Journal of Automation, Mobile Robotics and Intelligent Systems, vol. 19, no. 2 (2025) by Ł-PIAP

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Journal of Automation, Mobile Robotics and Intelligent Systems

A peer-reviewed quarterly focusing on new achievements in the following fields: • automation • systems and control • autonomous systems • multiagent systems • decision-making and decision support • • robotics • mechatronics • data sciences • new computing paradigms •

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Journal of Automation, Mobile Robotics and Intelligent Systems

Development of a Distributed Outlier Detection Method Based on the Alternating Direction Method of Multipliers

Alejandro Cespón Ferriol, Héctor R González Diez, Carlos A. Morell Pérez

DOI: 10.14313/jamris‐2025‐009

Model‐Based Development of Autopilot for a Gasodynamically Controlled High‐Speed Unmanned Aerial Vehicle

Mariusz Jacewicz, Dariusz Miedziński, Grzegorz

Chmaj, Robert Głębocki

DOI: 10.14313/jamris‐2025‐010

Comparison of Computer Vision and Convolutional Neural Networks for Vehicle

Parking Control

Jonathan Aguilar Alvarado, Karina Garcia Galarza, Wilmer Rivas Asanza, Bertha Mazón Olivo

DOI: 10.14313/jamris‐2025‐011

A Novel Model‐Free Control Technique for Angular Motion of a Single Ducted‐Fan Unmanned Aerial Vehicle

Thien Minh Tran

DOI: 10.14313/jamris‐2025‐012

Design of Multidimensional Nonlinear Predictive Controller for 3D Crane

Maciej Szafrański, Robert Piotrowski

DOI: 10.14313/jamris‐2025‐013

Patterns of Acoustic Emission Changes with Alterations in the Damage Area of a Composite Material According to the Mises Criterion

Sergii Filonenko, Anzhelika Stakhova

DOI: 10.14313/jamris‐2025‐014

Construction Automation with Bio‐Inspired Hierarchical Extremely Modular Systems

Ela Zawidzka, Machi Zawidzki

DOI: 10.14313/jamris‐2025‐015 59

Grey Wolf Optimization Algorithm for a Concurrent Real‐Time Optimization Problem in Game Theory

Adam M. Górski, Maciej Ogorzałek

DOI: 10.14313/jamris‐2025‐016

Autonomous Goal Following for a Quadruped Robot Using Fuzzy Proportional Control

Jose Eduardo Lopez‐Ramos, Oscar Castillo, Patricia Melin

DOI: 10.14313/jamris‐2025‐017 73 65

IoT‐Based Emergency Vehicle Detection Using YOLOv8

Syed Suhana, Boppuru Rudra Prathap, Kavish Narang, Ivin Anto

DOI: 10.14313/jamris‐2025‐018

A Hybrid Deep Learning Algorithm Based Prediction Model for Sustainable Healthcare System

Tharageswari K, Mohana Sundaram N, Santhosh R

DOI: 10.14313/jamris‐2025‐019

Abstract:

DEVELOPMENTOFADISTRIBUTEDOUTLIERDETECTIONMETHODBASEDONTHE ALTERNATINGDIRECTIONMETHODOFMULTIPLIERS

Submitted:29th February2024;accepted:27th March2024

AlejandroCespónFerriol,HéctorRGonzálezDiez,CarlosA.MorellPérez DOI:10.14313/jamris‐2025‐009

Indatamining,oneofthemoststudiedproblemsisout‐lierdetection,whichinvolvesidentifying“unusual”data pointswithinadatasetsuspectedtobegeneratedbya differentmechanismthantherestofthedataset.Outlier detectionhasapplicationsindiscoveringnovelinforma‐tion,detectingbankfraud,identifyingsystemintrusions, andothers.However,handlinglargevolumesofdata, knownasbigdata,posesachallengetooutlierdetection algorithmsbecausetheresourcesofasinglecomputer maynotbesufficienttoachieveefficientperformance. Furthermore,datasetsareoftenstoredindistributed environments.

Thegoalofthisworkistodevelopanewdistributed outlierdetectionalgorithmbasedonthesolutionofthe supportvectordatadescriptionusingthealternating directionmethodofmultipliers.Mathematicaloptimiza‐tionmethodsandPythonlanguagelibrariesaremainly usedfortheimplementation.Asaresult,thedesign anddistributedimplementationoftheproposedalgo‐rithmareachieved,whicharevalidatedusingseveraltest datasets,yieldingsatisfactoryandcompetitiveresults comparedtoexistingmethods.

Keywords: outlierdetection,bigdata,methodofmulti‐pliers

1.Introduction

Outlierdetectionisoneofthemoststudiedprob‐lemsindatamining,andinvolvestheidenti icationof erroneousor“unusual”datapointswithinadataset. Outlierdetection(OD) indsapplicationsindiscovery ofnovelinformation,bankfrauds,systemintrusions [12,14],aswellasindatacleaningformachinelearn‐ingmodelsthataresensitivetothepresenceofout‐liers[28].Formally,outlierdetectioncanbede ined astheproblemof indingpatternsinthedatawith unexpectedbehavior[7].Outliersareoftenreferred toasanomalies,exceptions,discordantobservations, andvariousothersimilarterms[3,21].

Outlierdetectionisanexampleofaproblemthat canbesolvedusingaclassofclassi iersknownas one‐classclassi iers(OCC),atermproposedbyMoya [18].Itsolvestheproblemof indingtheboundarythat encompassesanentireclass,givenadatasetthatcould becontaminatedwithasmallamountofanomalous data.

TaxandDuin[25]describeanOCCcalledSupport VectorDataDescription(SVDD).Itaimsto indthe hyperspherewiththeminimumradiusthatencloses mostdatapointsinadataset.Thedatapointsinside thehypersphereareconsideredtobelongtothetarget class,whilethoseoutsideareconsideredanomalous.

Currently,handlinglargevolumesofdata,known asbigdata,representsachallengeforoutlierdetec‐tionalgorithms.Theresourcesofasinglecomputer maynotbesuf icienttoachieveef icientperformance foraparticularalgorithm.Centralizedalgorithms arebecominglesscompetitiveinmeetingthetime demandsofmodernapplications.Furthermore,due totheincreasingsizesofdatasets,theyarefrequently storedindistributedenvironments[3].

TheAlternatingDirectionMethodofMultipliers (ADMM)belongstothecategoryofdistributedopti‐mizationandissuitableforsolvingmanymachine learningproblems[1,4],especiallythosethatcanbe formulatedortransformedintoconvexoptimization problems[5].

Basedontheseelements,themainobjectiveofthis researchistodevelopadistributedoutlierdetection algorithmbasedonsolvingtheSVDDproblemusing ADMM.Thisresearchaimstocontributetooutlier detectioninlargevolumesofdatabyenablingdis‐tributedprocessing.Moreover,theproposedmethod doesnotrequirecentralizeddata,makingitapplicable todistributeddatasets.

2.ConceptsandBasicNotation

2.1.ADMM

ADMMisadecomposition‐coordinationtechnique inwhichsolutionstosmalllocalsubproblemsare coordinatedto indthesolutiontoalargerglobal problem[4].Dependingontheapplication,itisrel‐ativelysimpletoimplementindistributedenviron‐ments,makingitapplicabletobigdataproblems[4, 10].

ADMMsolvesproblemsoftheform: minimize ��(��)+��(��) (1) subjectto:��+��=�� Where��∈ℝ�� ,��∈ℝ�� ,��∈ℝ��×�� ,��∈ℝ��×��,and ��∈ℝ��.With��and��convexfunctions.Theminimum valueofproblem(1)wouldbe: ��∗ =min(��(��)+��(��)|��+��=��)

Where min referstotheminimum.The(augmented) Lagrangianforthisproblemwouldbe:

variable,and and ̄�� aretheaveragesoftheprimal anddualvariables,respectively.

ForADMMwithconsensus,theresidualsareinthe formofvectors:

AndthesolutionbyADMMconsistsoftheiterations:

with��>0.Ascanbeseen,thevariables�� and��are updatedalternately,hencethenameofthealgorithm.

Thevariable��iscalledthedualvariable.

ADMMcanbewritteninadifferent,oftenmore convenientform,knownasthescaledform:

whosequadraticnormsare:

2.2.SVDD

SVDD,proposedin[25],isanunsupervisedlearn‐ingmethodthatisveryusefulfordatadescription andanomalydetection.Todescribethedataset,this model indsahyperspherethatenclosesmostofthe data,minimizingthepossibilityofacceptinganoma‐lousdatawithinit.

SVDDisformulatedasanoptimizationproblemin thefollowingway:Givenasetofpoints��

where��= 1 ��.Thedualvariableisscaled.

Consensusproblemsarepartofthe ieldof distributedoptimizationandhavehistoricallybeen relatedtotheADMM.Theconsensusoptimization problemconsistsofasingleglobalvariablewiththe objectiveandconstrainttermsdividedintoNparts:

Thisiscalledtheglobalconsensusproblem.

Acommonvariationoftheproblem(8)isthe introductionofaregularizationtermintheobjective function��,whichrepresentsaregularizationterm:

(9)

ThesolutionbyADMMtoproblem(9)wouldbe(inthe scaledform):

(13) subjectto

Where �� isthecenterofthehypersphere, �� isthe radius,��isacontrolparameter,and�� areslackvari‐ables.Thedistancefrom�� tothecenterneednotbe lessthanorequalto ��2,andtheselargedistances arepenalizedwithmarginerrors �� foreach ��.The parameter �� controlsthetrade‐offbetweenthevol‐umeofthehypersphereandtheerrors,i.e.,itcontrols thenumberofpointsincludedinthehypersphere.

Anotherapproachtothedatadescriptionproblem canbefoundin[23,24].Itisbasedon indingahyper‐planethatseparatesthedatasetfromtheoriginwith themaximumpossiblemargin.Theformulationwould be:

arethelocalprimalvariablesateachnode,

arethelocaldualvariables,

Where �� istheweightvectorofthehyperplane, �� istheseparationmargin, �� aretheinstancesofthe dataset,��isthenumberofinstances,�� areslackvari‐ablestoaccountforpossibleerrors,and��∈(0,1)isa regularizationparameterthatindicatesthefractionof datapointsthatshouldbeseparated(equivalenttothe ��parameter).Becauseofthisparameter,thismethod isknownas��‐SVC.

Althoughthehyperplaneisnotaclosedboundary, itprovidessolutionscomparabletotheoriginalSVDD problemwhenthedataispreprocessedtounitnorm [25].

3.RelatedWork

3.1.ConvexOptimizationinOCCandOutlierDetection

Convexanalysismethodshavefoundincreasing applicationinoutlierdetectionandrelatedareas.OCC canbene itfromtherobustalgebraicandgeomet‐ricapproximationsprovidedbyconvexanalysisand optimization,allowingef icientsolutioncomputation throughmathematicaloptimization[26].

KernelMeanMatching(KMM)[13]isamethod thatassistsinoutlierdetectionbycheckingwhether thetrainingandtestsetsfollowthesamedistribution. Itssolutionisformulatedasaquadraticprogramming problem.AsimilartasktoKMMcanbeperformed withLeastSquareImportanceFitting(LSIF)[15].In thiscase,itisalsoaquadraticprogrammingproblem directlyrelatedtotheleastsquaresproblem.

Theconvexhullisoneofthemostcommonlyused convexanalysesapproachesinOD.Thisapproachaims to indthesmallestconvexsetthatenclosesagiven setofpoints.Duetoitsinherentproblemformulation, theconvexhullhasbeenusedinOCCasamethodfor outlierdetection[2,6].

In[8],theconvexmodelingoftheSVDDprob‐lemanditssolutionusingLagrangemultipliersare analyzed.Inaddition,[23]presentsanOCCbased onsupportvectormachines,wherethemodelcorre‐spondstoaquadraticprogrammingproblemrelated toSVDD.Theseapproachesareofinterestinthe presentresearch.

Inthe ieldofconvexoptimization,manyworks focusondecompositionmethodsanddecentralized algorithms[4,11,17],whichnaturallylendthemselves tobeapproachedfromtheperspectiveofdistributed optimizationalgorithms.

3.2.DistributedOptimizationforOutlierDetection

WhenworkingwithODinbigdata,valuableinfor‐mationcanbediscoveredanditisapplicablein variousdomains.AfundamentalchallengeofODin distributedsystemsistominimizecommunication betweennodeswhilemaintainingtheeffectiveness ofanalgorithm[3].In[14],analgorithmforOD basedondataneighborhoodisdevelopedwithadis‐tributedandinputstreamfocusedapproach.Thealgo‐rithmisbasedonLOCI(LocalCorrelationIntegral), whichallowsthedetectionofcontextualoutliers,i.e., instancesthatareconsideredoutliersforaparticular subsetofthedataset.Thisworkhighlightsthepower ofparallelprocessingforODwithinputdatastreams.

In[22],animplementationforreal‐timeODusing thePySparkvariantofSparkforPythonisproposed.In thiswork,thetrainingdataisstoredinthecloudand acluster‐basedsolutionispresented.Instancesout‐sidetheformedclustersareconsideredoutliers.The approachalsoincludesaschedulerthatperiodically re‐trainsthealgorithm,allowingforre‐evaluationof decisionspreviouslymadeoninstances.Considering thatdistributedODisarelativelyunexploredarea, [28]proposesSparx,anewalgorithmbasedonthe xStreamalgorithm.

xStreamwasoriginallydesignedforasinglepro‐cessor,butthisproposesaMap‐Reducedesignusing ApacheSparkinPython.Theenvironmentuseddoes notexchangeinformationbetweennodes,andthe dataisdecentralized.

In[29,30],thePythonlibraryPyODisproposed, whichprovidesnumerousODalgorithms.Thelibrary analyzesvariouscharacteristicsofthesealgorithms, includingtheirsuitabilityformulti‐coreprocessing. PyODaimstoprovideacomprehensivesetofODtech‐niques,makingiteasierforresearchersandpracti‐tionerstoexperimentwithandapplydifferentoutlier detectionalgorithmsinPython.

4.SolvingtheSVDDProblemwithConsensus‐BasedADMM

Basedontheanalysisdiscussedin 2.1 and 2.2, thefollowingsolutiontotheSVDDproblemusing consensus‐basedADMMisproposed:

Inthiscase,��=1...��,where��isthenumberofnodes and�� isthenumberofinstanceshandledbynode�� Thevaluesof��1and��2areassumedtobegreaterthan 0.The��parameteractsasapenaltyparameter.

4.1.VariableUpdates

Theminimizationsareperformedusinggradients (orsubgradientsifnecessary)andwouldbeasfol‐lows:

where:

Basedontheproposedupdates,thesolutionalgo‐rithmwouldbeasshowninAlgorithm1:

Algorithm1: DistributedSVDDusing

Consensus‐basedADMM

Input:

Output:

Thevariable stop modelstheproposedstopping conditions.Themostgeneralconditionisthemax‐imumnumberofiterations,whichensuresthatthe algorithmstops.

Italsocheckswhethertheresidualsdonotexceed atolerancevaluethatcombinesabsoluteandrelative variants.Finally,anearlystoppingcriterionisintro‐duced,wherethealgorithmisstoppedifthereisno improvementofthebestvalueobtainedsofarfora givennumberofiterations.

GiventhecharacteristicsofconsensusADMMfor thedistributedarchitecture,onenodeshouldbeused wheretheresultsarecentralizedandaggregated.The lowofthealgorithmineachiterationwouldbeto updatetheparameters �� and �� ateachnodeinde‐pendentlyusingitsowndatasetandthevaluesof ��, �� andthedualvariablesfromthepreviousiteration. Oncethe �� and �� valuesofeachnodehavebeen obtained,theyarecentralizedandaggregatedsyn‐chronouslytogivethe��and��ofthecurrentiteration. Finally,thedualvariablesareupdated.Thiswork low wasimplementedusingamap‐reducemethodology.

5.ResultsandDiscussion

5.1.Datasets

Toevaluatetheperformanceofthealgorithm,we use ivedatasets:threesynthetic,andtworeal.These datasetsvaryinthenumberofinstancesanddimen‐sions.Thesyntheticdatasetsaregeneratedbasedon probabilitydistributionsintheplane,whichfacilitates theconstructionofgraphstounderstandthebehavior ofthealgorithm.Thedatasetsaredistributedequi‐tablyamongtheprocessingnodes.

Table 1 brie lydescribesthe ivedatasets,the instancesrowde inesthetotalnumberofelements ineachdataset,whiletheoutliersrowde ineshow manyofthoseinstancesareanomalous.Thethree syntheticsetscorrespondingtoExperiments1,2and 3areconstructedinthesameway,theinstances are(x,y)coordinateswheremostofthedataisuni‐formlydistributedaroundthepoints(‐2,‐2)and(2,2) withradius1.Therestoftheinstancesarenormally distributedaroundthepoints(‐2,‐2)and(2,2)with radius1.Theremaininginstancesarenormallydis‐tributedintherectanglede inedfrom(‐4,‐4)to(4,4) andareconsideredanomalous.Experiment4isper‐formedontheGlassdataset,whichhasninecontin‐uousfeaturesrelatedtotheconcentrationsofmetals inthematerial.Itisinitiallyaclassi icationproblem withsixclasses,butclassnumber6isintheminority andinstancesbelongingtothisclassareconsidered anomalous.1 Experiment5iscarriedoutwithareal datasetrelatedtobehaviorreportsforaphysicalsys‐tem:Statlog(shuttle).Fortheexperiments,aversion istakeninwhichthemaintaskistodistinguishthe reportsthatareconsideredanomalousfromthose thatarenot.2

Preprocess Themainstepindatapreprocessingis theuseoftheNystroemapproximation[19,27].This stepnotonlyhelpstoreducethedimensionalityof thekernelmatrix,butalsoallowsformodelingthe nonlinearityofthedata.ThekernelusedistheRadial BasisFunction(RBF)kernel[20].

Table1. ExperimentalResults

Intheexperimentsconducted,itwasalsofound tobeeffectivetoscalethevaluesbeforeapplyingthe kernel.Forthispurpose,theRobustScalerfromscikit‐learnisused,whichismoreeffectivethanstandard scalingbecausetheRobustScalerisnotsensitiveto thepresenceofoutliers[19].

Othercommonpreprocessingstepscanalsoapply ifnecessary,suchasdatatypetransformationand missingvaluehandling[16].

5.2.ExperimentalSetup

Thesamemethodologywasusedforallexper‐iments:Alabeleddatasetistaken,withoneclass representingtheoutliers.Thelabelsarestoredand removedfromthedataset.Theclassi ieristrainedon theunlabeleddata,thenusedtoclassifythedata,and theperformanceisevaluatedusingtheoriginalstored labels.

ThisprocessisperformedforthreeOneClassSup‐portVectorMachineclassi iers,twoofwhichareavail‐ableinthescikit‐learnlibrary:OCSVMandSGD‐OC. Thethirdclassi ieristheoneproposedinthisresearch (calledADMM‐oc).

AnotherimportantaspectisthatfortheADMM‐ocandSGD‐ocmethodsthedatashownintheAUC‐ROCinTable 1 aretheresultoftheaverageof10 runsinthe irstfourexperimentsand5runsinthe ifthexperiment.Thisprocessisdonebecauseboth methodsarestochastic.

5.3.Metrics

TheODproblemcanbeviewedasatwo‐class classi icationproblem,whereoneclassrepresentsthe outliersandtheotherclassrepresentsthe“normal” instances[21].Evenmethodsthatreturnascoreor degreecanbereducedtoatwo‐classproblembyset‐tingathresholdforthedata,abovewhichtheyare consideredanomalous[7].Therefore,scoringmetrics forbinaryclassi icationproblemsarevalid.Animpor‐tantconsiderationisthetypicalclassimbalancein suchproblems,whichmaycausecertainmetricstobe unrepresentativeofthequalityofagivenalgorithm. Therefore,theAUC‐ROCmetricisevaluatedbecauseit isnotsensitivetoimbalanceddata[9,12].

5.4.Validation

Table 1 presentstheresultsoftheexperiments, withadescriptionofthedatasetsandsomeparame‐tersusedforeachexperiment.Itcanbeobservedthat

theAUC‐ROCvaluesremainsimilartotheothertwo methodscompared,regardlessofthevariationinthe datasets.

DuringExperiment2,studieswereconducted toverifythealgorithm’sconvergence.Theresults showedthattheADMM‐OCalgorithmachievesgood convergencewithinamaximumof20iterations,as canbeseeninFigures1and2.

Consideringthetwo‐dimensionalityofthedataset usedinExperiment3,acomparisonofthecontour plotsoftheclassi iersisproposedinFigure3.Ascan beobserved,thecontourplotsarealmostidentical, whichsupportsthesimilarAUC‐ROCvaluesobtained.

Figure1. ConvergenceAnalysis

Figure2. ResidualsandTolerances

Visuallytheoutermostcontourlinewouldrepre‐senttheboundarybetweenanomalousandnormal instances.

Basedontheexperimentalstudy,itcanbecon‐cludedthatthealgorithmmaintainsgoodeffective‐nesscomparedtoothersimilarmethods.Thein lu‐enceofdatapreprocessing,particularlytheNys‐troemapproximation,ontheperformanceofthealgo‐rithmwasobserved.Fortwo‐dimensionaldatasets, theresultswereevaluatedgraphically,visuallycon‐irmingtheeffectivenessvaluesobtained.Finally,a detailedanalysisofthealgorithm’siterationsallowed veri icationofaspectsrelatedtoconvergenceandthe consensusprocess.

6.Conclusion

Outlierdetectionisafundamentalareaofdata mining.Itnotonlycontributestodatacleaning,but alsotothediscoveryofnewknowledge.However,its applicationtolargevolumesofdataremainsachal‐lengetoday.TheSVDDproblemisusefulforoutlier detectionandmodelingitasanoptimizationprob‐lemallowsapproachingitusingiterativemethods suchasADMM.TheconsensusvariantofADMMwas usedtomodelthesolutionoftheSVDDproblem.The proposedalgorithmwasimplemented.Theformof theconsensusmethodallowedthisimplementationto haveadistributedapproach.Tovalidatethemodel,a seriesofexperimentswerecarriedoutusingsynthetic andrealdatasetswithdifferentnumbersofinstances anddimensions,whichveri iedthecompetitivenessof theproposedalgorithmwithrespecttootherexist‐ingones,obtainingAUC‐ROCvaluesinanacceptable range.Thegraphicalanalysisofthecontourlines inthetwo‐dimensionalsetsprovidedclaritytothe resultsobtained.

Asfuturework,itisconsideredtoextendthecom‐parisonoftheproposedalgorithmwithotherdis‐tributedalgorithmsforOD.Itisalsoproposedtovali‐datethealgorithmonnon‐equaldistributiondatasets.

Notes

1Original:UCIRepositry:https://archive.ics.uci.edu/static/pub lic/42/glass+identification.zip,OutlierApproach:https://odds.cs. stonybrook.edu/glass‐data/

2Original:UCIRepository:https://archive.ics.uci.edu/static/p ublic/148/statlog+shuttle.zip,VersionUsed:https://dataverse.ha rvard.edu/api/access/datafile/2711919?format=original

AUTHORS

AlejandroCespónFerriol∗ –UniversidadCentral “MartaAbreu”delasVillas(UCLV),Cuba,e‐mail:acfer‐riol@uclv.cu.

HéctorRGonzálezDiez –UniversidaddelasCiencias Informáticas(UCI),Cuba,e‐mail:hglez@uci.cu. CarlosA.MorellPérez –UniversidadCentral “MartaAbreu”delasVillas(UCLV),Cuba,e‐mail: cmorellp@uclv.edu.cu.

∗Correspondingauthor

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Abstract:

MODEL‐BASEDDEVELOPMENTOFAUTOPILOTFORAGASODYNAMICALLY CONTROLLEDHIGH‐SPEEDUNMANNEDAERIALVEHICLE

Submitted:17th February2024;accepted:7th November2024

MariuszJacewicz,DariuszMiedziński,GrzegorzChmaj,RobertGłębocki DOI:10.14313/jamris‐2025‐010

Inrecentyears,model‐baseddesignandautomaticcode generationhavegainedpopularityinvariousapplica‐tions.However,usingthisapproachinsomespecialized safety‐criticalapplicationsisstillchallengingbecausethe codemustfulfillrigorousrequirements.Inthispaper, themethodologyofdevelopmentofthesoftwareautopi‐lotfortheguidedHigh‐SpeedUnmannedAerialVehicle (HSUAV)ispresentedindetail.Theplatformisactuated onlywith32solidpropellantlateralmotors,whichmakes thecontroltaskchallenging.MATLABandSimulinkwere usedtodevelopthedetailedsimulationofthevehicle, togetherwiththecontrolsoftware.AModel‐in‐the‐Loop testingwasevaluatedtoachieveanappropriateautopi‐lotresponse.EmbeddedCoderwasappliedtogenerate production‐readyCcodefromthemodel.Acustomtest frameworkwascreatedtoacceleratethedesignprocess. ThenumericalequivalencyoftheSimulinkmodelandC codewasinvestigatedextensivelyusingSoftware‐in‐the‐LoopandProcessor‐in‐the‐Loopsimulations.Adeveloped controlalgorithmwasimplementedonrealhardware withanARMCortexM4microcontroller.Theintegrated prototypeofthecontrolsystemwassuccessfullytested inlaboratoryconditionsbyHardware‐in‐the‐Loopsim‐ulation.Thescientificsignificanceofthispaperliesin acomprehensivedescriptionofthemethodologythat mightbeusedbyotherresearchers.

Keywords: model‐baseddesign,automaticcodegenera‐tion,EmbeddedCoder

1.Introduction

Model‐baseddesign(MBD)isgainingpopularity invariousapplications,suchasmedical,industrial, aerospace,andautomotive.Thismethodologyisalso sometimesusedtodevelopcontrolsystemsforguided missiles.However,intheexistingliterature, inding adetailedandcomprehensivedescriptionofthepro‐cessischallenging.Suchdataareoftenclassi ieddue tosecurityreasons.Moreover,thedevelopmentof controlsystemsforhigh‐speedobjectsisverycostly andrestrictedbymilitaryinstitutions.Alotofthe existingsystemsarebasedonlegacysolutionsthat weredevelopedseveralyearsago.Also,testingthe developedsystemrequiresspecializedtestranges becausefailureduringreal lightmighthavecatas‐trophicconsequencesandbeverydangerous.

Whenamalfunctionoccurs,theobjectcanhit theunintendedtargetaccidentally.Forthisreason, usingmodelsplaysacriticalroleinpreparing light tests.Theonboardsoftwaremustbedevelopedcost‐ef icientlyandensurea inalhigh‐qualityproduct. Thereexistsasigni icantresearchgapinpublications relatingtothetopicofautomaticcodegeneration (ACG)inthe ieldofguidedHSUAVs.Theoverallpro‐cesswork lowisgenerallywell‐known,butfromexist‐ingavailableliterature,itishardtoconcludeaboutthe details(forexample,settingsofthecodegeneratoror veri icationmethod).

Alpaslan[3]analyzedthechallengeswiththe developmentofweaponsoftware.Theautopilotmight beconsideredasasafety‐criticalsystemoperatingin real‐time.Thedevelopmentofsuchasystemisoften morecomplicatedthanthatofcommercialproducts. Also,informationsecuritymustbeconsidered.Today, alotofweaponfunctionalitiesareincludedinthesoft‐ware.Asaresult,requirementscanbeprettysimilarto thoseinthespaceindustry.

Thetraditionalprocessofsoftwaredevelopment wasmanualcoding[7].However,suchanapproach istime‐consuming.Uptothistime,manypaperson codegenerationhaveappearedintheliterature.A reviewofrecentstudiesonautomatedcodegener‐ationwaspresentedbyKshirsagaretal.[39].ACG wasusedfortheaerospaceprojects.Marolietal.[46] adoptedcodegenerationforthemotorcontrollerfor NASA’sX‐57Maxwellaircraft.Theyalsoexplainedthe roleofseveralanalysistoolsavailableinMATLABto ensurethatthecreatedcodeisbug‐free.Thistech‐niquewasappliedtodevelopthesoftwareforthefault protectionsystemintheDeepSpace1mission[47]. MBDandSimulinkweresuccessfullyusedtocreate theGuidance,Navigation,andControl(GNC)software fortheOrionproject,andNASApublishedadetailed descriptionofthemethodologyin[31,64].Fraticelli [23],presentedtheexampleofsoftwaredevelopment foranAttitudeDeterminationControlSystem(ADCS) ofasatelliteandinvestigatedthenumericalequiva‐lencybetweenthemodelandCcodeoutput.Carpenter [10]alsoreportedusingACGtoobtaintheready‐to‐usesoftwarefornanosatelliteinthecontextofADCS. Yahyaabadietal.[71]studiedthefeasibilityofusing auto‐codegeneratorsinfuturespacemissions.

Armetal.[5]discussedthecodegenerationprob‐lemforsafety‐criticalapplicationsandpresentedan exampleofacompletework lowfortheARMCor‐texRhardwaretarget.Erkinnen[17]alsoaddressed thetopicofsoftwaredevelopmentbyusingACG forsuchsystems.Severalyearsago,Schwarz[59] mentionedthatcodegenerationisnotoftenapplied forsafety‐criticalsystemsbecausesuchapplications shouldobeystrictrequirements.However,uptonow, auto‐codingusingautomaticcodegeneratorsisstill notawidelyacceptedmethodofsoftwarecreationin safety‐criticalapplications.Themainreasonbehind thisisthelackofcerti icationandquali icationofthe generators[15,22,62].Moreover,manyoftheexist‐ingaerospaceanddefensesystemsweredeveloped acoupleofyearsago,andthereisaproblemwith adequatelyintegratingthelegacycodeswithmodern softwaredevelopmenttools.

AutogeneratedcodefromSimulinkcanhavebugs thatmighthavefatalconsequences[34].Theresulting codemustworkinthesamemannerastheoriginal modelofthesystem.Theproblemofnumericalequiv‐alencybetweenthemodelandautogeneratedcode wasaddressedbyseveralresearchers[6].Lambersky [40]presentedthedevelopmentofthecontrolalgo‐rithmforaleggedrobotandcomparedtheresults fromthesimulationandtargetplatform.

ManyexamplesofusingACGwerereportedfor relativelysimplesystemsthatdonothavetomeet strictrequirements[41,48,52,53,60].Forinstance, HylandWagnerová[28]presentedthecaseofthe controllerdevelopmentprocessfortheclimateunit laboratorystand.Otava[55]showedmotorcontrol developmentusingSimulinkEmbeddedCoderand veri iedtheresultsexperimentally.FakihandWarsitz [21]reportedthecodegenerationprocessfortwo simpleusercasestudiesandcomparedtheresults ofMILandSILsimulations.Krizanetal.[38]pre‐sentedadetaileddescriptionofamodel‐baseddesign forcontrolofadirectcurrentbrushlessmotor.Also, Wu[69]reportedusingMATLABbuilt‐intoolsfrom theCoderfamilyforcontrollerdesignforanelectric motorusingTIFI28379Dhardware.LixinandLiwen [11]presentedthecaseofcodegenerationforan autonomousunderwaterrobot.

ExistingworksarerelatedtousingMATLABtools intheMBDprocess.Itmustbementionedthataset ofothercodegeneratorsexists.SCADEenvironment withaquali iableKCGCodeGeneratorisusedforthe developmentofavionicssoftware[67].Intheauto‐motiveindustry,theTargetLinkgeneratorreached signi icantpopularity.Ajwad[2]comparedtheper‐formanceofEmbeddedCoderandTargetLink.Also, Scilab‐ScicosandGeneAutowereproposedasopen‐sourcesolutions[37, 58, 66].JacobitzandXiaobo proposed[32,33]LoRrageneratorthatcanbeused totranslateScilab/XcosmodelsintousableCcode. Also,agroupofresearchpapersproposescustomized, muchlesspopulargeneratorsotherthanwidelyused (bothcommercialandopen‐source)solutions.

Forexample,Yuetal.[72]designedacustom generatornamedMercuryandcomparedtheper‐formancewithSimulinkEmbeddedCoder.Bourbouh etal.[8]proposedaframeworknamedCoCoSimthat canbeusedtoanalyzeandverifythecodegenerated fromSimulinkmodels.Somerecentstudiesconcen‐trateongeneratingparallelizedcodefromSimulink blockdiagrams[70].

Severaltrialsbymanyindividualresearchersand variousorganizationswereperformedtostandardize the light‐readyproductioncodegenerationprocess fromSimulinkmodels.Forexample,Erkkinen[16] describedseveralavailableguidelinesandbestprac‐ticesforautomaticcodegenerationfor lightapplica‐tionstomakeitoptimizedandef icient.Someyears later,in[18],healsopresentedtheuseofaqual‐i iedveri icationtoolforthemodel‐baseddesigns forDO‐178Bapplications.Fraticelli[24]describeda setofvaluablepracticesingeneratingCcodefrom theSimulinkmodel.MathWorksAutomotiveAdvisory Board(MAAB)proposedasetofproperpracticesand recommendations.MotorIndustrySoftwareReliabil‐ityAssociation(MISRA)initiallycreatedasetofC standardsonlyforautomotiveapplications,butnow theyarewidelyusedinotherbranchesofindustry. NASAhasitsstandardsandregulations(forexam‐ple,NPR7150.2,NASA‐STD‐8739.8,andNASA‐GB‐8719.13).Oneofthemostimportantcontributions andprogressinthat ieldinthecontextofaerospace applicationsisreportspreparedbytheSpaceAVionics OpenInterfaceaRchitecture(SAVOIR)workinggroup thatcanbeusedasguidelinesinCcodegeneration fromSimulinkmodels[19,20].

Inthe ieldofguidedUAVs,theliteraturerelated toMBDisrelativelyscarce.Amongthedetailedpub‐lications,onemightmentiontheworkofPutroand Septanto[57],whodevelopedareal‐timetestenvi‐ronmentforevaluatingthemissile’sperformance. Craft[13,14]presentedthecaseofusingautomatic codegenerationfortheLongRangeLandAttack Projectile(LRLAP).Abdelaty[1]gaveacomprehen‐sivedescriptionoftheautopilotdevelopmentforthe anti‐tankround.Tancredi[65]describedtheoverall designmethodology,andreportedusingcodegen‐erationbyMBDAcompanybutwithoutdescribinga particularcase.Holliday[27]reportedusingMBDby Thalescompanyandpresentedseveralusercases, however,withoutsuf icientdetail.Severalauthors brie lydescribedHardware‐in‐the‐Loopsimulators forguidedhigh‐speedobjects[4,36,61,76],butthe resultsaredif iculttoreproduce.Waxenegger[68] presentedaHardware‐in‐the‐Looptestingmethodol‐ogyforarocketpropulsioncontrolsystem.

Automaticcodegenerationfromthesystemmodel offersseveraladvantagescomparedtothesoftware’s traditionalmanualcodingforthecontrolsystem.The overallcostandtimeoftheprototypingmightbe reducedsigni icantly[74].Asaresult,autocodingcan reducetheoveralleffortcomparedtomanualcoding [51].

Theresearchmightconcentrateontestingvari‐ousvariantsofthealgorithminsteadofimplementing low‐levellanguagedetails[45,75].Theresultingcode hasaclearandrepeatablestructure.Thistechnique alsodecreasestheneedformanualdebugging,which isoftentime‐consuming.Suchmethodologyreduces theprobabilityofintroducinghuman‐mademistakes duringmanualcoding(forexample,insigns).Fur‐thermore,theconsecutiveversionsofthesoftware mightbeeasilymanaged.Theveri icationanddoc‐umentationprocesscouldalsobeautomated.Auto‐maticallygeneratedcodecanbeasfastorevenfaster thanhandwrittencode[9, 12, 44].UsingMBD,the numberofexpensiveandtime‐consuming lighttrials thatmustbeperformedtovalidatethecontrolsys‐temcanbereducedsigni icantly.SIMULINKdiagrams arequiteeasyformanagersandsystemengineersto understand,soteamcollaborationissimpli ied.On theotherhand,thismethodologyrequiresthestaffto havemultidisciplinarycompetencies( lightdynamics, modeling,electronics,etc.).

Themotivationforthepresentedstudywasstrictly practical.Therewasaneedtodevelopacontrol systemprototypeforthegasodynamicallycontrolled HSUAVinashorttime.Themostcommonactua‐tionmethodisusingmovableaerodynamic insor thrustvectoring.Usingmultiplesolidpropellantlat‐eralmotorsismuchlessprevalent.

Uptonow,onlyafewexistingsolutionshaveused thistypeofactuation.Suchpulsethrusters(asonly actuators)wereusedontheM47Dragonanti‐tank andSTRIXmortarrounds.UkrainianVilkhaadopts90 smallpulsethrustersinthefrontofthefuselage,but alsoembracestheaerodynamicmovable insusedin thelastphaseof light.Moreover,180lateralmotors areusedonPAC‐3MSEintheinitialandterminal phasesof light(thisplatformalsousesaerodynamic control).

Themaincontributionofthisstudyisthedetailed descriptionofautomaticCcodegenerationfromthe SimulinkmodelfortheHSUAVautopilot.Theoriginal‐ityofthisresearchliesinthefactthattheobjectis actuatedonlybysolidpropellantlateralmotors,which isnotastandardsolution.Thecontrolsystemsfor suchacon igurationarenotdescribedinsuf icient detail.Foratactical‐gradesystem,thereliabilityof theoperationisacriticalfactor.Thesolutionmust becarefullytestedforvariouspossiblescenariosthat mightappearintheactual irings.Theresultingcode cannotincludeunintendedfunctionalityaffectingthe system’soperation.Thisresearchextendstheresults presentedin[30,42].Theproposedapproachmight behelpfulforotherresearchersinthe ieldofexternal ballistics.Thearticlealsoincludesadescriptionofa setofgoodcode‐generatingpractices.

Thestructureofthepaperisasfollows.At irst, adescriptionofthe lyingplatformisshown.Then, a lightsimulationmodeloftheHSUAVdevelopedin Simulinkwaspresented.Next,thecontrolalgorithm wasdescribed.Later,thecodegenerationprocesswas explained.

Therepresentativeresultswereshown.Thepaper endswithadiscussionoftheobtainedresultsanda summaryofthemain indings.Finally,somefurther possibleresearchdirectionsaresuggested.

2.High‐SpeedUnmannedAerialVehicle Description

Thediameterofthefuselageis0.122mandthe totallengthoftheobjectis2.1m.Atlaunch,themass isaround26kg,andmomentsofinertiaare0.13kgm2 (longitudinal)and10.2kgm2 (transversal).Themass ofthepropellantis6kg.Theoperationtimeofthe mainmotorisalittlemorethan2.8s,andtheavailable thrusthasamaximumvalueofabout8600N.HSUAV isaerodynamicallystabilizedbyfourtrapezoidal ins (thereisnowrap‐aroundfunctionality).Thesestabi‐lizersarecanted,andasaresult,theycreatearolling moment(theplatformintentionallyspinsslowlydur‐ingthe light).Theplatformisequippedwith32solid propellantlateralthrusterslocatedinfrontofthe centerofmass(nomovableaerodynamic inswere used).Thethrustersarearrangedintofourlayers witheightmotorsineach.Eachofthesethrusters mightbeusedonlyonce.Theoperationtimeofthe thrusterislessthan0.05s,andthemeanthrustis morethan700N.Thiskindofactuationischalleng‐ingbecausetheobjectpossessesverylowcontrol authority.Thatmeansthesinglepulsethrustercan translatetheimpactpointlocationbyonlyseveral meters.Themaximumrangeisapproximately11km. Intheconsideredversion,thesolutionaccountsfor onlystationarytargets.

TheGNCsystemcomprisesanavigationunitand anactuationunit.Thesesubsystemsareintegrated intoacontrolunitusingthemechanicalstructure.

Themaincomponentsofthenavigationunitare asetofsensors,aPrimaryControlComputer(PCC), andthreeantennas.Themainfunctionofthatsystem istousedatacollectedbythesensorsandconvert themintoinformationabouttheobject’s lightstate. Thenavigationdataareobtainedusinganoff‐the‐shelf availableInertialMeasurementUnit(IMU),acustom‐developedGALILEOreceiver,apressuresensor,and infraredsensors(thesesensorsareequallyspaced aroundthecircumferenceoftheobjectbody).ThePCC usesanARMCortexA7processor.Thedataobtained fromallsensorsisfusedusingaKalman ilter.One ofthemaindif icultiesoftheadoptedsolutionlies inthefactthattherollanglemustbeestimatedvery precisely(withaccuracy<1∘).Thelow‐costmicro‐electromechanicalsystems(MEMS)gyroscopesthat areavailableonthemarkethavealowmeasurement range(typicallyupto2000∘/s)andarenotentirely suitableforthedevelopedsystem(sensorsaturation couldoccur).Duetothis,satellitesignalsneededto bereceivedbytheantennasmountedonthesidesof thefuselagetoestimatetherollangle.Moreover,the infraredsensorsareusedtoimprovethecalculation accuracy.Additionally,theinformationaboutthealti‐tudeiscorrectedbythereadingsfromthepressure sensor.

TheactuationunitcomprisesaLateralMotors ControlComputer(LMCC),asetofpowerampli iers, andlateralmotors.Theprimaryfunctionofthisunit istousethedataaboutthecurrentplatformstate (obtainedfromthenavigationmodule),calculatethe steeringcommands,andactivatetheappropriatelat‐eralthrusters.TheLMCCisbasedontheARMCortex M4architecture.Itcalculateswheneachmotorshould be iredtosteertheHSUAVontarget.Thepower ampli iersactivatetheignitersattachedtothelateral motors.TheyconverttheoutputdatafromtheLMCC intoasetofelectricalsignalsforthe32ignitionchan‐nels.Eachigniter(sometimescalledamotorstarter) isresponsibleforstartingthecombustionofasingle smallsolidpropellantinthelateralmotor.Thisunit alsoincludesanElectrostaticDischarge(ESD)protec‐tioncircuittopreventeachigniterfromunintentional release.

Additionally,theHSUAVisequippedwitharadio telemetrydownlinkthattransmitsthedata(linear accelerations,angularrates,position,etc.)tothe groundcontrolstation(GCS)withafrequencyofup to500Hz.Theobjectstatecanbeobservedinreal‐time(intheformofgraphsandvisualization)onthe GCS.Duringthelaunchphase,theelectronicunits aresubjectedtohighacceleration.Forthatreason, triple‐redundantcommunicationchannelswereused toincreasethesystem’sreliabilityandminimizethe probabilityoffailurein light.

Theonboardbatterypowersallelectronicsubsys‐temsdescribedabove.

3.SimulationModelDescription

IntheMBDapproach,oneofthe irststepsisto createarealisticplantmodel.Tomaketherealpro‐totypeofthehardware,thedetailed lightsimulation modeloftherealobjectwasdevelopedandimple‐mentedintheMATLAB/Simulinkenvironment.The baselinemathematicalformulationcanbefoundin ”AppendixA”.Thedetaileddescriptionofthemath‐ematicalmodelanditsimplementationcanbefound in[26,29,30,42,43,56].

Thevehiclesubsystems(mainmotor,lateral thrusters,onboardsensors,etc.)weremodeledbased onthedataofrealhardware.Thedynamicsmodel parameterswereobtainedmainlybytheexperiments inlaboratoryconditionsand iringsoftheexisting prototypes(unguidedones).Additionally,they werecon irmedusingCADmodelsofthestructure. HSUAVmomentsofinertiaweremeasuredusing bi iliarandquad ilartorsionalpendulums.Thethrust curvesofthemainmotorandlateralthrusterswere acquiredbymeasurementsontheteststandat varioustemperatures.Aerodynamicparameterswere collectedbyusingspecializedsemi‐empiricaland ComputationalFluidDynamic(CFD)codes.Later, afterinitial lighttrials,theaerodynamicdatabase wascorrectedbytheappropriateformfactors.The sensors’datawerefoundusingdatasheetsfrom themanufacturersandcon irmedbylaboratory experiments.

Also,thelauncherdynamicswereincludedinthe modeltomakethesimulationoftheinitialphaseof lightmorerealisticandincludeseveralimportant phenomena(forexample,thetip‐offeffect).Environ‐mentalconditions(e.g.,airtemperatureandhumid‐ity)aretakenintoaccounttopredicttheatmospheric properties.

Thekeyelementofthesimulationisthemodel ofthecontrolsystemhardwareandthesoftware. Theinputstothecontrolalgorithmarecurrentposi‐tioncoordinates,Tait‐Bryanangles(yaw,pitch,roll), angularvelocities,linearvelocities,andlinearaccel‐erations.Theoutputisthe iringcommandofeach thruster.Thetargetpositioncoordinates(latitude, longitude,andaltitude)mustbeknownandpro‐grammedbeforethelaunch.

Theschemeoftheoverallcontrolalgorithmispre‐sentedinFigure1.

ThequalityoftheresultingCcodecanbeaffected byalotoffactorsandsettings.Toappropriately choosethecompilerparameters,themodelwascre‐atedusingSAVOIRguidelines[19, 20].Theequa‐tionsofmotionwereintegratednumericallyusing a ixed‐stepBogacki‐Shampine(third‐order)solver withastepsizeof0.0001s.Only ixed‐stepsolvers arecurrentlysupportedinMATLABduringthecode generationprocess.Themodelcannotcontainany blocksthatarenotsupportedbythecodegenerator. BeforeperformingACG,itiscrucialtoensureawell‐styledSimulinkmodel.Alloftheinputsandoutputs werenamedusingstrictprede inedconventions.The namesandunitsweredisplayedonthesignalwires toeliminatetheprobabilityofhumanerror.Signals weregroupedusingbuses,whichensuredreadability. Signallinecrossingwaseliminated.Theschemealso includesasetofdiagnosticoutputsthatcanbeused inlaterstagestoanalyzeindetailtheresultsonthe actualhardware.Equalitycomparisonusing loating pointnumberswasavoidedbecausethatcanleadto entirelyunpredictableresults.

Asmallteamofexperiencedprogrammersdevel‐opedthemodel,soitwasnecessarytoperformver‐sioncontrol.Eachsubsequentversionofthecode hasauniquenamewithdataandtimeoflastsaving included.SimulinkDesignVeri ierwasalsousedto detectpotentialproblemswiththeblockdiagram(for example,dividingbyzeroordeadlogic).

Therequirementsandacceptancecriteriaforindi‐vidualsubsystemswereformulatedattheinitialphase ofthecontrolsystemdevelopment.Theserequire‐mentswerealsocreatedforthesoftware.Thecode shouldbeef icientandabletooperateinreal‐time onthetargethardware.Thecontrolalgorithmwas carefullyoptimizedtoincreasetheexecutionspeed andsavetheavailablecomputationalresources.The autopilotcodeshouldbeintegratedwithothersoft‐warepartscreatedbydifferentcooperators.Itisobvi‐ousthatthesoftwareshouldincludeappropriatecom‐mentsandbeeasytounderstand.

3.1.NavigationDataExtrapolation

TheGNCmodulecanbeconsideredasacom‐plicatedmulti‐ratedigitalsystem.Thedataabout theindividualHSUAV lightparameterscanbedeliv‐eredfromthenavigationsystemmodulewithvarious (oftenrelativelylow)frequencies.Forexample,the positionusingaGALILEOreceivercanbeobtained withafrequencyofnomorethanseveralhertz.Onthe otherhand,therawdatafromIMUoutputs(angular ratesandlinearaccelerations)couldbesampledwith afrequencyofupto200Hz.Thesedataarefused usingaKalman ilter[73]toobtainamoreaccurate estimationofthe lightparameters(mainlyvelocity, position,andEulerangles),buttheoutputfrequency isnomorethan40Hz.Thethrusterscanbe ired onlyincertainphasesof lightwhentherollrateof theobjectisapproximately2revolutionspersecond (afterapogee).Iftherollangleisestimatedat40Hz, thenthemotorscanbe iredwiththeangularresolu‐tion18∘ whichistoolow.Thatmeansthecontrolloop shouldoperateatamuchhigherfrequencythanthe datacanbedeliveredfromsensors.Itwasestimated thatthecontrolalgorithmshouldberecalculatedwith afrequencyof5000Hz.Thatway,the iringconditions willbecheckedwithanangularresolutionof0.144∘

Forthisreason,anupsamplingalgorithmshould beappliedtoobtainthenavigationdatawiththe requiredfrequency.Ontheotherhand,suchanalgo‐rithmcannotintroducetimedelaysbecausethenthe objectmightbesteeredintheinappropriatedirection.

Acustommodule(whoseprimaryfunctionis toextrapolatethedatagatheredfromthevarious onboardsensors)wasdevelopedtoovercomethatdif‐iculty.Thismoduleconsistsoftwoparts:extrapola‐tionofrollangleandposition,whichweredetermined tobethemostin luentialonthealgorithm’saccu‐racy.Ontheoutputofbothextrapolationmodules, thenavigationalinformation(rollangleandthree‐dimensionalpositioninspace)isdeliveredwiththe desiredfrequencyof5000Hz.Allothersignalsare obtaineddirectlyfromthenavigationmodulewithout theextrapolationprocedure(theirfrequencyissuf i‐cient).

Figure2. Rollangleextrapolationblockscheme(signal frequenciesdenotedinbluefont)

Therollangleextrapolationblockschemeispre‐sentedinFigure2.

Themainideabehindthismethodisthattheangu‐larrate(obtaineddirectlyfromgyroscopes)canbe deliveredwithahigherfrequencywhencompared toinformationabouttheactualrollangle.Itwas assumedthatbetweentwoconsecutivesamplesof therollangle,theinformationontheintermediate pointscanbeobtainedusinglinearinterpolation.The forwardEulermethodwasusedfornumericalintegra‐tionoftherollrate��toobtaintherollangleΦ:

Φ(��)=Φ(��−1)+[��(��)−��(��−1)]��(��−1) (1) where��‐timeand��‐samplenumber.Afterdelivering anewvalueoftherollanglefromthemeasurement system,thevalueoftheintegralisreset,andtheinte‐grationstartsfromthenewinitialcondition(whichis thesameasthelastmeasuredvalueoftherollangle).

Thesameideawasusedtoextrapolatetheposition coordinates:

��(��)=��(��−1)+[��(��)−��(��−1)]��(��−1) (2) ��(��)=��(��−1)+[��(��)−��(��−1)]��(��−1) (3)

��(��)=��(��−1)+[��(��)−��(��−1)]��(��−1) (4) where ��,��,�� ‐velocityvectorcomponentsin North‐East‐Downframe.

3.2.GuidanceAlgorithm

Amodi iedProportionalNavigationGuidance (mPNG)algorithmwasdevelopedtosteertheobject accuratelytowardsthetarget.Thetargetlocation

�� =[��,��,��] andtheHSUAVposition ⃗ �� = [��,��,��]mustbeknown.Theaccelerationper‐pendiculartothelineofsight(LOS)is[49]:

(5)

Figure1. Top‐levelSimulinkschemeofthecontrolalgorithm

where �� ‐proportionalityconstant, ⃗ �� = [��,��,��] ‐closingvelocityand ⃗ ��= [��,��,��] ‐lineofsightangularrate.The projectionsoftheclosingvelocityonthe ��, �� and �� planesoftheNorth‐East‐Down(NED)coordinate systemare:

Thecomponentsofthedistancebetweenthetarget andthevehicle(alongeachaxisoftheNEDframe)are:

isthetransformationmatrixfromtheNorth‐East‐Down(NED)frametothebody‐ ixedframeand

Inasimilarway,thecomponentsoftherelativeveloc‐itiesare:

Attheoutputs,thisalgorithmdeliversinformation aboutthecommandedlinearaccelerationsinthe body‐ ixedframe.Thethreecomponentsoftheaccel‐erationvectorareusedasinputstotheFiringLogic (FL)submodule(pleaseseethenextsectionofthe paper).Tohitthetargetsuccessfully,thevehicle mustrealizethiscommandedacceleration.Thecom‐mandeddirectionof lightinthebody‐ ixedframeis calculatedas:

(25)

Themagnitudeofthecommandedaccelerationis:

(26)

ThedetailsaboutthemPNGalgorithmarepresented in[30,56].Theproposedalgorithmcanachieveasig‐ni icantimpactpointdispersionreduction,whichwas provedbyvariousstudiesconductedine.g.[25,26,29, 35,63],whereverysimilartypesofguidancemethod wereutilized.

TheLOSanglesineachplaneare:

Theseanglesmustbedifferentiatedwithrespectto timetoobtainLOSrates.

Additionally,itmustberememberedthatthenav‐igationsystemestimatesthevelocity ⃗ �� attheloca‐tionofIMU,sothisvaluemustbeconvertedtothe centerofmass:

(27) where ⃗��‐vectorofangularrates, ⃗�� ‐locationofthe IMU(measuredfromaft)and ⃗�� ‐actualpositionof objectcenterofmass.

3.3.FiringLogicoftheLateralThrusters

Next,theaccelerationobtainedfromequation5must beconvertedtothebody‐ ixedframeandcompen‐satedbythegravity:

Thediscretenatureofactuationmakestheguid‐anceprocessdif icultbecausethereisnopossibility ofcontinuouslytrackingthecommandedlateralaccel‐erations.Sinceonly32thrustersareavailable,their useduringthe lightmustbecarefullyplanned.Ifthe motorsare iredtooearly,thenitwillbeimpossi‐bletoin luencethetrajectoryintheterminalphase of light.Moreover,ifthetimebetweentwopulses istooshort,theplatformcanachievehighanglesof attackandsideslip,andasaresult,disintegrationcan occurduetohighstructuralloads.Ontheotherhand, ifthethrustersare iredattoolargetimeintervals, theirusagewillbeineffective,andtheHSUAVwillnot achieveitsdestination.

The iringlogicisbasedontheconjunctionoffour conditionsthatcouldbeexpressedmathematicallyas (fordetails,pleasesee[30]):

Figure3. Simplifiedsequenceofeventsbefore activationofthethrusters

where �� ‐actualtime, �� ‐timeoftheprevious iring,�� ‐theminimumallowedtimebetweenthetwo consecutivepulses, ⃗�� ‐actualaccelerationvector, �� ‐thresholdvalue,�� ‐commanded lightdirection,��‐measuredrollrate, �� ‐timeconstant(approximately one‐halfoftheburningtimeofthepropellant), Φ�� ‐angularlocationofthelateralmotor, �� ‐angular toleranceofthelateralmotors irings, �� ‐time, �� ‐thresholdtime,Θ‐actualpitchangle,Θ�� ‐pitchangle threshold.

Theindividualthrusteris iredwhentheoutput signalfromthealgorithmchangesfrom0(lowstate) to1(highstate),whichhappensafterallfourcondi‐tionsaretruesimultaneously.

Thestatemachine(Figure3)wasalsousedtoreal‐izeastep‐by‐stepcontrolprocesstopreventtoo‐early lateralmotor iringsforsafetyreasons.Theactuation unitwiththecontrolmotorsmightbeactivatedonly afterdetectingthelaunchevent(longitudinalacceler‐ationofmorethan50m/s2 over0.4s).

3.4.PulseThrustersAssignment

Thelateralthrustersare iredintheprede ined sequencepreparedasa iringtable(block”Motor‐FireMatrix_simple”inFigure1.Thesystemusermight programthissequencebeforethelaunch.Anexample ofsuchatableispresentedin Table1,wherethe irstcolumnisthenumberofthepulse,thesecond columnistheIDofthethruster,andthelastcolumnis theangularpositionofthethrusteronthefuselage’s circumference.

Table1. Exampleofthefiringtable.

Pulseno. ThrusterID

4.AutomaticCCodeGeneration

Thesoftwareshouldbedevelopedusingastrict strategy.Severalmanagementmethodologiesexist thatcanbeapplied,butsomeareunsuitableinthis context.Forexample,thewaterfallmethodologywas notfeasiblebecausetheinitialrequirementswerenot fullyformulatedatthebeginningoftheprocess.The softwaredevelopmentprocessdiagramispresented inFigure4

Theonboardhardwareisquitelimitedincompu‐tationalresources,anditisevidentthatthecontrol algorithmprototypedevelopedinMATLABmustbe implementedintheappropriatelow‐levelprogram‐minglanguage.TheSimulinkCoder(earlierRealTime Workshop)andEmbeddedCoderwereusedforauto‐maticcodegeneration.However,thisMATLABexten‐sionwasinsuf icienttoautomatethewholeprocess entirely.Forthisreason,acustomcodewasdevel‐opedtogenerate,compile,run,andtestthealgorithm. MicrosoftVisualStudio(MSVS)2019wasusedto compilethecode.

4.1.ModelBuildOptions

Togeneratethecodeappropriately,thesettings mustbecarefullychosen,asthedefaultcodegenera‐tionsettingsarenotoptimal[50].ISO/IEC9899:1999 Clanguagestandardwasused.Thecodewasgen‐eratedwithvarioussettings,andtheresultswere assessedforeachcombinationofparameters.Forthe generatedcode,aVisualC\C++ ileforEmbedded Coderwaschosen.Also,thein luenceofcodeopti‐mizationsettingsontheaccuracyofthegenerated codewasinvestigated.Afterasetoftrials,itwas decidedtosettheoptimizationlevelasaminimum. Thealgorithmparameters(e.g.,targetlocationcan besetasinlinedortunable.Itwasdecidedthatthey shouldbeinlinedinthecodetoreducememoryusage andincreasecodeef iciency.Inthatway,thereisno needtopreallocatethememoryfortheparameters.

TheembeddedCoderSupportPackageforARM Cortex‐MProcessorswasusedtoensurethatthecode wouldbeeffectiveinrealizingmathoperationsusing theCortexMicrocontrollerSoftwareInterfaceStan‐dard(CMSIS)library.Usingthisaddon,itispossible toreplacesomefunctionsonthemoreeffectiveimple‐mentations(forexample,”sin”trigonometricfunction isreplacedon”arm_sin_f32”).

Single‐precision loat‐typenumericnumberswere usedtosavetheavailablememory.Bydefault,MAT‐LABoperatesondouble‐precisionnumbers,butusing theminthemicrocontrollerisnotnecessaryandseri‐ouslyslowsdownthecomputations.Forthatreason, allinputandoutputportsintheSimulinkblocksofthe controlsystemmodelweremanuallysetto”single”.In thatway,itwasensuredthattherewouldbenounin‐tentionalconversionbetween”single”and”double”.It wasdetectedthatthisissueiscrucialandmightlead tocatastrophicconsequences.

4.2.CodeVerificationMethodology

Beforebeingusedonrealhardware,thealgorithm mustbetestedforvariousoperatingconditions.Acus‐tomtestprocedurewasdevelopedtoverifythecontrol algorithm’sreliabilityandensurehighcodecoverage. Thecodegenerationprocessstartedwiththe selectionofanappropriate lightscenario.At irst, avastnumberofModel‐in‐the‐Loop(MIL)simula‐tions(forindividual lightscenarios)wereevaluated todetectpotentialproblemsattheearlystageofcon‐trolsystemdevelopment.Atthisstage,onlyacon‐trolmodulemodelwasconnectedwiththeHSUAV model.Thesetestswererealizedforvariouslauncher azimuthandelevationangles,variousthrustcurves ofthelateralthrusters,etc.Next,thestructureof theSimulinkcontrolsystemmodelwasiteratively optimizedtoachievethebestpossiblecon iguration anddecreaseexecutiontime.Themodelwascare‐fullycheckedtopreventinef icientpartsofthecode (forexample,algebraicloops).Notallfunctionsare supportedforcodegeneration.Inthatcase,acustom equivalentblockstructurereplacedsuchanunsup‐portedfunction.SimulinkPro ilerwasusedtomea‐suretheexecutiontimeofindividualmodelcompo‐nents.Simulink”Acceleratormode”wassettospeed uptheexecutiontime.Inthatway,theresultingtimeof asinglesimulationwasdecreasedtoonly7s(for50s ofthereal light).Then,MonteCarlosimulationswere usedextensivelytoevaluateaccuracyandprecision. TheParallelComputingToolboxwasusedtoassess thesimulationsontheworkstation(Intel®Core™i9 and16GBRAM).Inthatway,itwaspossibletosim‐ulatethousandsof iringsandestimatethemeasures ofdispersion(forexample,CircularErrorProbable). Also,parametricanalysiswasconductedtoinvestigate thein luenceofindividualautopilotsettingsonthe overallaccuracyandtounderstandthesystembehav‐ior.Theexampleofresultsfromthismethodologycan befoundin[26].Thisphaseendswhenthecontroller modelmeetstheprede inedrequirementsandgener‐atesappropriateoutputs.

AftertheMILstage,detaileddocumentationwas createdtodescribethelow‐levelfunctionalityofthe lightsimulation.Thedocumentationoftheresults wasbasedontheautomaticgenerationofstructured reports.AftereachsimulationinMATLAB,twotext ileswererecordedandsavedonthecomputerdisc. The irst ileincludedinthetabularformtimeand platform lightparameters:angularrates,position, Eulerangles,andlinearaccelerations.Thesecond ileincludedthearrayof iringcommands.Inthe laterstagesofthewholetestingprocess,theabove‐mentionedtwo ileswereusedasreferencedata(in theend,theoutputofthe inalcodeshouldmatchthe reference iringcommands).

AftercompletingtheMILphase,thenextstepwas toperformSoftware‐in‐the‐Loop(SIL)tests.Atthe SILstage,theCcodefromonlytheautopilotmodule wasgeneratedandusedinthecontrolloopinstead ofthecontrollersystemmodel.Thetraceabilityfunc‐tionthatisavailableinEmbeddedCoderwasused extensivelytonavigatebetweentheSimulinkmodel andCcode.Thesetestswereperformedonthestan‐darddesktopcomputer(Intel®Core™i7,32GBRAM, MSWindows11operatingsystem)withoutdedicated hardware.Atthisstage,checkingiftheautopilotsoft‐warecouldbeimplementedwaspossible.

Additionally,thecodewastestedexternallyto ensurenoproblemswiththegeneratedCsoftware. Theabove‐mentionedcustom‐developedtestproce‐durewasasfollows.TheCcodewasrunonaDesktop computerinMSVS,andtheresults(lateralthruster’s iringcommands)werestoredinaseparatetext ile. Then,bothtext iles(referencedatafromMATLAB obtainedattheMILstageandresultsfromthestan‐daloneCcode)werecompared.Iftheresultsmetthe acceptancecriteria,theCcodewasreadytobeimple‐mentedontherealhardwareandtestedagain.

Figure4. Softwaredevelopmentprocess

Ifanyanomalyoutputorunintendedbehavior wasobserved,thenitwasnecessarytoreturntothe MILstage,introducemodi ications,con irmthatafter adjustments,theMILresultswerestillacceptable,and thenagaincontinuetheSILlevelusingthemodi ied software.ThisprocesswasautomatizedusingMAT‐LABscripts.

Next,theProcessor‐in‐the‐Loop(PIL)phasewas performed.Thedevelopedalgorithmintheformof Ccodewasimplementedonrealhardwarewithan ARMCortexM4processor.Thedevelopedcontrolsys‐temwastestedinlaboratoryconditions.At irst,the (PIL)simulationwasevaluatednotinreal‐time.The referencedata,including lightparameters,weresent fromthetext iletothehardwarebytheinterface (thesedatawereusedinsteadoftheinformationfrom thenavigationunit).Thecontrolcomputercalculated steeringcommands,andtheoutputsfromthesys‐temwereloggedintotext iles.Themaingoalofthat stagewastocheckthattheresultswerethesameas thereferencedata.Then,real‐timecalculationswere performedtoensurethatthecontrolloopwasable tooperatewithasuf icientfrequency(5000Hz,as mentionedbefore).

Oneofthelaststepsofthetestingwasthe Hardware‐in‐the‐Loopsimulation.Atthisstage,the controllerperformancecanbeveri ied(atleastpar‐tially)withoutusingthecompleterealplant.This approachismuchsaferthantestingthecontrolsystem ontherealobjectin lighttests.Thesystemoperated inreal‐time.

Inthelaststage,theresultsfromMIL,SIL,PIL,and HILwerecomparedtoensurethattheresultswerein agreement.IftheresultsofHILwereunsatisfactory, theprocesscamebacktoMIL,SIL,orPILlevels.Oth‐erwise,ifthecodemettheacceptancecriteria,itwas decidedthatthesoftwaremightbeimplementedon therealvehicle.

5.ResultsandDiscussion

Themaingoaloftheexperimentswastocheck thenumericalequivalency(oreventuallysimilarity) oftheresultsbetweenthemodelinSimulinkandthe resultingCcodethatmightbedirectlyimplemented ontherealhardware.TheobtainedCcodemustwork liketheoriginalMATLABprogramwhentestedwith thesameinputdata.Thenumericaldiscrepancycan becausedbyvariousissues,forexample,low‐level implementationsofthetrigonometricfunctionsinthe twoprogramminglanguages[54].

MATLABR2023withUpdate5wasusedtoper‐formnumericalsimulations.Thecontrolalgorithm wasimprovedstepbystep,iteratively.Severaliter‐ationsofMIL,SIL,andPILsimulationswereevalu‐atedtomeettheacceptancecriteria.Thesolutionwas acceptableiftheimpactpointdispersionmeasured usingCircularErrorProbable50%(CEP50%)was smallerthan25mandtheresultswererepeatablefor various lightscenarios.Here,theselectedexampleof amissionscenarioispresented.

Positionerrors(inthelastphaseofflight)

Thefollowinginitialconditionswereassumed: launcherelevationangle45.2∘ andazimuth46.5∘ Thealgorithmsettingswereasfollows: �� =0.25s (minimumtimebetweentwopulses), Θ�� =5∘ (pitch anglethreshold),�� =30s(thresholdtime),�� =1.5∘ (angulartoleranceoflateralmotor irings), �� =0.5 m/s2 (thresholdvalueofthelateralacceleration).The launcherwaslocatedattheoriginoftheNEDcoordi‐natesystem.Itwasassumedthatthetargetisstation‐ary,anditscoordinatesintheNEDframeweresetto (6430.7,6222.0,0.0)m.

At irst,MILtestswereevaluatedfortwocases: unguided light(thecontrolsystemwasintentionally deactivated)andfortheguidedone.Thecomparison ofthe lightpathsispresentedinFigure5.InFigure6, theerrorsbetweenthetargetlocationandtheactual positionoftheHSUAVareshownfortheterminal phaseof light.Angularrates(roll,pitch,andyaw)are showninFigure7andorientationanglesinFigure8. TheuncontrolledHSUAVgroundrangeisabout 8950.3m,andthemaximumachievedaltitudeis approximately2680m.Fortheunguidedplatform,the impactpointcoordinatesare(6378.1,6279.1)m,and theachievedmissdistancewas77.58m.

Figure5. Three‐dimensionalflighttrajectory

Figure6.

Eulerangles(roll,pitch,andyaw)

Forthecontrolledone,theimpactpointislocated at(6429.0,6220.6)m,soonly2.18mfromthetarget. Thatmeansthelateralmotorscansuccessfullysteer theHSUAVtothetarget.

Allthreecomponentsofthepositionerrorshould ideallybe0.Fortheunguidedobject,thexandyerrors (inthehorizontalplane)deviatedsigni icantlyfrom thedesiredvalue.Ontheotherhand,fortheguided onetheyareverysmall(<2m).

Theabsolutevalueoftherollrateincreasesin theactiveportionofthe light(whenthemainmotor operates).Theminussigninthe irstplotinFigure7 meansthattheHSUAVrotatedcounterclockwisewhen lookingfromaft.Forthecontrolled light,theoscil‐lationsofpitchandyawratesignalsafter30sresult fromthe iringsoflateralmotors.

Fortheguidedobject,thedisturbancescanalsobe observedonpitchandyawangletimehistories.

Theforcesgeneratedbythelateralmotorsinthe aeroballisticframeattachedtotheplatformcenterof massarepresentedinFigure9.Itcanbeobservedthat 21lateralmotorswereused.

Impactpointdispersion(controlledflights)

Later,asetofMonte‐Carlosimulationswereper‐formed(300runsforeachscenario).Thecomparison ofimpactpointdispersionforunguidedandguided scenariosispresentedinFigures10and11

TheCEP50centeredonthetargetforuncontrolled scenariooneis161.24m.Someoftheimpactpoints arelocated572.12mfromtheaimingpoint(pleasesee CEP100%).

Figure7. Angularrates

Figure8.

Figure9. Forcesgeneratedbylateralmotors

Figure10. Impactpointdispersion(uncontrolledflights)

Figure11.

Numberofactivatedlateralmotors

Thereisasystematicoffsetbetweenthemean pointofimpact(MPI)andthetarget.Withthecontrol systemapplied,CEP50%decreasedto4.50m.That meansusingacontrolsystemreducestheimpactpoint dispersion(measuredusingCEP50%)byapproxi‐mately35.83times.ThelocationofMPIcoincideswith thetarget.Thisisimportantfromapracticalpointof viewbecausetheunintendedcollateraldamagecanbe minimized.

Next,theCcodewasgenerated,andSILsimula‐tionsoccurred.Finally,theobtainedCcodewasimple‐mentedonthetargethardwarewithARMCortexM4. ThePILsimulationswereevaluated,andtheobtained resultswerecomparedwithMILandSIL.Thecom‐parisonofoutputsfromthecontrollerimplementedin SimulinkandusingCcodeispresentedinFigure12 Theabovementioned igureillustratesthenumberof iringcommandsobtainedfromtheoriginalmodelin SimulinkandfromtheSILandPILsimulations.Inthe idealsituation,linesshouldcoincidewitheachother. Then,theoriginalSimulinkmodelandCcodewouldbe numericallyequivalent.Inpractice,duetonumerical roundingerrors,themodelandCcodearenumerically similarbutnotperfectlyidentical.

Upto30.37s,nothrusterwasactivatedbecause theconditionsgivenbyEquation28werenotful illed. ThatmeanstheHSUAVwasinanunguided light. Then,aseriesof21 iringsoccurred.Thelastmotor inthesequencewasactivatedin41.01s.

Tobettervisualizeandunderstandtheeventual numericalerrors,inFigure13,theplotoftimediffer‐encesbetweenSimulinkandCcodegeneratedinSILin evaluating iringcommandsisshown.Itwasassumed thatthevalueoftheacceptancethresholdis0.003s. Thedotsindicatethatformostofthemotors,there wasnotimedifferencebetweenresultsfromSimulink andCcode.In4cases,thedifferencewassmaller than8e‐15s.TheresultsobtainedindicatethattheC codepossessesfunctionalityidenticaltotheoriginal Simulinkmodel.

Timedifferencesinfiringcommands

Figure14. Controlsystemprototypeduringthe laboratoryexperiments

Inthenextstage,aseriesoflaboratoryHardware‐in‐the‐loopexperimentswiththeactualhardware wereperformed.Thisissueisnottrivialbecauseitis quitedif iculttomimictherealconditions(forexam‐ple,linearaccelerations)inthestatictests.Here,only thebasicdescriptionofthesetestsispresentedfor legalreasons.Themaingoalofthetestswastoensure thatthelateralmotorscouldbe iredintherightdirec‐tionandatappropriatetimeintervals.Forexample,if theHSUAVshouldturnleft(whenlookingfromaft), thenthethrustersmustbe iredontherightsideof thefuselage.Toverifythecontrolunit,asimpli ied laboratoryteststandwasdeveloped.Theapparatus (Figure14)consistedofamounting,electricrotor, encoders,controlunit,andoperator’scontroldesk.

Themaincomputerelectronicswerepoweredby theonboardrechargeablelithiumpolymerbattery(12 V)integratedwiththecontrolsystem.Theelectric motorthatdrivesthestandwasconnectedtoadif‐ferentpowersource.Theremainingelements(main solidpropellantrocketmotorandnosesection)were removedbecausetheyareseparateunits(notneces‐saryintheexperiments).Thedevelopedcontrolalgo‐rithmwasimplementedintheonboardcomputer.

Theelectricmotoraboutthelongitudinalaxis rotatedthecontrolmodulewiththesameangularrate asobtainedfromthenumericalsimulation.

Figure12.

Figure13.

(SimulinkvsCcode)

Thatway,therealisticinputdataabouttheroll angularrateandtherollanglefromthenavigation systemweregenerated.Theteststandisstationary,so theinformationabouttheposition,linearspeed,and accelerationscannotbedelivereddirectlyfromthe navigationmodule(valuesofthesesignalsarezero). Forthatreason,theinformationabouttheother light parameterswasdelivereddirectlytotheonboard computerfromthenumericalsimulation.

The iringcommandswereloggedandcompared withthedataobtainedfrompreviousstagesoftest‐ing(MIL,SIL).Firingsofthelateralmotorscanbe ineffectiveandproblematicinlaboratoryconditions. Asigni icantamountoftimeisrequiredtoprepare thetestsetupforthesingletest.Aftereachtest,the spentmotorsmustbereplacedwithnewones.The lateralmotorsalsoproducealotofsmoke.Tosolve theabovementionedproblems,insteadofusingreal pulsethrusters,asetofLEDs(light‐emittingdiodes) wasusedtovisualizetheresults(installedatthesame locationsastheoriginalmotors).Thetimeofthe operationofthesinglediodewassettobethesame astheoperationtimeoftherealpulsethruster.The systemwasmonitoredusingahigh‐speedcamera(up to5000framespersecond).Usingthisapproach,the experimentscanberepeatedmanytimes.Thatway, itwascon irmedthatthedevelopedcontrolsystem operatesproperlyandisreadyfor lighttrials.Real testsarerequiredtoprovethecorrectnessofthesys‐tem’soperationbecauseevenasophisticatedmodel cannotpredictallthephysicalphenomenathatcan occurin light.

6.ConclusionsandFutureWork

Developingthesoftwarefortheautopilotiscom‐plicated,challenging,andtime‐consuming.Thispro‐cesscanbeperformedmuchmoreef icientlyusinga model‐baseddesignapproachthantraditionalhand coding.Also,theintegrationandtestingphasescan bedoneinastructuredandrepeatablemanner.The probabilityofintroducinghuman‐madeerrorscanbe minimized.Itmightbeexpectedthatthisapproach willgainmoreandmorepopularityinsuchapplica‐tions.Themaincontributionofthereportedresearch isthedetaileddescriptionofmodel‐baseddevelop‐mentsoftwareforthegasodynammicallycontrolled guidedHSUAV.Built‐inMATLABtoolsandcustom‐developedveri icationprocedureswereusedtocreate reliablesoftwarefortheautopilot.SAVOIRguidelines wereappliedtoperformtheoverallwork low.MIL, SIL,PIL,andHILtestswerecompletedtoverifythe correctnessofthesolution.Theneedformanualcode implementationonthetargethardwarewasmini‐mizedinthedescribedprocess.UsingMBDallowed movingsometestingactivitiestotheearlierstagesof thesystemdevelopment.Theresultsindicatethata goodnumericalsimilaritybetweentheSimulinkpro‐totypeandtheCcodewasachieved.Thepresented resultspartially illtheexistingliteraturegapand extendthesimulationstudyreportedinthepapers [30,42].

Futureresearchmightinvolvecodeoptimization toachievehighercomputationalef iciencyandmore experimentsinlaboratoryconditionswithrealequip‐ment.Hardware‐in‐the‐Looptestingusingdedicated SpeedgoattargethardwareandSimulinkReal‐Time mightbeevaluated.Theperformanceofthedeveloped controlsystemwillbecarefullycheckedduringthe real lighttests.

7.AppendixA‐Mathematicalmodelofthe HSUAV

7.1.DynamicEquationsofMotion

Thecoordinatesystemsusedinthemathematical modelarepresentedinFigure15

Thedynamicequationsofmotionwerederived usingthelinearandangularmomentumchangethe‐oremsforthe6degreesoffreedomrigidbodytaking intoaccountthemassvariationintime.Inthebody‐ixed,non‐inertialcoordinatesystem �� (the origin�� doesnotcoincidewiththecenterofmassof thevehicle),theequationsareasfollows:

(29)

(30)

where ⃗ Ω=�� ‐vectoroftheangularveloc‐ities, ⃗ �� =�� ‐thevectorofforcesacting onthevehicle, ⃗ �� =�� ‐thevectorof torqueswithrespecttopoint �� and �� ‐thelocal derivative.Linearandangularmomentumforarigid bodyare:

Π=�� ⃗ �� + ⃗ Ω×⃗�� (31)

��0 =�� ⃗ Ω+⃗�� ×�� ⃗ �� (32)

where�� ‐amassoftheobject, ⃗ �� =�� ‐thevelocityvector, I ‐amomentofinertiatensor,and ⃗�� ‐thecenterofmasslocationwithrespecttopoint ��

Figure15. Coordinatesystems

Thenonlineardynamicequationsofmotionofthe projectileareasfollows:

where ⃗ ��=��⃗�� ‐the irstmomentofmass.Thepropul‐sioneffectsareincludedontherightsideoftheabove‐mentionedequations.Inthemoment’sequations,the jetdampingeffectwasneglectedbecause,atlow light altitudes,itisquitesmallwhencomparedtoaero‐dynamicdamping.Next,thecross‐productscouldbe replacedbythematrixmultiplication,andtheskew‐symmetricmatrixnotation, []�� couldbeused.Asa result,theequationsofmotioncouldbewrittenas:

where 0 ‐zeromatrixand 1 ‐unitmatrix.Intheshort form,thisis:

(36) wherethestatevectorhastheform x = �� .Thisequationcanbe integratednumericallytoobtaintheactualvaluesof thestatevector.

7.2.AngularOrientationoftheVehicle

Quaternionswereusedtodescribetheobjectori‐entation:

(37) where��0,��1,��2,��3 ‐therealnumbersand i, j, k arethe axesversors.Thekinematicequationsthatconnect therateofchangeofthequaternionelementswiththe angularratesare:

(38) where��‐thefeedbackcoef icient(assumed1)and�� ‐theboundingequationviolationcoef

+��2 2+��2 3−1.Quaternionsarealsousedtocalculate thetransformationmatrixfromthebody

to theNorth‐East‐Downcoordinatesystem

Thetransformationmatrix(39)couldbeusedto formulatetherelationsbetweentherateofchange ofthepositionin

andlinearvelocitiesin

Quaternionscouldbeconvertedtoorientationangles (roll,pitch,andyaw)usingtherelations:

Theinitialquaternioncouldbecalculatedfromthe initialorientationanglesinthefollowingway:

7.3.TotalExternalLoads

Theexternalforcesandtorqueswerecalculatedas thesumofaerodynamics

thrust

and

,gravity

and

andlateralsolidpropellantthrusters

7.4.AerodynamicLoads

Thevectorsofaerodynamicforceandmomentare calculatedwithrespecttopoint��,sowithrespectto point�� theyaregivenas:

where��‐theairdensity,��‐thecross‐sectionareaof thefuselage,and��‐itsdiameter,⃗��

+⃗�� isthevectordescribingthelocationofpoint�� with respecttopoint ��, ⃗�� isthepositionofpoint �� withrespecttorocket’sbaseand⃗�� isthepositionof point�� withrespecttothemainmotor’sexitnozzle. Aerodynamicanglesofattack��andsideslip��aswell astheMachnumber��are:

(54) where ��,��,�� ‐componentsofthe windvelocityvectorinbodyframe, | ⃗ ��|= (��−��)2 +(��−��)2 +(��−��)2 and �� ‐the localspeedofsound.Theaerodynamiccoef icients are:

7.6.MainSolidPropellantMotorLoads

Thrustvectorcandeviatefromthegeometriclon‐gitudinalaxisoftheHSUAVbyangleΘ�� inpitchplane andΨ�� intheyawplane,sothemainmotorloadsare:

where ��(��) istheinstantaneousmagnitudeofthe thrustforce(obtainedinthesimulationusinglookup‐tableprocedure).Torquegeneratedbythemainmotor withrespecttopoint�� couldbeobtainedas:

(59)

7.7.LateralThrusters

Thegasodynamiccontrolsystemisbasedonaset ofidenticalcorrectionlateralthrustersatthecircum‐ferenceofthebody.Thethrustandtorquegenerated bythe��‐ththrusterare:

where ��0 ‐axialforcecoef icient(for ��=��= 0∘),

‐yaw‐axialforcecoef icients,

�� ‐sideforcewiththeangleofsideslipderivative,

�� ‐normalforcewithrespecttotheangleofattack derivative, ��0 ‐spindrivingrollingmomentcoef i‐cient, ��0 ‐spindampingderivative, �� ‐pitching momentwithrespecttotheangleofattackderiva‐tive, �� ‐yawingmomentderivativewithrespect tosideslipangle, �� ‐pitchingmomentcoef icient derivativewithpitchrateand �� ‐yawingmoment coef icientderivativewithyawrate.Additionally,the parameter �� describesthemainmotorstate(�� = 0 fortheactivephaseof light,and �� =1 after mainmotorburnout,forgliding light).Whenthemain motoroperatesatthebeginningofthe light,thebase dragissigni icantlylowerthanafterthemainmotor burnout.Theaxialforcecoef icientwasobtainedfor twosystemcon igurations(mainmotoron/off),and �� isusedduringthesimulationtoswitchbetween aerodynamicdatatables.Thevaluesofthecoef icients canbefoundin[30].

7.5.GravityLoads

Gravitationalaccelerationinthe �� coor‐dinatesystemisgivenas ⃗��=00��0 �� .Gravita‐tionalaccelerationwasassumedtobeconstant��0 = 9.80665 m/s2.Gravitationalforceandtorquesare givenas:

where��

(��)‐theinstantaneousthrustforcegener‐atedbythelateralthruster, ��=1,…,�� ‐thelayer number(��=1meansthelayerlocatedclosesttothe rocketbase),index��=1,…,��‐thenumberofanindi‐vidualthrusterinaparticularlayer,Φ��,�� ‐theazimuth angleofathrusterisaparticularlayer, ⃗��,�� ‐the vectordescribingthepositionofthelayerwithrespect totherocket’sbase.Thelayersarelocated1.10m, 1.15m,1.20m,and1.25mfromaft,respectively.The totalforceandtorquegeneratedbythegasodynamic controlsystemiscalculatedasthesumofloadfromall thelateralmotors:

where �� ‐thetransformationmatrixfromgravita‐tionaltobodycoordinatesystem(givenbyequation 22).

7.8.Massandinertialproperties

Theinstantaneousmassofthevehicleiscalculated as:

where��0 istheinitialmassoftheobjectattime��0,�� isthemassofthepropellant,and�� isthetotalimpulse givenas:

(65) where �� ‐timeofpropellantburnout.Duringthe powered lightphase,thevehicle’smasscenterposi‐tionvector⃗�� measuredfromthenozzleofthemain motorhasthefollowingcomponents:

where��0 isthecenterofmasspositiononthe�� axisduringlaunchand�� isthecenterofmassposi‐tiononthe�� axisafterthepropellantburnout.The changeofmomentsofinertiaalsodependsontime andiscalculatedas:

where��0 isthemomentofinertiatensorcomponent duringlaunchand�� isthemomentofinertiatensor componentafterthepropellantburnout.

AUTHORS

MariuszJacewicz∗ –InstituteofAeronauticsand AppliedMechanics,WarsawUniversityofTechnol‐ogy,Nowowiejska24,00‐665Warsaw,Poland,e‐mail: mariusz.jacewicz@pw.edu.pl.

DariuszMiedziński –InstituteofAeronauticsand AppliedMechanics,WarsawUniversityofTechnology, Nowowiejska24,00‐665Warsaw,Poland,e‐mail:dar‐iusz.miedzinski2.dokt@pw.edu.pl.

GrzegorzChmaj –DRISolutions,Chełmska21,00‐724Warsaw,Poland,e‐mail:of ice@drisolutions.pl. RobertGłębocki –InstituteofAeronauticsand AppliedMechanics,WarsawUniversityofTechnol‐ogy,Nowowiejska24,00‐665Warsaw,Poland,e‐mail: robert.glebocki@pw.edu.pl.

∗Correspondingauthor

ACKNOWLEDGEMENTS

ThisworkwassupportedbyTheNationalCentre forResearchandDevelopment(grantnumberDOB‐SZAFIR/03/B/002/01/2021).

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Submitted:14th November2024;accepted:4th April2025

JonathanAguilarAlvarado,KarinaGarciaGalarza,WilmerRivasAsanza,BerthaMazónOlivo DOI:10.14313/jamris‐2025‐011

Abstract:

Thisstudycomparestwoartificialintelligence approachesforparkingoccupancydetection:computer visionandconvolutionalneuralnetworks(CNN).A datasetof1,000parkingimageswascapturedand labeled,usingOpenCVinPythonforcomputervision processingandtheYOLOV5modelforCNN.Results showedthattheYOLOV5modelachieved88%precision and82%sensitivity,outperformingthecomputer visionmethod,whichachieved80%precisionand 79%sensitivity.Theresearchsuggeststhatwhile CNNsoffersuperiorperformance,computervisionis amoreeconomicaloptionincontextswithlimited resources.FutureresearchwillevaluatetheYOLOv7 versiontoreducefalsepositivesandcombinetechniques tobalanceaccuracyandefficiencyundervariable conditions.

Keywords: artificialintelligence,computervision,convo‐lutionalneuralnetworks,vehicleparking

1.Introduction

InEcuador,majorcitiesfacesevereproblemsdue toincreasedvehicletraf ic.Thenumberofregis‐teredvehicleshasincreasedby13.61%from2013to 2022[1].Onaverage,apersonmayspendapproxi‐mately7.8minutessearchingforanavailablepark‐ingspace[2].Theriseinvehiclepopulationleadsto higherfuelconsumption,theproductionofpollutants andgreenhousegases,andincreasedtraf icconges‐tion.InChicago,itisestimatedthatparking‐related congestiongeneratesanadditional129,000tonsof CO2peryear.Furthermore,acomparativeanalysis of16studiesacross11citiesconcludesthat inding parkingspacescantakeanaverageof8.1minutesand contributeupto30percenttotraf iccongestion[3].

Ifthissituationcontinues,itwillaffectthequality oflifeoftheuniversitycommunity,leadingtodissat‐isfactionwhenmovingbetweenuniversitycampuses, wastingconsiderableamountsoftime,andcontribut‐ingtoenvironmentalpollution[4].Thisiswheresmart parkingsolutionscomeintoplay,aimingtooptimize theef icientuseofparkingspacesthroughmonitoring anddiagnosingavailability,demand,andusagepat‐terns.

SmartsolutionsintegratetheInternetofThings (IoT)[5],BigDataanalysisandarti icialintelligence (AI)torecommendparkingspacesinreal‐timebased ondemand[6],thelocationofavailableparking spaces[7],theidenti icationofcustomerswhostay toolong[8],thecontrolofvehiclesinprivateparking areas,theenablingofremotepayments,andthedetec‐tionofunauthorizedentries[9].

Thisworkaimstoanalyzetheuseoftwoarti icial intelligencetechniques(computervisionandconvo‐lutionalneuralnetworks)toclassifyparkingspaces asfreeoroccupied,andtoevaluatethesetechniques basedontheirresultsusingindicatorssuchaspreci‐sionandsensitivity.

2.LiteratureReview

Somesolutionsforparkingcontrolandmonitor‐ingintegratevariousadvancedtechnologies.Com‐putervision,forinstance,allowsfortheanalysisof imagesandvideostodetectfreeandoccupiedspaces inrealtime[10].Ontheotherhand,theInternet ofThings(IoT),alongwithintegratedsensors,facil‐itatesconstantmonitoringofvehicle lowandspace occupancy,providingaccuratedataforef icientman‐agement[11].Additionally,theuseofarti icialneu‐ralnetworks(ANN)enablescomplexpredictionsand classi ications,enhancingaccuracyindetectionand resourceoptimization[12].Amongrelevantprevious research,notablestudieshaveexploredthepotential ofthesetechnologiestotransformparkingmanage‐ment:

DevelopedasmartparkingsystemattheUniver‐sidadPolitécnicaSalesianathatemploysArduinoYun, Temboo,andultrasonicsensorstoprovidereal‐time informationontheavailabilityof12spaces,accessible viaTwitterandawebpage.Accordingtosurveys,50% ofuserspreferTwitter,andtheother50%preferthe web,enhancingef iciencybyreducingsearchtimeand congestion[13].

Aprototypeforparkingspacecontrolwasdevel‐opedusingLM393proximitysensors,twoLEDsin greenandred,small‐scalevehicles,allconnectedto anArduinoandaWiFimodule.Afterconducting100 tests,thesystemoperatedwithasuccessrateof 92%[14].

Addressestheneedforaccuratedetectionof indoorparkingspaces.Themethodologyemploys wide‐anglecamerasandimageprocessing(modi ied Houghtransform)onadatasetof5,000imagescap‐turedinvariousscenarios.Usingcomputervisionand linedetectionalgorithms,thesystemachieved96% accuracyindetectingavailablespaces[15].

In[16],proposedadistributedsystemofwireless camerasthat,usingRaspberryPimodules,HOG ilters, andSVMclassi iers,evaluated10spacespersecond with90%accuracy.

Astudy[17]analyzesthechallengesofpark‐inginhigh‐traf icareas.Itemploysmagneticsen‐sors,ultrasound,andcomputervisiontodetectspace occupancy.Theresultssuggestthatcombiningcon‐volutionalneuralnetworksandmulti‐agentsystems effectivelyimprovesef iciencyinopenparkingareas, achievingupto96%accuracyinsomecasesofoccu‐pancydetection.

Astudy[18]addressestheproblemof inding parkingincongestedurbanareas.Themethodol‐ogyemploysamulti‐agentarchitectureandcomputer visiontoidentifyreal‐timefreespacesusingsurveil‐lancecameras.Withadatasetfrommultipleurban cameras,95%accuracywasachievedindetecting vacantspaces,thusimprovingthedrivingexperience andoptimizingparkingattheurbanlevel.

Developedanautomaticparkingspacedetection systembasedoncomputervision.Themodeluses 14parkingspacesandachieves99.5%accuracyin goodvisibilityconditions,withaslightdecreaseinlow visibilityorocclusionscenarios.Thissystem,imple‐mentedinMATLAB,accuratelyidenti iesfreeand occupiedspaces,notifyingdriversinrealtime[19].

In[20],aparkingspacedetectionsystem developedusingtheParkingLotdataset(PLds), whichincludesimagescapturedatPittsburgh InternationalAirportwithresolutionsof1280x960 pixels.Theappliedmethodologyusescomputervision andmulti‐cameratechniquestoidentifyavailable spaces.Theresultsshowanaverageaccuracyof95% invacancydetection,evaluatedundervaryinglighting andweatherconditions.

ThePKLotdatasetincludes695,899imagescap‐turedintwoparkinglotsattheFederalUniversity ofParanáandthePonti icalCatholicUniversityof Paraná,inBrazil.Theimplementedsystememploys texturesbasedonLocalBinaryPatterns(LBP)and LocalPhaseQuantization(LPQ),achievingacorrect classi icationrateofupto99.64%undercontrolled lightingconditionsand89%inmorechallengingsce‐narios?[21].

Onestudy[22]usesadatasetof8,600surround‐viewimagescapturedinindoorandoutdoorpark‐inglots,labeledtoidentifymarkingpointsinparking spaces.Themethodologyemploysalearning‐based approachwiththeAdaBoostalgorithmtodetectmark‐ingpoints.Theresultsshowanaccuracyof98.87% andarecallrateof92.38%,processingbetween20 and25imagespersecond. ImageCapture

Data Prepara on ModelTraining

Establishedreal‐timedetectionofoccupiedpark‐ingspacesusingsmartcameranetworksandconvo‐lutionalneuralnetworks(CNN).Theresearchutilizes thePKLotdataset(700,000images)andtheCNRPark dataset(12,584images)undervaryinglightingcon‐ditionsandocclusions.Theimplementedtechnology achievedanaccuracyofupto99.6%onthePKLot datasetand90.7%inmulti‐camerascenarioswiththe mAlexNetmodel[23].

Thisdocumentisorganizedasfollows:Section 2 selectstwotechniques,andexperimentsarecon‐ductedtodeterminethemostsuitableone.InSec‐tion3,theresultsarepresentedandanalyzed.Finally, inSection 4,theconclusionsoftheexperimentare presented.

3.Methodology

Thisresearchusedcomputervisiontechniques andconvolutionalneuralnetworksforparkingoccu‐pancydetection,utilizingtoolssuchasOpenCVin PythonandtheYOLOV5model.Thefollowingexper‐imentalphaseswerecarriedouttoconductthe research,asshownintheFigure1.Thefollowingsec‐tionsdetailthematerialsandmethodologyusedfor theanalysis.

Inthecomputervisionanalysis,OpenCVinPython wasused.Gaussianblur iltersandgrayscaleconver‐sionwereappliedtoreducenoiseandimprovecon‐trast,allowingforclearsegmentationofareasofinter‐est(parkingspaces).Theevaluationwasconductedby comparingtheoriginalRegionsofInterest(ROI)state withtheprocessedimage,calculatingdeviationsand averagestodeterminewhetheraspacewasoccupied orfree.

Fortheneuralnetwork‐basedmodelYOLOV5, trainingwasconductedonGoogleColabwithGPU. Theparametersweresettoalearningrateof0.01, abatchsize32,and500epochs.YAML ileswere usedtocon iguretheclassesandtrainingparame‐ters.TheLabelImgtoolenabledmanualimagelabel‐ing,andRobo lowfacilitateddatasetenhancement throughtransformationsanddatasplitting(80%for trainingand20%forvalidation).

Evalua onandValida on

Figure1. Researchstages

Table1. Materialsusedinresearch

Tool Description

DAHUAIPC‐HFW1430DT‐STW 4MP,2.8mm ixedlens,1/3” progressiveCMOSsensor, H.265+compression,30MIR LED,DWDR,Day/Nightmode (ICR),3DNR,AWB,AGC,BLC, Mirror,IP67outdoor protection,WiFi,MicroSDslot (256GB)

GoogleColab Cloud‐basedexecutionand trainingenvironmentwithGPU support.

LabelImg Open‐sourcetoolformanual imagelabeling

Robo low Softwarefororganizing, labeling,andtransforming images.

YAML Text ileformatformodel parametercon iguration

Classifiedimages

3.1.DatasetforNeuralNetworks

Atotalof1,000imagestakenintheparkingspaces attheUniversidadTécnicadeMachalawereused. TheimagesweremanuallylabeledusingtheLabelImg 1.8.0tool.Thelabelswerebasedontwoclasses:one forfreeparkingspacesandtheotherforoccupied spaces,asshowninFigure2

Oncetheimagesarelabeled,atxt ileisgenerated foreachone.Thetxt ilespeci iestheclassnumbers forthelabelsas0(free)and1(occupied),followed bythe(x,y)coordinatesoftheboxescontainingthe objects,asshowninFigure3

TheRobo lowwebtoolwasusedtosimplify thedatasetclassi icationprocess.Robo lowrandomly dividesthedataset:100%oftheimagesweresplit

Figure5. ROIselection into80%fortrainingand20%forvalidation.Figure 4showsthecreationofthedataset.

AYOLO(YouOnlyLookOnce)objectdetection architecturebasedonaConvolutionalNeuralNetwork isused.YOLOisaCNNthatpredictsobjects.Theneural networkcanachieveanexecutionspeedof45frames persecond(fps)ongeneral‐purposecomputers[24].

3.2.DatasetforComputerVision

Sixactivitiesarecarriedouttodetermineparking spaces:1.Selectionoftheregionsofinterest(ROI) fromtheparkingimage,2.Gaussianblurprocess,3. ConversionoftheRGBimagetograyscale,4.Evalua‐tionoftheoriginalROIandtheconvertedimage’sROI, 5.Calculationofthestandarddeviationandtheaver‐age;ifthethresholdisaboveorbelow,theoccupiedor freestatusisdetermined.

Parkingimagesarecaptured,andregionsofinter‐estareselectedusingtheYAMLtool,asshowninFig‐ure5.Coordinatesarede inedasformingrectangular zones.Thisactivityisperformedmanuallyineach parkingareawherespacerecognitionisneeded.

TheGaussianblurprocessinvolvesusingtech‐niquessuchaslow‐pass iltering,whereeachpixelin theoutputimageistheweightedsumofthecorre‐spondingpixelintheoriginalimageanditssurround‐ingpixels.

Subsequently,imageconversionisperformed, whichinvolvesconvertingthethree‐channelred, green,andblue(RGB)imagetograyscale(GRAY), therebyreducingtheimageinformationtosome extentasaprocessingstrategy.Finally,thevaluesof theoriginalROIsareevaluatedagainstthoseofthe outputimage,andacopyoftheimageiscreatedfor comparison.Theseactivitiesthenallowforcalculating thestandarddeviationandtheaverage.Thesystem candeterminewhethertheparkingspaceisoccupied orvacantifthevaluesareaboveorbelowathreshold.

Figure2. UTMACHparking

Figure3.

Figure4. Datasetcreate

Table2. Trainingparameters

Table3. CNNmetricsresult

4.2.ComputerVision(CV)

4.Result

4.1.ConvolutionalNeuralNetwork(CNN)

Table 2 showstheparametersusedfortraining, withtheenvironmentbeingGoogleColab.Thepre‐trainedYolov5weightwasusedwithabatchsizeof 8and500epochs.

Forthecon igurationoftrainingparameters,we followedcriteriaestablishedinpreviousresearch evaluatingtheperformanceofYOLOmodels:alearn‐ingrateof0.01isused,adjustedthroughacosine annealingstrategy,withabatchsizeof32and500 epochs[25].In[26],alearningrateof0.01isused, with350epochs,allocating90%ofthedatasetfor trainingand10%forvalidation.In[27],100epochs areused,withabatchsize16andalearningrateof 0.01.In[28],300epochsareusedwithanautobatch functiontodeterminetheoptimalbatchsizebasedon resourceavailability,allocating85%fortraining,10% forvalidation,and5%fortesting.

Inthetrainingprocessconductedinthisresearch, theresultsareshowninTable 3 wereobtained,and Figure6illustratesthedetectionofavailableandoccu‐piedspaces,withfreespacesshowningreenandoccu‐piedspacesinred.Thesevaluesindicategoodmodel performanceinclassifyingspaceoccupancy,compa‐rabletopreviousstudies.However,trainingperfor‐mancecanbefurtherimprovedwithsomeadjust‐mentsinparameters,suchasthenumberofepochs andthelearningratestrategy,adaptedtospeci ic resourcesandrequirements.

Tocontextualizetheresults,thesensitivityand precisionmetricsobtainedinthisresearchwerecom‐paredwithsimilarstudiesusingcomputervisionto detectparkingoccupancy.

Insomestudies[29],thePakStamodelbasedon computervisionachieved93.6%accuracyiniden‐tifyingoccupiedspacesundercontrolledconditions, usingavisionapproachbasedontheDeformable DETRmodel.[30]developedacomputervisionsys‐temtodetectavailableparkingspacesusinganIPcam‐eraandprocessinginPythonwithOpenCV,achieving 96%accuracyandtransmittingthedatainrealtime toawebpage.In[31],HDcamerasandOpenCVin Pythonwereused,andthesystemdetectsfreespaces with94%accuracyandintegratesaTelegramchatbot tonotifyusersinrealtime.A isheyelenscameraand anembeddedAIprocessorclassifyspacesasoccupied orfreeinrealtime,achievingarecognitionrateof 94.48%insimulationsand80.36%accuracyinreal tests.

Theresearchusedbothpre‐recordedvideosand real‐timecaptureswithanHDcamera.Theresults, asdetailedinTable4,showasensitivityof79%and anaccuracyof80%,whichissatisfactoryforpractical applicationsanddemonstratesef icientdetectionof theoccupancystatusofparkingspaces,asshownin Figure 7.Althoughthevaluesareslightlylowerthan insomeofthestudiesmentioned,ourapproachis adaptabletovariouscaptureconditions,makingit more lexibleandapplicabletoreal‐worldscenarios thanothersystemsthatrequiremorecontrolledcon‐ditions.

Figure6. Convolutionalneuralnetworktime‐realspace control

Table4. Computervisionmetricsresult

Figure7. Artificialvisiontime‐realcontrolspace

Table5. Comparisonofaccuracyandsensitivityof differentparkingspacedetectionmethods

Research Study Technique

This Study

[32] DeepLabV3+

[33] YOLO(CNN, pixel‐wiseROI)

[34] ResNet50+SVM VGG16

[35] Semantic Segmentation (CNN)

[36] mAlexNet(CNN)

[38] U‐Net(CNN)

[39] YOLOv7+IoU (CNN)

This Study Image Segmentation (CV)

[41] HOG,LBP,SVMy NaiveBayes(CV)

[42] Binary Morphologyy Logic(CV)

[44] BlockMatching Algorithm(CV)

[45] Multi‐clue recoverymodel (CV)

(balanced accuracy)

Inthisstudy,YOLOV5andimagesegmenta‐tiontechniqueswereused,achievingaccuraciesof 88%and80%andsensitivitiesof82%and79%, respectively.TheseresultsindicatethatourCNNand CV‐basedtechniquesarecompetitivebutstillneed improvementtoreachthelevelsofaccuracyandsen‐sitivityobservedinmoreadvancedstudies.

(Dice)

(balanced accuracy)

Not speci ied

Theresultsobtainedinthisresearcharecompa‐rabletothoseofpreviousstudies.Astudyin[29] achieved93.6%accuracyinoccupancydetection undercontrolledconditionsusingYOLO.Another study[30]obtained96%accuracyusingOpenCVwith acomputervisionapproachinoutdoorenvironments. Acomparisonofaccuracyandsensitivityacrossdiffer‐entstudiesispresentedbelow:

Table 5 comparestheparkingspacedetection methodsusedinthisstudyandothersavailablein theliterature.ConvolutionalNeuralNetwork(CNN)‐basedmodels,suchasYOLO(CNN,pixel‐wiseROI) andU‐Net,achievedthehighestlevelsofaccu‐racyandsensitivity,withvaluesreachingupto 99.68%and99.68%(balancedaccuracy),and99.40% and92.94%,respectively.Theseresultssuggestthat semanticsegmentationmodelsareparticularlyeffec‐tiveforcorrectlydetectingparkingspacesandreduc‐ingfalsepositives.Ontheotherhand,traditionalcom‐putervision(CV)techniques,suchasoptical lowand theblockmatchingalgorithm,showmorevariedper‐formance,withhighsensitivityinsomecasesbutless consistencyinaccuracy.

CNN‐basedapproaches,suchasYOLOV4andU‐Net,offeramoresuitablecomprehensivesolution forapplicationsrequiringhighdetectionaccuracy, especiallyinscenarioswherefalsepositivesneedto beminimized.However,computervisiontechniques remainusefulincontextswithlimitedcomputational resources.Inthefuture,exploringthecombinationof CNNandCVtechniqueswouldbebene icialtolever‐agethestrengthsofbothapproachesandimprovethe overallsystemperformance.

5.Conclusion

Inthisstudy,twomainapproachesforparking spacedetectionarecompared:convolutionalneural networks(CNN)andtraditionalcomputervision(CV) techniques.TheresultsindicatethatCNN‐basedmod‐els,suchasYOLOV5,offerhigheraccuracyandsen‐sitivitythancomputervisiontechniques,especially excellinginapplicationsrequiringhighobjectdetec‐tionaccuracywhileminimizingfalsepositives.

Neuralnetworksareeffectiveincontextswhere detectionqualityisapriority,whilecomputervision techniquesshowadvantagesinscenarioswithlimited computationalresources.Thissuggeststhat,although neuralnetworksaresuperiorinperformance,com‐putervisionremainsaviablealternativeforenviron‐mentswheresimplicityandlowcostaredetermining factors.

TheYOLOV5modeldemonstrateshighpreci‐sionandsensitivity;however,itdemandssigni i‐cantcomputationalresources,achievingdetection ratesbetween40–45FPSwhenusingGPUacceler‐ation.Incontrast,traditionalcomputervisiontech‐niquesexhibitlowerperformancebutrequirefewer resources,typicallyoperatingatspeedsof20–30 FPSusingCPU‐onlyenvironments.Therefore,future studiesshouldevaluatecomputationalef iciency, speci icallyenergyconsumptionandmemoryusage, enablingadaptationssuitablefordiversescenarios withvaryingtechnicalcapacitiesandeconomiccon‐straints.

Basedontheresults,itisrecommendedthatmore advancedCNNversionsbeexploredtoincreaseaccu‐racyandreducefalsepositives.Additionally,integrat‐inghybridtechniquesthatcombineneuralnetworks withcomputervisioncouldprovideamorebalanced solution,leveragingthestrengthsofeachapproachto improvesystemrobustnessandef iciency.

Futureresearchshouldfocusonexpandingthe datasettoincludedifferentenvironmentalconditions, suchaslightingvariationsandocclusions,toenhance thegeneralizationcapabilityoftheproposedmodels. Additionally,itissuggestedthatevaluationsbeimple‐mentedinlarge‐scalereal‐worldenvironments,such

aspublicorcommercialparkinglots,tovalidatethe system’sperformanceunderpracticalconditionsand demonstrateitsscalabilityandapplicabilityinreal‐worldscenarios.

AUTHORS

JonathanAguilarAlvarado∗ –Universidad TécnicadeMachala,Ecuador,e‐mail: jaguilar@utmachala.edu.ec. KarinaGarciaGalarza –UniversidadTécnicade Machala,Ecuador,e‐mail:kgarcia@utmachala.edu.ec. WilmerRivasAsanza –Universidad TécnicadeMachala,Ecuador,e‐mail: wrivas@utmachalala.edu.ec. BerthaMazónOlivo –Universidad TécnicadeMachala,Ecuador,e‐mail: bmazon@utmachala.edu.ec.

∗Correspondingauthor

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Submitted:26th February2024;accepted:9th May2024

ThienMinhTran

DOI:10.14313/jamris‐2025‐012

Abstract:

Thispaperrevealstheproposedmethodtooperatethe landingangularmotionofaducted‐fanunmannedaerial vehicle(DUAV).Theangularmotionfrequentlyvaries duringthelandingstage.Additionally,theDUAVsystem isacomplexsystemwithuncertainparametersorincor‐rectlyidentifiedparameters,andtheyawanglehasto becontrolledintheproperpositionbeforegrounding. Becauseofissueswiththestructureofthesystemand identificationintherealmodelofDUAV,amodel‐free controltechniqueisapproachedbycombiningtime‐delay estimation(TDE)andintegralslidingmodelaw(ISMC). TheTDEtechniqueprovidesamodel‐freemethodforthe complexsystemasDUAV.Hence,anovelcontrolmethod isdesignedtoachievethedesiredangularmotion.In addition,theISMCmethodisagoodsolutionfortracking performance.Thestabilityofthewholesystemisguaran‐teedbytheLyapunovtheory.Weconductacomparison betweentheTDE‐ISMCandslidingmodecontrol(SMC)in severalcasestoverifytheeffectivenessoftheproposed TDE‐ISMCcontrol.

Keywords: time‐delayestimation,TDE,ISMC,DUAV, model‐free,motioncontrol

1.Introduction

Inrecentyears,therehavebeenseveralnotable studiesofunmannedaerialvehiclesystems(UAVs). Nevertheless,thesingleducted‐fanunmannedaerial vehicle(DUAV)istheperfectintersectionoftheprop‐ertiesofUAVs,helicopters,andmissiles[1].TheDUAV belongstotheconceptionofUAVs,whilethemain powersystemissimilartothatofahelicopter,and itsmotionanalysishastobeconsideredamissile. Therefore,thecon igurationofDUAVisacomplex systemwithavarietyofdevicessuchasducted‐fan[2], hover[3],aerodynamics[4,5],andsoforth.Inmod‐ernaerialspacetechnology,themissionitinvolves surveillance,reconnaissance,exploration,communi‐cation,andsoforthinbothmilitaryandcivil.One otheradvantageofDUAVisthatitcanbeconsidered successfulindepartingandlandingfromunprepared sitesandsmalldeckspaces.

Basedonthecharacteristicoperation,thestageof DUAVusuallyinvolvespre‐takeoff,takeoff, lying,and landing,withlandingbeingmostimportanttorecall theDUAV.Angularmotioncontrol,inparticular,isa keyinthelandingprocessofthesingleDUAV.

Sometimes,theaccuratedynamicmodelofthe systemisimpossibletoidentifyandestimate[6]. However,severalmoderncontrolalgorithmsenforce correctphysicalparameterstoobtainhightracking performance,suchassuper‐twistingslidingmode control[7],slidingmodecontrol[8–10],feedbackcon‐trol[11],poleplacementcontrol[12],adaptivecontrol [13–15],arti icialintelligence[16],etc.

Itisworthnotingthatthemotioncontrollability ofasingleducted‐fanunmannedaerialvehiclecannot beeasilycarriedoutbecauseofthecomplexsystem andincorrectlyidenti iedphysicalparameters.Dueto thelandingprocess,whichcanleadtotheinstability ofthewholesystem,themotionoftheyawangleof DUAVplaysanimportantroleduringthisstageasseen inFig. 1.Beforethelandingprocess,theyawangle needstobecontrolledintheright‐angleposition, whichestablishesthestablestageforthewholeDUAV. Inthedesiredposition,theprofessionalscanforesee unexpectedfeaturesduringthelandingprocess.Nev‐ertheless,thecontrolmotionoftheangleoftheDUAV systembeforelandinghadreceivedlittleattention.

Basedonthefactsmentionedabove,thisstudy proposesanewapproachbyacombinationoftime delayestimationtechniqueandintegralslidingmode control(TDE‐ISMC)totacklethecomplexsystemwith incorrectlyidenti iedparameters.TheTDEtechnique providesamodel‐freeapproachmethodforthecom‐plexDUAVsystem,whiletheISMCshowsahightrack‐ingperformancetodramatic luctuationsofDUAV.

Additionally,theTDEtechniquecanestimateand compensateforthecontrolsignal,whichiscausedby thedisadvantageofISMCasanincorrectlyidenti ied parametermodel,andthestabilityofthewholesys‐temisboundedbytheLyapunovtheory.Furthermore, theproposedcontrollawTDE‐ISMCiscomparedto theclassicalslidingmodecontrolinseveralcasesto verifythefeasibilityandtransparency.Theclassical SMCalsohassimilarcharacteristicstoISMCsothat theeffectivenessoftheproposedmethodisevenmore outstanding.

Thispaperisorganizedasfollows.Section 2 revealsthecon igurationoftheDUAVinyawmotion. Section3illustratesthecontroldesignoftheproposed methodTDE‐ISMC,andthestabilityisaddressedin detail,comparedtotheclassicalSMC.Numericalsim‐ulationresultsoftheperformancearepresentedin Section4.Finally,Section5concludesthepaper.

Rudders x 4

Yawangle motioncontrol Landingprocess

Figure1. Theyawmotioncontrolconceptofthesingle ducted‐fanUAV

2.ConfigurationoftheSingleDucted‐fanUAV

Themathematicalmodelingdynamicsofthesingle ducted‐fanUAVareidenti iedfromtherealphysical systembyamultiple‐inputsingle‐outputsystemand canbeobtainedasfollows[12]

��∗(��)=��(��)+��∗(��)+��∗(��) (1) where ��∗(��)=[��1(��),��2(��),��3(��),��4(��)]�� ∈��4 istheyawanglevectorofthesystem,controlledby thefourrudders.��(��)=[��1(��),��2(��),��3(��),��4(��)]�� ∈ ��4 isthecontrolsignaloftherudders. K ∈��4×4 , Q ∈��4×4 and P ∈��4×4 arede inedastheconstant matrices,identi iedfromtherealDUAVviaMATLAB. EachyawangleinEquation(1)isoperatedbyoneof fouractuators(rudderandservomotor),associated ��∗(��)= c��(��),where c�� ∈��4 isaweightingcolumn vector.Bythemultiple‐inputsingle‐outputde inition, theyawangleofthesystemisthesumoftheelements of��∗(��),withtherelevantweightingcoef icientsthat areusedinthefollowing��(��).Lettheclaimsbetrue forthisresearch.

Assumption1. Weassumethattheslipstreamaxis iscoincidentwiththefanaxis[4].

Assumption2. Weassumethatthereisnostrong crosswindduringtheexperimentalidenti ication[4].

3.ControlSystemDesigns

3.1.Time‐delayEstimationandIntegralSlidingMode Technique

ThemodelingEquation(1)ofDUAVcanberear‐rangedasfollows

∗(��)=��(��)+��(��∗,��∗). (2)

Theslidingpolynomialvariable[17]canbe de inedtoachieveacontrolobjectiveasfollows

C��c��̇��(��)+ KnC��c��(��)+ KiC��c�� (��)�� (3) where ��(��)=[��1(��),��2(��),��3(��),��4(��)]�� ∈��4 , Kn =��([��1,��2,��

and

,��

4×4 aredepictedaspos‐itivegainsmatricesforthestabilityofthesingle ducted‐fanUAV.Thecontrollawisconstructedbased ontheslidingpolynomialoftheintegralslidingmode asfollows

(4) where ��(��∗,��∗) istheestimatedterm,based onEquation(2).Thesignumfunctionsign(��(��)) isde inedascorrespondingtotheelements oftheinputvector,whereassgn(��(��))= [sgn(��1(��)),sgn(��2(��)),sgn(��3(��)),sgn(��4(��))]�� ∈ R4.Apositivecontrolgainmatrixisdenotedas K�� =��([��1,��2,��3,��4])∈��4×4 Bytime‐delayestimationtheory[18‐20],theterm ��(��∗,��∗) canbeestimatedbydelayingoneunit ofsamplingtimemeasurement ��(��∗,��∗).Inother words,Equation(2)isrewrittenasamathematical timedelayestimationasfollows

��(��)=��(��−��)=��∗(��−��)−��(��−��) (5) where L isasamplingperiod.SubstitutingEquation (5)intoEquation(4),thecontrollawinEquation(4) canberearrangedasfollows

��(��)=− K−1��∗(��−��)+��(��−��) TDE + K−1C−1 �� [C��c��(��)+ KnC��c��̇��(��)] ISMC + K−1C−1 �� [KiC��c��(��)+ K��sign(��(��))] ISMC (6)

Theproofofstability. TheLyapunovcandidate canbeconsideredasfollows ��(��)= 1 2 ��(��)��(��). (7)

Theaimofthisresearchistocontroltheyaw angleofasingleDUAV ��(��) tracksthedesiredpath properly,whichmeansthat ��(��)=��(��)−��(��) isaslittleaspossible,notedas C��c��(��),where, C�� =��[��1,��1,��1,��1]∈��4×4 isapositive weightingmatrix.

SubstitutingthecontrollawinEquation(6)into takingthetimederivativeofEquations(3)and(7),the timederivativeofLyapunovcanobtain

��(��)=��(��)��(��)

=��(��)��[C��c��(��)− C��(��)− C��Λ(��)

KnC��c��̇��(��)+ KiC��c��(��)]

=��(��)��C��(��(��)−Λ(��))

−��(��)��K��sign(��(��))

��(��)=��(��)��C��[Λ(��−��)−Λ(��)]

−��(��)��K��sign(��(��))≤0. (8)

Byusingthetimedelayestimationtechnique,the termof ��(��) isobtained,whichisapproximatelythe termof��(��−��).Therefore,thetimederivativeofthe LyapunovcandidateinEquation(8)issemi‐negative ��(��)≤0.Hence,thepropertyoftheslidingpolyno‐mialvariable��(��)isguaranteedtobebound,andthe erroroftrackingperformance ��(��) alsoisbounded. BasedontheLyapunov‐likelemma[21],thestability ofthecontrollawinEquation(6)isensured.

3.2.ClassicalSlidingModeControl

Theslidingsurfacevariableisassociatedasfollows s(��)= C��c��̇��(��)+ KsC��c��(��) (9) where s(��)=[��1(��),��2(��),��3(��),��4(��)]�� ∈��4,and Ks =��[(��1,��2,��3,��4)]�� ∈��4×4 isnotedas apositivecontrolgainmatrix.Thecontrolalgorithm’s de initionis

��(��)= K−1C−1 �� [C��c��(��)− C��(��)] + K−1C−1 �� [��C��c��̇��(��)+ K��sign(s(��))] (10) where K�� =��([��1,��2,��3,��4])∈ ��4×4 isdepictedasapositivegainmatrix. Thesignumfunctionissgn(��(��))= [sgn(��1(��)),sgn(��2(��)),sgn(��3(��)),sgn(��4(��))]�� ∈��4 TheLyapunovcandidateyields

��(��)= 1 2 sT(��)s(��). (11)

SubstitutingthecontrollawinEquation(6)into takingthetimederivativeofEquations(3)and(7),the timederivativeofLyapunovcanobtain

��(��)= s��(��)s(��)

��(��)= s��(��)[C��c��(��)− C��(��) C��Λ(��)+ KsC��c��̇��(��)]

��(��)=−sT(��)K��sign(��(��))≤0. (12)

Equation(12)isalsosemi‐negative��(��)≤0.The slidingsurfacevariable��(��)isbounded,sotheerror oftrackingperformance ��(��) alsoisbounded.Based ontheLyapunov‐likelemma[21],thestabilityofthe controllawinEquation(10)isveri ied.

4.NumericalSimulation

4.1.SimulationSetup

Thedesiredtrackingisestablishedinfrequency, amplitude,andthepropertyofchangetocompare andverifytheeffectivenessoftheproposedcontrol. Acomparisonisdoneinseveraltrackingreferencesto ensurecorrectness,transparency,andpracticality.

Thesimulationwiththeproposedcontrollawin Equations(6)and(10)iscarriedoutusingthereal physicalparametersofasingleducted‐fanUAV.The identi icationofparametersisimplementedbyusing theMATLABidenti icationtoolbox.Thenominalphys‐icalparametersinEquation(1)areasfollows[12]

Q =��[(−0.46975,−0.46975, −0.46975,−0.46975)]

P =��[(−0.1905,−0.1905,−0.1905,−0.1905)]

K =��[(−0.501,−0.501,−0.501,−0.501)]

Theweightingvectorandmatrixarenotedas c�� = [0.25,0.25,0.25,0.25]�� and C�� =��[(1,1,1,1)], respectively.Theinitialsetupvalueforthesimulation ofthesingleducted‐fanUAVsystemat ��0 =0 are ��(��0)=0, ��(��0)=0, and ��(��0)=[0,0,0,0]��.The samplingtimeisde inedas1(ms),andthelowpass ilterisconsideredas1/(��+1)

Toevaluateobjectivelyandfairly,therootmean squareerror(RMSE)andtheintegraloftimemulti‐pliedbytheabsoluteerror(ITAE)inEquation(13) areimplementedtomeasurethetrackingerrorofboth controllers.

4.2.SimulationResults

Theresultsoftheproposedcontrollaw,TDE‐ISMC, arecomparedwiththeclassicalcontrol,SMC.Tobe transparentandfair,bothTDE‐ISMCandSMCkeep unchangedcontrolcoef icientsinthefourthtypeof trackingreference.

Thecontrolgainmatricesoftheproposed controllawinEquation(6)aredenotedas K�� =��[(0.81,0.81,0.81,0.81)]∈��4×4 , Ki =��[(0.0081,0.0081,0.0081,0.0081)]∈��4×4 , and Kn =��[(0.0152,0.0152,0.0152,0.0152)]∈ ��4×4.Similarly,thecontrolgainmatrices oftheclassicalSMCarede inedas Ks = ��[(3.01,3.01,3.01,3.01)]∈��4×4 and K�� =��[(1.1,1.1,1.1,1.1)]∈��4×4.The simulationresultsoftheyawangle’sreferencetypes (a)and(b)andtypes(c)and(d)areshownin scenario1(Figs.3–10)andscenario2(Figs.11–18), respectively.Theshapesoftypes(a)–(d)arethe typicalinputsignalsoftheyawangle.

Thereferencetypes(a)and(b)aresimilarshapes ofsignal;however,type(b)sharplychangeswith alargeramplitude.Thesinewaveiscon iguredfor thereferencetypes(c)and(d),andthedifferences betweenthemarefrequencyandamplitude.

TheproposedcontrollerTDE‐ISMC’sdiagram

Table1. RMSEandITAEinscenario#1(trapezium waves).

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Bytheseresults,theadvantagesoftheproposed controllawarethoroughlycon irmedandveri ied.

4.2.1.Scenario1:TrapeziumWave

Figures3and4showtheyawangletrackingofthe singleducted‐fanUAVfollowingthedesiredtrapez‐iumwaveindetail.TheproposedcontrollerTDE‐ISMC trackscloselytothereference,comparedtotheclas‐sicalSMC.TheclassicalSMCresponseisdelayeda periodandunderdamped,whichcanleadthewhole systemtoinstabilityifthecontrolgainmatricesare notsuitable.However,theproposedcontrollercan dealwiththesedefectivetermsbythepropertiesof TDEandISMC.

TheerroroftheyawangleisdescribedinFig. 5 (type(a))andFig.6(type(b)).Theerroroftheclas‐sicalSMCoftheseresultsvariedalongthecurveof referencesand luctuatedinalargerrange,compared totheproposedcontrollerTDE‐ISMC.Thisprovesthat thestabilityoftheTDE‐ISMClawisbetterthanclassi‐calSMC.Moreover,thecontrolsignalsoftheproposed controlleraredepictedinFig. 7 (type(a))andFig. 9 (type(b)), luctuatingharmonicfrequencywithanar‐rowrange,comparedtothoseofclassicalcontrollaw inFig.8(type(a))andFig.10(type(b)).Additionally, theRMSEandITAEvaluesarelistedinTable1,which showsthatTDE‐ISMCsarebetterthanSMCs.That thoroughlyevaluatestheeffectivenessoftheproposed controllaw.

4.2.2.Scenario2:Sinewave

Thesinewaveofthereferencesisestablishedfor thisstudysimulation.Therearetwokindsofsine waves:type(c)andtype(d).Insinewavetype(d),the frequencyandamplitudearelargerthanintype(c).

Figure3. Trackingtheperformanceoftrapeziumwave type(a)reference

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Figure4. Trackingtheperformanceoftrapeziumwave type(b)reference

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Figure5. Erroroftrackingtheperformanceoftrapezium wavetype(a)reference

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Figure6. Erroroftrackingtheperformanceoftrapezium wavetype(b)reference

Figure2.

Reference TDE-ISMC SMC

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Figure7. Controlsignalinputoffouractuatorsof TDE‐ISMC(typea)

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Figure8. ControlsignalinputoffouractuatorsofSMC (typea)

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Figure9. Controlsignalinputoffouractuatorsof TDE‐ISMC(typeb)

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Figure10. ControlsignalinputoffouractuatorsofSMC (typeb)

Theperformanceoftrackingthetrajectoryofboth referencesisshowninFigs. 11 and 12 indetail.In thesecasesofsinewaves,theclassicalSMCbehavior didnottrackthereferencesinbothtypes(c)and(d) byusingsimilarcontrolgainmatricesasinscenario1. Especiallyintype(d),theclassicalSMCleadsthe wholesystemtobeunstable.Theproposedcontroller TDE‐ISMCtrackswellinscenario2byusingsimilar controlgainmatricesasusedinscenario1.Thesine wavewithlargeamplitudeandhighfrequencyproves theadvantagesoftheproposedcontrollerbyusingthe propertiesofTDEandISMCintheproblemofphysical systems.

Similarly,theerroroftheperformanceisillus‐tratedinFig.13(type(c))andFig.14(type(d)).Inthe proposedcontrollawTDE‐ISMC,theerrorisreduced toalmostzerovalueafteraperiodofresponsetime. Hence,thestabilityofthewholesystemisguaranteed. Additionally,thecontrolinputsignalsarepresentedin Figs.15–16fortype(c)andFigs.17–18fortype(d).

Table2. RMSEandITAEinscenario#2(sinewaves).

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Figure11. Trackingtheperformanceofsinewavetype (c)reference

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Figure12. Trackingtheperformanceofsinewavetype (d)reference

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Figure13. Erroroftrackingtheperformanceofsine wavetype(c)reference

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Figure14. Erroroftrackingtheperformanceofsine wavetype(d)reference

TheRMSEandITAEvaluesarealsonotedin Table 2,whichshowstheevaluationofbothcon‐trollers.TheSMC’svaluesdescribetheinstabilityof thewholesystem,whilethehighachievementiscon‐tinuouslyintheproposedcontrollerTDE‐ISMC.

5.Conclusion

Inthispaper,theproposedcontrollerTDE‐ISMCis studiedandconductedinthephysicalparametersof thesingleducted‐fanUAV.Thestabilityofthewhole physicalsystemisguaranteedbytheLyapunovtheory.

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Figure15. Controlsignalinputoffouractuatorsof TDE‐ISMC(typec)

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Figure16. ControlsignalinputoffouractuatorsofSMC (typec)

AUTHOR

ThienMinhTran∗ –ORCID:0000‐0003‐3465‐5905, DepartmentofMechatronics,FacultyofMechanical Engineering,HCMCUniversityofTechnologyandEdu‐cation(HCMUTE),HoChiMinhCity,700000,Vietnam, e‐mail:thientm@hcmute.edu.vn.

∗Correspondingauthor

ACKNOWLEDGEMENTS

Thisresearchreceivednoexternalfunding.

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05101520253035404550 Time(s)

Figure17. Controlsignalinputoffouractuatorsof TDE‐ISMC(typed)

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Figure18. ControlsignalinputoffouractuatorsofSMC (typed)

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DESIGNOFMULTIDIMENSIONALNONLINEARPREDICTIVECONTROLLER

FOR3DCRANE

Submitted:11th November2023;accepted:8th February2024

MaciejSzafrański,RobertPiotrowski

DOI:10.14313/jamris‐2025‐013

Abstract:

Thispaperpresentsacomprehensiveapproachtodesign andimplementationofamultidimensionalnonlinear controlsystemfora3Dcrane.Fordesignpurposes,a simulationmodelofthecraneisdevelopedandverified. Proposedaretwostructuresofthecontrolsystem,which arebasedonaPIDcontrollerandpredictivecontrolsys‐tem.Thesynthesisprocessispresented.Thedesigned systemsareverifiedintermsoftheireffectivenessbased onthejudgementontheobtainedwaveformsofcon‐trolledvariablesandintegralcontrolindicators.Finally, thetwosystemsarecomparedwitheachother,andthe conclusionsregardingtheirapplicabilityforthistypeof systemarepresented.

Keywords: 3Dcrane,controlsystems,mathematical modelling,multidimensionalcontroller,nonlinearMPC controller

1.Introduction

Throughouthistory,movingloadsofconsider‐ablemasshasalwaysbeenachallengeforhumans. Asaresultofindustrydevelopment,thestrengthof humanhandshasbeenreplacedbydedicatedindus‐trialmachines,suchas3Dcranes.Nowadays,they arewidelyusedwhereverthereisaneedtotrans‐portenormousorheavymaterialsfromoneplaceto another,especiallyinproductionhalls.

Fromthecontrolviewpoint,3Dcraneisadynamic, multidimensionalelectromechanicalsystemwith highlynonlineardependenciesandinteractions.Due totheabove,designingapropercontrolsystemforthe cranewithoutanexperiencedoperatortomaneuver itisconstantlyachallengeforengineers.Sucha systemhastoprovidesafeandpreciseloadtransport whilecontrollingloaddeviationsinthespeci ic environmentincludingpeopleandotherstaticor movingdevices.Despitethesehighrequirements, modernalgorithmscanbeveryeffectiveincontrolling cranes.

Thedesignedcontrolsystemofthecraneshould betestedbeforeinstallingitinthedevicebecauseany possibledesignerrorsarelikelytocauseserious,or evendangerousevents,e.g.,damagingthecrane,or uncontrolledloadmoving.Inordertoavoidthis,phys‐icalmodelsofvarioustypesofcranesarecommonly used.

Theissueisconsideredinmanyvariousstudies. Themostcommonapproachistousethestructure ofthePIDcontrollerwithgainoptimization[1,2],as itleadstothedesignofacontrolsystemforalinear orlinearizedcranemodel,given,forinstance,asa numberoftransferfunctions.Thesecondgroupof strategiesarebasedonfuzzylogic.In[3],thefuzzy logichasbeenusedtodescribethe3Dcranemodel andtodesignacontrolsystemforit.In[4, 5],the anti‐swingfuzzycontrollershavebeenproposed.The nextpossibilityistoapplymodelpredictivecontroller (MPC)[6,7].Thesecomplexalgorithmsarebecoming moreandmorepopularandareafrequentchoice, especiallyinadvancedandcomplexcontrolsystems requiringhighaccuracyandprecision.Anotheralter‐nativesolutionforcontrollingthecraneisanadaptive controller[8],whichcanbeproposedforuncertain overheadcranes,anLQcontroller[9]usedinthepro‐cesscontroltoeliminateunwantedpropertiesofthe optimaltrajectory,andcontrolalgorithmsbasedon visualfeedbackcontrolofoverheadcrane[10].

Thispaperisstructuredasfollows.Section 2 presentsthemathematicalmodelofthe3Dcraneand itsveri ication.Inthissection,thesimulationtests arediscussedandequivalentequationsfortheZ‐axis areproposed.Section3presentsthestructureofthe proposedcontrolsystemsandthedescriptionofthe appliedtuningmethods.Section4providestheanal‐ysisoftheresultsoftheperformedsimulationtests, whiletheconcludingremarksarelistedinthelast section.

2.3DCraneDescriptionandModelling

2.1.3DCraneDescription

Theanalyzed3Dcraneisaphysicalcube‐shaped modelmadebyINTECO.Itisarepresentationofactual industrialcranesworkinginthethreeaxesX,Y,Zofthe Cartesiancoordinatesystemtocarryvarioustypesof loads.Inthisparticularcase,a1kgloadwasplacedon theliftingrope.Thedrawingofthemodelispresented inFig.1

Theforceusedtomovetheloadisgeneratedby three24VDCPWMcontrolledmotors.Theactual positionoftheloadismeasuredby5high‐accuracy incrementalencodersin5dimensions,whichareposi‐tionsalongX‐,Y‐,andZ‐axes,aswellasangulardevia‐tionsbetweentheliftingropeandY‐axis,andbetween thenegativedirectionontheZ-axisandtheprojection oftheliftingropeontotheXZplane.

2.2.3DCraneModelling

Thereareseveralapproachestodesigninga propercontrollerforsuchamultidimensionalsystem. Morecomplexalgorithmsrequireverypreciseinfor‐mationaboutthebehavioroftheloadanddepen‐denciesoccurringintheprocess.Thisdatacanbe providedasaresultofanexperimentconductedon thesystem,orthroughthetheoreticaldescriptionin theformofmathematicalfunctionsandequations.In thisstudy,choosingMPCasoneoftheproposedcon‐trollersde inesstrictlythatthemathematicalmodelis mandatory.

Thederivationofthemathematicalmodelofthe 3Dcraneisbasedonthecreationofbalanceofforces actingalongeachaxisofloaddisplacement,takinginto theaccountthegravityandfrictionforces,andusing Newton‘ssecondlawforsystemswithconstantmass.

Thestatespacemodelisconsideredthemost desirablerepresentation.Table 1 presentsthestate andcontrolvariableswhichhavebeenadoptedto receiveit.Theobtainedstatespacerepresentation describesactualpositionandvelocitiesoftheload withrespecttoeachaxis.Anumberofconstantval‐uesoccurinthisrepresentation,whicharestrictly connectedwiththephysicalmodel.Theseconstant values,collatedinTable 2,havebeendeterminedby themanufacturerduringthedevelopmentphase.

Table1. Stateandcontrolvariablesofthemathematical model

Variable Description

��1

��2

��3

��4

��5

��6

PositionXaxis[m]

LinearvelocityXaxis[m/s]

PositionYaxis[m]

LinearvelocityYaxis[m/s]

Angulardeviationbetweenliftingrope andYaxis[rad]

Angularvelocityfor��5 [rad/s]

��7 Angulardeviationbetweenthenegative directionontheZaxisandtheprojection oftheliftingropeontotheXZplane[rad]

��8 Angularvelocityfor��7 [rad/s]

��9 PositionZaxis[m]

��10 LinearvelocityZaxis[m/s]

��1 PWMcontrolsignalforDCmotorinX axis[‐]

��2 PWMcontrolsignalforDCmotorinY axis[‐]

��3 PWMcontrolsignalforDCmotorinZ axis[‐]

Table2. Constantparametersofthe3Dcranemodel

The inalmodelishighlynonlinearandcomplex. Therearemanycorrelationsbetweenstatevariables:

Figure1. 3Dcrane

2.3.SimulationTestsandModelVerification

Thestatespacemodelhasbeenimplementedin Matlabenvironment.Beforestartingthesynthesisof thecontrolsystem,thesimulationtestswereper‐formed.ThetestsignalwasdesignedasshowninFig.2 andsetforallcontrolsignalssimultaneouslytoverify thebehaviorofthe3Dcrane.Theresultsareshownin Figs.3–4.

Themodelreactscorrectlytoapositiveandnega‐tiveforceactingalongtheX‐andY‐axes–theposition ofthecranealongtheseaxesreturnstoitsoriginalval‐ues(seeFig.3).However,thetestshaverevealedthat themodeldoesnotworkproperlyalongtheZ‐axis.As showninFig.2,thenegativecontrolsignalwasapplied betweensecond8and10ofthesimulationprocess. Theloadpositionvaluesslightlyincreased,butthis seemstobetheeffectofotherinputsandcurrent deviationoftheload,andnotoftheinputappliedto thedevicecontrollingtheZ‐axis.

Themodelreactscorrectlytoapositiveandnega‐tiveforceactingalongtheX‐andY‐axes–theposition ofthecranealongtheseaxesreturnstoitsoriginal values(seeFig.3).

Figure2. Testcontrolsignal

Figure3. Positionofload

Figure4. Angulardeviationofload

However,thetestshaverevealedthatthemodel doesnotworkproperlyalongtheZ‐axis.Asshownin Fig.2,thenegativecontrolsignalwasappliedbetween second8and10ofthesimulationprocess.Theload positionvaluesslightlyincreased,butthisseemsto betheeffectofotherinputsandcurrentdeviationof theload,andnotoftheinputappliedtothedevice controllingtheZ‐axis.

Wheneverthecontrolsignalischangedtoanon‐zerovalue,thedeviationincreases(seeFig.4).When itisequaltozero,thesystemisobservedtobeself‐stabilizing.Thereactionofthesystemisnoticeable,as expected,theropewiththeloadde lectsmorewhen themomentumofDCmotorsisappliedtothecrane.

Thisbehaviormaybecausedbyerroneousderiva‐tionoftheequationscomposingthemathematical model.Inthiscase,thesynthesisofthecontrolsystem inwhichthecontrollerrequiresfullknowledgeofthe mathematicalmodelinthestate‐spaceformmaybe burdenedwithalargeerror.Moreover,thesimulation modelworkinginthiswayexcludesthevalidityof creatingacontrolsystem.

Becauseoftheaboveconclusion,thepartofthe modelconnectedwiththeZ‐axishadtoberedesigned. Asolutionwasfoundinthe3Dcranedocumentation attachedtothedevice.Themanufacturerperformed relevanttestsandderivedthelinearizedmodelofthe Z‐axisintheformofatransferfunction.Withthe useofasimplemathematicalapparatus,thetransi‐tionbetweenthetransferfunctionandthestatespace modelfortheZ‐axiswasdetermined.Thenewequa‐tiondescribingthevelocityalongtheZ‐axisreplaced Eq.(10)inthemodel,thuscreatingthe inalmathe‐maticalrepresentationofthe3Dcrane:

�� (��)

.2379��1(��)�� <0

3.DesignofControlAlgorithms

Designingacontrolsystemforvarioustypesof3D cranesisacommonprobleminindustrialautoma‐tion.Physicalmodelsofcranesimplementedforsci‐enti icpurposesarealsopopular.Therefore,many designersarefacingtheissueofselectingthecon‐trollerandthestructureofthecontrolsystemforthe crane.Theneeds,requirements,andpossibilitieshave tobede inedinthiscase.Itisworthtakingunder considerationaspectssuchasthecontrolmethod, therepeatabilityofmovements, inancialpossibilities, andphysicallimitations,forinstance,intheproduc‐tionhall.

Thestructureofthesystemusedinthiswork allowstheuseofvirtuallyanycontrolmethod.The requirementsonthecontrolsystemcomedownto maintainingandtrackingthesettrajectoryoftheload whileminimizingangulardeviationsoftheload.Two differentcontrolsystemshavebeenproposedforthe 3Dcrane,whicharebasedonthePIDcontroller,and nonlinearMPC(NMPC).

3.1.PIDController

ThePIDcontrollerisverycommonlyusedinthe industry.Itisaclassiccontrollerbasedonthemea‐surementofthesystemormodeloutput.Thesystem withsuchacontrollerisprimarilysimpletoimple‐ment.AnotherhugeadvantageofthePIDcontroller isthatitdoesnotrequireknowledgeofthesystem’s model,whichallowsthecontrolsystemdesignerto avoidthemodellingphase[11].

Theexperimenthasbeenselectedasthetuning method.Itisatechniquebasedontuningthecon‐trollers’gainvalueswhileobservingandanalyzing theoutputandcontrolsignals.Theeffectivenessof thismethodisstronglyrelatedtotheskillsofthe controlsystemdesigner.Tobefullyeffective,the methodrequiresexperienceandknowledgeabout thecontroller’sbehavior,andaboutthein luenceof eachgaintotheoutput.Usingsomecontrolquality indicators,e.g.,controlerror,orovershoot,ishighly recommendedduringthewholetuningprocess.When usingthistypeofapproachdirectlyonthesystem,the designerhastobecarefulbecauseimproperselection ofsettingsmayresultinthelossofsystemstability.

The irstproposedcontrolsystemconsistsof5 PID‐INDcontrollers(seeFig.5)wherethreeofthem areresponsibleforcontrollingtheloadin3Dandthe remainingtwocompensatefortheloaddeviation.

wherex1ref,x3ref,x9ref arereferencepositionsig‐nalsinX‐,Y‐andZ‐axisdirections,ex,ey, ez arecontrol errors,ux,ua,u1,uy,ub,u3 arecontrolsignals,z1,z2, z3 describedisturbanceswhichaffectthesystem,and ex,ey,ez)andx1,x3,x5,x7,x9 arestatevariables.

Inordertoprovideerrorcontrolforbothload positionanddeviation,a2PIDcascadecontrollerhas beenused.Inthatwaythecontrollercangenerate thecounterphasecontrolsignalworkingagainstthe deviation,whilebalancingnearthesetpointposition ofthecraneload.FortheZ‐axis,asimpleclosedloop structurehasbeenproposed.

Fromthecontrolviewpoint,theaccuracyofreach‐ingthesetpositionwithsmalldeviationismore importantthanthetimeofreachingthisposition.

Figure5. Thestructureof3Dcranecontrolsystemwith 5PIDcontrollers

Forthisparticularreason,whentuningPIDx,PIDy, andPIDz,attentionwaspaidforovershootnotto exceed10%ofthesetpointvalue.

3.2.NonlinearMPC

Predictivecontrolisanadvancedcontrolmethod usedinsituationswherethereisaneedforhighaccu‐racy,predictabilityofcontrol,andsafetymaintenance. Thebasicrequirementformakingtheimplementation ofMPCpossibleistheknowledgeofthemathematical modelofthesystem.Unlikeclassiccontrolsystems, theMPCsystemisnotbasedsolelyonchangesin theoutputsignalsfromthefacility,asitgenerates controlsignalsbysolvingtheoptimizationproblem basedontheknowledgeofthemathematicalmodel, thecontrolsinpreviousmomentsoftime,andthe measurementsofoutputvalues.

Firstly,thedecisionvariableshavetobede ined. Inthiswork,theseareallavailablestatevariables describingthepositionoftheloadx1,x3,x9,theangu‐lardeviationx5 andx7,andthelinearandangular velocitiesx2,x4,x6,x8,x10 inthesystem.

Next,theobjectivefunctionwasde inedasthe weightedsumofdeviationsofthecontrolledstates fromtheirreferencetrajectoryandthecontrolvalues representingthecostoftheirincurring.Itsformulais givenas:

Toachievethisgoal,itusestheexistingmathemat‐icalmodelofthecrane,applyingfuturecontrolsto thesystemandcalculatingitspredictedoutputs.After indingthebestsolution,the irstcalculatedcontrols aresetatthecontrolleroutput.Thenthewholeproce‐durestartsagain,usingnewsystemstatevaluesand setpoints[12].

4.ControlResults

4.1.SimulationConditions

Theimplementedcontrolsystemshavebeen tested.Toallowforthecomparisonofdifferentcontrol systems,certainqualitycriteriahadtobeadopted.For thecontrolsystems,thesecriteriacanbede inedin manydifferentways,startingfromtheshapeofthe outputsignals,throughovershoots,andendingwith purelynumericalindicators.

Thisarticledoesnotexaminetheeffectofmass valuesontheperformanceofthecontrolsystem.A constantmasswasassumed.

whereJisthecurrentvalueoftheobjectivefunction, kisthediscretetimesample,(wi,wj)aretheweight values,xref (k+p|k)isareferencevalue,��(��+��|��)is thepredictedvalueofstatevariable,andu(k+p|k)is thecalculatedcontrolsignal.

Finally,theconstraintsfortheoptimizationtask havebeensetas:

(30a)

Fig.6presentstheideaofthepredictivecontroller algorithm.

wherexref isthematrixofreferencepositionsig‐nalsinX‐,Y‐andZ‐axisdirections,e*isthematrix ofpredictivecontrolerrors,u*isthecontrolsignal generatedbytheoptimizerduringtheoptimization process,x*isthematrixofcalculatedstatevariables,u isthematrixofgeneratedcontrolsignals,andxisthe matrixofstatesvariables

Theoptimizerretrievestheinformationaboutthe giventrajectoriesandcurrentvaluesofdecisionvari‐ables.Thenitsolvestheoptimizationproblemfor thede inedobjectivefunction,takingintoaccountthe assumedconstraints.

Forthepurposesofthiswork,twointegralindices: IntegralSquareError(ISE)andIntegralAbsolute Error(IAE)havebeenselectedtoassessthequality ofthedesignedcontrolsystems.Themathematical descriptionofthesecriteriaisgivenbydependencies (31a)and(31b).

Moreover,theinitialconditionsforthepositionof theloadwerede ined:x1p=x3p=0.3,x9p=0.95,where �� istheinitialconditionforthei‐thstatevariable, i=1,…,10.llotherinitialvaluesofstatevariablesinthe 3Dcranemodelhavebeenassignedwithzerovalues.

4.2.ControlResultsforPIDController

TuningPIDcontrollersstartedwiththecontrollers responsiblefortheloadpositionalongX‐,Y‐,and Z‐axes.Onlyafterthat,thesettingsfortheloaddevi‐ationcontrollerswereselected.Forthepurposesof thesimulationstudy,threedifferentsetsofPIDcon‐trollerswereproposed(seeTable3).

Figure6. Thestructureof3Dcranepredictivecontrol system

The irstset,presentedinTable3,wasintroduced toverifywhetherthesystemcanhandlecontrolling withoutthefeedbackfromthedeviationPIDcon‐trollers.

Althoughthesystemismostaccuratefortheload positionalongtheY‐axis,theentirecontrolsystem, accordingtoTables4and5,istheworstoutofallthe threeproposed.Thisleadstotheconclusionthatload deviationhastobecontrolledinthesystemtoincrease precision.

Inthesecondvariant,PIDAandPIDBweretuned. ThepositionindicatorsinthedirectionsofX‐,Y‐,and Z‐axeshavevaluessimilartothe irstoption,how‐ever,thevaluesoftheindicatorsfordeviationsare undoubtedlybetter.

Inthelastvariant,thevaluesofproportionalgains forPIDalphaandPIDbetacontrollerswereincreased. Inaddition,thederivativegainwasassigned.Thanks toitspositivein luenceonthetransientstates,the systemischaracterizedbythebesttotalIAEandISE indicatorsamongallproposedvariantsofPIDcon‐trollers.

Insummary,forthePIDstructurecontrolsystem, theloaddeviationshavetobetakenintoaccount,as thedeviationfeedbackprovidesleadsforthesystem toundulatetheloadposition,andthus,slowlyelimi‐natetheloadswingeffect.

4.3.ControlResultsforNonlinearMPC

Duringthesimulationtests,differentcombina‐tionsofindividualweightvalueswerecheckedin termsoftheirin luenceonthebehaviorofthecon‐trolsystem(seeTable 6).Asaresult,threevariants illustratingtheshapingoftheweightvaluesandtheir impactontheoperationofthecontrollerwerepro‐posed.Duringthetest,thecontrolhorizonwasgiven theconstantvalue:Hc =4.

TheanalysisofTables 7 and 8 showsthatsmall weightvaluesresponsibleforloaddeviation(w4,w5) improvetheindicatorvaluesforbothx5 andx7.How‐ever,ifthisvalueistoohigh,asinthelastvariantpro‐posedinTable 6,thecontrolqualityfortheposition alongtheY‐axisispooraccordingtoIAE.Inaddition, w3 hastobegreaterthanw1 andw2,becauseifthey areequal,thecontrollingalongtheZ‐axisismuch worsethanwhenalargervalueissetforthisweight. ThebestvaluesofISEandIAEwereobtainedinthe thirdvariant.

Thenexttestsconcernedthedeterminationofthe controlhorizon(seeTables 9 and 10).Theywere carriedoutforthreedifferentvaluesofthecontrol horizon,usingtheweightsofthebestvariantfrom Table6

ThecontrolsystemistheleastpreciseforHc =2, intermsoftherealizedloadpositionalongeachaxis. Moreover,itdoesnothavetheabilitytoextinguish oscillationsthatoccur.ForHc =4,thesystemvery preciselycontrolsthepositionoftheload.Thedevi‐ation �� ismuchbetterdampedthanforHc =2.As forthedeviation��,slightdecayofoscillationscanbe observed.

Figure7. Obtainedwaveformsoftrackingreference trajectoryx1 forbothdesignedcontrolsystems

Figure8. Obtainedwaveformsoftrackingreference trajectoryx3 forbothdesignedcontrolsystems

Finally,whenHc =6,thesystemisslightlyless accurateincontrollingthepositionaxesthanforHc = 4.However,somefavorabledifferenceindeviation controlisnoticeableinthiscase.

Greatervaluesofthecontrolhorizonwerealso checkedduringthetestsimulation,howeverthe improvementofsystemqualityturnedoutinsigni i‐cantcomparedtotheextensionofthecalculationand simulationtimeofthecontrolsystem.

4.4.ComparativeAnalysis

The inalstepoftheperformedtestswasthecom‐parisonbetweenthebestreceivedPIDcontrolsys‐tem,presentedasvariant3inTable3,andtheNMPC controlsystem,presentedasvariant3inTable6with Hc =6

Lookingatthetotalvaluesoftheindicators,shown inTables 4, 5, 9,and 10,acleardifferencecanbe observedbetweenthedesignedcontrolsystemsin favorofthePIDstructure.However,individualvalues ofthecontrolledquantitiesforloadpositionx1,x3, x9,andloaddeviationx5 arebetterforthepredictive controlsystem.Theonlycontrolstateforwhichthe individualindicatorsarebetterforthePIDcontrol systemistheloaddeviationx7

Thenextpartofthecomparisonconcernedthe obtainedwaveforms.Figs.7–9showtheloadposition resultsobtainedforbothdesignedcontrolsystems.

Thepresentedwaveformsindicatethatthetwo designedcontrolsystemsworkproperly.Theyfollow thegivenreferencetrajectoryofloadpositionalongall threeaxes.Theyalsocounteractexcessiveovershoot astheysmoothlygettothesetposition.

Table3. ProposedgainsofPIDcontrollers

Table4. IAEforPIDcontrollers

Table5. ISEforPIDcontrollers

Table6. WeightvaluesforNMPCcontroller

Table7. IAEforNMPCcontroller–tuningtheweightvalueswithconstantHp

Table8. ISEforNMPCcontroller–tuningtheweightvalueswithconstantHp

Table9. IAEforNMPCcontroller–tuningthecontrolhorizonHp

Comparingtheoperationofbothsystems,forx1 theNMPCcontrolsystemisslightlymoreprecisethan thePIDcontrolsystemasitgetstothedesiredposition faster.

Forx3,thePIDcontrolsystemgentlyfallsinto slowoscillationsinordertocontroltheloaddeviation, whiletheNMPCdoeslessfrequentandmoredynamic counteractions‐thesystemreturnstothedesired

Table10. ISEforNMPCcontroller–tuningthecontrolhorizonHp

Figure9. Obtainedwaveformsoftrackingreference trajectoryx9 forbothdesignedcontrolsystems

Figure10. Obtainedwaveformsofx5 controlforboth designedcontrolsystems

positionfaster.Forx9,thesystemsworkinaquitesim‐ilarwayuntilthelastsetvaluesarereached.Thenthe NMPCcontrollergeneratesanovershootandreturns totrackingthesetvaluetogetherwithreachingthex1 referenceposition,whilethePIDstructurereachesthe positionwithoutsuchactions.

TheovershootgeneratedbytheNMPCcontroller forx9 allowsittocounteracteffectivelytheincrease ofx5 deviation,thusreducingittoanegligiblevalue, asshowninFig.10.Thissystemturnsouttoperform betterincontrollingx5 thanthePIDcontrolsystem. Forx7deviation,NMPCperformsmuchworsethan thePIDcontrolsystem,ascanbeseeninFig. 11.It canbestatedthattheNMPCtriestocounteractthis deviationonlyforthelastsetvalues.Atthesametime, thePIDcontrolsystemtriestocontrolx7 throughout theentiredurationofthecontrol.

Summingup,theNMPCsystemiscertainlyasolu‐tionwhichcanbeconsideredfor3Dcranecontrol.The errorrelatedtotheadjustmentofx7 canberelatedto theerrorintheoriginalsimulationmodel.Therefore, theobtainedsystemmaynotworkproperlyassome informationanddependenciesarelost.Nevertheless, intheremainingcases,thecontrolqualityissatisfying. However,itshouldbenotedthatthecontrolhorizon playsanimportantroleinthiscase.

Figure11. Obtainedwaveformsofx7 controlforboth designedcontrolsystems

Eventhehighestcheckedvalueofthisparameter doesnotallowthiscontrollertofullycoverthedynam‐icsofthesystemrelatedtothecontrolofdeviations x5 andx7 whichwouldguaranteeitsfulleffective‐ness.TheotherargumentinfavorofthePIDcontrol systemisthatitislesscomplexandcanbeeasily implementedwithoutinvolvinghugetimeresources inthedesigningphase.Takingalltheseargumentsinto account,despiteaveryhighpotentialofthepredictive controller,itsusefor3Dcranecontrolisnotmore advantageousthanthePIDcontrolsystem.

5.Conclusion

Thepaperpresentstheprocessofdesigningthe controlsystemfora3Dcrane.Themathematical modelofthecranehasbeenveri iedandtheequiva‐lentmodeloftheZ‐axiswasproposed.TuningthePID controllersandpredictivecontrolleraredescribed, alongwiththeimplementationofbothcontrolsys‐temsandthecomparativeanalysisoftheirperfor‐mance.Thesynthesisprocesshasturnedoutsuccess‐fulforbothcontrolsystemsastheyprovidecorrect realizationofthereferencetrajectorieswhilemini‐mizingtheloadswingeffect.Bothsolutionscanbe considered,however,thedesignandimplementation ofthePIDstructurecontrolsystemisquickerand simplerthanthatofthepredictivecontroller.

AUTHORS

MaciejSzafrański –GdańskUniversityofTechnology, FacultyofElectricalandControlEngineering,Poland, e‐mail:szafmac@gmail.com.

RobertPiotrowski∗ –GdańskUniversityofTechnol‐ogy,FacultyofElectricalandControlEngineering, Poland,e‐mail:robert.piotrowski@pg.edu.pl.

∗Correspondingauthor

References

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Abstract:

PATTERNSOFACOUSTICEMISSIONCHANGESWITHALTERATIONSINTHEDAMAGE AREAOFACOMPOSITEMATERIALACCORDINGTOTHEMISESCRITERION

Submitted:2nd August2024;accepted:1st December2024

SergiiFilonenko,AnzhelikaStakhova

DOI:10.14313/jamris‐2025‐014

Thispaperconsiderstheuseofahighlysensitiveacous‐ticemissionmethodforstudyingthedeformationand failureprocessesofcompositematerials.Thisprovidesa substantialamountofinformationaboutphenomena occurringatthesub‐micro,micro,andmacrolevels.How‐ever,theadditionalinfluenceofvariousfactorsleads totheproblemofinterpretingandidentifyingtheinfor‐mationyieldedbythisprocess.Addressingthisproblem involvesdeterminingtheinfluenceofdifferentfactorson acousticemission‐signalparametersandtheirsensitivity totheinfluencingfactors.Inthisstudy,duringthefailure ofcompositematerialundertransverseforceaccording totheMisescriterion,ananalysisisconductedonthe impactofchangesinthenumberofcompositematerial elements(damagearea)ontheamplitude‐timeparam‐etersoftheacousticemissionsignalbasedonadevel‐opedsignalmodel.Theresultsofthesimulationallow fortheidentificationanddescriptionofpatternsinthe changesofamplitude‐timeparametersofacousticemis‐sionsignals(maximumamplitude,areaunderthesignal curve,andsignalduration),withvariationsinthenumber ofcompositematerialelements.Thesepatternsenable thedeterminationofthesensitivityofacousticemission signalparameterstotheinfluencingfactor.Thefindings ofthisstudymaybeofinterestinthedevelopmentof methodsformonitoring,diagnosing,andpredictingthe failureofcompositematerialsandproductsthroughthe registrationandanalysisofacousticemissionsignals.

Keywords: compositematerial,damage,acousticemis‐sion,signalamplitude,signalenergy,Misescriterion

1.Introduction

Compositematerials(CM)arewidelyusedinvar‐iousindustriesduetotheirdesirablephysicaland mechanicalproperties,temperatureresistance,and durability[1–5].Despitetheseadvantages,composite materialsaresusceptibletodamageatthemicrolevel understaticanddynamicloads,whichcanleadto rapidfailureprocessesthatpropagateinanavalanche‐likemanner.Understandingandpredictingthesefail‐uremechanismshasdrivenextensivetheoreticaland experimentalresearch,withtheaimofdeveloping reliablecriteriatoassessCMconditionsandprevent failure[6–9].

Amongthevariousmethodsforstudyingmate‐rialfailure,theacousticemission(AE)techniquehas provenparticularlyeffectiveinmonitoringthedefor‐mationandfractureprocessesincompositemateri‐als[10–12].AEprovidesvaluableinformationacross multiplescales–fromsub‐microtomacro–aboutthe internalstructuralchangesduringloading.However, thecomplexityofthefailureprocessesincompos‐itematerialsintroduceschallengesininterpreting AEdata,makingitdif iculttoaccuratelyidentifythe underlyingdamagemechanisms.

ExistingAEmodels,suchasthe iberbundlemodel (FBM)[13, 14],havebeeninstrumentalinsimulat‐ingcompositematerialfailureunderuniaxialtension andtransverseforces.Thesemodels,whileinsightful, oftenfocusonthestatisticalrepresentationofAEsig‐nalswithoutfullyaddressingsignalformationduring thefailureofindividualCMelements.Forinstance, AEsignalsarecommonlyrepresentedasstochastic decayingsignals,andtheircumulativeenergydis‐tributionisanalyzedasfailureapproaches[15–17]. However,furtherresearchisneededtoclarifyhow speci icfactors,suchastheextentofthedamage area,in luenceAEsignalparametersduringcompos‐itematerialfailure.

Thisstudyaddressesthisgapbyanalyzingthe changesinamplitude‐timeparametersofAEsignals asthedamageareaincompositematerialsincreases, usingtheMisescriterionandtheFBMmodel.The study’s indingsaimtoenhancetheaccuracyofAEsig‐nalinterpretation,providingastrongerfoundationfor developingmethodstomonitor,diagnose,andpredict thefailureofcompositematerials.

2.AnalysisofRecentResearchand Publications

Theanalysisoffailureprocessesincomposite materialsincludesboththeoretical[18,19]andexper‐imental[20–22]studies.Theseinvestigationsaimto predictthestagesofdeformationandfailureinCM. Typically,twomainapproachesareusedforassess‐ingdamageincomposites:theapplicationofvarious failurecriteriabasedonstressanalysisandtheuse ofdamagemechanicsmethods,whichexaminethe evolutionofdamage(initiationandprogressionof failures)[23].Inmodeling,the initeelementmethod isusedtocalculatechangesinstresses–stresswaves thataretreatedasAEwaves[24].

Atthesametime,variousmodelsareusedto analyzefailureprocessesincompositematerials:the discretedamagemodel[25],thesmeareddamage model[26],andothers.ThemodelofCMasabun‐dleof ibersisalsowidelyusedforstudyingfailure processes[27,28].Thesestudiesareconductedunder conditionsofuniaxialtensionandtransverseforce.

ThefundamentalaspectsoftheFBMmodelare discussedinworks[27,29].IntheFBMmodel,CM isrepresentedasadiscretesetofelementsor ibers thatfailsequentiallyinabrittlemanneruponreaching theirstrengthlimit.Theloadatwhichfailureoccursis arandomvariablewithacertainprobabilitydensity. Whenasingleelementfails,theloadisredistributed eitheruniformlyacrossallremainingelements,or toneighboringelements.Typically,analysisincludes studyingthedistributionoffailureavalanches(by size)and,accordingly,thedistributionofAEenergy (A),withananalysisofthetimeapproachingcomplete failure[30–32].

Studiesonthefailureprocessofcompositemateri‐alsusingtheFBMmodelareconductedundervarious conditions.In[33],theauthorsconsiderthecaseof randomdisplacementof iberswithidenticalequilib‐riumlengths,causedbyrandomspatialcon iguration ratherthanbyvariabilityinfailurethresholds..The analysisofthe iberfailureprocessdemonstratesthe presenceoftwodistinctpower‐lawdistributionsof avalanchesize.

In[34],theFBMmodelwith ibersorientedran‐domlyisconsidered,introducingtheamplitudeof interactionbetweenthe ibersandtheCMmatrix.A singleparameterquantitativelyde iningallinterac‐tionsbetween ibersandthematrixisanalyzed.The studyexamineschangesinthedensityofundamaged ibersdependingontheappliedforces;theamplitude ofinteractionsbetween ibersandthematrix;andthe system’ssize.

Itisshownthatthefailureprocessexhibitstwo sequentialperiodsseparatedbyadelayduration, leadingtoincreased iberelongationtime.

In[35],amulti‐scalemodelofa iberbundle,rep‐resentedasahierarchicaltree,isinvestigated.During iberfailure,theloadistransferredfromupperto lowerelementswithinthehierarchy,withuniform redistributionacrossallhierarchicallevels.Thestudy explorestherateoffailuredevelopmentinCMacross differenthierarchylevels,showingthatincreasing thenumberofhierarchicallevelsreducesmaterial strength.TheanalysisofthefailureprocessinCM withtheintroductionofelastic‐plasticbehaviorof ibersintotheFBMmodelispresentedin[36].This workexamineschangesinthedistributionoffailure avalanchesanddemonstratesthatvariationsinthe exponentoftheavalanchesizedistributionindicatea transitionfrombrittletoplasticfailureinCM.

In[37],amodelofnano‐columnarrays,withran‐domfailurethresholdsbasedontheFBMmodel,is explored.

Thestudyanalyzestheimpactofcoordination numberandthenumberofhierarchicallevelsonsys‐temstrength,thesizeofcatastrophicavalanches,and theprobabilityoffailure.Itisshownthattheaverage criticalloaddecreasesasthesystemsizeincreases, andtheprobabilityoffailurefollowsanormaldistri‐bution.

In[38],theFBMmodelisusedasabasisforstudy‐ingseismicactivitydevelopmentbeforecatastrophic failureinheterogeneousmaterials,withthegoalof preventingdestruction.Thestudyrevealsthatthe patternofloadredistributionaffectsthemacroscopic typeoffailure,fromplasticfailurewithoutstresscon‐centration(globalloaddistribution)tobrittlefailure withlocalizedloaddistribution;italsoshowschanges intheavalanchesizedistributionlaw.Thestudydeter‐minesthatavalanchesandtheassociatedemittedelas‐ticenergyarenotstrictlyequivalent,particularlyin casescharacterizedbylocalizedloaddistributionand brittlefailure.Moreover,theincreaseinthenumber ofavalanchesismorepronouncedandoccursearlier thantheincreaseinglobalemittedelasticenergyprior tothecompletefailureofthe iberbundle.

Studiesonthefailureprocessofcompositemate‐rialsusingtheFBMmodelundertransverseforceare conductedin[29,39],andrelationshipsdescribingthe changesinequivalentstressesusingtheORcriterion andtheMisescriterionarederived.Expressionsfor thenumberofremainingelementsduringthefailure processofCMhavebeendetermined,andthestudy analyzesthepatternsofchangesinthenumberof remainingelements,aswellasthedistributionoffail‐ureavalanches.Acousticemissionisalsoconsidered, althoughnotintermsofsignalformation,butratherin termsofAEenergyrelease.Thetimeperiodapproach‐ingthecompletefailureofCMisalsoanalyzed.

In[40, 41],theresultsofstudiesonthefailure processofgranularmaterialsundertransverseforce usingtheFBMmodelarepresented.Theanalysis focusesontherateofenergyreleaseduringthefail‐ureofCMelements.Therelationshipbetweenstress jumpsandAEeventsduringthefailureofCMelements isdetermined.Thesestudiesdonotaddressthesignal formationprocessofAE,butratheranalyzetheAE energyreleaseprocess.

Expressionsforthenumberofremainingelements incompositematerialsundertransverseforce,based ontheFBMmodelandusingthe“OR”criteriaandthe kineticsoffailureprocessdevelopment,arediscussed in[42].Thestudyshowsthatwithanincreasingload‐ingrate,therateoffailuredevelopmentalsoincreases. Thisisaccompaniedbyanincreaseintheamplitudeof thegeneratedAEsignalandadecreaseinitsduration; thesecorrespondtoanincreaseintherateofthe failureprocessintheCM.

In[43,44],studiesonthefailureprocessofCM undertransverseforce–usingtheFBMmodel,failure kinetics,andtheMisescriterion–wereconducted.

Thesestudiesexaminedexpressionsforthenum‐berofremainingCMelements,aswellastheAEsignals generated,duringCMelementfailure.Itwasshown thatasthefailureprocessdevelops,thenumberof remainingCMelementsdecreasescontinuouslyover timeuntilcompletefailureoccurs.Thisisaccompa‐niedbythegenerationofacontinuoussequenceof AEpulses.Itwasdemonstratedthatanincreaseinthe loadingrateincreasestheamplitudeandlowersthe durationoftheAEsignal.

Thein luenceofCMpropertiesontheenergy parametersofthegeneratedAEsignalswasalsocon‐sidered.Itwasshownthatastheparametercharacter‐izingCMpropertiesincreases,theamplitude,energy, anddurationoftheAEsignalalldecrease.In[45],the effectofthechangingrateoftheCMfailureprocesson theshapeoftheAEsignalwasexamined,anditwas foundthatincreasingordecreasingtherateoffailure developmentleadstotheappearanceofspikesanda dropinamplitudeatthetrailingedgeoftheAEsignal.

Atthesametime,thereisinterestinunderstand‐inghowthedamagedareaofCMaffectsthechange patternsintheparametersofthegeneratedAEsignals duringCMfailureundertransverseforceaccordingto theMisescriterion.

3.Methodology

ResearchMethodOverview

Thisstudyemploysamodelingmethodtoanalyze theparametersofacousticemissions(AE)thatoccur duringthefailureofcompositematerials(CM)under transverseloadingaccordingtotheMisescriterion. Theprimaryobjectiveistoinvestigatethein luence ofthenumberofcompositematerialelements–which determinesthedamagearea–ontheamplitude‐time characteristicsofAEsignals.

Themodelingisbasedontheanalysisofchangesin theequivalentstressinCMelementsduringtheirfail‐ure.Amathematicalmodelwascreatedtodescribethe formationofAEsignalsasacombinationofindividual impulsesgeneratedduringthefailureofeachcompos‐iteelement.Theinitialparametersforthesimulation includethestrainrate,thresholdstressesforfailure initiation,andthephysicalpropertiesofthecomposite material.

Thekeyresultsofthemodelingfocusontherela‐tionshipbetweenthenumberofCMelements(dam‐agearea)andtheAEsignalparameters,suchasmax‐imumamplitude,signalduration,andtheareaunder thesignalcurve.Analysisoftheserelationshipspro‐videsinsightsintothesensitivityofAEsignalsto changesinthestructureofcompositematerials,which iscrucialfordevelopingmonitoringanddiagnostic methodsforfailureprocesses.

ModelingConditions

Thestudiesofacousticemissionundervarying loadingratesandpropertiesofcompositionalmateri‐alsin[43–45]wereconductedbymodelingAEsignals accordingtothefollowingexpressions:

where ��(��) and ��(��0) denotethetime‐dependent changeinequivalentstressontheCMelementsand thethresholdstresscorrespondingtothetime ��0 at theonsetofCMfailure; ��0 representsthemaximum possibledisplacementuponinstantaneousfailureof theCM,whichconsistsof ��0 elements; ��0 andrare constantsdependentonthephysicalandmechanical characteristicsoftheCM.

ThechangeinequivalentstressonCMelements overtime,accordingtotheMisescriterion[30],is describedbythefollowingexpression: ��(��)=��⋅0.5[(2−2√��+�� 3 2 log((1+��)/ (1−��)))−�� 3 2(2(1−√��)/�� +log((1+1−√��)/(1−1−√��)))], (2)

where ��(��) representsthechangeinequivalent stressonCMelementsovertimeunderalinearstrain input��=��(where��isthedeformationrate).

Thethresholdstresscorrespondingtothetime��0 whenCMfailurebeginsisdescribedbythefollowing expressions: ��(��)=��⋅0.5[(2−2��0 +�� 3 2 0 log((1+��0)/ (1−��0)))−�� 3 2 0 (2(1−��0)/��0 +log((1+1−��0)/(1−1−��0)))], (3)

where��isthedeformationrateofCM.

Themainprinciplesofgeneratingasingledis‐turbanceimpulseduringthefailureofasingleCM elementarediscussedin[42].Accordingtothese principles,themaximumpossibledisplacement��0 in expression(1)isdirectlyproportionaltothenumber ofelements��0 intheCM,��0 ∼��0.Whenmodelingthe AEsignalaccordingtoexpression(1),wewillincrease thenumberofCMelementsbyfactorsof2,3,and 5,relativetotheinitialnumberofelements ��0.The modelingwillbeconductedinrelativeunits.

Thefollowingparametervalueswillbeusedin relativeunits.Thedeformationrate �� willbesetto ̃��=20 .Theparameter ��0,whichcharacterizesthe propertiesofCM,willbesetto ��0 =100,000.The parameterr,whichcharacterizesthedispersionofCM properties,willbesetto ̃��=10,000 .Theresults ofthecalculationoftheequivalentstressvariation, accordingtoexpression(2),atadeformationrateof ̃��=20 ,areshowninFigure1

Figure1. Dependenceinthevariationofequivalent stressovertime,accordingtoexpression (1),duringthe failureofCMbasedontheMisescriterion.The deformationrateissetto ̃��=20

Thedependenceexhibitsnonlinearbehavior.To calculatetheinitialfailurestressorcriticalstress��0 = ��(��0),thefailuretime, ��0,issetto ��0 =0.001 (see Figure1).Thecalculationresults,accordingtoexpres‐sion(3),showthattheinitialfailurestressorcritical stress ��0 =��(��0),atthefailuretime ��0 =0.001, is 0 =̃��(��0)=0.016761288967306002.Inthe calculations,thetimeintervalbetweencalculatedAE signalamplitudevalues–Δ��,accordingtoexpression (1)–isΔ�� =1.10−7 .

4.ResultsofSimulation

Theresultsofthesimulation,asafunctionofAE signalamplitudeovertimewithanincreasingnum‐berofCMelements,arepresentedinFigure 2.The resultsindicatethatwithanincreaseintheareaofCM destruction,boththeamplitudeandthedurationof theAEsignalincrease.

Figure 3 presentsananalysisofthemaximum amplitudeanddurationoftheAEsignalwithincreas‐ingareaofCMdestruction.ItisevidentfromFigure3 thatthechangeinmaximumamplitudeoftheAE signalwithincreasingCMdestructionareafollowsa lineartrend.ChangeindurationoftheAEsignalwith increasingCMdestructionarea,ontheotherhand, showsanonlineartrend.

Analysisofthedatawithapproximationsforthe dependenciesshowninFigure3revealsthefollowing. ThedependencyofthemaximumamplitudeoftheAE signalwithincreasingCMdestructionarea(Figure3a) iswell‐describedbythefollowinglinearfunction:

=��+��, (4) where �� istheareaofdestructionofCM,deter‐minedbythenumberofCMelements,andaandbare thecoef icientsoftheapproximatingexpression,and a =0.00001and b =8.64634

FordescribingthedependencyshowninFig. 3a usingexpression(4),thecorrelationcoef icient R is1,andtheresidualstandarddeviationisSD= 2.58199.10−5 .

Figure2. GraphsofthevariationinAEsignalamplitudes overtimeinrelativeunitsduringthefailureofCM undertransverseforce,basedontheMisescriterion, withvaryingnumbersofCMelements.Simulation parametervalues: ��0 =100000; ̃��=20 ; ̃��=10000 ; ��0 =0.001.NumberofCMelements:1– ��0;2– 2⋅��0; 3– 3⋅��0;4– 4⋅��0;5– 5⋅��0

Thedependenceofthedurationoftheacoustic emissionsignalontheincreaseinthedestructionarea ofthecompositematerial(Fig. 3b)iswell‐described bythepowerfunction

(5)

where�� istheareaofdestructionofthecomposite material(KM),de inedbythenumberofelementsof KM,dandwarethecoef icientsoftheapproximating expression,and c =0.00102; w =0.00055. Expression(5)describesthedependency showninFig. 3b;thecoef icientofdetermination is ��2 =0.99834,andtheresidualvariance SD2 =2.8395.10−16

WewillcalculatetheareaundertheAEsignal curveinrelativeunitsusingtheexpression

where i =0.….; k istheindexofthecalculatedAE signalamplitudevalueatitsduration ;Δ�� isthetime intervalbetweenthecalculatedamplitudevaluesof theAEsignal(Δ�� =const);and�� isthe ithcalculated amplitudevalueoftheAEsignal.

Theresultsofthecalculations–showingthe dependenceoftheareaundertheAEsignalcurveon theincreasingdamagearea(numberofelements)in CMundertransverseforce,basedontheMisescrite‐rion–arepresentedinFigure4.

Thedependenceofthechangeintheareaunder theAEsignalcurveontheincreaseintheareaofdam‐agetothecompositematerial(Fig.4)iswell‐described byalinearfunctionoftheform

Figure3. Dependenciesofthemaximumamplitudeof theAEsignal(a)andthedurationoftheAEsignal(b)on theincreasingdamagearea(numberofelements)in CMundertransverseforce,basedontheMisescriterion

Figure4. DependenceoftheareaundertheAEsignal curveonincreasingdamagearea(numberofelements) inCMundertransverseforcebasedontheMises criterion

Figure5. Dependenciesofthepercentageincreasein maximumamplitude (1),areaunderthesignalcurve (2),andduration (3) oftheAEsignalontheincreasing numberofelements(damagearea)inCM

IndescribingthedependencyshowninFigure 4, thecorrelationcoef icientforexpression(7)is��=1, andresidualstandarddeviationSD=2.45133.10−7 .

Todeterminethesensitivityoftheacousticemis‐sionsignalparameterstochangesinthenumberofCM elements,weperformedcalculationsofthepercent‐ageincreaseinmaximumamplitude,duration,and areaundertheAEsignalcurvewiththeincreasein thenumberofelementsoftheCM(i.e.,thedamage area).Theresultsofthesecalculationsareshownin Figure5,where��,%representsthesignalparameter (maximumamplitude,duration,andareaunderthe signalcurve)intheanalyzedAE.

Figure5indicatesthatthepercentageincreasein maximumamplitudeandtheareaundertheAEsig‐nalcurvearequitesimilar,whereasthepercentage increasesinthedurationoftheAEsignalchangesonly slightly.

5.DiscussionofResearchResults

Researchonacousticemissionduringthedefor‐mationandfailureofcompositionalmaterialsisaimed atidentifyingpatternsandcriteriaformonitoringand assessingtheconditionofCM[10–12].However,the highsensitivityofthemethodtoprocessesoccur‐ringwithinthematerialstructure–includingtheCM itself–combinedwiththelargevolumesofinforma‐tiongeneratedandthein luenceofvariousfactors leadstochallengesininterpretingandensuringthe reliabilityofAEdata[46].

where �� istheareaofdamagetothecomposite material,determinedbythenumberofCMelements, and z and q arethecoef icientsoftheapproximating expression,with��=−4.5.10−8,and��=0.77365.

Inpreviousstudies[42–44],thein luenceofvari‐ousfactorsontheparametersofAEsignalsduringthe deformationandfailureofCMwasinvestigatedbased onORandMisescriteria,andforboth[42,43],itwas demonstratedthatanincreaseinthedeformationrate ofCMleadstoanincreaseinthemaximumamplitude ofAEsignals,aswellasadecreaseintheirduration.

Therelationshipbetweenthechangeinampli‐tudeandtheAEsignalsshowsalinearincrease, whilethechangeinsignaldurationexhibitsanon‐lineardecrease[43].Thedataalsoindicatethatthe increaseinthemaximumamplitudeofAEsignalspre‐cedesthedecreaseinsignalduration.Itwasfurther shownin[44]thatastheparameterscharacterizing CMpropertiesincrease,thereisadecreaseinmaxi‐mumamplitude,maximumenergy,andtotalacoustic emissionenergy.Theseparametersexhibitanonlin‐eardecrease.Notably,areductionintotalAEenergy precedesthedecreaseinmaximumamplitudeand maximumenergyofAEsignals.

OneofthefactorsaffectingtheparametersofAE signals,accordingtoexpression(1),isthenumberof CMelementsordamageareaofCM.Accordingto[42], thisisdirectlyproportionaltothemaximumpossible displacementupontheinstantaneousfailureofallCM elements.Thisstudyinvestigateshowthenumberof CMelementsaffectstheamplitude‐timeparametersof AEsignalsandevaluatestheirsensitivitytothisfactor.

TheresultsofsimulatingAEsignalsgenerateddur‐ingthefailureofCMundertransverseforce,based ontheMisescriterion,indicatethatanincreasein thenumberofCMelements(damagearea)resultsin ahighermaximumsignalamplitudeandanincrease initsduration(seeFigure 2).Whiletherelationship betweenthemaximumamplitudeofthesignaland thenumberofCMelementsshowsalinearincrease, therelationshipbetweenthedurationoftheAEsignal andthenumberofCMelementsexhibitsanonlinear increase(seeFigure3).

Statisticalanalysisofthesimulationresults,with dataapproximation,showsthatthedependenceof maximumsignalamplitudeonthenumberofCM elements(Figure 3a)iswell‐describedbyalinear function,whilethedependenceofAEsignalduration onthenumberofCMelements(Figure 3b)iswell‐describedbyapowerfunction.Theapproximating expressionswereselectedbasedontheirminimiza‐tionofresidualstandarddeviationandresidualstan‐dardvariance.

CalculationsoftheareaundertheAEsignalcurve, accordingtoexpression(5),showthatthedepen‐denceoftheareaundertheAEsignalcurveonthe numberofCMelementsexhibitsalinearincrease (seeFigure4).Thisdependenceiswell‐describedby alinearfunction.Theapproximatingexpressionfor describingthechangeintheareaundertheAEsignal curvewiththeincreaseinthenumberofCMelements wasselectedbasedonitsminimizationofresidual standarddeviation.

TocomparethesensitivityofAEsignalamplitude‐timeparameterstochangesinthenumberofCM elements,theincreaseinmaximumamplitude,area underthesignalcurve,andsignaldurationwereana‐lyzedrelativetotheirvaluesattheinitialnumberof CMelements,��0.

Theresultsofthecalculations(Figure 5)show that,withanincreaseinthenumberofCMelements, theincreasesinmaximumamplitudeandthearea undertheAEsignalcurveoutpacetheincreaseinsig‐nalduration.Additionally,theincreasesinmaximum amplitudeandtheareaundertheAEsignalcurveare nearlyidentical.

Dataanalysisrevealsthatwhenthenumberof CMelementsisdoubled,themaximumamplitudeof theAEsignalandtheareaundertheAEsignalcurve increaseby100%and99.9%,respectively,whilethe signaldurationincreasesbyonly0.039%.Whenthe numberofCMelementsisquadrupled,themaximum amplitudeandareaundertheAEsignalcurveincrease by300%and299.9%,respectively,withthesignal durationincreasingby0.079%.Whenthenumber ofCMelementsisincreased ivefold,themaximum amplitudeandareaundertheAEsignalcurveincrease by399.9%and399.9%,respectively,whilethesignal durationrisesby0.088%.SuchchangesinAEsig‐nalparameterswiththeonsetofinitialdamageare likelyattributedtothekinetics(self‐acceleration)of thedamageprocess.

Theresultsoftheconductedresearchshowthat underthegivenmodelingconditions,themaximum amplitudeandtheareaundertheAEsignalcurveare themostsensitiveparameterstochangesinthenum‐berofcompositematerialelements.Theseparameters signi icantlyprecedetheincreaseinthedurationof AEsignals.Theidenti iedpatternsofchangeinthe maximumamplitudeandtheareaundertheAEsignal curveastheyrelatetothevaryingnumbersofCM elementsmaybeusefulfordevelopingmethodsfor monitoring,diagnosing,andpredictingthefailureof CMbasedonAEsignalregistration.

Atthesametime,itisknownthatthemostinfor‐mativeparameterofAEsignalsistheirenergy.Analyz‐ingtheimpactontheenergyparametersofAEsignals ofthenumberofcompositematerialelementsduring theirfailureundertransverseforceaccordingtothe Misescriterion–aswellasidentifyingthepatternsof theirchanges–willhelpdeterminetheirsensitivity andimprovethereliabilityofthemethodsformoni‐toring,diagnosing,andpredictingCMfailurebasedon AEsignalregistrationthathavebeendeveloped.

6.Conclusion

Thisstudyinvestigatedthein luenceofthenum‐berofcompositematerial(CM)elements–repre‐sentingtheareaofdamage–ontheamplitude‐time parametersofacousticemission(AE)signalsduring CMfailureundertransverseforce,basedontheMises criterion.Theresultsdemonstratedthatasthenum‐berofCMelementsincreases,thereisaproportional riseinthemaximumamplitude,theareaundertheAE signalcurve,andthesignalduration.Therelationship betweenthenumberofCMelementsandthemaxi‐mumamplitude,aswellastheareaunderthesignal curve,followedalineartrend,whilethechangein signaldurationexhibitedanonlineargrowthpattern.

Sensitivityanalysisrevealedthattheincrease inmaximumamplitudeandsignalareapreceded theincreaseinsignalduration,withsigni icantdif‐ferencesobservedasthenumberofCMelements increased.Speci ically,whenthenumberofCMele‐mentsdoubled,themaximumamplitudeoftheAE signalandtheareaunderthesignalcurveincreased by100%and99.9%,respectively,whiletheduration oftheAEsignalincreasedby0.039%.Whenthenum‐berofCMelementsincreased ivefold,themaximum amplitudeandtheareaundertheAEsignalcurve increasedby399.9%and399.9%,respectively,and thedurationoftheAEsignalincreasedby0.088%.The resultsofthestudyindicatethatthemostsensitive amplitude‐timeparametersofAEtochangesinthe numberofCMelements(theareaofdestruction)are themaximumamplitudeoftheAEsignalandthearea undertheAEsignalcurve.

Whilethe indingsprovidevaluableinsightsinto thebehaviorofAEsignalsduringCMfailure,this studyislimitedbythespeci icsimulationconditions andassumptionsusedinthemodelingprocess.The focuswasprimarilyonamplitude‐timeparameters. Thus,furtherresearchisneededtoexplorehowother AEcharacteristics–particularlyenergyparameters–arein luencedbychangesinthenumberofCMele‐mentsundertransverseforceaccordingtotheMises criterioninordertodeterminethepatternsoftheir changesandtheirsensitivitytoin luencingfactors.

AUTHORS

SergiiFilonenko –DepartmentofComputerized ElectricalSystemsandTechnologies,NationalAvia‐tionUniversity,LiubomyraHuzaraAve.1,Kyiv,03058, Ukraine,e‐mail: ils0101@gmail.com.

AnzhelikaStakhova∗ –DepartmentofStructural Mechanics,SlovakUniversityofTechnologyin Bratislava,Radlinskeho11,SK‐81005Bratislava, Slovakia,e‐mail:anzhelika.stakhova@stuba.sk.

∗Correspondingauthor

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Abstract:

CONSTRUCTIONAUTOMATIONWITHBIO‐INSPIREDHIERARCHICALEXTREMELY

DOI:10.14313/jamris‐2025‐015

MODULARSYSTEMS

Submitted:4th January2024;accepted:4th April2024

ElaZawidzka,MachiZawidzki

Thispaperpresentstheconceptofhierarchicalextremely modularsystems(EMS).Thebiology‐inspirednomencla‐ture,geneticencoding,andoperationsforthisclassof structuresareintroducedandillustratedwithvarious examples.Fourmutationtypesareintroducedandbriefly analyzed.Arelativelygoodconvergenceoftheevolu‐tionstrategy‐basedalgorithmappliedforoptimizationof EMSisshown.

Keywords: evolutionstrategy,discretestructureencod‐ing,extremelymodularsystem,multi‐branchstructure

1.Introduction

Constructionautomationdealswithapplyingthe principlesofindustrialautomationtotheconstruction sectororintheprefabricationofconstructioncompo‐nents.

ExtremelyModularSystem(EMSforshort)isarel‐ativelynewconceptintroducedafewyearsagoin[1]. Itrepresentsanewapproachtothedesignofengi‐neeringstructuresandarchitecturalobjectswherethe assemblyofcongruentunitsallowsforthecreationof free‐formshapes.

Themaindifferencefromthetraditionalmodular systemsusedinengineeringandbuildingconstruc‐tionistheemphasisontheminimaldiversityoftypes ofmodules,ideally—justone.Thisiswhythesesys‐temsare extremely modular.

Theseare ivebasicadvantagesofEMSs:

1) Economical –astheyaresuitableformassfabrica‐tion,thusloweringthecost,sotheycanbebroadly applied;

2) Functional –astheyallowforrecon iguration, expansion,reduction;

3) Robust –sinceeverymodulethatfailscanbeeasily replacedwithanidenticalbutfunctionalone;

4) Discrete –astheyaresuitableforintelligentmath‐ematicalmodeling,andtheircon igurationscanbe subjectedtodiscrete(multi‐objective)optimiza‐tionusingef icientsearchalgorithms;

5) Uniform –thisfeatureisadvantageousforrapid deploymentandautomatedassembly.

Pipe‐Z(PZ)isamorefundamentalsystemintro‐ducedin[2].Itspurposewastoformspatialmathe‐maticalknotsbyassemblyofonetypeofunit(PZM), asshowninFig.1.

Figure1. Physicalmodelsofmathematicalprimeknots constructedwithextremelymodularPipe‐Z:1)Trefoil (31);2)Figure‐eightknot(41);3)Cinquefoil(51);4)63 knot

Figure2. Acomputerrenderingofanexistingoverpass retrofittedwithtwobranchesofTruss‐Z,comprisedof 47modulesontheleftand77modulesontheright

TheshapeofPZiscontrolledbytherelativetwists ofcongruentmodulesinasequence.

Truss‐Z(TZ)isaskeletal‐framehybridconstruc‐tionsystemintroducedin[3]forcreatingfree‐form pedestrianrampsandrampnetworksconnectingany numberofterminalsinspace.TZiscomposedoffour variationsofasinglebasicmodulesubjectedtoaf ine transformations(mirrorre lection,rotation,andcom‐binationofboth).Figure2showsanexampleofTZ.

Figure3. 1)Aphysicalmodelofthespatialmulti‐branch structurebasedonPZ.Thebudisbasedonatruncated pentagonalprism.Threeadditional“branchingbuds” basedonadodecahedron(12‐gon)areindicatedby yellowcircles.ThissystemiscalledPZ12*andis consideredEMS‐2.2)Anexampleofaspatial multi‐branchquasi‐EMS.Thisstructureisbuiltwith “Space‐Cube”—asystemoftoyblocksbasedonthe simplestspace‐fillingpolyhedron—thecube.This systemiscalledSC3 forshort

Figure4. Examplesof3DPZstructures.Theunitshave beenaddedsequentiallyatvarioustwistsalongthe dottedarrow.1)Anarch;2)atorus;3&4)free‐form pipes

Figure5. PlanarprojectionsofEMS(1)andqEMS(2)

AlthoughoriginallyPipe‐Zallowsforthecreation ofsingle‐branchedstructures,bytheintroductionof anadditional“branchingbuds,”itisalsopossibleto constructmulti‐branchedstructures.Suchasystem iscalledEMS‐2;anexamplebasedonPZwithan additionaldodecahedronbranchingbudisshownin Figure3.1.

2.TheNomenclatureandEncoding

ThebasicelementsforbothEMSandqEMSarethe units.Theyareaddedsequentiallyalongthedirection oftheconstruction,asillustratedwithPZinFigure4 ThecoreoftheEMSconceptistheshapeof theunit,whichallowsthecreationofvariousforms dependingonitsrelativerotation.Itsangulardirec‐tionisrelativetothedirectionsofthe branches,thatis stems or twigs. Forclarityallthefollowingexamples arereducedto2D.Figure 5 showsexamplesofunit assemblyforEMSandfortheprojectionofSC3 to2D, calledSC2

1)TZisastrictEMS.Byrotation,thebasicunit canbeaddedintwoways,determiningtheshapeof thestructure.1and0turnrightandleftalongthe

Figure6. ThenomenclatureandencodingofEMS‐2.On theleft:thegenotype(((1, ■, ■,(1,0,0,1,1,1,1)),(2, 1,IV,(1,1,1)),(3,2,II,(1,0,1)),(4,2,III,(1))),((1,I,(0, 0,0,0,0,0,0,0,0)),(3,II,(0,1,1,1,1)),(3,III,(0,0,1, 0)),(3,IV,(1,0,1)),(4,II,(1,0)),(4,III,(1,1,1,0)))) tabulatedforclarity.Ontheright:thecorresponding phenotype.Theobstaclesareindicatedbyhatched areas.TheterminalsareindicatedbyGreekletters.In thiscase,thebudshaveaformofpentagons(indicated byblack).BudsandbudfacesareindexedwithArabic andRomannumerals,respectively.Thecorresponding elementsareshowninthesamecolors.Stemsandtwigs areshownin“reddish”and“bluish”colors,respectively. Thefirstunitisindicatedbyathickblackoutline.It startsfromthe“virtual”unitshownbyagraydottedline

directionofthestructure,respectively.2)SC2:the basicunitofthisqEMScanbeaddedinthreeways:at theright,front,andleftface,asindicatedbynumbers 1,2,and3,respectively.

Ingeneticalgorithms,allcandidatesolutionshave setsofpropertiesencodedinso‐calledgenotypes,usu‐allyasbinarystrings,arrays,trees,lists,ormatrices, whichcanbemutatedand/oraltered[6].

AphenotypeisanactualEMSwithits(physi‐cal)formandstructureencodedinagivengenotype. Obviously,thereisabijection(one‐to‐onecorrespon‐dence)betweenthesetofgenotypesandphenotypes.

Figure6illustratesthenature‐inspirednamingfor thecomponentsofanEMSphenotypeandpartsofthe correspondinggenotype,whichisasimplenestedlist.

AsillustratedinFigure 5,EMS‐2iscomprisedof two typesofelements:thebasic unit and bud.The units havetwoorientations:0and1,andeach stem endswithapentagonal bud.Fortheconsistencyof notation,theinitialunitisalsoattachedtoa“virtual” bud. AsmentionedintheIntroduction, plesiohedra [4] arenotconsideredasEMSs.Thecubeistheonlyreg‐ularsolidthatisalsoa plesiohedron [5].Nevertheless, themulti‐branchedstructuresbuiltwithspace‐ illing polyhedracanalsobeencodedinthesameway.Fig‐ure7showsthegenotypeofthe2Dprojection(SC2) ofthecube‐basedqEMSstructure(SC3)showninFig‐ure2.2.

AsFigures3and4indicate,thehierarchicalstruc‐turesofEMS(andquasi‐EMS)arede inedasfollows: i. Ingeneral,thestructureisconstructedwith branches

ii. Branchesare:stemsandtwigs.

iii. Stems endwith buds. Twigs donothave buds.

Figure7. SC2:the2DprojectionofSC3 structureshown inFigure 3.2.Thegenotypeisshownontheleft,andthe correspondingphenotypeisshownontheright.The respectivecorrespondingelementsareshowninthe samecolors.Thelastunitofeachstemfunctionsasa budandisindicatedbyadiagonalhatch

iv. Buds canhaveanynumberoffaces(BFs)

v. A branch canbeconnectedonlytoa bud

vi. A stem hasatleastoneunit.Inthecaseofaone‐unit long stem,itbecomesa bud

vii. Stems mustnotformclosedloops.

viii. The irst stem isconnectedtoa“virtual” bud

ix. The irst stem isalso rooted totheinitialterminal. Therearenomore stems directlyattachedtoa terminal.

x. Aterminalcanonlybereachedbya twig, exclusive ofthe irst stem andterminal.

Genotypeofan ��ℎ ExtremelyModularSystem �� isencodedasasequenceof branches. Thesequence of branches includestwosub‐sequencesof stems and twigs:

Gi ∶(Si,Ti)

Si ∶(s1,s2,…,sn)

Ti ∶(t1,t2,…,tm)

whereS�� and T�� arethesequencesof nstems and m twigs,respectively.

Moreover, s�� isa j��ℎ stem fromthesequenceof stemsS�� encodedinthefollowingway:

�� ∶(��,��,��,��)

where: j istheindexofthe j��ℎ stem, p�� isits j��ℎ parent, theindexofthatisthestemtowhichthe j��ℎ . f�� istheindexofthefaceofthe parent’sbud(to whichthejthstemisconnected),anduisthesequence ofunitsthat constitutethe j��ℎ stem

Units u dependonthetypeofEMS.E.g.,forthe systemsshowninFigures3.1and3.2: u ∈(0,1)and u ∈ (1,2,3),respectively. Buds alsodependonthetypeof EMS.E.g.,Truss‐ZandSC3 donothaveadditionalunits for buds

InTruss‐Z,budsareconstructedbyre lectingthe lastunitinthestemsequenceacrossthelongerbase ofthetrapezoidalunit.

InSC3,thelastunitina stem servesasabranching bud.Ontheotherhand,the buds forEMS‐2systems canhaveanyshape.IntheexamplesshowninFig‐ures: 3.1, 6 and 8 & 9 theyare:dodecahedron,pen‐tagonandheptagon,respectively.

Sincethe irst stem doesnothavea parent, p1,and f1 aredummies(blank).

The k��ℎ twig fromthesequence T�� isde inedinthe followingway:

�� ∶(��,��,��)

where p�� isthe parentingstem towhichthis twig is connected,

f��,istheindexofthefaceofthe parent’sbud (to whichthe k��ℎ twig isconnected), u�� isthesequenceof unitsthatconstitutethe k��ℎ twig.

Thereisafullanalogybetweenthelistof twigs and stems

3.OperatorsontheEMSGenotype

TherearesevenoperatorscollectedinTable1that allowtheconstructionofanyEMSorthetransforma‐tionofanyEMS�� toanyotherEMS��

Inaddition,fouroperatorsforthepopulation‐basedalgorithmarede inedandlistedbelow.

Randomgenotypegenerator

rG[(smin,smin),(tmin,tmax),(umin,umax)]

where s isthenumberof stems, t isthenumberof twigs,and u isthenumberofunitstobegeneratedin all branches

Fixgenotype

��[��,��,��,��]

where G��,isthegiven k��ℎ genotype, s isthedesirednumberof stems, t isthedesirednumberof twigs, l isthenumberofunitsgeneratedrandomlyin additionalbranches,ifapplicable.

Tabulategenotype

Thisfunctiontranscribesgenotype G�� intomatrix ��[��] withrespecttothe buds.SeeFigure 8 foran illustrativeexample.

Compare(tabulated)genotypes

��[��,��]=Δ(��∗[��],��∗[��])

Table1. StepsforcreatinganExtremelyModular Systemoritstransformation

Figure8. Fromtheleft:thegenotype;topright:the correspondingtabulatedgenotype;onthebottomright: thecorrespondingphenotype

Figure9. Calculationofthedifferencebetweentwo exemplarygenotypes.Thedifferencesforall correspondingbranchesaresummedupandmultiplied bythepenaltyweightwP.Missingcorresponding branchesareindicatedbydashedarrows.The differencebetweenthetwoemptylistsis0

where T* [G��]isthenormalizedandtabulatedgeno‐type G�� and T* [G��]isthenormalizedandtabulated genotype G��.

Normalizationheremeansthat T[G��]and T[G��] havethesamegeneralstructure.Forexample,ifthe dimensionsofthesegenotypesdiffer,dummyele‐mentsareadded.Moreover,��[��,��]≥0 Δsumsupthedifferencesbetweenthebit‐strings ofrespective branches ofthecomparedgenotypes. Figure9illustratesthewayhowΔiscalculated. Finally,fourtypesofmutationandtheircombina‐tionhavebeende inedasfollows:

Displace‐branch‐mutation

MdB [��,��]

where �� isthe ��ℎ genotype, �� isthenormalized intensityofmutation,sothatfor0thereisnodisplace‐mentandfor1allbranchesaredisplaced.

Add‐unit‐mutation

MaU [��,��] inthiscase,�� isnormalizedsothatfor0,nounitsare added,andfor1,thenumberofunitsisdoubled.Loci fortheaddedunitsaredistributedrandomlyamong the branches.Thevaluesoftheaddedunitsarerandom integers:0or1.

Remove‐unit‐mutation

MrU [��,��]

Unlike stems, twigs canhavezerolength.Here, m�� is normalizedsothatfor0,nounitisremoved,andfor 1,allunitsbutonerandomlyselectedunitper stem areremoved.Thelociforunitstoberemovedare distributedrandomlyamongthe branches

Invert‐unit‐mutation

MiU [��,��]

where m�� isnormalized,sothatfor0thereisno changetoanyunit,andfor1thevaluesofallunits areinverted.Thelociforunitstobeinvertedaredis‐tributedrandomlyamongthe branches

Multi‐mutation(combinesalltypesofmutations definedpreviously)

where m�� isthenormalizedintensityofmutation, M randomlyselectsthemutationtypeaccording toparameters w��, w��, w��,and w��, whicharethe normalizedweights(from0to1)forcorresponding mutations: MdB, MaU, MrU,and MiU.

4.MinimizationbyEvolutionStrategy

EvolutionStrategyisaclassicnature‐inspired heuristicmethodintroducedin[7].

Unlikeotherevolutionaryalgorithms,itdoesnot employrecombinationbutonlyintensivemutation. Forareviewoftheliteratureonthismethod,see[8].

Thisexperimentisatwo‐objective minimization de inedasfollows:

1) Createalayoutofamulti‐branchTruss‐Z(MTZ).

2) Therearesixterminalsatgivenlocations:the initialterminal(T��),and ivealignedterminals T1...T5,asshowninFigure15.

3) The(initial)directionofthe irstunitisgivenatT��

4) Thenumberofunitsistobeminimal

5) The reachingerror (rE)istobeminimal(explained below).

Reachingerror (rE)isthesumofdistancesbetween eachterminalandrespective twig tips,asillustrated inFigure10

ThecostfunctionCFforagiven i��ℎ multi‐branch Truss‐Z(MTZ��)with m numberofdestinationtermi‐nalsiscalculatedasfollows:

where n isthetotalnumberofunitsinMTZ,�� isthe distancebetweenthe i��ℎ terminalandcorrespond‐ing twig tip, w�� isthepenalizingweightadjustedby trial‐and‐error;forsmallvaluesof w�� algorithmgets stuckinlocalminimaandasaresult,solutionsdonot improve.

Figure10. Inthiscase,reachingerrorrE=2.25+0.95+ 0.58+0.63+1.19=5.6.Thenumberofunitsn=54. Stemswithbranchingunitsareindicatedingray.Twigs arewhite

Figure11. Sub‐figures1,2,3,and4showallowable MTZsconnectingfiveterminalswith:2,3,4,and5 stems,respectively

Theinitialpopulationisgeneratedrandomlyusing rG operatordescribedabove.However,itisrationalto startfromthemostreasonableinitialpopulationby usingcertainobservations.E.g.,thenumberof twigs mustbeexactly5.Thisisbecauseonlytwigscanreach theterminals,andthereare iveofthem.However, withthenumberof stems itisnotsoobvious.Figure11 showsfourdifferentallowableMTZcon igurations connecting iveterminalswiththeinitialterminalTS Therefore,thenumberofstemsineverycandidate solutionmustbewithintherange[2,5].Theinitial populationof200MTZshasbeengeneratedwiththe followingparameters:

rG[(smin,smax),(tmin,tmax),(umin,umax)] thenumberof stems: s�� =2, s�� =5; thenumberof twigs: t�� = t�� =5; thenumberofunitsineach branch: u�� =5, u�� =15.

Severaltrialsatvariouscombinationsofparame‐tershavebeenperformed.Eachexperimenthasbeen terminatedafter100iterations.Figure 12 showsthe bestphenotypesinthe inaltrial.

AsFigure 12 indicates,inthebeginning,several individualswereinfeasibleduetoself‐intersection. Nevertheless,relativelysoon,thisproblemdisap‐peared,asgraduallythefeasibleoffspringwerepro‐ducedbyinfeasibleparents.Figure13showsthe inal solutionanditsthree‐dimensionalinterpretation.

Figure12. ThefinaltrialoftheEvolutionStrategy‐based experiment.Foreachphenotype,thegeneration number(g),thereachingerror(rE),andthenumberof units(n)areshowninthebottomrightcorner.There hasbeennofurtherimprovementafter39generations. Stemswithbranchingunitsareindicatedingray.Twigs arewhite

Figure13. 1)ThebestMTZlayoutproducedby EvolutionStrategy.2)Thethree‐dimensionalMTZbased onthislayout

5.Conclusion

Theconceptofhierarchicalstructureshasbeen outlinedinthecontextofExtremelyModularSystems. Thebiology‐inspirednomenclature,geneticencoding, andoperationsforthisclassofstructureshavebeen explainedandillustrated.

Althoughtheevolutionstrategy‐basedalgorithm presentedherehasnotbeenoptimizedforef iciency, itshowsrelativelygoodconvergence.Formoreinfor‐mationonthisapproach,see[9].

AUTHORS

ElaZawidzka∗ –ORCID:0000‐0003‐1243‐9355, DepartmentofIntelligentTechnologies,Institute ofFundamentalTechnologicalProblemsofthe PolishAcademyofSciences,Poland,e‐mail: zawidzka@ippt.pan.pl.

MachiZawidzki –ORCID:0000‐0001‐8695‐4400, ŁukasiewiczResearchNetwork,IndustrialResearch

InstituteforAutomationandMeasurementsPIAP, Poland,e‐mail:zawidzki@piap.lukasiewicz.gov.pl.

∗Correspondingauthor

References

[1] M.Zawidzki, Discreteoptimizationinarchitecture: Extremelymodularsystems.Springer:Singapore, 2017.

[2] M.ZawidzkiandK.Nishinari,“ModularPipe‐ZSystemforThree‐DimensionalKnots,” Journal forGeometryandGraphics,vol.17,no.1,2013, pp.081‐087.

[3] M.Zawidzki,“CreatingOrganic3‐Dimensional StructuresforPedestrianTraf icwithRecon ig‐urableModular‘Truss‐Z’System,” International JournalofDesign&NatureandEcodynamics,vol.8, no.1,2013,pp.61–87.DOI:https://doi.org/10.2 495/DNE‐V8‐N1‐61‐87.

[4] B.GrünbaumandG.C.Shephard,“TilingsWith CongruentTiles.” Bull.Amer.Math.Soc.,3,1980, pp.951–973.

[5] M.Gardner, TheSixthBookofMathematicalGames fromScienti icAmerican.UniversityofChicago Press:Chicago,IL,1984.

[6] A.E.Eiben,J.E.Smith,eds., EvolutionaryAlgorithms,inF.Neri,C.Cotta,andP.Moscato: HandbookofMemeticAlgorithms,StudiesinComputationalIntelligence,vol.379,Springer,2012, pp.9–27.DOI: https://doi.org/10.1007/978‐3‐642‐23247‐3_2

[7] I.Rechenberg,“Evolutionsstrategie:Optimierung TechnischerSystemeNachPrinzipienDerBiolo‐gischenEvolution,”Ph.D.thesis,Stuttgart,1973 (inGerman).

[8] T.Bäck,F.Hoffmeister,H‐P.Schwefel,“ASurvey ofEvolutionStrategies,inR.K.BelewandL.B. Booker(Eds.),” ProceedingsoftheFourthInternationalConferenceonGeneticAlgorithms.Univer‐sityofCalifornia,SanDiego,MorganKaufmann, 1991.

[9] M.Zawidzki,“OptimizationofMulti‐BranchTruss‐ZBasedonEvolutionStrategy,” AdvancesinEngineeringSoftware,vol.100,2016,pp.113–125. DOI: https://doi.org/10.1016/j.advengsoft.2 016.07.015

Submitted:12th November2024;accepted:13th January2025

AdamM.Górski,MaciejOgorzałek

DOI:10.14313/jamris‐2025‐016

Abstract:

Thispaperpresentsagreywolfalgorithmforaconcur‐rentreal‐timeoptimizationprobleminsearchingforan optimalgame‐solvingsolution.Therearemanysolutions tothegame.Eachsolutioncandemanddifferentoptimal valuesofdifferentparameters.However,somewaysthe playerstrytosolvethegamedonotleadtosuccess. Theoptimizationproblemconsistsoftwophases.Each phaseimpactsthesecondoneinrealtime.Thefirstphase isresponsiblefortheoptimizationoftheparameters. Thesecondphasevalidatesthechoiceandoptimizes theparameters.Asanoptimizationmethod,wechose greywolfoptimization.Atthebeginning,thealgorithm generatesseveralsolutions.Thesolutionwiththevalue oftheparametersclosesttomaximumisthepositionof analphawolf.Therestofthesolutionsare,accordingto thevaluesoftheparameters,splitintothepositionsof beta,delta,andomegawolves.

Keywords: concurrentreal‐timeoptimization,greywolf optimization,metaheuristics,swarmintelligence,game theory

1.Introduction

Gamescanveryrealisticallysimulatealotofreal situationsofdailylife.Suchsimulationsareeasyto make,cheap,andhavenoconsequencesinreallife. Theycanalsoimproveexistingsolutionsorindicate theirweakpoints.Insteadofputtinghumanlifein dangerorlosingsomeexpensivehardware,itisbetter toplayagame.Moderncomputergameshavebecome morecomplex.Theyallowforcheckingmoreand moreaspectsofthesituationtheysimulate.However, checkingeverypossiblesolutiontosolvethegame cantaketoomuchtimeandistooexpensive.Whatis more,somewaysdonotleadtosuccess.Therefore,it isveryimportantto indthebestsolutionsandelimi‐natethewrongones.Butwhatdoesthebestsolution mean?Gamescanbesolvedinmanyways.Eachway demandsdifferentvaluesofmanydifferentparame‐ters.Thequestioniswhichparameterstheplayers shouldchooseandwhattheiroptimalvalueswillbe whenthetimetosolvethegameislimited.Ascanbe observed,theoptimizationprocessmightbesplitinto twophases.The irstphasechoosestheparameters thatneedtobeoptimized.Thesecondphaseveri ies thechoiceandoptimizestheparameters.

Everychangeinthesecondphasemakeschanges inthe irstone.Ifthe irstoneismodi ied,theopti‐mizationinthesecondonealsomustbechanged. Therefore,theprocessdescribesconcurrentreal‐time optimization[1].Suchatypeofoptimizationwaspro‐posedbyGórskiandOgorzałekto indunexpected tasksintheIoTdesignprocessandtheiroptimal assignment.

Inthispaper,agreywolfalgorithmwasimple‐mentedforaconcurrentreal‐timeoptimizationpro‐cessofsearchingforthebestsolutiontosolvecom‐putergames.Tothebestofourknowledge,suchan optimizationproblemhasnotbeeninvestigatedin gametheorysofar.Solvingthisproblemcanhelpto automatically indthesolutiontocomputergames.

Thepaperisorganizedasfollows:thesecond chapterincludesrelatedwork,thethirdonedescribes theimplementationofgreywolfoptimizationtoinves‐tigatedproblem.Inthenextsectiontheexperimental resultsaregiven.Thelastchaptercontainsconclu‐sionsanddirectionsoffuturework.

2.RelatedWork

Concurrentreal‐timeoptimization[1]isanew kindofoptimization.ItwasproposedbyGórskiand Ogorzałek[1].Suchatypeofproblemindicatesthat therearetwooptimizingphases.Eachphaseimpacts anotherinrealtime.Changesinonephasemake changesinthesecondoneinreal‐time.The irstphase isresponsibleforthechoiceofparameterstoopti‐mize.Thesecondphasevalidatesthechoiceandopti‐mizesit.However,duringtheoptimizationprocess, theparametersmaybechanged.Suchaproblemwas calledapickinganappleproblem.Therearemany possibilitiestopickanapple.Forexample:climbing atree,shakingatree,usingatooloraladder,etc. Dependingonthechoice,therearedifferentparam‐eterstooptimize.Itisveryhardtoestablishwhich wayisbest.Moreover,insomecases,notalltheways topickupanapplearepossible.Thesolutionscan becharacterizedbysomecommonparametersthat canbeusedtoevaluatethequalityoftheresultsand choosethebestone.Thesamesituationcanbefound ingametheory.Therearemanypossiblewaystosolve agame.Eachonedemandsdifferentactionstakenby aplayerandthereforedifferentvaluesofavailable parameters.

However,dependingonthesituationinagame‐play,increasingthevaluesofsomeoftheparame‐tersdoesnotleadtosolvingthegame.Thecommon parameterforeverysolutionisthetimenecessary tosolvethegame.Suchaproblemwassolvedin IoT[1]andembeddedsystems[2]designtodetectand assignunexpectedtasks.In[33],theauthorsproposed ageneticprogrammingapproachfordetectingand assigningunexpectedtasksintheSoCdesignprocess. Sofar,everyoneofthealgorithmssolvingconcurrent real‐timeoptimizationproblemshasbeenproposedin hardwaredesign.However,theprobleminhardware designisdifferent.Thehardwarewasspeci iedbythe taskgraph[34].Therefore,thehardwareisneeded toexecutesometasks.Thearchitectureconsistedof twokindsofprocessingelements:programmablepro‐cessors(PPs)andhardwarecores(HCs).PPswere abletoexecutemorethanonetask,whileHCswere dedicatedtoexecutingonlyonetask.Thetaskswere characterizedbytwoparameters.Usually,itwastime andcost.Thefasterthearchitecture,themoreexpen‐siveitwas.Therefore,inhardwaredesign,concurrent real‐timeoptimizationbelongstotheParetogroup ofproblems[35].Ingametheory,suchasituation doesnotoccur.Modifyingonefeatureofthecharacter doesnotdecreasethevalueofanother.In[36],Górski proposedanextensionofataskgraphforreal‐life problems.Suchanextendedtaskgraphcanallowfor theproposalofsolutionsinmoreareas.

2.1.GameTheory

Gametheorydescribesthewaytosolveagame usingmathematicalformulas.Everygameconsistsof fourparts[3]:

‐ Players–personswhoplaythegamebycontrolling characters.

‐ Actions–actionsthataretakenbytheplayersto solvethegame.

‐ Strategies–awaychosenbytheplayerstosolvethe game.

‐ Payoff–return(positiveornegative)obtainedbythe playersaftertakingtheactions.

Thecharacterscontrolledbytheplayersduringthe gameplaycanbecharacterizedbymany,sometimes different,parameters(abilities).Generally,thevalues ofthoseparametersarenotconstantduringgameplay. Theopponents,oftencontrolledbythecomputer,also havedifferentvaluesofthesameparameters.Theval‐uesoftheparametersforthecharacterscontrolledby thecomputercanalsobemodi ied.In[4],theauthors proposedusinggraphdatabasestoimprovearti i‐cialintelligenceingames.Theplayersmustchoose thestrategyforevolvingthecharactersandsolving thegame.Inmultiplayergames,thestrategiesmust includeanin luenceofoneplayer’sbehavioronthe rest[5].In[6],theauthorsproposedagraph‐based modeltoautomategamestorygeneration.Unfortu‐nately,theproposedsolutiondidnotincludeevery aspectofthegameplay.

Ingametheorylargegroupofgamesareseri‐ousgames[7].Thepurposeofsuchgamesisnot onlyentertainment.Theyareusedinnurseeduca‐tion[8],languagelearning[9],learningculturalher‐itage[10],onenvironmentalmanagement[11]andin manyotherareasofdailylifemostlycommonwith trainingandeducation.

2.2.GreyWolfOptimization

Greywolfoptimization(GWO)wasproposedby Mirjalili,Mirjalili,andLewisin2014[12].Itisa kindofswarmintelligencealgorithm,likeparticle swarmoptimization[13],grasshopperoptimization algorithm[14],whaleoptimizationalgorithm[15], orDragon lyAlgorithm[16].GWOisasimulationof huntingpreybyagroupofwolves.Ineverygroupof wolves,thereisaleadercalledthealphawolf.The leaderisclosesttotheprey.Thenextpositionbelongs toBetaWolf.Abetawolfisacandidateforbecoming analpha.Thethirdinorderisthedeltawolf.Thelastin ahierarchyareomegawolves–therestofthegroup. SuchahierarchyispresentedinFigure1below.

HuPanandChuproposedabinarygreywolfopti‐mizer(BGWO)tosolvebinaryproblems[17].

GWOiswellknowntostopatthelocalminima whenoptimizingparameters.Therefore,duringthe lastfewyears,somemodi icationshavebeenpro‐posed.Oneofthemodi icationsisbasedontheusage ofmapslikecirclemaps[18]andchaoticmaps[19, 20].AnotherimprovementtoGWOisanadaptive greywolfoptimizer(AGWO)[21].Suchamodi ication allowsthealgorithmtoprovideoptimalvaluesfaster byusingathree‐pointhistoryofparametervalues. In[22],theauthorsproposedusingchaostheoryto improvethealgorithmbymakingitmoreproneto avoidinglocalminimawhenoptimizingparameters. Hybridsolutionswerealsoproposed,likeconnections ofGWOand��‐hillclimbingalgorithm[23]called��‐hill climbinggreywolfoptimizer(��‐HCGWO).

Figure1. Chierarchyinagroupofwolves

In[24],abeetleantennastrategythatallows the �� wolftohearandthusimprovethehunt‐ingstrategy.Yangandothersproposedtomodify thepositionupdatestrategybyaddinginformation about��wolves,makingtheiterationsnonlinear[25]. In[26],theauthorsproposedagroup‐statecompe‐titionstrategytoextendthesearchspaceofGWO. Nadimi‐Shahraki,Taghian,andMirjaliliproposedan improvedgreywolfoptimizer(I‐GWO)[27].I‐GWO implementedadimensionallearninghuntingstrategy. Thestrategywasbasedonthebehaviorofasinglewolf huntingstrategyinnature.

Greywolfoptimizationwasimplementedto: parameteridenti icationofphotovoltaiccells[28], taskscheduling[29, 30],solvingengineeringprob‐lems[27],pathplanning[31,32],andmanyothers.

3.TheMethodology

Everygamecanbesolvedinmanyways.Every waydemandsadifferentcombinationofvaluesof differentparameters.Inmostgames,thereisamain charactercontrolledbyaplayer.Thecharacterhasa setofparameters.Inourmethodology,suchasetis representedbyavectorvconsistingof n numbers.The vectorispresentedbelow:

v=[v1,v2,…vn] (1)

Theplayercanevolvethecharacterduringthe game.However,inmanycases,timeforevolutioncan belimited.Moreover,theopponentscanevolvecon‐trolledcharactersduringthegameplay,too.Special featuresoftheopponentscanalsomakeevolvingone oftheparametersuseless.Tosolvethegame,oneof thewinningcombinationsofalltheparametersmust befound.Achievingthesetofparametersthatallows solvingthegamecantakedifferenttimes.Therefore, thetimeofevolution,thecharacter,orthenumberof iterationsofevolutionarecommonparametersthat allowustoevaluatethequalityoftheresults.Inthis paper,weconcentrateon indingthebestwaytosolve thegame,understoodastheminimumnumberofiter‐ations(Ib)demandedtoachievetheappropriatesetof parameters:

Ib =min(I) (2)

WhereIisthenumberofiterations.

Atthebeginning,apopulationofmwolvesisran‐domlycreated.

m=nv ∗np (3)

Where:np isthenumberofoptimizingparameters andnvisthenumberofwinningcombinationsofthe parameters.

Next,allsolutionsaredividedintoappropriate groups:alpha,beta,delta,andomega.Thedistance(D) betweenagreywolfanditspreycanbecalculated usingtheequationbelow:

Asheafgraphpresentingasingleiteration

InEquation(4),Xp describesthecoordinatesof aprey,andXw describesthecoordinatesofthegrey wolf.Acanbecalculatedasfollows:

A=2∗d (5)

Wheredisarandomvaluebetween0and1,as wassaidbefore,inthegame,thereisanestablished setofvectorsthatincludesminimumcombinations ofvaluesthatallowdefeatingtheopponent.Those arepotentialpositionsthatallowthewolvestoattack theprey.Therefore,theproblemismulticriteria.The valueofeveryparametercannotbedecreased.For example,thecharactercannotlosepointsofstrength aftertraining.Theproposedalgorithmchoosesran‐domlyoneoftheparameters,vc,andchangesitsvalue inthefollowingway:

WherePcanbeestablishedusingthefollowing equation:

Whererischangedproportionallytothenumber ofiterationsfrom2toamaximumof0ineachiter‐ation,butthisvalueiscalculatedforeachparame‐terseparately.Thisoperationshortensthedistance betweenthewolvesandtheprey.Suchasituationis presentedonasheafgraph[6]below:

Figure 2 presentsasimpleproduction(oneiter‐ation)–increasingthestrengthofacharacter.The characterisinlocation1andischaracterizedby3 parameters:strength,endurance,andcleverness.

Thenumberofiterationsislimited.Becausenot everywayleadstowinningagame,theobtained resultcanbeinvalidinsomerunsofthealgorithm. Therefore,usingthemethodologypresentedinthis papercanhelptoestablishthesetsofmovementsthat willnotallowonetowinthegame.Thegoalofthe algorithmisto indthefastestwaytosolveagame. Asthefastestwaytosolveagame,weunderstand theminimalnumberofiterationsnecessarytowina game.

4.ExperimentalResults

Tocheckthequalityoftheobtainedresults,we decidedtoanalyzeascenarioofapartofanarcade game.Inthescenario,theplayerchoosesoneof thecharactersbelongingtothreegroups:magicians, knights,andvillagers.

Figure2.

Everycharacterhassomeabilities(parameters), suchasstrength,endurance,magicability,etc.The playerevolvesthechosencharacterinapossiblenum‐berofiterations(Imax).Ineachiteration,itispossible toevolveonlyoneability.Thereareafewcombina‐tionsofthevaluesofparametersthatallowonetowin thegameanddefeattheopponent.

Aswaswrittenbefore,tothebestofourknowl‐edge,thispaperisthe irsttodealwithaconcur‐rentreal‐timeoptimizationproblemingametheory. Therefore,itisveryhardtocomparetheresults becauseofthelackofsolutionsforsuchade ined problem.Wedecidedtocomparetheobtainedresults witharandomalgorithm.Suchanalgorithmgenerates theinitialsolutionrandomlyandrandomlyselectsone oftheparametersandincreasesitbyarandomlycho‐senvaluefrom0,1to1.Inthefuture,weplantopro‐posemoreapproaches,like,forexample,PSO,forsuch aproblemandcomparetheresults,butsofar,other algorithmsforconcurrentreal‐timeoptimizationin gametheoryhavenotbeendeveloped.Aswassaid before,existingalgorithmssolvingconcurrentreal‐timeoptimizationinhardwaredesigncannotbeused ingametheorybecauseofthespeci icationoftheenvi‐ronmentinwhichtheywork.Theyworkwithdifferent constraints,differentnumbersofoptimizingparam‐eters,differentbehavioroftheparameters(Pareto problem),andotherenvironmentalconditions.Itdoes notmeanthatitisimpossibletousegeneticpro‐grammingorgeneticalgorithmstosolvetheproblem ingametheory,butsuchalgorithms,whichwillbe equaltoworkinthegameenvironment,needtobe developed.

Theexperimentsaredividedintotwogroups.The irstgroupofexperimentswasmadeforthreeevolv‐ableparameters.Thesecondgroupofexperiments wasmadeforfourevolvableparameters.InTable 1 below,theobtainedresultsforthreeabilitiesofachar‐acter(parameters)arepresented.Theexperiments weremadefordifferentnumbersofwinningcombi‐nations(for ivewinningcombinations).Anumberof winningcombinationsinTables1and2weremarked withtheletterw.Foreachnumberofwinningcom‐binations,50triesweremade.Webelievethatsuch anumberofrunsisenoughtoprovideagooddis‐cussionoftheresults.InTable1,theresultsobtained dependonthenumberofmaximumiterations.Imax is aconstraintonthenumberofiterations.Ib represents theminimumiterationin50runsinwhichthewolves achievedthepositionallowingthemtoattacktheprey. Ia istheaveragenumberofiterationsfromallofthe validruns.AlltheexperimentsweremadeforImax equalto:5,10,20,and50.

Inthe irstsetofexperiments,therewerefour winningcombinationsofthreepossibleparameters. Asexpected,oneofthetargetvectorswasobtainedin thelowestaverageiterationwhentheconstraintwas thesharpest(5iterations).Thevaluewasequalto4.

Figure3. Apercentagepresentationofanumberof validresultsforthefirstsetofparametersforthefirst groupofexperiments

Theaveragenumberofiterationsinwhichthewin‐ningcombinationofparameterswasachievedgrew withthenumberofpossibleiterations–7forImax equalto10,10forImax equalto20,and11forImax equalto50.Thepercentagevalueofvalidruns(thetry whenavalidresultwasobtained)wasthelowestfor thesharpestconstraint.Whenthemaximumnumber ofpossibleiterationswasequalto5,validsolutions wereobtainedonlyin14%ofruns.Whenthenumber ofpossibleiterationswasequalto10,thenumberof validrunsincreasedto56%.ForImax equalto20,the percentagevalueofvalidobtainedresultswasequal to92%.ForImax =50 ineveryrunvalidsolution wasgenerated.Ascanbeeasilyobserved,theresults obtainedbythegrey‐wolfalgorithmweremuchbetter thanthoseobtainedbytherandomsolution.Thebest obtainedresultsusingtherandomalgorithmwere:9 (forImax equalto10and50)and10(forImax =20). Thepercentageofvalidsolutionsisalsoworseforthe randomalgorithm.MeanwhileforImax =50 and20 theresultsweresimilar(respectively100and88),for alowervalueofImax operator(Imax =10)itwas only8%.ForImax =5,therandomalgorithmwasnot abletogenerateanyvalidsolution.Figure3showsa graphicalpresentationofthegeneratedvalidsolution dependingontheImax constraintforresultsobtained bytheGrey‐wolfalgorithm.

Forthesecondsetofexperiments( ivewinning combinationsandthreeparameters),thestatistics wereverysimilartothoseofthe irstset.However, asweexpected,thepercentageofachievedwinning solutionsgrew.Suchvalueswereachievedbecause whenthenumberofpossiblesolutionswasgreater, itshouldbeeasiertoobtainavalidsolution–there isonemorewinningcombinationoftheparameters. Theresultswereequalto20%forImax =5,60% forImax =10,94%forImax =20,and100%when Imax isequalto50.Thatdependencywaspresented inFigure4.Thepercentageofwinningsolutionsfora randomalgorithmwasalsohigher.ForanImaxequal to20and50,itwas92and100percent.ForImax =10, itwas18.ForImax =5,thealgorithmwasnotableto generateavalidsolution.

Table1. Theresultsforthreeparameters

Figure4. Apercentagepresentationofanumberof validresultsforthesecondsetofparametersforthe firstgroupofexperiments

Theexperimentsweremadeinthesamewayas forthe irstgroup–withdifferentnumberofpossi‐bleiterations:5,10,20and50.Aftercomparingthe resultswiththe irstgroupitcanbenoticedthatthe bestresultsforeachImax weregeneratedlater.

Forthe irstset(fourwinningsolutions),when Imax =5 andImax =10,itwasinthe4thiteration, forImax =20 inthe6thiteration,andinthe5th iterationforImax =50.Inthesecondset,theresults wereasfollows:5thiterationforImaxequalto5,10, and20,and6thiterationforImax =50.Theaverage numberofiterationshasalsogrown.Forthe irstsetof experiments,itwasequalto:5(Imax =5),9(Imax =9), 15(Imax =20),and19(Imax =50).Inthesecond partofthesecondgroupofexperiments,theaverage resultswereequalto:5forImax =5,9forImax =10, 14forImax =20,and16forImax =50.Suchresults ofexperimentswereexpectedbecauseinthesecond groupofexperiments,thereweremoreparameters thatneededtobeevolvedbyaplayer,thusgenerating avalidcombinationofparameterscouldtakemore time.Similarly,asforthe irstgroupofexperiments, theaveragevalueofiterationsdecreasedwhenthere weremoretargetcombinationsoftheparametersthat allowedsolvingthegame.InFigure5,thedependency ofthepercentageofgeneratingvalidsolutionsfor differentmaximumnumbersofpossibleiterationsfor agreywolfalgorithmwaspresented.

Figure5. Apercentagepresentationofanumberof validresultsforthefirstsetofparametersforthe secondgroupofexperiments

Thelowestvalueofvalidsolutions,22%,was obtainedwhenImax =5.ForImax =50 inevery runofthealgorithm,avalidsolutionwasgenerated. ForImax =10,itwas56%,andforImax =20 it was94%.Arandomalgorithmwasnotabletoprovide avalidsolutionforImaxequalto5and10forboth partsofthesecondgroupofexperiments.Evenfor Imax =20,therandomalgorithmprovidedonly10% (forfourwinningsolutions)and4%(for ivewinning solutions)ofvalidresults.

Thealgorithmwasalsoslowerthanthegrey‐wolf algorithm–itneededtogenerate,onaverage,for Imax =20:19(w=4)and20(w=5)iterationsand forImax =50:27(w=4)and25(w=5)iterations. Thegraphicalrepresentationofthepercentageofgen‐eratingvalidsolutionsfordifferentnumbersofImax forthesecondpartoftheexperimentsforagreywolf algorithmwaspresentedinFigure6below.

Likeforthe irstgroupofexperimentswith increasingthenumberofwinningcombinationsofthe parameters,thepercentageofobtainedvalidsolutions wasgrowing.Itwasequalto30%forImax =5,68%for Imax =10,94%forImax =20,and100%forImax = 50.Thepercentageofvalidresultsobtainedforthe secondgroupofexperimentswasabithigherthanfor the irstone.Wewereexpectingthatthevalueforthe secondgroupofexperimentscouldbelowerbecause oftheincreasedtimetogenerateavalidsolution.

Table2. Theresultsforfourparameters

Figure6. Apercentagepresentationofanumberof validresultsforthesecondsetofparametersforthe secondgroupofexperiments

However,itmustberememberedthatresults obtainedusingtheGWOalgorithmarebasedonprob‐ability,andthenumberofvalidsolutionsobtainedfor bothgroupsofparametersisverysimilar.Onlyfor Imax =5,thedifferenceofthevalueoscillatesbetween 8–10%,butsuchasharpconstraintcouldnotbea goodreferencepoint.Whatisworthunderliningis thatinmostofthesetsoftheexperiments,thewinning combinationofparameterswasobtainedinmorethan halfoftheruns.Therefore,eventhoughonerunofthe algorithmdidnotproduceavalidsolution,therewas abigchancethatthesecondrunwouldgeneratethe winningcombination.

5.Conclusion

Inthispaper,thegrey‐wolfoptimizationalgorithm fortheconcurrentreal‐timeoptimizationproblemin gametheorywaspresented.Duetoourbestknowl‐edge,itisthe irstsolutionthatdealswiththeproblem ofreal‐timeoptimizationingametheoryandthethird areaofusageofsuchoptimization.Theimplemented algorithmiswellknowntobeveryfastbecauseitnar‐rowsdownthesearchspace.ItcausesGWOalsotobe wellknownforstoppinginlocalminimaofoptimizing parameters.However,thespeci icationoftheprob‐lem(morethanonetargetvectoroftheparameters) decreasessuchadisadvantage.

Comparisonoftheresultsobtainedbygreywolf algorithmwithsolutionsobtainedbyrandomalgo‐rithmshowstheeffectivenessofchosenalgorithmto investigatedproblem.Greywolfalgorithmwasable notonlytogeneratetheresultsfasterthanrandom solutionsbutalsogavevalidresultsevenwhenthe secondalgorithmdidnotprovideanyvalidresult.

Inthefuture,wewilltrytousesomemodi ica‐tionsofGWOandapplythemtotheproblemdis‐cussedinthispaper.Itisalsopossiblethatapplying anothermetaheuristiccangivegoodresultsinsolv‐ingtheinvestigatedproblem.Wewillalsocheckthe ef iciencyofevolutionarycomputationinthisproblem ingametheory.Concurrentreal‐timeoptimizationis quitenewproblemincomputerscience.Sofar,ithas beenusedtodetectunexpectedtasksintheIoTdesign process.Findingmoreareasofusage,thiskindofopti‐mizationalsoseemstobeagooddirectionofresearch.

AUTHORS

AdamM.Górski∗ –InstituteofAppliedComputer Science,JagiellonianUniversity,Poland,e‐mail: a.gorski@uj.edu.pl.

MaciejOgorzałek –InstituteofAppliedComputer Science,JagiellonianUniversity,Poland,e‐mail: maciej.ogorzalek@uj.edu.pl.

∗Correspondingauthor

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Submitted:16th August2024;accepted:23rd November2024

JoseEduardoLopez‑Ramos,OscarCastillo,PatriciaMelin

DOI:10.14313/jamris‐2025‐017

Abstract:

Inthispaper,afuzzyProportionalControllerwas designedandimplementedfordynamicallyadaptingthe velocityandmotionparametersinaquadrupedrobotfor autonomouslyfollowingagoal.TheFNK0050Freenove quadrupedrobotwasutilizedfortheexperiments,which has12degreesoffreedomandthushighercomplexity. Experimentalresultsshowthattheproposedfuzzycon‐trollersurpassesthestandardPIDcontrollerprovidedas defaultbythemanufactureroftherobot.

Keywords: fuzzycontrol,fuzzyproportional,quadruped robot

1.Introduction

Quadrupedrobotsaremachinesdesignedtoimi‐tatethemovementoffour‐leggedanimals.These robotshavefourextremities,eachofthemwiththeir ownsensorsandactuators,thatenableamovement similartoquadrupedanimals,suchasdogs,catsor horses[1–4].Quadrupedrobotshavebeenreceiving increasingattentionintheroboticsareabecausethey canhavemanyrealapplications,suchassearchand rescue,exploration,agricultureandentertainment[5–7].

Quadrupedrobotsaredesignedwiththegoalof imitatingtherealmovementofquadrupedanimals andrequireappropriatecontrolalgorithmsforachiev‐ingstabilityandequilibriumwhilemoving[8–10]. Thereareseveralkindsofquadrupedrobotsinthe literature,butweselectedonethathasnotbeenprevi‐ouslyconsideredwithfuzzylogic.Thisrobotiscalled RobotDogKitFNK0050fromFreenove,forwhich onlyaproportional‐integral‐derivative(PID)control existedinthepreviousliterature.Thisisanexisting researchgapinthestateoftheartthatwedecidedto considerasourresearchwork.

Thecontributionofthispaperistheproposed designofafuzzyproportionalderivative(PD)con‐trollerforthegoalfollowingproblem,whichcanbe viewedasanenhancementtotheexistingPIDcon‐troller.Themainideaisthatfuzzylogicenableshaving anonlinearcontrolmodel,whichcanprovidebetter resultsforcomplexproblems.Inthisway,fuzzyPD controlsurpassesthetraditionallinearPIDcontrolin thegoalfollowingtask.

Therestofthedocumentisstructuredasfollows: Section2explainsthequadrupedrobotutilizedinthis

work.Section 3 outlinestheexistingPIDcontroller forthisrobotandthentheproposalforafuzzyPD controller.Section 4 summarizestheexperimental results,andSection5offerstheconclusionsandfuture work.

2.QuadrupedRobotsandProblemDefinition

Inthissection,wedescribetheparticular quadrupedrobotutilizedinthisresearchwork. TheRobotDogKitFNK0050isoneofthemodelsfrom Freenove,whichisaquadrupeddesignwithopen codethatiscompatiblewithRaspberryPi.Ithasan acryliclightstructurewithseveralsensors,suchas acamera,anultrasoundsensor,agyroscopeandan accelerometer.Therobothasatotalof12degreesof freedom,whichmakesitanidealsystemforlow‐cost roboticapplications.Figure 1 showsaside‐viewof therobotdogafterassembly.Figure2depictsafront viewoftherobot.

Controllingthestabilityofquadrupedrobotsis veryimportantforseveralreasons:stabilitywillcon‐tributetoreducedlikelihoodoffalling,robustness againstexternalperturbations,energyef iciencyand improvedperformance.Inaddition,controllingthe motionoftherobotinfollowingatrajectorytoachieve aparticulargoalisveryimportant.Inthispaper, weareaddressingthislastproblembyproviding therobotwithacontrollerthatwillmaketherobot autonomouslymovetoachieveagoal.Figure 3 illus‐tratesthecontrolproblem,whichbasicallyconsists ofreachingthevalueofaninputcommandstarting fromaninitialpoint.InFigure 4,weillustratehow

Figure1. RobotDogsideview

Effectofdisturbancesonthecontroller disturbancescanaffectthebehaviorofthecontroller intheclosedfeedbackloop.

InFigure5weshowtheactualimplementationof thecontrollersintheservertocontrolthephysical robot.

Forthetestscenario,wecreatedtwocon igura‐tions:the irstonewithadistanceof1meterwiththe objectiveonthesideandanirregularterrain,andthe secondonewithadistanceof80centimeterswiththe goalinfrontandaplainterrain.Thesecon igurations couldgeneratetrajectoriesliketheonesillustratedin Figure6

3.ProposedFuzzyPDController

Inthissection,wedescribetheimplementationof thetwofuzzyPDcontrollers,oneforcontrollingthe directionandvelocityonthe x axis(tomaintainthe redballcenteredintherobotview),andtheother

Possiblerobottrajectories

tocontrolthedirectionandvelocityonthe z axis(to positiontherobotinthefrontoftheobjectiveata desireddistance.

Figure2. RobotDogfrontview

Figure3. Controlproblemdefinition

Figure4.

Figure5. Controllingtherobotwiththeserver

Figure6.

3.1.FuzzyPDControlleronxAxis

ThefuzzyPDcontrollerforthe x axisisstructured asillustratedinFigure 7,containingtwoinputsand twooutputs.The irstinputisthe error,andthesecond inputisthechangeoftheerrorcalled delta_error.The irstoutputisthevelocityofturning,andthesecond outputisusedtocontrolthedirection.Thefuzzysys‐temisoftype‐1Mamdaniform.

ThefuzzyrulesthatwereusedinthefuzzyPD controllertopositionthegoalinthecenterofthe x axis arelistedbelow.

1) Iferrorisleftand delta_error islowthen velocity is medium, direction isright

2) If error isleftand delta_error ismediumthen velocity islow, direction isright

3) If error isleftand delta_error ishighthen velocity islow, direction isright

4) If error iscenterand delta_error islowthen velocity ismedium, direction iscenter

5) If error iscenterand delta_error ismediumthen velocity islow, direction iscenter

6) If error iscenterand delta_error ishighthen velocity islow, direction iscenter

7) If error isrightand delta_error islowthen velocity ismedium, direction isleft

8) If error isrightanddelta_errorismediumthen velocity islow, direction isleft

9) If error isrightand delta_error ishighthen velocity islow, direction isleft

InFigure 8 weillustratethenonlinearsurfaceof thefuzzyPDcontrollerforthe x axis.

3.2.FuzzyPDControlleronxAxis

ThefuzzyPDcontrollerforthe z axisisstructured asillustratedinFigure 9,containingtwoinputsand twooutputs.The irstinputisthe error,andthesecond inputisthechangeoftheerrorcalled delta_error.The irstoutputisthe velocity ofmotioninthe z axis,and thesecondoutputisusedtocontrolthedirection.The fuzzysystemisoftype‐1Mamdaniform.

Figure9. InputandoutputsofthefuzzyPDcontroller(z axis)

ThefuzzyrulesthatwereusedinthefuzzyPD controllertopositionthegoalinthecenterofthe z axis arelistedbelow

1) If error isleftand delta_error islowthen velocity is medium, direction isbackward

2) If error isleftand delta_error ismediumthen velocity islow, direction isbackward

3) If error isleftand delta_error ishighthen velocity islow, direction isbackward

4) If error iscenterand delta_error islowthen velocity ismedium, direction isstay

5) If error iscenterand delta_error ismediumthen velocity islow, direction isstay

6) If error iscenterand delta_error ishighthen velocity islow, direction isstay

7) If error isrightand delta_error islowthen velocity ismedium, direction isforward

8) If error isrightand delta_error ismediumthen velocity islow, direction isforward

9) If error isrightand delta_error ishighthen velocity islow, direction isforward

InthesameformaswiththefuzzyPDcontroller forthe x axis,therulesforthe z axiswereobtainedby physicallyexperimentingwiththeFNK0050robotto avoidslippingandcollisionduringthemovementon thetrajectory.

InFigure10,weillustratethenonlinearsurfaceof thefuzzyPDcontrollerforthe z axis.

Figure7. StructureofthefuzzyPDcontroller(xaxis)

Figure8. Surfaceofthecontrollerforthevelocity

4.2.TestwithFuzzyPDControl

4.ExperimentalResults

Inthissection,wesummarizetheresultsthatwere obtainedwiththecontrollersmentionedinSection3. Theseresultswereachievedbyperformingphysical testswiththeFNK0050robotplatformatdistances of80cmand100cm,respectively.InFigure 11,we illustratethetestscenarioforexperimentingwiththe controllers.

4.1.TestwithPIDControl

ThePIDcontrollerwastestedwithtwodifferent scenarios,the irstoneisto indtheobjectiveina straightlinewithadistanceof80cmonaplainsur‐face,andthesecondoneisto indtheobjectivethatis positionedonthesidesatadistanceof1monarough surface.

Inthe irstcase,weperformed30testswitha distanceof80cmandtheobjectivepositionedinfront oftherobot,andinallcases,therobotreachedthe objectivewithanaveragetimeof24.2056seconds.It isworthmentioningthatthiscontroller(bydefault) givesprioritytothedistancetotheobjectivebefore centeringtheobjectiveonthe x axis.

Inthesecondcase,weperformed40testswitha distanceof1mandtheobjectivepositionedontheleft sideoftherobot.Inthissituation,therobotwasnot abletoreachtheobjectiveinallthetests,whichwe believeisbecausethedefaultcontrollergivespriority todistanceovercenteringtheobjective.

ThefuzzyPDcontrollersweretestedwiththe samescenariosasforthedefaultcontrollerofthe robot:the irstonewiththestraight‐linetrajectoryof 80cmonaplainsurface,andthesecondonewitha lateraltrajectoryonaroughsurface.

4.2.1.Trackof80cm

Weperformed30testswithadistanceof80cm andtheobjectivepositionedinfrontoftherobot,and inallcases,therobotreachedtheobjectivewithan averagetimeof13.4796seconds.Theacceleration oscillatedbetween2and5,andthevelocitybetween2 and3.ThemainadvantagesofthefuzzyPIDcontroller werethedynamicadjustmentofvelocitiesandthe adjustmenttothepositionoftheobjectiveinthe x axis,whichenabledbettermovementoftherobot,as showninFigure12.

4.2.2.Trackof100cm

ThefuzzyPDcontrollerwasusedin40testsona roughsurface,whichcouldrandomlyaddnoisetothe motionoftherobotbyaffectingthelegmovementof therobot.Evenwiththenoise,thecontrollerwasable toreachtheobjectiveinallcaseswithanaveragetime of29.5325seconds.InFigure13,weseetheresultof oneofthetests.

4.3.Comparisonofresults

Tables 1 and 2 showtheresultsofeachtestfor theabove‐mentionedcontrollers,respectively.The resultswithunderlineandboldaretheminimaltimes inreachingtheobjective,andinboldarethemaximum times.

Figure10. Controlsurfaceforthevelocityforthezaxis

Figure11. Testscenariofortheexperiments

Figure12. FuzzyPDcontrolleradjustingtheposition withrespecttotheballinxaxis

Figure13. FuzzyPDcontrollerperformanceinthe1m distancecase

Table1. Resultsfortheexperimentswith80cm

Theresultsobtainedintheexperimentswitha scenarioof80cmshowaclearadvantageintheaver‐agetimesofthefuzzyPDcontrollerwithrespectto thePIDcontroller.Thisstatementistruedespitethis scenariobeingidealforthePIDcontroller.Notethat thePDcontrollerwasbetterinallcasesaswellason average.Thereasonforthesuperiorityofthefuzzy PDcontrolleristhatitdynamicallychangestheveloc‐ityvaluesaccordingtothesituation.Astatisticaltest comparingtheaveragesproducesatvalueof17.96 andpvalueof3.82×10−23,whichareevidenceofthe superiorityoftheproposedfuzzycontroller.

InTable2,theacronymNAO(notableobjective) isusedtorepresentthatthecontrollerisnotableto reachtheobjective.TheresultsfromTable2showthat thePIDcontrollerisnotabletoreachtheobjectivein allcases,whichisduetothelimitedcapabilitythatit hastoadapttonoisysituations(terrainwithpertur‐bations).Ontheotherhand,thefuzzyPDcontrolleris abletoreachtheobjectiveinallcases,althoughittakes moretimethanintheprevioustable,anditisableto adapttonoisysituations.

Table2. Resultsfortheexperimentswith1m

Trackof1m Tests FuzzyPD PID 1 26.28 NAO 2 28.12 NAO 3 18.62 NAO

32.56 NAO

NAO

25.78 NAO

36.65 NAO

25.83 NAO

NAO

28.07 NAO

23.83 NAO

29.32 NAO 40 28.15 NAO �� 29.5325 NAO �� 4.6036 NAO

5.Conclusion

Inthispaper,wepresentedfuzzyPDcontrolforthe problemofaquadrupedrobot.AfuzzyPDcontroller wasdesignedandimplementedwithfuzzylogicto enhanceitsperformancewithrespecttotraditional linearcontrollers.Theproblemisveryimportantto achieveef icientmovementoftherobot,aswellasto minimizeenergyusage.Acomparisonofthedesigned fuzzyPDcontrollerwithrespecttothePIDcontroller waspresentedtoverifythesuperiorityofthepro‐posal.

Theexperimentationwasperformedwitharobot calledFNK0050forwhichonlyaPIDcontrollerwas previouslyused,sothecontributionisintheenhance‐mentofthecontrolusingfuzzylogic.Futureworks includeoptimizingthedesignofthefuzzyPIDcon‐troller,aswellaselevatingitsdesigntotype‐2[12–15] andpossiblytype‐3fuzzylogic[16–18]withthegoal ofhandlinghigherlevelsofuncertaintyinthecontrol process.Finally,weenvisionoptimizingthefuzzyPID designwithmetaheuristics,asin[19–21].

AUTHORS

JoseEduardoLopez-Ramos –TijuanaInstituteof Technology,TecNM,Tijuana,22379,Mexico,e‐mail: m22210010@tectijuana.edu.mx.

OscarCastillo∗ –TijuanaInstituteofTechnology, TecNM,Tijuana,22379,Mexico,e‐mail: ocastillo@tectijuana.mx.

PatriciaMelin –TijuanaInstituteofTechnology, TecNM,Tijuana,22379,Mexico,e‐mail: pmelin@tectijuana.mx.

∗Correspondingauthor

ACKNOWLEDGEMENTS

ThisworkwassupportedbyTecNMwitharesearch grantandConacytwithanscholarshipforJose EduardoLopezRamos.

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Submitted:24th May2023;accepted:17th July2023

SyedSuhana,BoppuruRudraPrathap,KavishNarang,IvinAnto

DOI:10.14313/jamris‐2025‐018

Abstract:

Therapidresponseofemergencyservicesplaysacritical roleinsavinglivesandminimizingtheimpactofemer‐gencies.However,identifyingandlocatingemergency vehiclesinreal‐timecanbechallenging,especiallyincon‐gestedurbanareas.Thispaperfocusesontheemergency vehicleidentificationusingtheYouOnlyLookOncever‐sion8(YOLOv8)algorithmandisfocusedonInternetof Things(IOT).Thegoalofthisresearchistodevelopareal‐timeandpreciseemergencyvehicledetectionsystem usingYouOnlyLookOnceversion8(YOLOv8)algorithm, trainedandtestedwithadatasetfromacameraplaced onabusyroad,toenhanceemergencyserviceresponse times.Thefindingsdemonstratethesuggestedsystem’s abilitytorecognizeemergencyvehiclesataspeedof 31framespersecondandwitha95%accuracyrate. ModernobjectidentificationalgorithmsincludetheYou OnlyLookOnceversion8(YOLOv8)algorithm,which hasshownpromisingresultsinvariousapplications.The proposedsystemisbuiltonaRaspberryPi,whichactsas anedgedeviceandprocessesthevideostreaminreal‐time.ThesystemconsistsofanInternetofThings(IOT) devicewithacamerathatcapturesthelivevideostream, whichisthenfedintothealgorithmforobjectdetec‐tion.Onceanemergencyvehicleisdetected,thesystem sendsanemailnotificationtothenearbyemergency services,likeapolicestation,usingSimpleMailTransfer Protocol(SMTP),whocanthentakeappropriateaction. TheresultsofthisinvestigationshowthattheInternet ofThingsandYouOnlyLookOnceversion8(YOLOv8) algorithmshavegreatpromiseforcreatingeffectiveand dependableemergencyvehicledetectionsystems.The proposedsystempossessesthecapacitytosavelives andimprovetheeffectivenessofemergencyresponseby speedingupresponsetimesforemergencyservices.The suggestedsolutionisalsoinexpensive,simpletoimple‐ment,andadaptabletoexistinginfrastructure.Through thedevelopmentofintelligenttransportationsystems, emergencyservicescanoperatemoresafelyandeffec‐tively.Moresophisticatedmachinelearningalgorithms maybeincorporatedintotheproposedsystem,andfur‐thersensorscanbeaddedtoutilizealternativemethods beyondcamera‐baseddetectiontoidentifyemergency vehicles.Overall,thisresearchshowsthepotentialof InternetofThings(IOT)andmachinelearningincreating creativeemergencyservicessolutions.

Keywords: YouOnlyLookOnce(YOLOv8),RaspberryPi, PiCamera,InternetofThings(IoT),emergencyvehicles, simplemailtransferprotocol(SMTP),emailnotifications

1.Introduction

Thesurgeinaccidents,disasters,andmedical crisesinrecentyearshasmadeemergencyservices moreandmorecrucial.Thepromptactionofemer‐gencyservicescanpreventfatalitiesandlessenthe effectsofcatastrophes.However,heavytraf icand lagtimesinlocatingthesceneoftheincidentfre‐quentlycompromisetheeffectivenessofemergency services.Tospeedupreactiontimesandboostthe effectivenessofemergencyservices,anapproachthat cantrackemergencyvehiclesontheroadinreal‐time isrequired.Tomeetthisneed,wepresentanIoT‐basedemergencyvehicleidenti icationsystembased ontheYOLOV8algorithm.Thesuggestedsystemuses anIOTcameradevice,PiCamera,torecordthelive videostream,whichissubjectedtoobjectdetection processingbytheYOLOV8algorithm.Whenanemer‐gencyvehicleisdetected,thealgorithmisdesigned sothatthesystemsendsalertstotheemergencyser‐vices,likepolicestations,sothattheycanrespond appropriately.

ARaspberryPiservesasanedgedeviceforthe systemandperformsreal‐timeprocessingofthevideo feed.Modernobjectidenti icationalgorithmslike YOLOV8haveproducedencouragingresultsinvari‐ousapplications.Itisaquickandaccuratereal‐time objectdetectiontechnique.Thepicturecapturedby thecameraispartitionedintoagridofcellstoidentify thevehicle,andboundingboxesareestimatedforeach ofthem.Additionally,itassignseachobjecttoapre‐determinedcategoryandforecaststhelikelihoodthat itwillbepresentineachbox.TheYOLOV8algorithm canaccuratelyidentifyavarietyofitemssinceitwas trainedonavastcollectionofphotos.

Thesuggestedsystemhasa95%detectionaccu‐racyandcanidentifyemergencyvehiclesataspeedof 31framespersecond.Thetechnologymaybeinstalled onabusyroutetoidentifyemergencyvehiclesand shortenemergencyserviceresponsetimesquickly. Thistechnologycanhelpsavelivesandincreasethe effectivenessofemergencyresponsebycuttingdown onresponsetimes.Inaddition,thesuggestedsolution isaffordable,simpletoimplement,andadaptableto existinginfrastructure.Duetoitspotentialtoboost emergencyservices’effectiveness,researchonemer‐gencyvehicledetectionsystemshasattractedinterest recently.Severalexperimentshavebeencarriedout tocreateeffectiveandtrustworthyemergencyvehicle detectionsystems.

However,themajorityofthesestudieshavecon‐centratedontheusageofconventionalmachinelearn‐ingapproaches,whichareinaccurateandexpensive tocompute.Incontrast,thesuggestedsystemuses acutting‐edgeobjectidenti icationalgorithmthatis bothquickandextremelyaccurate.

Thecontributionofthisresearchisthecreationof anIoT‐basedemergencyvehicleidenti icationsystem basedontheYOLOV8algorithm.Thesuggestedsys‐temhasbeenproventoidentifyemergencyvehicles ontheroadaccuratelyand,hence,sendalerts.The suggestedmethodisacutting‐edgeideathatmight improvetheeffectivenessandsafetyofemergency services.Thesuggestedsystemcancoverahugearea sinceitisscalableanddeployableatalargescale. Thesubsequentsectionsoftheessayareorganized asfollows.Wewilltalkaboutrelatedresearchon theYOLOV8algorithmandemergencyvehicledetec‐tionsystemsinthepartthatfollows.Oneofthe recentresearchstudiesinthisdomainwasdoneusing YOLOv4inapapertitled“Animprovedandef icient YOLOv4methodforobjectdetectioninvideostream‐ing,”inwhichtheauthorstalkabouthowthisYOLOv4 algorithmiscombinedwithvariousInferencemeth‐ods,whichleadstoasigni icantincreaseintheef i‐ciency.Further,weshallreviewtheresearchapproach inpart3ofthisarticle.Wewilldiscussthestudy’s indingsandanalysesinsection 4.Wewillofferthe verdictandsuggestionsforfurtherstudyinsection5. Finally,weshalllistthereferencesusedforthisstudy insection6.

InternetofThings,whichlinksvariousgadgetsand sensorsthroughtheinternet,hascompletelychanged thewayweliveandwork.IoThasrecentlygained moreimportanceinemergencyservices,especially whenitcomestotherecognitionofemergencyvehi‐cles.Real‐timeemergencyvehicledetectioncanspeed upemergencyresponsetimesandlowerthelike‐lihoodofaccidents.Objectrecognitionalgorithms, suchastheYOLOfamilyofmodels,areawell‐liked methodforlocatingemergencyvehicles.Speci ically, YOLOv8isacutting‐edgeobjectidenti icationmodel thatperformsreal‐timeobjectrecognitionusingdeep convolutionalneuralnetworks.Numerousapplica‐tions,suchastraf icmanagement,surveillance,and autonomousvehicles,haveextensivelyusedit.Inthis article,wesuggestanIoT‐basedYOLOv8emergency vehicledetectionsystem.Ourtechnologyusescam‐erasandsensorsplacedonroadstoidentifyemer‐gencyvehiclesinreal‐time.Wewillgothroughhow ourapproachwasimplementedandassesshowwellit workedtoidentifyemergencyvehicles.Ultimately,we hopethatourresearchwilladdtotheincreasingbody ofknowledgeonIoT‐basedemergencyvehicleidenti‐icationandshedlightonhowtoemployYOLOv8for objectdetectioninreal‐timecircumstances.

2.LiteratureReview

Emergencyvehicledetectionsystemshavedrawn moreattentionrecentlybecausetheycanincreasethe effectivenessofemergencyservices.Severalexperi‐mentshavebeencarriedouttocreateeffectiveand trustworthyemergencyvehicledetectionsystems. ThissectionreviewstheYOLOV8algorithmandasso‐ciatedstudiesonemergencyvehicledetectionsys‐tems.

EmergencyVehicleDetectionSystems

Researchershavebeeninterestedintheapplica‐tionoftechnologyinemergencyservices.Onesuch pieceoftechnologythatcanhelpspeedupemergency serviceresponsetimesisemergencyvehicledetection systems.Systemsforidentifyingon‐roademergency vehiclesmakeuseofavarietyofsensors,including cameras,radar,andGPS.

Bagheletal.[1]exploretheeffectivenessofthe Ex‐YOLOalgorithmfordetectingemergencyvehicles comparedtootherreal‐timealgorithms.Theauthors thenproposeanimprovedversionofYOLO,called Ex‐YOLO,whichusesconvolutionalneuralnetworks toimproveaccuracy.TheauthorscompareEx‐YOLO withreal‐timealgorithmslikeFasterR‐CNNandSSD foremergencyvehicledetection.The indingsindi‐catethattheEx‐YOLOalgorithmperformsbetterthan otherreal‐timealgorithmsintermsofaccuracyand speed.Theauthorsalsodiscussthelimitationsoftheir study,suchasthelimitedsizeoftheirdataset.Overall, thepaperpresentsawell‐researchedstudyonthe effectivenessoftheEx‐YOLOalgorithmforemergency vehicledetection.

Theresearch“Audio‐VisionEmergencyVehicle Detection”proposesanewapproachforemergency vehicledetectionbyintegratingaudioandvisual information.Theauthorsuseadatasetoftraf ic videoswithaccompanyingaudiosignalsandcon‐trasttheperformanceoftheirproposedapproach withtraditionalvisual‐onlymethods.Theoutcomes demonstratethattheproposedapproachisbetter thantraditionalvisual‐onlymethodsintermsofaccu‐racy,recall,andprecision.Thepaperthoroughly explainstheproposedapproach,includingtheaudio featureextractionprocess,andutilizesdeepneural networksforclassi ication.Theresultssuggestthat suchanapproachcanimprovetheaccuracyandreli‐abilityofemergencyvehicledetectionsystems,which canhavesigni icantimplicationsfortraf icsafetyand emergencyresponse.However,itwouldbeusefulto evaluatetheproposedmethodonalargerandmore diversedatasettofurtherassessitseffectiveness[2].

ManagingTraf icisahugechallengeonaglobal scale.Traf iccongestionproblemsarerisingquickly, particularlyinIndia,duetourbanization,population increase,andanincreaseinthenumberofautomo‐biles.Asaresult,itissometimesdif icultforthe ambulancetoreachthehospitalontime.Technologi‐caladvancementshavecreatednumeroussolutionsto addressseriousproblemsandhelpsavepeople.

TheIoTsurelyhasthepotentialtomakethesitu‐ationbetter.ThisstudyaimstoexamineseveralIoT movementcontrolstrategiesandvariousmethodsfor helpingemergencyvehiclesarriveatnearbymedical facilitiesintime.Findingthebestpossiblemethodsto lessentraf iccongestionisthekeygoal[3].

Mostoftheindividualswhogethurtinautoacci‐dentsgethelpfromotherdriversorpassengers.How‐ever,incaseofacaraccidentthattookplaceina remoteareaorifthedriveristheonlyoneinside thevehicleandisunconscious,noonewillbearound toalerttheappropriateauthoritiesintimeformedi‐caltreatment.Atechniqueforidentifyinghigh‐speed head‐onandsingle‐vehiclecrashes,assessingthecon‐text,andsoundinganalertisrequiredinlightof theseproblems.Chang,W.J[4]proposestheInter‐netofVehicles(IoV)systemnamedDeepCrashto addresstheseissues.DeepCrashconsistsofanin‐vehicleinfotainment(IVI)telematicsplatformwith avehicleself‐collisiondetectionsensorandafront camera,acloud‐baseddeeplearningserver,anda cloud‐basedmanagementplatform.Whenahead‐on orsingle‐carcollisionisfound,accidentdetectiondata istransferredtothecloudforself‐collisionvehicle accidentrecognition,andacorrespondingemergency alertissentout.Accordingtotheexperimental ind‐ings,traf iccollisiondetectionaccuracymayapproach 96%,andthetypicalnoti icationreactiontimefor emergenciesisaround7s.

Thedesireforquickerandmoreprecisedetec‐torsisincreasingasautonomousvehiclesandracing becomeincreasinglypopular.Eventhoughevenfrom greatdistances,ournakedeyescannearlyquickly extractcontextualinformation,picturequalityand processingresourcerestrictionsmakerecognizing tinyobjects(thatis,thingsthat illlessthanonesquare aconstrainedregionofpixelsintheinputimage),ajob thatisdif icultformachinesandisanopentopicfor investigationThestudy[5]looksatwaystoenhance thewell‐knownYOLOv5objectdetectortobetteriden‐tifyupsmallthingswithafocusonautonomousrac‐ing.Todothis,welookintohowchangingsomeof themodel’sstructuralcomponents(alongwiththeir linksandvariousfactors)mightimpacteffectiveness andthetimetogetinferences.Consequently,wesug‐gestasetofmodelsofvaryingsizesthatwecall “YOLO‐Z.”Whenrecognizingsmallerobjectsat50% IOUforjust3mslongerinferencetimethantheorig‐inalYOLOv5model,thesemodelsdemonstratean improvementofupto6.9%inmAP.Theobjective istocontinueinvestigatingthepossibilityofmodi‐fyingawell‐knowndetectorlikeYOLOv5tohandle certainjobsandofferperceptionsonhowparticular alterationsmightaffectsmallitemidenti icationin thefuture.Such indingsmayincreasetheamountof contextualdatathatautonomousvehiclesystemshave accesstowhentheyareappliedtoalargercontext.

Currentobjectdetectionnetworksuseregion proposaltechniquestopredictthelocationsof objects.InnovationslikeSPPnetandFastR‐CNN havereducedtherunningtimeofthesedetection networks,exposingregionproposalcomputation asabottleneck.TheareaProposalNetwork(RPN) wascreatedinthecurrentstudytocooperate withthedetectionnetworktoexchangefull‐image convolutionalfeaturesandprovidealmost‐freearea recommendations.AnRPN,orfullyconvolutional network,predictsobjectboundsandobjectness scoresforeachlocationsimultaneously.Byutilizing RPNsthathavecompletedend‐to‐endtraining,Fast R‐CNNconductsdetectionemployinghigh‐quality regionsuggestions.RPNandusingjustalternating optimization,afastR‐CNNmaybetrainedtoshare convolutionalfeatures.Thisdetectiontechnique deliverscutting‐edgeitemrecognitionwith300 proposalsperimage.TheaccuracyofPASCALVOC 2007(73.2%mAP)and2012(70.4%mAP)while operatingataframerateof5fps(includingallphases) onaGPU[6].

Thenumberofautomobilesontheroadwill increasesigni icantlyeveryyear.Accordingtodata fromMalaysia’sroadtransportdepartment(JPJ),asof December31,2019,therewerearound31.2million motorvehicleunitsregisteredinthecountry.Asof themiddleof2017,Malaysiahadatotalofabout 28.18millionmotorvehicleunits.Sincetraf icconges‐tionmaybeidenti iedbyusingthevolumeofcarsas bene icialdata,itiscrucialtoswiftlyandeffectively detectvehiclesontheroad.Thisisbecauseitwill helpwithtraf icmanagement.Muhammadetal.[7] useTensorFlow,aframeworkformachinelearning, togetherwiththeobjectidenti icationmethodYOLO, toconstructdeeplearningforreal‐timecarrecogni‐tion.Thesuggestedmethodinthisstudycombines thesetwoandotherrequirementsusingPythonasthe programminglanguagetoassesshowwelltheYOLOv4 algorithmperformsincomparisontotheprevious modelinthevehicleidenti icationsystem.Toeffec‐tivelycountthenumberofcarspassinginthevideo, thisvehicleidenti icationalsoemploystheDeep‐SORTmethod.Yolov4,thetopYOLOmodelfromthis research,achievedcutting‐edgeperformancewith 82.08%AP50atareal‐timeframerateofroughly 14FPSonaGTX1660ti.Yolov4employedacustom datasettoachievetheseresults.

Detectionofvehiclesforaerialphotoshasbecome animportantengineeringapproachanddemonstrates theworthofacademicstudybyusingUAVsinintel‐ligenttransportationsystems.Thisstudyprovides aYOLOdeeplearning‐basedapproachforidentify‐ingvehiclesinaerialimages.Themethodcombines threeopen‐sourceaerialpicturedatasetsintoone suitablefortrainingtheYOLOalgorithm.Experiments showthatthetrainedmodelmatchesthereal‐time requirementsandworkswellonunknownaerialpho‐tographs,especiallyforsmallobjects,rotatingobjects, andcompactanddenseobjects[8].

Oneofthekeyfacetsofaneconomyistransporta‐tion.Alargenumberofeconomicsectorsstruggle becauseofalooselyorganizedtransportationnet‐work.Thisisanimportantchallengethatemerging nationsmustdealwith.Thereisnoquestionthat highwaysshouldbebuilttoincreasethethroughput ofthetransportationnetwork,butexpandingalready‐existingroadsisalsonotpracticalincountrieslike SriLankabecauseoftheirshrinkinggeographicalarea andgrowingpopulation.Hence,forustoresolvethis problem,amoreeffective,technologicallyadvanced approachmustbeembraced.Thecurrentpandemic turmoilhasproventheneedtoprioritizeambulances whenitisinvolvedinatraf iccongestion,inaddition tothenormalcongestionscenarios.Anothercrucial aspectoftheroadsystemispedestrians.Roadacci‐dentswillbedecreasedthrougheffectiveandsafe crosswalksforpedestrians,whichwillalsoimprove thecurrenthightraf ic.Thebestoptioninthissce‐narioisasophisticatedtraf icmonitoringsystemwith integratedtraf iclightmanagement.Todetectcars andpedestriansandprovideprioritytoemergency vehicles,thisarticlesuggestsamethodforintelligent, dynamictraf icmonitoringandcontrol.Toachieve 91.3%detectionprecision,anewCNNistrainedusing theYOLOV3architecture[9].

Acomputervision‐basedmethodforreal‐time identi icationofseveralkindsofemergencyvehi‐clesincongestedtraf icispresentedinthisstudy.It enablesthetraf iccontrollertogiveemergencyvehi‐clespreferredpathclearance,whichcouldpossibly savelives,safeguardproperty,andsimplifytheeffort topreventcrimes.Theproposedmodelisbasedon fourclasses:Firetrucks,Ambulances,PoliceCars,and NormalCars.TheYOLOalgorithm’stoplayerswere redesignedandretrainedtogetnewlearnedweights, whereasthebottomlevelsremainedlocked.The modelhasdemonstratedgoodoutcomesandexcellent metricsinrecognizingandcategorizingemergency vehiclesandregularcarsafterretrainingusingthe suggestedmodi iedYOLOv5.UsingthemAPmetric, policecarsachieved98%,96%for iretrucks,89%for ambulances,and97%fornormalcars[10].

Thispaperpresentsalightweightversionof thepopularobjectdetectionalgorithmYOLO,called YOLO‐LITE,thatisoptimizedfornon‐GPUcomputers. Theauthorsproposeseveraloptimizationmethodsto reducethecomputationalrequirementsoftheoriginal YOLOalgorithm,suchassubstitutingfullyconnected layerswithconvolutionallayersandusingasmaller inputresolution.Theyalsointroduceanewapproach foranchorboxclusteringtoimproveobjectdetection accuracy.InanexperimentalcomparisonofYOLO‐LITEandothercutting‐edgeobjectidenti icationalgo‐rithms,thearticleshowsthatYOLO‐LITEperforms aswellasorbetterwhileoperatinginreal‐timeon low‐powerdevices.Overall,theresearchprovidesa practicalandef icientmethodforreal‐timeobject identi icationondeviceswithlimitedresources[11].

Thisresearchsuggestsanewobjectdetection techniquenamedTinier‐YOLO,whichisacompact versionofthepopularYOLOalgorithmdesignedfor real‐timeobjectdetectioninresource‐constrained environments.Theauthorsintroduceseveralmod‐i icationstotheYOLOarchitecture,suchasreduc‐ingtheconvolutional iltersandthedimensionsof anchorboxes,toachieveasmallermodelsizeand fasterinferencespeed.Theyalsoproposeanewdata augmentationtechniquetoincreasethestabilityofthe model.Thearticleoffersexperimental indingsfrom severaldatasets,demonstratingthatTinier‐YOLOper‐formsbetterthanotherleadingobjectdetectionmeth‐odswhilerunningatreal‐timespeedsonlow‐power devices.Overall,thepaperoffersanef icientandeffec‐tivesolutionforreal‐timeobjectdetectionincon‐strainedenvironments[12].

Thisstudysuggestsanovelobjectdetection approachforlandslideidenti icationinsatellite remotesensingpictures.Theauthorsintroducea smallattentionalYOLO(YouOnlyLookOnce)model thatimprovestheprecisionofitemrecognition incomplicatedbackdropsbyusinganattention method.Themodelusesseveralconvolutionallayers andattentionmodulestoreducethecomputational requirementsandachievereal‐timeperformance.The suggestedmethodsurpassesexistingcutting‐edge objectdetectiontechniquesintermsofdetection accuracyandcomputingef iciency,asshownby experimental indingsonalandslipdetectiondataset inthestudy.Theproposedapproachhasthepotential toassistinearlywarningandmitigationoflandslide disasters,providingavaluablecontributiontothe ieldofdisastermanagement[13].

Theproposedapproachhelpsimprovetheaccu‐racyoftraf icsignidenti icationusingYOLOv4and arti icialtrainingdatageneratedbynumerousGANs. Theauthorstrainedtheirproposedmodelonan availabletraf icsigndatasetandassesseditonboth thesamedatasetandareal‐worlddataset.Thetest‐ing indingsdemonstratedthattheirstrategyoutper‐formedanumberofcutting‐edgetechniquesinterms ofaccuracy.Theauthorsalsoconductedablationstud‐iestoinvestigatetheeffectivenessofusingsynthetic trainingdatageneratedbydifferentGANs.Thepaper concludesthattheirproposedapproachusingYOLO v4andsynthetictrainingdatageneratedbyvarious GANscansigni icantlyimprovetheaccuracyoftraf‐icsignrecognition,whichiscrucialforthesafetyof autonomousvehicles[14].

Thepaperrecommendsanimprovedversionof theYOLOnetworkforreal‐timevehicledetection inembeddedsystems.Thesuggestedstrategyalters thenetwork’stopologytokeepdetectionaccuracy whileloweringcomputationalcomplexity.Themod‐i iednetworkisthenimplementedonanembed‐dedsystemusingaheterogeneouscomputingplat‐form,whichincludesanFPGAandaCPU.Accord‐ingtoexperimental indings,thesuggestedtechnique detectsvehicleswithhighaccuracy,using30%less processingtimethantheoriginalYOLOnetwork.

Thesuggestedmethodsurpassesothermodern objectidenti icationtechniquesintheresearchwhen comparedtobothdetectionaccuracyandprocess‐ingspeed.Theoutcomesshowthatthesuggested approachisappropriateforembeddedsystems’real‐timevehicledetectionapplications[15].

3.Methodology

Thereal‐timeobjectidenti icationtechnique, YOLO,was irstimplementedin2016.Thesystem locatesobjectsinimagesorvideosbybreakingthe inputimageupintoseveralcellsandestimating boundingboxesandclasslikelihoodsforeach cell.Oneoftheprimarybene itsofYOLOisjust howquickitis.YOLOisbuilttoprocessphotosin real‐time,makingitappropriateforuseinrobots, autonomousvehicles,andsurveillancesystems, amongotherthings.Additionally,YOLOisasingle‐stagedetectiontechnique,unlikeotherobject identi icationalgorithmslikeFasterR‐CNNorSSD, whichbothneedanadditionalregionproposal phase.Thismakesthingssimplerandcreatesafaster pipeline.

Accuracyisanotherbene itofYOLO.Onwell‐knownobjectidenti icationbenchmarkslikeCOCO andVOC,YOLOv4,themostrecentalgorithmiteration, performsatthecuttingedge.YOLOdoeshavecertain restrictions,though.Itssensitivitytotinythingsis oneofitslimitations.YOLOmayoverlooklittlethings thatarepositionedbetweencellssinceitsplitsthe pictureintoagridofcells.Anotherdrawbackishow wellitperformsindensesituationswithoverlap‐pingitems,whichmightresultinseveraldetections ofthesamething.YOLOisoftenquickerthanother objectidenti icationalgorithmsbutmaygiveupsome accuracywhencomparedtotwo‐stagemethodslike QuickerR‐CNNorMaskR‐CNN.SingleShotMultibox Detector(SSD)andRetinaNetaretwomorewell‐likedobjectidenti icationalgorithmsthatlikewisetry tocompromisespeedandaccuracy.Inconclusion, YOLOisawell‐likedobjectidenti icationtechnique renownedforitsquicknessandprecision.Itssingle‐stagearchitectureandreal‐timeperformancemakeit suitedforavarietyofapplications.Still,incomparison tootheralgorithms,itcouldhavetroublehandling smallobjectsorclutteredsituations.

YOLOv8isthelatestversion,whichisaddedto theYOLOfamily.Thismodelisparticularlyusedfor objectdetectionandsegmentation.Theperformance and lexibilityhavebeenimprovedwithadditional features.YOLOv8isquick,precise,andsimpletouse, henceprovingtobethebestchoiceforavarietyof objectrecognitionandtracking,segmentation,clas‐si ication,andmanyothertasks.YOLOv8ismuch fasterandgivesaccurateresultscomparedtoprevi‐ousversionsofYOLOAnadditionalfeatureaddedto YOLOv8isinstanceSegmentation,throughwhichmul‐tipleobjectscanbedetectedinanimage.Thearchitec‐tureofYOLOv8extendsontheYOLOobjectdetection modelsfrompreviousreleases.Afullyconvolutional neuralnetwork,or“backboneandhead,”thatYOLOv8 usesforprocessingimages.Amodi iedformofthe CSPDarknet53architectureprovidesthefoundationof YOLOv8.YOLOv8hasintroducedDarknet‐53,which ismuchfasterandprecise.DarkNet‐53isa53‐layer CNNthatcancategorizephotosinto1000different objectcategories.Variousconvolutionallayersanda collectionoffullyconnectedlayerscomprisethehead oftheYOLOv8algorithm.Theselayersareinchargeof predictingtheobjectdetectionboundaries,objectness scores,andclassprobabilities.

YOLOv8usesaboundingboxpredictionmech‐anismjustlikeanyotherimagesegmentation.An anchor‐freedetectionheadwasintroducedtoachieve this.ThemodelismoreeffectivebecauseYOLOv8 makesuseofabiggerfeaturemapandamoreeffective neuralnetwork.Alargerfeaturemapsimplyindicates thatthemodelcancapturecomplicatedconnections betweenvariouscharacteristicsandcanrecognize patternsandobjectsinthedatamoreeffectively.In additiontothis,italsoreducestheover ittingand reducesthetimeittakestotrainthemodel.Theactive useofaself‐attentionmechanisminthenetwork’s brainisoneofYOLOv8’sdistinguishingcharacteris‐tics.Inadditiontoaidingthisprocess,themodelhas theabilitytodirectitsattentiontovariousfeaturesof theimagebasedontheirrelevancetothetaskathand. ThecapabilityofYOLOv8tocarryoutmulti‐scale objectidenti icationisafurtheressentialcharacteris‐tic.Themodelemploysuseofafeaturepyramidnet‐worktoidentifyitemsinanimagethathavedifferent dimensionsandscales.Multiplelayersofthisfeature pyramidnetworkdetectitemsatdifferentdimensions, permittingthemodeltorecognizelargeandsmall thingsinanimage.Figure2showstheproposedmodel oftheExperiment.Theentireresearch,aspresented inthenextsectionsfrom3.1to3.6,isbasedonthis proposedmodel.

Figure1. YOLOarchitecture

3.1.ExperimentalSetup

TheExperimentwasconductedona2kmstretch ofaroadthatisknowntohavefrequentemergency vehicletraf ic.ThePiCamerawasmountedataheight of5meters,facingtheroad.Themicrocontroller, RaspberryPiwasconnectedtoacellularnetworkto transmitdatatoacloudserver.

3.2.SystemArchitecture

Oursystemconsistsofacameramountedona pole,amicrocontroller,andacloudserver.Thecam‐eracapturesimagesoftheroad,andthemicrocon‐trollerprocessestheimagesandsendsthemtothe cloud.ThisserverrunstheYOLOv8objectdetection algorithmtodetectemergencyvehiclesintheimages.

3.3.Dataset

Thedatasetisobtainedbylivecapturingof EmergencyVehiclesontheRoad.Whiletrainingour YOLOv8model,thedatasetwasdividedintotrain, valid,andtestsetsinaratioof70:15:15.Ourmodel istrainedtodetectfourclassesofvehicles:ambu‐lances,Policecars,FireEngines,andandVIPVehicles. Figure 3 showsthesampledatasetimagesusedfor experimentalpurposes.

3.4.DataPreprocessing

Thedatasetwaspreprocessedbeforeitunderwent trainingusingtheYOLOv8algorithm.Thefollowing stepswereincludedasapartofpreprocessinga) Resizingimages:Theimageswereresizedto416X

416pixelssothatalltheimagesinthedatasethave equaldimensions.Thisnotonlyspeedsupthetrain‐ingprocessbutalsoimprovesourmodel’saccuracy. OpenCVwasusedtoresizetheimages.b)Converting imagestoYOLOformat:TheYOLOalgorithmdemands aspeci icformatforthedataset.Itiscrucialtotrans‐formourrawdataintoaformatthattheYOLOalgo‐rithmcanuseinordertocreateaYOLOmodel.The prepareddatasetmustincludeImagedataandlabel data.c)Imagedata:Incommon,theImagedatacan beinanyimageformatlikeJPEGorPNG.Itisjust likeamatrixthatrepresentsthepixelsoftheinput image.Here,ourdatahas416X416pixels.d)Label data:Thelabeldatacontainstheannotationsforeach image,whichtypicallyincludesboundingboxcoordi‐natesandclasslabels.Thefollowingclasslabelswere given:Ambulance,FireEngine,Police,VIP.Thelabel datawillbestoredinatext ilehavingtheexactname asthecorrespondingimage ile,andhavinga“.txt” extension.Eachrowinthelabel ilerepresentsone objectintheimageandhasthefollowinginformation: ObjectClassIndex,ObjectCenterCoordinates,Object width,andheight.Thisdatasetwaspreparedusing Robo low.Robo lowisacloud‐basedsoftwareplat‐formthatprovidestoolsforcreatingandmanaging customobjectdetectiondatasets,includingdatasets forYOLOmodels.SomeofthefeaturesofRobo low includeDataAugmentation,Labellingtools,Dataset management,ExporttoYOLOformat,andIntegration withdeeplearningframeworks.Thedatasetwasdis‐tributedintoTrain,Valid,andTestsetsinaratioof 70:15:15.

3.5.YOLOAlgorithmandConfiguration

YOLOisanobjectdetectionmodel,andthemost recentadditiontothefamilyofYOLOalgorithmsis YOLOv8.TheYOLOv8algorithmisusedtotrainour model.YOLOv8usesDarkNet‐53asitsCNN,whichis 53layersdeep.Itgivesmorepreciseresultsandis moreef icientthanpreviousYOLOversionsandother objectdetectionalgorithms.Theproposedemergency vehicledetectionsystemusestheYOLOV8algorithm todetectemergencyvehiclesinthevideostream. Thissystemconsistsoftwocomponents:thetraining componentandthedetectioncomponent.Thetrain‐ingpartusestheYOLOv8algorithmonadatasetof emergencyVehicles.Thedetectionmoduledetects theemergencyvehiclesinreal‐timeusingatrained YOLOv8algorithm.Thepre‐trainedYOLOv8model was ine‐tunedonouremergencyvehicledataset.The Adamoptimizerwasusedtotrainthemodel.

Mathematicalmodel: MathematicsbehindYOLO Itisnecessarytounderstandthefollowingsteps:

1) TounderstandtheYOLOalgorithm,oneshould knowthattheobjectclass,alongwithitsbounding box,ispredicted.

2) Theboundingboxhascentercoordinates,width, height,andvaluec,whichrepresentstheclassof theobject.

3) Alongwiththat,wepredictpc,arealnumber, whichcorrespondstotheprobability.

Figure2. Proposedsystemmodel

Figure3. Sampledataset

4) YOLOdoesn’tsearchforspeci icplacesinanimage butinsteaddividestheimageintocells,eachcell wouldtakeuptheresponsibilityforpredicting boundingbox.

5) Thecentercoordinatesarecalculatedconsidering theentirecell,buttheheightandwidtharecal‐culatedwithrespecttothecompleteimagesize. Hence,anobjectwillbeconsideredtoresideina particularcellonlyifitscentercoordinatesliein thatcell.

6) YOLOdeterminestheprobabilitythatacellcan containaclassduringitsonepassofforwardprop‐agationusingtheequationbelow:

SCOREc,i=PcX

Ciiswherecisacertainclass.

7) Thenextstepafter indingprobabilitiesofclassis non‐maxsuppression,itisanapproachtoremove unwantedboundingboxes.

8) ByperformingIoU(IntersectionoverUnion)on theboundingboxeswiththegreatestclassproba‐bility,non‐maxsuppressionreducesthebounding boxesthatareveryneartooneanother.

9) Thisalgorithmhence indstheIoUvaluesofall boundingboxesand inallyretsridofunwanted boxesbydeletingtheoneswhoseIoUvalueis greaterthanacertainthreshold.

10) Thisisdonerepeatedlyuntilthereareonlydiffer‐entboundingboxesleft.

11) Thealgorithm inallyshowstheboundingboxesof therespectiveclass.

3.6.Training

ThePreparedDatasetwastrainedusingYOLOv8 algorithmusingDarknetFramework.TheDarknet Frameworkisanopen‐sourceframework.Themodel wastrainedfor200epochswithabatchsizeof64. TheRateoflearningwaschangedto0.001,andthe Momentumwassetto0.9.Thelossfunctionused wasYOLOv3lossfunction.Thetrainedalgorithmwas eventuallyevaluatedonasetofvalidationimages.The EvaluationMetricsusedwerePrecision,F1Score,and Recall.

4.ResultsandDiscussion

Thesystemwasabletodetectemergencyvehicles accuratelyandef icientlyinrealtime.The indings showtheFeasibilityandeffectivenessofourIOT‐basedEmergencyVehicleDetectionusingYOLOv8.Our SystemachievedanmAPscoreof0.5.

4.1.SampleDataset

4.2.Detection

Thedetectionmodulewasimplementedusingthe YOLOv8algorithmandtheOpenCVlibrary.Thismod‐uletakesavideostreamasinputandprovidesemer‐gencyvehicledetectioninrealtime.

ThedetectedVehiclesarehighlightedusingbound‐ingboxesandarehencelabelledwiththeirclasses. Figure 6 showsasampleframefromthedetected videostream.Thedetectedemergencyvehiclesare highlightedwithboundingboxesandlabeledwith theirrespectiveclasses.

4.3.PerformanceAnalysis

Theeffectivenessofoursystemismeasuredbythe meanaverageprecision(mAP)metric.Theef iciency ofoursystemiscomparedagainsttheYOLOv3model andabaselinesystemthatusestraditionalcomputer visiontechniques.

4.4.ConfusionMatrix

Aconfusionmatrixisaperformanceevaluation toolthatprovidesinsightsintohowwellaYOLOmodel isperformingforobjectdetectiontasks.

Figure4. Imagescapturedonroads

Figure5. (a),(b),(c),(d)Sampledataset

Figure6. EmergencyvehicleidentificationusingYOLOV8

Figure8. F1Confidencecurveonthevehicle identification

Aconfusionmatrixisatablethatcomparesthe YOLOmodel’spredictedlabelstothetestset’strue labels.Figure 7 showstheConfusionMatrixofthe experimentalsetup.Hereiswhateachcategoryrep‐resents:TruePositive(TP):TheYOLOmodelcorrectly detectedanobjectintheimage.FalsePositive(FP): TheYOLOmodelpredictedanobjectintheimage,but therewasnoobjectinthegroundtruthlabel.True Negative(TN):TheYOLOmodelcorrectlypredicted thattherewasnoobjectintheimage.FalseNegative (FN):TheYOLOmodelfailedtodetectanobjectinthe imagethatwaspresentinthegroundtruthlabel.By analyzingthevaluesintheconfusionmatrix,onecan getinsightsaboutPrecisionandRecall,Accuracy,False Positiverate,andErroranalysis.

4.5.F1ConfidenceandPrecisionCurve

F1CurveplotstheF1Scoreagainstarangeof con idencethresholdsforobjectdetectioninaYOLO model.TheF1scoreisa

ThismetriccombinesRecallandPrecisionandis usedtoassesshowwellthemodelisworking.Figure8 showstheF1Con idencecurveforvehicleidenti ica‐tion,witharangeof0to1.

ThePcurverepresentsaYOLOmodel’sobject detectionprecisionvs.recallplot.Precisionandrecall aretwoimportantindicatorsforassessingtheeffec‐tivenessofobjectidenti icationalgorithms,andtheP curvecanprovideseveralinsightsintoaYOLOmodel’s performance.Figure9showsthePrecisioncon idence curveforvehicleidenti ication.

Precisionconfidencecurveforthevehicle identification

Precision‐Recallcurvefordifferent emergencyvehicleidentification

Recall‐Confidencecurveondifferentvehicles

4.6.Precision–Recall&Recall–ConfidenceCurve

ThePR(Precision‐Recall)curveplotsprecision againstrecallforobjectdetectioninaYOLOmodel. Therecall‐con idencecurveplotsrecallversus con idenceforobjectdetectioninaYOLOmodel.While con idenceisthelikelihoodthatanobjectwillactually befoundwithinaprojectedboundingbox,recallisthe proportionoftheactualobjectsthatthemodeleffec‐tivelydetects.Figure 10 showsthePrecision‐Recall curvefordifferentemergencyvehicleidenti ication.

Figure7. Confusionmatrix

Figure9.

Figure10.

Figure11.

4.7.EmailNotification

WeusedtheSMTPserverofIoTtodeliveremail noti ications.EmailclientsuseSMTPtosendand receiveemailmessages.InthecontextofIoT,anSMTP servercanbeusedtosendalerts,noti ications,and otherinformationviaemail.

5.Conclusion

Tosumup,theproposedemergencyvehicledetec‐tionsystemusestheYOLOV8algorithmtodetect Emergencyvehiclesinreal‐time.Animagecollection ofemergencyvehicleswasusedtotrainthesystem, anditachievedaprecisionof0.85andarecallof 0.91.Inthisresearchwork,wesuggestedanIoT‐basedYOLOv8emergencyvehicledetectionsystem. TheproposedsystemutilizesIoTsensorsandcloud‐basedcomputingtoenablereal‐timedetectionand responsetoemergencyvehicles.Usingareal‐time imagecollectionofemergencyvehicles,weassessed thesuggestedsystem’sperformanceandcomparedit tootherleading‐edgeobjectidenti icationalgorithms. Thissystemhassuccessfullyattaineditsobjective ofdetectingemergencyvehiclesstuckintraf icand hashencegeneratedalertstosavepeople’slives.The analysisshowedthatthesuggestedsystemperformed betterthanothermodelsintermsofaccuracy,pre‐cision,recall,andF1score,makingitapromising solutionforemergencyvehicledetectioninvarious settings.FromtheConfusionmatrix,wecanconclude thatthesystempredictedvaluesareascloseasthe actualvalues,andthevaluesheredirectlypointtothe emergencyvehicles.TheF1Con idence,precisioncon‐idence,precision‐Recall,andtheRecall‐Con idence curvespresentthemodel’sperformanceindetecting variousemergencyvehicles,asmentioned.

Theproposedsystem’sadvantagesoverother modelscanbeattributedtoitsabilitytodetectemer‐gencyvehiclesaccuratelyinreal‐time,eveninlow‐lightconditionsandchallengingangles.TheYOLOv8 method,whichenablestheidenti icationofmany objectsinasingleframe,isasophisticatedcomputer visionapproachtoachievethis.Theproposedsystem alsohasthepotentialtosigni icantlyimproveemer‐gencyresponsetimes,therebyincreasingthechances ofsavinglivesinemergencies.Byprovidingreal‐time informationaboutthelocationandtypeofemergency vehicles,thesystemcanhelpemergencyservices respondquicklyandef iciently,reducingthetimeit takesforemergencyvehiclestoreachtheirdestina‐tion.Moreover,theproposedsystem’suseofIoTsen‐sorsandcloud‐basedcomputingallowsforscalability and lexibility,makingitsuitablefordeploymentin varioussettings,includingurbanandruralareas.This isparticularlyimportantinareaswheretraditional emergencyresponsesystemsmaybelimitedbyinfras‐tructureorresources.Inconclusion,theproposedIoT‐basedemergencyvehicledetectionsystemusingthe YOLOv8algorithmhasthepotentialtorevolutionize Emergencyresponsesystemsbyprovidingreal‐time informationaboutthelocationandtypeofemergency vehicles.

Thesystemperformsbetterthanotherpioneer‐ingobjectdetectionmodels,anditsscalabilityand lexibilitymakeitapromisingsolutionforemergency vehicledetectioninvarioussettings.

Futureworkcanfocusonimprovingthepro‐posedsystem’sperformancebyincorporatingaddi‐tionaldatasources,suchastraf iccamerasand aerialimagery,toenhancethesystem’sabilityto detectemergencyvehiclesinreal‐time.Addition‐ally,thesystem’sintegrationwithexistingemergency responsesystemscanbeexploredtofurtherimprove emergencyresponsetimesandcoordination.Future researchcannotonlybelimitedtocamera‐based emergencyvehicledetectionbutcanalsobeextended toothersensorslikesounddetectingsensors.Overall, theproposedsystemhasthepotentialtosavelives andimproveemergencyresponsetimes,makingita valuablecontributiontothe ieldofemergencyman‐agementandIoT‐basedsystems.

AUTHORS

SyedSuhana –DepartmentofComputerScienceand Engineering,CHRIST(DeemedtobeUniversity),India, e‐mail:syed.suhana@btech.christuniversity.in.

BoppuruRudraPrathap∗ –Departmentof ComputerScienceandEngineering,M.S.Ramaiah UniversityofAppliedSciences,India,e‐mail: brprathap@gmail.com.

KavishNarang –DepartmentofComputerScience andEngineering,CHRIST(DeemedtobeUniversity), India,e‐mail:kavish.narang@btech.christuniversity. in.

IvinAnto –DepartmentofComputerScienceand Engineering,CHRIST(DeemedtobeUniversity),India, e‐mail:ivin.anto@btech.christuniversity.in.

∗Correspondingauthor

References

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Submitted:28th September2023;accepted:15th May2024

TharageswariK,MohanaSundaramN,SanthoshR

DOI:10.14313/jamris‐2025‐019

Abstract:

Inthepresentera,maintainingahealthyanddisease‐freelifeiscomplexduetomultiplepersonalandenvi‐ronmentalimpacts.Earlyidentificationanddiagnosiswill helphumanbeingsleadasustainablelife.However,to achievethis,healthcaredatahavetobeprocessedinan efficientmannerwithmoreaccuracy.Thus,theimpacts ofdiseasesorfutureimpactscanbepredictedordetected andpropermedicationcanbeprovidedbythephysi‐cians.Handlingmedicaldataoverconventionaldata analysisisquitedifferentduetodatadiversity.Efficient featureextractiontechniquesmustbeemployedwith minimumcomputationcostsothattheextractedfea‐turescanbeclassifiedinabetterway.Machinelearning modelsperformwellinhealthcaredataanalysis.How‐ever,theperformancecanbeimprovedifdeeplearning modelsreplacemachinelearningmodels.Thus,inthis researchwork,ahybriddeeplearningapproachispro‐posedusingconvolutionalneuralnetworks(CNN)andthe randomforest(RF)algorithm.Thefinalclassifierblockin theCNNarchitectureisreplacedwithaRFclassifierto enhancethepredictionaccuracyof0.975andoverallper‐formance.Standardbenchmarkhealthcaredatasetsare employedintheproposedmodelsimulationanalysisand theperformancesarecomparedtoexistingtechniques suchasaMNN(multi‐neuralnetwork),CNN‐multilayer perceptron(CNN‐MLP),CNN‐longshort‐termmemory (CNN‐LSTM),supportvectormachines(SVM),andKNN tovalidatethesuperiorperformance.

Keywords: diseaseprediction,featureextraction,deep learning,convolutionalneuralnetwork,machinelearn‐ing,randomforest

1.Introduction

Themassivedevelopmentoftheworld’spopula‐tionrequiresawell‐sustainedhealthcaresystemfor humanbeingstomaintaintheirlifetimehealth.As thepopulationincreases,thegrowthofvariousdis‐easescanalsoincrease.Thiscreatesacrucialtask forhumansinthehealthcareindustry:Maintaininga largevolumeofmedicaldataandpredictinganaccu‐ratediseaseatanearlierstage.Sincethemanualpre‐dictionofdiseasetakesalongtime,thereisaneedfor anautomatedhealthcaresystem.

Ahealthcaresystemismainlyconstructedfor thebettermentofthehealthrequirementsofhuman

beingsandprovidesserviceslikemaintaining,restor‐ing,andmonitoringthehealthrecordsofasingleper‐sonoragroupofpeople.Thissystemcomprisesthe caregivenbyclinicsandphysicians.Itattemptstohold healthfactorswhilealsoprovidingdirectpursuitto improvepeople’shealth.Themainsigni icanceofthe healthcaresystemisthatthevalueoflifecanbeiden‐ti iedbyasinglepersonorcorporationaswellasby thepublicorthestate.Hence,designinganexhaustive healthcaresystemprovidesbene itstoasingleperson orcorporationaswellastothepublicorstate.

Moreover,therearevariousbene itsfrom healthcaresystems,butsharinginformationmutually betweenpatientsanddoctorsintraditionalhealthcare systemsisstillcomplex.Duetothepatient’sbelief indoctors,theknowledgesharingbetweenthem createsinformationdissymmetry.Thismakesthe healthcaresystemunsustainable.Inordertohave agoodrelationshipbetweenthedoctorandthe patient,theknowledgesharingbetweenthemshould bemutual,sothatthepatientcangetabetter understandingoftheirhealthandfurtherfollowthe doctor’sinstructionstocureandimprovetheirhealth bythemselves[1].Forthispurpose,aneasyand well‐organizedhealthcaremodelistobeconsidered. Toattainthismotive,apredictivemethodcouldbethe bestoption,whichmakesthepredictionofdisease easierandprovidesbetterinformationsharing betweenthedoctorandthepatient[2,3].

Thehealthcaresystemisbeingmadedigitallycen‐tricbyusingIoTandcloudcomputingtechniques.The InternetofThings(IoT)playsanimportantroleinthe healthsystemsinceitallowsdoctorstomonitorthe healthlevelofpatientsdailyfromanywhereatany timeusingIoTsensors.Cloudcomputingalsoplaysa speci icroleinstoringandmaintainingthemassive amountsofdatainthehealthcaresystem[4].Theexe‐cutionofdigitalprinciplesinhealthcaresystemsmini‐mizesthedif icultiesintheservice ieldandimproves effectiveness,whichinturnextensivelyimprovesthe sustainabilityofhealthcaresystems.

Withtherapidgrowthofarti icialintelligence, theanalysisofdatainvariousdomainapplications becomessimpleandef icient.Arti icialintelligence utilizesvariousmachinelearningapproachestoana‐lyzeandpredictdata[5,6].Inparticular,thelearn‐ingapproachworksmuchmoreef icientlythanother traditionalmodelsinthehealthcaresystem.

Thehealthcaresystemrequiresabetterunder‐standingofcomplexmedicaldata,whichishardto obtainbytraditionalapproaches.Toovercomethis problem,deeplearningtechniqueshavebeenwidely adoptedinrecentyearsformedicaldataanalysis[7, 8].Basedonthis,areliableconvolutionneuralnet‐work(CNN)hasbeenusedasaclassi icationmodel inthiswork,whichclassi iesmedicaldata.Ahybrid CNNmodelispresentedinthisworkinorderto attainabetterpredictionofdiseaseandtodecrease themanpowerneedsinhealthcaredataanalysis.The mainobjectiveofthisworkistoimproveprediction accuracyasasustainablehealthcaresystem,which shouldreducehumaneffortsandincreasediagnostic accuracy.Thecontributionsofthisresearchworkare summarizedasfollows:

‐ Presentedadiseasepredictionmodelforasustain‐ablehealthcaresystemusinghybriddeeplearning algorithmwhichincludesaCNNandrandomforest (RF)techniques.

‐ Presentedanintenseexperimentalanalysisto exhibittheperformanceoftheproposedmethod usingbenchmarkdatasets.

‐ Presentedrelativecomparativeanalysisofthepro‐posedmodelwithotherconventionalprediction modelsforbettervalidation.

Therestofthesectionisorderedasfollows:Avast surveyaboutdifferenthealthcaresystemsanddisease predictionmodelsispresentedinSection2.Thepro‐posedpredictionmodelispresentedinSection3,and itsperformanceanalysisispresentedinSection4.The inalobservationsareconcludedinSection5

2.RelatedWorks

Themassivedevelopmentoftheworld’spopula‐tionrequiresawell‐sustainedhealthcaresystemfor humanbeingstomaintaintheirlifetimehealth.As thepopulationincreases,thegrowthofvariousdis‐easescanalsoincrease.Thiscreatesacrucialtask forhumansinthehealthcareindustry:maintaininga largevolumeofmedicaldataandpredictinganaccu‐ratediseaseatanearlierstage.Sincethemanualpre‐dictionofdiseasetakesalongtime,thereisaneedfor anautomatedhealthcaresystem.

Ahealthcaresystemismainlyconstructedfor thebettermentofthehealthrequirementsofhuman beingsandprovidesserviceslikemaintaining,restor‐ing,andmonitoringthehealthrecordsofasingleper‐sonoragroupofpeople.Thissystemcomprisesthe caregivenbyclinicsandphysicians.Itattemptstohold healthfactorswhilealsoprovidingadirectpursuitto improvingpeople’shealth.Themainsigni icanceof thehealthcaresystemisthatthevalueoflifecanbe identi iedbyasinglepersonorcorporationaswellas bythepublicorthestate.Thus,designingacompre‐hensivehealthcaresystemisgoodforbothindividuals andthepublicorthestateasawhole.

Moreover,therearevariousbene itsfrom healthcaresystems,butsharinginformationmutually betweenpatientsanddoctorsintraditionalhealthcare systemsisstillcomplex.Duetothepatient’sbelief indoctors,theknowledgesharingbetweenthem createsinformationdissymmetry.Thismakesthe healthcaresystemunsustainable.Inordertohave agoodrelationshipbetweenthedoctorandthe patient,theknowledgesharingbetweenthemshould bemutual,sothatthepatientcangetabetter understandingoftheirhealthandfurtherfollowthe doctor’sinstructionstocureandimprovetheirhealth bythemselves[1].Forthispurpose,aneasyand well‐organizedhealthcaremodelistobeconsidered. Usingapredictivemethodcouldbethebestwayto reachthisgoal.Thismethodmakesiteasiertopredict diseaseandallowsforbetterinformationsharing betweenthedoctorandthepatient[2,3].

Awidesurveyhasbeenconductedtoinvestigate theconventionaldiseasepredictionmodels’perfor‐mances.Themethodology,featureadvantagesand disadvantagesareconsideredforinvestigation,and inally,thedrawbacksarediscussedtoincreasethe researchmotivation.Machinelearninganddatamin‐ingmethodsarebroadlyusedinthemedicalindus‐try.UsingbothMLandDM,medicaldataaretrained andclassi iedinthemedicalindustry.ACNN‐LSTM methodisconsideredin[9]forpredictingheartdis‐easeinthehealthcaresystem.Asustainablehealth‐caresystemhasbeenconstructedin[10]usingatriple bottomlineandstackholdertheory,andthecommu‐nicationbetweenthehealthcaresystemsisprovided bymeansofFuzzy,DEMATEL,andISMmodels.In[11], targetpredictionofmiRNAhasbeenobtainedbycon‐sideringthecombinationofsupervisedandunsuper‐visedmachinelearningalgorithmsandanSVMclassi‐ier.Varioustypesoflearningapproacheshavebeen comparedin[12]topredictthetimeseriesblood glucoseleveloftype1diabetesdisease.IoTisafas‐cinatingimprovementinconsiderationinthedomain ofhealthservices.IoTmakesdoctorsworksmarterby usingthecollecteddataintheIoTenvironment.

Theuseoftobaccoinhumanscauseschronicdis‐easeslikecardiovasculardisease,arthritis,cancer,and diabetes.Thefeatureextractionofthisdiseaseand theidenti icationofchronicdiseasesareobtainedby usingaCNNandK‐NearestNeighborin[13].

Thelessconsumptionofwaterformoredaysinthe humanbodycausesakidneyproblem,whichcauses kidneydamageand,inturn,requireskidneytrans‐plantation.Toavoidthis,earlydetectionofkidney diseaseisneeded,whichcanbeachievedbyusing machinelearningalgorithmslikeLogisticRegression (LR),DecisionTree,andK‐NearestNeighbor[14].

WiththehugeadoptionofElectronicHealth Records(EHR)insmarthealthcare,amassivequantity ofelectronicmedicaldataiscollected.Fortheinter‐pretablepredictionofthoseclinicaldata,theattention mechanism‐basedneuralnetworkisused[15].The predictionofcardiovasculardiseaseisanextremely dif iculttaskinthehealthcaresystem.Thisresearch work[10]comparedmanymachinelearningalgo‐rithmslikeREPTree,M5PTree,RandomTree,Linear Regression,NaiveBayes,J48,andJRIPandobtained betterresultsfortheRandomTreeapproach.Nowa‐days,manyvarietiesofbraindiseasesarecreated.The earlydetectionofbraindiseasesaveshumanlives. VariousMLandDLapproachesarediscussedinthis work[16]topredictthedifferenttypesofbraindis‐eases.Ariskpredictionsystemfordifferentchronic diseaseshasbeendevelopedinthework[17]using thelong‐termshort‐memory(LSTM)algorithm.

Theimbalancedclassofdatasetscontaining chronickidneydiseasedatahasbeenbalancedby usingtheSMOTEalgorithm[18].Themissingvalue inclinicaldatadecreasestheaccuracyofthesystem. Thatcanbeconsideredthemainfocusin[19],and theresearchtriedtoovercomethatproblembyusing theSMOTEalgorithmbasedLR‐KNNsystem.The abnormallevelofmicrobesinhumanscanaffect humanhealth,whichcanbepredictedbyusingthe randomwalkalgorithm[20].In[21],thepresence andabsenceofarterialeventshavebeenidenti ied forthepredictionofin lammatoryboweldiseases usingSVMandXGBoostalgorithms.In[22],theSlime MouldAlgorithm(SMA)isutilizedintheworktotrain theSVMforthebetterclassi icationofCOVID‐19data. Theclassi icationofParkinson’sdiseaseisachieved byusingthemulti‐sourceensemblelearningandCNN method[23].ForpredictingAlzheimer’sdisease,[24] usesaGAN(GenerativeAdversarialNetwork)forthe classi icationofbrainimages.

Fromtheliteraturereview,itisnotedthatthe accuracyofthepredictiondependsontheselectionof asuitablelearningalgorithmandclassi iers.Various typesofmachinelearningalgorithmsaremostlyused intheresearch.Fromtheabovesurvey,itisobserved thatLSTMandSVMalgorithmsperformbetter.In someofthecases,CNNsperformedbetter,butthe performancewasnotmuchbetter.Inordertoextend theperformanceoftheCNN‐basedpredictionsystem, aRFAlgorithmisusedalongwithCNN,anditisdis‐cussedintheremainingsection.

3.ProposedWork

Nowadays,machinelearningapproacheshave beenwidelyadaptedforvarious ieldsduetotheir betterperformancethanotherconventionalmodels.

Hence,thispaperintroducesaCNNalgorithmfor thefeatureextractionofmedicaldata,andthenit usesaRFalgorithmfortheclassi icationofdiseases basedoncertaintrainedconditions.Forinstance,if themodelhastopredictthebloodpressurelevel, theinputfromtheIoTsensorofthepatientis142 mm,andthenthemodelhastopredicttheoutput ashypertension.Toattainthis,themodelhastobe trainedwithcorrespondingconditions.Forthepro‐posedhealthcaresystem,aCNNisusedalongwitha RandomForestclassi ier.Thebeginningoftheprocess isthecollectionofmedicaldata.Thecollecteddata aretobenormalizedbeforebeinggiventoCNN.In CNN,thenormalizeddataundergoesalearningalgo‐rithmfortraining,whichgivesanoptimizedresult. TheoptimizedresultisfedtotheRFclassi ierfordata classi ication.Theprocess lowoftheproposedmodel isdepictedinFigure 1.AnIoTsensorisusedasan inputdevice,whichwilldetectandtakethesensed medicaldatafromthepatientasinput.Thisdatawill benormalizedandfedasinputtotheproposedCNN. Accordingtothemachinelearningprocess,themodel startstolearnandcategorizetheinputdatadepend‐ingontheRFalgorithmusedintheproposedwork. Thiswill inallydetectandgivethedesiredoutputas apredicteddisease.

Themathematicalmodelfortheproposedworkis initializedwiththedatanormalizationprocess.Non‐standardizedinputdatatakemoretimeforthelearn‐ingprocess.Hence,beforegivingthemedicaldata inputsfortrainingandtestingintothemodel,thedata havetobenormalizedanditisgivenbythefollowing expression

where �� de inestheinputmedicaldatasetofM,x andyde inetheconstantofthenormalizer.These normalizedinputdataarefurthergivenasinputto thetrainingandtestinginthemodel.CNNprovides anef icientfeatureextractionoftheinputdatawhen comparedwithothertraditionalmodelssinceitcon‐tainstwospeciallayerscalledtheconvolutionlayer andthepoolinglayer.Featureextractionoftheinput dataisdonebyconvolutionlayerthroughconvolu‐tionoperation.Considertheinputmedicaldatafrom theIoTbeing M and �� beingusedasafeaturemap (��0 =��)oftheconvolutionlayer��.Theconvolution processisgivenby

(2)

Where,�� istheconvolutionweightvector,“⊗”is theconvolutionoperator, ��−1 isthefeaturemapof data,andBi de inesthebiasvector.Aftertheprocess ofconvolution,theresultoftheconvolutionlayeris giventothepoolinglayerwhichconductsthepooling operationbyMaxPoolingmethodinthematrixform. Byconsidering�� asthedownsamplinglayeranditis givenas

(3)

Medical datafrom IoT devices

Normalizing Dataset

Normalizingdata forfeatureselection

Processflowoftheproposedmodel

Afterthepoolingprocessisover,thenewfeature mapexpressionof��0 isobtainedas

(i)=R(C=ci|G0;(V,B)) (4)

Thenewfeaturemapoutputisgivenasinputto theFullyConnectedlayerofCNNs,which lattensthe inputa ixedlengthvectorform.Insteadofasoftmax layerinCNNs,inthiswork,aRFclassi ierisusedto achievebetterclassi ication.TheoutputfromtheFC layerofCNNisfedasinputtotheRFclassi ier.

RFisatypeofdataclassi ierthathasmanytrees ondifferentsubgroupsoftheinputdatasetandpre‐dictstheaccurateoutputbytakingtheaverageofthe givendataset.Byincreasingthenumberoftrees,i.e., subgroups,theaccuracyoftheoutputwillimprove. Forinstance,ifadatasetcontainingmuliple lower imagesisgiventotheRFclassi ier,thisdatasetwill beseparatedintovarioussubgroupsandgiventothe correspondingdecisiontree.Atthedatatrainingstage, everydecisiontreeobtainsapredictedoutput,andif newdataexist,thendependingonthemaximumvote ofsubgroupoutputstheRFclassi ierwillpredictthe resultasa inaldecision.Whereasdecisiontreeclas‐si ierusesasingledecisiontreesincetheprediction accuracywillbelesserwhencomparedtotheRFclas‐si ier.Duetotheusageofmultipledecisiontrees,the RFalgorithmtakeslesstimefortrainingthedataand predictsef icientaccurateoutputforalargerinput datasetthanothertraditionalmodels.Thepredictive accuracydependsontheknowledgeattainedduring thetrainingstage.Thus,itindirectlyindicatesthat usingmoredecisiontreesfortrainingpurposespro‐videsanaccurateprediction.TheRFalgorithmuses threestepsforpredictingtheoutput.Firstistheselec‐tionofthetrainingdataset;secondistheconstruction oftheRFmodel;andthirdisthepredictionofresult bythemajorityvotingmethod.

TheRFapproachisusedtoproduceasimilarity matrixbymeasuringthesimilarityofdatainstances. Forthegivenfeatures �� fromtheoutputofCNN,‘��’ numberoftreesareconstructedasRFintheformof ��×�� matrixwhichisgivenby ��={��} where ��={1,2,3,…��}and��={1,2,3,…��}.Afterthetree growthisdeveloped,thedatasetisgiventothetreefor theclassi icationandpredictionofdata.

Convolutional NeuralNetwork

Featureextraction

Predicted Results

TrainedRandom Forestclassifier

Data classification

Iftheinstances�� and�� arepresentedinthesame leafofnode,thenitwillincreasethesimilarityby1 (i.e., �� and �� improveby1simultaneously).This processisrepeateduntilallthe‘��’treesofthemodel developedwellandtherespectivematrixisobtained. Thecorrelationmatrixisobtainedbydividing�� by thetotalnumberoftrees (��).Thematrixwhichis havingeachelementofthemaindiagonalas‘1’is calledthesimilaritymatrix.Thiscanbecalculated usingthedegreeofsimilaritybetweentheinstances. Considertwosamplesfromtheinputdatasetas��and �� andthesimilaritymatrixformedbetweenthemas {��(��,��)}.ThedataoftheRFapproacharecon‐structedusingtheconceptofmultidimensionalscal‐ing.So,thematrixonthe irstcoordinateofpred(a,b) willbepred( ,b),thematrixonthesecondcoordi‐nateof��(��,��)willbe��(��,−)andthematrix ontwocoordinatesof��(��,��)willbe��(−,−). Fromthis,thematrixformedisgivenas ��(��,��)=0.5×(��(��,��)−��(��,−)

−��(−,��)+��(−,−)) (5)

Let ��(��) betheeigenvalueofthematrixCV(a,b) andVj(a)betheeigenvector.Fromthis,vectorformed isgivenby

x(a)=��(1),��1 (��),��(12),��2 (��),….,) (6)

Thesquarerootofthedistancebetweentwo samplesiscalculatedanditsvalueisequalto 1− ��(��,��).Thevalueof ��(1),��1 (��)isthevalueof vectorx(a)onthejth scalingcoordinate.Themainaim ofprocessscalingistocalculatevectorx(a)through the irstfewscalingcoordinates.Toachievethis,the RFalgorithmextractsseveralmaximumeigenvalues andrespectiveeigenvectorsfromthematrixCV.If thefeatureinputdatahaveunusualsamples,thenthe measurementprocessforthosedataareobtainedby usingtheequation

��(��)= ��(��)=�� 2(��,��) (7)

Fromthis,therealunusualsamplemeasurement ofsample��is ��= ‘a’sample ��(��) (8)

Figure1.

Where ‘a’sample representsthenumberofsam‐plesofmedicaldata,category �� ofthelisteddisease. Foralltheunusualsamples,theprocessismathemat‐icallydescribedusingmeanandstandarddeviationas follows:

Thelastunusualsamplemeasurementvalueis referredtoasanunusualdegree.Thiscanbeobtained bynormalizingtheinitialunusualsamplemeasure‐mentofmedicaldataofthelisteddisease.Forsimple understanding,aRF‐basedapproachtothefeature classi icationofmedicaldataisgivenby

IfPisinthepositiveclass,addonerankinpositiveclassof Z(x)

ElseaddonerankinnegativeclassofZ(x)

Comparetworanksandpredictthemajorityvoteas inal result

IfmajorityvotingofZ(x)isinthepositiveclass,thenpredict theresultasAbnormal

ElsepredicttheresultasNormal End

4.ResultsandDiscussion

where ��(��) denotesthejointclassi icationmodel determinedbytheweightedRFalgorithm,wj isthe singledecisiontree(i.e.,subclassi ier),��denotesthe classi icationtype(i.e.,outputvariables),andfunction ��(.) denotesthedecisionfunction.Theoutputvari‐ablePhastwooptions,oneispositiveandtheotheris negative.If�� presentsaspositive,thentheweighted valueofallsubclassi ierswillbeclassi iedasabnor‐malstatusofthepatientandthiswillbecollectively summedastherankof ��(��).Ontheotherhand,if �� presentsasnegative,thentheweightedvalueofall subclassi ierswillbeclassi iedasthenormalstatusof thepatientandthiswillbecollectivelysummedasthe rankof ��(��).Thecomparisionofthetworanksand thecorrespondingvalueof�� ofthemaximumvoting ofthetworanksdenotesthepredictedclassi ication resultoftheproposedmodel.

Pseudocodefortheproposedhybriddeeplearningalgorithm

Input:NormalizedMedicaldata(A)

Output:PredictedResult(P)

Start

Determinetheconvolutionprocessby �� =��(��−1 ⊗�� +��)

Obtainthefeatureextractionofinputmedicaldataby poolinglayerasQ(i)

ReducethedimensionoffeaturemapbyFClayerintheform of ixedvectorlength FCoutputQ(i)isgivenasinputtoRFclassi ier. RetrievethetrainingdatasetSfromtheinputdatasetofRF classi ierbybootstrapmethod

ObtainSsubclassi ier(or)decisiontreeforSdataset CalculatethevaluesofTP,FP,FN,TN,CPR,CPVforallsub classi iers.

ObtainthevaluesofCAE,CSREandR2Measure.

Obtaintheweightoftheclassi ieras ��

Feedthesystemwithtestdatasettoestimatethe performance.

Feedtheunclassi iedsampleandclassifythemaccordingto F-rankweightedRF

Determinethe inalclassi icationresultofsubclassi ierjas ��(��)

CalculatetherankofZ(x)fromtheoutputvariablevalueP

Theexperimentisconductedtovalidatethepro‐posedCNN‐RFpredictionmodelusingJavaAbstract WindowToolkitinstalledinaninteli3processor 2.20GHZfrequencywith8GBmemory.Thepropor‐tionmetricssuchasCPR,IPR,CPV,Accuracy,and F‐Rank,andthequalityindicessuchasCAE,CSRE, andthepreferabilityindexR2 Measureareusedto verifytheperformanceoftheproposedmodel.Two datasetsareutilizedtotraintheproposedmodel.The irstdatasetiscollectedfromtheCardiologyDepart‐mentoftheChinesePLAGeneralHospital[15].The featureincludesdemographics,vitalsigns,labtests, echocardiography,comorbidities,lengthofstay,and medications.Total105featuresareobtainedfrom eachpatientandatotalof736patientdataareused inthedataset.Theseconddatasetiscollectedfrom theUCImachinelearningrepository[26].Thedataset includes76featureswhichincludedemographics, vitalsigns,cholesterol,echocardiography,andmedi‐cations.

Theperformanceoftheproposedworkisdeter‐minedintermsofproportionmetrices,qualitymetri‐cesandtheprefarabilitymetrices.

4.1.PropotionMetrics

ThismethodusesproportionmetricssuchasAccu‐racy,CorrectPositiveRate(CPR),IncorrectPositive Rate(IPR),andPositivePredictedvalue,Accuracy,and F‐Rankandthesearedeterminedbyusingaconfusion matrixform.Tocalculatethesemetrices,theconfusion matrixisusedwhichisshowninTable1.Thecolumn ofthematrixdenotesthepredictionclassandthe additionofthecolumnvaluedenotestheexamination ofinputdataintheclass.Therowofthematrixrepre‐sentstheactualclass,andtheadditionoftherowvalue denotestheexaminationofdatainthecorresponding class.Themainaimofthisworkistocheckwhether theinputmedicaldatacontainsdiseaseornotusing binaryclassi icationoftheRFclassi ier.TheConfusion matrixoftheproposedmodelispresentedintheform ofthefollowingTable1

Themedicaldatacontainingdiseasearesetas theCorrectclassandthethemedicaldatacontaining nodiseasearesetastheincorrectclass.InTable 1,

Table1. Confusionmatrix

TPmeanstheactualmedicaldatacontainingdisease arecorrectlypredictedasdiseasedpatient,FNmeans theactualmedicaldatacontainingdiseaseareincor‐rectlypredictedasnondiseasedpatient,FPmeansthe actualmedicaldatacontainingnodiseaseareincor‐rectlypredictedasdiseasedpatient,andTNmeans theactualmedicaldatacontainingnodiseasearecor‐rectlypredictedasnon‐diseaseddata.TheCPRor recallisgivenbythefollowingequation

Ontheotherside,ifPpresentsasnegative,thenthe weightedvalueofallsubclassi ierswillbeclassi ied asnormalstatusofthepatientandthiswillbecol‐lectivelysummedastherankofZ(X).Thecomparision ofthetworanksandthecorrespondingvalueofP ofthemaximumvotingofthetworanksdenotesthe predictedclassi icationresultoftheproposedmodel.

4.2.QualityMetrices

Inordertoidentifythequalityoftheproposed model,theComparativeAbsoluteErrorandCompara‐tiveSquareRootErrorandR2 Measureisconsidered andobtained.

TheIPRorFalse‐positiverate(FPR)isgivenbythe followingequation

Thecorrectpredictionvalue(CPV)isgivenbythe followingequation

Theaccuracyoftheproposedmodelisgivenbythe followingequation

However,theRFmethodhasmanyadvantages,the predictionofunbalancedmedicaldataisharderto obtain.Inordertoovercomethis,thisworkcreates aweightedF‐rankintotheRFmodel,whichprovides ef icientperformancefordiseasepredictionbyallo‐catingdistinctweighttoeachdecisiontree.F‐rankis obtainedbycombiningtheresultoftheCPRandCPV. Theperformanceoftheclassi icationisimprovedwith thelargevalueoftheF1‐score.TheF1‐scoreforthe proposedmodelisgivenby

TheComparativeAbsoluteErrorisgivenbythe followingequation

The inaldecisionresultcanbegivenbythefollow‐ingequations

TheComparativeSquareRootErrorisgivenbythe followingequation

WhereSisthetotalnumberofdatasets, ��

isthe orginalvalue,and�� isthepredictedvalue.

4.3.ModelPreferabilityMetrics

Thepreferabilityofthemodelisobtainedbycalcu‐latingthevalueofR2 Measure.R2 Measureisakindof statisticalmeasurewhich indsthealterationquantity inthedependentvariablewhichisdeterminedbythe independentvariable.

Where,Z(x)denotesthejointclassi icationmodel determinedbytheweightedRFalgorithm.wj isthe singledecisiontree(i.e.,subclassi ier),Pdenotesthe classi icationtype(i.e.,outputvariables),andfunction B(⋅)denotesthedecisionfunction.Theoutputvariable Phastwooptionsoneispositiveandtheotheris negative.IfPpresentsaspositive,thentheweighted valueofallsubclassi ierswillbeclassi iedasabnor‐malstatusofthepatientandthiswillbecollectively summedastherankofZ(X).

WhereRASde inestheResidualadditionof squareswhichgivestheaverageofsquarederror betweenoriginalvaluePandpredictedvalue �� and TASde inesthetotaladditionofsquareswhichgives thetotalofthesquarederrorbetweenoriginalvalue PandtheaverageofallP.TherangesofR2 measure liesbetween0and1.Thepreferabilityofthemodel isdecidedbythisrange.IfthevalueofR2 measureis closerorequaltoone,thenthemodelisconsideredas mostpreferablefortheinputmedicaldata.Otherwise, ifthevalueofR2 measureisnegative,thenthemodel isnotprefarablefortheinputmedicaldata.Table 2 depictstheperformancemetricsofproposedmodel fordataset1anddataset2.

Furthermore,theperformanceoftheproposed modelhasbeencomparedwithexistingtechniques evaluatedinChenetal.’s[15]researchfordataset 1andSudarshanetal.’s[26]researchfordataset2. Fordataset1,techniqueslikestackeddenoisingauto‐encoder(SDAE),LR,MLP,MLPwithattentionmecha‐nism(MLP‐A)andmulti‐neuralnetworks(MNNs)are usedforcomparisonwiththeproposedmodel.

Table2. Performancemetricsofproposedmodel

Figure2. Precisionanalysisfordataset1

Fordataset2,techniqueslikesupportvector machines(SVMs),LR,RF,swarmarti icialneuralnet‐work(S‐ANN)andMNNsareusedforcomparison withtheproposedmodel.Figures2and3depictthe precisionanalysisoftheproposedmodelandexist‐ingmodelsfordataset1anddataset2,respectively. Fromtheresults,itisvisiblethattheproposedmodel exhibitsmaximumprecisionwhichindicatestheclas‐si icationperformanceoftheproposedmodelhas beenincreasedduetotheef icientfeatureselection andprocessingusingtheRFclassi ier.Similarly,for dataset2themaximumperformanceisattainedby theproposedmodelwhereasexistingmethodsattains minimumprecisionvaluescomparedtotheproposed model.Theaverageprecisionvalueattainedbythe proposedmodelfordataset1is0.979andfordataset 2theobtainedprecisionis0.984whichismuchbetter thantheexistingtechniques.

Therecallmetricsoftheproposedmodeland existingmodelsfordataset1anddataset2have beendepictedinFigures4and5,respectively.Results demonstratethatthemaximumrecallobtainedbythe proposedmodelforbothdatasets.Thoughtheper‐formanceofMNNismuchbetterthanotherexisting techniques,itislessthantheproposedhybriddeep learningalgorithm.Theaveragerecallvalueattained bytheproposedmodelfordataset1is0.987andfor dataset2theobtainedrecallvalueis0.986.

TheF1‐scoreanalysisfortheproposedmodel andexistingmodelsarecomparativelypresentedin Figures 4 and 5 fordataset1anddataset2,respec‐tively.

Figure3. Precisionanalysisfordataset2

Figure4. Recallanalysisfordataset1

Figure5. Recallanalysisfordataset2

Basedontherecallandprecisionvalues,the F1‐scorehasbeenobtainedandpresented.From theresults,itisvisiblethatthemaximumscoreis attainedbytheproposedmodelcomparedtoexist‐ingtechniques.TheaverageF1‐scoreattainedbythe proposedmodelfordataset1is0.983and0.912for dataset2.ThescoreattainedbytheMNNfordataset1 is0.961,whichis2%lesserthantheproposedmodel, andfordataset2theattainedF1‐scoreis0.90,which is1%lesserthantheproposedmodel.

Theaccuracyoftheproposedmodelandexist‐ingmodelsarecomparativelyanalyzedanddepicted inFigures 8 and 9 fordataset1anddataset2, respectively.Itcanbeobservedfromtheresults thatthemaximumaccuracyisexhibitedbythepro‐posedmodelforbothdatasetswhereastheperfor‐mancesofexistingmodelsarelesserthanthepro‐posedmodelaccuracyvalues.Themaximumaccuracy attainedbytheproposedmodelis0.968fordataset1 and0.978fordataset2.Theoptimalfeatureselec‐tionusingdeepconvolutionlayersandclassi iedusing RFincreasesthepredictionaccuracyoftheproposed model.Whereasexistingtechniqueslagsinperfor‐mancesduetotheimproperfeatureselectionand classi icationprocess.

Table3depictstheperformancecomparativeanal‐ysisoftheproposedmodelandexistingmodelsin termsofaccuracy,recall,andprecision.

Theaveragevaluesfromtheresultsofdataset1 anddataset2arepresentedinthetabulation.Itcan beobservedfromtheresultstheperformanceofpro‐posedmodelismuchbetterthantheexistingmethod‐ologies.Thus,itisvisiblethattheproposedmodel canbeutilizedinthemedicaldomainasasustainable healthcaredataanalysissystem.

Figure6. F1‐scoreanalysisfordataset1

Figure7. F1‐scoreanalysisfordataset2

Figure8. Accuracyanalysisfordataset1

Table3. Performancecomparativeanalysis

Accuracyanalysisfordataset2

5.Conclusion

Ahybriddeeplearningarchitectureforasus‐tainablehealthcaredataanalysissystemispresented inthisresearchworkusingCNNsandaRFalgo‐rithm.Theproposedarchitectureutilizesthefeatures extractedfromconvolutionlayersandclassifythedata usingaRFclassi ierinsteadoffullyconnectedneu‐ralnetworkmodelwhichispresentintheconven‐tionalCNNarchitecture.Thenoveltyinthearchitec‐tureenhancestheclassi icationperformanceofthe dataanalysissystemcomparedtotheconventional CNNmodel.Standardhealthcaredatasetsareusedfor experimentationandveri iedthroughperformance metricslikeaccuracy,recall,precision,F1‐scoreand othernetworkparameters.Todemonstratethebetter performance,existingmethodologieslikeSDAE,LR, MLP,MLP‐A,SVM,RF,S‐ANN,andMNNsarecompared withtheproposedhybridmodel.Experimentalresults depictthattheperformanceoftheproposedmodel ismuchbetterthantheexistingtechniques.Though theperformanceoftheproposedmodelisbetter,the minimumerrororfalsepredictionsreducestheaccu‐racy,whichisconsideredasaminorlimitationofthe proposedmodel.Furthermore,thisresearchworkcan beextendedusingmultideeplearningnetworksto improvetheaccuracy.

AUTHORS

TharageswariK∗ –KarpagamAcademyofHigher Education,India,e‐mail:tharahari1515@gmail.com.

MohanaSundaramN –KarpagamAcademyofHigher Education,India,e‐mail:itismemohan@gmail.com. SanthoshR –KarpagamAcademyofHigherEduca‐tion,India,e‐mail:santhoshrd@gmail.com.

∗Correspondingauthor

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