A Traffic Flow Prediction Method Based on Adaptive Graph Fusion Convolutional Network

Abstract

The present invention relates to a traffic flow prediction method based on an adaptive graph fusion convolutional network, comprising the following steps: constructing a road network to be predicted as a graph model, which is called a road network graph model; inputting the historical traffic of the node into an adaptive graph fusion convolutional module for processing, the adaptive graph fusion convolutional module is used to establish an adaptive static adjacency matrix and an adaptive dynamic adjacency matrix according to the generated road network graph model, and the static-dynamic graph fusion layer performs fusion operation to extract corresponding spatial features; the road network spatial features extracted by the adaptive graph fusion convolutional module are organized by using the residual enhanced gated recurrent unit; a hidden state vector sequence is processed by a node embedded self-attention layer; a fully connected layer is constructed for dimensional conversion, and the obtained hidden state sequence is input into the fully connected layer to obtain the prediction results on each road section.

Description

Technical Field

[0001] The present invention relates to a traffic flow prediction method. Background Art

[0002] The traffic flow prediction problem mainly predicts the traffic flow information of the current target node in the future for a period of time by considering the historical time series characteristics of the traffic flow. As a research hotspot in the field of intelligent transportation, traffic flow prediction is of great significance for traffic guidance and route planning. With the development of artificial intelligence and deep learning, neural network models based on deep learning have gradually been applied to traffic prediction. Compared with traditional time series prediction methods, deep learning technology with autonomous feature representation ability and powerful function approximation ability has greater advantages in spatio-temporal data mining and improves the accuracy of traffic prediction.

[0003] Traditional methods based on mathematical statistics and classical machine learning methods often model, analyze and predict the time series data of a certain observation point in the road network. More representative methods include historical average [1], autoregressive integrated moving average model [2], Kalman filter model [3], etc. Subsequently, with the development of deep learning, end-to-end neural network models have been widely used in time series prediction problems. Researchers have applied various deep learning methods to traffic prediction tasks. Many studies use convolutional neural networks to learn the spatial features of different nodes in time slices, and apply convolutional neural networks or recurrent neural networks to extract the time features of traffic data. Reference [4] converts the traffic network into a grayscale image and applies a model based on convolutional neural network to predict traffic speed. Reference [5] applies long short-term memory network and gated recurrent unit to extract the dependencies of time series data.

[0004] Although the above models have made great progress in traffic prediction tasks, convolutional neural networks are more suitable for processing Euclidean space data, such as image and grid data. And it is not suitable for data processing in non-Euclidean space, such as the structural data in graphs. The emergence of graph neural networks enables the model to process data in non-Euclidean space and provides a new way for processing data with complex non-uniform structures such as road networks. Reference [6] proposes a gated graph convolutional network for traffic prediction based on this method, and this model is applicable to traffic prediction problems with different topological structures. Reference [7] successfully improves the traffic prediction performance under complex spatio-temporal relationships by designing a spatio-temporal synchronous modeling mechanism to merge spatio-temporal blocks. Reference [8] performs a fusion operation on various spatio-temporal graphs parallel in different time periods to learn hidden spatio-temporal dependencies.

[0005] References:

[0006] [1]B.L.Smith and M.J.Demetsky,“Traffic flow forecasting:comparison ofmodeling approaches,”J.Transp.Eng.,vol.123,no.4,pp.261–266,1997

[0007] [2]M.M.Hamed,H.R.Al-Masaeid,and Z.M.B.Said,“Short-term prediction oftraffic volume in urban arterials,”J.Transp.Eng.,vol.121,no.3,pp.249–254,1995.

[0008] [3]C.P.Van Hinsbergen,T.Schreiter,F.S.Zuurbier,J.Van Lint,and H.J.VanZuylen,“Localized extended kalman filter for scalable real-time traffic stateestimation,”IEEE Trans.Intell.Transp.Syst.,vol.13,no.1,pp.385–394,Mar.2011.

[0009] [4]X.Ma,Z.Dai,Z.He,J.Ma,Y.Wang et al.,"Learning traffic as images:adeep convolutional neural network for large-scale transportation networkspeed prediction,"Sensors,17(4),p.818,2017.

[0010] [5]R.Fu,Z.Zhang,and L.Li,“Using lstm and gru neural network methodsfor traffic flow prediction,”in Proc.31st Youth Acad.Annu.Conf.Chin.Assoc.Autom.(YAC),2016,pp.324–328.

[0011] [6] B.Yu, H.Yin, and Z.Zhu, "Spatio-temporal graph convolutional networks: A deep learning framework for traffic forecasting," arXiv preprint arXiv:1709.04875, 2017.

[0012] [7] C.Song, Y.Lin, S.Guo, and H.Wan, “Spatial-temporal synchronous graph convolutional networks: A new framework for spatial-temporal network data forecasting,” in Proc. AAAI Conf. Artif. Intell., vol. 34, no. 01, 2020, pp. 914–921.

[0013] [8] M.Li and Z.Zhu, “Spatial-temporal fusion graph neural networks for traffic flow forecasting,” in Proc. AAAI Conf. Artif. Intell., vol. 35, no. 5, 2021, pp. 4189–4196. Summary of the Invention

[0014] The object of the present invention is to provide a traffic flow prediction method based on an adaptive graph fusion convolutional network. Compared with other methods, this method has a smaller prediction error on road network structures of various different scales, indicating that this method can be more flexibly applied to actual prediction and can achieve accurate prediction results. The technical solution is as follows:

[0015] A traffic flow prediction method based on an adaptive graph fusion convolutional network, comprising the following steps:

[0016] Step 1, construct the road network to be predicted into a graph model, which is called the road network graph model. The road network sections are modeled as the nodes of the graph, and each road section node is equipped with a road network sensor. The connection relationship between road sections is modeled as the edges of the graph, and the traffic flow of each road section is described as the attribute characteristics of the nodes;

[0017] Step 2: Input the historical traffic of the nodes into the adaptive graph fusion convolution module for processing. The adaptive graph fusion convolution module is used to establish an adaptive static adjacency matrix and an adaptive dynamic adjacency matrix based on the generated road network graph model, and perform a fusion operation by the static-dynamic graph fusion layer to extract the corresponding spatial features. The method is as follows:

[0018] 1) For a traffic flow sequence input X = (X 1 , X 2 , …, X I ) ∈ R I×N containing I time steps, where the traffic flow at the i-th time step is denoted as X i ;

[0019] 2) Construct the static adjacency matrix of the road network graph model, which is called the adaptive static adjacency matrix. The adaptive static adjacency matrix A S in the adaptive graph fusion convolution layer is ReLU(tanh(a 1 (EE T ))), where E ∈ R N×D represents a randomly initialized learnable node embedding, defined in the network according to the number of nodes N and the custom dimension D. E T is the transpose of E, and a 1 is a network parameter;

[0020] 3) A residual-enhanced gated recurrent unit is designed after the adaptive graph fusion convolution module. The residual-enhanced gated recurrent unit takes the road network spatial features extracted by the adaptive graph fusion convolution module as input and outputs a hidden state vector;

[0021] 4) Construct the dynamic adjacency matrix of the road network graph model, which is called the adaptive dynamic adjacency matrix. Combine the traffic flow X i at the i-th time step with the hidden state vector output by the residual-enhanced gated recurrent unit at the (i - 1)-th time step to generate the adaptive dynamic adjacency matrix A D , and the formula is as follows: A D = ReLU(tanh(a 2 (DE·DE T ))), a 2 is a network parameter, where represents the Hadamard product, [·, ·] represents the concatenation operation, W ∈ R is a learnable weight parameter, and a 3 is a network parameter;

[0022] 5) Perform feature fusion through the static-dynamic graph fusion layer, and combine the traffic flow X i at the i-th time step, the adaptive static adjacency matrix A S and the adaptive dynamic adjacency matrix AD Input into the static-dynamic graph fusion layer for feature extraction, and extract the spatial feature Z of the road network at the i-th time step. Z is represented as where α and β are learnable parameters, and Z represents the output of the static-dynamic graph fusion layer, that is, the output of the adaptive graph fusion convolution module; W 1 ∈R D×F and b ∈ R D×F are both learnable parameters, F is the feature dimension predefined in the network, and W 2 is a learnable weight with dimension F;

[0023] Step 3: Use the residual enhanced gated recurrent unit to organize the spatial features of the road network extracted by the adaptive graph fusion convolution module. The residual enhanced gated recurrent unit takes the output of the adaptive graph fusion convolution module as the input, and at the same time establishes a linear connection between the input and output of each residual enhanced gated recurrent unit. The finally generated hidden state vectors are merged together as the output, and the spatio-temporal features of the corresponding road network are generated;

[0024] Step 4: Process the sequence of hidden state vectors obtained in Step 3 with the self-attention layer of node embeddings; Connect the hidden state sequence H and the node embedding E as the input to perform self-attention operation in the self-attention layer to generate the attention score γ, and dot-product the attention score γ with the original hidden state sequence to obtain the new hidden state sequence H';

[0025] Step 5: Construct a fully connected layer for dimension conversion, and input the hidden state sequence H' obtained in Step 4 into the fully connected layer to obtain the prediction results on each road segment.

[0026] Furthermore, the method of Step 3 is as follows:

[0027] 1) Take the spatial feature at the i-th time step as the input vector and input it into the residual enhanced gated recurrent unit;

[0028] 2) In the residual enhanced gated recurrent unit, the spatial feature updates the candidate hidden state through the tanh activation function which is expressed as: where represents the corresponding hidden state vector in the (i - 1)-th time step, r t is the corresponding weight, and is the network parameter of the residual enhanced gated recurrent unit;

[0029] 3) In the residual enhanced gated recurrent unit, according to and generate the hidden state vector corresponding to the i-th time step and is expressed as: z t is Combination and weight, α x , α h , W h , W ox is the residual weight;

[0030] 4) After all the spatial features of I time steps are processed in the residual enhanced gated recurrent unit, all time steps are obtained and represented as a sequence of hidden state vectors

[0031] The present invention can not only simulate the overall change trend of traffic flow, but also capture the tiny changes in traffic flow. The prediction results are close to the actual values, and it has excellent prediction performance regardless of the change of prediction time step in the prediction task. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 Overall structure diagram of the proposed method

[0033] Figure 2 One-hour average prediction results of different nodes in the PeMS04 dataset, (a) Node 1; (b) Node 99 DETAILED DESCRIPTION OF THE INVENTION

[0034] At present, various traffic flow prediction methods based on graph neural networks have achieved certain effects. However, most models rely on a predefined graph structure generated by node distances to extract spatial relationships, unable to capture the hidden spatial features in the road network structure. At the same time, it does not fully consider the highly dynamic spatial dependence of the traffic network over time. To solve this problem, this patent provides a traffic flow prediction method based on adaptive graph fusion convolution.

[0035] In this method, a traffic prediction modeling scheme is proposed. The model can adaptively simulate the temporal and spatial features of traffic flow data and provide accurate prediction results for the intelligent transportation system. In this model, an adaptive graph fusion convolution module, a residual enhanced gated recurrent unit, and a node embedding self-attention module are respectively constructed. The adaptive graph fusion convolution module uses learnable node embeddings to generate an adaptive static graph adjacency matrix and combines the current and historical states to generate an adaptive dynamic graph adjacency matrix at each time step. At the same time, the static-dynamic graph fusion layer in the module uses the generated static and dynamic adjacency matrices to fully explore the spatial relationships of the traffic network without prior knowledge. The residual enhanced gated recurrent unit is designed to capture fine-grained long-term dependencies, and the node embedding self-attention module will further adjust the prediction mode of each node..

[0036] The overall structure of the present invention is as Figure 1As shown below. To make the technical solution of the present invention clearer, the following further describes the specific implementation manner of the present invention. The present invention is specifically implemented according to the following steps:

[0037] Step 1: Construct the road network to be predicted into a graph model, which is called the road network graph model. The road network segments are modeled as nodes of the graph, and each road segment node is equipped with a road network sensor. The connection relationship between road segments is modeled as the edge of the graph, and the traffic flow of each road segment is described as the attribute feature of the node;

[0038] Step 2: Input the historical traffic flow of the nodes in Step 1 into the adaptive graph fusion convolution module for processing. The adaptive graph fusion convolution module will respectively generate the adaptive static adjacency matrix and the adaptive dynamic adjacency matrix of the road network graph model and perform a fusion operation by the static-dynamic graph fusion layer in the module to extract the corresponding spatial features. The method is as follows:

[0039] 1) For a traffic flow sequence input X = (X 1 , X 2 , …, X I ) ∈ R I×N , which contains I time steps. Among them, the traffic flow at the i-th time step is expressed as X i ;

[0040] 2) Construct the static adjacency matrix of the road network graph model, which is called the adaptive static adjacency matrix. The adaptive static adjacency matrix A S in the adaptive graph fusion convolution layer is ReLU(tanh(a 1 (EE T ))), where E ∈ R N×D represents a randomly initialized learnable node embedding, which is defined in the network according to the number of nodes N and the custom dimension D. E T is the transpose of E, and a 1 is the network parameter;

[0041] 3) Construct the dynamic adjacency matrix of the road network graph model, which is called the adaptive dynamic adjacency matrix. A residual enhanced gated recurrent unit is designed after the adaptive graph fusion convolution module. The residual enhanced gated recurrent unit takes the road network spatial features extracted by the adaptive graph fusion convolution module as the input and outputs the hidden state vector. Step 3 will specifically explain it. Combine the traffic flow X i at the i-th time step with the hidden state vector output by the residual enhanced gated recurrent unit at the (i - 1)-th time step to generate the adaptive dynamic adjacency matrix A D . The specific formula is as follows: A D = ReLU(tanh(a 2 (DE·DE T ))), a 2is a network parameter, where represents the Hadamard product, [·, ·] represents the concatenation operation, W ∈ R is a learnable parameter, a 3 is a network parameter;

[0042] 4) Construct a static-dynamic graph fusion layer for feature fusion. Input the traffic X at the i-th time step i as well as the adaptive static adjacency matrix A S and the adaptive dynamic adjacency matrix A D into the static-dynamic graph fusion layer for feature extraction, and the spatial feature Z of the road network at the i-th time step can be extracted. Z is represented as where α and β are learnable parameters, Z represents the output of the static-dynamic graph fusion layer, that is, the output of the adaptive graph fusion convolution module; W 1 ∈ R D×F and b ∈ R D×F are both learnable parameters, F is the feature dimension predefined in the network, and W 2 is a learnable weight of dimension F.

[0043] Step 3: Organize the spatial features of the road network extracted by the adaptive graph fusion convolution module using a residual-enhanced gated recurrent unit. The residual-enhanced gated recurrent unit takes the output of the adaptive graph fusion convolution module as input and establishes a linear connection between the input and output of each unit. The finally generated hidden state vectors are combined together as the output, and the spatio-temporal features of the corresponding road network are generated. The method is as follows:

[0044] 1) Take the spatial feature at the i-th time step as the input vector and input it into the residual-enhanced gated recurrent unit;

[0045] 2) In the residual-enhanced gated recurrent unit, the spatial feature updates the candidate hidden state through the tanh activation function which is expressed as: where represents the corresponding hidden state vector in the (i - 1)-th time step, r t is the corresponding weight, and is the network parameter of the residual-enhanced gated recurrent unit;

[0046] 3) In the residual-enhanced gated recurrent unit, according to and generate the hidden state vector corresponding to the i-th time step and is expressed as: z t is the weight of the combination and , α x , α h,W h ,W ox is the residual weight.

[0047] 4) After all the spatial features of I time steps are processed in the residual enhanced gated recurrent unit, all the time step representations are obtained as a sequence of hidden state vectors

[0048] Step Four: Process the sequence of hidden state vectors obtained in Step Three with the self-attention layer of node embeddings. Connect the hidden state sequence H and the node embedding E as inputs and perform self-attention operation in the self-attention layer to generate attention scores γ, and obtain a new hidden state sequence H' by taking the dot product of the attention scores γ and the original hidden state sequence.

[0049] Step Five: Construct a fully connected layer for dimensional transformation, input the hidden state sequence H' obtained in Step Four into the fully connected layer, and obtain the prediction results on each road segment. Then, based on the historical time step traffic flow X ∈ R I×N predict the future time step traffic flow X ∈ R J ×N .

[0050] In a specific embodiment, first, the model needs to be supervised trained. After obtaining the best model, new data is used for prediction. The steps are as follows:

[0051] First Step: Use road sensors to collect the traffic flow data of the traffic road network to be predicted, preprocess the collected traffic flow data, and aggregate the traffic flow data with a 5-minute time window.

[0052] Second Step: Use a sliding window with a length of 12 (12 is the number of time steps, and the interval is 5 minutes) to slide along the time dimension of the aggregated traffic flow data to intercept and generate time series data.

[0053] Third Step: Use the time series as the input of the model, set the number of nodes and the length of the decoder output sequence (in this embodiment, the interval of the sliding window is 5 minutes. If you want to predict the traffic flow information within the next hour, the input sequence length of the decoder is taken as 12. If you want to predict the traffic flow information within the next two hours, the input sequence length of the decoder is taken as 24, and so on) for the supervised learning of the model. Adjust the model parameters. As the number of model training iterations increases, the loss function value gradually decreases and reaches stability. At this time, the fitting degree between the predicted value and the true value of the traffic flow data output by the model is good and stable. After the model training is completed, save the model structure and parameters.

[0054] Step 3: When predicting the traffic flow of a certain road network structure, first train according to its historical flow data by the above method, and then input the current flow data into the trained model, and run the model to obtain the predicted output.

[0055] Experiments were conducted on four public real-world traffic datasets, PeMS03, PeMS04, PeMS07, and PeMS08, which were collected once by the California Performance Measurement System. Traffic data was collected at 5-minute intervals.

[0056] Model training and prediction were carried out on the above datasets. The traffic flow in the next 5 minutes to 1 hour was predicted based on the historical traffic flow data of 1 hour. The results show that the mean absolute percentage error on the PeMS03 dataset was 14.68%, the root mean square error was 26.98, and the mean absolute error was 15.31; the mean absolute percentage error on the PeMS04 dataset was 12.53%, the root mean square error was 31.38, and the mean absolute error was 19.13; the mean absolute percentage error on the PeMS07 dataset was 8.65%, the root mean square error was 33.99, and the mean absolute error was 20.37; the mean absolute percentage error on the PeMS08 dataset was 9.93%, the root mean square error was 24.63, and the mean absolute error was 15.52. The error of this result is smaller compared with other prediction models, indicating that the model can learn and accurately predict the traffic flow of road networks with different scales and structures. The predicted results obtained by the proposed method at different nodes of the PeMS04 dataset were compared with the real values, and the results are as Figure 2 shown. The results show that the model of the present invention not only simulates the overall change trend of traffic flow, but also captures the small changes in traffic flow. The predicted results are close to the actual values. At the same time, the model has achieved excellent prediction performance regardless of the change of the prediction time step in the prediction task.

Claims

1. A traffic flow prediction method based on an adaptive graph fusion convolutional network, comprising the following steps: Step 1: Construct the road network to be predicted into a graph model, called the road network graph model. Model the road network segments as nodes of the graph, install road network sensors at each road segment node, model the connection relationship between road segments as the edges of the graph, and describe the traffic flow of each road segment as the attribute features of the nodes. Step 2: Input the historical traffic flow of the nodes into the adaptive graph fusion convolutional module for processing. The adaptive graph fusion convolutional module is used to establish an adaptive static adjacency matrix and an adaptive dynamic adjacency matrix according to the generated road network graph model, and perform a fusion operation by the static-dynamic graph fusion layer to extract the corresponding spatial features. The method is as follows: 1) For a traffic flow sequence input X = (X 1 , X 2 , …, X I ) ∈ R I×N , which contains I time steps, where the traffic flow at the i-th time step is denoted as X i ; 2) Construct the static adjacency matrix of the road network graph model, which is called the adaptive static adjacency matrix, and the adaptive static adjacency matrix A in the adaptive graph fusion convolutional layer S = ReLU(tanh(a 1 (EE T ))), where E ∈ R N×D represents the randomly initialized learnable node embedding, defined in the network according to the number of nodes N and the custom dimension D, and E T is the transpose of E, and a 1 is the network parameter; 3) A residual enhanced gated recurrent unit is designed after the adaptive graph fusion convolutional module. The residual enhanced gated recurrent unit takes the road network spatial features extracted by the adaptive graph fusion convolutional module as input and outputs a hidden state vector. 4) Construct the dynamic adjacency matrix of the road network graph, called the adaptive dynamic adjacency matrix, and combine the flow X at the i-th time step i with the hidden state vector output by the residual enhanced gated recurrent unit at the (i-1)-th time step to generate the adaptive dynamic adjacency matrix A D , and the formula is as follows: A D = ReLU(tanh(a 2 (DE·DE T ))), where a 2 is the network parameter, ⊙ represents the Hadamard product, [·,·] represents the concatenation operation, W ∈ R is the learnable weight parameter, and a 3 is the network parameter; 5) Feature fusion is performed through the static-dynamic graph fusion layer, and the traffic volume X at the i-th time step i and the adaptive static adjacency matrix A S and the adaptive dynamic adjacency matrix A D are input into the static-dynamic graph fusion layer for feature extraction, and the spatial feature Z of the road network at the i-th time step is extracted. Z is expressed as where α and β are learnable parameters, and Z represents the output of the static-dynamic graph fusion layer, that is, the output of the adaptive graph fusion convolution module; W 1 ∈R D×F and b ∈ R D×F are both learnable parameters, F is the feature dimension predefined in the network, and W 2 is a learnable weight with dimension F; Step 3: Organize the road network spatial features extracted by the adaptive graph fusion convolutional module by using the residual enhanced gated recurrent unit. The residual enhanced gated recurrent unit takes the output of the adaptive graph fusion convolutional module as input, and at the same time establishes a linear connection between the input and output of each residual enhanced gated recurrent unit. The finally generated hidden state vectors are merged together as output, and the spatio-temporal features of the corresponding road network are generated. Step 4: Process the hidden state vector sequence obtained in Step 3 with the self-attention layer of node embedding: Connect the hidden state sequence H and the node embedding E as input to perform self-attention operation in the self-attention layer to generate an attention score γ, and dot the attention score γ with the original hidden state sequence to obtain a new hidden state sequence H'. Step 5: Construct a fully connected layer for dimensionality conversion, input the hidden state sequence H' obtained in Step 4 into the fully connected layer, and obtain the prediction results on each road segment.

2. The traffic flow prediction method according to claim 1, characterized in that the method of Step 3 is as follows: 1) Take the spatial features at the i-th time step as the input vector and input them into the residual enhanced gated recurrent unit. 2) In the residual enhanced gated recurrent unit, the spatial features update the candidate hidden state through the tanh activation function It is expressed as: Where represents the corresponding hidden state vector at the (i - 1)-th time step, and r t is the corresponding weight, and is the network parameter of the residual enhanced gated recurrent unit; 3) In the residual enhanced gated recurrent unit, according to and generate the hidden state vector corresponding to the i-th time step and is expressed as: z t is the weights of the combination sum and , α x , α h , W h , W ox are the residual weights; 4) After all the spatial features of I time steps are processed in the residual enhanced gated recurrent unit, all the time step representations are obtained as a sequence of hidden state vectors

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