An Internet of Things Approach for Extracting Featured Data Using AIS Database: An Application Based on the Viewpoint of Connected Ships

2017·3.7 MB·

by  Wei He

SS
symmetry
Article
An Internet of Things Approach for Extracting
Featured Data Using AIS Database: An Application
Based on the Viewpoint of Connected Ships
WeiHe1,2,3,ZhixiongLi4,5,† ID,RezaMalekian6,* ID,XinglongLiu3,7,*andZhiheDuan8
1 CollegeofMarineSciences,MinjiangUniversity,Fuzhou350108,China;[email protected]
2 TheFujianCollege’sResearchBasedofHumanitiesandSocialScienceforInternetInnovationResearch
Center(MinjiangUniversity),Fuzhou350108,China
3 FujianProvincialKeyLaboratoryofInformationProcessingandIntelligentControl(MinjiangUniversity),
Fuzhou350121,China
4 SchoolofMechatronicEngineering&JiangsuKeyLaboratoryofMineMechanicalandElectricalEquipment,
ChinaUniversityofMining&Technology,Xuzhou221116,China;[email protected]
5 DepartmentofMechanicalEngineering,IowaStateUniversity,Ames,IA50010,USA
6 DepartmentofElectrical,Electronic&ComputerEngineering,UniversityofPretoria,Pretoria0002,
SouthAfrica
7 DepartmentofPhysicsandElectronicInformationEngineering,MinjiangUniversity,Fuzhou350108,China
8 SchoolofMechanicalEngineering,Xi’anJiaotongUniversity,Xi’an710001,China;[email protected]
* Correspondence:[email protected](R.M.);[email protected](X.L.);
Tel.:[phone](R.M.);[phone](X.L.)
† Currentaddress:Fuzhou350108,China.
Received:19July2017;Accepted:28August2017;Published:7September2017
Abstract: Automatic Identification System (AIS), as a major data source of navigational data, is
widelyusedintheapplicationofconnectedshipsforthepurposeofimplementingmaritimesituation
awarenessandevaluatingmaritimetransportation. EfficientlyextractingfeatureddatafromAIS
databaseisalwaysachallengeandtime-consumingworkformaritimeadministratorsandresearchers.
Inthispaper,anovelapproachwasproposedtoextractmassivefeatureddatafromtheAISdatabase.
An Evidential Reasoning rule based methodology was proposed to simulate the procedure of
extractingroutesfromAISdatabaseartificially. First,thefrequencydistributionsofshipdynamic
attributes,suchasthemeanandvarianceofSpeedoverGround,CourseoverGround,areobtained,
respectively, according to the verified AIS data samples. Subsequently, the correlations between
the attributes and belief degrees of the categories are established based on likelihood modeling.
Inthiscase,theattributeswerecharacterizedintoseveralpiecesofevidence,andtheevidencecan
becombinedwiththeEvidentialReasoningrule. Inaddition,theweightcoefficientsweretrained
in a nonlinear optimization model to extract the AIS data more accurately. A real life case study
wasconductedatanintersectionwaterway,YangtzeRiver,Wuhan,China. Theresultsshowthatthe
proposedmethodologyisabletoextractdataveryprecisely.
Keywords: AutomaticIdentificationSystem(AIS);EvidentialReasoningrule;likelihoodmodeling;
beliefdistribution;non-linearoptimization
1. Introduction
TheAutomaticIdentificationSystem(AIS)isabroadcast-stylecommunicationsystemdeveloped
for exchanging navigational data automatically and autonomously. It was originally designed
for ship collision avoidance and maritime regulatory, and now it is gradually being used as an
importantconnected-shiptechniquebyshipownerstomonitortheshiplocationandcargos. TheAIS
Symmetry2017,9,186;doi:10.3390/sym9090186 www.mdpi.com/journal/symmetry
Symmetry2017,9,186 2of15
communicationnetworkcanbeseparatedintotwoparts,theshipborneAISstationandtheshore
station. TheshipborneAISstationsbroadcastshiprelatedstaticanddynamicinformationonVery
HighFrequency(VHF)bandatregularfrequencyaccordingtotheInternationalTelecommunication
Union (ITU) specification. The static information, which is manually entered or updated, mainly
include identifier, call sign, ship name, dimensions, type, etc. The dynamic information, which is
fromtheGlobalNavigationSatelliteSystem(GNSS),includestimestamp,SpeedoverGround(SOG),
CourseoverGround(COG),position(presentbylongitudeandlatitude),etc. Theshorestationsare
mainlysetupbyshoreauthorities. WhiletheshipborneAISstationissendingoutmessages,ships
andshorestationsaroundcanreceivethesemessagesanddisplayingthemonElectricalNavigation
Chart(ENC).Therefore,theAISenablesthecommunicationbetweenshipsandshoreauthorities,and
helpthemaritimeadministrators,shipowner,andshippilottodetectthepositionandstateofvessels.
AccordingtothemandatoryrequirementoftheConventionontheSafetyofLifeatSea(SOLAS)
conventionin2002,allshipsof300grosstonnageandupwardsengagedoninternationalvoyages,cargo
shipsof500grosstonnageandupwardsnotengagedoninternationalvoyages,aswellaspassenger
shipsirrespectiveofsizeshallbefittedwithanAIS.Hence,theAISbecameoneofthemostwidelyused
piecesofequipmentonboard. BecausetheAISprovidesabundantshipvoyagerelatedinformation,
itisrecognizedastheprimarydatasourceinmaritimesituationawareness. TheAISdataiswidely
usedinriskanalyses,accidentprevention,motionpatternrecognition,routeprediction,andanomaly
detection,etc.Quetal.[1]introducedtheAISdatabaseintoquantitativelyevaluatingthecollisionrisks
intheSingaporeStrait. Balmatetal.[2]proposedafuzzyapproachtoassessthemaritimeriskatsea
basedonthedecision-makingsystemwiththerealAISdata. Wangetal.[3]exploitedthecontextual
AISdatainacoupledspatial–temporalperspectivemicroscopicanalyticalschemeforatwo-vessel
collisionaccidentinvestigation. Mouetal.[4]madeastatisticalanalysisforcollisioninvolvedshipsby
usingAISdatainRotterdamPorttoinvestigatetheaccurateandactualbehaviorofcollision-involved
ships. Risticetal.[5]extractedmotionpatternsbythestatisticalanalysisoftherealhistoricAISdata,
inordertoconstructthecorrespondingmotionanomalydetectorsofshipsinportsandwaterways.
Pallottaetal.[6]proposedanunsupervisedandincrementallearningapproachtoextractmaritime
movementpatterns,forthepurposeofconvertingrawdatatoinformationsupportingdecisions,such
astrafficrouteextractionandanomalydetection. Inthesepreviousstudies,theextractionofvaliddata
fromtheAISdatabaseisalwaystheprimaryandfundamentalstep. However,theextractionofvalid
dataisalsothemosttime-consumingandlaborioustaskbeforeconductingstudies.
Many researchers gave their solutions on this problem. Demšar et al. [7] introduced a 3D
space-timedensityoftrajectoriestovisualizingthetemporal-spatialdata,andpresentedanapplication
tovessels’trajectoriesacquiredbyAIS.Scheepensetal.[8]proposedamethodthatcanexplorethe
attributesalongtrajectoriesbycalculatingadensityfieldformultiplesubsetsofthedata. Inorder
todiscoversimilargroupsofsub-trajectoriesinthespatialdatabase,Debnathetal.[9]proposeda
frameworktoclustersub-trajectoriesbycombiningtechniquesfromgridbasedapproaches,spatial
geometry, and string processing. Kim et al. [10] developed a maritime traffic gridded database
byprojectingtrafficdataonageographiccoordinatesystem. However, ingeneral, thegrid-based
methods for extracting AIS data need a prior definition on optimal grid size, which is difficult to
get. To solve this problem, Arguedas et al. [11] proposed an algorithm to automatically produce
hierarchical graph-based representations of maritime shipping lanes extrapolated from historical
AISdata,butthegrid-basedmethodbecameinefficientasthescaleexpands. Theimprovementof
grid-basedmethodsondataclassificationandextractionisthevector-basedmethods. Inthisaspect,
Gerbenetal.[12]appliedapiecewiselinearsegmentationmethodtocompressthetrajectoriesobtained
fromAISdata. Zhangetal.[13]usetheDouglas-Peucker(DP)algorithmtosimplifyAIStrajectoriesby
extractingthecharacteristicpoints. Comparedwiththegrid-basedmethod,thecomputationalburden
ofthevector-basedmethoddecreasedalotindeed. However,thesemethodsdidn’tfullyutilizethe
contentsoftheAISdata,suchastheSOG,COG,etc. Xiaoetal.[14]proposedastatisticalapproach
toextractingshiptrafficbehaviorswithAISdata,includingspatialdistribution,speeddistribution,
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coursedistribution,averagespeed,andtrafficdensity,theresearchcontributedalotfordataextraction
fromtheAISdatabase. Liuetal.[15]providesasolutionforextractinganomalymovementinthe
maritime traffic domain based on the clustering, in the study, the position, SOG, and COG were
utilizedinextractingAISdataintandem,i.e.,theroleofposition,SOG,andCOGinAISdatapoint
areunrelated.
In daily administration, maritime administrators are capable of extracting featured AIS data
accordingtotheirexperienceondynamicattributesofthevessels,suchasSOG,COG,andposition.
However, it is impossible and inefficient to extract the massive AIS data timely by manual labor.
Referringtotheprocedureofvesselclassificationofmaritimeadministrators,itisfeasibletosimulate
theexperiencesofadministratorsbasedonartificialintelligencethatshouldbeabletomakeconjunctive
inferencewiththeSOG,COG,andposition. Focusedontheextractionofvesseltargetsinradarimages,
Maetal.[16]giventhesimilarcognitionofbuildinganartificialintelligencebaseonBayesianNetwork.
Therefore,buildinganartificialintelligenceforextractingfeaturedAISdataisatypicalprobabilistic
inferenceissueappliedinvessels’spatial-temporaldata. Basedontheaboveanalysis,aprobabilistic
methodologywasproposedtoclassifyshipswithAISdynamicinformation. Theposition,SOG,and
COGaretreatedaspiecesofevidencetomakethefinaldecisioninacooperativeway. However,in
contrasttotheSOGandCOG,thepositionishardtobeconvertedintopiecesofevidence.Nevertheless,
astheshipsailinginthewaterway,theSOGandCOGofthevesselswouldbefeatured.Inconsideration
ofthetwofactors,thetrajectoryevidencewasdiscardedandtheAISdatawiththeSOGandCOG
evidencewasextracted. Inthiscase,thecomputationalburdenoftheAISdatawillbedecreasegreatly.
Thescopeofthisstudyistoproposeanartificialintelligenceforextractingfeatureddatafromthe
AISdatabase. Thepaperisorganizedasfollows: Section2givestheproposedapproachforextracting
featuredAISdatawithvalidatesamples. Section3deliversanapplicationoftheproposedapproach,
whichlocatedintheWuhanwaterway,middlestreamoftheYangtzeRiver. Finally,Section4contains
theconclusionsofthisproposal.
2. AProposedApproach
Asmentionedabove,thispaperisdedicatedtointroducingtheartificialintelligenceofmaritime
administratorsintoextractingfeaturedAISdata. Themaritimeadministratorsmaketheirinferences
onfeatureddataaccordingtotheirexperience,whichcomesfromthedailyobservationofmassive
vessels. Theartificialintelligenceistypicallyakindofprobabilisticinference[16].
BayesianInferenceisoneofthemostclassicalmethodologiesintheprobabilisticinferencedomain,
anditiscapableofhandlingthenoisedataofmovingtargets[16]. However,thelimitationofBayesian
Inference is that it requires the frame of discernment being mutually exclusive and independent.
Dempster-Shafer (DS) theory is considered as an improvement of Bayes Inference, it is able to
makerigorousprobabilisticinference,whichconstitutesaconjunctiveprobabilisticprocess[17,18].
ThereliabilitiesofevidencesinDStheoryareconsideredtobefullyreliable. Hence,DStheorycannot
combinetwopiecesofevidenceincompleteconflict[19]. Toaddressthisproblem,Dezertetal.[20,21]
developed the Dezert-Smarandache Theory (DSmT) by introducing coefficient of reliabilities and
weights,andmakestheDSmTcapableofcombiningpiecesofevidenceincompleteconflictionby
redistributingtheconflictsofevidences. However,DSmTneitherkeepstheconsistencieswiththe
Bayesianrule,norisacknowledgedasrigorousreasoning[22]. OriginatedfromtheDempster’sand
Bayesianrule,Yangetal.[22]developedtheEvidentialReasoning(ER)ruleinwhichthecoefficients
ofweightandreliabilityareinheritedfromDSmT,andtheirdiscountingmethodaremodified,hence
there is no more deficiency in the inference process, meanwhile keeping the consistency with the
Bayesianrule. Moreover,comparedwiththeconventionalBayesianinference,theERruledoesnot
need the prior probability of patterns or states, because it constitutes a likelihood modelling [23].
Therefore, the ER rule provides a rigorous way to build the artificial intelligence of experienced
maritimeadministrators. Inthissection,thedetailsonintroducingtheERruleintoextractingfeatured
AISdatawillbepresent. Theprocessingflowoftheapproachisdepictedwithfoursteps,including
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featureextracting,likelihoodmodeling,conjunctiveinference,andnonlinearoptimizationonweights,
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i=1 i
Table1.Attributevaluesforverifiedsampleinthehypotheses.
Table 1. Attribute values for verified sample in the hypotheses.
VerifiedSampleAttributeDistributionValue
ClassCifilcaastsiiofnication Verified Sample Attribute Distribution Value ToTtaolta l
ValueV1 alue 1. .. … VaVluaeliue i ..…. VVaalluuee LL
ClassC(1l)ass (1) y11 y1 ... … y1i y1 ..…. yy11L Q1Q=1=∑LiL=y11y 1i
Class(2) y2 1 ... y2 i ... yL2 Q2 =∑i=1L i y2
1 i L i=1 i
... Class (2) ... y12 ... … ... yi2 ...… y...L2 Q2 =iL...=1yi2
Class(j)… yj … ... … yj… .….. …yj Q…j =∑L yj
1 i L i=1 i
... Class (j) ... y1j ... … ... yij ...… y...Lj Qj =iL...=1yij
Class(m…) ym … ... … ym… .….. …ym Qm…=∑L ym
1 i L i=1 i
Class (m) ym … ym … ym Qm =L ym
1 i L i=1 i
Similarly,thefrequencydistributionofvarianceofSOG,meanofCOG,andvarianceofCOGfor
thedatasamplescanalsobepresentedlikeTable1.
Similarly, the frequency distribution of variance of SOG, mean of COG, and variance of COG
for the data samples can also be presented like Table 1.
2.2. Step2: LikelihoodModelling
2.2. SAtefpte 2r: aLciqkeuliihrionogd Mthoedferleliqnuge ncydistributionsofshipmotionattributesdemonstratedpresentin
Table1,thesecharacterizeddistributionsshouldthenbetransferredtosupportdegreesofthecategories.
After acquiring the frequency distributions of ship motion attributes demonstrated present in
Thatistosay,themappingfunctionsbetweensupportdegreesandstatisticaldistributionsshouldbe
Table 1, these characterized distributions should then be transferred to support degrees of the
foundout.
categories. That is to say, the mapping functions between support degrees and statistical
distributions should be found out.
{ }
The concepts description of DS theory is introduced as follows. Suppose Θ= θ,θ,,θ is a
1 2 m
set of mutually exclusive and collectively exhaustive propositions. Where θ，θ，，θ denote to
1 2 m
Symmetry2017,9,186 5of15
TheconceptsdescriptionofDStheoryisintroducedasfollows. SupposeΘ = {θ ,θ ,··· ,θ }isa
1 2 m
setofmutuallyexclusiveandcollectivelyexhaustivepropositions. Whereθ ,θ ,··· ,θ denotetothe
1 2 m
categories,respectively. Letφrepresenttheemptyset. Then,Θisreferredtoasaframeofdiscernment.
ThepowersetofΘconsistsof2m subsetsofΘ,isdenotedbyP(Θ). Differentfromtheconventional
probabilisticinferencemethods,abeliefdegreeoraprobabilitymightbealsoassignedtothepower
setP(Θ)intheERrulewhenthereisareliabilityprobleminevidence[22].
ABasicProbabilityAssignment(bpa)isafunctionp: 2Θ → [0,1] thatsatisfies,
∑
p(φ) =0, θ⊆Θp(θ) =1 (1)
wherethebasicprobability p(θ)isassignedexactlytoapropositionφandnottoanysmallersubset
of φ. p(θ) is generated from the frequency distributions. Referring to the research conducted by
Yangetal.[23],thelikelihoodsbasedonthefrequencydistributionscanbepresentedasfollows.
Thecoreoflikelihoodmodelingistofindtheprobabilisticrelationshipsbetweenthevaluesof
afrequencydistributionandtheclassification(i.e.,Class1,Class2,... ,Classm)ofaAISdatacell.
ThelikelihoodtransformationapproachestablishedbyYangetal.[23]underpinsanewlikelihood
modelingmethodforclassifyingvessels,whichisdescribedasfollows.
BasedonthefrequencydistributionsgiveninTable1,thelikelihoodthatanattributeisequalto
valueiforaclassjiscalculatedinEquation(2).
cj = yj/Qj i =1,2,··· ,L,j =0,1,··· ,m (2)
i i
j
wherec denotesthelikelihoodtowhichattributedistributionisexpectedtobeequaltovalueiin
i
classj.
j
Letp denotetheprobabilitythatanattributewithvalueipointstoclassj,whichisindependentof
i
j
thepriordistributionoftheclassification. p isthenacquiredasnormalizedlikelihoodasfollows[23].
i
pj = cj/∑m ck i =1,2,··· ,L,j =1,2,··· ,m (3)
i i k=1 i
Beliefdistributions,givenbyEquation(3)representtheprobabilisticrelationshipsbetweenthe
motion attributes and its classification. Note that a belief distribution reduces to a conventional
probability distribution when p0 is equal to zero, or there is no ambiguity about the classification.
i
Followingtheaboveprocedure,anattributevaluecanbemappedtoabeliefdistribution,whichis
regardedasapieceofevidence.
2.3. Step3: ConjunctiveInference
Subsequently,theERruleisusedtoprocessthesepiecesofevidence,anditalsotakesthereliability
andweightofevidenceintoconsiderations. Apieceofevidencee isrepresentedasarandomsetand
i
profiledbyaBeliefDistribution(BD)asfollows:
ei = (cid:8)(θ,pθ,i),∀θ ⊆ Θ,∑θ⊆Θpθ,i =1(cid:9) (4)
where (θ,p ) is an element of evidence e, representing that the evidence points to proposition θ,
θ,i i
whichcanbeanysubsetofΘoranyelementofP(Θ)exceptfortheemptyset,tothedegreeof p ,
θ,i
referredtoasprobabilityordegreeofbeliefingeneral. (θ,p )isreferredtoasafocalelementofe,if
θ,i i
p > 0. Inthisoccasion, p isexactlycomingfromtheprobabilitiesobtainedfromthequantified
θ,i θ,i
characterizeddistributionsofdifferentclassification,givenbyEquations(2)and(3).
In addition, the reliability is associated with evidence e, denoted by r, which represents the
i i
abilityoftheevidence,wheree isgenerated,toprovideacorrectassessmentorsolutionforagiven
i
problem[21]. Thereliabilityofapieceofevidenceistheinherentpropertyoftheevidence,andinthe
ERframeworkitmeasuresthedegreeofsupportfor,oroppositionto,apropositiongiventhatthe
Symmetry2017,9,186 6of15
evidencepointstotheproposition. Inotherwords,theunreliabilityofapieceofevidencesetsabound
withinwhichanotherpieceofevidencecanplayaroleinsupportfor,andoppositionagainst,different
propositions. On the other hand, evidence e can also be associated with a weight, denoted by w.
i i
Theweightofapieceofevidencesharesthesamedefinitionasthatofitsreliability[22].Whendifferent
pieces of evidence are acquired from different sources, or measured in different ways, the weight
of evidence can be used to reflect its relative importance in comparison with other evidence and
determinedaccordingtowhousestheevidence.
Tocombineapieceofevidencewithanotherpieceofevidence,itisnecessarytotakeintoaccount
threeelementsoftheevidence;itsbeliefdistribution(probability),reliability,andweight. IntheER
rule,thisisachievedbydefiningaso-calledweightbeliefdistributionwithreliabilityasfollows:
(cid:110) (cid:16) (cid:17)(cid:111)
mi = (θ,m(cid:101)θ,i),∀θ ⊆ Θ; P(Θ),m(cid:101)P(Θ),i (5)
wherem measuresthedegreeofsupportforθfrome withboththeweightandreliabilityofe taken
(cid:101)θ,i i i
intoaccount,definedasfollows:

0 θ = φ
m(cid:101)θ,i = crw,imθ,i θ ⊆ Θ,θ (cid:54)= φ (6)
c (1−r ) θ = P(Θ)
rw,i i
c =1/(1+w −r ) (7)
rw,i i i
wherec denotesanormalizationfactor,w denotesforweight,andr denotesreliability. m isthe
rw,i i i θ,i
degreeofsupportforpropositionθfromevidencei,whichisgivenbym = w p ,with p beingthe
θ,i i θ,i θ,i
degreeofbeliefthatevidenceipointstoθ. Asdescribedpreviously, p canbeobtainedusingTable1,
θ,i
Equations(2)and(3)P(Θ)isthepowersetoftheframeofdiscernmentΘthatcontainsallmutually
exclusive hypotheses in question. It is worth mentioning that P(Θ) is treated as an independent
elementintheERrule[22].
Ifeverypieceofevidenceisfullyreliable,e.g.,r =1foranyi,theERrulereducestoDempster’s
i
rule. EvidencesgivenbyAISarenotfullyreliable,sor <1. Thecombinationoftwopiecesofevidence
i
e ande (definedinEquation(4))willbeconductedasfollows:
1 2

0 θ ⊆ φ
pθ,e(2) = ∑D⊆mˆΘθ,meˆ(2D),e(2) θ ⊆ Θ (8)
mˆθ,e(2) = [(1−r2)mθ,1+(1−r1)mθ,2]+∑B∩C=θmB,1mC,2∀θ ⊆ Θ (9)
wherem ,m ,m andm aregivenbyEquations(5)–(7);B,CandDdenoteanyelementsinthe
θ,1 θ,2 B,1 C,2
powersetP(Θ)exceptfortheemptyset;the p isthesyntheticbeliefdistributiontoproposition
θ,e(2)
θ whentakingthetwopiecesofevidencee ande intoconsideration. Yangetal.[23]provedthat
1 2
the belief distribution here is equivalent to the probability in Bayesian rule if belief is assigned to
singletonstatesonlyand pθ iscalculatedbyEquation(4). Therefore,theERrulecanbeusedtoobtain
i
theprobabilityofanAISdatacellindicatestowhichclassification,byusingthemeanandvarianceof
SOG,COGextractedfromtheAISdata,respectively.
2.4. Step4: NonlinearOptimization
Weightcoefficientsweretrainedthroughanon-linearoptimization,withverifiedsamplestogeta
higheraccuracyofclassification. Asdiscussed,inEquations(6)and(7),thereliabilityandweightof
evidenceareparametersusedtomeasureevidencequality. InStep2,theevidencefromnormalized
likelihoodswasgeneratedindependentlyofthepriordistributionofhypothesesbyassumingthat
eachsetofsampledataisfullyreliable.
Symmetry2017,9,186 7of15
In practice, the data provided by AIS is not completely reliable. Hence the evidences are
not completely reliable either. As mentioned above, a weight of a piece of evidence is a relative
importance which determined by whom is making the inference. In practice, such importance is
exactlyrelatedtoaverifiedsampleandacertainoptimizationobjective[23]. Toagroupofverified
samples,appropriateweightsofevidenceshouldmakethefinalresultmorelikelytoachieveasetting
objective. Hence, appropriateweightcoefficientscanbeobtainedonlyifanobjectiveandverified
samplesaredetermined.
A typical objective is set to minimize a global deviation. All of the classification results were
comparedwiththereality,theaimofoptimizingtheweightcoefficientisthat,foracertainnumberof
validatedsamples,thenumberofincorrectclassificationdividethenumberofvalidatesamples,i.e.,the
errorrate,isminimized. Infact,theglobaldeviationinquestiongenerallyincludestheclassification
onobject. Thus,asignfunctionisoftenusedtodetermineadiscretestate(usuallytrueoffalse)of
objectbasedontheirbeliefdistributions(probability)tocorrespondinghypotheses. However,thesign
functionisverydifficulttobemodeledinrelatedalgorithms[24]. Hence,inthisresearch,theweight
coefficientcanbesolvedinacompromisedwayasfollows.
Let S betheverifiedsamplesindicatetovesselsbelongtoclassj, wherej=1,2, ... , m. And
j
N isthenumberofsamplesforclassj. LetSk denotesthesamplekinclassj,wherek=1,2,... ,N.
j j j
(cid:16) (cid:17) (cid:16) (cid:17)
p Sk,wT denotestheprobabilitytopropositionθ ,whereθ indicatestotheclassj. p Sk,wT
θj,e j j j θj,e j
isobtainedbytheconjunctivereasoningprocessusingtheERrule. Thus,foreachjudgmentonthe
(cid:16) (cid:17) (cid:16) (cid:17)
sampleSk,thedeviationcanbepresentsas1− p Sk,wT . Alloftheprobability p Sk,wT share
j θj,e j θj,e j
thesameweightvectorwT={w ,w ,w ,w },whichdenotestheweightcoefficientsofmeanofSOG,
1 2 3 4
varianceofSOG,meanofCOG,varianceofCOG,respectively. Hence,theglobalaccuracyorsumof
inferredprobabilitiesthathavebeenassignedtothecorrectpropositionsispresentedas,
φ(cid:16)wT(cid:17) = ∑m ∑Nj (cid:104)1−p (cid:16)Sk,wT(cid:17)(cid:105) (10)
j=1 k=1 θj,e j
Tominimizethedeviation,wTshouldmakeEquation(10)minimum. Therefore,theoptimization
formulationcanbepresentedas,
(cid:16) (cid:17)
wT =argmin φ wT (11)
wT:feasible
Asdiscussed,withoutasignfunction,thisoptimizationcanonlyprovideacompromisedsolution
toweights. SinceEquation(10)iscontinuousandderivable, Equation(11)canbesolvedwiththe
‘fmincon’functionofMATLAB.Withthisprocedure,moreappropriateweightsofpiecesofevidence
canbesolved. Actually,theweightsofpiecesofevidencecanalsobesetthroughoptimizingother
objectives, depending on the requirements, for example, to achieve a higher accuracy of class 1.
Otheroptimizationobjectiveswillbediscussedinthefollowingcasestudy.
3. ACaseStudy
Tovalidatetheproposedmethodology,acasestudywasconductedatWuhanwaterway,located
atmiddlestreamofYangtzeRiver,China. Forthepurposeoffollowingthenavigationalrulesand
fuelprudent,captainstendtomaneuvertheirvesselswithafixedpatternwhichmaketheSOGand
COGofvesselsindifferentroutescharacterized. ThecharacteristicSOGandCOGcouldbequantified
bystatisticalanalysisofdynamicAISinformation. Takethemarinetrafficsceneattheintersection
waterwayinWuhan,China,forexample. AsshowninFigure2,therearesixdirectionsofthetraffic
flowattheintersectionwaterway,whicharelabeledbynumber1to6. Forvesselsindirections4and
6,thevesselswillkeepthespeedanddirectionsteadywhentheygothroughthechannelofYangtze
River,hencethevarianceofSOGandCOGwouldbesmall,andthemeanoftheCOGwouldbesimilar
tothedirectionofchannel,whatismore,fortherushofcurrent,themeanofSOGindirection4willbe
Symmetry 2017, 9, 186 8 of 15
of the traffic flow at the intersection waterway, which are labeled by number 1 to 6. For vessels in
Symmetry2017,9,186 8of15
directions 4 and 6, the vessels will keep the speed and direction steady when they go through the
channel of Yangtze River, hence the variance of SOG and COG would be small, and the mean of the
COG would be similar to the direction of channel, what is more, for the rush of current, the mean of
lowerthanthatindirection6. Forvesselsindirection1,i.e.,voyagingdownstreamfromHanRiverto
SOG in direction 4 will be lower than that in direction 6. For vessels in direction 1, i.e., voyaging
YangtzeRiver,fortherushofcurrentandturningdirection,themeanofSOGshouldbehigherthan
downstream from Han River to Yangtze River, for the rush of current and turning direction, the
vesselsindirection3,andthevarianceofCOGshouldbelargerthanvesselsindirections4and6.
mean of SOG should be higher than vessels in direction 3, and the variance of COG should be larger
Forvesselsindirection5,i.e.,voyagingfromupstreamofYangtzeRivertotheHanRiver,duetothe
than vessels in directions 4 and 6. For vessels in direction 5, i.e., voyaging from upstream of Yangtze
impaRctivoefr ctou rthreen Ht,atnh Reisvpere,e dduwe toou thlde idmepcraecat soef csuorrthenatt, tthhee svpaereida nwcoeuoldf SdOecGreagseet ssol athrgaet rt,hae nvdartiahnecve aorfi ance
of COSOGGa glseots blaercgoemr, eanldar tgheer v.aSriiamniclea rolfy C,OotGh earlsfoe baetucormese claarngebre. Sfiomuinladrlyfr, oomthetrh feeamtuereasn caann dbev faoruinadn ce of
SOG,frComO Gth,er mesepaenc atinvde vlya.riIanncceo onfs SeOquGe, nCcOeG,b, ryessptaectitsivtieclya.l Iann caolnysseiqsuoefntche,e bfyo sutrataistttirciabl uatneaslyosfist ohfe thvee ssels
indifffoeurre natttrriobuutteess ,otfh theeh videsdseelns imn odtiifofenrepnat trtoeurtnesw, tihlel bheidedxepno mseodti,onan pdatctearnn bweiltl rbaen esxfopromseedd, atnodp ciaenc esof
be transformed to pieces of evidence to make the inference.
evidencetomaketheinference.

(a) (b) (c)

(d) (e) (f)
FigurFeig2u.rTe h2e. Tdhiere dcitrieocntisonosf ovfe vsseesslselisn int htheei nintteerrsseeccttiioonn wwaateterwrwaya,y W,Wuhuahna, nC,hCinhai.n Tah.eT bhlaecbk llainckesl winieths with
arrows in (a–f) present the directions for vessels in different routes. (a) The direction 1 of vessels go
arrowsin(a–f)presentthedirectionsforvesselsindifferentroutes. (a)Thedirection1ofvessels
downstream from Han River to lower reaches of Yangtze River; (b) The direction 2 of vessels go
go downstream from Han River to lower reaches of Yangtze River; (b) The direction 2 of vessels
downstream from Han River to upper reaches of Yangtze River; (c) The direction 3 of vessels go
godownstreamfromHanRivertoupperreachesofYangtzeRiver;(c)Thedirection3ofvesselsgo
upstream from Yangtze River to Han River; (d) The direction 4 of vessels go upstream of Yangtze
upstreamfromYangtzeRivertoHanRiver;(d)Thedirection4ofvesselsgoupstreamofYangtzeRiver,
River, (e) The direction 5 of vessels go downstream from Yangtze River to Han River; (f) The
(e)Thedirection5ofvesselsgodownstreamfromYangtzeRivertoHanRiver;(f)Thedirection6of
direction 6 of vessels go downstream of Yangtze River.
vesselsgodownstreamofYangtzeRiver.
The verified samples were acquired from Wuhan Maritime Administrator from 1 January 2014
to 31 August 2016. The samples from 1 January 2014 to 31 May 2014 (including 5486 verified
TheverifiedsampleswereacquiredfromWuhanMaritimeAdministratorfrom1January2014to
samples) were applied to obtain the frequency distributions for the four attributes. The samples from
31August2016. Thesamplesfrom1January2014to31May2014(including5486verifiedsamples)
1 June 2014 to 31 October 2014 (including 3015 verified samples) were used to train the weight
wereappliedtoobtainthefrequencydistributionsforthefourattributes. Thesamplesfrom1June
coefficient of evidence. The samples from 1 November 2015 to 31 August 2016 (including 17,723
2014to31October2014(including3015verifiedsamples)wereusedtotraintheweightcoefficientof
samples in total) were invited to validate the accuracy of methodology proposed in Section 2.
evidence. Thesamplesfrom1November2015to31August2016(including17,723samplesintotal)
were3i.n1v. Sitteepd 1t:o Svtaatlisidticaatle Athnaelyascisc uofr tahcey Aottfrmibuettehs ofrdooml oVgeryifipedro ApIoSs Dedatain Section2.
In order to extract the frequency distributions from historical AIS data, 220 samples for
3.1. Step1: StatisticalAnalysisoftheAttributesfromVerifiedAISData
direction 1, 117 samples for direction 2, 244 samples for direction 3, 2260 samples for direction 4, 108
Isnamorpdleesr ftoor edxirteractcitotnh 5e, farnedq u25e3n7c ysadmisptlreisb fuotri odnirsefcrtoiomn 6h, iwsteorrei csaelleActIeSdd aantda ,a2n2a0lyszaemd.p lesfordirection1,
117sa mplesfordirection2,244samplesfordirection3,2260samplesfordirection4,108samplesfor
direction5,and2537samplesfordirection6,wereselectedandanalyzed.
• Attribute1: MeanofSOG
WhentheaccuracyofmeanofSOGwassetto0.1,thefrequencydistributionsofmeanofSOGfor
sixdirectionsareshowninFigure3.
Symmetry 2017, 9, 186 9 of 15
Symmetry 2017, 9, 186 9 of 15
•• AAttttrriibbuuttee 11:: MMeeaann ooff SSOOGG
SymmeWWtryhh2ee0n1n7 t,th9h,ee1 8aa6ccccuurraaccyy ooff mmeeaann ooff SSOOGG wwaass sseett ttoo 00..11,, tthhee ffrreeqquueennccyy ddiissttrriibbuuttiioonnss ooff mmeeaann ooff 9 SSoOOf1GG5
for six directions are shown in Figure 3.
for six directions are shown in Figure 3.

((aa)) ((bb)) ((cc))

((dd)) ((ee)) ((ff))
FFFiiiggguuurrreee 33.3..F rFFerrqeeuqqeuuneecnnyccydy isddtirisisbttrruiibtbiuuotntiiosonnosfs moofef ammneoeaafnnS OooGff fSSoOOrGGve sffsooerrl svvienesssdseeifllsfse riiennn tdddiififfrfeeercreteinnottn sdd.iir(raee)cctTtiiohonenssf.r. e((qaau)) eTnThchyee
dfrisetqruibeuntciyo ndisotfrivbeustsioenls oifn vedsisreelcst iionn di1r;ec(tbio)nT 1h; e(bf)r eTqhuee fnrecyqudenisctyri bduisttiroinbuotifonv eosfs velesssienls dinir edcitrieocntio2n;
frequency distribution of vessels in direction 1; (b) The frequency distribution of vessels in direction
(2c;) (Tc)h Tehfere fqreuqeunecnycdy idstirsitbriubtuiotinono fofv vesesseselslsi nin ddiirreeccttiioonn 33;; ((dd)) TThhee frfreeqquueennccyy ddisitsrtirbiubutitoino nofo vfevsesesslse lisn
2; (c) The frequency distribution of vessels in direction 3; (d) The frequency distribution of vessels in
idnirdeicreticotnio n4; 4(;e()e T)hTeh efrferqeuqeunecnyc yddisitsrtirbibuutitoionn oof fvveesssseelsls inin ddiirreeccttiioonn 55;; ((ff)) TThhee ffrreeqquueennccyy ddiissttrriibbuuttiioonn ooff
direction 4; (e) The frequency distribution of vessels in direction 5; (f) The frequency distribution of
vveesssseellss iinn ddiirreeccttiioonn6 6..
vessels in direction 6.
••• AAAtttrttitrbriiubbtuuette2e : 22V:: VaVraairariniaacnnecceoe f ooSff O SSOGOGG
The frequency distribution of variance of SOG is shown in Figure 4, where the accuracy of
TThhee ffrreeqquueennccyyd idsitsrtirbiubtuiotinono fovfa rviaanricaenocfe SoOf GSOisGsh oisw snhionwFnig iunr eF4ig,wurhee r4e, twhehaecrceu trhaec yaocfcuvraarciayn coef
variance of SOG was set to 0.2.
ovfarSiOanGcew oafs SsOetGto w0a.2s .set to 0.2.

((aa)) ((bb)) ((cc))

Figure4.Cont.
Symmetry2017,9,186 10of15
Symmetry 2017, 9, 186 10 of 15
Symmetry 2017, 9, 186 10 of 15

(d) (e) (f)
(d) (e) (f)
Figure 4. Frequency distribution of variance of SOG for vessels in different directions. (a) The
FFiigguurree 44..F Frerqeuqeunecnycyd isdtirsitbruibtiuotnioonf voafr ivaanrcieanofceS OoGf fSoOrGve sfsoerl sviensdseiflfse rienn tddififreercetinotn sd.ir(ae)ctTiohnesf.r e(qau) eTnhcye
frequency distribution of vessels in direction 1; (b) The frequency distribution of vessels in direction
dfriesqtruibenuctiyo ndisotfribvuetsisoenls ofi nvedsisreelcst iino ndi1re;c(tibo)n T1h; e(bf) rTeqhue efnrecqyuednisctyr idbiusttiroibnutoifonv eosf sveelssseinls dinir decirteiocntio2n;
(22c;;) ((ccT))h TTehhfeer effrrqeeuqqeuuneecnnyccyyd iddsiitssrttirrbiiubbutuittoiinoonno oofffv vveeesssssseeellslss iiinnn dddiiirrreeeccctttiiiooonnn 333;;; (((ddd))) TTThhheee ffrrfeerqqequuueennecncyyc yddiidssttisrriitbbriuubttuiiootinno nooff ovvfeessvsseeesllssse iilnns
idnirdeicrteicotnio 4n; 4(e;)( eT)hTeh ferefrqeuqeunecnyc ydidsitsrtibriubtuiotino nofo fvevsesseslesl sinin ddirierecctitoionn 55; ;((ff)) TThhee ffrreeqquueennccyy ddiissttrriibbuuttiioonn ooff
direction 4; (e) The frequency distribution of vessels in direction 5; (f) The frequency distribution of
vveesssseellss iinn ddiirreeccttiioonn 66..
vessels in direction 6.
• Attribute 3: Mean of COG
•• AAtttrtirbiubtuete3 :3M: Meaenano foCf COOGG
The frequency distribution of mean of COG is shown in Figure 5, where the accuracy of the
TThhee ffrreeqquueennccyyd disitsrtirbibuutitoionno fomf meaenanof oCf OCGOiGs sihs oswhnowinnF iing uFrieg5u,rwe h5,e rwehtheerea cthcue raacccyuorfatchye omf etahne
mean of COG was set to 6.
omfeCaOn Gof wCaOsGse wttaos 6s.et to 6.

(a) (b) (c)
(a) (b) (c)

(d) (e) (f)
(d) (e) (f)
Figure 5. Frequency distribution of mean of COG for vessels in different directions. (a) The frequency
Figure 5. Frequency distribution of mean of COG for vessels in different directions. (a) The frequency
Fdiigsturribeu5t.ioFnre oqfu venescsyedlsi sintr idbiurteicotnioonf 1m; e(ban) TohfeC fOreGqufoernvcyes dseislstriinbudtiifofenr eonf tvdeisrseecltsi oinn sd.i(rae)cTtihoen f2re; q(cu)e Tnhcye
distribution of vessels in direction 1; (b) The frequency distribution of vessels in direction 2; (c) The
dfriesqtruibenuctiyo dnisotfribvuetsisoenls ofi nvedsisreelcst iino ndi1re;c(tibo)n T3h; e(df) rTeqhue efnrecqyuednisctyr idbiusttiroibnutoifonv eosf sveelssseinls dinir decirteiocntio2n;
frequency distribution of vessels in direction 3; (d) The frequency distribution of vessels in direction
(c) The frequency distribution of vessels in direction 3; (d) The frequency distribution of vessels
4; (e) The frequency distribution of vessels in direction 5; (f) The frequency distribution of vessels in
4; (e) The frequency distribution of vessels in direction 5; (f) The frequency distribution of vessels in
indirection4;(e)Thefrequencydistributionofvesselsindirection5;(f)Thefrequencydistributionof
direction 6.
direction 6.
vesselsindirection6.
• Attribute 4: Variance of COG
• Attribute 4: Variance of COG
• Attribute4: VarianceofCOG
The frequency distribution of variance of COG is shown in Figure 6, where the accuracy was
The frequency distribution of variance of COG is shown in Figure 6, where the accuracy was
set toT 1h0e0f. requencydistributionofvarianceofCOGisshowninFigure6,wheretheaccuracywasset
set to 100.
to100.