehicle average velocity), then passing to control program selects and the data allocations module, control program is selected and the data allocations module is determined traffic bottlenecks according to these data, and formulation regulation and control scheme, then with enable signal, control program and traffic flow data are passed to each computing module, each computing module receives behind the enable signal simultaneously to be predicted and the result is deposited in register traffic flow density and vehicle average velocity, modules is passed to synchronization module to calculating end signal separately after calculating and finishing, synchronization module is finished at all computing modules and is calculated predicting the outcome of rear transmitted signal informing case selection and data allocations module reception traffic flow data, proceed prediction, at predicted time T _cIn, if traffic bottlenecks are removed, then adopt this scheme that actual traffic is regulated and control, if can not remove, control program select and the data allocations module according to traffic flow data and last time regulation and control scheme formulate new regulation and control scheme, and traffic flow data and regulation and control scheme are passed to each computing module, re-start prediction, repeatedly predict and adjust regulation and control scheme after select a suitable regulation and control scheme output that traffic bottlenecks are regulated and control, and the highway section of having regulated and control is in time T _cIn no longer regulate and control, then continue traffic is predicted, seek new traffic bottlenecks, and control;

Determine traffic bottlenecks in the described step 3 and to its method of controlling be: find the solution || η (x, t) || _∞=η _m(x _m, t _m), work as η _mGreater than given threshold value η _MThe time, highway section x is described _mAt t _mConstantly will become traffic bottlenecks, then at t _m-T ₀The moment is to the x of vehicle heading _mFront and back enter, go out the circle mouth and the variable information display board carries out speed limit (highway section, bottleneck road the place ahead Speed Reduction, highway section, rear Speed improving), restriction enters bottleneck road even bottleneck road is rolled in pressure away from; Or find the solution ‖ σ (x, t) || _∞=σ _m(x _m, t _m), work as σ _mGreater than given threshold value σ _MThe time, highway section x is described _mAt t _mConstantly will become traffic bottlenecks, then at t _m-T ₁The moment is to the x of vehicle heading _mFront and back go out, enter the circle mouth and the variable information display board carries out speed limit (highway section, bottleneck road the place ahead Speed Reduction, highway section, rear Speed improving), restriction enters bottleneck road even bottleneck road is rolled in pressure away from;

T in the formula ₀, T ₁For time of applying in advance control so that || η (x, t) || _∞=η _m(x _m, t _m)≤η _M, ‖ σ (x, t) || _∞=σ _m(x _m, t _m)≤σ _M, η _M, σ _MBe respectively the positive number that makes according to roading density maximum saturation, friction;

The priority principle of control is: 1. at first adjust highway section speed by the variable information display board, the car speed that enters bottleneck road is reduced, the car speed that rolls bottleneck road away from improves, 2. in the time of only can not reaching the control index by variable information display board adjustment highway section speed, then enter the bottleneck road flow by circle mouth restriction and adjust highway section speed with the variable information display board and control simultaneously, 3. adjust highway section speed and control simultaneously can not reach control and require the time when enter bottleneck road flow and variable information display board by circle mouth restriction, be controlled at interrupting time by the circle mouth and force part highway section vehicle to roll road away from, simultaneously circle mouth restriction is entered the bottleneck road vehicle flowrate and the variable information display board is adjusted highway section speed to reach the control index request.

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