In search of the severity dimension of traffic events: Extended Delta-V as a traffic conflict indicator

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Accident Analysis and Prevention

j o ur na l h o me pa g e :w w w . e l s e v i e r . c o m / l o c a t e / a a p

In search of the severity dimension of traffic events: Extended Delta-V as a traffic conflict indicator

Aliaksei Laureshyn

, Tim De Ceunynck

, Christoffer Karlsson

, Åse Svensson

, Stijn Daniels

aTransportandRoads,DepartmentofTechnologyandSociety,FacultyofEngineering,LTHLundUniversity,Box118,SE-22100Lund,Sweden

bInstituteofTransportEconomics,Gaustadalléen21,NO-0349Oslo,Norway

cTransportationResearchInstitute,HasseltUniversity,Wetenschapspark5,bus6,BE-3590Diepenbeek,Belgium

a r t i c l e i n f o

Articlehistory:

Received18February2016 Receivedinrevisedform 22September2016 Accepted23September2016 Availableonline28September2016 Keywords:

Trafficsafety

Surrogatesafetymeasures Trafficconflicts

Extendeddelta-V Crashseverity

a b s t r a c t

Mostexistingtrafficconflictindicatorsdonotsufficientlytakeintoaccounttheseverityoftheinjuries resultingfromacollisionhaditoccurred.Thusfar,mostoftheindicatorsthathavebeendeveloped expresstheseverityofatrafficencounterastheirproximitytoacollisionintermsoftimeorspace.

ThispaperpresentsthetheoreticalframeworkandthefirstimplementationofExtendedDelta-Vasa measureoftrafficconflictseverityinsite-basedobservations.ItisderivedfromtheconceptofDelta-Vas itisappliedincrashreconstructions,whichreferstothechangeofvelocityexperiencedbyaroaduser duringacrash.TheconceptofDelta-Visrecognisedasanimportantpredictorofcrashoutcomeseverity.

Thepaperexplainshowthemeasureisoperationalisedwithinthecontextoftrafficconflictobserva- tions.TheExtendedDelta-Vtrafficconflictmeasureintegratestheproximitytoacrashaswellasthe outcomeseverityintheeventacrashwouldhavetakenplace,whicharebothimportantdimensionsin definingtheseverityofatrafficevent.Theresultsfromacasestudyarepresentedinwhichanumberof trafficconflictindicatorsarecalculatedforinteractionsbetweenleftturningvehiclesandvehiclesdriv- ingstraightthroughasignalisedintersection.TheresultssuggestthattheExtendedDelta-Vindicator seemstoperformwellatselectingthemostseveretrafficevents.Thepaperdiscusseshowtheindicator overcomesanumberoflimitationsoftraditionalmeasuresofconflictseverity.Whilethisisapromising firststeptowardsoperationalisinganimprovedmeasureoftrafficconflictseverity,additionalresearch isneededtofurtherdevelopandvalidatetheindicator.

©2016TheAuthor(s).PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Traditionally,roadsafetyanalyseshavereliedmostlyoncrash dataastheirprimarydatasource.Crashdata,however,havesome well-knownlimitations froman analytical pointof view.These limitationsincludetheirrelativelylowfrequency,leadingtosta- tisticalissuesrelatedtosmalldatasamples,(unevenlydistributed) under-reportingofcrashesandthelimitedinformationtheypro- vide on behavioural and environmental aspects of the crashes (Laureshynetal.,2010;SvenssonandHydén,2006;Tarkoetal., 2009).Theseissueslimitthepossibilitiesfordrawinginferences

∗ Corresponding authorat:TransportandRoads,DepartmentofTechnology andSociety,FacultyofEngineering,LTHLundUniversity,Box118,SE-22100Lund, Sweden.

E-mailaddress:[email protected](A.Laureshyn).

aboutthecausalityofthecrashesandhowtheycanbeprevented inthefuture(Davis,2004;Elvik,2007;Hauer,2010;Tarko,2012).

Therefore, a number of researchers argue that road safety analysescanstronglybenefit fromreliablemethodsthat utilise observablenon-crasheventsasasurrogateoracomplementto crashes(Laureshynetal.,2010;Tarkoetal.,2009).Theideabehind thisisthattrafficcanbeseenasanumberofelementaryevents thatdifferintheirdegreeofseverity(unsafety),andthatarela- tionshipexistsbetweenthefrequencyandtheseverityoftheevents (SvenssonandHydén,2006).Differentconceptsdescribingthisidea haveemergedover theyears.Hydén(1987)describesthisrela- tionshipwitha‘safetypyramid’,wherethebaseofthepyramid isformedbynormaltrafficencountersthatarequitesafeandfre- quent,whilethetipofthepyramidcontainsthemostsevereevents, suchascrashesresultingin injuriesorfatalities,thatarehighly infrequent.Otherresearchers,suchasGlauzandMigletz(1980) andSvensson(1998),alsoconsidertheeventsofthelowestseverity (‘perfectlysafe’events)tobequiterare,too.Theystatethatitisthe

http://dx.doi.org/10.1016/j.aap.2016.09.026

0001-4575/©2016TheAuthor(s).PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.

0/).

eventsofmoderateseveritythataremostfrequent,becauseroad usersaimatoptimisingtheirbehaviourinrespecttobothsafety andmobility.Thisexplainsthepreferenceforencountersofmod- erateseveritybecauseacceptingsmallergapscanleadtogainsin traveltime(Svensson,1998).Acommongroundofallconceptsis, however,thatthelessseveretrafficevents:i)aremorefrequent thancrashes;andii)haveaninterdependencywithcrashesthat, onceitissufficientlyunderstood,canbeusedtoestimateriskand infercausesoftrafficcrasheswithouthavingtoobservecrashes themselves.Thereis,indeed,abulkofliteraturesuggestingthat astrongcorrelationexistsbetweenthefrequencyof‘seriouscon- flicts’(thoughdefinedinavarietyofways)andthefrequencyof crashes(Brown,1994;El-BasyounyandSayed,2013;Hydén,1987;

Lord,1996;Migletzetal.,1985;Sacchietal.,2013).

Theliteraturerevealsthatdozensoftrafficconflictseverityindi- catorshavebeendeveloped over thepastdecades(Allenetal., 1978;Hayward,1972;Kraayetal.,1986;Laureshynetal.,2010;

Minderhoudand Bovy,2001;Zhenget al.,2014).Mostofthese indicatorsexpresstheseverityofatrafficencounterasitsprox- imity toacrashin termsof timeor space(Zhenget al.,2014).

However,proximitytoacrashisonlyone dimensionof ‘sever- ity’.Intuitively,gettingclosetoacollisionthatwouldlikelyhave resultedinaslighttouchshouldnotbeconsideredassevereasget- tingequallyclosetoacollisionthatwouldlikelyhaveresultedina severeinjury.Therefore,thepotentialseverityoftheconsequences intheeventthatacrashwouldhavetakenplaceneedstobetaken intoaccountinsomeway(Laureshynetal.,2010).Accordingto initiativessuchasVisionZero,policymakersand roaddesigners shouldstrivetowardsatrafficsystemwithoutfatalitiesorseri- ousinjuries(Johansson,2009).TheprimarygoalofVisionZerois, therefore,toavoidseverecrashes,ratherthanallcrashes.Thus,the trafficconflictseveritycalculatedfromanindicatorshouldexpress theproximitytoaserious/fatalinjuryratherthantheproximity toacrashalone.Veryfewoftheexistingtrafficconflictindicators andtechniquestaketheoutcomeseverityintoaccountin some way.Forexample,theSwedishTrafficConflictTechnique(Hydén, 1987)usesboththeproximityintimeandthespeedatwhichthe conflicttakesplace,whichindirectlyreflectsthepossibleconse- quences.TheDutchtechnique,DOCTOR(vanderHorstandKraay, 1986),andtheCanadianTrafficConflictTechnique(Brown,1994) useasubjectivescoreforpotentialconsequencesthatisaddedto theobjectivenearness-in-timeindicator(s).However,theseexam- plesareexceptionsandthewaystheycombinetheprobabilityofa collisionanditsconsequencesarenotcompletelyproblem-free.

Inordertodevelopatrafficconflictseverityindicatorthatmeets thissuggesteddefinition,threequestionsneedtobeaddressed:

1)Howcanwemeasuretheproximityofanencountertoacrash?

2)Howcanwemeasuretheconsequencesintheeventa crash wouldhavetakenplace?

3)Howcanweweighbothelementstogether?

Thesethreequestionswillbeaddressedinthefollowingsub- sections.

2. Extendeddelta-Vasameasureoftrafficconflictseverity 2.1. Howtomeasurenearness-to-collision?

Asindicated,thenearnesstoacollisionhasbeenstudiedexten- sively,sincemosttrafficconflictindicatorsareexclusivelybased onsomemeasureofproximityintimeorspace.Fromamethod- ologicalperspective,thetime-basedmeasuresarepreferred,since theyaretheresultofacombinationofroadusers’speedsanddis- tances(Laureshynetal.,2010).Oneofthemostfrequentlyused

Fig.1. SimplifiedillustrationoftheT2concept.Detailedcalculationsthattakeinto accountthedimensionsoftheroaduserscanbefoundinLaureshynetal.(2010).

indicatorsintrafficconflictstudiesisTime-to-Collision(TTC).TTC isdefinedas‘thetimeuntilacollisionbetweenthevehicleswould occuriftheycontinuedontheirpresentcourseattheirpresent rates’(Hayward,1972).IntheSwedishtrafficconflicttechnique, theTTCvalueatthemomentoftheevasiveactionstart(TA,Time- to-Accident)togetherwiththedrivingspeeddefinetheseverityof atrafficconflict(Hydén,1987),whiletheminimumvalueofthe Time-to-Collision(TTC_min)duringanencounterisusedasapartof theDOCTORtechnique(vanderHorstandKraay,1986).Inmany recentstudiesusingautomatedtrafficconflictobservations(Autey etal.,2012;Ismailetal.,2010;Sayedetal.,2013),TTC_minhasalso beencommonlyusedasatrafficconflictindicator.

Post-encroachmenttime(PET)isapplicableinsituationswhere tworoaduserspassthe‘conflictzone’withatimemargin(Allen etal.,1978).Itisdefinedasthetimebetweenthefirstroaduser leavingthe‘conflictzone’andthesecondonearrivingatit.APET valueequaltozeroindicatesnomargin,i.e.acrash.

Inorderforacrashtotakeplace,acollisioncourseofthetwo roadusersisapre-condition;withoutit,acollisionisnotpossi- ble.However,encounterswithouta collisioncoursemighthave crashpotentialaswell,sinceevenminorchangesinthespatialor temporalrelationshipsbetweentheroaduserscanleadtoacolli- sioncourse.ThismeansthattheuseofTTCaloneisnotsufficient fordetectingallpotentiallydangeroussituations.Thisisalsosup- portedbytheobservationsoftheactualconflictsintraffic(vander Horst,1990).Svensson(1998)noticedthatinsituationswheretwo vehicledriverswereabouttomisseachotherbyaveryshorttime margin,theirevasivebehaviourwasthesameasiftheywereon acollisioncourse.Inotherwords,eventhoughtherewasstrictly speakingnocollisioncourse,thedriversperceivedand actedas iftheywereonacollisioncourse.Laureshynetal.(2010),inan attemptofstudyingindetailtheprocessoftrafficconflicts,noted thataninteractionbetweentworoaduserscouldsmoothlyswitch frombeingacollisioncourseeventtobeinganon-collisioncourse event,andviceversa.Sincethiswasaresultofveryminor(and reversible)speedchanges,itappearscounter-intuitiveifthedan- gerousnessofthesituationwouldchangedramaticallyfromone timeinstancetothenext.Also,itwasnotedthatinfactthemajor- ityofthesituationsthatatrainedconflictobserverwouldselect asconflictsandhavingacollisioncoursehadinfactsmalltime marginsrevealed ifmore accuratetoolsfor speed and position measurementswereused(Laureshynetal.,2016).

Therefore,measuresusedtodescribetheseverityofanyinter- action should be flexible enough to include both the collision courseandnon-collisioncoursestate,andallowasmoothtrans- ferbetweenboth.TheindicatorT2suggestedbyLaureshynetal.

(2010)isanattempttofillthisgap.T₂describestheexpectedtime forthesecond(latest)roadusertoarriveattheconflictpoint,given unchangedspeedsand‘planned’trajectories(seeFig.1).Iftheroad usersareonacollisioncourse,T₂equalsTTC.Intheeventthatthe tworoaduserspasstheconflictpointwithatimemargin,T₂reflects themaximumtimeavailabletotakeevasiveactionsandalleviate

theseverityofthesituation.Itisnotstatedintheoriginalpaper explicitly,butthecurrentpracticeoftheapplicationofT2isthatit isnolongercalculatedafterthefirstroaduserhaslefttheconflict zone(sincethecollisionisnolongerpossible).Thisputanatural limitforhowlowaT2valuecanbereachedduringaninteraction

−forsituationswithalargetimemarginT₂remainslarge,while whenthemarginissmallT₂canalsoreachsmallvalues.

TheT2indicatorextendstheconceptofTTC,sinceitscalcula- tiondoesnotrequireacollisioncourse,andthereforeallowsfor asmooth transferfrom collision-courseandno-collision-course situationswithinthesameinteractionwithoutaneedtochange indicators(unlikethetraditionalTTCversusPETdichotomy).

SimilartoTTC,T₂isacontinuousindicatorandcanbecalculated foranytimeinstanceaslongasbothroadusersareheadingtowards thecommon‘conflictarea’.Thisraisesthequestionofwhichvalue (orwhatcombinationofvalues)ismostrelevantandshouldbe used.ThelatestpossiblevalueofT₂duringaninteraction,i.e.the momentwhenthefirstroaduserleavesthe‘conflictzone’andafter whichacollisionisnolongerpossiblewithoutachangeoftrajec- tories,haspracticallythesamemeaningasthePETandreflects themomentwhenthetworoadusersareclosestinspacetoeach other.Alternatively,theminimumvalueofT₂ (T₂^min)duringthe encounterreflectsthemomentwhentheyareclosestintime.In mostcases,thesetwovaluescoincide(asT2normallydecreasesas theroadusersapproacheachother),butinthecaseofsignificant speedchangesduringaninteraction,e.g.duetohardbraking,they mightrepresentdifferenttimeinstances.

BecauseofthemoreextensivescopeofT2comparedTTC,theT2

indicatorwillbeappliedtoexpressthenearnesstoacollision.More specifically,theminimumvalueofT₂(T₂^min)willbeused,sincethis valuerepresentsthepointwhereroadusershaveapproachedeach otherclosestintime,whichcanthereforebeconsideredthemost criticalinstantoftheirinteraction.

2.2. Howtomeasureconsequencesintheeventacrashwould havetakenplace?

Delta-V(v)isanotationoftenusedinphysicstodenotean object’schangeofvelocity(forexample,becauseofanimpactwith anotherobject).Inthecontextofroadcrashes,Delta-Vrefersto

thechangeofavelocityvectorexperiencedbyaroaduserduring acrash.Arapidchangeinthemagnitudeandthedirectionofthe speedimpliesextensiveforcesactingontheroaduserandcanbe expectedtohaveastrongeffectonpersonalinjuries. Moreover, Delta-Vissensitivetothe‘vulnerability’oftheroaduser,sincea lightobjectcollidingwithaheavyonewill‘bounceback’,whilethe heavyobject’sspeedwillremainquiteunchanged.Thisisavery importantpropertyinstudiesofcrashesbetween,forinstance,a carandapedestrianoraheavytruckandacar.

Numerous examples in crash safety research support this assumption(Evans,1994;GabauerandGabler,2008;Johnsonand Gabler,2012).TherelationshipbetweenDelta-Vandtheprobabil- ityofaseriousinjuryisvisualisedbyalogisticregressioncurvein Fig.2.TheexampleisadoptedfromGabauerandGabler(2006), buttherelationshipbetweenDelta-Vandtheriskofseriousinjury isconfirmedbyvariousauthors(Augensteinetal.,2003;Evans, 1994;GabauerandGabler,2008;Joksch,1993;Rybetal.,2007).

Joksch(1993) defineda rule ofthumb, showingthat themean rateofpercentageoftwo-vehiclecollisionsresultinginafatalityis approximatelyproportionaltoDelta-Vtothefourthpower.Studies byEvans(1994)andO’DayandFlora(1982)confirmthatJoksch’s ruleprovidesagoodapproximatefit.

Becauseofthisstrongevidence,variousresearchersconsider Delta-Vthebestsinglepredictorofcrashseverity(Evans,1994;

Shelby,2011).

TheestimationofDelta-Vforcrashesthathavetakenplaceis relativelystraightforward.Inthesecases,thereisa‘true’valueof Delta-Vthathastakenplaceduringthecrash.Basedonevidence aboutthepost-collisiontrajectoriesoftheinvolvedroadusersand otherinformation,suchasvehiclespecifications,expertscanmake abackwardreconstructionofthepre-,duringandpost-collision phase.AnestimationoftheDelta-Vvaluesexperiencedbythevehi- clesinthatparticularcrashcanbecalculated,forexample,byusing themomentumconservationprinciple(BurgandMoser,2007).

Itshouldbementionedthatanimportantcharacteristicofthe collisionwhichwouldaffecttheDelta-Vvaluesishowmuchenergy isabsorbed bythedeformationofthecollidingbodies, i.e.how

‘elastic’thecollisionis.Asafirstsimplifiedapproach,wecalculate Delta-Vasifitwasacompletelyinelasticcollision,i.e.bothobjects sticktogetherandmoveasoneafterthefirstcontact.Delta-V(abso-

Fig.2.IllustrationofrelationshipbetweenDelta-Vandprobabilityofasevereinjury(GabauerandGabler,2006).

( + )

Δ Δ

Fig.3.CalculationofDelta-Vbasedonmomentumconservationprinciple(inelasticcollision,i.e.twoobjects“sticktogether”afterthefirstcontact).

lutevalues)fortworoadusersinvolvedinaninelasticcollisioncan becalculated(seeFig.3):

v1= m2

m1+m2 ·

v²₁₊v²₂₋2v1v2cos˛ and

v2= m1

m1+m2 ·

v²₁₊v²₂₋2v1v2cos˛

wherem1,m2–themassesoftheroadusers1and2respectively, v₁,v₂–theirspeeds,

␣−theapproachangle.

SinceeachroaduserhasitsownDelta-Vvalue,todescribethe interactionseveritythehighestvaluecanbeused.

TheprobleminapplyingthisconceptofDelta-Vfortrafficcon- flictstudiesis thatno‘true’Delta-Vvaluehasmanifesteditself.

However,whenassumptionsaremadeabouttheroadusers’future movements,itispossibletocalculateahypotheticalor‘expected’

Delta-Vvaluethatwouldhaveemergedfromacrash.Forexample, assumingthatbothvehicleswillcrashwiththesamespeedasthey haveatacertainmomentduringaninteraction,theirrespective

‘expected’Delta-Vvaluescanbeestimated.This,however,creates anumberofissuestoresolve:i)the‘expectedDelta-V’becomes acontinuousvariablethatcanbecalculatedforeachinstantdur- ingtheinteraction;andii)foreveryinstantduringtheinteraction, differentvaluescanbecalculatedbasedontheassumptionsthat aremadeabouthowtheinteractionwilldevelop(primarily,ifthe plannedpathsandspeedwillstaythesameorchange).

Delta-Vhasnotbeenappliedasatrafficconflictindicatoruntil recentlywhenitwasincorporatedintotheautomatedconflictanal- ysisalgorithmsoftheSurrogateSafetyAssessmentModel(SSAM) (Gettmanetal.,2008;Shelby,2011).Itismeasuredbycalculating theexpectedchangeinvelocitybetweenthepre-andpost-crash phaseoftheroadusersinvolvedintheconflictassumingahypo- theticalcollisionofthetworoadusersattheangleandvelocitythey haveatthemomentTTC_mintakesplace.However,thisapproach hasanumberoflimitations,particularlywhenappliedontrajec- torydataobservedinfieldratherthangeneratedbyamicroscopic model. Firstly,the useof TTC_min as thetime at which Delta-V isestimatedlimitsitsapplicationtointeractions inwhichthere isacollisioncourseonly.Asmentionedintheprevioussection, experiencefromfieldobservationstudieslearnsthatmany(even close)encountersintrafficdonothaveanactualcollisioncourse (Laureshynetal.,2016;Svensson,1998).Secondly,inthisform, theindicatoronlyrepresentsthepotentialoutcomeseverityinthe eventanaccidentwouldhavetakenplace,butitdoesnotinclude thenearnesstoacollision.AneventwithalargeTTC_minvalueof severalsecondscanthereforehavethesamecalculatedvalueasa

consequences

'Expected' Delta-V, m/s

T2min, sec.

severity levels

nearness to collision

Fig.4.Conceptualillustrationofthemaindimensionsofconflictseverity.

verycloseinteractionwithaTTC_minlessthanonesecond.Because ofthis,itislesssuitableasastand-aloneindicatortodistinguish severefromnon-severeeventsintraffic.Ithasbeenacknowledged thattheimplementationofDelta-VinSSAMstillneedssubstantial improvements(Shelby,2011)andleadstosomecounter-intuitive resultsinexperiments(Zhaetal.,2014).

A framework that extends to non-collision course eventsis thereforetobepreferred.TheuseofT2min insteadofTTC_minas thebasisforexpressingthenearnesstoacollisioninourindicator overcomesthislimitation.Toovercomethesecondlimitation,the nearnesstoacollisionandtheestimatedseverityoftheoutcomein theeventanaccidentwouldhavetakenplaceshouldbeweighed togetherintoasingleindicator.

2.3. Extendeddelta-V−anattempttoweighnearnessand potentialoutcomeseverity

Fig.4 conceptually plotsthe twomain dimensions oftraffic conflictseveritythathavebeenidentifiedintheprevioussections (T₂^minand‘expected’Delta-Vatthesametimeinstant).Quiteintu- itively,theseverityofanencounterincreasesastheT₂^minvalue goesdown(astheroadusersareclosertoacollision)andasthe

‘expected’Delta-Vvaluegoesup(astheconsequencescanbemore severe).Encountersthat combinealow T₂^min value anda high

‘expected’Delta-Vvaluecanbeconsideredverydangeroussitu- ations.The “severitylevel”-linesrepresent theeventsof “equal severity”.Howexactlythe“severity” canbecalculatedrequires clarifications.

Fig.5. ScreenshotT-Analyst(onlyonecameraviewshown).

Theproblemofthe‘expected’Delta-Visthatitassumesacrash atthecurrentspeedsoftheinvolvedroadusersanddoesnottake intoaccountanyavailableopportunitytotakeanevasiveaction anddecreasetheconsequencesofthehypotheticalcollision.We suggestanewseverityindicator−ExtendedDelta-V−thatiscal- culatedwithspeedsthatarereducedbasedontheassumptionthat thetworoadusersspentthetimeavailabletobrakebeforearriving atthecollisionpoint.Thefinalspeed,v,isthencalculatedas

v=

0,if(v0−at)<0, wherev₀istheinitialspeed;

aistheassumeddecelerationrate;

t−timeremainingfortheevasivemanoeuvre.

Thedefinitionofthetimeavailableisquitestraightforwardin situationswithacollisioncourse;here,thecurrentTTCvaluecanbe used.Ifthereisnostrictcollisioncourse,thetworoadusersactually havedifferenttimesuntiltheyarriveatthepotentialcollisionpoint.

Inthiscontext,itisthetimeforthelatest-to-arriveroaduser,i.e.

T2indicator,thatappearstobemostrelevant,asitisobjectively themaximalavailabletimeuntilacollisionmayhappen(incase thefirstroaduserwould‘freeze’atthecollisionpoint).

Onefinalpointthatneedstobeaddressedistheassumeddecel- erationoftheinvolvedroadusers.Firstofall,itdependsonthe behaviouroftheinvolvedroadusers.Willtheybrakeinanormal way,orwilltheyapplymaximumbrakingforce?Inthispaper,we willtest twosimplifieddeceleration assumptionsasafirstcase study.Wewillapplyadecelerationof4m/s²fornormalbraking, andadecelerationof8m/s²foremergencybraking;thelatterisa

conservativevalueformaximumdecelerationthatnearlyallauto- mobilescanachieve(BurgandMoser,2007).Thesetrafficconflict measureswillbereferredtoasExtendedDelta-V₄ andExtended Delta-V8,respectively.ThebaseDelta-Vvalues,assumingnobrak- ing,willbereferredtoasDelta-V₀.

3. Thedatasetusedtoillustratetheconcept

Asafirsttestcase,anintersectioninthecityofMinsk(Belarus) wasanalysedforthreefulldays(6a.m.till9p.m.).Theintersection isafour-legintersectionequippedwithclassictwo-phasetraffic lights.Videofootageoftwocameras,installedatarooftopcloseto theintersection,wasusedfortheanalyses.

ThevideoswereanalysedusingT-Analyst,asemi-automated videoanalysistooldevelopedatLundUniversity(T-Analyst,2016).

Thesoftwareallowsformanuallysettingup3Dmodelsofroad usersinvideoimagesandprojectingtheirpositiononreal-world coordinates.Inthisway,thesoftwareallowsmanualtrackingof roadusersin oneor morecameraviews andthecalculationof somesafetyindicatorssuchasTTC,TimeAdvantage,T2 andrel- ativespeed(Laureshynetal.,2010).Itallowsfordealingwithlarge numbersofdetectionsinonedatabase.Fig.5showsascreenshot oftheprogramme.

Forillustrativepurposes,itwasdecidedtofocusonlyonsitu- ationswithaleft-turningvehicleapproachingfromtheleft-hand sideinthecameraview,andastraight-travellingvehiclecoming fromtheright-handsideinthecameraview.Thisprovidedarela- tivelylargenumberofinteractionsforanalysis,whilemostofthe ambiguityindefiningthe‘planned’trajectorieswasavoided.

12 342 1 165

564 104 Extended Delta-V8>0

all simultaneous arrivals ('exposure') all 'potential' conflicts

(Delta-V₀> 0) Extended Delta-V₄>0

Fig.6. Frequencyofeventsbyseverity.

The two cameras’ view allowedobserving two approaching vehicles approximately 3–4s beforethe potentialconflict area.

Simultaneousarrivals(situationsofavehicleintendingtomake a left-turn while there wasa visible straight-travelling vehicle approaching)werecountedas‘elementaryexposureunits’(Elvik et al.,2009).If theleft turnwasdone infront ofthe straight- travellingvehicle,itwasconsidereda‘potentialconflict’andthe trajectoriesforthetwovehicleswereextractedandanalysedusing T-Analyst.Freepassageswithnostraight-travellingvehiclepresent werenotconsidered‘exposureunits’andwerenotincludedinthe analyses.

4. Results

Threefull days of observations resulted in a total exposure of12,342 simultaneousarrivals.Of thesesimultaneousarrivals, 1165involvedavehicleturningleftinfrontofavehicledriving straightthrough.Forallofthesesituations,anon-zeroDelta-V0

valuecouldbecalculated.Ofthese1165situations,564hadanon- zeroExtendedDelta-V₄ valueand104hadanon-zeroExtended Delta-V8 value.ExtendedDelta-Vbecomes zeroin caseboth of thevehicleswould cometoafullstopbeforereachingthecol- lisionpointiftheyhadbrakedattheassumed decelerationrate (obviously,thehigheradecelerationratethatisassumed,theear- liervehiclescanstopandthusthemoresituationswillhavezero valueoftheExtendedDelta-V).Aclearsafetyhierarchycouldbe observed:eventsoflowseverityweremuchmorecommonthan eventsofhigherseverity(seeFig.6).

Allvariablesthathavebeencollectedfortherecordswithnon- zeroDelta-V₀valuesandtheirdescriptivestatisticsarepresented inTable2.

ThedistributionoftheDelta-V₀ valuesisshowninFig.7.The scatterplotinwhichtheDelta-V₀valuesareplottedagainsttheir correspondingT2minvaluesdoesnotshowveryclearpatterns.The histogramshowsatwo-tailedbellcurve,meaningthatboththe verylowvaluesandtheveryhighvaluesofDelta-V₀arerelatively uncommon.

The patterns become clearer when Extended Delta-V4 and ExtendedDelta-V₈ areusedtosettheseverityoftheindividual interactions(Fig.8andFig.9,respectively).Bothhistogramsshow aone-tailedshapewithahighnumberoflowvaluesandafewhigh values.ThispatternisabitmoredistinctintheExtendedDelta-V₈ histogramthanintheExtendedDelta-V₄histogram.

Thescatterplots shown in Fig.8 and Fig. 9are thesame as thescatterplotofDelta-V₀ values(Fig.7), butinteractions with non-zero Extended Delta-V₄ and Extended Delta-V₈ values are highlightedincolour.Thecolourofthesepointsprovidesthemag- nitudeoftheExtendedDelta-V₄andExtendedDelta-V₈valuesina categoricalway(incrementsof2m/sarechosenbecausetheypro- videasuitabletrade-offbetweenaccuracyandreadabilityofthe

graphs).Also,thehorizontalaxis(T₂^min)hasbeenadjustedtofocus ontherangeinwhichthesevaluesoccurtomaketheplotmore readable.Thedashedlinesindicatethetrendlineoftheselected Delta-V₀versusT₂^minvalues(basedonordinarylinearregression) foreachcategoryoftheExtendedDelta-V4andExtendedDelta-V8

values andmaybeseen asa firstapproximationof the“sever- itylevels”conceptuallyintroducedonFig.4(weomitR² values andregressionequationsasthetrendlinesarebasedonalimited numberofdatapointsandtheirpurposeismainlyillustrative).

ThetrendlinesofhighercategoriesofExtendedDelta-V₄and ExtendedDelta-V₈valuesarepositionedmoretothetopleftofthe graphthanthetrendlinesoflowercategoriesofExtendedDelta- V₄ andExtendedDelta-V₈.Thisshifttowardsthetopleftofthe graphshouldbeinterpretedthatgenerallyeventsofhigherseverity correspondwithhighervaluesofExtendedDelta-V4andExtended Delta-V₈.ThegraphsthereforeshowthatbothExtendedDelta-V₄ andExtendedDelta-V₈ identifyquitewellwhatcanbebelieved tobethemostdangerousconflictsfromthedataset.Theeventsof highestseverityareacombinationofhighDelta-V₀valuesandlow T₂^minvaluesandare,asmentionedearlier,assumedtobeclosestto aseverecrash.WhileExtendedDelta-V4leadstoahighernumberof selectedevents,itseemsthatExtendedDelta-V8ismoreselective.

Also,itisworthnotingthatthetrendlinesforExtendedDelta-V₈are steeperthanforExtendedDelta-V₄whichmeansthatinweighing togetherthetwodimensionsoftheseveritymoreweightisgiven toT₂^min.

Table1showsthe20mostsevereExtendedDelta-V₈situations, andhowthesesituationsrankforanumberofotherindicators.

Quitesomedisagreementcanbeseenamongtheindicators.The mostseveresituationaccordingtoExtendedDelta-V₈isalsocon- sideredthemostseveresituationaccordingtoTTC_minandT2min, whilethissituationisthesecondmostseveresituationaccording toExtendedDelta-V₄.However,accordingtoExtendedDelta-V₀, thissituationisonlyaverage;thisresultsfromthefactthatitis acar–carsituation(nodifferencesinmass),withonlyamoderate relativespeed.Theextremeclosenessintimemoststronglydefines theseverityofthissituation;aT₂^minof0.08simpliesaverynarrow miss.ThevalueconsideredthesecondmostseverebyExtended Delta-V₈isconsideredthemostseverebyExtendedDelta-V₄.This situationhasaratherhighDelta-V₀value,causedbyamoderate relativespeedincombinationwithalargedifferenceinmass(car- HGVsituation).Thereis,however,aslightlyhighertimemarginthat canstillbeusedtobrake,whichexplainsthedifferenceinranking betweenthetwoExtendedDelta-Vindicators.

Asaresultofthedifferenceintheassumeddecelerationrate betweenExtendedDelta-V₈andExtendedDelta-V₄,itcanbeseen thattheExtendedDelta-V4indicatorplacesabitmoreemphasison thecombinationoftherelativespeedandthemassratioofthesit- uation,whiletheclosenessintimeisamuchstrongerdeterminant fortheExtendedDelta-V₈situations.

Ingeneral,itcanbeseenthattheclosenessintimestillhighly definestheseverityofaninteraction.The20mostseveresituations accordingtoExtendedDelta-V₈ allhaveaT₂^minvalueof1.5sor lower,andallrankinthetop80mostseveresituationsaccordingto T₂^min.Ahighclosenessintimeis,therefore,stillanimportantpre- requisiteforanencountertobeconsideredseverebytheExtended Delta-Vindicators.Thisisanimportantcharacteristicfromatheo- reticalpointofview,sincemedium-severitytimemarginsarenot tobeconsidereddangerous.Rather,theyrepresentthenormaltraf- ficprocesswhereroadusersbalancetheneedtobehavesufficiently safewiththedesiretomaintainasufficientlyhighlevelofmobility (Hydén,1987;Laureshynetal.,2010;SvenssonandHydén,2006).

Ontheotherhand,ahighExtendedDelta-V₀ valueislessessen- tialtobeconsideredaratherseveresituation;aslongasthetime

0 50 100 150 200 250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 More

Frequency

Delta-V0(m/s)

N = 1,165

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10

Delta-V0(m/s)

T₂^min(sec.)

a) b)

Fig.7. Delta-V0values:a)histogram;b)scatterplotagainstT2min.b.

a) b)

0 20 40 60 80 100 120 140

1 2 3 4 5 6 7 8 9 10 More

Frequency

Extended Delta-V4(m/s)

N = 564

0 2 4 6 8 10 12 14 16 18 20

0 1 2 3 4 5

Delta- V

( m/s )

T

(sec.)

0 < Extended Delta-V4 < 2 2 < Extended Delta-V4 < 4 4 < Extended Delta-V4 < 6 6 <Extended Delta-V4

Fig.8. ExtendedDelta-V4values:a)histogram;b)markedonDelta-V0scatterplot.

Fig.9. ExtendedDelta-V8values:a)histogram;b)markedonDelta-V0scatterplot.

Table1

Comparisonrankingofthe20mostsevereExtendedDelta-V8situations(“ExtendedDelta-V”isabbreviatedto“V”).

Rank V8

Value V8

(m/s)

Rank V4

Value V4

(m/s)

Rank V0

Value V0

(m/s)

Rank T2min

Value T2min(s)

Rank TTCmin

Value TTCmin(s)

Rank relative speed

Value relative speed (m/s)

Typeof situation

mass ratio^*

1 9 2 9.3 409 9.6 1 0.08 1 0.98 191 19.2 car-car 1.00

2 7.7 1 11.1 17 16 23 1.09 58 3.99 135 20.2 car-HGV 3.85

3 5.8 3 8.7 119 12.3 12 0.91 – novalue 577 15.5 car-HGV 3.85

4 5 7 7.6 202 11.3 19 1.04 35 3.42 293 18 car-

minivan 1.69

5 4.7 24 5.8 908 6.9 2 0.32 12 2.87 741 14.1 car-car 1.00

6 4.5 8 7.3 194 11.4 40 1.27 – novalue 38 22.8 car-car 1.00

7 4.4 19 6.2 561 8.8 8 0.85 – novalue 327 17.7 car-car 1.00

8 4.3 17 6.3 561 8.8 7 0.81 – novalue 338 17.6 car-car 1.00

8 4.3 4 8.2 27 15.2 28 1.16 – novalue 390 17.2 car-HGV 3.85

10 4.2 11 6.9 367 9.9 11 0.91 9 2.29 154 19.8 car-car 1.00

10 4.2 6 7.8 75 13.3 72 1.48 – novalue 5 26.6 car-car 1.00

12 3.9 16 6.4 327 10.2 16 0.98 66 4.1 491 16.2 car-

minivan 1.69

13 3.7 13 6.5 367 9.9 59 1.4 31 3.4 154 19.8 car-car 1.00

13 3.7 20 6.1 628 8.5 5 0.69 4 1.92 413 17 car-car 1.00

15 3.6 5 8 43 14.1 57 1.38 – novalue 327 17.7 car-HGV 3.85

16 3 14 6.5 202 11.3 49 1.33 – novalue 44 22.6 car-car 1.00

17 2.9 23 5.9 353 10 79 1.5 – novalue 146 20 car-car 1.00

17 2.9 31 5.5 516 9 47 1.31 14 2.91 293 18 car-car 1.00

17 2.9 15 6.4 194 11.4 59 1.4 – novalue 38 22.8 car-car 1.00

17 2.9 53 5 724 8 13 0.92 20 3.17 526 16 car-car 1.00

*Massoftheheaviestvehicledividedbythemassofthelightestvehic.

marginissmallenough,moderatevaluesofDelta-V₀canalsobe consideredsituationsoffairlyhighseverity.

It isnoteworthythat there islittle correspondence between ExtendedDelta-V₈andTTC_min.ManyofthemostsevereExtended Delta-V8situationshavenoTTCvalueatall,i.e.therewasnocol- lisioncourse.Ontheonehand,thereisstrongevidenceforTTCto berelatedtotheseverityofthesituation.Forexample,inacali- brationstudycomparingtheseverityrankingofsituationsusing differenttrafficconflicttechniques,TTC_minwasfoundtobeadom- inantcomponentthatthescoresofalltechniquescorrelatedwith (Grayson,1984).¹ Ontheotherhand,theremightbeadvantages inincludingsituationswithoutacollisioncourse,too.Forexam- ple,theDOCTORtechnique(vanderHorstandKraay,1986)uses TTC_min asoneofthemainvaluestoassesstrafficconflictsever- ity,butalsoconsiderscloseencounterswithoutacollisioncourse seriousconflicts.

5. Discussion

5.1. Strengthsandapplications

TheExtendedDelta-Vindicatorbuildsonwell-establishedcon- cepts ofcrashreconstructions in order torepresent therisk of seriousinjuriesorfatalitiesascloselyaspossible(Augensteinetal., 2003;Evans,1994;GabauerandGabler,2008;Joksch,1993;Ryb etal.,2007).Integratingthe‘Delta-V’elementwiththetimeprox- imity to crashesadds a severitydimension toexisting conflict indicators.Asthebiggestsocietalburdencomesfromcrasheswith themostsevere outcomes,attempts topredictand preventthe highestlevelinjurieshavebeenatthecoreoftrafficsafetypolicy andresearchforalongtime.Therefore,validtrafficconflictindi- catorsshouldbynaturebecapableofpredictingthemostrelevant crashscenarios,i.e.thosewiththemostsevereoutcomes.Thus,

1Onecouldspeculate,however,abouttheaccuracyofthemeasurementsdone inthecalibrationstudy.Eventhoughthemeasurementswereactuallytakenfrom videos,manyfactors,suchasasimplifiedcameracalibrationmodelandcalculation proceduresforTTC,lowresolutionoftheimages,etc.,couldcontributetosituations wherebyverysmalltimegapsarelabelledashavingacollisioncourse.

Table2

Descriptivestatisticsofthedataset.

Variable Descriptivestatistics(N=1165) Delta-V0(m/s) None-zerovalues=1165

Mean=8.98;St.Dev.=2.66;

Min=1.5;Max=19.2 ExtendedDelta-V4(m/s) None-zerovalues=564

Mean=2.56;St.Dev.=1.79;

Min=0.1;Max=11.1 ExtendedDelta-V8(m/s) None-zerovalues=104

Mean=1.76;St.Dev.=1.59;

Min=0.1;Max=9.0

T2min(s) Availablevalues=1163

Mean=4.05;St.Dev.=13.99;

Min=0.08;Max=473.33

TTCmin(s) Availablevalues=247

Mean=5.19;St.Dev.=2.38;

Min=0.98;Max=32.83 Relativespeed(m/s) Mean=15.5;St.Dev.=3.96;

Min=3.1;Max=29.9 Left-turningvehicletype Availablevalues=1132

Car=1024;

Heavygoodsvehicle(HGV)=78;

Bus=0;Van=62

Left-turningvehiclespeed(m/s) Mean=5.35;St.Dev.=1.79;

Min=0.4;Max=12.9 Straightthroughvehicletype Availablevalues=1132

Car=844;HGV=170;

Bus=56;Van=94 Straightthroughvehiclespeed(m/s) Mean=12.02;St.Dev.=3.76;

Min=0.1;Max=21.7

addingaseveritydimensiontoaconflictindicatormightimprove thevalidityofconflictindicatorsaspredictorsforcrashes.Obvi- ously,furtherassessmentisneededtoverifythis.

TheExtendedDelta-Vindicatorissufficientlyflexibletoinclude collisioncourseandnon-collisioncourseevents,aswellascrash andnon-crashevents.T₂hasbeendevelopedexplicitlywiththe aimofallowingforthesmoothtransferbetweencollision-course and non-collisioncourseevents(Laureshynet al.,2010).In the eventofanactualcrash,T₂^minbecomeszero,andallvariationsof theExtendedDelta-Vvaluesconvergetothe‘true’Delta-Vvalue

experiencedbythevehiclesinvolvedintheactualcrash.Thisseems tomake theindicatorflexible enoughtocoverthewholespec- trumofsafetyrelevantsituations,rangingfromnormalencounters overseriousconflictsuptoandincludingcrashes.Thisisamajor strengthofthedevelopedindicator,anditisanadaptationtowards useinreal-worldobservations(thatoftenhavenocollisioncourse) aswellasanextensionoftheDelta-Vconceptasithasbeenimple- mentedinmicrosimulation(Gettmanetal.,2008).

Anoticeablefeatureoftheindicatoristhattheseverityofsome conflicts,thosewithhighExtendedDelta-Vvalues, maybecon- sideredhigherthantheseverityofsomeactualcrashes.Imagine acollisionbetweentwocarsmanoeuvringatverylowspeedsina parkinglot.Inthissituation,theriskforasevereinjuryislowand theactualDelta-Vvaluesthattakeplaceduringthecrasharealso low.Ontheotherhand,anarrowmissbetweentwovehicleswith highdifferencesinmassandspeedislikelytohaveamuchhigher (calculated)ExtendedDelta-Vvalue.Althoughthereisnoactual crash,thesituationisstillseveresincetheroaduserscomevery closetoasituationwithahighriskofseriousinjury.However,this doesmakesenseifone’spurposeistoassesstheseverityofatraffic situation,notonlyintermsofitsproximitytoacrash,butinterms ofitsclosenesstoaseriousinjury.

Thesuggestedindicatorcanbeusedinfullyautomatedtraffic conflictanalyses,sinceallrequiredparameters(speeds,trajecto- ries,roadusertypeestimates)canberetrievedfromvideofootage, and withslight alterations, also from data fromother sensors.

Giventherapidevolutionofthetrafficconflictobservationdomain towardsautomatedanalyses(Laureshynetal.,2010;Saunieretal., 2010),thisisanimportantadvantageoftheindicator.

5.2. Challengesandfutureresearch

For reasons of feasibility, this first operationalisation of the Extended Delta-V indicator accepted a number of simplified assumptions.Makingthemreflectrealisticsituationsmoreclosely shouldimprovetheperformanceoftheindicator:

1)Theassumedbrakingforceisnowaconstant.Thetruemaximum brakingforce,however,dependsonthemaximumtyre-roadway frictionwhich,inturn,dependsontheweather,thetypeand conditionofthepavement,thevehicletype,thetypeandcondi- tionofthetyres,thespeedofthevehicle,etc.(Roeetal.,1991;

Warneretal.,1983).Whileitwillnotbefeasibletoincludeall oftheseaspects(forinstance,videofootagedoesnotallowfor retrievinginformationaboutthetyresofthevehicle),anumber ofrefinementscanbeintroduced;

2)WhileitisexpectedthatExtendedDelta-Vwillespeciallyhigh- lightvulnerableroaduser(VRU)-relatedconflicts,theevasive actionsofpedestriansandcyclistsarenotthesameasmotor vehicles.Forexample,cyclistswerefoundtoswerveratherthan brake(Laureshynetal.,2016)whilepedestrianshaveanability toliterallystopinafractionofasecondandevenchangedirec- tiontotheopposite(jumpback).Assumptionsof‘atyrebraking ondryasphalt’aredefinitelynotidealhere;

3)Onlyfourdifferentvehiclemassesweredistinguished(car,HGV, bus,minivan).Theseassumptionscanberefined.Information aboutthemassofvehiclescanusuallyberetrievedfromvarious databases.Forefficiencyreasons,itwouldbebestiftheesti- matedmassofvehiclescouldberetrievedautomaticallybythe videoanalysissoftware.Onepossibilitycouldbetorelatethe massofthevehicletoitslength,whichisafeaturethatcanbe retrievedautomaticallyrelativelyeasily;

4)In thecurrentcalculations, acompletelyinelasticcollision is assumed.Thiscanbeseenasacollisionbetweentwoclayballs, whichwillsticktogetherafterthepointofcollisionandproceed

alongthesamepost-collisiontrajectory.Whilethisisareason- ableapproximation,inreality,motorvehiclecrashesexhibita somewhatelasticeffect,wherethevehiclesslightlyreboundoff eachotheragain(Shelby,2011).Thiseffectismodelledusing a so-called coefficientof restitution,which equalszero (0.0) forcompletelyinelasticcollisions(aswasassumedhere),and one(1.0)forcompletelyelasticcollisions.Inpractice,lowspeed collisionshaveacoefficientofrestitutionofaround0.4,while thiscoefficientdecreasesathigherimpactspeedstoaround0.1 (Nordhoff,2005);

5)Itshouldbepointedoutthat,whilethereisaclearcorrelation betweenthe(actual)Delta-Venduredbya roaduserduring acrashand thelikelihoodof(severe)injury, therelationship betweencrashimpactandinjuryoutcomeisquitecomplexand theresultingseverityofinjuries fromacrashareaffectedby manyfactors.Forexample,elderlyvehicleoccupantsaremore likelythanyoungeroccupantstobeseverelyinjuredinsimilar crashes(Evans,2001;Farmeretal.,1997;Lietal.,2003).The crashworthinessofavehicle(includingpassivesafetysystems) alsosignificantlyaffectstheprobabilityandseverityofinjuries inagivencrash.Additionally,motorvehiclescanabsorbmore impactenergyinfrontalimpactsthaninsideimpactsdueto thepresenceofcrumplezonesinthefrontofthevehicle.Occu- pantswhoareseatedmorecloselytothepointofimpacthavea higherprobabilityofsustainingsevereinjuriesthanoccupants fartheraway fromtheimpactpoint (Evans and Frick,1988).

Whilesomeoftheseaspectscouldbetakenintoaccountwhen furtheradvancingtheconflictindicator,otherscannot.

Apart from optimising the theoretical framework and the parameters of the calculation,validation researchis neededto checkwhetheratrafficconflictindicatorcanbeusedasatruemea- sureofsafety.Thisimpliesthatasufficientlylargebodyofevidence mustbefound, showingclosecorrelationsbetweencrashesand conflicts.Thisneedforvalidityresearchdoesnotonlyapplytothe ExtendedDelta-Vindicatorasitwasintroducedinthispaper,but alsotomanyoftheindicatorsthatareappliedtoday(Laureshyn etal.,2016;Zhengetal.,2014).

WhilethispapershowsthattheappliedExtendedDelta-Vindi- catorsallowforrankingtheseverityoftrafficencounters,itisnot yetclearhowthevaluesshouldbeinterpretedfromasafetyper- spective.For instance,itis unclearwhethera border shouldbe definedbetweenwhatisconsideredaseriousoranon-seriouscon- flict,orthattheresultsshouldbeinterpretedfromacontinuous perspective.

Oneoftheapproachesinsurrogatesafetyanalysisistheuseof extremevaluetheory,i.e.calculationsofprobabilitiestogetvery extreme(havinglowprobability)valuesofanindicatorbasedon thedistributionofthe‘normal’values(SongchitruksaandTarko, 2006).Forexample,ifthePETindicatorisused,onecouldformulate theproblemas‘whatistheprobabilityofobservingPET<0s’,which meansacollision.WhilestudyingtheDelta-Vsfromactualcolli- sions,onecanfindathresholdafterwhichsevereinjuriesbecome veryprobable;however,in thecaseof ahypotheticalExtended Delta-Vvalue,itisnotclearhowthethresholdshouldbedefined, andoncedefined,howitshouldbeinterpreted.

Thecasestudyonlyappliedtoonetypeofmanoeuvre,onetype ofintersection,andonlytomotorisedvehicles.Itwillbenecessary totesttheindicatorinothercircumstancesandforothertypesof roadusers.Itwillbeespeciallyrelevanttoseehowtheindicator willbehavewhenappliedtosituationswithVRUs.Existingtraffic conflicttechniquesareusuallyoptimisedforencountersamongcar drivers,butareoftenlesssuitableforapplyingtoVRUs(Shbeeb, 2000).