CN112201035A - Signal control intersection periodic flow estimation method driven by track data - Google Patents
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- G—PHYSICS
- G08—SIGNALLING
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- G08G1/00—Traffic control systems for road vehicles
- G08G1/01—Detecting movement of traffic to be counted or controlled
- G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
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- G—PHYSICS
- G08—SIGNALLING
- G08G—TRAFFIC CONTROL SYSTEMS
- G08G1/00—Traffic control systems for road vehicles
- G08G1/01—Detecting movement of traffic to be counted or controlled
- G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
- G08G1/0125—Traffic data processing
- G08G1/0129—Traffic data processing for creating historical data or processing based on historical data
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- G08G—TRAFFIC CONTROL SYSTEMS
- G08G1/00—Traffic control systems for road vehicles
- G08G1/065—Traffic control systems for road vehicles by counting the vehicles in a section of the road or in a parking area, i.e. comparing incoming count with outgoing count
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- G—PHYSICS
- G08—SIGNALLING
- G08G—TRAFFIC CONTROL SYSTEMS
- G08G1/00—Traffic control systems for road vehicles
- G08G1/07—Controlling traffic signals
- G08G1/081—Plural intersections under common control
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- G08G—TRAFFIC CONTROL SYSTEMS
- G08G1/00—Traffic control systems for road vehicles
- G08G1/07—Controlling traffic signals
- G08G1/085—Controlling traffic signals using a free-running cyclic timer
Abstract
The invention relates to a trajectory data-driven signal-controlled intersection periodic flow estimation method, which comprises the following steps: 1) dividing the periodic flow into a known part and an unknown part according to the parking position and the expected arrival time of the last queuing sampling track; 2) extracting parameters related to flow of the known part and the unknown part in each period, constructing a three-dimensional tensor comprising the flow of the unknown part in each period, and converting the periodic flow estimation problem into a data repair problem; 3) and repairing the constructed tensor based on a tensor decomposition method to obtain the flow of each period. Compared with the prior art, the method has the advantages of track data driving, high effectiveness, wide applicability and the like.
Description
Technical Field
The invention relates to the field of traffic information, in particular to a trajectory data-driven signal control intersection periodic flow estimation method.
Background
Traffic flow is one of important inputs of urban road planning, operation and management, periodic traffic flow estimation is very important for dynamic evaluation and optimization of urban road signal control intersections, existing traffic flow detection modes mainly rely on fixed-point detectors, such as fixed-point coils, microwave radars, electric alarms and the like, however, the coverage range of the fixed-point detectors in reality is extremely limited due to factors such as installation and maintenance costs, and in addition, practical application of the fixed-point detectors is also influenced by faults and data quality.
In recent years, due to the rapid development of technologies such as mobile internet, intelligent internet and the like, the acquisition of massive high-frequency vehicle track data is possible, generally, vehicles which are provided with a GPS, a Beidou and the like and can upload position information in real time are called internet vehicles or sampling vehicles, at present, such sampling vehicles can upload the instantaneous positions and speeds of the vehicles at intervals of 1-5 s, so that abundant traffic flow information is provided, compared with a traditional fixed-point detector, the track of the sampling vehicle can provide an economic and efficient data source for monitoring the traffic running condition of a road network, and meanwhile, the track of the sampling vehicle has great potential in the aspects of dynamic evaluation and optimization of signal control intersection running, and it needs to be explained that the positioning accuracy of the sampling vehicle is still not enough to realize lane-level positioning of the vehicles at present.
In the last few years, much research has focused on the use of sampled vehicle trajectories to evaluate the behavior of signalized intersections, where a lot of research has focused on estimating the length of queues at signalized intersections, using deterministic or stochastic methods based mainly on traffic wave theory (such as Cheng et al, 2012; Ramezani and gerrolimminis, 2015; Li et al, 2017; Yin et al, 2018), which achieves the estimation of the length of queues per cycle by determining the critical motion points of the sampled vehicle trajectories, i.e. joining or leaving queues, and reconstructing the signalized intersections to control the formation and dissipation processes of the queues at intersections, but when reconstructing the traffic, it is generally necessary to assume that the remaining vehicles between two consecutive sampled vehicles arrive at a constant flow rate, which may generate large errors in low permeability conditions (< 10%), and stochastic methods by assuming that the arrival of vehicles obeys a time-varying distribution, therefore, the periodic queuing length is constructed as a random variable based on methods such as probability theory and the like so as to estimate the maximum possible queuing length or the expected value of the queuing length in the period (such as Commert and Cetin, 2009, 2011; Hao et al, 2013; Hao et al, 2014; Tan et al, 2019; Zhang et al, 2019), the method is generally more robust than a deterministic method, but generally needs other inputs such as permeability, signal timing and the like, in addition, the estimation precision of the method under low permeability still cannot meet the practical application, recently, for different traffic states, Zhang et al (2019) assume different arrival distributions, estimate the arrival rate of each period by adopting an expected value maximization algorithm, then estimate the maximum queuing length and the residual queuing length based on the traffic wave theory, the method can still generate a more accurate estimation result even under a sparse environment, and in addition, tan et al (2019) fully utilize historical trajectory data to obtain arrival distribution in a period, then convert a queuing length estimation problem into a parameter estimation problem based on a probability theory, and finally realize the estimation of the maximum queuing length and the red light tail queuing length.
In addition to queue length estimation, some scholars have attempted to estimate traffic flow based on sample trajectories, Zheng and Liu (2017) et al have translated the flow estimation problem into a maximum likelihood estimation problem based on the assumption that vehicle arrivals obey time-varying poisson, and finally solved using an expectation maximization algorithm, which is the first attempt to estimate traffic flow based on sample trajectories, but have limitations in that given that the arrivals of each cycle within each time interval are consistent and do not achieve estimation of cycle-level flow, Wong et al (2019) and Zhao et al (2019) achieve estimation of signal control intersection vehicle permeability by analyzing the parking positions of the sample vehicles queued within the time interval, and then Zhao et al (2019) have proposed various extended methods to further estimate the number of queued vehicles and the time interval flow based on the estimated permeability, since the proposed methods do not require information such as signal timing, the method can be easily expanded to large-scale road network application, and recently Yao et al (2019) propose a probability model and traffic wave theory hybrid estimation method, the method realizes periodic flow estimation for the first time, the method firstly estimates the queuing length, namely parking flow, based on the traffic wave theory, then converts the parking flow estimation into a parameter estimation problem based on the assumption that the vehicle arrives and obeys bounded time-varying Poisson distribution, and finally realizes the periodic queuing length estimation.
In summary, the existing methods for estimating the queuing length and the flow based on the sampling trajectory have obvious advantages and disadvantages, and the main limitation is that the existing methods generally rely on the assumption of the vehicle arrival process, and such assumption usually requires that the arrival of the vehicles with different flow directions on different lanes are consistent and the queuing principle of first-in first-out is followed, which causes that a plurality of lanes exist in each flow direction of a signal control intersection, and when the queuing trajectory of first-in first-out is not suitable, such methods generate large errors, and furthermore, the more important factor is that the arrival distribution of the vehicles is rather uncertain and unknown in practice, the existing methods assume that a specific arrival distribution is difficult to accurately describe the arrival situation of real vehicles, and the existing methods are limited in that they are all traffic flow model-driven methods, which directly causes the problem that their estimation accuracy under low permeability is insufficient, therefore, a trajectory data driven method is needed to realize accurate estimation of the periodic traffic flow of the signalized intersection.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a signal control intersection periodic flow estimation method driven by track data.
The purpose of the invention can be realized by the following technical scheme:
a signal control intersection periodic flow estimation method driven by track data comprises the following steps:
1) dividing the periodic flow into a known part and an unknown part according to the parking position and the expected arrival time of the last queuing sampling track;
2) extracting parameters related to flow of the known part and the unknown part in each period, constructing a three-dimensional tensor comprising the flow of the unknown part in each period, and converting the periodic flow estimation problem into a data repair problem;
3) and repairing the constructed tensor based on a tensor decomposition method to obtain the flow of each period.
In step 1), the flow rate in each period is divided into a known part and an unknown part by the last queued sampling trajectory, and then:
wherein v iskIs the flow rate of the k-th cycle,
the number of vehicles arriving before the last queued sample trajectory, i.e. the known flow,
the number of vehicles arriving after the last queued sample trajectory, i.e. the unknown flow,
parking position of the sampling trajectory for the last queue, d0The average parking headway distance is shown, and omega is the number of lanes in the lane group.
The step 2) specifically comprises the following steps:
21) for the period of observing the queued sampling track, extracting two known and unknown parameters related to the flow in each period, including the number of the observed sampling tracks and the length of an observation period, and constructing a period characteristic matrix;
22) for the period of the sampling track which is not observed in the queue, replacing the periodic feature matrix of the previous observed track;
23) and finally, constructing a three-dimensional tensor by using the feature matrix of each period in the study period.
In the step 21), the periodic feature matrix is specifically:
wherein, XkA feature vector for the kth observed queued sampling trajectory period;
and
corresponding to the number of observed sample traces for the known and unknown portions respectively,
and
the lengths of the observation periods corresponding to the known and unknown portions, respectively.
In said step 22), for the period in which no queued sampling trace is observed, the period feature matrix of the previous observed trace is replaced, so that:
Xi＝Xi-1
wherein, XiIs the eigenvector of the ith cycle, which does not observe the queued sample traces, Xi-1The feature vector for the i-1 th cycle, which has observed the queued sample traces.
In the step 23), the constructed three-dimensional tensor expression is as follows:
wherein the content of the first and second substances,
for an initial tensor composed of K cycles of eigenvectors over the study period, vbefAnd vaftVector consisting of known and unknown flow for K cycles in the study period, nbefAnd naftRespectively, a vector consisting of the number of sampling trajectories observed for the K periods of known and unknown flow components within the study period, tbefAnd taftRespectively, vectors consisting of the lengths of observation periods corresponding to the K periods of known and unknown flow portions within the study period.
The step 3) specifically comprises the following steps:
31) initial tensor containing unknown partial flow based on Tucker decomposition
Decomposing the data into a form of multiplying a kernel tensor by a factor matrix in three dimension directions, and converting a Tucker decomposition process into an optimization problem;
32) solving an optimization problem based on a gradient descent method, and realizing Tucker decomposition of an initial tensor;
33) and restoring the initial tensor based on the kernel tensor and the factor matrix, realizing tensor repair, obtaining the flow of the unknown part of each period, and finally finishing the estimation of the periodic flow of the intersection.
In the step 31), the initial tensor
The expression of the Tucker decomposition of (1) is:
wherein the content of the first and second substances,
is the decomposed nuclear tensor, an
I.e. a non-negative tensor of size P x Q x R,
and
respectively factor matrices with corresponding dimensions of 3 XP, 2 XQ and KXR, respectively, a reference bookξAnd xi is 1,2 and 3, which is the direction product calculation and represents the inner product of the tensor and the matrix in the dimension xi.
In the step 32), the Tucker decomposition process is converted into an optimization problem, and the following steps are performed:
wherein λ is a regularization strength parameter, | | · |. non-calculation2The norm of L2 is shown,
is a regularization term.
In step 33), the initial tensor is restored based on the kernel tensor and the factor matrix, and then:
the flow rate estimates for each cycle are as follows:
wherein the content of the first and second substances,
in order to restore the initial tensor in the original state,
to investigate the flow estimate for period k over the period,
is an unknown partial flow estimated based on a tensor decomposition method.
Compared with the prior art, the invention has the following advantages:
firstly, driving track data: the method is different from the existing model-driven flow estimation method based on the traffic flow theory, converts the periodic flow estimation problem into the pure track-driven problem of tensor repair, does not need any prior traffic flow hypothesis, and can be used by non-traffic background professionals.
Secondly, the effectiveness is high: the flow estimation method provided by the invention has higher precision than the existing method in the aspects of cycle-level estimation and time-period-level estimation.
Thirdly, the applicability is wide: the sampling track adopted by the method comprises a network car booking track, data of various geomap navigation companies and the like, the coverage of the whole road network can be basically realized at the present stage, and the method has no requirement on the signal control type, so the method can be applied to the urban road network in a large scale.
Drawings
FIG. 1 is a schematic diagram of the periodic flow division in the present invention.
FIG. 2 is a schematic diagram of the periodic feature extraction in the present invention.
Fig. 3 is a schematic diagram of the construction of the three-dimensional tensor according to the present invention.
Fig. 4 is a decomposition diagram of tensor Tucker in the present invention.
FIG. 5 is a diagram illustrating an exemplary verification scenario.
Fig. 6 is a comparison diagram of results of example verification and the conventional method, wherein fig. 6a is a comparison diagram of cycle-level results, fig. 6b is a comparison diagram of 10-minute results, fig. 6c is a comparison diagram of 30-minute results, and fig. 6d is a comparison diagram of 60-minute results.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Examples
The invention provides a track data-driven signal-controlled intersection periodic flow estimation method, which adopts a data driving method to estimate the passing flow of a signal-controlled intersection in each signal period based on sampled vehicle track data and comprises the following steps:
1) the periodic flow is divided into two parts, known and unknown, according to the parking position and the expected arrival time of the last queued sample trajectory, as shown in fig. 1:
wherein v iskA flow rate of period k;
the number of vehicles arriving before the last queued sample trajectory is the known flow;
the number of vehicles arriving after the last queued sampling trajectory is the unknown flow;
parking position of the sampling trajectory queued for the last; d0The average parking vehicle head distance is obtained; ω is the number of lanes in the study lane group.
2) And extracting parameters related to the flow, such as the number of sampling tracks and the time interval length of each part of each period, constructing a three-dimensional tensor comprising the flow of the unknown part of each period, and converting the periodic flow estimation problem into a data repair problem. The method specifically comprises the following steps:
21) for the period of observing the queued sampling track, extracting two parts of parameters related to the flow, namely the number of the observed sampling tracks and the length of an observation period, of each period, and constructing a period feature matrix, as shown in fig. 2:
wherein, XkA feature vector for the kth observed queued sampling trajectory period;
and
respectively corresponding to the observed sampling track numbers of the known flow part and the unknown flow part;
and
the lengths of the observation periods corresponding to the known and unknown flow portions, respectively.
22) For the period of the sample trace not observed in the queue, the periodic feature matrix of the previous observed trace is replaced by:
Xi＝Xi-1
wherein, XiNo queued sampling trajectory is observed for the feature vector of the ith cycle; xi-1The queued sample traces are observed for the i-1 th cycle of the feature vector.
23) Finally, a three-dimensional tensor is constructed by the feature matrix of each period in the study period, as shown in fig. 3:
wherein the content of the first and second substances,
for K cycles in the study periodAn initial tensor composed of eigenvectors; v. ofbefAnd vaftOne-dimensional vectors consisting of known and unknown flows of K periods in a research period respectively; n isbefAnd naftRespectively forming one-dimensional vectors by the number of sampling tracks correspondingly observed by K periods of known and unknown flow parts in a research period; t is tbefAnd taftAnd the one-dimensional vectors are respectively formed by the lengths of observation periods corresponding to the known and unknown flow parts of K periods in the research period.
3) And (4) repairing the constructed tensor based on a tensor decomposition method, so that the flow of each period can be obtained. The method specifically comprises the following steps:
31) the problem is converted into an optimization problem by decomposing an initial tensor containing unknown flow into a kernel tensor multiplied by a factor matrix of three dimensional directions based on the Tucker decomposition.
As shown in fig. 4, the Tucker decomposition of the initial tensor is as follows:
wherein the content of the first and second substances,
to be the decomposed nuclear tensor,
i.e., a non-negative tensor of size P × Q × R;
and
the dimensions of the factor matrixes are three, and the sizes of the factor matrixes are 3 multiplied by P, 2 multiplied by Q and K multiplied by R respectively; is prepared fromξ(xi ═ 1,2,3) is the directional product, representing the inner product of the tensor over dimension xi with the matrix.
This Tucker decomposition process can be translated into an optimization problem as follows:
wherein λ is a regularization strength parameter; the second term of the objective function is a regularization term.
32) And solving the optimization problem based on a gradient descent method to realize tensor Tucker decomposition.
Inputting: initial tensor
An error threshold epsilon;
initializing a kernel tensor with random values
And factor matrix A, B, C, initializing learning rate
Marking theta as a target function value;
if Δ θ > ε, cycle:
β←β+1
for the initial tensor
Each of which is not null
When the cycle is over, return to
A、B、C。
Wherein the content of the first and second substances,
representing the outer product; Δ θ is the difference between the two iterations; β is a parameter for initializing the learning rate.
33) And restoring the initial tensor based on the kernel tensor and the factor matrix, and realizing tensor repair, namely estimating the known flow of each period. And restoring the initial tensor based on the nuclear tensor and the factor matrix:
finally, the flow rate estimates for each cycle are as follows:
wherein the content of the first and second substances,
is the flow estimation value of period k in the research period;
is an unknown partial flow estimated based on a tensor decomposition method.
4) And taking the Shenzhen emperor Lufu middle road intersection as a case to verify the precision of the flow estimation method provided by the invention.
The case verification scene of the invention is 4 straight lanes of the north approach at the Fuzhonglu-Huang post road intersection in Shenzhen city, as shown in FIG. 5. The sampling vehicle is a drip operating vehicle, and the track uploading frequency is 3 seconds. The data acquisition period is 2017, 4 and 13, and 10: 30 to 14: 30. the real traffic flow is recorded by a high-definition camera erected on the spot. The average permeability is 8.6%, and the cart ratio is 4.2%. The intersection is controlled by a SMOOTH self-adaptive control system widely applied in Shenzhen city, and the time length of each period and the time length of green light fluctuate.
The Mean Absolute Error (MAE) and Mean relative Error (MAPE) were used to evaluate the estimation accuracy, calculated as follows:
the values of the algorithm-related parameters are shown in the following table:
TABLE 1 Algorithm-related parameters
| Parameter(s) | Value taking |
| P | 3 |
| Q | 2 |
| |
5 |
| λ | 0.01 |
| ε | 0.001 |
| |
108 |
Two existing representative methods are selected for comparison, namely the periodic-level flow estimation method of Yao et al (2019) and the time-interval-level flow estimation method of Zheng et al (2017), and the results are shown in fig. 6 and table 2. Therefore, the method provided by the invention is obviously higher than the existing method in the flow estimation precision of the periodic level and the time interval level. The periodic error is only 15.3%, and the hourly estimation error is only 5.1%.
TABLE 2 comparison of the estimation results of the present invention with the prior art methods
Claims (10)
1. A signal control intersection periodic flow estimation method driven by track data is characterized by comprising the following steps:
1) dividing the periodic flow into a known part and an unknown part according to the parking position and the expected arrival time of the last queuing sampling track;
2) extracting parameters related to flow of the known part and the unknown part in each period, constructing a three-dimensional tensor comprising the flow of the unknown part in each period, and converting the periodic flow estimation problem into a data repair problem;
3) and repairing the constructed tensor based on a tensor decomposition method to obtain the flow of each period.
2. The method for estimating the periodic flow of the signal-controlled intersection driven by the track data according to claim 1, wherein in the step 1), the flow in each period is divided into a known part and an unknown part by a last queued sampling track, and the method comprises the following steps:
wherein v iskIs the flow rate of the k-th cycle,
the number of vehicles arriving before the last queued sample trajectory, i.e. the known flow,
the number of vehicles arriving after the last queued sample trajectory, i.e. the unknown flow,
parking position of the sampling trajectory for the last queue, d0The average parking headway distance is shown, and omega is the number of lanes in the lane group.
3. The trajectory data-driven signal-controlled intersection periodic flow estimation method according to claim 2, wherein the step 2) specifically comprises the following steps:
21) for the period of observing the queued sampling track, extracting two known and unknown parameters related to the flow in each period, including the number of the observed sampling tracks and the length of an observation period, and constructing a period characteristic matrix;
22) for the period of the sampling track which is not observed in the queue, replacing the periodic feature matrix of the previous observed track;
23) and finally, constructing a three-dimensional tensor by using the feature matrix of each period in the study period.
4. The method for estimating the periodic traffic of the signal-controlled intersection driven by the trajectory data according to claim 3, wherein in the step 21), the periodic feature matrix is specifically:
wherein, XkA feature vector for the kth observed queued sampling trajectory period;
and
corresponding to the number of observed sample traces for the known and unknown portions respectively,
and
the lengths of the observation periods corresponding to the known and unknown portions, respectively.
5. The method for estimating the periodic traffic of the signalized intersection driven by the track data as claimed in claim 4, wherein in the step 22), for the period in which the queued sampling track is not observed, the period feature matrix of the previous observed track is replaced by the period feature matrix of the previous observed track, and the method comprises the following steps:
Xi＝Xi-1
wherein, XiIs the eigenvector of the ith cycle, which does not observe the queued sample traces, Xi-1The feature vector for the i-1 th cycle, which has observed the queued sample traces.
6. The method for estimating the periodic traffic of the signal-controlled intersection driven by the track data according to claim 4, wherein in the step 23), the constructed three-dimensional tensor expression is as follows:
wherein the content of the first and second substances,
for an initial tensor composed of K cycles of eigenvectors over the study period, vbefAnd vaftVector consisting of known and unknown flow for K cycles in the study period, nbefAnd naftRespectively, a vector consisting of the number of sampling trajectories observed for the K periods of known and unknown flow components within the study period, tbefAnd taftRespectively, vectors consisting of the lengths of observation periods corresponding to the K periods of known and unknown flow portions within the study period.
7. The trajectory data-driven signal-controlled intersection periodic flow estimation method according to claim 6, wherein the step 3) specifically comprises the following steps:
31) initial tensor containing unknown partial flow based on Tucker decomposition
Decomposing the data into a form of multiplying a kernel tensor by a factor matrix in three dimension directions, and converting a Tucker decomposition process into an optimization problem;
32) solving an optimization problem based on a gradient descent method, and realizing Tucker decomposition of an initial tensor;
33) and restoring the initial tensor based on the kernel tensor and the factor matrix, realizing tensor repair, obtaining the flow of the unknown part of each period, and finally finishing the estimation of the periodic flow of the intersection.
8. The method for estimating the periodic traffic of the signal-controlled intersection driven by the track data as claimed in claim 7, wherein in the step 31), an initial tensor is used
The expression of the Tucker decomposition of (1) is:
wherein the content of the first and second substances,
is the decomposed nuclear tensor, an
I.e. a non-negative tensor of size P x Q x R,
and
respectively factor matrices with corresponding dimensions of 3 XP, 2 XQ and KXR, respectively, a reference bookξXi is 1,2,3 is directionThe product computation represents the inner product of the tensor over dimension ξ with the matrix.
9. The trajectory data-driven signal-controlled intersection periodic flow estimation method according to claim 8, wherein in the step 32), if a Tucker decomposition process is converted into an optimization problem, the method comprises the following steps:
wherein λ is a regularization strength parameter, | | · |. non-calculation2The norm of L2 is shown,
is a regularization term.
10. The method for estimating the periodic traffic of the signal-controlled intersection driven by the track data according to claim 9, wherein in the step 33), the initial tensor is restored based on the kernel tensor and the factor matrix, and the method includes:
the flow rate estimates for each cycle are as follows:
wherein the content of the first and second substances,
in order to restore the initial tensor in the original state,
to investigate the flow estimate for period k over the period,
is an unknown partial flow estimated based on a tensor decomposition method.
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| CN113240902A (en) * | 2021-03-25 | 2021-08-10 | 同济大学 | Signal control road network path flow estimation method based on sampled vehicle trajectory data |
| CN114141013A (en) * | 2021-11-25 | 2022-03-04 | 东南大学 | Intersection signal timing method based on low-permeability network connection track data |
| CN114141013B (en) * | 2021-11-25 | 2022-12-13 | 东南大学 | Intersection signal timing method based on low-permeability network connection track data |
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