43
1 INTRODUCTION
Tanjung Perak Port area is located in Madura Strait
betweenJavaIslandandMaduraIsland,inSurabaya,
EastofJava,Indonesia. Theportplaysan important
role as the central port of Indonesia. The port
provides transportation services to and from the
centerofinternationaltradinginSingapore,aswellas
domestic tra
ding services between the western and
eastern parts of Indonesia. The port is expected to
handle ships without transit in Singapore.
Accordingly, larger ships could be handled. A
multipurposeport was builtin Lamong Baynear to
theTanjungPerakPort.Thepositionsoftheportsand
anchoragezonesareshowninFigure1.Thetra
jectory
ofashiponthefairwayisplottedinFigure1based
ontheautomaticidentificationsystem(AIS)data.The
positionsindicatedinbluearecreatedasthelimitof6
areas representing 3 paths of course keeping A, C,
andE,and3pa
thsofturningB,D,andF.
Figure 1 shows that two anchored ships are
located out of the anchorage zones and close to the
fairway, indicating an increasing number ship calls.
The increasing number of ship calls and the lack of
traffic scheme in the developing port area will
increase thenumber of collision candidates, andthe
causationprobabilit
y,andsubsequentlywillincrease
the number of ship collisions. The causation
probabilityofshipcollisionsinMaduraStraitisabout
1.08 × 10
4
(Mulyadi et al., 2014). The probability
representsthefrequencyoffailingtoavoidacollision
when on collision course. The high causation
probabilityalsodenotesthehighprobabilityofships
losing control. The high number of ship calls and
ships losing control as well as the limited area will
make course changes more difficult when the ships
areexposedtoashipshipcollisionsituation.Besides
course changes and course keeping, a crash ast
ern
maneuver may be chosen by the navigator to avoid
accidents.
Probability of Ship on Collision Courses Based on the
New PAW Using MMG Model and AIS Data
I.P.S.Asmara
GraduateSchoolofMaritimeSciences,KobeUniversity,Japan
PoliteknikPerkapalanNegeriSurabaya,Indonesia
E.Kobayashi&N.Wakabayashi
GraduateSchoolofMaritimeSciences,KobeUniversity,Japan
K.B.Artana
InstitutTeknologiSepuluhNopemberSurabaya,Indonesia
ABSTRACT: This paper proposes an estimation method for ships on collision courses taking crash astern
maneuversbased onanewpotential areaofwater (PAW)for maneuvering.A crashasternmaneuveris an
emergencyoptionashipcantakewhenexposedtotheriskofacollisionwithothershipstha
thavelostcontrol.
However,lateralforcesandyawmomentsexertedbythereversingpropeller,aswellastheuncertaintyofthe
initial speed and initial yaw rate, will move the ship out of the intended stopping position landing it in a
dangerousarea.AnewPAWforcrashast
ernmaneuversisthusintroduced.ThePAWisdevelopedbasedona
probabilitydensityfunctionoftheinitialyawrate.Distributionsoftheyawratesandspeedsareanalyzedfrom
automatic identification system (AIS) data in Madura Strait, and estimated paths of the maneuvers are
simulatedusingam
athematicalmaneuveringgroupmodel.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 9
Number 1
March 2015
DOI:10.12716/1001.09.01.05
44
Figure1.Shiptrajectoryintheresearcharea.
This study aims at developing a method to
estimate the probability of collision when using a
crash astern maneuver. The proposed method was
developed based on the combination of the two
typical methods introduced by Fujii (1974) and
Kristiansen(2005),andtheconceptofpotentialareaof
water (PAW) introduced by
Inoue (1990). The
frequency of a subject ship on a collision course is
estimated based on the distributions of initial speed
and initial yaw rates. The uncertainty of the initial
conditions significantly affects the paths of the
maneuvers(Asmara et al.,2012).The trajectoriesare
estimated using mathematical maneuvering group
(MMG) model and initial conditions of speed and
yaw rate are analyzed from automatic identification
system(AIS)data.Theaimofthisstudyistopropose
a method for estimating the probability of collision
resultingfromcrashasternmaneuvers intheresearch
area, of a ship on a collision course that
attempts
crashasternmaneuvers.
2 LITERATUREREVIEW
Theformulausedfortheassessmentofcollisionrisk
isshownbyEquation1(Goerlandtetal.,2011).
RPC (1)
where R is the collision risk; P, the probability of
collision; and C, the factor representing the
consequences of collision such as collision energy
losses.
Several researchers have introduced methods for
estimating the number of collisions. Generally, the
methods were developed based on Fujii’s model
(1974), where the number
of expected collisions is
calculated from the number of collision candidates
multiplied by the probability of failing to avoid a
collision when on a collision course, as shown by
Equation2.
coll A C
NNP
(2)
whereN
collisthenumberofcollisionsforagiventime
period;N
A,thenumberofencountersduringthetime
period; and P
C, theprobability of failure of collision
avoidance,generallyknownascausationprobability.
Inthisapproach,thenumberofcollisioncandidatesis
estimated usinggeometrical probability based onan
encounter segment of the lateral distribution of the
ship’s trajectory. The probability of collision
avoidance failure, the causation probability, is
estimatedbased
onspecificerrorsituationanalysisof
several factors leading to the probability of wrong
actionandsteeringfailure.
In another approach, the probability of steering
failure is defined as the probability of a loss of
control. It estimates the collision probability by
multiplyingitwiththeprobabilityofaship
collision
uponthelossofvesselcontrol(Kristiansen,2005).In
this method, the probability of loss control is
determinedfromhistoricaldata.Theprobabilityofa
collisionupon thelossofvesselcontrolis calculated
usingageometricalprobabilitybasedondimensions
offairwayandships,trafficdensity,andships’speed,
aswellasthetypeofcollision.Inthisapproach,first,
theprobabilityofcollisionPaisdeterminedbasedon
the historical accident data, and second, the
probabilityofcollisionuponthelossofvesselcontrol
Pi is calculated based on geometrical probability of
collision.Finally,theprobabilityofcontrol
lossPcin
the port area is determined. Collision probability is
defined as the probability of a loss of control Pc
multiplied by the probability of an incident (the
probabilityofaccidentuponthelossofvesselcontrol)
Pi(Kristiansen,2005)asfollows:
aci
PPP
(3)
wheretheindexesdenoteaccident(a),lossofcontrol
(c)andimpact(i).Inthisapproach,theprobabilityof
control loss seems to be treated as the collision
candidate frequency, which is determined based on
the historical statistic data. The probability of an
incident, probability of
accident upon the loss of
vessel control, acts as the probability of failing to
avoid accident. However, the method used for
determiningtheincidentprobabilityisdifferentfrom
that usedfor estimating causation probability in the
previousapproach.Itwasusedinthefirstapproach
to calculate the collisioncandidate frequency,
which
depends on the type of encounter, fairway
dimensions,andthe speedanddimensions ofships,
basedonageometricalprobability.
Figure 2 shows the approaches of the described
methods and the proposed method. Both of the
existing