Research Article A Novel Traffic Flow Forecasting Method Based on RNN-GCN and BRB

As an important part of a smart city, intelligent transport can eﬀectively reduce energy consumption and environmental pollution. Traﬃc ﬂow forecasting provides a reliable traﬃc dispatch basis for intelligent transport, and most of the existing prediction methods only predict a single saturation or speed and do not use the saturation and speed in a uniﬁed way. This paper proposes a new traﬃc ﬂow prediction method based on RNN-GCN and BRB. First, the belief rule base (BRB) is used for data fusion to obtain new traﬃc ﬂow data, then the recurrent neural network (RNN) and graph convolution neural network (GCN) model is used to obtain the time correlation of the traﬃc data, and ﬁnally, the traﬃc ﬂow is predicted by the topology graph. The experimental results show that the method has a better performance than ARIMA, LSTM, and GCN.


Introduction
Urban traffic congestion not only wastes people's time and pollutes the environment but also easily leads to traffic accidents. erefore, it is important to predict traffic flow effectively, which is a key step to solve the problems. It means that traffic flow prediction is an important part of an intelligent traffic information system. e change in road traffic flow is a real-time, nonlinear, nonstationary random process. e shorter the sampling interval, the stronger the randomness and uncertainty of traffic flow changes, which makes it difficult to accurately analyze the laws of changes and algebraic expressions. erefore, the study of the traffic flow forecast has important practical significance.
In order to predict traffic flow, many researchers have proposed various prediction models. Generally speaking, the existing models can be divided into two categories: prediction models based on classical statistics and data-driven prediction models. e former mainly uses limited data to analyze the traffic flow data, regress and optimize the parameters of the traffic flow data, and realize the fitting prediction of the traffic data. Kumar and Vanajakshi [1] combined short-term traffic flow forecasting with seasonal ARIMA models and used limited input data to solve the applicability of the ARIMA model in traffic flow forecasting. In 2017, Kumar [2] proposed another forecasting model based on the Kalman filter; it overcomes the shortcomings that the SARIMA model is relying on a large amount of data for development. Li et al. [3] established a deep feature fusion model and used heterogeneous data to predict the average speed of time and space. Fei et al. [4] proposed a dynamic linear model (DLM) based on Bayesian inference to predict online short-term travel time on highways. Feng et al. [5] proposed a short-term traffic flow prediction algorithm based on an adaptive multikernel support vector machine (AMSVM) with spatial-temporal correlation. e second one is a data-driven predictive model, which uses intelligent calculation methods to mine the evolution trend of historical traffic flow data to predict the future trend of the data. When using deep learning to build models, convolutional neural networks are usually used to predict traffic flow. Li et al. [6] applied a multimodal deep learning model to the estimation of missing values in heterogeneous traffic data. Li et al. [7] used an advanced multiobjective particle swarm optimization algorithm to optimize certain parameters in the deep belief network to achieve traffic flow prediction for the next day. Zhang et al. [8] proposed an ST-ResNet deep learning inverse method to predict the number of mobile populations in each region using the residual convolutional neural network. Wu et al. [9] combined CNN and LSTM to obtain spatial dependence using onedimensional CNN and designed a short-term convolutional neural network forecasting model. Traditional convolutional neural networks can effectively extract local features of data, but they can only be applied to standard grid data. We are dealing with nongrid traffic data points, and graph convolution can directly implement convolution operations on graph-structured data. Currently, the main graph convolution methods include spatial methods and spectral methods. e spatial method directly applies the convolution kernel to the nodes on the graph and its neighborhood. e core of this method is how to select the neighborhood of the node [10,11]. e spectral method generalizes the convolution operation on the grid data to the graph structure data through the graph Laplacian matrix [12,13].
Although people have made great progress in traffic flow prediction using graph convolution, there are still the following problems: First, these models are for a single traffic flow data, and multiple traffic flow factors are not considered for integration. Due to the complexity and nonlinear correlation of traffic scenarios, multiple indicators of traffic flow are closely related; this paper considers them as a new traffic factor in the dataset to be used for prediction. Secondly, traffic flow is predicted at a particular period (T + 1) in the future. rough the traffic factor at time T, the historical traffic flow of (T n ) and T is not considered to predict traffic flow; that is, the time correlation is not considered, which makes the accuracy of traffic flow forecasting somewhat reduced.
To the above problems, this paper gives the following solutions. First, this paper adopts a new data fusion method, and the information fusion method based on the BRB expert system is adopted for the first time. In this method, multiple indicators are combined to obtain a new dataset of traffic flow. e distribution characteristics of the output result are obtained, and the clustering analysis is performed on the output result of the sample data. Yang et al. [14] proposed a BRB system based on the evidence reasoning (ER) algorithm in 2006. In the BRB, every possible outcome of the rule is associated with the degree of belief. Such a belief rule can capture more complex and continuous causal relationships between different factors, and the traditional IF-THEN rule is its special case. BRB can be used to capture nonlinear causality as well as continuity, incompleteness, and ambiguity. It has been widely used in many fields, such as safety assessment [15], fault diagnosis [16], risk analysis [17], health assessment of engineering systems [18], fault prediction [19], system behavior prediction [20], network security prediction [21], medical and medical evaluation [22], and identification of uncertain nonlinear system [23]. Second, in this paper, a new traffic flow forecasting model based on a recurrent neural network and graph a convolutional neural network (RNN-GCN) is designed for the first time. GCN is used to implement convolution operations directly on the data of the graph structure. e topological relationship is established in any data in the normed space, the structural features of the graph are captured, and the spatial features are effectively extracted for learning. Seo et al. [24] proposed a graph convolutional recurrent network (GCRN), but it is difficult to determine the optimal combination of recurrent network and graph convolution under certain settings. Cui et al. [25] proposed a novel deep learning framework, namely, the flow graph convolutional long short-term memory neural network (TGC-LSTM), which solves the time-varying traffic patterns and the complex space constraints on the road network. Zhou et al. [26] provide a detailed review of existing graph neural network models and systematically categorize the applications. Subsequently, Yu et al. [27] proposed a GCN network of control mechanisms and applied it to traffic volume forecasting problems. RNN contains a feedback input compared to previous neurons. Guo et al. [28] propose a novel attention-based spatialtemporal graph convolutional network (ASTGCN) model to solve the traffic flow forecasting problem. e single neuron of the RNN is similar to a series of weight-sharing feedforward neurons. After the connection, the input and output will change at the same time as the traditional neurons. But the difference is that the "historical information" of neurons at the moment on the RNN will be connected to the neurons at the next moment by weights. In this way, the RNN completes the mapping of the input and output at time t and refers to the influence of all input data on the network before t, forming a feedback network structure. erefore, the RNN can process the sequence data; that is, the RNN will consider the information that appears before processing the current information. To sum up, the RNN-GCN traffic flow forecasting model proposed in this paper has fully considered the traffic flow status of the current and historical time nodes and established the traffic topology map to facilitate feature extraction and learning. e model is feasible and accurate, and it has been verified that the accuracy of traffic flow forecasting is improved. In summary, a new traffic flow forecasting method based on RNN-GCN and BRB was designed for the first time.
e complexity of traffic scenarios and the time correlation of traffic flow was fully considered, and the traffic flow forecasting problem was effectively solved. e paper is organized as follows: In Section 2, a feasibility analysis of the traffic flow forecast is presented, including the fusion process of the traffic flow data and the prediction of the traffic flow under the RNN-GCN model. In Section 3, a model for traffic information fusion based on BRB is given. In Section 4, a prediction model based on RNN-GCN is established. e model's effectiveness is validated by experiments and case studies in Section 5. Conclusion and future work are reported at the end of this paper.

Description of the Problem
Traffic flow is predicted as shown in Figure 1. First, in order to better describe the traffic congestion problem, multiple traffic flow indicators are merged to obtain new traffic indicators. Second, in order to predict the traffic flow more accurately, a new traffic flow prediction model is constructed. Finally, the predicted result is output.

Traffic Flow Information Fusion Process.
In traffic flow forecasting, the datasets used in the past were only for a single indicator. Due to the complexity of the traffic scene, the forecast results are different from the real values. To this end, BRB technology is adopted in this paper, multiple indicators are merged, a nonlinear relationship between input and output is established, and a new traffic flow indicator is acquired. e BRB fusion process is shown in Figure 2.
In this process, two hypotheses are defined to describe the information fusion of traffic flow: (1) y(t) is defined as the output of the information fusion, which can be expressed as (2) X(t) is defined as the input set of the information fusion and can be expressed as where x n (t)(n � 1, . . . , N) represents the value of the n th traffic flow indicator at time t. f(·) denotes the BRB-based nonlinear transformation. α denotes the parameter set of the BRB.

RNN-GCN Traffic Flow Forecasting Process.
RNN-GCN is defined to describe the problem of traffic flow forecasting, and the forecast process of traffic flow is shown in Figure 3. In this process, two hypotheses are defined to describe the traffic flow forecasting: (1) y(t + 1) is defined as the forecasting result of traffic flow and can be expressed as (2) Y(t) is defined as the input of traffic flow forecasting and can be expressed as where y(t − T) is the traffic flow at time T. g(·) denotes the RNN-GCN-based nonlinear transformation. β denotes a parameter set of the RNN-GCN.

e Basic Structure of the Model.
e BRB is composed of a series of belief rules. Initially, the belief rules are constructed. In a rule, each result has its belief degree; hence, all the results of a rule can be presented in a belief distribution. Each rule is set with a rule weight, which is defined as its relative importance to other rules. e k th rule of the BRB is shown as follows: With a rule weight θ k , and attribute weights δ 1 , δ 2 , . . . , δ N .
is the k th rule of the BRB. L is defined as the number of rules in the BRB. N) is the input of the BRB. θ k denotes the rule weight of the k th rule, reflecting the relative importance of kth rule. A k i is the reference value of the ith antecedent attribute. A i � A i,j , j � 1, . . . , J i represents the set consisting of J i reference values. D j (j � 1, . . . , M) is the evaluation level of the output. β j,k denotes the belief degree

Input
Output y(t + 1) of D j ; if N j�1 β j,k � 1, then the k th rule is complete; otherwise, it is incomplete. δ n (n � 1, . . . , N) is the attribute weight of the kth rule, which represents the importance of the antecedent attribute.

Model Reasoning Process.
e belief rule is used by BRB to realize the storage and expression of knowledge, and then the ER algorithm is used to inductive reasoning of existing knowledge. e reasoning process can be summarized as the following process: Step 1.
e rule matching calculation for the input sample is described as where a k i is the matching degree of the input information with the kth rule; x i (t) denotes the i th antecedent attribute value in the input data; A l i and A l+1 i are defined as the reference value of the neighboring state of the i th antecedent attribute; K is the number of belief rules.
Step 2. e weight of the matching degree and the belief rule is used to calculate the activation weight of the belief rule, which is described as where w k is the activation weight of the k th rule. θ k denotes the rule weight of the kth rule. δ i is represented as the i th antecedent attribute weight. M is the number of antecedent attributes.
Step 3. e ER iterative algorithm is used to combine rules to generate belief levels for different output levels.
Step 4. Using the activation weight of the belief rule, the belief degree is converted to the basic probability mass, which is described as where m m,I(k+1) is the basic probability mass of the evaluation result D m after combining the k rules.
Step 6. e results of information fusion are calculated.
Step 7. e belief degree in calculating the evaluation results is described as where β m denotes the belief degree of the evaluation result D m .
Step 8. Utility calculation is used and fusion results are generated. is process can be described as where U(·) denotes the utility formula.
In summary, the reasoning process is shown in Figure 4. e ER algorithm uses the normalized idea when calculating the activation weight of the rule based on the input information. Compared to the traditional D-S evidence combination method, the system's ability to deal with conflict evidence is enhanced. In addition, the computational complexity of the D-S evidence combination method is an N-P difficult problem. e rule combination method of the ER algorithm is linear, and the computational complexity of the rule combination is greatly reduced. e BRB synthesizes the activated rules through the ER algorithm. e nonlinear relationship between the input and the output is established, and the feedback mechanism of the rule base is established, which realizes the possibility of self-learning.

Traffic Flow Forecasting Model
Based on RNN-GCN 4.1. Model Structure. One of the key issues in traffic flow forecasting is the correlation of acquisition time, which is generally obtained using RNN. RNN is a special neural network structure in which the output of temporally contiguous states can be described with memory functions. In this paper, a new RNN-GCN model is proposed. e model structure is shown in Figure 5. It is using the nodes between the hidden layers of the RNN to have connectivity. e input of the hidden layer contains not only the input of the input layer but also the output of the hidden layer at the previous moment. It mainly consists of an input layer, a hidden layer, and an output layer. e data is updated cyclically in the hidden layer. is is the way to implement the time memory function. e hierarchical expansion of the hidden layer is shown in Figure 6. e memory function of the sample can be described as where S t denotes a memory of the sample at t. y(t) is an input sample. W is the weight of the input. U is the weight of the (y t− 2 , y t− 1 , y t ) T . rough the RNN model, a piece of historical time series fragment [y t−n , y t−n+1 , . . . , y t−1 , y t ] directly adjacent to the forecasting period is obtained. e convergence and divergence of vehicles on the road are gradually taking shape. erefore, the traffic of the next moment of a node will be affected by the traffic at the previous moment. e traffic flow forecasting of the road network is aimed at the graph structure. e structure of the graph is    Figure 6: Hidden layer hierarchy expansion diagram. Journal of Advanced Transportation 5 considered as irregular infinite-dimensional data, and the surrounding structure of each node is considered unique, so it has no translation invariance. e surrounding structure of each node may be considered unique. e data of this structure prevents traditional CNN and RNN from obtaining good prediction results. To solve the irregularity of the graph structure, GCN is introduced to learn by effectively extracting spatial features. e structure of GCN is shown in Figure 7. GCN is considered as a kind of neural network dealing with the graph data structure. e core idea of GCN is considered to be to aggregate node information by using edge information, so as to generate new node representations.
e essence of GCN is used to extract the spatial features of the topological graph. For graph data, node information and structural information must be considered. So GCN can automatically learn not only the characteristics of node characteristics but also the associated information between nodes. rough the RNN model, a piece of historical time series fragment [y t−n , y t−n+1 , . . . , y t−1 , y t ] directly adjacent to the forecasting period is obtained. When processing the graph structure, the spectrum analysis method [13] is considered. e graph structure of the spectrogram method is analyzed mainly by transforming the graph into an algebraic form. In this paper, the connectivity and mutual influence between nodes in the graph structure are mainly concerned. In the spectrogram method, a graph can be represented by its corresponding Laplacian matrix (L), and the properties of the graph structure can be obtained by analyzing L and its eigenvalues. e Laplacian matrix of the graph is obtained, which can be shown as e canonical form is described as where A is the adjacency matrix. I N is the unit matrix. e degree matrix D ∈ R N×N is a diagonal matrix composed of node degrees. e Laplacian matrix and its eigenvalues are analyzed, and the properties of the graph structure are obtained. en, the graph signal y � y f t ∈ R N is transformed through Fourier, and the result is expressed as y � U T y. Graph convolution is a kind of convolution operation that is implemented by defining a diagonal linear operator in the Fourier domain to equivalently replace the classic convolution operator [29]. e specific operation is defined as a convolution operation on the graph with the convolution kernel g θ : where ∧ � diag([λ 0 , . . . , λ N−1 ]) ∈ R N×N is a diagonal matrix composed of the eigenvalues of L. U is the Fourier basis [27]. But when the scale of the graph is large, it is expensive to decompose the Laplacian matrix directly. erefore, the approximate expansion of Chebyshev polynomials is used to solve the problem: where θ k ∈ R k is the coefficient of Chebyshev polynomial. λ max is the largest eigenvalue of L. T k (y) is the recursive definition of Chebyshev polynomial. To sum up, the GCN can be used to convolute the undirected graph, and the traffic flow data can be topologically processed. e GCN model is trained and learned to predict the traffic flow, which solves the problem that the traditional neural network cannot predict the complex traffic network in real time and accurately.

Model Implementation Process.
According to the complex characteristics of the traffic scene, the RNN-GCN traffic forecasting model is constructed, and the specific implementation process is shown in Figure 8. e detailed steps are described as follows: (1) Obtain the time correlation: through the RNN model, historical time series are constructed, and continuous output in time is obtained (2) Serialize the graph structure: the dataset is converted into a form of a topological graph structure as a data input to the GCN model includes two parts: one is a 156 * 156 adjacency matrix, which describes the spatial relationship between roads, each row represents a road, and the value in the matrix represents the connectivity between roads. e other is the feature matrix, which describes the change of the speed on each road over time. Each row represents the traffic speed on the road at different times, and each column is a road. e traffic speed and traffic saturation are calculated on each road every 15 minutes. Traffic speed is the calculated average speed of all cars on a certain road. Traffic saturation is the ratio of the current number of road vehicles to the current street carrying capacity.
is case includes two parts. Firstly, BRB is used to fuse the two indicators of traffic speed and traffic saturation to get a traffic flow fusion result. Secondly, the results of BRB fusion are put into RNN-GCN for prediction. Finally, the prediction results are obtained. Figure 9 shows the traffic flow prediction process of the experiment.

BRB Data Fusion Case.
In the case of BRB data fusion, traffic saturation and traffic speed were combined to obtain a new dataset of traffic flow. e output result of the sample data is analyzed, the distribution characteristics of the output result are acquired, and the system rule number and the result evaluation level related parameter are determined.
To express domain knowledge in BRB, reference points and reference values need to be given. In this BRB model, two indicators of traffic speed (x 1 ) and traffic saturation (x 2 ) are selected as the input of the BRB system, and y is the output to reflect traffic conditions. e selection of reference points and reference values is based on expert knowledge.  (Tables 1-3).
According to the expert system, a belief rule table as shown in Table 4 is constructed, and there are 48 belief rules.
By inputting the traffic data samples, the matching degree calculation is performed. e belief rule table is used. e traffic saturation is merged with traffic speed. And the nonlinear relationship between the input and the output is established. And a new traffic flow forecasting index is obtained.

Prove the Performance of the Model.
rough the analysis of experimental results and comparative test analysis, the traffic information at the next moment can be predicted based on the traffic data at the historical time point. is section evaluates the prediction performance of the RNN-GCN model compared to other prediction models. Without loss of generality, only the traffic speed is used as the traffic information for the experimental part.
We compare our model with the following three baselines: (i) ARIMA: autoregressive integrated moving average method is a well-known time series analysis method for predicting future values. (ii) GCN: graph convolutional neural network uses graph convolution operation to process topological graph structure data. (iii) LSTM: long short-term memory network is a special RNN model. Figure 10 is a comparison diagram of traffic speed prediction results and real values in a day. It can be seen from the figure that the forecasting result of the model in the day is close to the true value of the data. It shows that the RNN-GCN model can obtain the best forecasting performance through training. Figure 10 demonstrates the effectiveness of the RNN-GCN model.

Define Evaluation Indicators.
To effectively evaluate the performance of RNN-GCN, three evaluation indicators are used to measure the prediction effect of the model, where y t represents the actual traffic flow data at time t and y t represents the output of traffic flow forecasting by the model. NUM is the total number of test samples, including the following: (i) Mean absolute error (MAE): MAE can well reflect the actual situation of predicted value error and is the first choice for model Journal of Advanced Transportation prediction effect evaluation: the smaller the value is, the better the prediction effect is. (ii) Root mean square error (RMSE): RMSE is used to measure the deviation between the predicted value and the true value and is more sensitive to outliers in the data: the smaller the value is, the better the prediction effect is.
ACC is used to detect the prediction precision: the larger the value is, the better the prediction effect is. ‖ · ‖ F represents the norm of this matrix which is Frobenius norm, y is a matrix of true values, and y is a matrix of predicted values.

Analysis of Experimental
Results. Traffic indicators are fused by BRB, and a dataset of traffic flow is generated. In the experiment of traffic flow forecasting, 80% of the dataset is used for model training and 20% of the dataset is used for model testing. Figures 11-13 show the decrease of RAME and MAS and the increase of ACC with the increase of training times. is shows the effectiveness of the model when the BRB fusion data is input into RNN-GCN.
We compare our models with the three baseline methods. Table 5 shows the average results of traffic flow prediction performance. It can be seen from Table 5 that our RNN-GCN achieves the best performance in the same datasets in terms of all evaluation metrics. We can observe that the prediction results of the traditional time series analysis methods are usually not ideal, demonstrating those methods' limited abilities to model nonlinear and complex traffic data.

Conclusions
In this paper, a new traffic flow forecasting method based on RNN-GCN and BRB is proposed. First, the BRB model is used for data fusion, and new traffic flow data is obtained; second, the RNN model is used to obtain time correlation; finally, the GCN model is used for traffic forecasting. rough experiments, the method proposed in this paper is better than other forecasting models; the accuracy has improved. But obtaining temporal correlation through the time attention mechanism is not considered. erefore, our next step will be to optimize the predictive model by adding strategies such as time attention mechanisms and further improve the predictive ability of the model.

Data Availability
In the study of this paper, the dataset used is a public dataset, and the access address is https://github.com/lehaifeng/T-GCN/tree/master/data.

Conflicts of Interest
e authors declare that they have no conflicts of interest.