an improved deep learning model for traffic crash...

Research ArticleAn Improved Deep Learning Model for Traffic Crash Prediction

Chunjiao Dong 123 Chunfu Shao12 Juan Li1 and Zhihua Xiong 1

1MOE Key Laboratory for Urban Transportation Complex Systems eory and Technology Beijing Jiaotong UniversityBeijing 100044 China2Key Laboratory of Industry of Big Data Application Technology for Comprehensive Transport Ministry of TransportBeijing Jiaotong University Beijing 100044 China3Center for Transportation Research Tickle College of Engineering University of Tennessee 600 Henley Street Knoxville37996 Tennessee USA

Correspondence should be addressed to Chunjiao Dong cjdongbjtueducn

Received 12 June 2018 Accepted 12 November 2018 Published 10 December 2018

Guest Editor Hamzeh Khazaei

Copyright copy 2018 ChunjiaoDong et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Machine-learning technology powersmany aspects of modern society Compared to the conventionalmachine learning techniquesthat were limited in processing natural data in the raw form deep learning allows computational models to learn representationsof data with multiple levels of abstraction In this study an improved deep learning model is proposed to explore the complexinteractions among roadways traffic environmental elements and traffic crashes The proposed model includes two modulesan unsupervised feature learning module to identify functional network between the explanatory variables and the featurerepresentations and a supervised fine tuning module to perform traffic crash prediction To address the unobserved heterogeneityissues in the traffic crash prediction a multivariate negative binomial (MVNB)model is embedding into the supervised fine tuningmodule as a regression layer The proposed model was applied to the dataset that was collected from Knox County in Tennesseeto validate the performances The results indicate that the feature learning module identifies relational information between theexplanatory variables and the feature representations which reduces the dimensionality of the input and preserves the originalinformationThe proposedmodel that includes theMVNB regression layer in the supervised fine tuningmodule can better accountfor differential distribution patterns in traffic crashes across injury severities and provides superior traffic crash predictions Thefindings suggest that the proposed model is a superior alternative for traffic crash predictions and the average accuracy of theprediction that was measured by RMSD can be improved by 8458 and 15827 compared to the deep learning model withoutthe regression layer and the SVMmodel respectively

1 Introduction

Road traffic injuries are a leading cause of preventable deathespecially for the young people In the United States trafficcrashes were the number one cause of death among peoplefrom 16 to 24 years old for each year from 2012 to 2014 [1]In 2015 the nation lost 35092 people in traffic crashes a 72-percent increase from 32744 in 2014 which is the largestpercentage increase in nearly 50 years [2]This is an average ofapproximately 96 people being killed on the nationrsquos roadwaysevery day of the year and an average ofmore than four peopleper hour In other words one person dies on roadways every15 minutes

To understand the relationship between the influencefactors and traffic crash outcomes with the extracted datafrom police reports and state highway-asset-managementdatabases the analyses of traffic safety estimate and predicatethe likelihood of a traffic crashThe number of crashes occur-ring on a defined spatial entity over a specific time period(for example the number of crashes per year occurring at aroadway intersection over a specified roadway segment orin a region) would be considered as the dependent variablesand some of the many factors affecting the likelihood ofa traffic crash are analyzed and examined (see [3ndash5] for acomprehensive review) Though more and more factors thatare relevant to the traffic crashes have been incorporated and

HindawiJournal of Advanced TransportationVolume 2018 Article ID 3869106 13 pageshttpsdoiorg10115520183869106

2 Journal of Advanced Transportation

the proposed models became more and more sophisticatedthere are still some factors that are not available to theresearchers and the models result in bias estimations anderroneous predictions In this study we proposed an innova-tive approach for traffic crash prediction which incorporatesa multivariate regression layer into a dynamic deep learningmodel that contains an unsupervised feature learningmoduleand a supervised fine tuning module governing the statedynamics to improve the performances of prediction

2 Literature Review

The statistical methodologies such as the Poisson negativebinomial (NB) and their variants in univariate andmultivari-ate regression frameworks have been successfully applied incrash count analyses [4 6ndash8] which attempt to deal with thedata and methodological issues associated with traffic crashestimations and predictions and enhance our understandingon the relationship between the influence factors and trafficcrash outcomes However current research in traffic safetyindicates that the applied statistical modeling fails whendealing with complex and highly nonlinear data [9] whichcould suggest that the relationship between the influencefactors and traffic crash outcomes is more complicated thancan be captured by a single statistical approach In additionmost of the statistical methods are based on some strongassumptions such as specifying a priori and the error dis-tribution Moreover a problematic issue is multicollinearityie the high degree of correlation between two or moreindependent variables Furthermore statistical models havedifficulty when dealing with outliers missing or noisy data[10]

To deal with the limitations of statistical methodologiesthe machine learning methods including Artificial NeuralNetwork (ANN) Support Vector Machine (SVM) modelsand deep learning models have been applied to varioustraffic safety problems and used as data analytic methodsbecause of their ability to work with massive amounts ofmultidimensional data In addition because of the modelingflexibility learning and generalization ability and good pre-dictive ability the machine learning has been considered asgeneric accurate and convenientmathematicalmodels in thefield of traffic safety

Because the commonly used Poisson or NB regres-sion models assume the predefined underlying relationshipbetween dependent and independent variables and the viola-tion of the assumption would lead to erroneous estimationANN and Bayesian neural network (BNN) models havebeen employed to analyze the traffic safety problems formany years Although both ANN and BNN models havesimilar multilevel network structures they are different inpredicting the outcome variables For ANN the weightsare assumed to fix However the weights of BNN followa probability distribution and the prediction needs to beintegrated over all the probability weights Basically the ANNcan be characterized by three features network architecturemodel of a neuron and learning algorithms Chang [11]compared the performances of NB regression model andANN in crash frequency analyses The results showed that

ANN is a consistent alternative method for analyzing crashfrequency Abdelwahab and Abdel-Aty [12] employed twowell-known ANN paradigms [the multilayer perceptron andradial basis functions (RBF) neural networks] to analyzethe traffic safety of toll plazas and evaluate the impacts ofelectronic toll collection (ETC) systems on highway safetyThe performance of ANN was compared with calibratedlogit models Modeling results showed that the RBF neuralnetwork was the best model for analyzing driver injuryseverity Xie Lord and Zhang [13] evaluated the applicationof BNN models for predicting traffic crashes by using datacollected on rural frontage roads in TexasThe results showedthat back-propagation neural network (BPNN) and BNNmodels perform better than the NB regression model interms of traffic crash prediction The results also showedthat BNNs could be used to address other issues in high-way safety such as the development of crash modificationfactors and enhance the prediction capabilities for evalu-ating different highway design alternatives Kunt Aghayanand Noii [14] employed a genetic algorithm (GA) patternsearch and ANN models to predict the severity of freewaytraffic crashes The results showed that the ANN providedthe best predictions Jadaan Al-Fayyad and Gammoh [15]developed a traffic crash prediction model using the ANNsimulation with the purpose of identifying its suitability forpredicting traffic crashes under Jordanian conditions Theresults demonstrated that the estimated traffic crashes areclose to actual traffic crashes Akin and Akbas [16] proposedan ANN model to predict intersection crashes in MacombCounty of the State of Michigan The predictive capabil-ity of the ANN model was determined by classifying thecrashes into these types fatal injury and property damageonly (PDO) crashes The results were very promising andshowed that ANN model is capable of providing an accurateprediction (909) of the crash types In summary thoughANN and BNNmodels show better linearnonlinear approx-imation properties than traditional statistical approachesthese models often cannot be generalized to other data sets[3]

The SVMmodels have recently been introduced for trafficsafety analyses [17 18] which are a new class of models thatare based on statistical learning theory and structural riskminimization [19] These models are supposed to approxi-mate any multivariate function to any desired degree of accu-racywith a set of related supervised learningmethods Li et al[17] evaluated the application of SVM models for predictingmotor vehicle crashes The results showed that SVM modelspredict crash data more effectively and accurately thantraditional NB models In addition the findings indicatedthat the SVM models provide better (or at least comparable)performance than BPNNmodels and do not over-fit the dataTo identify the relationship between severe crashes and theexplanatory variables and enhance model goodness-of-fitYu and Abdel-Aty [20] developed three models to analyzecrash injury severity which include a fixed parameter logitmodel a SVM model and a random parameter logit modelThe results showed that the SVM models and the randomparameter models provide superior model fits compared tothe fixed parameter logit model Findings also demonstrate

Journal of Advanced Transportation 3

that it is important to consider possible nonlinearity andindividual heterogeneitywhen analyzing traffic crashes Chenet al [21] employed the SVM models to investigate driverinjury severity patterns in rollover crashes using two-yearcrash data collected in New Mexico The results showed thatthe SVM models produce reasonable predictions and thepolynomial kernel outperforms the Gaussian RBF kernelDong Huang and Zheng [22] proposed a SVM model tohandle multidimensional spatial data in crash predictionThe results showed that the SVM models outperform thenonspatial models in terms of model fitting and predictiveperformance In addition the SVM models provide bettergoodness-of-fit compared with Bayesian spatial model withconditional autoregressive prior when utilizing the wholedataset as the samples Ren and Zhou [23] proposed a novelapproach that combines particle swarm optimization (PSO)and SVM for traffic safety predictionThe results showed thatthe predictions of PSO-SVM are better than that from BPneural network Yu and Abdel-Aty [24] proposed the SVMmodels with different kernel functions to evaluate real-timecrash risk The results showed that the SVMmodel with RBFkernel outperformed the SVM model with linear kernel andBayesian logistic regression model In addition the findingsshowed that smaller sample size could improve the classifi-cation accuracy of the SVM models and variable selectionprocedure is needed prior to the SVM model developmentOverall it has been found that the SVM models showedbetter or comparable results to the outcomes predicted byANNBNN and other statistical models [19] However likeANN and BNN the SVMmodels often cannot be generalizedto other data sets and they all tend to behave as black-boxes which cannot provide the interpretable parameters asstatistical models do

Other than the ANNBNN and SVM models othermachine learning methods have been introduced intraffic safety analyses Abdel-Aty and Haleem [25]introduced a recently developed machine learningtechniquemdashmultivariate adaptive regression splines (MARS)to predict vehicle angle crashes using extensive data collectedon unsignalized intersections in Florida The results showedthat MARS outperformed the NB models The proposedMARS models showed promising results after screeningthe covariates using random forest The findings suggestedthat MARS is an efficient technique for predicting crashes atunsignalized intersections

Deep learning is a recently developed branch of machinelearning method and has been successfully applied in speechrecognition visual object recognition object detection andmany other domains such as drug discovery and genomics[26 27] Compared to the conventional machine learningtechniques that were limited in their ability to process naturaldata in their raw form deep learning constructs compu-tational models aiming to extract inherent features in datafrom the lowest level to the highest level Though the deeplearning methods have shown outstanding performances inmany applications [26] the applications of deep learningin the field of transportation are relatively few and onlyfocusing on the topic of traffic flow prediction [28ndash30] Inthis study we proposed an improved deep learning model

for traffic crash prediction The proposed model includestwo modules an unsupervised feature learning module anda supervised fine tuning module To discover nonlinearrelationship between the investigated variables and identifythe impacts of influence factors on traffic crashes for roadwaynetwork a DAE model is proposed in the unsupervisedfeature learning module to learn the features of explana-tory variables In addition a multivariate negative binomial(MVNB) regression is embedding into the supervised finetuning module to address the heterogeneity issues Theproposed model performances are evaluated by comparingto the deep learning model without the MVNB layer andSVM models by using five-year data from Knox County inTennessee

3 The Modeling Framework Formulation

A novel model is proposed for the traffic crash predictionand Figure 1 illustrates the modeling framework The pro-posed model includes two modules One is the unsuper-vised feature learning module and another is the super-vised fine tuning module The obtained encoded featurerepresentations from the unsupervised feature module areused as the input for the supervised fine tuning mod-ule

31 Unsupervised Feature Learning Module Compared tothe commonly used deep learning architectures includingdeep belief network [31] stacked autoencoder [32] andconvolutional neural networks [27] the symmetrical neuralnetworks in an unsupervised manner have shown betterperformances which can automatically learn an appropriatesparse feature representation from the raw data [33] Theunsupervised feature learning module includes a denoisingautoencoder (DAE) model to learn the underlying struc-ture of the dynamic pattern among the characteristics ofroadway traffic and environment With the explanatoryvariables such as roadway geometric design features trafficfactors pavement factors and environmental characteristicsas the input the designed DAE model can identify thenonlinear relationship between the investigated variables inan unsupervised and hierarchical manner and the robustfeature representations can be obtained In addition thedesigned DAE model can encode the explanatory variablesinto an embedding low-dimensional space The proposedDAE model contains a visible layer a hidden layer an outputlayer and a reconstruction layer Unlike the conventionalDAE model with K hidden layers [34] the proposed modeluses a reconstruction error optimizing the output layer andthe noisy input layer to generate higher level representa-tions

Assume Φ = [k119894 u119894]119899119894=1 is a training set that containsn roadway entities where k119894 isin R119863 is the explanatoryvariable vector with dimension D and ui is the multi-variate traffic safety outcomes for roadway entity i Giventhe training set the proposed DAE model is trained todevelop a robust feature representation by reconstructing the


(1) Traffic factors(2) Roadway geometric design features(3) Pavement factors(4) Environmental characteristics(5) Crash data(6) Other data

Unsupervised feature learning

Supervised fine tuning

Feature representations

Traffic crash estimation and prediction

Input Visible layer Output

Reconstruction error

Hidden layer

Output layer

Input Output

Hidden Representation

Regression function

1

2

D

2

D

1

ℎ1

ℎ2

ℎj

ℎF

x1

x2

xp

x1

x2

xp

x1

x2

xp

ℎ1

ℎ2

ℎj

ℎF

yi1

yi2

yim

yi1

yi2

yim

Figure 1 Flowchart of the proposed model for traffic crash prediction

input vi from its noisy corrupted version V119894 as shown inFigure 1

There are D units in the visible layer and F units in thehidden layer and the proposed model can be defined by aparameter set Θ = W a b c where W = [119882119894119895] isin R119863times119865 isthe interlayer connection weights a = [119886119894] isin R119863 is the visibleself-interactions or biases b = [119887119895] isin R119865 is the hidden biasesand c = [119888119896] isin R119870 is the reconstruction error The jointprobability distribution between the noisy input variables and

hidden variables is defined as

119875 (k h Θ) = 1119885 (Θ) exp [minus120576 (k h Θ)] (1)

where 120576(k h Θ) is an energy function defined by symmet-ric interactions between the noisy input variable hiddenvariables and a set of interaction parameters Θ Z(Θ) is anormalized factor


For a binary variable a Bernoulli-Bernoulli energy func-tion [34 35] and the conditional distribution of a singlestochastic hidden variable are given by

120576 (k h Θ) = k119879Wh minus a119879k minus b119879h119875 (ℎ119895 = 1 | k Θ) = 1

1 + exp [minus (119887119895 + sum119863119894=1119882119894119895V119894)](2)

For a continuous variable a Gaussian-Bernoulli energyfunction [31] and the conditional distribution of a singlestochastic hidden variable are given by

120576 (k h Θ) = minusk1015840119879Wh + a1015840119879a1015840 minus b119879h119875 (ℎ119895 = 1 | k Θ) = 1

1 + exp [minus (119887119895 + sum119863119894=1 (119882119894119895V119894120590119894))](3)

where k1015840 = (V11205901 V21205902 sdot sdot sdot V119894120590119894 sdot sdot sdot V119863120590119863)119879 a1015840 = ((V1 minus1198861)1205901 (V2minus1198862)1205902 sdot sdot sdot (V119894minus119886119894)120590119894 sdot sdot sdot (V119863minus119886119863)120590119863) and 120590119894is the standard deviation of the i-th visible variable vi centeredon the bias ai

The conditional distribution over hidden units can befactorized and computed by

119875 (h | k Θ) = 119865prod119895=1

119875 (ℎ119895 | k Θ) (4)

To estimate the parameters the method proposed byHjelm et al [35] which maximizes the log-likelihood ofthe marginal distribution of the hidden units to find thegradient of the log-likelihood is employed in this researchTo simplify the estimation process the free energy in termsof the probability at a data point vn can be used to replace theenergy function and the gradient has the following form

120597120597Θ sumkisin119863 log119901 (k) = minussumkisin119863⟨120597120597Θ120593 (k h Θ)⟩

119901(h|kΘ)

+ sumkisin119863⟨ 120597120597Θ120593 (k h Θ)⟩

119901(kh|Θ)

(5)

where 120593(k h Θ) = minus logsumℎ exp[minus120576(k = k119899 h Θ)] and theconditional distribution over hidden units should be replacedby a loss function

120593 (h | k119899) =

minusa119879k119899 minus 119865sum119895=1

log [1 + exp (k119879119899119882119895 + 119887119895)] k119899 is binary

minus 1003817100381710038171003817a minus k11989910038171003817100381710038172 minus119865sum119895=1

log [1 + exp (k119879119899119882119895 + 119887119895)] k119899 is continuous(6)

Considering the hidden layer as the input layer for theoutcome layer and outcome layer as the hidden layer thejoint probability distribution between the hidden variablesand outcome variables energy function the conditional dis-tributions of the outcome variables and units and parameterestimation process can be obtained as those for hiddenlayer The model will stop training when ck satisfies thereconstruction error requirements or the dimension of thefeature representation achieves the designed goals

32 Supervised Fine Tuning Module The supervised finetuning module is a supervised fine tuning procedure thatincludes a regression layer on the top of the resulting hiddenrepresentation layers to estimate the likelihood of the crashoccurrences as shown in Figure 1 The obtained encodedfeature representations from the unsupervised feature mod-ule are used as the input for the supervised fine tuningmodule To jointly estimate the occurrence likelihood formore than one type of crashes simultaneously and addressthe potential heterogeneity issues in the interdependent crashdata amultivariate negative binomial (MVNB)model is usedin the supervised fine tuning module to estimate and predictthe traffic crashes across injury severities Assume yi=(yi1yi2 yim)1015840 is a vector of crash occurrence likelihood forroadway entities i which includes m types of crashes The

particular NB regression model employed in this study hasthe following form

119901 (119910119894119895)= Γ (120582119894119895120590 + 119910119894119895)Γ (120582119894119895120590) Γ (119910119894119895 + 1) (

11 + 120590)120582119894119895120590 ( 1205901 + 120590)

119910119894119895 (7)

where Γ(sdot) is the gamma function yij is the crash number ofcrash type j for roadway segment i and E[yij]=120582ij=exp(120573119895X119894119895+120576119894119895) exp(120576119894119895) is a multivariate gamma-distributed error termwith mean 1 and variance 120572minus1

As described in Shi and Valdez [36] and Anastasopouloset al [37] with the expected number of crashes120582ij theMVNBmodel has a joint probability function

119901 (1199101119895 1199102119895 sdot sdot sdot 119910119894119895)= min(1199101119895 1199102119895sdotsdotsdot 119910119894119895)sum

119896=0

119901 (119896) 119873prod119894=1

119901 (119910119894119895 minus 119896)(8)

The model parameters can be estimated by maximizing thelog-likelihood function


119871 = sum119894119895

log [Γ (120590minus1 + 119910119894119895)] minus log [Γ (120590minus1)] minus log (119910119894119895)

minus120590minus1 ln [1 + 120590 exp (120573119895X119894119895)] minus 119910119894119895 log [1 + 120590minus1 exp (120573119895X119894119895)]

(9)

The MVNB regression layer is added on the top ofthe resulting hidden representation layers to perform trafficcrash prediction This yields a deep learning model tailoredto a task-specific supervised learning Then we fine tunethe module 2 using backpropagation by minimizing thefollowing cost function

119891 (120579)= minus1119899

119899sum119894=1

119898sum119895=1

119904 (1199101015840119894119895 = 119910119894119895) log[ exp (ℎ120579 (119909119894))sum119865119897=1 exp (ℎ120579 (119909119894))]

+ 1205722119901 [10038171003817100381710038171003817119882119903119890119892119903119890119904119904119894119900119899100381710038171003817100381710038172

119865+ 119865sum119897=1

100381710038171003817100381711988211989710038171003817100381710038172119865](10)

where s(sdot) is an indicator function if yijrsquo=yij then s(sdot)=1otherwise s(sdot)=0 120572 is a regularization parameter and 119865 isthe Frobenius normThe first term refers to the cross entropyloss for the regression layer the second term is the weightdecay penalty and ℎ120579(119909119894) is the output of deep learning foran input 119909119894rsquo

The cost function isminimized with amin-batch gradientdescent algorithm [27] The parameters in module 2 120579 =W119897 bW119903119890119892119903119890119904119904119894119900119899 are estimated by initializing the weightsW119903119890119892119903119890119904119904119894119900119899 of the regression layer to small random valuesand the weights of the F hidden layers are initialized bythe encoding weights obtained in the unsupervised featurelearning module

4 Data

Thedata are obtained from the Tennessee Roadway Informa-tion Management System (TRIMS) and the Pavement Man-agement System (PMS) which are maintained by the Ten-nessee Department of Transportation (TDOT) The datasetincludes crash data traffic factors geometric design featurespavement factors and environmental characteristics Thetraffic geometric pavement and environmental characteris-tics are linked to the crash data through the common variableid number An extensive and comprehensive data screeningthat includes cleaning consistency and accuracy checks isprocessed and performed to ensure the data are useablereliable and valid for the analyses After the initial datascreening in total 635 roadway segments in Knox County arechosen for the analyses For the selected roadway segmentseach of them has a completed dataset that links to thecrash data In other words the dataset contains detailedinformation on traffic factors geometric design featurespavement characteristics and environment factors

In TRIMS the crash data have been classified into fivecategories fatal crashes incapacitating injury crashes nonin-capacitating injury crashes possible-injury crashes and PDO

crashes Because the category of fatal crashes has only a fewobservations the categories of fatal crashes and incapacitat-ing injury crashes have been combined and referred to asmajor injury crashes The possible-injury crashes and PDOcrashes have been combined and referred to as no-injurycrashes The nonincapacitating injury crashes are referred toas minor injury crashes A few of pervious literature [38ndash40]has used a similar classification for injury outcomes For thoseselected 635 roadway segments from 2010 to 2014 a total of5365 traffic crasheswere reported by the police officers whichinclude 135 (251)major injury crashes 1312 (2446)minorinjury crashes and 3917 (7302) PDO crashes Individualroadway segment experienced from 0 to 23 crashes peryear with a mean of 154 and a standard deviation of 189As expected a significant amount of zeros is observedThe dependent variables and their descriptive statistics areshown in Table 1 The descriptive statistics of continuousindependent variables and categorical independent variablesare shown in Tables 1 and 2 respectively

The considered traffic factors include the logarithm ofannual average daily traffic (AADT) per lane truck traf-fic percentage and posted speed limits Roadway segmentAADT per lane from 2010 to 2014 varies from 851 to 32359vehicles with a mean of 338844 and a standard deviationof 549541 Other than the TRIMS dataset maintained by theDDOT traffic flow information can be obtained from httpswwwtdottngovAPPLICATIONStraffichistory which is anAADT map providing traffic volumes based on a 24-hourtwo-directional count at a given location The website alsoprovides the traffic history of any specific count station Thevariable of posted speed limit has a mean of 3865 and astandard deviation of 669 with a minimum value of 30 anda maximum value of 70 The truck traffic percentage variesfrom 1 to 33 with a mean of 671 and a standard deviation of498

Important measurements of geometric design featuresconsidered in this study include segment length degreeof horizontal curvature median widths outsider shoulderwidths number of through lanes lane widths number ofleft-turn lanes median types and shoulder type Amongthem the segment length degree of horizontal curvaturemedian widths and outsider shoulder widths are consideredas the continuous variables and the others are consideredas the categorical variables Other than the traffic factorsand geometric design features the impacts of pavementsurface characteristics are considered to better address trafficsafety issues for roadway design and maintenance Theconsidered pavement surface characteristics include inter-national roughness index (IRI) and rut depth (RD) Theanalyzed IRI varies from 2545 to 18258 with a mean of6585 and a standard deviation of 2775 which is calculated


Table 1 Summary statistics of analyzed continuous variables

Variable Mean Std Dev Min MaxIndependent variableThe number of major injury crashes per year per roadway segment 004 032 0 3The number of minor injury crashes per year per roadway segment 041 054 0 9The number of no injury crashes per year per roadway segment 123 174 0 22Traffic factorsThe logarithm of AADT per lane 353 374 293 451Truck traffic percentage 671 498 1 33Posted speed limits 3865 669 30 70Geometric design featuresSegment length (miles) 081 103 002 1231Degree of horizontal curvature 151 323 0 1400Median widths 112 202 0 12Outside shoulder widths 306 188 352 8Pavement factorsInternational roughness index 6585 2775 2545 18258Rut depth (in) 013 005 006 041

Table 2 Summary statistics of analyzed categorical variables

Variable Category Frequency PercentGeometric design featuresNumber of through lanes 3 585 1843

2 1660 52281 930 2929

Lane widths (ft) 12 915 288211 1650 519710 610 1921

Number of left-turn lanes 2 920 28981 650 20470 1605 5055

Median type 1 for non-traversable median 1185 37320 for traversable median 1990 6268

Shoulder type 2 for pavement 760 23941 for gravel 1595 50240 for dirt 820 2583

Environmental factorsTerrain type 1 for mountainous 1206 3797

0 for rolling 1969 6203Land use type 2 for residential 1622 5110

1 for commercial 775 24410 for rural 778 2449

Indicator for lighting 1 for lighting exists on the roadway segments 1304 41060 for others 1871 5894

using a quarter-car vehicle math model and the response isaccumulated to yield a roughness index with units of slope(inmi) Another pavement condition indicator is the RDwhich is measured at roadway speeds with a laserinertialprofilograph The analyzed RD varies from 006 to 041 witha mean of 013 and a standard deviation of 005

The environmental factors including terrain types light-ing condition and land use type are considered Two terraintypes are examined which include rolling terrace (6203)and mountainous terrace (3797) Lighting condition wasconsidered as a category variable which indicated whetherlighting devises are provided at the roadway segments


Three types of land use are considered including commer-cial (2441) rural (2449) and residential (5110) Thesevariables are considered because they might have potentialsignificant effects on traffic safety

5 Modelling Results

The MATLAB was employed for model development Four-year data from 2010 to 2013 were used as the training setand one-year data the year of 2014 were used as the testingset In order to obtain the model with superior performancemodule 1 was developed using 9 Gaussian visible units 13binary visible units and a number of hyperbolic tangenthidden units ranging from 32 to 128 in steps of 2 Thenumber of hidden units was setting based on two rulesgreater than the input data dimensionality and the powers oftwo The parameters for learning rate and weight decay wereselected to optimize reduction of reconstruction error overtraining Module 1 was trained with a sample size of 2540(four-year crash data) to allow for full convergence of theparametersThe input data were processed by using module 1to capture the relationship between traffic factors geometricdesign features pavement conditions and environmentalcharacteristics Module 2 was developed using 4 Gaussianvisible units and a number of hyperbolic tangent hiddenunits The initial number of hyperbolic tangent hiddenunits ranging from 8 to 32 was tested and examined Thelearning procedure will stop when the number of featurerepresentations is achieved to four or the reconstruction erroris less than 001

51 Results of Unsupervised Feature Learning Module Forthe final model the reconstruction error is less than 001and four hidden layers are included The weights betweenthe input layer and output layer can be calculated asW32times16W16times8W8times4=W32times4 The results are shown in Table 3The negative sign represents a crash-prone condition and apositive sign represents a safe-prone condition The valuednumber indicates an evaluation score Because the featurelearning module identifies relational information betweeninput variables and output feature representations the con-nection weights between visible units and hidden units canbe interpreted as the functional networks [35] The resultsshow that each of the output units is significant associatedwith traffic factors geometric factors pavement factors andenvironmental factors

Since the proposed feature learning module has sym-metric connection between visible and hidden layers andthe units in both layers have the probabilistic characteristicsthe proposed feature learning module also can be called asan auto-encoder Thus the values of output units can beinterpreted as a feature representation and the results areshown in Table 4 The number of output units is smallerthan the number of visible units which indicates the featurerepresentation with the values of output units has reduced thedimensionality of the input but still preserving the originalinformation Hence the four output units are defined as traf-fic feature representation geometric feature representation

pavement feature representation and environmental featurerepresentation

The results show that the signs of themeans of four featurerepresentations are negative which indicate that the featurerepresentations are associated with crash-prone condition Inother words the current traffic geometric pavement andenvironmental features are the main factors that attribute tothe risk of crash occurrences The findings indicate that thetraffic geometric pavement and environmental factors havea direct influence on traffic safety and need to be improved

The traffic feature representations have a wide range witha minimum value of -4420 and a maximum value of 6650which indicate the traffic factors have a significant impacton traffic safety The pavement factors have comparativeimpacts on traffic safety with a minimum value of -12076and a maximum value of 6753 The ranges of geometricand environmental feature representations are from -1386 to1280 and from -1805 to 0847 respectively which indicatethat the geometric and environmental feature representationshave comparative effects on traffic safety Compared to thosecrash modeling techniques that use only geometric designfeatures as the input factors the current research revealsnew insights that would benefit the development of updatedguidelines

52 Results of the Supervised Fine Tuning Module For thesupervised fine tuning module the visible units of theinput layer use the feature representations as the input andthe crash counts across injury severities are used as thetraining target The aggregate weights between the inputlayer and output layer are shown in Table 5 The resultsshow that the traffic and geometric feature representationshave positive effects and pavement and environmental featurerepresentations have negative effects on traffic crashes acrossinjury severities The findings indicate that decreasing thevalues of traffic and geometric feature representations willincrease the likelihood of crashes and increasing the valuesof geometric and environmental feature representations willincrease the likelihood of crashes The comparison resultsshow that traffic feature representation and geometric featurerepresentation have significant impact on PDO crashes Thepavement feature representation and environmental featurerepresentation have significant impact on minor injurycrashes Among four feature representations the geometricfeature representation pavement feature representation andtraffic feature representation have most direct impacts onmajor injury minor injury and PDO crashes respectively

Considering the data in the year of 2014 as the inputvariables the developed deep learning model is used topredict the crash counts for the year of 2014 To validatethe superiority of the proposed models the predicted resultsare compared to the observed values In addition a deeplearning model without the regression layer and a supportvector machine (SVM) model are also developed to predictcrash counts across injury severities There are two key issuesrelated to the development of SVR models kernel selectionand parameters optimization To address the nonlinear rela-tionship between the outcomes and attributes the commonly


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vironm

entalfeature

representatio

nTraffi

cfactor

Thelogarith

mof

AADTperlane

-052

9-0007

-0016

-0034

Trucktraffi

cpercentage

-0659

-0002

-0024

-0010

Poste

dspeedlim

its-0030

-0010

0175

-0047

Geometricfactors

Segm

entlength(m

iles)

000

7-0580

-0007

-0003

Degreeo

fhorizon

talcurvature

0002

-0918

-0006

-0009

Medianwidths

0002

0826

006

80015

Outsid

esho

ulderw

idths

000

50419

0016

006

4Num

bero

fthrou

ghlanes

3lanes

-0021

-0891

-0006

-0026

2lanes

-0015

-0864

-0022

-0060

Lane

widths

12ft

000

40776

000

5000

111ft

000

90592

0076

000

4Num

bero

fleft

-turn

lanes

2left-turn

lanes

-0003

-0212

-0019

-0017

1left

-turn

lane

0002

-0783

0028

0016

Mediantype

Non

-traversablem

edian

0013

0247

000

6000

7Sh

oulder

type

Pavement

-0035

-014

4-0027

-0016

Gravel

000

5-074

30011

006

0Pa

vementfactor

Internationalrou

ghnessindex(in

mile)

0101

000

7-018

3-0001

Rutd

epth

(in)

-0004

-0004

-0341

-0038

Environm

entalfactor

Terraintype

Mou

ntaino

us-0014

-0011

-0010

-0954

Land

usetype

Resid

entia

l004

20015

0011

0847

Com

mercial

0058

000

1000

6-0915

Indicatorfor

lighting

Ligh

tingexistso

nroadway

0018

000

80027

0781


Table 4 Summary statistics of feature representations

Statistics Mean Std Dev Min MaxTraffic feature representation -0697 1464 -4420 6650Geometric feature representation -1620 0521 -1386 1280Pavement feature representation -5388 2441 -12076 6753Environmental feature representation -2167 0442 -1805 0847

Table 5 The functional network between the feature representation and different crash types

Variable Major injury crashes Minor injury crashes PDO crashesTraffic feature representation -0109 -0421 -1535Geometric feature representation 0129 0261 0539Pavement feature representation -0033 -0872 -0315Environmental feature representation 0113 0298 0146

used RBF kernel is chosen to develop the SVM model Toprecisely reflect the performance on regressing unknowndata and prevent the overfitting problem the k-fold cross-validation approach is employed for optimizing the twoparameters in RBF kernelsmdashC and 120576 [41 42] The optimizedparameters are (4230 3709) and the optimized SVM modelyields to a training mean absolute error (MAE) less than001 and a training root-mean-squared deviation (RMSD) lessthan 5

To evaluate the accuracy and reliability of the predictionresults the predicted means for each injury severity level bythe proposed model the deep learning model without theregression layer and the SVM model are compared to theobservedmeans and two evaluationmeasures are used whichinclude MAE and RMSD The comparison and validationresults are shown in Table 6 Results in Table 6 indicate thatthe predicted means from the proposed model (0110 05731335 and 2019 for major injury minor injury no-injuryand all crashes respectively) are very close to the observedmeans (0096 0556 1306 and 1986) We believe that avery importation feature of the proposed model is that theincluded regression layer can provide a good estimate of thechance that the roadway segment is in the crash-free state orsome crash-prone propensity states

For all the observed samples the proposed model resultsin a MAE of 0030 0080 0071 and 0150 and a RMSD of17298 29961 27206 and 43652 for major injuryminor injury PDO and all crashes respectively The deeplearning mode without the regression layer results in a MAEof 0043 0202 0405 and 0520 and a RMSD of 2062051741 65086 and 82862 for major injury minorinjury PDO and all crashes respectively The SVM modelresults in a MAE of 0055 0257 0471 and 0660 and aRMSD of 26022 61350 72416 and 96636 for majorinjury minor injury PDO and all crashes respectively Theresults suggest that the proposed model predicts better thanthe deep learning model without the regression layer and theSVM model In summary compared to the deep learningmodel without the regression layer and the SVM model the

proposed model results in the smallest prediction MAE andRMSD no matter for the crash types across injury severitiesWe hypothesize that the proposed model better addresses theissue of heterogeneity and allows for excess zero counts incorrelated data

The findings indicate that the predictions from the pro-posed model have significant improvements over all com-parison models in both accuracy and robustness The best-performing result of the proposed model for major injurycrashes has a MAE of 0030 which indicates an 42105 and84211 improvement from the deep learning model withoutthe regression layer and the SVM model respectively Theproposedmodels performworse for theminor injury crasheswith a 0080 RMSD for all observed samples However itis still better than the evaluation measurements from thedeep learning model without the regression layer and theSVM model which are 0202 and 0257 respectively Thisrepresents a MAE improvement of 150980 and 219608for minor injury crash prediction For the PDO crashesthe MAE improvements of the proposed models over thecomparison models range from 471111 to 564444 Forall the observed samples the MAE improvements rangefrom 247368 to 341053 Clearly the improvement issignificant for the traffic crash predictions Therefore theproposed model seems to be a better alternative for crashcount predictions

The proposed model has better performances in termsof small error variances than the comparison models sincethe regression model is imbedding into the proposed modelThe overall performances of the proposed model for allcrashes show an 89824 RMSD improvement over the deeplearning mode without regression layer and an 121378RMSD improvement over the SVMmodel It is clear that thepredictions obtained from the proposed models are superiorto those obtained from the comparison models The greatestdifference is demonstrated for the PDO crashes where theproposed model yields a RMSD of 27206 compared to a65086 RMSD value from the deep learning model withoutthe regression layer and a 72416 RMSD value from the


Table 6 Results of roadway segment crash count prediction

Major injury Minor injury No injury TotalObservation mean 0096 0556 1306 1986Proposed model

Estimated mean 0110 0573 1335 2019MAE 0030 0080 0071 0150RMSD () 17298 29961 27206 43652

Deep learning model without the regression layerEstimated mean 0101 0556 1332 1989MAE 0043 0202 0405 0520RMSD () 20620 51741 65086 82862

SVMmodelEstimated mean 0101 0513 1329 1943MAE 0055 0257 0471 0660RMSD () 26022 61350 72416 96636

SVM model The differences in the proposed model and theSVM model for the minor injury crashes are also significant(29961 versus 61350)

6 Conclusions

Because traffic crashes are a big concern of the publicagencies and policy makers and result in countless fatalitiesand injuries there is a need to perform a comprehensiveanalysis that aims to understand the relationship between theinfluence factors and traffic crash outcomes In this study wepresented an innovative approach for traffic crash predictionMethodologically we demonstrated a novel deep learningtechnique embedded within a multivariate regression modelcan be used to identify relationship between the examinedvariables and the traffic crashes Future applications of thisapproach have the potential to provide insights into basicquestions regarding roadway spatial and temporal dynamicfunction and practical questions regarding countermeasuresThe investigation results provide sufficient evidence for thefollowing conclusions(1) The results show that the feature learning moduleidentifies relational information between input variables andoutput feature representations The findings indicate that thefeature representations have reduced the dimensionality ofthe input but still preserving the original information(2)Theproposedmodel that includes aMVNB regressionlayer in the supervised fine tuning module can better accountfor different patterns in crash data across injury severitiesand provide superior traffic crash predictions In additionthe proposed model can perform multivariate estimationssimultaneously with a superior fit(3) The proposed model has superior performances interms of prediction power compared to the deep learningmodel without a regression layer and the SVM model Theoverall performances of the proposed model for all crashesshow an 89824RMSD improvement over the deep learningmodel without a regression layer and an 121378 RMSDimprovement over the SVM model

(4) The findings suggest that the proposed model is asuperior alternative for traffic crash predictions The pro-posed model can better account for heterogeneity issues intraffic crash prediction

Theproposedmodels can perform traffic crash predictionfor a given facility The proposed methodology could beapplied to other roadway networks if appropriate attributevariables are available Traffic and transportation engineeringagencies can employ the proposed models with relative casesand develop them to their needs to obtain traffic crashpredictions for various time periods Further investigationof the proposed models includes the predictions of spatial-temporal dynamic pattern in crash data

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

Special thanks are due to TDOT for providing the TRIMSdata This research is supported by funding provided bythe Southeastern Transportation Centermdasha Regional UTCfunded by the USDOTmdashResearch and Innovative Technol-ogy Administration Additional funding was provided by theNational Natural Science Foundation of China (Grant Nos51678044 51338008 71621001 71210001 and 71501011)

References

[1] NHTSA Motor Vehicle Traffic Crashes as a Leading Cause ofDeath in the United States 2012-2014 Department of Trans-portation National Highway Traffic Safety AdministrationTraffic Safety Facts DOT HS 812 297 2016


[2] NHTSA 2015 Motor Vehicle Crashes Overview US Depart-ment of Transportation National Highway Traffic SafetyAdministration Traffic Safety Facts DOT HS 812 318 2016

[3] D Lord and F Mannering ldquoThe statistical analysis of crash-frequency data a review and assessment of methodologicalalternativesrdquo Transportation Research Part A Policy and Prac-tice vol 44 no 5 pp 291ndash305 2010

[4] F L Mannering and C R Bhat ldquoAnalytic methods in accidentresearch methodological frontier and future directionsrdquo Ana-lytic Methods in Accident Research vol 1 pp 1ndash22 2014

[5] F L Mannering V Shankar and C R Bhat ldquoUnobservedheterogeneity and the statistical analysis of highway accidentdatardquo Analytic Methods in Accident Research vol 11 pp 1ndash162016

[6] J C Milton V N Shankar and F L Mannering ldquoHighwayaccident severities and the mixed logit model an exploratoryempirical analysisrdquo Accident Analysis amp Prevention vol 40 no1 pp 260ndash266 2008

[7] C Dong D B Clarke X Yan A Khattak and B Huang ldquoMul-tivariate random-parameters zero-inflated negative binomialregression model an application to estimate crash frequenciesat intersectionsrdquo Accident Analysis amp Prevention vol 70 pp320ndash329 2014a

[8] CDongD B Clarke S S Nambisan andBHuang ldquoAnalyzinginjury crashes using random-parameter bivariate regressionmodelsrdquo Transportmetrica A Transport Science vol 12 no 9pp 794ndash810 2016

[9] M G Karlaftis and E I Vlahogianni ldquoStatistical methodsversus neural networks in transportation research differencessimilarities and some insightsrdquo Transportation Research Part CEmerging Technologies vol 19 no 3 pp 387ndash399 2011

[10] J C Principe N R Euliano and W C Lefebvre Neural andAdaptive Systems Fundamentals through Simulations vol 672Wiley New York NY USA 2000

[11] L-Y Chang ldquoAnalysis of freeway accident frequencies Negativebinomial regression versus artificial neural networkrdquo SafetyScience vol 43 no 8 pp 541ndash557 2005

[12] H T Abdelwahab and M A Abdel-Aty ldquoArtificial neuralnetworks and logit models for traffic safety analysis of tollplazasrdquo Transportation Research Record no 1784 pp 115ndash1252002

[13] Y Xie D Lord and Y Zhang ldquoPredicting motor vehiclecollisions using Bayesian neural network models an empiricalanalysisrdquo Accident Analysis amp Prevention vol 39 no 5 pp 922ndash933 2007

[14] M M Kunt I Aghayan and N Noii ldquoPrediction for trafficaccident severity Comparing the artificial neural networkgenetic algorithm combined genetic algorithm and patternsearch methodsrdquo Transport vol 26 no 4 pp 353ndash366 2011

[15] K S Jadaan M Al-Fayyad and H F Gammoh ldquoPredictionof Road Traffic Accidents in Jordan using Artificial NeuralNetwork (ANN)rdquo Journal of Traffic and Logistics Engineeringvol 2 no 2 pp 92ndash94 2014

[16] D Akin and BAkbas ldquoA neural network (NN)model to predictintersection crashes based upon driver vehicle and roadwaysurface characteristicsrdquoScientific Research and Essays vol 5 no19 pp 2837ndash2847 2010

[17] X Li D Lord Y Zhang and Y Xie ldquoPredicting motor vehiclecrashes using Support VectorMachine modelsrdquo Accident Anal-ysis amp Prevention vol 40 no 4 pp 1611ndash1618 2008

[18] Y Zhang and Y Xie ldquoForecasting of short-term freeway vol-ume with v-support vector machinesrdquo Transportation ResearchRecord vol 2024 no 1 pp 92ndash99 2007

[19] V Kecman ldquoSupport Vector Machines ndash An Introductionrdquo inSupport Vector Machines eory and Applications vol 177 ofStudies in Fuzziness and So Computing pp 1ndash47 SpringerBerlin Heidelberg Berlin Heidelberg 2005

[20] R Yu and M Abdel-Aty ldquoAnalyzing crash injury severity fora mountainous freeway incorporating real-time traffic andweather datardquo Safety Science vol 63 pp 50ndash56 2014

[21] C Chen G Zhang Z Qian R A Tarefder and Z TianldquoInvestigating driver injury severity patterns in rollover crashesusing support vector machine modelsrdquo Accident Analysis ampPrevention vol 90 pp 128ndash139 2016

[22] N Dong H Huang and L Zheng ldquoSupport vector machine incrash prediction at the level of traffic analysis zones assessingthe spatial proximity effectsrdquo Accident Analysis amp Preventionvol 82 pp 192ndash198 2015

[23] G Ren and Z Zhou ldquoTraffic safety forecasting method byparticle swarm optimization and support vector machinerdquoExpert SystemswithApplications vol 38 no 8 pp 10420ndash104242011

[24] R Yu and M Abdel-Aty ldquoUtilizing support vector machine inreal-time crash risk evaluationrdquoAccidentAnalysis amp Preventionvol 51 pp 252ndash259 2013

[25] M Abdel-Aty and K Haleem ldquoAnalyzing angle crashes atunsignalized intersections using machine learning techniquesrdquoAccident Analysis amp Prevention vol 43 no 1 pp 461ndash470 2011

[26] Y LeCun Y Bengio and G Hinton ldquoDeep learningrdquo Naturevol 521 no 7553 pp 436ndash444 2015

[27] J Schmidhuber ldquoDeep learning in neural networks anoverviewrdquoNeural Networks vol 61 pp 85ndash117 2015

[28] W Huang G Song H Hong and K Xie ldquoDeep architecturefor traffic flow prediction deep belief networks with multitasklearningrdquo IEEE Transactions on Intelligent Transportation Sys-tems vol 15 no 5 pp 2191ndash2201 2014

[29] Y Lv Y Duan W Kang Z Li and F-Y Wang ldquoTraffic FlowPrediction with Big Data A Deep Learning Approachrdquo IEEETransactions on Intelligent Transportation Systems vol 16 no 2pp 865ndash873 2015

[30] N G Polson and V O Sokolov ldquoDeep learning for short-term traffic flow predictionrdquo Transportation Research Part CEmerging Technologies vol 79 pp 1ndash17 2017

[31] G E Hinton S Osindero andY Teh ldquoA fast learning algorithmfor deep belief netsrdquoNeural Computation vol 18 no 7 pp 1527ndash1554 2006

[32] P Swietojanski A Ghoshal and S Renals ldquoConvolutionalneural networks for distant speech recognitionrdquo IEEE SignalProcessing Letters vol 21 no 9 pp 1120ndash1124 2014

[33] MMARahhal Y BaziHAlhichriNAlajlan FMelgani andR R Yager ldquoDeep learning approach for active classification ofelectrocardiogram signalsrdquo Information Sciences vol 345 pp340ndash354 2016

[34] H-I Suk C-Y Wee S-W Lee and D Shen ldquoState-spacemodel with deep learning for functional dynamics estimationin resting-state fMRIrdquo NeuroImage vol 129 pp 292ndash307 2016

[35] R D Hjelm V D Calhoun R Salakhutdinov E A Allen TAdali and S M Plis ldquoRestricted Boltzmann machines for neu-roimaging An application in identifying intrinsic networksrdquoNeuroImage vol 96 pp 245ndash260 2014


[36] P Shi and E A Valdez ldquoMultivariate negative binomial modelsfor insurance claim countsrdquo Insurance Mathematics amp Eco-nomics vol 55 pp 18ndash29 2014

[37] P C Anastasopoulos V N Shankar J E Haddock and F LMannering ldquoA multivariate tobit analysis of highway accident-injury-severity ratesrdquo Accident Analysis amp Prevention vol 45pp 110ndash119 2012

[38] L Chang and J Chien ldquoAnalysis of driver injury severity intruck-involved accidents using a non-parametric classificationtree modelrdquo Safety Science vol 51 no 1 pp 17ndash22 2013

[39] J Pahukula S Hernandez and A Unnikrishnan ldquoA time ofday analysis of crashes involving large trucks in urban areasrdquoAccident Analysis amp Prevention vol 75 pp 155ndash163 2015

[40] Q Wu F Chen and G H Zhang ldquoMixed logit model-based driver injury severity investigations in single- and multi-vehicle crashes on rural two-lane highwaysrdquo Accident Analysisamp Prevention vol 72 pp 105ndash115 2014

[41] N Cristianini and J Shawe-Taylor An Introduction to SupportVector Machines Cambridge University Press CambridgeUK2000

[42] C Campbell ldquoKernelmethods A survey of current techniquesrdquoNeurocomputing vol 48 pp 63ndash84 2002

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom


the proposed models became more and more sophisticatedthere are still some factors that are not available to theresearchers and the models result in bias estimations anderroneous predictions In this study we proposed an innova-tive approach for traffic crash prediction which incorporatesa multivariate regression layer into a dynamic deep learningmodel that contains an unsupervised feature learningmoduleand a supervised fine tuning module governing the statedynamics to improve the performances of prediction

2 Literature Review

The statistical methodologies such as the Poisson negativebinomial (NB) and their variants in univariate andmultivari-ate regression frameworks have been successfully applied incrash count analyses [4 6ndash8] which attempt to deal with thedata and methodological issues associated with traffic crashestimations and predictions and enhance our understandingon the relationship between the influence factors and trafficcrash outcomes However current research in traffic safetyindicates that the applied statistical modeling fails whendealing with complex and highly nonlinear data [9] whichcould suggest that the relationship between the influencefactors and traffic crash outcomes is more complicated thancan be captured by a single statistical approach In additionmost of the statistical methods are based on some strongassumptions such as specifying a priori and the error dis-tribution Moreover a problematic issue is multicollinearityie the high degree of correlation between two or moreindependent variables Furthermore statistical models havedifficulty when dealing with outliers missing or noisy data[10]

To deal with the limitations of statistical methodologiesthe machine learning methods including Artificial NeuralNetwork (ANN) Support Vector Machine (SVM) modelsand deep learning models have been applied to varioustraffic safety problems and used as data analytic methodsbecause of their ability to work with massive amounts ofmultidimensional data In addition because of the modelingflexibility learning and generalization ability and good pre-dictive ability the machine learning has been considered asgeneric accurate and convenientmathematicalmodels in thefield of traffic safety

Because the commonly used Poisson or NB regres-sion models assume the predefined underlying relationshipbetween dependent and independent variables and the viola-tion of the assumption would lead to erroneous estimationANN and Bayesian neural network (BNN) models havebeen employed to analyze the traffic safety problems formany years Although both ANN and BNN models havesimilar multilevel network structures they are different inpredicting the outcome variables For ANN the weightsare assumed to fix However the weights of BNN followa probability distribution and the prediction needs to beintegrated over all the probability weights Basically the ANNcan be characterized by three features network architecturemodel of a neuron and learning algorithms Chang [11]compared the performances of NB regression model andANN in crash frequency analyses The results showed that

ANN is a consistent alternative method for analyzing crashfrequency Abdelwahab and Abdel-Aty [12] employed twowell-known ANN paradigms [the multilayer perceptron andradial basis functions (RBF) neural networks] to analyzethe traffic safety of toll plazas and evaluate the impacts ofelectronic toll collection (ETC) systems on highway safetyThe performance of ANN was compared with calibratedlogit models Modeling results showed that the RBF neuralnetwork was the best model for analyzing driver injuryseverity Xie Lord and Zhang [13] evaluated the applicationof BNN models for predicting traffic crashes by using datacollected on rural frontage roads in TexasThe results showedthat back-propagation neural network (BPNN) and BNNmodels perform better than the NB regression model interms of traffic crash prediction The results also showedthat BNNs could be used to address other issues in high-way safety such as the development of crash modificationfactors and enhance the prediction capabilities for evalu-ating different highway design alternatives Kunt Aghayanand Noii [14] employed a genetic algorithm (GA) patternsearch and ANN models to predict the severity of freewaytraffic crashes The results showed that the ANN providedthe best predictions Jadaan Al-Fayyad and Gammoh [15]developed a traffic crash prediction model using the ANNsimulation with the purpose of identifying its suitability forpredicting traffic crashes under Jordanian conditions Theresults demonstrated that the estimated traffic crashes areclose to actual traffic crashes Akin and Akbas [16] proposedan ANN model to predict intersection crashes in MacombCounty of the State of Michigan The predictive capabil-ity of the ANN model was determined by classifying thecrashes into these types fatal injury and property damageonly (PDO) crashes The results were very promising andshowed that ANN model is capable of providing an accurateprediction (909) of the crash types In summary thoughANN and BNNmodels show better linearnonlinear approx-imation properties than traditional statistical approachesthese models often cannot be generalized to other data sets[3]

The SVMmodels have recently been introduced for trafficsafety analyses [17 18] which are a new class of models thatare based on statistical learning theory and structural riskminimization [19] These models are supposed to approxi-mate any multivariate function to any desired degree of accu-racywith a set of related supervised learningmethods Li et al[17] evaluated the application of SVM models for predictingmotor vehicle crashes The results showed that SVM modelspredict crash data more effectively and accurately thantraditional NB models In addition the findings indicatedthat the SVM models provide better (or at least comparable)performance than BPNNmodels and do not over-fit the dataTo identify the relationship between severe crashes and theexplanatory variables and enhance model goodness-of-fitYu and Abdel-Aty [20] developed three models to analyzecrash injury severity which include a fixed parameter logitmodel a SVM model and a random parameter logit modelThe results showed that the SVM models and the randomparameter models provide superior model fits compared tothe fixed parameter logit model Findings also demonstrate


















Hidden layer

Output layer

Input Output


Regression function

1

2

D

2

D

1

ℎ1

ℎ2

ℎj

ℎF

x1

x2

xp

x1

x2

xp

x1

x2

xp

ℎ1

ℎ2

ℎj

ℎF

yi1

yi2

yim

yi1

yi2

yim










1 + exp [minus (119887119895 + sum119863119894=1119882119894119895V119894)](2)



1 + exp [minus (119887119895 + sum119863119894=1 (119882119894119895V119894120590119894))](3)



119875 (h | k Θ) = 119865prod119895=1

119875 (ℎ119895 | k Θ) (4)



119901(h|kΘ)

+ sumkisin119863⟨ 120597120597Θ120593 (k h Θ)⟩

119901(kh|Θ)

(5)


120593 (h | k119899) =








119901 (119910119894119895)= Γ (120582119894119895120590 + 119910119894119895)Γ (120582119894119895120590) Γ (119910119894119895 + 1) (

11 + 120590)120582119894119895120590 ( 1205901 + 120590)

119910119894119895 (7)




119896=0

119901 (119896) 119873prod119894=1

119901 (119910119894119895 minus 119896)(8)



119871 = sum119894119895



(9)


119891 (120579)= minus1119899

119899sum119894=1

119898sum119895=1

119904 (1199101015840119894119895 = 119910119894119895) log[ exp (ℎ120579 (119909119894))sum119865119897=1 exp (ℎ120579 (119909119894))]

+ 1205722119901 [10038171003817100381710038171003817119882119903119890119892119903119890119904119904119894119900119899100381710038171003817100381710038172

119865+ 119865sum119897=1

100381710038171003817100381711988211989710038171003817100381710038172119865](10)



4 Data











2 1660 52281 930 2929

Lane widths (ft) 12 915 288211 1650 519710 610 1921












5 Modelling Results










Table3Th

efun

ctionaln

etwo

rkbetweentheinp

utvaria

bles

andthefeature

representatio

ns

Varia

ble

Traffi

cfeature

representatio

nGeometric

feature

representatio

nPavementfeature

representatio

nEn

vironm

entalfeature

representatio

nTraffi

cfactor

Thelogarith

mof

AADTperlane

-052

9-0007

-0016

-0034

Trucktraffi

cpercentage

-0659

-0002

-0024

-0010

Poste

dspeedlim

its-0030

-0010

0175

-0047

Geometricfactors

Segm

entlength(m

iles)

000

7-0580

-0007

-0003

Degreeo

fhorizon

talcurvature

0002

-0918

-0006

-0009

Medianwidths

0002

0826

006

80015

Outsid

esho

ulderw

idths

000

50419

0016

006

4Num

bero

fthrou

ghlanes

3lanes

-0021

-0891

-0006

-0026

2lanes

-0015

-0864

-0022

-0060

Lane

widths

12ft

000

40776

000

5000

111ft

000

90592

0076

000

4Num

bero

fleft

-turn

lanes

2left-turn

lanes

-0003

-0212

-0019

-0017

1left

-turn

lane

0002

-0783

0028

0016

Mediantype

Non

-traversablem

edian

0013

0247

000

6000

7Sh

oulder

type

Pavement

-0035

-014

4-0027

-0016

Gravel

000

5-074

30011

006

0Pa

vementfactor

Internationalrou

ghnessindex(in

mile)

0101

000

7-018

3-0001

Rutd

epth

(in)

-0004

-0004

-0341

-0038

Environm

entalfactor

Terraintype

Mou

ntaino

us-0014

-0011

-0010

-0954

Land

usetype

Resid

entia

l004

20015

0011

0847

Com

mercial

0058

000

1000

6-0915

Indicatorfor

lighting

Ligh

tingexistso

nroadway

0018

000

80027

0781



















6 Conclusions




Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



















Hidden layer

Output layer

Input Output


Regression function

1

2

D

2

D

1

ℎ1

ℎ2

ℎj

ℎF

x1

x2

xp

x1

x2

xp

x1

x2

xp

ℎ1

ℎ2

ℎj

ℎF

yi1

yi2

yim

yi1

yi2

yim










1 + exp [minus (119887119895 + sum119863119894=1119882119894119895V119894)](2)



1 + exp [minus (119887119895 + sum119863119894=1 (119882119894119895V119894120590119894))](3)



119875 (h | k Θ) = 119865prod119895=1

119875 (ℎ119895 | k Θ) (4)



119901(h|kΘ)

+ sumkisin119863⟨ 120597120597Θ120593 (k h Θ)⟩

119901(kh|Θ)

(5)


120593 (h | k119899) =








119901 (119910119894119895)= Γ (120582119894119895120590 + 119910119894119895)Γ (120582119894119895120590) Γ (119910119894119895 + 1) (

11 + 120590)120582119894119895120590 ( 1205901 + 120590)

119910119894119895 (7)




119896=0

119901 (119896) 119873prod119894=1

119901 (119910119894119895 minus 119896)(8)



119871 = sum119894119895



(9)


119891 (120579)= minus1119899

119899sum119894=1

119898sum119895=1

119904 (1199101015840119894119895 = 119910119894119895) log[ exp (ℎ120579 (119909119894))sum119865119897=1 exp (ℎ120579 (119909119894))]

+ 1205722119901 [10038171003817100381710038171003817119882119903119890119892119903119890119904119904119894119900119899100381710038171003817100381710038172

119865+ 119865sum119897=1

100381710038171003817100381711988211989710038171003817100381710038172119865](10)



4 Data











2 1660 52281 930 2929

Lane widths (ft) 12 915 288211 1650 519710 610 1921












5 Modelling Results










Table3Th

efun

ctionaln

etwo

rkbetweentheinp

utvaria

bles

andthefeature

representatio

ns

Varia

ble

Traffi

cfeature

representatio

nGeometric

feature

representatio

nPavementfeature

representatio

nEn

vironm

entalfeature

representatio

nTraffi

cfactor

Thelogarith

mof

AADTperlane

-052

9-0007

-0016

-0034

Trucktraffi

cpercentage

-0659

-0002

-0024

-0010

Poste

dspeedlim

its-0030

-0010

0175

-0047

Geometricfactors

Segm

entlength(m

iles)

000

7-0580

-0007

-0003

Degreeo

fhorizon

talcurvature

0002

-0918

-0006

-0009

Medianwidths

0002

0826

006

80015

Outsid

esho

ulderw

idths

000

50419

0016

006

4Num

bero

fthrou

ghlanes

3lanes

-0021

-0891

-0006

-0026

2lanes

-0015

-0864

-0022

-0060

Lane

widths

12ft

000

40776

000

5000

111ft

000

90592

0076

000

4Num

bero

fleft

-turn

lanes

2left-turn

lanes

-0003

-0212

-0019

-0017

1left

-turn

lane

0002

-0783

0028

0016

Mediantype

Non

-traversablem

edian

0013

0247

000

6000

7Sh

oulder

type

Pavement

-0035

-014

4-0027

-0016

Gravel

000

5-074

30011

006

0Pa

vementfactor

Internationalrou

ghnessindex(in

mile)

0101

000

7-018

3-0001

Rutd

epth

(in)

-0004

-0004

-0341

-0038

Environm

entalfactor

Terraintype

Mou

ntaino

us-0014

-0011

-0010

-0954

Land

usetype

Resid

entia

l004

20015

0011

0847

Com

mercial

0058

000

1000

6-0915

Indicatorfor

lighting

Ligh

tingexistso

nroadway

0018

000

80027

0781



















6 Conclusions




Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





1 + exp [minus (119887119895 + sum119863119894=1119882119894119895V119894)](2)



1 + exp [minus (119887119895 + sum119863119894=1 (119882119894119895V119894120590119894))](3)



119875 (h | k Θ) = 119865prod119895=1

119875 (ℎ119895 | k Θ) (4)



119901(h|kΘ)

+ sumkisin119863⟨ 120597120597Θ120593 (k h Θ)⟩

119901(kh|Θ)

(5)


120593 (h | k119899) =








119901 (119910119894119895)= Γ (120582119894119895120590 + 119910119894119895)Γ (120582119894119895120590) Γ (119910119894119895 + 1) (

11 + 120590)120582119894119895120590 ( 1205901 + 120590)

119910119894119895 (7)




119896=0

119901 (119896) 119873prod119894=1

119901 (119910119894119895 minus 119896)(8)



119871 = sum119894119895



(9)


119891 (120579)= minus1119899

119899sum119894=1

119898sum119895=1

119904 (1199101015840119894119895 = 119910119894119895) log[ exp (ℎ120579 (119909119894))sum119865119897=1 exp (ℎ120579 (119909119894))]

+ 1205722119901 [10038171003817100381710038171003817119882119903119890119892119903119890119904119904119894119900119899100381710038171003817100381710038172

119865+ 119865sum119897=1

100381710038171003817100381711988211989710038171003817100381710038172119865](10)



4 Data











2 1660 52281 930 2929

Lane widths (ft) 12 915 288211 1650 519710 610 1921












5 Modelling Results










Table3Th

efun

ctionaln

etwo

rkbetweentheinp

utvaria

bles

andthefeature

representatio

ns

Varia

ble

Traffi

cfeature

representatio

nGeometric

feature

representatio

nPavementfeature

representatio

nEn

vironm

entalfeature

representatio

nTraffi

cfactor

Thelogarith

mof

AADTperlane

-052

9-0007

-0016

-0034

Trucktraffi

cpercentage

-0659

-0002

-0024

-0010

Poste

dspeedlim

its-0030

-0010

0175

-0047

Geometricfactors

Segm

entlength(m

iles)

000

7-0580

-0007

-0003

Degreeo

fhorizon

talcurvature

0002

-0918

-0006

-0009

Medianwidths

0002

0826

006

80015

Outsid

esho

ulderw

idths

000

50419

0016

006

4Num

bero

fthrou

ghlanes

3lanes

-0021

-0891

-0006

-0026

2lanes

-0015

-0864

-0022

-0060

Lane

widths

12ft

000

40776

000

5000

111ft

000

90592

0076

000

4Num

bero

fleft

-turn

lanes

2left-turn

lanes

-0003

-0212

-0019

-0017

1left

-turn

lane

0002

-0783

0028

0016

Mediantype

Non

-traversablem

edian

0013

0247

000

6000

7Sh

oulder

type

Pavement

-0035

-014

4-0027

-0016

Gravel

000

5-074

30011

006

0Pa

vementfactor

Internationalrou

ghnessindex(in

mile)

0101

000

7-018

3-0001

Rutd

epth

(in)

-0004

-0004

-0341

-0038

Environm

entalfactor

Terraintype

Mou

ntaino

us-0014

-0011

-0010

-0954

Land

usetype

Resid

entia

l004

20015

0011

0847

Com

mercial

0058

000

1000

6-0915

Indicatorfor

lighting

Ligh

tingexistso

nroadway

0018

000

80027

0781



















6 Conclusions




Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



119871 = sum119894119895



(9)


119891 (120579)= minus1119899

119899sum119894=1

119898sum119895=1

119904 (1199101015840119894119895 = 119910119894119895) log[ exp (ℎ120579 (119909119894))sum119865119897=1 exp (ℎ120579 (119909119894))]

+ 1205722119901 [10038171003817100381710038171003817119882119903119890119892119903119890119904119904119894119900119899100381710038171003817100381710038172

119865+ 119865sum119897=1

100381710038171003817100381711988211989710038171003817100381710038172119865](10)



4 Data











2 1660 52281 930 2929

Lane widths (ft) 12 915 288211 1650 519710 610 1921












5 Modelling Results










Table3Th

efun

ctionaln

etwo

rkbetweentheinp

utvaria

bles

andthefeature

representatio

ns

Varia

ble

Traffi

cfeature

representatio

nGeometric

feature

representatio

nPavementfeature

representatio

nEn

vironm

entalfeature

representatio

nTraffi

cfactor

Thelogarith

mof

AADTperlane

-052

9-0007

-0016

-0034

Trucktraffi

cpercentage

-0659

-0002

-0024

-0010

Poste

dspeedlim

its-0030

-0010

0175

-0047

Geometricfactors

Segm

entlength(m

iles)

000

7-0580

-0007

-0003

Degreeo

fhorizon

talcurvature

0002

-0918

-0006

-0009

Medianwidths

0002

0826

006

80015

Outsid

esho

ulderw

idths

000

50419

0016

006

4Num

bero

fthrou

ghlanes

3lanes

-0021

-0891

-0006

-0026

2lanes

-0015

-0864

-0022

-0060

Lane

widths

12ft

000

40776

000

5000

111ft

000

90592

0076

000

4Num

bero

fleft

-turn

lanes

2left-turn

lanes

-0003

-0212

-0019

-0017

1left

-turn

lane

0002

-0783

0028

0016

Mediantype

Non

-traversablem

edian

0013

0247

000

6000

7Sh

oulder

type

Pavement

-0035

-014

4-0027

-0016

Gravel

000

5-074

30011

006

0Pa

vementfactor

Internationalrou

ghnessindex(in

mile)

0101

000

7-018

3-0001

Rutd

epth

(in)

-0004

-0004

-0341

-0038

Environm

entalfactor

Terraintype

Mou

ntaino

us-0014

-0011

-0010

-0954

Land

usetype

Resid

entia

l004

20015

0011

0847

Com

mercial

0058

000

1000

6-0915

Indicatorfor

lighting

Ligh

tingexistso

nroadway

0018

000

80027

0781



















6 Conclusions




Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







2 1660 52281 930 2929

Lane widths (ft) 12 915 288211 1650 519710 610 1921












5 Modelling Results










Table3Th

efun

ctionaln

etwo

rkbetweentheinp

utvaria

bles

andthefeature

representatio

ns

Varia

ble

Traffi

cfeature

representatio

nGeometric

feature

representatio

nPavementfeature

representatio

nEn

vironm

entalfeature

representatio

nTraffi

cfactor

Thelogarith

mof

AADTperlane

-052

9-0007

-0016

-0034

Trucktraffi

cpercentage

-0659

-0002

-0024

-0010

Poste

dspeedlim

its-0030

-0010

0175

-0047

Geometricfactors

Segm

entlength(m

iles)

000

7-0580

-0007

-0003

Degreeo

fhorizon

talcurvature

0002

-0918

-0006

-0009

Medianwidths

0002

0826

006

80015

Outsid

esho

ulderw

idths

000

50419

0016

006

4Num

bero

fthrou

ghlanes

3lanes

-0021

-0891

-0006

-0026

2lanes

-0015

-0864

-0022

-0060

Lane

widths

12ft

000

40776

000

5000

111ft

000

90592

0076

000

4Num

bero

fleft

-turn

lanes

2left-turn

lanes

-0003

-0212

-0019

-0017

1left

-turn

lane

0002

-0783

0028

0016

Mediantype

Non

-traversablem

edian

0013

0247

000

6000

7Sh

oulder

type

Pavement

-0035

-014

4-0027

-0016

Gravel

000

5-074

30011

006

0Pa

vementfactor

Internationalrou

ghnessindex(in

mile)

0101

000

7-018

3-0001

Rutd

epth

(in)

-0004

-0004

-0341

-0038

Environm

entalfactor

Terraintype

Mou

ntaino

us-0014

-0011

-0010

-0954

Land

usetype

Resid

entia

l004

20015

0011

0847

Com

mercial

0058

000

1000

6-0915

Indicatorfor

lighting

Ligh

tingexistso

nroadway

0018

000

80027

0781



















6 Conclusions




Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




5 Modelling Results










Table3Th

efun

ctionaln

etwo

rkbetweentheinp

utvaria

bles

andthefeature

representatio

ns

Varia

ble

Traffi

cfeature

representatio

nGeometric

feature

representatio

nPavementfeature

representatio

nEn

vironm

entalfeature

representatio

nTraffi

cfactor

Thelogarith

mof

AADTperlane

-052

9-0007

-0016

-0034

Trucktraffi

cpercentage

-0659

-0002

-0024

-0010

Poste

dspeedlim

its-0030

-0010

0175

-0047

Geometricfactors

Segm

entlength(m

iles)

000

7-0580

-0007

-0003

Degreeo

fhorizon

talcurvature

0002

-0918

-0006

-0009

Medianwidths

0002

0826

006

80015

Outsid

esho

ulderw

idths

000

50419

0016

006

4Num

bero

fthrou

ghlanes

3lanes

-0021

-0891

-0006

-0026

2lanes

-0015

-0864

-0022

-0060

Lane

widths

12ft

000

40776

000

5000

111ft

000

90592

0076

000

4Num

bero

fleft

-turn

lanes

2left-turn

lanes

-0003

-0212

-0019

-0017

1left

-turn

lane

0002

-0783

0028

0016

Mediantype

Non

-traversablem

edian

0013

0247

000

6000

7Sh

oulder

type

Pavement

-0035

-014

4-0027

-0016

Gravel

000

5-074

30011

006

0Pa

vementfactor

Internationalrou

ghnessindex(in

mile)

0101

000

7-018

3-0001

Rutd

epth

(in)

-0004

-0004

-0341

-0038

Environm

entalfactor

Terraintype

Mou

ntaino

us-0014

-0011

-0010

-0954

Land

usetype

Resid

entia

l004

20015

0011

0847

Com

mercial

0058

000

1000

6-0915

Indicatorfor

lighting

Ligh

tingexistso

nroadway

0018

000

80027

0781



















6 Conclusions




Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Table3Th

efun

ctionaln

etwo

rkbetweentheinp

utvaria

bles

andthefeature

representatio

ns

Varia

ble

Traffi

cfeature

representatio

nGeometric

feature

representatio

nPavementfeature

representatio

nEn

vironm

entalfeature

representatio

nTraffi

cfactor

Thelogarith

mof

AADTperlane

-052

9-0007

-0016

-0034

Trucktraffi

cpercentage

-0659

-0002

-0024

-0010

Poste

dspeedlim

its-0030

-0010

0175

-0047

Geometricfactors

Segm

entlength(m

iles)

000

7-0580

-0007

-0003

Degreeo

fhorizon

talcurvature

0002

-0918

-0006

-0009

Medianwidths

0002

0826

006

80015

Outsid

esho

ulderw

idths

000

50419

0016

006

4Num

bero

fthrou

ghlanes

3lanes

-0021

-0891

-0006

-0026

2lanes

-0015

-0864

-0022

-0060

Lane

widths

12ft

000

40776

000

5000

111ft

000

90592

0076

000

4Num

bero

fleft

-turn

lanes

2left-turn

lanes

-0003

-0212

-0019

-0017

1left

-turn

lane

0002

-0783

0028

0016

Mediantype

Non

-traversablem

edian

0013

0247

000

6000

7Sh

oulder

type

Pavement

-0035

-014

4-0027

-0016

Gravel

000

5-074

30011

006

0Pa

vementfactor

Internationalrou

ghnessindex(in

mile)

0101

000

7-018

3-0001

Rutd

epth

(in)

-0004

-0004

-0341

-0038

Environm

entalfactor

Terraintype

Mou

ntaino

us-0014

-0011

-0010

-0954

Land

usetype

Resid

entia

l004

20015

0011

0847

Com

mercial

0058

000

1000

6-0915

Indicatorfor

lighting

Ligh

tingexistso

nroadway

0018

000

80027

0781



















6 Conclusions




Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




















6 Conclusions




Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


an improved deep learning model for traffic crash...

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