CN113240902B - Signal control road network path flow estimation method based on sampled vehicle trajectory data - Google Patents
Signal control road network path flow estimation method based on sampled vehicle trajectory data Download PDFInfo
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Abstract
The invention relates to a signal control road network path flow estimation method based on sampling vehicle track data, which comprises the following steps: 1) obtaining prior matrix of flow direction flow according to sampling vehicle track data in road network2) Obtaining the flow prior estimation value of each path according to the sampled path flow in the road network, and constructing the prior matrix of the path flow3) And constructing a generalized least square model taking the error minimization of the path flow and the flow direction flow as a target, and solving the model through a gradient search algorithm to obtain an optimal path flow estimation value. Compared with the prior art, the method has the advantages of pure track data input, less assumed conditions, wide applicability and the like.
Description
Technical Field
The invention relates to the field of traffic operation evaluation, in particular to a method for estimating the path flow of a signal control road network based on sampled vehicle trajectory data.
Background
OD flow is an important index representing traffic demand of a road network, path flow refers to flow of traffic flow between any OD pair distributed on all actual driving paths, and compared with OD flow, path selection of travelers in the road network is further considered, and spatial flow and aggregation of the traffic flow in the road network can be more finely positioned by the OD.
The accurate path flow matrix is a key link for refining traffic control, and plays an important role in identifying key elements (such as road sections, channels, paths and the like) of the road gateway. In the traffic planning level, the OD traffic and the path traffic are usually obtained by the conventional "four-step" method, and the traffic volume of a selected specific path is obtained by the path allocation, so that the research of estimating the path traffic by directly using the detection data is less. For the research of OD flow estimation, most of the inputs of the existing OD flow estimation model are the cross-sectional flow of the fixed detector, and a priori OD matrix needs to be acquired through historical data or survey data. The relation of OD to flow and path flow obtained based on a traffic distribution theory is realized by relying on user balance and perfect information game, and whether the distribution relation is in accordance with the distribution relation in actual operation or not cannot be known. With the development of new detection technologies such as mobile positioning (GPS), vehicle communication, etc., data input of OD traffic estimation has more options. In order to solve the uncertainty of the OD estimation problem, the utilization of the existing model to the novel data such as the trajectory is often limited to the calibration of the traditional model parameters or the reinforcement of the constraint conditions by the sample flow or the travel time information, and the dynamic information of the traffic flow contained in the trajectory data is not fully mined and utilized. Therefore, a method for estimating the traffic of the signal control road network path, which has important theoretical and practical significance for the accurate traffic control in the new generation of network connection big data environment, needs to be established.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for estimating the traffic of a signal control road network based on sampled vehicle trajectory data.
The purpose of the invention can be realized by the following technical scheme:
a signal control road network path flow estimation method based on sampling vehicle track data comprises the following steps:
1) obtaining prior matrix of flow direction flow according to sampling vehicle track data in road network
2) Obtaining the flow prior estimation value of each path according to the sampled path flow in the road network, and constructing the prior matrix of the path flow
3) And constructing a generalized least square model taking the error minimization of the path flow and the flow direction flow as a target, and solving the model through a gradient search algorithm to obtain an optimal path flow estimation value.
The step 1) specifically comprises the following steps:
11) calculating to obtain left-turn and straight-going sampling rate estimated values of all the inlet roads of all the intersections;
12) calculating a sampling rate estimation value of the right turning flow direction of each inlet channel of each intersection;
13) calculating a prior flow estimation value of the right turning flow direction of each inlet channel at each intersection;
14) and forming a priori road section flow direction flow matrix by the priori flow estimation values of the flow directions of all the inlet roads of all the intersections.
The step 11) is specifically as follows:
calculating to obtain the left-turn and straight-going sampling rate estimated values of the intersection i and the intersection j according to the number of sampled vehicle tracks in the road network and the prior flow estimated values of the left-turn and straight-going flow directions of all the intersection inlet roads, wherein the sampling rate estimated values comprise:
wherein i is the number of the intersection, j is the number of the entrance lane,the number of sampling traces for the left turn flow direction of the entrance lane j at the intersection i,the number of sampling traces of the straight flow direction of the inlet lane j of the intersection i,respectively are prior flow estimated values of left turn and straight flow direction of an inlet channel j of an intersection i,the left turn and straight run sample rate estimates for the intersection i entrance lane j, respectively.
In step 12), taking the average value of the sampling rate estimation values of the controlled flow directions of the same inlet passage as the sampling rate estimation value of the right-turn flow direction, the following steps are performed:
wherein, the first and the second end of the pipe are connected with each other,is an estimate of the sampling rate of the right turn flow direction for the intersection i, the entrance lane j.
In the step 13), calculating a prior flow estimation value of the right turn flow direction of each inlet channel at each intersection, including:
wherein the content of the first and second substances,the number of sampling traces for the right turn direction of the entrance lane j at the intersection i,is a priori flow estimate of the right turn flow direction of the inlet lane j at the intersection i.
In the step 2), according to the prior flow estimation value of each flow direction of each inlet of each intersection obtained in the step 1), the distribution proportion of the flow direction flow among different paths is approximated by the flow of the sample track, and the flow prior estimation value of each path is obtained according to the quantity proportion of the sample tracks passing through the same flow direction and different paths, so that the method comprises the following steps:
wherein, the first and the second end of the pipe are connected with each other,as a priori estimate of the flow of path k, i.e. a priori matrix of the path flowsThe elements (A) and (B) in (B),is the flow estimate, d, of path k from the prior flow estimate of the turn m at the intersection i entry lane jkThe number of flow directions that the path k passes, nkIs the number of sampling trajectories of the path k,the set of paths for flow direction m through intersection i, entrance lane j, and m ∈ { l, t, r }, representing left turn, straight run, and right turn flow directions, respectively.
In the step 3), the matrix form expression of the generalized least square model is as follows:
wherein Z is an optimization objective function, ω1,ω2The method comprises the steps of calculating a weight coefficient of two error terms in an objective function, wherein X is an estimated value matrix of flow direction traffic of each intersection of a road network in a TOD time period, Y is an estimated value matrix of flow direction of each path of the road network in a TOD time period, and A is a parameter matrix of incidence relation between the flow direction and the path.
Constructing a parameter matrix A of the incidence relation between the flow direction and the path according to the topological corresponding relation between the flow direction and the path in the road network structure, wherein the elements in the parameter matrix AThe expression of (c) is:
wherein the content of the first and second substances,the element in the parameter matrix a represents the correlation coefficient of the path and the road section flow direction.
In the step 3), an iterative method based on gradient search is adopted to solve the generalized least square model.
The method for solving the generalized least square model by adopting the iteration method based on the gradient search specifically comprises the following steps of:
31) a priori matrix giving flow direction trafficA priori matrix of path trafficWeight coefficient omega1、ω2Parameter matrix A, learning rate alpha and precision epsilon;
32) let the iteration number a equal to 0 and initialize Xa=X0,Ya=Y0;
33) When gradient of target function | | gaStopping iteration when | < epsilon, otherwise, orderPerforming step 34);
if | | | Za+1-ZaIf | | is less than epsilon or the difference between the decision variable and the last iteration is less than epsilon, stopping the iteration, and Xa+1I.e. the optimal solution X*、Y*Otherwise, go to step 35);
35) let a be a +1, return to step 33).
Compared with the prior art, the invention has the following advantages:
firstly, inputting pure track data: compared with the technical scheme that the sampling trajectory data is only used as data supplement or parameter calibration of the method which takes the section flow detection data of the road section as the main data condition in the existing research, the method fully utilizes the characteristics of wide-area continuity and fine perception of the trajectory data, excavates the traffic flow real-time running state information carried by the trajectory data, and provides an innovative exploration direction in a theoretical method for the wide application of individual sample mobile detection data.
II, assuming few conditions: the existing arrival flow estimation method based on sampling trajectory data can be used for achieving estimation of flow direction flow, so that a priori path flow matrix is obtained, the cost and data source requirements of a technical scheme of a priori OD matrix obtained from historical data or investigation commonly used in existing research are omitted, conditions of a known sampling ratio or a preset traffic distribution model are not needed, the constraint of a plurality of assumed conditions is reduced, meanwhile, sources possibly influenced by estimation accuracy are controlled, and the complexity of analysis of estimation error reasons is reduced.
Thirdly, the applicability is wide: the invention adopts the sampled vehicle track data as input, and the popularization rate and the coverage rate of the vehicle track data are gradually improved under the background of popularization of the internet vehicle communication and mobile positioning detection technology, so that the method has larger potential and wide application range in urban traffic operation evaluation in the future.
Drawings
Fig. 1 is verification case road network information, wherein fig. 1a is verification road network topology information, and fig. 1b is a verification road network simulation model.
Fig. 2 is a visualization of the estimation result of the path flow estimation method, wherein fig. 2a is a flow direction flow estimation regression fitting curve, and fig. 2b is a path flow estimation regression fitting curve.
FIG. 3 is a flow chart of the method of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
As shown in fig. 3, the present invention provides a method for estimating a traffic flow of a signal control road network based on sampled vehicle trajectory data, which obtains the traffic flow of the signal control road network through the sampled vehicle trajectory data, and comprises the following steps:
1) calculating to obtain a prior matrix of flow direction and flow rate based on sampled vehicle track data in a road network and the flow direction and flow rate of each inlet road at each intersectionThe method specifically comprises the following steps:
in a TOD time period, knowing the time period flow rates of the controlled left turn and straight flow in each intersection, calculating and obtaining an estimated value of the sampling rate of the controlled flow according to the sampling track number of the controlled flow as follows:
wherein i is the number of the intersection, j is the number of the entrance lane,a sample trajectory number (veh) indicating the left-turn flow direction of the entrance lane j at the intersection i,the number of sampling traces (veh) representing the straight-going flow direction of the entrance lane j at the intersection i,respectively, a priori flow rate estimated values (veh) of the left turn and the straight flow direction of the inlet channel j of the intersection i,which represent the sample rate estimates for the left turn and straight run, respectively, of the intersection i, the entrance lane j.
Thus, the sample rate for a right turn flow direction may be expressed as the average of the sample rate estimates for the controlled flow direction for the same inlet port as follows:
wherein the content of the first and second substances,a sample rate estimate representing the right turn flow direction of the intersection i entry lane j.
Therefore, the a priori flow estimate for the right turn flow is calculated as follows:
wherein the content of the first and second substances,the number of traces (veh) indicating the right turn direction of the entrance lane j at the intersection i,a priori flow estimate (veh) representing the right turn flow direction of the approach lane j at intersection i.
2) Based on the topological corresponding relation between each flow direction and each path, a parameter matrix A of the incidence relation between the flow direction and the path is constructed, and a priori estimated value of the path flow is obtained based on the sampled path flow, which specifically comprises the following steps:
modeling the distribution relation of the flow in the road section flow direction among different paths, and aiming at the static path flow estimation in a TOD time period, the flow in the road section flow direction can be regarded as the sum of the flow of different paths flowing through the road section, and the expression is as follows:
wherein the content of the first and second substances,flow (veh) representing the flow direction m (including left turn, straight run, right turn, i.e., m e { l, t, r }) of the approach j at the intersection i,the correlation coefficient representing the flow direction of the path and the section, i.e. the element in the parameter matrix A, ykThe path flow rate (veh) of the path K is shown, and K is a path set of the entire road network.
Numbering the flow directions of all intersection entrance roads of the road network to obtain a correlation coefficient matrix A between the flow directions and the paths, wherein the selection relation between the flow directions and the flow rates of the paths can be expressed in a matrix form as follows:
X=AY
according to the prior estimation value of the flow direction flow in the step 1), the flow rate of the sample track is adopted to approximate the distribution proportion of the flow direction flow among different paths, and the flow rate prior estimation value of each path can be obtained according to the quantity proportion of the sampling tracks passing through the same flow direction and different paths as follows:
wherein the content of the first and second substances,represents the a flow prior estimate (veh) for path k,flow estimate (veh), d) representing path k from a prior estimate of flow for turn m at intersection i, entrance lane jkDenotes the number of flow directions, n, through which the path k passeskIndicates the number of sampling trajectories (veh) of the path k,a set of paths representing flow direction m through the intersection i entrance lane j,a flow prior estimate (veh) representing the flow direction m of the approach j to the intersection i.
3) Constructing a generalized least square model taking the error minimization of the path flow and the flow direction flow as a target, wherein the expression is as follows:
wherein Z is an optimization objective function, I is an intersection index set, J is an entrance way index set, m belongs to { l, t, r }, and is a variable symbol set representing flow direction, omega1,ω2Are the weight coefficients of the two error terms in the objective function.
The variables in the least squares model are expressed in a matrix form, and the following can be obtained:
wherein Z is an optimization objective function,respectively representing an estimation value matrix and a prior value matrix of different flow direction flows of each intersection of the road network in a TOD time period,respectively representing an estimated value matrix and a prior value matrix of each path flow of the road network in a TOD time period, wherein A represents a path-flow direction correlation matrix.
Solving the least square model by adopting an iterative method based on gradient search, and giving a flow direction flow prior valuePath flow prior valueWeight coefficient ω1,ω2The correlation coefficient A, the learning rate alpha and the precision epsilon, and the solution method comprises the following steps:
i) setting the iteration number as a to 0, and initializing Xa=X0,Ya=Y0,
ii) calculating the gradient of the objective function:
if | | | Za+1-ZaIf | | < epsilon or the difference between the decision variable and the last iteration is less than epsilon, stopping the iteration, and Xa+1,Ya+1Is the optimal solution X*,Y*(ii) a Otherwise, performing step (iv);
iv) let a be a +1 and return to step (ii).
4) And verifying the intersection timing scheme estimation method through the empirical data.
Examples
The invention verifies the path flow estimation method through the following simulation case, as shown in fig. 2, a simulation model is established by using VISSIM software with a four-longitudinal-three-transverse road network of south China of Qingdao city as a background, 25 intersections are arranged in the road network range, wherein 18 signal control intersections (shown by circles in the figure) are arranged, 190 flow directions are arranged, 28 OD points are arranged in the whole network, and 311 paths to be estimated are arranged. The simulation model is calibrated at the early peak time (7: 00-9: 00) of the timing scheme of 3 months in 2019, the detection data of 1 day to 12 days in 3 months in 2019 are selected for statistics, and the vehicle input of the simulation model is calibrated according to the average traffic flow level. The simulation time period is set to 9000s, with the first 1800s as the preheat period and the remaining 7200s as the verify period. The uploading frequency of the vehicle track in the simulation model is set as 1s, and the weight coefficient in the model is taken as omega1=0.1,ω21.0, precision ∈ 10-6Sampling the track data after the whole network simulation operation by adopting a sampling ratio of 0.1 to obtain three groups of parallel groups, and adopting average absolute error (MAE), weighted average percent error (WMAPE) and root mean square error (RMS)E) The estimation effect of the invention is evaluated as an evaluation index of the flow direction flow and the path flow.
TABLE 1 Path flow estimation results
As can be seen from table 1 and the fitted curve of fig. 2, under the condition that the sampling rate is 0.1, the accuracy of the flow direction and flow rate estimation obtained by the present invention can reach more than 95%, and the average absolute error of 190 flow direction and flow rate in the verification period of 2h is about 52 veh. In the aspect of path estimation, the average estimation precision can reach 92.3%, the average absolute error is only 7veh, and from the index of RMSE, the model has small fluctuation and stable estimation effect.
Claims (7)
1. A signal control road network path flow estimation method based on sampling vehicle track data is characterized by comprising the following steps:
1) obtaining prior matrix of flow direction flow according to sampling vehicle track data in road network
2) Obtaining the flow prior estimation value of each path according to the sampled path flow in the road network, and constructing the prior matrix of the path flow
3) Constructing a generalized least square model taking the error minimization of the path flow and the flow direction flow as a target, wherein a matrix form expression of the generalized least square model is as follows:
wherein Z is an optimization objective function, ω1,ω2The weight coefficients of two error items in the objective function are set, X is an estimation value matrix of each flow direction flow of each intersection of the road network in a TOD time period, Y is an estimation value matrix of each path flow of the road network in a TOD time period, and A is a parameter matrix of the incidence relation between the flow direction and the path;
solving the generalized least square model by adopting an iterative method based on gradient search, and specifically comprising the following steps:
31) a priori matrix giving flow direction trafficA priori matrix of path trafficWeight coefficient omega1、ω2Parameter matrix A, learning rate alpha and precision epsilon;
32) let the iteration number a equal to 0 and initialize Xa=X0,Ya=Y0;
33) When gradient of target function | | gaStopping iteration when | < epsilon, otherwise, orderProceed to step 34), gradient gaThe calculation formula of (A) is as follows:
if | | | Za+1-ZaIf | | is less than epsilon or the difference between the decision variable and the last iteration is less than epsilon, stopping the iteration, and Xa+1、Ya+1Is the optimal solution X*、Y*Otherwise, go to step 35);
35) let a be a +1, return to step 33).
2. The method for estimating the traffic of the signal control road network based on the sampled vehicle trajectory data according to claim 1, wherein the step 1) specifically comprises the following steps:
11) calculating to obtain the left-turn and straight-going sampling rate estimated values of all the entrance roads of all the intersections;
12) calculating a sampling rate estimation value of the right turning flow direction of each inlet channel of each intersection;
13) calculating a prior flow estimation value of the right turning flow direction of each inlet channel at each intersection;
14) and forming a priori road section flow direction and flow matrix by the priori flow estimation values of the flow directions of all inlet roads of all intersections.
3. The method for estimating the traffic of the signal control road network based on the sampled vehicle trajectory data according to claim 2, wherein the step 11) is specifically as follows:
calculating to obtain the left-turn and straight-going sampling rate estimated values of the intersection i and the intersection j according to the number of sampled vehicle tracks in the road network and the prior flow estimated values of the left-turn and straight-going flow directions of all the intersection inlet roads, wherein the sampling rate estimated values comprise:
wherein i is the number of the intersection, j is the number of the entrance lane,the number of sampling traces for the left turn flow direction of the entrance lane j at the intersection i,the number of sampling traces of the straight flow direction of the inlet lane j of the intersection i,respectively are prior flow estimated values of left turn and straight flow direction of an inlet channel j of an intersection i,the left turn and straight run sample rate estimates for the intersection i entrance lane j, respectively.
4. The method as claimed in claim 3, wherein the step 12) of taking the average of the sampling rate estimation values of the controlled flow direction of the same inlet road as the sampling rate estimation value of the right turn flow direction comprises:
5. The method for estimating the route traffic of the signal control road network based on the sampled vehicle trajectory data according to claim 4, wherein in the step 13), the prior traffic estimation value of the right turn traffic direction of each entrance road at each intersection is calculated by:
6. The method for estimating the traffic of the signal control road network based on the sampled vehicle track data according to claim 5, wherein in the step 2), according to the prior traffic estimation value of each flow direction of each inlet and outlet at each intersection obtained in the step 1), the distribution proportion of the flow direction and the traffic among different paths is approximated by the traffic of the sample track, and the flow prior estimation value of each path is obtained according to the quantity proportion of the sampled tracks passing through the same flow direction and different paths, and then:
wherein the content of the first and second substances,as a priori estimate of the flow of path k, i.e. a priori matrix of the path flowsThe elements (A) and (B) in (B),is the flow estimate, d, of path k from the prior flow estimate of the turn m at the intersection i entry lane jkThe number of flow directions that the path k passes, nkIs the number of sampling trajectories of the path k,the set of paths for flow direction m through intersection i, entrance lane j, and m ∈ { l, t, r }, representing left turn, straight run, and right turn flow directions, respectively.
7. The method as claimed in claim 1, wherein the parameter matrix A of the correlation between the flow direction and the path is constructed according to the topological correspondence between the flow direction and the path in the road network structure, and the element in the parameter matrix A is thenThe expression of (a) is:
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