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
areexposedtoaship‐shipcollisionsituation.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 methods do not specifically show the
probability of collision upon using crash
astern
maneuvers, whichmay be adopted by navigatorsto
avoidacollisionindensetraffic.Thelateraldeviation
of the maneuvers may be considered as a wrong
action included in the causation probability, and
losing control in the first and second approaches,
respectively. However, the specific estimation of
probability of a
ship on a collision course when
performingcrashasternmaneuvershasnotyetbeen
analyzed.
45
Figure2.Flowchartofexistingandproposedmethods.
This paper proposes a method to estimate the
probabilityofshiponacollisioncourse,upontaking
crash astern maneuvers, based on a new PAW for
maneuvering. The PAW for maneuvering is defined
as the water area that would be used before the
intended ship’s movement is achieved, assuming
that
the navigator will encounter an emergency
involvingtheapplicationofcrashasternmaneuveror
such other emergency action as may be necessary
should the ship encounter an unexpected situation
during the maneuver (Inoue, 1990). The number of
collisioncandidatesduetoacrashasternmaneuveris
the number of ships
taking crash astern maneuvers
multiplies by the probability of ships on collision
courses performing crash astern maneuvers. The
numberofshipstakingcrashasternmaneuversisthe
numberofshipsenteringtheresearchareamultiplies
by the probability of them taking crash astern
maneuvers. However, the probability of taking a
crash
asternmaneuverisnotdiscussedinthispaper.
ThePAWwasdevelopedbysuperimposingtheship
pathsbytheirpositionswhencrashasternmaneuvers
areordered (Inoue, 1990).The newPAW developed
in thisstudy is developed not onlyby the positions
when the maneuvers are ordered but also by
the
distributionofinitialspeedandinitialyawrate.
3 METHODS
3.1 AISData
TheAISdataistakenfromanAISreceiverinstalledat
the Institut Teknologi Sepuluh Nopember (ITS)
campusinIndonesiathroughacollaborationbetween
ITSandKobeUniversity.Thenumberofshipcallsin
theportarea
onapeakdayinJanuary2011wasmore
than 120, as shown in Figure 3. The number of
enteringshipsishigherthanleavingshipsbecauseof
the high number of anchored ships, as indicated by
the ships anchoring out of the anchorage zones, as
shown in Figure 1.
The number of entering and
leaving ships is identified from AIS data by
distinguishing the ship courses in the research area.
Theaveragenumberofenteringandleavingshipsper
dayis49and42,respectively.
Figure3.Numberofshipcallsintheportarea.
Table1.Distributionofspeed
_______________________________________________
AreaDistribution ParameterofDistribution
Mean(kt) Standard Deviation(kt)
_______________________________________________
A Normal 9.8139 3.3600
B Normal 9.6653 3.4433
C Normal 9.4936 3.0687
D Normal 7.7335 3.9185
E Normal 6.0941 2.8388
F Normal 5.6742 2.4777
_______________________________________________
The distribution of ship speeds in the 6 areas is
presented in Table 1.The distribution fitsto normal
distributions with a mean of between 10 to 5 knots
decreasing from area A to area F. The average ship
speed is more than 9 knots before entering the
anchoragezonesin
areaA,BandC.Itismorethan7
knotsintheareabetweenthenewportandanchorage
zones,areaD,andabout6knotsintheexistingport
area,areaEandF.
3.2 MMGModel
The mathematical model for the simulation of ship
maneuvering was developed
based on Yoshimura’s
model for medium high‐speed merchant ships and
fishing ships (Yoshimura & Masumoto, 2012). The
coordinatesystemforthismodelisshowninFigure4.
The equations of surging, swaying and yawing
motion are expressed by Equations 4 to 6. The
subscripted H, P, and R for longitudinal
force X,
lateral force Y, and yaw moment N, represent the
hull, propeller and rudder, respectively. The hull,
propeller, and rudder forces and moments are
calculated based on Kijima’s and Yoshimura’s
regressionequationsandempiricalformsformedium
high‐speed merchant ships and fishing ships
(Yoshimura&Masumoto,2012).
46
Figure4.CoordinatesystemofMMGmodel.
Themodelalsoconsiderstheeffectoftheshallow
wateronshipmaneuvering(Kobayashi,1995).
Surge:
x
GyGGHPR
mmu mmvr X X X
(4)
Sway:
yG xGG H P R
mmv mmur Y Y Y
(5)
Yaw:
˙
zz zz G H P R G
I
JrN N N xY
(6)
Hull forces and moment are expressed in
Equations7to9.
2' '2 ' ' ' '''2 ' 4
0
0.5
HyGG ry rrGy
Xmvr LdUXX X mrXxmrX
(7)
2' ' ' ' 3 ' 2 ' '2 ''3
0.5
H x G G r x r rr rrr
Ymur LdUY YmrY Y rYrYr
(8)
22' ' ' 3 ' 2 ' '2''3
0.5
H r r rr rrr
NLdUNNrNNrNrNr
(9)
where:
r
=dimensionlessyawrate=r(L/U)
'
G
x
=dimensionlesslongitudinalcenterofgravity
= /
G
x
L
ρ =densityofwater
L =shiplength
d =meandraught
''
,
x
y
mm=dimensionlessaddedmass
=
2
, /0.5
xy
mm Ld
'
0
X
=dimensionlessresistance=
2
0
/0.5
X
LdU
Therelationbetweentrustcoefficientandapparent
advanceconstantforareversingpropellerisadopted
fromK
T‐JSdiagram for containership(Yoshimura &
Nomoto,1978;Yoshimura,1980).
Figure5.KT‐JSdiagramforacontainership.
Figure6. Lateral force and yaw moment exerted by a
reversingpropeller.
The trust coefficient for a reversing propeller is
presentedinthefourthquadrantofFigure5.
Lateral force and yaw moment exerted by a
reversingpropelleraretakenfromYoshimuragraphs
(1980).ThegraphsarefittoEquations10to15andare
showninFigure6.
*2
0.005125 0.006629 0.000978
PSS
YJJ
: 0.5653
S
for J
(10)
*
0.074153 0.043076
PS
YJ
: 0.5653 0.5
S
for J
(11)
*2
0.037007 0.031084 0.000054
PSS
YJJ
: 0.5 0
S
for J
(12)
*2
0.001255 0.000734 0.000519
PSS
NJJ
: 0.5625
S
for J
(13)
47
*
0.049018 0.028116
PS
NJ
: 0.5625 0.5429
S
for J (14)
*
0.000319 ln 0.001774
PS
NJ
: 0.5429 0
S
for J (15)
*
P
Y and
*
P
N aretypicalnon‐dimensionalformof
lateralforceandyawmomentexertedbyreversinga
propelleraspresentedbyEquations16and17below.
*2
/ ( )
2
PP
YY LdnD
(16)
*22
/ ()
2
PP
NN LdnD
(17)
where n is propeller revolution and D is propeller
diameter.
3.3 SubjectShipSelection
A pure car carrier (PCC) ship was selected as the
subject ship based on the maximum size of ships
voyagingintheresearcharea.Inaddition,theship’s
primary dimensions fit the requirement of the
nonlinear hull derivatives for the MMG model,
includingthebeamtolength(L/B),beamtodraught
ratio (d/B) and block coefficient (Cb). The principle
dimensionsofthesubjectshiparepresentedinTable
2. The subject ship is simulated to follow the AIS
based trajectoryof anentering ship usingthe
MMG
model.Thedistributionsofyawrateinthe6areasare
analyzedbasedonthetimeseriesofyawrateresulted
fromthesimulation.
Table2.PrincipledimensionofPCCship.
_______________________________________________
ShipParticularsDimension
_______________________________________________
Length(Lpp)180m
Breadth(B)32.2m
Draft(d)8.2m
CoefficientBlock(Cb)0.548
Displacement
26,650tons
Speed(Vs)18kt
PropellerDiameter(Dp)5.7m
RudderArea(A
R)37.76m
2
_______________________________________________
3.4 PAWforCrashAsternManeuvers
Originally, the concept of PAW for crash astern
maneuvers was introduced as an area covered by
possible paths of a ship upon taking several
emergency actions of crash astern maneuvers. The
possible paths are developed based onthe positions
when maneuvers are ordered (Inoue,
1990). Each
position actually represents a specific course, speed,
andyawrate.However,aPAWisintroducedasthe
superpositionofthepathsofthemaneuversordered
atseveralinitialpositions.Thispaperproposesanew
PAW that is developed based on not only the
positions when maneuvers are ordered
but also the
distributionsofspeedandyawrateinanareaofthe
positions. The distribution of a ship’s speed is
analyzedfromAISdata.Howeverthedistributionof
yawrateisnotprovidedintheAISdata.Accordingly,
amethod isproposed toestimate thedistributionof
yawrate
intheresearchareaasfollows:
1 Thesubjectshipissimulatedintheresearcharea
tofollowthetrajectoryofashipbelongingtothe
sameclassderivedfromAISdata.
2 Thetrajectoryandtimeseriesofthesubjectship’s
yawangleshouldbesimilartothosederived
from
AISdata.
3 The trajectory is divided into several paths of
areas. The distribution of yaw rate of the subject
shipin the areacalculated in theMMG model is
analyzed.Thedistributionistreatedasarandom
initialconditionofcrashsternmaneuverstakenin
thearea.
4 RESULTS
ANDDISCUSSIONS
Thedistributionsoftheyawrateofthesubjectshipin
the6areaswereestimatedinthesimulationusingthe
MMG model to follow the trajectory of an entering
shipplotbasedontheAISdata.
Figure7.Timeseriesofrudderangle.
-2000 0 2000 4000 6000 8000
-6000
-4000
-2000
0
2000
4000
y
0
(m)
x
0
(m)
:AIS-based trajectory
:MMG-based trajectory
:Limit of area A,B,C,D,E,and F
Figure8.Trajectoryofsubjectship.
Thetimeseriesofrudderanglesofthesubjectship
followingthetrajectoryoftheenteringshipisshown
48
inFigure7andthecomparisonofthetrajectoriesare
presented in Figure 8. Figure 8 shows that subject
ship’s trajectory is almost the same as the entering
ship’strajectory.Thesubjectship’stimeseriesofyaw
angle results from the MMG model are also almost
the same with the
entering ship’s true heading
derivedfromAISdata,aspresentedinFigure9.
The time series of yaw rates of the subject ship
basedontheMMGmodelisshowninFigure10,and
thedistributionoftheyawratesinthe6areasarefit
tonormalanduniform
distributions,aslistedinTable
3.Basedonthedistributionofyawratespresentedin
Tables 3, the initial of yaw rate, at the time of
reversingthepropeller,israndomized.
Figure9.Timeseriesofyawangle.
Figure10.Timeseriesofyawrate.
Table3.Distributionofyawrate.
_______________________________________________
AreaDistribution DistributionParameters(rad/s)
_______________________________________________
A Normal =4.8582E‐5 σ=4.0774E‐4
B Uniforma=‐0.00141b=1.5265E‐4
C Normal =6.5377E‐5 σ=3.8861E‐4
D Normal =7.9368E‐4 σ=3.4995E‐4
E Uniforma=‐6.2509E‐4 b=3.6763E‐4
F Uniforma=‐0.00148b
=0.00239
______________________________________________
-1000 0 1000 2000 3000 4000
-3000
-2000
-1000
0
1000
2000
y
0
(m)
x
0
(m)
:Slow astern trajectories
:Half astern trajectories
:Full astern trajectories
:Normal trajectory
:Limit of area A, B, C, D, E, and F
Figure11.PAWsbypositionandinitialyawrate.
Figure12.Timeseriesofshipspeed.
The reversing of the propeller is ordered at 4
positions in each area. Three types of crash astern
maneuvers including slow, half, and full are
simulatedforthesubjectship.ThePAWofslow,half
andfullasternmaneuversbasedontherandomvalue
ofinitialyawratearepresentedin
Figure11.
Figure 11 shows that the PAW becomes smaller
whenenteringtheareaofTanjungPerakPort,areasE
andF,becausethespeedsignificantlydecreases.The
timeseriesofshipspeedispresentedinFigure12.In
area B, the PAW of a slow crash astern maneuver
covers
the opposite line of the fairway lying at the
port side of the entering ship. Some of the possible
pathsentertheexitinglaneofthe100mwidefairway.
InareasCandD,thePAWsdonotcovertheopposite
lanebutentertheareaofLamongBayPort.
InareaD,
thepathscrossthelineofportstructure,whichmeans
theshipcollideswiththestructure.Theprobabilities
oftheshiponcollisioncourseinthedangerareasofB
andDisanalyzedasfollows:
49
4.1 ProbabilityofShiponCollisionCourseuponTaking
CrashAsternManeuversinAreaB
AreaBistheareawhereacoursealterationistaken
before a short straight path of area C and the long
turningpathofareaD.Fourpositionsareselectedin
areaBas
initialpositions,whicharewhenthe crash
asternmaneuversareorderedatthesimulationtimes
t,oft=410s,t= 500s,t=590s,andt=680s.Inarea
B,takingaslowcrashasternatthelastinitialposition,
t=680
s,causedaPAWcoveringtheoppositelane,as
showninFigure13.
However, if a half or a full astern maneuver is
ordered, the lateral deviation is not significant. The
maximum lateral deviation was only 0.24 times the
shipwidth B, and 0.13B, forthe halfand full astern
maneuvers,
respectively.Itisasmalldeviationwhen
comparedtothewidthofthelane,whichis100m,or
about 3B. Dangerous situations will occur if a slow
crash astern is ordered. The distribution of lateral
deviation from thenormal position is shown by the
barchartpresentedinFig.
14.Thedistributionfitstoa
uniform distribution with maximum deviation of
4.165Bandminimumdeviationof2.114B.About77%
of the possible paths will enter the opposite line by
consideringthattheallowablelateraldeviationishalf
oflanewidth,whichisabout2.5B.
-1500 -1000 -500 0 500 1000
0
500
1000
1500
2000
2500
y
0
(m)
x
0
(m)
:Slow astern trajectories
:Half astern trajectories
:Full astern trajectories
:Normal trajectory
Figure13.PAWsbyinitialyawrateinareaB.
Figure14.Barchartoflateraldeviationforslowcrashastern
att=680.
4.2 ProbabilityofShiponCollisionCourseuponTaking
CrashAsternManeuversinAreaD
AreaD depictsa long turningpath locatedbetween
anchorage area and the new port. If a slow crash
astern maneuver is taken at positions between the
firstandsecondinitialpositionsofareaD,at
t=1250
sandt=1500s,thePAWswillcoverthestructureof
Lamong Bay port. The ship’s speeds at the initial
positionsare7.98and7.00knots,respectively.
Figure15shows,atthesameyawratedistribution,
thelowertheinitialspeedthesmallerthePAW.
The
bar chart of lateral deviations from the normal
positionofsimulationofthePAWofinitialpositionat
t=1250 sisshown in Figure16.Thedistribution of
the lateraldeviation atthis positionfits to a normal
distribution with the mean of‐5.894B and the
standard deviation
of 0.342B. The distance between
the fairway and the Lamong Bay port’s structure is
about4.9BandallofthepossiblepathsonthePAW
attack the port structure. However, the maximum
lateraldeviationforhalfandfullcrashasternare1.9B,
and0.23B,respectively.
-2000 -1000 0 1000 2000 3000
-4000
-3000
-2000
-1000
0
1000
2000
y
0
(m)
x
0
(m)
:Slow astern trajectories
:Half astern trajectories
:Full astern trajectories
:Normal trajectory
Figure15.ThePAWsbyinitialyawrateinareaD.
Figure16.Barchartoflateraldeviationforslowcrashastern
att=1250.
Theinitialspeedsatthetwootherinitialpositions,
att=1750s,andt=2000s,are6.35and6.03kt.The
maximumlateraldeviationsatthesepositionsare3.14
Band1.64B.Thedeviationsarelessthanthedistance
betweenthefairwayandportstructure.It
meansthat
50
the safe speed at this area is around 6 kt. The
probabilityof ships oncollision coursesof attacking
the new port structure upon taking a slow crash
asternmaneuverisabout50%.Itisestimatedbased
ontheprobabilityofshipshavingspeedhigherthan
the safe speed
upon entering the existing port area,
areaE,aspresentedbyTable1.
5 CONCLUSIONSANDFUTUREWORKS
AnewmethodofdevelopingthePAWisintroduced.
The method was developed based on the position
whenthemaneuverisorderedandthedistributionof
yawrateintheareaof
theposition.Thedistribution
of yaw rate is estimated using a maneuvering
simulation and AIS data. The new PAW is
implemented to propose a method to estimate the
probabilitiesof ship oncollision course upontaking
crash astern maneuvers. The methods were
implemented in Madura Strait and conclusions
obtained from the
analysis of PAW in the research
areaareasfollows:
1 Area B, the area located before the anchorage
zones,andareaD,theareabetweentheanchorage
zones and the new port of Lamong Bay, are
considereddangerareas.
2 The accident probability of the subject ships on
collision
coursesupon taking aslow crashastern
maneuverattheendpartofareaBwillbe77%if
theinitialspeedofthemaneuverisabout8knots.
3 The subject ship will attack the structure of the
new port upon performing the maneuver at the
firsthalfofarea
D.
4 The maximum safe speed of the subject ship to
avoidcollisionwithportstructureisabout6knots.
5 Theprobabilityofshipsoncollisioncoursesatthe
portareaisestimatedbasedonthedistributionof
ships’ speed in the area, and the probability of
shipsto
attackthenewportstructureupontaking
theslowcrashasternmaneuveris50%.
Thesubsequentphaseofthisresearchwillanalyze
the probability of ships taking a crash astern
maneuver, develop the PAW for maneuvering of
othertypesofships,andanalyzetheimplementation
ofthemethodinany
otherdevelopingportareas.
ACKNOWLEDGMENTS
The authors wish to thank the members of the
Maritime Safety System Laboratory of Kobe
University for their assistance. The research is
supported by the Overseas Doctoral Scholarship of
the Indonesian Ministry of Education No.
373/E/T/2011.
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