CN102945606A - On-line predictive control method of traffic bottlenecks based on field programmable gate array (FPGA) and improved Kerner-Konhauser model - Google Patents

Abstract

The invention discloses an on-line predictive control method of traffic bottlenecks based on an FPGA and an improved Kerner-Konhauser model, and aims to solve the technical problem that on-line predictive control is difficult to perform on the traffic bottlenecks on actual highways or blocked roads in the existing method. According to the method, the Kerner-Konhauser model is improved, a variable information display board is integrated into the Kerner-Konhauser model, predictive analysis is performed on highways or blocked roads based on an FPGA platform and the improved Kerner-Konhauser model, the traffic bottlenecks are found according to a defined state variable, and then control schemes of ramp control and the variable information display board are provided and taken to prediction models according to priority to find reasonable control schemes to perform on-line control on the traffic bottlenecks, so that the traffic bottlenecks on the actual highways or blocked roads can be effectively controlled.

Description

Online traffic bottlenecks forecast Control Algorithm based on FPGA and improvement Kerner-Konhauser models

Technical field

The present invention relates to a kind of FPGA control methods, more particularly to a kind of online traffic bottlenecks forecast Control Algorithm based on FPGA and improvement Kerner-Konhauser macroscopic traffic flows.

Background technology

Traffic congestion has turned into the common focus of attention in countries in the world and has been badly in need of the major issue of solution, traffic bottlenecks problem is to restrict one of main problem of the magnitude of traffic flow, due to the limitation or the influence of emergency situations of hardware facility, so that some sections turn into the bottleneck of whole road, such as without regulation and control, then it can accelerate the fluid accumulation of bottleneck road, deteriorate traffic, get congestion, even result in whole transportation network paralysis.

At present, the mode of freeway traffic regulation and control only has variable information display board to carry out two kinds of rate limitation and circle mouthful control, and in order to effectively relieve traffic congestion, improve the service efficiency of highway, normal use information display board is used as Traffic information demonstration and the means of control；Generally, presentation of information board and variable speed-limit sign are issued as the important information of intelligent transportation system, remote control is carried out by communication network by Surveillance center's computer, transmit and show various graph text informations, issue the different surface conditions and all kinds of transport information of different sections of highway in time to driver, traffic law, the publicity of Traffic knowledge are carried out, the influence for reducing highway reappearance obstruction, reducing the non-reappearance accident of highway is reached, improves traffic safety；Such as document, " Hai Yilatibala is carried, and Expressway Information display board sets Discussion on Technology, and the land bridge visual field, in October, 2010,139-140 " is described, and the setting mechanism of presentation of information board system is：(1) sensor information is collected and processing system, the offer of (2) presentation of information board information, (3) communication system, (4) central control system；Setting for presentation of information board should take into full account associating for leading and control, take the comprehensive benefit of surface road and overpass, formulation globality, reasonability, the leading scheme of high efficiency into consideration from the angle of whole traffic navigation system Construction；Presentation of information board uses different forms according to the difference in the place and purpose that set；One kind is mounted on main line, carries out main line induction and outlet induction, is shown for example unimpeded, crowded, delay of the traffic in front section etc. with character style, so that driver can turn to surface road, is avoided crowded area；Another to be arranged on ring road entrance, queue length and crowded prediction case ring road porch are reported to driver, the traffic conditions on neighbouring main line can be also shown to the driver on ring road entrance, reasonably be induced so as to be provided for them；In addition, in the case where road congestion risk is very high, circle mouthful input can be controlled, or even some vehicles are forced to roll highway away from road circle mouthful, to avoid congestion；But, these schemes, the induction of super expressway entrance, the induction of road main line, the induction of road way outlet are demarcated only in accordance with information requirement, there is no organic phase combination, particularly the display information of presentation of information board is not according to the automatic setting of macro traffic model prediction output, it is difficult to carry out bottleneck road traffic control from global angle, the results of regulation and control is often that the section of regulation and control is unimpeded, but traffic jam phenomenon occurs for non-regulation and control section.

In order to analyse in depth traffic system, domestic and international a large amount of scholar's research traffic flow models, wherein the both macro and micro model analysis traffic characteristics person set up using hydromechanical viewpoint is in the majority；In macroscopic traffic flow, traffic flow is considered as the compressible continuous fluid medium being made up of a large amount of vehicles, and the average behavior of research vehicle collective, the individual character of single unit vehicle are not highlighted；Macroscopic traffic flow portrays traffic flow with the averag density ρ, average speed v and flow q of vehicle, studies the equation that they are met；Macromodel can preferably portray the collective behavior of traffic flow, so that the traffic engineering problem such as effect to design effective traffic control strategy, simulation and estimation road geometry modification provides foundation；It is unrelated with number of vehicles in studied traffic system the time required to simulation Macro-traffic Flow in terms of numerical computations, with studied road, numerical method choose and its hollow x, time t discrete steps are relevant.So, macroscopic traffic flow is more suited to handle the traffic flow problem of the traffic system of a large amount of vehicle compositions；This class model is used for discussing the traffic behavior of blocked road by Most scholars in the world.

Found by retrieval, number of patent application 200810117959.8, publication date on January 14th, 2009, record " a kind of control method and device at traffic bottlenecks ", this method is by setting buffering area, limit the traveling rule of vehicle in buffering area, the vehicle number in buffering area is controlled to be controlled vehicle flowrate, with certain effect, but this method could not point out how to detect in traffic bottlenecks, real road, traffic bottlenecks are not fixed, each section is likely to become traffic bottlenecks, and therefore, this method has limitation；Document " analysis, control and the simulation of Zeng Guangxiang road traffic bottlenecks; 2010; Guangxi University's Master's thesis " based on LWR models, analyze road and reduce the disturbance that the one-way traffic bottleneck produced is produced, and propose to improve the method for traffic bottlenecks in pedestrian traffic based on this, and the harm or economic loss that road traffic bottleneck is caused are bigger, the document does not analyze its solution；

In highway or blocked road, traffic can only be adjusted by variable information display board or circle mouthful control, and each section is likely to turn into traffic bottlenecks, most simply to the traffic bottlenecks producing cause analysis of current research is only how to solve the problems, such as specific road section traffic bottlenecks, simply the intensive traffic section is emulated, bottleneck forecasting and traffic control are not combined real-time monitoring is carried out to the intensive traffic section, and mostly operate in computer and its with upper mounting plate, it is bulky, there is the technical problem for being difficult to that in actual highway or blocked road traffic bottlenecks are carried out with on-line prediction and regulation and control in these researchs.

The content of the invention

The technological deficiency that in actual highway or blocked road traffic bottlenecks are carried out with on-line prediction regulation and control in order to overcome existing method to be difficult to, the present invention provides a kind of online traffic bottlenecks control method based on FPGA and improvement Kerner-Konhauser models, this method is improved to Kerner-Konhauser models, variable information display board is dissolved into Kerner-Konhauser models, analysis is integrally predicted to highway or blocked road by improved Kerner-Konhauser models based on FPGA platform, road bottleneck is found according to the state variable of definition, and then provide the control program of circle mouthful control and variable information display board, and these control programs are according to priority brought into forecast model, find rational control program, so as to carry out On-line Control to traffic bottlenecks, can effectively solve the technical problem that existing scheme is difficult to traffic bottlenecks be carried out in actual highway or blocked road on-line prediction regulation and control.

The technical solution adopted for the present invention to solve the technical problems：Online traffic bottlenecks forecast Control Algorithm based on FPGA and improvement Kerner-Konhauser models, is characterized in comprising the following steps：

Step 1: according to Kerner-Konhauser models：

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\frac{V_e\left(\mathrm{\ρ}\right)-v}{T}-\frac{c_0^2}{\mathrm{\ρ}}\frac{\∂v}{\∂x}+\frac{\mathrm{\μ}}{\mathrm{\ρ}}\frac{{\∂}^{2}v}{{\∂x}^2}\end{array}\right.$

In formula, t is the time, and x is the distance with emulating road starting point, ρ is traffic current density and is x, t function, ρ=ρ (x, t), v be vehicle average speed and be x, t function, v=v (x, t), π [r (x, t), s (x, t)] it is due to rate of change of the density function caused by the vehicle flowrate that circle mouthful enters or rolls away from, r (x, t)=r₀(x,t)-r_q(x, t) is t, x sections by the vehicle flowrate of circle mouthful entrance, s (x, t)=s₀(x,t)+s_qThe vehicle flowrate that (x, t) is t, x sections are rolled away from by circle mouth, r₀(x,t)、s₀(x, t) is to drive into the normal vehicle flowrate rolled away from, r by circle mouthful_q(x, t) is circle mouthful control No entry flow-reduction amount that expressway causes, s_q(x, t) is the flow increment that circle mouthful control forces that outgoing vehicles are caused, V_e(ρ) be equivalent speed and with free stream velocity v_fIt is related to traffic flow density p, T,

μ is constant, and full application symbol definition is identical；

Variable display board display speed is incorporated Kerner-Konhauser models, with variable display board display speed v_indInstead of the free stream velocity v in equivalent speed_f, obtain improved Kerner-Konhauser models as follows：

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\frac{V_e(\mathrm{\ρ},v_{\mathrm{ind}})-v}{T}-\frac{c_0^2}{\mathrm{\ρ}}\frac{\∂v}{\∂x}+\frac{\mathrm{\μ}}{\mathrm{\ρ}}\frac{{\∂}^{2}v}{{\∂x}^2}\end{array}\right.$

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

When tending to be infinite, representing traffic density tends to saturation traffic density, produces traffic congestion, works as state variable

When tending to be infinite, represent vehicle average speed and go to zero, produce traffic congestion；

In formula, ρ_jamTraffic current density when blocking for traffic；

Step 3: the improved Kerner-Konhauser models that a. is obtained according to step one, differential term is represented with difference scheme and higher order term is omitted, obtained：

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

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

$\frac{{\∂}^{2}v}{\∂x^2}=\frac{v(x+h,t)-2v(x,t)+v(x-h,t)}{h^2}+o\left(h^2\right)=\frac{v_{i+1}^n-{2v}_i^n+v_{i-1}^n}{h^2}$

In formula：ξ is t differential, and h is x differential, and o (ξ) is ξ higher-order shear deformation, and o (h) is h higher-order shear deformation, o (h²) it is h²Higher-order shear deformation, road is divided into multiple sections, each road section length is h, and the sampling period is ξ,

For i-th of section [n ξ, (n+1) ξ] interior vehicle averag density,

For i-th of section [n ξ, (n+1) ξ] vehicle average speed；

The difference form for obtaining improved Kerner-Konhauser models is：

$\left\{\begin{array}{c}{\mathrm{\ρ}}_i^{n+1}=\mathrm{\ξ\π}(r_i^n,s_i^n)-\frac{\mathrm{\ξ}}{h}[v_i^n({\mathrm{\ρ}}_{i+1}^n-{\mathrm{\ρ}}_i^n)+{\mathrm{\ρ}}_i^n(v_{i+1}^n-v_i^n)]+{\mathrm{\ρ}}_i^n\\ v_i^{n+1}=v_i^n+\mathrm{\ξ}[\frac{V_e({\mathrm{\ρ}}_i^n,v_{\mathrm{ind}}(i,n))-v_i^n}{T}-\frac{c_0^2(v_{i+1}^n-v_i^n)}{{\mathrm{\ρ}}_i^{n}h}-\frac{v_i^n(v_{i+1}^n-v_i^n)}{h}+\frac{\mathrm{\μ}(v_{i+1}^n-2v_i^n+v_{i-1}^n)}{{\mathrm{\ρ}}_i^n{h}^2}]\end{array}\right.$

In formula：

The vehicle flowrate that i-th of section is entered at [n ξ, (n+1) ξ] by circle mouthful is represented,

Represent the vehicle flowrate that i-th of section is rolled away from [n ξ, (n+1) ξ] by circle mouth, v_ind(i, n) represents i-th of section variable display board display speed in [n ξ, (n+1) ξ]；

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

E is constant in formula；

C. write in FPGA based on the PREDICTIVE CONTROL module for improving Kerner-Konhauser models, as shown in Figure 1, including data reception module, control program selection and data allocation module, computing module 1- computing modules N, synchronization module, data outputting module, road is divided into N number of section, one computing module of each section correspondence, computing module 1- computing modules N is the forecasting traffic flow computing module combined according to the Difference Method of foregoing partial differential equations using floating point arithmetic device in figure, and the data flow of PREDICTIVE CONTROL module is：Data reception module receives the traffic flow data in each section that host computer is transmitted（Traffic current density, vehicle average speed）, it is then passed to control program selection and data allocation module, control program is selected and data allocation module determines traffic bottlenecks according to these data, and formulate regulation and control scheme, then signal will be enabled, control program and traffic flow data are transmitted to each computing module, each computing module is received after enable signal while being predicted to traffic current density and vehicle average speed and result being stored in register, respective calculating end signal is transmitted to synchronization module by modules calculating after terminating, synchronization module sends the selection of signal informing case after all computing modules complete to calculate and data allocation module receives predicting the outcome for traffic flow data, proceed prediction, in predicted time T_cIt is interior, if traffic bottlenecks are released, then actual traffic is regulated and controled using the program, if can not release, control program is selected and data allocation module formulates new regulation and control scheme according to traffic flow data and last time regulation and control scheme, and traffic flow data and regulation and control scheme are transmitted into each computing module, re-starts prediction, the suitable regulation and control scheme output of selection one regulates and controls to traffic bottlenecks after multiple prediction and adjustment regulation and control scheme, and the section regulated and controled is in time T_cInside no longer regulated and controled, then proceed to be predicted traffic, find new traffic bottlenecks, and be controlled；

Traffic bottlenecks are determined in the step 3 and the method controlled it is：Solve | | η (x, t) | |_∞=η_m(x_m,t_m), work as η_mMore than given threshold value η_MWhen, illustrate section x_mIn t_mMoment will turn into traffic bottlenecks, then in t_m-T₀X of the moment to vehicle heading_mFront and back enter, go out circle mouthful and variable information display board progress speed limit（Speed reduction in section in front of bottleneck road, rear section speed is improved）, limitation enter bottleneck road even force roll bottleneck road away from；Or solve ‖ σ (x, t) | |_∞=σ_m(x_m,t_m), work as σ_mMore than given threshold value σ_MWhen, illustrate section x_mIn t_mMoment will turn into traffic bottlenecks, then in t_m-T₁X of the moment to vehicle heading_mFront and back go out, enter circle mouthful and variable information display board progress speed limit（Speed reduction in section in front of bottleneck road, rear section speed is improved）, limitation enter bottleneck road even force roll bottleneck road away from；

T in formula₀、T₁Cause for time for applying control in advance | | 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_MThe positive number being respectively made according to roading density maximum saturation, friction；

The priority principle controlled is：1. section speed is adjusted by variable information display board first, reduce the car speed into bottleneck road, the car speed for rolling bottleneck road away from is improved, when 2. can not reach Con trolling index only by variable information display board adjustment section speed, then enter bottleneck road flow by circle mouthful limitation and adjust section speed with variable information display board and be controlled simultaneously, 3. when controlling to reach that control is required simultaneously into bottleneck road flow and variable information display board adjustment section speed by circle mouthful limitation, part way vehicle is forced to roll road away from interrupting time by circle mouthful control, enter bottleneck road vehicle flowrate to circle mouthful limitation simultaneously and variable information display board adjusts section speed to reach Con trolling index requirement.

The beneficial effects of the invention are as follows：The present invention is by improving the equivalent speed in Kerner-Konhauser models, variable information display board display speed is dissolved into equivalent speed, analysis is integrally predicted to highway or blocked road by improved Kerner-Konhauser models based on FPGA platform, road bottleneck is found according to the state variable of definition, and then provide the control program of circle mouthful control and variable information display board, and these control programs are according to priority brought into forecast model, to ensure that regulation and control scheme is practical, and then solve the technical problem that existing method is difficult to traffic bottlenecks be carried out in actual highway or blocked road on-line prediction regulation and control.

Brief description of the drawings

Fig. 1 is that FPGA of the present invention based on FPGA and the online traffic bottlenecks forecast Control Algorithm for improving Kerner-Konhauser models realizes block diagram；

Fig. 2 is control method flow chart of the present invention based on FPGA and the online traffic bottlenecks forecast Control Algorithm for improving Kerner-Konhauser models.

Embodiment

1,2 describe the present invention in detail referring to the drawings.

Control method flow chart of the present invention is as shown in Figure 2, in the case where no traffic bottlenecks are produced, control program shows the free stream velocity that road allows by variable display board, circle mouthful control does not limit input and output, by traffic current density, vehicle average speed, variable display board display speed and circle mouthful control program to the traffic current density and vehicle average speed prediction in each section T for a period of time_c（T_cTake T₀、T₁Between big value）And judge whether traffic bottlenecks occur, if occurring without traffic bottlenecks, regulated and controled using current control program, variable display board display speed and circle mouthful control program then are adjusted according to aforementioned priority principle if there is bottleneck, and continues to predict a period of time T_cIf traffic bottlenecks can not be released, continue to adjust control program, traffic bottlenecks problem is can solve the problem that until finding a kind of control program, and traffic bottlenecks are controlled using the program, its method detailed is as follows：

1. according to Kerner-Konhauser models：

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\frac{V_e\left(\mathrm{\ρ}\right)-v}{T}-\frac{c_0^2}{\mathrm{\ρ}}\frac{\∂v}{\∂x}+\frac{\mathrm{\μ}}{\mathrm{\ρ}}\frac{{\∂}^{2}v}{{\∂x}^2}\end{array}\right.$

In formula, t is the time, and x is the distance with emulating road starting point, ρ is traffic current density and is x, t function, ρ=ρ (x, t), v be vehicle average speed and be x, t function, v=v (x, t), π [r (x, t), s (x, t)] it is due to rate of change of the density function caused by the vehicle flowrate that circle mouthful enters or rolls away from, r (x, t)=r₀(x,t)-r_q(x, t) is t, x sections by the vehicle flowrate of circle mouthful entrance, s (x, t)=s₀(x,t)+s_qThe vehicle flowrate that (x, t) is t, x sections are rolled away from by circle mouth, r₀(x,t)、s₀(x, t) is to drive into the normal vehicle flowrate rolled away from, r by circle mouthful_q(x, t) is circle mouthful control No entry flow-reduction amount that expressway causes, s_q(x, t) is the flow increment that circle mouthful control forces that outgoing vehicles are caused, V_e(ρ) be equivalent speed and with free stream velocity v_fIt is related to traffic flow density p, T,

μ is constant, and full application symbol definition is identical；

Variable display board display speed is incorporated Kerner-Konhauser models, with variable display board display speed v_indInstead of the free stream velocity v in equivalent speed_f, obtain improved Kerner-Konhauser models as follows：

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\frac{V_e(\mathrm{\ρ},v_{\mathrm{ind}})-v}{T}-\frac{c_0^2}{\mathrm{\ρ}}\frac{\∂v}{\∂x}+\frac{\mathrm{\μ}}{\mathrm{\ρ}}\frac{{\∂}^{2}v}{{\∂x}^2}\end{array}\right.$

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

When tending to be infinite, representing traffic density tends to saturation traffic density, produces traffic congestion, works as state variable

When tending to be infinite, represent vehicle average speed and go to zero, produce traffic congestion；

In formula, ρ_jamTraffic current density when blocking for traffic；

3. according to the improved Kerner-Konhauser models obtained in 1, differential term is represented with difference scheme and higher order term is omitted, obtained：

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

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

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

$\frac{{\∂}^{2}v}{\∂x^2}=\frac{v(x+h,t)-2v(x,t)+v(x-h,t)}{h^2}+o\left(h^2\right)=\frac{v_{i+1}^n-{2v}_i^n+v_{i-1}^n}{h^2}$

In formula：ξ is t differential, and h is x differential, and o (ξ) is ξ higher-order shear deformation, and o (h) is h higher-order shear deformation, o (h²) it is h²Higher-order shear deformation, road is divided into multiple sections, each road section length is h, and the sampling period is ξ,

For i-th of section [n ξ, (n+1) ξ] interior vehicle averag density,

For i-th of section [n ξ, (n+1) ξ] vehicle average speed；

The difference form for obtaining improved Kerner-Konhauser models is：

$\left\{\begin{array}{c}{\mathrm{\ρ}}_i^{n+1}=\mathrm{\ξ\π}(r_i^n,s_i^n)-\frac{\mathrm{\ξ}}{h}[v_i^n({\mathrm{\ρ}}_{i+1}^n-{\mathrm{\ρ}}_i^n)+{\mathrm{\ρ}}_i^n(v_{i+1}^n-v_i^n)]+{\mathrm{\ρ}}_i^n\\ v_i^{n+1}=v_i^n+\mathrm{\ξ}[\frac{V_e({\mathrm{\ρ}}_i^n,v_{\mathrm{ind}}(i,n))-v_i^n}{T}-\frac{c_0^2(v_{i+1}^n-v_i^n)}{{\mathrm{\ρ}}_i^{n}h}-\frac{v_i^n(v_{i+1}^n-v_i^n)}{h}+\frac{\mathrm{\μ}(v_{i+1}^n-2v_i^n+v_{i-1}^n)}{{\mathrm{\ρ}}_i^n{h}^2}]\end{array}\right.$

In formula：

The vehicle flowrate that i-th of section is entered at [n ξ, (n+1) ξ] by circle mouthful is represented,

Represent the vehicle flowrate that i-th of section is rolled away from [n ξ, (n+1) ξ] by circle mouth, v_ind(i, n) represents i-th of section variable display board display speed in [n ξ, (n+1) ξ]；

4. set up 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 formula；

5. write in FPGA based on the PREDICTIVE CONTROL module for improving Kerner-Konhauser models, traffic flow conditions are predicted, find traffic bottlenecks, traffic bottlenecks are controlled, in the present embodiment, fpga chip selects the EP4CE115F29C8 chips of altera corp, with other road information acquisition modules（Host computer）By wireless GPRS communication, road is divided into 40 sections, as shown in Figure 1, including the selection of data reception module, control program and data allocation module, computing module 1- computing modules 40（N takes 40 in embodiment）, synchronization module, data outputting module, computing module 1- computing modules 40 are the forecasting traffic flow computing module that is combined using floating point arithmetic device of Difference Method according to foregoing partial differential equations, and the data flow of PREDICTIVE CONTROL module is：Data reception module receives the traffic flow data in each section that host computer is transmitted（Traffic current density, vehicle average speed）, it is then passed to control program selection and data allocation module, control program is selected and data allocation module determines traffic bottlenecks according to these data, and formulate regulation and control scheme, then signal will be enabled, control program and traffic flow data are transmitted to each computing module, each computing module is received after enable signal while being predicted to traffic current density and vehicle average speed and result being stored in register, respective calculating end signal is transmitted to synchronization module by modules calculating after terminating, synchronization module sends the selection of signal informing case after all computing modules complete to calculate and data allocation module receives predicting the outcome for traffic flow data, proceed prediction, in predicted time T_cIt is interior, if traffic bottlenecks are released, then actual traffic is regulated and controled using the program, if can not release, control program is selected and data allocation module formulates new regulation and control scheme according to traffic flow data and last time regulation and control scheme, and traffic flow data and regulation and control scheme are transmitted into each computing module, re-starts prediction, the suitable regulation and control scheme output of selection one regulates and controls to traffic bottlenecks after multiple prediction and adjustment regulation and control scheme, and the section regulated and controled is in time T_cInside no longer regulated and controled, then proceed to be predicted traffic, find new traffic bottlenecks, and be controlled；

6. the method found traffic bottlenecks in above-mentioned 5 and regulated and controled to bottleneck is：Solve | | η (x, t) | |_∞=η_m(x_m,t_m), work as η_mMore than given threshold value η_MWhen, illustrate section x_mIn t_mMoment will turn into traffic bottlenecks, then in t_m-T₀X of the moment to vehicle heading_mFront and back enter, go out circle mouthful and variable information display board progress speed limit（Speed reduction in section in front of bottleneck road, rear section speed is improved）, limitation enter bottleneck road even force roll bottleneck road away from；Or solve ‖ σ (x, t) | |_∞=σ_m(x_m,t_m), work as σ_mMore than given threshold value σ_MWhen, illustrate section x_mIn t_mMoment will turn into traffic bottlenecks, then in t_m-T₁X of the moment to vehicle heading_mFront and back go out, enter circle mouthful and variable information display board progress speed limit（Speed reduction in section in front of bottleneck road, rear section speed is improved）, limitation enter bottleneck road even force roll bottleneck road away from；

T in formula₀、T₁Cause for time for applying control in advance | | 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_MThe positive number being respectively made according to roading density maximum saturation, friction；

The priority principle controlled is：1. section speed is adjusted by variable information display board first, reduce the car speed into bottleneck road, the car speed for rolling bottleneck road away from is improved, when 2. can not reach Con trolling index only by variable information display board adjustment section speed, then enter bottleneck road flow by circle mouthful limitation and adjust section speed with variable information display board and be controlled simultaneously, 3. when controlling to reach that control is required simultaneously into bottleneck road flow and variable information display board adjustment section speed by circle mouthful limitation, part way vehicle is forced to roll road away from interrupting time by circle mouthful control, enter bottleneck road vehicle flowrate to circle mouthful limitation simultaneously and variable information display board adjusts section speed to reach Con trolling index requirement.

Claims (1)

1. a kind of online traffic bottlenecks forecast Control Algorithm based on FPGA and improvement Kerner-Konhauser models, it is characterised in that comprise the following steps：

Step 1: according to Kerner-Konhauser models：

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\frac{V_e\left(\mathrm{\ρ}\right)-v}{T}-\frac{c_0^2}{\mathrm{\ρ}}\frac{\∂v}{\∂x}+\frac{\mathrm{\μ}}{\mathrm{\ρ}}\frac{{\∂}^{2}v}{{\∂x}^2}\end{array}\right.$

In formula, t is the time, and x is the distance with emulating road starting point, ρ is traffic current density and is x, t function, ρ=ρ (x, t), v be vehicle average speed and be x, t function, v=v (x, t), π [r (x, t), s (x, t)] it is due to rate of change of the density function caused by the vehicle flowrate that circle mouthful enters or rolls away from, r (x, t)=r₀(x,t)-r_q(x, t) is t, x sections by the vehicle flowrate of circle mouthful entrance, s (x, t)=s₀(x,t)+s_qThe vehicle flowrate that (x, t) is t, x sections are rolled away from by circle mouth, r₀(x,t)、s₀(x, t) is to drive into the normal vehicle flowrate rolled away from, r by circle mouthful_q(x, t) is circle mouthful control No entry flow-reduction amount that expressway causes, s_q(x, t) is the flow increment that circle mouthful control forces that outgoing vehicles are caused, V_e(ρ) be equivalent speed and with free stream velocity v_fIt is related to traffic flow density p, T,

μ is constant, and full application symbol definition is identical；

Variable display board display speed is incorporated Kerner-Konhauser models, with variable display board display speed v_indInstead of the free stream velocity v in equivalent speed_f, obtain improved Kerner-Konhauser models as follows：

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\frac{V_e(\mathrm{\ρ},v_{\mathrm{ind}})-v}{T}-\frac{c_0^2}{\mathrm{\ρ}}\frac{\∂v}{\∂x}+\frac{\mathrm{\μ}}{\mathrm{\ρ}}\frac{{\∂}^{2}v}{{\∂x}^2}\end{array}\right.$

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

When tending to be infinite, representing traffic density tends to saturation traffic density, produces traffic congestion, works as state variableWhen tending to be infinite, represent vehicle average speed and go to zero, produce traffic congestion；

In formula, ρ_jamTraffic current density when blocking for traffic；

Step 3: the improved Kerner-Konhauser models that a. is obtained according to step one, differential term is represented with difference scheme and higher order term is omitted, obtained：

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

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

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

$\frac{{\∂}^{2}v}{\∂x^2}=\frac{v(x+h,t)-2v(x,t)+v(x-h,t)}{h^2}+o\left(h^2\right)=\frac{v_{i+1}^n-{2v}_i^n+v_{i-1}^n}{h^2}$

In formula：ξ is t differential, and h is x differential, and o (ξ) is ξ higher-order shear deformation, and o (h) is h higher-order shear deformation, o (h²) it is h²Higher-order shear deformation, road is divided into multiple sections, each road section length is h, and the sampling period is ξ,

For i-th of section [n ξ, (n+1) ξ] interior vehicle averag density,

For i-th of section [n ξ, (n+1) ξ] vehicle average speed；

The difference form for obtaining improved Kerner-Konhauser models is：

$\left\{\begin{array}{c}{\mathrm{\ρ}}_i^{n+1}=\mathrm{\ξ\π}(r_i^n,s_i^n)-\frac{\mathrm{\ξ}}{h}[v_i^n({\mathrm{\ρ}}_{i+1}^n-{\mathrm{\ρ}}_i^n)+{\mathrm{\ρ}}_i^n(v_{i+1}^n-v_i^n)]+{\mathrm{\ρ}}_i^n\\ v_i^{n+1}=v_i^n+\mathrm{\ξ}[\frac{V_e({\mathrm{\ρ}}_i^n,v_{\mathrm{ind}}(i,n))-v_i^n}{T}-\frac{c_0^2(v_{i+1}^n-v_i^n)}{{\mathrm{\ρ}}_i^{n}h}-\frac{v_i^n(v_{i+1}^n-v_i^n)}{h}+\frac{\mathrm{\μ}(v_{i+1}^n-2v_i^n+v_{i-1}^n)}{{\mathrm{\ρ}}_i^n{h}^2}]\end{array}\right.$

In formula：

The vehicle flowrate that i-th of section is entered at [n ξ, (n+1) ξ] by circle mouthful is represented,

Represent the vehicle flowrate that i-th of section is rolled away from [n ξ, (n+1) ξ] by circle mouth, v_ind(i, n) represents i-th of section variable display board display speed in [n ξ, (n+1) ξ]；

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

E is constant in formula；

C. write in FPGA based on the PREDICTIVE CONTROL module for improving Kerner-Konhauser models, including data reception module, control program selection and data allocation module, computing module 1- computing modules N, synchronization module, data outputting module, road is divided into N number of section, one computing module of each section correspondence, computing module 1- computing modules N is the forecasting traffic flow computing module combined according to the Difference Method of foregoing partial differential equations using floating point arithmetic device, and the data flow of PREDICTIVE CONTROL module is：Data reception module receives the traffic flow data in each section that host computer is transmitted（Traffic current density, vehicle average speed）, it is then passed to control program selection and data allocation module, control program is selected and data allocation module determines traffic bottlenecks according to these data, and formulate regulation and control scheme, then signal will be enabled, control program and traffic flow data are transmitted to each computing module, each computing module is received after enable signal while being predicted to traffic current density and vehicle average speed and result being stored in register, respective calculating end signal is transmitted to synchronization module by modules calculating after terminating, synchronization module sends the selection of signal informing case after all computing modules complete to calculate and data allocation module receives predicting the outcome for traffic flow data, proceed prediction, in predicted time T_cIt is interior, if traffic bottlenecks are released, then actual traffic is regulated and controled using the program, if can not release, control program is selected and data allocation module formulates new regulation and control scheme according to traffic flow data and last time regulation and control scheme, and traffic flow data and regulation and control scheme are transmitted into each computing module, re-starts prediction, the suitable regulation and control scheme output of selection one regulates and controls to traffic bottlenecks after multiple prediction and adjustment regulation and control scheme, and the section regulated and controled is in time T_cInside no longer regulated and controled, then proceed to be predicted traffic, find new traffic bottlenecks, and be controlled；

Traffic bottlenecks are determined in the step 3 and the method controlled it is：Solve | | η (x, t) | |_∞=η_m(x_m,t_m), work as η_mMore than given threshold value η_MWhen, illustrate section x_mIn t_mMoment will turn into traffic bottlenecks, then in t_m-T₀X of the moment to vehicle heading_mFront and back enter, go out circle mouthful and variable information display board progress speed limit（Speed reduction in section in front of bottleneck road, rear section speed is improved）, limitation enter bottleneck road even force roll bottleneck road away from；Or solve ‖ σ (x, t) | |_∞=σ_m(x_m,t_m), work as σ_mMore than given threshold value σ_MWhen, illustrate section x_mIn t_mMoment will turn into traffic bottlenecks, then in t_m-T₁X of the moment to vehicle heading_mFront and back go out, enter circle mouthful and variable information display board progress speed limit（Speed reduction in section in front of bottleneck road, rear section speed is improved）, limitation enter bottleneck road even force roll bottleneck road away from；

T in formula₀、T₁Cause for time for applying control in advance | | 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_MThe positive number being respectively made according to roading density maximum saturation, friction；

The priority principle controlled is：1. section speed is adjusted by variable information display board first, reduce the car speed into bottleneck road, the car speed for rolling bottleneck road away from is improved, when 2. can not reach Con trolling index only by variable information display board adjustment section speed, then enter bottleneck road flow by circle mouthful limitation and adjust section speed with variable information display board and be controlled simultaneously, 3. when controlling to reach that control is required simultaneously into bottleneck road flow and variable information display board adjustment section speed by circle mouthful limitation, part way vehicle is forced to roll road away from interrupting time by circle mouthful control, enter bottleneck road vehicle flowrate to circle mouthful limitation simultaneously and variable information display board adjusts section speed to reach Con trolling index requirement.

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