A Traffic Crash Warning Model for BOT E-Tolling Operations Based on Predictions Using a Data Association Framework

Abstract

As a result of the increasing use of artificial intelligence technology in transportation, numerous real-time crash prediction techniques have been developed. In the context of highway traffic management, machine learning models and classifiers are used to analyze electronic toll collection (ETC) and vehicle detector (VD) data to predict crash occurrences. However, traffic accidents are influenced by multiple factors, such as traffic speed differences, traffic density, and weather conditions, and direct associations may not exist between sensor data and crash incidents. Therefore, data integration and association methods must be used to examine ETC and VD data through traffic flow theories, to extract key data from datasets and to facilitate model training. In this study, a data association method and framework combined with deep learning was proposed to construct a crash prediction and warning model for national highways in Taiwan. The results revealed a model accuracy of 94%, indicating that the model had a low error rate and was suitable for the prediction of traffic accidents. Overall, this study provides referential data for the Freeway Bureau of Taiwan to conduct comprehensive assessments and develop strategies for crash prevention.

1. Introduction

Highways are a vital component of intercity transport and commutes. Despite the allocation of various resources by governments to improve highway traffic safety, multiple problems persist [1]. According to statistics compiled by the Freeway Bureau of Taiwan (https://data.gov.tw/dataset/31028, accessed on 11 December 2021), 32,965 traffic accidents occurred on highways in Taiwan in 2021, 18,479 of which were caused by insufficient headway and inattentional blindness. These accidents can primarily be attributed to speed differences between upstream and downstream traffic flows, resulting in an uneven traffic density and an increased likelihood of accidents. Multiple studies have focused on the development of effective real-time crash prediction models [2,3], including the use of feature extraction techniques to examine variables in such models [4]. Scholars in related fields have also used traffic speed and speed differences as crucial variables. If we can verify the correlation between the aforementioned causes of accidents and the research literature on traffic accidents, it will be of great help to highway speed management or accident warning. In this study, to investigate the associations between highway traffic accidents and review relevant literature, upstream and downstream traffic intervals were designated in accordance with the locations of electronic toll collection (ETC) gantries and vehicle detectors (VDs), which are installed every 2 km on highways. Sensor data recorded between 8:00 AM and 10:00 PM in 2021 were processed to calculate the speed difference every 5 min and identify patterns in traffic flow data. The processed data were then filtered to label the time periods and locations where speed differences occurred. The results were further examined with data collected in 2019 and 2020 to identify patterns of association, which revealed that insufficient headway and inattentional blindness accounted for 35% to 45% of the accident causes. It can be seen that if the accident can effectively reduce the speed difference factor, the highway traffic safety will be improved.

Machine learning/deep learning (ML/DL) has many similarities with statistical learning. For example, both analyze large amounts of data, construct models and make predictions. ML/DL and statistics differ in their purpose. ML/DL models are designed to make accurate predictions. Statistical modeling focuses on the relationship between data and output variables, while ML/DL focuses on what the model predicts. As far as this study is concerned, it is known that speed, traffic shock waves, and other factors are related to the occurrence of accidents. This is done through the data detected by ETC and VD of expressways. Models with statistical bases are less applicable. Therefore, it is more appropriate to use ML/DL to construct an early warning model.

Given this, this paper uses the filtering and association method of data analysis to label the periods and locations of the accident, and deep learning was used to create a crash prediction and warning model. The model was then applied to specific road sections to provide road users with warning notifications of accidents occurring in downstream traffic. The goal was to prevent the occurrence of severe traffic accidents due to traffic speed differences caused by uneven traffic densities. However, although the developed model was able to warn users about traffic conditions ahead, some road users experienced alert fatigue after receiving excessive warnings. Therefore, intervals of speed at different thresholds were defined to minimize the number of warnings while maximizing the number of accidents prevented. Notably, in highway traffic flow data, the amount of data recording traffic speed differences is considerably less than that of data recording normal traffic conditions. When such imbalanced data are processed with deep learning, biased training results may be obtained [5]. Therefore, in this study, the effectiveness of focal loss, class weight, and oversampling methods was evaluated in terms of processing imbalanced data. Data association and machine learning methods were also used to resolve problems pertaining to crash prediction. Compared with other planning and engineering solutions, the developed model is more effective in improving highway traffic safety in a short time by stabilizing traffic flow, sending warnings to road users, and predicting traffic accidents.

2. Literature Review

The increasing demand for highways has resulted in complex traffic flows, leading to a wide scope of research on modeling and predicting traffic accidents [6,7]. Generally, the occurrence of a traffic accident on a highway is associated with the upstream and downstream traffic flow status. Specifically, an increase in the downstream traffic density (road occupancy rate) results in differences in the upstream traffic speed and causes traffic accidents [8]. Before an accident occurs, vehicles in the traffic flow are in relative motion. When the speed of a vehicle substantially varies from the mean speed of the traffic flow, the probability of a crash increases [9,10]. Therefore, traffic speed differences should be considered in the prediction of traffic accidents and establishment of warning mechanisms.

Real-time crash prediction methods typically rely on statistical and machine learning approaches. Statistical methods include logistic models and Bayesian logistic models [11,12]. With the emergence of big data analysis and artificial intelligence, various machine learning methods, including artificial neural networks [13], support vector machines [14], and random forest models [15], have been used in real-time crash prediction to achieve high prediction accuracy. Relevant studies have indicated that deep learning can further enhance the real-time prediction of traffic accidents by machine learning models [16] and that machine learning is more accurate than statistical approaches [17]. For instance, Theofilatos et al. [2] used real-time traffic and weather parameters to examine factors affecting highway traffic accidents. They reported that, compared with shallow neural networks and other machine learning methods, deep learning models yielded more accurate results. Ren et al. [18] used spatiotemporal correlation models to develop a highly accurate deep learning model for predicting the risk of traffic accidents. They confirmed that their model was able to effectively predict accidents. Chen et al. [19] proposed a structure learning method to constructing Bayesian networks. The network can fully illustrate the causal relationship between risk contribution characteristics and risk events on the vehicle road. The results indicate that the optimal network has achieved satisfactory results in terms of structure complexity and prediction accuracy. In addition, compared with the networks constructed by other state-of-the-art structural learning methods, the optimal networks show superior performance in terms of causality interpretation. In the present study, the data recorded for traffic accidents and normal traffic were highly imbalanced, which means that direct use of this dataset in model training will produce prediction results that do not reflect the actual condition, resulting in false-positive (indicating the occurrence of an accident although none occurred) or false-negative (indicating the absence of an accident although one did occur) errors. Therefore, the imbalanced dataset used in this study must be balanced first. In the current development of prediction models, data balancing methods have received increasing attention. Undersampling and oversampling methods have been used to convert imbalanced training data to balanced data. Notably, previous studies have predominantly used manually balanced data to train and verify models. However, manual balancing through undersampling methods may result in the loss of crucial data recording the occurrence of normal events. By contrast, oversampling methods may repeat or excessively emphasize crash event data, resulting in overfitting [20].

Class weight and focal loss methods do not process imbalanced data directly. Instead, they involve the use of loss functions to adjust the weights of imbalanced data in neural networks and resolve the problem of imbalanced data. Arbabzadeh and Jafari [21] used driver risk prediction datasets to prepare training data and extract features in order to increase the accuracy of their model. They used a class weight method to assign appropriate weights to imbalanced data and obtain accurate prediction results. Zhang et al. [22] demonstrated that datasets based on adverse events such as accidents, aircraft damage, or deaths have the problem of data imbalance. They embedded class weights in a long short-term memory model to create a classifier and effectively address the problem of imbalanced data. Ovi et al. [23] examined datasets recording traffic accidents in the United States by using a DNN with class weights to adjust the weights of specific data. They tested the model with data from major US cities and reported a considerable improvement in the prediction of abnormal traffic events. Yu et al. [6] explored the problem of imbalanced data in the expressway system of Shanghai, which prevented the comprehensive capturing of spatiotemporal traffic flow characteristics. They used binary cross-entropy, α-weighted cross-entropy, and focus loss to optimize the loss function of a convolutional neural network (CNN). They also used datasets with different ratios of crash and non-crash data to test the model. Their results indicated that CNN models with focal loss functions exhibited high classification performance with imbalanced data.

This study makes the following contributions. First, time-series datasets for traffic accidents were established using the traffic flow data and geographical locations of ETC and VD devices and records of highway traffic accidents, thereby verifying the ratio of speed difference-related traffic accidents to all traffic accidents. Second, the identified association was used to label the periods and locations of traffic accidents. Third, data balancing techniques were used to address problems pertaining to imbalanced data. Finally, a DNN was established using the ETC and VD datasets to predict highway traffic accidents. The goal was to send accurate warnings to road users in advance and effectively prevent the occurrence of traffic accidents.

The rest of this paper is organized as follows. First, crash prediction problems are examined and evaluated, followed by a description of the sources of immense multidimensional temporal data used in this study and their data processing procedures, data analysis methods, and research rationales. Subsequently, the use of data analysis and mining techniques to further explore the associations between traffic accidents, traffic speed differences, and shock wave propagation on national highways is presented. The aforementioned methods for processing imbalanced data are also discussed to establish a DNN model and predict the occurrence of traffic accidents. Finally, conclusions and recommendations for future applications of the proposed method and promotion of traffic safety are presented.

3. Dataset Generation

3.1. Basic Traffic Dataset

The data used in this study were established using three sources. The first source was the traffic flow data of National Freeway No. 1. This highway connects northern and southern Taiwan and is therefore crucial to national economic development. A VD is installed every 2 km along the highway, and ETC gantries are installed at each interchange. Data collected from ETC and VD devices are analyzed by traffic controllers to formulate adequate traffic control strategies. For this study, the 2021 ETC and VD data of National Freeway No. 1 were downloaded from the database of the Freeway Bureau of Taiwan, which contains 210,240 records of the mean travel time, mean speed, quantity, occupancy rate, and toll of each vehicle type. After negative speed, negative traffic flow, and other irrelevant data were excluded, an average of 14 million data entries were generated for the basic traffic dataset each day.

The following methods were used to generate essential data for the basic traffic dataset:

• Traffic flow volume: Depending on ETC and VD data, the number of vehicles passing through two neighboring gantries was calculated for each vehicle type. The results were then converted into passenger car equivalents in accordance with the road capacity manual published by the Taiwanese government. (https://thcs.iot.gov.tw/WebForm3.aspx#gsc.tab=0, accessed on 15 November 2022).
• Mean speed: Mean speed is pointed to every 5 min between adjacent ETC gantry through all average vehicle speed detection ($mean\_spee{d}_t^l={\sum }_{i}spee{d}_i^t/veh$). Where $spee{d}_i^t$ is the speed detected by the ith car at time t. $veh$ is the total number of vehicles detected in five minutes. In addition, t is the time index, which distinguishes the time interval of every 5 min.
• Mean speed difference: Depending on ETC and VD data, the mean speed differences of all vehicles passing through a gantry were calculated as follows: $mean\_speed\_dif{f}_t^l=mean\_spee{d}_t^l$ − $mean\_spee{d}_{t-1}^l$, where l is a gantry label, t is a time label, $speed\_dif{f}_t^l$ is the mean traffic speed difference of gantry l at time t, $mean\_spee{d}_t^l$ is the traffic speed of gantry l at time t, and $mean\_spee{d}_{t-1}^l$ is the traffic speed of gantry l at time t − 1.
• Mean passing time: Depending on daily ETC data, the durations spent by all vehicles passing through two neighboring gantries were summed every 5 min and averaged to determine the mean travel time. The following equation was used: $ave\_passtim{e}_l=\frac{{\sum }_{veh}passtim{e}_t^{veh}}{veh}$, where $passtim{e}_t^{veh}$ is the travel time of each vehicle passing through two neighboring gantries at time t and veh is the number of vehicles passing through the gantries within 5 min.
• Lane occupancy: Depending on VD data, the identification code of each VD was acquired to determine the lane occupancy rate at each VD location. This rate was calculated every 5 min, and its association with that at each ETC gantry was determined to derive the occupancy of each lane between every two neighboring gantries.
• Number of accidents: The associations between gantry location and accident number (were determined to identify the distribution of accidents at each gantry.)

3.2. Accident Labeling Dataset

An accident labeling dataset containing data selected using a proposed filter was established on the basis of the basic traffic dataset. The following factors were considered during the development of the filter.

• Vehicles typically travel at high speeds on highways. Changes in traffic density can considerably reduce vehicle speed, potentially resulting in traffic accidents. Therefore, data analysis must be performed to determine the association between changes in vehicle speed and the occurrence of traffic accidents [24]. In this study, a basic traffic dataset was used to calculate the mean vehicle speed difference in each 5 min period between every two neighboring gantries to determine whether a drastic speed change occurred. This speed difference was then used as the first criterion for the filter to select useful data.
• In low-density traffic, vehicles travel at high speeds, allowing them to catch up with vehicles in high-density downstream traffic. The interaction of these two flows creates a discontinuous traffic wave, also known as a shock wave, which travels back upstream at a negative propagation velocity. In this study, ETC and VD data were used to obtain the traffic flow volume q and mean traffic speed v. The relational equation 𝑞 = 𝑘 × 𝑣 was used to derive the traffic density k. Subsequently, data conversion was performed to derive the velocity of the shock wave propagating toward the upstream traffic, v_sw. This propagation velocity was used as the second criterion for data filtration. The following equation was used:

  $$v_{sw}=\frac{q_b-q_a}{o_b-o_a}$$

  (1)

$v_{sw}$ represents the propagation velocity of the shock wave (km/hour), and $q_a$ and $q_b$ respectively represent the vehicle flow before and after the condition changes (vehicles/hour). $o_a$ and $o_b$ respectively represent lane occupancy before and after the condition changes (vehicles/length).

3.

As indicated by Risto and Martens [25], the relationship between space headway s and time headway h (Figure 1) can be used in combination with vehicle density k data to determine the mean headway. Figure 1 shows the space-time diagram of the relationship between space headway s and time headway h. The horizontal axis represents time t and the vertical axis represents space x. $s_i$ represents the space headway of the ith car and the i+1th car. $h_i$ represents the time headway of the ith car and the i+1th car. $v_i$ and $v_{i-1}$ respectively represent the change in speed between car i and car i+1. According to the vehicle characteristics and relevant regulations in Taiwan, when the mean traffic speed is 60 km/h, the maximum speed limit is 110 km/hr, the headway threshold should be 50–100 m/veh. Therefore, in this study, a mean headway of <50 m/veh was used as the third criterion for data filtration.

4.

In summary, three filtration criteria, namely drastic decreases in mean traffic speed, shock wave propagation velocity, and mean headway of <50 m/veh, were used in this study to identify and label traffic accidents.

3.3. Model Training and Validation Dataset

The process of generating a model training and validation dataset involved several steps. First, traffic accidents caused by insufficient headway and inattentional blindness in 2021 were selected and chronologically sorted depending on their occurrence time. Second, the relationship between the geographical data of gantries and the accident label data was analyzed to establish a model training and validation dataset. This dataset contained traffic flow data for all lanes on National Freeway No. 1, as well as upstream and downstream traffic flow data between neighboring gantries, with a 5 min interval. The traffic flow data contained information on 11 labels: the date of each record, the time of each record, the number of vehicles passing through upstream gantries, the lane occupancy of upstream gantries, the mean traffic speed at upstream gantries, the current number of vehicles passing through each gantry, the current lane occupancy of each gantry, the number of vehicles passing through downstream gantries, the lane occupancy of downstream gantries, the mean traffic speed at downstream gantries, and whether a traffic accident occurred. Figure 2 presents the flowchart of dataset generation.

4. Prediction Model and Numerical Testing

4.1. Testing Site

Numerical testing was conducted using the highway traffic accident data highlighted in Section 3. Data from all gantries in the northbound and southbound lanes of National Freeway No. 1 were visualized to create area charts and demonstrate the association between the total number of traffic accidents and the number of accidents caused by traffic speed differences (Figure 3). The results indicated that traffic accidents caused by traffic speed differences accounted for a large proportion of all accidents in each highway section. Therefore, to effectively manage highway sections and reduce the number of traffic accidents, a national highway crash prediction and warning model was developed. To verify the accuracy of this model, the highway section between Wangtian and Changhua interchanges (Gantry 01F10906S) was selected as the test site. Figure 4 depicts the geographical location and road network of the test site. The characteristics of this section are shown in

Table 1. Section characteristic between Wangtian and Changhua interchanges.

Regional Section	The Number of Kilometers	Number of Southbound Lanes	Number of Northbound Lanes	Speed Limit (km/h)
Wangtian interchange	189	4	4	110
Changhua system interchange	192	3	3	100
Changhua interchange	198	4	4	110

. It contains information such as the location of the area, the number of kilometers, the number of lanes, and the speed limit. As shown in Figure 3b, association rule mining revealed that this section had the highest proportion of traffic accidents caused by traffic speed differences. Notably, traffic accidents occurring on interchange ramps instead of main highway lanes were excluded and classified as accidents unrelated to traffic speed differences.

4.2. National Highway Crash Prediction and Warning Model

Developing prediction and accident warning models for shock wave propagation is a challenging task. In this study, the data analysis results discussed in Section 3 were used to confirm the causal relationship between shock wave propagation and traffic accident occurrence. The associations between traffic flow, shock wave propagation, mean speed difference, space headway, time headway, and gantry location were examined, and the dataset of traffic accidents related to speed differences was used as the training dataset. After the problem of imbalanced data was addressed, a DNN model was trained to detect the occurrence of shock waves, send early warnings to road users, and thereby prevent traffic accidents. The model development process focused on two stages: (1) the processing of imbalanced data and (2) the prediction of traffic accidents and announcement of early warnings. Figure 5 depicts the model framework. In Figure 5, the balanced dataset in the second stage includes traffic flow information for the upstream gantry area, the current gantry area, and the downstream gantry area. Traffic flow information includes vehicle number, lane occupancy, and average speed. The above information is used as input to the deep learning model to train the model.

Table 2. Deep learning model summary description.

Layer (Type)	Output Shape	Param
dense (Dense)	(None, 11)	110
dense_1 (Dense)	(None, 11)	132
dense_2 (Dense)	(None, 1)	12
Total params: 254
Trainable params: 254
Non-trainable params: 0

describes the content and parameter summary of the deep learning model.

The examined data were imbalanced because the numbers of data labeled with traffic accidents and no-accident instances differed substantially. For instance, at gantry 01F1960S and its neighboring upstream and downstream gantries (01F1906S and 01F2011S, respectively), of the 105,119 data entries obtained in this study, only 703 were labeled with traffic accidents. To address the problem of imbalanced data, three methods, namely class weight, oversampling, and focal loss methods, were evaluated. The class weight and oversampling methods assigned large weights to specific categories of data, thereby allowing these data to have a greater effect on model training and fitting compared with other categories of data. By contrast, the focal loss method adjusted the loss function of a prediction model to address imbalanced data. Comparison of the three methods indicated that the class weight method was the most appropriate for training and validating the proposed model.

A DNN was used to develop the prediction model. Nine types of traffic characteristic data in the accident labeling dataset were used for model construction. Specifically, the data were randomly divided into a model training dataset (80%) and a validation dataset (20%). The developed DNN had a multilayer perceptron structure, and its configuration is described as follows:

• Due to the different units of traffic flow volume, density, and speed data, min–max normalization was used to standardize the input eigenvalues.
• DNN parameters were initialized. The DNN model consisted of four fully connected layers (i.e., one input layer, two hidden layers, and one output layer) and included parameters such as connection weights and bias.
• The input layer had 10 eigenvalues, and each of the two hidden layers had 11 neurons. Since the accident prediction results were binary solutions (indicating whether an accident occurred), the model had only one output layer.
• DNN forward propagation
  • The input layer receives normalized data and transmits them to the hidden layers. The data then undergo multiplication with a connection weight matrix and addition with a bias term (i.e., a column vector) to produce a set of values. These values are then input into an activation function to obtain the final output of a hidden layer as follows:

    $$z_i^l={{\displaystyle \sum }}_i^{}{{\displaystyle \sum }}_j^{}{w}_{ij}^l·a_i^{l-1}+b_i^l{v}_{sw}=\frac{q_b-q_a}{o_b-o_a}$$

    (2)

    $$\sigma \left(z_i^l\right)=\mathrm{ReLu}\left(z_i^l\right)=a_i^l$$

    (3)

    where $w_{ij}^l$ is the weight of the ith perceptron in the lth layer, $a_i^{l-1}$ is the output of the lth layer, $a_i^l$ is the output of the ith perceptron in the lth layer, $a_i^{l-1}$ is the output of the lth layer, $b_i^l$ is the bias term of the ith perceptron in the lth layer, and $\sigma \left(·\right)$ is an activation function. The activation function of each hidden layer is a rectified linear unit.
  • Since the model outputs are binary solutions, the activation function of the output layer is a sigmoid function. The output $\widehat{y}$ of the output layer is calculated as

    $$\widehat{y}=\mathrm{Sigmoid}\left({{\displaystyle \sum }}_j^{}{w}_j^o·a_i^h+b_{}^h\right)$$

    (4)

    where $w_j^o$ is the weight of the output layer perceptron and $a_i^h$ is the output of a hidden layer.
  • Binary cross-entropy is used as the loss function, which is defined as follows:

    $$Loss\left({\widehat{y}}_k,y_k\right)=-\frac{1}{K}{\sum }_k^{}\left({\widehat{y}}_k·\log \left(p\left(y_k\right)\right)+\left(1-{\widehat{y}}_k\right)·\log \left(1-p\left(y_k\right)\right)\right),$$

    (5)

    where ${\widehat{y}}_k$ is the kth output of the output layer and $y_k$ is the label of the kth accident in the dataset. When an accident occurs, the output value is 1; otherwise, it is 0. Here, $p\left(y_k\right)$ represents the probability of accident occurrence. The loss function determines the prediction accuracy of the model.
• DNN back propagation
  • In accordance with Kingma and Ba [26], adaptive moment estimation (Adam) was used in this study as an optimizer to update DNN parameters. The loss function uses the chain rule to determine the partial derivative of parameters ($w_{ij}^l,b_i^l$) in each layer:

    $$\frac{\partial Loss\left(·\right)}{\partial w_{}^l}=\frac{\partial Loss\left(·\right)}{\partial p\left(y_k\right)}\frac{\partial p\left(y_k\right)}{\partial z_{}^{l+1}}\frac{\partial z_{}^{l+1}}{\partial w_{}^l},$$

    (6)

    $$\frac{\partial Loss\left(·\right)}{\partial {\mathrm{b}}_{}^l}=\frac{\partial Loss\left(·\right)}{\partial p\left(y_k\right)}\frac{\partial p\left(y_k\right)}{\partial {\mathrm{z}}_{}^{l+1}}\frac{\partial {\mathrm{z}}_{}^{l+1}}{\partial {\mathrm{b}}_{}^l}$$

    (7)
  • Generally, the Momentum optimizer adjusts the speed of change in the gradient descent direction, and AdaGrad uses an adaptive method to adjust the learning rate ($\eta$) of gradient descent. The Adam optimizer integrates both Momentum and AdaGrad and updates the exponential moving average $m_t$ and squared gradient $v_t$. Parameters ${\beta }_1$ and ${\beta }_2$, which belong to the interval [0, 1), are used to control the learning rate decay of ($m_t$, $v_t$), update the estimated values (${\widehat{m}}_t,\widehat{v_t}$), and thereby update each parameter ($w_{ij}^l,b_i^l$) in the neural network:

    $$w_{ij}^l=w_{ij}^l-\eta \frac{{\widehat{m}}_t}{\sqrt{\widehat{v_t}}+\epsilon }$$

    (8)

    $$b_i^l=b_i^l-\eta \frac{{\widehat{m}}_t}{\sqrt{\widehat{v_t}}+\epsilon }$$

    (9)

4.3. Model Validation and Testing

A confusion matrix is commonly used to evaluate the performance of DNN models. In this study, testing was conducted on the road section passing through gantry 01F10906S, located on the Changhua Interchange, which connects the southbound lanes of National Freeway No. 1 and National Freeway No. 3. After the developed DNN model was trained, its performance was evaluated using the following indicators based on the true-positive (TP), false-negative (FN), false-positive (FP), and true-negative (TN) rates:

• Sensitivity: The ratio of true traffic accidents predicted by the model to all true traffic accidents:

  $$\mathrm{Sensitivity}=\frac{TP}{TP+FN}$$

  (10)
• Precision: The ratio of true traffic accidents predicted by the model to all traffic accidents predicted by the model:

  $$\mathrm{Precision}=\frac{TP}{TP+FP}$$

  (11)
• False alarm rate: The ratio of false traffic accidents predicted by the model to all no-accident instances:

  $$\mathrm{FAR}=\frac{FP}{FP+TN}$$

  (12)
• Accuracy: The ratio of true traffic accidents to no-accident instances correctly predicted by the model:

  $$\mathrm{Accuracy}=\frac{TP+TN}{TP+FN+FP+TN}$$

  (13)

Table 3. Confusion matrix and performance indicators of the proposed prediction model.

(a) Training dataset
Total Number of Data: 84,048
Classification		Model Prediction
		Accident Occurs	No Accident
Actual situation	Accident occurs	499 (TP)	68 (FN)
	No accident	4,725 (FP)	78,576 (TN)
Sensitivity:	88%	False alarm rates:	6%
Precision:	10%	Accuracy:	94%
(b) Testing dataset
Total Number of Data: 21,071
Classification		Model Prediction
		Accident Occurs	No Accident
Actual situation	Accident occurs	119 (TP)	17 (FN)
	No accident	1,144 (FP)	19,791 (TN)
Sensitivity:	88%	False alarm rates:	5%
Precision:	9%	Accuracy:	94%

summarizes the results of the confusion matrix and aforementioned indicators. In both the training and the validation stages, the developed model achieved an accuracy of 94%, a sensitivity of 88%, a precision of <10%, and a false alarm rate of <6%. The above values show that this model predicts accurately, and the false alarm rate is low. When the model is trained and verified, the real-time data of the detection facilities can be used to predict accident symptoms. If a symptom is found, the predicted result can be broadcast, for example on a changeable message sign or a smart mobile phone. In this way, highway users are informed in advance, so that serious accidents are reduced and the safety of road users is improved.

5. Conclusions

In this study, a DNN was used to develop a highway crash prediction and warning model. A data association framework was used to create datasets comprising large volumes of ETC and VD data, which included information on shock wave propagation, mean traffic speed, and headway defined by traffic flow theories. To obtain training data for the proposed model, the associations between these data and gantry information, accident location, and accident quantity were examined. Generally, the adopted framework can be used to establish the relationships between actual sensor data (e.g., mean traffic speed, lane occupancy rate, and traffic flow volume) and traffic accident occurrences. For example, when the traffic density is uneven, shock waves are generated, which in turn affect changes in the mean traffic speed of vehicles. Therefore, to identify the occurrence of traffic accidents, drastic decreases in vehicle headway and mean traffic speed recorded in datasets must be examined. In this study, sensor data and traffic flow theories were combined to label all data entries as either accident or no-accident instances in order to create datasets for testing and validating the developed DNN model. The class weight method was used to address the problem of imbalanced data, thereby allowing the proposed model to accurately predict traffic accidents. The test results indicated that the proposed model exhibited high accuracy and sensitivity and a low false alarm rate. Specifically, the model accurately predicted 88% of traffic accidents while generating a false alarm rate of 6% and 5% during the training and validation stages, respectively. Overall, the model exhibited an accuracy of 94%. However, only the data recorded at gantry 01F1960S and its neighboring upstream and downstream gantries (01F1906S and 01F2011S, respectively) were examined. Therefore, future studies should focus on all lanes and sections of highways to develop a model that produces different prediction results depending on regional characteristics, thereby increasing the flexibility of the model construction method proposed in this study. In conclusion, the data association framework and prediction model proposed in this study have high potential for smart highway management aiming to improve the safety of road users.