Overview of a part of Maasvlakte I, Port of Rotterdam ...
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OverviewofapartofMaasvlakteI,PortofRotterdam
Source:http://www.skyscrapercity.com/showthread.php?t=164137&page=11
(accessed27/6/2010)
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An analysis of vessel behaviour based on AIS data
Application of AIS data in a nautical traffic model
Document: Finalreport
Placeanddate: Delft,June28th2010
Author: ThijsdeBoer
Email: [email protected]
University: DelftUniversityofTechnology
Faculty: FacultyofCivilEngineering&Geosciences
Department: HydraulicEngineering
Graduationcommittee:
Prof.ir.H.Ligteringen(graduationcommitteechair) Professor Ports & Waterways, Delft University of Technology
Dr.ir.W.Daamen Assistant professor Transport & Planning, Delft University of Technology
Ir.R.W.P.Seignette Program manager, Port Planning & Development, Port of Rotterdam
Ir.C.VanderTak Senior Project Manager, Marin’s Nautical Centre MSCN
Ir.Y.Koldenhof Project Manager, Marin’s Nautical Centre MSCN
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An analysis of vessel behaviour based on AIS data
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Preface
ThismasterthesisisthelastpieceofworkinmymastereducationinHydraulicEngineeringattheDelftUniversityofTechnology.ThelargestpartoftheresearchhasbeencarriedoutinDelftandWageningen,althoughIhavehadseveralthesis-relatedmeetingsatotherlocationsintheNetherlands.
InthereportacasestudyofananalysisofAIS(AutomaticIdentificationSystem)isgiven.Bydoingthisanalysis,moreinsightisobtainedintothepaththatvesselstakeandtheaccompanyingvesselspeed,inportareas.Theresultsoftheanalysisaremadegeneric,tomakeitpossibletoimplementtheminmaritimemodels.
Iwouldliketothankthemembersofmygraduationcommittee,Prof.ir.H.Ligteringen,Dr.ir.W.DaamenfromtheDelftUniversityofTechnology,Ir.R.W.P.SeignettefromthePortofRotterdamandIr.C.VanderTakandIr.Y.KoldenhoffromMarinfortheirsupportandfeedbackgivenduringthetimespanofmythesis.
Furthermoremygratitudegoestofollowingpeoplethathelpedmewithvariouspartsofmyresearch.ErnstBoltfromRijkswaterstaat,forprovidinginformationandinsightinthemaritimemodelsthatexistnowadays.BenvanScherpenzeelfromthePortofRotterdam,forextendingmyknowledgeinthepracticalsideofthestory.DannydeRooandCorvanderScheldefromthePortofRotterdamforprovidingtheportmapandcurrentdata.
IwouldalsoliketothankErwinvanIperenfromMarin,forhisvaluable‘onthejob’supportandfeedback.Nexttohim,IwouldliketogiveabigthankstoallmycolleaguesatMarin,whogavemeaveryenjoyabletimeinWageningen.And,lastbutnoleast,mygirlfriendandfamilyfortheirsupportduringtheexecutionofmythesis!
ThijsdeBoer Delft,June2010
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SummaryFromDecember2004onwardseveryseagoingvesselover300GrossTonnage(GT)isobligedtobeequipedwithanAutomaticIdentificationSystem(AIS).NowadaysalsoinlandvesselsareincreasinglyusingAIS.ThemainfunctionsofAISarecollisionavoidanceandanaidtonavigation.Alsocoastalauthori-ties(security)andVesselTrafficServices(trafficmanagement)useAIS.Thesystemisvaluableforsearchandrescueactionsandinmaritimemodellingaswell.
ThequalityofAISmessageshasbeentopicofseveralresearches.AnAISmessagecanbedividedintothreetypesofdata:static,voyagerelatedanddynamic.MosterrorsarefoundinthedescriptionofDes-tination,Estimatedtimeofarrival,Draught,VesselTypeandNavigationalStatus.Exceptforvesseltype,thesedataarevoyagerelated.Thistypeofdatahastobechangedmanually,whichisasourceoferrors.Thestaticdataareaddedduringinstallationofthesystemanddonotchangehereafterandarethuslesspronetoerrors.Thedynamicdatadependonthevessel’snavigationalinstrumentsandarequitereliable.
MaritimemodelsuseAISdatamainlytodeterminethetrafficinput.AISdataalsoimprovetheinsightintothenauticalnetworksthathavetobemodelled.Inportareas,AISdataisnotoftenusedforthesepur-poses,asintheseareasthetrafficimageisdisturbedbyvesselsthatarenotAISequipped.AISdatacanpotentiallybeusedtoinvestigateindividualvesselbehaviour,butnoextensiveuseismadeofthisyet.
Roughlytwotypesofmaritimemodelsexist.Onetypesimulatestheoverallnauticaltrafficandtheotherusesindividualvessels.Aproblemforthemodelsthatsimulatevesselbehaviouristhesocalledhumanfactor.MostmodelstrytosimulatethisbehaviourusingFuzzy-technologyorBayesiannetworks.
AcasestudyisperformedtoseeifananalysisofAISdatacandescribevesselbehaviourinthePortofRotterdamarea.Ascasearea,thepathbetweentheNorthSeaandtheAmazonehaven(MaasvlakteI)isused.Thevesselpathandspeed,aswellastheinfluenceofvesselsize,wind,currentandvisibilityisdetermined.Theinfluenceofthevesselsizeistakenintoaccount,bycreatingfivedifferentclasses(<10,000;10,000-40,000;40,000-70,000;70,000-100,000;>100,00dwt).
Therearesignificantdiferencesbetweenthesizeclasses,aswellforthevesselpathasthevesselspeed.Ingeneral,largervesselssailmoretothemiddleofthechannelandsailslower.Theyalsohaveamorenarrowdistributionoverthewaterway.Thevesselpositionandthevesselspeedarenormallydistributedoverthewaterway.Thereisnosignificantrelationshipfoundbetweenthelocationinthecrosssectionandthevesselspeed.
Therearesomeexceptionstothegeneralconclusionsdescribedinthepreviousparagraph.Vesselsofthesizeclass70,000-100,000dwtsailsignificantlyslowerthanvesselsofthelargestsizeclass.Thismightbecausedbythefactthatthelargestvesselsusemoretugsandthereforehavealargermanoeuvrabilityintheportarea.Thismakesitpossibleforthemtomaintainahigherspeed.
IncomingvesselssailbackwardsorforwardsintotheAmazonehaven,dependingonhowtheyareloaded.ThiscausesroughlytwodifferentvesselpathsintheBeerkanaal,becauseinbothcasesthevesselswanttotakethewidestbend,asthisisamoreeasymanoeuvre.Vesselsthatleavetheportclearlyshowsomedeviationtowardsthenorthorsouth.Thisindicatesthattheyalreadyadapttheircoursetowardstheirnextdestination(e.g.directionofAntwerporHamburg).
Alsotheinfluenceoftheexternalcircumstanceswind,currentandvisibilityareexamined.Allthreearefoundtohaveaninfluenceonbothvesselpathandspeed.Exceptforthevisibilitynosignificantdiffer-
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An analysis of vessel behaviour based on AIS data
encesininfluencearefoundbetweenthedifferentsizeclasses.IntheMaasmond,highcrosswindsandcrosscurrentsleadtoadeviationfromtheaveragepathinthedirectiontheexternalinfluenceisworkingandtoalowerspeed.Ingeneral,windandcurrentfrombehindthevesselleadtoahighervesselspeed.
Toobtainmoregenericrules,Thecaseareaissplitintoseveralparts.Ineverypart,thegeneralisedvesseldistributionandvesselspeeddistributionarederivedinanumberofcrosssections.Theinfluenceoftheexternalcircumstancesisgeneralisedaswell.Thesecauseashiftinthenormaldistributionsoverthewater-way.Finally,theinteractionbetweenvesselscanbeanalysedbyusingAISdata.Inthisthesisanexampleofthisisgiven.
Fourcurrentlyexistingmaritimemodels(Samson,HarbourSim,MartramandDymitri)aretestedtotheoutputofthecasestudy,toseeiftheresultscanbeimplemented.Noneofthemodelscanimmediatelyimplementtheresults.InMartram,theresultscanbeimplementedbymakingonlyasmallamountofadjustments.HarbourSimneedstobeadaptedmore,mainlytoincludethevessel(speed)distributionoverthewaterway.Itisverydifficulttoimplementtheresultsintheothertwomodels,astheyarenotmeantfornauticaltrafficsimulation(Samson)orhaveadifferentapproachforsimulating(Dymitri).
Therearethreeimportantrecommendationsforfutureresearch.First,differenttypesofvesselsshouldbeinvestigated,asinthisthesisonlycontainervesselswheretakenintoaccount.Secondly,moreresearchshouldbeperformedtoobtainabetterinsightintheinfluenceoftheexternalcircumstances.Inthisway,externalinfluencescanbedescribedmorepreciseandalsorelationshipbetweenthemandthevesselsizemightbederived.Finally,thevessel-vesselinteractionshouldbeexamined.Thisclearlyisthenextstepindescribingthevesselbehaviourinaportarea.
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Preface
Summary
Tableofcontents
Listoffigures
Listoftables
1 Introduction............................................................................................................................ 21.1 Background................................................................................................................ 21.2 Nauticaltrafficmodellingprograms.......................................................................... 31.3 Problemdefinition..................................................................................................... 31.4 Researchquestions.................................................................................................... 31.5 Researchapproach.................................................................................................... 41.6 Reportoutline........................................................................................................... 5
2 AutomaticIdentificationSystem............................................................................................. 82.1 Introduction............................................................................................................... 82.2 AISmessage............................................................................................................... 82.3 ErrorsinAISmessages............................................................................................... 92.4 Improvingsafetyofnavigationandotherapplications........................................... 102.5 Conclusions.............................................................................................................. 11
3 Maritimemodelling.............................................................................................................. 143.1 Thebasicprincipleofmaritimemodellingprograms.............................................. 143.2 TypeI:Thegeometricmodel................................................................................... 163.3 TypeII:MaritimeTrafficSimulationPrograms......................................................... 173.4 UseofAISinmodels................................................................................................ 193.5 Existingmaritimemodels........................................................................................ 20
4 Casestudysetup.................................................................................................................. 264.1 Approachcasestudy................................................................................................ 264.2 Location................................................................................................................... 264.3 Casestudyoutline................................................................................................... 29
5 Averagevesselpathandspeed............................................................................................. 325.1 Datasets.................................................................................................................. 325.2 Accuracyofthedatasets......................................................................................... 335.3 Theinfluenceofvesselsize..................................................................................... 375.4 Vesselandvesselspeeddistribution....................................................................... 425.5 Conclusions............................................................................................................. 54
Table of contents
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6 Externalinfluences............................................................................................................... 586.1 Wind........................................................................................................................ 586.2 Current.................................................................................................................... 666.3 Visibility................................................................................................................... 706.4 Conclusions.............................................................................................................. 72
7 Interaction............................................................................................................................ 747.1 Interactioninthecasestudyarea........................................................................... 747.2 MethodI.................................................................................................................. 747.3 MethodII................................................................................................................. 777.4 Conclusion............................................................................................................... 78
8 Genericrules......................................................................................................................... 808.1 Definingwaterways................................................................................................. 808.2 Averagebehaviour................................................................................................... 838.3 Externalinfluences.................................................................................................. 858.4 Implementationinmaritimemodels....................................................................... 868.5 Conclusions.............................................................................................................. 87
9 Conclusions&recommendations......................................................................................... 909.1 Conclusions.............................................................................................................. 909.2 Recommendations................................................................................................... 90
References
Appendices
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Figure1.1 Worldseabornetrade1968-2008,.......................................................................... 2
Figure1.2 Reportoutline.......................................................................................................... 5
Figure3.1 Twovesselswithdifferent,overlappingsafetydomains........................................ 14
Figure3.2 Thebasicprincipleofthecalculationofcollisionrisk............................................ 15
Figure3.3 Thebasicprincipleofthecalculationofcollisionrisk,reflectedinprobabilities... 16
Figure3.4 Crossingwaterwayswithriskareaofship-shipcollision........................................ 17
Figure4.1 OverviewoftheportofRotterdam,theMaasvlakteIisindicated
bytheredcircle;................................................................................................... 27
Figure4.2 OverviewofMaasvlakteI,theAmazonehavenisindicatedbyaredellipse;........ 27
Figure4.3 PlotofthevesseltracksattheentranceoftheBeerkanaal.................................. 28
Figure4.4 PlotofthevesseltracksattheentranceoftheAmazonehaven............................ 28
Figure5.1 Calculationdifferencesbetweenaveragevesselpaths.......................................... 34
Figure5.2 Thecumulativedistributionfunctionofthedifferencesbetween
two average tracks, ............................................................................................... 35
Figure5.3 Averagepathofoutgoingvessels,sizeclasses<10,000dwt(green)
and>100,000dwt(blue)....................................................................................... 37
Figure5.4 Speeddevelopmentandtherelativedifferencebetweenthetracks(blue)......... 41
Figure5.5 OverviewofallAISmessagessentfromspecificareas.......................................... 43
Figure5.6 Crosssectionsonthevesseltrajectories,............................................................... 44
Figure5.7 Spatialdistributiononlocation3(seeFigure73),................................................ 45
Figure5.8 Spatialdistributionforthevesselsizeclass<10,000;incomingatlocation3(left)
and>100,000;outgoingatlocation2(right)......................................................... 47
Figure5.9 Thespatialvesseldistributionofthevesselsizeclass10,000-40,000,.................. 47
Figure5.10 Thespatialvesseldistributionofthevesselsizeclass40,000-70,000;
incomingatlocation3........................................................................................... 49
Figure5.11 Thespatialvesseldistributionofthevesselsizeclass70,000-100,000;outgoingat
location1(left)and3(right).................................................................................. 50
Figure5.12 Thespatialdistributiononlocation4forincoming(left)andoutgoing(right)
vesselsfromsizeclass>100,000dwt..................................................................... 51
List of figures
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Figure5.13 Thedifferenceinthevesselpathwhensailingforwards(red)orbackwards(blue)
intotheAmazonehaven......................................................................................... 51
Figure5.14 Vesselspeeddistributiononlocations1to4,forsizeclass70,000-100,000dwt;
incomingvessels.................................................................................................... 53
Figure5.15 Vesselspeeddistributionoverthecrosssectionsatlocations1to4................... 54
Figure6.1 PartIandpart2...................................................................................................... 58
Figure6.2 AverageheadinginMaasmondandBeerkanaal.................................................... 59
Figure6.3 Influenceofcrosswindonthechosenpathofindividualvesselsat
the’Maasmond’trajectory.................................................................................... 60
Figure6.4 BoxplotoftheinfluenceofcrosswindsintheMaasmond..................................... 61
Figure6.5 LinearrelationshipregardingtheinfluenceofcrosswindsintheMaasmond........ 62
Figure6.6 TheinfluenceofcrosswindsonthevesselspeedintheMaasmond...................... 62
Figure6.7 Developmentoftheaveragevesselheadingforthewholesizeclass>100,000dwt
andthepartofthevesselsthatencounterstrongcrosswindfromstarboardside.63
Figure6.8 Theinfluenceofparallelwindonthechosenpathandvesselspeedinthe
Maasmond............................................................................................................ 64
Figure6.9 Theinfluenceofcrosswindsonthevesselpathandvesselspeed
intheBeerkanaal................................................................................................... 64
Figure6.10 Theinfluenceofwindfrombehindandfromthefrontofthevessel
onthevesselpathintheBeerkanaal..................................................................... 65
Figure6.11 TheinfluenceofparallelwindonthevesselspeedintheBeerkanaal
forincoming(left)andoutgoing(right)vessels..................................................... 65
Figure6.12 Overviewofthedifferentcurrentregimesinthecasearea................................. 67
Figure6.13 Theinfluenceofcrosscurrentonthevesselpath(left)
andspeed(right)inpart1..................................................................................... 68
Figure6.14 Developmentofthevesselheadingunderinfluenceofastrongcrosscurrent
(green)comparedtotheaverageheading(blue).................................................. 68
Figure6.15 Theinfluenceofparallelcurrentonthevesselpath(left)
andspeed(right)inpart1.................................................................................... 69
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Figure6.16 Theinfluenceofparallelcurrentonthevesselpath(left)andspeed(right)
inpart2................................................................................................................ 69
Figure6.17 Theinfluenceofparallelcurrentonthevesselpathinpart4(Beerkanaal)......... 70
Figure6.18 Theinfluenceoflowvisibilityonthedeviationfromtheaveragepath
intheBeerkanaal.................................................................................................. 71
Figure7.1 ExplanationCPAandTCPA...................................................................................... 75
Figure7.2 AnexampleofinteractionshortlybeforetheentranceintotheBeerkanaal......... 75
Figure7.3 Developmentofthevesselspeed(left)andvesselheading(right)compared
totheaverageofthesizeclass70,000-100,000dwt(discontinuousline)............ 76
Figure7.4 Exampleoftheinteractionofanoutliers(purpletriangle)withanothervessel,
afterplottingthewholetrafficimage.................................................................... 78
Figure8.1 Overviewofthedifferentcurrentregimesinthecasearea................................... 80
Figure8.2 Overviewofthesimplifiedwaterway(blue)inpart1........................................... 81
Figure8.3 Overviewofthesimplifiedwaterwayinpart2...................................................... 81
Figure8.4 Overviewofthesimplifiedwaterwayinpart3...................................................... 82
Figure8.5 Overviewofthesimplifiedwaterwayinpart4...................................................... 82
Figure8.6 Thecrosssectionsthatareinvestigatedinpart1................................................. 83
Figure8.7 Distributionoverthewaterwayatcrosssection1-C.............................................. 84
Figure8.8 Thespeeddistributionforincomingvesselsatcrosssection1-C.......................... 84
Figure8.9 Theinfluenceofcrosscurrentonthevesselpathatpart1.................................. 86
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Table2.1 Numbersofvesselstransmittingerrorsbyyear...................................................... 10
Table5.1 Numberoftracksineachdataset............................................................................ 33
Table5.2 Comparisonoftheaveragetracks,calculatedbyrespectively50%and100%
ofthedata............................................................................................................. 34
Table5.3 The95%confidenceintervalsinmetersforthedistancebetweentwoaverage
tracksofonevesselsizeclass................................................................................ 35
Table5.4 Comparisonofthespeedoftheaveragetracks,calculatedbyrespectively50%
and100%ofthedata............................................................................................ 36
Table5.5 The95%confidenceintervalsinpercentagesforthespeeddifferencebetween
twoaveragetracksofonevesselsizeclass............................................................ 36
Table5.6 Comparisonoftheaveragetracksfromdifferentvesselsizeclasses,forincoming
vessels................................................................................................................... 38
Table5.7 Comparisonoftheaveragetracksfromdifferentvesselsizeclasses,foroutgoing
vessels................................................................................................................... 38
Table5.8 95%confidenceintervalsinmetersforthedifferencebetweentheaverage
trajectoriesoftwovesselsizeclasses.................................................................... 39
Table5.9 95%confidenceintervalsinmetersforthedifferencebetweentheaveragetrajecto-
riesoftwovesselsizeclasses,forthetrajectorywithintheport’sbreakwater.... 39
Table5.10 Comparisonoftheaveragespeedfromdifferentvesselsizeclasses,for
incomingvessels................................................................................................... 40
Table5.11 Comparisonoftheaveragespeedfromdifferentvesselsizeclasses,for
outgoingvessels................................................................................................... 40
Table5.12 95%confidenceintervalsinpercentagesforthedifferencebetweenthespeeds
oftwovesselsizeclasses....................................................................................... 40
Table5.13 Skewnessforthedifferentdatasetsatlocations1to4........................................ 46
Table5.14 Excesskurtosisforthedifferentdatasetsatlocations1to4................................ 46
Table5.15 Resultsoftheχ2-testsforthefittingoftheassumednormaldistributionto
thedifferentdatasets........................................................................................... 48
List of tables
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Table5.16 Coefficientsofdetermination(R2)forthespatialvesseldistribution................... 49
Table5.17 Coefficientsofdetermination(R2)forthevesselspeeddistributionin
locations1to4...................................................................................................... 52
Table6.1 Windspeedclasses.................................................................................................. 59
Table6.2 Currentvelocityclasses............................................................................................ 67
Table8.1 Characteristicsofthedifferentsizeclassesincrosssection1-C.............................. 85
Table8.2 Vesselspeedcharacteristicsofthedifferentsizeclassesincrosssection1-A......... 85
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Chapter 1
Chapter 8
Chapter 5
Descrip�on the func�ons of AIS and an inves�ga�on of the quality of AIS messages
Research ques�on 1: What are the possibili�es and limita�ons of AIS data, when using it in mari�me modelling research?
Chapter 4
Chapter 3
Chapter 2 Subques�on 1-A: What are the possibili�es and limita�ons of AIS (data)?
Introduc�on of AIS , mari�me traffic simula�on programs. Problem defini�on and research ques�ons .
Explana�on of the characterics of mari�me models and how AIS is used in the models nowadays.
Subques�on 1-B: What are the main characteris�cs of mari�me traffic simula�on programs?
Subques�on 1-C: How is AIS used in the development of mari�me models nowadays?
Research ques�on 2: Can the exact nau�cal behaviour of vessels in the port of Ro�erdam be described using sta�s�cal equa�ons, following from an analysis of AIS data ?
A descrip�on of the case study that is used in this thesis
Analysis of the average vessel path and vessel speed, as well as an inves�ga�on of the influence of vessel size.
Subques�on 2-A: What factors are important in a vessel’s exact path and vessel speed an to what extent?
Deriva�on of generic rules, based on the outcomes of the case study. Also a discussion of the possibility to implement
these rules into currently exis�ng mari�me models. Subques�on 3-B: Is it possible to implement the derived equa�ons into a currently exis�ng mari�me model or should a new model be developed?
Research ques�on 3: Is it possible to develop derive generic mari�me model rules that describe the vessel behaviour in a port area?
Subques�on 3-A: How can these specific equa�ons be made generic?
Chapter Content Subques�on answered
Chapter 6 Analysis of the influence of the external circumstances wind, current and visibility on the vessel path and speed
Subques�on 2-B: How do interac�ons with other vessels influence a vessel’s course?Chapter 7 Analysis of the influence of the vessel-vessel interac�on.
Introduction
Chapter1
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Introduction
1 Introduction
1.1 Background
Maritimetransporthasalwaysbeenveryimportantininternationaltrade.Especiallysincetheintroductionofthecontainerinthefifties,maritimetransporthasrapidlyincreasedduetoitscost-efficiency(Figure1.1).Thishasledtoanenormousgrowthofthetrafficintensityinportsallovertheworld.Notonlythenumberofvesselshasincreased,alsothevessel-sizehasbeendeveloping.1
Figure 1.1 World seaborne trade 1968-2008, source: www.marisec.org
Withtheabovementioneddevelopmentsinmaritimetransport,safetyandcapacityissuescomeup.TheInternationalMaritimeOrganization(IMO)2hasbeenveryimportantfortheimprovementofsafetyatsea.Thisorganisation,establishedin1948inGeneva,maintainsseveraltreatiesthataimtoimprovethenauti-calsafety.AnexampleofsuchatreatyisSOLAS(SafetyofLifeatSea),whichgivesrulesandguidelinestopreventaccidents.Oneoftheserulesistheobligationforseagoingvesselslargerthan300GrossTonnage(GT)tocarryanAutomaticIdentificationSystem(AIS)sinceDecember2004.
VesselsequippedwithAIScarryaninstrumentwhichtransmitsandreceivesdataaboutthevesseloveradedicatedVHF(VeryHighFrequency)radioband.Thetimeintervalinwhichthisisdonedependsonthespeedofthevesselandrangesfrom2secondsto10secondswhensailing.Thedatacontainsthegeneralinformationofavesselaswellasitsposition,speed,heading,originanddestination,cargoandcurrentdraft.Thisinformationispickedupbyothervesselsandcoastalauthorities.Theothervesselsuseitfornavi-
1 Internationalchamberofshipping(ICS)&Internationalshippingfederation(ISF),
http://www.marisec.org/shippingfacts/,accessed:26/1/2010
2 MoreinformationregardingtheIMOandtheSOLAStreatycanbefoundinAppendixA.
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gationalpurposes,whiletheauthoritiescanuseitforidentification(security)andcommunication.3 More informationregardingthecharacteristicsanduseofAIScanbefoundinchapter2.
1.2 Nautical traffic modelling programs
Besidesinternationalrulesandguidelines,awaytoimproveanddeterminesafetyandcapacityisbytheuseofmaritimemodels.Especiallyinportplanninganddesign,modellingprogramscanbeaveryvaluabletool.Theycanforexampledemonstratetheeffectivenessofdifferentriskcontrolmeasures;therebyassistingtheevaluationofalternatives(Seignette,2005).Differenttypesofmodelsexisttosupportdecisionsinthedevelopmentofportinfrastructure.Someofthesemodels(FastTimeManoeuvringSimulationPrograms)describeavessel’smotioningreatdetail,bytakingintoaccountexternalinfluencessuchaswindandcur-rents.Animportantoutputofsuchamodelistheprecisepathasinglevesseltakesinacertainportareaandthecontrolsitapplies.Therisksfollowingfromtheinteractionbetweenvesselshoweverisnotsimu-lated,becausemostlythemodellingofmultiplevesselssimultaneouslyisnotdone(Pimontel,2007).
Inanothertypeofmodel,themaritimetrafficmodellingprograms,multiplevesselsaretakenintoaccount.Thismakesitpossibletocalculatesafetyandcapacityofacertainwaterway.Theseprogramshoweverdonotreachthesamelevelofdetailofthefasttimemanoeuvringmodels.Somemodelstrytoapproximatethevesselbehaviour,butmostofthemdonotsimulateexactvesselmovements.Thismeansthatalsothevesselinteractionwithothervesselsandinfrastructureisnotsimulated.Especiallyinbusy,closedwater-wayslikeportsthismakesitverydifficulttoquantifynauticalriskssufficiently.
1.3 Problem definition
Asmentionedabove,currentmaritimemodelsdonotsufficientlysimulatetheexactvesselbehaviourandinteractionwithothervessels.WiththeintroductionofAIS,anewpossibilityisavailabletogetmoreinsightintothisnauticalbehaviour.AISmessagesaresentonaveryregularbaseandthereforealotofprecisedataispresent.Thismakesitpotentiallypossibletostatisticallydescribevesselbehaviour.AIShoweverisnotoriginallydevelopedforresearchpurposes.Itisnotsurewhicherrorsanduncertaintiesarepresentandifandhowthislimitsthepossibilityofusingitinmodelling.Thereforethesedatashouldbeexaminedverycriticalbeforeusing.Thisleadstotheproblemdefinitionofthisresearch:
Theexactcourseofavesselanditsinteractionwithothervesselsandinfrastructureisnotalwayssimulatedinsufficientdetailincurrentmaritimemodels,ananalysisofAISdatamayimprovetheinsightinandmod-ellingoftheexactnauticalbehaviour.
1.4 Research questions
Theproblemdefinitionissplitupintothreeresearchquestions.Becausemodellingexactvesselbehaviourisespeciallyimportantinportareas,theportofRotterdamareaisusedasacasestudy.Eachofthequestionsisdividedintoseveralsubquestions.
3 Internationalmaritimeorganization(IMO),
www.imo.org,accessed:26/1/2010
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Introduction
1. WhatarethepossibilitiesandlimitationsofAISdata,whenusingitinmaritimemodellingresearch?
1-AWhatarethepossibilitiesandlimitationsofAIS(data)?
1-BWhatarethemaincharacteristicsofmaritimetrafficmodellingprograms?
1-CHowisAISusedinthedevelopmentofmaritimemodelsnowadays?
2. CanthedetailednauticalbehaviourofvesselsintheportofRotterdambedescribedusingstatistical equations,followingfromananalysisofAISdata?
2-AWhichfactorsareimportantinavessel’sexactpathandspeedandtowhatextent?
2-BHowdointeractionswithothervesselsinfluenceavessel’spathandspeed?
3. Isitpossibletoderivegenericmaritimemodelrulesthatdescribevesselbehaviourina portarea?
3-AHowcanthesespecificrulesbemadegeneric?
3-BIsitpossibletoimplementthederivedequationsintoacurrentlyexistingmaritimemodelor shouldanewmodelbedeveloped?
1.5 Research approach
Theapproachusedinthisthesistoanswerthethreemainresearchquestions,canalsobesplitintothreesections.First,aliteraturestudyisneededtoobtaininsightintoAISandmaritimemodels.Afactualdescrip-tionofAIS(messages)isgiven,butalsoinsightinthequalityofAISdata,toanswersubquestion1-A.Togetinformationregardingmaritimemodels,anoverviewisgivenoftheapproachofmaritimemodelsnowa-days.AlsotheuseofAISdatainthesemodelsisinvestigated.
Researchquestion2isansweredbyusingacasestudy.Byusingaspecifiedarea,aselectioninvesseltracksthatareexaminedcanbemade.Itmakesitalsopossibletocomparethederivedresultswitheachothermoreeasy.Inthiscasestudy,firsttheinfluenceofthevesselsizeisinvestigated.Thisisdone,becauseafterthisisknown,thevesselscanbebroughttogetherinsuitablesizeclasses.Theaveragevesselpathandspeediscalculatedforthedifferentsizeclasses.
Whentheaveragebehaviourisknown,itcanberesearchedwhatotherinfluencesdoexistthatinfluenceavessel’spathandspeed.Mainfocuswillbeontheinfluenceofexternalcircumstances,likewind.Alsothevessel-vesselinteractionwillbetakenintoaccount.Thisisdifferentfromtheotherinfluences,asinteractionsituationsaremostlyverycasespecific.Thecalculationoftheinfluenceofinteractionwillthereforeneedanapproachthatfocussesonthedetailedanalysisofindividualsituations.
Researchquestion3isdividedintotwosubquestions.Thefirstsubquestionhandlesthederivationofgener-icrules.Thesecanbemade,bysimplifyingthenauticalinfrastructurefromthecasestudytomorestandardtypesofwaterways.Theresultsfromthecasestudycanthanbegeneralised.Thesecondquestionscon-cernsthepossibilitytoimplementtheserulesinanexistingmaritimemodel.Toanswerthisquestion,thespecificcharacteristicsofseveralmaritimemodelsusednowadaysareelaborated.
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An analysis of vessel behaviour based on AIS data
1.6 Report outline
Researchquestions1anditssubquestionswillbeansweredinchapters2and3.Question2,includingsubquestions,ishandledinchapters4-7.Theanswertoquestion3anditssubquestionsisgiveninchapter8.Figure1.2showsthereportoutlinegraphically.
Chapter 1
Chapter 8
Chapter 5
Descrip�on the func�ons of AIS and an inves�ga�on of the quality of AIS messages
Research ques�on 1: What are the possibili�es and limita�ons of AIS data, when using it in mari�me modelling research?
Chapter 4
Chapter 3
Chapter 2 Subques�on 1-A: What are the possibili�es and limita�ons of AIS (data)?
Introduc�on of AIS , mari�me traffic simula�on programs. Problem defini�on and research ques�ons .
Explana�on of the characterics of mari�me models and how AIS is used in the models nowadays.
Subques�on 1-B: What are the main characteris�cs of mari�me traffic simula�on programs?
Subques�on 1-C: How is AIS used in the development of mari�me models nowadays?
Research ques�on 2: Can the exact nau�cal behaviour of vessels in the port of Ro�erdam be described using sta�s�cal equa�ons, following from an analysis of AIS data ?
A descrip�on of the case study that is used in this thesis
Analysis of the average vessel path and vessel speed, as well as an inves�ga�on of the influence of vessel size.
Subques�on 2-A: What factors are important in a vessel’s exact path and vessel speed an to what extent?
Deriva�on of generic rules, based on the outcomes of the case study. Also a discussion of the possibility to implement
these rules into currently exis�ng mari�me models. Subques�on 3-B: Is it possible to implement the derived equa�ons into a currently exis�ng mari�me model or should a new model be developed?
Research ques�on 3: Is it possible to develop derive generic mari�me model rules that describe the vessel behaviour in a port area?
Subques�on 3-A: How can these specific equa�ons be made generic?
Chapter Content Subques�on answered
Chapter 6 Analysis of the influence of the external circumstances wind, current and visibility on the vessel path and speed
Subques�on 2-B: How do interac�ons with other vessels influence a vessel’s course?Chapter 7 Analysis of the influence of the vessel-vessel interac�on.
Figure 1.2 Report outline
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AutomaticIdentificationSystem
Chapter2
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AIS
2 Automatic Identification System
ThischapterexplainstheworkingoftheAutomaticIdentificationSystem(AIS).Itindicatestheseveralfunc-tionsofAISandhowthemessagesaretransmitted.Alsothedataincludedinamessageandthequalityofthedataisdescribed.
2.1 Introduction
InDecember2000IMOdecidedtostartimplementingAISintheinternationalseatrade.TheobjectivesfortheimplementationofAISwere‘toenhancesafetyandefficiencyofnavigation,safetyoflifeatsea,andmaritimeenvironmentalprotectionthroughbetteridentificationofvessels,assistedtargettracking,andimprovedsituationalawarenessandassessmentthroughsimplifiedandadditionalinformation.AIScanalsoimprovethequalityofvesseltrafficsurveillance(VTS)andwaterwaymanagement’.(Harati-Mokhtari,et.al.2007,p.374)
FromtheobjectivesmentionedaboveroughlythreefunctionsofAIScanbedistinguished.
1.Toassistinnavigationandcollisionavoidance.
2.Topassinformationaboutavesselanditscargotocoastalstates.
3.TohelpintrafficmanagementasaVTStool.
EspeciallythefirstfunctionisaveryimportantcharacteristicofAIS.ByreceivingAISmessagesfromnearbyvessels,apreciseoverviewofthetrafficsituationaroundthevesselisderived.Becauseidentificationisdoneautomatically,communicationiseasier.Thismakesitpossibletosolvepotentiallydangeroussituationsmuchquicker.Thisandotheradvantagesareelaboratedmoreintodetailinthenextsection.
ThetimeschemeoftheintroductionofAISisdescribedintheSOLAStreaty.FromDecember2004onwardsallsea-goingvesselslargerthan300grosstonnages(GT)areobligedtohaveAISonboard.Inpracticealmosteverysea-goingcargovesselexceedsthisweightlimitandcarriesAISnowadays.FishingandinlandvesselsaswellaspleasureyachtsuseAISlessoften.TheuseofAISby-especially-inlandvesselsishoweverexpectedtoincreaserapidly.4
2.2 AIS message
VesselsthathaveanAIScarryatransponderwhichtransmitsmessagesaboutthevesseloveradedicatedVHF(VeryHighFrequency)radioband.ThefrequenciesintheVHFrangearemuchlowerthanthefrequen-ciesusedbymarineradar(whichusesSuperHighFrequencies).ThismeansthatAISmessagesaresentwithalargerwavelengthaswell.DuetothislargerwavelengthAISisabletodetecttargetsinsituationswhereradardetectionislimited.Thisisthecasearoundbends,behindhillsandothervesselsandinconditionsofrestrictedvisibilityinportsandrestrictedwaterways.
4 Currently3%oftheinlandvesselsthatvisittheportofRotterdamareequippedwithiAIS(inlandAIS).The
expectationisthat,duetonationalandEuropeanstimulationprograms,attheendof2012thisnumberhas
increasedtoalmost80%.Source:R.W.P.Seignette,portofRotterdam.
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An analysis of vessel behaviour based on AIS data
TherearethreetypesofdatainanAISmessages:staticdata,voyagerelateddataanddynamicdata.Thecategoriesarevalidfordifferenttimeperiodsandthereforehavedifferentupdateintervals.Staticdataandvoyagerelateddataaretransmittedevery6minutes,onrequestofacompetentauthorityandwhenthedataarechanged.Thetimeintervalofthedynamicdatamessagedependsonthespeed,coursealterationandnavigationalstatusofthevessel.Whenthevesselismooredamessageissentevery3minutes.Whensailing,thistimeintervalrangesfrom2seconds(speed>23knots≈11.8m/s)to10seconds(speed<14knots≈7.2m/sandnocoursealterations).Ifneededalsoshortsafety-relatedmessagescanbesent.
StaticdataareenteredintothesystemduringtheAISinstallationandneedonlytobechangedifthenameofavesselchangesorifthevesselundergoesaconversiontoanothershiptype.Examplesofstaticdataarename,MMSI-number(MaritimeMobileServiceIdentity),vesseltype,lengthandpositionoftheAIStrans-mitteronthevessel.Voyagerelatedinformationconcernsissueslikethevessel’sdraught,destinationandETA(EstimatedTimeofArrival).Thisinformationneedstobekeptuptodatemanuallybytheship’screw,whichmakesitsensitivetoerrorsanduncertainties.
Dynamicdataoriginatefromthevesselsnavigationalinstruments;examplesarethevessel’sposition,head-ingandrateofturn.Thepositionofthevesselisreportedbythreeparameters:longitude,latitudeandapositionaccuracyreport.Thelongitudeandlatitudearegivenin1/10,000minute,whichis-inlatitudinaldi-rection-equaltoapproximately20cm.Inlongitudinaldirectionthisnumberdependsonthedistancetotheequator(Netherlands≈11cm).Thepositionaccuracyreportindicateshowaccuratethetwomentionedpositionreportsare(IALAandAISM,2004).
AdetailedoverviewofthedatainsideanAISmessagecanbefoundinAppendixB.
2.3 Errors in AIS messages
ToinvestigatethequalityofthedatainAISmessagessomesurveyshavebeenundertaken.Mostsurveysonlylookattheerrorsthatoccurinalimitednumberofparameters.Bailey,etal.(2008)studytheinfluenceoftheintroductionofAIS.InthisstudyAISmessagestransmittedbyvesselsintheDoverStraitarejudgedinthreedifferentyears.Harati-Mokhtarietal.(2007)investigatederrorsinAISmessagesbyusingthreediffer-entdatasets.Intheirstudy,static,voyage-relatedanddynamicdataareexamined.
Bailey,etal.(2008)lookedtothemaritimetrafficofoneweekintheDoverStraits.Thiswasdoneinthreedifferentyears,leadingtodatasetsof806(2004),901(2005)and940(2007)vessels.Afteranalysis,errorswerefoundinMMSI-number,CallSign,Name,Draught,DestinationandCourse.Byfarthemosterrorsoc-curredinthecategoriesDestinationandDraught.ErrorsinDestinationincludedmisspelling,emptydatafields,incomprehensibleabbreviationsandreferencestothepreviousport.Mostoftheerrorsindraughtwerelessthan1meter,butinsomecasesadifferenceofmorethan3mwasfound.
Becausethereweredatafromthreedifferentyears,itwaspossibletocreateacomparisonbetweenthoseyears.Bydoingso,theyfoundthatthepercentageofvesselsthattransmittederrorsdecreasedfrom10.4%in2004to3.5%in2007.Howevertheauthorsremarkthat,duetoseveralreasons,thislastnumbermaytosomeextentunderestimatetheactualnumberoferrors.Thisdoesnotinfluencetheirconclusionthatthenumberoferrorsisdecreasingyearonyear.ThenumbersaresummarisedinTable2.1.
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AIS
Table 2.1 Numbers of vessels transmitting errors by year. Source: Bailey, Ellis et al., 2008
YearTotal number
of vesselsNumber of vessel
transmitting errorsPercentage of vessels
transmitting errorsNumber of errors
2004 806 84 10.4% 122
2005 901 71 7.9% 99
2007 940 33 3.5% 44
Harati-Mokhtarietal(2007)usethreedifferentdatasetstoinvestigateerrorsandinaccuraciesinthediffer-entfieldsofanAISmessage.Inoneoftheuseddatasets(‘Data-miningstudy’),8%fromatotalof400,059reportscontainederrorsconcerningMMSInumber,IMOnumber,position,courseoverground(COG),andspeedoverground(SOG).Theseerroneousreportswereinvestigatedfurther.Anotherdataset(VTS-basedstudy),containinginformationfrom94differentAISequippedvessels,wasusedfortheinvestigationoftheMMSInumber,vesseltype,ship’snameandcallsign,length,beamandnavigationalstatus.Athirddataset(ProactiveAISstudy)waspresent,butonlyusedtoinvestigateerrorsinMMSI-number.
Inthestaticdata,errorswerefoundinMMSI-number,vesseltype,vesselname,callsign,lengthandbeam.Mainsourceoferrorswasthevesseltype,whichdescriptionwasfoundtobevagueorincorrectinrespec-tively74%(VTS-basedstudy)and56%(Data-miningstudy)ofthecases.
Intheanalysisofvoyage-relateddata,thefocusoftheauthorsisondestination,ETA(EstimatedTimeofArrival)anddraught.Inthedata-miningstudy,49%containederrorsconcerningdestinationandETA.In31%oftheinvestigatedmessagesobviouserrorsinthevesselsdraughtswerereported.Theanalysisofdynamicdatafocusesonlyontheerrorsinthecategory‘NavigationalStatus’,whichforexampleindicatesifavesselissailingoranchored.Incorrectnavigationalstatusinformationwasgivenby30%ofthevessels(VTS-basedstudy).
Solvsteen(2009)alsoshowssomeresultsaboutthequalityofAISdata.HeconcludesthatmosterrorsoccurinETA(21.7%oftheobservationswerewrong),IMO-number(14.1%)andDestination(11.0%).HealsofounderrorsinRateofTurn(8.9%),Heading(7.1%),Dimensions(6.2%),Draught(5.7%),CourseoverGround(0.8%),SpeedoverGround(0.8%)andamissingshipname(0.04%).ItisnotsureifSolvsteendidnotfindanyerrorsintheotherparameters,liketheNavigationalStatus,ordidnottakethemintoaccount.
2.4 Improving safety of navigation and other applications
Asdescribedinthefirstsectionofthischapter,theprimaryfunctionofAISistoassistinnavigationandcol-lisionavoidance.OtherfunctionsarepassinginformationtocoastalauthoritiesandhelpingVTSsintrafficmanagement.Nexttothesethreefunctions,otherapplicationshavecomeupthatuseAIS.Insearchandrescueoperationsforexample,SAR(Search&Rescue)aircraftstransmittheirpositionbyAIS.
TheuseofAISbyVTSs,coastalauthoritiesandSearch&RescueoperationsisdescribedinAppendixC.Anotherexample,alreadymentionedinthefirstsection,istheuseofAISdatainmaritimemodelling;thissubjectishandledinchapter3.BelowadescriptionisgivenhowAISfulfilsitsprimaryfunctionandim-provessafetyofnavigation.
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An analysis of vessel behaviour based on AIS data
ThereareseveralwaysinwhichAISimprovesthesafetyofnavigation.Oneofthemhastodowiththeinformationexchangebetweenvessels.VesselsautomaticallypickupAISmessagesfromnearbyequippedvessels.OtherapplicationsmakeuseofthefactthatanAISsignalcanalsooriginatefromothersourcesthanvessels,forexampleabuoy.
WhenvesselsreceiveanAISmessagetheyautomaticallydecodeanddisplaytheinformationtotheofficeronwatch.InthiswayacompletepictureofallAISequippedshipswithinVHFrangecanbederived.BeforeAISwasused,thetrafficsituationaroundavesselwasderivedbyplottingaradarimage.TheadvantageofAIScomparedtothisradarimageisthatthevesselsareautomaticallyidentified.Inthisidentificationnotonlythenameofothervesselsisprovided,butalsoothercharacteristicssuchasshiptypeandsize.NexttothisadvantageAISisalsoabletodetecttargetsonplaceswheretheradardetectionis(temporarily)limited.
Thisgivesabetteroverviewofthesituationaroundthevessel.Becausetheidentityofthesurroundingves-selsisknownitalsoiseasiertocallonothervesselsandcommunicate.Thereforeevasivemanoeuvrescanbeagreeduponquicker,whichreducescollisionrisk.ThisclearlyshowstheadvantagesofAISoverradar.ItishowevernotpossibletorelycompletelyonthetrafficimagederivedfromAIS.ThishastodowiththefactthatAISmessagesaresentactively.IfavesselisnotequippedwithAIS,itwillnotbedetected.Radarwavesdonothavethisproblem,becausetheyaresimplyreflectedbyeveryobstacle.
ThisdisadvantageofAISismostvisibleinsituationswherealotofvesselswithandwithoutAISarepresent.Thishappensmainlyinandaroundportareas,wherecargoistransferredbetweenlargeoceanvesselsandothertransportmodessuchasinlandwaterwaytransport.Especiallyinlandvessels,butalsofishingves-eslsandrecreationalvesselsdosometimesinterfereintheseplaceswithseagoingcargovessels.InthesesituationsAISdoesnotgiveasufficienttrafficoverviewanditisbettertorelyontheradarimage.AIScanhoweverstillbeusedasanadditionalsourceofinformation,mainlyforidentificationpurposes.
AnotherinterestingabilityofAISisthetransmittingofpositionsandnamesofobjectsotherthanvessels,forexamplenavigationalaidsaslighthousesandbuoys.Thiscanbedoneintwoways.OneoptionisthatthenavigationalaidsendsAISmessageswithitsowntransmitter.Anotherwayisthathissignalissentbyanearbybasestation.Topassingshipsthisseemstocomefromtheaiditself.Thismethodisknownassyn-theticAISandcanbeinterestingwhenitisnotpossibletoequipanavigationalaidwithitsownAIStrans-mitter.AIScanalsobeusedtogivelocationswhicharenotvisible,likeawreckedship.Againabasestationsendsoutamessageandthenon-visibletargetappearsonavesselitsscreen.ThisisknownasvirtualAIS.5
2.5 Conclusions
AISisawellknownsysteminmaritimetransportnowadays.Especiallyseagoingcargovesselsareequippedwiththesystem.ThemainfunctionofAISiscollisionavoidanceandaidtonavigation.ItisalsousedbycoastalauthoritiesandVTSsforrespectivelysecurityandtrafficmanagementreasons.OtherapplicationsofAISare,amongstotherthings,searchandrescueandtheuseofdatainmaritimemodelling.
5 UKGovernmentStrategyforAIS,Departmentfortransport,UnitedKingdom,
http://www.dft.gov.uk/pgr/shippingports/ports/modern/ais/ukgovernmentstrategyforais?page=2,
accessed:17/12/2009
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AIS
SincetheintroductionofAIS,severalresearcheshavebeenperformedtoinvestigatethequalityofAISmes-sages.Everyresearchfocussesondifferentparametersandusesdatasetsfromdifferentyearsandlocations.Thereforeitisdifficulttocomparethemanddrawconclusions.Therearehoweversomesimilaritiesbe-tweenthethreeresearchesmentioned.OnecommonconclusionisthatasignificantamountofAISmes-sagescontainerrors.MostproblemswerefoundinthecategoriesDestination,ETA,Draught,VesselTypeandNavigationalStatus.ExceptfortheVesselType,thesecategoriescontaindatathathavetobeupdatedmanually.
Duetothedifferencesbetweenthethreestudiesmentioned,itisdifficulttoconcludesomethingaboutthedevelopmentofthequalityofAISdata.Harati-Mokhtarietal.(2007)findforexamplemuchhighererrorpercentagesthanBailey,EllisandSampson(2008).ThefindingsofSolvsteen(2009)lieinbetween.OnlyBai-ley,EllisandSampsonetal(2008)lookatthequalityofthedataindifferentyearsandfromtheirresearchitispossibletostatethattheAISdataqualityisimproving.Moreresearchishoweverneededtosupportthisstatement.
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Number of collisions to be expected
Number of encounters Causa�on probability
Collision probability
Probability a ‘model’ encounter becomes a real
encounter
Probability that a real encounter becomes an
accident
Maritimemodelling
Chapter3
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Maritimemodelling
3 Maritime modelling
Mostnauticalsafety-andcapacitystudiesusemaritimemodelsforthemodellingofnauticaltraffic.Almostallprogramsusethesamebasicprinciple,especiallyforthedeterminationofcollisionrisk.Thereishoweveramaincharacteristicthatdividestheseprogramsintotwotypes.Thischaracteristicconcernsthequestionifindividualvesselmovementsaresimulated.
Thefirsttype,thegeometricmodel,usesstatisticalknowledgeoftrafficintensitiesanddistributions.Noindividualvesselmovementsaresimulated.However,maritimetrafficsimulationprograms,simulateindi-vidualvesselmovements.Thischapterdescribesthebasicprincipleofmaritimemodellingprogramsaswellasthecharacteristicsandlimitationsofthetwotypesofmodelsmentioned.
3.1 The basic principle of maritime modelling programs
Moststudiesthatusemaritimemodels,aimtoderivethenauticalsafetyofacertainwaterway.Inpracticethismeansthecalculationofcollisionriskswithinapredefinedtimespan.Forthedeterminationofthis,modelscalculatethenumberofaccidentsthatcanbeexpected;thisisdoneintwosteps.Firstanumberofpotentialdangeroussituationsiscalculated.Secondly,thisnumberisusedtocalculateanumberofcolli-sionsthatistobeexpected.
Thepotentiallydangeroussituationsarecalledencounters.Inpractice,whentwovesselscometooclosetoeachother,thisiscalledanencounter.Thisraisesthequestionhowclosevesselscansailtoeachother,be-forethisis‘tooclose’.Forthis,theprincipleofvesselsafetydomainsisused.Asafetydomainisaprescribedareaaroundavessel.Iftwosafetydomainsoverlaporifavesselentersthedomainofanothervessel,theyaretooclosetoeachother;thiscountsasanencounter(seeFigure3.1).So,thesizeofthevesselsafetydomainisaleadingparameterinthedeterminationofthenumberofencounters.
Figure 3.1 Two vessels with different, overlapping safety domains.
Itishowevernotveryeasytodeterminethesizeandshapeofthisdomain,becauseitdependsonalotofparameters:characteristicsofthevesselsinvolved(e.g.speed,dimensions,manoeuvrability),thetrafficsituation(e.g.trafficintensity,widthofwaterway)andexternalinfluences(e.g.visibility,wind,waves).Dif-ferentstudieshavebeenperformedtodeterminevesselsafetydomains.However,noconsensushasbeenreachedyetonthesizeandshapeofthedomains(Pimontel,2007).
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An analysis of vessel behaviour based on AIS data
Differenttypesofmaritimemodelscalculatethenumberofencountersindifferentways.Thishasespeciallytodowiththemodellingofindividualvesselmovementsandtheabilityofvesselsinamodeltomanoeu-vre,therebypreventingencounters.Ingeometricmodels,wherenoindividualmovementsaresimulated,thisleadstoanoverestimationofthenumberofencountersinreality.Theothermodelsdosimulatevesselmovements,butthemanoeuvringpossibilitiesareoftenveryrestricted.Therefore,theyalsoover-estimatethenumberofencounters.
Thisover-estimationiscompensatedbythecausationprobability.Thisnumberincludestheprobabilitythatanaccidenthappens,giventheoccurrenceofanencounterinthemodel.Thecausationprobabilitycanbedividedintwoparts.Thefirstpartcompensatestheover-estimationofthenumberofencountersfollowingfromamodelrun.Thisisreflectedbytheprobabilityanencounterhappens,giventhefactthatanencoun-tersoccursinthemodelrun.Thesecondpartconcernsthefactthatanencounterisnotequaltoanacci-dent.Thisisreflectedbytheprobabilityanaccidenthappens,giventheoccurrenceofarealencounter.
Thephysicalmeaningofthecausationfactoristhepercentageofvesselsthatdoesnotmakeasufficientevasivemanoeuvrewhenneeded,topreventanaccident.Thisprincipleisusedbymaritimemodelsinthecalculationofthecausationfactor,whichisdoneintwoways.OneoptionistheuseofBayesiannetworks.Thesenetworksarebuiltinsuchawaythattheycalculatetheprobabilityavesseldoesnotrespondsuffi-cientlytopreventanaccident.Factorssuchasvisibility,stresslevelandVTSassistanceareincluded.
Anotheroptionforthederivationofthecausationfactoristheuseofhistoricalaccidentdata.Inthismethodthecausationfactorisdeterminedinsuchawaythattheoutcomeofthemodel(collisionprobabi-lity)isplausible.Historicaldataisalsousedinthefirstmethod,forthevalidationoftheBayesiannetworks.Theproblemofaccidentdataisthefactthatthesearenotalwaysavailable.Withoutthedataitisnotpos-sibletochecktheoutcomeofthemodel.Inthesesituationsitisnotpossibletoquantifynauticalrisk;onlyconclusionscanbedrawnontherelativesafetyofdifferentalternatives.
So,bycombiningthenumberofencountersandthecausationprobability,anumberofaccidentsisob-tained.Finallythistotalnumberofaccidentsisconvertedtoacollisionrisk(seeFigure3.2andFigure3.3).
Number of collisions to be expected
Number of encounters Causa�on probability
Collision probability
Probability a ‘model’ encounter becomes a real
encounter
Probability that a real encounter becomes an
accident
Figure 3.2 The basic principle of the calculation of collision risk.
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Figure 3.3 The basic principle of the calculation of collision risk, reflected in probabilities
C = Collision; Em = Encounter in model run; Er = Encounter to be expected in reality.
3.2 Type I: The geometric model
Insomemodelsnoindividualvesselmovementsaresimulated.Vesselssailalongapredefinedtrack,ac-cordingtoaspatialdistributionoverthewaterway.Theydonothavetheabilitytodeviatefromthesestandardroutes.Whenavesselmeetsanobstaclelikeanothervesselorashoal,italsodoesnotreact.Thisprincipleisknownasthegeometricmodel,becausethecalculationsarebasedongeometricprobability.TheprincipleisrootedintheapproachdefinedbyFujii,etal.(1974)andMacDuff(1974).(Kujala,etal.,2009,p.1353).AnexampleofamodelthatworkswiththisprincipleisSAMSON(SafetyAssessmentModelforShippingandOffshoreontheNorthSea),usedbyMarin6,mainlyfornauticalsafetystudies.
Thecalculationofcollisionriskisdonefollowingthebasicprinciplediscussedintheprevioussection.ThecausationfactorisderivedbyusingBayesiannetworksandhistoricalaccidentdataasexplained.Becausenoindividualvesselmovementsaresimulated,itisnotpossibletosimplycountthenumberofencounters.Thedeterminationofthisnumberisthereforeofinterestinthesekindofmodels.Thisisdonebyusingtwoassumptionsmentionedbefore.(Friis-HansenandSimonsen,2001)
1. Vesselssailaccordingtoanassumedorpre-specifiedspatialdistributionofthevesseltraffic overthewaterway;
2. Vesselsarenavigatingblindlywhentheseareoperatingattheconsideredwaterway.
6 MaritimeResearchInstituteNetherlands
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Afterthedistributionsoverthedifferentwaterwayshavebeenspecified,itispossibletocalculatethenumberofencounters.Thisisdonebydefiningariskarea,wherevesselscanpotentiallyencountereachother(seeFigure3.4).Subsequently,thenumberofencountersiscalculated,usingthedimensions,speedsandthespatialdistributionoverthewaterways.Thisisdoneforallcombinationsofdifferentvesselclasses.
Figure 3.4 Crossing waterways with risk area of ship-ship collision. f (z)= vessel distribution over the waterway, different vessel classes are
denoted by i and j; z = distance to the centreline of the waterway; V = velocity of vessel; θ = angle between the waterways 1 and 2. Source: Pedersen et al. (1999), p. 4, figure 2.1 (Pedersen and Zhang, 1999)
Theexactcalculationisnottreatedhere,becausethemainfocusofthisthesisliesonmodelsthatdosimu-lateindividualvesselmovements.
3.3 Type II: Maritime Traffic Simulation Programs
Themaindifferencebetweenthegeometricmodelandmaritimetrafficsimulationprograms(MTSPs)issimulationofvesselmovements.InMTSPsthenumberofencountersiscalculatedbycountingthenumberofencountersthathappeninasimulationrun.Theoutputofasimulationrunisnotonlyanumberofencounters,butmakesitalsopossibletotakeacloserlookattheencountersituation.Thisleadstoabet-terinsightintothedifferentcausesofanencounter.Thiscanbevaluableinevaluatingtheefficiencyof,forexample,infrastructuralimprovements.
AnotheradvantageisthatthenumberofencountersiscalculatedmorepreciselybyMTSPsthanbythegeometricmodels.Thisisduetothefactthatvesselsareabletomanoeuvreinordertopreventencounters,whereasthisisnotpossibleinthegeometricmodels.Theaccuracyofthecalculationdependsonthequal-ityofthevesselsimulation.TheimprovementofthissimulationisoneofthemaintargetsforMTSPs.
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Mostsimulationprogramsusesimplerulestosimulatevesselbehaviour.Themostimportantrulesforves-selbehaviourfollowfromtheinternationallyrecognisedCollisionRegulations(COLREGs)7.Theseregula-tionsprescribethesupposedvesselbehaviour,especiallyregardingtheinteractionwithothervessels.
TheCOLREGsgiveagoodfirstindicationofvesselbehaviour,buttwolimitationscomeup.First,theseregulationsonlygivegeneralguidelineshowvesselsshouldbehave.Nodetailedinformationconcerningtheprecisepathofavesselanditsinteractionwithothervesselsisgiven.Secondly,vesselsdonotalwaysobeytheCOLREGs.Sometimestheydeviatefromtheseguidelinesforsomereason.
So,tosimulatevesselbehaviourinamoredetailedway,additionalrulesandguidelinesshouldbeformu-lated.Itisnotveryeasytodoso,becausethevesselbehaviourgreatlydependsonthedecisionsthataremadebythehumansthatcontrolthevessel.Theirdecisionsarebasedonknowledge,experienceandcapabilities,whicharedifferentforeveryone:thehumanfactor.Neverthelessseveralmethodstodescribevesselbehaviourcanbedistinguishednowadays:fuzzylogic,rulesbasedonexpertknowledge,andBaye-siannetworks.
Fuzzylogicisamathematicaltechniquethatisusedinmodelsforthedeterminationofthehumanbehav-iour.“Infuzzylogicmodelling,largeamountsofinputdataareprocessedaccordingtovarious‘If-Then’rules,similartothosethatoccurinthehumanbrain.Weightingandaveragingoftheresultingoutputsthenleadstoasingleoutputsignal.Thisabilityoftakinginandevaluatinglargeamountsofdata,leadingtoadecisiononhowtoactiswhatmakesfuzzylogicmodellingsosuitableformodellinghumanbehaviour.”(Pimontel,2007,p.10).Nowadays,thesimulationprogramsDYMITRIusesfuzzytechnologytosimulatethehumanelement(Bolt,2006).
AnotherwayofsimulatingthehumanelementisbyusingBayesiannetworks.BarauskisandFriis-Hansen(2007)usedynamicBayesiannetworksforthemodellingofvesselbehaviourintheirmodel,calledthenumericalnavigator.Anadvantageofusingthosenetworksisthepossibilityofhavingincompleteinforma-tion.Inthenumericalnavigatormodelthevesselsarereflectedbyagents.Thoseagentshavetheabilitytointeract,anticipateandlearn.Tomodelandtotraintheagents,COLREGS’sandAISdataanalysesareused.ThepossibilitytouseAISdatainmaritimesimulationishandledinchapter4.
Athirdoptiontogetmoreinsightintovesselbehaviouristheuseofsimplelogicalrules.Theserulesareestablishedbyusingexpertknowledge.Ininterviewsseveralcaptainsgiveanoverviewoftheirbehaviourindifferentpresentedsituations.Fromthisknowledgegenericrulesthatdescribevesselbehaviourarederived.Bydoingso,itisnotneededtosimulatethehumanbrain.Thisproblemisbypassed,becauseitisalreadyincludedbytheobtainedrules.SIMDASisanexampleofamodelthatworkslikethis.
ChauvinandLardjane(2008)didsomeresearchonvesselmovementsandinteractionaswell.ByusingtheRPD(Recognition-Primed-Decision)modelofKlein8theyinvestigatedtheinteractionbetweenvesselsintheDoverStrait.Theycomeupwithsomeconclusionregardingcollisionavoidancebehaviour.Anexampleisatwhatdistancefromeachothervesselsstarttochangecoursetopreventanaccident.TheirvesseltrackdatawerebasedonmotionsobservedbyaVTS.
7 InternationalMaritimeOrganization,IMO,
http://www.imo.org/conventions/contents.asp?doc_id=649&topic_id=257,accessed:10/3/2010
8 GaryA.Klein,ARecognition-PrimedDecision(RPD)ModelofRapidDecisionMaking,
http://www.ise.ncsu.edu/nsf_itr/794B/papers/Klein_1989_AMMSR_RPDM.pdf,accessed:8/1/2010
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3.4 Use of AIS in models
SincetheintroductionofAIS,studieshavebeenperformedonthereliabilityofAISdata,forexamplebyHarati-Mokhtarietal.(2007).Nevertheless,AISdataarealreadyusedinmanyresearchesconcerningmari-timemodels.Mostlytodeterminethenauticaltrafficdemand,animportantinputintheseprograms.AIScanhoweveralsobeusedtoanalysevesselmovements,assuggestedbyBarauskisandFriis-Hansen(2007).
3.4.1 Traffic input
InMTSPsitisveryimportantthatthetrafficdemandisassumedasrealisticaspossible.Athoroughanalysisshouldbedoneaboutvesseltype,size,destination,interarrivaldistribution,etc.AnAISmessagecontainsallthisinformationandisthereforeveryvaluabletogeneratethisinput.Alotofriskassessmentsnowadaysthereforeusethesedata,buttheyoftenalsomentionlimitations.ForexampleVanderTak(2009)usesotherdatasourcesthanAIStoobtaininformationaboutthedensityoffishingvessels.BothKujalaetal.(2009)andYlitalo(2009)mentionthelackofAISdatafromfishingvesselsaswellaspleasureboats,whichmakesitmoredifficulttoderivegoodaccidentrisks.
MoststudiesusingAISdata,investigatesafetyattheopensea.TherearefarlesssurveysconcerningportsorinlandwaterwaysthatuseAISdata.Thisiseasytounderstandfromthefactthatalotofsmallervessels(mainlyinlandvessels)donotcarryAISequipment.ForexampleIperenandKoldenhof(2008)useradardatafortheirriskassessmentstudyintheportofRotterdamarea.However,AISdataareusedinaresearchintheportarea‘Eemshaven’fortheriskassessmentofLNGvessels.Thisisonlypossiblebecausetheves-selsthatdonotcarryAISaretoosmalltodamageanLNGvessel(KoldenhofandVanderTak,2007).
AISdatacanalsobeusedtoimproveroutemodelling.Thehugeamountofavailabledata,especiallyregard-ingthepositionsofvessels,makesitpossibletogetabetterinsightintotheroutesvesselstake.VanDorpandMerrick(2009)usethispossibilityandexplainhowtheydealwitherrorsandinaccuraciesinthedata.Althoughthisimprovesthemodellingofthemaritimenetwork,itdoesnotgivemoreinformationregardingtheexactvesselbehaviour(e.g.theinteractionwitheachother).
3.4.2 Vessel movement and interaction
WithAISdata,theexactposition,headingandspeedofavesselareknownatalmosteverymoment.Thismakesittheoreticallypossibletodostatisticalanalysesonvesselbehaviour.Themostimportantcharac-teristicofthismethodisthatitdoesnottrytosimulatehumanbehaviour,becausethevesselbehaviourisalreadyknownfromtheAISdataanalysis.
DifferenterrorsthatoccurinthemessagesareaproblemwhenusingAISdataforthemodellingofvesselbehaviour.Assaidinchapter2,mosterrorsconcerntheDestination,ETA,Draught,VesselTypeandNaviga-tionalStatus.Forthemodellingofvesselbehaviourthemostimportantinformationregardsposition,speedandheading.Thesefieldscontainfewererrors.However,itmustbesaidthatinformationlikedestinationandnavigationalstatuscanmakethemappingofthenauticaltrafficmucheasier.
Oneofthemodelsthattrytoimprovethemodellingofvesselmovementsisthenumericalnavigator.BarauskisandFriis-Hansen(2007,p.5)concludethat‘StudieswillalsobeinitiatedthatbyuseofobservedAIStracksshalladjustandvalidatethewaythenumericalnavigatoroperatesthevesseltrafficinanarea’.ByadjustingtheBayesiannetworksthatdescribevesselbehaviour,theywanttotrainvessels(‘agents’)withtheresultsofAISdataanalyses.Sofarnoevidencehasbeenfoundifthisisalreadydone.
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AlsoMouetal.(2010)useAISdata,tostatisticallyanalysevesselbehaviour.ThefocusoftheauthorsisonthecorrelationoftheClosestPointofApproach(CPA)withvesselsize,speedandcourse.Fortheassess-mentofrisks,theyuseadynamicmethodbasedonSAMSON(seesection3.5forexplanationofthismari-timemodel).
3.4.3 Conclusions
AISdataarepotentiallyaveryinterestingsourceofinformationformaritimemodels.Nowadaysitismainlyusedinmaritimemodellingforthederivationofthetrafficinput,suchasinter-arrivaltime.AISdataisalsousedtogetabetterinsightintothenauticalnetworkthathastobemodelled.Inrestrictedwaterways,likeports,lessuseismadeofthedata.ThiswillbemainlyduetothefactthatintheseareasalotofvesselsarepresentthatarenotAISequipped.
ThereisaclearpotentialtouseAISdatatoobtainmoredetailedinsightinvesselbehaviour.ErrorsinAISdatamainlyoccurinfieldsthatareuseful,butnotindispensibleforthispurpose.ThereforetheycanmaketherequiredAISanalysismoredifficult,butcertainlynotimpossible.Noextensiveuseismadeofthispos-sibilityhoweversofar.Thereareplanstoincludeitinthenumericalnavigatormodel,butthestatusofthismodelisunsure.
3.5 Existing maritime models
Oneofthegoalsofthisthesisistoseeifstatisticalequationsthatdescribevesselbehaviour,canbeim-plementedincurrentlyexistingmaritimemodels.Thissectiongivesanoverviewofdifferentmodelsthatexistnowadays.Fourofthemareelaboratedabitmoreintodetail:SAMSON,HarbourSim,MARTRAMandDymitri.
Thesemodelsarechosen,becausetheygiveagoodinsightintherangeofmodelsthatisusedatthemo-ment.SAMSONclearlyisatypeImodel,thatdoesnotsimulate(individual)vesselmovements.Dymitriisattheothersideofthespectrum,asinthismodelthevesselsaresimulatedandhavealargefreedomtomanoeuvre.The4modelsarealsochosenbecausetheyare‘proventechnology’.Allofthemareworkingandhavebeenusedinseveralstudies.
3.5.1 Characteristics
ResultsoftheAISanalysisshouldincludeinformationconcerningthevesselpathandvesselspeed,butalsotheinfluenceofexternalinfluenceslikewindandcurrents.Besidesthis,itisalsotriedtoobtaininsightintheprocessofinteractionwhentwovesselsencountereachother.Oneoftheresearchquestionsistoseeiftheobtainedbehaviouralrulescanbeimplementedinacurrentlyexistingmodel.Thissectiondescribesthecharacteristicsthatareneededtodoso.
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Type1-Nauticalinfrastructure Describevesseldistributionoveracrosssectionoverthewaterway. Describethevesselspeeddistributionoverandinacrosssectionoverthewaterway. Type2-Vesselrelatedcharacteristics Distinguishbetweenstaticcharactericsasvesselsizeandvesseltype. Distinguishbetweendynamiccharacteristics,forexamplevesseldestination. Type3-Externalcircumstances Takeexternalinfluenceslikewind,currentandvisibilityintoaccount. Type4-Theinteractionwithothervessels Abilitytoincludedeviationfromthepredefinedpathandspeedbecauseofinteractionwithother vessels.
Thefirsttypeisimportantasthevesselswillhavea‘naturaldeviation’.Thismeansthattwovesselsthathaveexactlythesamecharacteristicsandarebothsubjecttothesameexternalinfluences,willnotchoosetesamerouteandspeed.Thisisforexampleduetointernalcircumstances,likethetraining,experienceandpreferencesofthecaptainsofthevessels.Thismeansthatmodels,iftheywanttoimplementthebehav-iouralrules,shouldnotfixatethevessellocationatonepointinthecrosssectionoverthewaterway.Alsoforthevesselspeeditshouldbepossibletodescribeanaturaldeviationfromtheaverage.
Thesecondtypehandlestheinfluenceofthevesselcharacteristics.Thevesselpathandspeedneedtohaveacertaindistributionoveracrosssectioninthewaterway,asexplainedabove.Thisshapeandlocationofthisdistributionmighthoweververywellbedependentonthevesselcharacteristics.Amodelshouldthereforebeabletomakeadivisioninvesselclasses.Theseclassesshouldincludevesselandvesselspeeddistributionsoveracrosssectioninthewaterway,differentforeachvesselclass.
Thethirdtypeindicatesthatexternalinfluencesshouldbetakenintoaccount.Thisiscanbedonesimilarlyasthetypehandledabove.Externalinfluencescanalterthevesselpathandspeedandamodelshouldbeabletocopewiththosechanges.Differentfromtypetwoisthatthisonedoesnotdescribetheaverage,generalbehaviourofacertainvesselclass.Incontrary,externalinfluencescansometimesleadtoverydi-vergentvesselpathandvesselspeed.Althoughonlyalimitednumberofvesseltrackswillbethatdifferent,itisimportantforamodeltobeabletodescribethem.
Thelasttypeconcernstheinteractionbetweenvessels.Thisisthemostcomplicatedissue,asthisimpliesadeviationfromthepredefinedvesselpathandvesselspeed.Vesselclassesand-toalesserextent-externalinfluencesareconstantduringtheexaminationofacertainvesseltrack.Interactionwithothervesselsiscompletelyincontrastwiththis,asitcanhappenatalmostanypointintimeandspace.Nexttothis,therearealotofdifferentmannersinwhichaninteractioninfluencesthepathandspeedofthevesselsinvolved.Thisdependsforexampleonthetypeofinteraction(e.g.head-on,overtaking),thetypeandsizeofvesselsinvolvedandthelocationonthewaterway.Tosimulatetheinteractionsufficiently,vesselsshouldhavealotoffreedomtomanoeuvreanddeviatefromtheirpathandspeed.
3.5.2 SAMSON
SAMSONisamodelfortheriskassesmentofnauticaltransportatsea.Itevaluatestheriskeffectsofchang-esinforexampleshippingroutesandoffshoreconstructions.Themodeldividesthevesselaccidentsthatareconsideredintodifferenttypes,forexamplecollisions,fireandstranded.SAMSONisaTypeImodel,inwhichthecausationfactor(whichiscalledthecasualtyrateinSAMSON)isbasedonhistoricaldata.Thismeansthatitdoesnotsimulatenauticaltraffic.Themodelfocussesonthecalculationofrisksatsea,butby
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adjustingthecasualtyratealsoportareascanbeexamined.(Bolt,2006)
SAMSONistestedtothe4typesmentionedintheprevioussection.Thecharacteristicsoftype1arepartlymetbythemodel.Thevesseldistributionoverthewaterwayisclearlyincluded.ThiscanbeseenfromFigure3.4,whichisanexampleofhowthistypeofmodelsdeterminesthecollisionrisk.Itisclearthatthedistributionoverthewaterwayistakenintoaccount.Alsothevesselspeedisincluded;withasmalladjust-mentthedistributionofthevesselspeedoveracrosssectioninthewaterwayisimplementedaswell.
Theinfluenceofthevesselcharacteristicsisalsopresentinthemodel,asdifferentvesselclassesaredis-tinguished.Thedistributionoverthewaterwayisalsodifferentfortheseveralvesselclasses.Theexternalinfluencesarealsotakenintoaccount.Itishoweverdifficulttoincludetheinfluenceofsomesituationswithextremeexternalcircumstances,asSAMSONisnotmeantfortheinvestigationofindividualvesselbehav-iour.Asimilarproblemariseswhenlookingatthepossibilitytomodelinteraction.SAMSONisnotasimula-tionprogramandthereforeitisnotpossibletoincludeadetaileddescriptionoftheinteractionbetweenvessels.
3.5.3 Harboursim
HarboursimisasimulationmodelusedbytheTUDelft,mainlytodeterminewaitingtimes.Themodelfocussesonportareasanddescribesthenauticalinfrastructurebyfixatedwaterways.Somecharacteristicsareassignedtothesenauticallanes,forexamplethenumberofvesselsthatcansailinonelaneatthesamemoment.Themodelalsoincludestheservicetimeofvessels,whichmakesitpossibletoderivecapacityandwaitingtimes.
InHarbourSim,thevesselssailinacertainlaneanddonotdeviatefromthis.Insidethelanetherearealsonodifferentpathsavesselcantake.Thereisalsono‘naturaldeviation’invesselspeed.Theissuefromtype1arethereforenotdealtwithatthemoment.Itmighthoweverbepossibletoincludethisinthemodel,bycalculatingvesselpathsforeveryvesselthatiscreated.Thesepathscanthenbemadedependendonthevesseldistributionoverthewaterway.Thesamecanbedoneforthevesselspeed.Thisishoweveramajormutationofthemodel.
Thesecondtypeispartlymet.Thereisacleardistinctioninvesselclassesinthemodel,butthisdistinc-tionismainlyusedforthedifferenceinservicetimeanddestination.Thisisverylogical,asthegoalofthisprogramistocalculatewaitingtimes.If,followingfromissueone,individualvesselpathsareincludedinthemodel,itshouldnotbetoocomplicatedtoincludetheinfluencesofvesselclassdifferencesaswell.Thesameistrueforissuethree,whichcanpotentiallybeimplemented.
Theinteractionwithothervesselsishandledinthecurrentmodel,butinaverylimitedway.Itconsistsofbehaviouralruleswhetheravesselcanenteracertainwaterwaysegment.Thisdependsonthepresenceofothervesselsinthissegmentandthemaximalpermissiblenumberofvesselsinthatspecificsegment.Itdoesnotincludeanydeviationsfromthevesselpath.Toincludethis,averylargemutationofthemodelshouldbemade.
3.5.4 MARTRAM
MARTRAM(MarineTrafficRiskAssessmentModel)isdevelopedandusedbyRoyalHaskoningforaswellriskassesmentsascapacitystudies.Itcansimulatenauticaltrafficindifferentareas,inwhichforeverynewareathenauticalinfrastructureshouldbeimplementedinthemodel.Theconstructionoftheinfrastructure
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inthemodelcanbedonebyaddingnodesandconnectingsegments.Duringasimulationrunthenumberofencountersiscounted,whichisameasureforthenauticalsafety.
MARTRAMdoesincludeadistributionoverthewaterway.Everyvesselsmaintainsafixeddistancefromthecenterlineofthenavigationchannel.Thisdistanceisrandomlypickedfromanassumeddistributionofthevesselsoverthewaterway.Alsothevesselspeedhassomevariation,asthemodelkeeps10%variationaroundaninsertedvalue.Themodeldoesthereforecertainlykeepupwiththerequirementsoftype1.
Thecharacteristicsofissue2areclearlymetaswell,asdifferentvesseltypesaredistinguishedinMAR-TRAM.Forthesevessels,thecharacteristicdimensions,speedandvesselsafetydomaincanbeset.So,acleardistinctioninvesselclassesismade.Itishoweverunsureifthisclassesalsohavedifferentdistributionsoverthewaterway,whichshouldbeapossibilityinthemodel.Type3,theinfluenceofexternalcircum-stancesisnotincludedinthemodel.Becausethereisalreadyadistributionoverthewaterwayandadevia-tioninthevesselspeed,itshouldnotbealargesteptoincludethisinthemodel.
TheinteractionwithothervesselsistosomeextentpresentintheMARTRAMmodel.Ifavesselsdetectsan-othervesselinhis‘observationdomain’(whichis5-10%largerthanthesafetydomain),itmakesacollisionavoidancemanoeuvre.Thisconsistsofaspeedreduction,whileitmaintainsitscourse(Pimontel,2007).Thisisnotenoughtogiveadetailedinsightinrealvesselbehaviourduringaninteraction.Itishoweveragoodstartingpoint;mostimportantadditionisthepossibilitytodeviatefromthepredefinedpath.
3.5.5 Dymitri
Dymitri,ownedbyBritishMaritimeTechnologylimited,simulatesthenauticaltrafficwiththemaingoaltoindentifycollisionandgroudingrisk.Themodelisbasedonanautonomousagentsimulationofthemarimetraffic.Alsothehumanelementismodelled,byusing(Fuzzy)technologythatsimulatesthehumanbrain.Thevesselshavealargefreedomtomanoeuvre.Theincidentriskisbasedonthenumberandnatureofavoidanceactionsthathavebeenundertakenduringthesimulationrun.
Themodelcomplieswithtypeone,asthereisalotoffreedomtomanoeuvreforvesselsinthemodel.Dymitriishowevernotbasedonspecificvesseldistributionsoverthewaterway,butontheindividualbe-haviourofvessels.Thisbehaviourisbasedonthesimulateddecisionsmadebythevessel’sfirstmate.Thisisadifferentapproachthanthestatisticalwhichisusedinthisthesis.Thereishowevernodoubtthatthevesselsdohavesomedistributionoverthewaterway.
InDymitriitispossibletosetdifferentshiptypesandsizeclasses.Alsoexternalinfluencescanbeincluded.Boththevesselsclassesandtheexternalcircumstancesinfluencethewayinwhichthevessels(theautono-mousagents)sail.Types2and3arethereforeclearlymetbythemodel.TheinteractionbetweenvesselsisalsosimulatedbyDymitri.Thedistanceatwhichtheinteractionstartsisfoundfrommarinerreviewsanddigitalradarassessment.TheinteractionitselfisdrivenbytheFuzzylogicthatdeterminesthemarinersdecisions(Bolt,2006).
3.5.6 ConclusionMaritimemodellingprogramscanbedividedintwogroups:Geometricmodelsandthemaritimetrafficsimulationprograms.Thegeometricmodelisananalyticalcalculation,whichusesgeometricdistributionsoverthewaterwaystoderivenauticalsafety.MTSPssimulatetheindividualvesselsandtheirbehaviour,todifferentextents.Insomesimulationprogramsvesselsfollowpredefinedtracksandarebarelyallowedtochangespeedorcourseinordertopreventcollisions.
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Othersimulationprogramstrytosimulatethevesselbehaviourmoreindetail.Itishoweververydifficulttodoso,becausethisbehaviourdependsgreatlyonthedecisionshumansmake,thehumanfactor.Thereareseveralpossibilitiespresenttodealwiththis.Somesolutionsaimtosimulatethehumanbrain.Thisismain-lydonebyfuzzytechnologyand-toalesserextent-byBayesiannetworks.Othersolutionstrytobypasstheproblemofsimulatingthehumanfactor,byderivingsimpleruleswhere,inpractice,mostvesselsobeyto.
InbothtypesofmaritimemodelsAISisused,butinaverylimitedway.IfAISisused,themainpurposeisthederivationoftrafficinputortoincreasetheunderstandingoflargertrafficpatterns.Atthemoment,someattemptsaremadetouseAISfortheanalysisofindividualvesselbehaviour,butnoclearresultsofthisareyetfound.
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Casestudysetup
Chapter4
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4 Case study set up
Thischapterexplainsthesetupofthecasestudydoneinthismasterthesis.Theaimofthisstudyistoob-tainmoreinsightintothevesselpathandvesselspeedandhowthisisinfluencedbydifferentfactors.Intheend,theresultsaregeneralised:genericrulesareformulatedtodescribevesselbehaviourinaportarea.Inthischapter,itisexplainedhowthechoiceforthisspecificlocationwasmadeandwhatthelocalcharacter-isticsare.
4.1 Approach case study
Thegoalofthecasestudyistodescribetheexactpathvesselstakeandtheircorrespondingspeed.Theresultsshouldbeformulatedinsuchaway,thattheyaregeneralapplicableandcanbeusedasinputforamaritimemodel.Thereforethecasestudyaimstoderivegeneralrulesregardingvesselpathandves-selspeed.Itisimportantthattheobtainedsetofrulesissufficienttoreliablydescribeavessel’spathandspeedinamaritimemodel.Todoso,thedifferentrulesshouldcomplywiththefollowingissues:
1. Describethespatialdistributionofvesselsinacertaincrosssection;2. Describethelateralvesselspeeddistributionofvesselsinacertaincrosssection;3. Describethevesselspeeddistributiononacertainlocation;4. Takeintoaccountthatthe3distributionsmentionedabovedependon:
a. Vesseltype;b. Vesselsize;c. Vesselheading/destination;d. Typeofwaterwaysegment(straight/bend)e. Widthofthe(forthatspecificvesseltypeandsize)navigablewaterway;f. Windspeedandwinddirection;g. Currentspeedandcurrentdirection;h. Visibility;i. otherexternalinfluences;j. Interactionwithothervessels.
5. Describethemutualdependencebetweentwospatialsuccessivedistributions(toconnectthedifferentcrosssections,inordertoassembleanindividualvesselpathandcorrectspeeddevelopment)
Itcanbeseenfromthelistthattherulesdonottrytodescribedecisionsmadebypeoplethataresteeringtheindividualvessels.Byapplyingstatisticallyderiveddistributionsthisisbypassed;onlytheresults of this behaviourareformulated.Inthiscasestudynotthecompletelistofissuesmentionedaboveishandledfully.First,onlycontainervesselsareinvestigatedasavesseltype.Thisisbecauseonlythistypeofvesselsvisitsthelocationchoseninthecasestudy(see4.2).Second,nootherexternalinfluences(e.g.waves,rain)areinvestigated.Thisisbecause-inaportarea-thoseinfluencesareassumedtohaveasmallinfluenceonthevesselpathandspeedcomparedtotheotherexternalinfluences(wind,currentandvisibility).Third,theinteractionbetweenvesselsisnothandledinthisthesis.Theresultsfromthecasestudycanhoweverbeusedtoinvestigatetheinteraction.Anillustrativeexampleofthisisgiveninsection9.
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An analysis of vessel behaviour based on AIS data
4.2 Location
Inthecasestudy,itistriedtoderivethegeneralrulesasdescribedintheprevioussection.Thereforethelocationshouldcomplywithsomeconditionsfollowingfromtheissueslistedbefore.Atfirst,enoughdatamustbeavailabletoderivethecrosssectionsmentioned(issues1-3).ThismeansthatthelargemajorityofthenauticaltrafficthatvisitsthechosenportlocationshouldbeequippedwithAIS.Nexttothis,thetrafficimageshouldnotbetoomuchdisturbedbyvesselsthatdonotcarryAIS(e.g.inlandvessels).Anotherpointofinterestistherequiredvarietyinvesselsize,tohandleis-sue4.b.Differenttypesofwaterwaysegmentsshouldbepresentinthepathtowardstheterminalaswell(issue4.d).Itisalsopreferablethatalotofinteractionbetweenvesselsistobeexpectedonthispath(issue4.j).
Afterdeliberatingtheseconditions,theAmazonehavenischosenasthecaselocation.Figure4.1andFigure4.2showthelocationoftheAmazonehavenintheportofRotterdam,atthe'MaasvlakteI'.ThevesselpathsthatwillbeinvestigatedarethetracksfromNorthSeatotheAmazonehavenandtheotherwayaround.Below,thisiselaboratedmoreintodetail,togetherwithamoreintodepthexplanationwhythislocationsuitsthepredefinedconditions.
WhenvesselscomingfromtheNorthSeavisittheAmazonehaven,theycrossseveralinterestinglocationswhereinterestingvesselbehaviourmightbeexpected.ShortlybeforeenteringtheportofRotterdamintheMaasmond,apilotembarksmostvessels(1).AfterthisthevesselscometosailbetweenthenorthernbreakwaterandtheMaasvlakteI(2).Theseofferprotectionfromcurrentsandwavesandvesselswillhavetoadjusttheirbehaviourtothechangedexternalinfluences.
Figure 4.1 Overview of the port of Rotterdam, the Maasvlakte I is indicated by the red circle; source: Google Earth
Figure 4.2 Overview of Maasvlakte I, the Amazonehaven is indicated by a red ellipse;
source: Google Earth
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Every(seagoing)vesselthatvisitstheportofRotterdameventuallyhastosailthroughtheMaasmond(3).Thereforethisisabusywaterwayinwhichitislikelythatvesselshavequitesomeinteractionwitheachother.Thisisalsotheplacewheretugsfastentomost(bigger)containervessels,aprocessthatcaninflu-encevesselcourseandspeed.AftertheMaasmond,thevesselsheadingfortheAmazonehaventakeaturnintotheBeerkanaal(4).Inthisbendquitesomeinteractionscanoccur,becausethereisalotof(sometimes
Figure 4.3 Plot of the vessel tracks at the entrance of the Beerkanaal on 14 July 2009, between 10:00 and 16:00 hours.
Figure 4.4 Plot of the vessel tracks at the entrance of the Amazonehaven (indicated by the red ellipse) on 14 July 2009, between 10:00
and 16:00 hours.
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An analysis of vessel behaviour based on AIS data
crossing)nauticaltrafficpresent.SeeFigure4.3foratrafficimageatthislocation.
IntheBeerkanaal(5)andattheentranceoftheAmazonehaven(6)thenauticaltrafficintensityislowerthanintheareasmentionedbefore.TherearehoweverstillalotofvesselsthatvisitoneoftheterminalsatMaasvlakteI,orareaimingforthe‘Hartelkanaal’.Interactionwillthereforealsooccurhere,forexampleduringaturningmanoeuvreofalargevessel-tugscombinationinfrontoftheAmazonehaven.Figure4.4showsanimageofthenauticaltrafficatthislocation.
Asdescribedabove,thereareseveralreasonswhythevesseltrajectoriestowardsandawayfromtheAma-zonehavenareinterestingintheanalysisofvesselbehaviour.Nexttothepathvesselstake,alsothevarietyinsizeofthevesselsthatvisitthiscontainerterminalisagoodreason.Alotoflargecontainervesselsvisitthisterminal,becauseitiseasytoreachandtheAmazonehavenoffersenoughdepthfordeepdraughtves-sels.Firstofall,thisisinterestingbecauseinthiswaythebehaviourofthelargestcontainervesselscanbeinvestigated.Itisverylikelytheyreactdifferentone.g.highwindorcurrentsthansmallervessels.
Nexttothis,theselargevesselsonlyvisittheterminalintheAmazonehaven,afterwhichtheycontinuetheirjourneyontheNorthSea.Theseareexactlythetracksthatareinvestigatedinthiscasestudy.SmallercontainervesselsmostlyvisitalsoothercontainerterminalsintheportofRotterdam,tracksthatareonlyconfusingandnotexaminedinthisstudy.
AnotheradvantageoftheAmazonehavenisthatitislocatedatthemostWesternpartoftheport,awayfromthecitycentreandthesmallerterminals.Thisisadvantageousbecausethesmallerterminalsareoftenvisitedbyinlandvessels.Asmentionedbefore(chapter2)mostofthesevesselsdonottransmitAISmessag-esnowadays.ThereforethesevesselscannotbeseenwhenlookingpurelyatAISdata.Sowhensuchaves-selinteractswithanAISequippedvessel,thismakesitdifficulttoexplainthebehaviouroftheAISequippedvessel.Thisproblemcouldtheoreticallybeovercomebyusingradarimages,butitismuchmorepracticaltochooseanareawerelessinteractionwithinlandvesselsistobeexpected.
MostoftheadvantagesmentionedbeforedoalsoapplyforthedrybulkterminalthatispresentintheMis-sissippihaven(7).VesselsvisitingthisterminaldofollowlargelythesamerouteasthevesselsthatvisittheAmazonehaven.Thesedrybulkvesselsarealsoingeneralverylarge.Thisterminalishowevernotchosen,becausethenumberofvesselsthatvisititismuchlowerthanforthecontainerterminal.Thismakesitmoredifficulttomakestatisticalsignificantcalculations.Besides,drybulkvessels(especiallyverylargeones)arelesspresentinportsallovertheworldthancontainervessels.Itisthereforemorebeneficialtoformulategenericrulesforcontainervesselsthanfordrybulkvessels.
TheconsiderationsmentionedabovehaveledtothechoicetolookatthecontainerterminalintheAma-zonehaven.Thismakesitpossibletoderiveinsightinthebehaviourofcontainervesselsofdifferentsizeclasses.Duetothelargerangeinsizeclassesalsothedifferentinfluencesofwind,currentsandvisibilitycanbegivenacloserlook.
4.3 Case study outline
Theselectedtracks(fromvesselsthatvisittheAmazonehaven)arefurtheranalysedandinformationregard-ingvesselbehaviourisobtainedfromthisanalysis.First,thevesselsaremappedintodifferentvesselsizeclasses.Foreachoftheseclassestheaveragepathisdetermined,foraswellincomingasoutgoingvessels(section5.3).Theaveragevesselspeedisobtainedforeverysizeclassaswell.Alsothespatialdistributionofvesselsoverthewaterwayiscalculatedforseveralcrosssectionsovertheinvestigatedwaterway.Attention
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ispaidtothevesselspeedaswell,byderivingthespeeddistributionsoncertainlocationsontheaveragepath(Section5.4).
Withtheaveragepathandcorrespondingspatialandspeeddistributionsknown,attentionispaidtothefactorsthatinfluencetheseresults.Severalfactorsareinvestigated:wind,currents,visibilityandtheinter-actionwithothervessels.First,theinfluenceoftheinteractionwithothervesselsisleftoutofconsidera-tion.Severaltracksofvesselsthatweresailingduringhighwinds,currentsorlowvisibilityarecomparedtotheaveragepathofvesselsfromthesamesizeclass(Chapter6).Tomaptheinfluenceofvessel-vesselinteractionanexampleofasituationinwhichinteractionoccurredisexamined(chapter7).
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Blue: < 8 AIS messagesYellow: 8-13Red: 14-30Black: >30
Average vesselpathandspeed
Chapter5
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Averagevesselpathandspeed
5 Average vessel path and speed
Inthischaptertheaveragevesselbehaviourisdetermined.First,thedatasetsusedforthisaredescribed(section5.1)andtheirqualityischecked(section5.2).Insection5.3theinfluenceofthevesselsizeontheaveragepathandvesselspeedisinvestigated.Insection5.4thespatialdistributionofvesselsindifferentcrosssectionsiselaborated.Thissectionalsotreatsthevesselspeeddistributioninthesecrosssections.
5.1 Data sets
WiththeuseoftheprogramShowRoute9aselectionofAISmessagesismade.TheselectionissetupbythemessagesofcontainervesselsthatvisitedthecontainerterminalintheAmazonehaveninFebruary,March,April,July,August,October,NovemberorDecember2009.Thesemonthsarechosentogetinformationfromdifferentseasons.Finally,atotalof4,105,821uniqueAISmessagesisderived.Thesearehoweverrawdata;differentimprovementshavetobemadebeforethedatacanbeanalysed.
ThemostimportantoperationistheremovaloftracksotherthanbetweenNorthSeaandAmazonehaven.Especiallysmallercontainervesselscausethesedisturbingtracks,becausetheyvisitdifferentterminalsintheportofRotterdam.Nexttotheremovaloftracks,twootheradjustmentsaremade.Thefirstonecon-cernsthetransformationofgeographicalcoordinatestoRijksdriehoeksgridcoordinates.TheRijksdriehoeks-grid(RD)isthenationalgridoftheNetherlands.Itisusedasabasisforgeographicalindicationsandfiles,likeGeographicInformationSystems.AlsotheportofRotterdamsinfrastructureisexpressedinRDcoordi-nates.So,toevaluateavesselspositioncomparedtotheportsinfrastructureitisneededtorecalculatethegeographicalcoordinatestoRDcoordinates.
Thesecondadjustmentisarecalculationofthevesselsposition,bytakingintoaccounttheexactantennapositiononthevessel.ThepositionofthevesselthatisshownintheAISmessagereflectsthepositionofthetransmittingantenna.Thisantennamostlyisnotpositionedinthemiddleofthevessel;thereforearecalculationisneededtoretrievethecorrectpositioncoordinatesofthevessel.Thepositioncoordinatesthatarefinallyderivedreflectthemiddleofthevessel.TheoperationsareexecutedbyaMatlabmodel,whichisexplainedindetailinAppendixD.
AftertheadjustmentstotherawAISdata,805differentincomingtracks(NorthSeatoAmazonehaven)and663outgoingtracks(AmazonehaventoNorthSea)areleft.Toinvestigatetheinfluenceofthevesselsize,thevesselsarecategorisedintofivesizeclasses:
1.Smallerthan10,000Deadweighttonnage(dwt).10
2.10,000–40,000dwt. 3.40,000–70,000dwt. 4.70,000–100,000dwt. 5.Largerthan100,000dwt.
9 ShowRouteisasoftwareprogram,ownedbyMarin,whichcanbeusedtomakeselectionsofAISdata.Itcan
alsoplotselectedAISmessages,whichmakesitpossibletoreplaysituations.Thisishelpfulinthejudgement
ofinteractionbetweenvesselsinchapter9.Itisalsopossibletocalculateothercharacteristics,likethe
ClosestPointofApproach(usedintheCPAanalysisinchapter9).
10 Deadweighttonnageisameasurehowmuchavesselcan(safely)carry.Itisthesumofthecargo,fuel,water,
provisions,passengersandcrew.
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An analysis of vessel behaviour based on AIS data
Thesizeclassesarechoseninsuchawaythatineverydatasetapproximatelythesameamountoftracksisavailable.Theonlyexceptiontothisisthesmallestsizeclass,inwhich2-3timesasmuchtracksarepresent.Thisisdoneonpurpose,becausethesmallestvesselshavealargerfreedomtomanoeuvre.Itisthereforeexpectedthatmoredataisneededbeforereliableandaccuratecalculationscanbemade.
Thenumberoftracksavailableineachofthe10differentdatasetsisshowninTable5.1
Table 5.1 Number of tracks in each dataset
SizeClass(dwt) Incoming Outgoing
<10,000 307 250
10,000-40,000 173 109
40,000-70,000 89 98
70,000-100,000 124 132
>100,000 112 119
5.2 Accuracy of the data sets
Thequestionarisesifthereareenoughdataineachdatasettocalculateareliableaveragevesselpathandspeed.Toanswerthisquestion,theaveragevesselpathandspeedarefirstcalculatedbyusingonly50%oftheavailabledata(thetracksusedforthisarechosenatrandom).Afterthis,thesamecalculationisdone,nowusing100%oftheavailabletracks.So,theamountofdatathatisusedisdoubled.Thetwoderivedav-eragesarecomparedwitheachother.Ifthereisnosignificantdifferencebetweenthem,apparentlyagoodapproximationoftheaveragevesselpathandspeedwasalreadygivenbyusingonly50%oftheavailabledata.Inthatcasetheconclusionisdrawnthatenoughdataareavailabletoobtainareliableresult.
5.2.1 Accuracy average track calculation
Theabovedescribedprocedureisperformedforeverydataset.ForthecalculationoftheaveragepaththesameMatlabmodelisusedasmentionedbefore(AppendixD).Inthismodelagridisapplied,withadistancebetweenthegridpoints(gridsize)of50meters.Thismeansthatevery50meterstheaveragelocationinacrosssectionoverthewaterwayofavesselwithinacertainsizeclassisdescribed.ThepathtowardstheAmazonehavenisinthiswaydescribedby234datapoints.Whencomparingtwoaveragepathswitheachother,thedifferenceateachgridpointisdetermined(Figure5.1).Itshouldhoweverberemarkedthatthesedifferencesarenotindependentfromeachother.Forexample,ahighvalueforΔnmakesitverylikelyalsoΔn-1andΔn+1havehighvalues,becausetheyarealllinkedtooneaveragepath.
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Averagevesselpathandspeed
Δyi-2
Path 1
Path 2
Δyi-1 Δyi Δyi+1Δyi+2
Δyi+3
Δyi+4
Figure 5.1 Calculation differences between average vessel paths.
Fromthe234differencesthatareobtained,themeanandstandarddeviationarecalculated,seeequation(5.1).Themeanvalueandstandarddeviationofthetotalofthesedifferencesareanindicationhowwellthetwovesselpathsmatch.Table5.2showsforthedifferentdatasetsthevaluesofthemeanandstandarddeviation.Anegativevalueforthemeanindicatesthatthepathbasedon50%ofthedatapointslies,onaverage,onthestarboardsideofthepaththatisbasedon100%ofthedatapoints.
(5.1)
n
ii 1
n 2ii 1
where n numberof tracks
1Mean y
n
1St.Dev. ( y ) ,
n
µ
µ
=
=
=
= = ∆
= ∆ −
∑
∑
Table 5.2 Comparison of the average tracks, calculated by respectively 50% and 100% of the data.
SizeClass(dwt) Incoming Outgoing
Mean(m) StDev(m) Mean(m) StDev(m)
<10,000 0.5 5.2 -5.2 4.8
10,000-40,000 0.6 9.6 1.1 8.7
40,000-70,000 2.8 5.7 8.4 7.8
70,000-100,000 3.0 6.2 -1.9 5.8
>100,000 -1.8 10.3 -3.2 4.8
Table5.2showsthatthemaximummeandifferencebetweenthecomparedaveragetracksis8.4meters.Themaximumstandarddeviationis10.3meters.Thesenumbersalonearehowevernotenoughtodrawclearconclusionsregardingtheaccuracyofthedatasets.Forthisacloserlookattheouterlimitsofthedif-ferencesisneeded.Bycalculatingconfidenceintervals11(cdf’s)thiscanbeachieved.
11 Aconfidenceintervalisthelikelihoodaparameterisincludedinacertainintervalinsideaprobabilitydistribu
tion.Theconfidencelimitsaretheendpointsoftheconfidenceinterval.Aconfidenceintervalisalwayspre
cededbyapercentage,theconfidencelevel,whichreflectsthelikelihood.
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An analysis of vessel behaviour based on AIS data
Todoso,itisneededtosetupcumulativedistributionfunctionsofthedifferences,foreverydataset.AnexampleofsuchafunctionisgiveninFigure5.2.
−20 −15 −10 −5 0 5 10 15 200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Mean
X = Differences between two datasets (m)
P (X
)
95% lower limit 95% upper limit
Figure 5.2 The cumulative distribution function of the differences between two average tracks,
Vessel size class <10,000; outgoing.
Withthiscdf,itispossibletocalculatethe95%confidenceinterval.Thismeansthatthereisa95%likeli-hoodthatarandomchosendifferencebetweenthetwoaveragepathsiswithinthoselimits.Inthisthesis95%iskeptasathresholdvalueforthedeterminationoftheaccuracy12.TheresultsareshowninTable5.3.Fromthistableitcanbeconcludedthat-foreverysizeclass-itisfor95%certainthatthedifferencebe-tweentwoaveragetracksisintheinterval[-26;27].Thus,theaccuracythatcanbederivedbyusingonly50%oftheavailabledatais±30metersatleast.Inthecasestudy,alldataisusedanditisthereforeverylikelythattheaccuracyisevenhigher.
Table 5.3 The 95% confidence intervals in meters for the distance between two average tracks of one vessel size class.
SizeClass(dwt) Incoming Outgoing
<10,000 [-11;10] [-17;4]
10,000-40,000 [-26;12] [-16;18]
40,000-70,000 [-11;13] [-7;24]
70,000-100,000 [-6;18] [-14;7]
>100,000 [-15;27] [-15;5]
12 Whatconfidencelevelistakenasarepresentativevalueissubjectiveanddependsonthenatureofthestudy.
Mostcommonishowevertousea95%confidencelevel.
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Averagevesselpathandspeed
5.2.2 Accuracy average vessel speed calculation
Anotherimportantoutcomeofthecalculationoftheaveragetrackistheaveragespeed.Theaveragespeeddevelopsalongthevesselpath.Valuesforthisspeedarethereforecalculatedateverygridpoint(onceevery50meters).Thedifferencesarecomputedinthesamewayasdescribedabove.Table5.4showsthemeanandstandarddeviationofthedifferencesfortheseveralsizeclasses(incomingandoutgoing).Thedifferencesinvesselspeedaregiveninpercentages,tocopewiththefactthatthevesselspeedrangesfromalmostzerointheAmazonehaventoaround15knots13justoutsidethenorthernbreakwater.
Table 5.4 Comparison of the speed of the average tracks, calculated by respectively 50% and 100% of the data. The speed differences are reflected in percentages .
SizeClass(*1,000dwt)
Incoming Outgoing
Mean(%) Stand.Dev.(%) Mean(%) Stand.Dev.(%)
<10 -2.2 1.2 0.0 1.0
10-40 1.5 2.2 -1.0 1.8
40-70 1.7 2.1 -2.6 1.8
70-100 -2.6 1.7 0.0 2.1
>100 1.4 3.2 -0.7 1.0
Togetanindicationoftheaccuracythatcanbeobtainedinaveragespeedcalculations,the95%confidencelevelsarecalculated.Table5.5showstheresultsforthedifferentsizeclasses.Atthe95%confidencelevelthespeeddifferencesforalldatasetsareinthe[-6.2;6.3]interval,so±6.5%.At15knots,whichisaproxi-matelythefastestthatvesselssailintheobservedcasearea,thisisequaltoanaccuracyof±1.0knots.
Table 5.5 The 95% confidence intervals in percentages for the speed differ-ence between two average tracks of one vessel size class.
SizeClass(*1,000dwt)
Incoming Outgoing
<10 [-6.2;-0.2] [-1.1;2.5]
10-40 [-3.1;5.5] [-4.8;3.8]
40-70 [-4.7;4.9] [-5.6;1.2]
70-100 [-5.4;0.6] [-2.2;6.3]
>100 [-6.1;4.9] [-3.4;0.5]
5.2.3 Conclusions
Theaccuracyoftheaveragepaththatiscalculatedisatleast±30meters.Theaccuracyofthevesselspeedis±6.5%.Bothvaluesarelowenoughtoconcludethatenoughdataisavailabletomakeareliableanalysisofthevesselpathandvesselspeed.Thederivedaccuraciesshouldhoweverbekeptinmindwhenevaluat-ingthosetwocharacteristics.
13 1knot=1nauticalmileperhour=1.852kilometerperhour=0.514meterspersecond.
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5.3 The influence of vessel size
Toinvestigatetheinfluenceofvesselsize,theaveragetracksofthedifferentsizeclassesarecomparedwitheachother.Aswelltheaveragepaththatvesselstakeastheaccompanyingspeedisinvestigated.Thiscom-parisonisagaindonebycalculatingthemeanandstandarddeviationofthedifferencesbetweenthetwoaveragevesselpathsandvesselspeedsatthedifferentgridpoints(seeFigure5.1).Thegoalistoseeiftherearesignificantdifferencesbetweenthesizeclassesand,iftherearenot,whichsizeclassescanbebroughttogether.
InFigure5.3theaveragepathforoutgoingvesselsfromthesmallest(<10,000dwt)andthelargest(>100,000dwt)sizeclassareplotted.Itcanbeobservedthatthedifferencesbetweenthetwotrajectoriesincreaserapidlywhenthevesselshavelefttheprotectedportarea(PartA).Outsidethe(northern)break-waterthewaterwayismuchwiderandthesmallervessels(withasmallerdepth)arelessrestrictedanddeviatetothenorth.Insidetheprotectedportareatherearealsodifferencesbetweenthetwotracks,butthesearesmallerandlesssuitableforavisualinspection.AnexampleisintheBeerkanaal,wherethesmall-estvesselssailmoretotheeast.Nexttothis,thesevesselstakeasharpercurveintotheBeerkanaal,whentheyareleavingtheAmazonehaven.
TheabovedescribeddifferencesmakeitclearthatforadetaileddescriptionofthedifferencesitisneededtosplitthetrajectorybetweentheNorthSeaandtheAmazonehaveninseveralparts.Itisespeciallyworth-whiletolookseparatelyatthepartsoutside(PartA)andinsidetheprotectionofthebreakwater.
5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.84.4
4.41
4.42
4.43
4.44
4.45
4.46
4.47
4.48
4.49
4.5
Part A
Figure 5.3 Average path for outgoing vessels, size classes <10,000 dwt (green) and >100,000 dwt (blue)
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Averagevesselpathandspeed
5.3.1 Influence on the average path
Tobeabletodrawvalidconclusions,aquantativeanalysisofthedifferencesismade.Theresults,thedif-ferencesbetweenthesizeclassesforbothincomingandoutgoingvessels,aresummarisedinTable5.6andTable5.7
Table 5.6 Comparison of the average tracks from different vessel size classes, for incoming vessels. A positive value for the mean indicates that the size class on that row sails more to the starboard
side of the vessel class in the column.
SizeClass(*1,000dwt)
10-40 40-70 70-100 >100
Mean(m)St Dev (m)
Mean(m)St Dev (m)
Mean(m)St Dev (m)
Mean(m)St Dev (m)
<10 16 11 75 47 84 66 93 77
10-40 59 39 68 59 77 70
40-70 9 27 18 39
70-100 9 14
Table 5.7 Comparison of the average tracks from different vessel size classes, for outgoing vessels. A positive value for the mean indicates that the size class on that row sails more to the starboard
side of the vessel class in the column.
SizeClass(*1,000dwt)
10-40 40-70 70-100 >100
Mean(m)St Dev (m)
Mean(m)St Dev (m)
Mean(m)St Dev (m)
Mean(m)St Dev (m)
<10 39 41 62 56 83 92 103 114
10-40 23 19 44 53 65 75
40-70 21 37 41 61
70-100 20 26
Itcanbeseenthatallmeandifferenceshaveapositivevalue.Thismeansthatthesizeclassontherowsailstothestarboardsideofthecorrespondingclassinthecolumn(whichisthelargestofthetwocomparedclasses).Toseewhetherthesizeclassesdiffersignificantlyfromeachother,theaccuracydeterminedintheprevioussectionisused:±30meters.Tocomparethedifferenceswiththisaccuracy,the95%confidenceintervalsarecalculated(Table5.8).
Itcanbeseenthatallconfidenceintervalsareoutsidethe[-30;30]accuracyinterval.Onlythecombina-tionof<10,000dwtand10,000-40,000dwtandthecombinationof70,000-100,000dwtand>100,000dwt,bothforincomingvessels,comeclosetotheaccuracyinterval.Sowhenlookingatthewholetrajectory,itcanbeconcludedthatallsizeclassesdiffersignificantlyfromeachotherconcerningthepaththeychoose.
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An analysis of vessel behaviour based on AIS data
Table 5.8 95% confidence intervals in meters for the difference between the average trajectories of two ves-sel size classes
SizeClass(*1000dwt)
10-40 40-70 70-100 >100
In Out In Out In Out In Out
<10 [1;39] [-19;120] [4;153] [-8;164] [-5;251] [-26;251] [1;245] [-14;251]
10-40 [-1;121] [-19;55] [-8;219] [-42;150] [-5;251] [-31;244]
40-70 [-19;103] [-21;103] [-22;137] [-11;192]
70-100 [-10;44] [-5;92]
Assaidbefore,themajorityofthedifferencesisfoundinthepartofthetrajectoryoutsidetheprotectionoftheportsbreakwater(PartA).Itisthereforeworthwhiletoinvestigatethedifferencesthatoccurwithintheprotectedportarea.Thisisdonebyagaincalculating95%confidenceintervals,nowleavingoutthepartoutsidetheprotectionofthebreakwater(Table5.9).
Table 5.9 95% confidence intervals in meters for the difference between the average trajectories of two ves-sel size classes, for the trajectory within the port’s breakwater
SizeClass(*1000dwt)
10-40 40-70 70-100 >100
In Out In Out In Out In Out
<10 [0;39] [-20;37] [2;116] [-14;74] [-7;104] [-34;89] [-4;97] [-24;88]
10-40 [-1;82] [-27;38] [-10;69] [-47;53] [-7;79] [-37;49]
40-70 [-21;9] [-22;17] [-23;15] [-11;16]
70-100 [-10;14] [-6;22]
Table5.9showsthatthecombinationsofthethreehighestvesselsizeclassesareinsidetheaccuracyinter-val.Thecombinationofthesizeclasses<10,000dwtand10,000-40,000dwtalsogivesasmallinterval,butthisisoutsidethedeterminedaccuracylimits.Thereforetheconclusionisdrawnthatthevesselsizeclasses40,000-70,000dwt,70,000-100,000dwtand>100,000dwtdonotdifferfromeachothersignificantly.So,whenevaluatingthepaththatvesselstake,theycanbebroughttogether.Itshouldhoweverbekeptinmindthatthisisonlyvalidfortheareainsidetheport’snorthernbreakwater.Outsidetheprotectionoftheport,everysizeclassshouldbeinvestigatedindividually.
5.3.2 Influence on the average speed along the path
Alsotheaveragespeedisinvestigatedforthecombinationsofdifferentsizeclasses.Thisisdoneinthesamemannerasforthetrajectoriesabove.Againthemeanandstandarddeviationofthedifferencesarecalculat-ed.Thedifferencesareagainreflectedinpercentages,toobtaintherelativedeviationofthevesselspeed.Table5.10andTable5.11showthemeanandstandarddeviationforrespectivelyincomingandoutgoingvessels.
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Averagevesselpathandspeed
Table 5.10 Comparison of the average speed from different vessel size classes, for incoming vessels. A positive value for the mean indicates that the size class on that row sails faster than the other
vessel class in the column.
SizeClass(*1,000dwt)
10-40 40-70 70-100 >100
Mean(%)St Dev (%)
Mean(%)St Dev (%)
Mean(%)St Dev (%)
Mean(%)St Dev (%)
<10 3.3 6 25.6 10.6 29 8.9 26.9 10.6
10-40 23.3 7.6 26.7 5.8 24.7 7.2
40-70 4.2 3.9 1.6 3.5
70-100 -2.8 4.5
Table 5.11 Comparison of the average speed from different vessel size classes, for outgoing vessels. A positive value for the mean indicates that the size class on that row sails faster than the other
vessel class in the column
SizeClass(*1,000dwt)
10-40 40-70 70-100 >100
Mean(%)St Dev (%)
Mean(%)St Dev (%)
Mean(%)St Dev (%)
Mean(%)St Dev (%)
<10 5.4 12.1 20.8 14.5 28.5 12.7 21.2 18.6
10-40 16.7 7.2 24.6 7.6 17.8 11.2
40-70 9.6 4.1 1.6 6.4
70-100 -9 8.8
Itcanbeseenthatforincomingvesselsthethreelargestsizeclasseshaveagoodresemblance(Mean<5%).Alsothetwosmallestsizeclassesdiffernottoomuch.Foroutgoingvesselstheequalityisless,butthemeansofthementionedsizeclasscomparisonsarestillwithin10%ofeachother.Thesedifferencesseemhowevertoolargetostatethatthereisnosignificantspeeddifference.Toproofthispoint,the95%confi-denceintervalsarederived.Table5.12clearlyindicatesthatnoconfidenceintervaliswithinthepredefinedaccuracyintervalof±6.5%.
Table 5.12 95% confidence intervals in percentages for the difference between the speeds of two vessel size classes.
SizeClass(*1000dwt)
10-40 40-70 70-100 >100
In Out In Out In Out In Out
<10 [-4;11] [-5;32] [12;40] [5;48] [17;41] [14;54] [11;42] [0;54]
10-40 [11;35] [8;34] [15;36] [13;44] [14;36] [5;42]
40-70 [-3;14] [-5;16] [-5;12] [-6;15]
70-100 [-13;8] [-18;17]
Figure5.4showsanexampleofthespeeddevelopmentalongthetrajectoryfortwosizeclasses:70,000-100,000dwtand>100,000dwt,outgoingvessels.Fromthisfigureitbecomesclearthatthereindeedisasignificantspeeddifferencebetweenthesizeclasses.Itisobviousthatthedifferencesdonotlargelyoccuroutsidetheprotectedportarea,aswiththeaveragepath.Thereisacontinuous,significantspeeddiffer-
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An analysis of vessel behaviour based on AIS data
ence.Thisisalsofoundfortheothercombinationsofsizeclasses.Thereforeasplittingofthetrajectoryintodifferentparts(e.g.insideandoutsidetheport’sbreakwater)willnotleadtoahugelyimprovedresem-blence.
0 50 100 150 200 2502
4
6
8
10
12
14
16
Development along average path, 1 (grid)point = 50m
Spee
d ov
er g
roun
d (k
nots
)
port entrance
Entrance Beerkanaal
Entrance Amazonehaven
−20
−18
−16
−14
−12
−10
−8
−6
−4
−2
Diff
eren
ce (%
)
Figure 5.4 Speed development and the relative difference between the tracks (blue).
Size class 70,000-100,000 dwt (green) and size class >100,000 dwt (black)
Nexttothedifferences,Figure5.4showssomeinterestingagreementsinthespeeddevelopment.Altoughthespeedisdefinitelydifferent,theshapeofthetwolinesisverysimilar.Moststrikingisthespeeddipclosetotheportentrance.Thisdipispresentinthegraphsofallsizeclasses,butonlyforoutgoingvessels.Thisisbecauseatthislocationpilotsleavethevessel,byapilotboatthatcomesalongside.Forthisma-noeuvre,thevesselshavetoreducespeedduringashorttimeinterval.
AlsointerestingisthestrongreductioninspeedattheentranceoftheAmazonehaven.ThishastodowiththefactthatthesevesselshavetomakeaturntowardstheBeerkanaal,aftertheyhavelefttheAmazone-haven.Thisisespeciallytrueforlargervessels,thatcannotmakethisturnwhentheyaresailingtoofast.Therefore,thesmallervesselsizeclassesshowthisdiptoo,butforthemthespeedreductionismuchless.Incomingvesselsalsoshowthisspeedreduction,butlesssharpthantheoutgoingvesselsdo.
5.3.3 Conclusions
Thevesselsizedefinitelyhasaninfluenceonaswellthechosenpathasthevesselspeed.Concerningtheaveragepaththefollowingconclusionscanbedrawn.First,thesmallervesselssailtothestarboardsideofthelargervesselonaverage.Inpractice,thismeansthattheysailmoreclosetotheshore.Inabend,smallervesselstakeashorterpaththanthelargervessels,astheymakeasharpercurve(smallerradius).Thethreelargestsizeclassesshowaverygoodresemblence,whenlookingattheiraveragepathinsidethe
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Averagevesselpathandspeed
port’sbreakwater.Outsidethebreakwaterthereishoweverasignificantdifference.Theothersizeclassesbehavesignificantlydifferentinbothareas.
Thedifferencesbetweenthesizeclassesinvesselspeedarelargerthanthedifferencesfoundfortheaver-agepath.Nocombinationofsizeclasseshasaresemblencethatiswithintheaccuracyinterval.Althoughthethreelargestsizeclassesshowthesesignificantdifference,theyhavearelativelygoodagreementwitheachother,comparedtotheothersizeclasses.Ingeneralitcanbesaidthatvesselspeeddecreasedwhenthevesselsizeincreases.Anexceptiontothisissizeclass70,000-100,000dwt,whichhasaloweraver-agespeedthansizeclass>100,000dwt.Themostprobablereasonforthisisthatvesselsfromsizeclass>100,000dwtdousemoretugs,whichincreasestheirflexibilitytoalterforexampletheirspeed.Thismakesitpossibleforthemtonavigatewithalargerspeedinsidetheportarea14.
Althoughtheaveragepathsofsomevesselsizeclasseshaveaverygoodresemblence,nosizeclassesarebroughttogetherintoonegroup.Thisisbecausethevesselspeedsaresignificantlydifferentforallsizeclasses.Besidesthis,theaveragepathsoutsidetheprotectionoftheport’sbreakwaterarealsoverydiffer-entfromeachother.
5.4 Vessel and vessel speed distribution
Nexttotheaveragepathvesselstake,itisimportanttoderiveinsightintothedeviationfromthispath.InFigure5.5agridhasbeenlaidoverthedeterminedcasearea.Thedimensionsofagridcellare25X25meters(0.5Xgridsize).ThecolorsoftheplottedpointsindicatehowmanyvesselshassendanAISmessagewhentheywhereinsidethatspecificgridarea.Thedatausedinthisfigureisfromsizeclass70,000-100,000dwt,forincomingvessels.
Itcanalreadybeseenfromthispicturethatmostvesselschooseapproximatelythesamepath,butthatthereisalsoadeviationfromthispath.Thisdeviationissometimesverylarge,forexampleoutsidetheport.Onotherlocationthedistributionoverthewaterwayisrelativelynarrow,whichisforexamplethecaseintheMaasmond.IntheBeerkanaal,thereisclearly1pathmostvesselstake,butsomevesselschooseacompletelydifferent,morewestwards,route.Thisfiguremakesitclearthatitisneededtoinvestigatethedistributionoverthewaterwayindifferentcrosssections.Inthisway,amoredetailedinsightinthediffer-entvesselpathscanbeobtained.
14 ThispracticalexplanationoftheresultsfoundisderivedfromaninterviewwithBenvanScherpenzeel(Port
ofRotterdam).Otherpracticalinterpretationsofthetheoreticalresultsfoundinthisthesisareconcluded
fromthisinterviewaswell.
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An analysis of vessel behaviour based on AIS data
Blue: < 8 AIS messagesYellow: 8-13Red: 14-30Black: >30
Figure 5.5 Overview of all AIS messages sent from spe-cific areas.
Size class 70,000-100,000, ingoing vessels
Ateverygridpoint(each50meters)adistributionoverthecrosssectionoverthewaterwayiscalculatedfromtheavailabledatapoints.For4locationsontheincomingandoutgoingtrajectoriesthedistributionsareelaboratedfurther.ThelocationswherethisisdoneareindicatedinFigure5.6
Location1ischosen,becauseitgivesmoreinsightintothebehaviourofvesselsjustoutsidetheport.Influ-encesofforexampletheirdestination(e.g.Hamburg,Antwerp)mightbevisibleinthiscrosssection.Loca-tion2showshowthevesselsbehaveinarelativelywidewaterway(e.g.howdotheypreparebeforetakingthebendintotheBeerkanaal).Theotherlocationsarechosenbecausetheygiveinsightinhowvesselsbehaveinabend(location3)andmoreclosetotheirdestination(location4).
Nexttothepaththatvesselstake,alsothevarianceinthevesselspeedisimportant.Thereforethedistri-butionofthevesselspeedisalsoinvestigatedforthecrosssectionsindicatedinFigure5.6.Thisisdoneintwoparts.First,thedistributionofthevesselspeedinacertaincrosssectionisdetermined.Hereafter,this
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Averagevesselpathandspeed
islinkedtothespatialdistributionbycalculatingthedistributionoftheaveragevesselspeedover a cross section.
1
4
3
2
Figure 5.6 Cross sections on the vessel trajectories, which are used to obtain more insight into the
spatial vessel distribution and the distribution of the vessel speed. Source: Google Earth
5.4.1 Spatial vessel distribution on cross-sections
Figure5.7showsanexampleofaspatialdistribution,derivedfromtheempiricaldataatacertaincrosssec-tion.OntheX-axis,avalueofzerocorrespondentstothecalculatedvaluefortheaveragetrack.Thisfigureshowsthereforethedeviationfromtheaverage.ApositivevalueforXmeansthatthevesselsailsmoretothestarboardside.
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An analysis of vessel behaviour based on AIS data
−400 −300 −200 −100 0 100 200 300 4000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
X = devia�on from average (m)
P (X
)
Figure 5.7 Spatial distribution on location 3 (see Figure 5.6),
Size class 10,000-40,000; In-coming.
Byvisualinspectingthedifferentdistributions,itseemsanormaldistributionfunctionwouldmakeagoodfit.Toobtain(besidesthevisualinspection)asecondindicationhowthedataisdistributed,theskewnessandkurtosisarecalculated.Theskewnessisameasureoftheasymmetryofthedistributionoftheempiricaldata.Anormaldistributionissymmetrical;thereforetheskewnessofthisdistributionis0.Valuesbetween-1and1indicatethatthedataareapproximatelynormaldistributed.Thekurtosisgivesanindicationofthepeakednessofadistributionfunction.Anormaldistributionhasakurtosisof3.Inthisthesisthekurtosisiscorrectedbysubtracting3,becauseinthiswayvaluesaround0aretobeexpectedforanormaldistribution.Thisisalsoknownastheexcesskurtosis.Equation(5.2)and(5.3)showtheformulasfortheskewnessandkurtosis(Groenveld,2001).
Theskewnessandexcesskurtosisarecalculatedforthedifferentdatasetsatalllocations.TheresultsaresummarizedinTable5.13andTable5.14respectively.
n3
i ii=1n
3 3/2i i
i=1
Skewness =
(x - ) *p(x )
(x - ) *p(x )[ ]
µ
µ
∑
∑(5.2)
n4
i ii 1n
2 2i i
i 1
Excess kurtosis
where n=numberofdatapoints
(x ) *p(x )3
(x ) *p(x )[ ]
µ
µ
=
=
=−
−−
∑
∑(5.3)
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Averagevesselpathandspeed
Table 5.13 Skewness for the different datasets at locations 1 to 4.
Location<10,000 10,000-40,000 40,000-70,000 70,000-100,000 >100,000
In Out In Out In Out In Out In Out
1 -0.16 -0.5 -0.64 -0.17 -0.24 -0.26 -0.21 -0.07 0.09 0.02
2 -0.1 -0.44 -0.36 -0.46 0.01 -0.78 -0.05 -0.07 -0.28 0.08
3 -1.24 -0.02 -0.63 0.52 0.09 0.04 -0.17 0.21 0.02 -0.14
4 -0.24 -0.73 -0.07 -0.49 1.06 -0.91 0.32 -0.58 0.94 -0.4
Table 5.14 Excess kurtosis for the different datasets at locations 1 to 4.
Location<10,000 10,000-40,000 40,000-70,000 70,000-100,000 >100,000
In Out In Out In Out In Out In Out
1 -0.43 0.12 -0.09 -0.48 -0.5 -0.62 -0.72 -0.79 -0.51 -0.68
2 -0.06 -0.17 0.05 -0.03 -0.4 1.81 -0.36 -0.86 -0.71 -0.98
3 3.07 -0.57 0.44 -0.13 -0.69 -0.4 -0.21 0.28 -0.62 -0.37
4 0.09 0.17 -0.54 -0.12 0.8 1.17 0.06 2.57 0.72 0.75
Itcanbeseenthattheskewnessis,exceptfor2values,alwaysinsidethe[-1;1]-interval.Thismeansthat,basedontheskewness,itcanbeconcludedthatthedistributionsareindeedapproximatelynormaldis-tributed.Itisremarkabletoseethattheskewnessformostdatasetshasanegativevalue.Thismeansthattheyhaveatailtotheleftsideofthedistribution.Inpractice,thistailistowardstheportsideofthevessels.Thismeansthatthereareoftensomevesselsthatdeviatemoretothemiddleofthechannel,whereasthedeviationtowardstheshoreismorestrictlybounded.Fromapracticalpointofviewthisseemsalogicalconclusion.
Theexcesskurtosisisformostdatasetsaround0.Therearehoweversomenoticeablelowandhighvalues.Mosteye-catchingisthevalueof3.07forsizeclass<10,000dwt;incomingatlocation3.Figure5.8(left)showsthegraphofthisdistribution.Thismakesitclearthatthishighvalueiscausedbyarelativesmallpeakattheleftsideofthedistribution.Duetotheverysmallstandarddeviationofthisdistribution,thispeakhasabiginfluenceontheexcesskurtosis.(whichisthecomparisonbetweenthe4thmomentrela-tivetothemeanandthe4thpowerofthestandarddeviation).Thisalsoexplainstheothervalueslargerthan1.Inpractice,thissmallpeakiscausedby1or2vesselsthatsailalongthispath.Thefactthatsuchasmallamountofvesselshaveaccidentallysailedatthislocationisnoreasontorejecttheassumednormaldistribution.
Valuesaroundandlowerthan-1arefoundaswell.Thesedatasetshaveanexcesskurtosisthatindicatestheyaremainlyuniformdistributed(theexcesskurtosisforauniformdistributionis-1.2).Mostclosetothisaretheoutgoingvesselsfromsizeclass>100,000atlocation2,withanexcesskurtosisof-0.98.Figure5.8(right)showsthisdistribution,whichmakesitclearthatindeedauniformdistributedmightbeabetterfitforthisdatasetatthisspecificlocation.Byfarmostdatasetsdohoweverindicatethatanormaldistribu-tionisexpectedtogiveagoodfit.Itisthereforetriedtodoso.
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An analysis of vessel behaviour based on AIS data
−400 −300 −200 −100 0 100 200 300 4000
0.05
0.1
0.15
0.2
0.25
X = devia�on from average (m)P
(X)
Skewness = 0.08Kurtosis = -0.98
−400 −300 −200 −100 0 100 200 300 4000
0.05
0.1
0.15
0.2
0.25
X = devia�on from average (m)
P (X
)
Skewness = -1.24Kurtosis = 3.07
Thenormaldistributionthatisusedtofittheobserveddistributionfunctionsisafreetruncatednormaldistribution.Itisdescribedbythreeparameters:themean(μ),thevariance(σ2)andascalingparameter(A).Thefactthatitistruncatedmeansthatthedistributionisboundedbelowandabove.Normally,anormaldistributionisnotboundedandvaluesontheX-axiscangoto(minus)infinity.Inpractice,vesselswillnotdeviatethatmuchfromtheirpath,becausethentheyaregrounded.Ofcoursethismight(veryrarely)hap-peninreality,butinsuchcasesothermechanismsthanastatisticaldeviationfromtheaveragepathwillbeleading.Thisisthereforenottakenintoaccountinthenormaldistributionsthatdescribethevesselstrajectories.
Figure5.9andshowsthefittingofanormaldistributiononthefourpredefinedlocations.Thedataset10,000-40,000;incomingischosenasanexample.Thevaluesintheupperrightcornerofthegraphsde-scribethefittednormaldistribution(reddottedline).TheR2valuesmentionedindicatethegoodnessoffitforthisdistribution.Thecalculationofthisparameteriselaboratedbelow.
−400 −300 −200 −100 0 100 200 300 4000
0.05
0.1
0.15
0.2
0.25
X = devia�on from average (m )
P (X
)
R 2=0.9443
µ = −2.9σ = 72.5A = 0.14
−400 −300 −200 −100 0 100 200 300 4000
0.05
0.1
0.15
0.2
0.25
X = devia�on from average (m)
P (X
)
R 2=0.8663
µ=0σ=86.2A=0.12
Figure 5.9 The spatial vessel distribution of the vessel size class 10,000-40,000, incoming based on observed values (blue) and the fitted normal distri-
bution (red dotted), on location 1 (left) and location 4 (right).
Figure 5.8 Spatial distribution for the vessel size class <10,000; incoming at location 3 (left) and >100,000; outgoing at location 2 (right)
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Averagevesselpathandspeed
Assaidbefore,thenormaldistributionsaredescribedbythreeparameters.Nexttothis,theyareboundedbyX-valuesonbothsides.Equation(5.4)showstheformulathatdescribesthenormaldistribution,derivedforlocation4(Figure5.9;right).
fit
2-(X- )
22*
X = deviationfromthemeaninmetersforX = [-250;250] 2.9
72.5A 0.14
P (X) A*e
µ
σ
µσ
→ = −==
=
(5.4)
Theskewnessandexcesskurtosisgaveanindicationthatnormaldistributionswouldgiveagoodfit.Nowtheyarederived,thedistributionscanbetested.TheirgoodnessoffitisfirstdeterminedbyperformingaChi-squaretest(χ2).Thistestdeterminesthedegreeofagreementbetweentheempiricaldistributionandthetheoretical(normal)distribution.Thehypothesisisthatthereisnosignificantdifferencebetweenthosedistributions.Theconfidencelevel(answeringthequestionwhatissignificant)isseton95%,thesameasusedpreviously.
Thedetailedelaborationofthedifferentχ2-testscanbefoundinAppendixE.Table5.15showswhetherthedifferentdatasetsandlocationspasstheχ2-test(OK)ornot(FAIL).
Table 5.15 Results of the χ2-tests for the fitting of the assumed normal distribution to the different data sets.
Location<10,000 10,000-40,000 40,000-70,000 70,000-100,000 >100,000
In Out In Out In Out In Out In Out
1 OK OK OK OK OK OK OK OK OK OK
2 OK OK OK OK OK OK OK OK OK OK
3 OK OK OK OK FAIL OK OK OK OK OK
4 OK OK OK OK OK OK OK FAIL FAIL OK
Clearly,mostdistributionshaveasufficientfit.Therearethreedatasetsthatdonotpasstheχ2-test.Thefailsforthedatasets70,000-100,000dwt;outgoingand>100,000dwt;incomingatlocation4arenotverysurprising.Thecalculatedskewness(-0.58and0.94)andkurtosis(2.57and0.72)forthesedatasetswerealreadynotcompletelyindicatinganormaldistribution.Thisiscausedbyrelativelysmallpeakstotheouterlimitsofthedistribution,asexplainedbefore.Thedataset40,000-70,000dwt;incomingalsofailstheχ2-test atlocation3.Figure5.10showsthereasonforthis:alargepeaktotherightsideofthedistribution.Suchapeakisveryunlikelytooccurwhenthevesseldistributionisnormaldistributed.ThesmallpeakattheouterleftsideofthegraphisanoutlierthatisnotfilteredoutbytheMatlabcode.Thisoutlierdoeshowevernotinfluencetheoutcomeoftheχ2-testverymuch.Asalmosteverydatasetpassestheχ2-test,itisconcludedthatthenormaldistributionisagoodapproximationofthevesseldistributionoveracrosssectioninthewaterway.
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An analysis of vessel behaviour based on AIS data
−400 −300 −200 −100 0 100 200 300 4000
0.05
0.1
0.15
0.2
0.25
X = devia�on from average (m)
P (X
)
R2=0.8292
µ=7.9σ=72A=0.14
Figure 5.10 The spatial vessel distribution of the vessel size class 40,000-70,000; incoming at location 3
Besidesthediscusseddatasets,itisprovenbytheχ2-test-testthateverydatasetiscorrectlyapproximatedbyitsspecificnormaldistribution.Thereforethesedistributionsareusedinthefollowing.Itishoweverstillinterestingtoinvestigatehowwellthenormaldistributionsfittheempiricaldata.Theχ2-test-tests have providedanindicationforthis,butmoreinsightisobtainedbycalculatingthecoefficientofdetermination,R2.Thiscoefficientdependsontherelationbetweenthesumofthesquaredresiduals(SSR)andthesumofthesquarederrors(SSE).Equation(5.5)showsthecalculationofR2,SSRandSSE.
2
n2
X 1
n2
fitX 1
SSRR
SSE SSR
SSR
SSE
(P (X) P( ))
(P (X) P(X))
µ=
=
=+
=
=
−
−
∑
∑
(5.5)
ValuesofR2rangefrom0to1;inwhichvaluescloseto1indicateastrongcorrelationbetweenthetwodistributioncurves.Thegoodnessoffitisthereforedependentonthisvalue.Table5.16showsR2foralldatasets.
Table 5.16 Coefficients of determination (R2) for the spatial vessel distribution
Location<10,000 10,000-40,000 40,000-70,000 70,000-100,000 >100,000
In Out In Out In Out In Out In Out
1 0.88 0.85 0.87 0.77 0.83 0.76 0.95 0.76 0.85 0.79
2 0.94 0.85 0.96 0.88 0.97 0.87 0.99 0.91 0.94 0.95
3 0.97 0.82 0.96 0.88 0.83 0.91 0.91 0.86 0.96 0.86
4 0.95 0.96 0.94 0.93 0.94 0.98 0.94 0.97 0.88 0.97
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Averagevesselpathandspeed
Mostdatasetshaveanaveragevaluehigherthan0.8.Forthedatasetsthatdidnotpasstheχ2-test values above0.8arefoundaswell.Therearehoweversomeinterestingpatternsthatcanbeobservedfromthetable.Moststrikingarethelowervaluesthatoccurforoutgoingvesselsatlocation1and-toalesserextent-atlocation2and3.Figure5.11showsthedistributionforthesizeclass70,000-100,000dwt;outgoing,atlocations1(left)and3(right).Atlocation1,thedistributionisverywide(σ=123.9m).Becauseofthis,onlyasmallamountofdatapoints(afewvessels)canalreadycauseasmallpeak.Nexttothis,clearlytwopeakscanbedistinguished,both±100awayfromX=0.Thismightgiveanindicationthatvesselsarealreadyadaptingtheirpositionatthewaterwaytotheirdestination,towardstheSouth(e.g.Antwerp)ortowardstheNorth(e.g.Hamburg).
Atlocation3,thebendattheentranceoftheBeerkanaal,thedistributionismuchmorenarrowthanatlocation1.Anotherremarkablefindingisthefactthatthedistributionclearlyhastwopeaks.ThiscanbeexplainedbythefactthatthosevesselshavebeenhinderedbyvesselscomingfromtheCalandkanaal.Be-causeofthistraffic,theyhadtochoosea(lesspreferable)pathmoretotheinnerbend.
−400 −300 −200 −100 0 100 200 300 4000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8571
µ=−5.4
σ=74.9
A=0.13
−400 −300 −200 −100 0 100 200 300 4000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
X = devia�on from average (m)
P (X
)
R 2=0.7592
µ=10.5
σ=123.9
A=0.08
Figure 5.11 The spatial vessel distribution of the vessel size class 70,000-100,000; outgoing at location 1 (left) and 3 (right)
Ingeneral,theincomingvesselshaveahigherR2valuethanoutgoingvessels.Thisismainlybecausetheoutgoingvesselshaveawiderdistributionoverthewaterway.Inpractice,they‘spreadout’moreoverthewaterwaydependingonforexampletheirdestination.Thereishoweveroneexceptiontothisobservation.Forthethreelargestsizeclasses,atlocation4theoutgoingvesselsaremorenormallydistributed(higherR2 value)thantheincomingvessels.
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An analysis of vessel behaviour based on AIS data
−400 −300 −200 −100 0 100 200 300 4000
0.05
0.1
0.15
0.2
0.25
X = devia�on from average (m)
P (X
)
R 2=0.971
µ=2.1σ=35A=0.27
−400 −300 −200 −100 0 100 200 300 4000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8768
µ=−18.9
σ=55.3
A=0.17
Figure 5.12 The spatial distribution on location 4 for incoming (left) and outgoing (right) vessels from size class >100,000 dwt.
Figure5.12showsthedistributionsatthislocationforthesizeclass>100,000dwt,incoming(left)andout-going(right).Thedistributionfortheincomingvesselsclearlyshowsonepeak,butalsotwosmallerpeakstotherightsideofthedistribution.Apparently,apartofthevesselschoosestotakeanotherpathinsidetheBeerkanaal.ThiswasalreadyobservedfromFigure5.5onpage43.Thepresenceofthese‘preferencelanes’iscausedbythewaythevesselssailintotheAmazonehaven.Dependingonhowtheyareloaded,vesselshavetosailforwardsorbackwardsintotheAmazonehaven.Whentheysailinforwards,whatmostvesselsdo,theychoosethepathclosesttotheshore(thelargestpeakinFigure5.12).Thisisdonebecauseinthiswaythewidestbendcanbetaken,whichispreferred.Iftheysailinbackwards,thisistheotherwayaround,asthewidestbendisnowattheothersideofthewaterway(seeFigure5.13).
Figure 5.13 The difference in the vessel path when sailing forwards (red) or backwards (blue) into the Amazonehaven.
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Averagevesselpathandspeed
5.4.2 Vessel speed distribution
Nexttothespatialvesseldistribution,alsothedistributionofthevesselspeedoverthecrosssectiononthe4predefinedlocationshasbeeninvestigated.Theaccuracyofspeedcalculationsis±6.5%,whichisataspeedof15knotsequivalentto±1.0knot(seesection5.2).Thereasonforthisinaccuracyisthelargedeviationoftheindividualvesselspeedfromthecalculatedaveragespeed.Thislargedeviationwillbeinvestigatedmoreintodetailinthissection.Bycalculatingtheskewnessandexcesskurtosis,togetherwithperformingaχ2-testitisinvestigatedifthedatacanagainbeapproximatedbynormaldistributions(seeAp-pendixE).
Theskewnessandexcesskurtosisindicatethatanormaldistributionisagoodindicationforalmosteverydataset.Alsotheχ2-testsupportsthisconclusion.Toinvestigatehowwellanormaldistributionmatchesthedatasets,coefficientsofdeterminationarecalculated.TheseareshowninTable5.17.
Table 5.17 Coefficients of determination (R2) for the vessel speed distribution in locations 1 to 4
Location<10,000 10,000-40,000 40,000-70,000 70,000-100,000 >100,000
In Out In Out In Out In Out In Out
1 0.88 0.85 0.87 0.77 0.83 0.76 0.95 0.76 0.85 0.79
2 0.94 0.85 0.96 0.88 0.97 0.87 0.99 0.91 0.94 0.95
3 0.97 0.82 0.96 0.88 0.83 0.91 0.91 0.86 0.96 0.86
4 0.95 0.96 0.94 0.93 0.94 0.98 0.94 0.97 0.88 0.97
Itcanbeseenfromthetablethatallempiricaldistributionshavequiteagoodfitforanormaldistribution.Thesmallestvaluesarefoundatlocation1,wherevesselshavemorefreedomtomanoeuvreandtoaltertheirspeeds.ThehighestvaluesforR2arefoundforincomingvesselsfromthethreelargestsizeclasses,atlocations3and4.Attheselocationsthedifferentvesselsspeedshaveconvergedmoretowardseachother.ThisisalsoshownbyFigure5.14,whichshowthedistributionofthevesselspeedinthedifferentcrosssec-tions.Inthefigurealsothefittednormaldistributionisplotted(discontinuousredline).Thethreeparam-etersintherightuppersideofthefigures(μ,σandA)describethisdistribution.
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An analysis of vessel behaviour based on AIS data
0 2 4 6 8 10 12 14 16 18 200
0.05
0.1
0.15
0.2
0.25
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8833µ=10.2
σ=1.9
A=0.1
0 2 4 6 8 10 12 14 16 18 200
0.05
0.1
0.15
0.2
0.25
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8865µ=7.5
σ=1.4
A=0.14
0 2 4 6 8 10 12 14 16 18 200
0.05
0.1
0.15
0.2
0.25
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9097µ=6.0
σ=0.8
A=0.23
0 2 4 6 8 10 12 14 16 18 200
0.05
0.1
0.15
0.2
0.25
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9533µ=5.6
σ=0.7
A=0.27
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure 5.14 Vessel speed distribution on locations 1 to 4, for sizeclass 70,000-100,000 dwt; incoming vessels.
Thegraphsmakeclearthatthevesselspeedhasawidedistribution.Thewidthofthespeedintervalisforthefirsttwolocationsaround10knots.ItcanbeseenthatthisintervaldecreaseswhenthevesselssailsfurthertowardstheAmazonehaven.Thisisalsoshownbytheσ(standarddeviation)thatdevelopsfrom1.9atlocation1tofinally0.7atlocation4.Itcanbeseenaswellthatthelargestreductioninspeedisobtainedbeforelocation3,sobeforethevesselsailsintothestraightpartoftheBeerkanaal.Theothersizeclassesshowthesamebehaviour,althoughitmustberemarkedthatforthesmallervesselsthedeviation(σ)isclearlylarger.
Nexttothedistributionofthevesselspeedinacrosssection,itisalsointerestingtoobtaininsightinthedistributionofthevesselspeedoveracrosssection.Todoso,graphsareproducedthatshowtheaveragespeedondifferentlocationsofacrosssection.Figure5.15givesanexampleofthis,forthecrosssectionsatlocation1to4,againforincomingvesselsfromsizeclass70,000-100,000dwt.
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Averagevesselpathandspeed
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)−200 −100 0 100 200
0
5
10
15
X = devia�on from average (m)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Vess
el s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
MeanMean
Mean Mean
Vess
el s
peed
(kn)
Vess
el s
peed
(kn)
Vess
el s
peed
(kn)
Figure 5.15 Vessel speed distribution over the cross sections at locations 1 to 4, for incoming vessels from size class 70,000-100,000 dwt.
Thefigureshowsthatthevarianceofthevesselspeedoverthesecrosssectionsisnotverylarge.Especiallyatlocations3and4,thevesselspeedisclearlyindependentfromthelocationinthecrosssections.Forlocation2and-especially-location1thisimageissomewhatmorepeaky.Theirregularbehaviourattheouterlimitsoriginatesfromthefactthatthosepointsarecalculatedfromasmallamountofvessels.Thismakesthosepointslessaccurateandmostpeaksthatoccurattheouterlimitsarethereforenotsignificant.Thedistributionsoftheothersizeclassesareinvestigatedaswell.ThoseshowasimilarpatternasshowninFigure5.15.Foroutgoingvesselsandforsmallersizeclassesasomewhatmorepeakydistributionisfoundsometimes.Noproofishoweverfoundthatthelocationinthecrosssectionhasasignificantinfluenceonthevesselspeed.
ThevesseldistributionsandvesselspeeddistributionsthatarenotshowninthischaptercanbefoundinAppendixF.
5.5 Conclusions
Inthischaptertheaveragebehaviourofvessels,visitingtheAmazonehaven,isinvestigated.Theamountofdatausedmakesitpossibletodrawconclusionsregardingaveragevesselpathwithanaccuracyof±30m.Forvesselspeed,anaccuracyof±6.5%canbeachieved.Thesevaluesarebasedona95%significancelevel;thisiskeptasatresholdvaluethroughoutthisthesis.Theaccuraciesthatarefoundareacceptedas
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An analysis of vessel behaviour based on AIS data
sufficientinthisthesis.
Itisfoundthatthevesselsizeclearlyinfluencestheaveragepathandspeed.Aslongasthevesselsarewith-intheprotectionoftheport’sbreakwater,theaveragepathsofthethreelargestsizeclasseshaveagoodresemblence.Inthepartofthetrajctoryoutsidetheport’sprotection,thesedohowevertakeasignificantdifferentpath.Thevesselspeedisdifferentforall5sizeclasses.
Ingeneral,thefollowingcanberemarkedconcerningtheinfluenceofvesselsize.Largervesselssailmoreintothemiddleofthechannel.TheyalsotakealargerbendattheentranceoftheBeerkanaal.Onaverage,vesselsfromthelargestsizeclass(>100,000dwt)sailabout100metersmoretothemiddlethanvesselsfromthesmallestsizeclass(<10,000dwt).Thisistrueforbothincomingandoutgoingvessels.
Thevesselsizedoesalsoinfluencetheaveragevesselspeed.Ingeneralitistruethatlargervesselssailslow-erthansmallervessels.Thereisoneexceptiontothis:vesselsfromsizeclass70,000-100,000sailslowerthanallothervessels,includingthesizeclass>100,000dwt.Thespeeddifferencebetweenbothincomingandoutgoingvesselsfromthefastest(andsmallest)sizeclassandtheslowestsizeclass(70,000-100,000dwt)isalmost30%.
Thespatialdeviationoverthewaterwayisverywellapproximatedbyanormaldistribution.Thisissup-portedbycalculatingvaluesfortheskewnessandexcesskurtosisoftheempiricaldatasets.Aχ2-testshowedaswellthattheassumednormaldistributionsareagoodapproximation.Nexttothis,R2 values for the goodnessoffitarecalculatedon4differentcrosssections.Thesevaluesdemonstrateagainthatthenormaldistributionisagoodfitfortheempiricaldata.
Thedeviationfromtheaveragespeedisquitelarge.Inmostcrosssectionsthewidthofthespeeddistribu-tioncangoupto10knots,dependingonthelocationandvesselsize.Theskewness,excesskurtosis,χ2-test andR2valueshaveshownthatthevesselspeedinacrosssectionisbyagoodapproximationnormallydistributed.Alsothevesselspeeddistributionoverthecrosssectionsisexamined.Inthesedistributionsnosignificantproofisfoundthatthelocationinthecrosssectionhasinfluenceonthevesselspeed.Itisthere-foreconcludedthatthevesselspeedisuniformdistributedoveracrosssection.
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Northern breakwater Start bend into Beerkanaal95
100
105
110
115
120
125
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Development along average path -->
head
ing
(deg
rees
), 0
/ 36
0 =
Nor
th
Part 1 Part 2
Externalinfluences
Chapter6
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Externalinfluences
6 External influences
Inthepreviouschaptertheaveragevesselbehaviourfordifferentsizeclassesisobtained.Thisaveragebe-haviourissplitintothevesselpathandtheaccompanyingvesselspeed(speedoverground).Itisverylikelythatexternalcircumstanceslikewindandcurrenthaveaninfluenceonthesecharacteristics.Ifthisisindeedthecaseandtowhatextent,isinvestigatedinthischapter.Thefactorsthatareexaminedare:wind,currentandvisibility.Thesearechosen,becausethelargestinfluenceonthevesselpathandspeedisexpectedforthesefactors.ThetrajectorybetweenNorthSeaandtheAmazonehavenis,whereneeded,splitintodiffer-entparts.Thismakesitpossibletodrawconclusionsregardingtheexternalinfluenceonthevesselbehav-iouroncertaintypesofwaterways.Theseconclusionsareusedinchapter8,fortheformulationofgenericrules.
6.1 Wind
6.1.1 Split up of the trajectory
Fortheinvestigationoftheinfluenceofwind,thetrajectorybetweentheNorthSeaandtheAmazonehavenissplitintotwoparts.Part1(‘Maasmond’)isbetweentheNorthSeaandtheentranceoftheBeerkanaal.Part2(‘Beerkanaal’)isbetweentheentranceoftheBeerkanaalandtheentranceoftheAmazonehaven.ThetrajectoryinsidetheAmazonehavenisnottakenintoaccount,asthemanoeuvrabilityisverylimitedatthispoint.ItisthereforeexpectedthatnosignificantresultsshallbefoundregardingthedeviationfromthevesselpathandvesselspeedinsidetheAmazonehaven.
TheMaasmondandBeerkanaalarelookedatseparately,becausethevesselheadingisclearlydifferentfortheseparts(Figure6.1).Thisisimportant,becauseitmeansthatthewindalsoworksfromdifferentdirec-tionsonthevessels.Forexample,anincomingvesselthatsailsintheMaasmondencountersastrongwindfrombehind.WhenthevesselenterstheBeerkanaalthissamewindnowcomesfromhisstarboardside,throughwhichthiswindislikelytohaveadifferentinfluence.
5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.84.4
4.41
4.42
4.43
4.44
4.45
4.46
4.47
4.48
4.49
4.5
Part I - ‘Maasmond’
Part 2 - ‘Beerkanaal’
Figure 6.1 Part I and part 2
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An analysis of vessel behaviour based on AIS data
6.1.2 Wind data
ThewinddatathatisusedtomaptheinfluenceofthisexternalcircumstanceisobtainedfromtheKNMI15.ThisdatasetcontainstheinformationregardingthewindclimateatHoekvanHollandin2009.HoekvanHollandisseenasagoodapproximationofthewindclimateinthewholecasearea.Everyhourthehourlymeanwindspeedisknownwithanaccuracyof1m/s.Alsothemeanwinddirectionisgiveneveryhour,withanaccuracyof10degrees.BycouplingthepointsintimeoftheindividualAISmessagesandthewinddataset,thewindspeedanddirectionisknownforeveryAISmessage.
Theinfluenceofwindisexaminedfordifferentwinddirectionsandwindspeeds.Thedivisioninwinddirectionsismade,dependendonthevesselheading.Forthetwotrajectories(MaasmondandBeerkanaal)thewinddirectionissplitintofourgroups:windfrombehind,front,portsideandstarboardside.Forthecouplingofthesegroupstothewinddata(whichisgivenindegrees),theaverageheadinginthetwoportsiscalculated.Figure6.2showsthistranslationtoaspecificrangeofdegrees.Forincomingandoutgoingvesselsthesameaverageheadingsareused,buttherangeofdegreesisexactlytheoppositeofeachother(250o-340oiswindfrombehindforincomingvessels,butwindfromthefrontforoutgoingvessels).
Port side (in)Starboard side (out)
Starboard side (in)Port side (out)
Front (in)Behind (out)
Behind (in)Front (out)
0 / 360
Average heading: 115 (in) 295 (out)
Port side (in)Starboard side (out)
Starboard side (in)Port side (out)
Front (in)Behind (out)
Behind (in)Front (out)
0 / 360
Average heading: 195 (in) 15 (out)
Figure 6.2 Average heading in Maasmond and Beerkanaal
Thewindspeedisdividedintothreeclasses(Table6.1).Byusingthisdivision,everywindclasshasapproxi-matelythesameamountoftracks.Togetherwiththesplitupofthewinddirection,everyvesselsizeclassnowisdividedinto12differenttypesofwindinfluence.Itmustberemarkedthatnoteveryofthose12datasetshavethesameamountoftracks.Thisdependsverymuchonthewinddirection,asthereisforexamplelessfrequentwindfromtheeastthanfromthewest.
Table 6.1 Wind speed classes
Windspeedclass Beaufort Windspeed(m/s) Windspeed(kn)
I 0-3 0-5.4 0-10
II 4 5.5-7.9 11-15
III >5 >8.0 >15
15 RoyalNetherlandsMeteorologicalinstitute,thewinddataisobtainedfromtheirwebsite,www.knmi.nl,
at1April2010
5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.84.4
4.41
4.42
4.43
4.44
4.45
4.46
4.47
4.48
4.49
4.5
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Externalinfluences
6.1.3 Results
Foreverywindregimeandvesselsizeclass,aselectionoftracksisobtained.Theseselectionsarecomparedtotheaveragevesselpathandvesselspeedforthatspecificsizeclass.Thiscomparisonismadeforthechosenpathaswellasthedevelopmentofthevesselspeedalongthispath.Theresultsarepresentedinthesamewayaswasdoneinthepreviouschapter.Anaveragedeviationfromthevesselpathiscalculated.Inthis,apositivevaluemeansthattheobservedselectionsailsmoretothestarboardsideoftheaveragepathofthatspecificsizeclass.Thespeeddifferencesarecalculatedinpercentages.TheresultsarehandledseparatelyfortheMaasmondandBeerkanaalbelow.
Maasmond
Figure6.3showsthedeviationfromtheaveragepathforthedifferentsizeclasses,whentheyaresubjecttocrosswind.OntheX-axisthecrosswinddevelopsfromastrongwindfromportsidetoastrongwindfromstarboardside.Thefigureclearlyshowsthequiteextensiveamountofscatterthatispresentintheresults,mainlybecauseofthenaturaldistributionofvesselsoverthewaterway.Thedifferentsizeclassesarealsoindicatedinthefigure,toseeifsignificantconclusionsconcerningthespecificclassescanbedrawn.Afteradetailedinspectionofthefigureitisconcludedthatnosignificantdifferencesbetweenthesizeclassescanbefound.Thereforethesizeclassesarebroughttogether.Alsothewindspeedisbroughttogetherinthethreeclassesderivedintheprevioussection.
< 10,000 dwt
10,000 - 40,000 dwt
40,000 - 70,000 dwt
70,000 - 100,000 dwt
> 100,000 dwt
<-- Wind from port side Wind from starboard side -->
−15 −10 −5 0 5 10 15
−400
−300
−200
−100
0
100
200
300
400
500
Wind speed (m/s)
Dev
ia�o
n fr
om a
vera
ge tr
ack
(m)
Figure 6.3 Influence of cross wind on the chosen path of individual vessels at the ’Maasmond’ trajectory
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An analysis of vessel behaviour based on AIS data
Figure6.4showsaboxplotofthegroupedresults.Thehorizontalredlinereflectsthemeanvalue.Theblueboxindicatesthe25%and75%percentile.Therangeofresultsisindicatedbythehorizontalblackline.Theredplussesareoutliers.Everypointthatisfurtherawayfromthemeanthanapproximately2.7timesthestandarddeviationisseenasanoutlier.ThisisdeterminedbyMatlab.Itisobviousfromtheboxplotthattheinfluenceofcrosswindissmallcomparedtothenaturaldeviation,whichisintheorderofhundredsofmeters.
Figure 6.4 Boxplot of the influence of crosswinds in the Maas-mond
<-- Wind from port side Wind from starboard side -->
> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −600
−400
−200
0
200
400
600
Dev
ia�o
n fr
om a
vera
ge tr
ack
(m)
Wind speed (m/s)
Toobtainamoregenericresult,alinearfunctionisfittothemeanvaluesderivedbytheboxplot.Alinearfunctionischosen,becausethisisasimplefunctionanditisstatisticallydifficulttoderiveamorecomplexrelationshipduetotheamountofscatter.Avisualinspectionofthefiguresupportsthisconclusion,asalinearfunctionseemtogiveareasonablefit.Figure6.5showsthelinearfit.Inchapter8thisrelationshipisfurtherelaboratedandgeneralised.Intheremainderofthisthesistheboxplotandtheindividualvesseltracksarenotelaborated.Itisassumed,basedonthisexamplethatitiscorrecttodoso.
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Externalinfluences
<-- Wind from port side (m/s).......wind from starboard side (m/s) −−>
> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −40
−20
0
20
40
60
devi
a�on
from
ave
rage
trac
k (m
)
Figure 6.5 Linear relationship regarding the influence of crosswinds in the Maasmond
Thevesselspeedisaffectedbycrosswindsaswell.Figure6.6showstheresultsforthedifferentsizeclasses(left)andtheirgroupedaverages(right).Thesamepatternwithareasonableamountofscatterispresent.However,thecalculatedmeanvaluesdonotshowalinearrelationshipthistime.Thevesselspeedisclearlysmalleratbothsidesofthegraph.Inpracticethismeansvesselsarelikelytosailslowerwhenthereisastrongcrosswind,regardlessifthewindcomesfromportsideorstarboardside.Therelationshipusedtodescribethecalculatedmeanvalues,isasecondorderpolynomial.
> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −15
−10
−5
0
5
10
15
<--Wind from port side (m/s)....wind from starboard side (m/s) -->
devi
a�on
from
ave
rage
spe
ed (%
)
> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −4
−3
−2
−1
0
1
2
o <-- Wind from port side (m/s).......wind from starboard side (m/s) −−>
devi
a�on
from
ave
rage
spe
ed (%
)
Figure 6.6 The influence of crosswinds on the vessel speed in the Maasmond The black lines in the left figure represent the results for the different size classes. The
red line in the left figure indicates the average, whereas the red lines in the right graph shows the fitted second order polynomial
Afterinvestigatingthevesselpathandvesselspeed,itcanbeconcludedthatcrosswindsdefinitelyhaveanoticeableinfluence.Forthevesselpaththisinfluenceishowevernotverylarge,especiallycomparedtothenaturaldeviationoverthecrosssection.Forlargewindspeedsthedeviationfromtheaveragepathisin
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An analysis of vessel behaviour based on AIS data
theorderof30meters.Themaximalvesselspeedreductionisapproximately4%.Anexplanationforbothresultscanbefoundwhenlookingattheaverageheadingofvessels.Figure6.7showsthedevelopmentoftheaverageheadingintheMaasmondforsizeclass>100,000dwt,forincomingvessels.Thebluelineistheaverageforthewholesizeclass.Thegreenlinereflectsthedevelopmentoftheheadingwhenthereisawind(windspeed>8m/s)blowingfromstarboardside.Itcanbeseenthatthevesselsobviouslyhaveadifferentheadingwhentheyareencounteringastrongcrosswind.
Northern breakwater
Fastening tugs Start bend into Beerkanaal100
105
110
115
120
125
130
Development along average path
head
ing
(deg
rees
), 0˚
/ 3
60˚
= N
orth
Figure 6.7 Development of the average vessel heading for the whole sizeclass >100,000 dwt and the part of the vessels that encounter strong crosswind from star-board side.
Thesevesselscorrecttheirheadinginordertostayoncourse.Iftheydonotcorrecttheircourse,thestrongcrosswindwouldblowthem‘away’.Itcanbeseenthattheheadingdifferenceislargestoutsidetheprotec-tionofthenorthernbreakwater.WhenthevesselsapproachthebendtowardstheBeerkanaal,theheadingdifferencebecomessmaller.Thisprincipleisalsofoundfortheothersizeclasses,butonlyforincomingves-sels.Outgoingvesselsdonot,ortoafarlesserextent,adapttheirheadingtothewindcircumstances.Inter-estingpeaksinheadingarefoundatlocationswheretugsfasten.ThefasteningoftugssometimesdisturbsthetransmittingofAISmessages,leadinginthiscasetosomepeaksinthevesselheading.
Thefactthatvesselsdoadapttheirheadingtokeeponcourseexplainswhythereisnotalotofdeviationfromtheaveragepath.Besidesthis,itdoesalsoexplainwhythevesselspeeddecreasesifthecrosswindspeedincreases.Becausethevesselscorrecttheirheading,theyareusingapartoftheirenginetocoun-terweightthewindforce.So,theyarenotusingtheirfullpowertosailahead;therebyreducingthevesselspeed.Anotherresultoftheadaptedheadingisthefactthatthepathwidthincreases.Thiscanalsohaveaninfluenceontheinteractionwithothervessels,asthevesselusesmorespace.Thisissueisnothandledinthisstudy,butitisworthwhiletoanalyseitinafuturestudy.
Alsotheinfluenceofwindcomingfrombehindorfromthefrontofthevessel(‘parallelwind’)isinvesti-gated.Thisisdoneinthesamewayasthecrosswindhandledabove.Figure6.8showsthefinalresults,inwhichalinearrelationshipisfoundandfitted.Thewindinfluenceishowevermuchlowerthanfoundforthecrosswinds.Thefactthatwindfrombehindleadstoahigherspeedfeelsverylogical.Thedeviationfromtheaveragepaththatisfoundishoweververylow(maximal11meters)andthelinearrelationshipdoesnotfitwell.Itisthereforedifficulttodrawsignificantconclusionsconcerningtheinfluenceofthiswindtypeonthevesselpath.
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Externalinfluences
> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −10
−5
0
5
10
15
devi
a�on
from
ave
rage
trac
k (m
)
<-- Wind from behind (m/s).....wind from front (m/s) −−>> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −3
−2
−1
0
1
2
3
<-- Wind from behind (m/s).....wind from front (m/s) −−>
devi
a�on
from
ave
rage
spe
ed (%
)
Figure 6.8 The influence of parallel wind on the chosen path and vessel speed in the Maasmond.
Beerkanaal
IntheBeerkanaaltheinfluenceofwindisinvestigatedinthesamewayasfortheMaasmond.Figure6.9showstheinfluenceofcrosswindsatthislocation.ItcanbeseenthattheinfluenceonthevesselpathisthesameasfoundfortheMaasmond.Windcomingfromstarboardsideblowsthevesselsmoretowardsportsideandtheotherwayaround.Thedifferencesarehowevermuchlower(<10meters).Thelinearrelation-shipseemstofitbothgraphsinasufficientmanner.TheinfluenceonthevesselspeedisdifferentfromtheresultsfoundfortheMaasmond.Whenthewindblowsmorefromstarboardside,thevesselspeedseemstodecrease.Thelinearrelationshipdoesnotgiveagoodfitforthevesselspeedanditisalsoimpossibletofitothersimplerelationships.
> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −8
−6
−4
−2
0
2
4
6
8
o <-- Wind from port side (m/s).....wind from starboard side (m/s) -->
devi
a�on
from
ave
rage
trac
k (m
)
> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −4
−3
−2
−1
0
1
2
3
4
5
r <-- Wind from port side (m/s)......wind from starboard side (m/s) −−>
devi
a�on
from
ave
rage
spe
ed (%
)
Figure 6.9 The influence of crosswinds on the vessel path and vessel speed in the Beer-kanaal.
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An analysis of vessel behaviour based on AIS data
TheinfluenceofparallelwindisinvestigatedfortheBeerkanaalaswell(seeFigure6.10).AswasalsofoundintheMaasmond,thistypeofwinddoesnothavealotofinfluenceonchosenvesselpath.Itisaswellnotpossibletofindagoodandsimplerelationship.
> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −20
−15
−10
−5
0
5
o <-- Wind from behind (m/s).....wind from front (m/s) −−>
devi
a�on
from
ave
rage
trac
k (m
)
Figure 6.10 The influence of wind from behind and from the front of the vessel on the vessel path in the Beerkanaal.
Theinfluenceonthevesselspeedisanotherstory,asatthislocationthereisadifferencebetweenincom-ingandoutgoingvessels.Figure6.11showstheinfluenceoftheparallelwindontheincoming(left)andoutgoing(right)vessels.Clearlytheincomingvesselsfollowalinearrelationship,whereastrongwindfrombehindleadstoahighervesselspeedandastrongheadwindcausesalowervesselspeed.Foroutgoingvesselstherelationshipismorecomplex;inthefigureasecondorderpolynomialistriedtofit.Thisseemstogiveagoodapproximation.Thisisaninterestingresult,becauseitissimilartotheinfluencefoundattheMaasmond,butnowforparallelwindinsteadofcrosswind.
> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −6
−5
−4
−3
−2
−1
0
1
2
3
> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −4
−2
0
2
4
6
8
o
devi
a�on
from
ave
rage
spe
ed (%
)
<-- Wind from behind (m/s).....wind from front (m/s) −−> <-- Wind from behind (m/s).....wind from front (m/s) −−>
devi
a�on
from
ave
rage
spe
ed (%
)
Figure 6.11 The influence of parallel wind on the vessel speed in the Beerkanaal for incom-ing (left) and outgoing (right) vessels.
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Externalinfluences
6.1.4 Conclusions
Thewindcircumstancesdefinitelyhaveaninfluenceonthevesselspeedandvesselpath.Thedeviationfromtheaveragevesselpathisnotverylarge,mainlybecausethevesselscorrecttheirheadingwhentheyareencounteringastrongcrosswind.Thisisconcludedbycomparingtheheadingofthosevesselswiththeaverageheading.Strongcrosswindsalsocauseadecreasedvesselspeed,asvesselsuseapartoftheirenginepowertocompensateforthewindforce.Moreinsidetheportarea,attheBeerkanaal,theinfluenceofcrosswindsisclearlylessthanattheMaasmond.
Windcomingfrombehindandfromthefrontofthevessel,parallelwind,hardlyinfluencesthevesselpath,butdoesinfluencethevesselspeed.Generally,headwindcausesadecreaseinvesselspeedandastrongerwindfrombehindthevesselleadstoahighervesselspeed.ExceptiontothisaretheoutgoingvesselsintheBeerkanaal.Thesevesselsshowadecreaseinvesselspeed,whenthewindisstronger,regardlessthedirec-tionoftheparallelwind.
6.2 Current
6.2.1 Currents in the case study area
Forthewindinfluence,itwasassumedthatthewindonlyvariesintime.Thisimpliedthatwithintheexaminedcasearea,thewindspeedandwinddirectionwereassumedtobeconstantoverthetotalarea,foracertainmomentintime.Forcurrentthisisnottrue,asthecurrentvariesintimeand inspace,bothhorizontallyandvertically.Thehorizontalvariationinspacedependsmainlyontheportsnauticalinfrastruc-ture.Theverticalvariationinspacedependsforalargepartontheinteractionbetweentheriver(NieuweWaterweg)andthetide.
Thesetwofactors(riverdischargeandtide)arethedrivingfactorsofthecurrentsthatoccurinthecasestudyarea,resultingindifferentdirectionsforthecurrentondifferentdepths.Thismightbeexplainedbythefollowing.Wherethesaltseawaterandthefreshriverwatermeeteachother,thefirstone‘dives’un-derthelayerofriverwater.Thisisbecausesaltwaterisheavierthanfreshwater.Becauseofthisprincipletherearemomentsintimewherethetoplayerofthewaterandthelayersbeneathhaveoppositecurrentdirections.Wheninalllayersthecurrentdirectionisapproximatelyequal,therecanstillbehugedifferencesincurrentvelocity.
6.2.2 Current data
FromthePortofRotterdam,dataisobtainedregardingtheexpectedcurentvelocitiesanddirectionsatthreedifferentsdepths.Thisinformationisknownfor10importantlocationsalongthecasetrajectory,fornormativetidalcyclesandriverdischarges(indicatedwithreddotsinFigure6.12.These10locationsaregrouped,bylookingatsimilaritiesintheircurrentregimes.Bydoingso,thehorizontalvariationinspaceistakenintoaccount.Finally,5differenttrajectoriesarepointedoutwhereasimilarregimeispresent(seeFigure6.12).Inpart5,theAmazonehaven,thecurrentinfluenceisnotfurtherinvestigated,asthecurrentvelocitiesareverylowatthislocation.
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An analysis of vessel behaviour based on AIS data
5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.84.4
4.41
4.42
4.43
4.44
4.45
4.46
4.47
4.48
4.49
4.5
Part 1
Part 5
Part 2
Part 3
Part 4
Figure 6.12 Overview of the different current regimes in the case area.
The red dots indicate the points where current data is available
FromtheServicedeskData(Rijkswaterstaat)thewaterlevelsatthecaselocationareobtainedover2009.Bycouplingthesewaterlevelstothenormativecurrentinformation,thecurrentvelocityanddirectionisknownateverychosenlocation,forthethreedifferentdephts.Afterthis,selectionsaremadefromvesselsthathavesailedthroughthecaseareawhileencounteringdifferentcurrentvelocitiesanddirections.Whichlayers(depths)arechosentobetakenintoaccountforthisdependsonthevesselsize.
Thecurrentdirectionissplitupinto4categories,thesameasusedforthewindinfluence:currentfrombe-hind,front,portsideandstarboardside.Thecurrentvelocityissplitintothreeclasses(seeTable6.2).Theseclassesarechosen,becausenoweverysizeclasshasaboutthesameamountofvesseltracks.Theamountofvesseltracksinoneselectiondependsofcourseverymuchonthecurrentdirection.Hardlyanycrosscur-rentcanforexamplebefoundinpart2.
Table 6.2 Current velocity classes
ClassCurrentvelocity
(m/s)Currentvelocity
(kn)
I <0.3 <0.6
II 0.3-0.5 0.6-1.0
III >0.5 >1.0
6.2.3 Results
Theresultsaregiveninthesamewayasforthewindinfluence.Figure6.13showstheresultsfortheareaoutsidetheprotectionofthenorthernbreakwatertheinfluenceofcrosscurrentonthevesselpathandthevesselspeed.Theinfluenceonthevesselpathisveryclearandinlinewiththefindingsfortheinfluenceofcrosswind.Theinfluenceonthevesselspeedgivesamorescatteredimage.Thebestsimplefitisgivenbyasecondorderpolynomial,butitisobviousthatthisfitisfarfromperfect.
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Externalinfluences
> 0.5 0.3−0.5 0−0.3 0−0.3 0.3−0.5 > 0.5−6
−5
−4
−3
−2
−1
0
1
2
3
devi
a�on
from
ave
rage
spe
ed (%
)> 0.5 0.3−0.5 0−0.3 0−0.3 0.3−0.5 > 0.5
−30
−25
−20
−15
−10
−5
0
5
10
15
<-- Current from port side (m/s)...current from starboard side (m/s) −−>
devi
a�on
from
ave
rage
trac
k (m
)
<-- Current from port side (m/s)...current from starboard side (m/s) −−>
Figure 6.13 The influence of cross current on the vessel path (left) and speed (right) in part 1.
Althoughthedeviationfromtheaveragepathclearlyhasadowngoingtrend,theabsolutedeviationisnotverylarge,about25metersmaximal.Againthiscanbeexplainedbythefactthatvesseladapttheirhead-ingtostayoncourse.Thiswasalreadyfoundwheninvestigatingtheinfluenceofwind,butalsoduringhighcrosscurrentvelocitiesthevesselheadingissignificantlydifferentfromtheaverageheading.Figure6.14showsanexampleofthis,forthesizeclass40,000-70,000dwt.
Northern breakwater Start bend into Beerkanaal95
100
105
110
115
120
125
130
Development along average path -->
head
ing
(deg
rees
), 0
/ 36
0 =
Nor
th
Part 1 Part 2
Figure 6.14 Development of the vessel heading under influence of a strong cross cur-rent (green) compared to the average heading (blue), both for vessels of size class 40,000-70,000 dwt
TheinfluenceofthecurrentthatflowsparalleltothevesselisshowninFigure6.15.Bothgraphsdonothaveaperfectfitforalinearrelationship,butclearlyshowatrend.Thenegativevaluesforthedeviationfromtheaveragepath(leftfigure)indicatethatvesselssailmoretoportsidewhentheyexperienceastrongcurrentfrombehind.Inpracticethismeansthattheyaresailingmoretothemiddleofthewaterway.Thevesselspeeddecreaseswhenthecountercurrentincreases.
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An analysis of vessel behaviour based on AIS data
> 0.5 0.3−0.5 0−0.3 0−0.3 0.3−0.5 > 0.5−6
−5
−4
−3
−2
−1
0
1
2
3
<-- Current from behind (m/s).......current from front (m/s) −−>de
via�
on fr
om a
vera
ge s
peed
(%)
> 0.5 0.3−0.5 0−0.3 0−0.3 0.3−0.5 > 0.5−20
−10
0
10
20
30
40
devi
a�on
from
ave
rage
trac
k (m
)
<-- Current from behind (m/s).......current from front (m/s) −−>
Figure 6.15 The influence of parallel current on the vessel path (left) and speed (right) in part 1
Inpart2onlyparallelcurrentsarepresentduetothefactthatatthislocationthewaterwayisclosedatbothsides.Theinfluenceofthiscurrentonthevesselpathandvesselspeedissimilartotheinfluencefoundinpart1,butsmaller(seeFigure6.16).
> 0.5 0.3−0.5 0−0.3 0−0.3 0.3−0.5 > 0.5−6
−4
−2
0
2
4
6
devi
a�on
from
ave
rage
spe
ed (%
)
> 0.5 0.3−0.5 0−0.3 0−0.3 0.3−0.5 > 0.5−8
−6
−4
−2
0
2
4
6
8
10
12
devi
a�on
from
ave
rage
trac
k (m
)
<-- Current from behind (m/s).......current from front (m/s) --> <-- Current from behind (m/s).......current from front (m/s) -->
Figure 6.16 The influence of parallel current on the vessel path (left) and speed (right) in part 2
Inpart3,thebendattheentranceoftheBeerkanaal,andpart4(Beerkanaal)thecurrentvelocitiesaremuchlower.Alsotheinfluenceofthecurrentonthevesselpathandspeeddecreases.Forpart3,nosig-nificantinfluencesarefound.IntheBeerkanaal(part4)thereissomeinfluenceofparallelcurrent,mainlyregardingthevesselpath.Figure6.17showsthisresult,whichisquitesimilartothefindinginpart1and2.Thereisnosignificantinfluencefoundonthevesselspeedatthislocation.ThecrosscurrentsarehardlypresentintheBeerkanaal;thereforenoinfluenceofthesecurrentdirectionsisfound.
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Externalinfluences
> 0.5 0.3−0.5 0−0.3 0−0.3 0.3−0.5 > 0.5−15
−10
−5
0
5
10
devi
a�on
from
ave
rage
trac
k (m
)
<-- Current from behind (m/s).......current from front (m/s) -->
Figure 6.17 The influence of parallel cur-rent on the vessel path in part 4 (Beerkanaal)
6.2.4 Conclusions
Itisverycomplextoanalysetheinfluenceofthecurrentonthevesselpathandvesselspeed.Thisisbe-causethecurrentishugelyaffectedbythelocalinfrastructure,especiallyinaportarea.Inthiscasealsotheinteractionbetweentheriverandtheseaisimportant:thisleadstoalargedeviationincurrentvelocityanddirectionoverthewaterdepth.Bysplittinguptheexaminedcaseareaandbyusingseveralsimplificationsitishoweverpossibletoobtainsomegoodresults.
Theinfluenceofcrosscurrentscouldonlybeobservedinpart1,outsidethenorhernbreakwater.Attheotherlocationscrosscurrentsarehardlypresent,duetothelocalinfrastructure.Inpart1theinfluenceofthecrosscurrentissimilartotheinfluenceofthewind.Thereisadeviationfromthevesselpathfound.Thisdeviationisnotverylarge,becausevesselsadapttheirheadinginordertostayoncourse.Theinfluenceofthecrosscurrentonthevesselspeedislessclear.
Currentcomingfrombehindorthefrontofavessel,parallelcurrent,hasaninfluenceaswell.Astrongcur-rentfrombehindmakesvesselssailmoretothemiddleofthewaterway.Astrongheadcurrentmakesthemsailmoretowardstheshore.Thevesselspeedisalsoaffected:astrongcurrentfrombehindincreasesthevesselspeedandtheotherwayaround.Thesefindingsaresupportedbytheresultsforpart1,part2andpart3.Inpart4,theBeerkanaal,onlytheconclusionsregardingthevesselpatharefound.
6.3 Visibility
6.3.1 Visibility data
Visibilitydatafor2009areobtainedfromtheKNMI.Theinvestigationoftheinfluenceofvisibilityismorestraightforwardthanforwindandcurrent.Visibilitydoesonlyvaryintimeandithasnodirectioninwhichitworks.ThevaluesforvisibilityaredefinedbytheKNMIasthe‘horizontalvisibilityatthetimeofobserva-tion’.Thisvisibilityisknownasthe‘meteorologicvisibility’andisdefinedasthelargestdistanceatwhichablackobjectcanbeseenandrecognised.Theintervalbetweentheobservationsisonehour.
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An analysis of vessel behaviour based on AIS data
Thevisibilityisnotsplitintodifferentclasses,asisdonewiththewindandcurrent.Thisisbecausebyfar,mostvesselsmeetclearvisibilityconditions.Onlywhenthevisibilitybecomesverylow,thereisanoticeableinfluence.Thisiswhythereareareonlytwoclassesmade:badvisibilityandsufficientvisibility.Badvisibilitymeansthatthemeteorologicvisibilityislowerthan2kilometers.Bycomparingthemomentsintime,theAISmessagesfromthevesselsandthevisibilitydataarecoupled.
6.3.2 Results
Forthedeterminationoftheinfluenceontheaveragepath,thecaseareaisagainsplitintotwoparts:the MaasmondandtheBeerkanaal.Forthecalculationofthedeviationfromtheaveragespeednosplitupofthecaseareaisused.Vesselsthatenterorleavetheportwithsufficientvisibilitydonotdeviatefromboththeaveragepathandaveragespeed.Forvesselsthatencounteradecreasedvisibilityaninfluenceispresent;itistriedtofindarelationshipbetweenthevesselsizeandthisinfluence.
IntheMaasmonditisnotpossibletofindaclearrelationshipbetweenthevesselsizeandtheinfluenceonthevesselpath.Thereishoweveracleardifferencebetweenincomingandoutgoingvessels.Incomingves-selsdonotsignificantlydeviatefromtheaveragepathduringtimesoflowvisibility.Contrarytothis,outgo-ingvesselsdohaveadeviationtostarboardside(theshore),intheorderof50meters.
IntheBeerkanaaltheinfluenceofthevesselsizeismoreobvious(seeFigure6.18).Thereisnodifferencebetweenincomingandoutgoingvessels.Thelineartrendlinefitsquitegoodandadowngoingtrendcanbeobserved.Inpractice,thismeansthatlargervesselssailmoretothemiddleofthechannelunderlowvis-ibilitycircumstancesthansmallervessels.
<10,000 10,000−40,000 40,000−70,000 70,000−100,000 >100,000−60
−50
−40
−30
−20
−10
0
10
20
Vessel size class (dwt) −−>
devi
a�on
from
ave
rage
trac
k (m
)
Figure 6.18 The influence of low visibility on the deviation from the average path in the Beerkanaal.
Fortheinfluenceoflowvisibilityonthevesselspeednosignificantdifferencesbetweenincomingandoutgoingvesselsarefound.Inthiscaseadivisioncanbemadeinsmallandlargevessels.Thesmallvessels,containingthesizeclasses<10,000dwt,10,000-40,000dwtand40,000-70,000dwtareclearlyhamperedbyalowvisibility.Thesevesselsdecreasetheirspeed,onaverage,with6%.Thelargervessels(sizeclasses70,000-100,000dwtand>100,000dwt)havenosignificantspeeddifference.
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Externalinfluences
6.3.3 Conclusion
Itisdifficulttofindaveryclearrelationshipfortheinfluenceoflowvisibility.MostimportantfindingisthatvesselssailintheBeerkanaalmoretothemiddleofthewaterway,whenthevesselsizeincreasesincaselowvisibility.GoodrelationshipsforthedeviationsfromtheaveragepathintheMaasmondandfromtheaveragespeedarenotfound.Therearehoweveraveragevaluesobtainedthatgivesomeinsightinthisves-selbehaviour.
6.4 Conclusions
Forallthreeexternalcircumstancesinfluencesonthevesselpathandvesselspeedarefound.ThelargestdeviationsfromthevesselpatharefoundforcrosswindandcrosscurrentintheMaasmond,outsidetheprotectionoftheNorthernbreakwater.Thesedeviationsarelimited,becausevesselsadapttheirheadingtostayoncourse.Inthiswaytheypreventfrombeingblownor‘flowed’awaybythewindorcurrent.AsecondlargedeviationisfoundintheBeerkanaal,intimesoflowvisibility.Especiallylargervesselssailmoretothemiddleofthewaterwayinthesecircumstances.
Alsoforthedeviationfromtheaveragespeedtheinfluenceofwindandcurrentisquitesimilar.Highcross-windandcrosscurrentvelocitiesleadtoalowervesselspeed.Thisresultismostvisibleforwind,butalsothecurrentinfluenceshowsthispattern.Largewindandcurrentvelocitiesfrombehindleadtoahighervesselspeed,wherewindandcurrentfromthefrontcauseadecreasedspeed.
Exceptforthevisibility,nosignificantdifferencesbetweenthesizeclassesarefound.Thisismainlyduetoalackofdatawhensplittinguponesizeclassintoseveralselections.Insomeoftheseselections,therearenotalotofvesseltracksavailable.Thisiscausedbythelackofoccuranceofaexternalinfluence,forexamplewindfromtheeastorcrosscurrentintheBeerkanaal.Alsowhentheexaminedexternalinfluencedoesoccurfrequent,theamountofdataismostlytoosmalltodrawsignificantconclusionsforonlyonesizeclass.
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6.3 6.35 6.4 6.45 6.5 6.55
4.425
4.43
4.435
4.44
4.445
4.45
4.455
X−posi�on in "Rijksdriehoeksgrid" [m]
Y−po
si�on
in "R
ijksd
rieho
eksg
rid" [
m]
x105
x104
Interaction
Chapter7
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Interaction
7 Interaction
Oneoftheresearchquestionsistoinvestigatetheinfluenceofvessel-vesselinteractioninastatisticalway.Duetotimeconsiderationsthestatisticalanalysisofthisinteractionisnotperformed.Someresearchontheinfluenceofinteractionishoweverperformed,mainlytoshowhowindividualcasescanbefoundandanalysed.Forthisexaminationthesimilarcasestudyareaisused.
7.1 Interaction in the case study area
Vessel-vesselinteractiontakesplacewhenavesseldeviatesfromitsnormalpath,speedorheading,be-causeofthepresenceofanothervessel.Sometimesthevesselsreactoneachotherinanearlystage;thesesituationsaredifficulttotrackdown.Otherinteractionsituationsaremoreobviousandarealsomoreeasilyfound.InthetrackthatvesselssailbetweentheNorthSeaandtheAmazonehaven,thereareseveralplaceswhereinteractionislikelytooccur.ForexampleinthebendattheentranceoftheBeerkanaalorintheBeerkanaalitself.Amoredetaileddescriptionofthepathanditsinterestinglocations,togetherwithsometrafficimages,hasbeengiveninsection4.2.
Thefirststepistoidentifyinteractionsituations.Therearemainlytwowaystodoso,basedonthecalcula-tionprinciplesusedinthisthesis.Bothmethodsinvestigatedifferenttypesofvesselsthatareinvolvedintheinteraction.Thefirstway(MethodI)isbasedontheinteractionbetweentwocontainervesselsthatbothvisittheAmazonehaven.ThisanalysisusesCPA(ClosestPointofApproach)andTCPA(TimetoClosestPointofApproach)characteristics.Thesecondway(MethodII)investigatestheinteractionbetweenaves-selthatvisitstheAmazonehavenandavesselthatlikelydoesnot(thus,thissecondvesselisnotanalysedinthecasestudy).Thisanalysismakesuseofthecalculated‘outliers’,vesselsthatclearlydeviatefromtheaveragepathorspeed.
Inthecasestudyareaseveraltypesofinteractionarepresent.Theseareconnectedtothetypesofencoun-tersvesselscanexperience:head-on,crossingorovertaking.Allofthesetypesofinteractionwillbepresent,andshouldbelookedat,wheninvestigatingtheinfluenceofinteraction.
7.2 Method I
Ofallvesselsthatareanalysedinthecasestudy,alsodataareknownconcerningtheCPAandTCPA.TheCPAisthesmallestdistancethatvesselswillhavetoeachother,iftheykeeptheirheadingandspeedcon-stant.TheTCPAisthetimeuntilthismomentisreached(seeFigure7.1).Inpracticethesetwoparametersgiveanindicationaboutthepossibleclosestdistancetoothervesselsandthetimethatislefttoadaptcourseandspeed,ifthisdistanceistoosmall.
AsanoutputofShowRoute,theCPAandTCPAcanbeobtainedforeverycombinationoftwovesselsthatarerelativelyclosetoeachother.AverysmallCPAandTCPAindicatethattwovesselsareclosetoeachother;thereforevessel-vesselinteractionisexpected.Tofindsomeoftheseinteractionsituations,lowerlimitsaresetfortheCPAandTCPA.FortheCPAthislimitissetat0.05nauticalmile,roughly100meters.ThelimitfortheTCPAissetat5minutes.ItisalsoworthwhiletoreducetheCPAandTCPAevenmore.Inthiscase,onlyafewinteractionsituationwillbefound,buttheseareprobablyveryhelpfullintheanalysisofsituationswhereacollisionwasnarrowlyavoided(nearmisses).
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An analysis of vessel behaviour based on AIS data
Figure 7.1 Explanation CPA and TCPA
Closest Point of Approach, CPA (m)Distance
Vessel speed
TCPA = Distance / Vessel speed
Theselectionthatisobtainedbytheselimitsconsistsofseveralvesseltracks.Figure7.2showsthecombina-tionoftwooftheseinteractingtracksaroundtheentranceoftheBeerkanaal.Thebluelineshowstheindi-vidualtrackofanincomingvessel,fromthesizeclass70,000-100,000dwt.Theredlineindicatesthetrackofanoutgoingvessel,alsofromsizeclass70,000-100,000dwt.Thediscontinuouslinesshowtheaveragepathsforthissizeclass,incoming(blue)andoutgoing(red).Themarkersindicatesimilarmomentsintime,thetriangleindicatesthereforethepositionofthevesselswhentheyaretheclosesttoeachother.
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m]
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Figure 7.2 An example of interaction shortly before the entrance of the Beerkanaal
Afewthingscanbeconcludedfromthisexample.Firstofall,itisobviousthatthereisaninteractionbetweenthevessels,becausebothdeviateclearlyfromtheiroriginalpath.Thisisnotaverystrangecon-
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Interaction
clusion,whenlookingatthedimensionsofthevessels.Botharelargecontainervesselsofthesizeclass70,000-100,000dwt.Theyhavetopasseachotherinarathernarrowwaterway.Thisconclusionisbasedonthedeviationfromtheaveragepath.Beforeitspathisdisturbedbytheoutgoingvessel,theincomingvesselsailsquiteclose(alittlebittothesouth)totheaveragepathofitssizeclass.Atacertainmomentitdeviatesquitestrongtotheshore;afterithastakenthebendintotheBeerkanaalitreturnsattheaveragetrack.Theoutgoingvesselundergoesaboutthesame.Atfirstinstance,italmostexactlyfollowstheaveragepath.Inthebenditdeviatesstronglytothestarboardsideoftheaveragepath.Contrarytotheincomingvessel,itdoesnotcomebackatthepathaftertheinteraction.Soinitscase,theinteractionhasastructuraleffect.
Theinteractionsituationhasnowbeendescribedqualitatively.Toobtainstatisticalequationsconcerningthevesselbehaviourduringaninteractionsituation,itisalsoimportanttodoquantitativeanalyses.Inthisanalysis,afewquestionsshouldbeanswered.First,atwhatdistanceinspaceand timedotheinteractionmanoeuvresstart.Whenthisisknown,itisimportanttoinvestigatewhatthebehaviourexactlyincludes.Thiscanbedescribedbyanadjustmentofthevesselspeed(knots/minute)andvesselheading(degreesperminute).Itshouldalsobederivedatwhatmoment(forexampleadistancebetweenthetwovesselsinvolved)theseadjustmentsareseenasbeingsufficient.Finally,thequestionshouldbeansweredhowves-selsbehaveaftertheinteractionsituationhaspassed.
Inthisexamplethefollowingresultsarefound.Theincomingvesselstartswithhisdivergentbehaviourwhenthedistancebetweenthetwovesselsisabout1000meters.Atthispointthetimetoclosestpointofapproachis1.5minute.Theoutgoingvesselalreadystartsdeviatingfromhispathwhenthedistancebetweenthevesselsisapproximately4kilometers.TheactionsthatareundertakenbytheincomingvesselcanbequantifiedbylookingatFigure7.3.OntheX-axisofthisfiguretheareainwhichtheinteractiontakesplaceisshown;thiscanbecomparedtotheX-axisofFigure7.2.Regardingthevesselspeedtwoconclusionscanbedrawn.First,thevesselsailsfasterthantheaverageofitssizeclass.Thisdeviation(±1knot)canhoweverbeexplainedbythenaturalspreadinvesselspeed.
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Figure 7.3 Development of the vessel speed (left) and vessel heading (right) compared to the average of the sizeclass 70,000-100,000 dwt (discontinuous line).
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An analysis of vessel behaviour based on AIS data
Thegraphontheright,theheading,givesagoodindicationhowthevesseldeviatesfromhispath.ClearlyaroundX=64,000mthevesselheadingquicklyincreasesandafterabout250meters,theheadinghasrisenwith4degreesfrom115degreesto119degrees.Thismeansthattheratiooftheheadingadjustmentisabout1degreeper60meters.Withavesselspeedof9knotsthisimpliesapproximately4degreesperminute.Inthefigureitcanbeseenthatafter600meters(X=65,000m.)theheadingisagainalmostthesameastheaverageheading.Atthatmoment,thedistancebetweenthevesselsis300meters.
Afterthevesselshavepassedeachother,theinteractionisover.Theresultsoftheinteractionarehow-everstillpresent.About2kilometersafterthevesselshavepassedeachother,theincomingvesselisbackaroundtheaveragetrack.Theoutgoingvesseldoesnotconvergetowardstheaveragetrackanymore.
Anotherremarkcanbemade.Theincomingvessel,thattakestheinnerbendintotheBeerkanaaldevi-ateslessfromitsoriginalpaththantheoutgoingvessel.Bothvesselssailbeforetheinteractionalongtheaveragepathoftheirsizeclass,byapproximation.Themaximaldeviationfromthisaveragepathisfortheincomingvessel100meters,fortheoutgoingvessel200meters.Thishasverylikelytodowiththespacethatisavailableforthevessels.Theincomingvesselisintheinnerbendandsailsalreadyquiteclosetothesideofthewaterway,whereastheoutgoingvesselhassome‘reserve’spaceleftathisstarboardside.
7.3 Method II
Asexplainedinthefirstsectionofthischapter,themethodIIinteractionsituationsarederivedbycalculat-ingoutliers.Theseoutliershavebeenfoundduringthecalculationoftheaveragevesselbehaviourinchap-ter5.Duringthiscalculationsomevesselswerefoundthathadsuchadifferentvesselpathorvesselspeed,thatthesewerecalledoutliers.Theideaisthatthelargedeviationsofthesevesselsoriginatefromthefactthattheyhadtoaltercourseorspeedbecauseofavessel-vesselinteraction.
TheCPAandTCPAdataisonlyknownforthevesseltracksthatwereinvestigatedinthecasestudy.Iftheoutliersindeedhadinteraction,thiswillverylikelynotbewithanotherinvestigatedvessel.Thisisbecausethesevesselsareonlyaverysmallpartofthetotalamountofvesselsthatsailthroughthecasearea.So,infirstinstancethereisnoinformationconcerningthevesselsthatpossiblyhadinteractionwiththedeter-minedoutliers.Toobtainthisinformation,thetotaltrafficimagearoundanoutlierisplayedinShowRoute(seeFigure7.4).
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Interaction
Figure 7.4 Example of the interaction of an outliers (purple triangle) with another vessel, after plotting the whole traffic image.
Thisgivestwooptions.Thefirstoptionistoseewhethertherehavebeenvesselspresentthatsailedclosetotheoutliers.Secondly,ifinteractionsituationsareindeedfound,theinformationofinteractingvesselscanbeobtained.ThesecanthenbeusedtoproducethesamenumbersandfiguresasinmethodI,fromwhichaquantativeanalysiscanbeperformed.
7.4 Conclusion
Theexampleshowsthatitispossibletodoaquantitativeanalysisconcerningvesselbehaviourinaninter-actionsituation.Thedataderivedherearehoweveronlyvalidforthisspecificsituation.Forthederivationofstatisticalequations,itisneededtoobserveandanalysemanymoreofthesesituations.Differenttypesofinteractionshouldbeinvestigatedaswell.Thiswouldalsomakeitpossibletoincludethevesselspeedintheanalysis.Duetothelargenaturalspreadinvesselspeeditisdifficulttodrawconclusionsbasedonasmallnumberofsituations.
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> 100,000 dwt
North South
Incoming: µ = 1100 m σ = 90 mOutgoing: µ = 460m σ = 120 m
Incoming: µ = 970 m σ = 90 mOutgoing: µ = 630m σ = 160 m
Genericrules
Chapter8
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Genericrules
8 Generic rules
Inthischapterthevesselbehaviouranalysedinthecasestudyistransformedintogenerallyapplicablerules.Inthiswaythevesselbehaviourinotherwaterwaysandportscanbedescribed,basedonthefind-ingsofthecasestudy.Togeneralisetheresultofthecasestudy,thefirstissuetobehandledisthemappingofthenauticalinfrastructure.Theinfrastructureisdifferentateverylocation.Thetrackofthecasestudyissplitinseveralpartsinsection8.1.Afterdealingwiththeinfrastructure,theaveragevesselbehaviourisgeneralised(section8.2)andtheexternalinfluencesareincluded(section8.3).
8.1 Defining waterways
Thetrackinthecaseareaissplitinto5differentparts,whichwerealsousedfortheexaminationoftheinfluenceofcurrent(seeFigure8.1).Inthissectionthedifferentpartsaregeneralisedtospecifictypesofwaterways.Itistriedtofindouterboundariesforeverypart,therebyfindingthewidthofthecharacterisedwaterway.Inthiswayitispossibletodescribethevessel’spositioninrelationtoitspositiononthewater-way.
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Part 1
Part 5
Part 2
Part 3
Part 4
Figure 8.1 Overview of the different current re-gimes in the case area.
8.1.1 Part 1 - Outside the northern breakwater
Inthispartthewidthofthewaterwayisnotreallydefinedbyanacceptabledepth.ThefactthatvesselswanttoenterorleavetheportofRotterdam,andthereforeconvergetowardstheentranceoftheport,isnormative.Thereforethewidthofthewaterwayisdefinedbytakingacertainanglefromtheentranceoftheport.Thisanglehasbeendeterminedbylookingatthe98%contoursfromtheincomingandoutgo-ingvessels.Inportareaswherethesecontourlinesarenotavailable,thisangleshouldbedeterminedbyinvestigatingthedepthprofiles,navigationalaidspresent(e.g.buoys),theorigin,destination,expectedtypeandsizeofthevesselsthatvisitthatport.Whentherearesimilaritiesfoundwiththiscasestudyarea,thancontourlinesofthiscasestudycanbeusedtogiveafirstinsightintheangleoftheline.Sizeclass<10,000dwtischosenforthis,asthesevesselsusethewidestspaceandthereforehavethenormativecontourlines.Figure8.2showsthesecontours(red)andtheaveragepath(greendotted,incomingandoutgoing).Thebluelineshowsthedefinitionofthewidthofthewaterway.
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Figure 8.2 Overview of the simplified waterway (blue) in part 1.
Also indicated are the average path (green dash dotted), the 98% contours (red) and the buoys (red).
Byusingthe98%contours,itisinevitablethatsomevesselswillsailoutsidethedeterminedlimits.Othervesselswillsailveryclosetotheselimits.Theseouterlimitsshouldthereforenotseenasastrictborder.Vesseldonotrunagroundiftheygooutside.Thelimitsrepresentthemostlikelyareatocontainvesseltracks,whiletherearenonauticalinfrastructurerestrictions.
8.1.2 Part 2 - ‘Maasmond’
Thewaterwayinpart2isclearlyindicatedbybuoys.Bydrawingstraightlinesbetweenthosebuoys,itispossibletoobtainthewidthofthewaterway.Thiswidthisdecreasing,asallvesselsconvergetowardstheentranceoftheBeerkanaal.Figure8.3showsanoverviewofthebuoys(reddots)andthedeterminedwa-terway.Atsomelocations,the98%contourlinesarenotstraight,butquite‘peaky’.ThisisprobablybecauseoferrorsindisturbedAISmessages,causedbythefactthattugsfastentothecargovesselsatthatlocation.
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Figure 8.3 Overview of the simplified waterway in part 2.
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Genericrules
8.1.3 Part 3 - Bend at entrance Beerkanaal
Alsothispartisdistinguishedasseparatepart,asthisiscompletelydifferentfromtherelativelystraightwa-terwaysintheMaasmondandBeerkanaal.Intheinnerbendaswellastheouterbend,buoysarepresentthatshowtheouterlimitsofthewaterway(seeFigure8.4).Thelimitsintheouterbendare‘cutof’,theselimitsdonotexistinreality,becausethisistheentrancetoanotherwaterway,theCalandkanaal.Inthiscaseuseismadeofabuoytopredictthelimitsofthewaterwayintheouterbend.Inotherportareas,thesenavigationalaidscouldbeusedaswell.Whenthesearenotpresent,the98%contourlinesgiveagoodindi-cation.Anotheroptionistoinvestigateandsettheouterbendtoacertaindistancefromtheinnerbend.
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Figure 8.4 Overview of the simplified wa-terway in part 3.
8.1.4 Part 4 - the Beerkanaal
TheschematisationofthewaterwayintheBeerkanaalisshowninFigure8.5.Thewidthisapproximatelyconstantforthewholesegment.OnlyattheentranceoftheAmazonehaven,thewidthdecreases.Useismadeofexistingbuoys,shorecontourlinesand98%vesselpathcontourstodeterminetheouterlimitsofthewaterway.Thispartisquitesimilartopart2,themaindifferenceisthefactthatthevesselnowap-proachtheirgoal,theAmazonehaven,whichinfluencestheirbehaviour(e.g.sailinginbackwards).
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Figure 8.5 Overview of the simplified wa-terway in part 4.
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An analysis of vessel behaviour based on AIS data
8.2 Average behaviour
Withthetotaltrajectoryschematisedintodifferentparts,itispossibletoobtainthevessellocationwithrespecttothewaterway.Thedistributionofvesselsoveracrosssectioninthewaterwayishandled,aswellasthedistributionoveracrosssectionofthevesselspeed.Toobtainasufficientinsight,thesegeneraliseddistributionsarederivedforseveralcrosssectionsineverypart.Theshapeandsizeofmostofthesedistri-butionswasalreadyfoundinchapter5,butheretheyarecoupledtothesimplifiednauticalinfrastructure.
8.2.1 Part 1 - Outside the northern breakwater
Inthissectionanexamplewillbegivenhowthedistributionsofbothlocationandvesselspeedarederived.Fortheothercrosssectionsinthisandintheotherparts,thisapproachremainsthesame.Inpart1,4dif-ferentcrosssectionsareinvestigated(seeFigure8.6).AsanexampleCrosssection1-Ciselaboratedbelow.
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Figure 8.6 The cross sections that are investigated in part 1.
Atcrosssection1-C,thedeviationoverthewaterwayisinvestigated,forbothincomingandoutgoingves-selsfromsizeclasses<10,000dwtand>100,000dwt.Thenormaldistributionsarebasedontherealvesseltracks,asexplainedinchapter5.Figure8.7showsthesedistributions.Severalcharacteristicsareimportantinthederivationofgenericrules.First,thewidthofthewaterway.ThiscanbeseenontheX-axis(0isontheportsideoftheincomingvessels)andisatthislocationequalto1300m.Next,themeanandstandarddeviationofthedistributions.Itcanimmediatelybeseenthatthelargestsizeclasssailmoretothemiddleofthechannel.Thisresultsinasubstantialoverlapbetweentheincomingandoutgoingvesseldistributionforthissizeclass.Thesmallestsizeclasssailsmoretotheouterlimitsandhasalmostnooverlap.
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Genericrules
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> 100,000 dwt
North South
Incoming: µ = 1100 m σ = 90 mOutgoing: µ = 460m σ = 120 m
Incoming: µ = 970 m σ = 90 mOutgoing: µ = 630m σ = 160 m
Figure 8.7 Distribution over the waterway at cross section 1-C
Fromtheresultsshowninthefigure,itispossibletoformulaterulesregardingtheprobablepositionofavesselonthewaterwayinthiscrosssection,dependingonitssizeclass.Nexttothevesseldistributionoverthecrosssection,alsothevesselspeeddistributionshouldbeexamined.Thisisalsobasedontheresultsfromchapter5.Figure8.8showsthenormalisedspeeddistributionsincrosssection1-Cforthesmallestandlargestsizeclass,forincomingvessels.Thedistributionsaretruncatedinsuchawaythattheirtotalwidthisabout14knots.Moststrikingisthefactthatthesmallestvesselssailabout2knotsfasterthanthelargestvessels.Forthevesselspeedthemeanandstandarddeviationgiveenoughinformationtoformulategeneralisedrules.
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µ = 11.0 knσ = 2.4 kn
Figure 8.8 The speed distribution for incoming vessels at cross section 1-C
Theexampleshowsthatnowenoughinformationisavailabletocalculatetheprobabilitythatavessel,fromacertainsize,sailsataspecificlocationinthecrosssection,withaspecificspeed.Figure8.7andFigure8.8alsoofferinformationconcerningforexampletheoverlapbetweenincomingandoutgoingvessels.Allcrosssectionswillbehandledinthesamewayastheexampleabove.Theresultsarepresentedintables,inwhichthemostimportantcharacterics(mean,standarddeviation,widthofthewaterway)canbefound.
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ThesetablescanbefoundinAppendixG;anexampleisgivenbelowforcrosssection1-C,Table8.1.
Table 8.1 Characteristics of the different size classes in cross section 1-C
Widthofthewaterway(B):1300meters
Sizeclass(dwt)
Incoming Outgoing
Spatialdistr.(m) Speeddistr.(kn) Spatialdistr.(m) Speeddistr.(kn)
Mean(μ) StDev(σ) Mean St Dev Mean St Dev Mean St Dev
<10,000 1100 90 13.9 2.1 460 120 14.7 2.1
10,000-40,000 1080 100 14.6 2.4 520 130 15.0 2.1
40,0000-70,000 1000 90 11.1 1.5 560 120 13.6 2.3
70,000-100,000 980 90 10.6 1.8 600 140 12.0 2.4
>100,000 970 90 11.0 2.4 630 160 14.3 2.0
μ/B σ/B μ/μV0 σ/σV0 μ/B σ/B μ/μV0 σ/σV0
<10,000 0.85 0.07 0.96 1.11 0.35 0.09 1.06 0.95
10,000-40,000 0.83 0.08 0.97 1.14 0.40 0.10 1.02 0.84
40,0000-70,000 0.77 0.07 0.93 0.65 0.43 0.09 1.03 0.92
70,000-100,000 0.75 0.07 0.92 0.82 0.46 0.11 1.04 1.26
>100,000 0.75 0.07 0.87 0.89 0.48 0.12 1.05 0.87
InthesecondpartofTable8.1ageneralisationismadetorespectivelythewidthofthewaterwayandthe‘starting’vesselspeedcharacteristics.Thewidthofthewaterwaythatisusedisindicatedatthetopofthetable.The‘starting’vesselspeedcharacteristicsused,arethemean(μV0)andstandarddeviation(σV0)ofthevesselspeedincrosssection1-A(seeTable8.2).Bydividingthemeanandstandarddeviationofthevesselspeedwiththeoriginalmeanandstandarddeviation,insightintothedevelopmentofthevesselspeedisobtained.
Table 8.2 Vessel speed characteristics of the different size classes in cross section 1-AWidthofthewaterway:3000meters
Sizeclass(dwt)
Incoming Outgoing
Speeddistr.(kn) Speeddistr.(kn)
μV0 σV0 μV0 σV0
<10,000 14.5 1.9 13.9 2.2
10,000-40,000 15.1 2.1 14.7 2.5
40,0000-70,000 11.9 2.3 13.2 2.5
70,000-100,000 11.5 2.2 11.5 1.9
>100,000 12.6 2.7 13.6 2.3
8.3 External influences
Theexternalcircumstancesdonotchangetheshapeofthenormaldistributionsthatarefoundforthespa-tialandspeeddistributions.Thisisbecausetheinvestigationoftheexternalinfluencesinchapter6didnotincludethe individualdeviationfromtheaveragepathandspeed.Thiswasnotpossible,becausetherewas
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notenoughdatainmostselectionstoobtainsignificantresults.Inmostcases,nodifferencesbetweensizeclassesarefound.Thereisoneexceptiontothis,theinfluenceofvisibilityonthevesselspeed.
Theabovementionedmeansthattheexternalcircumstancesmainlycauseashiftofthenormaldistribu-tions.Thesizeoftheshiftdependsontheexternalinfluenceitself.Inchapter6already,mostlylinear,relationshipswerefound.Theyhavetobetransformedtoobtainamoregeneralinsightintheexternalinfluence.Figure8.9showswhatismeantbythistransformation.Theleftfigureistheoriginalinfluence,asfoundinchapter6.Therightfigureshowsthegeneralisedinfluence,inwhichtheX-axisisnolongerdividedin6sizeclasses.ThevaluesontheY-axisseemlarger,butthisisbecausetheresultsareextrapolated.Withthisrelationshipitispossibletoadaptthespatialvesseldistributiontothecurrentthatispresentatacer-tainmomentintime.
<-- Current from port side (m/s).......current from starboard side (m/s) -->
Part 1 - Outside the northern breakwater
> 0.5 0.3−0.5 0−0.3 0−0.3 0.3−0.5 > 0.5−30
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<-- Current from port side (m/s)...current from starboard side (m/s) −−>
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Figure 8.9 The influence of cross current on the vessel path at part 1.
Theinfluenceofthecrosscurrentatpart1isanexampleofhowtheinfluencesaregeneralised.Theotherinfluencesandlocationsareelaboratedinthesameway.ThesegraphscanbefoundinAppendixG.
8.4 Implementation in maritime models
InSection3.5,thecharacteristicsoffourmaritimemodelswerediscussed,concerningthepossibilitytoim-plementtheresultsofthisthesis.Forthedescriptionofthemodels,thefollowingissueswerementioned:
Type1-Nauticalinfrastructure Describelateralvesseldistributionoveracrosssectionoverthewaterway. Describethevesselspeeddistributionoverandinacrosssectionoverthewaterway. Type2-Vesselrelatedcharacteristics Distinguishbetweenstaticcharactericsasvesselsizeandvesseltype. Distinguishbetweendynamiccharacteristics,forexamplevesseldestination. Type3-Externalcircumstances Takeexternalinfluenceslikewind,currentandvisibilityintoaccount. Type4-Interactionwithothervessels Abilitytoincludedeviationfromthepredefinedpathandspeedbecauseofinteractionwithother vessels.
Nowtheresultsofthecasestudyareknown,thesetypescanbeelaboratedabitfurther.Type1,thenauti-
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calinfrastructure,isdescribedindetailinthecasestudy.Resultshavebeenobtainedconcerningthevesselandvesselspeeddistributionoverthewaterway,dependentonthetypeandwidthofthespecificwater-way.Type2,thevesselcharacteristicsaretreatedpartly,asonlytheinfluenceofvesselsizeanddestination(tosomeextent)aretreated.Resultsforthedestinationareobtainedtosomeextent,asthesailingdirec-tionofvessels(incomingoroutgoing)hasbeentakenintoaccount.
Externalcircumstancesdonotchangethesizeandshapeofthevesseldistributions,butshiftthemtoport-sideorstarboardside.Thevessel-vesselinteraction,type4,isnotelaboratedstatistically.Althoughexam-plesaregivenhowtofindandanalysethesesituations,nostatisticalresultsareavailable.
Thefirstmaritimemodelhandledinchapter3wasSAMSON.Thismodelisabletoincludetheresultsfromthecasestudyconcerningthetype1,type2andtype3characteristics.ThemaindisadvantageofSAMSONistheinabilitytosimulatethenauticaltraffic.Thischaracteristicishowevermainlyneededforthemodel-lingofinteraction.Becausenointeractionresultsarefound,thisisnotalargedrawbackfortheimplemen-tationoftheavailablecaseresults.However,ifafuturestudywouldobtainmoreinsightintheprocessofvessel-vesselinteraction,simulatingnauticaltrafficispreferable.
ForHarbourSim,themostseriousdrawbackswerethe(speed)distributionoverthewaterway.Becauseseveralresultsarefoundforthisdistributionoverthewaterway,themodelshouldbeadjustedlargelytobeabletoimplementthis.AlsotheinteractionisverylimitedinHarbourSim,butsinceinteractionresultshavenotbeendetermined,thisisnoproblematthemoment.Again,futurestudiesmightchangethis.
MARTRAMwasfoundtomeetmostofthecriteriamentioned.Themodelsimulatesthenauticaltrafficandthereisadistributionoverthewaterway,alsoforvesselspeed.Thedistributionsusedshouldbeadaptedtotheresultsfoundinthecasestudy.Ifthisisdone,itcanalsohandletheinfluenceoftheexternalcircum-stances.MARTRAMalsosimulatesinteraction,butonlyinverylimitedway(vesselscanonlyreducespeed).Iflateroninteractionresultsarefound,MARTRAMshouldbeextendedtocopewiththis,butatthemo-mentthemodelkeepsupwiththecriteria.
Thefourthmodelthatwasinvestigated,Dymitri,simulatesnauticaltrafficinmostdetail.Itrunsonbehav-iouralrules,thatarebasedonthesimulationofthehumanbrain.Thismakesitdifficulttoimplementtheresultsthatarefoundinthecasestudy.Theresultsthatarefound(mainlydistributionsandfactorsthatinfluencethesedistributions)arenotlinkedtobehaviouralrules.Inotherwords,Dymitriisnotbasedoncertaindistributionsoverthewaterway,butonthedecisionsofindividualvessels.Contrarytothis,resultsoffutureinteractionresearchcanbeimplementedmoreeasilyinthemodel.Thisisbecausetheseresultswillbemorelikebehaviouralrules,astheyareclosertothe(casespecific)natureoftheinteractionprocess.
8.5 Conclusions
Theresultsofthecasestudyhavebeenusedtoderivegenericrulesregardingthevesselpathandves-selspeedinsideaportarea.Forthis,thetotaltrajectorybetweenNorthSeaandAmazonehavenissplitintodifferentcharacteristicwaterways.Itisnotalwayspossibletoassignreal,physicalouterlimits.Thisisbecausesometimesthephysicalrestrictions,likedepth,arenotnormative.Thisisforexamplethecaseoutsidethebreakwater,whenvesselsconvergetowardstheportentrance.
Thevesselpathandspeedaredescribedbynormaldistributions,obtainedinchapter5.Visualrepresenta-tionsofthesedistributionsquicklygiveinsightintodifferencesbetweensizeclassesandbetweenincomingandoutgoingvesselsfromonesizeclass.Theexternalinfluencesaregeneralisedand,inmostcases,causea
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horizontalshiftofthespatialandspeeddistributionforeverysizeclass.
Thegenericrules,thatarederivedfromthecasestudy,canbeimplementedmosteasilyinamodellikeMARTRAM.AmodellikeSAMSONdoesnotsimulatenauticaltraffic,becausethisisnotthepurposeofthemodel.Thisisespeciallydifficultinthelightofapossiblyincreasedfutureinsightintheinteractionprocess,whereasnowadaysSAMSONwouldbesufficientlyabletoimplementtheresultsofthecasestudy.Harbour-Simdoesnotallowdeviationfromtheaveragepath,animportantresultofthecasestudy.Dymitrisimu-latesthenauticaltrafficingreatdetail,buttheapproachofthemodelisdifferentthanwhatfollowsfromtheresultsfromthecasestudy.
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Chapter 9
Conclusions&recommendations
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Conclusions&recommendations
9 Conclusions & recommendations
9.1 Conclusions
AfterperformingtheAISanalysisandformulatinggenericresults,finalconclusionscanbedrawn.Theyaresplitupinsuchawaythattheseparateresearchquestionsareansweredand,finally,theproblemdefinitionoftheresearchishandled.
AIS and maritime models
ThisresearchquestionwasdividedintothepossibilitiesandlimitationsofAIS,characteristicsofmaritimemodelsandtheuseofAISinmaritimemodelling.NexttothemainfunctionsofAIS,beingcollisionavoid-anceandnavigationalaid,thesystemisalsousedinmaritimemodelling.Untilnow,AISdataaremainlyusedtodeterminethenauticaltrafficinput(e.g.interarrivaltime)andthebehaviourofnauticaltrafficatalargerscale(e.g.insightintothetrafficnetwork).Notmuchuseismadeofthepossibilitytoobtaininsightintoindividualvesselbehaviour,somethingwhatisdoneinthisthesis.Indoingso,itispossibletodealwiththehumanfactorinmaritimemodels.ProblemsthatexistwhenusingAISdatainthesemaritimemodelsarecausedbythefactthatsomeAISdatacontainerrorsandthereforearenotcompletelyreliable.
AIS data analysis
Thisresearchquestionwasdividedintotheinfluencesofvesselsize,externalinfluencesandinteractiononthevesselpathandvesselspeed.ThisstudyhasshownthepossibilitiestodescribetheindividualvesselbehaviourintheportofRotterdamareastatistically,byusingananalysisofAISdata.Inthisthesisthebe-haviourinaspecificcaseareaisinvestigated,butitisalsopossibletodosofortheotherareasintheportofRotterdam.Theinvestigatedfactorsvesselsize,wind,currentandvisibilityallhaveasignificantinfluenceonthevesselpathandspeed.Noconclusionsregardingtheinteractioncanbemade,asnostatisticalanalysisofthevessel-vesselinteractionhasbeenperformed.
Generic rules
Thisreserachquestionwasdividedintothetransferfromspecifictogenericrulesandthepossibilitytoimplementtheminmaritimemodels.Withtheapproachusedinthisthesis,itispossibletoobtaingenericrulesthatdescribethevesselpathandvesselspeedinaportarea.Todoso,thecasestudyareaissplitintoseveralcharacteristicwaterwaysegmentsandthelocationspecificresultsaregeneralisedtotheirspecificsegments.Currentlyexistingmaritimemodelsarenotabletodirectlyimplementthegenericrulesfound,butwithasmallnumberofadjustmentsitispossibleforsomeofthemtodoso.
Finally,itcanbeconcludedthatbyusingananalysisofAISdata,clearlymoreinsightisobtainedinthede-tailedindividualvesselbehaviour.Thisunderstandingofthebehaviourcanbeformulatedingenericrules.Theserulescanbeimplementedinmaritimemodels,whichimprovesthesimulationoftheindividualvesselpathandvesselspeed.
9.2 Recommendations
ThisthesishasshownthatitispossibletoobtaininsightinvesselbehaviourbyusingAISdata.Oneofthemainfinalgoalsofthethesisistousethisinsighttoobtaingenericrules,whichcanbeimplementedinamaritimemodel.Somerulesarederivedinthisthesis,butthereareseveralissueswherefurtherresearchisneeded.
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Firstofall,onlycontainervesselsareinvestigatedinthecasestudy.Othertypesofvesselswillhavediffer-entbehaviour,astheyhaveotherdimensions.Forexampledrybulkvessels,thathavealargerdepthandasmallerheight.Thismakesthem,theoretically,moresensitivetotheinfluenceofcurrentsandlesssensitivetowind.Thissamedepthcouldalsorestrictthemmoretothemiddleofthewaterway,wherealargerwaterdepthcouldbeexpected.
Rulesconcerningtheinfluencesofexternalcircumstancesareobtainedinthisthesis.Additionalresearchwouldhoweverbeverybeneficialfortheinsightintotheseandotherexternalinfluences.First,onlywind,currentandvisibilityareexamined,asthesewereexpectedtobethemostimportantinthecasestudy.Thevisibilitydatainthecasestudydependedmainlyonthepresenceofweatherinfluenceslikefogandrain.Thequestionifavesselsailedbydaylightornot,isnottakenintoaccount.Thisisaninterestingissue,asvesselsmightbehavedifferentlyiftheysailbynight(despitegoodlightingintheportarea).Theinfluenceofwavesisalsoapossiblesubjectoffutureresearch,butitisofminorimportancewhenlookingataportarea;thereforethisisnotafirstnecessity.
Fortheexternalinfluences,thereisnorelationshipfoundbetweenthedifferentsizeclasses(exceptforvisibility).Itmightbethecasethatthereisnoclearrelationship,butitismorelikelythat-tosomeextent-arelationshipexist.Thereishoweveralotofdataneededbeforethiscanbeshownstatistically,astheinflu-enceoftheexternalcircumstancesonthevesselpathandspeedissmallcomparedtothenaturaldeviationfromtheaverage.Anothercharacteristicthatshouldbelookedatmorecloselyisthepathwidth,ascrosscurrentsandcrosswindscausealargerpathwidth.Moreresearchisthereforeworthwhile.Thisresearchshouldnothaveacaseareabetweentheseaandaterminal,butshouldfocusonaspecificwaterwayseg-ment.Everyvesselthatsailsthroughthissegmentshouldbeanalysed;inthiswayenoughdatacouldbeobtained.
Thegenericrulesthatareobtainedinthisthesisdescribethevesselpathandvesselspeedbyusingdistribu-tionsoverdifferentcrosssections.Amaritimemodelshouldbeabletousethesedistributionstosimulatenauticaltraffic.Atthemoment,noresearchisdoneontherelationofthevessel’spositionbetweentwosuccessivecrosssections.Amaritimemodelneedsthisinformationbeforeitcansimulateindividualvessels.
Nostatisticalresultsofvessel-vesselinteractionareobtainedinthecasestudy.Thisisthenextstepinobtaininginsightinthevesselbehaviourinportareas.Anexamplehasalreadyshownthatitispossibletotrackdowninteractionsituationsandhowtheycanbeanalysed.Toobtainstatisticalvalidresultshowevermanymoresituationsshouldbeelaborated.
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References
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References
References
Bailey,N.J.,N.Ellis,N.andSampson,H.(2008):TrainingandTechnologyOnboardShip:HowseafarerslearnedtousetheshipboardAutomaticIdentificationSystem(AIS),Cardiff,Lloyd’sRegisterEduca-tionalTrustResearchUnit,SeafarersInternationalResearchCentre(SIRC)andCardiffUniversity.
Barauskis,G.andFriis-Hansen,P.(2007):Baysiannetworksforshipsmanoeuvringcontrol,SafetyatSeaproject,Coastal,MaritimeandStructuralEngineering/MEK,TechnicalUniversityofDenmark.
Bolt,E.(2006):Modeldescriptions,Safetyatseaproject.strand1,reportNo1.08.http://www.safetyatsea.se/index.php?section=results
Chauvin,C.andLardjane,S.(2008):Decisionmakingandstrategiesinaninteractionsituation:Collisionavoidanceatsea,TransportationResearchPartF11:259-270.
Dorp,R.J.vanandMerrick,J.R.W.(2009):OnaRiskManagementAnalysisofOilSpillRiskusingMaritimeTransportationSystemSimulation,AnnalsofOperationsResearch.
Friis-Hansen,P.andSimonsen,B.C.(2001):GRACAT:softwareforgroundingandcollisionriskanalysis, MarineStructures15:383-403.
Fujii,Y.,Yamanouchi,H.andMizuki,N.(1974):SomeFactorsAffectingtheFrequencyofAccidentsinMarineTraffic.II–TheProbabilityofStrandingandIII–TheEffectofDarknessontheProbabilityofCollisionandStranding,JournalofNavigation27(2):239-247.
Harati-Mokhtari,A.,Wall,A.,Brooks,P.,Wang,J.(2007):AutomaticIdentificationSystem(AIS):DataReli-abilityandHumanErrorImplications,JournalofNavigation60:373-389.
Groenveld,R.(2001).ServiceSystemsinPortsandInlandWaterways.Delft,TUDelft,FacultyCiTG.
IALAandAISM(2004):IALAguidelineNo.1028onTheAutomaticIdentificationSystem(AIS),Volume1,PartI:Operationalissues,Ed.1.France.
Iperen,W.H.van,Koldenhof,Y.,Saladas,J.,Tak,C.vander(2008):NetwerkevaluatieNoordzee2008.Wage-ningen,Marin.
Koldenhof,Y.andC.v.d.Tak(2007):Nautischerisicostudievoordeaanloopstudienaardelng-terminalindeeemshaven,Wageningen,Marin,10-11.
Kujala,P.,Hänninen,M.,Arola,T.,Ylitalo,J.(2009):AnalysisofthemarinetrafficsafetyintheGulfofFin-land,ReliabilityEngineeringandSystemSafety94:1349-1359.
Macduff,T.(1974):Theprobabilityofvesselcollisions,OceanIndustry1974:144-148.
Mou,J.M.,Tak,C.Vander,Ligteringen,H.(2010):StudyoncollisionavoidanceinbusywaterwaysbyusingAISdata,OceanEngineering37:483-490
Pedersen,P.T.andZhang,S.(1999):CollisionAnalysisforMSDEXTRA.MSDEXTRA.Lyngby,DepartmentofNavalArchitectureandOffshoreEngineering,TechnicalUniversityofDenmark.
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Pimontel,L.(2007):Astudyintomaritimecollisionprobability,CEG,Delft,DelftUniversityofTechnology,MScthesis.
Seignette,R.W.P.(2005):Comprehensivetrafficmodelling,InternationalConferenceonPort-MaritimedevelopmentandInnovation,WTC,Rotterdam
Solvsteen,C.(2009):AnalysisofAISdataquality.PresentationatBOOSWorkshop2009Sopot,Poland.
Tak,C.Vander(2009):Safetyassessmentstudyforoffshorewindfarmducalvados.Wageningen,Marin:12-19.
Ylitalo,J.(2009):Ship-ShipcollisionprobabilityofthecrossingareabetweenHelsinkiandTallin.Helsinki,HelsinkiUniversityofTechnology.
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Appendices
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Appendices
Appendix A Safetyatsea................................................................................................... A7
Appendix B DatainanAISmessage................................................................................ A11
Appendix C ApplicationsandpossibilitiesofAIS............................................................ A15
Appendix D MatlabmodelfortheAISanalysis............................................................... A19
Appendix E χ2tests,skewnessandexcesskurtosis......................................................... A29
Appendix F Vesselandvesselspeeddistributions.......................................................... A35
Appendix G Genericrules................................................................................................ A53
Table of contents
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FigureC.1 Theprincipleofaradardirectionfinder(left)andRadarwavesblockedbyan-othervessel(right)........................................................................................................ A19
FigureC.2 AISSART,asdevelopedbyJotronAS................................................................... A19FigureD.1 GUItomakeavesseltrackselection.................................................................... A24FigureF.1 Vesseldistributionovercrosssections1-4forincomingvesselsfromsizeclass
<10,000dwt.................................................................................................................. A38FigureF.2 Vesseldistributionovercrosssections1-4foroutgoingvesselsfromsizeclass
<10,000dwt.................................................................................................................. A39FigureF.3 Vesseldistributionovercrosssections1-4forincomingvesselsfrom
sizeclass10,000-40,000dwt......................................................................................... A39FigureF.4 Vesseldistributionovercrosssections1-4foroutgoingvesselsfrom
sizeclass10,000,40,000-dwt........................................................................................ A40FigureF.5 Vesseldistributionovercrosssections1-4forincomingvesselsfrom
sizeclass40,000-70,000dwt......................................................................................... A40FigureF.6 Vesseldistributionovercrosssections1-4foroutgoingvesselsfrom
sizeclass40,000-70,000dwt......................................................................................... A41FigureF.7 Vesseldistributionovercrosssections1-4forincomingvesselsfrom
sizeclass70,000-100,000dwt....................................................................................... A41FigureF.8 Vesseldistributionovercrosssections1-4foroutgoingvesselsfrom
sizeclass70,000-100,000dwt....................................................................................... A42FigureF.9 Vesseldistributionovercrosssections1-4forincomingvesselsfromsizeclass
>100,000dwt................................................................................................................ A42FigureF.10 Vesseldistributionovercrosssections1-4foroutgoingvesselsfromsizeclass
>100,000dwt................................................................................................................ A43FigureF.11 Vesselspeeddistributiononlocation1-4,forincomingvesselsfromsizeclass
<10,000dwt.................................................................................................................. A44FigureF.12 Vesselspeeddistributiononlocation1-4,foroutgoingvesselsfromsizeclass
<10,000dwt.................................................................................................................. A44FigureF.13 Vesselspeeddistributiononlocation1-4,forincomingvesselsfrom
sizeclass10,000-40,000dwt........................................................................................ A45FigureF.14 Vesselspeeddistributiononlocation1-4,foroutgoingvesselsfrom
sizeclass10,000-40,000dwt........................................................................................ A45FigureF.15 Vesselspeeddistributiononlocation1-4,forincomingvessels
fromsizeclass40,000-70,000dwt................................................................................ A46FigureF.16 Vesselspeeddistributiononlocation1-4,foroutgoingvessels
fromsizeclass40,000-70,000dwt................................................................................ A46FigureF.17 Vesselspeeddistributiononlocation1-4,forincomingvessels
fromsizeclass70,000-100,000dwt.............................................................................. A47FigureF.18 Vesselspeeddistributiononlocation1-4,foroutgoingvessels
fromsizeclass70,000-100,000dwt.............................................................................. A47
List of figures
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FigureF.19 Vesselspeeddistributiononlocation1-4,forincomingvesselsfromsizeclass>100,000dwt................................................................................................................ A48
FigureF.20 Vesselspeeddistributiononlocation1-4,foroutgoingvesselsfromsizeclass>100,000dwt................................................................................................................ A48
FigureF.21 Vesselspeeddistributionovercrosssections1-4,forincomingvessels fromsizeclass<10,000dwt.......................................................................................... A49
FigureF.22 Vesselspeeddistributionovercrosssections1-4,foroutgoingvessels fromsizeclass<10,000dwt.......................................................................................... A49
FigureF.23 Vesselspeeddistributionovercrosssections1-4,forincomingvessels fromsizeclass10,000-40,000dwt................................................................................ A50
FigureF.24 Vesselspeeddistributionovercrosssections1-4,foroutgoingvessels fromsizeclass10,000-40,000dwt................................................................................ A50
FigureF.25 Vesselspeeddistributionovercrosssections1-4,forincomingvessels fromsizeclass40,000-70,000dwt................................................................................ A51
FigureF.26 Vesselspeeddistributionovercrosssections1-4,foroutgoingvessels fromsizeclass40,000-70,000dwt................................................................................ A51
FigureF.27 Vesselspeeddistributionovercrosssections1-4,forincomingvessels fromsizeclass70,000-100,000dwt.............................................................................. A52
FigureF.28 Vesselspeeddistributionovercrosssections1-4,foroutgoingvessels fromsizeclass70,000-100,000dwt.............................................................................. A52
FigureF.29 Vesselspeeddistributionovercrosssections1-4,forincomingvessels fromsizeclass>100,000dwt........................................................................................ A53
FigureF.30 Vesselspeeddistributionovercrosssections1-4,foroutgoingvessels fromsizeclass>100,000dwt........................................................................................ A53
FigureG.1 Thecrosssectionsthatareinvestigatedinpart1................................................ A56FigureG.2 Thecrosssectionsthatareinvestigatedinpart2................................................ A58FigureG.3 Thecrosssectionsthatareinvestigatedinpart3................................................ A60FigureG.4 Thecrosssectionsthatareinvestigatedinpart4............................................... A62FigureG.5 InfluenceofcrosswindsintheMaasmondontheaveragepath.Theleftfigure
showsthesplitupindifferentwindspeedclasses...................................................... A64FigureG.6 InfluenceofcrosswindsintheMaasmondontheaveragespeed.Theleftfigure
showsthesplitupindifferentwindspeedclasses...................................................... A64FigureG.7 InfluenceofparallelwindsintheMaasmondontheaveragepath.Theleftfig-
ureshowsthesplitupindifferentwindspeedclasses................................................ A65FigureG.8 InfluenceofparallelwindsintheMaasmondontheaveragespeed.Theleft
figureshowsthesplitupindifferentwindspeedclasses............................................ A65FigureG.9 InfluenceofcrosswindsintheBeerkanaalontheaveragepath(left)andspeed
(right)............................................................................................................................ A66FigureG.10 InfluenceofparallelwindsintheBeerkanaalontheaveragepath................... A66FigureG.11 InfluenceofparallelwindsintheBeerkanaalontheaveragespeed,forincom-
ing(left)andoutgoing(right)vessels.......................................................................... A67FigureG.12 Influenceofcrosscurrentinpart1onthevesselpath(left)andvesselspeed
(right)............................................................................................................................ A67
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FigureG.13 Influenceofparallelcurrentinpart1onthevesselpath(left)andvesselspeed(right).................................................................................................................. A68
FigureG.14 Influenceofparallelcurrentinpart2onthevesselpath(left)andvesselspeed(right).................................................................................................................. A68
FigureG.15 Influenceofparallelcurrentinpart4onthevesselpath................................. A69
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TableB.1 DatainanAISmessage.......................................................................................... A12TableE.1 ExampleofapartoftheChi-squaredistributiontable.......................................... A31TableE.2 χ2testsperformedforthevesseldistributionsoverthecrosssectionsonlocation
1-4,Sizeclass<10,000dwt.......................................................................................... A31TableE.3 χ2testsperformedforthevesseldistributionsoverthecrosssectionsonlocation
1-4,Sizeclass10,000-40,000dwt................................................................................ A31TableE.4 χ2testsperformedforthevesseldistributionsoverthecrosssectionsonlocation
1-4,Sizeclass40,000-70,000dwt................................................................................ A32TableE.5 χ2testsperformedforthevesseldistributionsoverthecrosssectionsonlocation
1-4,Sizeclass70,000-100,000dwt.............................................................................. A32TableE.6 χ2testsperformedforthevesseldistributionsoverthecrosssectionsonlocation
1-4,Sizeclass>100,000dwt........................................................................................ A32TableE.7 χ2testsperformedforthevesselspeeddistributionsoverthecrosssectionson
location1-4,Sizeclass<10,000dwt............................................................................. A32TableE.8 χ2testsperformedforthevesselspeeddistributionsoverthecrosssectionson
location1-4,Sizeclass10,000-40,000dwt.................................................................. A33TableE.9 χ2testsperformedforthevesselspeeddistributionsoverthecrosssectionson
location1-4,Sizeclass40,000-70,000dwt.................................................................. A33TableE.10 χ2testsperformedforthevesselspeeddistributionsoverthecrosssectionson
location1-4,Sizeclass70,000-100,000dwt................................................................ A33TableE.11 χ2testsperformedforthevesselspeeddistributionsoverthecrosssectionson
location1-4,Sizeclass>100,000dwt........................................................................... A33TableE.12 Skewnessforthevesselspeeddistributionsoverthecrosssectionsatlocations
1to4,,forthedifferentdatasetsatlocations1to4.................................................... A34TableE.13 Excesskurtosisforthevesselspeeddistributionsoverthecrosssectionsat
locations1to4,forthedifferentdatasetsatlocations1to4...................................... A34TableG.1 Characteristicsofthedifferentsizeclassesincrosssection1-A........................... A54TableG.2 Characteristicsofthedifferentsizeclassesincrosssection1-B............................ A55TableG.3 Characteristicsofthedifferentsizeclassesincrosssection1-C............................ A55TableG.4 Characteristicsofthedifferentsizeclassesincrosssection1-D........................... A55TableG.5 Characteristicsofthedifferentsizeclassesincrosssection2-A........................... A56TableG.6 Characteristicsofthedifferentsizeclassesincrosssection2-B............................ A56TableG.7 Characteristicsofthedifferentsizeclassesincrosssection2-C............................ A57TableG.8 Characteristicsofthedifferentsizeclassesincrosssection3-A........................... A57TableG.9 Characteristicsofthedifferentsizeclassesincrosssection3-B............................ A58TableG.10 Characteristicsofthedifferentsizeclassesincrosssection4-A......................... A58TableG.11 Characteristicsofthedifferentsizeclassesincrosssection4-B.......................... A59TableG.12 Characteristicsofthedifferentsizeclassesincrosssection4-C.......................... A59
List of tables
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AppendixA
Safetyatsea
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Page-A8-
Safetyatsea
Appendix A Safety at sea
A.1 History of maritime transport1 2
Alreadythousandsofyearsagoseatransportwasimportantintrade.Intheseancienttimesthistradewasmainlyonaregionalornationalscale.Peoplewerenotabletosailacrossbigwaters,liketheAtlanticOcean.Lackofknowledgeoftheseaandallitsexternalfactorsmadesailingonopenseaaverydangerousactivity.Somewhatlater,inRomantimes,vesselsstayedmostofthetimequiteclosetothecoast,butthiswasnotaguaranteeforsafenavigation.Inbadweatherwindandcurrentscouldstilldestroyashipandalsopiracywasextensivelypresent.
FromtheMiddleAgesuntilthe18thcenturytheshippingindustrydeveloped,butsafetyatseastayedlow.Inthe19thcenturythelossofcargoandlifebyshipwreckwasstillenormous.Onlyduringthewinterof1820over2,000shipswerelostintheNorthSea,causingthedeathof20,000people.Theproblemswereinternationallyrecognisedandin1840thefirstnavigationrules,dealingwiththelightingofships,wereapplied.InthenextdecadesmainlyEnglandandFranceformulatedmoreguidelinesandrulestoaidnaviga-tionalsafety.
Theinternationalisationoftheshippingindustryperseveredinthe20thcentury.Itbecameclearthattheshippingbusinessneededgeneralagreements,toimprovesafetyandensurefaircompetition.TheBerlinconventionofNovember1906gaverisetothefirstrulesonwirelesstelegraphy.In1910conventionsoncol-lisionandlifesavingandassistanceweresigned.However,adisasterwasneededtoacceleratethedevelop-mentsonthefieldofstandardssetting.
A.2 SOLAS3 4
On14April1912theRMSTitanicsanknearNewfoundland.Noonehadexpectedtheworld’snewestandlargestpassengervesseltosink.Nexttothefactthatsomany–sometimesrichandfamous-peopledied,thisledtothequestionwhetherindividualcountriescouldsettheirownsafetystandards.AconferencewasheldinLondonwhichledtothefirstInternationalConventionfortheSafetyofLifeatSea(SOLAS).Thiswasoneofthefirsttreatiesthatfocussedontheprotectionofhumanlifeinsteadofproperty.
TreatieslikeSOLASwereimportant,butalsoverydependentonthededicationandenthusiasmofthedif-ferentgovernments.Inthefirstpartofthe20thcenturythesegovernmentsweremainlyoccupiedbythetwoworldwars.Howeverbetweenthesewars,in1929,anewerversionoftheSOLASwasaccepted.AftertheSecondWorldWartheinternationalisationoftheshippingbusinessincreasedrapidly.KeydevelopmentwasthefoundingoftheInter-GovernmentalMaritimeConsultativeOrganization(IMCO).
1 TheUNAtlasoftheOceans,www.oceansatlas.org,accessed:27/10/2009
2 Thehistoryofsafetyatsea,PhilippeBoisson,theUNAtlasoftheOceans,http://www.oceansatlas.com/unat
las/issues/safety/transport_telecomm/history_safety/history_safety.htm,accessed:27/10/2009
3 IMO’s50thanniversary:shippingandtheoceans,Overviewofshippingandnavigationhistory,World
MaritimeDay1998,InternationalMaritimeOrganization,http://www.imo.org/About/contents.asp?topic_
id=320&doc_id=886&header=false,accessed:27/10/2009
4 Internationalconventionforthesafetyoflifeatsea(SOLAS),1974,InternationalMaritimeOrganization,Inter
nationalMaritimeOrganization,http://www.imo.org/Conventions/contents.asp?topic_id=257&doc_id=647,
accessed:27/10/2009
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TheIMCOwasestablishedinGenevain1948.Thefirstofficialmeetingoftheneworganisationwasheldin1959.In1982thenamewaschangedinhowweknowitnowadays:theInternationalMaritimeOrganiza-tion,IMO.TheIMOisaspecialisedagencyoftheUnitedNations;herheadquarterislocatedinLondon.ThemaingoalforIMOis‘todevelopandmaintainacomprehensiveregulatoryframeworkforshippinganditsremittodayincludessafety,environmentalconcerns,legalmatters,technicalco-operation,maritimesecu-rityandtheefficiencyofshipping’.5
Toreachtheabovedescribedmainpurpose,internationalconventionshavebeensetup.ItisIMOhistasktomaintainandupdatetheseconventionsaswellassetupnewonesifneeded.Threetypesoftreatiesaredistinguished.Firstthereareconventionswhichaimtopreventaccidents.Second,treatiesprescribewhattodoifanaccidenthappens.Third,thereareconventionsthatestablishcompensationandliabilityregimes.TheSOLASconventionisaconventionofthefirsttype:topreventaccidents.OtherkeytreatiesofthistypeareMARPOL(InternationalConventionforthePreventionofPollutionfromShips)andSTCW(InternationalConventiononStandardsofTraining,CertificationandWatchkeepingforSeafarers)6.
TheSOLASconventionwasoneofthefirsttasksofIMO.Itcameintoforcein1965.Theideawastokeeptheconventionuptodatebyadjustingandexpandingitwithamendments.Theprocedurestodosoappearedtobeveryslow;thereforeafifthconventionwassetupin1974,inwhichtheamendmentprocesswasmadequicker.
TheSOLASconventioncurrentlyconsistsof12chapters.InDecember2000anumberofamendmentswasadopted.OneoftherevisedchaptersoftheconventionwaschapterV:‘SafetyofNavigation’.Thisbroughtinnewmandatoryrequirementsconcerningtheuseofvoyagedatarecorders(VDR’s)andautomaticidenti-ficationsystems(AIS).Atimeschemewasintroducedtoclarifywhichvesselsshouldbeequippedwiththeseitemsatwhattime.
AccordingtothenewchapterVinSOLAStheAISis“designedtobecapableofprovidinginformationabouttheshiptoothershipsandtocoastalauthoritiesautomatically”.IntheDecember2000amendmentthesevesselswererequiredtoinstalltheAISdependingontheirsizebetweenbetweenJuly2005andJuly2007.TheimplementationoftheAISwasfurtheracceleratedbyanewamendmentadoptedinDecember2002.Inthisamendment,allvesselsbetween300and50,000grosstonnagewereobligedtobefittedwithAISon31December2004atthelatest.
5 InternationalMaritimeOrganization,IntroductiontoIMO,http://www.imo.org/About/mainframe.asp?topic_
id=3,accessed:31/1/2010
6 InternationalMaritimeOrganization,Conventions,http://www.imo.org/Conventions/mainframe.asp?topic_
id=148,accessed:27/10/2009
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AppendixB
DatainanAISmessage
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DatainanAISmessage
Appendix B Data in an AIS message
Table B.1 Data in an AIS message
Static information Sent every 6 minutes and on request of a competent authority
MMSI MaritimeMobileserviceIdentity.Setduringinstallation.
Callsign Setduringinstallation
Name Ship’sname
IMOnumber InternationalMaritimeOrganizationnumber
Lengthandbeam Setduringinstallationorifchanged
Locationofpositionfixingantenna
Setduringinstallationormaybechangedforbi-directionalvesselsorthosefittedwithmultiplepositionfixantennae.
Dynamic information Sent every 3-10 seconds, dependent on speed and course alteration
Ship’spositionwithaccu-racyindicationandintegritystatus
AutomaticallyupdatedfromthepositionsensorconnectedtotheAIS.
PositionTimestampinUTCAutomaticallyupdatedfromship’smainpositionsensorconnectedtoAIS.(e.g.GPS)
Courseoverground(COG)
Automaticallyupdatedfromship’smainpositionsensorconnectedtotheAIS,providedthatsensorcalculatesCOG.(Thisinformationmightnotbeavailable)
Speedoverground(SOG)AutomaticallyupdatedfromthepositionsensorconnectedtotheAIS,pro-videdthatthesensorcalculatesSOG(Thisinformationmightnotbeavail-able).
Heading Automaticallyupdatedfromtheship’sheadingsensorconnectedtotheAIS.
Navigationalstatus
Navigationalstatusinformationhastobemanuallyenteredbytheofficeronwatch(OOW)andchanged,asnecessary,forexample:
underwaybyengines,restrictedinabilitytomanoeuvre(RIATM),aground,atanchor,moored,engagedinfishing,notundercommand(NUC),con-strainedbydraughtandunderwaybysail.
Inpractice,sincealltheserelatetotheCOLREGS,anychangethatisneed-edcouldbeundertakenatthesametimethatthelightsorshapeswerechanged.
Rateofturn(ROT)Automaticallyupdatedfromtheship’sROTsensororderivedfromthegyro-compass.(Thisinformationmightnotbeavailable).
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An analysis of vessel behaviour based on AIS data
Voyage related information Sent Every 6 minutes, when data is amended or on request
Ship’sdraughtTobemanuallyenteredatthestartofthevoyageusingthemaximumdraftforthevoyageandamendedasrequired;e.g.afterde-ballastingpriortoportentry.
Hazardouscargo(type)
Asrequiredbycompetentauthority.Tobemanuallyenteredatthestartofthevoyageconfirmingwhetherornothazardouscargoisbeingcarried,namely:
- DangerousGoods(DG) - HarmfulSubstances(HS) - MarinePollutants(MP) - Indicationsofquantitiesarenotrequired.
DestinationandETAAtMaster’sdiscretion.Tobemanuallyenteredatthestartofthevoyageandkeptuptodateasnecessary.
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AppendixC
Applicationsand possibilitiesofAIS
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ApplicationsandpossibilitiesofAIS
Appendix C Applications and possibilities of AIS
ThisappendixshortlydescribeshowAISisorcanbeusedbycoastalauthoritiesandVTSsorinsearchandrescueoperations.
C.1 Aiding coastal authorities
AISoffersagoodopportunityforcoastalauthoritiestomonitorthevesselssailingthroughthecoastalwa-tersofanation.Alargerrangeandmoreinformation(e.g.typeofcargoanddestination)canbeobtainedthanwithradar;thisleadstoagoodoverviewofmaritimeactivity.Inthiswaytheycankeepcontrolofforexamplehazardouscargo.AdisadvantageofAISisthefactthatAISmessagesaresentbythevesselsthem-selves(comparedtoradar,wherethesignalisreflectedbythevessels).Althoughmostvesselsarenotlikelytodoso,itispossibletotransmitincorrectmessagesonpurpose.
ShoresideestablishedAISstationscansimplymonitor,butalsoactivelyrequestdatafrompassingvessels(ship-shore).Thesestationscanalsotransmitinformationtovessels(shore-ship),forexampletidesandweatherforecasts.
C.2 Vessel Traffic Services
InmostbusyportsandwaterwaysaVTSexiststokeepcontrolofthenauticaltraffic.Theseservicesuseradartomapthetraffic.Identificationisdonebyradioandradarinformation.VTSuseAISmessagesforadditionalinformationandasbackupwhenradarisnotworkingsufficient.AISdataisusedincreasingly,butradarstillisthemainsourceofinformationforVTSoperators1.Therearemainlytworeasonsforthis.First,thetechnicalreliabilityofthesignalisnotalwaysveryhigh.Thisisforexamplethecaseundercontainercranesandwhentugsarefasteningtothevessel.ThesecondreasonthatAISisnotfullyreliedonbyVTSoperatorsisduetoerrorsandinaccuraciesintheAISmessages.
Mostoftheseerrorsoccurinthestaticdataofamessage.Theoretically,itispossibletoidentifyvesselsquicklyandcorrectlywithAIS,whichcanbeveryuseful,especiallyincrowdedwaterways.ThevesselnameinAISmessagesdoessometimesnotexactlymatchwiththenameintheportitsdatabase.ThismakesitdifficulttousetheAISdataforidentifyingvessels.Thereforenowadaysidentificationis,atleastfortheportofRotterdam,stilldonemanually,withhelpfromradarandradio.Thisisdonebydeterminingtheloca-tionfromwherearadiosignalistransmitted(radardirectionfinder,seeFigureC.1(left).Whenthetargetisidentifiedontheradar,avesselnamecanbeplacedmanually.
1 InformationderivedfromavisittotheVTSHoekvanHolland,portofRotterdam,Netherlands
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An analysis of vessel behaviour based on AIS data
VTSPort area
Radar Direc�on Finder
Radar Direc�on Finder
Radar Sta�on
Shadow area
Figure C.1 The principle of a radar direction finder (left) and Radar waves blocked by another vessel (right)
VTSscanalsouseAISdatatomapthetrafficsituationinsideandaroundtheportarea.AdvantageofAISoverradaristhatthepositionofthevesselsismuchmoreprecise.Nexttothis,AISdetectionisnotlimitedbyobstacleslikeothervesselsorlandmass(e.g.aroundcorners),seeFigureC.1(right).DisadvantageofAISistheoccurrenceofalotoferrorsinthedata,whichmakesitdifficulttorelyon.Furthermore,notallvesselssailinginorthroughtheportareequippedwithAIS(e.g.fishing,recreationalandinlandshippingvessels).
C.3 Search and rescue
Duringamarinesearchandrescueoperationitisimportanttoknowthepositionandnavigationalstatusofallshipsinvicinityoftheshiporpersonindistress.WithAIS,thisinformationisavailableforthevessels.AlsoSearchandRescue(SAR)aircraftcantransmittheirpositionbyAIS.Latelyanewtoolisdevelopedtolo-catepersonsindistress:theAIS-SART(FigureC.2).ThisdevicetransmitsAISmessagescontainingtheactualpositionoftheperson2.
Figure C.2 AIS SART, as de-veloped by Jotron AS.
2 InternationalMaritimeOrganization,IMO,
http://www.imo.org/includes/blastDataOnly.asp/data_id%3D20463/246%2883%29.pdf,
accessed:24/12/2009
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AppendixD
MatlabmodelfortheAISanalysis
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MatlabmodelfortheAISanalysis
Appendix D Matlab model for the AIS analysis
ThematlabmodelusedfortheanalysisofAISdatatransformsinseveralstepstheavailableroughAISmes-sagesintodataconcerningthevesselbehaviourofaspecifiedselectionofvessels.Inthisappendix,firsttheconvertingfromroughAISmessagestowardsanumberofreadytousevesseltracksishandled.Hereafteritisshownhowdifferentselectionscanbemadefromthesevesseltracks.Finally,theselectedvesseltracksareanalysed.
D.1 Transformation rough AIS data
SomeadjustmentshavetobemadebeforetheAISmessagesthatareobtainedasoutputfromShowRoutecanbeusedintheAISanalysis.Thevessel’spositionisgiveninlongitudeandlatitudecoordinates.Disad-vantageofthesecoordinates,isthattheyaremeasuredindegrees,minutesandseconds.Thereisalsothedifficultythatonedegreeinlateraldirectionisadifferentdistancethanonedegreeinlongitudinaldirec-tion.Thismakesitverydifficulttocomparethemandbecausetheresultsconcerningthevesselbehaviourshouldbeobtainedinmeters,itisdecidedtorecalculatethecoordinates.Theyaretransformedtocoordi-natesinthe‘Rijksdriehoeksstelsel’(RD).Thisnationalgridisusedasabasisforgeographicalindicationsandfiles,likeGeographicInformationSystems.AlsotheportofRotterdamsinfrastructureisexpressedinRDco-ordinates.So,toevaluateavesselspositioncomparedtotheportsinfrastructureitisneededtorecalculatethegeographicalcoordinatestoRDcoordinates.TheMatlabcodethatisusedtodosoispresentedbelow:
function [A0] = transform_to_RD(A0)
disp(‘Transform to RD...’)
Latitude = A0(:,1);
Longitude = A0(:,2);
dF = 0.36 * (Latitude - 52.15517440);
dL = 0.36 * (Longitude - 5.38720621);
for i=1:size(A0)
A0(i,2)= 155000+(190094.945 * dL(i)) + (-11832.228 * dF(i) * dL(i)) + (-144.221 * dF(i)^2 * dL(i)) + (-32.391 * dL(i)^3) +
(-0.705 * dF(i)) + (-2.340 * dF(i)^3 * dL(i)) + (-0.608 * dF(i) * dL(i)^3) + (-0.008 * dL(i)^2) + (0.148 * dF(i)^2 * dL(i)^3);
A0(i,1) = 463000+(309056.544 * dF(i)) + (3638.893 * dL(i)^2) + (73.077 * dF(i)^2 ) + (-157.984 * dF(i) * dL(i)^2) +
(59.788 * dF(i)^3 ) + (0.433 * dL(i)) + (-6.439 * dF(i)^2 * dL(i)^2) + (-0.032 * dF(i) * dL(i)) + (0.092 * dL(i)^4) + (-0.054 *
dF(i) * dL(i)^4);
end
AfterthetransformationtowardstheRDcoordinates,thelocationoftheantennethattransmitsthemes-sagesonthevesselshouldbetakenintoaccount.Thisantennaismostlynotsituatedexactlyinthemiddleofthevessel;itcanbeatadifferentplaceateveryvessel.Thiscausesinaccurieswhencomparingvesselpositionswitheachother.Theseinaccurariescanbenegligibleatopensea,butinaportarea,theyaredefi-nitelynot.Itisthereforeneededtoadjustthevessel’scoordinatesbytakingintoaccountthepositionoftheantennainthevessel.ThisexactpositionisfortunatelyincludeintheAISmessage,whichmakesitpossibletodoso.TheMatlabcodebelowshowshowthiscalculationisdone.
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An analysis of vessel behaviour based on AIS data
function [A2] = AntennaLocation(A1)
disp(‘Antenna Location...’)
pf = 0.8;
sf=1 ;
for i=1:size(A1)
bow(1) = A1(i,1) + A1(i,8)*cos(A1(i,7)*pi()/180)*sf;
bow(2) = A1(i,2) + A1(i,8)*sin(A1(i,7)*pi()/180)*sf;
starfor(1) = A1(i,1) + A1(i,8)*cos(A1(i,7)*pi()/180)*pf*sf - A1(i,10)*sin(A1(i,7).*pi./180)*sf;
starfor(2) = A1(i,2) + A1(i,8)*sin(A1(i,7)*pi./180).*pf.*sf + A1(i,10)*cos(A1(i,7)*pi./180).*sf;
staraft(1) = A1(i,1) - A1(i,9)*cos(A1(i,7)*pi()/180)*s - A1(i,10)*sin(A1(i,7)*pi./180).*sf;
staraft(2) = A1(i,2) - A1(i,9)*sin(A1(i,7)*pi./180).*sf + A1(i,10)*cos(A1(i,7)*pi./180).*sf;
portaft(1) = A1(i,1) - A1(i,9)*cos(A1(i,7)*pi./180).*sf + A1(i,11)*sin(A1(i,7)*pi./180).*sf;
portaft(2) = A1(i,2) - A1(i,9)*sin(A1(i,7)*pi./180).*sf - A1(i,11)*cos(A1(i,7)*pi./180).*sf;
portfor(1) = A1(i,1) + A1(i,8)*cos(A1(i,7)*pi./180).*pf.*sf + A1(i,11)*sin(A1(i,7)*pi./180).*sf;
portfor(2) = A1(i,2) + A1(i,8)*sin(A1(i,7)*pi./180).*pf.*sf - A1(i,11)*cos(A1(i,7)*pi./180).*sf;
A1(i,1)=(starfor(1)+staraft(1)+portaft(1)+portfor(1))/4;
A1(i,2)=(starfor(2)+staraft(2)+portaft(2)+portfor(2))/4;
end
D.2 Track selection
Aftertheoperationsmentionedabove,anumberoftracksisleftwithwhichtheanalysiscanbeperformed.Beforeanycalculationsregardingforexampletheaveragevesselpathcanbemade,aselectionoftracksmustbedetermined.Thisselectioncandependonthevesselsizeandthedirectionofthevessel(incomingoroutgoing).Itishoweveralsopossibletoincludetheexternalcircumstancesintheselectionprocess.ByusingaGraphicalUserInterace(GUI)theselectioncriteriaarefilledin,seeFigureD.1.
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MatlabmodelfortheAISanalysis
Figure D.1 GUI to make a vessel track selection
AfterfillingintheGUI,thefollowingMatlabcodeisrun.
function [A4,f,h,tracks_data,GeenInfo] = route_toewijzing(A2,a,ondergrens,bovengrens,r,LowLim_wind,UpLim_
wind,LowLim_dir,UpLim_dir,LowLim_visibility,UpLim_visibility,Current_track,Current_dir,Current_size_max,Current_
size_min,Cur)
disp(‘Chosing tracks...’)
tf=strcmp(a,’ingaand’);
if tf==1
s=200;
t=100;
end
if tf==0
s=100;
t=200;
end
n=1;
k=1;
for i=1:size(A2)-1
if abs(A2(i+1,3)-A2(i,3))<600
A2(i,6)=n;
else
A2(i,6)=n;
n=n+1;
if (and(A2(i,2)<62000,A2(i,1)>444300))
A2(i,13)=200;
else
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A2(i,13)=300;
end
if and((A2(i,1)<441500),and(A2(i,1)>440000,and(A2(i,2)<66000,A2(i,2)>62200)))
A2(i,13)=100;
end
if (and(A2(i+1,2)<62000,A2(i+1,1)>444300))
A2(i+1,13)=200;
else
A2(i+1,13)=300;
end
if and((A2(i+1,1)<441500),and(A2(i+1,1)>440000,and(A2(i+1,2)<66000,A2(i+1,2)>62200)))
A2(i+1,13)=100;
end
b{1,n}=A2(k+1:i,:);
k=i;
end
end
load Input/Grootte
b{1,1}=0;nnn=0;GeenInfo=0;
for i=2:n
c=size(b{1,i});
d=b{1,i};
for x=1:size(Grootte)
if d(1,5)==Grootte(x,1)
d(:,12)=Grootte(x,2);
end
end
b{1,i}=d;
if or(d(1,12)<ondergrens,or(d(1,12)>bovengrens,c(1,1)<10))
b{1,i}=0;
end
if d(1,12)==0;b{1,i}=0;nnn=nnn+1;GeenInfo(nnn)=d(1,5);end
if or(d(1,14)<LowLim_wind,d(1,14)>UpLim_wind)
b{1,i}=0;
end
if UpLim_dir-LowLim_dir>0
if or(d(1,15)<LowLim_dir,d(1,15)>UpLim_dir)
b{1,i}=0;
end
else
if and(d(1,15)<LowLim_dir,d(1,15)>UpLim_dir)
b{1,i}=0;
end
end
if or(d(1,16)<LowLim_visibility,d(1,16)>UpLim_visibility)
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MatlabmodelfortheAISanalysis
b{1,i}=0;
end
if or(b{1,i}==0,Cur~=1);else
[Check] = Current_check(d,Current_track,Current_dir,Current_size_max,Current_size_min);
if Check(1,1)==0;
b{1,i}=0;
end
end
end
j=1;b{1,1}=0;tracks_data(1,1)=0;
for i=1:n
c=size(b{1,i});
d=b{1,i};
if size(b{1,i})<100;b{1,i}=0;end
if b{1,i}==0;
else
if or(d(1,13)~=s,d(c(1,1),13)~=t)
b{1,i}=0;
else
tracks_data(j,1)=i-1;
tracks_data(j,2)=d(1,5);
j=j+1;
end
end
end
y=0;f{1,1}(1,1)=0;
for i=1:n
if b{1,i}==0
else
y=y+1;
f{y,1}=b{1,i};
end
end
if f{1,1}(1,1)~=0
g=randperm(round(numel(f)));
h=f(g(1:numel(f)*r));
A4=cell2mat(h);
else
h{1,1}=0;A4(1,1)=0;
end
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An analysis of vessel behaviour based on AIS data
D.3 Analysis selected tracks
Theanalysisoftheselectedtrackscontainsseveralaspects.Firsttargetistodeterminetheaveragevesselpathandtheaccompanyingaveragevesselspeed.Togetherwiththis,alsothedeviationofthevesselsoverthedifferentcrosssectionsinthewaterwayisdetermined.Thesameisdoneforthevesselspeed.TheMat-labcodeinwhichthisisdone,ispresentedbelow.
function [Tracks,B1] = bepaling_gem_positie_snelheid_final_v4(a,gridsize,gridsize_verdeling,h)
disp(‘Calculate average track (1)’)
tf=strcmp(a,’ingaand’);
if tf==1
route=180;
else route=0;
end
load Input/RefLine
Xstart=59000;
Xeind=68000;
Ystart=440000;
Yeind=450000;
Xtotal=Xeind-Xstart;
Ytotal=Yeind-Ystart;
Xkruis=65500;
Ykruis=4.441*10^5;
Deviation=cell(numel(RefLine(:,1)),3);
n=0;
for xxx=1:numel(RefLine(:,1))
disp(xxx)
x=RefLine(xxx,1);
n=n+1;
v=0;
vv=0;
bb=0;pp=0;bbb=0;
for iii=1:size(h)
if xxx==1;Tracks{iii,2}=h{iii,1}(1,6);end
clear a
a(:,1)=h{iii,1}(:,1);
a(:,2)=h{iii,1}(:,2);
a(:,3)=h{iii,1}(:,4);
a(:,4)=h{iii,1}(:,7);
a(:,5)=h{iii,1}(:,6);
b=a;
v=0;
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MatlabmodelfortheAISanalysis
bb=0;
for i=1:size(a)
Bpar=a(i,1)-a(i,2)*tan((RefLine(xxx,3)-90)*pi/180);
CrossX=(Bpar-RefLine(xxx,4))/(tan((RefLine(xxx,3))*pi/180)-tan((RefLine(xxx,3)-90)*pi/180));
CrossY=tan((RefLine(xxx,3)-90)*pi/180)*CrossX+Bpar;
Dist=sqrt((CrossY-a(i,1))^2+(CrossX-a(i,2))^2);
if or(Dist>gridsize/2,or(abs(RefLine(xxx,1)-a(i,2))>2000,abs(RefLine(xxx,2)-a(i,1))>2000))
b(i,:)=0;
else
v=v+1;
bb(v,1:5)=a(i,:);
bb(v,7)=CrossX;bb(v,8)=CrossY;
end
end
vv=vv+1;
if numel(bb(:,1))~=1;bbb(vv,1:8)=mean(bb(:,1:8));bbb(vv,6)=v;Tracks{iii,1}(xxx,1)=mean(bb(:,8));Tracks{iii,1}(xxx,2)=m
ean(bb(:,7));Tracks{iii,1}(xxx,3)=mean(bb(:,3));
else
if bb(1,1)~=0;bbb(vv,1:8)=bb(:,1:8);bbb(vv,6)=v;Tracks{iii,1}(xxx,1)=bb(:,8);Tracks{iii,1}(xxx,2)=bb(:,7);Tracks{iii,1}
(xxx,3)=bb(:,3);
else
bb=0;
for i=1:size(a)
Bpar=a(i,1)-a(i,2)*tan((RefLine(xxx,3)-90)*pi/180);
CrossX=(Bpar-RefLine(xxx,4))/(tan((RefLine(xxx,3))*pi/180)-tan((RefLine(xxx,3)-90)*pi/180));
CrossY=tan((RefLine(xxx,3)-90)*pi/180)*CrossX+Bpar;
Dist=sqrt((CrossY-a(i,1))^2+(CrossX-a(i,2))^2);
if or(Dist>gridsize,or(abs(RefLine(xxx,1)-a(i,2))>2000,abs(RefLine(xxx,2)-a(i,1))>2000))
b(i,:)=0;
else
v=v+1;
bb(v,1:5)=a(i,:);
bb(v,7)=CrossX;bb(v,8)=CrossY;
end
end
if numel(bb(:,1))~=1;bbb(vv,1:8)=mean(bb(:,1:8));bbb(vv,6)=v;Tracks{iii,1}(xxx,1)=mean(bb(:,8));Tracks{iii,1}(xxx,
2)=mean(bb(:,7));Tracks{iii,1}(xxx,3)=mean(bb(:,3));
else if bb(1,1)~=0;bbb(vv,1:8)=bb(:,1:8);bbb(vv,6)=v;Tracks{iii,1}(xxx,1)=bb(:,8);Tracks{iii,1}
(xxx,2)=bb(:,7);Tracks{iii,1}(xxx,3)=bb(:,3);else vv=vv-1;end
end
end
end
end
e=bbb;
if numel(e)~=1;
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An analysis of vessel behaviour based on AIS data
eX=mean(e(:,7));
eY=mean(e(:,8));
Deviation{n,2}=eX;Deviation{n,3}=eY;
Deviation{n,1}(1,:)=-400:gridsize_verdeling:400;
Deviation{n,1}(2,:)=0;Deviation{n,1}(3,:)=0;
for eee=1:numel(e(:,1))
if or(and(e(eee,4)>45,and(e(eee,4)<=135,e(eee,8)<eY)),or(and(e(eee,4)>135,and(e(eee,4)<=225,e(eee,7)<eX)),or(a
nd(e(eee,4)>225,and(e(eee,4)<=315,e(eee,8)>eY)),and(or(e(eee,4)>315,e(eee,4)<=45),e(eee,7)>eX))))
e(eee,9)=sqrt((e(eee,7)-eX)^2+(e(eee,8)-eY)^2);
else e(eee,9)=-sqrt((e(eee,7)-eX)^2+(e(eee,8)-eY)^2);
end
nnn=0;
for nnn=1:numel(Deviation{n,1}(1,:))
if abs(e(eee,9)-Deviation{n,1}(1,nnn))<gridsize_verdeling/2
Deviation{n,1}(2,nnn)=Deviation{n,1}(2,nnn)+1;
Deviation{n,1}(3,nnn)=Deviation{n,1}(3,nnn)+e(eee,3);
end
end
end
Afw2=prctile(e(:,9),2);Afw98=prctile(e(:,9),98);
f(n,12)=Afw2;f(n,13)=Afw98;
if route==180;
Prct2X=eX-Afw2*cos(RefLine(xxx,3)*pi/180);Prct2Y=eY-Afw2*sin(RefLine(xxx,3)*pi/180);
Prct98X=eX-Afw98*cos(RefLine(xxx,3)*pi/180);Prct98Y=eY-Afw98*sin(RefLine(xxx,3)*pi/180);
else Prct2X=eX+Afw2*cos(RefLine(xxx,3)*pi/180);Prct2Y=eY+Afw2*sin(RefLine(xxx,3)*pi/180);
Prct98X=eX+Afw98*cos(RefLine(xxx,3)*pi/180);Prct98Y=eY+Afw98*sin(RefLine(xxx,3)*pi/180);
end
f(n,1)=mean(e(:,7));
f(n,2)=mean(e(:,8)); %average path
f(n,3)=Prct2X;
f(n,4)=Prct2Y;
f(n,5)=Prct98X;
f(n,6)=Prct98Y;
f(n,7)=mean(e(:,3)); %average speed
f(n,8)=prctile(e(:,3),2);
f(n,9)=prctile(e(:,3),98);
f(n,10)=vv;
f(n,11)=mean(e(:,4));
u{n,1}(:,1)=e(:,3);
end
end
g=find(f==0);
f(g)=NaN;
B1=f;
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AppendixE
χ2tests,skewnessandexcesskurtosis
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χ2tests,skewnessandexcesskurtosis
Appendix E χ2 tests, skewness and excess kurtosis
Thisappendixgivesthemoredetailedelaborationoftheχ2teststhatareperformedinthecasestudy.Nexttothis,alsotheresultsfromthecalculationoftheskewnessandexcesskurtosisthatarenotshowninthemainreport,areshownhere.
E.1 χ2 tests
χ2testsareperformedforaswellthevesseldistributionasthevesselspeeddistributionoverthewaterway(seesection5.4).Thistestexaminesthedegreeofagreementbetweentheempiricaldistributionandaspe-cifictheoreticaldistribution.Equation(E.1)showshowthevalueforχ2iscalculated.
(E.1) 2k2 o e
1 e
(f f )
fχ
−=∑
where
fo=observedfrequencyofeachclassorinterval; fe=expectedfrequencyforeachclassorintervalpredictedbyatheoretical distribution; k=totalclassesorintervals.
Ifthevalueforχ2isequaltozero,thentheempiricalentheoreticaldistributionhaveaperfectmatch.Ifthisisnotthecase,thesizeofχ2determinesthedegreeofagreement.Thehypothesisthatismadewhenperformingaχ2test,isthatnosignificantdifferenceexistsbetweenthecompareddistributions.Ifthecalcu-latedvalueforχ2istoolarge,thishypothesisisrejected.Beforeitcanbeseenifthisisthecase,twoques-tionsshouldbeanswered.First,thedegreeoffreedomofthedistributionsshouldbeobtained.Thedegreesoffreedomreflectthenumberofclassesinwhichthetwodistributionsarecomparedtoeachotherandthenumberofparametersthatisneededtodescribethetheoreticaldistribution,equation(E.2)).
(E.2) k 1 mθ = − − where
θ=degreesoffreedom; k=numberofclassesorintervals; m=numberofparametersneededtocalculatetheexpected frequencies.
Afterthedegreesoffreedomaredetermined,thesignificancelevelhastobeset.Thisreflectsthecon-fidencelevelthatisusedtorejectoracceptthehypothesis.Thislevelcanbesetbyatdifferentvalues,dependingonforexamplethenatureofthestudie.Throughoutthisthesisalevelof95%isused;thisisalsodonefortheχ2tests.
Whenthevalueforχ2,thedegreesoffreedomandthesignificancelevelareknown,thehypothesiscanbetested.Thisisdonebycomparingthevaluefoundforχ2toavalueobtainedfromaChi-squaredistribu-tion.ThisisvaluefromtheChi-squaredistributionismostlyderivedfromatable,inwhichalsothedegreesoffreedomandthesignificancelevelareincluded.TableE.1showsanexampleofhowapartofthistable
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An analysis of vessel behaviour based on AIS data
lookslike.Itcanbeseenthattheasignificancelevelof95%combinedwith5degreesoffreedom,leadstoavalueof11.1.
Table E.1 Example of a part of the Chi-square distribution table
Degrees of free-dom
Significancelevel
99.5% 99% 95% 90%
1 7.88 6.63 3.84 2.71
2 10.6 9.21 5.99 4.61
3 12.84 11.34 7.81 6.25
4 14.96 13.28 9.49 7.78
5 16.7 15.1 11.1 9.2
6 18.5 16.8 12.6 10.6
Thisvaluecanhereafterbecomparedtothevaluefoundforχ2.Ifthevalueforχ2islargerthanthevaluefoundinthetable,theirisasignificancedifferencebetweenthetwodistributions.Thehypothesisofnodif-ferenceisinsuchacaserejected.
Inthethesis,theabovedescribedχ2testisperformedseveraltimes.Aswelthevesseldistributions,asthevesselspeeddistributionsoverdifferentcrosssectionsaretested.TableE.2toTableE.11showtheresultsforthesetests.Thecolumn‘χ2’showsthevaluethatwasfoundforχ2and‘Freedom’reflectsthedegreesoffreedom.Thecolumn‘χ2table’showsthevaluethatwasreadfromtheChi-squaredistribuiontable.Thecolumn‘Check’reflectstheresultofthecomparisonbetweenthefirsttwo:thehypothesisisaccepted(OK)orrejected(FAIL).
Table E.2 χ2 tests performed for the vessel distributions over the cross sections on location 1-4Size class < 10,000 dwt.
LocationIncoming Outgoing
χ2 Freedom χ2table Check χ2 Freedom χ2table Check
1 12.9 19 30.1 OK 16.2 24 36.4 OK
2 8.8 11 19.7 OK 16.3 22 33.9 OK
3 16.6 15 25 OK 14.8 25 37.7 OK
4 7.9 16 26.3 OK 11.6 12 21 OK
Table E.3 χ2 tests performed for the vessel distributions over the cross sections on location 1-4Size class 10,000-40,000 dwt.
LocationIncoming Outgoing
χ2 Freedom χ2table Check χ2 Freedom χ2table Check
1 18.2 17 27.6 OK 34.2 29 42.6 OK
2 9.7 8 15.5 OK 17.0 16 26.3 OK
3 11.8 12 21 OK 12.4 23 35.2 OK
4 6.2 15 25 OK 15.4 9 16.9 OK
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χ2tests,skewnessandexcesskurtosis
Table E.4 χ2 tests performed for the vessel distributions over the cross sections on location 1-4Size class 40,000-70,000 dwt.
LocationIncoming Outgoing
χ2 Freedom χ2table Check χ2 Freedom χ2table Check
1 17.4 17 27.6 OK 25.3 20 31.4 OK
2 7.2 6 12.6 OK 20.2 14 23.7 OK
3 28.9 15 25 FAIL 9.7 16 26.3 OK
4 17.2 10 18.3 OK 10.8 8 15.5 OK
Table E.5 χ2 tests performed for the vessel distributions over the cross sections on location 1-4Size class 70,000-100,000 dwt.
LocationIncoming Outgoing
χ2 Freedom χ2table Check χ2 Freedom χ2table Check
1 7.8 17 27.6 OK 29.7 26 38.9 OK
2 2.5 6 12.6 OK 13.8 15 25 OK
3 12.0 12 21 OK 19.5 15 25 OK
4 16.0 12 21 OK 13.6 6 12.6 FAIL
Table E.6 χ2 tests performed for the vessel distributions over the cross sections on location 1-4Size class >100,000 dwt.
LocationIncoming Outgoing
χ2 Freedom χ2table Check χ2 Freedom χ2table Check
1 16.5 17 27.6 OK 16.3 27 40.1 OK
2 9.9 9 16.9 OK 16.3 15 25 OK
3 9.9 13 22.4 OK 21.8 15 25 OK
4 23.1 11 19.7 FAIL 8.2 6 12.6 OK
Table E.7 χ2 tests performed for the vessel speed distributions over the cross sections on location 1-4Size class <10,000 dwt.
LocationIncoming Outgoing
χ2 Freedom χ2table Check χ2 Freedom χ2table Check
1 18.4 17 27.6 OK 7.9 15 25 OK
2 17.7 20 31.4 OK 10.9 12 21 OK
3 10.3 16 26.3 OK 14.5 16 26.3 OK
4 3.8 17 27.6 OK 6.5 13 22.4 OK
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An analysis of vessel behaviour based on AIS data
Table E.8 χ2 tests performed for the vessel speed distributions over the cross sections on location 1-4Size class 10,000-40,000 dwt.
LocationIncoming Outgoing
χ2 Freedom χ2table Check χ2 Freedom χ2table Check
1 30.7 20 31.4 OK 22.5 15 25 OK
2 22.2 26 38.9 OK 9.2 13 22.4 OK
3 11.9 19 30.1 OK 18.9 16 26.3 OK
4 7.3 18 28.9 OK 9.7 13 22.4 OK
Table E.9 χ2 tests performed for the vessel speed distributions over the cross sections on location 1-4Size class 40,000-70,000 dwt.
LocationIncoming Outgoing
χ2 Freedom χ2table Check χ2 Freedom χ2table Check
1 29.7 13 22.4 FAIL 23.8 18 28.9 OK
2 7.7 8 15.5 OK 11.2 15 25 OK
3 8.3 7 14.1 OK 15.5 11 19.7 OK
4 13.7 4 9.49 FAIL 13.1 9 16.9 OK
Table E.10 χ2 tests performed for the vessel speed distributions over the cross sections on location 1-4Size class 70,000-100,000 dwt.
LocationIncoming Outgoing
χ2 Freedom χ2table Check χ2 Freedom χ2table Check
1 17.4 14 23.7 OK 31.0 18 28.9 FAIL
2 17.8 10 18.3 OK 23.0 16 26.3 OK
3 13.4 6 12.6 FAIL 12.9 12 21 OK
4 2.5 4 9.49 OK 13.1 9 16.9 OK
Table E.11 χ2 tests performed for the vessel speed distributions over the cross sections on location 1-4Size class >100,000 dwt.
LocationIncoming Outgoing
χ2 Freedom χ2table Check χ2 Freedom χ2table Check
1 13.9 18 28.9 OK 18.4 14 23.7 OK
2 15.3 11 19.7 OK 12.7 11 19.7 OK
3 4.7 5 11.1 OK 6.6 11 19.7 OK
4 9.1 3 7.81 FAIL 8.2 8 15.5 OK
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χ2tests,skewnessandexcesskurtosis
E.2 Skewness and kurtosis
Forthevesseldistributionsoverthecrosssectionsatthedifferentlocations,theskewnessandkurtosiswerealreadygiveninthemainreport.Forthevesselspeeddistributionthisishowevernotdone.Thereforethesetwoparametersareshownbelow(TableE.12andTableE.13).
Table E.12 Skewness for the vessel speed distributions over the cross sections at locations 1 to 4, for the different datasets at locations 1 to 4
Location<10,000 10,000-40,000 40,000-70,000 70,000-100,000 >100,000
In Out In Out In Out In Out In Out
1 -0.68 -0.05 -0.63 -0.1 0.2 0.02 0.22 0.33 0.12 -0.28
2 -0.59 -0.12 -0.17 -0.72 0.58 0.47 0.66 0.24 0.12 0.02
3 -0.38 -0.65 0.12 -0.54 -0.43 0.24 0.13 0.16 0.25 0.41
4 -0.36 -0.54 -0.11 -0.21 0.03 -0.17 -0.97 0.44 -0.21 0.22
Table E.13 Excess kurtosis for the vessel speed distributions over the cross sections at locations 1 to 4, for the different datasets at locations 1 to 4
Location<10,000 10,000-40,000 40,000-70,000 70,000-100,000 >100,000
In Out In Out In Out In Out In Out
1 0.33 -0.4 -0.28 -0.48 0.5 -0.79 0.34 -0.33 -0.41 -0.57
2 -0.25 -0.45 -0.65 2.31 0.66 0.69 0.95 -0.62 0.26 -0.63
3 -0.04 0.59 -0.39 0.36 0.9 -0.74 0.5 0.82 0.52 0.18
4 0.18 0.91 -0.35 -0.38 0.73 0.1 3.45 1.03 0.52 0.51
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AppendixF
Vesselandvesselspeeddistributions
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Vesselandvesselspeeddistribution
Appendix F Vessel and vessel speed distributions
Thisappendixshowsalldistributionsthatareusedthroughoutthecasestudy,toobtaininsightintheaver-agevesselbehaviour.First,thevesseldistributionsoverthewaterwayatthefourpredefinedlocationsisgivenforeverysizeclass.Second,thevesselspeeddistributions,againatthefourspecifiedlocationsisshown.Forboth,aswellthetheempiricalasthefittednormaldistributionaregiven.Finallyalsothespeeddistributionoverthewaterwayispresented.
F.1 Vessel distribution over the waterway
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8845µ=11.3σ=84.1A=0.12
Loca�on 1
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)R 2=0.939µ=0σ=39.1A=0.25
Loca�on 2
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9654µ=23σ=42.9A=0.21
Loca�on 3
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9526µ=7.7σ=72.9A=0.13
Loca�on 4
Figure F.1 Vessel distribution over cross sections 1-4 for incoming vessels from sizeclass <10,000 dwt
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An analysis of vessel behaviour based on AIS data
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8464µ=21.9σ=111.9A=0.09
Loca�on 1
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8546µ=0σ=95.1A=0.1
Loca�on 2
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8159µ=−1.4σ=120.8A=0.08
Loca�on 3
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9631µ=9.5σ=58.7A=0.17
Loca�on 4
Figure F.2 Vessel distribution over cross sections 1-4 for outgoing vessels from sizeclass <10,000 dwt
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8663µ=0σ=86.2A=0.12
Loca�on 1
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9644µ=6.8σ=36A=0.27
Loca�on 2
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9553µ=13.2σ=57.1A=0.17
Loca�on 3
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9443µ=−2.9σ=72.5A=0.14
Loca�on 4
Figure F.3 Vessel distribution over cross sections 1-4 for incoming vessels from sizeclass 10,000-40,000 dwt
![Page 150: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/150.jpg)
Page-A38-
Vesselandvesselspeeddistribution
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.7726µ=0σ=139.6A=0.07
Loca�on 1
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8835µ=2.6σ=79A=0.12
Loca�on 2
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8848µ=−5.8σ=112A=0.09
Loca�on 3
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9267µ=7.7σ=50.6A=0.19
Loca�on 4
Figure F.4 Vessel distribution over cross sections 1-4 for outgoing vessels from sizeclass 10,000,40,000- dwt
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.7592µ=10.5σ=123.9A=0.08
Loca�on 1
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9071µ=5.3σ=76.3A=0.13
Loca�on 2
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8571µ=−5.4σ=74.9A=0.13
Loca�on 3
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9716µ=0σ=27.8A=0.32
Loca�on 4
Figure F.5 Vessel distribution over cross sections 1-4 for incoming vessels from sizeclass 40,000-70,000 dwt
![Page 151: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/151.jpg)
Page-A39-
An analysis of vessel behaviour based on AIS data
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.7635µ=20.9σ=98.5A=0.1
Loca�on 1
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8737µ=16.6σ=59.9A=0.16
Loca�on 2
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9094µ=6.4σ=82.2A=0.12
Loca�on 3
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9829µ=8.1σ=34.2A=0.27
Loca�on 4
Figure F.6 Vessel distribution over cross sections 1-4 for outgoing vessels from sizeclass 40,000-70,000 dwt
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.952µ=−1.3σ=82.7A=0.12
Loca�on 1
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9921µ=3.3σ=37A=0.27
Loca�on 2
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9109µ=4.9σ=58.7A=0.17
Loca�on 3
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.935µ=−15.5σ=51.9A=0.18
Loca�on 4
Figure F.7 Vessel distribution over cross sections 1-4 for incoming vessels from sizeclass 70,000-100,000 dwt
![Page 152: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/152.jpg)
Page-A40-
Vesselandvesselspeeddistribution
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.7592µ=10.5σ=123.9A=0.08
Loca�on 1
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9071µ=5.3σ=76.3A=0.13
Loca�on 2
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8571µ=−5.4σ=74.9A=0.13
Loca�on 3
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9716µ=0σ=27.8A=0.32
Loca�on 4
Figure F.8 Vessel distribution over cross sections 1-4 for outgoing vessels from sizeclass 70,000-100,000 dwt
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8535µ=−4.6σ=84.9A=0.12
Loca�on 1
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9444µ=2σ=49A=0.21
Loca�on 2
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9599µ=5.4σ=63.8A=0.16
Loca�on 3
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8768µ=−18.9σ=55.3A=0.17
Loca�on 4
Figure F.9 Vessel distribution over cross sections 1-4 for incoming vessels from sizeclass >100,000 dwt
![Page 153: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/153.jpg)
Page-A41-
An analysis of vessel behaviour based on AIS data
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.7885µ=1σ=131.5A=0.08
Loca�on 1
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.9451µ=−5.6σ=76.8A=0.14
Loca�on 2
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.8553µ=−4.6σ=68.6A=0.14
Loca�on 3
−400 −200 0 200 4000
0.1
0.2
X = devia�on from average (m)
P (X
)
R 2=0.971µ=2.1σ=35A=0.27
Loca�on 4
Figure F.10 Vessel distribution over cross sections 1-4 for outgoing vessels from sizeclass >100,000 dwt
![Page 154: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/154.jpg)
Page-A42-
Vesselandvesselspeeddistribution
F.2 Vessel speed distribution on a location on the waterway
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8593
µ=13.7
σ=2.1
A=0.09
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8406
µ=12.7
σ=2.5
A=0.08
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8997
µ=10.5
σ=2.2
A=0.09
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9269
µ=9.2
σ=2.3
A=0.09
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.11 Vessel speed distribution on location 1-4, for incoming vessels from size class <10,000 dwt
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9553
µ=14.8
σ=2.1
A=0.1
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9348
µ=14.3
σ=1.7
A=0.12
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9324
µ=11.8
σ=1.9
A=0.1
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9018
µ=10.4
σ=1.7
A=0.12
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.12 Vessel speed distribution on location 1-4, for outgoing vessels from size class <10,000 dwt
![Page 155: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/155.jpg)
Page-A43-
An analysis of vessel behaviour based on AIS data
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8541
µ=14.4
σ=2.5
A=0.07
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8262
µ=11.5
σ=3.4
A=0.06
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9221
µ=9
σ=2.7
A=0.08
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8577
µ=8.1
σ=2.5
A=0.08
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.13 Vessel speed distribution on location 1-4, for incoming vessels from size class 10,000-40,000 dwt
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8044
µ=15.3
σ=2.2
A=0.09
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.947
µ=14.5
σ=1.7
A=0.11
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9019
µ=11.1
σ=2.1
A=0.09
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8647
µ=9.8
σ=2
A=0.1
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.14 Vessel speed distribution on location 1-4, for outgoing vessels from size class 10,000-40,000 dwt
![Page 156: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/156.jpg)
Page-A44-
Vesselandvesselspeeddistribution
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.7607
µ=10.8
σ=1.8
A=0.11
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9149
µ=7.4
σ=1.3
A=0.16
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9545
µ=6.2
σ=1.1
A=0.19
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)R 2=0.9592
µ=5.9
σ=0.6
A=0.28
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.15 Vessel speed distribution on location 1-4, for incoming vessels from size class 40,000-70,000 dwt
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8221
µ=13.7
σ=2.4
A=0.09
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9022
µ=12.4
σ=2
A=0.1
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9398
µ=8.5
σ=1.7
A=0.12
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9114
µ=7
σ=1.4
A=0.14
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.16 Vessel speed distribution on location 1-4, for outgoing vessels from size class 40,000-70,000 dwt
![Page 157: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/157.jpg)
Page-A45-
An analysis of vessel behaviour based on AIS data
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8833
µ=10.2
σ=1.9
A=0.1
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8865
µ=7.5
σ=1.4
A=0.14
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9097
µ=6
σ=0.8
A=0.23
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9533
µ=5.6
σ=0.7
A=0.27
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.17 Vessel speed distribution on location 1-4, for incoming vessels from size class 70,000-100,000 dwt
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.7979
µ=12
σ=2.4
A=0.08
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8766
µ=10.7
σ=2.2
A=0.09
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8898
µ=7.6
σ=1.5
A=0.13
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.923
µ=6
σ=1.1
A=0.17
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.18 Vessel speed distribution on location 1-4, for outgoing vessels from size class 70,000-100,000 dwt
![Page 158: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/158.jpg)
Page-A46-
Vesselandvesselspeeddistribution
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9157
µ=10.5
σ=2.5
A=0.08
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8944
µ=7.4
σ=1.6
A=0.12
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9817
µ=6.2
σ=0.8
A=0.23
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9838
µ=5.7
σ=0.7
A=0.27
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.19 Vessel speed distribution on location 1-4, for incoming vessels from size class >100,000 dwt
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8813
µ=14.3
σ=2
A=0.1
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.8761
µ=12.3
σ=1.6
A=0.12
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9386
µ=8.3
σ=1.5
A=0.13
0 5 10 15 200
0.1
0.2
X = Vessel speed (kn) −−>
P (X
)
R 2=0.9604
µ=6.6
σ=1.3
A=0.15
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.20 Vessel speed distribution on location 1-4, for outgoing vessels from size class >100,000 dwt
![Page 159: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/159.jpg)
Page-A47-
An analysis of vessel behaviour based on AIS data
F.3 Vessel speed distribution over cross section
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.21 Vessel speed distribution over cross sections 1-4, for incoming vessels from size class <10,000 dwt
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.22 Vessel speed distribution over cross sections 1-4, for outgoing vessels from size class <10,000 dwt
![Page 160: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/160.jpg)
Page-A48-
Vesselandvesselspeeddistribution
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.23 Vessel speed distribution over cross sections 1-4, for incoming vessels from size class 10,000-40,000 dwt
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.24 Vessel speed distribution over cross sections 1-4, for outgoing vessels from size class 10,000-40,000 dwt
![Page 161: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/161.jpg)
Page-A49-
An analysis of vessel behaviour based on AIS data
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.25 Vessel speed distribution over cross sections 1-4, for incoming vessels from size class 40,000-70,000 dwt
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.26 Vessel speed distribution over cross sections 1-4, for outgoing vessels from size class 40,000-70,000 dwt
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Page-A50-
Vesselandvesselspeeddistribution
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.27 Vessel speed distribution over cross sections 1-4, for incoming vessels from size class 70,000-100,000 dwt
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.28 Vessel speed distribution over cross sections 1-4, for outgoing vessels from size class 70,000-100,000 dwt
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Page-A51-
An analysis of vessel behaviour based on AIS data
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.29 Vessel speed distribution over cross sections 1-4, for incoming vessels from size class >100,000 dwt
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
−200 −100 0 100 2000
5
10
15
X = devia�on from average (m)
Ave
rage
ves
sel s
peed
(kn)
Loca�on 1 Loca�on 2
Loca�on 3 Loca�on 4
Figure F.30 Vessel speed distribution over cross sections 1-4, for outgoing vessels from size class >100,000 dwt
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AppendixG
Genericrules
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Page-A54-
Genericrules
Appendix G Generic rules
Thisappendixshowsthecharacteristicsofthederivedgenericnormaldistributionsforthedifferentpre-definedcrosssections.Theresultsarepresentedintables,inwhichthedistributionforeverysizeclassispresent.Alsotheinfluenceoftheexternalcircumstancesishandledinthisappendix.Severalfiguresshowtherelationshipbetweentheexternalinfluenceandthedeviationfromtheaveragevesselpathandvesselspeed.
G.1 Vessel and vessel speed distribution
Thedifferentpartsinwhichthetotalcaseareaissplit,areintroducedinChapter8.Belowfirstafigureofthespecifiedpartisgiven,togetherwiththecrosssectionsthatarehandled.
G.1.1 Part 1
5.9 6 6.1 6.2 6.34.45
4.455
4.46
4.465
4.47
4.475
4.48
4.485
4.49
X−posi�on in "Rijksdriehoeksgrid" [m]
Y−po
si�o
n in
"Ri
jksd
rieh
oeks
grid
" [m
]
1 - A
1 - B
1 - D
1 - C
Figure G.1 The cross sections that are investigated in part 1
Table G.1 Characteristics of the different size classes in cross section 1-A
Widthofthewaterway:3000meters
Sizeclass(dwt)
Incoming Outgoing
Spatialdistr.(m) Speeddistr.(kn) Spatialdistr.(m) Speeddistr.(kn)
Mean St Dev Mean St Dev Mean St Dev Mean St Dev
<10,000 2310 210 14.5 1.9 880 190 13.9 2.2
10,000-40,000 2240 310 15.1 2.1 970 230 14.7 2.5
40,0000-70,000 2100 290 11.9 2.3 1080 300 13.2 2.5
70,000-100,000 1960 250 11.5 2.2 990 370 11.5 1.9
>100,000 1900 270 12.6 2.7 1250 880 13.6 2.3
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Page-A55-
An analysis of vessel behaviour based on AIS data
Table G.2 Characteristics of the different size classes in cross section 1-B
Widthofthewaterway:2200meters
Sizeclass(dwt)
Incoming Outgoing
Spatialdistr.(m) Speeddistr.(kn) Spatialdistr.(m) Speeddistr.(kn)
Mean St Dev Mean St Dev Mean St Dev Mean St Dev
<10,000 1630 130 14.1 1.9 680 160 14.3 2.1
10,000-40,000 1600 130 14.7 2.4 760 180 15.1 2.4
40,0000-70,000 1490 140 11.5 2.1 820 210 13.4 2.4
70,000-100,000 1430 140 11 2.1 860 260 11.8 2.4
>100,000 1400 130 11.7 2.8 910 260 14.2 2.2
μ/B σ/B μ/μV0 σ/σV0 μ/B σ/B μ/μV0 σ/σV0
<10,000 0.74 0.06 0.97 1.00 0.31 0.07 1.03 0.95
10,000-40,000 0.73 0.06 0.97 1.14 0.35 0.08 1.03 0.96
40,0000-70,000 0.68 0.06 0.97 0.91 0.37 0.10 1.02 0.96
70,000-100,000 0.65 0.06 0.96 0.95 0.39 0.12 1.03 1.26
>100,000 0.64 0.06 0.93 1.04 0.41 0.12 1.04 0.96
Table G.3 Characteristics of the different size classes in cross section 1-C
Widthofthewaterway:1300meters
Sizeclass(dwt)
Incoming Outgoing
Spatialdistr.(m) Speeddistr.(kn) Spatialdistr.(m) Speeddistr.(kn)
Mean St Dev Mean St Dev Mean St Dev Mean St Dev
<10,000 1100 90 13.9 2.1 460 120 14.7 2.2
10,000-40,000 1080 100 14.6 2.4 520 130 15 2.1
40,0000-70,000 1000 90 11.1 1.5 560 120 13.6 2.3
70,000-100,000 980 90 10.6 1.8 600 140 12 2.4
>100,000 970 90 11 2.4 630 160 14.3 2
μ/B σ/B μ/μV0 σ/σV0 μ/B σ/B μ/μV0 σ/σV0
<10,000 0.85 0.07 0.96 1.11 0.35 0.09 1.06 0.95
10,000-40,000 0.83 0.08 0.97 1.14 0.40 0.10 1.02 0.84
40,0000-70,000 0.77 0.07 0.93 0.65 0.43 0.09 1.03 0.92
70,000-100,000 0.75 0.07 0.92 0.82 0.46 0.11 1.04 1.26
>100,000 0.75 0.07 0.87 0.89 0.48 0.12 1.05 0.87
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Page-A56-
Genericrules
Table G.4 Characteristics of the different size classes in cross section 1-D
Widthofthewaterway:800meters
Sizeclass(dwt)
Incoming Outgoing
Spatialdistr.(m) Speeddistr.(kn) Spatialdistr.(m) Speeddistr.(kn)
Mean St Dev Mean St Dev Mean St Dev Mean St Dev
<10,000 660 60 13.6 2.2 230 110 15 1.9
10,000-40,000 640 60 13.8 3 240 110 15.3 2
40,0000-70,000 580 80 10.1 1.7 280 70 13.3 2.2
70,000-100,000 560 60 9.2 1.6 320 100 11.8 2.6
>100,000 560 70 9.4 2 320 110 14 1.9
μ/B σ/B μ/μV0 σ/σV0 μ/B σ/B μ/μV0 σ/σV0
<10,000 0.83 0.08 0.94 1.16 0.29 0.14 1.08 0.86
10,000-40,000 0.80 0.08 0.91 1.43 0.30 0.14 1.04 0.80
40,0000-70,000 0.73 0.10 0.85 0.74 0.35 0.09 1.01 0.88
70,000-100,000 0.70 0.08 0.80 0.73 0.40 0.13 1.03 1.37
>100,000 0.70 0.09 0.75 0.74 0.40 0.14 1.03 0.83
G.1.2 Part 2
Figure G.2 The cross sections that are investigated in part 2
6.2 6.25 6.3 6.35 6.4 6.45 6.5 6.554.435
4.44
4.445
4.45
4.455
4.46
4.465
4.47
X−posi�on in "Rijksdriehoeksgrid" [m]
Y−po
si�o
n in
"Ri
jksd
rieh
oeks
grid
" [m
]
2 - A
2 - B
2 - C
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Page-A57-
An analysis of vessel behaviour based on AIS data
Table G.5 Characteristics of the different size classes in cross section 2-A
Widthofthewaterway:850meters
Sizeclass(dwt)
Incoming Outgoing
Spatialdistr.(m) Speeddistr.(kn) Spatialdistr.(m) Speeddistr.(kn)
Mean St Dev Mean St Dev Mean St Dev Mean St Dev
<10,000 700 50 13.2 2.3 360 100 14.7 1.6
10,000-40,000 680 40 12.4 3.4 410 100 14.8 1.5
40,0000-70,000 650 50 8 1.1 420 60 12.8 2.1
70,000-100,000 640 40 7.5 1.4 460 90 11.2 2.4
>100,000 640 60 7.1 1.4 460 100 13.2 2
μ/B σ/B μ/μV0 σ/σV0 μ/B σ/B μ/μV0 σ/σV0
<10,000 0.82 0.06 0.91 1.21 0.42 0.12 1.06 0.73
10,000-40,000 0.80 0.05 0.82 1.62 0.48 0.12 1.01 0.60
40,0000-70,000 0.76 0.06 0.67 0.48 0.49 0.07 0.97 0.84
70,000-100,000 0.75 0.05 0.65 0.64 0.54 0.11 0.97 1.26
>100,000 0.75 0.07 0.56 0.52 0.54 0.12 0.97 0.87
Table G.6 Characteristics of the different size classes in cross section 2-B
Widthofthewaterway:650meters
Sizeclass(dwt)
Incoming Outgoing
Spatialdistr.(m) Speeddistr.(kn) Spatialdistr.(m) Speeddistr.(kn)
Mean St Dev Mean St Dev Mean St Dev Mean St Dev
<10,000 480 30 12.4 2.5 250 70 14 1.8
10,000-40,000 470 30 10.7 3.3 280 60 14.1 1.8
40,0000-70,000 440 40 7 1.4 290 60 11.7 1.9
70,000-100,000 440 40 6.8 1.1 310 60 10.2 2
>100,000 430 40 6.8 1.2 320 70 11.7 1.5
μ/B σ/B μ/μV0 σ/σV0 μ/B σ/B μ/μV0 σ/σV0
<10,000 0.74 0.05 0.86 1.32 0.38 0.11 1.01 0.82
10,000-40,000 0.72 0.05 0.71 1.57 0.43 0.09 0.96 0.72
40,0000-70,000 0.68 0.06 0.59 0.61 0.45 0.09 0.89 0.76
70,000-100,000 0.68 0.06 0.59 0.50 0.48 0.09 0.89 1.05
>100,000 0.66 0.06 0.54 0.44 0.49 0.11 0.86 0.65
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Page-A58-
Genericrules
Table G.7 Characteristics of the different size classes in cross section 2-C
Widthofthewaterway:450meters
Sizeclass(dwt)
Incoming Outgoing
Spatialdistr.(m) Speeddistr.(kn) Spatialdistr.(m) Speeddistr.(kn)
Mean St Dev Mean St Dev Mean St Dev Mean St Dev
<10,000 340 40 11.7 2.4 190 80 12.9 1.7
10,000-40,000 320 30 10.1 2.8 190 70 12.3 1.7
40,0000-70,000 270 50 6.6 1.2 190 60 10.1 1.8
70,000-100,000 270 40 6.7 1.1 200 50 8.6 1.6
>100,000 270 40 6.5 1.3 200 40 9.6 1.5
μ/B σ/B μ/μV0 σ/σV0 μ/B σ/B μ/μV0 σ/σV0
<10,000 0.76 0.09 0.81 1.26 0.42 0.18 0.93 0.77
10,000-40,000 0.71 0.07 0.67 1.33 0.42 0.16 0.84 0.68
40,0000-70,000 0.60 0.11 0.55 0.52 0.42 0.13 0.77 0.72
70,000-100,000 0.60 0.09 0.58 0.50 0.44 0.11 0.75 0.84
>100,000 0.60 0.09 0.52 0.48 0.44 0.09 0.71 0.65
G.1.3 Part 3
6.48 6.5 6.52 6.54 6.56 6.58 6.6 6.62
4.43
4.432
4.434
4.436
4.438
4.44
4.442
4.444
X−posi�on in "Rijksdriehoeksgrid" [m]
Y−po
si�o
n in
"Ri
jksd
rieh
oeks
grid
" [m
]
3 - A
3 - B
Figure G.3 The cross sections that are investigated in part 3.
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Page-A59-
An analysis of vessel behaviour based on AIS data
Table G.8 Characteristics of the different size classes in cross section 3-A
Widthofthewaterway:900meters
Sizeclass(dwt)
Incoming Outgoing
Spatialdistr.(m) Speeddistr.(kn) Spatialdistr.(m) Speeddistr.(kn)
Mean St Dev Mean St Dev Mean St Dev Mean St Dev
<10,000 820 40 10.8 2.3 650 130 11.9 1.9
10,000-40,000 800 50 9.3 2.8 620 120 11.4 2.2
40,0000-70,000 710 70 6.3 1.1 630 90 8.8 1.7
70,000-100,000 720 50 6.2 0.9 630 70 7.7 1.5
>100,000 700 60 6.2 1 650 70 8.6 1.6
μ/B σ/B μ/μV0 σ/σV0 μ/B σ/B μ/μV0 σ/σV0
<10,000 0.91 0.04 0.74 1.21 0.72 0.14 0.86 0.86
10,000-40,000 0.89 0.06 0.62 1.33 0.69 0.13 0.78 0.88
40,0000-70,000 0.79 0.08 0.53 0.48 0.70 0.10 0.67 0.68
70,000-100,000 0.80 0.06 0.54 0.41 0.70 0.08 0.67 0.79
>100,000 0.78 0.07 0.49 0.37 0.72 0.08 0.63 0.70
Table G.9 Characteristics of the different size classes in cross section 3-B
Widthofthewaterway:550meters
Sizeclass(dwt)
Incoming Outgoing
Spatialdistr.(m) Speeddistr.(kn) Spatialdistr.(m) Speeddistr.(kn)
Mean St Dev Mean St Dev Mean St Dev Mean St Dev
<10,000 480 40 10 2.1 320 80 11.5 2.1
10,000-40,000 450 60 8.6 2.5 310 60 11 2
40,0000-70,000 380 60 6.1 0.7 310 40 8.3 1.6
70,000-100,000 380 60 5.7 0.8 320 40 7.1 1.5
>100,000 380 60 6 0.9 330 60 7.8 1.6
μ/B σ/B μ/μV0 σ/σV0 μ/B σ/B μ/μV0 σ/σV0
<10,000 0.87 0.07 0.69 1.11 0.58 0.15 0.83 0.95
10,000-40,000 0.82 0.11 0.57 1.19 0.56 0.11 0.75 0.80
40,0000-70,000 0.69 0.11 0.51 0.30 0.56 0.07 0.63 0.64
70,000-100,000 0.69 0.11 0.50 0.36 0.58 0.07 0.62 0.79
>100,000 0.69 0.11 0.48 0.33 0.60 0.11 0.57 0.70
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Page-A60-
Genericrules
G.1.4 Part 4
6.44 6.46 6.48 6.5 6.52 6.54 6.56 6.58 6.6 6.62 6.64
4.41
4.415
4.42
4.425
4.43
X−posi�on in "Rijksdriehoeksgrid" [m]
Y−po
si�o
n in
"Ri
jksd
rieh
oeks
grid
" [m
]
x10⁵
x10⁴
4 - A
4 - C
4 - B
Figure G.4 The cross sections that are investigated in part 4
Table G.10 Characteristics of the different size classes in cross section 4-A
Widthofthewaterway:700meters
Sizeclass(dwt)
Incoming Outgoing
Spatialdistr.(m) Speeddistr.(kn) Spatialdistr.(m) Speeddistr.(kn)
Mean St Dev Mean St Dev Mean St Dev Mean St Dev
<10,000 400 70 9.2 2.3 290 60 10.4 1.7
10,000-40,000 370 70 8.1 2.5 300 50 9.8 2
40,0000-70,000 300 50 5.9 0.6 310 30 7 1.4
70,000-100,000 310 50 5.6 0.7 320 30 6 1.1
>100,000 300 60 5.7 0.7 330 30 6.6 1.3
μ/B σ/B μ/μV0 σ/σV0 μ/B σ/B μ/μV0 σ/σV0
<10,000 0.57 0.10 0.63 1.21 0.41 0.09 0.75 0.77
10,000-40,000 0.53 0.10 0.54 1.19 0.43 0.07 0.67 0.80
40,0000-70,000 0.43 0.07 0.50 0.26 0.44 0.04 0.53 0.56
70,000-100,000 0.44 0.07 0.49 0.32 0.46 0.04 0.52 0.58
>100,000 0.43 0.09 0.45 0.26 0.47 0.04 0.49 0.57
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Page-A61-
An analysis of vessel behaviour based on AIS data
Table G.11 Characteristics of the different size classes in cross section 4-B
Widthofthewaterway:700meters
Sizeclass(dwt)
Incoming Outgoing
Spatialdistr.(m) Speeddistr.(kn) Spatialdistr.(m) Speeddistr.(kn)
Mean St Dev Mean St Dev Mean St Dev Mean St Dev
<10,000 350 80 8 2.1 290 80 9.9 1.6
10,000-40,000 320 70 7 2.3 300 60 8.6 2
40,0000-70,000 250 40 5.1 0.9 310 60 6 1.1
70,000-100,000 250 40 4.9 0.7 300 30 5.2 0.9
>100,000 260 40 5.1 0.8 320 30 5.4 0.8
μ/B σ/B μ/μV0 σ/σV0 μ/B σ/B μ/μV0 σ/σV0
<10,000 0.50 0.11 0.55 1.11 0.41 0.11 0.71 0.73
10,000-40,000 0.46 0.10 0.46 1.10 0.43 0.09 0.59 0.80
40,0000-70,000 0.36 0.06 0.43 0.39 0.44 0.09 0.45 0.44
70,000-100,000 0.36 0.06 0.43 0.32 0.43 0.04 0.45 0.47
>100,000 0.37 0.06 0.40 0.30 0.46 0.04 0.40 0.35
Table G.12 Characteristics of the different size classes in cross section 4-C
Widthofthewaterway:750meters
Sizeclass(dwt)
Incoming Outgoing
Spatialdistr.(m) Speeddistr.(kn) Spatialdistr.(m) Speeddistr.(kn)
Mean St Dev Mean St Dev Mean St Dev Mean St Dev
<10,000 350 90 6.3 1.9 310 90 8.6 1.8
10,000-40,000 320 90 5.8 1.7 310 70 6.7 2
40,0000-70,000 230 30 4.3 0.9 320 70 4.6 0.8
70,000-100,000 280 70 4 0.8 300 50 3.7 0.6
>100,000 250 40 4 0.9 300 40 3.8 0.9
μ/B σ/B μ/μV0 σ/σV0 μ/B σ/B μ/μV0 σ/σV0
<10,000 0.47 0.12 0.43 1.00 0.41 0.12 0.62 0.82
10,000-40,000 0.43 0.12 0.38 0.81 0.41 0.09 0.46 0.80
40,0000-70,000 0.31 0.04 0.36 0.39 0.43 0.09 0.35 0.32
70,000-100,000 0.37 0.09 0.35 0.36 0.40 0.07 0.32 0.32
>100,000 0.33 0.05 0.32 0.33 0.40 0.05 0.28 0.39
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Page-A62-
Genericrules
G.2 External influences
Asexplainedinchapter8ofthemainreport,theresultsfromthecasestudyconcerningtheexternalinflu-encesaretranformedintogenericrules.ThisisdonebygeneralisingtheX-axis,afterwhichaquantifiedlinearrelationshipisobtained.Belowthisisdoneforeveryexternalinfluencethatisfound.
G.2.1 Wind influences
−15 −10 −5 0 5 10 15−40
−20
0
20
40
60
devi
a�on
from
ave
rage
trac
k (m
)
<-- Wind from port side (m/s).......wind from stern side (m/s) −−>
> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −40
−20
0
20
40
60
devi
a�on
from
ave
rage
trac
k (m
)
<-- Wind from port side (m/s).......wind from stern side (m/s) −−>
y (x) = 6.25 - 2.1861 * x
Figure G.5 Influence of cross winds in the Maasmond on the average path. The left figure shows the split up in different wind speed classes.
> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −4
−3
−2
−1
0
1
2
o <-- Wind from port side (m/s).......wind from starboard side (m/s) −−>
devi
a�on
from
ave
rage
spe
ed (%
)
−15 −10 −5 0 5 10 15−12
−10
−8
−6
−4
−2
0
2
4
o
devi
a�on
from
ave
rage
spe
ed (%
)
<-- Wind from port side (m/s).......wind from starboard side (m/s) −−>
y (x) = 2.11 + 0.13 * x
Figure G.6 Influence of cross winds in the Maasmond on the average speed. The left figure shows the split up in different wind speed classes.
![Page 175: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/175.jpg)
Page-A63-
An analysis of vessel behaviour based on AIS data
> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −10
−5
0
5
10
15
−15 −10 −5 0 5 10 15−10
−5
0
5
10
15
<−− wind from behind (m/s).... ...wind from front (m/s) −de
via�
on fr
om a
vera
ge tr
ack
(m)
<−− wind from behind (m/s).... ...wind from front (m/s) −
devi
a�on
from
ave
rage
trac
k (m
)
y (x) = 3.7 - 0.61 * x
Figure G.7 Influence of parallel winds in the Maasmond on the average path. The left figure shows the split up in different wind speed classes.
> 8 5.5−8 0−5.5 0−5.5 5.5−8 > 8 −3
−2
−1
0
1
2
3
<-- Wind from behind (m/s).....wind from front (m/s) −−>
devi
a�on
from
ave
rage
spe
ed (%
)
−15 −10 −5 0 5 10 15−3
−2
−1
0
1
2
3
4
devi
a�on
from
ave
rage
spe
ed (%
)
<-- Wind from behind (m/s).....wind from front (m/s) −−>
y (x) = 0.64 - 0.20 * x
Figure G.8 Influence of parallel winds in the Maasmond on the average speed. The left figure shows the split up in different wind speed classes.
![Page 176: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/176.jpg)
Page-A64-
Genericrules
−15 −10 −5 0 5 10 15−10
−5
0
5
10
<-- Wind from port side (m/s).....wind from stern side (m/s) −−>
devi
a�on
from
ave
rage
trac
k (m
)
−15 −10 −5 0 5 10 15−4
−2
0
2
4
6
<-- Wind from port side (m/s).....wind from stern side (m/s) −−>de
via�
on fr
om a
vera
ge s
peed
(m/s
) y (x) = 1.08 - 0.56 * x y (x) = 0.41 - 0.25 * x
−15 −10 −5 0 5 10 15−14
−12
−10
−8
−6
−4
−2
0
2
p<-- Wind from port side (m/s).....wind from starboard side (m/s) −−>
devi
a�on
from
ave
rage
trac
k (m
)
y (x) = -4.81 + 0.14 * x
Figure G.9 Influence of cross winds in the Beerkanaal on the average path (left) and speed (right).
Figure G.10 Influence of parallel winds in the Beer-kanaal on the average path.
![Page 177: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/177.jpg)
Page-A65-
An analysis of vessel behaviour based on AIS data
j
G.2.2 Current influence
−15 −10 −5 0 5 10 15−16
−14
−12
−10
−8
−6
−4
−2
0
2
4
devi
a�on
from
ave
rage
spe
ed (m
/s)
<-- Wind from port side (m/s)......wind from starboard side (m/s) −−>
−15 −10 −5 0 5 10 15−6
−4
−2
0
2
4
6
8
<-- Wind from port side (m/s)......wind from starboard side (m/s) −−>
devi
a�on
from
ave
rage
spe
ed (m
/s)
y (x) = 1.01 - 0.43 * x
y (x) = 2.03 + 0.10 * x -0.069*x^2
Figure G.11 Influence of parallel winds in the Beerkanaal on the average speed, for incoming (left) and outgoing (right) vessels.
−1.4−1.2 −1−0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4−30
−20
−10
0
10
20
<−− current from port side(m/s).......current from starboard side(m/s) −−>
devi
a�on
from
ave
rage
trac
k (m
))
−1.2 −0.8 −0.4 0 0.4 0.8 1.2−12
−10
−8
−6
−4
−2
0
2
4
devi
a�on
from
ave
rage
spe
ed (%
)
<−− current from port side(m/s).......current from starboard side(m/s) −−>
y (x) = -8.87 - 23.4 * x
y (x) = 0.34 +1.47* x-5.35*x^2
Figure G.12 Influence of cross current in part 1 on the vessel path (left) and vessel speed (right)
![Page 178: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/178.jpg)
Page-A66-
Genericrules
Appendix H
−1.4−1.2 −1−0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4−40
−20
0
20
40
60
devi
a�on
from
ave
rage
trac
k (m
))
−1.4−1.2 −1−0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4−6
−4
−2
0
2
4
6
<−− current from behind (m/s).......current from front (m/s) −−>de
via�
on fr
om a
vera
ge s
peed
(%)
<−− current from behind (m/s).......current from front (m/s) −−>
y (x) = -11.18 + 38.08 * x y (x) = -0.33 - 3.93 * x
Figure G.13 Influence of parallel current in part 1 on the vessel path (left) and vessel speed (right)
−1.4−1.2 −1−0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4−20
−10
0
10
20
−<-− current from behind (m/s).......current from front (m/s) −−>
devi
a�on
from
ave
rage
trac
k (m
)
−1.4−1.2 −1−0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4−6
−4
−2
0
2
4
6
devi
a�on
from
ave
rage
spe
ed (%
))
<-− current from behind (m/s).......current from front (m/s) −−>
y (x) = 1.41+ 11.53 * x y (x) = -0.52 - 3.98 * x
Figure G.14 Influence of parallel current in part 2 on the vessel path (left) and vessel speed (right)
![Page 179: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/179.jpg)
Page-A67-
An analysis of vessel behaviour based on AIS data
−1.4 −1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4−20
−15
−10
−5
0
5
10
15
<−− current from behind (m/s).......current from front (m/s) −−>
devi
a�on
from
ave
rage
trac
k (m
)
y (x) = -1.88 + 12.08 * x
Figure G.15 Influence of parallel current in part 4 on the vessel path.
![Page 180: Overview of a part of Maasvlakte I, Port of Rotterdam ...](https://reader030.fdocuments.in/reader030/viewer/2022032610/623a1a729f3cfe07fa658d63/html5/thumbnails/180.jpg)