2010 WASE International Conference on Information Engineering Bayesian Networ-Based Road Traffic Accident Causality Analysis Xu Hongguo e-mail: xhg335@163.com Zong Fang (Contact Author) Abstract Traffic accident causality analysis is an important aspect in the traffic safety research field. Based on data survey and statistical analysis, a Bayesian networ for traffic accident causality analysis was developed. The structure and parameter of the Bayesian networ was learnt with K2 algorithm and Bayesian parameter estimation respectively. With the Junction Tree algorithm, the effect of road cross-section on the accident casualties was inferred. The results show that the Bayesian networ can express the complicated relationship between the traffic accident and the causes, as well the correlations among the factors of causes. The results of analysis provide the valuable information on how to reveal the traffic accident causality mechanisms and how to tae effective measures to improve the traffic safety situations. Keywords-traffic accident; bayesian networ; K2 algorithm; accident causality Ⅰ. INTRODUCTION With the development of economy and society in China, the car ownership and the road traffic accidents have increased greatly. In order to reduce the traffic accidents, it is necessary to analyze traffic accident causality in the theory. The activity can reveal the correlation between the traffic accident and the elements of traffic system, and provide the valuable information for road construction, traffic safety control, vehicle safety design, and so on. The causes of traffic accident include the subjective factors and objective one. The subjective one is human factors, composed of motor driver, non-motor driver, Zhang Huiyong e-mail: jluzhy@yahoo.com.cn e-mail: zongfang@jlu.edu.cn passenger and pedestrian. The objective one consists of vehicle, road environment and environment: The vehicle factors, for example vehicle performance; The road elements include types, alignment, intersection, pavement conditions, etc.; The environment factors consist of natural conditions, traffic volume, etc. Road traffic system is a complex dynamic coupling one, composed of human, vehicle, road and environment. Road accident is caused by disturbance of these elements. As a result, it has the characteristic of randomness and uncertainty. This paper will give the theory of traffic accident causality with Bayesian networ. It is organized as follows: In section 2, the previous researches are reviewed. In section 3, the Bayesian model is introduced. This is followed by developing a Bayesian networ for traffic accident causality analysis in section 4. In section 5, the correlation between the traffic accident and the causes is analyzed. Summary and conclusions are made in section 6. Ⅱ. REVIEW A. Traffic Accident Causality Theory The traditional accident causality theories include Accident Proneness theory, Accident Causality Sequence theory, Energy Transfer theory, Surry's Accident model, Orbit Intersecting theory, Haddon model, etc. Based on these, many researchers have given the traffic accident causality theory in recent years. The main methods include Principle Component Analysis, Layer-Interrelating Analysis method, Grey Forecasting 978-0-7695-4080-1/10 $26.00 2010 IEEE DOI 10.1109/ICIE.2010.276 413
Model, BP Neural Networ, Fuzzy Clustering Analysis and so on. For instance, Chong Miao and Abraham Ajith (2004, 2005) studied the methods of traffic accident causality and traffic accident data mining with machine learning paradigm [1,2]. Zhang Haiyi et al. (2001) designed a traffic accident analysis system based on association rules [3]. Han Wenbin (2007) studied on the relationship between road alignment and traffic accidents with Principle Component analysis and Multivariate Linear Regression method [4]. Sha aimin (2006) analyzed the accident causes by the accident data,and developed a Grey forecasting model predicting traffic accident [5]. Yuan Chunmiao et al. (2005) analyzed the causes of accidents based on BP Neural Networ [6]. Wei Qingyao et al. (2005) analyzed road factors in traffic accident using Layer-Interrelating Analysis method [7]. Yu hongqi (2005) analyzed traffic accident causality factors using the Clustering Method in data mining and the technique of the Open Database Connectivity (ODBC) [8]. B. Bayesian Method In terms of traffic safety, the Bayesian method is mainly applied to traffic accident duration prediction. Qin Xiaohu (2005) developed a traffic accident prediction model based on Bayesian networ [9]. Wang Fazhi(2006) created a Bayesian networ assessing traffic accidental event situation and analyzed the effect of several factors, such as whether, traffic volume, vehicle type, etc., on the traffic accident duration [10]. Ji Yang Beibei (2008) studied traffic accident duration prediction method with Bayesian method-based decision tree classification algorithm [11]. Above reviews show that most of the researches are unitary analysis. This can only reveal the inherent laws of traffic accident on a certain aspect. However, the traffic accident causality is multidimensional and there are correlation and logic relationships among the causality factors. The existing wors are practice-oriented, but without the character of generality. Although some studied the traffic accident causality based on the theory of complex systems, the whole road traffic system are not taen as complex systems. In addition, most of the existing wors are static analysis that ignore the time-variation of the factors. The application of Bayesian networ in the accident duration forecasting indicates that: (1) Comparing with the other methods, Bayesian networ can describe the logic relationships among the variables in the networ. (2) The networ can embody the dynamic coupling mechanism among the variables; (3) Bayesian method provides a way to introduce more information into the model, such as expert suggestions, other studies and empirical distributions. The above merits show that Bayesian networ can solve the problems in the existing researches. Therefore, a Bayesian networ for traffic accident causality analysis will be developed in this study, in order to explore the application of Bayesian method in the field of traffic accident reasons. Ⅲ. METHODOLOTY A. Bayesian Networ A Bayesian networ, belief networ or directed acyclic graphical model is a probabilistic graphical model that represents a set of random variables and their conditional dependencies via a directed acyclic graph (DAG). A Bayesian networ consists of the following elements: (1)A set of variables and a set of directed lins among variables; (2)The variables coupled with the directed lins construct a DAG; (3) Each variable with parents has a conditional probability table. The basis of Bayesian networ is Bayes' formula for conditional probability: H) D H ) H D) = (1) D) H is a hypothesis, and D is the data. H) is the prior probability of H: the probability that H is correct before the data D was seen. D H) is the conditional probability of seeing the data D given that the hypothesis H is true. D H) is called the lielihood. D) is the marginal probability of D. H D) is the posterior probability: the probability that the hypothesis is true, given the data and the previous state of belief about the hypothesis. B. Modeling of Bayesian Networ The modeling of Bayesian networ consists of two steps: structure learning and parameter learning. 414
The purpose of structure learning is to define the directed lins between the nodes in order to form the structure of the Bayesian networ. The main methods of structure learning are Exhaustive search, K2 algorithm, Hill-climbing, etc. The most popular method is K2 algorithm (Cooper and Hersovits, 1992), which is a ind of greedy search algorithm that wors as follows: Initially each node has no parents. It then adds incrementally the parent whose addition most increases the score of the resulting structure. When the addition of no single parent can increase the score, it stops adding parents to the node [12]. The aim of parameter learning is to estimate the posterior distribution of the nodes when the structure of the Bayesian networ and the prior distribution of some nodes are already nown. In many previous researches, the conditional probability tables were defined by the experts. However, there is a big deviation between the estimated results and the actual one. The popular method is to learn the distribution of the variables from the data, which maes the parameter learning more universal. When learning parameter, the prior distribution of the nodes can be defined by experts or by analyzing and estimating. The main methods of parameter learning are maximum lielihood parameter estimation and Bayesian parameter estimation. Ⅳ. CONSTRUCTION STRUCTION OF BAYESIAN NETWORK A. Data Based on traffic accidents data of some main expressways (including Chang-Ping, Chang-Ji, Yan-Tu, Jing-Ha, etc.) in Jilin province during 2003~2006, the training data, consisting of 3019 sample data, are set up. The main data items (shown in TableⅠ) indicate that the data about road condition and the consequence of the accident are in detail. Data type Environment factors Road factors Traffic accident TABLEⅠ. DATA ITEMS OF THE TRAINING DATA Data items Terrain, Weather, Traffic control Road type, Pavement type, Road alignment, Type of intersection and road section, Road cross-section, Road condition Cause of accident, Accident form, Accident type, deaths, serious, light, Property damage No data about driver, passenger and pedestrian, vehicle types, speed, traffic volume, etc. are given, which maes the modeling difficult. B. Structure Learning Using the K2 algorithm and the Full-BNT toolbox of Matlab, the structure of the Bayesian networ is learnt with the training data, as shown in Figure 1. Road cross-section Cause of accident Figure 1. The structure of the Bayesian networ The Bayesian networ is composed of ten nodes and concerned lins. The ten nodes come from the ten variables in Table Ⅱ, and the lins represent the correlations between the nodes. For instance, as shown in the networ, road type has influence on accident form and accident type; accident type affects the number of deaths. TABLE Ⅱ. VARIABLES IN THE BAYESIAN NETWORK Terrain 1.Plains, 2.Hills, 3.Mountains 1.Expressway, 2.Class Ⅰ highway, 3. Class Ⅱ highway, Road type 4.Class Ⅲ highway, 5. Class Ⅳ highway, 6. Sub-standard road, 7.Urban road Road 1.Road divided by lanes and directions, 2.Road divided by cross-section lanes, 3.Road divided by directions, 4.Lane-direction mixed 1.Vehicle breadown, 2.Violation of motor vehicle, Cause of 3.Violation of non-motor vehicle, passenger or pedestrian, accident 4.Unexpected reasons, 5.Others 1. Front collision, 2. Side collision, 3. Rear collision, 4. Scraping in the opposite direction, 5. Scraping in the same Accident form direction, 6. Rolling over, 7. Rolling, 8. Hitting a stationary object, 9. Hitting a stationary vehicle, 10. Falling, 11. Catching fire, 12. Others Accident type 1. Injury, 2. Property damage, 3. Fatal 1. 0 2. 1 3. 2 4. 3 5. than 4 deaths serious 1. 0 2. 1 3. 2 4. than 3 1. 0 2. 1 3. 2 4. than 3 light Property damage (Yuan) Number of deaths Terrain Road type Accident form Accident type serious light Environment factors Road factors Traffic accident Accident casualties Property damage 1. 0 2. 0-1000 3. 1 000-10 000 4. 10 000-100 000 5. No less than 100 000 415
C. Parameter Learning The variables in the Bayesian networ are estimated by the Bayesian parameter estimation method and the Full-BNT toolbox in Matlab. During the process of parameter learning, the prior distributions of all the variables are assumed to be Dirichlet distribution (see reference [12] for the detailed content about the Dirichlet distribution). The variable of accident type will be taen as an example to illustrate the parameter learning process. TABLE Ⅲ. ESTIMATIONS OF THE ACCIDENT TYPE Road type Conditional probability Conditional probability of Training data of injury accident property damage accident Conditional probability Training data Training data Sample size of fatal accident Expressway 0.3362 0.3362 0.4598 0.4598 0.2040 0.2040 1044 Class Ⅰ highway 0.5625 0.5626 0.1195 0.1194 0.3180 0.3180 695 Class Ⅱ highway 0.4848 0.4848 0.1566 0.1565 0.3587 0.3587 1118 Class Ⅲ highway 0.3816 0.3817 0.0309 0.0305 0.5875 0.5878 131 Class Ⅳ highway 0.3333 0.3333 0.1146 0.1111 0.5521 0.5556 9 Sub-standard road 0.8217 0.8333 0.0078 0.0000 0.1705 0.1667 6 Urban road 0.6635 0.6667 0.2013 0.2000 0.1352 0.1333 15 D. Validity Test The validity of the estimations will be tested by two methods: (1) Comparing the forecasts with the training data; (2) Calculating the Hit Ratio of the model. The comparing of the forecasts and the training data are shown in Table Ⅲ. Results show that the maximum absolute error of the forecasts compared with the training data is 0.0116, and the mean absolute error is 0.0018. Because of the sample size of the property damage accidents on sub-standard road is 0, the error in this case is very large, and the relative error is 1. If the data is not taen into account, the maximum relative error of the model is 0.0223, and the mean relative error is 0.0060. The parameter of Hit Ratio is calculated as: Defining P i as the forecasting probability of the accident type i for the piece of data. Defining d = i. If Pi is the max for all the values of i, defining if and only if P i traverses all i. Then S The Hit ratio is: 1, = d = 0, d = i, (2) R h n Si = = 1 (3) n The reference [15] shows that if the Hit Ratio is greater than 80%, the estimation can be considered to be credible. Based on formula (3), the Hit Ratio of the model in accident type forecast is calculated as 100%. The estimations of other variables in the model are tested with the same two methods. The results show high accuracy of the model. Ⅴ. APPLICATION IN THE ACCIDENT CASUALTIES ANALYSIS Based on the Bayesian networ, the conditional probability of any node in the networ can be inferred. The main methods of inference include Junction Tree algorithm, Variable Elimination algorithm, Global Inference methods and so on. The Junction Tree algorithm, which is the basis of all the inference methods, is most widely used. Therefore, the Junction Tree algorithm will be selected. The inferred results of the accident casualties under the influence of the road cross-section are shown in Table Ⅳ, which is taen as an example to illustrate the inferring process. 416
Road crosssection TABLE Ⅳ. THE CONDITIONAL PROBABILITY OF ACCIDENT CASUALTIES UNDER THE INFLUENCE OF ROAD CROSS-SECTION deaths 0 1 2 3 than 4 serious 0 1 2 than 3 light 0 1 2 than 3 lanes and directions 0.769 0.189 0.030 0.009 0.005 0.852 0.123 0.021 0.004 0.634 0.234 0.086 0.046 lanes 0.746 0.207 0.033 0.009 0.005 0.841 0.132 0.022 0.005 0.606 0.251 0.093 0.050 directions 0.647 0.288 0.045 0.013 0.007 0.794 0.170 0.029 0.007 0.493 0.323 0.120 0.065 Lane-directio n mixed 0.624 0.307 0.048 0.014 0.007 0.798 0.166 0.029 0.007 0.506 0.314 0.117 0.064 Assuming the number of deaths, serious and light are all 0, the effect of the road cross-section on the accident casualties is shown in Figure 2. The results show that the better the condition of road cross-section, the greater the lielihood of no accident casualty. 0.9 0.8 0.7 0.6 0.5 0.4 lanes and directions no death no serious injury no light injury lanes directions Lane-direction mixed Figure 2. The effect of the road cross-section on the accident casualties With the same method, the analysis of the other sets of data in Table Ⅳ indicates that the road cross-section is an important factor for accident casualties. When the road cross-section is divided by lanes and directions, the casualties are reduced to a great extent. The casualties increase gradually with the worsening of the road cross-section. It means that the better the condition of road facilities, the lower the casualties. The influence of other factors on the traffic accident can be inferred with the same method. Ⅵ. CONCLUSIONS Based on data survey and statistical analysis, a Bayesian networ for traffic accident causality analysis was given. The structure and parameter of the Bayesian networ is learnt with K2 algorithm and Bayesian parameter estimation method respectively. With the Junction Tree algorithm, the effect of the factor of road cross-section on the accident casualties is inferred. It is an attempt to explore new methods for traffic accident causality analysis. The results of analysis provide the valuable information on how to reveal the traffic accident causality mechanism and how to tae effective measures to improve the traffic safety conditions. The limitations include: (1) Due to the lac of some data, the factors of human, vehicle, speed and traffic volume, etc. are not introduced in the Bayesian networ. This problem results in the incompletion of the Bayesian networ. The required data should be complemented to improve the model in the future. (2) It can be improved in prior distribution definition and Bayesian networ application. ACKNOWLEDGEMENTS The research is funded by National High Technology Research and Development Program (2009AA11Z201). REFERENCES [1] C. Miao, A. Ajith, Traffic accident analysis using machine learning paradigms, Computational Intelligence in Data Mining, 2005, vol. 29, No. 5, pp. 89-98. [2] C. Miao, A. Ajith, Traffic Accident Data Mining Using Machine Learning Paradigms, Fourth International Conference on Intelligent Systems Design and Applications (ISDA'04), Hungary, 2004, pp. 415-420. [3] H. Zhang, B. Bac, W. Zhou, The Design and Implementation of a Traffic Accident Analysis System, Proceedings of the 14th International conference on Industrial and engineering applications of artificial intelligence and expert systems: engineering of intelligent systems, 2001, pp. 476-481. [4] H. Wenbin, Research on the Relation between Road Alignment and Traffic Accident, Master Degree Dissertation of, 2005. [5] S. Aimin, Research on the Freeway Traffic Accidents and Countermeasures, Master Degree Dissertation of Dongnan University, 2006. [6] Y. Chunmiao, C. Baozhi, L. Chang, Analyzing Methods of Contributing Causes for Accidents Based on BP Neural Networ, Industrial Safety and Dust Control, 2005, vol. 31, No. 10, pp. 54-56. [7] W. Qing-yao, C. Bin, J. Weidong, F. Rui, Y. Wei, Analyzing Road Factor in Traffic Accident Based on Layer-interrelating Analysis Method, Journal of Changsha Communications University, 2005, vol. 21, No. 1, pp. 82-86. [8] Yu hongqi, Analysis of the Road Traffic Accident Reason in Clustering, Master Degree Dissertation of, 2005. [9] Qin Xiaohu, The Model and Application of Urban Traffic Emergency Management and Safety System, Doctor Degree Dissertation of Chongqing University, 2005. [10] W. Fazhi, Methods Based on the Bayesian Networs for Traffic Accidental Event Situation Assessment, Master Degree Dissertation of Dalian University of Technology, 2006. [11] J. Beibei, Research on Prediction Method of Traffic Incident Duration, Doctor Degree Dissertation of Tongji University, 2008. [12] G.Cooper, E. Hersovits, A Bayesian Method for the Induction of Probabilistic Networs from Data, Machine Learning, 1992, No. 9, pp. 309. 417