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Accident Detection and Flow Prediction for Connected and Automated Transport Systems

Accident Detection and Flow Prediction for Connected and Automated Transport Systems Hindawi Journal of Advanced Transportation Volume 2023, Article ID 5041509, 9 pages https://doi.org/10.1155/2023/5041509 Research Article Accident Detection and Flow Prediction for Connected and Automated Transport Systems 1 2 3 3 3 Yi Zhang , Fang Liu , Sheng Yue , Yuxuan Li , and Qianwei Dong Zhejiang Gaoxin Technology Company Limited, Hangzhou 310002, China Liaoning Provincial Transportation Planning and Design Institute Company Limited, Shenyang 110111, China College of Transportation, Jilin University, Changchun 130012, China Correspondence should be addressed to Qianwei Dong; dongqw21@mails.jlu.edu.cn Received 2 February 2023; Revised 26 February 2023; Accepted 5 April 2023; Published 17 April 2023 Academic Editor: Wenxiang Li Copyright © 2023 Yi Zhang et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Efective accident detection and trafc fow forecasting are of great importance for quick respond, impact elimination and intelligent control of the trafc fow consisting of autonomous vehicles. Tis paper proposes a trafc accident detection method for connected and automated transport systems by conducting a grid-based parameter extracting and SVC-based trafc state classifcation. Allowing for the dynamic spread of trafc fow over time, from upstream to downstream and from accident lanes to other lanes, a spatiotemporal Markov model is established to predict the evolution of trafc fow after accident by introducing the grid as state detection unit and ftting the spatiotemporal evolution with the parameter space mean speed to match the need of both detection accuracy and monitoring scope. Compared with actual accident data, the validation results indicate that the proposed methods present a good performance in accident detection with the accident detection rate as 87.72% and a higher precision rate than both SVM (support vector machine) and ANN (artifcial neural network) models in trafc fow prediction. With the active trafc accident identifcation and dynamic trafc fow prediction, it is benefcial to shorten detection time, reduce possible impacts of trafc accidents and carbon emissions from congestion. Te methods can be implied to trafc state recognition and trafc fow prediction, which is one of the signifcant sections of connected and automated transport systems, and serve as references for accident handling and urban trafc management. In recent years, the rapid development of automatic 1. Introduction driving technology, intelligent network technology and With the rapid increment of motor vehicles, congestion and satellite positioning technology, etc., enriches the sources of secondary accidents caused by slow accident response seriously data acquisition. Integration of these multisource big-data afect urban trafc safety and efciency and have become ofers new data-driven ways to obtain real-time location a social problem, which attracts much attention [1]. Efective information of autonomous vehicles and trafc motion trafc condition monitoring is vital to decrease the adverse characteristics. In this case, the methods for accident de- impact of accidents, as the faster an accident is detected, the tection and management should be improved from aspects more quickly managers can respond, thereby shortening of global state diagnosis and postaccident trafc fow handling time, relieving trafc pressure, and lessening the prediction. occurrence probability of massive congestion and secondary However, most of the previous studies focus on local accidents [2]. Terefore, trafc condition monitoring and state monitoring based on roadside devices and trafc fow trafc fow prediction have become essential parts of urban prediction with macroscopic parameters [3–7]. Except for trafc management, which is conducive to improving trafc the accidents happen at the place with monitoring devices efciency, ensuring trafc safety, and reducing energy con- which can be informed, most accidents occurring at the sumption and carbon emissions of transportation system. place without any detection device still remains insensitive. 2 Journal of Advanced Transportation tracking, how to conduct an accurate and large-scale de- In order to make a quick accident response, the real-time abnormal state monitoring of wide range in the road net- tection with the reduction of algorithm complexity has become a problem that cannot be ignored. work should be noted enough. Besides, the trafc fow prediction after an accident is also vital for efcient accident After a trafc accident occurs, it is necessary to predict its disposing and trafc guidance. Terefore, to reduce negative impact and take emergency management measures to clear impact of trafc accidents, it is necessary to investigate the up the accident and reduce losses. Some studies used trafc methods for timely and accurate trafc state identifcation, wave models and fuid mechanics models to predict the accident detection, and postaccident impact prediction in impact of trafc accidents, while most of the others esti- autonomous transport systems. mated the impact degree by using neural network [12], decision tree [13], and other machine learning methods [14]. According to the data types used, the research in this feld can be divided into two aspects. One is accident de- Among them, Markov is one of the most popular approaches to predict trafc condition. For example, Yao et al. [15] tection by using macroscopic trafc fow parameters, such as trafc volume, speed, density, and occupancy, and the other divided a day into multiperiods and predicted trafc in each period by using Markov chain. Li et al. [16] used a Grey- is utilizing the videos taken by on-road cameras to learn accident features concerning collision image and driving Markov model to predict highway trafc variation based on trajectory, etc. historical data and obtained an acceptable accuracy and With respect to the macro trafc parameters-based re- reliability. Zhao et al. [17] combined Bayesian information search, data collected by sensors such as loop sensors are criterion and HMM (hidden Markov model) to predict used mostly in obtaining historical trafc parameters. Te trafc. Te results indicate that the method yields a better methods employed mainly include state recognition [4], performance than SVM and LSTM-RNN (long short-term memory-recurrent neural network). Although previous statistics [5], and machine learning [6]. For example, Ki et al. [4] conducted an ANN (artifcial neural network)-based studies indicated that Markov method performs well in short-term trafc prediction, they only focused on the accident detection by using trafc parameters exacted from loop sensors on the freeway in South Korea. Fang et al. [6] postaccident evolution of trafc condition over time; few involved the dynamic spatial spread of trafc fow. Actually, determined trafc accidents by training deep-loop neural network involving the parameters of trafc fow, speed, and the movement process of trafc fow is naturally from up- occupancy of downstream of urban expressway. As most of stream to downstream and from accident lanes to other the parameters used in this type of research are extracted lanes. It is necessary to deduce the propagation of trafc fow from cross-sectional trafc fow data, it is limited by partially from the view of both time and space dimension in trafc data missing and low data quality. In order to avoid this fow prediction. problem, some scholars combined the cross-sectional fow Considering the limited number of sensors and moni- toring range of video detection, this paper aims at de- data with video tracking data to improve the accuracy of accident detection and position. For example, Yang and Wu veloping a lane-level detection method based on big data resources, which is intended to use GPS data of autonomous [7] constructed a BP neural network for preliminary acci- dent recognition by using trafc parameters obtain from vehicles to obtain road-level trafc fow parameters, so as to optimized distribution of loop sensors, and established the detect accidents. As grid-based lane level analysis is proved Camshift algorithm for vehicle tracking to make a fnal to be helpful for detection accuracy improvement [11, 18], determination. However, the detection range of these studies we divide lanes into grids and express the trafc state of each is at the regional and road level, with a lack of lane-level state grid with macro trafc fow parameters, considering both monitoring and accident identifcation [8]. In fact, the oc- monitoring granularity and computational complexity. currence and subsequent impact of accidents on trafc fow With a machine learning process, the trafc state is then are mostly at lane level. On the other hand, the image combined with historical data to distinguish accidents from other events, such as regular congestion. It is worth noting feature-based accident detection and positioning mainly rely on deep learning of the abnormal characteristics of the trafc that the use of gridded roads can make the detection of trafc accidents refned to the lane level. Tereby, it can not only accidents, such as the vehicle collision features [9] and the abnormal vehicle trajectories in video images [10]. For ex- realize global accident detection but also accurately locate ample, Zou et al. [9] proposed a detection method based on trafc accidents, and efectively refect the variations in the imagine signal processing and hidden Markov classifying trafc conditions before and after the trafc accident. to detect the trafc incidents at signal intersections. Ren et al. Heeding the limitations of previous studies in trafc pre- [11] divided the highway video images into a cluster of cells diction, a spatiotemporal trafc fow prediction model will and used fuzzy-identifcation to determine the state of cells be constructed based on Markov theory, which allows for the dynamic spread of trafc over both spatial and temporal and then constructed an SVM (support vector machine) classifer to position and detect the trafc accidents. Al- dimensions. In conclusion, this paper will propose methods to monitor the trafc status of wide-range road network though this type of studies is proved to have a good accuracy performance, there is a limitation that it will be constrained based on real-time vehicle location information. Ten, the negative postaccident efect will be predicted based on the by the installation position and number of on-road cameras. Moreover, the popularization of this method also faces the evolution of trafc state after accidents. Te results will be problem of computing resources. With the promotion of helpful to improve the range and real-time of accident demand for performance of detection and trajectory detection and the accuracy of trafc prediction, thus Journal of Advanced Transportation 3 contributing to rapid accident responses, which is conducive result of the density of queued vehicles under diferent trafc to enhancing trafc efciency, ensuring trafc safety, re- conditions, the length of the unit L is determined to be the grid ducing energy consumption and carbon emissions of sum of the body length of fve vehicles and the minimum transportation system, and the incidence of trafc conges- safety car-following distance d in free fow, which in the min tion and even secondary accidents. urban road condition is 22.8 m [19], while in the highway Te remainder of this paper is organized as follows: In condition is 127.2 m [20]. Considering that the vehicle Section 2, we present trafc accident diagnosis method. length is generally less than 5.0 m, the length of the state Section 3 proposes a grid-based spatiotemporal deduction detection unit L for urban road and the highway con- grid model for postaccident fow prediction. Section 4 simulates ditions is set to be 139.0 m and 661.0 m, respectively. Te and verifes the efectiveness of the methods. Tis paper is adjacent interval dg denotes the distance between two ad- concluded with Section 5, in which we summarize our jacent grids, which is calculated by the distance of 1 s at the fndings and discuss our study limitations and directions for maximum allowable speed in corresponding condition. future research. Ten, dg under the urban road and highway condition is calculated to be 10.0 m and 33.3 m, respectively. In general, trafc state is time-varying, and the number of vehicles in the 2. Traffic Accident Detection Model grid varies with the trafc state, as shown in Figure 1. 2.1. Defnition of State Detection Unit. Although the image Terefore, trafc fow indicators calculated by grids will feature-based methods are proved to have relatively high objectively refect real-time trafc state changes. accuracy in accident detection according to existing studies, they are limited by the fnite location and sparse distribution 2.2. Expression of Trafc State. In order to transfer the con- density of video detectors, as they identifed the occurrence tinuous trafc fow on a lane into discrete state detection units, and location of trafc accidents using video images obtained we need to select an appropriate trafc state indicator to by on-road devices. Te limitation of detection range and represent the real-time trafc state of a grid and its changes computational resources makes these methods unable to over time and space. As shown in HCM [21], the parameter of carry out large-scale and high-precision accident detection. average speed of trafc fow, which consists of time mean speed However, the Internet of vehicles (IoV) and big data en- and space mean speed, is often used in a trafc state classif- vironment makes it possible to obtain large-scale trafc cation and real-time trafc state estimation. Taking account status information based on multisources vehicular that the defned length of a grid is a fxed value, using the space positioning data. mean speed will be more convenient to express and calculate Tis section will establish dynamic models for accident the trafc state under this circumstance. Ten, we defne v as detection and postaccident impact prediction, of which, the the space mean speed of a grid, which is calculated as follows: frst step is to propose a state detection unit to express the trafc condition. After a trafc accident occurs, the trafc grid v � , (1) state will get worse with the gathering of vehicles and the n (1/n)􏽐 t i�1 trafc congestion may come into being and spread from the downstream to the upstream on the accident lanes, while where t denotes the time that it takes for vehicle i to go also spreading from the accident lanes to adjacent lanes and through the grid during the detection interval. n is the total even the entire road section. Terefore, a lane-level detection number of vehicles which pass the grid during the sampling unit, named as grid, is proposed. Except for meeting the interval. Considering that the normal accident sampling granularity requirements of trafc propagation analyzing, it interval is 5 min, and the equipment’s acquisition time is 1 s, is well suited to be employed in examining the trafc state taking into account real-time and computational con- variation between micro vehicle and macro trafc fow, and sumption, the sampling interval is selected as 10 s. optimizing calculation speed on the basis of ensuring de- According to previous research [22, 23], trafc state is tection precision. divided into the following four levels: unblocked, lightly Although Ren et al. [11] and Wang et al. [18] also utilized congested, congested, and severely congested. Te corre- grid in trafc fow analysis, the size of grid is set to be small sponding space mean speed ranges on the main urban roads and lack of enough theoretical basis. For example, in the are, respectively, higher than 30 km/h, 20 km/h-30 km/h, analysis based on multiagent method, the size of grid is 10 km/h-20 km/h, and less than 10 km/h. Tus, when the defned as vehicle level, which causes that the state of a grid space mean speed of a grid is less than 20 km/h, its trafc directly refects that of the corresponding vehicle. Tis state will be determined as congested state. We then use the microscopic analysis results in a large amount of overall grid to sample, record, and store data including space mean calculation and is inconvenient to macroscopic trafc fow speed, trafc state, and state duration at a sampling interval analysis. In order to decrease defective impact, we can of 10 s. Te historical data stored by the grid will be used as consider dividing larger grids and express the state of each the data set for trafc accident detection. grid with meso parameters. At the same time, considering the analysis accuracy, the space between adjacent grids can be set to be relatively small. As shown in Figure 1, we divide 2.3. Detection of Trafc Accident. Te reasons for trafc a lane into a number of overlapping grids with a unit length congestion can be divided into the following two main types: of L and adjacent interval of dg. According to the analysis normal congestion and abnormal congestion. Normal grid 4 Journal of Advanced Transportation L dg grid State detection unit Driving Direction Figure 1: Illustration of the state detection unit. congestion refers to the congestion caused by the inability of where the frst term 1/2‖ω‖ is the regularized term, which is road capacity to meet the trafc demand, which often has used to adjust the function fatness, while the second term regular characteristics. For example, regular trafc conges- R [f] is the loss function which measures the empirical emp tion usually occurs in the morning and evening rush hour. error. C is a regularization parameter that determines the Abnormal congestion refers to the congestion caused by trade-of between structural error and empirical error. sudden events, which is unpredictable and accidental. In Considering that a generalization error cannot be obtained order to detect trafc accident, the mission of this section is by simply minimizing the training error, we then allow bits to distinguish abnormal congestion from the normal one of examples assigned wrongly and introduce soft margin to according to the characteristic of diferent trafc states. respite the overftting dilemma as following: Based on the real-time and historical data of space mean |y − f(x)| � max 􏼈0, |y − f(x)| − ε􏼉, (4) speed for each grid, we employ SVC (support vector clas- sifcation) [3] to detect trafc accidents according to the which is defned as the minimal distance of a sample to the characteristics of spatiotemporal distribution and its dy- decision surface. Te loss is the diference between the namic change. SVC is an application of SVM in the aspect of predicted value and the radius ε of the soft margin. It will be data analysis and pattern recognizing, which is widely used 0 if the predicted value is within the region of margin. Both C in accident detection by previous studies [24]. Te data we and ε are user-determined parameters. Te positive slack use are extracted from a sample library, which is built to variables ξ is introduced to indicate the degree of classif- store the historical data for each grid, with the information cation error. Terefore, equation (3) is transferred to of space mean speed, state duration, weekly simultaneous data and monthly simultaneous data, etc. According to the 2 min J � ‖ω‖ + C 􏽘 ξ􏼁 , distinguished characteristics of normal congestion and ab- 2 i�1 normal one caused by trafc accidents, we assign the sample (5) data to positive and negative classes correspondingly. Ac- ⎧ ⎪ y ω∙ϕ x􏼁 + b ≥ ε − ξ 􏼁, i i i cordingly, the input-output training data pairs in training s.t. samples are labeled as D � 􏼈(x , y ), . . . , (x , y ), . . . , 0 ≤ ξ . 1 1 i i (x , y )}, where x ∈ X⊆R and y is the label of con- N N i i t t Te constrained optimization problem is then converted gestion type with yϵ{−1, 1}, in which a sample is assigned to into a convex quadratic optimization problem and solved class 1 if a congestion is normal congestion and to the class with the primal Lagrangian from the following equation: −1 otherwise. N is the number of training samples. Ten, we estimate a function as follows: m m L � ‖ω‖ + C 􏽘 ξ − 􏽘 η ξ , 􏼁 􏼁 i i i f(x) � ω∙ϕ(x) + b x ∈ R , (2) 2 i�1 i�1 (6) where ϕ(x) represents the high-dimensional feature spaces m that are nonlinearly mapped from the input space x, ω − 􏽘 α ε + ξ −y + ω∙Φ x􏼁 + b􏼁, i i i i i�1 denotes the parameter vector, and b is the threshold. Te best estimation function that one can obtain can minimize where L is the Lagrangian function and η and α are i i the expected risk. However, the small sample size might Lagrange multipliers. Hence, equation (6) satisfes the occur overftting dilemma. One way to avoid the problem is positive constraints. to restrict the complexity of the estimation function. One introduces the regularization term as a solution. So, the 0≤ η , α . (7) i i SVC’s linear algorithm is to solve the following regularized risk function: Te above problem is thereby converted into a dual problem, in which the Lagrangian multipliers η , a , and a i i j min J � ‖ω‖ + CR [f] , (3) needed to be optimized. Tis dual problem contains emp 2 Journal of Advanced Transportation 5 ∗ ∗ a quadratic objective function of α and a with the linear Ten, we get the optimal solutions ω and b of ω and b, i j constraint. respectively, m m m ∗ ∗ max J � 􏽘 a − 􏽘 a a y y ϕ x , ϕ x , ω � 􏽘 a y ϕ x , 􏼐 􏼁 􏼐 􏼑􏼑 􏼁 i i j i j i j i i i i�1 i,j�1 i�1 (15) ∗ ∗ 0≤ α ≤ C (8) b � y − 􏽘 a y 􏼐ϕ x􏼁 , ϕ􏼐x 􏼑􏼑, ⎧ ⎪ i i i i i j ⎨ i�1 s.t. , i � 1, 2, . . . , m. ⎪ and separation hyperplane. 􏽘 a y � 0 ⎩ i i i�1 ∗ ∗ . (16) ω ϕ x􏼁 + b � 0 Let Eventually, we construct decision function to classify the m m following equation: min J � 􏽘 a a y y 􏼐ϕ x􏼁 , ϕ􏼐x 􏼑􏼑 − 􏽘 a , (9) i j i j i j i ∗ ∗ i,j�1 i�1 f(x) � sign ω ϕ x􏼁 + b 􏼁. (17) 0 ≤ α ⎧ ⎪ 3. Prediction of Postaccident Traffic Flow s.t. , i � 1, 2, . . . , m. (10) 􏽘 a y � 0 ⎩ i i i�1 3.1. Spatial Correlation Test. Trough the analysis of existing research and related accident data, it is found that the Introducing kernel function κ(x , x ) into equation (9), i j congestion caused by trafc accidents has a trend of we get spreading from downstream to upstream and from accident m m lanes to other lanes. We construct a spatiotemporal Markov min J � 􏽘 a a y y κ􏼐x , x 􏼑 − 􏽘 a , i j i j i j i model to predict the impact of accidents based this trend. i,j�1 i�1 Before modeling, we investigate the spatial characteristics of accident propagation by calculating the Moran’ I index to (11) 0 ≤ α ⎧ ⎪ i ⎪ conduct a spatial correlation test. s.t. , i � 1, 2, . . . , m , ⎪ N N 􏽘 a y � 0 w v − v v − v 􏽐 􏽐 􏼁 􏼁 ⎩ i i N i�1 j�1 ij i i I � × , i�1 S 􏽐 v − v 0 i i�1 where κ(x , x ) is the kernel function which is equal to the (18) i j N N inner product of two vectors, i.e., x and x , in the feature i j S � 􏽘 􏽘 w , 0 ij space ϕ(x ) and ϕ(x ). Tat is, i j i�1 j�1 κ x , x � ϕ x ∙ ϕ x . (12) 􏼐 􏼑 􏼁 􏼐 􏼑 i j i j where v is the space mean speed of the i-th grid and v is the mean of space mean speed of all the grids in the area where To simplify the calculating complexity, some common the accident occurred. N denotes the number of grids in the kernel functions, such as linear kernel, polynomial kernel, study segment. Te spatial weight matrix of the grids W and radial-basis function (RBF) kernel, are introduced to the ij refects the spatial relation of the grids. computation of ϕ(x). Choosing diferent kernel functions Te form of the rules determining W is that w � 1 if will form diferent learning machines. Considering that the ij ij grid i and j are adjacent in space, otherwise w � 0. Te data set is nonlinear, the RBF kernel function, which is ij value of Moran’ I index is between −1 and 1. Te value is a nonlinearly kernel function, is chosen in this study. positive indicates that the space mean speed of diferent � � � �2 � � � � x − x grids is positively correlated in spatial distribution, while � i j� ⎜ ⎟ ⎛ ⎜ ⎞ ⎟ ⎝ ⎠ (13) κ􏼐x , x 􏼑 � exp − , i j negatively correlated in space when negative, and 0 indicates 2σ that the space mean speed is independent of each other in spatial distribution. where σ is a parameter that determines the area of infuence Te statistical signifcance Z is calculated as follows: this support vector has over the data space. To get the optimal solution, equation (9) needs to meet 1 − E(I) KKT (Karush-Kuhn-Tucker) conditions. 􏽰������ Z � , Var(I) 0≤ a , 0 ≤ μ, ⎧ i 1 (19) ⎨ y f x􏼁 − ε + ξ ≥ 0, i i i E(I) � , (14) 1 − n a y f x − ε + ξ � 0, 􏼁 􏼁 i i i i 2 2 Var(I) � E􏼐I 􏼑 − E(I) , ξ ≥ 0, μ ξ � 0. i i i 6 Journal of Advanced Transportation where E(I) is the mean of Moran’ I indexes, and Var(I) is a grid is infuenced by its side grid. Meanwhile, the the variance of Moran’ I indexes. Based on the post- historical data for a grid also associates with its cur- accident trafc fow data, we obtain that Moran’ rent trafc fow state because of periodic variation of I � 0.0362910 and Z � 2.2587. When the value of I is trafc fow [16]. Terefore, we examine the evolution of positive, it denotes that there is spatial correlation be- state in each grid considering the impact of its upstream tween the space mean speed of diferent grids. And if grid, side grid, and adjacent previous period, as shown in 1.96 ≤ Z ≤ 2.58, it means that 95% of spatial features that Figure 2. are sure to reject statistics are randomly distributed as- sumptions. Tey confrm that there is a signifcant spatial 3.2.1. Infuence of Downstream Grid. Given the recurrence correlation between the space mean speed of diferent relation between upstream grids and downstream ones, we grids in the area where the accident occurred. Terefore, i⟶i+1 introduce the transition probability P to express the we can predict the postaccident trafc fow according to infuence of the downstream grid i to the upstream one i + 1 the characteristics of the spatial evolution process of the at time t, which is expressed as follows: space mean speed value. i+1,j i⟶i+1 P � . (21) i,j 3.2. Model Construction. Te prediction of trafc fow variation under accident condition is a crucial means for accident management, since a real-time overlook at the 3.2.2. Infuence of Side Grid. In addition to the congestion variation of trafc state in the accident area contributes for propagation within the accident lanes, there is also impact of quick accident disposal and congestion evacuation. Re- j⟶j+1 the grids in the accident lanes to its side grid. We use P ferring to [25], Markov model has a high accuracy in short- to denote the impact of the side grid. Formally, it is time prediction for trafc condition based on the historical and real-time data. Terefore, this paper will establish i,j+1 j⟶j+1 P � . (22) a spatiotemporal Markov model to deduce the trafc state i,j after the trafc accident happens. Markov process is often used to describe the state of 3.2.3. Infuence of Adjacent Previous Period. Likewise, a system and the transition between diferent states. And Markov chain refers to the Markov process whose time considering the infuence of a grid’s state from time t-1 to t⟶t+1 time t, the transition probability P is defned and and state parameters are discrete. It satisfes the following two assumptions: (1) the nonafterefect property of the calculated as follows: t+1 Markov model, which refers to that the state U of the t+1 i,j t⟶t+1 system at time t + 1 is relevant to the state at time t, re- P � . (23) gardless of the state before time t. Tis means that the i,j t+1 t value of U is only related to the value of U , but not t− 1 t− 2 Considering all the three factors, the compound tran- related to the value of U , U , . . .; (2) the state tran- sition probability is sition from time t to time t + 1 is independent with the state at time t. α β c t i⟶i+1 j⟶j+1 t⟶t+1 P � 􏼐P 􏼑 + 􏼐P 􏼑 + 􏼐P 􏼑 . i,j Tus, we denote a matrix composed by space mean speed (24) of q adjacent units at p adjacent lanes as a system. Te state of s.t. α + β + c � 1, the system at time t, refers to U , is expressed as follows: where α, β, and c are the weight coefcients. Substituting t t t v · · · v · · · v q,p i,p 1,p equations (21)–(23) into (24), we get ⎜ ⎞ ⎟ ⎛ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⋮ ⋮ ⋮ ⎟ ⎜ ⎟ ⎜ ⎟ ⎟ α β c ⎜ ⎟ ⎜ ⎟ t t t+1 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ v v v ⎜ ⎟ ⎜ ⎟ t ⎜ t t t ⎟ i+1,j i,j+1 i,j ⎜ ⎟ t ⎜ ⎟ ⎜ ⎟ ⎛ ⎝ ⎞ ⎠ ⎛ ⎝ ⎞ ⎠ ⎛ ⎝ ⎞ ⎠ ⎜ ⎟ . (25) U � ⎜ v · · · v · · · v ⎟ , (20) ⎜ ⎟ P � + + ⎜ ⎟ ⎜ q,j i,j 1,j ⎟ i,j ⎜ ⎟ t t,h t ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ v v ⎜ ⎟ ⎜ ⎟ v ⎜ ⎟ i,j i,j ⎜ ⎟ i,j ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⋮ ⋮ ⋮ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ t t t Ten, the transition probability matrix at time t is v · · · v · · · v q,1 i,1 1,1 t t t P · · · P · · · P n,m i,m 1,m where v denotes the space mean speed of the i-th grid in the ⎜ ⎟ i,j ⎛ ⎜ ⎞ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⋮ ⋮ ⋮ ⎜ ⎟ j-th lane at time t. ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ t ⎜ t t t ⎟ By calculating the spatial correlation of space mean ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ P � ⎜ P · · · P · · · P ⎟ , (26) ⎜ ⎟ ⎜ ⎟ ⎜ n,j i,j 1,j ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ speed of trafc state in diferent grids, we fnd that the ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⋮ ⋮ ⋮ ⎟ ⎜ ⎟ ⎜ ⎟ postaccident propagation of trafc fow has certain spatial ⎝ ⎠ t t t characteristics. Tat is, the state of trafc fow is spreading P · · · P · · · P n,1 i,1 1,1 from upstream to downstream, which means that the state of a grid is directly infuenced by its upstream grid. P denotes the transition probability of the i-th state de- i,j Besides, the congestion state of accident-impacted lanes tection unit in the j-th lane at time t. Ten, the state matrix at will spread to other lanes, which means that the state of time t is Journal of Advanced Transportation 7 t t t+1 t+1 v v v v 1,2 2,2 1,2 2,2 t→t+1 j→j+1 j→j+1 p p t t t+1 t+1 v v v v 1,1 2,1 1,1 2,1 i→i+1 i→i+1 p p t–moment t+1–moment Figure 2: Te conduction process of the state between diferent grids. Driving Direction 1 2 4 8 10 11 12 13 3 5 6 7 9 14 15 16 17 18 19 L=384 m the underpass section of Qinggang Overpass of the Northern Expressway in Changchun The Grid 1 The Grid 8 where the traffic accident occurred Figure 3: Te case study section and unit partition. t t− 1 t Here we present a case by taking the accident occurred at (27) U � U ∙P . 15:25:35 on Aug. 16th, 2019, as an example. First, we cal- culate the space mean speed for each grid of the target According to the state change of each grid and of the spatial distribution, the duration and infuence scope of section once per 10 seconds during the period of 15:22: 49−16:35:59. Te results indicate that all the lanes were congestion caused by trafc accident can be predicted. congested after 15:25:39. Notably, there are two zero-speed vehicles at the 8-th grid on the 1-st lane, which is shown in 3.3. Model Calibration. We obtained the trafc accident data Figure 3, during the period of 15:25:39−16:07:19. Te state of and the corresponding trafc fow data of the underpass section this grid is illustrated in Figure 4. in Qinggang Overpass of the northern expressway in As shown in Figure 4, the state variation of the grid goes Changchun in 2019 from trafc management department, through four states, i.e., (1) uncongested from about 15:22:49 to which has GPS and mobile signaling big data resources. Tere 15:25:39; (2) extremely congested from about 15:25:39 to 16:07: are totally 502 valid samples in which 164 in the positive class 19, as the space average speed suddenly dropped to 0, and the and the others in the negative class according to the method in lane began to be congested; (3) congestion evacuation from Section 2.3. Ten, 400 samples including 131 positive samples about 16:07:19 to 16:08:59, during which period the trafc are selected and composed the training set for model training accident was handled; and (4) free fow state after 16:09:29. and parameter calibrating, and the remaining 102 samples are With the proposed SVC model, the accidents were de- taken as testing set for validating performance. Based on the termined, and the performance comparing to the testing 400 training samples, the parameter of α, β, and c in the data is shown in Table 1. spatiotemporal Markov model is estimated by utilizing the According to the testing results, the precision is calcu- MLE (maximum likelihood estimation) method, with the value lated to be 77.78%, the recall is 84.8%, and the accuracy is being 0.39, 0.47 and 0.14, respectively. 87.72%. Te results prove that the accident detection model can recognize trafc accidents with a low error rate. It re- 4. Simulation and Model Validation fects that the accident detection model can identify ab- normal congestion caused by a trafc accident efciently and 4.1. Trafc Accident Detection. Based on the 102 testing then send a notifcation to trafc management department samples mentioned in Section 3.3, the trafc accident de- timely and precisely. tection model proposed in Section 2.3 is validated. As shown in Figure 3, the road section is divided into grids. Since the total length of the target section is 384 m, we draw 19 grids 4.2. Postaccident State Prediction. Based on the testing data, for each lane beginning from the downstream stop line to we predict the trafc state after the 102 accidents in the upstream. testing dataset by using the spatiotemporal Markov model 8 Journal of Advanced Transportation systems, this paper predicts the trafc state from lane level with detection unit as grid and detection parameter as space mean speed. After determining the trafc state of each grid, we formulate a trafc state matrix to integrate the states of all the grids both in lateral and longitudinal direction. Con- 40 sidering the impacts of upstream grid, side grid and time t − 1, a Markov model is presented, in the transition state matrix of which, time and space evolution of trafc state are simultaneously deduced. Te results indicate that the methods improve the accuracy on accident detection and trafc fow prediction corresponding to 2.6% and 9.2% lower 0 16 50 100 150 200 266 291 mean absolute percentage error compared with SVM and 15:22:49 15:25:39 16:07:19 16:11:29 time step ANN model, respectively. Te active detection and prediction method developed Figure 4: Te state variation of a grid in case study. matches the need of both spatial accuracy and computa- tional efciency to identify trafc accidents and predict the Table 1: Confusion matrix of classifcation results. postaccident trafc fow with calculated precision as 77.78%, Prediction recall as 84.8%, and accuracy as 87.72%. It also shortens the Ground-truth detection time and reduces possible impacts of accidents and Positive Negative carbon emissions from congestion, which is helpful to Positive 28 5 monitor the accident situation, identify abnormal trafc Negative 8 71 condition and ensure trafc safety. Moreover, this paper can serve as a reference for accident handling, trafc control and Table 2: Algorithms comparison results. management in autonomous transport systems. It should be mentioned that there still existing some Indicator ANN SVM Spatiotemporal Markov limitations in this paper. Even though we have verifed the MAE 16.7 11.3 9.4 spatial correlation of congestion caused by an accident, we RMSE 18.2 15.5 16.4 will involve the quantitative spatiotemporal spread mech- MAPE (%) 26.3 19.7 17.1 anism of postaccident in future research. In addition, we can also conduct a more detailed calibration for the parameters in rectangular grid analysis given diferent trafc status. proposed above. Taken space average speed as dependent variable and based on the historical data, we also develop an SVM and an ANN [26], respectively, for evaluation of the Data Availability prediction performance with parameter of MAE (mean abso- Te data supporting the study are provided by trafc lute error), RMSE (root mean squared error) and MAPE (mean absolute percentage error). Te results are shown in Table 2. management department. Comparing the prediction efects of the three algorithms, we fnd that the prediction results provided the spatio- Conflicts of Interest temporal Markov model is most close to the real data. Te reason may be that the spatiotemporal Markov model Te authors declare that they have no conficts of interest. considers not only the evolution of trafc state in time dimension, but also that in spatial dimension which includes Acknowledgments trafc fow spreading both from upstream to downstream and from accident lanes to other lanes. And based on Tis work was supported by the National Natural Science Markov theory, the deduction in three dimensions is Foundation of China (52272349 and U21B2090). expressed simultaneously in a single model. References 5. Conclusions [1] G. N. Xiao, Q. W. Lu, and A. N. Ni, “Exploring the infuence of COVID-19 on residents’ choice behavior of public trans- Tis paper proposes a trafc accident detection method for portation,” Journal of Advanced Transportation, vol. 106, connected and automated transport systems by conducting a grid-based parameter extracting and SVC-based trafc [2] C. Dong, C. Shao, H. Huang, X. Chen, and N. N. Sze, state classifcation. 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Yang, Research on Driving Safety Distance and Rear-End Collision Warning of Urban Roads, M.S. Nanjing University of Information Science and Technology, Nanjing, China, 2018. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Advanced Transportation Hindawi Publishing Corporation

Accident Detection and Flow Prediction for Connected and Automated Transport Systems

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10.1155/2023/5041509
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Hindawi Journal of Advanced Transportation Volume 2023, Article ID 5041509, 9 pages https://doi.org/10.1155/2023/5041509 Research Article Accident Detection and Flow Prediction for Connected and Automated Transport Systems 1 2 3 3 3 Yi Zhang , Fang Liu , Sheng Yue , Yuxuan Li , and Qianwei Dong Zhejiang Gaoxin Technology Company Limited, Hangzhou 310002, China Liaoning Provincial Transportation Planning and Design Institute Company Limited, Shenyang 110111, China College of Transportation, Jilin University, Changchun 130012, China Correspondence should be addressed to Qianwei Dong; dongqw21@mails.jlu.edu.cn Received 2 February 2023; Revised 26 February 2023; Accepted 5 April 2023; Published 17 April 2023 Academic Editor: Wenxiang Li Copyright © 2023 Yi Zhang et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Efective accident detection and trafc fow forecasting are of great importance for quick respond, impact elimination and intelligent control of the trafc fow consisting of autonomous vehicles. Tis paper proposes a trafc accident detection method for connected and automated transport systems by conducting a grid-based parameter extracting and SVC-based trafc state classifcation. Allowing for the dynamic spread of trafc fow over time, from upstream to downstream and from accident lanes to other lanes, a spatiotemporal Markov model is established to predict the evolution of trafc fow after accident by introducing the grid as state detection unit and ftting the spatiotemporal evolution with the parameter space mean speed to match the need of both detection accuracy and monitoring scope. Compared with actual accident data, the validation results indicate that the proposed methods present a good performance in accident detection with the accident detection rate as 87.72% and a higher precision rate than both SVM (support vector machine) and ANN (artifcial neural network) models in trafc fow prediction. With the active trafc accident identifcation and dynamic trafc fow prediction, it is benefcial to shorten detection time, reduce possible impacts of trafc accidents and carbon emissions from congestion. Te methods can be implied to trafc state recognition and trafc fow prediction, which is one of the signifcant sections of connected and automated transport systems, and serve as references for accident handling and urban trafc management. In recent years, the rapid development of automatic 1. Introduction driving technology, intelligent network technology and With the rapid increment of motor vehicles, congestion and satellite positioning technology, etc., enriches the sources of secondary accidents caused by slow accident response seriously data acquisition. Integration of these multisource big-data afect urban trafc safety and efciency and have become ofers new data-driven ways to obtain real-time location a social problem, which attracts much attention [1]. Efective information of autonomous vehicles and trafc motion trafc condition monitoring is vital to decrease the adverse characteristics. In this case, the methods for accident de- impact of accidents, as the faster an accident is detected, the tection and management should be improved from aspects more quickly managers can respond, thereby shortening of global state diagnosis and postaccident trafc fow handling time, relieving trafc pressure, and lessening the prediction. occurrence probability of massive congestion and secondary However, most of the previous studies focus on local accidents [2]. Terefore, trafc condition monitoring and state monitoring based on roadside devices and trafc fow trafc fow prediction have become essential parts of urban prediction with macroscopic parameters [3–7]. Except for trafc management, which is conducive to improving trafc the accidents happen at the place with monitoring devices efciency, ensuring trafc safety, and reducing energy con- which can be informed, most accidents occurring at the sumption and carbon emissions of transportation system. place without any detection device still remains insensitive. 2 Journal of Advanced Transportation tracking, how to conduct an accurate and large-scale de- In order to make a quick accident response, the real-time abnormal state monitoring of wide range in the road net- tection with the reduction of algorithm complexity has become a problem that cannot be ignored. work should be noted enough. Besides, the trafc fow prediction after an accident is also vital for efcient accident After a trafc accident occurs, it is necessary to predict its disposing and trafc guidance. Terefore, to reduce negative impact and take emergency management measures to clear impact of trafc accidents, it is necessary to investigate the up the accident and reduce losses. Some studies used trafc methods for timely and accurate trafc state identifcation, wave models and fuid mechanics models to predict the accident detection, and postaccident impact prediction in impact of trafc accidents, while most of the others esti- autonomous transport systems. mated the impact degree by using neural network [12], decision tree [13], and other machine learning methods [14]. According to the data types used, the research in this feld can be divided into two aspects. One is accident de- Among them, Markov is one of the most popular approaches to predict trafc condition. For example, Yao et al. [15] tection by using macroscopic trafc fow parameters, such as trafc volume, speed, density, and occupancy, and the other divided a day into multiperiods and predicted trafc in each period by using Markov chain. Li et al. [16] used a Grey- is utilizing the videos taken by on-road cameras to learn accident features concerning collision image and driving Markov model to predict highway trafc variation based on trajectory, etc. historical data and obtained an acceptable accuracy and With respect to the macro trafc parameters-based re- reliability. Zhao et al. [17] combined Bayesian information search, data collected by sensors such as loop sensors are criterion and HMM (hidden Markov model) to predict used mostly in obtaining historical trafc parameters. Te trafc. Te results indicate that the method yields a better methods employed mainly include state recognition [4], performance than SVM and LSTM-RNN (long short-term memory-recurrent neural network). Although previous statistics [5], and machine learning [6]. For example, Ki et al. [4] conducted an ANN (artifcial neural network)-based studies indicated that Markov method performs well in short-term trafc prediction, they only focused on the accident detection by using trafc parameters exacted from loop sensors on the freeway in South Korea. Fang et al. [6] postaccident evolution of trafc condition over time; few involved the dynamic spatial spread of trafc fow. Actually, determined trafc accidents by training deep-loop neural network involving the parameters of trafc fow, speed, and the movement process of trafc fow is naturally from up- occupancy of downstream of urban expressway. As most of stream to downstream and from accident lanes to other the parameters used in this type of research are extracted lanes. It is necessary to deduce the propagation of trafc fow from cross-sectional trafc fow data, it is limited by partially from the view of both time and space dimension in trafc data missing and low data quality. In order to avoid this fow prediction. problem, some scholars combined the cross-sectional fow Considering the limited number of sensors and moni- toring range of video detection, this paper aims at de- data with video tracking data to improve the accuracy of accident detection and position. For example, Yang and Wu veloping a lane-level detection method based on big data resources, which is intended to use GPS data of autonomous [7] constructed a BP neural network for preliminary acci- dent recognition by using trafc parameters obtain from vehicles to obtain road-level trafc fow parameters, so as to optimized distribution of loop sensors, and established the detect accidents. As grid-based lane level analysis is proved Camshift algorithm for vehicle tracking to make a fnal to be helpful for detection accuracy improvement [11, 18], determination. However, the detection range of these studies we divide lanes into grids and express the trafc state of each is at the regional and road level, with a lack of lane-level state grid with macro trafc fow parameters, considering both monitoring and accident identifcation [8]. In fact, the oc- monitoring granularity and computational complexity. currence and subsequent impact of accidents on trafc fow With a machine learning process, the trafc state is then are mostly at lane level. On the other hand, the image combined with historical data to distinguish accidents from other events, such as regular congestion. It is worth noting feature-based accident detection and positioning mainly rely on deep learning of the abnormal characteristics of the trafc that the use of gridded roads can make the detection of trafc accidents refned to the lane level. Tereby, it can not only accidents, such as the vehicle collision features [9] and the abnormal vehicle trajectories in video images [10]. For ex- realize global accident detection but also accurately locate ample, Zou et al. [9] proposed a detection method based on trafc accidents, and efectively refect the variations in the imagine signal processing and hidden Markov classifying trafc conditions before and after the trafc accident. to detect the trafc incidents at signal intersections. Ren et al. Heeding the limitations of previous studies in trafc pre- [11] divided the highway video images into a cluster of cells diction, a spatiotemporal trafc fow prediction model will and used fuzzy-identifcation to determine the state of cells be constructed based on Markov theory, which allows for the dynamic spread of trafc over both spatial and temporal and then constructed an SVM (support vector machine) classifer to position and detect the trafc accidents. Al- dimensions. In conclusion, this paper will propose methods to monitor the trafc status of wide-range road network though this type of studies is proved to have a good accuracy performance, there is a limitation that it will be constrained based on real-time vehicle location information. Ten, the negative postaccident efect will be predicted based on the by the installation position and number of on-road cameras. Moreover, the popularization of this method also faces the evolution of trafc state after accidents. Te results will be problem of computing resources. With the promotion of helpful to improve the range and real-time of accident demand for performance of detection and trajectory detection and the accuracy of trafc prediction, thus Journal of Advanced Transportation 3 contributing to rapid accident responses, which is conducive result of the density of queued vehicles under diferent trafc to enhancing trafc efciency, ensuring trafc safety, re- conditions, the length of the unit L is determined to be the grid ducing energy consumption and carbon emissions of sum of the body length of fve vehicles and the minimum transportation system, and the incidence of trafc conges- safety car-following distance d in free fow, which in the min tion and even secondary accidents. urban road condition is 22.8 m [19], while in the highway Te remainder of this paper is organized as follows: In condition is 127.2 m [20]. Considering that the vehicle Section 2, we present trafc accident diagnosis method. length is generally less than 5.0 m, the length of the state Section 3 proposes a grid-based spatiotemporal deduction detection unit L for urban road and the highway con- grid model for postaccident fow prediction. Section 4 simulates ditions is set to be 139.0 m and 661.0 m, respectively. Te and verifes the efectiveness of the methods. Tis paper is adjacent interval dg denotes the distance between two ad- concluded with Section 5, in which we summarize our jacent grids, which is calculated by the distance of 1 s at the fndings and discuss our study limitations and directions for maximum allowable speed in corresponding condition. future research. Ten, dg under the urban road and highway condition is calculated to be 10.0 m and 33.3 m, respectively. In general, trafc state is time-varying, and the number of vehicles in the 2. Traffic Accident Detection Model grid varies with the trafc state, as shown in Figure 1. 2.1. Defnition of State Detection Unit. Although the image Terefore, trafc fow indicators calculated by grids will feature-based methods are proved to have relatively high objectively refect real-time trafc state changes. accuracy in accident detection according to existing studies, they are limited by the fnite location and sparse distribution 2.2. Expression of Trafc State. In order to transfer the con- density of video detectors, as they identifed the occurrence tinuous trafc fow on a lane into discrete state detection units, and location of trafc accidents using video images obtained we need to select an appropriate trafc state indicator to by on-road devices. Te limitation of detection range and represent the real-time trafc state of a grid and its changes computational resources makes these methods unable to over time and space. As shown in HCM [21], the parameter of carry out large-scale and high-precision accident detection. average speed of trafc fow, which consists of time mean speed However, the Internet of vehicles (IoV) and big data en- and space mean speed, is often used in a trafc state classif- vironment makes it possible to obtain large-scale trafc cation and real-time trafc state estimation. Taking account status information based on multisources vehicular that the defned length of a grid is a fxed value, using the space positioning data. mean speed will be more convenient to express and calculate Tis section will establish dynamic models for accident the trafc state under this circumstance. Ten, we defne v as detection and postaccident impact prediction, of which, the the space mean speed of a grid, which is calculated as follows: frst step is to propose a state detection unit to express the trafc condition. After a trafc accident occurs, the trafc grid v � , (1) state will get worse with the gathering of vehicles and the n (1/n)􏽐 t i�1 trafc congestion may come into being and spread from the downstream to the upstream on the accident lanes, while where t denotes the time that it takes for vehicle i to go also spreading from the accident lanes to adjacent lanes and through the grid during the detection interval. n is the total even the entire road section. Terefore, a lane-level detection number of vehicles which pass the grid during the sampling unit, named as grid, is proposed. Except for meeting the interval. Considering that the normal accident sampling granularity requirements of trafc propagation analyzing, it interval is 5 min, and the equipment’s acquisition time is 1 s, is well suited to be employed in examining the trafc state taking into account real-time and computational con- variation between micro vehicle and macro trafc fow, and sumption, the sampling interval is selected as 10 s. optimizing calculation speed on the basis of ensuring de- According to previous research [22, 23], trafc state is tection precision. divided into the following four levels: unblocked, lightly Although Ren et al. [11] and Wang et al. [18] also utilized congested, congested, and severely congested. Te corre- grid in trafc fow analysis, the size of grid is set to be small sponding space mean speed ranges on the main urban roads and lack of enough theoretical basis. For example, in the are, respectively, higher than 30 km/h, 20 km/h-30 km/h, analysis based on multiagent method, the size of grid is 10 km/h-20 km/h, and less than 10 km/h. Tus, when the defned as vehicle level, which causes that the state of a grid space mean speed of a grid is less than 20 km/h, its trafc directly refects that of the corresponding vehicle. Tis state will be determined as congested state. We then use the microscopic analysis results in a large amount of overall grid to sample, record, and store data including space mean calculation and is inconvenient to macroscopic trafc fow speed, trafc state, and state duration at a sampling interval analysis. In order to decrease defective impact, we can of 10 s. Te historical data stored by the grid will be used as consider dividing larger grids and express the state of each the data set for trafc accident detection. grid with meso parameters. At the same time, considering the analysis accuracy, the space between adjacent grids can be set to be relatively small. As shown in Figure 1, we divide 2.3. Detection of Trafc Accident. Te reasons for trafc a lane into a number of overlapping grids with a unit length congestion can be divided into the following two main types: of L and adjacent interval of dg. According to the analysis normal congestion and abnormal congestion. Normal grid 4 Journal of Advanced Transportation L dg grid State detection unit Driving Direction Figure 1: Illustration of the state detection unit. congestion refers to the congestion caused by the inability of where the frst term 1/2‖ω‖ is the regularized term, which is road capacity to meet the trafc demand, which often has used to adjust the function fatness, while the second term regular characteristics. For example, regular trafc conges- R [f] is the loss function which measures the empirical emp tion usually occurs in the morning and evening rush hour. error. C is a regularization parameter that determines the Abnormal congestion refers to the congestion caused by trade-of between structural error and empirical error. sudden events, which is unpredictable and accidental. In Considering that a generalization error cannot be obtained order to detect trafc accident, the mission of this section is by simply minimizing the training error, we then allow bits to distinguish abnormal congestion from the normal one of examples assigned wrongly and introduce soft margin to according to the characteristic of diferent trafc states. respite the overftting dilemma as following: Based on the real-time and historical data of space mean |y − f(x)| � max 􏼈0, |y − f(x)| − ε􏼉, (4) speed for each grid, we employ SVC (support vector clas- sifcation) [3] to detect trafc accidents according to the which is defned as the minimal distance of a sample to the characteristics of spatiotemporal distribution and its dy- decision surface. Te loss is the diference between the namic change. SVC is an application of SVM in the aspect of predicted value and the radius ε of the soft margin. It will be data analysis and pattern recognizing, which is widely used 0 if the predicted value is within the region of margin. Both C in accident detection by previous studies [24]. Te data we and ε are user-determined parameters. Te positive slack use are extracted from a sample library, which is built to variables ξ is introduced to indicate the degree of classif- store the historical data for each grid, with the information cation error. Terefore, equation (3) is transferred to of space mean speed, state duration, weekly simultaneous data and monthly simultaneous data, etc. According to the 2 min J � ‖ω‖ + C 􏽘 ξ􏼁 , distinguished characteristics of normal congestion and ab- 2 i�1 normal one caused by trafc accidents, we assign the sample (5) data to positive and negative classes correspondingly. Ac- ⎧ ⎪ y ω∙ϕ x􏼁 + b ≥ ε − ξ 􏼁, i i i cordingly, the input-output training data pairs in training s.t. samples are labeled as D � 􏼈(x , y ), . . . , (x , y ), . . . , 0 ≤ ξ . 1 1 i i (x , y )}, where x ∈ X⊆R and y is the label of con- N N i i t t Te constrained optimization problem is then converted gestion type with yϵ{−1, 1}, in which a sample is assigned to into a convex quadratic optimization problem and solved class 1 if a congestion is normal congestion and to the class with the primal Lagrangian from the following equation: −1 otherwise. N is the number of training samples. Ten, we estimate a function as follows: m m L � ‖ω‖ + C 􏽘 ξ − 􏽘 η ξ , 􏼁 􏼁 i i i f(x) � ω∙ϕ(x) + b x ∈ R , (2) 2 i�1 i�1 (6) where ϕ(x) represents the high-dimensional feature spaces m that are nonlinearly mapped from the input space x, ω − 􏽘 α ε + ξ −y + ω∙Φ x􏼁 + b􏼁, i i i i i�1 denotes the parameter vector, and b is the threshold. Te best estimation function that one can obtain can minimize where L is the Lagrangian function and η and α are i i the expected risk. However, the small sample size might Lagrange multipliers. Hence, equation (6) satisfes the occur overftting dilemma. One way to avoid the problem is positive constraints. to restrict the complexity of the estimation function. One introduces the regularization term as a solution. So, the 0≤ η , α . (7) i i SVC’s linear algorithm is to solve the following regularized risk function: Te above problem is thereby converted into a dual problem, in which the Lagrangian multipliers η , a , and a i i j min J � ‖ω‖ + CR [f] , (3) needed to be optimized. Tis dual problem contains emp 2 Journal of Advanced Transportation 5 ∗ ∗ a quadratic objective function of α and a with the linear Ten, we get the optimal solutions ω and b of ω and b, i j constraint. respectively, m m m ∗ ∗ max J � 􏽘 a − 􏽘 a a y y ϕ x , ϕ x , ω � 􏽘 a y ϕ x , 􏼐 􏼁 􏼐 􏼑􏼑 􏼁 i i j i j i j i i i i�1 i,j�1 i�1 (15) ∗ ∗ 0≤ α ≤ C (8) b � y − 􏽘 a y 􏼐ϕ x􏼁 , ϕ􏼐x 􏼑􏼑, ⎧ ⎪ i i i i i j ⎨ i�1 s.t. , i � 1, 2, . . . , m. ⎪ and separation hyperplane. 􏽘 a y � 0 ⎩ i i i�1 ∗ ∗ . (16) ω ϕ x􏼁 + b � 0 Let Eventually, we construct decision function to classify the m m following equation: min J � 􏽘 a a y y 􏼐ϕ x􏼁 , ϕ􏼐x 􏼑􏼑 − 􏽘 a , (9) i j i j i j i ∗ ∗ i,j�1 i�1 f(x) � sign ω ϕ x􏼁 + b 􏼁. (17) 0 ≤ α ⎧ ⎪ 3. Prediction of Postaccident Traffic Flow s.t. , i � 1, 2, . . . , m. (10) 􏽘 a y � 0 ⎩ i i i�1 3.1. Spatial Correlation Test. Trough the analysis of existing research and related accident data, it is found that the Introducing kernel function κ(x , x ) into equation (9), i j congestion caused by trafc accidents has a trend of we get spreading from downstream to upstream and from accident m m lanes to other lanes. We construct a spatiotemporal Markov min J � 􏽘 a a y y κ􏼐x , x 􏼑 − 􏽘 a , i j i j i j i model to predict the impact of accidents based this trend. i,j�1 i�1 Before modeling, we investigate the spatial characteristics of accident propagation by calculating the Moran’ I index to (11) 0 ≤ α ⎧ ⎪ i ⎪ conduct a spatial correlation test. s.t. , i � 1, 2, . . . , m , ⎪ N N 􏽘 a y � 0 w v − v v − v 􏽐 􏽐 􏼁 􏼁 ⎩ i i N i�1 j�1 ij i i I � × , i�1 S 􏽐 v − v 0 i i�1 where κ(x , x ) is the kernel function which is equal to the (18) i j N N inner product of two vectors, i.e., x and x , in the feature i j S � 􏽘 􏽘 w , 0 ij space ϕ(x ) and ϕ(x ). Tat is, i j i�1 j�1 κ x , x � ϕ x ∙ ϕ x . (12) 􏼐 􏼑 􏼁 􏼐 􏼑 i j i j where v is the space mean speed of the i-th grid and v is the mean of space mean speed of all the grids in the area where To simplify the calculating complexity, some common the accident occurred. N denotes the number of grids in the kernel functions, such as linear kernel, polynomial kernel, study segment. Te spatial weight matrix of the grids W and radial-basis function (RBF) kernel, are introduced to the ij refects the spatial relation of the grids. computation of ϕ(x). Choosing diferent kernel functions Te form of the rules determining W is that w � 1 if will form diferent learning machines. Considering that the ij ij grid i and j are adjacent in space, otherwise w � 0. Te data set is nonlinear, the RBF kernel function, which is ij value of Moran’ I index is between −1 and 1. Te value is a nonlinearly kernel function, is chosen in this study. positive indicates that the space mean speed of diferent � � � �2 � � � � x − x grids is positively correlated in spatial distribution, while � i j� ⎜ ⎟ ⎛ ⎜ ⎞ ⎟ ⎝ ⎠ (13) κ􏼐x , x 􏼑 � exp − , i j negatively correlated in space when negative, and 0 indicates 2σ that the space mean speed is independent of each other in spatial distribution. where σ is a parameter that determines the area of infuence Te statistical signifcance Z is calculated as follows: this support vector has over the data space. To get the optimal solution, equation (9) needs to meet 1 − E(I) KKT (Karush-Kuhn-Tucker) conditions. 􏽰������ Z � , Var(I) 0≤ a , 0 ≤ μ, ⎧ i 1 (19) ⎨ y f x􏼁 − ε + ξ ≥ 0, i i i E(I) � , (14) 1 − n a y f x − ε + ξ � 0, 􏼁 􏼁 i i i i 2 2 Var(I) � E􏼐I 􏼑 − E(I) , ξ ≥ 0, μ ξ � 0. i i i 6 Journal of Advanced Transportation where E(I) is the mean of Moran’ I indexes, and Var(I) is a grid is infuenced by its side grid. Meanwhile, the the variance of Moran’ I indexes. Based on the post- historical data for a grid also associates with its cur- accident trafc fow data, we obtain that Moran’ rent trafc fow state because of periodic variation of I � 0.0362910 and Z � 2.2587. When the value of I is trafc fow [16]. Terefore, we examine the evolution of positive, it denotes that there is spatial correlation be- state in each grid considering the impact of its upstream tween the space mean speed of diferent grids. And if grid, side grid, and adjacent previous period, as shown in 1.96 ≤ Z ≤ 2.58, it means that 95% of spatial features that Figure 2. are sure to reject statistics are randomly distributed as- sumptions. Tey confrm that there is a signifcant spatial 3.2.1. Infuence of Downstream Grid. Given the recurrence correlation between the space mean speed of diferent relation between upstream grids and downstream ones, we grids in the area where the accident occurred. Terefore, i⟶i+1 introduce the transition probability P to express the we can predict the postaccident trafc fow according to infuence of the downstream grid i to the upstream one i + 1 the characteristics of the spatial evolution process of the at time t, which is expressed as follows: space mean speed value. i+1,j i⟶i+1 P � . (21) i,j 3.2. Model Construction. Te prediction of trafc fow variation under accident condition is a crucial means for accident management, since a real-time overlook at the 3.2.2. Infuence of Side Grid. In addition to the congestion variation of trafc state in the accident area contributes for propagation within the accident lanes, there is also impact of quick accident disposal and congestion evacuation. Re- j⟶j+1 the grids in the accident lanes to its side grid. We use P ferring to [25], Markov model has a high accuracy in short- to denote the impact of the side grid. Formally, it is time prediction for trafc condition based on the historical and real-time data. Terefore, this paper will establish i,j+1 j⟶j+1 P � . (22) a spatiotemporal Markov model to deduce the trafc state i,j after the trafc accident happens. Markov process is often used to describe the state of 3.2.3. Infuence of Adjacent Previous Period. Likewise, a system and the transition between diferent states. And Markov chain refers to the Markov process whose time considering the infuence of a grid’s state from time t-1 to t⟶t+1 time t, the transition probability P is defned and and state parameters are discrete. It satisfes the following two assumptions: (1) the nonafterefect property of the calculated as follows: t+1 Markov model, which refers to that the state U of the t+1 i,j t⟶t+1 system at time t + 1 is relevant to the state at time t, re- P � . (23) gardless of the state before time t. Tis means that the i,j t+1 t value of U is only related to the value of U , but not t− 1 t− 2 Considering all the three factors, the compound tran- related to the value of U , U , . . .; (2) the state tran- sition probability is sition from time t to time t + 1 is independent with the state at time t. α β c t i⟶i+1 j⟶j+1 t⟶t+1 P � 􏼐P 􏼑 + 􏼐P 􏼑 + 􏼐P 􏼑 . i,j Tus, we denote a matrix composed by space mean speed (24) of q adjacent units at p adjacent lanes as a system. Te state of s.t. α + β + c � 1, the system at time t, refers to U , is expressed as follows: where α, β, and c are the weight coefcients. Substituting t t t v · · · v · · · v q,p i,p 1,p equations (21)–(23) into (24), we get ⎜ ⎞ ⎟ ⎛ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⋮ ⋮ ⋮ ⎟ ⎜ ⎟ ⎜ ⎟ ⎟ α β c ⎜ ⎟ ⎜ ⎟ t t t+1 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ v v v ⎜ ⎟ ⎜ ⎟ t ⎜ t t t ⎟ i+1,j i,j+1 i,j ⎜ ⎟ t ⎜ ⎟ ⎜ ⎟ ⎛ ⎝ ⎞ ⎠ ⎛ ⎝ ⎞ ⎠ ⎛ ⎝ ⎞ ⎠ ⎜ ⎟ . (25) U � ⎜ v · · · v · · · v ⎟ , (20) ⎜ ⎟ P � + + ⎜ ⎟ ⎜ q,j i,j 1,j ⎟ i,j ⎜ ⎟ t t,h t ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ v v ⎜ ⎟ ⎜ ⎟ v ⎜ ⎟ i,j i,j ⎜ ⎟ i,j ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⋮ ⋮ ⋮ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ t t t Ten, the transition probability matrix at time t is v · · · v · · · v q,1 i,1 1,1 t t t P · · · P · · · P n,m i,m 1,m where v denotes the space mean speed of the i-th grid in the ⎜ ⎟ i,j ⎛ ⎜ ⎞ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⋮ ⋮ ⋮ ⎜ ⎟ j-th lane at time t. ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ t ⎜ t t t ⎟ By calculating the spatial correlation of space mean ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ P � ⎜ P · · · P · · · P ⎟ , (26) ⎜ ⎟ ⎜ ⎟ ⎜ n,j i,j 1,j ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ speed of trafc state in diferent grids, we fnd that the ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⋮ ⋮ ⋮ ⎟ ⎜ ⎟ ⎜ ⎟ postaccident propagation of trafc fow has certain spatial ⎝ ⎠ t t t characteristics. Tat is, the state of trafc fow is spreading P · · · P · · · P n,1 i,1 1,1 from upstream to downstream, which means that the state of a grid is directly infuenced by its upstream grid. P denotes the transition probability of the i-th state de- i,j Besides, the congestion state of accident-impacted lanes tection unit in the j-th lane at time t. Ten, the state matrix at will spread to other lanes, which means that the state of time t is Journal of Advanced Transportation 7 t t t+1 t+1 v v v v 1,2 2,2 1,2 2,2 t→t+1 j→j+1 j→j+1 p p t t t+1 t+1 v v v v 1,1 2,1 1,1 2,1 i→i+1 i→i+1 p p t–moment t+1–moment Figure 2: Te conduction process of the state between diferent grids. Driving Direction 1 2 4 8 10 11 12 13 3 5 6 7 9 14 15 16 17 18 19 L=384 m the underpass section of Qinggang Overpass of the Northern Expressway in Changchun The Grid 1 The Grid 8 where the traffic accident occurred Figure 3: Te case study section and unit partition. t t− 1 t Here we present a case by taking the accident occurred at (27) U � U ∙P . 15:25:35 on Aug. 16th, 2019, as an example. First, we cal- culate the space mean speed for each grid of the target According to the state change of each grid and of the spatial distribution, the duration and infuence scope of section once per 10 seconds during the period of 15:22: 49−16:35:59. Te results indicate that all the lanes were congestion caused by trafc accident can be predicted. congested after 15:25:39. Notably, there are two zero-speed vehicles at the 8-th grid on the 1-st lane, which is shown in 3.3. Model Calibration. We obtained the trafc accident data Figure 3, during the period of 15:25:39−16:07:19. Te state of and the corresponding trafc fow data of the underpass section this grid is illustrated in Figure 4. in Qinggang Overpass of the northern expressway in As shown in Figure 4, the state variation of the grid goes Changchun in 2019 from trafc management department, through four states, i.e., (1) uncongested from about 15:22:49 to which has GPS and mobile signaling big data resources. Tere 15:25:39; (2) extremely congested from about 15:25:39 to 16:07: are totally 502 valid samples in which 164 in the positive class 19, as the space average speed suddenly dropped to 0, and the and the others in the negative class according to the method in lane began to be congested; (3) congestion evacuation from Section 2.3. Ten, 400 samples including 131 positive samples about 16:07:19 to 16:08:59, during which period the trafc are selected and composed the training set for model training accident was handled; and (4) free fow state after 16:09:29. and parameter calibrating, and the remaining 102 samples are With the proposed SVC model, the accidents were de- taken as testing set for validating performance. Based on the termined, and the performance comparing to the testing 400 training samples, the parameter of α, β, and c in the data is shown in Table 1. spatiotemporal Markov model is estimated by utilizing the According to the testing results, the precision is calcu- MLE (maximum likelihood estimation) method, with the value lated to be 77.78%, the recall is 84.8%, and the accuracy is being 0.39, 0.47 and 0.14, respectively. 87.72%. Te results prove that the accident detection model can recognize trafc accidents with a low error rate. It re- 4. Simulation and Model Validation fects that the accident detection model can identify ab- normal congestion caused by a trafc accident efciently and 4.1. Trafc Accident Detection. Based on the 102 testing then send a notifcation to trafc management department samples mentioned in Section 3.3, the trafc accident de- timely and precisely. tection model proposed in Section 2.3 is validated. As shown in Figure 3, the road section is divided into grids. Since the total length of the target section is 384 m, we draw 19 grids 4.2. Postaccident State Prediction. Based on the testing data, for each lane beginning from the downstream stop line to we predict the trafc state after the 102 accidents in the upstream. testing dataset by using the spatiotemporal Markov model 8 Journal of Advanced Transportation systems, this paper predicts the trafc state from lane level with detection unit as grid and detection parameter as space mean speed. After determining the trafc state of each grid, we formulate a trafc state matrix to integrate the states of all the grids both in lateral and longitudinal direction. Con- 40 sidering the impacts of upstream grid, side grid and time t − 1, a Markov model is presented, in the transition state matrix of which, time and space evolution of trafc state are simultaneously deduced. Te results indicate that the methods improve the accuracy on accident detection and trafc fow prediction corresponding to 2.6% and 9.2% lower 0 16 50 100 150 200 266 291 mean absolute percentage error compared with SVM and 15:22:49 15:25:39 16:07:19 16:11:29 time step ANN model, respectively. Te active detection and prediction method developed Figure 4: Te state variation of a grid in case study. matches the need of both spatial accuracy and computa- tional efciency to identify trafc accidents and predict the Table 1: Confusion matrix of classifcation results. postaccident trafc fow with calculated precision as 77.78%, Prediction recall as 84.8%, and accuracy as 87.72%. It also shortens the Ground-truth detection time and reduces possible impacts of accidents and Positive Negative carbon emissions from congestion, which is helpful to Positive 28 5 monitor the accident situation, identify abnormal trafc Negative 8 71 condition and ensure trafc safety. Moreover, this paper can serve as a reference for accident handling, trafc control and Table 2: Algorithms comparison results. management in autonomous transport systems. It should be mentioned that there still existing some Indicator ANN SVM Spatiotemporal Markov limitations in this paper. Even though we have verifed the MAE 16.7 11.3 9.4 spatial correlation of congestion caused by an accident, we RMSE 18.2 15.5 16.4 will involve the quantitative spatiotemporal spread mech- MAPE (%) 26.3 19.7 17.1 anism of postaccident in future research. In addition, we can also conduct a more detailed calibration for the parameters in rectangular grid analysis given diferent trafc status. proposed above. Taken space average speed as dependent variable and based on the historical data, we also develop an SVM and an ANN [26], respectively, for evaluation of the Data Availability prediction performance with parameter of MAE (mean abso- Te data supporting the study are provided by trafc lute error), RMSE (root mean squared error) and MAPE (mean absolute percentage error). Te results are shown in Table 2. management department. Comparing the prediction efects of the three algorithms, we fnd that the prediction results provided the spatio- Conflicts of Interest temporal Markov model is most close to the real data. Te reason may be that the spatiotemporal Markov model Te authors declare that they have no conficts of interest. considers not only the evolution of trafc state in time dimension, but also that in spatial dimension which includes Acknowledgments trafc fow spreading both from upstream to downstream and from accident lanes to other lanes. 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Journal of Advanced Transportation – Hindawi Publishing Corporation

Published: Apr 17, 2023

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