CN115798198B - Urban road network travel time distribution estimation method based on data fusion - Google Patents
Urban road network travel time distribution estimation method based on data fusion Download PDFInfo
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Abstract
According to the urban road network travel time distribution estimation method based on data fusion, the path rsk is firstly obtained based on the network-connected vehicle track data uploaded by the floating vehicle, then the travel time distribution probability density of any path is calculated, and the calibration time for AVI data is acquired through the electric warning bayonet equipment.
Description
Technical Field
The invention relates to the technical field of traffic state estimation, in particular to an urban road network travel time distribution estimation method based on data fusion.
Background
The travel time and the travel time distribution are important evaluation indexes of the traffic running state of the urban road network, travelers in the urban road network can make more reliable path selection based on accurate estimation of the travel time, and the travel time distribution can intuitively indicate the ground benefit and the running reliability of the urban road network and can also be used for determining the road network bottleneck, so that active control measures are applied and the overall traffic condition is improved. In the existing research, a single data source of floating car or AVI data is generally adopted to estimate the travel time distribution of a road section, and the method is mainly oriented to continuous flow (such as expressway) scenes. The floating car is a bus and a taxi which are provided with a vehicle-mounted GPS positioning device and run on an urban arterial road, and the data uploaded by the floating car is network-connected vehicle track data. However, the online vehicle track data uploaded by the floating vehicle has the problems of low uploading frequency, low market permeability, biased samples and the like, and the estimated stability and the accuracy of the estimated travel time distribution cannot be ensured; the electric warning bayonet device is based on AVI data (also called automatic identification data of vehicles, hereinafter referred to as AVI data), because the distribution density of the electric warning bayonet device in the urban road network is very limited, the universality of the travel time distribution estimation in the road network based on the AVI data cannot be ensured, and the estimation can be carried out only for the road sections with better distribution conditions of the local electronic bidding device.
Disclosure of Invention
In order to solve the problems of inaccuracy or low universality in the existing travel time estimation method due to the fact that stability of floating car data cannot be guaranteed and coverage rate of electric police monitoring equipment is limited in the prior art, the invention provides a city road network travel time distribution estimation method based on data fusion, which is not limited by the density factors of detector arrangement in a road network and can flexibly and accurately estimate travel time distribution of any given path in the road network.
The technical scheme of the invention is as follows: the urban road network travel time distribution estimation method based on data fusion is characterized by comprising the following steps of:
s1: determining a road network to be analyzed;
s2: obtaining a road network diagram of the road network to be analyzed, wherein the road network diagram comprises all flow directions of roads;
s3: constructing a path unit travel time distribution function;
the path unit is as follows: defining two continuous flow directions in the road network as a path unit;
based on the travel time of the network-connected vehicle track data in the road network to be analyzed, fitting the travel time distribution of an initial path unit by using a double-variable Gaussian mixture model GMM, wherein the probability density function PDF form of the travel time distribution function of the initial path unit is given by the following formula:
wherein t is - And t + Respectively representing the travel time of the upstream and downstream flows; c represents the number of component distributions in GMM, lambda c Is the weight of component c; τ c A two-variable gaussian distribution probability density function representing the component distribution c; mu (mu) c Andis the mean and variance of the component distribution c; τ () represents the overall two-variable gaussian distribution probability density function;
s4: fitting the initial path unit travel time distribution function GMM through a maximized likelihood function L based on network-connected vehicle track data of each path unit in the road network;
wherein E is all the roads included in the road network to be analyzedA path unit set of paths; n is n e The number of the observation network train connection samples on the path unit E E; t is t i- And t i+ Representing travel time of an ith internet protocol vehicle in the upstream and downstream flow directions;
s5: calculating the average travel time t of each flow direction m in the road network to be analyzed m ：
Wherein,for the mapping relation between the path unit e and the flow direction m, if the path unit e contains the flow direction m, the path unit e is +.>1, otherwiseIs 0;
s6: acquiring a target path rsk;
setting: the number of path units included in the target path rsk is NUM;
s7: GMM tau from initial path element travel time distribution 0 (t - ,t + ) Randomly generated N samples
Initializing a variable nu to 0;
s8: make the following stepsAnd from the condition distribution->Sampling;
s9: let nu=nu+1;
s10: steps S8 to S9 are circularly executed until all NUM path units in the target path rsk are listed;
s11: approximate t obtained by using nuclear density estimation KDE method to sample distribution rsk Probability density function τ (t) rsk ,b)：
Wherein t is rsk For the average travel time variable of path rsk, κ (·) is a gaussian kernel function, b is a smoothing parameter called bandwidth, M represents flow direction, M rsk A set of flow directions contained for path rsk;
s12: constructing an objective function based on the AVI data:
wherein P represents a local path, P is a path set, RS is a traffic start and stop OD pair set, K rs The path set between the OD pair rs is obtained; z is the function of the object to be measured,
as a decision variable, the remaining travel time of path rsk through AVI sequence p is represented;
in the objective function, the first termIs a typical OLS item;
second itemIs the variance that minimizes the residual error of different paths of the same flow direction combination between p;
w' 1 ,w' 2 the weights of the first term and the second term, respectively, v being the standard deviation of the vehicle travel time between the recorded AVI data pair p;
s13: solution minimization based on constraintsObjective function minZ, decision variable is obtainedSolution of (2);
the decision variables are determined using the following formulaThe solution of (2) is converted into an adjustment of the average flow direction travel time;
wherein,indicating the adjustment ratio of the flow direction m allocated to the path rsk within the range of AVI versus p; t is t m Travel time for flow direction m; />Represents the average travel time adjustment amount of the flow direction m; />Indicating whether the flow direction m is passed by rsk and the occurrence within the range of AVI sequence p; m is a set of all flow directions included in the road network to be analyzed;
s14: each component assigned to the GMM containing the target flow direction will be adjusted according to the component weights:
wherein c is the constituent in GMM, μ c Is the average value of the component distribution c, lambda c Is the weight of component c;
s15: based on the adjusted GMM, t is recalculated rsk Probability density function τ (t) rsk And b) obtaining the average travel time of the target path rsk.
It is further characterized by:
the value of the smoothing parameter b is as follows:
wherein,is the sample variance for doing the KDE;
the constraint conditions are as follows:
wherein t is p An average value representing the travel time recorded between any pair of AVI detectors;representing the travel time between a target pair of AVIs along path rsk; RS is OD pair set, K rs For the set of paths between OD and rs +.>Indicating whether the partial path p is passed by the path rsk; />Is an occurrence indicating whether the flow direction m is passed by rsk and within the range of AVI sequence p; />Defining as a residual term, which is the residual travel time of the path rsk through the AVI sequence p; f (f) rsk Representing path traffic data;
in step S12, the ratio of the two weights is defaulted to w' 1 :w' 2 ＝1:1。
According to the urban road network travel time distribution estimation method based on data fusion, the path rsk is firstly obtained based on the network-connected vehicle track data uploaded by the floating vehicle, then the travel time distribution probability density of any path is calculated, and the calibration time for AVI data is acquired through the electric warning bayonet equipment; in the method, the link of the upstream continuous flow direction and the downstream continuous flow direction is defined as a path unit, and the path unit is used as a basic unit of path travel time distribution, so that more refined modeling is performed, the travel time correlation relationship in the modeling unit is simplified, and the requirement on the network connection sample size is reduced; the technical route starts from the flow direction and the travel time distribution of the path units, and the sample set of the path unit combination is generated by the Monte Carlo sampling method, so that the travel time distribution of any given path in the road network can be flexibly estimated without being limited by factors such as the distribution density of detectors in the road network, and the method can be widely applied to urban road networks in the future, and has larger potential and wide application range.
Drawings
Fig. 1 is a schematic diagram of an urban road network travel time distribution estimation process in the present application;
FIG. 2 is an embodiment of a path element;
FIG. 3 is a network satellite map of embodiment 2;
FIG. 4 is a schematic diagram of the topology of the road network and the distribution points of the AVI in embodiment 2;
FIG. 5 is a VISUM network in example 2;
fig. 6 is a VISSIM network in example 2.
Detailed Description
The invention comprises a data fusion-based urban road network travel time distribution estimation method, which is characterized by comprising the following steps of:
s1: and determining the road network to be analyzed.
S2: and obtaining a road network diagram of the road network to be analyzed, wherein the road network diagram comprises the flow directions of all roads.
S3: constructing a path unit travel time distribution function;
the path unit is as follows: two continuous flow directions in the road network are defined as one path unit. As shown in fig. 2, the upstream is in a straight flow direction, and the downstream is in a left-turn fashion, so that a path unit is formed; the left turn flow direction and the downstream straight flow direction form a path unit.
Based on the definition of the path unit, the travel path of the vehicle can be characterized by a sequence of flow directions or a sequence of path units. By defining path elements, the travel time correlation between successive flows can be estimated explicitly.
Determining the probability density function (Probability Density Function, PDF) form of the initial path-unit travel-time distribution function given by the following equation using a two-variable gaussian mixture model GMM to fit the initial path-unit travel-time distribution in view of the bivariate nature of the path-unit travel-time:
wherein t is - And t + Respectively representing the travel time of the upstream and downstream flows; c represents the number of component distributions in the GMM, represents the number of modes in the distribution modeling, lambda c Is the weight of component c; τ c A two-variable gaussian distribution probability density function representing the component distribution c; mu (mu) c Andis the mean and variance of the component distribution c; τ () represents the overall two-variable gaussian distribution probability density function.
In particular, the data samples (t - ,t + ) The component quantity C can be set according to specific requirements, and is usually set to be between 2 and 5.
S4: fitting an initial path unit travel time distribution function GMM by using a maximized likelihood function L based on the network-connected vehicle track data of each path unit in the road network and an EM algorithm;
e is a path unit set of all paths included in the road network to be analyzed; n is n e The number of the observation network train connection samples on the path unit E E; t is t i- And t i+ Representing travel time of an ith internet protocol vehicle in the upstream and downstream flow directions; GMM parameters (λ, μ, σ) can be achieved by employing classical expectation maximization algorithms 2 ) And (5) estimating.
S5: calculating the average travel time t of each flow direction m in the road network to be analyzed m ：
Wherein,for the mapping relation between the path unit e and the flow direction m, if the path unit e contains the flow direction m, the path unit e is +.>1, otherwiseIs 0;
in general, given the path unit travel time distribution, the path travel time can be estimated correspondingly through convolution, but because of the difficulty in convolution and integration of GMM, the invention proposes to use a Monte Carlo Simulation (MCS) method to approach the path travel time distribution:
deriving a GMM distribution form;
as shown in equation (4), by integration, it can be inferred that the marginal distribution of the bivariate GMM is a univariate GMM, which has the same component number and weight as the corresponding bivariate GMM.
Given a double-variant gaussian condition distribution τ c (t + |t - ) Still a gaussian distribution after parameter adjustment, while the conditional distribution of GMM is still a gaussian mixture model.
The conditional distribution given by equation (5) is also a univariate GMM whose composition is a weight normalized univariate gaussian distribution.
Wherein ρ is a correlation coefficient, which is a fixed parameter in a binary gaussian distribution probability density function.
Because of the double-variable gaussian condition distribution τ given by equation (6) c (t + |t - ) Still a gaussian distribution after parameter adjustment, while the conditional distribution of the GMM is still a gaussian mixture model.
Then, based on formulas (4) to (6), the present application proposes the following steps to generate samples of arbitrary paths.
S6: acquiring a target path rsk;
setting: the number of path units included in the target path rsk is NUM;
s7: GMM tau from initial path element travel time distribution 0 (t - ,t + ) Randomly generated N samples
Initializing a variable nu to 0;
s8: make the following stepsAnd from the condition distribution->Sampling;
s9: let nu=nu+1;
s10: steps S8 to S9 are circularly executed until all NUM path units in the target path rsk are listed;
s11: approximate t obtained by using nuclear density estimation KDE method to sample distribution rsk Probability density function τ (t) rsk ,b)：
Wherein t is rsk For the average travel time variable of path rsk, κ (·) is a gaussian kernel function, b is a smoothing parameter called bandwidth, M represents flow direction, M rsk A set of flow directions contained for path rsk;
the value of the smoothing parameter b is as follows:
wherein,is the sample variance for doing the KDE;
as shown in fig. 1, in the method, estimation of the travel time distribution of a path unit is completed based on formulas (1) to (3), and the travel time distribution of any path of the road network is estimated by formulas (4) to (8), namely, the method is marked as follows: path travel time distribution estimation (prior); however, the estimation of the travel time distribution of the path unit and the estimation of the travel time distribution of any path of the road network are both performed by adopting the network-connected vehicle track data information, and the consistency of the travel time parameter and the parameter observed by the automatic identification of the vehicle cannot be ensured. In addition, since the network-connected vehicles in the urban road network are usually a biased sample, the method in the present application needs to further propose the step of aligning and adjusting the travel time of data fusion. The path travel time alignment model is derived first and then the flow direction travel time is adjusted.
The path travel time alignment model derivation process is as follows.
Based on external acquisition of path traffic data f rsk (OD versus path flow for path k between rs) the travel time adjuster aims to align the a priori travel time provided by the previously fitted GMM to coincide with the travel time between observed AVI detectors.
Therefore, the present invention uses the constraint conditions of the optimizing formula (11) in the formulas (9) and (10). Wherein equation (9) describes that the average travel time recorded between any pair of AVI detectors is constant equal to the weighted sum of travel times of paths through the AVI detectors, and equation (10) describes that the local path travel time is constant equal to the sum of flow direction travel times on the local path. The constraint of the formula (11) through the system equation formula (9) and the formula (10) can ensure that the initial travel time distribution obtained based on the network-connected vehicle estimation is still consistent with the AVI under the condition of bias. Meanwhile, the method fully combines the travel time information of AVI local observation with the global distribution information provided by the internet-connected vehicle, and solves the problem that AVI single data source is difficult to realize the whole-path network travel time estimation.
The constraint conditions are as follows:
wherein t is p An average value representing the travel time recorded between any pair of AVI detectors;representing the travel time between a target pair of AVIs along path rsk; RS is OD pair set, K rs For the set of paths between OD and rs +.>Indicating whether the partial path p is passed by the path rsk; />Is an occurrence indicating whether the flow direction m is passed by rsk and within the range of AVI sequence p; f (f) rsk Representing path traffic data; />The residual term is defined as the residual travel time of the path rsk passing through the AVI sequence p, and is the basis for adjusting the flow direction travel time.
S12: constructing an optimization objective function based on the least square error based on AVI data:
wherein P represents a local path, P is a path set, RS is a traffic start and stop OD pair set, K rs The path set between the OD pair rs is obtained; z is the function of the object to be measured,
as a decision variable, the remaining travel time of path rsk through AVI sequence p is represented;
in the objective function, the first termIs a typical OLS item;
second itemIs the variance that minimizes the residual error of different paths of the same flow direction combination between p;
w' 1 ,w' 2 the weights of the first and second terms, respectively, v is the standard deviation of the vehicle travel time between the recorded AVI data versus p. The ratio of the two weights defaults to w' 1 :w' 2 In specific implementation, the confidence level of the two targets may be set in actual operation, in this embodiment, w' 1 ,w' 2 The optimal weight ratio of (2) is 1:100.
the optimization target constructed by the formula (11) can be solved through a basic quadratic programming solving method, and the solution with the minimum travel time mean value difference between the same AVI pair of different paths, namely the optimal solution with the common compatibility of the multi-source data, is innovatively found under the condition that the average travel time observables of the multi-source data (network-connected vehicle track data and AVI data) are ensured to be consistent.
In the concrete implementation, the optimization model MinZ is a standard convex quadratic programming, and can be directly solved by adopting classical methods such as an interior point method or an external solver is called for solving. Wherein t is p And v are obtained by counting the mean and standard deviation of the differences between the matched vehicle timestamps between AVI pairs p,based on road network topology (whether the path passes through two sections in AVI pair p), f rsk By external input (path flow estimate or traffic survey statistics).
The flow direction travel time is adjusted as follows.
S13: based on constraint conditions, solving an objective function minimization objective function minZ to obtain a decision variableSolution of (2);
the decision variables are determined using the following formulaThe solution of (2) is converted into an adjustment of the average flow direction travel time;
wherein,indicating the adjustment ratio of the flow direction m allocated to the path rsk within the range of AVI versus p; t is t m Travel time for flow direction m; />Represents the average travel time adjustment amount of the flow direction m; />Indicating whether the flow direction m is passed by rsk and the occurrence within the range of AVI sequence p; m is a set of all flow directions included in the road network to be analyzed;
s14: each component assigned to the GMM containing the target flow direction will be adjusted according to the component weights:
wherein c is the constituent in GMM, μ c Is the average value of the component distribution c, lambda c Is the weight of component c.
In the method, the adjustment quantity of the local path p is distributed to each flow direction forming the local path according to the physical space mapping relation through a formula (12) and a formula (13), so that the flow direction adjustment quantity is obtained, and the new flow direction travel time is calculated; after obtaining the new flow direction travel time, the mean value of the GMM is correspondingly adjusted through the formula (14), namely, the step of "path-flow direction adjustment distribution" in fig. 1.
In other words, in the method, after the space full-coverage internet-access sample data and the space partial-coverage full-sample data AVI data are complemented, an accurate recognition result is obtained.
S15: finally, based on the adjusted GMM, t is recalculated rsk Probability density function τ (t) rsk B), obtaining the average travel time of the target path rsk.
In the urban road network travel time distribution estimation method, firstly, two-dimensional path unit travel time distribution is obtained through Gaussian mixture model fitting based on network-connected vehicle track data of each path unit in a road network; then, based on the travel time distribution of each path unit, constructing an arbitrary path travel time sample set in the road network by a Monte Carlo sampling method, and generating path travel time distribution probability density by a kernel density estimation method; and finally, combining the average travel time from point to point obtained by the automatic identification data of the vehicle, aligning and adjusting the path travel time distribution, and finally, distributing the travel time of all flow directions and any paths in the data path network. Compared with the prior art, the invention has the advantages of fully fusing and mining the existing observation data, finer travel time distribution modeling unit, easily acquiring fused input data, low cost, stronger use flexibility and the like.
The calculation procedure of the method of the present application is described below with example 1.
As shown in table 1, an example of the obtained AVI data.
Table 1: embodiments of AVI data
Table 2 is an example of vehicle track data for a networked vehicle.
Table 2: embodiment of vehicle track data of Internet-connected vehicle
| Vehicle ID | Time stamp | Road section | Distance travelled by road section |
| #V558 | 2022/02/02 10:31:20 | 112 | 35.6 |
| #V558 | 2022/02/02 10:31:23 | 112 | 62.1 |
Based on the data of tables 1 and 2, the post-path element (intersection 1-north straight, intersection 2-north left turn) GMM was fitted, with a group score C of 2:
is brought intoIn (1), the following steps are obtained:
0.4*τ 1 (t - ,t + |[26.2,30.5],[7.3,3.4] 2 )+0.6*τ 2 (t - ,t + |[28.5,32.2],[3.1,0.7] 2 )
the average travel time of the flow direction intersection 1-north straight is 27.4 seconds;
path flow (OD vs r=1, s=7, total of 7 alternative paths) example:
f rsk ＝[5,12,6,74,32,2,68]
the optimization model outputs each path flow adjustment example:
flow direction intersection 1-north straight average travel time adjustment example:
the average travel time of the flow direction intersection 1-north straight is 27.4+0.7=28.1 seconds
The adjusted GMM is:
0.4*τ 1 (t - ,t + |[26.5,30.5],[7.3,3.4] 2 )+0.6*τ 2 (t - ,t + |[28.9,32.2],[3.1,0.7] 2 )
sample 3 sample examples from the GMM:
[(27.3,30.7),(29.5,32.1),(24.1,34.5)]
OD versus 3 sample examples of path travel time of r=1, s= 7,k =1:
[170.5,186.2,199.2]
the final output OD versus path travel time profile r=1, s= 7,k =1:
the simulation case is taken as example 2, and the travel time distribution estimation method of the present application is verified, as shown in fig. 3, the road network is located in the southern area of a city, and is composed of 25 intersections, wherein 18 of the road network are signal intersections (including 14 four-arm intersections and 4T-shaped intersections). The invention establishes a simulation model by using VISUM and VISSIM to comprehensively evaluate the travel time distribution estimation effect. The simulation model is calibrated in the TFLOWFUZZY module of the VISUM using traffic collected from the electric warning bayonets, travel time collected from local taxi rentals, and signal timing schemes collected from local law enforcement. All data were collected at month 3 of 2019.
Fig. 4 shows the AVI layout position. According to the calibration result, the absolute error of the flow is smaller than 6veh/h, and the relative error is smaller than 9%. In a calibrated network, there are 28 OD nodes and 305 paths. To generate the required data sources, some vehicles are randomly sampled as networked vehicles. The simulation model was run for a total of two (simulation) hours and the required data file was output.
All experiments below were performed on a server with a 2.8GHz six-core CPU and 8GB memory. The method adopts an average absolute error (MAE) and an average percentage error (MAPE) evaluation index to evaluate the estimation effect of the invention.
In this embodiment, the bimodal GMM (i.e., component number 2) is used to fit the flow direction travel time distribution, so it divides the path element distribution into four modes (slow-slow, slow-fast, fast-slow, fast-fast). In this case, the number of components per unit time of the path of GMM fitting is set to 4, and the path time distribution is approximated from the distribution of 2,000 samples generated by the KDE. The evaluation results are shown in the following table 3, and it can be known that the road network travel time estimation method provided by the invention can realize better travel time distribution estimation both in the flow direction and in the path layer.
Table 3: evaluation results
Because the floating car has the problems of low uploading frequency, low market permeability, biased samples and the like, the estimated stability and the reliability of the estimated travel time distribution cannot be ensured; meanwhile, the distribution density of AVI data represented by electric police bayonets in the urban road network is very limited, and the universality of travel time distribution estimation in the road network cannot be guaranteed. In the technical scheme of the invention, after a path rsk is acquired based on track data of a floating car, the travel time distribution probability density of any path is calculated, and then the AVI data is used for calibrating time.
Claims (4)
1. The urban road network travel time distribution estimation method based on data fusion is characterized by comprising the following steps of:
s1: determining a road network to be analyzed;
s2: obtaining a road network diagram of the road network to be analyzed, wherein the road network diagram comprises all flow directions of roads;
s3: constructing a path unit travel time distribution function;
the path unit is as follows: defining two continuous flow directions in the road network as a path unit;
based on the travel time of the network-connected vehicle track data in the road network to be analyzed, fitting the travel time distribution of an initial path unit by using a double-variable Gaussian mixture model GMM, wherein the probability density function PDF form of the travel time distribution function of the initial path unit is given by the following formula:
wherein t is - And t + Respectively representing the travel time of the upstream and downstream flows; c represents the number of component distributions in GMM, lambda c Is the weight of component c; τ c A two-variable gaussian distribution probability density function representing the component distribution c; mu (mu) c Andis the mean and variance of the component distribution c; τ () represents the overall two-variable gaussian distribution probability density function;
s4: fitting the initial path unit travel time distribution function GMM through a maximized likelihood function L based on network-connected vehicle track data of each path unit in the road network;
e is a path unit set of all paths included in the road network to be analyzed; n is n e The number of the observation network train connection samples on the path unit E E; t is t i- And t i+ Representing travel time of an ith internet protocol vehicle in the upstream and downstream flow directions;
s5: calculating the average travel time t of each flow direction m in the road network to be analyzed m ：
Wherein,for the mapping relation between the path unit e and the flow direction m, if the path unit e contains the flow direction m, the path unit e is +.>1, otherwise->Is 0;
s6: acquiring a target path rsk;
setting: the number of path units included in the target path rsk is NUM;
s7: GMM tau from initial path element travel time distribution 0 (t-,t + ) Randomly generated N samplesInitializing a variable nu to 0;
s8: make the following stepsAnd from the condition distribution->Sampling;
s9: let nu=nu+1;
s10: steps S8 to S9 are circularly executed until all NUM path units in the target path rsk are listed;
s11: approximate t obtained by using nuclear density estimation KDE method to sample distribution rsk Probability density function τ (t) rsk ,b)：
Wherein t is rsk For the average travel time variable of path rsk, κ (·) is a gaussian kernel function, b is a smoothing parameter called bandwidth, M represents flow direction, M rsk A set of flow directions contained for path rsk;
s12: constructing an objective function based on the AVI data:
wherein P represents a local path, P is a path set, RS is a traffic start and stop OD pair set, K rs The path set between the OD pair rs is obtained; z is the function of the object to be measured,
as a decision variable, the remaining travel time of path rsk through AVI sequence p is represented;
in the objective function, the first termIs a typical OLS item;
second itemIs the variance that minimizes the residual error of different paths of the same flow direction combination between p;
w’ 1 ,w' 2 the weights of the first term and the second term, respectively, v being the standard deviation of the vehicle travel time between the recorded AVI data pair p;
s13: based on constraint conditions, solving a minimized objective function minZ to obtain a decision variableSolution of (2);
the decision variables are determined using the following formulaThe solution of (2) is converted into an adjustment of the average flow direction travel time;
wherein,represents the adjustment ratio of the flow direction m allocated to the path rsk within the range of AVI versus pExamples are; t is t m Travel time for flow direction m; />Represents the average travel time adjustment amount of the flow direction m; />Indicating whether the flow direction m is passed by rsk and the occurrence within the range of AVI sequence p; m is a set of all flow directions included in the road network to be analyzed;
s14: each component assigned to the GMM containing the target flow direction will be adjusted according to the component weights:
wherein c is the constituent in GMM, μ c Is the average value of the component distribution c, lambda c Is the weight of component c;
s15: based on the adjusted GMM, t is recalculated rsk Probability density function τ (t) rsk And b) obtaining the average travel time of the target path rsk.
2. The urban road network travel time distribution estimation method based on data fusion according to claim 1, wherein the method is characterized by comprising the following steps: the value of the smoothing parameter b is as follows:
wherein,is the sample variance for doing the KDE.
3. The urban road network travel time distribution estimation method based on data fusion according to claim 1, wherein the method is characterized by comprising the following steps: the constraint conditions are as follows:
wherein t is p An average value representing the travel time recorded between any pair of AVI detectors;representing the travel time between a target pair of AVIs along path rsk; RS is OD pair set, K rs For the set of paths between OD and rs +.>Indicating whether the partial path p is passed by the path rsk; />Is an occurrence indicating whether the flow direction m is passed by rsk and within the range of AVI sequence p;defining as a residual term, which is the residual travel time of the path rsk through the AVI sequence p; f (f) rsk Representing path traffic data.
4. The urban road network travel time distribution estimation method based on data fusion according to claim 1, wherein the method is characterized by comprising the following steps: in step S12, the ratio of the two weights is defaulted to w' 1 :w' 2 ＝1:1。
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