A Bayesian Network Approach to Causation Analysis of Road...

Research ArticleA Bayesian Network Approach to Causation Analysis ofRoad Accidents Using Netica

Xin Zou and Wen Long Yue

School of Natural and Built Environments University of South Australia Adelaide SA 5095 Australia

Correspondence should be addressed to Xin Zou zouxy011mymailunisaeduau

Received 4 June 2017 Revised 7 October 2017 Accepted 31 October 2017 Published 12 December 2017

Academic Editor Alexandre De Barros

Copyright copy 2017 Xin Zou andWen Long Yue This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Based on an overall consideration of factors affecting road safety evaluations the Bayesian network theory based on probabilityrisk analysis was applied to the causation analysis of road accidents By taking Adelaide Central Business District (CBD) in SouthAustralia as a case the Bayesian network structure was established by integrating K2 algorithm with expertsrsquo knowledge andExpectation-Maximization algorithm that could process missing data was adopted to conduct the parameter learning in Neticathereby establishing the Bayesian network model for the causation analysis of road accidents Then Netica was used to carry outposterior probability reasoning the most probable explanation and inferential analysis The results showed that the Bayesiannetwork model could effectively explore the complex logical relation in road accidents and express the uncertain relation amongrelated variables The model not only can quantitatively predict the probability of an accident in certain road traffic condition butalso can find the key reasons and the most unfavorable state combination which leads to the occurrence of an accident The resultsof the study can provide theoretical support for urban road management authorities to thoroughly analyse the induction factors ofroad accidents and then establish basis in improving the safety performance of the urban road traffic system

1 Introduction

With the expansion of urban development and the surgingof vehicle ownership urban travel becomes vulnerable tothree ldquochronic diseasesrdquo which are congestion accidentand pollution Among the above three accident has beenrecognised as the most negative aspect in particular in andaroundCentral Business District (CBD) According toGlobalPlan for the Decade of Action for Road Safety 2011ndash2020developed by the UN Road Safety Collaboration in 2011nearly 13 million people die as a result of road trafficcollisions per annum whichmeansmore than 3000 fatalitiesper day And 20 to 50 million more people sustained nonfatalinjuries from collisions and these injuries were an importantcause of disability worldwide The case in Australia is alsoat an alarming level there were around 25 deaths and 700serious injuries per week and cost to tax payers was morethan 32 billion dollars a year [1] Unless immediate andeffective action is taken road traffic injuries are predictedto become the fifth leading cause of death in the world

Therefore the analysis and evaluation on the influencingfactors on traffic accident estimation of the potential safetyhazards and selection of appropriate measures in advanceso as to reduce the frequency and severity of traffic accidentsare important research topics in road safety engineering

Previous studies showed that there are many reasonsbehind road accidents these causes may be coherent to eachother and for instance poor road alignments and unex-pected vehicle compositions or behaviours may result in theconfusion of road users which may lead to traffic accidentsHowever many official records of road accidents indicatedthat most of the crashes are only pointed to single causesespecially human errors For example according to a crashcausation survey released by the USNational Highway TrafficSafety Administration (NHTSA) in 2015 [2 3] drivers are tobe criticised for 94 of crash cases Apparently the 94 ofsuch accidents are also related to other causes from commonexperience such as road alignment [4ndash6] traffic sign [7ndash9]and weather condition [10ndash12] Therefore the existing roadaccident statistics cannot fully reveal the causes and traffic

HindawiJournal of Advanced TransportationVolume 2017 Article ID 2525481 18 pageshttpsdoiorg10115520172525481

2 Journal of Advanced Transportation

engineers and road infrastructure designers are providedwith limited information for the accident mechanism and theformulation of improvement plans It is of great importanceto take full advantage of the traffic accident statistics andminepotential information so as to provide a basis for the analysisof accident mechanism and the improvement of road safety

Bayesian network is one of the effective methods in thefield of artificial intelligence to express uncertainty analysisand probability reasoning of a system It can exploit thedependence relationships based on local conditions in amodel to conduct bidirectional uncertainty investigation forprediction classification and diagnostic analyses At presentthere are some software platforms available for the con-struction of a Bayesian network such as Bayes Net Toolbox(BNT) BayesBuilder and JavaBayes of which the MATLAB-based BNT developed by Murphy [13] is extensively usedThis toolbox provides a lot of underlying basic functionlibraries for Bayesian network learning but it does notintegrate the basic functions for Bayesian network learninginto a system Moreover BNT does not have Graphical UserInterface (GUI) which is not user-friendly nor can it be wellgeneralized Netica is a Bayesian network learning softwaredeveloped by Norsys Software Corporation in Canada whichhas been extensively applied in uncertaintymanagement suchas business engineering medicine and ecology [14ndash16] dueto its powerful functions friendly GUI reliable computationand good performance In this paper a model is formulatedusing Bayesian network for road accident studies and then aBayesian network learning process posterior probability rea-soning most probable explanation and inferential analysisare conducted by using Netica

This paper is organized as follows Section 2 reviews therelated literature on causation analysis of road accidentsSection 3 describes the construction of a Bayesian networkmodel Section 4 presents a case study on Bayesian networkmodel application for Adelaide Central Business District(CBD) in South Australia the findings of this study aresummarized in Section 5

2 Literature Review

The use of causation theory for road accident analysis aimsto extract the accident mechanisms and accident modelsfrom a large number of typical accidents so as to providetheoretical basis for the qualitative and quantitative analysesthe predication and prevention of accidents and the improve-ment of safety management Scholars across the world havedone some researches in road accident causation analysis andvarious data sources variables sample sizes and analyticalmodels such as aggregated models which include FrequencyAnalysis [17ndash19] and 1205942 Test [20 21]

In terms of disaggregated models as the frequency ofroad accidents is in a form of nonnegative discrete andabnormal distribution and based on experience the frequencyof accidents follows Poisson distribution the Poisson regres-sion model can be applied to analyse the influence of eachrisk factor on the frequency of accidents [22] The negativebinomial distribution regression is based on Poisson distribu-tion but its specification error follows Gamma distribution

The negative binomial regression model has been extensivelyapplied in traffic safety analysis model [23ndash27] However theassumption that the mean value of Poisson distribution isequal to the variance is often inconsistent with realities Andin the analysis of longitudinal data samples the adoptions ofPoisson regression model and negative binomial regressionmodel are likely to generate biased estimate and even incor-rect results When the explained variables only take a limitednumber ofmultiple discrete values the established regressionmodel is a discrete choice model in which Logit model isthe earliest discrete choice model and is one of the widelyused models [28ndash31] For an applicable statistical modelresearch object is required to be in independent distributionwhile the safety data has a complex spatial distribution theaccuracy and robustness of safety level estimation will begreatly affected if the spatial feature is neglected

Through the review of the existing literature it has beendiscovered that past researches on the causation analysis oftraffic accidents are gradually evolving from the descriptivesimple analysis based on aggregated models to the multi-variable complex modeling analysis based on disaggregatedmodels However the deficiencies of the existing studiesare the following the influencing factors on accidents arenot fully considered most are based on specific isolatedsuperficial single-factor analysis considering only the maininfluence factors These studies revealed the inherent rules ofthe occurrence of accidents in one aspect or case but ignoredthe multidimensionality of accident relationships and theircorrelations so that the complex logical relationship betweencauses accident occurrence and accident consequence wasnot reflected Therefore research methods and analysis tech-nologies are not generally applicable Although some scholarsused Decision Tree [26 32 33] Bayesian network [34ndash36]and other complex systems to research the correlation betweenaccident causes the theoretical systems and related support-ing technologies have not been systematically established

3 Construction of Bayesian Network Model31 Basic Principles of Bayesian Network Bayesian networkalso referred to as belief network is considered as one of themost effective theoretical models in the fields of uncertaintyknowledge representation and reasoning It is a directedacyclic network topology consisting of node set and directededge and each node denotes one variable state while directededge denotes the dependence between variables The corre-lation intension or confidence coefficient between variablesis described by using Conditional Probability Table (CPT)Prediction diagnosis classification and other tasks can beachieved by using learning and statistical inference functionsof Bayes theorem Bayesian network uses probability todenote the uncertainty of all forms and uses the probabilisticrules to achieve learning and reasoning process It has thefollowing relationship

119901 (119883) = 119899prod119894=1

119901 (119883119894 | 119901119886119894) (1)

A set of variables 119883 = 1198831 1198832 119883119899 of Bayesian networkconsists of the following components [37] 119878 is a network

Journal of Advanced Transportation 3

X1

X2

X3

X4

X5

X6

X7

X8

Figure 1 Graph of a valid Bayesian network (no cycle exists)

structure which denotes the conditional independent asser-tion in variable set 119883 119875 is a set of local probability distribu-tions associated with each variable 119883119894 denotes the variablenode and 119901119886119894 denotes the father node of119883119894 in 119878119878 and 119875 define the joint probability distribution of 119883119878 is a directed acyclic graph (DAG) and each node in 119878corresponds to a variable in 119883 (Figure 1) The default arcbetween nodes of 119878 denotes conditional independence

Use 119875 to denote the local probability distribution in (1)namely the product term 119901(119883119894 | 119901119886119894) (119894 = 1 2 119899)then the binary group (119878 119875) denotes the joint probabilitydistribution 119901(119883)

The construction of a Bayesian network mainly involvesthe following steps

(1) Structure learning determine the factor variables(nodes) related to the study object and then deter-mine the dependent or independent relationshipbetween the nodes so as to construct a directed acyclicnetwork structure

(2) Parameter learning based on the given Bayesiannetwork structure learn the Conditional ProbabilityTable (CPT) at each node of the Bayesian networkmodel

32 Structure Learning As the network structure and data setcan be used to determine the parameters structure learningis the basis of Bayesian network learning and the effectivestructure learning is the key to constructing the optimalnetwork structure

The construction of Bayesian network structure includesthe following three points

(1) Based on expert experience and prior knowledgedetermine the variable nodes of Bayesian network soas to determine the structure of Bayesian network

(2) Through the learning of sample data automaticallyacquire the Bayesian network structure by usingmachine learning algorithm

(3) Based on expert experience and machine learning ofdata acquire the Bayesian network structure by usingdata fusion method

As the third point combines the advantages of expertexperience and machine learning and avoids the disad-vantage of using one method to determine the Bayesiannetwork structure only in this paper the third method todetermine the Bayesian network structure for the causationanalysis of road accidents will be used Common machinelearning methods include K2 algorithm MCMC algorithmand hill-climbing algorithm K2 algorithm is based on thescoring function and hill-climbing algorithm which lies inthe basic principle from an empty network according tothe predefined order of nodes select the node with themost posterior probability as the father node of this nodesequentially traverse all nodes and gradually add the optimalfather node to each variable K2 algorithm uses posteriorprobabilities as the scoring function which is described asfollows

119875 (119863 | 119861119878) = 119899prod119894=1

score (119894 119901119886119894) (2)

where

score (119894 119901119886119894)= 119902119894prod119895=1

[ Γ (120597119894119895)Γ (120597119894119895 + 119873119894119895)

119903119894prod119896=1

Γ (120597119894119895119896 + 119873119894119895119896)Γ (120597119894119895119896) ] (3)

119863 is a set of variables119861119878 is the network structure119899 are the numbers of nodes in the graph119902119894 are configurations (states) of the parents of the 119894thnode119903119894 are mutual exclusive states of the 119894th node119873119894119895119896 are instances of the 119894th node being in the 119896th statewhen its parents are in their 119895th configuration and119873119894119895 = sum119903119894

119896=1119873119894119895119896120597119894119895119896 are the hyperparameters of the Dirichlet distri-

bution and correspond to the a priori probabilitydistribution of 119883119894 taking on its 119896th state while itsparents are in their 119895th configuration 120597119894119895 = sum119903119894

119896=1120597119894119895119896

The gamma function Γ(119883) = int+infin0

119905119883minus1119890minus119905119889119905 satisfiesΓ(119883 + 1) = 119883Γ(119883) and Γ(1) = 1K2 algorithmuses a variable order 120588 and a positive integer119906 to limit the search space which seeks the optimal modelweierp that meets the following two conditions (1) the number

of father nodes of any variable in weierp should not be greaterthan 119906 and (2) 120588 is a topological order of weierp However as K2


algorithm adopts greedy search strategy which may easilyfall into the local optimal solution and cannot guarantee thatthe network acquired is the optimal network the knowledgeand experience of experts need to be integrated so as toacquire the optimal network structure In this paper thecombination of expert experience and K2 algorithm willperform the Bayesian network structure learning for thecausation analysis of road accidents

33 Parameter Learning After determining the topologicalstructure of Bayesian network the parameter learning ofBayesian network can be performed In the process of col-lecting road accidents information missing data often occursdue to various reasons for instance recording instrumentsmalfunction and confusion of respondents in answeringquestions Most of statistical models cannot directly anal-yse the data with missing values and in the case of anymissing values the record with missing values is generallyeliminated directly to ensure that the statistical model canbe properly fitted If the missing values are less this will notgreatly affect the results if the record with missing valuesis directly eliminated However if the multivariate analysisis performed more variables will be studied which meansthat more records will be eliminated it may cause a loss ofinformation reduce the power of test and cause some bias toresearch results [38]

The Expectation-Maximization (EM) algorithm isan asymptotic deterministic estimation method for theunknown parameter 120579 with missing data It can be used toperform maximum likelihood estimation on the parametersfrom incomplete data set which is a practical learningalgorithm [39] EM algorithm can be widely used to dealwith incomplete data such asmissing data and censored dataEM algorithm mainly involves two steps Expectation Step(119864-Step) and Maximization Step (119872-Step) The algorithm isdescribed as follows

(1) Initialize 120579(0) Set accuracy 120576 and correction value 1205791015840 ofestimated value 120579

While 10038161003816100381610038161003816120579 minus 120579101584010038161003816100381610038161003816 gt 120576do 120579 larr997888 1205791015840 (4)

(2) 119864-Step Calculate the expected sufficient statistic of miss-ing value 119890lowast

The probability distribution of 119890lowast is119875 (119890lowast | 119890 120579) = 119875 (119890 | 119890lowast 120579) 119875 (119890lowast | 120579)

sum119890lowast 119875 (119890 | 119890lowast 120579) 119875 (119890lowast | 120579) (5)

where

119875 (119890 | 119890lowast 120579) = 119875 (119890 119890lowast 120579)119875 (119890lowast 120579)

119875 (119890lowast | 120579) = 119875 (119890lowast 120579)119875 (120579)

(6)

The sufficient statistic is

119864119875(119883|119890120579)119873119894119895119896 = sum119895119896

119875 (119883119894119895 120587 (119883119894119896) | 120579) (7)

where 119875(119890 | 119890lowast 120579) is the probability distribution of 119890 underthe condition that 119890lowast and 120579 are known 119875(119890lowast 120579) is the jointdistribution of 119890lowast and 120579 119883119894 is the 119894th variable 119873119894119895119896 is thecount of all possible joint instantiations between119883119894 and120587(119883119894)denoted by 119895 and 119896 respectively(3) 119872-Step Calculate the new maximum likelihood (ML)or maximum a posteriori (MAP) values of 1205791015840 in the givencondition 119875(119890lowast|119890 120579)

In Expectation-Maximization we have the following

ML

1205791015840119894119895119896 = 119864119875(119883|119890120579)119873119894119895119896sum1198961015840 119864119875(119883|119890120579)1198731198941198951198961015840 (8)

MAP

1205791015840119894119895119896 = 120572119894119895119896 + 119864119875(119883|119890120579)119873119894119895119896sum1198961015840 (1205721198941198951198961015840 + 119864119875(119883|119890120579)1198731198941198951198961015840) (9)

where 120572119894119895119896 is the Dirichlet parameter that can beobtained through the iteration process of 119864-Step and119872-Step

119864-Step is used to calculate the expected sufficient statisticof 119890lowast and 119872-Step is used to conduct new estimation oflearning parameter by using the statistic obtained in 119864-StepIn this paper the Bayesian network parameter learning ofroad accidents is performed by using EMalgorithm inNetica

4 Case Studies

41 Study Area and Data Source Adelaide Central BusinessDistrict (CBD) in South Australia is selected as the studycase as it attracts 22 of metropolitan Adelaidersquos worktrips [40] and has the first and the second most dangerousaccident concentration areas which are North Terrace andWest Terrace in the CBD [41]

The crash data of South Australia from 2006 to 2008were provided by theDepartment of Planning Transport andInfrastructure (DPTI) and ArcGIS 105 software was used tolocate the precise crash sites as shown in Figure 2

42 Variable Selection and Data Preprocessing By usingArcGIS 105 1558 and 756 data sets of road accidents inAdelaide CBD from 2006-2007 and 2008 are obtainedrespectively The statistical data from 2006 to 2007 will beused for the construction of Bayesian network model andcalibration and the statistical data in 2008 will be used forthe model validation process

Previous studies [33 42ndash45] provided some in-depthinsights to guide the variable selection discretization and


CBD

Adelaide

Figure 2 The location and region of Adelaide CBD

classification in this research As a result fourteen variablesare selected from the data sets as having ldquosignificant influ-encerdquo that is ldquocrash typerdquo ldquodriverrsquos apparent errorrdquo ldquoroadgeometryrdquo ldquovehicle typerdquo and others as shown in Table 1However according to the statistical result in Table 1 it canbe seen that the percentage of ldquoinattentionrdquo reaches up to3984 which is the biggest contributing factor in ldquodriverrsquosapparent errorrdquo category In our daily routine ldquoinattentionrdquois explained as ldquofailure to give attention or negligencerdquoGenerally such usage is quite convenient for record purposeshowever from the perspective of psychology and physiologythe usage is not clear and definite There are lots of otherreasons that may be behind traffic accidents such as humanfactors (driverrsquos physical and mental state knowledge andskill and the operational approach) objective factors (vehi-cles roads and road facilities) and safety management If allabove factors are simply summarized as ldquoinattentionrdquo thenthe causes of traffic accidents are to be extremely simplifiedAnd the prevention measures will be hardly developedTherefore in this research the factor of ldquoinattentionrdquo will beexcluded and all variables used for modeling are shown inTable 2

Bayesian network can be used to process continuous vari-ables and discrete variables As the classification result of traf-fic accident variables obviously has the discrete characteristicdiscrete variables are adopted for Bayesian network analysisof road accidents Before structure learning discretizationprocessing has to be conducted for road accident variableThe discretization values and value descriptions of processedvariables are shown in Table 2

43 Structure Learning In this paper the method combiningK2 algorithm and expertsrsquo knowledge is used to formulatethe Bayesian network structure Based on K2 algorithm

FullBNT-107 is utilized to conduct structure learning viaMATLAB Through repeated selection and sequencing ofvariables by experts the Bayesian network structure is finallydeveloped as shown in Figure 3The network is composed by14 nodes and several lines The 14 nodes refer to 14 variablesand lines between these nodes indicate the relationshipsamong the variables

It can be seen from Figure 3 that some road accidentvariables have demonstrated clear hierarchical relations ofaffecting others and being affected by others Road acci-dents result from the interaction of variables from ldquotrafficparticipant vehicle road and environmentrdquo which is fullyreflected by the Bayesian network structure as well Forinstance ldquovehicle movementrdquo is affected by ldquoroad geometryrdquoand ldquodriverrsquos apparent errorrdquo but it can also affect ldquototalunits involvedrdquo at the same time The actual situation ofroad accidents can be fully embodied by the interactionalhierarchical relationship of variables in Bayesian network

44 Parameter Learning Once a Bayesian network struc-ture is formed parameter learning can be carried out TheBayesian network structure can be created in Netica andthen parameter learning can be conducted thus obtainingthe conditional probability distribution of nodes Finallythe Bayesian network model for the road accident causationanalysis can be determined as shown in Figure 4

45 Model Calibration and Validation To validate theparameter learning accuracy and prediction accuracy ofthe Bayesian network model sensitivity analysis is used toidentify the sensitive factors with a significant impact on thetarget node from a number of uncertain factors and then thetarget node is set as the evidence variable to conduct modelfitting and prediction with these sensitive factors


Table 1 Variables of road accidents Adelaide CBD 2006ndash2008

Variable class Variable name Discretization value Value description Frequency Percentage

Driver Apparent error (1198831)

1 Fail to stand 307 1325

2 Change lanes toendanger 221 954

3 Incorrect turn 31 134

4 Reverse without duecare 92 397

5 Follow too closely 173 747

6 Overtake without duecare 52 224

7 Disobey traffic lights 171 7388 Disobey stop sign 23 0999 Disobey give way sign 47 20310 Inattention 923 398411 DUI 23 09912 Fail to give way 254 1096

Road

Road geometry (1198832)

1 Cross road 1116 48172 Y junction 57 2463 T junction 450 19424 Multiple 33 1425 Divided road 349 15066 Not divided 294 12697 Pedestrian crossing 18 078

Road moisturecondition (1198833)

1 Wet 237 10232 Dry 2080 8977

Traffic control (1198834)1 Traffic signals 1282 55332 Stop sign 42 1813 Give way sign 118 5094 No control 875 3776

Environment

Weather condition(1198835)1 Raining 151 6522 Not raining 2166 9348

Light condition (1198836) 1 Daylight 1716 74062 Night 601 2594

Vehicle

Vehicle type (1198837)1 Heavy 172 7422 Medium 901 38893 Light 1244 5369

Vehicle movement(1198838)

1 Right turn 426 18392 Left turn 95 4103 U turn 122 5274 Swerving 242 10445 Reversing 77 3326 Straight ahead 1238 5343

7 Entering privatedriveway 15 065

8 Leaving privatedriveway 50 216

9 Overtaking on right 39 16810 Overtaking on left 13 056


Table 1 Continued


Road crash

Crash type (1198841)

1 Rear end 1010 43592 Hit fixed object 59 2553 Side swipe 392 16924 Right angle 377 16275 Head on 5 0226 Hit pedestrian 50 2167 Right turn 333 14378 Hit parked vehicle 91 393

Crash severity (1198842) 1 PDO (propertydamage only) 1748 7544

2 Injury 569 2456

Total units (involvedin a road crash) (1198843)

1 Two units 2012 86842 Three units 258 11143 Four units 40 1734 Five units 7 030

Total casualties(fatalities and treated

injuries) (1198844)1 None 1748 75442 One casualty 495 21363 Two casualties 62 2684 Three casualties 12 052

Total serious injuries(1198845)1 None 2267 97842 One serious injury 50 216

Total estimateddamage (A$) (1198846)

1 [0 5000) 1139 49162 [5000 10000) 795 34313 [10000 +infin) 383 1653

Road geometry

Vehicle movement

Driverrsquos apparent error

Light condition

Crash type

Total units involved

Weather condition

Road moisture condition

Traffic control

Total casualties

Total estimated damage

Vehicle type

Crash severity

Total serious injuries

Figure 3 The Bayesian network structure for the road accident analysis


Table 2 Variables used for the Construction of Bayesian Network









7 Disobey traffic lights 115 12418 Disobey stop sign 18 1949 Disobey give way sign 27 29110 DUI 9 09711 Fail to give way 179 1931

Road

Road geometry (1198832)1 Cross road 454 48982 Y junction 11 1193 T junction 196 21144 Multiple 13 1405 Divided road 132 14246 Not divided 121 1305


1 Wet 100 10792 Dry 827 8921


Environment



Vehicle








Table 2 Continued


Road crash




2 Injury 238 2567







1 [0 5000) 423 45632 [5000 10000) 342 36893 [10000 +infin) 162 1748

Vehicle_movementRight turnLeft turnU turnSwervingReversingStraight aheadEntering private drivewayLeaving private drivewayOvertaking on rightOvertaking on left

277617803155693259174246344208

Driverrsquos_apparent_errorFail to standChange lanes to endangerIncorrect turnReverse without due careFollow too closelyOvertake without due careDisobey traffic lightsDisobey stop signDisobey give way signDUIFail to give way

215152259658128378124194291097193

Road_moisture_conditionWetDry

108892

Weather_conditionRainingNot raining

701930

Crash_severityPDOInjury

707293

Total_casualtiesNoneOne casualtyTwo casualtiesThree casualties

691260341150

Total_estimated_damageFrom 0 to 5000From 5000 to 10000Above 10000

455363181

Vehicle_typeHeavyMediumLight

680409523

Total_serious_injuriesNoneOne serious injury

963373

Light_conditionDaylightNight

730270

Crash_typeRear endHit fixed objectSide swipeRight angleHead onHit pedestrianRight turnHit parked vehicle

172598187166597848208635

Road_geometryCross roadY junctionT junctionMultipleDivided roadNot divided

490119211140142131

Traffic_controlTraffic signalsStop signGive way signNo control

515291604396

Total_units_involvedTwo unitsThree unitsFour unitsFive units

930563091042

Figure 4 The Bayesian network model after parameter learning in Netica 602


Table 3 Sensitivity analysis result of the node ldquocrash typerdquo

Node Mutual info Percent Variance of beliefsCrash type 282978 100 07195390Driverrsquos apparent error 057217 202 00869963Vehicle movement 033948 12 00351281Total casualties 021563 762 00057073Crash severity 017897 632 00037534Road geometry 004044 143 00008944Total serious injuries 001888 0667 00004707Traffic control 001125 0398 00001573Road moisture condition 000503 0178 00001027Light condition 000417 0147 00000915Total estimated damage 000407 0144 00000533Total units involved 000394 0139 00002397Weather condition 000313 0111 00000638Vehicle type 000000 0000 00000000

451 Sensitivity Analysis In Bayesian network the sensi-tivity analysis refers to the analysis of the influence andinfluence degrees of multiple causes (node states) on result(target node) Based on sensitivity analysis the elementaryevents with relatively greater contribution to the probabilitiesof the consequential events can be determined to facilitatethe reduction of probabilities of these elementary events bytaking effective measures so that the probabilities of theconsequential events will be reduced

The sensitivity analysis function of Netica can be used toidentify which factors have more important safety manage-ment values in analyzing traffic accidents In Netica selectthe target node and then analyse the impact degrees of othernodes on the target node in a descending order Taking thenode ldquocrash typerdquo as an example make sensitivity analysis ofit and the result is as shown in Table 3

The mutual information refers to the direct or indirectinformation flow rate andmeasures the degree of dependencebetween nodes In other words the mutual informationbetween two nodes can indicate if the two nodes are depen-dent on each other and if so how close their relationship is[46] As shown in Table 3 it can be seen that the mutualinfo (=057217) of node ldquodriverrsquos apparent errorrdquo is the largestwhich means that it has the strongest impact on ldquocrash typerdquofollowed by ldquovehicle movementrdquo and ldquoroad geometryrdquo whichhave mutual info = 033948 and 004044 respectively

452 Model Fitting and Prediction Based on the sensitivityanalysis result of ldquocrash typerdquo the posterior probabilitiesof ldquodriverrsquos apparent errorrdquo ldquovehicle movementrdquo and ldquoroadgeometryrdquo obtained from the Bayesian network are comparedwith the actual calculations from 2006 to 2007 and from2008 respectively Due to the large amount of data ldquorear endrdquofrom the parameter learning results of ldquocrash typerdquo is used forexemplificative explanation

Figures 5 6 and 7 show the posterior and actual prob-ability distributions of ldquodriverrsquos apparent errorrdquo ldquovehicle

1 2 3 4 5 6 7 8 9 10 110

1020304050607080

Driverrsquos apparent error (discretization value)

Prob

abili

ty d

istrib

utio

n (

)

Posterior probabilityActual probability (2006-2007)Actual probability (2008)

Figure 5The comparison of posterior and actual probability curvesof driverrsquos apparent error when the evidence variable is ldquorear endrdquo


2 3 4 5 6 7 8 9 101Vehicle movement (discretization value)

01020304050607080

Prob

abili

ty d

istrib

utio

n (

)

Figure 6The comparison of posterior and actual probability curvesof vehicle movement when the evidence variable is ldquorear endrdquo



15 2 25 3 35 4 45 5 55 61Road geometry (discretization value)

0

10

20

30

40

50

60

Prob

abili

ty d

istrib

utio

n (

)

Figure 7The comparison of posterior and actual probability curvesof road geometry when the evidence variable is ldquorear endrdquo

movementrdquo and ldquoroad geometryrdquo respectively when theevidence variable is ldquorear endrdquo Compared with the actualcomputational results from2006 to 2007 themaximummeanabsolute error (MAE) of Bayesian network model is 558Similarly compared with the actual computational resultsof 2008 the maximum MAE is 614 which suggests thatthe Bayesian network model has both high fitting accuracyand high prediction accuracy Therefore it is feasible to usethe Bayesian network model to conduct result predictionand inferential analysis of each variable of road accidentsaccordingly

46 Bayesian Network Model Application

461 Posterior Probability Reasoning Bayesian networkmodel can be used to perform probability reasoning includ-ing posterior probability calculations Precisely it aims tocalculate the posterior probabilities of some targeted nodescontrol the influence degrees of determined specific nodeson the nodes of interest predict the possibility of accidentoccurrence and analyse the major accident sources underthe condition that states of specific nodes are determined Inbrief the posterior probabilities in inferring the result fromcause and inferring the cause from result are referred to asaccident prediction and causal inference respectively

(1) Accident Prediction Figure 8 is the accident predictionon the assumption that a driver ldquodisobeys traffic lightsrdquowhen driving in Adelaide CBD Input the evidence variables(ldquotraffic signalsrdquo and ldquodisobey traffic lightsrdquo) emerging fromthis circumstance into the Bayesian network so it becomesa problem to solve the posterior probabilities of other nodeswith the known status of some evidence variables

In Netica set both the statuses of ldquotraffic signalsrdquo andldquodisobey traffic lightsrdquo as 100 that is the statuses of theevidence variables are determinedThen update the probabil-ities of the whole network the probability change of relevantnodes namely the probability change of ldquocrash typerdquo andother nodes can be observed In this case the probability

of ldquoright anglerdquo in ldquocrash typerdquo is found to increase fromthe initial 166 to 580 This suggests that if the driverldquodisobeys traffic lightsrdquo the probability of ldquoright anglerdquo willsignificantly increase

As shown in Figure 9 in addition to ldquodisobey trafficlightsrdquo assume that the driving time is at night namely thestatus of ldquonightrdquo in ldquolight conditionrdquo is set as 100 After auto-matically updating the probabilities of the whole networkthe probability of ldquoright anglerdquo is found to further increasefrom 580 to 594 which means that the probability ofldquoright-anglerdquo traffic accident is higher Go one step furtherand assume that it is also a rainy night (namely set the statusof ldquorainingrdquo in ldquoweather conditionrdquo as 100) According toFigure 10 once again it can be found that the probabilityof ldquoright anglerdquo further increases from 594 to 633 Thissuggests that ldquodriverrsquos apparent errorrdquo ldquolight conditionrdquo andldquoweather conditionrdquo will all affect the probability of ldquorightanglerdquo to various degrees Therefore it can be found thatthe status change of evidence node variables will affect theprobabilities of query nodes which is consistent with theengineering practice

(2) Causal Inference Another important application of theBayesian network is fault diagnosis of the system Thebidirectional reasoning technology of the Bayesian networkcan calculate not only the probability of a system failure undercombined fault conditions but also the posterior probabilitiesof various components under the system fault conditionand easily find out the most likely combination that causedsystem failure thereby making the computational analysismore intuitive and flexible

Conduct causal inference by taking the ldquoside swiperdquoin ldquocrash typerdquo as an example In this case the evidencevariable is ldquoside swiperdquo so its status probability is 100 Asshown in Figure 11 after inputting the evidence the prob-ability of ldquochange lanes to endangerrdquo in ldquodriverrsquos apparenterrorrdquo increases greatly from 152 to 467 through theautomatic updating function of Netica And the probabilityof ldquoswervingrdquo in ldquovehicle movementrdquo also increases from155 to 449which reaches themaximumprobabilityThissuggests that in the absence of other evidences the mostprobable cause to ldquoside swiperdquo is ldquoswervingrdquo (vehicle) causedby ldquochange lanes to endangerrdquo (driver)

462 Most Probable Explanation Bayesian network modelcan be used to make the most probable explanations pre-cisely from sets of multiple causes (node states) which arelikely to lead to a conclusion use Netica to identify the setthat is most likely to lead to the result and this set with themaximum likelihood will be the most probable explanation

In the example of ldquoside swiperdquo as illustrated in Figure 12use ldquoMost Probable Explanationrdquo function in Netica to findout the most probable cause set As shown in Figure 12 themost probable explanation cause (node state) set of ldquosideswiperdquo is [cross road change lanes to endanger swervingdaylight not raining dry traffic signals] It explicitly showsthat most probable explanation and causal inference arehighly consistent when the evidence variable is ldquoside swiperdquoand the set is also consistent with the engineering practice



102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


698302


688267334108


443366191


680409523


965345


730270


418362474580362719150362


490119211140142131


100 00 0


890938130032

Figure 8 Road accident prediction when the evidence variables are ldquotraffic signalsrdquo and ldquodisobey traffic lightsrdquo


102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


708292


698258332107


442367191


680409523


966337


0100


374374374594374563162374


490119211140142131


100 00 0


890938130032

Figure 9 Road accident prediction when the evidence variables are ldquotraffic signalsrdquo ldquodisobey traffic lightsrdquo and ldquonightrdquo

47 Inferential Analysis of Accidents Based on ldquoSeriousInjuriesrdquo and ldquoTotal Estimated Damagerdquo The application ofthe Bayesian network model in Netica to solve the pos-terior probability reasoning problem maximum posteriorhypothesis problem andmost probable explanation problem

highlighted the inferential capability of the Bayesian networkmodel To further analyse the factors contributing to trafficaccidents especially serious traffic accidents the Bayesiannetwork model was used to calculate the probabilities ofldquoserious injuriesrdquo and ldquototal estimated damage over 10000



102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


1000+


1000


724276


714244323104


441369190


680409523


968323


0100


374374374633374374143374


490119211140142131


100000

Total_units_involvedTwo unitsThree unitsFourunitsFive units

890938130032

Figure 10 Road accident prediction when the evidence variables are ldquotraffic signalsrdquo ldquodisobey traffic lightsrdquo ldquonightrdquo and ldquorainingrdquo


125799852449245906139246740330


512467606206268952566128188052185


909909


591941


841159


841159

0+ 0+


454377169


680409523


988120


746254


00

1000000 0


468103212106161138


525211577396


945410065080

Figure 11 The posterior probability when the evidence variable is ldquoside swiperdquo

AUDrdquo under the influence of ldquodriverrsquos apparent errorrdquo ldquoroadgeometryrdquo ldquoweather conditionrdquo ldquolight conditionrdquo and ldquocrashtyperdquo respectively The results are shown in Table 4

471 Driverrsquos Apparent Error Theresults presented in Table 4indicate that ldquodriving under the influencerdquo (DUI) will most

likely cause serious injuries and heavy property damage asDUI is more easily to lead to dangerous behaviours includingspeeding not wearing a safety belt and reckless or erraticdriving According to the inference results DUI is most likelyto cause traffic accidents on cross roads with the inferenceprobability of 490 As for the crash types the inference



125719123100

451728080342215569


561 100102451304215728158136079125


355100


355100


100219


100219

0+ 0+


100966324


155848 100


100178


100369


00

10000000


100264452312214211


100122117313


100302167322

Figure 12 The most probable explanation when the evidence variable is ldquoside swiperdquo

probabilities of rear-end and head-on crashes are the twohighest (resp 156 and 154) In previous studies amongall traffic accidents caused by DUI unrestrained occupantswere 470 times more likely to die or 466 times more likelyto be injured than restrained occupants [47] Besides drunkdrivers show weak control ability of vehicles and the higherethanol content in their blood the higher probability thatthey will have illegal actions mentioned previously [48]which are more likely to cause serious traffic accidents withheavy casualties and property damage

472 Road Geometry Intersections are an important part ofroad system and are potentially the most dangerous locationsin a network as well Previous studies have shown thatintersections especially cross roads have higher crash ratesand greater crash severity particularly in urban areas [49ndash51]As shown in Table 4 the most dangerous ldquoroad geometryrdquoin Adelaide CBD also is ldquocross roadrdquo which means that theprobabilities of causing serious injuries and heavy propertydamage at ldquocross roadsrdquo are both the biggest According tothe accident records in Adelaide CBD among serious trafficaccidents caused at cross roads there are two main crashtypes ldquoright anglerdquo and ldquoright turnrdquo respectively accountingfor 4435 and 4261 while ldquofail to standrdquo and ldquodisobeytraffic lightsrdquo become the twomain reasons of traffic accidentscaused at cross roads respectively accounting for 3826 and3478

473 Weather Condition Rainfall will not only decrease theeffectiveness of driversrsquo visual search [12] but also lower thefriction coefficient of roads which makes roads slipperyincreases braking distance greatly and thus results in the

possibility of traffic accidents A study for Melbourne Aus-tralia by Keay and Simmonds [10] found that rainfall wasthe strongest factor that correlated to weather parameter andit had the greatest impact in winter and spring Keay andSimmonds [52] also found a contributing parameter whichis the lagged effect of rain Symons and Perry [53] found thatwet roads or raining is increasing the probability of trafficaccidents which can reach up to 70 percent Similarly Qiuand Nixon [11] found that rain can increase the crash rateby 71 and the injury rate by 49 This coincides with theresults found in this research which indicate that rainfall isassociated with traffic accidents that had serious injuries andheavy property damage

474 Light Condition (Urban Heat Island) Traditional bitu-minous pavement can absorb and store large amounts ofheat during the day and continuously output the heat to theexternal environment at night whichwill result in an increasein external environment temperature and lead to urban heatisland (UHI) UHI might have some impacts on road dura-bility and safety such as accelerating bituminous pavementaging and exacerbating road high-temperature rutting maylead to road accidents With the continuous expansion of citysize the comprehensive phenomenon of such microclimaticvariationwill become increasingly obvious [54] As one of themajor Australian cities Adelaide is also affected by UHI [55]And as waste heat from vehicles and temperature regulationof buildings is an important determinant of UHImagnitudesAdelaideCBDwhich has the largest density of traffic networkand the largest number of buildings has become the centerof UHI As shown in Table 4 the number of road accidentsthat occurred at night demonstrates a larger proportion of


Table 4 Inference results for variables that are associated with ldquoserious injuriesrdquo and ldquototal estimated damagerdquo in serious traffic accidents

Variable class Variable name Serious injuries Total estimated damage (ge10000 AUD)


Fail to stand 354 175Change lanes to endanger 283 175

Incorrect turn 361 171Reverse without due care 403 179

Follow too closely 391 200Overtake without due care 336 187

Disobey traffic lights 415 194Disobey stop sign 481 195

Disobey give way sign 468 189DUI 517 204

Fail to give way 391 172

Road geometry

Cross road 447 196Y junction 369 182T junction 327 180Multiple 417 184

Divided road 405 181Not divided 412 183

Weather condition Raining 422 184Not raining 369 181

Light condition Daylight 365 181Night 393 182

Crash type

Rear end 340 190Hit fixed object 276 174Side swipe 120 169Right angle 248 176Head on 154 260

Hit pedestrian 937 186Right turn 293 172

Hit parked vehicle 034 169

5556 than by daylight Under the influence of UHI Jusufet al [56] found that at nighttime commercial area has thehighest ambient temperature among the four land use types(commercial residential industrial and airport) SimilarlyParker [57] also found that the urban heat island is strongestat night in high-rise city centers Therefore the correlationanalysis between road accidents and nighttime UHI is apotential research direction

475 Crash Type Head-on crashes are among the mostsevere collision types and are of great concern to road safetyauthorities [58] For instance according to an annual reportpresented by NHTSA in 2015 head-on crashes occupied only23 of total crashes however they accounted for 96 offatal crashes As shown inTable 4 nomatter ldquoserious injuriesrdquoor ldquoproperty damage over 10000 AUDrdquo the possibility ofldquohead-onrdquo crashes always takes the first place and is largelyhigher than other types of traffic accidents As for the roadgeometry the head-on crashes are most likely to happen oncross roads with the inference probability of 396 while theinference probability of ldquodisobey traffic lightsrdquo is the biggest indriversrsquo apparent errors which cause head-on crashes These

results agree with Bham et al [59] who found that head-oncollisions were at a higher risk for severe injuries comparedwith other collision types And Rizzi et al [60] concludedthat 31 and 21 of crashes at intersections could have beenavoided entirely or influenced by anti-lock braking system(ABS) however the head-on crashes were the only crash typefor which ABS seemed to be ineffective

5 Conclusion and Future Work

As road accidents are unexpected random complex andlatent it is necessary to conduct investigations on accidentmechanism and accurately identify the exact causes TheBayesian network combining the probability theory withgraph theory not only has a rigorous mathematical consis-tency but also has the structure chart that can intuitivelyidentify problems Therefore it is one of the most powerfuland effective tools to deal with uncertainties

The occurrence of road accident results from the interac-tions of ldquotraffic participant vehicle road and environmentrdquoand there is a potential hierarchical relation (impacting andimpacted) among the variables In Bayesian network the


directed acyclic graph is a visual expression form that iscloser to the characteristics of thought and reasoning modeof human In the study the Bayesian network structure forthe road accident causation analysis was achieved by usingK2 algorithm and expertsrsquo knowledge which combines theadvantages of machine learning and expertsrsquo knowledgeThe structure learning result of the Bayesian network fullyreflects the hierarchical relations among the accident relatedvariables and allows for better prediction and analysis of thecharacteristics of road accidents

In this study the Bayesian network model for the roadaccident causation analyses was established by using Net-ica Bayesian network-based software with friendly GUIThe Expectation-Maximization algorithm that can deal withmissing data was adopted to process the parameter learningand then the calibration and validation posterior probabilityreasoning most probable explanation and inferential anal-ysis were carried out after the construction of the BayesiannetworkmodelThe results showed that the Bayesian networkmodel is feasible and effective for road accident causationanalyses in particular the use of posterior probability of theBayesian network can not only more precisely and quicklyfind the key causes for traffic accidents but also identify themost likely cause (state) combination The result can be usedas an important theoretical basis in developing road trafficmanagement strategies so as to improve road traffic safety

Follow-up studies will consider the rationality of theBayesian model and other factors that may lead to trafficaccidents and establish a more accurate and comprehensivemodel As the Bayesian model is a probabilistic modelmore comprehensive and extensive basic data are needed toenhance its reliability in which some data can be obtainedonly by carrying out experiments despite the ability of theBayesian mode to make up for missing data Moreover as theinfluencing road accident factors in reality are more than thefactors used in this study and as Netica is also suitable for theestablishment of a larger and more complex accident analysismodel the model can be expanded to a more sophisticatedmodel that can consider more factors

Conflicts of InterestThe authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] Australasian College of Road Safety 2017 ACRS Submission toFederal Parliamentarians Retrieved from httpacrsorgauwp-contentuploads2017-ACRS-Submission-to-Federal-Parlia-mentarians-FINALpdf

[2] National Highway Traffic Safety Administration (NHTSA)ldquoCritical reasons for crashes investigated in the national motorvehicle crash causation surveyrdquo vol 85 101 pages 2015

[3] National Highway Traffic Safety Administration (NHTSA)ldquoTraffic safety facts 2014 a compilation of motor vehicle crashdata from the fatality analysis reporting system and the generalestimates systemrdquo 2015

[4] M G Karlaftis and I Golias ldquoEffects of road geometry andtraffic volumes on rural roadway accident ratesrdquo AccidentAnalysis Prevention vol 34 no 3 pp 357ndash365 2002

[5] R Fu Y Guo W Yuan H Feng and Y Ma ldquoThe correlationbetween gradients of descending roads and accident ratesrdquoSafety Science vol 49 no 3 pp 416ndash423 2011

[6] J P Gooch V V Gayah and E T Donnell ldquoQuantifying thesafety effects of horizontal curves on two-way two-lane ruralroadsrdquo Accident Analysis Prevention vol 92 pp 71ndash81 2016

[7] H Al-Madani and A R Al-Janahi ldquoRole of drivers personalcharacteristics in understanding traffic sign symbolsrdquo AccidentAnalysis Prevention vol 34 no 2 pp 185ndash196 2002

[8] D de Waard F J J M Steyvers and K A Brookhuis ldquoHowmuch visual road information is needed to drive safely andcomfortablyrdquo Safety Science vol 42 no 7 pp 639ndash655 2004

[9] T Ben-Bassat and D Shinar Ergonomic Guidelines for TrafficSign Design Increase Sign Comprehension Human Factors vol48 no 1 pp 182ndash195 2006

[10] K Keay and I Simmonds ldquoThe association of rainfall andother weather variables with road traffic volume in melbourneaustraliardquo Accident Analysis Prevention vol 37 no 1 pp 109ndash124 2005

[11] L Qiu and W Nixon ldquoEffects of adverse weather on trafficcrashes systematic review and meta-analysisrdquo TransportationResearch Record Journal of the Transportation Research Boardpp 139ndash146 2008

[12] P Konstantopoulos P Chapman and D Crundall ldquoDriverrsquosvisual attention as a function of driving experience and visibil-ity Using a driving simulator to explore driversrsquo eye movementsin day night and rain drivingrdquo Accident Analysis amp Preventionvol 42 no 3 pp 827ndash834 2010

[13] K PMurphy ldquoThe bayes net toolbox forMATLABrdquoComputingScience and Statistics vol 33 no 2 pp 1024ndash1034 2001 httpwwwinterfacesymposiaorgI01I2001ProceedingsKMurphyKMurphypdf

[14] O Arsene I Dumitrache and IMihu ldquoMedicine expert systemdynamicBayesianNetwork andontology basedrdquoExpert Systemswith Applications vol 38 no 12 2011

[15] G Buyukozkan G Kayakutlu and I S Karakadılar ldquoAssess-ment of lean manufacturing effect on business performanceusing bayesian belief networksrdquo Expert Systems with Applica-tions vol 42 no 19 pp 6539ndash6551 2015

[16] H Mcheick H Nasser M Dbouk and A Nasser ldquoStrokeprediction context-aware health care systemrdquo in Proceedingsof IEEE First International Conference on Connected HealthApplications Systems and Engineering Technologies (CHASE)pp 30ndash35 Washington Wash USA 2016

[17] S Jensen ldquoPedestrian Safety in Denmarkrdquo TransportationResearch Record Journal of the Transportation Research Boardvol 1674 pp 61ndash69 1999

[18] M Stone and J Broughton ldquoGetting off your bike cyclingaccidents in great britain in 1990ndash1999rdquo Accident AnalysisPrevention vol 35 no 4 pp 549ndash556 2003

[19] D E Lefler andHCGabler ldquoThe fatality and injury risk of lighttruck impacts with pedestrians in the United Statesrdquo AccidentAnalysis Prevention vol 36 no 2 pp 295ndash304 2004

[20] O THolubowycz ldquoAge sex and blood alcohol concentration ofkilled and injured pedestriansrdquo Accident Analysis amp Preventionvol 27 no 3 pp 417ndash422 1995

[21] A S Al-Ghamdi ldquoPedestrianndashvehicle crashes and analyticaltechniques for stratified contingency tablesrdquo Accident AnalysisPrevention vol 34 no 2 pp 205ndash214 2002

[22] D Lord S P Washington and J N Ivan ldquoPoisson Poisson-gamma and zero-inflated regression models of motor vehicle


crashes balancing statistical fit and theoryrdquo Accident Analysisamp Prevention vol 37 no 1 pp 35ndash46 2005

[23] M Poch and F Mannering ldquoNegative binomial analysis ofintersection-accident frequenciesrdquo Journal of TransportationEngineering vol 122 no 2 pp 105ndash113 1996

[24] J-L Martin ldquoRelationship between crash rate and hourly trafficflow on interurbanmotorwaysrdquoAccident Analysis amp Preventionvol 34 no 5 pp 619ndash629 2002

[25] K-s Ng W-t Hung and W-g Wong ldquoAn algorithm forassessing the risk of traffic accidentrdquo Journal of Safety Researchvol 33 no 3 pp 387ndash410 2002

[26] L-Y Chang and W-C Chen ldquoData mining of tree-basedmodels to analyze freeway accident frequencyrdquo Journal of SafetyResearch vol 36 no 4 pp 365ndash375 2005

[27] G Lovegrove and T Sayed ldquoMacrolevel collision predictionmodels to enhance traditional reactive road safety improvementprogramsrdquoTransportationResearchRecord Journal of the Trans-portation Research Board pp 65ndash73 2007

[28] M J M Sullman M L Meadows and K B Pajo ldquoAberrantdriving behaviours amongst new zealand truck driversrdquo Trans-portation Research Part F Traffic Psychology and Behaviour vol5 no 3 pp 217ndash232 2002

[29] J-K Kim S Kim G F Ulfarsson and L A Porrello ldquoBicyclistinjury severities in bicyclemotor vehicle accidentsrdquo AccidentAnalysis amp Prevention vol 39 no 2 pp 238ndash251 2007

[30] P Savolainen andFMannering ldquoProbabilisticmodels ofmotor-cyclists injury severities in single- and multi-vehicle crashesrdquoAccident Analysis amp Prevention vol 39 no 5 pp 955ndash963 2007

[31] R K Young and J Liesman ldquoEstimating the relationshipbetween measured wind speed and overturning truck crashesusing a binary logit modelrdquoAccident Analysis amp Prevention vol39 no 3 pp 574ndash580 2007

[32] P M Kuhnert K-A Do and R McClure ldquoCombining non-parametric models with logistic regression an application tomotor vehicle injury datardquo Computational Statistics amp DataAnalysis vol 34 no 3 pp 371ndash386 2000

[33] J Abellan G Lopez and J de Ona ldquoAnalysis of traffic accidentseverity using decision rules via decision treesrdquo in ExpertSystems with Applications vol 40 pp 6047ndash6054 2013

[34] J de Ona R O Mujalli and F J Calvo ldquoAnalysis of traffic acci-dent injury severity on spanish rural highways using bayesiannetworksrdquo Accident Analysis Prevention vol 43 no 1 pp 402ndash411 2011

[35] S Heydari L FMiranda-Moreno D Lord and L Fu ldquoBayesianmethodology to estimate and update safety performance func-tions under limited data conditions A sensitivity analysisrdquoAccident Analysis Prevention vol 64 pp 41ndash51 2014

[36] A C Mbakwe A A Saka K Choi and Y-J Lee ldquoAlternativemethod of highway traffic safety analysis for developing coun-tries using delphi technique and Bayesian networkrdquo AccidentAnalysis amp Prevention vol 93 pp 135ndash146 2016

[37] K G Olesen and A L Madsen ldquoMaximal prime subgraphdecomposition of Bayesian networksrdquo IEEE Transactions onSystems Man and Cybernetics Part B (Cybernetics) vol 32 no1 pp 21ndash31 2002

[38] S Demissie M P LaValley N J Horton R J Glynn and L ACupples ldquoBias due to missing exposure data using complete-case analysis in the proportional hazards regression modelrdquoStatistics in Medicine vol 22 no 4 pp 545ndash557 2003

[39] R S Pilla and B G Lindsay ldquoAlternative EMMethods for Non-parametric Finite Mixture Modelsrdquo Biometrika vol 88 no 2

pp 535ndash550 2001 Retrieved from httpwwwjstororgstable2673498

[40] A Allan ldquoLand Use Planning and its Role in Transformingthe Adelaide-Gawler Line into a Transit Corridor of ConnectedTransit Oriented Developmentsrdquo in Paper presented at the 34thAustralasian Transport Research Forum (ATRF) ProceedingsAdelaide Australia 2011 httpwwwworldtransitresearchinforesearch4335

[41] Australian AssociatedMotor Insurers Limited ldquoAdelaidersquos mostdangerous accident hotspots revealedrdquo 2015 Retrieved fromhttpswwwaamicomauaami-answerspress-releasesadelaide-most-dangerous-accident-hotspots-revealedhtml

[42] R O Mujalli and J De Ona ldquoA method for simplifying theanalysis of traffic accidents injury severity on two-lane highwaysusing Bayesian networksrdquo Journal of Safety Research vol 42 no5 pp 317ndash326 2011

[43] A Gregoriades and K C Mouskos ldquoBlack spots identificationthrough a bayesian networks quantification of accident riskindexrdquo Transportation Research Part C Emerging Technologiesvol 28 pp 28ndash43 2013

[44] R O Mujalli G Lopez and L Garach ldquoBayes classifiersfor imbalanced traffic accidents datasetsrdquo in Accident AnalysisPrevention (Supplement C) vol 88 pp 37ndash51 URL https 2016

[45] A Iranitalab and A Khattak ldquoComparison of four statisticalandmachine learningmethods for crash severity predictionrdquo inAccident Analysis amp Prevention 108 (Supplement C) pp 27ndash362017

[46] J Cheng R Greiner J Kelly D Bell and W Liu ldquoLearningBayesian networks from data an information-theory basedapproachrdquoArtificial Intelligence vol 137 no 1-2 pp 43ndash90 2002

[47] E Desapriya I Pike and S Babul ldquoPublic attitudes epidemi-ology and consequences of drinking and driving in britishcolumbiardquo IATSS Research vol 30 no 1 pp 101ndash110 2006

[48] R Hingson and M Winter ldquoEpidemiology and consequencesof drinking and drivingrdquo Alcohol Research and Health vol 27no 1 pp 63ndash78 2003 httpspubsniaaanihgovpublicationsarh27-163-78htm

[49] Transport Canadarsquos Motor Vehicle Safety Directorate ldquoRoadSafety inCanadardquo 2011 Retrieved fromhttpswwwtcgccaengmotorvehiclesafetytp-tp15145-1201htm

[50] R Tay and S M Rifaat ldquoFactors contributing to the severity ofintersection crashesrdquo Journal of Advanced Transportation vol41 no 3 pp 244ndash265 2007

[51] E Hoareau N Candappa and B Corben ldquoIntersection SafetyMeeting Victoriarsquos Intersection Challengerdquo Stage 1 - Task 1ProblemDefinition vol 1 2011 httpwwwmonashedumuarcresearchour-publicationsmuarc316a

[52] K Keay and I Simmonds ldquoRoad accidents and rainfall in a largeAustralian cityrdquo Accident Analysis amp Prevention vol 38 no 3pp 445ndash454 2006

[53] L Symons and A Perry ldquoPredicting road hazards caused byrain freezing rain and wet surfaces and the role of weatherradarrdquoMeteorological Applications vol 4 no 1 pp 17ndash21 1997

[54] A M Rizwan L Y C Dennis and C Liu ldquoA review onthe generation determination and mitigation of Urban HeatIslandrdquo Journal of Environmental Sciences vol 20 no 1 pp 120ndash128 2008

[55] N Earl I Simmonds and N Tapper ldquoWeekly cycles in peaktime temperatures and urban heat island intensityrdquo Environ-mental Research Letters vol 11 no 7 Article ID 074003 p 102016


[56] S K Jusuf N H Wong E Hagen R Anggoro and YHong ldquoThe influence of land use on the urban heat island inSingaporerdquo Habitat International vol 31 no 2 pp 232ndash2422007

[57] D E Parker ldquoUrban heat island effects on estimates ofobserved climate changerdquo Wiley Interdisciplinary Reviews Cli-mate Change vol 1 no 1 pp 123ndash133 2010

[58] M Hosseinpour A S Yahaya and A F Sadullah Exploring theeffects of roadway characteristics on the frequency and severityof head-on crashes Case studies from Malaysian Federal RoadsAccident Analysis Prevention vol 62 pp 209ndash222 2014

[59] G H Bham B S Javvadi and U R RManepalli ldquoMultinomiallogistic regression model for single-vehicle and multivehiclecollisions on urban us highways in arkansasrdquo Journal ofTransportation Engineering vol 138 no 6 pp 786ndash797 2012

[60] M Rizzi J Strandroth and C Tingvall ldquoThe effectiveness ofantilock brake systems on motorcycles in reducing real-lifecrashes and injuriesrdquoTraffic Injury Prevention vol 10 no 5 pp479ndash487 2009

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



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Journal of

Advances inOptoElectronics


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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



engineers and road infrastructure designers are providedwith limited information for the accident mechanism and theformulation of improvement plans It is of great importanceto take full advantage of the traffic accident statistics andminepotential information so as to provide a basis for the analysisof accident mechanism and the improvement of road safety

Bayesian network is one of the effective methods in thefield of artificial intelligence to express uncertainty analysisand probability reasoning of a system It can exploit thedependence relationships based on local conditions in amodel to conduct bidirectional uncertainty investigation forprediction classification and diagnostic analyses At presentthere are some software platforms available for the con-struction of a Bayesian network such as Bayes Net Toolbox(BNT) BayesBuilder and JavaBayes of which the MATLAB-based BNT developed by Murphy [13] is extensively usedThis toolbox provides a lot of underlying basic functionlibraries for Bayesian network learning but it does notintegrate the basic functions for Bayesian network learninginto a system Moreover BNT does not have Graphical UserInterface (GUI) which is not user-friendly nor can it be wellgeneralized Netica is a Bayesian network learning softwaredeveloped by Norsys Software Corporation in Canada whichhas been extensively applied in uncertaintymanagement suchas business engineering medicine and ecology [14ndash16] dueto its powerful functions friendly GUI reliable computationand good performance In this paper a model is formulatedusing Bayesian network for road accident studies and then aBayesian network learning process posterior probability rea-soning most probable explanation and inferential analysisare conducted by using Netica

This paper is organized as follows Section 2 reviews therelated literature on causation analysis of road accidentsSection 3 describes the construction of a Bayesian networkmodel Section 4 presents a case study on Bayesian networkmodel application for Adelaide Central Business District(CBD) in South Australia the findings of this study aresummarized in Section 5

2 Literature Review

The use of causation theory for road accident analysis aimsto extract the accident mechanisms and accident modelsfrom a large number of typical accidents so as to providetheoretical basis for the qualitative and quantitative analysesthe predication and prevention of accidents and the improve-ment of safety management Scholars across the world havedone some researches in road accident causation analysis andvarious data sources variables sample sizes and analyticalmodels such as aggregated models which include FrequencyAnalysis [17ndash19] and 1205942 Test [20 21]

In terms of disaggregated models as the frequency ofroad accidents is in a form of nonnegative discrete andabnormal distribution and based on experience the frequencyof accidents follows Poisson distribution the Poisson regres-sion model can be applied to analyse the influence of eachrisk factor on the frequency of accidents [22] The negativebinomial distribution regression is based on Poisson distribu-tion but its specification error follows Gamma distribution

The negative binomial regression model has been extensivelyapplied in traffic safety analysis model [23ndash27] However theassumption that the mean value of Poisson distribution isequal to the variance is often inconsistent with realities Andin the analysis of longitudinal data samples the adoptions ofPoisson regression model and negative binomial regressionmodel are likely to generate biased estimate and even incor-rect results When the explained variables only take a limitednumber ofmultiple discrete values the established regressionmodel is a discrete choice model in which Logit model isthe earliest discrete choice model and is one of the widelyused models [28ndash31] For an applicable statistical modelresearch object is required to be in independent distributionwhile the safety data has a complex spatial distribution theaccuracy and robustness of safety level estimation will begreatly affected if the spatial feature is neglected

Through the review of the existing literature it has beendiscovered that past researches on the causation analysis oftraffic accidents are gradually evolving from the descriptivesimple analysis based on aggregated models to the multi-variable complex modeling analysis based on disaggregatedmodels However the deficiencies of the existing studiesare the following the influencing factors on accidents arenot fully considered most are based on specific isolatedsuperficial single-factor analysis considering only the maininfluence factors These studies revealed the inherent rules ofthe occurrence of accidents in one aspect or case but ignoredthe multidimensionality of accident relationships and theircorrelations so that the complex logical relationship betweencauses accident occurrence and accident consequence wasnot reflected Therefore research methods and analysis tech-nologies are not generally applicable Although some scholarsused Decision Tree [26 32 33] Bayesian network [34ndash36]and other complex systems to research the correlation betweenaccident causes the theoretical systems and related support-ing technologies have not been systematically established

3 Construction of Bayesian Network Model31 Basic Principles of Bayesian Network Bayesian networkalso referred to as belief network is considered as one of themost effective theoretical models in the fields of uncertaintyknowledge representation and reasoning It is a directedacyclic network topology consisting of node set and directededge and each node denotes one variable state while directededge denotes the dependence between variables The corre-lation intension or confidence coefficient between variablesis described by using Conditional Probability Table (CPT)Prediction diagnosis classification and other tasks can beachieved by using learning and statistical inference functionsof Bayes theorem Bayesian network uses probability todenote the uncertainty of all forms and uses the probabilisticrules to achieve learning and reasoning process It has thefollowing relationship

119901 (119883) = 119899prod119894=1

119901 (119883119894 | 119901119886119894) (1)

A set of variables 119883 = 1198831 1198832 119883119899 of Bayesian networkconsists of the following components [37] 119878 is a network


X1

X2

X3

X4

X5

X6

X7

X8













119875 (119863 | 119861119878) = 119899prod119894=1

score (119894 119901119886119894) (2)

where

score (119894 119901119886119894)= 119902119894prod119895=1

[ Γ (120597119894119895)Γ (120597119894119895 + 119873119894119895)

119903119894prod119896=1

Γ (120597119894119895119896 + 119873119894119895119896)Γ (120597119894119895119896) ] (3)




119896=1120597119894119895119896













where


119875 (119890lowast | 120579) = 119875 (119890lowast 120579)119875 (120579)

(6)


119864119875(119883|119890120579)119873119894119895119896 = sum119895119896

119875 (119883119894119895 120587 (119883119894119896) | 120579) (7)



ML

1205791015840119894119895119896 = 119864119875(119883|119890120579)119873119894119895119896sum1198961015840 119864119875(119883|119890120579)1198731198941198951198961015840 (8)

MAP

1205791015840119894119895119896 = 120572119894119895119896 + 119864119875(119883|119890120579)119873119894119895119896sum1198961015840 (1205721198941198951198961015840 + 119864119875(119883|119890120579)1198731198941198951198961015840) (9)



4 Case Studies






CBD

Adelaide




















Road




1 Wet 237 10232 Dry 2080 8977


Environment



Vehicle








Table 1 Continued


Road crash




2 Injury 569 2456







1 [0 5000) 1139 49162 [5000 10000) 795 34313 [10000 +infin) 383 1653

Road geometry

Vehicle movement


Light condition

Crash type


Weather condition


Traffic control

Total casualties


Vehicle type

Crash severity














Road



1 Wet 100 10792 Dry 827 8921


Environment



Vehicle








Table 2 Continued


Road crash




2 Injury 238 2567







1 [0 5000) 423 45632 [5000 10000) 342 36893 [10000 +infin) 162 1748


277617803155693259174246344208


215152259658128378124194291097193


108892


701930


707293


691260341150


455363181


680409523


963373


730270


172598187166597848208635


490119211140142131


515291604396


930563091042










1 2 3 4 5 6 7 8 9 10 110

1020304050607080


Prob

abili

ty d

istrib

utio

n (

)





01020304050607080

Prob

abili

ty d

istrib

utio

n (

)





0

10

20

30

40

50

60

Prob

abili

ty d

istrib

utio

n (

)















102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


698302


688267334108


443366191


680409523


965345


730270


418362474580362719150362


490119211140142131


100 00 0


890938130032



102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


708292


698258332107


442367191


680409523


966337


0100


374374374594374563162374


490119211140142131


100 00 0


890938130032






102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


1000+


1000


724276


714244323104


441369190


680409523


968323


0100


374374374633374374143374


490119211140142131


100000


890938130032



125799852449245906139246740330


512467606206268952566128188052185


909909


591941


841159


841159

0+ 0+


454377169


680409523


988120


746254


00

1000000 0


468103212106161138


525211577396


945410065080







125719123100

451728080342215569


561 100102451304215728158136079125


355100


355100


100219


100219

0+ 0+


100966324


155848 100


100178


100369


00

10000000


100264452312214211


100122117313


100302167322

















Road geometry





Crash type















References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










X1

X2

X3

X4

X5

X6

X7

X8













119875 (119863 | 119861119878) = 119899prod119894=1

score (119894 119901119886119894) (2)

where

score (119894 119901119886119894)= 119902119894prod119895=1

[ Γ (120597119894119895)Γ (120597119894119895 + 119873119894119895)

119903119894prod119896=1

Γ (120597119894119895119896 + 119873119894119895119896)Γ (120597119894119895119896) ] (3)




119896=1120597119894119895119896













where


119875 (119890lowast | 120579) = 119875 (119890lowast 120579)119875 (120579)

(6)


119864119875(119883|119890120579)119873119894119895119896 = sum119895119896

119875 (119883119894119895 120587 (119883119894119896) | 120579) (7)



ML

1205791015840119894119895119896 = 119864119875(119883|119890120579)119873119894119895119896sum1198961015840 119864119875(119883|119890120579)1198731198941198951198961015840 (8)

MAP

1205791015840119894119895119896 = 120572119894119895119896 + 119864119875(119883|119890120579)119873119894119895119896sum1198961015840 (1205721198941198951198961015840 + 119864119875(119883|119890120579)1198731198941198951198961015840) (9)



4 Case Studies






CBD

Adelaide




















Road




1 Wet 237 10232 Dry 2080 8977


Environment



Vehicle








Table 1 Continued


Road crash




2 Injury 569 2456







1 [0 5000) 1139 49162 [5000 10000) 795 34313 [10000 +infin) 383 1653

Road geometry

Vehicle movement


Light condition

Crash type


Weather condition


Traffic control

Total casualties


Vehicle type

Crash severity














Road



1 Wet 100 10792 Dry 827 8921


Environment



Vehicle








Table 2 Continued


Road crash




2 Injury 238 2567







1 [0 5000) 423 45632 [5000 10000) 342 36893 [10000 +infin) 162 1748


277617803155693259174246344208


215152259658128378124194291097193


108892


701930


707293


691260341150


455363181


680409523


963373


730270


172598187166597848208635


490119211140142131


515291604396


930563091042










1 2 3 4 5 6 7 8 9 10 110

1020304050607080


Prob

abili

ty d

istrib

utio

n (

)





01020304050607080

Prob

abili

ty d

istrib

utio

n (

)





0

10

20

30

40

50

60

Prob

abili

ty d

istrib

utio

n (

)















102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


698302


688267334108


443366191


680409523


965345


730270


418362474580362719150362


490119211140142131


100 00 0


890938130032



102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


708292


698258332107


442367191


680409523


966337


0100


374374374594374563162374


490119211140142131


100 00 0


890938130032






102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


1000+


1000


724276


714244323104


441369190


680409523


968323


0100


374374374633374374143374


490119211140142131


100000


890938130032



125799852449245906139246740330


512467606206268952566128188052185


909909


591941


841159


841159

0+ 0+


454377169


680409523


988120


746254


00

1000000 0


468103212106161138


525211577396


945410065080







125719123100

451728080342215569


561 100102451304215728158136079125


355100


355100


100219


100219

0+ 0+


100966324


155848 100


100178


100369


00

10000000


100264452312214211


100122117313


100302167322

















Road geometry





Crash type















References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















where


119875 (119890lowast | 120579) = 119875 (119890lowast 120579)119875 (120579)

(6)


119864119875(119883|119890120579)119873119894119895119896 = sum119895119896

119875 (119883119894119895 120587 (119883119894119896) | 120579) (7)



ML

1205791015840119894119895119896 = 119864119875(119883|119890120579)119873119894119895119896sum1198961015840 119864119875(119883|119890120579)1198731198941198951198961015840 (8)

MAP

1205791015840119894119895119896 = 120572119894119895119896 + 119864119875(119883|119890120579)119873119894119895119896sum1198961015840 (1205721198941198951198961015840 + 119864119875(119883|119890120579)1198731198941198951198961015840) (9)



4 Case Studies






CBD

Adelaide




















Road




1 Wet 237 10232 Dry 2080 8977


Environment



Vehicle








Table 1 Continued


Road crash




2 Injury 569 2456







1 [0 5000) 1139 49162 [5000 10000) 795 34313 [10000 +infin) 383 1653

Road geometry

Vehicle movement


Light condition

Crash type


Weather condition


Traffic control

Total casualties


Vehicle type

Crash severity














Road



1 Wet 100 10792 Dry 827 8921


Environment



Vehicle








Table 2 Continued


Road crash




2 Injury 238 2567







1 [0 5000) 423 45632 [5000 10000) 342 36893 [10000 +infin) 162 1748


277617803155693259174246344208


215152259658128378124194291097193


108892


701930


707293


691260341150


455363181


680409523


963373


730270


172598187166597848208635


490119211140142131


515291604396


930563091042










1 2 3 4 5 6 7 8 9 10 110

1020304050607080


Prob

abili

ty d

istrib

utio

n (

)





01020304050607080

Prob

abili

ty d

istrib

utio

n (

)





0

10

20

30

40

50

60

Prob

abili

ty d

istrib

utio

n (

)















102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


698302


688267334108


443366191


680409523


965345


730270


418362474580362719150362


490119211140142131


100 00 0


890938130032



102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


708292


698258332107


442367191


680409523


966337


0100


374374374594374563162374


490119211140142131


100 00 0


890938130032






102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


1000+


1000


724276


714244323104


441369190


680409523


968323


0100


374374374633374374143374


490119211140142131


100000


890938130032



125799852449245906139246740330


512467606206268952566128188052185


909909


591941


841159


841159

0+ 0+


454377169


680409523


988120


746254


00

1000000 0


468103212106161138


525211577396


945410065080







125719123100

451728080342215569


561 100102451304215728158136079125


355100


355100


100219


100219

0+ 0+


100966324


155848 100


100178


100369


00

10000000


100264452312214211


100122117313


100302167322

















Road geometry





Crash type















References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










CBD

Adelaide




















Road




1 Wet 237 10232 Dry 2080 8977


Environment



Vehicle








Table 1 Continued


Road crash




2 Injury 569 2456







1 [0 5000) 1139 49162 [5000 10000) 795 34313 [10000 +infin) 383 1653

Road geometry

Vehicle movement


Light condition

Crash type


Weather condition


Traffic control

Total casualties


Vehicle type

Crash severity














Road



1 Wet 100 10792 Dry 827 8921


Environment



Vehicle








Table 2 Continued


Road crash




2 Injury 238 2567







1 [0 5000) 423 45632 [5000 10000) 342 36893 [10000 +infin) 162 1748


277617803155693259174246344208


215152259658128378124194291097193


108892


701930


707293


691260341150


455363181


680409523


963373


730270


172598187166597848208635


490119211140142131


515291604396


930563091042










1 2 3 4 5 6 7 8 9 10 110

1020304050607080


Prob

abili

ty d

istrib

utio

n (

)





01020304050607080

Prob

abili

ty d

istrib

utio

n (

)





0

10

20

30

40

50

60

Prob

abili

ty d

istrib

utio

n (

)















102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


698302


688267334108


443366191


680409523


965345


730270


418362474580362719150362


490119211140142131


100 00 0


890938130032



102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


708292


698258332107


442367191


680409523


966337


0100


374374374594374563162374


490119211140142131


100 00 0


890938130032






102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


1000+


1000


724276


714244323104


441369190


680409523


968323


0100


374374374633374374143374


490119211140142131


100000


890938130032



125799852449245906139246740330


512467606206268952566128188052185


909909


591941


841159


841159

0+ 0+


454377169


680409523


988120


746254


00

1000000 0


468103212106161138


525211577396


945410065080







125719123100

451728080342215569


561 100102451304215728158136079125


355100


355100


100219


100219

0+ 0+


100966324


155848 100


100178


100369


00

10000000


100264452312214211


100122117313


100302167322

















Road geometry





Crash type















References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















Road




1 Wet 237 10232 Dry 2080 8977


Environment



Vehicle








Table 1 Continued


Road crash




2 Injury 569 2456







1 [0 5000) 1139 49162 [5000 10000) 795 34313 [10000 +infin) 383 1653

Road geometry

Vehicle movement


Light condition

Crash type


Weather condition


Traffic control

Total casualties


Vehicle type

Crash severity














Road



1 Wet 100 10792 Dry 827 8921


Environment



Vehicle








Table 2 Continued


Road crash




2 Injury 238 2567







1 [0 5000) 423 45632 [5000 10000) 342 36893 [10000 +infin) 162 1748


277617803155693259174246344208


215152259658128378124194291097193


108892


701930


707293


691260341150


455363181


680409523


963373


730270


172598187166597848208635


490119211140142131


515291604396


930563091042










1 2 3 4 5 6 7 8 9 10 110

1020304050607080


Prob

abili

ty d

istrib

utio

n (

)





01020304050607080

Prob

abili

ty d

istrib

utio

n (

)





0

10

20

30

40

50

60

Prob

abili

ty d

istrib

utio

n (

)















102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


698302


688267334108


443366191


680409523


965345


730270


418362474580362719150362


490119211140142131


100 00 0


890938130032



102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


708292


698258332107


442367191


680409523


966337


0100


374374374594374563162374


490119211140142131


100 00 0


890938130032






102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


1000+


1000


724276


714244323104


441369190


680409523


968323


0100


374374374633374374143374


490119211140142131


100000


890938130032



125799852449245906139246740330


512467606206268952566128188052185


909909


591941


841159


841159

0+ 0+


454377169


680409523


988120


746254


00

1000000 0


468103212106161138


525211577396


945410065080







125719123100

451728080342215569


561 100102451304215728158136079125


355100


355100


100219


100219

0+ 0+


100966324


155848 100


100178


100369


00

10000000


100264452312214211


100122117313


100302167322

















Road geometry





Crash type















References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table 1 Continued


Road crash




2 Injury 569 2456







1 [0 5000) 1139 49162 [5000 10000) 795 34313 [10000 +infin) 383 1653

Road geometry

Vehicle movement


Light condition

Crash type


Weather condition


Traffic control

Total casualties


Vehicle type

Crash severity














Road



1 Wet 100 10792 Dry 827 8921


Environment



Vehicle








Table 2 Continued


Road crash




2 Injury 238 2567







1 [0 5000) 423 45632 [5000 10000) 342 36893 [10000 +infin) 162 1748


277617803155693259174246344208


215152259658128378124194291097193


108892


701930


707293


691260341150


455363181


680409523


963373


730270


172598187166597848208635


490119211140142131


515291604396


930563091042










1 2 3 4 5 6 7 8 9 10 110

1020304050607080


Prob

abili

ty d

istrib

utio

n (

)





01020304050607080

Prob

abili

ty d

istrib

utio

n (

)





0

10

20

30

40

50

60

Prob

abili

ty d

istrib

utio

n (

)















102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


698302


688267334108


443366191


680409523


965345


730270


418362474580362719150362


490119211140142131


100 00 0


890938130032



102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


708292


698258332107


442367191


680409523


966337


0100


374374374594374563162374


490119211140142131


100 00 0


890938130032






102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


1000+


1000


724276


714244323104


441369190


680409523


968323


0100


374374374633374374143374


490119211140142131


100000


890938130032



125799852449245906139246740330


512467606206268952566128188052185


909909


591941


841159


841159

0+ 0+


454377169


680409523


988120


746254


00

1000000 0


468103212106161138


525211577396


945410065080







125719123100

451728080342215569


561 100102451304215728158136079125


355100


355100


100219


100219

0+ 0+


100966324


155848 100


100178


100369


00

10000000


100264452312214211


100122117313


100302167322

















Road geometry





Crash type















References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















Road



1 Wet 100 10792 Dry 827 8921


Environment



Vehicle








Table 2 Continued


Road crash




2 Injury 238 2567







1 [0 5000) 423 45632 [5000 10000) 342 36893 [10000 +infin) 162 1748


277617803155693259174246344208


215152259658128378124194291097193


108892


701930


707293


691260341150


455363181


680409523


963373


730270


172598187166597848208635


490119211140142131


515291604396


930563091042










1 2 3 4 5 6 7 8 9 10 110

1020304050607080


Prob

abili

ty d

istrib

utio

n (

)





01020304050607080

Prob

abili

ty d

istrib

utio

n (

)





0

10

20

30

40

50

60

Prob

abili

ty d

istrib

utio

n (

)















102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


698302


688267334108


443366191


680409523


965345


730270


418362474580362719150362


490119211140142131


100 00 0


890938130032



102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


708292


698258332107


442367191


680409523


966337


0100


374374374594374563162374


490119211140142131


100 00 0


890938130032






102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


1000+


1000


724276


714244323104


441369190


680409523


968323


0100


374374374633374374143374


490119211140142131


100000


890938130032



125799852449245906139246740330


512467606206268952566128188052185


909909


591941


841159


841159

0+ 0+


454377169


680409523


988120


746254


00

1000000 0


468103212106161138


525211577396


945410065080







125719123100

451728080342215569


561 100102451304215728158136079125


355100


355100


100219


100219

0+ 0+


100966324


155848 100


100178


100369


00

10000000


100264452312214211


100122117313


100302167322

















Road geometry





Crash type















References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Table 2 Continued


Road crash




2 Injury 238 2567







1 [0 5000) 423 45632 [5000 10000) 342 36893 [10000 +infin) 162 1748


277617803155693259174246344208


215152259658128378124194291097193


108892


701930


707293


691260341150


455363181


680409523


963373


730270


172598187166597848208635


490119211140142131


515291604396


930563091042










1 2 3 4 5 6 7 8 9 10 110

1020304050607080


Prob

abili

ty d

istrib

utio

n (

)





01020304050607080

Prob

abili

ty d

istrib

utio

n (

)





0

10

20

30

40

50

60

Prob

abili

ty d

istrib

utio

n (

)















102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


698302


688267334108


443366191


680409523


965345


730270


418362474580362719150362


490119211140142131


100 00 0


890938130032



102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


708292


698258332107


442367191


680409523


966337


0100


374374374594374563162374


490119211140142131


100 00 0


890938130032






102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


1000+


1000


724276


714244323104


441369190


680409523


968323


0100


374374374633374374143374


490119211140142131


100000


890938130032



125799852449245906139246740330


512467606206268952566128188052185


909909


591941


841159


841159

0+ 0+


454377169


680409523


988120


746254


00

1000000 0


468103212106161138


525211577396


945410065080







125719123100

451728080342215569


561 100102451304215728158136079125


355100


355100


100219


100219

0+ 0+


100966324


155848 100


100178


100369


00

10000000


100264452312214211


100122117313


100302167322

















Road geometry





Crash type















References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















1 2 3 4 5 6 7 8 9 10 110

1020304050607080


Prob

abili

ty d

istrib

utio

n (

)





01020304050607080

Prob

abili

ty d

istrib

utio

n (

)





0

10

20

30

40

50

60

Prob

abili

ty d

istrib

utio

n (

)















102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


698302


688267334108


443366191


680409523


965345


730270


418362474580362719150362


490119211140142131


100 00 0


890938130032



102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


708292


698258332107


442367191


680409523


966337


0100


374374374594374563162374


490119211140142131


100 00 0


890938130032






102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


1000+


1000


724276


714244323104


441369190


680409523


968323


0100


374374374633374374143374


490119211140142131


100000


890938130032



125799852449245906139246740330


512467606206268952566128188052185


909909


591941


841159


841159

0+ 0+


454377169


680409523


988120


746254


00

1000000 0


468103212106161138


525211577396


945410065080







125719123100

451728080342215569


561 100102451304215728158136079125


355100


355100


100219


100219

0+ 0+


100966324


155848 100


100178


100369


00

10000000


100264452312214211


100122117313


100302167322

















Road geometry





Crash type















References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












0

10

20

30

40

50

60

Prob

abili

ty d

istrib

utio

n (

)















102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


698302


688267334108


443366191


680409523


965345


730270


418362474580362719150362


490119211140142131


100 00 0


890938130032



102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


708292


698258332107


442367191


680409523


966337


0100


374374374594374563162374


490119211140142131


100 00 0


890938130032






102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


1000+


1000


724276


714244323104


441369190


680409523


968323


0100


374374374633374374143374


490119211140142131


100000


890938130032



125799852449245906139246740330


512467606206268952566128188052185


909909


591941


841159


841159

0+ 0+


454377169


680409523


988120


746254


00

1000000 0


468103212106161138


525211577396


945410065080







125719123100

451728080342215569


561 100102451304215728158136079125


355100


355100


100219


100219

0+ 0+


100966324


155848 100


100178


100369


00

10000000


100264452312214211


100122117313


100302167322

















Road geometry





Crash type















References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


698302


688267334108


443366191


680409523


965345


730270


418362474580362719150362


490119211140142131


100 00 0


890938130032



102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


108892


701930


708292


698258332107


442367191


680409523


966337


0100


374374374594374563162374


490119211140142131


100 00 0


890938130032






102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


1000+


1000


724276


714244323104


441369190


680409523


968323


0100


374374374633374374143374


490119211140142131


100000


890938130032



125799852449245906139246740330


512467606206268952566128188052185


909909


591941


841159


841159

0+ 0+


454377169


680409523


988120


746254


00

1000000 0


468103212106161138


525211577396


945410065080







125719123100

451728080342215569


561 100102451304215728158136079125


355100


355100


100219


100219

0+ 0+


100966324


155848 100


100178


100369


00

10000000


100264452312214211


100122117313


100302167322

















Road geometry





Crash type















References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











102285285285285671285285285285


0 0 0 0 0 0

100 0 0 0 0


1000+


1000


724276


714244323104


441369190


680409523


968323


0100


374374374633374374143374


490119211140142131


100000


890938130032



125799852449245906139246740330


512467606206268952566128188052185


909909


591941


841159


841159

0+ 0+


454377169


680409523


988120


746254


00

1000000 0


468103212106161138


525211577396


945410065080







125719123100

451728080342215569


561 100102451304215728158136079125


355100


355100


100219


100219

0+ 0+


100966324


155848 100


100178


100369


00

10000000


100264452312214211


100122117313


100302167322

















Road geometry





Crash type















References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











125719123100

451728080342215569


561 100102451304215728158136079125


355100


355100


100219


100219

0+ 0+


100966324


155848 100


100178


100369


00

10000000


100264452312214211


100122117313


100302167322

















Road geometry





Crash type















References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















Road geometry





Crash type















References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














References

































































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









A Bayesian Network Approach to Causation Analysis of Road...

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