325
1 INTRODUCTION
With the rapid development of the world economy,
the rapid increase in the number of ships, the
increasing traffic on the water, the frequent port
accesstoshipsandsomehumanfactorshavecaused
the frequent occurrence of water traffic accidents,
which has aroused widespread concern. In the
investigationofthecausesofcollisionaccidents,more
than 80% were caused by human factors that could
notfullyassessthecollisionrisk ofthe shipandthe
implementationofefficientdecision‐making
[1]
.
Atpresent,in orderto solvethe problemof ship
navigationsafety,domesticandforeignscholarshave
done a lot of research and made some progress in
ship collision avoidance. Scholars use methods such
as forecasting and identifying collision collision risk
areas
[2‐3]
,shipdynamicsteeringmodelmethod
[4]
,and
shipautomaticcollisionavoidancemodelmethod
[5‐7]
to achieve effective collision avoidance. In addition,
Liao bingjun
[8]
identified and controlled the risk of
ship collision according to the law of situational
awareness in practice, and proposed the related
conceptsandbasicusageofsafetysituationchart.Hu
Shenping
[9]
basedontheanalysisofshipʹsencounter,
put forward with the Distance to Closest Point of
Approach (DCPA) and Time to Closest Point of
Approach (TCPA)on thebasis of ship maneuvering
freedomofcollision avoidanceaction stage,stage of
riskofcollision,qualitativeandquantitativeanalysis
of the urgent
situation, for ship collision liability
divisionandshipmaneuveringactiontoprovidethe
reference.HuQiaoeretal.
[10]
,aimedatmutualbenefit
and overall optimization, proposed to solve the
problem of ship collision avoidance from a more
humanized and practical perspective based on the
theory of negotiated ship collision avoidance, and
Ship Collision Avoidance Decision Model and
Simulation Based on Collision Circle
J
.Zhang&Q.Hu
M
erchantMarineCollege,ShanghaiMaritimeUniversity,Shanghai,China
B.Liao
COSCOShippingSeafarerManangementCO,LTD,Shanghai,China
ABSTRACT:Inordertogiveconsiderationtobothcomprehensiveevaluationandefficientdecision‐makingin
collisionavoidancedecision‐makingprocess,acollisionavoidancedecision‐makingmodelbasedoncollision
circleisproposedbyintroducingtheconceptofcollisioncircle. Firstly,thefactorscausing ship
collisionare
analyzed.Secondly,thestaticanddynamiccharacteristicsofcollisioncirclesareanalyzedandsummarizedby
using collision circle simulation cases. Thirdly, based on the static characteristics, a reasonably distributed
collisionavoidancedecisionmodelof(PossiblePointofCollision,PPC)wasestablished.Finally,thespatialdata
operationscorealgorithm(Java
TopologySuite,JTS)isusedforlogicaloperationand visualization,soasto
realizetheshipcollisionavoidanceevaluationanddecision.Thedecisionmodelwasusedtoverifytheaccident
scenarioofʺSANCHIʺ,andthe resultsshowed that theobtained collisionavoidanceschemewasreasonable
andinlinewiththe
ʺInternationalRegulationsforPreventingCollisionsatSeaʺandsafetyrequirements,thus
providingareferenceformaritimeoperatorstoavoidcollisionsbetweenships.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 13
Number 2
June 2019
DOI:10.12716/1001.13.02.08
326
verified and analyzed the feasibility of the theory
through simulation data. Youngjun You et al.
[11]
proposed to take collision ratio as an indicator to
determine the time to start collision avoidance
maneuver, and to evaluate the effectiveness of
inferred collision ratio according to the dynamic
characteristics of the ship and collision prevention
algorithm. With the maturity and perfection of
artificialintelligenttechnology,throughthepeople
[12]
workers swarm algorithm, genetic algorithm
[13]
,
mimicryphysicsoptimizationalgorithm
[14]
,simulated
annealingalgorithm
[15]
,theparticleswarmalgorithm
[16]
based on depth competition Q learning algorithm
andA*algorithm
[17]
calculationofcollisionriskand
loss of voyage, such as the objective function to
achieve the optimal give way to the timing, safety,
avoidingcollision,andresumetoresumetime.Atthe
same time, scholars also use the advantages of
intelligent algorithms and models to combine the
theoryofship
collisionavoidancefield,shipdynamic
boundary theory, ship motion mathematical model
and domain model with various intelligent
algorithms
[18‐22]
toestablishtheoptimizationmodelof
ship automatic collision avoidance. In the above
studies, although relevant intelligent algorithms are
usedtoputforwardcollisionavoidanceschemes,the
changerulesofcollisioncirclesandpossiblecollision
points in collision avoidance process have not been
fully clarified, and the guiding significance of
collisionavoidancehasnotbeenfullyexplained.The
details are as follows: 1. The changing rules of
collisioncircleinvariousencountersofshipsarenot
fullyexplained;2.Limitedtothesingle‐shipanalysis,
the PPC of the two ships was not comprehensively
analyzed;3.The dynamic variation rulesofPPC
and
Possible Circle of Collision (PCC) and the specific
model used for Collision avoidance decision are not
fullyexplained.
When a ship is sailing at sea, its speed and
heading are greatly affected by external factors.
Therefore, it is difficult to make a comprehensive
evaluation and efficient decision for collision
avoidance.Thecollisioncirclemodelisdeterminedby
the speed, course, position and other factors of the
two ships, which is especially suitable for the
situationofunstablespeedandcoursechanges.Fully
sorting out the distribution rules of collision circle
greatly improves the comprehensive evaluation and
efficient decision‐making of
collision avoidance of
ships.Thispaperanalyzesthestaticdistributionand
dynamic distribution rules of PCC and PPC,
summarizes the static distribution and dynamic
changerulesofPCCandPPC,establishesthecollision
avoidancedecision‐making model of ships based on
collisioncircle,andappliesthemodeltotheaccident
scene ofʺSANCHIʺ to verify the reliability of the
modelwithanexample.
2 COLLISIONCIRCLEPRINCIPLEANDRELATED
CONCEPTS
2.1 DefinitionoftheApolloniuscircle
Apollonius circle theorem: the ratio of the distance
betweenthemovingpointPandthetwopointsAand
Bisequaltothefixed
valuek(k>1),thenthetrajectory
of point P is A circle with the diameter of the line
connectingthefixedvaluektotheinnerpointCand
theouterpointD,asshowninfigure1.
Figure1ModelofanApolloniuscircle
InFIG.1,thedistanceratiofrompointPtopointA
and point B is A fixed value k. According to the
theorem, all points satisfying this condition form A
circle.LetBbetheoriginofthecoordinate(0,0),Abe
thecoordinate(‐a,0),andthemovingpoint
P(x,y).
Equationofacircle:
222 2
()( )120kxyaxa
(1)
TheradiusRis:
2
1
ak
R
k
(2)
ThecentercoordinateOis:
2
2
(,0)
1
ak
k
(3)
2.2 Definitionofcollisioncircle
The collision circle is the specific application of the
Apolloniscircleincollisionavoidance.LetpointAbe
the position where ship A is located. The distance
frompointAtopointPisS1.PointBistheposition
whereshipBis
located.ThedistancefrompointBto
pointPisS2.S1isthedistancethatAshipsailswithin
acertaintimet,andS2isthedistancethatBshipsails
within the same time t ,then the distance ratio
problemisconvertedintoaspeedratioproblem.
In
thecollisioncircle:k>1,itmeansthatthespeed
ofthe Aship isfaster than thatofthe B ship; when
k=1,itmeansthatthesetofPisnotthecollisioncircle,
and it is the vertical bisector of the connection
betweentheAshipandthe
Bship;whenk<1,therole
oftheAshipandtheBshiparefastandslow,andthe
principle is the same. This paper only analyzes the
case of k>1, which can explain the relevant change
rules.
2.3 ConceptsanddefinitionsrelatedtoPCC,PPCand
PAD
PCCrefers
tothepossiblecollisioncircle.Itrefersto
the collection of all positions at the same place that
327
canbereachedatthesametimewhenthetwoships
havedifferentspeeds.Whenthetwoshipsareatthe
same speed, it is the vertical bisector of the line
connectingthetwoships.
PPC is a possible collision point, which refers to
the intersection of the two ship
ʹs heading lines with
thePCC.
PAD is the predicted danger area. Since the ship
needstopasswithinasafedistance,itisassumedthat
thetargetshipmaintainsspeedanddirection,andthe
target ship PPC is calculated through a certain
function to form an extended area, indicating
the
potentialcollisionareawhenthetargetshipmaintains
speed and direction. If avoiding this area, the two
ships can pass within a safe distance. However, the
formationprocessofPADinvolvescomplexfunction
calculation, and the avoidance effect of different
schemescannot be accurately evaluated, making it
difficulttomakedecisions
incomplicatedsituations.
2.4 Generationruleofcollisioncenterandradius
Accordingtotheformulaofthecenterandradiusof
the collision circle, the following rules are
summarized:
1 The coordinates and radius of the center of the
collisioncirclearerelatedtothedistanceDandthe
speed
ratio k between the two ships, and have
nothingtodowiththecourse.
2 Thecloserkisto1,thefartherthecenterisandthe
larger the radius is, When the two ships change
thespeed,thespeedratiochangesaccordingly.If
the speed ratio is increased, the
center distance
andradiusdecrease,thespeedratiodecreases,and
thecenterdistanceandradiusincrease.Whenkis
in infinite state, the radius of the collision circle
gradually shrinks to 0, which is the B ship
position; when k=1, the set of possible collision
pointsistheverticalbisector
oftheABconnection;
whenk<1,theAshipandtheBshiphasafastand
slow ship transition, and the collision circle is
locatedonthesideoftheAship.
3 When the speed ratio k is constant, the center
distance and radius are proportional to the
distance
betweenthetwoships.Thetwoshipswill
graduallyapproachthedistance,andthedistance
andradiusofthecenterofthecollisioncirclewill
graduallybecomesmaller.
4 Thecenter ofthe collisioncircle islocated onthe
side of the slow ship connecting the two ships.
Whenthe
relativepositionofthefastshipchanges,
when one ship crosses the bow line of the other
ship, the collision circle rotates accordingly and
the arc of the collision circle cutting by the slow
shipchanges.
5 ShipAisfastship,whichislocatedoutsidePCC.
Thereare0~2intersection
pointsbetweenshipAʹs
headinglineandPCC(representedbyEandF),as
showninFIG.2a,2band2c.ShipBisaslowship,
which is located in PCC. There is only one
intersection point between ship Bʹs heading line
and PCC (represented by M),
as shown in figure
2d.
a)Ashipproduces0PPC
b)Ashipproduces1PPC
c)Ashipproduces2PP
d)Bshipproduces1PPC
Figure2. Distribution rule of PPC generated by two ships
onthecollisioncircle
2.5 Establishcollisioncirclecollisionavoidancemodel
The collision circle is a collection of all possible
collisionpoints(the vertical bisector of the two ship
linesatconstantspeed),whichischaracterizedbythe
useofasimpleformulatoexhaustallpossibilities.
According to the production rules of PCC and
PPC,ifthePPCoftwoshipsoverlaps,itmeansthat
the two ships will collide at the overlapping PPC
point.IfthePPCoftwoshipsisveryclose,thenthere
isariskofcollisionbetweenthetwoships.Therefore,
whether the PPC distribution is reasonable plays a
crucialroleinthecollisionbetweentwoships.Based
328
onthis,theshipcollisionavoidancedecisionmodelis
establishedto judge whether the PPC distribution is
reasonableontheonehandandevaluatewhetherthe
decisionplaniseffectiveontheotherhand.
The establishment process of collision avoidance
model :(1) forming collision circle;(2) calculate the
PPCoftwo
ships;(3)takeallPPCasthecenterofthe
circleandsetthedistanceparameterastheradiusas
thecircle to formthecircleʺDistributiondiagram of
PPCʺ. (4) keep the course lines of both sides away
fromeachotherʹsʺPPCdistributionmodelʺ.
3 STATICDISTRIBUTION
LAWANDDYNAMIC
DEVELOPMENTLAWOFPCCANDPPCIN
TWOSHIPS
3.1 StaticdistributionlawofPPCofthetwoships
Byanalyzingthe PPCgeneratedbythetwoships at
thesametime,thecurrentsituationofthetwo ships
and the collision avoidance effect corresponding to
eachcourse
canbeevaluatedmorecomprehensively,
andthecollisionavoidanceproblemcanbeconverted
intothePPCdistributionproblemofthetwoships.
When evaluating the situation with the
distributionproblemoftwoshipsʹPPC,thefollowing
situationswillbedistinguished,asshowninfigure3:
1 When the PPC of
the two ships overlaps (N
denotes the overlap), it means that the two ships
willcollideattheoverlappingpointN,asshown
inFIG.3a;
2 Close PPC distance between the two ships
indicates the existence of collision risk, as shown
inFIG.3b;
3 Thedistancebetweenthe two
shipsʹ PPCislong,
radianandfarawayfromeachotherʹscourseline,
indicating that there is no risk of collision, as
showninFIG.3c;
4 ThePPCofthetwoshipsislocatedonbothsides
oftheconnectinglineofthetwoships,indicating
theobvious
trend,asshowninFIG.3d;
5 When ship A (clipper) has no intersection point
withthecollisioncircle,itmeansthatshipBhasno
abilitytocatchupwithshipAandtherewillbeno
collision,asshowninFIG.3e.
a)Collision
b)Riskofcollision
c)Nocollisionrisk
d)Obvioussecuritysituation
e)Clipperhasnointersectionwithcollisioncircle
Figure3InfluenceofPPCdistributiononthecollisioncircle
oftwoshipsonthesituation
3.2 DynamicdevelopmentrulesofPPCandPCCofthe
twoships
3.2.1 SimulationofdynamicdevelopmentrulewhenPPC
overlaps
The ship collision avoidance simulation platform
isbuiltbyJAVAlanguage,Xrepresentsthelongitude
of the coordinate axis, Y represents the coordinate
axis representing the latitude, and the scale
unit is
nauticalmile(nmile).Inordertoclearlyobservethe
change law, the A ship, the heading line and the
distributioncirclearemarkedinredcolor;theBship,
the heading line and the distribution circle are
markedinbluecolor;thecollisioncircleismarkedin
blackcolor.Throughthesimulationplatformtest,the
two ships collided and observe the dynamic
developmentofPCCandPPC.
Simulationscenariosareshownintable1.
329
Table1.Collisionscenarios
__________________________________________________________________________________________________
time shipsname shipspositionspeed/kn course/(°) PPCposition
__________________________________________________________________________________________________
00:00:00 Aship (32°0.0000´N,123°0.0000´E) 20000(32°3.3333´N,123°0.0000´E)
Bship (32°4.5000´N,123°0.0000´E) 10180(32°3.3333´N,123°0.0000´E)
00:06:00 Aship (32°2.0000´N,123°0.0000´E) 20000(32°3.3333´N,123°0.0000´E)
Bship (32°4.0000´N,123°0.0000´E) 10180(32°3.3333´N,123°0.0000´E)
00:09:00 Aship (32°3.0000´N,123°0.0000´E) 20000(32°3.3333´N,123°0.0000´E)
Bship (32°3.5000´N,123°0.0000´E) 10180(32°3.3333´N,123°0.0000´E)
00:09:36 Aship (32°3.2000´N,123°0.0000´E) 20000(32°3.3333´N,123°0.0000´E)
Bship (32°3.4000´N,123°0.0000´E) 10180(32°3.3333´N,123°0.
0000´E)
__________________________________________________________________________________________________
Thesimulationtestisshowninfigure4.
a)10minbeforecollision b)4minbeforecollision
c)1minbeforecollision d)0.4minbeforecollision
Figure4. Simulation of dynamic development rule of
collision
Accordingtothesimulationtest,whenthePPCof
twoshipsoverlaps,thecollisioncircleshrinkstothe
PPC point until the radius is 0 with the gradual
approach of the two ships;The position of the
commonPPCpointremainsunchanged,andthetwo
ships move towards the common PPC point
and
eventuallycollideatthePPCpoint.Thecourselines
ofthetwoshipswilldividethecollisioncircleinthe
sameradianratio.
The whole process of change is presented as a
wholeinonefigure,anddifferentcollisionsituations
canalsobedescribedinthesameway,as
shownin
figure5.
a)Collisionsituation
b)Crosscollisionsituation
c)Overtakingcollisionsituation
Figure5. Dynamic development rules of collision circles
whencollisionoccursindifferentsituations
3.2.2 Throughthesimulationoftheaccidentcaseof
ʺSANCHIʺ,thedynamicdevelopmentlawofPPC
intheneardistancewasanalyzed
Jan 6, 2018 at about 19:50 PM, Panamanian oil
tankerʺSANCHIʺ collided with Hong Kong bulk
carrierʺCFCRYSTALʺabout160nauticalmileseast
of the Yangtze
river estuary, resulting in the whole
ship ofʺSANCHIʺ caught fire and sank on January
14, 2018. The accident caused a large number of
casualties,propertylossesandseriousenvironmental
pollution. By collecting relevant information of
ʺSANCHIʺaccident,thesimulationsystemwasinput
to observe the dynamic development rules of
PCC
andPPCwhenthecollisionpointwasveryclose.The
simulationscenesareshownintable2.
330
Table2.SimulationscenariosofʺSANCHIʺaccident
__________________________________________________________________________________________________
time shipsname shipspositionspeed/kn course/(°) AshipPPCposition BshipPPCposition
__________________________________________________________________________________________________
19:40:08 Aship (30°49.3150´N,10.4 358 (30°51.2275´N,
124°57.6740´E)124°57.6072´E)
Bship (30°52.8032´N,
124°59.5038´E)13.2 226(30°51.1663´N,
124°57.8088´E)
19:43:08 Aship (30°49.8370´N,10.4 358 (30°51.2161´N,
124°57.6500´E)124°57.6018´E)
Bship (30°52.3096´N,13.2 226(30°51.1407´N,
124°58.
9917´E)124°57.7812´E)
19:47:09 Aship (30°50.5380´N,10.4 358 (30°51.1865´N,
124°57.6150´E)124°57.5923´E)
Bship (30°51.6706´N,13.2 226(30°51.1299´N,
124°58.2596´E)124°57.6997´E)
19:50:09 Aship (30°51.0580´N,10.4 358 (30°51.1515´N,
124°57.5830´E)124°57.5797´E)
Bship (30°51.1873´N,13.2 226
(30°51.1191´N,
124°57.6956´E)124°57.6250´E)
__________________________________________________________________________________________________
Table3Scenarioofsafepassageofthebowline
__________________________________________________________________________________________________
time shipsname shipspositionspeed/kn course/(°) PPCposition
__________________________________________________________________________________________________
00:00:36 Aship (32°0.2000´N,123°0.0000´E)20000(32°3.5645´N,123°0.0000´E)
Bship (32°4.9000´N,123°1.0000´E)10180(32°3.2960´N,123°1.0000´E)
00:03:00 Aship (32°1.0000´N,123°0.0000´E)20000(32°3.6410´N,123°0.0000´E)
Bship (32°4.5000´N,123°1.0000´E)10180(32°3.2728´N,123°1.0000´E)
00:06:36 Aship (32°2.2000´N,123°0.0000´E)20000
Bship (32°3.9000´N,123°1.0000´E)10180(32°3.2004´N,123°1.0000´E)
00:10:00 Aship (32°3.3333´N,123°0.0000´E)20000
Bship (32°3.3333´N,123°1.0000´E)10180(32°2.7592´N,123°1.0000´E)
__________________________________________________________________________________________________
SimulationofʺSANCHIʺaccident,seefigure6.
a)10minbeforecollision b)7minbeforecollision
c)3minbeforecollision d)0minbeforecollision
Figure6.AccidentsimulationofʺSANCHIʺ
Accordingtothesimulationtest,whenthePPCof
two ships is very close, the collision circle shrinks
towardsthePPCpointuntilthetwoshipsareclosest
as the two ships approach gradually. The change
range of PPC position generated by each ship is
relatedtothechangerangeof
relativeazimuthofthe
two ships. In this case, the change range is very
small.Thechange of the proportion of the collision
circledividedbythecourselinesofthetwoshipsis
very small. When the PPC generated by the two
ships is relatively close, there is a
risk of collision.
When the size of the two ships is large, the ship
cannot be regarded as a particle, because collision
maystilloccur.
3.2.3 SimulationofdynamicdevelopmentrulesofPPC
andPCCwhenthebowlinepassessafely
Through the simulation platform test, the two
ships can safely
pass through the bow line, and
observe the dynamic development law of PCC and
PPC.
Thesimulationscenariosareshownintable3.
Thesimulationtestisshowninfigure7.
331
a)Longdistancewithout b)Closertotheline
crossingtheline
c)Clippersoffthecollisiond)Drivepastandletclear
circle
Figure7Simulationofdynamicdevelopmentrulesforthe
safepassageofthebowline
Itcanbeseenfromthesimulationtestthatwhen
the two ships are far away from PPC and the bow
lineisnotreached:withthegradualapproachofthe
twoships,thediameterofthecollisioncircleshrinks
andreachesthenearestapproachpoint(CPA)ofthe
two ships;The
proportion of the clipper course line
dividingcollisioncirclechangesalot.Thecourseline
gradually separates from the collision circle and
moves away from the collision circle. The PPC
graduallycontractstoapointandfinallydisappears,
andgraduallymovesawayfromthecollisioncircle.
Theproportionofthe
collisioncircledividedbythe
slow shipʹs course line remains unchanged, PPC
gradually moves towards the course line, and the
changerangeisverysmallwhenarrivingattheCPA
point,andacceleratesafterarrivingattheCPApoint.
Thewholechangeprocessispresentedasawhole
in one
figure (the Angle between the two shipsʹ
courselineschangesslightly),asshowninfigure8.
a)Trueexercise
b)Relativemotion
Figure8 Shows the dynamic development rule when the
bowlinepassessafely
3.2.4 SimulationofdynamicdevelopmentrulesofPPC
andPCCwhencrossingthebowlinesafely
Through the simulation platform test, the two
ships can pass through the bow line safely, and
observe the dynamic development law of PCC and
PPC.
Thesimulationscenariosareshownintable4.
Thesimulation
testisshowninfigure9.
Table4Sceneofsafepassagethroughthebowline
__________________________________________________________________________________________________
time shipsname shipspositionspeed/kn course/(°) PPCposition
__________________________________________________________________________________________________
00:00:00 Aship (32°0.0000´N,123°0.0000´E)20000(32°3.8277´N,123°0.0000´E)
Bship (32°4.0000´N,123°1.5000´E)10270(32°4.0000´N,122°59.4989´E)
00:09:00 Aship (32°3.0000´N,123°0.0000´E)20000(32°3.6667´N,123°0.0000´E)
Bship (32°4.0000´N,123°0.0000´E)10270(32°4.0000´N,122°59.4259´E)
00:10:30 Aship (32°3.5000´N,123°0.0000´E)20000(32°4.0000´N,123°0.0000´E)
Bship (32°4.0000´N,122°59.7500´E) 10270(32°4.0000´N,122°59.3352´E)
00:12:00 Aship (32°4.0000´N,123°0.0000´E)20000
Bship (32°4.0000´N,122°59.5000´E) 10270(32°4.0000´N,122°59.0000´E)
__________________________________________________________________________________________________
332
a)Beforecrossingthe b)Crossingthebowline
stemline
c)Clippersheadingoffthe d)Drivepastandletclear
collisioncircle
Figure9 Simulation of dynamic development rules when
crossingthebowlinesafely
Through simulation test, it can be seen that this
casealsohasallkindsofchangeruleswhentwoships
pass through safely. Compared with the no‐break
bow line, the direction of the fast ship course line
fromthecollisioncirclechanges,whichincreasesthe
changeofarcdegreeof
thecuttingcollisioncircle.The
collisioncirclerotateswiththechangeoftheazimuth
ofthefastshiprelativetotheslowship,andthearcof
theslowshipcuttingthecollisioncirclealsochanges
duringtheconversionfromonesidetotheother.
The whole change process is
presented in one
picture(fortheconvenienceofdrawing,theincluded
angle of the course line of the two ships slightly
changes),asshowninfigure10.
a)Trueexercise
b)Relativemotion
Figure10 Dynamic development rules for safe passage
throughthebowline
3.2.5 Simulationconclusion
1 By comparing two kinds of collision simulation
and two kinds of safety simulation, the dynamic
developmentrulesofPCCandPPCareanalyzed.
Itcanbeseenthatwhetherthecollisionpointsof
two ships are reasonably distributed plays a
decisive role in the occurrence of collision.
The
distributionofcollisionpointsofthetwoshipsis
easytoobservethroughvisualprocessing,andcan
be used to comprehensively and efficiently
determinewhetherthereisacollisionrisk.
2 Inthestaticanalysis,thereasonabledistributionof
PPCbetweenthetwoshipspromotesthedynamic
change to
a favorable direction;On the contrary,
theunreasonable distribution makes the dynamic
changedevelopinanunfavorabledirection.
3 Inthedynamicanalysis,thePPCofthetwoships
is located on both sides of the connection line of
the two ships, and the process in which the arc
degree of the
collision circle of fast ship heading
linecuttingbecomes smaller, untilit is separated
from and far away from the collision circle is a
necessaryprocessforthedynamicchangerulesof
PCCandPPCinthecaseofnocollision.
4 SIMULATIONVERIFICATIONOFCOLLISION
AVOIDANCEMODELBASEDON
COLLISION
CIRCLE
ThedataofʺSANCHIʺ(A)andʺCFCRYSTALʺ(B)10
minutes before the collision were input into the
simulation platform as the initial state, and the
circularPPCdistributionmodelwassetastheradius
parameter of 1 nautical mile to obtain the collision
avoidancedecisionschemeandcompare
thecollision
avoidanceeffect.Atthismoment,itcanbeappliedto
theactionstrategyofspeedmaintainingsteering.The
decisionofcollisionavoidanceschemeandtheeffect
ofcollisionavoidanceareshownintable5.
333
Table5.“SANCHI”accidentusing “collision‐based ship collision avoidance model” decision‐makingcollisionavoidance
schemeandcollisionavoidanceindexscenario
__________________________________________________________________________________________________
Collisionavoidance ships shipsposition speed decision turning PPCposition DCPA/ TCPA/
schemename/kn course/(°) range/(°)nmile min
__________________________________________________________________________________________________
19:40:08Aship (30°49.3150´N, 10.4 358(30°51.2275´N, 0.19 10.94
Theinitialstate124°57.6740´E)124°57.6072´E)
Bship (30°52.8032´N, 13.2 226(30°51.1663´N,
124°59.5038´E)124°57.8088´E)
Ashipturnright Aship (30°49.3150´N, 10.4 039 +41 (30°50.6576´N, 1.03 9.69
124°57.6740´E)124°58.7612´E)
Bship (30°52.8032´N, 13.2 226(30°51.1663´N,
124°59.5038´E)124°57.8088´E)
Ashipturnleft Aship (30°49.3150´N, 10.4 331‐27(30°51.5897´N, 0.96 12.20
124°57.6740´E)124°56.4131´E)
Bship (30°52.8032´N, 13.2 226(30°51.1663´N,
124°59.5038´E)124°57.8088´E)
Bshipturnright Aship (30°49.3150´N, 10.4 358(30°51.2275´N, 0.96 12.36
124°57.6740´E)124°57.6072´E)
Bship (30°52.8032´N, 13.2 255 +29 (30°51.7139´N,
124°59.5038´E)124°55.4385´E)
Bshipturnleft Aship (30°49.3150´N, 10.4 358(30°51.2275´N, 1.11 9.83
124°57.6740´E)124°57.6072´E)
Bship (30°52.8032´N, 13.2 202‐24(30°50.7865´N,
124°59.5038´E)124°58.5218´E)
__________________________________________________________________________________________________
In theʺSANCHIʺ accident scene, theʺcollision
circlebasedshipcollisionavoidancedecisionmodelʺ
is used to determine the collision avoidance process
andthecollisionavoidanceeffect,asshowninfigure
11.
a)Aturnrightb)Aturnleft
c)Bturnrightd)Bturnleft
Figure11. Simulation of collision avoidance decision of
ʺSANCHIʺscene
In combination with the international regulations
for preventing collisions
[23]
, and both ship should
choosearightscheme,usingcollisioncirclecollision
avoidance decision‐making model to calculate fast
and efficient to amplitude and DCPA and
requirementoftheshipʹsindex,throughvisualization
canclearlyseethatthedistributionofPPCinanall‐
round way, the collision avoidance
decision‐making
schemeandtheresultsmeetthe requirementsofthe
ʺinternationalregulationsfor preventingcollisionsat
seaʺ,asshownintable6.
Table6.AvoidancedecisionschemeinʺSANCHIʺaccident
scenario
_______________________________________________
plan ships decision turning DCPA/ TCPA/
name course/(°) range/(°) nmile min
_______________________________________________
Aship Aship 039 +41 1.03 9.69
turnright Bship 226
Bship Aship 3580.96 12.36
turnright Bship 255 +29
_______________________________________________
5 CONCLUSION
Thecollisioncirclemodelhastheadvantagesofwell
adaptingtothechangeofspeed,courseandposition,
and theʺcollision circle ship collision avoidance
decisionmodelʺ is applied to evaluate and visualize
thedecision‐making,whichtosomeextentsolvesthe
problem of poor effect of comprehensive
evaluation
andefficientdecision‐makingforships.Thecollision
circlemodelwasusedtosimulatetheaccidentscene
ofʺSANCHIʺ, and the results showed that the
proposed collision avoidance scheme met the
requirements ofʺinternational rules for collision
avoidance at seaʺ and safety requirements, which
provedthe feasibility of
the model and provided an
objectiveandefficientmethodforcollisionavoidance.
ThePPCdistributionmodelcorrespondsto different
geometricrelationshipsindifferentsituations,andthe
parameter setting of the geometric model is highly
subjective based on experience. Therefore, how to
flexiblyselecttheappropriatemodelandimprovethe
334
setting of geometric parameters will require further
researchandexperiments.
REFERENCES
[1]Huang Ying, Li Lina, Chen guoquan. Design and
application of decision support module for collision
avoidance of urgent danger [J]. Journal of jimei
university:naturalscienceedition,2011,16(6).
[2]Wu Zhaolin. Selection of collision avoidance actions
based on PAD information and improvement of PAD
graphics [J]. Journal of dalian
maritime university,
1986(4):16‐26.
[3]Fang Xianglin, Fu Wanxuan. Danger zone model for
velocity ratio circle prediction and its application in
ARPAsystem[J].Chinamaritime,1984(2):5‐17.
[4]Wang Renqiang, Zhao Yuelin, Xie Baofeng.
Mathematical model of collision avoidance in ship
dynamic steering [J]. Journal of dalian maritime
university,
2014,40(1):17‐20.
[5]HeYixiong,HuangLiwen,MouJunmin,etal.Automatic
collision avoidance action plan for give‐way vessels in
cross‐encounter situation [J]. Journal of Harbin
engineeringuniversity,2015(08):1024‐1029.
[6]Xiong Yong, He Yixiong, Huang Liwen. Multi‐ship
automaticcollisionavoidancecontrolmethod basedon
speedobstacle
[J].Chinamaritime,2015,38(3).
[7]Chen Yaojie, Li Shuang, Fan Huan, et al. Research on
multi‐ship automatic collision avoidance based on
velocity vector coordinate system [J]. Computer
simulation,2015,32(6):420‐424.
[8]Liao Bingjun. Introduction to safety situation diagram
avoidancemethod[J].Navigationtechnology,2018.
[9]Hu Shenping. Classification and quantification
of
collision avoidance stage in ship encounter process [J].
Chinamaritimeindustry,2001(2):83‐87.
[10]Hu Qiaoer, Hu Qinyou. Design and analysis of ship
collision avoidance simulation system based on
negotiation[J].Chinamaritime,2009,32(1):54‐59.
[11]You Y, Rhee K. Development of the collision ratio to
inferthetime
atwhichtobeginacollisionavoidanceof
aship[J].AppliedOceanResearch,2016,60:164‐175.
[12]MaWenyao,WuZhaolin,YangJiaxuan,etal.Decision
support for collision avoidance path planning of
artificialfishswarmalgorithm[J].Chinamaritime,2014,
37(3):63‐67.
[13]Ni Shengke, Liu Zhengjiang, Cai Yao,
et al. Collision
avoidance decision support for ships based on genetic
algorithm [J]. Journal of Shanghai maritime university,
2017(1).
[14]YuJiagen,LiuZhengjiang,BuRenxiang,etal.Collision
avoidancedecisionofshipsteeringbasedonsimulation
physics optimization algorithm [J]. China maritime,
2016,39(1):36‐38.
[15]Yang Baicheng, Zhao Zhilei.
Multi‐ship collision
avoidance decision based on improved simulated
annealing algorithm [J]. Journal of dalian maritime
university,2018,44(2).
[16]Wang Deyan, liu Yian. Application of particle swarm
optimization in multi‐ship collision avoidance decision
[J].Computerengineeringanddesign,2009,30(14):3380‐
3382.
[17]Shen Haiqing, Guo Chen, Li Tieshan,
et al. Intelligent
collision avoidance navigation method for unmanned
ships considering rules of navigation experience [J].
Journal of Harbin engineering university, 2018,
260(06):48‐55.
[18]Huang Y, P. H. A. J. M. van Gelder, Wen Y. Velocity
obstacle algorithms for collision prevention at sea[J].
OceanEngineering,2018,151:308‐321.
[19]Liu
Renwei,Xue Yanzhuo, Liu Yang, et al. Automatic
collision avoidance model and its application in
restricted waters [J]. Journal of Harbin Institute of
Technology,2018(3).
[20]LiLina,XiongZhennan,GaoYansong,etal.Generation
and optimization method of single ship collision
avoidance intelligent decision [J]. Information and
control,2002,
32(2):189‐192.
[21]ZhuoYongqiang,andT.Tang.ʺAnintelligentdecision
support system to ship anti‐collision in multi‐ship
encounter.ʺWorld Congress on Intelligent Control &
AutomationIEEE,2008.
[22]LAZAROWSKA A. Ant Colony Optimization based
Navigational Decision Support System [J]. Procedia
ComputerScience,2014,35:1013‐1022.
[23]
Zhao jin‐song, wang feng‐chen, et al. Collision and
collision avoidance rules. Dalian maritime university
press,1997.
