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Lecture Notes in Electrical Engineering 919 Sio-Iong Ao Len Gelman   Editors Transactions on Engineering Technologies Proceedings of World Congress on Engineering 2021 Lecture Notes in Electrical Engineering Volume 919 SeriesEditors LeopoldoAngrisani,DepartmentofElectricalandInformationTechnologiesEngineering,UniversityofNapoli FedericoII,Naples,Italy MarcoArteaga,DepartamentdeControlyRobótica,UniversidadNacionalAutónomadeMéxico,Coyoacán, Mexico BijayaKetanPanigrahi,ElectricalEngineering,IndianInstituteofTechnologyDelhi,NewDelhi,Delhi,India SamarjitChakraborty,FakultätfürElektrotechnikundInformationstechnik,TUMünchen,Munich,Germany JimingChen,ZhejiangUniversity,Hangzhou,Zhejiang,China ShanbenChen,MaterialsScienceandEngineering,ShanghaiJiaoTongUniversity,Shanghai,China TanKayChen,DepartmentofElectricalandComputerEngineering,NationalUniversityofSingapore, Singapore,Singapore RüdigerDillmann,HumanoidsandIntelligentSystemsLaboratory,KarlsruheInstituteforTechnology, Karlsruhe,Germany HaibinDuan,BeijingUniversityofAeronauticsandAstronautics,Beijing,China GianluigiFerrari,UniversitàdiParma,Parma,Italy ManuelFerre,CentreforAutomationandRoboticsCAR(UPM-CSIC),UniversidadPolitécnicadeMadrid, Madrid,Spain SandraHirche,DepartmentofElectricalEngineeringandInformationScience,TechnischeUniversität München,Munich,Germany FaryarJabbari,DepartmentofMechanicalandAerospaceEngineering,UniversityofCalifornia,Irvine,CA, USA LiminJia,StateKeyLaboratoryofRailTrafficControlandSafety,BeijingJiaotongUniversity,Beijing,China JanuszKacprzyk,SystemsResearchInstitute,PolishAcademyofSciences,Warsaw,Poland AlaaKhamis,GermanUniversityinEgyptElTagamoaElKhames,NewCairoCity,Egypt TorstenKroeger,StanfordUniversity,Stanford,CA,USA YongLi,HunanUniversity,Changsha,Hunan,China QilianLiang,DepartmentofElectricalEngineering,UniversityofTexasatArlington,Arlington,TX,USA FerranMartín,Departamentd’EnginyeriaElectrònica,UniversitatAutònomadeBarcelona,Bellaterra, Barcelona,Spain TanCherMing,CollegeofEngineering,NanyangTechnologicalUniversity,Singapore,Singapore WolfgangMinker,InstituteofInformationTechnology,UniversityofUlm,Ulm,Germany PradeepMisra,DepartmentofElectricalEngineering,WrightStateUniversity,Dayton,OH,USA SebastianMöller,QualityandUsabilityLaboratory,TUBerlin,Berlin,Germany SubhasMukhopadhyay,SchoolofEngineering&AdvancedTechnology,MasseyUniversity,Palmerston North,Manawatu-Wanganui,NewZealand Cun-ZhengNing,ElectricalEngineering,ArizonaStateUniversity,Tempe,AZ,USA ToyoakiNishida,GraduateSchoolofInformatics,KyotoUniversity,Kyoto,Japan LucaOneto,DepartmentofInformatics,Bioengineering.,Robotics,UniversityofGenova,Genova,Genova, Italy FedericaPascucci,DipartimentodiIngegneria,UniversitàdegliStudi“RomaTre”,Rome,Italy YongQin,StateKeyLaboratoryofRailTrafficControlandSafety,BeijingJiaotongUniversity,Beijing,China GanWoonSeng,SchoolofElectrical&ElectronicEngineering,NanyangTechnologicalUniversity, Singapore,Singapore JoachimSpeidel,InstituteofTelecommunications,UniversitätStuttgart,Stuttgart,Germany GermanoVeiga,CampusdaFEUP,INESCPorto,Porto,Portugal HaitaoWu,AcademyofOpto-electronics,ChineseAcademyofSciences,Beijing,China WalterZamboni,DIEM-UniversitàdeglistudidiSalerno,Fisciano,Salerno,Italy JunjieJamesZhang,Charlotte,NC,USA The book series Lecture Notes in Electrical Engineering (LNEE) publishes the latest developments in Electrical Engineering - quickly, informally and in high quality. While original research reported in proceedings and monographs has traditionallyformedthecoreofLNEE,wealsoencourageauthorstosubmitbooks devoted to supporting student education and professional training in the various fieldsandapplicationsareasofelectricalengineering.Theseriescoverclassicaland emergingtopicsconcerning: (cid:129) CommunicationEngineering,InformationTheoryandNetworks (cid:129) ElectronicsEngineeringandMicroelectronics (cid:129) Signal,ImageandSpeechProcessing (cid:129) WirelessandMobileCommunication (cid:129) CircuitsandSystems (cid:129) EnergySystems,PowerElectronicsandElectricalMachines (cid:129) Electro-opticalEngineering (cid:129) InstrumentationEngineering (cid:129) AvionicsEngineering (cid:129) ControlSystems (cid:129) Internet-of-ThingsandCybersecurity (cid:129) BiomedicalDevices,MEMSandNEMS For general information about this book series, comments or suggestions, please [email protected]. To submit a proposal or request further information, please contact the PublishingEditorinyourcountry: China JasmineDou,Editor([email protected]) India,Japan,RestofAsia SwatiMeherishi,EditorialDirector([email protected]) SoutheastAsia,Australia,NewZealand RameshNathPremnath,Editor([email protected]) USA,Canada: MichaelLuby,SeniorEditor([email protected]) AllotherCountries: LeontinaDiCecco,SeniorEditor([email protected]) **ThisseriesisindexedbyEICompendexandScopusdatabases.** · Sio-Iong Ao Len Gelman Editors Transactions on Engineering Technologies Proceedings of World Congress on Engineering 2021 Editors Sio-IongAo LenGelman InternationalAssociationofEngineers SchoolofComputingandEngineering IAENGSecretariat TheUniversityofHuddersfield HongKong,HongKong Huddersfield,UK ISSN 1876-1100 ISSN 1876-1119 (electronic) LectureNotesinElectricalEngineering ISBN 978-981-19-3578-7 ISBN 978-981-19-3579-4 (eBook) https://doi.org/10.1007/978-981-19-3579-4 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SingaporePteLtd.2023 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSingaporePteLtd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Preface AlargeinternationalconferenceonAdvancesinEngineeringTechnologiesandPhys- icalSciencewasheldinLondon,UK,July7–9,2021,undertheWorldCongresson Engineering 2021 (WCE 2021). The WCE 2021 is organized by the International AssociationofEngineers(IAENG);theCongressdetailsareavailableat:http://www. iaeng.org/WCE2021.IAENGisanon-profitinternationalassociationforengineers andcomputerscientists,whichwasfoundedoriginallyin1968.TheWorldCongress on Engineering serves as good platforms for the engineering community to meet witheachotherandtoexchangeideas.Theconferenceshavealsostruckabalance betweentheoreticalandapplicationdevelopment.Theconferencecommitteeshave beenformedwithoverthreehundredcommitteememberswhoaremainlyresearch center heads, faculty deans, department heads, professors, and research scientists fromover30countries.Thecongressistrulyglobalinternationaleventwithahigh levelofparticipationfrommanycountries.TheresponsetotheCongresshasbeen excellent.Therehavebeenmorethanfourhundredmanuscriptsubmissionsforthe WCE 2021. All submitted papers have gone through the peer-review process, and theoverallacceptancerateis50.73%. This volume contains eleven revised and extended research articles written by prominent researchers participating in the conference. Topics covered include mechanicalengineering,engineeringmathematics,computerscience,electricalengi- neering,andindustrialapplications.Thebookoffersthestateoftheartoftremendous advancesinengineeringtechnologiesandphysicalscienceandapplicationsandalso servesasanexcellentreferenceworkforresearchersandgraduatestudentsworking onengineeringtechnologiesandphysicalscienceandapplications. HongKong Prof.Sio-IongAo Huddersfield,UK Prof.LenGelman v Contents Piecewise Monotonic Fitting for Covid-19 Data Analysis oftheUnitedKingdomDuring31-01-2020to19-11-2021 .............. 1 EvangelosE.Vassiliou,IoannisN.Perdikas,DemetriusE.Davos, andIoannisC.Demetriou OntheFreeBoundaryProblemfortheLowReynoldsNumber ........ 17 NinoKhatiashvili CommunityDetectiononProximityNetworks ........................ 33 GünceKezibanOrmanandOnurAkdog˘an A Machine-Learnt Approach to Market Segmentation andPurchasePredictionUsingPoint-Of-Sale(POS)Data ............. 49 IromiR.Paranavithana,ThashikaD.Rupasinghe,andDanielD.Prior FeasibilityandBenefitsofSmallPhotovoltaicSystemsinGhana ....... 63 KingsfordAtanga,GeorgeEduful,andDavidPulfrey DesignofMultipleBearingPlacementsforBrushCutterVibration Reduction ........................................................ 77 YukiKoikeandShingoTsuruoka ExperimentalDEMHybridApproachforPredictionofLandslide inUghelliSandstone ............................................... 87 AdeolaGraceOlugbenga,SimonJosephAntony,AbdulkarimNasir, MohammedUmarGarba,andMuibatDiekolaYahya ExtractingtheEfficientModelofCylindricalandConicalBasins fromDifferentAspectRatios ....................................... 101 ShahadatHossainZehad, SadmanAlFaiyaz, MdRedwanIslam, andIrfanAhmed vii Piecewise Monotonic Fitting for Covid-19 Data Analysis of the United Kingdom During 31-01-2020 to 19-11-2021 EvangelosE.Vassiliou,IoannisN.Perdikas,DemetriusE.Davos, andIoannisC.Demetriou Abstract The least squares piecewise monotonic data approximation method is applied to daily Covid-19 new cases and deaths data of the UK for the period 31- 01-2020to19-11-2021.Thedatademonstratewidevariationinpartsandnoticeable peaks over time. We are interested in estimating turning points of the data in that thefitisusefultoanalyzingtheprogressofthepandemic.Anenormousnumberof combinationsofturningpointsneedbeconsideredinordertofindanoptimalcombi- nation,butthemethodprovidesquiteefficientlyaglobalsolution.Ourresultsshow theefficacyofthepiecewisemonotonicitymethodinlocatingoptimalturningpoints that are significant to the Covid-19 analyses. We consider the facts that influence thechoiceofthenumberofpeaks.Ouranalysisprovideduswithinsightsregarding thedrivingforcesbehindtheturningpointsthatthemethoddetected,whichfurther maybehelpfultomanagement,aspartoftheinformationonwhichdecisionswill bemade. · · · Keywords Approximation Combinatorialproblem Covid-19pandemicdata · · · · Divideddifferenceoffirstorder Leastsquaresfit Peak Piecewisemonotonic · Turningpoint UnitedKingdom B E.E.Vassiliou( ) DepartmentofFinancialandManagementEngineering,UniversityoftheAegean,41 KountouriotouStreet,Chios82100,Greece e-mail:[email protected] I.N.Perdikas·D.E.Davos·I.C.Demetriou DepartmentofEconomics,NationalandKapodistrianUniversityofAthens,1Sofokleousand AristidouStreet,Athens10559,Greece e-mail:[email protected] D.E.Davos e-mail:[email protected] I.C.Demetriou e-mail:[email protected] ©TheAuthor(s),underexclusivelicensetoSpringerNatureSingaporePteLtd.2023 1 S.-I.AoandL.Gelman(eds.),TransactionsonEngineeringTechnologies,LectureNotes inElectricalEngineering919,https://doi.org/10.1007/978-981-19-3579-4_1 2 E.E.Vassiliouetal. 1 Introduction There has been an explosion of scientific publications on the Covid-19 pandemic (see,e.g.,[7]).Theapplicationandanalysisofthepiecewisemonotonicmethodto peakestimationofCovid-19data,whichweaddresshere,areconductedforthefirst time. Daily Covid-19 new cases and deaths data of the UK for the period 31-01- 2020to19-11-2021demonstratewidevariationintime,aswellassomenoticeable peaksofdifferentmagnitudealongthetimerange.Weareinterestedinestimating peaks and trends of these data that can assist in the decision making policy. Since the underlying laws are unknown, the estimation problem is made rather difficult. Weassume,though,thatiftheunderlyingfunctionispiecewisemonotonic,thenthe numberofitsturningpointsissubstantiallylowerthanthenumberofturningpoints ofthedata. Therefore, we apply the method of Demetriou and Powell [6] that makes least changestothedatabyimposingalimitonthenumberofsignchangesinthesequence of the first differences. Specifically, if k−1 is the limit, then the approximated values consist of at most k monotonic sections. Thus, if some value of k can be derived from the form of the underlying function, or if the user is willing to try several values of k, then no other knowledge of this function is required. In this paper, we define “least changes” to the data by minimizing the sum of squares of changes subject to the smoothness condition. Further, two consecutive monotonic sectionsmeetataturningpoint.Thepositionsoftheturningpointsarealsointeger variables of the optimization calculation whose optimal values have to be found automatically.However,aboutO(nk−1)combinationsofpositionscanoccur,which makes it impossible to test each and every one separately. Demetriou and Powell [6]havestudiedthisproblem,and,furthermore,Demetriou[1, 2, 4]hasdeveloped algorithms and software that obtain a global solution in only O(n2+knlog n) 2 computeroperations.Whenk =1(monotoniccase)ork =2(unimodalcase),this workisreducedtoO(n).Thisexcellentefficiencyisduetoadecompositionproperty ofthesolution.Indeed,themethodpartitionsthedataintoatmostk disjointsetsof adjacentvaluesandsolvesak =1problemforeachset. Besidesreductionofcomplexitywhenfindingtheoptimalturningpoints,piece- wisemonotonicapproximationmethodhassomemoreadvantagescomparedtoother approximationtechniques.First,itavoidstheassumptionthat f(x)hasaparametric form.Second,theapproximationprocessisaprojectionbecause,ifitisappliedto the approximated values, then no changes are made thereto. Third, the method of [6]issofastinpracticethatitallowsrunningforasequenceofintegersk ifasuit- ablevalueisnotknowninadvance.Fourth,duetothenatureoftheconstraintson theapproximationcomponents,anyirregularerrorsinthedatadonotcauseripples to the piecewise monotonic fit. Moreover, any peak in the data does not introduce perturbationsawayfromthepeak. ThepiecewisemonotonicapproximationmethodisoutlinedinSect.2.InSect.3, themethodisappliedtobothCovid-19newcasesanddeathsdataoftheUK,some technical aspects of the fit are provided, the estimation of peaks is illustrated, the PiecewiseMonotonicFittingforCovid-19DataAnalysis… 3 resultsofthecalculationareexplained,andtheeffectivenessofthemethodisdemon- strated.InSect.4,theresultsofSect.3areusedinfurtheranalyzingtheprogressof theCovid-19pandemicintheUK,inconjunctionwithvariousimportantdatesand eventspertainingtothetimelineofthepandemic.InSect.5,someconclusionsare presentedandthepossibilityofexpandingthisresearchisdiscussed. AlltheexperimentswerehandledroutinelybytheFortranprogramofDemetriou [2],whichimplementsavariantofthemethodoutlinedinSect.2.Weprovidedjust thedatasequencesandthevalueofk;theoptimalturningpointsandthesmoothed valueswereautomaticallydeliveredbythemethod. Piecewisemonotonicdataapproximationmaybeappliedtoavarietyofsituations inwhichpeakestimationsarerequired,butsufficientinformationislackingtostate a parametric form for the underlying function. Such situations are quite common, so applications of piecewise monotonic approximation can occur in several fields. Examplesarisefromtimeseries[8],fromspectroscopy[3, 5]andfromcurvefitting to physical data, to mention few. More applications appear in the reference list of [4]. 2 PiecewiseMonotonicApproximation Let {(x ,φ ): i =1,2,...,n} be pairs of real numbers, where the abscissae {x : i i i i =1,2,...,n} areinthestrictlyascending order x < x <···< x ,andwhere 1 2 n φ is the measurement of some unknown underlying function, or a process, f(x) i at x .Duetoerrorsofmeasurement,itispossiblethatthenumberofsignchanges i inthesequence{φi+1−φi : i =1,2,...,n−1}ismuchgreaterthanthenumber inthesequence{f(xi+1)− f(xi): i =1,2,...,n−1}.Thepiecewisemonotonic approximation method makes the least change to the data so that the new values {yi : i =1,2,...,n}haveatmostk−1signchangesinthesequence{yi+1−yi : i =1,2,...,n−1} , where k is any positive integer. In this paper we define the “least” change to the data that gives the smoothing condition by choosing the L 2 norm in Rn. Therefore, the piecewise monotonic method calculates numbers {y : i i =1,2,...,n}thatminimizetheexpression (cid:2)n (cid:3)(y ,y ,...,y )= (y −φ )2, (1) 1 2 n i i i=1 subjecttotheconstraints (cid:3) ytj−1 ≤ ytj−1+1 ≤···≤ ytj, j isodd , (2) ytj−1 ≥ ytj−1+1 ≥···≥ ytj, j iseven where{t : j =1,2,...,k−1}areintegersthatsatisfytheconditions j 1=t ≤t ≤···≤t =n. (3) 0 1 k

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