831
1 INTRODUCTION
Wind energy is an environment‐friendly and
sustainable energy. To develop this burgeoning
industry for electrical generation, many countries
have developed large numbers of offshore wind
farms (OWFs) near the coastal area. As a type of
human installation, the OWF leads to a potential
collisionriskwhenvessels
arepassingtheOWFarea,
it is the main issue amongst the OWF impacts to
navigation [1]. Current research works have
presented a general understanding knowledge of
OWF impacts to navigation. For example, several
studies used the vessel Automatic Identification
System database to assess OWFs influence on the
vessel traffic
in the Thames Estuary, the Penghu
waterway and the south coast of Busan [2][3][4].
Accordingtopastresearchworksofvesseltrafficflow
studies, vessels under different categories may
conduct different collision probabilities [5][6][7].
Althoughthereareseveralissueshavebeendiscussed
amountthese researchworks,thelackofa conceptual
framework of evaluating the ship allision risk, the
discussionaboutOWFimpactsoncollision
probabilities under different ship categories and
discussionoftheconsequenceofshipallisionaretoo
general.Thesedrawbackswereraisedwhenapplying
traditionalriskanalysesinOWFsafety studydue to
following reasons, the accident records
for vessel
collided with OWF turbines are rare and hard to
acquire; understanding of allision mechanism of
OWFs still uncompleted [8]. Therefore, this paper
introducesaBayesianNetwork(BN)modeltoanalyse
the vessel collision risk near the OWF area. On the
basisofthefailuremodeandeffectsanalysis(FMEA),
theBNmodelisestablishedtoprovideageneralrisk
An Expert Elicitation Analysis for Vessel Allision Risk
Near the Offshore Wind Farm by Using Fuzzy Rule-
Based Bayesian Network
Q.Yu&K.Liu
WuhanUniversityofTechnology,Wuhan,China
ABSTRACT:Thispaperdevelopsanexpertbasedframeworkforanalysingandsynthesisingtheshipallision
riskneartheoffshorewindfarm(OWF)onthebasisofagenericFuzzyBayesiannetworkandFMEAanalysis.
Thisframeworkisspecificallyintendedtoovercomethedifficultyofusing
traditionalriskassessmentmethods
in OWF allision. Under the introduced framework, subjective belief degrees are assigned to model the
incompletenessencounteredinestablishingtheknowledgebase.Thefuzzytransformationtechnologyisthen
usedtointroducealljudgementsresultsundervarioussituations.Fully,aBayesiannetworkisestablishedto
aggregate all
relevant attributes to the conclusion and to prioritise potential allision risk level of each ship
categories.Aseries ofcasestudiesofdifferent shipcategoriesare studiedto illustratethe applicationof the
proposedframework.Resultsshowthatthefishingvesselandtheservicevesselhaveahigherallisionriskthan
themerchantvesselduetoinsufficientriskdetection.Thecollisionconsequenceofthetankerissignificantly
higherthanothertypesofvessel.Theframeworkfacilitatessubjectiveriskassessmentwhenhistoricalfailure
dataisnotavailableintheirpractice,whichprovidessupporttoOWF‐safeguardinganddecision‐making.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 13
Number 4
December 2019
DOI:10.12716/1001.13.04.16
832
analysis framework. An expert‐based consulting
board is constructed to judge the vessel allision risk
under different categories based on expert`s
knowledge.Toimprovetheaccuracyoftransforming
thebeliefdegreeassignmentsofthevesselallisonrisk
in the vicinity of the OWF. A fuzzy transforming
technologyisusedto
transformtheexpertjudgement
of each attendance attribute into the conditional
probabilities to link the risk factors. The developed
BNmodelisthenimplementedtoprioritisethevessel
allisionriskunderdifferentcategories,whichextend
theunderstandingoftheOWFimpactstonavigation
environment.
The paper is presented as follows: Section 2
introduces the methodology of developing a hybrid
riskmodelbasedonFMEA.Insection3,theproposed
model is implemented to deal with a subjective
database to evaluate the allision risk of different
vessel categories. Section 4 gives a discussion of the
study
resultandconclusionfromthisstudyisdrawn
inSection5.
2 METHODOLOGY
Inthissection,arule‐basedBNmodelonthebasisof
the FMEA is introduced. The FMEA is one of the
earliest risk analysis method, it was widely used in
dealing with the potential risks that
conduct
mechanicalfailuresorengineeringaccidents [9]–[11].
TheriskstructureofFMEAconsistswiththreefactors
that include the probability of accident occurred (L),
theconsequence severity of the accident(C) and the
likelihood ranking of potential risks are detected
beforeithappens(P).Thekernelofthis
approachisto
introduce reliable database and transform the
databaseintotheconclusionbyusingtheriskpriority
number(RPN),thentheL,CandPareaggregatedto
conclude the risk priority of the scenarios. [12][13].
However, when applying the method in the OWF
area, the accuracy and
the reliability of the FMEA
approach is limited due to the insufficient database
bothof accident records or judgements.Therefore, a
fuzzy rule‐based BN and a transforming framework
aredevelopedtohelpexpertstoprovidemoreprecise
judgements and to transf orm the judgements into
marginalprobabilities[14].Thenthe
BNcanbeused
toaggregateallriskfactorsintoconclusion.
2.1 Fuzzymappingand transforming
When applying the expert elicitation, experts may
express their judgement in different ways. This
requiresamethodtointegratethejudgementresults
under various form into a consistent way before
introducing to the risk analysis
model [9]. We used
thefuzzymappingapproachtonormalisetheexpert
judgementandtoaggregatethedata.Onthebasisof
theFMEAapproach,threeriskfactorsofL, CandP
aredescribedusingthelinguisticvariables associated
withtheantecedent attributes. Referto the literature
survey,the
linguistic variables used to estimate L, C
andParedefinedasfollows:theLisdefinedwithfive
linguisticgradesas(L
1=verylow,L2=low,L3=average,
L
4=frequentandL5=veryfrequent);theCisdefinedas
(C
1=negligible, C2=marginal, C3=moderate, C4=critical
and C
5=catastrophic); the P is described as
(P
1=unlikely, P2=reasonable unlikely, L3=likely,
L
4=resealablelikelyandL5=definite)[14].Totransform
the expert judgement into the belief degree of
linguisticterms, the fuzzy mapping functionis used
and the membership function of each linguistic
variables is defined with an equal interval as
L
1=C1=P1=0.1, L2=C2=P2=0.3, L3=C3=P3=0.5 L4=C4=P4=0.7
L
5=C5=P5=0.9. Three examples of transforming the
expertjudgementsunderdifferentformsaregivenas
followings. For the shape of trapezoidal, antecedent
attributes are given with the format of the lowest
possible number lp, the lowest belief number lb, the
highest belief number hb and the highest possible
numberhp,
whichas(lp,lb,hb,hp).
lb
hb
hp
lp
S
1
S
2
S
3
S
4
S
5
r
5
r
2
r
4
r
3
Figure1. Fuzzy mapping for the shape of the trapezoidal
format
The Figure 1 graphically shows the transforming
function for the judgement J = (lp=0.15, lb=0.45,
hb=0.55, hp=0.95) gives by an expert. The J can be
transformed into the fuzzy mapping distribution set
DincludingeachlinguistictermS,andtheD=(S
1=0,
S
2= 0.5, S3= 1,S4= 0.625,S5=0.125).Normalisingthe
D, the belief degree distribution Q of each S is
computedasQ = (0 (S
1),0.22 (S2), 0.44 (S3), 0.28 (S4),
0.06(S
5)).
ap
hp
lp
S
1
S
2
S
3
S
4
S
5
r
5
r
2
r
4
r
3
Figure 2 Fuzzy mapping for the shape of the triangular
format
A judgement used the triangular format can be
transformed as shown in Figure 2. The judgement
expresses with three parameters: the lowest possible
number lp, the average possible number ap and the
highestpossiblenumberhp,showas(lp,ap,hp).Gives
aJ=(lp=0.15,ap=0.45,
hp=0.95),theDiscalculatedas
(S
1=0,S2=0.5,S3=0.9,S4=0.5,S5=0.1)andthentheQ
=(S
1=0,S2=0.25,S3=0.45,S4=0.25,S5=0.05)
833
Figure4BNforthevesselallisionriskinFMEA
S
1
S
2
S
3
S
4
S
5
r
2
r
3
a single deterministic
judgement
Figure3. Fuzzy mapping for the shape of the single
deterministicformat
Accordingtothefuzzymappingfunction,asingle
deterministic judgement can be transformed
according to the mean maximum method. It
graphicallyasFigure3:ifJ=0.45,thenD=Q=(S
1=0,
S
2=0.25,S3=0.75,S4=0,S5=0).
2.2 DevelopmentofrulebasesforBayesianstructuresin
FMEA
IntheFMEA,theallisionriskforvesselneartheOWF
is influenced by three factors as the probability of
allision(L) , consequenceseverity(C)and the chance
ofallisionriskbedetected(P) . TheFMEAbasedBN
structureisshowninFigure4.
TolinkedeachnodeintheBN,theIF‐THENruleis
used to develop the conditional probability table
(CPT) between parent nodes of P, L and C with the
finalnodeofallisionrisk[14].AsetofbeliefrulesBR
h
consistoftheIF‐THENrulewithabeliefstructurethat
applyinginFMEAcanbeexpressedas:
BR
h:IFPiandCjandLk,THENR
h
={(β1
h
,R1),(β2
h
,R2),
(β
3
h
,R3),(β4
h
,R4),(β5
h
,R5)},where(i,j,k=1,2,3,4,5,
h=1,2,…,125).
whereβ
n
h
(n=1,2,3,4,5)isthebeliefdegreetowhich
the R
h
is believed to be the consequence for the hth
rule with the combination of their parent nodes are
stated as P
i, Cj and Lk. To simplify the CPT for the
allision risk, the equivalence principle is used to
construct the rule base set, which is given as
followings:
BR1:IFP1andC1andL1,THENR
1
={(1,R1),(0,R2),(0,R3),
(0,R
4),(0,R5)},
BR
2:IFP1andC1andL2,THENR
2
={(0.67,R1),(0.33,R2), (0,
R
3),(0,R4),(0,R5)},
…
BR
124:IFP5andC5andL4,THENR
2
={(0,R1),(0,R2),(0,R3),
(0.33,R
4),(0.67,R5)},
BR
125:IFP5andC5andL5,THENR
2
={(0,R1),(0,R2),(0,R3),
(0,R
4),(1,R5)},
Theabovesetofrulebaseisestablishedandthen
usedtoconstructtheCPT,whichshowsasTable1.
2.3 Safetylevelprioritisation
Inordertorankthesafetyleveloftheresults,anovel
offunctionsisassignedtocalculatethebeliefdegree
distribution and the preference number
PN of each
stateinL,CandParedefinedwiththerangefrom1
to9.Thepreferencenumberfornodesareassignedas
PN(L
1)=PN(C1)=PN(P5)=9,PN(L2)=PN(C2)=PN(P4)=7,
PN(L
3)= PN(C3)= PN(P3)=5, PN(L4)= PN(C4)= PN(P2)=3
and PN(L
5)= PN(C5)= PN(P1)=1. Then a risk priority
functionisgivenasfollowings:
1551
111 1PN R poor PN L PN C PN P


2442
333 27PN R fair PN L PN C PN P


3333
555 125PN R average PN L PN C PN P

4224
777 343PN R Good PN L PN C PN P
2115
999 729PN R excellent PN L PN C PN P 
834
Table1.ConditionalprobabilitytablewithbeliefstructuresinFMEA
___________________________________________________________________________________________
RulesAntecedentattributesAllisionrisk
_________________________________________________________________________________________
Theprobabilityof ConsequencechanceofallisionPoor Fair Average`Good Excellent
allision(L)severity(C)riskbedetected(P)
___________________________________________________________________________________________
1 VerylowNegligibleUnlikely0.33 0.000 0.00 0.00 0.67
2 VerylowNegligibleReasonablyunlikely 0.00 0.333 0.00 0.00 0.67
3 VerylowNegligiblelikely0.00 0.000 0.33 0.00 0.67
4 VerylowNegligibleReasonablylikely 0.00 0.000 0.00 0.33 0.67
5 VerylowNegligibleDefinite0.00 0.000 0.00 0.00
 1.00
…  ………… …  ………
…  ………… …  ………
121 VeryfrequentCatastrophicUnlikely1.00 0.00 0.00 0.00 0.00
122 VeryfrequentCatastrophicReasonablyunlikely 0.67 0.33 0.00 0.00 0.00
123 VeryfrequentCatastrophiclikely0.67 0.00 0.33 0.00 0.00
124 VeryfrequentCatastrophicReasonablylikely 0.67 0.00 0.00 0.33 0.00
125 VeryfrequentCatastrophicDefinite0.67 0.00 0.00 0.00 0.33
___________________________________________________________________________________________
Table2.Expertjudgementsunderdifferentvesselcategories
__________________________________________________________________________________________
Vesselcategories ExpertsNo. Judgementresults
LCP
___________________________________________________________________________________________
FishingvesselE10.4,0.6,0.8,0.9 0.1,0.15,0.2,0.45 0.2,0.3,0.45,0.55
E20.6,0.7,0.75 0.1,0.2,0.50.2,0.3,0.5
E30.80.50.15
ServicevesselE10.75,0.8,0.85,0.950.25,0.4,0.5,0.55 0.35,0.45,0.65,0.85
E20.8,0.9,10.05,0.2,0.40.25,0.55,0.75
E30.90.150.45
TankerE10,0.05,0.15,0.2 0.65,0.7,0.85,0.95 0.65,0.7,0.85,0.95
E20,0.15,0.20.45,0.8,0.90.5,0.7,0.95
E30.050.950.85
Generalcargovessel E10,0.05,0.15,0.2 0.45,0.6,0.7,0.95 0.6,0.8,0.9,1
E20,0.25,0.30.5,0.75,0.90.7,0.75,0.95
E30.10.60.7
Passengervessel E10.25,0.45,0.5,0.550.65,0.75,0.8,0.95 0.65,0.7,0.85,0.95
E20.05,0.25,0.45 0.55,0.6,0.850.4,0.65,0.7
E30.20.750.55
___________________________________________________________________________________________
and
 
5
1
mm
m
SL R PN R

(1)
wheretheSL meansthe safetylevelindex. Ahigher
safety level means low risk of allision, the opposite
resultmeansahighriskofvesselallision.
3 IMPLICATIONANDDISCUSSION
Theaboveintroducedmethodsareusedtoinvestigate
thevesselallisionriskneartheOWFunderdifferent
categories.
According to the categories given in AIS
records,vesselsagroupedas‘thefishingvessel’,‘the
servicevessel’,‘thetanker’,‘thegeneralcargovessel’
and ‘the passenger vessel’. A group of three experts
from different background are invited to provide a
subjective evaluation of the allision risk of every
vessel type.
To test the transformation technology
introducedinsection2.1,theexpertsareaskedtogive
their judgement under a different format. The
judgementresultsetispresentedasTable2.
By using the fuzzy transformation technology,
judgementresultscanbetransformedintotheCPTfor
L,PandC,
whichgivenasTable3,Table4andTable
5:
Table3.CPTfornodeʹprobabilityofallisionʹ
____________________________________________
StatesofL Vesselcategories
Fishing Service Tanker GeneralPassenger
____________________________________________
Verylow 0.0000 0.0000 1.0000 1.0000 0.2500
Low0.0000 0.0000 0.0000 0.0000 0.4722
Average 0.1111 0.0000 0.0000 0.0000 0.2778
Frequent 0.7222 0.0000 0.0000 0.0000 0.0000
Veryfrequent0.1667 1.0000 0.0000 0.0000 0.0000
____________________________________________
Table4.CPTfornode‘consequenceseverity’.
____________________________________________
StatesofC Vesselcategories
Fishing Service Tanker GeneralPassenger
____________________________________________
Negligible 0.2778 0.3833 0.0000 0.0000 0.0000
Marginal 0.4444 0.3667 0.0000 0.0000 0.0000
Moderate 0.2778 0.2500 0.0556 0.2391 0.0000
Critical 0.0000 0.0000 0.5000 0.7174 0.7833
Catastrophic 0.0000 0.0000 0.4444 0.0435 0.2167
____________________________________________
Table5.CPTfornode‘chanceofallisionriskundetected’.
____________________________________________
StatesofP Vesselcategories
Fishing Service Tanker GeneralPassenger
____________________________________________
Unlikely0.2143 0.0000 0.0000 0.0000 0.0000
Reasonably 0.6429 0.1151 0.0000 0.0000 0.0000
unlikely
Likely 0.1429 0.5992 0.0000 0.0000 0.5833
Reasonably 0.0000 0.2857 0.5833 0.4444 0.3056
likely
Definite 0.0000 0.0000 0.4167 0.5556 0.1111
____________________________________________
835
WhenintroducingtheCPTsintotheBNmodel,the
conclusionofeachvesselcategoriescanbegenerated
andpresentedasaformatoftheposteriorprobability
distribution.Forinstance,theallisionriskforfishing
vessel is distributed as (0.13 (poor), 0.46 (fair), 0.18
(average), 0.15 (good), 0.09 (excellent)), which is
graphicalgiveninFigure5.
In the similar way, results for other four vessel
categoriesare‘servicevessel=(0.33(poor),0.04(fair),
0.28(average),0.22(good),0.13(excellent))’,‘tanker=
(0.15 (poor), 0.17 (fair), 0.02 (average), 0.19 (good),
0.47(excellent))’,‘generalcargovessel=(0.01(poor),
0.24 (fair), 0.08
(average), 0.15 (good), 0.52
(excellent))’, ‘passenger vessel = (0.07 (poor), 0.26
(fair),0.29(average),0.26(good),0.12(excellent))’,see
Figure6.
Thefunctionsintroducedinsection2.3areusedto
prioritise the vessel allision risk on different
categories based on the distribution result. For
example, the SL for the type of
fishing vessel is
calculatedasfollowings:
0.13*1 0.46 * 27 0.18*125 0.15*343 0.09*729
152.11
fishing
SL 
Similarcomputationsareperformedforotherfour
vessel categories in the study, which are
204.49
service
SL
, 417.91
tanker
SL ,
445.25
general
SL
,
219.48
passenger
SL
.
Consequently,theallisionriskofeachvesselcategory
are ranked as ‘fishing vessel’ > ‘service vessel’ >
‘passenger vessel’ > ‘tanker’ > ‘general cargo vessel’.
Therankingresultindicatesthetypeoffishingvessels
requires more attention to control the allision risk
than other vessel categories. The belief degree
distribution
forL, C and P on the fishing vesselcan
present a more information. The Figure 5 shows
although the fishing vessel has a low collision
consequence, but fishing vessels has a higher
probability of allision and low probability of risk
detectionbefore allision. Consulting the experts, this
state is
explained as two main reasons. In the study
OWF area, many fishing vessels takes a fishing
operationinsidetheOWFarea,whichisverycloseto
theturbinestructuresandfacilities.Itleadstoavery
highcollisionriskiffishingvesselslosstheircontrol
dueto themachinefailure
orbadweather occurred.
Meanwhile,anotherreasonistheabilityofdetecting
the risk for the fishing vessel is insufficient, which
may due to the insufficient training or lack of
facilities,whichallleadingtoalowtheprobabilityof
detectingthecollisionrisk.
Figure5.AnalysisresultforthefishingvesselinBN
836
Figure6.Allisionriskdistributiononvesselcategories
Figure7.Sensitivityanalysisofthechanceofriskbedetectedonthetypeoffishingvessels.
Thesensitivityanalysisisusedtotesttheeffectof
Ponthefishingvessel.Weassumethereisasecurity
controloptionisimplementedonthefishingvesselto
improve the risk detection probability. The security
controloptionsincludeimprovingtraining,equipping
with the collision warning system, etc. To
take a
sensitivity analysis, we first set the node vessel
category as ‘100% of the fishing vessel in the BN
model. Then the belief degree of P is equivalently
increasedfrom0.05to0.1,whichmeansthedetection
probabilityforfishingvesselincreasingfrom100%of
unlikelyto100%ofdefinite.
Asaresult(seeFigure7),
theSLincreasedfrom141.41to384.07,whichshowsa
significant increase in safety level for this type of
vessel. When belief degree of P less than 0.5, the
influencedegreeofPtotheconclusionisslight,which
increasedfrom141.41to182.74.
Theinfluencedegree
of P to the safety level is significant when P larger
than 0.5. It increased the safety level index from
182.74 to 384.07. Therefore, the result states that
securitycontrol options canimprove the safety level
forvessels.Itisnecessarytoensurethebeliefdegree
of P
for fishing vessels not smaller than 0.5, which
mean not worse than the state as ‘likely’. However,
this sensitivity analysis can be also used to test the
influence of risk factors on other vessel categories,
whichisworthtoanalysisinthefurtherstudy.
4 CONCLUSION
Thispaperintroduced a
fuzzyrule‐based BN model
based on FMEA analysis. In this model, the fuzzy
mapping and the rule base technology are to
transform the subjective judgement into conditional
probabilities, Three belief factors are developed to
modeltherelationshipbetweentheallisionrisklevel
associated with its risk attributes L, C
and P that
basedontheFMEAanalysis.
The proposed framework is then applied to
analyse the vessel allision risk near the OWF under
differentcategories.Inordertofacilitatethestudy,a
group of three experts has been invited to give
judgementundervariousformatshapes.Throughthe
fuzzy
mapping and transforming technology, the
judgement is then used to provide the conditional
probabilitytableforeachriskfactorsofL,CandPin
theBNmodel.Asetofrulebasesisgiventolinkeach
risk factor to the conclusion of allision risk. The
obtained posterior probability distributions
under
different vessel categories are then computed to
priorities the safety level, and sensitivity analysis is
implementedatlast.
When applying this BN model in practice, the
resultshowsthecategoryofthefishingvesselhasthe
highest allision risk than the other four types of
vessels. Fishing vessels have
a high probability of
collisionandalowchanceofdetectingtheriskbefore
allision. Meanwhile, the type of service vessel is
ranked as the second and following with the
passenger vessel, the tanker and the general cargo
837
vessel. Influence degree of risk detection on the
fishingvesselisanalysed,theresultshowsthatsome
security control options such as equipping the early
warning system, providing safety training can
reducingthevesselallisionrisk.
This paper discussed the probability of using a
rule‐based BN model to analyse
the vessel allision
riskneartheOWFwhenusingtheexpertjudgement.
Anexampleofstudyingvesselallisionriskisgivento
test the reliability of the model. However, there are
some insufficiencies should be studied in further
analyses. The example in this paper is simple and
general.Enhancingthe
BNstructurecansignificantly
improve the usage of the BN model. Methods of
mitigating the bias in the expert judgement are
required, which not discussed in this paper. Other
securitycontroloptionscanbetestedandprioritised
by using the BN model, which can provide support
forriskpreventionandsafety
control.
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