CN109858559B - Self-adaptive traffic analysis road network simplification method based on traffic flow macroscopic basic graph - Google Patents
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Abstract
The invention relates to a traffic flow macroscopic basic diagram-based self-adaptive traffic analysis road network simplifying method, which comprises the following steps: step S1: drawing a traffic flow macroscopic basic graph according to the road network traffic flow state data, and dividing time intervals of the MFD according to road network expression by applying a clustering method; step S2: simplifying the road network of each sub-period respectively; step S3: combining the simplified road networks with different resolutions, and performing dynamic traffic distribution based on simulation. Compared with the prior art, the method can adaptively adjust the time interval division according to different road network traffic conditions, better accords with the real traffic conditions, improves the traffic analysis efficiency by reducing the road network scale, and greatly reduces the calculation amount of simulation and distribution.
Description
Technical Field
The invention relates to the field of traffic engineering, in particular to a self-adaptive traffic analysis road network simplifying method based on a traffic flow macroscopic basic diagram.
Background
The complexity of the traffic analysis road network is closely related to the traffic analysis efficiency: on one hand, the dense road network can accurately reflect real traffic conditions, but the calculation amount is huge, and the calculation efficiency is low; on the other hand, a sparse road network can greatly reduce the computational burden, but may bring extra congestion at peak times. Therefore, a single analysis road network cannot give consideration to both analysis precision and analysis efficiency, so the research aims to adaptively divide heterogeneous time periods in a time dimension according to the dynamic traffic situation of the road network, simplify and obtain the road network matched with the traffic situation of each heterogeneous time period aiming at each heterogeneous time period, realize the traffic analysis method with adjustable precision in the time dimension, and improve the efficiency of traffic analysis while ensuring the analysis precision.
At present, most of road network simplification methods at home and abroad are static, and time heterogeneity of traffic conditions is not well considered, namely real road network traffic conditions always fluctuate and there are early and late peak periods and peak balancing periods, and the static simplification methods cannot obtain a road network matched with the traffic conditions at all the periods. In recent years, simple dynamic reduction methods have been proposed, but merely dividing the time slots evenly does not guarantee that the net appears the same in each time slot. A Macroscopic basic Map (MFD) of traffic flow is used as a basic map for describing the overall operation rule of the network traffic flow, and can reflect the overall level of the road network and the dynamic change of traffic. Therefore, the establishment of the MFD-based adaptive traffic analysis road network simplification method has important practical significance for real-time dynamic simplification of the road network.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a self-adaptive traffic analysis road network simplifying method based on a traffic flow macroscopic basic diagram, which comprises the following steps: a road network simplification method based on an improved Toeplitz inverse covariance multidimensional time series clustering method and a connectivity enhancement algorithm is disclosed, time heterogeneity of traffic conditions is considered in time series clustering based on MFD, and therefore a plurality of time periods with similar road network performance are obtained through division, and traffic dynamic characteristics of each time period are respectively reflected; the connectivity enhancement algorithm can extract important road sections of the road network in different time segments according to the clustering result to obtain the simplified road network matched with the traffic condition, the road network dense in the peak period can ensure the analysis precision of the simplified road network, the road network sparse in the peak flattening period can improve the calculation efficiency, and the problems of a static simplification method and a simple dynamic simplification method are well solved, so that the self-adaptive simplification of the traffic analysis road network is realized.
The purpose of the invention can be realized by the following technical scheme:
a self-adaptive traffic analysis road network simplification method based on a traffic flow macroscopic basic graph comprises the following steps:
step S1: drawing a traffic flow macroscopic basic graph according to the road network traffic flow state data, and dividing time intervals of the MFD according to road network expression by applying a clustering method;
step S2: simplifying the road network of each sub-period respectively;
step S3: combining the simplified road networks with different resolutions, and performing dynamic traffic distribution based on simulation.
The step S1 specifically includes:
step S11: selecting road network traffic flow data in an analysis time period to obtain average flow and average density;
step S12: clustering the average flow and the average density of the road network to minimize the objective function, and obtaining a plurality of clusters P ═ P with approximately same road network performance1,…,PKAn endpoint of each cluster is a time node of each sub-period;
step S13: presetting a reasonable time interval number S according to the actual traffic condition of the road network, selecting a scheme which minimizes the sum of the standard deviations of the density of the road network in each time interval as an optimal scheme, and simultaneously obtaining a corresponding penalty item;
step S14: the classification condition is embodied through a traffic flow macroscopic basic diagram, and different classification schemes are generated for different traffic conditions.
The mathematical expression of the average flow is:
wherein:
is the average flow, n is the number of road sections, qlFor the flow rate of the section i,
the mathematical expression for the average density is:
wherein:
is the average density of the road network, llFor the length of the section l, lanelNumber of lanes, k, of road section llIs the density of the section i.
In step S12, a penalty term β 'is introduced separately for the time range where the peak hours are located in the morning and evening, and β' is less than or equal to β, and the mathematical expression of the objective function is as follows:
wherein: thetaiAs inverse covariance matrix of class i, P being of all classesA time sequence distribution set is a covariance inverse matrix set of various types, K is the number of sub-time sequences, lambda is a regularization parameter, the sparsity of the matrix is determined, | | | & | survival1Is L1 norm, XtIs a sub-time series, -ll (X)t，Θi) Is a sub-time sequence XtLog-likelihood values belonging to class i, β being the current time series Xt-1A penalty term when not belonging to class i, β 'being the current sub-time series X't-1Penalty terms when not belonging to class i, PiFor the set of time series assigned to the ith class,
to judge the subsequence Xt-1Whether it belongs to class i, Xt-1Is a sub-temporal sequence not belonging to the morning-evening rush hour, X't-1Is a sub-time sequence belonging to the morning and evening peak hours.
The mathematical expression of the penalty term is as follows:
wherein: k is a radical oftThe road network density at time t is shown,
is the average density, k, of the road networkt(β') is a road network density at time t belonging to the morning and evening peak hours,
is the average road network density over time period s.
The step S2 specifically includes:
step S21: from the original road network NoExtracting an initial simplest road network N only containing high-level road sectionsp；
Step S22: on the basis of the time nodes obtained after clustering, the road network N of the sub-period spsAnd (3) carrying out road section expansion: taking the road section travel time reaching the dynamic user balance as the road section cost, and combining any start point and any end point in the road network with ODkIf the combined section l is connectedo(lo∈No) Time t of tripoLess than NpsSection of roadps(lps∈Nps) Time t of trippsThen will loAdding to set NpsIn the last time period, the simplified road network NrsOnly contains important road sections with obvious traffic influence;
step S23: obtaining a simplified road network set N consisting of a plurality of simplified road networks with different complexity degreesr＝{Nr1，…，Nrs}。
The step S3 specifically includes:
step S31: in the original road network NoOn the basis of the method, labels are added to each road section to distinguish the existence state of the road section at each moment;
step S32: will make up road network NcThe method is applied to mesoscopic traffic simulation software for operation, when the existing states of the road section in different time periods are inconsistent, for example, the existing states are changed from existing to non-existing, vehicles on the road section are stopped from moving, no vehicle enters the road section at the same time until the existing state of the road section is restored to exist, and iteration is carried out until NcA dynamic user balance state is achieved.
Compared with the prior art, the invention has the following beneficial effects:
1) the dynamic changes of the overall flow, density and speed of the road network in the analysis period are considered.
2) The whole analysis time period is divided into a plurality of sub time periods, and the road network traffic state of each sub time period is approximately the same.
3) The time interval division can be adaptively adjusted according to different road network traffic conditions, and the real traffic conditions are better met.
4) The reduction of the road network scale improves the efficiency of traffic analysis and greatly reduces the calculation amount of simulation and distribution.
Drawings
FIG. 1 is a schematic diagram of a traffic analysis road network according to an embodiment of the present invention;
FIG. 2 is a simplified flow chart of the adaptive road network according to the present invention;
fig. 3 is a macroscopic basic graph (MFD) of a road network traffic flow according to an embodiment of the present invention;
FIG. 4 is a diagram illustrating MFD clustering results according to the present invention;
FIG. 5 is a schematic view of traffic demand of each sub-period divided by the present invention;
FIG. 6 is a flow chart of the "connectivity enhancement algorithm" of the present invention;
FIG. 7 is a simplified road network diagram for each sub-period of the present invention;
FIG. 8 is a comparison graph of simulation time of the simplified road network and the original road network according to the present invention;
FIG. 9 is a comparison graph of the distribution time of the simplified road network and the original road network according to the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
A self-adaptive traffic analysis road network simplification method based on a traffic flow macroscopic basic graph comprises the following steps:
step S1: drawing a traffic flow macroscopic basic graph according to the road network traffic flow state data, applying a clustering method, and dividing time intervals of the MFD according to road network performance, wherein the method specifically comprises the following steps:
step S11: selecting road network traffic flow data in an analysis period to obtain average flow and average density, wherein the mathematical expression of the average flow is as follows:
wherein:
is the average flow, n is the number of road sections, qlFor the flow rate of the section i,
the mathematical expression for the average density is:
wherein:
is the average density of the road network, llFor the length of the section l, lanelNumber of lanes, k, of road section llIs the density of the section i.
Step S12: the method is characterized in that the average flow and the average density of the road network are clustered by applying an improved Toeplitz Inverse Covariance-Based multi-dimensional time series Clustering method (Advanced Toeplitz Inverse Covariance-Based Clustering, ATICC) to minimize an objective function and obtain a plurality of clusters P ═ { P ═ with approximately same road network performance1，…，PKAnd the end point of each cluster is the time node of each sub-period, wherein in order to reflect the traffic-specific early-late peak phenomenon, a penalty term β 'is introduced into the time range of the early-late peak period, and β' is less than or equal to β, and the mathematical expression of the objective function is as follows:
wherein: thetaiFor the covariance inverse matrix of the ith class, P is a time sequence distribution set of all classes, and is a covariance inverse matrix set of each class, K is the number of sub-time sequences, and lambda is a regularization parameter, and determines the sparsity of the matrix, | | · |1Is L1 norm, XtIs a sub-time series, -ll (X)t，Θi) Is a sub-time sequence XtLog-likelihood values belonging to class i, β being the current time series Xt-1A penalty term when not belonging to class i, β 'being the current sub-time series X't-1Penalty terms when not belonging to class i, PiFor the set of time series assigned to the ith class,
to judge the subsequence Xt-1Whether it belongs to class i, Xt-1Is a sub-temporal sequence not belonging to the morning-evening rush hour, X't-1Is a sub-time sequence belonging to the morning and evening peak hours.
The mathematical expression of the penalty term is:
wherein: k is a radical oftThe road network density at time t is shown,
is the average density, k, of the road networkt(β') is a road network density at time t belonging to the morning and evening peak hours,
is the average road network density over time period s.
Step S13: presetting a reasonable time interval number S according to the actual traffic condition of the road network, selecting a scheme which minimizes the sum of the standard deviations of the density of the road network in each time interval as an optimal scheme, and simultaneously obtaining a corresponding penalty item;
step S14: the classification condition is embodied through a traffic flow macroscopic basic diagram, and different classification schemes are generated for different traffic conditions.
Step S2: the method for simplifying the road network of each sub-period comprises the following steps:
step S21: from the original road network NoExtracting an initial simplest road network N only containing high-level road sectionsp；
Step S22: based on the time nodes obtained after clustering, applying a Connectivity Enhancement Algorithm (CEA) to the road network N of the sub-period spsAnd (3) carrying out road section expansion: taking the travel time of a road section reaching Dynamic User Equilibrium (DUE) as the road section cost, and combining any starting point and destination point OD in a road networkkIf the combined section l is connectedo(lo∈No) Travel time oftoLess than NpsSection of roadps(lps∈Nps) Time t of trippsThen will loAdding to set NpsIn the last time period, the simplified road network NrsOnly contains important road sections with obvious traffic influence;
step S23: obtaining a simplified road network set N consisting of a plurality of simplified road networks with different complexity degreesr＝{Nr1，…，Nrs}。
Step S3: combining the simplified road networks with different resolutions, and then performing dynamic traffic distribution based on simulation, specifically comprising:
step S31: in the original road network NoOn the basis of the method, labels are added to each road section to distinguish the existence state of the road section at each moment;
step S32: will make up road network NcThe method is applied to mesoscopic traffic simulation software for operation, when the existing states of the road section in different time periods are inconsistent, for example, the existing states are changed from existing to non-existing, vehicles on the road section are stopped from moving, no vehicle enters the road section at the same time until the existing state of the road section is restored to exist, and iteration is carried out until NcA dynamic user balance state is achieved.
And finally, comparing the road network performance of the simplified road network and the original road network, and verifying the accuracy of the simplified method.
Fig. 1 is a simulated road network of Alexandria used in the embodiment of the present invention, which is developed based on the traffic network of Alexandria city, virginia, and the whole road network includes 85 traffic analysis cells, 6,724 road segments, 2,573 nodes, and the road segments include various levels of roads, such as highways, expressways, branches, and the like.
The overall flow of the adaptive road network simplification method is shown in fig. 2, and a road network traffic flow macroscopic basic graph is drawn by utilizing the average flow and the average density of the road network according to the actual traffic flow condition of the traffic analysis road network, as shown in fig. 3. Secondly, carrying out multi-dimensional time series clustering on the average flow and the average density, and ensuring that the traffic state in each time period after clustering is as consistent as possible. In this embodiment, the whole analysis period (24h) is planned to be clustered into 6 sub-periods with different durations, that is, S is 6, given a penalty value β is 300, and β' of the optimal solution is calibrated to be 80, where the durations of the respective sections are: 255min, 150min, 195min, 380min, 225min, 235min, and the clustering results of MFDs are shown in FIG. 4. Fig. 5 is a traffic demand distribution situation of each sub-period, and it can be seen that there is a significant difference in traffic demand of each sub-period. Meanwhile, high-grade road segments are extracted from the original road network to form an initial simplest road network, then the road network simplification method-connectivity enhancement algorithm of FIG. 6 is respectively applied to each time interval to perform appropriate road network expansion on the simplest road network according to the segmentation result obtained after clustering, and the important road segments in the time interval are added to obtain 6 simplified road networks with different resolutions as shown in FIG. 7. Table 1 counts the coverage time range and road network status information of each simplified road network and the original road network. In combination with the traffic demands of the various sub-periods, it can be found that: the number of the simplified road network sections is in positive correlation with the traffic demand, and the simplified road network has more sections in the time period with large traffic demand. And finally, combining the 6 simplified road networks, and operating mesoscopic simulation software to perform traffic simulation and dynamic traffic distribution until a dynamic user balance state is achieved. In the specific simulation and distribution process, if a certain road section "disappears" in the simplified road network of the next time period, a "freezing method" is applied to the vehicle affected by the change of the state of the road section, that is: if the label of a certain road section is changed from 1 to 0, the vehicle originally running on the road section stops moving, and meanwhile, no vehicle enters the road section until the road section reappears.
Table 1 simplified road network and original road network information statistical table
In order to compare the road network performance of the adaptive simplification method and the original scheme, the simulation results of the combined simplified road network and the original road network are compared, and the simulation results comprise the average vehicle running time (ave. Table 2 records simulation and assignment results for the simplified road network and the original road network iterated 15 times:
table 2 road network performance verification statistical table
| Ave.time/min | Ave.dist/mile | Aff.time/min | CPU/sec | |
| Simplified road network | 5.904 | 5.086 | 5.935 | 10905.44 |
| Original road network | 5.605 | 4.812 | 5.803 | 14366.44 |
| Mean error (%) | 5.34 | 5.69 | 2.27 | — |
| Efficiency improvement (%) | — | — | — | 24.09 |
From comparison of simulation results, it is found that the driving states (average driving time and average driving mileage) of all vehicles in the simplified road network are about 5% of the error of the original road network, and the error of the affected vehicle is less than 3%, so that the simplified road network is considered to exhibit substantially the same performance as the original road network. Meanwhile, the CPU time used by the whole simulation and distribution is reduced by more than 20% compared with the original road network, and as can be seen from the graph 8 and the graph 9, the simplified scheme has great advantages in simulation and distribution efficiency, and the method is proved to be capable of remarkably improving the analysis efficiency.
Claims (5)
1. A self-adaptive traffic analysis road network simplification method based on a traffic flow macroscopic basic graph is characterized by comprising the following steps:
step S1: drawing a traffic flow macroscopic basic graph according to the traffic flow state data of the road network, applying a clustering method to divide time intervals of the MFD according to the road network performance,
step S2: the road network of each sub-period is simplified respectively,
step S3: combining a plurality of simplified road networks with different resolutions, and then performing dynamic traffic distribution based on simulation;
the step S1 specifically includes:
step S11: selecting traffic flow data of the road network in an analysis period to obtain average flow and average density,
step S12: clustering the average flow and the average density of the road network to minimize the objective function, and obtaining a plurality of clusters P ═ P with approximately same road network performance1，…，PKThe end point of each cluster is the time node of each subinterval,
step S13: presetting a reasonable time interval S according to the actual traffic condition of the road network, selecting a scheme which minimizes the sum of the standard deviations of the road network density in each time interval as an optimal scheme, and simultaneously obtaining corresponding punishment items,
step S14: the classification condition is embodied through a traffic flow macroscopic basic diagram, and different classification schemes are generated for different traffic conditions;
the step S2 specifically includes:
step S21: from the original road network NoExtracting an initial simplest road network N only containing high-level road sectionsp，
Step S22: on the basis of the time nodes obtained after clustering, the road network N of the sub-period spsAnd (3) carrying out road section expansion: taking the travel time of the road section reaching the dynamic user balance as the road section cost, combining ODk the start point and the end point of any one road network, and if the road section l of the combination is connectedoTime t of tripoLess than NpsSection of roadpsTime t of trippsThen will loAdding to set NpsIn the last time period, the simplified road network NrsOnly important road sections with significant traffic impact,
step S23: obtaining a simplified road network set N consisting of a plurality of simplified road networks with different complexity degreesr＝{Nr1，…，Nrs}。
2. The method for simplifying the adaptive traffic analysis road network based on the macroscopic basic graph of the traffic flow according to claim 1, wherein the mathematical expression of the average flow is as follows:
wherein:
is the average flow, n is the number of road sections, qlFor the flow rate of the section i,
the mathematical expression for the average density is:
wherein:
is the average density of the road network, llFor the length of the section l, lanelNumber of lanes, k, of road section llIs the density of the section i.
3. The method for simplifying the adaptive traffic analysis road network based on the macroscopic basic map of the traffic flow according to claim 1, wherein in the step S12, a penalty term β 'is introduced separately for the time range of the peak hours in the morning and the evening, and β' is less than β, and the mathematical expression of the objective function is as follows:
wherein: thetaiFor the covariance inverse matrix of the ith class, P is a set of time sequence distribution of all clusters, and is a set of covariance inverse matrix of each cluster, K is the number of sub-time sequences, and lambda is a regularization parameter, so as to determine the sparsity of the matrix, | | · |1Is L1 norm, XtIs a sub-time series, -ll (X)t，Θi) Is a sub-time sequence XtLog-likelihood values belonging to class i, β being the current time series Xt-1A penalty term when not belonging to class i, β 'being the current sub-time series X't-1Penalty terms when not belonging to class i, PiFor the set of time series assigned to the ith class,
to judge the subsequence Xt-1Whether it belongs to class i, Xt-1Is not a son of the morning and evening peak periodTime sequence, X't-1Is a sub-time sequence belonging to the morning and evening peak hours.
4. The method for simplifying the adaptive traffic analysis road network based on the macroscopic basic graph of the traffic flow according to claim 3, wherein the mathematical expression of the penalty term is as follows:
wherein: k is a radical oftThe road network density at time t is shown,
is the average density, k, of the road networkt(β') is a road network density at time t belonging to the morning and evening peak hours,
is the average road network density over time period s.
5. The method for simplifying the adaptive traffic analysis road network based on the macroscopic basic map of the traffic flow according to claim 1, wherein the step S3 specifically comprises:
step S31: in the original road network NoOn the basis of the method, labels are added to each road section to distinguish the existence state of the road section at each moment;
step S32: will make up road network NcThe method is applied to mesoscopic traffic simulation software for operation, when the existing states of the road section at different time intervals are inconsistent, the vehicles on the road section stop moving, no vehicle enters the road section at the same time until the existing state of the road section is restored to exist, and the iteration is carried out until NcA dynamic user balance state is achieved.
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