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A Systematic Series Development and Calm Water Resistance Prediction for a Fast Catamaran Ferry Utilizing Machine Learning Tools

Authors:
Amin Nazemian at University of Strathclyde
Amin Nazemian
Evangelos Boulougouris at University of Strathclyde
Evangelos Boulougouris
Myo Zin Aung at University of Strathclyde
Myo Zin Aung
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Abstract and Figures

The aim of article is to design a calm water resistance predictor based on Machine Learning Tools and development of a systematic series for battery-driven catamaran hull forms. Regression Trees (RT), Support Vector Machines (SVM), and Artificial Neural Network (ANN) regression models are applied for dataset training on developed systematic series of catamarans. A hullform optimization was implemented for various catamarans including dimensional and hull coefficient parameters based on resistance and structural weight reduction and battery performance improvement. This paper provides a diverse database of catamaran hullform. Hence, an automated Matlab program was coded for geometry generation and cost function evaluation. Design distribution based on Lackenby transformation fulfills all design space and sequentially a novel self-blending method reconstructs new hullforms based on two parents blending. Finally, a machine learning approach was conducted on generated data of case study. This study shows that ANN algorithm correlates well with the measured resistance. Accordingly, a general and unique tool is proposed for optimized and desired design in first design stage.
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Article Not peer-reviewed version
A Systematic Series Development and
Calm Water Resistance Prediction for a
Fast Catamaran Ferry Utilizing Machine
Learning Tools
Amin Nazemian * , Evangelos Boulougouris , Myo Zin Aung
Posted Date: 1 December 2023
doi: 10.20944/preprints202312.0049.v1
Keywords: Systematic series; Machine learning; Lackenby variation method; Self-blending method; Panel
method
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Article
ASystematicSeriesDevelopmentandCalmWater
ResistancePredictionforaFastCatamaranFerry
UtilizingMachineLearningTools
AminNazemian1,*,EvangelosBoulougouris1andMyoZinAung1
1MaritimeSafetyResearchCentre(MSRC),DepartmentofNavalArchitecture,OceanandMarine
Engineering,UniversityofStrathclyde,Glasgow,UK;evangelos.boulougouris@strath.ac.uk,
myo.aung@strath.ac.uk
*Correspondence:amin.nazemian@strath.ac.uk
Abstract:TheaimofarticleistodesignacalmwaterresistancepredictorbasedonMachine
LearningToolsanddevelopmentofasystematicseriesforbattery‐drivencatamaranhullforms.
RegressionTrees(RT),SupportVectorMachines(SVM),andArtificialNeuralNetwork(ANN)
regressionmodelsareappliedfordatasettrainingondevelopedsystematicseriesofcatamarans.A
hullformoptimizationwasimplementedforvariouscatamaransincludingdimensionalandhull
coefficientparametersbasedonresistanceandstructuralweightreductionandbatteryperformance
improvement.Thispaperprovidesadiversedatabaseofcatamaranhullform.Hence,anautomated
Matlabprogramwascodedforgeometrygenerationandcostfunctionevaluation.Design
distributionbasedonLackenbytransformationfulfillsalldesignspaceandsequentiallyanovelself‐
blendingmethodreconstructsnewhullformsbasedontwoparentsblending.Finally,amachine
learningapproachwasconductedongenerateddataofcasestudy.ThisstudyshowsthatANN
algorithmcorrelateswellwiththemeasuredresistance.Accordingly,ageneralanduniquetoolis
proposedforoptimizedanddesireddesigninfirstdesignstage.
Keywords:systematicseries;machinelearning;Lackenbyvariationmethod;self‐blendingmethod;
panelmethod
1.Introduction
TheEUfundedproject“TrAM‐Transport:AdvancedandModular”developsbattery‐driven
zeroemissionfastpassengervesselsforcoastalareasandinlandwaterways.Modulardesignand
manufacturingmethodsarethefocusofthisprojectwiththeobjectivestominimiseenvironmental
impactandlifecyclecost[1,2].Thedevelopmentofasystematicseriesofzero‐emissioncatamaran
hullformfordifferentdisplacementtonnageandshiptypescansignificantlyhelpthisprocess.
Enormouscatamaranhullformswillgenerateduringthesystematicseriesdevelopmentand
resistancecalculationtakestimeforeachdesign.Anaccurateandfastresistancepredictoryieldsto
convenienttoolforaclassofhullforms.Therefore,anewmodelforsuchdiversitywithan
appropriategeneralizationtonewpredictionsisdesiredinthisfield,thisleadsusthedatamining
approaches[3].
2.Background
Resistancecalculationsinpastdecadeshavebeenimplementedbymodeltestsorseatrial
measurements.Theclassicregressionmodelshavelimitedtoconventionalvesselswithspecified
generalparticulars.Besides,theaccuracyanditscostwerebarrierstoimplementEFDandCFD
measurementsfornewdesigns.Duringthepastdecades,somenonlineardynamicapproacheshave
beendeveloped,whichproducescomparableresultsandmoreflexibility[4,5]
Shipresistanceoptimizationplaysanimportantroleinthehullformdevelopment.Assessing
theshipresistanceinthefirststageofshipdesignallowsthedesignertoanalyzetheinfluenceof
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© 2023 by the author(s). Distributed under a Creative Commons CC BY license.
2
differenthullformsandparameters.Accordingly,differentmethodsofgeometryoptimizationand
designstudyhavebeendevelopedduringpastdecades[6].Papanikolaouetal.[7]implementeda
globalandlocalhullformoptimizationofthefastcatamaranintwodesignstudyscenarios.Inthe
firststageofoptimization,1000hullformswereelaboratedwithsurrogate‐baseddesignstudyusing
potentialtheory3Dpanelcode.Afterthat,twomostpromisingdesignshavebeenselectedasinitial
hullformoflocalmodificationfocusingonthesternregion.However,acomprehensivedesign
optimizationmightbeproposedaccordingtobalancebetweenaccuracyandtime,whichisdiscussed
indifferentpreviouspapers[8–10].Anall‐inclusivehullformoptimizationinthefieldofshipdesign
definesvarioushullformswithdifferentgeometricalparameters.Accordingly,marineindustry
needsanoptimizationplatformtominimizetherequiredpropulsionpoweraccordingtovarious
possibilitiesofhullform.Besides,asystematicseriesaredevelopedongeneratedgeometriesto
establisharesistancepredictor.
Lietal.[11]byusingSingle‐ParameterLagrangianSupportVectorRegression(SPL‐SVR)
developedametamodelonseakeepingdata.Amultidisciplinarydesignoptimizationinconcept
designstageofshipshasbeenproposed.Recently,FahrnholzandCaprace[12]conducteda
regressionanalysisonthreesailboatsʹ systematicseries.Basedonmachinelearningtechniques,a
resistancepredictorwasdesignedonresistancedata.NazemianandGhadimi[13]byusingaD‐
optimalDoEstudyinvestigatedresistanceperformanceofatrimaranhullseries.Aresistanceanalysis
anditsimprovementwasencompassedtoextractoptimumvalueofhullparametersandsidehull
arrangement.
Machinelearningtechniqueshavecommencedinthelastdecadeinthefieldofshipdesignand
hydrodynamics[14,15].Theresistancepredictionhasbeendevelopedandcomparedbytraditional
approachesbyRadojicetal.[16,17].AnArtificialNeuralNetworkregressionmethodwasdesigned
forplaningboatsatdifferentseriestypes.Themachinelearningmodelscanalsoimplementonadded
resistance[18]andiceresistance[19].Differentaspectsofshipdesigntargetscanbeconsideredin
datasetanalysis.LiuandPapanikolaou[20]developedasemi‐empiricalformula,approximatingthe
addedresistanceofshipsinregularwavesofarbitraryheading.Developofacatamaranclass
alongsideoptimizationprocesshasbeenconsideredinthecurrentstudywithanautomaticdesign
generation.
Thepresentpaperdividesintwophases,focusingonsystematicseriesdevelopmentforafast
passengerandfreightzero‐emissioncatamaranandapplyingmachinelearningongenerateddata.
Basedonsurveyedliterature,itcanbeconcludedthatahullformoptimizationprocessneedstobe
addedtoshipseries.Foreachtonnageconditionandshiptype,apredictivemachinelearningmodel
developstocalculatecalmwaterresistance.Besidesthefinaldesignwouldbethebestdesignwith
respecttothelowestresistanceatmulti‐designspeeds.Anautomatedoptimizationcodeiscarried
outinMatlabsoftwaretopreparedatasetofdifferenthullform.IntheframeofTrAMproject,various
optimizeddesignoptionspreparebasedonshipdimensionandcoefficientandhullformalteration.
Accordingly,designstudystartswithnumerousshiptypesandtonnageandofferdifferent
possibilityofcatamaranhullformasflexibilityforownerʹsselection.Ownerscanchoosetheir
optimizeddesignbasedontheirrequirements.
Performingparametrictransformationsandself‐blendingmethodcreatesaseriesofhullforms
withsystematicallyvaryingparameters.Parametrictransformationbymovingshipsectionsandself‐
blendingbymovingControlPointsimplementparametrictransformationstocreatenewhulls.A
regressionformulacalculatesstructuralweightofcatamaransforscantlinganddeckweights.The
steelweightofshellscomputesbasedonwettedsurfaceareawhendesigndraftisplacedonmain
deck.Weightofinstalledbatteryautomaticallydecreasesbyreductionoftotalresistanceand
consequentlypowerrequirement.
3.Methodology
Presentʹsoptimizationcodecapabilities,allowinganytypeofhullformtobemodeledincaseof
differentshipdesigntargets,offerscopeforthecreationofawiderangeofhullformsandprovide
anoptionalselectionforowners.Combinedwiththebuilt‐inresistance,structureweightandbattery‐
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3
drivensystemperformancecalculations,youhavethetoolstoexperimentwithshapesandexplore
designparameters.Accordingly,anextensivefastcatamaranserieshasbeendevelopedandforeach
selection,anoptimizedhullobtains.Thecasestudyisacatamaranhull[1,2]asaninitialdesignof
databaseproduction.Thedatabaseconsistsofthreetonnages(∆75,∆80,∆85)tons.Two
typesofpassengerandfreightcatamaranboatsaredefinedasinitialhullform.Generalarrangement
ofunder‐studiedcatamaransdepictsinFigure1.

Figure1.GeneralArrangementplanofpassengerandfreightcatamaranboat.
Threedesignstudyprocessesapplytothreehullforms(75ton,80ton,85ton).Afterthemodel
hasbeenalteredtotalresistancecalculatesviaslenderbodymethod.Structuralweightofeachdesign
isestimatedbyaregressionformulaandshellexpansionofhullsurface.Propulsionsystemofvessel
workswithelectricallypoweredbatteryspares.Performanceandbatteryweightcomputesbasedon
resistanceandconsequentlybreakpowerofthecatamaran[21–24].Outputofoptimizationprocess
isresistanceat12knotandresistanceat22knot,whichrepresentbyaweightingcostfunction:
𝐶𝑜𝑠𝑡
𝑓
𝑢𝑛𝑐𝑡𝑖𝑜𝑛󰇧󰇡




󰇢𝑊𝑡






𝑊𝑡

󰇛𝑊𝑒𝑖𝑔ℎ𝑡/𝑊𝑒𝑖𝑔ℎ𝑡0󰇜∗
𝑊𝑡

󰇜󰇨󰇡


_


󰇢
,
(1)
TheframeworkofdesignstudyandmachinelearningillustratesinFigure2.Foreachtonnage,
shipgeometryisdesignedanddistributedondesignspaceaccordingtomulti‐levelcombinationof
designvariables.Totalresistanceandweightestimationofstructureandbatteryweightcalculatefor
eachdesign.Pre‐processingprogressisappliedtoobtaineddatatodefinedifferentregression
schemes.Herein,RegressionTree(RT),SupportVectorRegression(SVR),andArtificialNeural
Network(ANN)methodsareusedtopredictotherinterestingdesignsandfindaresistance
predictivemodel.
Thecasestudycatamaranistheprototypehullform,whichisdesignedandbuiltinframeof
Horizon2020EuropeanResearchprojectTrAM[25].Themainpurposeofthiseffortistoreplicate
thishullformbasedonsmallmodifications.Optimizationprocessconductson6designvariablesand
2constraintsthatareshowninTable1.Asaresult,thedisplacementconstraintisdefinedasfollows:
∆

∆

∆

0.01,(2)
Anotherconstraintofthepresentstudyistotalbeamofthecatamarantosatisfyport
requirements,therefore:
2𝐷𝑒𝑚𝑖ℎ𝑢𝑙𝑙 𝑜𝑓𝑓𝑠𝑒𝑡𝑑𝑒𝑚𝑖ℎ𝑢𝑙𝑙 𝑏𝑒𝑎𝑚 9
,(3)
Demihulloffsetisthedistancebetweencenterlineofeachdemihull.
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Figure2.Frameworkofdesignstudyandmachinelearningmethodology.
Table1.Designparametersofthecatamarancasestudy.
OptimizationparameterSymbolspecifications
DesignVariableLwlWaterlinelength(m)
DesignVariableB DemihullBeam(m)
DesignVariableTDraft(m)
DesignVariableDTDemihulltransversedistance(m)
FreeVariableCb Blockcoefficient
DesignVariableCm Maxsectionareacoefficient
DesignVariableLCB(%ofLwl)LongitudinalCenterofBuoyancy
Constraint
𝞩
Displacement(Ton)
Constraint(DTx2)+BTotalBeam(m)
9designparametersofcatamaranshipareselectedasinputdataofregressionlearner.Total
resistancevalueisoutputparameterofthestudy,whichcalculatesthroughslenderbodymethod
[26,27].AttributeselectionisdepictedinTable2.Regressionmodelsimplementsoneachshipspeed
[12,13.25,14.5,15.75,17,18.25,19.5,20.75,22]knot.Finally,acomprehensiveregressionisappliedto
allgeneratedhullsatdifferentdraftsanddimensionstogeneralizethesystematicseries.
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Table2.Selectedattributesfordataminingwiththeirrespectivestatisticsvalues.
specificationsSymbolMinMaxMeanDeviation
Shipspeed[kn]V1222173.4232
Waterlinelength(m)Lwl283330.21391.2354
DemihullBeam(m)B2.09852.20652.14070.0352
Draft(m)T1.2831.3861.31520.0318
Demihulltransversedistance(m)DT3.353.4243.38890.0239
BlockcoefficientCb0.43490.50620.46630.0144
MaxsectionareacoefficientCm0.70910.76100.72930.0135
LongitudinalCenterofBuoyancy(%of
L)LCB0.53460.55490.54630.0047
Waterplanearea(m2)Aw96.235104.339100.4882.9536
Maximumsectionarea(m2)Ax3.9234.1534.0940.0582
4.Databasegenerationofcatamarancasestudy
Optimizationprocessconductsforeachdesignscenariotoobtainthebestdesignforeach
configuration.Thedevelopedgeometryreconstructionmodeloffersdesignerthepossibilityto
control/specifythemainparticularsofthedemihullalongwiththehullformdetailswithina
reasonablerangeofvariationofthedefineddesignvariables,whileatthesametime,adequatequality
offairnessandsmoothnessofthehullisensured.Thedesignerisenabledtoexplorethehugedesign
spaceofautomaticallygeneratedhullformsanddecideonthemostfavorableonesbasedonrational,
holisticcriteria.Regressionlearnersareappliedon5designconfigurationsevery1955hullforms,
whichturnsto9775designs.Thepre‐processingprocedurereformsdatabasetotheapplicationof
machinelearningtechniques.Linearnormalizationisimplementedoneachparameteraccordingto
Eq.(4):
𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 .
..,(4)
Anotherstepofpreprocessingisusingaprincipalcomponentanalysistechnique(PCA)and
OutlierdetectionusingthehotellingsT2test[28].Selectingtheoutlierscanbeusefultoremovethem
fromthedatasetorfordeeperinvestigation.Dimensionalityreductionisappliedtotheinputsto
projectdataintoaspaceoflowerdimensionwhilepreservingamaximumofinformation.Number
ofdatareducesfrom9775to8745recordsaccordingtoPCAandoutlierdetectionwithconfidence
intervalof0.05[29,30].Finally,thedatabaseisrandomlysplitintoalearningsetandtestset,which
contains70%and30%oftherecords,respectively.
Regressiontrees(RT),supportvectormachines(SVM),andartificialneuralnetwork(ANN)
regressionmodelsareappliedfordatasettrainingbasedon9predictorsand1response.The
regressiontreeisasupervisedlearningalgorithmwithtree‐structuredclassification.Thereisa
decision‐relatedalgorithmforeachnodebasedontheattributes.Eachstepinapredictioninvolves
checkingthevalueofonepredictorvariabletodeterminewhetheranattributeislargerthanor
smallerorequaltoavalueofthefollowingbranch.Theresponsevaluecontainsinthelastnode,
whichisknownasleafnode.Secondsupervisedregressiontoolislinearepsilon‐insensitiveSVM
regression.Thismethoddisregardspredictionerrorsthatarelessthansomefixedhyperplane.Data
pointsincludeinthesupportvectorsthathaveerrorslargerthanadmissibleerrorofthemodel.The
functiontheSVMusestopredictnewvaluesdependsonlyonthesupportvectorstominimizethe
error.Boxconstraint,Epsilonvalue,andKernelscaleparameteraresettoautomaticmodethatthe
applicationusesaheuristicproceduretoselectappropriatevalue.
Theartificialneuralnetworkisinter‐connectedneuronsthatorganizedinlayers.AnANN
algorithmworksbasedonhumanneuronsystem,whichconsistsofnumberoflayers,thekindof
neuralsynapsesandthelearningalgorithm[12,31].Theartificialneuralnetworkishereinappliedto
datasetusingmultilayerfeedforwardnetworks.Shiphullparametersdefineatfirstfullyconnected
layer,andeachsubsequentlayerhasaconnectionfromthepreviouslayer.Weightmatrixmultiplies
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toeachfullyconnectedlayer.Weightintensityiterativelychangesaimingtodecreasethefinalerror.
ThenumberoflayersandtheirneuronsisselectedbytheBayesianoptimizablealgorithm[32].
Internalparametersofregressionmodelcanbechosenmanually,however,theoptimized
regressionmethodscanselectoptimizedinternalvaluesbyusinghyperparameteroptimization.
Someoftheseoptionscanstronglyaffectregressionmethodʹsperformance.Accordingly,
OptimizableRegressionTree,OptimizableSVM,andOptimizableANNmethodsareappliedherein
[33].Modelevaluationisimplementedbystatisticalparametersandtestdatasets.Coefficientof
modeldeterminationconsistsofR‐squared(R2),meansquarederror(MSE),meanabsoluteerror
(MAE),androotmeansquareerror(RMSE):
𝑅1∑󰇛
󰇜
∑󰇛
󰇜
,(5)
𝑦
∑𝑦
 ,(6)
𝑀𝑆𝐸
∑󰇛
𝑦𝑥󰇜
 ,(7)
𝑀𝐴𝐸
∑|𝑦𝑥|
 ,(8)
𝑅𝑀𝑆𝐸
∑󰇛
𝑦𝑥󰇜
 ,(9)
Where𝑦ispredictedresistanceoftherecordi,𝑥isthecalculatedresistancefromdataset,and
nisnumberofsamples.
5.Results
Threeregressionmodelshavebeendevelopedaccordingtointernalparameterselectionto
minimizeMSEvalue.ThePCAdimensionalityreductionreducesnumberoffeaturesfrom9to6
features.Table3presentsevaluationresultsofmodelperformanceandinternalobtainedparameters
ofregressionmodels.
Table3.Internalparametersofoptimumregressionmodels.
OptimizableRegressionTreeOptimizableNeuralNetworkOptimizableSVM
RMSE:0.1043
R2:0.98
MSE:0.01088
MAE:0.057334
RMSE:0.03037
R2:1
MSE:0.000922
MAE:0.020429
RMSE:0.1168
R2:0.97
MSE:0.01365
MAE:0.06614
Minimumleafsize:3
Num.oflayers:2
Activation:Sigmoid
Lambda:1.5276e‐08
FirstLayersize:26
SecondLayersize:77
Boxconstraint:17.0223
Kernelscale:8.5763
Epsilon:8.17e‐4
Kernelfunction:Gaussian
Regressionevaluationresultsdepictthatthemodeldevelopedusingtheartificialneural
networksalgorithmhasbeenfittedmoresuitablethanotherimplementedmodels.Thismodelhas
R‐squareddeterminationequalto1,whiletheerrorsanddispersionmeasurementsareminimal.
Figure3illustrateshistoryofMSEparameterminimizationforthreeappliedmethods.Darkblue
pointcorrespondstoobservedminimumMSEandlightblueonerepresentsestimatedminimum
MSE.Numberofiterationsconsider30,whichbestpointofMSEvalueisshowninredcolor.
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(b)
(a)
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(c)
Figure3.MSEhistoryreductionthroughoptimizableregressionprocess(a)RegressionTree(b)
RegressionSVM(c)RegressionANN.
ResponseplotpresentsinFigure4,showsthemainandpredictedresponseversustherecord
number.Besides,Predictedvs.ActualandResidualplotsareshowninFigure5foreachregression
model.Theseplotshelptounderstandhowwelltheregressionmodelmakespredictionsfordifferent
responsevalues.ItcanbeindicatedthatANNmethodcanpredictresponsesclosetoactualonesdue
towell‐scatteredsamplesalongthediagonalline.Additionally,residualplotdepictsdifference
betweenthepredictedandtrueresponses,whichcanbeinterpretedasacleardistributionaround
zeroforANNregressionmethod.Assessmentofresponseplotsrepresentstheappropriate
performanceofANNmethodagainstotherimplementedmethods.
(a)
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(b)
(c)
Figure4.PredictionvsTruedesigncomparisonthroughoptimizableregressionprocess(a)
RegressionTree(b)RegressionSVM(c)RegressionANN.

(a)
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
(b)

(c)
Figure5.Residualplotcomparisonthroughoptimizableregressionprocess(a)Regression
Tree(b)RegressionSVM(c)RegressionANN.
5.1.Regressionmodelevaluation
5.1.1.Datasettestcases
AcomparisonconductsbetweenRT,SVM,andANNmethodsforevaluatingresistance
predictors.Twodesignsofdatasethavebeenselectedrandomlyforevaluationinthissubsection.
Figure6(a)showstheresultsforarandomhullinhullformseries.Inaddition,Figure6(b)depicts
theresultsforarandomcatamaranhullformfor85Dseries.
Theproposedmodelsfitwelltheobserveddatafortestcasesamongdataset.However,itcanbe
indicatedasmallunderestimatevaluesatspeeds15to18knot.R‐squareandRMSEvaluesforFigure
6(randomdesigntestmodel1&2)arepresentedinTable4.Theartificialneuralnetworksalgorithm
fitsobserveddataeffectivelyaccordingtolowervaluesofpredictionparameters.
Table4.Predictionparametersofmodeltestfordatasetdesigns.
Testmodel1Testmodel2
RTRMSE:0.6051
R2:0.9991
RMSE:1.4895
R2:0.9934
SVMRMSE:0.3185
R2:0.9996
RMSE:1.1625
R2:0.9971
ANNRMSE:0.8083RMSE:0.3606
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R2:0.9997R2:0.9994
(a)
(b)
Figure6.ModelcomparisonbetweenRT,SVM,andANNmethodsfor(a)randomdesignTestmodel
1and(b)randomdesignTestmodel2.
5.1.2.Interpolationtestcases
Inthissection,twointerpolateddesignsbasedonshiptonnagehavebeenimportedtoregression
models.Catamaranhullformsof77.5tonand82.5tonaredesignedforregressionmodelevaluation.
Threeimplementedregressionmodelsareadjustedon77.5tonhullform(Figure7(a))and82.5ton
hullform(Figure7(b)).RegressiondataiswelladjustedusingANNmethodforbothdesigns
accordingtopredictorparameterspresentedinTable5.However,aslightdifferencecanbeobserved
athigherspeedsofcase82.5ton,whichisslightlysuperior.
Table5.Predictionparametersofmodeltestforinterpolationdesigns.
77.5ton82.5ton
RTRMSE:0.7597
R2:0.9965
RMSE:1.4029
R2:0.9911
SVMRMSE:1.0426RMSE:1.4938
10
15
20
25
30
35
40
45
50
55
11 12 13 14 15 16 17 18 19 20 21 22 23
Resistance[KN]
Speed[kn]
SBMresults
RegressionTree
SVM
ANN
10
15
20
25
30
35
40
45
50
55
60
11 12 13 14 15 16 17 18 19 20 21 22 23
Resistance[KN]
Speed[kn]
SBMResults
RegressionTree
SVM
ANN
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12
R2:0.9976R2:0.9906
ANNRMSE:0.4677
R2:0.9988
RMSE:0.8633
R2:0.9977
(a)
(b)
Figure7.ModelcomparisonbetweenRT,SVM,andANNmethodsfor(a)interpolationdesign77.5
tonand(b)interpolationdesign82.5ton.
5.1.3.Extrapolationtestcases
Extrapolationdesignsdefinehullformsoutofdisplacementboundofdataset.Considering
displacementofalldesignsfromdatasetaredesignedbetween75to85tones.TwoCatamaran
hullformsof71.5tonand88.5tonareconsideredforregressionmodelevaluation.Thepurposeof
extrapolationtestisassessmentofregressionmodelsforout‐boundariescatamarans.Figure8(a)and
Figure8(b)showresistancevaluesagainstspeedforSlenderBodyMethodresultsandfitted
regressionsfor71.5tondesignand88.5tondesignrespectively.InFigure8(a),allregressionmodels
estimateresistancehigherthanactualvalues.Oncontrary,theproposedmodelsareinferiortoSBM
resultsinFigure8(b).Inthetransitiontohighspeeds,themodelsgetlessaccurate.Inaddition,Table
6presentspredictionvaluesoffittingquality,whichdepictsregressionsaremorepreciseinlower
displacementdesignthaninhigherone.
10
15
20
25
30
35
40
45
50
55
11 12 13 14 15 16 17 18 19 20 21 22 23
Resistance[KN]
Speed[kn]
SBMresults
RegressionTree
SVM
ANN
10
15
20
25
30
35
40
45
50
55
11 12 13 14 15 16 17 18 19 20 21 22 23
Resistance[KN]
Speed[kn]
SBMresults
RegressionTree
SVM
ANN
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13
Table6.Predictionparametersofmodeltestforextrapolationdesigns.
71.5ton88.5ton
RTRMSE:1.8147
R2:0.9964
RMSE:2.4631
R2:0.9975
SVMRMSE:1.6215
R2:0.9965
RMSE:2.7815
R2:0.9975
ANNRMSE:1.3860
R2:0.9968
RMSE:2.2180
R2:0.9983
(a)
(b)
Figure8.ModelcomparisonbetweenRT,SVM,andANNmethodsfor(a)extrapolationdesign71.5
tonand(b)extrapolationdesign88.5ton.
6.Conclusions
Asystematicseriesofnovelcatamaranshipshasbeendevelopedfortwotypesofpassengerand
freightboats.Threedifferentshiptonnages75,80,and85tonesareconsideredtoproducenew
designs.Ashifttransformationandself‐blendingmethodaresequentiallyappliedtogenerate
differenthullforms.Threedifferentsupervisedmachinelearningmethodshavebeenappliedto
10
15
20
25
30
35
40
45
50
55
11 12 13 14 15 16 17 18 19 20 21 22 23
Resistance[KN]
Speed[kn]
SBMresults
RegressionTree
SVM
ANN
10
15
20
25
30
35
40
45
50
55
60
11 12 13 14 15 16 17 18 19 20 21 22 23
Resistance[KN]
Speed[kn]
SBMresults
RegressionTree
SVR
ANN
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14
generateddatasetofcatamaranstopredictresistanceatdifferentshipspeeds.Generatedhullforms
havebeensortedbasedonacostfunctionofresistancetoobtaintheoptimumdesignforeach
displacementseries.Accordingly,9775catamaranhullformshavebeenproducedtomakeavast
optionalconditionforshipowners.Usingmachinelearningalgorithms,itisworthdevelopinga
continuoustotalresistancepredictorwellfittedtodatabaseofshipseries.Threeregression
algorithmsRegressionTree,SupportVectorMachine,andArtificialNeuralNetworkapproachesare
appliedtodataset.RegressionestimationhasgoodcompliancewithresultsofSBMmethodatwide
rangeofspeeds.However,RTandSVMmethodshavesomedifferencesinhigherspeed.TheANN
approachdepictswell‐adjustedregressiononthedata.Thevalidationoffittingmethodsevaluates
bycasetestofdataset,interpolation,andextrapolationcatamarans.Accordingly,ageneraland
uniquetoolisproposedtopredictresistanceoftheseriesatdifferentdisplacementsandhullforms.
Theproposedmodelisavaluabletooltoassesstheresistanceofcatamaranhullsduringtheearly
designstages.Finally,asophisticatedANNmodelisproposedbyexploringdifferentfeaturesand
training/optimizationalgorithms.Resistancecalculationsbymoreprecisemethodsincludingtrim
andsinkageeffectcanbecarriedoutforfutureworks.
AuthorContributions:Conceptualization,A.N.andM.Z.A.;methodology,A.N.;software,A.N.andM.Z.A.;
validation,A.N.;formalanalysis,A.N.;investigation,A.N.andM.Z.A.;writing—originaldraftpreparation,
A.N.andM.Z.A.andE.B.;supervision,E.B.Allauthorshavereadandagreedtothepublishedversionofthe
manuscript.
Funding:TheTrAMprojecthasreceivedfundingfromtheEuropeanUnion’sHorizon2020researchand
innovationprogramundergrantagreementNo769303.https://tramproject.eu/.
InstitutionalReviewBoardStatement:Notapplicable.
InformedConsentStatement:Notapplicable.
DataAvailabilityStatement:Notapplicable.
Acknowledgments:MaritimeSafetyResearchCentre(MSRC)atStrathclydeUniversityisanindustry‐
UniversitypartnershipinvolvingStrathclydeʹsDepartmentofNavalArchitecture,Ocean&MarineEngineering,
andsponsorsofRoyalCaribbeanGroupandDNVClassificationSociety.Theopinionsexpressedhereinare
thoseoftheauthorsanddonotreflecttheviewsofDNVandRCG.
ConflictsofInterest:Theauthorsdeclarethattheyhavenoknowncompetingfinancialinterestsorpersonal
relationshipsthatcouldhaveappearedtoinfluencetheworkreportedinthispaper.
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