Method of Evaluating and Predicting Traffic State of Highway Network Based on Deep Learning

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Introduction
With the increasing of vehicle ownership, the demand for transportation has also expanded rapidly, which not only brings great pressure to the highway traffic system, but also causes a series of congestion problems and safety issues. e 2019 Hebei Statistical bulletin on national economic and social development indicates that the mileage open to traffic increased by 1.9% in the province, but the vehicle ownership increased by 7.4% year-over-year [1]. erefore, it is particularly essential to be able to evaluate and predict the traffic state of the highway network accurately in real time. Traffic managers can develop prevention strategies in advance to effectively avoid the occurrence of traffic congestion and prevent the further expansion of the impact of congestion. How to realize the accurate evaluation and prediction of traffic state is the most important task faced by traffic managers and traffic problem researchers.
Appropriate indicators need to be selected for the evaluation of traffic state, mainly including service level [2], traffic flow parameters [3][4][5], and travel time [6]. In addition, a large number of scholars have studied the evaluation method of traffic state. e existing researches on the traffic state evaluation of road primarily focus on the intersection [7], road [8], and road network [9,10]. For transportation node, most studies focus on urban roads and use major intersections as the research object. Xu et al. have conducted in-depth research on the evaluation of road traffic state. ey used various theories and methods to estimate and predict the road traffic state [11][12][13][14]. In addition, D.W. Xu et al. proposed a novel deep learning framework for estimating road traffic state [15]. As the development of big data [16] and machine learning [17] advances, more methodologies will be applied to the evaluation of highway network traffic state. B. Hillel used cellular phone service provider information to measure traffic speed and travel time [18]. Based on a large amount of floating car data, G. Fusco et al. made short-term forecasts of traffic speed and carried out comparative analysis using a variety of methods [19]. A. Wu et al. adopted floating car data to identify the traffic state of signalized intersections [20]. M. Wang et al. used a large cell phone network data to estimate traffic flow [21]. A large number of loop detectors are installed in the highway network to collect traffic information. ese data can also be used to analyze traffic state [22,23]. In addition, based on machine learning theory, neural networks have been widely applied to traffic flow prediction [24,25]. J. Yu et al. presented a graph convolutional generative autoencoder model to estimate traffic speed in real time [26]. I. Laña et al. presented a method with an adaptation mechanism for longterm urban traffic volume forecasting [27]. e previously related research is mainly divided into two aspects including predicting traffic flow parameters, such as traffic volume, density, speed, and saturation, and evaluating the road traffic state. Little attention is paid to the evaluation and prediction of road network traffic state. Taking highway network as the research object, this study aims to conduct the evaluation and prediction model of highway network traffic state based on deep learning. e evaluating and predicting traffic state of highway network can comprehensively reflect the traffic condition of the entire highway network.
is study could be useful for future policy making.

Methods
e traffic state of the highway network is divided into four categories, namely, severe congestion state, congestion state, general state, and smooth state. e speed and density of traffic flow are selected as evaluation indicators to develop the proposed evaluation and prediction model of highway network traffic state based on deep learning. e model mainly includes the partition model of traffic state based on the Fuzzy C-means (FCM) algorithm, the prediction model of traffic state based on the Long Short-Term Memory (LSTM) algorithm, and the discriminant model of traffic state based on K-Means algorithm.

e Partition Model of Highway Network Traffic State Based on FCM Algorithm.
e traffic state of the highway network has certain fuzziness. e speed and density of traffic flow are used as evaluation indicators, and the FCM algorithm is used to evaluate the traffic state of the highway network. e FCM algorithm can well analyze the attribute characteristics of big data in practical problems, and it uses the membership function to cluster [28]. e FCM algorithm divides the n vectors x i (i � 1, 2, . . . , n) into c classes and calculates the cluster centers for each class. For ∀x i � (v i , k i ),v i , k i represent the speed and density of the ith sample, respectively, and 1 < c < n. e objective function defined by the membership function is as follows: where J(U, A) is the weighted value of the sample to each cluster center of the highway network traffic state; u ij is the membership function of the ith sample for the j class, and 1 ≤ j ≤ c,1 ≤ i ≤ n; A � [a 1 , . . . , a j , . . . , a c ] is the 2 × c order cluster center matrix; a j is the eigenvector of the jth cluster center of the highway network traffic state and a j � (v j , k j ); m is the fuzzy weighted index; (d ij ) 2 � ‖x i − a j ‖ is the Euclidean distance from the ith sample to a j ; and U � u ij is the c × n order fuzzy classification matrix. Construct the following formula by using Lagrange multiplication: Taking the derivatives for all input variables, we can get the following formula: (3)

Algorithm Implementation
(1) Initialization. Give the iterative standards ε > 0, set b as the number of iterations, and let b � 0. e membership matrix is calculated as (3) Use a matrix norm ‖ · ‖ to compare a (b+1) and  Journal of Advanced Transportation e driving speed and density of the vehicle on the highway network can well reflect the traffic state of the highway network. e faster the driving speed of the vehicle, the smaller the density, the better the highway condition, and the smoother the traffic state of the highway network. According to the above algorithm, the cluster center matrix and the classification result of the traffic state of the highway network can be obtained.

e Prediction Model of Highway Network Traffic State
Based on LSTM Algorithm. LSTM is a long-term and shortterm memory neural network. e model can be trusted for a long time, which is suitable for processing and predicting time series data and important events with relatively long delays. It has been used in many fields of science and technology. e model training methods proposed in this paper include forward calculation using activation function and backward estimation using the backpropagation through time (BPTT) according to the loss function [29]. e data are preprocessed by Z-score normalization method before training. e processed function has a mean value of 0 and a standard deviation of 1 as shown in (6). After outputting the predicted result, the data need to be antinormalized to obtain the true predicted values of the traffic state evaluation indicators. e antinormalization formula is shown in (7): x � x * * σ + μ, where μ is the mean of all sample data, and σ is the standard deviation of all sample data. In order to verify the accuracy of the prediction result and the feasibility of the prediction model, it is necessary to perform error analysis on this result. e relative error formula of each predicted point is shown in (8). e Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) of the highway or the highway network are calculated using (9) and (10), respectively.
where ε i is the relative error between the predicted value and the real value of the ith sample data, y i is the real value of the ith sample data,y * i is the predicted value of the ith sample data, and N is the number of sample data of the traffic state evaluation indicators.

e Discriminant Model of Highway Network Traffic State Based on K-Means Algorithm.
e K-Means algorithm is an unsupervised clustering algorithm, and the basic idea of the algorithm is that, for a given sample set, it is divided into multiple clusters according to the distance between the samples. Using the Euclidean distance as the measure of similarity, the shortest distance between each sample and each cluster center can be found. en, we can know the traffic state of each sample. e specific formula is as follows: where where x p is the pth highway traffic state prediction sample;v p and k p are, respectively, the speed and density parameters of the pth highway traffic state prediction sample; a j is the cluster center of the jth class of the highway traffic state; v a j and k a j are the speed and density of a j , respectively; β 1 and β 2 are the weight of the influence of speed and density, respectively, on the classification of the traffic state, and this paper considers the influence as the same, namely, In order to evaluate the traffic state of the highway network, the average speed and density of all highways need to be calculated. Based on the K-means algorithm, the average traffic state of the highway network can be obtained.

Dataset.
e dataset is collected by 233 continuous observation stations from September 5, 2016, to September 12, 2016. e original dataset has certain quality problems, so the dataset is cleaned and processed. e dataset is the comprehensive traffic flow information by direction, lane, and vehicle mode. e observation interval is set to be five minutes, and each observation station collects 288 pieces of data per day. us, 536,832 pieces of data are collected from 233 observation stations.
e layout of the observation stations in the highway network is shown in Figure 1. e main attribute information of the observation station is shown in Table 1.
e data for one day the at Babaihu observation station are listed in Table 2.
ere is an observation station on each highway, and the observation data of the observation station represent the traffic information of the highway on which it is located.

Partition of Highway Network Traffic State.
e highway network is composed of different highways, and each highway has its specific design speed. erefore, before using the FCM algorithm for clustering, the traffic flow speed and density of the highway network should be standardized. e standardized formula is as follows:

Journal of Advanced Transportation
When using FCM algorithm to classify traffic state of the highway network, the model parameters need to be selected first. As discussed previously, the number of clusters c � 4. For fuzzy weighted index m, numerous studies have been conducted, and it is widely accepted that, for general classification, m � 2 is rational [30]. Speed and density data collected by 233 observation stations from September 5, 2016, to September 11, 2016, are studied. e collected dataset contains 469,728 pieces of data. e calculated cluster center is shown below.
e first column of matrix A shows the normalized speed value of the cluster centers. e second column shows the normalized density value of the cluster centers. Since the faster the speed, the smaller the density, and the better the traffic, the four rows in matrix A show cluster centers with severe congestion state, congestion state, general state, and smooth state from top to bottom, respectively. e clusters found by FCM are shown in Figure 2.

Prediction of Highway Network Traffic State.
e LSTM algorithm is utilized to develop the short-term prediction. e data from September 5, 2016, to September 11, 2016, are the training set and the data from September 12, 2016, are the testing set. e speed and density of each observation station are predicted separately, and the prediction errors are calculated. e comparison of predicted speed and true speed in some observation stations is shown in Figure 3. And the comparison of predicted density and true density in some observation stations is shown in Figure 4. According to (9) and (10)

Discriminant of Highway Network Traffic
State. e speed and density of each highway are determined by the observations of the observation station where it is located. Before judging the traffic state of each highway, the predicted speed and density values should be normalized according to (13) and (14). e traffic state of each highway is discriminated based on the K-means algorithm. en, calculating the average speed and density of all highways can obtain the average traffic state of the highway network. e discriminant result of the average traffic state of each highway is shown in Figure 5. And the normalized average predicted speed and density of the highway network are 0.7719 and 0.0467, respectively. erefore, according to the proposed evaluation and prediction model of highway network traffic state based on deep learning, on September 12, 2016, the average traffic state of the highway network constituted by 233 highways is in general state.

Analysis of Evaluation Results.
To prove the accuracy of the proposed model, the true average traffic state of the highway network on September 12, 2016, needs to be analyzed. First, the true average speed and density of each highway on September 12, 2016, are calculated and normalized, and then the average traffic state of each highway is discriminated, which is shown in Figure 6. e true normalized average speed and density of the highway network are 0.7710 and 0.0471, respectively. And the predicted and true traffic state are consistent, and both are in general state. e predicted and real average traffic states of each highway are compared, and the proportion of each traffic state in the highway network is shown in Table 3. e results show that congestion state and general state account for the largest proportion. About 6% of highways are in severe congestion state, indicating that the speed of vehicles is restricted to a certain extent. e operating conditions are not good, and the highway is in high pressure. Such problem could be caused by the imbalance between supply and demand of existing highway infrastructure and traffic demand caused. e traffic management departments should pay attention to the reconstruction and development of these highways. Approximately 30% of the highways are in congestion state, and these highways should also be focused on. Reasonable traffic organization plans and control measures should be formulated in advance to alleviate traffic congestion. When the highways are in general state and smooth state, it means that the vehicles can travel at a faster speed and are in good operating condition. And in the highway network, more than 50% of the highways are not congested. It shows that the overall layout of the highway network is relatively reasonable, and the traffic condition is good. e evaluation and prediction of the traffic state of the highway network can play a role in prevention and planning in advance.

Conclusions
is paper proposes an evaluation and prediction model of highway network traffic state based on deep learning. e model consists of a FCM algorithm-based traffic state partition model, a LSTM algorithm-based traffic state prediction model, and a K-Means algorithm-based traffic state discriminant model. In this study, the traffic state of the highway network is divided into four categories: severe congestion state, congestion state, general state, and smooth state. e speed and density of traffic flow are selected as evaluation indicators. To validate the effectiveness of the proposed model, the traffic flow data of 233 observation stations in Hebei Province from September 5, 2016, to September 12, 2016, are collected. e observation interval is 5 minutes, and the total of data is 536,823 pieces. e main findings are concluded as follows: On September 12, 2016, the predicted average traffic state of the highway network constituted by 233 highways is in general state, which is consistent with the real traffic state. e overall layout of the highway network is relatively reasonable, and the supply and demand of transportation are basically balanced. e highway network traffic state is an objective reflection of the traffic condition. e evaluation and prediction of highway network traffic state provide the dynamic characteristic of traffic change. Based on this information, travelers can make their travel plans better and improve their travel efficiency. Traffic managers can also work out better traffic organization plans in advance to reduce traffic congestion.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.