CN109285346B - Urban road network traffic state prediction method based on key road sections - Google Patents
Urban road network traffic state prediction method based on key road sections Download PDFInfo
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Abstract
The patent discloses a method for predicting urban road network traffic states based on key road sections, which is characterized by comprising the following steps: the method comprises the following steps: preprocessing data; step two: establishing a road network space weight matrix; step three: establishing a time correlation matrix; step four: the key road segments are identified using a spatiotemporal correlation matrix. Step five: establishing a deep convolutional neural network, predicting the future road network state, and evaluating a prediction model; according to the method, the urban traffic flow state is predicted from a large-range road network level, the traffic flow is induced from a macroscopic view, the time-space correlation characteristics of the traffic flow are fully mined, and by identifying the key road sections in the road network, compared with the method that the historical states of all the road sections are used as input data, the training time of a model can be greatly reduced, and the prediction efficiency is improved; and a convolutional neural network is used as a prediction model, so that the prediction result is more accurate.
Description
Technical Field
The invention relates to the field of traffic. In particular to a method for predicting the whole traffic flow state of a road network by identifying key road sections from the urban road network by utilizing a space-time correlation algorithm.
Background
The urban traffic network congestion problem is increasingly serious due to the acceleration of the urbanization process and the continuous increase of the motor vehicle holding amount in China, and the urban traffic network congestion problem becomes one of the important factors for hindering the rapid development of urban health. The short-time traffic flow of the urban road network is predicted in real time, a real-time and reliable route is provided for travelers, the traveling efficiency is improved, and the traffic behavior is induced. Meanwhile, powerful technical support is provided for traffic information service, traffic guidance, traffic control and relieving of traffic jam problems of management departments.
With the rapid development and popularization of Intelligent Traffic technology (ITS), mass Traffic data collected from terminals such as toll stations, checkpoints, video detectors, mobile phones and the like urge the Traffic System to change intelligently, and provide a data base for the development of future Intelligent Traffic. In addition, with the rise of artificial intelligence algorithms and the successful application in the traffic prediction field, the data-driven model based on deep learning also provides algorithm support for the insight, understanding and prediction of complex traffic systems. The method is applied to new scenes such as real-time perception and prediction of traffic situation, traffic cloud computing and the like by combining big data and an artificial intelligence technology, and provides a new means for prediction and analysis of road network situation.
Short-term traffic flow prediction is always a hot point of research of scholars at home and abroad, and the existing methods are mainly divided into parametric models, nonparametric models, artificial intelligence methods, combined models and the like. The parameter model is simple and easy to construct, but for complex and changeable traffic flows, hysteresis exists, and emergencies cannot be dealt with; the non-parametric model is simple in structure, but is not suitable for the non-linearity and uncertainty characteristics of traffic flow; the artificial intelligence method can be adaptive to a complex and nonlinear traffic system, the prediction precision is high, but the training of the model needs a large amount of data, and the training time is long; the combined model combines the advantages of multiple models, but is more complex to construct. The deep learning is a method for automatically learning features from big data, has strong self-learning capability, has been successfully applied to the aspects of image and voice recognition and the like, and achieves certain results in traffic state prediction.
The characteristics of large scale, multiple types, low value density and the like of the traffic big data determine that a large amount of redundant information is contained in the mass information. In the current research for predicting the road network state by utilizing deep learning, mass data are directly applied to prediction, so that the model is complex but the accuracy is not remarkably improved. In research, it is found that traffic flow shows obvious correlation in time and space, and part of roads have great influence on adjacent road sections or local road networks. The invention provides a method for identifying key road sections in a road network by using a space-time correlation algorithm and predicting the state of the whole road network by using traffic parameters of the key road sections. The method fully considers the time-space correlation of traffic flow, can simplify model input on the premise of ensuring precision, improves prediction efficiency, and well overcomes the defects of long training time and large dependence on data quantity in the conventional method for predicting the road network state by utilizing deep learning.
Disclosure of Invention
The invention aims to solve the problems of long training time and low prediction efficiency in the current deep learning, fully excavate the time-space correlation characteristics of road network traffic, identify key road sections which have large influence on the states of adjacent road sections and regional road networks, and provide a prediction method for predicting the traffic state of the road network by using the time-space characteristics of the key road sections. According to the method, a floating car technology is utilized, original data are firstly cleaned, and the topological relation between the average speed of each road section in a road network and the road sections is obtained; then, identifying key road sections in the road network by utilizing a space-time correlation algorithm; and finally, building a deep learning network, converting the speed of the key road section into a space-time state matrix as input, training the prediction model, predicting the traffic flow state of the future whole road network, and evaluating the model. The method considers the time-space correlation of the road network, fully excavates the time-space characteristics of the road network, identifies the key road sections in the road network, predicts the whole road network state based on the time-space characteristics, is innovative in theory and has strong guiding significance to the reality.
In order to achieve the purpose, the invention adopts the following technical scheme:
the method comprises the following steps: and (4) preprocessing data. And cleaning the original data, calculating the average speed of each road section, matching the average speed to the road section, and selecting a road network to be researched.
In order to obtain accurate floating car data, the original data needs to be preprocessed, briefly, the error data is deleted, and the missing data is filled by a linear interpolation method.
Secondly, calculating the average speed of the road section in each time period, wherein the calculation method comprises the following steps: average speed of all vehicles in a certain section in a certain time period. The calculation formula is shown as (1)
In the formula: v. ofx，jRepresents the average speed of the road sections of the x road sections in the j time period, x epsilon (1, 2, …, l), namely, total l road sections.
Representing the average speed of vehicle i at Δ t and n representing the number of vehicles on the road segment.
Can be obtained from the formula (2).
In the formula: s represents the length of the road segment and Δ t represents the length of the time period.
The calculated speed values are matched to the road segments so that each road segment has an average speed value for each time segment.
Step two: and establishing a road network spatial weight matrix. According to a complex network theory, a k-order adjacency matrix between road sections is established by adopting a topological relation between the road sections, and a road network space weight matrix is established according to the k-order adjacency matrix.
When the edges x and y are directly connected, the relationship of the two edges is defined as a first-order adjacency. Similarly, a second-order adjacency may be described as a first-order adjacency of a first-order adjacency, and so on, a k-order adjacency matrix for a certain road segment may be established. The adjacency may be described as:
in the formula: omegax，yThe adjacent relation between the x-th road section and the y-th road section is shown, and the value ranges of x and y are both [1, l]I.e. on a road sectionAnd performing iteration.
The urban traffic network can be abstracted into an undirected graph and a directed graph, and the undirected graph is obtained if only static network topology is considered; if the traffic flow is considered, the map is a directed graph. In the method, the flow direction of the traffic flow is fully considered, so that the topological relation of the road network is abstracted by adopting a directed graph mode, and the spatial correlation of the traffic flow can be reflected more truly. Taking fig. 2 and fig. 3 as an example for explanation, given a network consisting of 8 edges and 9 nodes, when the network is an undirected graph, its first and second order adjacency matrices based on edges are shown in fig. 1; when the network is a directed graph, its adjacency matrix is as shown in fig. 2.
In the whole road network, when k-order adjacent road sections are considered, 1-k-order adjacent matrixes of space objects are established, and the matrixes are added to obtain a space weight matrix of the whole road network. In addition, the adjacent matrices of each order need to be weighted in addition in consideration of the fact that the farther the distance from the link, the weaker the mutual spatio-temporal influence. The distribution of the weights is given by equation (4).
In the formula: q. q.siRepresents the weight of the ith order adjacency matrix, and the value range of i is [1, k]And k is the order of the adjacency matrix.
The weighted spatial weight matrix representing the spatial correlation between the road segments can be calculated by equation (5):
in the formula: w is the weighted spatial weight matrix, qiWeight, Q, representing the ith order adjacency matrix(i)Is an i-order space matrix, and the value range of i is [1, k ]]。
Step three: a time correlation matrix is established. And measuring the time correlation among the road sections in the road network by using a Pearson correlation function to obtain a time correlation matrix of the road network.
Specifically, the average speed of the road sections in the road network in one day is subjected to correlation analysis to obtain the time correlation (correlation coefficient) of the flow of each road section, and then the correlation coefficient is used as the evaluation basis to measure the time correlation of the road sections. The time correlation coefficient of the two road segments can be calculated by equation (6).
In the formula: gamma rayx，yRepresenting the time-dependent coefficients of the links X and y, where X ═ X1，x2，…，xz]Is the average speed vector of a road section with a sampling period of p and x in one day, and Y is [ Y ═ Y [1，y2，…，yz]Is the average speed vector of y road sections in the road section per day, the number z of elements of X, Y is related to the sampling period,
respectively, are the arithmetic mean of the elements within the vector. And in the actual road network, gammax，yHas a value range of [ -1, 1 [)]Negative values indicate a tendency for the x and y segments to exhibit negative correlation, and closer to-1 indicates that the correlation is more pronounced. For calculation convenience, gamma needs to be matchedx，yTaking the absolute value of (a), i.e. gammax，yThe closer to 0, the less significant the correlation between the two road sections is; the closer to 1, the more significant the correlation between the two links.
And measuring the time correlation of the traffic flow states of the two road sections in one day by using a Pearson correlation function, and establishing a time correlation matrix T to represent the time correlation of the road network.
The elements in the matrix T represent the time correlation between two road segments. For the convenience of the next calculation, the autocorrelation of the road section is not considered, namely the diagonal element gamma of the matrix T1，1、γ2，2、γl，lAre all zero. Since in the history data, each timeThe traffic flow states of one day present features that are different, so in the calculation, a time correlation matrix T is established for the average speed of each day1，T2，…，TdI.e. d days of historical status correspond to d different time dependency matrices.
Step four: the key road segments are identified using a spatiotemporal correlation matrix.
Performing dot multiplication on the spatial weight matrix and the time correlation matrix of a certain day to obtain the time-space correlation matrix of the road network in the day, namely:
Ha＝W·Ta(8)
in the formula: haRepresenting the space-time state matrix of day a, W representing the spatial weight of the weighted road network, TaRepresents the time correlation matrix of the day a, and the value range of a is [1, d]. Then HaIs an l x l matrix, and the value range of each element in the matrix is [0, 1%]Closer to 1 indicates more significant spatio-temporal correlation.
After the road network space-time correlation matrix of the day a is obtained, the frequency of the space-time correlation index (namely, the numerical value of each column) of each road section between 0 and 1 and taking 0.1 as the step length is counted. Taking x road segments as an example, the number of the spatio-temporal correlation indexes of the x road segments, i.e. the correlation parameters of the row corresponding to the x road segments, is l (where the autocorrelation coefficient of the x road segments is set to 0). Statistics of l parameters at [0, 0.1 ]]、(0.1，0.2]、…、(0.9，1.0]Frequency of each interval. For comprehensively considering the influence of the time-space correlation among the road sections in all historical states, after the frequency distribution of the road sections in each day is counted, the frequency distribution is added, so that the sum of the frequency of a certain road section in each section in the historical state can be obtained and recorded as f1、f2、…、f10Respectively represent a certain road section at [0, 0.1 ]]、(0.1，0.2]、…、(0.9，1.0]Frequency of each interval. The evaluation criterion of the key road section is the weighted sum of the frequency of each section, namely:
ca＝0.95×f10+0.85×f9+0.75×f8+0.65×f7(9)
in the formula: c. CaRepresenting criticality of the road section a, f10、f9、f8、f7Respectively represent the road sections a at (0.9, 1.0)]、(0.8，0.9]、(0.7，0.8]、(0.6，0.7]The frequency sum in the interval.
By criticality caThe criticalities of all road sections can be sorted, the road sections sorted in the front are extracted as key road sections according to the percentage of the total number of the road sections, and the average speed of the key road sections is extracted as an input value of the prediction model.
Step five: and establishing a deep Convolutional Neural Network (CNN), predicting the future road Network state, and evaluating the prediction model.
First, a sample set is established, and the ratio of 2: the scale of 1 is divided into a training set and a test set.
Secondly, extracting average speed data of the key road sections from the historical data, converting the average speed data into a space-time state matrix, and using the space-time state matrix as the input of a prediction model. Specifically, the average speeds of all the links are arranged in a matrix in the form of the link number on the abscissa and the time on the ordinate. Then, modeling by adopting a neural convolution network, and comprising the following steps of:
(1) input and output variables are determined. The input variable is a time-space state matrix of a key road section in a road network, and the number of neurons in an input layer is the same as that of the key road section; the output variable is an integral state matrix of the future road network, the integral state matrix comprises average speeds of all road sections in the road network, and the number of neurons in an output layer is the same as that of all road sections in the road network.
(2) And (3) constructing an end to end deep convolutional neural network model, and setting the structural parameters of the convolutional neural network. Training a convolutional neural network with an input layer-convolutional layer-pooling layer-output layer structure under the input of a training set, measuring the difference between the output value of an output layer and the true value by using a loss function, and minimizing the loss function by using a BPTT algorithm to obtain the optimal model parameters.
(3) And predicting the overall state of the road network in a future period of time. And extracting the average speed of the key road sections from the test set, converting the average speed into a space-time state matrix, inputting the space-time state matrix into the trained prediction model in the second step, and obtaining an output vector, namely the overall traffic flow state of the road network in the next time period.
And finally, establishing a prediction model evaluation index system taking the Mean Square Error (MSE) and the Root Mean Square Error (RMAE) as standards, and evaluating the prediction precision of the model. MAE and RMSE were calculated according to the following equations (10) and (11).
In the formula: u represents the number of time slots, l is the number of road segments, npIs represented by the number of time periods, np＝l×u。
The invention has the advantages that:
(1) the method predicts the urban traffic flow state from the large-range road network level, can control the urban traffic situation evolution on the whole, and is favorable for inducing the traffic flow macroscopically;
(2) the time-space correlation characteristics of the traffic flow are fully mined, the quality of input data in prediction is improved by identifying key road sections in a road network, and more importantly, compared with the method that the historical states of all the road sections are used as the input data, the training time of a model can be greatly reduced, and the prediction efficiency is improved;
(3) compared with the traditional parameter model, non-parameter model and the like, the convolutional neural network is adopted as the prediction model, so that the complex and non-linear characteristics of the traffic flow can be better adapted, the robustness is better, and the prediction result is more accurate.
Drawings
FIG. 1 is a schematic diagram of an undirected graph adjacency matrix
FIG. 2 is a schematic diagram of a directed graph adjacency matrix
FIG. 3 is a graph of the average speed of the pre-processed road section
FIG. 4 is a road network of an area to be studied
FIG. 5 shows a first and second order adjacency matrix (part) of the road network
FIG. 6 is a spatial weight matrix (part) of road network
FIG. 7 is a time correlation matrix (part) between 6-month and 1-day road segments
FIG. 8 is a time correlation matrix (part) between 8-month and 1-day road segments
FIG. 9 is a spatiotemporal correlation matrix (part) between 6-month and 1-day road segments
FIG. 10 shows the criticality of the road segments
FIG. 11 is a key road segment distribution in road network
FIG. 12 is a schematic diagram of spatio-temporal state matrix transformation
FIG. 13 shows a CNN prediction model structure
FIG. 14 is a graph of MSE as a function of training times
FIG. 15 is a flow chart of the method.
Detailed Description
The present invention will be described in detail with reference to the following examples. The data used is floating car data of a certain area in beijing city provided by a certain company, and includes 278 road segments, the sampling frequency of the data is 2 minutes, and the data includes 92 days of data in three months of 6, 7 and 8. For ease of calculation, 6:00 to 23:00, namely, the night running time period with small traffic flow is eliminated.
The implementation route of the invention comprises the following steps:
the method comprises the following steps: and (4) preprocessing data. And cleaning the original data, calculating the average speed of each road section, matching the average speed to the road section, and selecting a road network to be researched.
In order to obtain accurate floating car data, the original data needs to be preprocessed, briefly, the error data is deleted, and the missing data is filled by a linear interpolation method.
Secondly, calculating the average speed of the road section in each time period, wherein the calculation method comprises the following steps: average speed of all vehicles in a certain section in a certain time period. The calculation formula is shown as (12)
In the formula: v. ofx，jRepresents the average speed of the road segments of the x road segments in the j time period, x e (1, 2, …, 278).
Representing the average speed of vehicle i at Δ t and n representing the number of vehicles on the road segment.
Can be obtained from the formula (13).
In the formula: s represents the length of the road segment and Δ t represents the length of the time period.
The calculated speed values are matched to the road segments so that each road segment has an average speed value for each time segment. The preprocessed input is shown in fig. 3 and includes three fields, time dt, link number linkid, and speed (km/h).
In the present invention, a road network composed of 278 road segments is taken as a research object, and a schematic diagram of the road network is shown in fig. 4.
Step two: and establishing a road network spatial weight matrix. According to a complex network theory, a 5-stage adjacency matrix between road sections is established by adopting a topological relation between the road sections, and a road network space weight matrix is established according to the 5-stage adjacency matrix.
When the edges x and y are directly connected, the relationship of the two edges is defined as a first-order adjacency. Similarly, a second-order adjacency may be described as a first-order adjacency of a first-order adjacency, and so on, a 5-order adjacency matrix for a certain road segment may be established. The adjacency may be described as:
in the formula: omegax，yThe adjacent relation between the x-th road section and the y-th road section is shown, and the value ranges of x and y are both [1, 278 ]]I.e. iterates between 278 road segments.
The urban traffic network can be abstracted into an undirected graph and a directed graph, and the undirected graph is obtained if only static network topology is considered; if the traffic flow is considered, the map is a directed graph. In the method, the flow direction of the traffic flow is fully considered, so that the topological relation of the road network is abstracted by adopting a directed graph mode, and the spatial correlation of the traffic flow can be reflected more truly. The first and second order adjacency matrices created according to the topological relation of the road network are shown in fig. 5. (road segment numbering is reduced to 1, 2, … …)
In this example, when 5 th-order neighboring links are considered, 1 to 5 th-order adjacency matrices of spatial objects are established, and the matrices are summed to obtain a spatial weight matrix of the whole road network. In addition, the adjacent matrices of each order need to be weighted in addition in consideration of the fact that the farther the distance from the link, the weaker the mutual spatio-temporal influence. The assignment of the weights is given by equation (15).
In the formula: q. q.siRepresents the weight of the ith order adjacency matrix, and the value range of i is [1, 5 ]]。
The weighted spatial weight matrix characterizing the spatial correlation between road segments can be calculated by equation (16):
in the formula: w is the weighted spatial weight matrix, qiWeight, Q, representing the ith order adjacency matrix(i)Is an i-order space matrix, and the value range of i is [1, 5 ]]. Fig. 6 is a partial spatial weight matrix after the weighting of the road network.
Step three: a time correlation matrix is established. And measuring the time correlation among the road sections in the road network by using a Pearson correlation function to obtain a time correlation matrix of the road network.
Specifically, the average speed of the road sections in the road network in one day is subjected to correlation analysis to obtain the time correlation (correlation coefficient) of the flow of each road section, and then the correlation coefficient is used as the evaluation basis to measure the time correlation of the road sections. The time correlation coefficient of the two road segments can be calculated by equation (17).
In the formula: gamma rayx，yRepresenting the time-dependent coefficients of the links X and y, where X ═ X1，x2，…，x481]Is the average speed vector of the x road section 6:00-23:00 with the sampling period of 2 minutes, and Y is [ Y ═ Y-1，y2，…，y481]Is the average speed vector for the y road segments 6:00-23:00 in the road segment,
respectively, the arithmetic mean value of elements in the vector, and the value ranges of x and y are both [1, 278 ]]. And in the actual road network, gammax，yHas a value range of [ -1, 1 [)]Negative values indicate a tendency for the x and y segments to exhibit negative correlation, and closer to-1 indicates that the correlation is more pronounced. For calculation convenience, gamma needs to be matchedx，yTaking the absolute value of (a), i.e. gammax，yThe closer to 0, the less significant the correlation between the two road sections is; the closer to 1, the more significant the correlation between the two links.
And measuring the time correlation of the traffic flow states of the two road sections in one day by using a Pearson correlation function, and establishing a time correlation matrix T to represent the time correlation of the road network.
The elements in the matrix T represent the time correlation between two road segments. For the convenience of the next calculation, the autocorrelation of the road section is not considered, namely the diagonal element gamma of the matrix T1，1、γ2，2、γ278，278Are all zero. Since the traffic flow status of each day shows a difference in characteristics in the history data, the average speed for each day is calculatedEstablishing a time correlation matrix T1，T2，…，T92I.e. a history of 92 days corresponds to 92 different time dependency matrices. Fig. 7 and 8 are partial link time correlation matrices for days 6/month 1 and days 8/month 1.
Step four: the key road segments are identified using a spatiotemporal correlation matrix.
Performing dot multiplication on the spatial weight matrix and the time correlation matrix of a certain day to obtain the time-space correlation matrix of the road network in the day, namely:
Ha＝W·Ta(19)
in the formula: haRepresenting the space-time state matrix of day a, W representing the spatial weight of the weighted road network, TaRepresents the time correlation matrix of the day a, and the value range of a is [1, 92 ]]. Then HaIs a 278 x 278 matrix, and the value range of each element in the matrix is [0, 1]Closer to 1 indicates more significant spatio-temporal correlation. FIG. 9 is a spatiotemporal correlation matrix for a 6 month 1 day segment.
After the road network space-time correlation matrix of the day a is obtained, the frequency of the space-time correlation index (namely, the numerical value of each column) of each road section between 0 and 1 and taking 0.1 as the step length is counted. Taking x-segment as an example, 278 spatio-temporal correlation indexes of the x-segment, that is, correlation parameters of the column corresponding to the x-segment (where the autocorrelation coefficient of the x-segment is set to 0) are provided. 278 statistical parameters are in [0, 0.1 ]]、(0.1，0.2]、…、(0.9，1.0]Frequency of each interval. For comprehensively considering the influence of the time-space correlation among the road sections in all historical states, after the frequency distribution of the road sections in each day is counted, the frequency distribution is added, so that the sum of the frequency of a certain road section in each section in the historical state can be obtained and recorded as f1、f2、…、f10Respectively represent a certain road section at [0, 0.1 ]]、(0.1，0.2]、…、(0.9，1.0]Frequency of each interval. The evaluation criterion of the key road section is the weighted sum of the frequency of each section, namely:
ca＝0.95×f10+0.85×f9+0.75×f8+0.65×f7(20)
in the formula: c. CaRepresenting criticality of the road section a, f10、f9、f8、f7Respectively represent the road sections a at (0.9, 1.0)]、(0.8，0.9]、(0.7，0.8]、(0.6，0.7]The frequency sum in the interval.
By criticality caThe criticalities of all road segments may be ranked. Fig. 10 shows the road segments at the top 9 of the criticality ranking in the road network, and according to the road segment numbers, the key road segments and the speed information thereof can be extracted. In the present example, the top 60%, i.e., 166 top-ranked road segments are extracted as the key road segments, as shown by the red road segments in fig. 11, and the average speed of the key road segments is extracted as the input value of the prediction model.
Step five: and establishing a deep Convolutional Neural Network (CNN), predicting the future road Network state, and evaluating the prediction model.
First, a sample set is established, and the ratio of 2: the proportion of 1 is divided into a training set and a test set, namely, data of 61 days in 6 and 7 months are extracted as the training set, and data of 31 days in 8 months are extracted as the test set.
Secondly, extracting average speed data of the key road sections from the historical data, converting the average speed data into a space-time state matrix, and using the space-time state matrix as the input of a prediction model. Specifically, the average speeds of all the links are arranged in a matrix in the form of the link number on the abscissa and the time on the ordinate. Fig. 12 shows the conversion of the speed of the key road section into a space-time state matrix and the visualization thereof. It can be seen that the traffic flow velocities of road segments exhibit strong spatiotemporal correlation.
Then, modeling by adopting a neural convolution network, and comprising the following steps of:
(1) input and output variables are determined. The input variable is a time-space state matrix of a key road section in a road network, and the number of neurons in an input layer is the same as that of the key road section, namely 166; the output variable is the overall state matrix of the future road network, including the average speed of all road segments in the road network, and the number of neurons in the output layer is the same as that of all road segments in the road network, namely 278. The schematic structural diagram of the model is shown in fig. 13, the left side is input as traffic flow speed information of the key road section, and the right side is output as the traffic flow state of the whole road network. The intermediate training and prediction is based on a deep convolutional neural network.
(2) An end to end deep convolutional neural network model is constructed, and the structural parameters of the convolutional neural network are set, wherein the specific structure is shown in table 1. Training a convolutional neural network with an input layer-convolutional layer-pooling layer-output layer structure under the input of a training set, measuring the difference between the output value of an output layer and the true value by using a loss function, and minimizing the loss function by using a BPTT algorithm to obtain the optimal model parameters.
TABLE 1 CNN model parameter settings
(3) And predicting the overall state of the road network in a future period of time. And extracting the average speed of the key road sections from the test set, converting the average speed into a space-time state matrix, inputting the space-time state matrix into the trained prediction model in the second step, and obtaining an output vector, namely the overall traffic flow state of the road network in the next time period.
And finally, establishing a prediction model evaluation index system taking the Mean Square Error (MSE) and the Root Mean Square Error (RMAE) as standards, and evaluating the prediction precision of the model. MAE and RMSE were calculated according to the equations (21) and (22).
In the formula: u-79846, l-278, npIs represented by the number of time periods, np＝l×u＝22197188。
The traffic flow speed of the road network consisting of 278 road segments is predicted 2 minutes later by using the 166 key road segment speeds in the example. During the training process of the model, the MSE gradually decreases with the increase of the training steps, as shown in fig. 14, that is, the prediction accuracy of the model is also continuously improved.
And (3) predicting the overall state of 278 road segments of the road network by adopting 166 key road segments, wherein the final prediction precision is that RMSE is 6.64, and the training time of the model is 370 seconds (based on four TITAN Xp video card parallel operation). Under the same settings of the number of model layers, hidden layer parameters (see table 1) and training times (100), compared with the method that the state of the 278 road segments 2 minutes later is predicted by adopting the average speed of the 278 road segments without adopting key road segments, the prediction precision is improved by 1.04%, and the time required by training is reduced by 10.62%.
TABLE 2 comparison of predicted effects using key road segments
Therefore, the method can improve the training efficiency of the model on the premise that the prediction precision of the method is not greatly different from that of the original method, even the prediction precision of the method is improved. When the urban road network is larger in scale, the method has the advantages that the method is more obvious in performance, the state of the road network in the future is more quickly predicted, and the method is very suitable for on-line training and real-time prediction of traffic states.
Claims (2)
1. A method for predicting traffic state of urban road network based on key road segments is characterized by comprising the following steps:
the method comprises the following steps: data pre-processing
Cleaning the original data, calculating the average speed of each road section, matching the average speed to the road section, and selecting a target road network; the data preprocessing comprises deleting error data and filling up missing data by using a linear interpolation method; and calculating the average speed of the road section in each time period;
step two: establishing a road network spatial weight matrix
Abstracting the topological relation of the road network by adopting a directed graph mode, and utilizing the topology among the road sectionsEstablishing a k-order adjacency matrix among road sections, and establishing a road network space weight matrix according to the k-order adjacency matrix; when the edges x and y are directly connected, defining the relation of the two edges as first-order adjacency; the second-order adjacency can be described as the first-order adjacency of the first-order adjacency, and by analogy, a k-order adjacency matrix of a certain road section is established; the adjacency is described as:
in the formula: omegax，yThe adjacent relation between the x-th road section and the y-th road section is shown, and the value ranges of x and y are both [1, l]I.e. iterate between 1 road segment;
in the whole road network, when k-order adjacent road sections are considered, 1-k-order adjacent matrixes of space objects are established, and the matrixes are added to obtain a space weight matrix of the whole road network; when the addition is carried out, the adjacent matrixes of all orders are weighted when the addition is carried out on the basis of the characteristic that the mutual spatio-temporal influence is weaker as the distance from the road section is farther; the weight is distributed by
To obtain, wherein: q. q.siRepresents the weight of the ith order adjacency matrix, and the value range of i is [1, k]K is the order of the adjacent matrix; the weighted spatial weight matrix characterizing the spatial correlation between road segments can be represented by
Calculated, in the formula: w is the weighted spatial weight matrix, qiWeight, Q, representing the ith order adjacency matrix(i)Is an i-order space matrix, and the value range of i is [1, k ]]；
Step three: establishing a time correlation matrix
Measuring time correlation among road sections in a road network by using a Pearson correlation function to obtain a time correlation matrix of the road network;
average speed of road sections in road network in one dayPerforming correlation analysis to obtain a correlation coefficient of the flow of each road section in time, and measuring the correlation of the road section in time by taking the correlation coefficient as an evaluation basis; the time correlation coefficient of the two road sections can be represented by formula
Calculation, in the formula: gamma rayx，yRepresenting the time-dependent coefficients of the links X and y, where X ═ X1，x2，…，xz]Is the average speed vector of a road section with a sampling period of p and x in one day, and Y is [ Y ═ Y [1，y2，…，yz]Is the average speed vector of y road sections in the road section per day, the number z of elements of X, Y is related to the sampling period,
respectively, the arithmetic mean of the elements in the vector; gamma rayx，yHas a value range of [ -1, 1 [)]Negative values indicate a tendency for the x and y segments to exhibit negative correlation, and closer to-1 indicates that the correlation appears more pronounced; for gammax，yTaking the absolute value of (a), i.e. gammax，yThe closer to 0, the less significant the correlation between the two road sections is; the closer to 1, the more significant the correlation between the two road sections is; measuring the time correlation of the traffic flow states of the two road sections in one day by using a Pearson correlation function, and establishing a time correlation matrix T to represent the time correlation of the road network
Diagonal element gamma of matrix T1，1、γ2，2、γl，lAre all zero, and in the calculation, a time correlation matrix T is established for the average speed of each day1，T2，…，TdThat is, the historical state of d days corresponds to d different time correlation matrixes;
step four: identifying a key road section by utilizing a space-time correlation matrix;
performing dot multiplication on the spatial weight matrix and the time correlation matrix of a certain day to obtain a time-space correlation matrix H of the road network in the daya＝W·Ta(ii) a In the formula: haRepresenting the space-time state matrix of day a, W representing the spatial weight of the weighted road network, TaRepresents the time correlation matrix of the day a, and the value range of a is [1, d]；HaIs an l x l matrix, and the value range of each element in the matrix is [0, 1%]Closer to 1 indicates more significant spatio-temporal correlation;
after a road network space-time correlation matrix of the day a is obtained, counting space-time correlation indexes of all road sections, namely the numerical value of each row, wherein the frequency is between 0 and 1 and takes 0.1 as the step length; after counting the frequency distribution of the road sections in each day, summing the frequency distribution to obtain the sum of the frequency of the road sections in each section in the historical state, and recording the sum as f1、f2、…、f10Respectively represent the road section at [0, 0.1 ]]、(0.1，0.2]、…、(0.9，1.0]Frequency of each interval; the evaluation criterion of the key road section is the weighted sum of the frequency of each section, ca＝0.95×f10+0.85×f9+0.75×f8+0.65×f7(ii) a In the formula: c. CaRepresenting criticality of the road section a, f10、f9、f8、f7Respectively represent the road sections a at (0.9, 1.0)]、(0.8，0.9]、(0.7，0.8]、(0.6，0.7]Frequency sum in the interval; by criticality caSorting the criticalities of all road sections, extracting the road sections sorted in the front as key road sections according to the percentage of the total number of the road sections, and extracting the average speed of the key road sections as an input value of a prediction model;
step five: establishing a deep convolutional neural network, predicting the future road network state, and evaluating a prediction model; firstly, establishing a sample set, and dividing the sample set into a training set and a testing set according to the ratio of 2: 1; secondly, extracting average speed data of the key road section from historical data, converting the average speed data into a space-time state matrix, and using the space-time state matrix as the input of a prediction model; the input variable is a time-space state matrix of a key road section in a road network, and the number of neurons in an input layer is the same as that of the key road section; the output variable is an integral state matrix of the future road network, the integral state matrix comprises average speeds of all road sections in the road network, and the number of neurons in an output layer is the same as that of all road sections in the road network.
2. The method for predicting the traffic state of the urban road network based on the key road segments according to claim 1, wherein the step five specifically comprises the following steps:
s501, sorting the average speeds of all road sections into a matrix in a mode that the abscissa is the road section number and the ordinate is the time;
s502 employs a neural convolutional network modeling, which includes:
(1) determining input and output variables
The input variable is a time-space state matrix of a key road section in a road network, and the number of neurons in an input layer is the same as that of the key road section; the output variable is an integral state matrix of a future road network, and comprises the average speed of all road sections in the road network, and the number of neurons in an output layer is the same as that of all road sections in the road network;
(2) constructing deep convolutional neural network model, and setting structural parameters of convolutional neural network
Training a convolutional neural network with an input layer-convolutional layer-pooling layer-output layer structure under the input of a training set, measuring the difference between an output value and a true value of an output layer by using a loss function, and minimizing the loss function by using a BPTT algorithm to obtain an optimal model parameter;
(3) predicting the whole state of road network in future period
Extracting the average speed of the key road sections from the test set, converting the average speed into a space-time state matrix, inputting the space-time state matrix into the trained prediction model in the second step, and obtaining an output vector, namely the traffic flow state of the whole road network in the next time period;
(4) establishing a prediction model evaluation index system taking the root mean square error and the root mean square error as standards, and evaluating the prediction precision of the model; the square root error is calculated as
The root mean square error is calculated by the formula
In the formula: u represents the number of time slots, 1 is the number of road segments, npIs represented by the number of time periods, np＝l×u。
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