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1 INTRODUCTION
Riskmetricsareimportantforcollisionpreventionat
sea. When one ship encounters with obstacles, the
Officer On Watch (OOW) needs to appraisal the
dangerous levels of these obstacles for decision
making,e.g.continuewithcurrentoperationsortake
new actions. The importance of risk metrics is also
stipulatedininternationalregulationsforprevention
collisionatsea(COLREGs),whichrequeststheOOWs
to “make a full appraisal of the situation and of the
riskofcollision”(Organization),1972).Hence,various
collision risk metrics have been developed and
proposed in past decades and these metrics have
become the core
of various collision alert systems
(Goerlandt,Montewka,Kuzmin,&Kujala,2015)and
automatic collision avoidance systems (Johansen,
Perez,&Cristofaro,2016).
Mostofthecollisionriskmetricsusuallychoosea
pairofshipsfromtraffictoevaluatetherisk.Ineach
pair,theshipunderourcontrolisusuallycalledown
ship (OS) and the other is target ship (TS). By
choosing different TSs, different pairs of ships are
obtained and the collision risk in each pair is
evaluated. That means the ship out of the pair is
temperately ignored. Researchers use numerous
indicatorstocalculatethecollisionriskwhichis
also
named as collision risk index (CRI). In these
indicators, two frequently used ones are Distance to
Closest Point of Approach (DCPA) and Time to
ClosestPointofApproach(TCPA).Bythisapproach,
theOOWscancalculatetheCRIofeachTS, findthe
TS in conflict with the OS (whose
CRI over the
threshold),andidentifythemostdangerousTS.
Thisgroupofmethods,however,havedifficulties
inshowingtheentirerisklevelofthetrafficfortheOS
Measuring Ship Collision Risk in a Dense Traffic
Environment
Y.Huang&P.H.A.J.M.vanGelder
DelftUniversityofTechnology,Delft,TheNetherlands
ABSTRACT:Collisionriskmeasurementisanessentialtopicforshipcollisionprevention.Manyriskmeasures,
i.e.DCPA/TCPA,etc.,decoupletheshiptrafficintoseveralpairsofshipsand thenevaluatetheriskineach
pair.Thiskindofmeasurementlosessomeinformationofthe
entiretrafficandmightincludesomebiasesin
risk measurement, especially in multiple‐ship scenarios. In this article, Imminent Collision Risk Assessment
(ICRA)isextended,whichformulatescollisionriskasaratioofreachablemaneuversleadingtoacollisionand
allreachablemaneuvers(velocities).Twogroupsofscenarioshavebeen
simulatedtoshowtheICRAissuitable
forassessingthecollisionriskinmultiple‐shipscenarios.Moreover,twoimprovementshavebeenintroduced:
(1)ageneralizedvelocityobstaclealgorithmisintroducedtocollectthemaneuversleadingtocollisions,which
considersshipdynamics;(2)theconstraintsofforcesareconsideredintheformulation
ofreachablemaneuvers.
As a result, the proposed measurement helps one ship assess the risk of approaching obstacles which are
difficulttoavoidthecollisionintermsofown‐ship’sdynamicsandkineticconstraints.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 13
Number 4
December 2019
DOI:10.12716/1001.13.04.05
738
when the OS encounters with multiple ships. In
technique level, there are no agreements on
combining various CRIs into one number which
representstheriskoftheentiretraffic.Therearesome
alternatives, such as average, sum, and maximum,
while they more or less have some drawbacks. The
“average”underestimates
themostdangerousTS;the
“maximum” ignores the influence from non‐
conflictingTSs;the“sum”offerslimitedinformation
aboutcollisioneventineachpair.
Furthermore, when we decouple the traffic in
severalpairsofships,welosesomeinformationabout
traffic and introduce some biases in collision risk
assessment. The
biases of risk are caused by two
aspects:(1)theriskcausedbyanon‐conflictingTSis
ignored. Although a non‐conflicting TS does not
directly have a conflict with the OS, it might block
some operations of the OSwhich mightresult in an
inevitableencounterbetweentheOS
andanotherTS;
(2)theriskcausedbytrafficcharacteristicsisignored.
Forexample,theCRIvalueineachpairofshipsare
thesame,butwell‐organizedtrafficseemstobesafer
thanothers(seeSection3.2fordetails).
Thispaperoffersanewperspectivetoevaluatethe
collision
riskfortheOS,whichconsidersallthetarget
ships together. The risk measurement presented in
literature(Y.Huang,Gelder,&Mendel,2016)and(Y.
Huang & van Gelder, 2019) is applied to multiple‐
ship cases, which is named as Immediate Collision
Risk Assessment (ICRA) in this paper. Moreover,
basedon
theoriginalICRA,theship’sdynamicsand
constraintsonforcesareconsidered.Thestructureof
thispaperisasfollows:thebackgroundandgapsof
existingcollisionriskassessmentarepresentedinthis
section;thedetailsof ICRA and theimprovedICRA
areshowninSection2;Section3collects
threegroups
of scenarios which show the performance of ICRA
and improved ICRA; at the end, discussion and
conclusion are presented in Section 4 and Section 5,
respectively.
2 COLLISIONRISKMEASUREMENT
2.1 ImmediateCollisionRiskAssessmentMethod
Immediate collision risk assessment (ICRA) (Y.
Huang et al., 2016) measures the collision
risk with
the aid of “room‐for‐maneuver” (Degre & Lefevre,
1981).In(Y.Huang&vanGelder,2019),thisconcept
is further developed. The construction of the ICRA
follows some steps: firstly, the encounter scenarios
have been projected from geography space into
velocityspace(V‐space)andthe
velocitiesleadingto
collision are collected in Velocity Obstacle (VO) set;
secondly,asetofvelocitiesthatoneshipcanachieve
is denoted as reachable velocity (RV) set; lastly, the
overlap of VO set and RV set are the reachable
velocity leading to collision and the collision risk is
measuredby
thepercentageoftheoverlap,i.e.:
VO RV
RV
S
ICRA
S
, (1)
where
S
represents an operation that calculates
the area ofthe inputted polygon, e.g.
RVS
is the
area of RV set;
VO RV
represents the overlap of
VOsetandRVset,asshowninFig.1.
The formulation of VO set is relying on velocity
obstacle algorithm. In some maritime studies, this
algorithmisalsonamedasCollisionThreatParameter
Area (CTPA) (Lenart, 1983; Szlapczynski & Krata,
2018) or Collision Danger Sector
(CDS)(Pedersen,
Inoue,&Tsugane,2003).Readerswhoareinterested
in this algorithm can read more in the literature
(Fiorini & Shiller, 1998) and its applications in
maritimestudiescanbefoundin(Y.M.Huang,van
Gelder,&Wen,2018)and(P.Chen,Huang,Mou,&
van Gelder, 2018). The construction
of RV set is
relatedwithtimetocollisionandmaneuverabilityof
the ship. For the sake of simplification, some
researchers use constant maximal speed and
instantaneousheadingchangestoconstructtheRVset
(Westrenen&Ellerbroek,2017).
Figure1TheillustrationofICRAmeasurement
In this paper, we employed the VO algorithm
proposedintheliterature(Fiorini&Shiller,1998),in
whichthetarget‐shipisassumedtokeeptheconstant
speedandcourse.TheRVsetissimplifiedasthehalf
ofthewholeV‐spaceoftheOS,i.e.velocityinsurge
direction
accepts
max
0,
u
vv
and velocity in sway
directionis
max max
,
v
vvv
.Oneexampleisshownin
Fig.3(2).
2.2 ImprovedICRA
In the previous section, the constructions of VO set
and RV set accept some simplifications. Specifically,
the ship’s dynamics is ignored and the RV set is
simply equal to the half of V‐space. However, these
simplifications influence the
performance of I‐ICRA
measurementincloserange.Forexample,theinclose
range, the many collision‐free solutions, i.e.
VO RVv , are not reachable regarding ship’s
dynamics.
Tosolvethisproblem,weusegeneralizedvelocity
obstacle (GVO) to collect the velocity set leading to
collisions, which was proposed in the literature
(Bareiss & van den Berg, 2015) and applied to ship
collision avoidance in the literature (Y. M. Huang,
Chen,&
vanGelder,2019).
2.2.1 Themotionmodeloftheshipusingvelocityasthe
input
The ship dynamics model used in this paper is
fromliterature(Fossen,2002).xand
τ
denotestates
of the ship and inputted forces. x consists of the
position of the ship, heading, surge speed, sway
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speedandyawrate,i.e.
T
,, ,,,
x
yuvr
.Theinputted
forceswillmodifythestatesoftheship,seeFig.2(1).
Figure2.Setthedesiredvelocityu*asinputstothesystem.
Since the VO set collects velocities instead of
forces, we introduce a PD controller to switch the
inputfromforcestothedesiredvelocitynotedasu*,
seeFig.2(2).Thecontrolisformulatedas:
*
VV
pd
KK
u xx
, (2)
here, K
p and Kd are feedback matrices; u* is desired
velocity contains the desired surge speed, sway
speed,andheading.Inreturn,wehaveanewmotion
model:
*
dp
p
BK V BK
KV
Rv
I0
xu
Cvv Dvv x
0M
, (3)
here,
T
,,uvrv
isvelocitystates;C(v),D(v),M,and
RareCoriolis,damping,mass,androtationmatrices,
respectively; I is a 3‐by‐3 identical matrix and
T
33 33
B,
0I
.Thisequationcanalsoberewrittenin
ageneralform:
**
12
,,, ,,
pd pd
f
xu fxKK fxKKu x
, (4)
where
f isnonlinear.
2.2.2 Thedesiredvelocityleadingtoacollision
Firstly,wedefinethecollisioneventattimetasan
eventthatoneshipviolatesaminimumsafetyregion
oftheothershipattimet,whichisformulatedas:
ij
P
t P t ConfP
, (5)
P
iandPjarethepositionoftheOSandtheTS;ConfP
istheminimumsafetyregion;
j
P
t ConfP
isaset
ofsafetyregionsurroundingthetargetship.
Secondly, we formulate the relation between P
i
and u* in the help of a linearization of equation (4)
arounditsinitialstatex
0
andinitialinputu
0
:
*0
ii
ttGt xx uu
, (6)
whereGisaresponsematrix;
i
tx
isthetrajectory
oftheOSgiventheinitialstateandinputs,whichis
calculatedviaRunge‐KuttaIntegration.Sinceweonly
needthepositionoftheOS,weintroduceamatrixC,
which:
*0
*0
iii
i
Pt C t C t CGt
Pt CGt
xx uu
uu
, (7)
here,
i
Pt
istheestimatedtrajectoryoftheOSwith
initialinputu
0
.
Thirdly,wesubstituteEquation(7)toEquation(5)
and formulate the changes on inputs leading to
collision:
1
*0
sUO
ji
CG P t P t ConfP t
uu
.
(8)
Thissetonlycollectsu*resultinginacollisionat
time t. Thus, if we sum the
sUO t
that
0,t
,
we obtain all u* leading to a collision in the future,
whichisnamedasUOset.
*0
0
sUO UO
t
t
uu
.
2.2.3 Consideringconstraintsonforces.
InSection2.2.2,wecollectthevelocitythatleading
toacollisioninthefuture,while,notallthevelocity
outofthissetarereachablefortheshipregardingits
dynamics and constraints. For instance, one ship
might not generate enough powers to achieve
the
desiredvelocity.Hence,inthissection,theconstraints
onforcesareconsidered.
Let say, the force in each direction is satisfying
constraints:
lb ub
τττ. (9)
Then,wecanformulatetheforcesasafunctionof
the states and the desired velocity according to
Equation(3)andEquation(2),i.e.:
*
21pd p d
KKVf KVKVf τux
. (10)
Combining Equation (9) and (10), we derive the
constraintsonthedesiredvelocityu*:
11
*
212 1pd p d pd p d
K
K Vf K V K Vf K K Vf K V K Vf
lb ub
τx u τ x
.
(11)
Equation (11) is the reachable velocity set
satisfying the constraints on forces given a PD
controller.
3 CASESTUDIES
Threegroupsofscenarioshavebeendesignedinthis
section. The performance of ICRA in multiple‐ship
encountersanddifferent traffic modesarepresented
inSection3.1andSection3.2,
respectively.InSection
3.3, a demonstration of I‐ICRA considering ship
dynamicsandconstraintsisshown.
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3.1 PerformanceofICRAinmultiple‐shipscenarios
Threeencounterscenarioshavebeensimulatedto
showtheperformanceoftheICRA.Ineachscenario,
the own‐ship is placed at the origin heading to the
North with speed at 10 knots, while the number of
targetshipsisincreasingfrom
onetothree.Inthefirst
scenario,theOSonlyencounterswithonetarget‐ship
(TS1)whoseDCPAis0.5[NM]andTCPAis0.25[h].
Inthesecondscenario,one extra target‐ship(TS2)is
introducedandtheDCPAandTCPAremainthesame
as that of the TS1.
In the last scenario, the OS
encounters with three target ships together, namely
TS1, TS2, and TS3. The details of the settings are
presentedinTable1.
Table1.Settingsofscenario
____________________________________________
Position Heading Speed DCPA TCPA
[NM] [deg] [knot] [NM][h]
____________________________________________
OwnShip (0,0)000 10.0‐‐
TS1(0.65,‐1.44)358 16.0 0.50.25
TS2(‐2.45,1.80)081 8.50.50.25
TS3(3.38,3.02) 268 14.7 0.50.25
____________________________________________
Inatwo‐shipscenario,theTS1 approachestheOS
fromitssternandtheshipblocksthestarboard‐turn
optionsoftheOS,asshowninFig.3(2).Thebluearea
is the VO set which collects the velocity of the OS
leadingtoacollisionwiththeTS1.
Therestofthearea
is collision‐free for the OS, which also can be
interpreted as the “room‐for‐maneuver”. According
to Section 2.1, the percentage of the VO shows the
dangerleveloftheOSwhichis0.749.Thatmeans,the
shipstillhas0.251chancetoavoid
thecollision.
Figure3TheV‐SpaceoftheOSwhenitencounterswithone
TS,twoTSsandthreeTSs
When we introduce one more ship (TS2) whose
DCPAandTCPAarethesameasthethatofTS1,the
entire collision risk is undefined by traditional
methods(CRImethods),especiallythenewshiphas
the same CRI with the TS1. As we can expect that
more ships in the same
area might increase the
collisionrisk,buthowdothenewCRIinfluencethe
originalCRIisunclear.ICRAoffersasolutiontothis
problem.Onemoreshipblockssomeextra“room‐for‐
maneuver” which leads to less chance to avoid
collisiondangers,asshowninFig.3(2).As
aresult,
the encounter scenario would be more dangerous
thanthepreviousscenario.Asweshow,theICRA,in
thiscase,raises from0.749to0.925,whichmeansthe
number of solutions for the OS to avoid collision
decrease and the OS is more dangerous than the
previous case. When the
OS encounters with three
ships together, the area of “room‐for‐maneuver” is
shrunkfurthermore.Whenthewholevelocityspaceis
occupiedbytheVOsets,thatmeans, the collisionis
inevitableinthefutureandtheICRAreaches1.
3.2 Well‐organizedtrafficversuschaotictraffic
In this section,
the influence of ship traffic on the
measurement of collision risk is shown. Three
scenarios are simulated, in which three target ships
are involved, namely TS1, TS2, and TS3. The same
shipindifferentscenarioshasthesameDCPA,TCPA,
andrelativedistance,whilethepositionandvelocity
are slightly different.
For example, the TS1 in each
scenario has different positions and speeds, but the
samesettingsofDCPA,TCPA,andrelativedistance.
Inthefirstscenario,threeshipsaregrouped as a
vessel train (L. Y. Chen, Hopman, & Negenborn,
2018),specificallythesevesselshavethesamevelocity
andkeep
theformationinpurpose.Inthesecondand
thethirdscenarios,eachtargetshipkeepsitsrelative
distance to the OS in the first scenario, but the
bearings of each target ship are changed. In the
second scenario, the bearing of the target ship is
changed in a small angle, say
an arbitrary angle
smaller than 60 degrees (See Fig. 4); in the last
scenario, the changing range is enlarged to 240
degrees.AnillustrationisshowninFig.4.TheTS3 is
locatedatPointAinthefirstscenario,whiletheTS3
is randomly located on the arc BC
and DE in the
secondandthirdscenariorespectively.Thedetailsof
thesettingsareshowninTable2.
Figure4. The illustration of the position of TS3 in three
differentscenarios
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Table2.Settingsofscenarios
____________________________________________
Case Ship Position Heading Speed DCPA TCPA
[NM] [deg] [knot] [NM][h]
____________________________________________
OwnShip (0,0)000 10.0‐‐
1 TS1 (‐0.29,4.99)174 10.0 0.05 0.25
TS2 (‐0.19,4.00)174 10.0 0 0.20
TS3 (‐0.10,3.00)174 10.0 0.05 0.15
2 TS1 (‐1.23,4.84)153 10.6 0.05 0.25
TS2 (0.14,4.00) 184 10.0 0 0.20
TS3 (‐0.46,2.97)161 10.1 0.05 0.15
3 TS1 (4.14,2.81) 265 16.5 0.05 0.25
TS2 (‐2.56,3.07)112 13.9 0 0.20
TS3 (2.98,0.40) 070 21.0 0.05 0.15
____________________________________________
Figurer5. the V‐Space of the OS when it encounters with
three ships in three cases, namely well‐organized case,
disorder case, and chaotic case. (the DCPA, TCPA and
relative distance of one ship, e.g. TS1 in case 1, are as the
sameastheshipinothercases.)
Fig.5(1)‐(3)showthelayoutsofeachscenarioand
(4)‐(6) show the V‐space of the OS in relevant
scenarios.Thefirstscenarioisacasethatthetrafficis
well‐organized; in the second scenario, the traffic is
relativelydisorderedcomparingwiththefirst;inthe
last
scenario,thetrafficisconsideredtobea chaotic
case.
ThetargetshipshavethesameDCPA,TCPAand
relativedistanceinthesescenarios.Thatimplieseach
pair in these scenarios has the same collision risk.
Hence, we might conclude the collision risk in each
scenario is the same. However,
the OS in the last
scenario seems more dangerous than the others
becausetheOSmightnoteasilyfindonecollision‐free
solution.
ICRA can catch the difference in collision risk in
these scenarios. The value of ICRA indicates the
collisionriskinthesescenarios,whichare0.61,0.62,
and0.93.
TheICRAshowsthedifficultyof avoiding
thecollisionineachcase.AlthoughtheDCPA,TCPA,
andrelativedistanceareallthesameineachscenario,
the room‐for‐maneuvers are different in each
scenario.
Three VO sets from three target‐ships have been
identifiedineachscenario.Inthe
firstscenario,traffic
iswell‐organizedandalltheseVOsetsarecontaining
inoneVOsetgeneratedbyTS3.Thatmeans,iftheOS
can avoid collision with the TS3, the ship can avoid
collision with TS2 and TS1, as well. In the last
scenario, each VO set blocks different
groups of
maneuvers. For instance, the collision‐free solutions
foravoidingTS3(thebottom‐leftarea)areblockedby
TS1.Thatmeans,evenifthesolutioncanhelptheOS
toavoidtheTS3,itmightnotavoidcollisionwithTS1.
As a result, the collision danger is more difficult
to
rejectandthecollisionriskishigh.
3.3 DemonstrationofICRAconsideringship’sdynamics
Inthepreviousscenarios,themaneuverabilityofthe
shipisignoredandtheshipisenabledtochangeits
velocity immediately. However, the real ship has
various constraints in kinematic and dynamics. For
example, the ship
has maximal speed, maximal
turningrate,maximalthrust,etc.
Inthisscenario,thedynamicmodeloftheshipis
considered. Theship model called “CyberShip II” is
consideredtobetheOS,whichisa1:70smallscaled
marine surface vehicle model. The mass of this ship
modelis
23.8kgandthemaximalforceinthesurge
and sway and yaw moment are [10; 10; 10],
respectively.Thesescalednumbersrepresentthefull‐
scale ship weights 8163400kg and forces/ moment
constraint to [3430000; 3430000; 240100000],
respectively. The scaled‐up law follows Froude
scalinglaw(Moreira,Fossen,&GuedesSoares,
2007).
The other parameters of this model ship are
presented in literature (Skjetne, Smogeli, & Fossen,
2004). The settings of PD controllers are: Kd=
diag([200,200,10]); Kp = diag([5,5,5]); The target‐ship
is assumed to keep its motion. The layout of this
scenarioispresentedinTable3.
Table3Settingsofscenario
_______________________________________________
Position Heading Speed DCPA TCPA
[NM] [deg] [knot] [NM][h]
_______________________________________________
OwnShip (0,0)000 10.0‐‐
TS1(4.24,4.24) 248 18.4 0 0.25
_______________________________________________
FollowingthemethodspresentedinSection2,we
generateVOsetandUOsetoftheTS1andpresentin
Fig.6(2)and(3).InFig.6(2),weignorethedynamic
model of the OS and assume the OS can change its
velocity immediately. In return, we calculate the
I‐
ICRA=0.38,whichmeanstheshiphasmorethanhalf
chance to avoid a collision and the encounter
scenario, which is not such urgent. However, if we
considertheship’sdynamicsandconstraints(e.g.the
maximalforcesandmoment),theI‐ICRArisesto0.63.
Thatisbecause
mostofthecollision‐freesolutionsin
Fig.6(2)arenotreachablegivenconstraintsandthe
PD controller. In the UO set, the shadow area
represents the velocity is reachable for the OS but
leadingtocollision;thewhiteregionisthereachable
andcollision‐freesolutiontotheship.
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Figure6. The encounter scenario when we consider the
manoeuvrabilityoftheOS.
4 DISCUSSION
4.1 ComparingbetweenICRAandotherCRImethods
(basedonCPA)
ThreedifferencebetweenCRImethodsandICRAare
identified in this paper. Firstly, ICRA defines the
collision risk as the chance of avoiding a collision
which considers the ability of the OS to avoid a
collision,whilemost
ofCRImethodsignorethispart.
Secondly,ICRAmapsalltheobstaclesintoresolution
space (i.e., V‐space) together and then measures the
collisionrisk,whereastheCRImethodsdecouplethe
traffic first and then assess the risk in each pair of
ships.Thirdly,the constructionofICRAis relatively
independentoftheexperts’judgment.
4.1.1 ICRAconsiderstheabilityoftheOStoavoida
collision
Fig. 7 shows the bow‐tie model of the OS
encounters with three target‐ships (TS1, TS2, and
TS3).ThecollisionbetweenTS1andtheOSmeansthe
path(sayPath1)between TS1
andthetopevent(or
“Collision”)isconnected.
TheCRIsindicatetheconnectivityofthese paths.
IfoneTS’sriskindexexceedsthethreshol d,thepath
between this TS and the OS is connected, which
implies this TS is dangerous for the OS. Then, a
collision alert is triggered. However,
this approach
ignores the “barriers” on the path which can block
these paths from TSs to the top event. Here, the
barriers can be interpreted as maneuvers. Before
collisionshappen,theOSiscapabletotakeallkinds
of maneuvers to block the paths, i.e. avoid the
collision. In Section 3.2,
we show that even the
upcomingship(e.g.TS3)hasthesameCRI,theroom‐
for‐maneuveroftheOStoavoidcollisionisdifferent.
Inthefirstscenario,theOScantakeeitherportturns
orstarboardturnstoavoidthecollision,whileinthe
last scenario, the OS
can avoid the collision if and
only if the ship chooses a hard port‐turn. Thus, the
last scenario should be more dangerous than in the
first scenario. The CRI methods only consider the
dangerslevelof“threats”(thea pproachingships)but
ignore the chance of the OS to avoid the
“threats”.
Therefore, CRI methods cannot distinguish the
difficultyoftheOStacklingthesethreats.
ICRAisdesignedtoconsidertheabilityoftheOS’s
maneuverability to prevent a collision. In returns,
ICRA not only measures the danger levels of the
threats (TSs) but also present the ability of the OS
blocks the paths. When the ICRA exceeds the
thresholds, it basically tellsthe officer on board that
thecoming threats (TSs)arenot only dangerousbut
alsodifficulttofindasolutiontopreventcollisions.
Figure7.Bow‐tiemodeloftheshipcollisionevent.
4.1.2 ICRAmeasures thecollisionriskoftrafficasa
whole
TheICRAmeasures the collision riskasa whole,
whichcanpreventtwodrawbacksofCRImethodsin
multiple‐shipcases.
Thedecouplingtechniquelosessomeinformation
about the traffic, which results in biases in collision
risk assessment. As Section
3.2 shown, a well‐
organizedscenarioislessdangerousthanthetrafficin
chaos, even the risk index of each pair in these
scenarios remains the same. The CRI cannot show
thesedifferencestotheOOW,buttheICRAcould.
Inconveniencein findingconflict resolutions. CRI
onlyshowstherisk
inpairsandignoretheimpactsof
other ships. Thus, when we find one solution
reducing the risk in one pair of ships, we cannot
guarantee this solution can also reduce the risk in
anotherpair.Insomeworsecases,thissolutionmight
create some new conflicts. Thus, the OOWs need
to
tryandtest the solutions ineachpair of ships,until
theycanfindtheonewhichreducesalltheconflictin
eachpairofships.Conversely,theICRAmeasuresthe
collision risk as a whole and it can directly identify
collision‐freesolutionstotheOOWs.Thetarget‐
ship
whoistemporarilynotinconflictisalsoconsideredin
theICRA.Asaresult,thesolutionsidentifiedbythe
ICRA method can solve all the conflicts and would
notcreateanewconflict.
4.1.3 Independentfromtheexperts’judgment
ThesettingandmeaningofICRAareindependent
of the
OOW and experts, while the construction of
CRI methods strongly relies on expert’s knowledge.
Moreover,thereisalackofgeneralagreementsonthe
settingsofCRI(Goerlandtetal.,2015).Thatmeansthe
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samescenariomighthavedifferentCRIsanddifferent
conclusions when the differentexperts are involved.
On the other hand, the construction of the VO set
relies on the obtained traffic data and the RV set
dependsonthemaneuverabilityoftheship,whichis
relativelyindependent of experts.Additionally, the
meaning of ICRA is also clear. When the value of
ICRAreaches1,thentheOSisinevitablecollidewith
obstacles, even the collision has not happened yet.
WhenICRA is 0.5,that means if theOS choosesthe
solutions randomly, the ship still has 50% to collide
withother
ships.
4.2 Potentialapplications
The ICRA offers a new perspective to measure
collision risk, which can rich the tools for risk‐
informed decision making on board. In literature
(Goerlandt et al., 2015), researchers proposed a
framework for risk‐informed collision alert, which
helps share situational awareness between experts
and OOWs. Some
widely used indicators are listed,
but few indicators reflect the ability of the ship to
avoidacollisionandconsidertheentiretraffic.ICRA
canbeusedasoneindicatorinthisframeworkwhich
offerssomeinformationaboutthedifficultyoftheOS
shipavoidingcollisionwiththeentiretraffic.
ICRA also can be used in risk‐based decision
making,e.g.collisionavoidance.ICRAconsistsofVO
setandRVsetwhichcanhelptheOOWstoeliminate
the solutions leading to collisions and find the
collision‐freesolutionstoalltheencounteringships.
5 CONCLUSION
In this paper, Immediate Collision
Risk Assessment
(ICRA) is proposed to meas ure collision risk in a
densetrafficenvironment,i.e.multiple‐shipscenarios.
Thecollisionriskismeasuredbythepercentageofthe
maneuvers(velocities)leadingtoacollision.Totackle
the dynamics of ship and constraints on forces, an
improved‐ICRA is proposed, where
the generalized
velocityobstacle(GVO)algorithmisapplied.
Threegroupsofscenarioshavepresented.Thefirst
group of scenarios shows the performance of ICRA
when the number of Target Ship (TS) is increasing;
the second group of scenarios shows the proposed
ICRA is enabled to measure the collision risk in
different
traffic modes, specifically well‐organized
traffic case and chaotic traffic case. These two cases
show ICRA is suitable to use in multiple‐ship
scenarios. The last scenario demonstrates the
improved‐ICRA that considers ship dynamics and
force constraints. It shows that the collision risk is
underestimated when we ignore the
ship dynamics
andconstraintsonforces.
ThreefeaturesofICRAhavebeenidentifiedinthis
paper: (1) it measures the collision risk considering
theabilityoftheOwnShip(OS)toavoiddangers;(2)
itmeasurescollisionriskoftheentiretrafficinsteadof
decoupling the traffic, which is more suitable
in
multiple‐ship scenarios; (3) the measurement is
independentfromexperts’opinions. We believethat
the proposed ICRA offers a new perspective in
collision risk measurement, which not only enriches
the choices in the developments of risk‐informed
collisionalert systems butalso cansupport the risk‐
basedcollisionavoidance
inmultiple‐shipscenarios.
Future research will consider the following
directions. Firstly, the influence of regulations, e.g.
COLREGs,willbeincluded.IftheOScomplies with
regulations, the size of RV set will be modified and
thenthemeasuredriskischanged,e.g.(Y.Huang&
van Gelder, 2019). Secondly, the
environmental
disturbancewouldbeconsideredtosupportcollision
avoidance in different environmental conditions.
Thirdly, the potentials of using ICRA on board ship
andinvesseltrafficservicecenterinvariousscenarios
needmorestudies.
ACKNOWLEDGMENT
This work is supported by the China Scholarship Council
underGrant:201406950010.
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