469
1 INTRODUCTION
Presently,variousmeasuresareavailabletoenhance
safetyofshiptraffic.TrafficSeparationSchemes(TSS)
andVesselTrafficServices(VTS)areestablishedand
sophisticated ship technologies are applied to
promote safety of navigation. Further measures are
investigated and tested in various domains and
initiatives.Toassesstheactualanda
nticipatedeffects
of the implementation of such measures, qualitative
methods depending on expert judgement are most
commonlyapplied.
Incontrasttothispracticeofsubjectiveevaluation,
this paper outlines an approach for establishing a
fuzzy‐logic‐based index intended to objectively
evaluate safety in maritime traffic. This first section
introducesthebackgroundofthi
sstudy,includinga
presentation of the originating STM Validation
researchproject,themotivationforthisstudyaswell
asthepresentstateofresearchinthisparticularfield.
This is followed by a description of the fuzzy logic
methodology applied in establishing the maritime
safety index as well of the q
uantitative numerical
variablesusedasinputdata.Thethirdsectioncovers
thedevelopedfuzzymodelwhichisusedtocalculate
the maritime safety index. This also includes the
results from a survey conducted with navigation
training experts for defining membership functions.
Validation of the established model as well as
calculat
ionresultsarediscussedinthefourthsection
followedbythestudy’sconclusionandoutlookinthe
finalsection.
1.1 TheSTMconcept
Inspired by air traffic management, the STM
Validation project and its predecessors have
produced a concept for sea traffic management. It
Developing a Maritime Safety Index using Fuzzy Logics
F.Olindersson
ChalmersUniversityofTechnology,Gothenburg,Sweden
W.C.Bruhn&T.Scheidweiler
FraunhoferCenterforMaritimeLogisticsandServicesCML,Hamburg,Germany
A.Andersson
SSPASwedenAB,Gothenburg,Sweden
ABSTRACT:Safeshippingisessentialforsocietyanddifferentmeasuresaretakentoimprovemaritimesafety,
forexamplethroughimplementationoftrafficseparationschemes,radarsurveillanceandtrafficmanagement
concepts.Buthowcanmaritimesafetybemeasuredtodeterminetheeffectsofthoseimplementations?Inthis
study,a real‐ti
memaritimesafety indexfor ashipisdeveloped,takingintoaccountboththeprobability of
grounding and the probability of collision. The index is developed using fuzzy integrated systems and
validatedinshiphandlingsimulatorscenarios.Itusesnumericaldatafromthesimulatorasaninputtoassess
thepresentt
rafficsituationfromthe perspectiveofa specificshipandoutputs acomprehensiveindex.This
paper describes the concept of sea traffic management as proposed and evaluated in the EU funded STM
Validationproject,themotivationfordevelopingamaritimesafetyindex,thenumericalinputvariablesand
modelpropertiesandalsovalidat
esthefeasibilityoftheapproach.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 11
Number 3
September 2017
DOI:10.12716/1001.11.03.12
470
consistsofanumberofcomponentservicesaimingat
improving safety and efficiency in the maritime
transport chain through traffic monitoring and
guidance. Through sharing of information between
involvedstakeholderswithinacommonenvironment
and structure, services such as route exchange
between ships as well as with shore‐based entities,
voyageandrouteplanningandoptimizationaswell
asportcollaborativedecision‐makingwillbeenabled.
This will benefit the overall maritime transport
domainatlarge.
1.2 Motivation
Within the STM Validation research project, large‐
scale trial runs are conducted with the European
Maritime Simulator Network (EMSN). This test
facility
connects more than 30 ship handling
simulator bridges from maritime training and
research facilities located throughout Europe. The
databeingproducedduringthesesimulationsreflects
thenavigators’decisionsindifferentmaritimetraffic
scenarios . For the assessment of navigators’
behaviourinencountersituationsbetweenshipsitis
requiredtodevelopan
approachthataccountsforthe
full complexity of the task. While most assessment
methods conventionally used depend to a large
degreeonexpertopinions,thisstudyaimsforamore
objectiveandquantitativeapproach.
1.3 Paperreview
A first attempt to use fuzzy logic on real time AIS
datahas
beendevelopedbyKaoetal.in2007.With
the four input parameters ship size, ship speed, sea
state and radius size of a guardian ring, a danger
indexisdeterminedtoestimatethelocationandtime
of potential collisions between vessels. Park et al.
developed a collision risk assessment system
using
fuzzy theory based on the input variables DCPA
(distance of the closest point of approach), TCPA
(timeoftheclosestpointofapproach)andindicators
for abnormally navigating ships, specified by
accumulatedchangesin thespeedand courseof the
vessels.
Since 2007, several more papers have been
published
focusing on fuzzy logic as a tool for
avoidingcollisionsinrealtimeoperations.Adifferent
approachtoassesssafetyinmaritimetraffichasbeen
done by Lopez‐Santander et al.estimating the risk
ofcollisionsvia a statisticalprobabilistic model. The
purpose of this paper is to present a fuzzy
logic
approach measuring the level of safety of different
traffic situations to finally validate the service
conceptsdevelopedintheSTMValidationproject.
2 METHODOLOGY
Theterm Fuzzy Logic wasintroducedbyL.A. Zadeh
deliveringthetheoryoffuzzysetsin1965andwas
appliedtocontrol automated steam engines
by E.H.
Mamdaniin1975.Insteadofdealingwiththebinary
termsof“true”and“false”thefuzzylogicapproach
extendsthesetermsontheunitintervalasdegreesof
truth.
2.1 FuzzyLogic
2.1.1 Fuzzysetsandmembershipfunctions
GivenaspaceofobjectsXwithx
XafuzzysetA
in X is characterized by a membership function
A(x):x
[0,1] with
A (x) representing the grade of
membership of x in the fuzzy set A ,,. Given two
fuzzysetsA,B
Xtheclassicalsetoperationsinclude
the complement, intersection and union. For x
i
X
(where i=1,…,n) and X being a discrete and finite
spacethemappingofthefuzzysetAisdenotedby
x
A
i
A
x
i
i
(1)
GivenacontinuousandinfinitespaceXthefuzzy
setAcanbeexpressedas
x
A
A
dx
x
(2)
With the classical set operations and x
X, the
operationsforfuzzysetsAandBaredefinedas
\
C
A
xXA (3)
min ,
AB AB
x
xxxAB
(4)
max ,
AB AB
x
xxxAB
(5)
2.1.2 Fuzzification
The first step of the fuzzy logic proceeding is to
map the non‐fuzzy input values to linguistic
variables. This fuzzification process is performed by
the pre‐derived membership functions for the input
and output variables which can have multiple
different types, such as triangular, trapezoidal or
Gaussian waveforms. With x
X the core, support
andboundariesofafuzzysetAaredefinedas
core | 1
A
AxX x
(6)
supp | 1
A
AxX x
(7)
b
nd | 1
A
AxX x
(8)
2.1.3 Fuzzyrules
By means of the linguistic variables generated
duringthefuzzificationrulescanbeusedtodescribe
theknowledgeofanexpert.Givenasetofconditions
471
c and a set of consequences z fuzzy rules can be
representedasasequenceofIF‐THENphrases:
IFxiscTHENyis (9)
with c
C and z
Z. Having rules with multiple
parts, the introduced fuzzy operators are used to
combinethesemultipleinputswith“AND”meaning
the minimum, “OR” meaning the maximum and
“not” delivering the additive complement of the
condition.
2.1.4 Defuzzification
Inordertoobtainanoutputthatsummarizes the
input variables, output membership
functions and
rules the linguistic output variable has to be
defuzzified. Centroid defuzzification is the most
commonly used method providing the centre of the
area under the curve of the membership function.
Given a membership function
i:x
[0,1] and an
outputvariablex
X,thedefuzzifiedoutputzo
canbecalculatedas
0
.
x
xdx
z
x
dx
(10)
3 FUZZYMODELFORESTIMATINGASAFETY
INDEX
Themaritimesafetyindexconsistsofthecombination
ofacollisionandagroundingindexeachrepresented
byaproposedfuzzymodel.Followingthedefinition
oftheinput variables,themembership functionsfor
the fuzzy models estimating a collision and
grounding
index are created based on the results of
pre‐conductedinstructorsurveys.
The fuzzy models estimate a safety index for a
specificvessel,theownship,ataspecifictime.Inthe
vicinity of the own ship, one or several target ships
could be present to affect the collision safety index
and land or shallow waters nearby could affect the
groundingsafetyindex.
3.1 Inputvariables
Givenamaritimetrafficsituationwithoneownship
andoneormultipletargetships,Table1,basedonthe
workbyLopez‐SantanderandLawry,liststheinput
variablesforthecollisionindex
whicharerepresented
by membership functions later on. Table 2 lists the
corresponding input variables for estimating the
groundingindex.
Tobeabletomeasurethesafetyindexinreal‐time
during a ship handling simulator exercise or using
liveAIS data,the inputvariableshave been derived
fromdataavailable
from the AIS system (exceptfor
environmentalconditions).
Table1.Inputvariablesforestimatingacollisionindex.
_______________________________________________
Variable Description
_______________________________________________
CPA ClosestPointofApproach
TCPA TimetoClosestPointofApproach
BCR BowCrossRangetothetargetship
ETEncountertype
ECEnvironmentalConditions
Intentions Previouslyshownintentionsforperforminga
collisionavoidancemanoeuver
GTS GeneralTrafficSituation
MANVessel’smanoeuvrability
_______________________________________________
Table2.Inputvariablesforestimatingagroundingindex
_______________________________________________
VariableDescription
_______________________________________________
UKCUnderKeelClearance
SMSafetyMargin
DADriftingAngle
DSDriftingSpeed
_______________________________________________
3.1.1 ClosestPointofApproach(CPA)
TheCPA isthe distancecalculatedfromtheown
ship’s and target ship’s position, course and speed.
ThedistanceismeasuredinmeterssothattheCPAis
definedby
2
22
sin cos sin cos
2sinsincoscos
uv y tw y uv x tv x
CPA
vw vw x y x y
(11)
wherexistheownship’scourse,yisthetargetship’s
course, v is the own ship’s speed, w is target ship’s
speed, t is the longitudinal distance and u is the
lateraldistancebetweenownshipandtargetship.
Fivemembershipfunctionsareusedtodefinethe
CPA;zero,small,medium,largeandverylarge.
3.1.2 TimetoClosestPointofApproach(TCPA)
TheTCPAisthetimeforthevesselsto reachthe
CPA.TocalculatetheTCPAtheownship’sandtarget
ship’s positions, courses and speeds are used. The
TCPAcaneitherbepositiveor
negativedependingon
whether the vessels are approaching or not and is
definedby
22
sin sin cos cos
2sinsincoscos
tv xtw yuv xuw y
TCPA
vw vw x y x y
(12)
withtheparametersx,y, v, w,t,anduasdefinedin
section 3.1.1. To define the TCPA six membership
functions are used; history, passed, zero, small,
mediumandlarge.
3.1.3 Bowcrossrange
The distance at which the target ship crosses the
own ship’s heading line is
called bow cross range
(BCR).ThevalueoftheBCRispositiveifthecrossing
isaheadoftheownshipandnegativeifthecrossing
isasternoftheownship.Fivemembershipfunctions
are used to define BCR; ahead, close ahead, zero,
closeasternandastern.
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3.1.4 Encountertype
Accordingtotheinternationalcollisionregulation
COLREGs , the rules that apply in a specific traffic
situationtoavoidcollisiondependsontheencounter
type. Encounter types can be defined using
differences in the course, speed and the relative
bearingfromtheownshiptothetarget
ship.
Six membership functions are used to define the
encounter type; head‐on, crossing from starboard,
crossing from port, overtaking, overtaken and safe
situation. In this context, a traffic situation is
considered to be safe when no potential risk of
collisionexists.
3.1.5 Environmentalconditions
The safety depends on some
environmental
factors, such as wind direction, wind speed, current
direction,currentvelocity,seastateandvisibility.All
environmental factors are condensed to an output
consisting of three membership functions
representing the environmental influence in the
situation; no influence, small influence and high
influence.
3.1.6 Intentions
The collision safety index of a
traffic situation is
not only a matter of geometrical and environmental
factors. If one vessel performs a large and positive
avoiding manoeuver in ample time in accordance
withCOLREGs,thesafetyindexincreasesduetothe
“communication” between the vessels. It indicates
thatthesituationhasbeenidentifiedand
thataction
willbetakenaccordingtotherules.
To classify pre‐shown intentions, first a
manoeuver must be identified and second, an
assessment whether this manoeuver is an avoiding
manoeuver or not has to be made. A manoeuver is
identified by the changes in course or speed over a
certain
periodoftimeusingamovingaveragevalue.
Todistinguishbetweenmanoeuversmadeaspart
of ordinary navigation and those of an avoiding
manoeuver,thefollowingcriteriaareused:
1 Riskofcollisionexistsbetweenthevessels
2 The manoeuver is performed within a specified
actionrangeforthe
typeofsituation
3 The manoeuver is performed when TCPA is
positive
4 TheCPAshouldincreaseduetothemanoeuver
5 There is no other target with higher risk of
collisionatthemoment
Shownintentionsalsotakeintoaccountthevessels
navigational status (power‐driven vessel, sailing
vessel, vessel
engaged in fishing, vessel constrained
by her draught, vessel with restricted ability to
manoeuver and vessel not under command) as well
asthesizeofthevessel.
Threemembership functionsareusedto describe
the shown intentions; no intentions shown, fuzzy
intentions,clearintentions.
3.1.7 Generaltrafficsituation
If the
traffic density is high, the risk of collision
increasesand thesafetylevel will belower than the
lowest safety indication for each individual traffic
situation.
Thetrafficdensityisdefinedbythreemembership
functions;low,mediumandhigh.
Figure2. Illustration of 15 UKC points used within the
model.
3.1.8 Manoeuvrability
Anavoidingmanoeuvernormallyisperformedby
acoursechangetostarboard.Accordingtorule14in
the COLREGsvessels meeting in a head‐on
situation should change their course to starboard.
According to rule 15 in COLREGsvessels which
havetheothervesselonstarboardside,shallkeep
out
ofway andavoidpassing aheadof theother vessel,
whichmeansaturntostarboard,normally.Iftheown
shiphasnooronlyasmallabilitytoturntostarboard
duetoothertargetshipsorshallowwater,thesafety
leveldecreasesintheindex.
Theability
toturntostarboardsideishandledby
an input variable called “manoeuvrability” and
consists of three membership functions; good, poor
andnone.
3.1.9 Underkeelclearance(UKC)
TheUKCiscalculatedasthedistancebetweenthe
keel and the sea bottom, the difference of the water
depthandtheship
draught.TheUKCismeasuredat
15differentlocationsaroundthevesselasillustrated
infigure2.Sevenpointsarelocated“3minutesaway”
and seven “12 minutes away” from the current
position.Thesevenpointsarelocatedstraightahead,
+90, +60, +30,‐30,‐60 and‐90 degrees from present
course over ground (including the vessel rotation).
The 15 points have the same five membership
functions; aground, low, medium, high and very
high.Figure3illustratesthetrapezoidalmembership
functionsfortheseinputparameters.
473
Figure3.MembershipfunctionsforUKC.
3.1.10 Safetymargin
The“safetymargin”inputparameterregulatesthe
UKCthatisconsideredtobesafeforthespecificship.
The “safety margin” input parameter has five
membership functions, four triangle and one
trapezoidal,whichareillustratedinfigure4.
Figure4.Membershipfunctionsforsafetymargin.
3.1.11 Drift
Avesselisdriftingduetotheeffectsofwindand
current,whichcouldbedividedintoadriftingangle
anddriftingspeed.
The input parameter “drifting angle” is the
direction that the ship would travel without any
propulsion. The parameter is the