MemoirsoftheFacultyofEngineerlng，KyushuUniversity，Vol．64，No．1，March ZOO4 AnalysisofMotorValveOperationsinFukuokaCityWater SupplyNetworkUsingSelf−OrganizingMap by HaythamAwAD＊，AkiraKAWAMURA＊＊，KenjiJINNO＊＊＊andYusukeKuNO＊（ReceivedDecember17，2003） Abstract ThewaterdistributionregulationsystemofFukuokaCityisasystem in which motor valves are operated by remote control while pressure gaugesandflowmetersattachedtodistributionpipesaremonit〔red．One ofthemain objectives ofthis systemis to regulate pressure jn allthe networknodesbetweenloweranduppertargetvalues． Withtheever−increaslngCOmplexityofthecity−Widedistributionpipe network，mOtOrValveoperationstoregulatepressureandflow cameto dependmoreandmoreontheexperienceandskillsofoperators．Forthis reason，animprovementofvalveoperationssupportshouldbed（）nebased onvalve operation planningfor flow andpressure regulation and the operationknowledgedatabasewhichisconstructedonthebasjsofpast experiencein order to prevent the events of pressure regula二ion falls outsidetherequiredtargetpressurerangeandalsotoreduceth∈effortof OperatOrS． Therefore in this study and with the assistance of three years of telemetrydata，ananalysisoftheexistingvalveoperationof a certain blockwithinthecitydistrictisperformedusingbothcorrelatiorLanalysis andanunsupervisedclassofArtificialNeuralNetworks（ANN）named Self−OrganizingMaps（SOM）．Resultsshowthatcorrelationan；11ysishas successfullyclassifiedtheoperationtypesofdifferentvalvesat［achedto thestudiednetworkintothreecategorieswhileSOMisaneffi・：ienttool in clustering the different complicated operationalpatterns（・f valves， visualizing the huge amount of telemetry valves data，dete二ting the patternswhichneedfutureimprovementandcouldpresentgoo・ialterna− tivesolutionsforimprovlngfuturevalveoperationalsupport・ Keywords：Waterdistributionnetworks，MotorvalvecontrolCorrela− tion analysis，Pressure regulation，Self−Organizilg Maps （SOM），ArtificialNeuralNetworks（ANN）＊GraduateStudent，Institute ofEnvironmentalSystems ＊＊Associate Professor，Institute ofEnvironmentalSystems ＊＊＊Professor，InstituteofEnvironmentalSystems 64 H．AwAD，A．KAWAMURA，K．JINNO and Y．KuNO 1．Introduction FukuokaCityispoorinwaterresourceswithnolargeriverswithinthecitydistrict．For thisreasonithastakenvariousmeasurestowardsthecreationofa“water−SaVlngCity”，a Cityinwhichvaluablewaterwillnotbewasted．Onesuchmeasurehasbeentheinsta11ation Ofthewaterdistributionregulationsystem；OneOftheleadingsystemsofitstypeinJapanl）． Withthissystem，rOund−the−Clockcentralizedmonitoringofdatafrompressuregaugesand flowmeters attachedto distributionpipesiscarried out，While onthebasis ofthis data， PreSSureandflowwithintheentirecitydistrictisregulatedbytheremoteoperationofmotor Valves・Byputtingthissystemintooperation，ithasbeenpossiblenotonlytosupplywater evenlytoconsumers，butbecausewaterpressurecanberegulatedappropriatelyithasalso beenpossibletoreduceexcesspressureandconservewater． Thepurposeofawatersupplynetworkistoconveywatertoconsumersintherequired quantityatappropriatepressure，Ofacceptablequality，aSeCOnOmicallyaspossible．There− foreinordertoimprovetheexistingsystemoperationandmanagementofFukuokaCity Water SuPply network，the Water Distribution ControICenter whichis responsible for operation and management of the whole city water distribution network has introduced SeVeraloperationalsupportfunctionstofurtherthereliabilityofwatersupplyanddistribu− tion・TablelshowsasummaryoftheusedoperationalsupportfunctionsusedinFukuoka City water supply system，their purposes and factors affecting the formulation of those functions・By centralizing the city network controland uslng the operationalsupport functions，thecenterseekstoachieveseveralobjectiveslikeregulatingflowbetweenwater purificationplants，reducingmanpowerrequiredforvalveoperationsduringwatershortages， makingearly discovery ofdistributionpipe abnormalities andrespondrapidlybyremote COntrOl；andgatheringandanalyzinginformationtomakewaterdistributionmoreefficient2）． Theultimategoalofwatersupplyoperationsistomakeallfacilitiesfunctionworkatthe peakofefficiency．Towardthisend，WOrkhascontinueduptopresentdaytoimproveallthe functionsoftheWaterDistributionControICenter，butvariouskindsofproblemsarestill encounteredduringoperations． Asoneofthoseproblems，istheproblemsrelatedtothemotorvalveoperationswhich TablelOperationalsupportfunctionsusedinFukuokaCitywaterdistributionnetwork． Function Demand Estimation Support BriefPurpose Affectedfactors −Estimate totalwater demandof −WeatherConditions． theCitywatersupplynetwork．一Timeperiodandamountofwater −Factorsaffectingtheday（WOrking from each purification plant. day，holiday，Month，etC・・・）・ーPastdataforthatparticularday． −Suggest recommended scenario −Hydraulicconditionsofthestudied Trouble−Shootlng Support incaseofpipebreakagecausedby PartOftheCitywaternetwork． accident or Bre，SuSPenSion of −Duration of the recommended WaterSuPPly，PIPeCleanslngand restoration of supply −Carried out the additional −Changlngthestageofelectricmotor ScheduleControl OPerationsforvalvesaperture Setting． ValveOperations Support −Suggestedsetofelectricmotor −Requiredwaterdemand． −Pressureregulationconstraints． ValveopenlngS． AnalysisofMotorValveOperationsinFukuokaCityWaterSupplyNetworkUsingSelf−OrganizingMap 65 aimtofindtheoptimalelectric openingsofdifferentmotorvalvesto achievetwotargets； feedconsumerswiththeirrequirementsofwaterdemandandtrytoregulatewaterpressure inthe entirewatersupplynetwork betweenupper andlowervalues．Approximately the loweranduppertargetvaluesintheFukuokaCitywatersupplynetworkaresetto24mand 32m，reSpeCtively．Thelowerpressuretargetvalueisassignedbecauseconsumerswantto receive water with adequate pressure while the upper target valueisintroduced for the purpose that higher pressures cause anincrease ofthe amount ofleakedwater from the network．Bycontrollingthedistributionofhydraulicpressuresinthenetwork，pipebreaking couldbelessened and water couldbe conserved． Available models that explore pressure regulation problem throughoptimalcontrol valve settings could be dividedinto two categories．In the first type，a mathematical statementisusedasanobjectivefunctiontobeminimized．Thismathematicalstatement couldbepresentedintheformofnetworkpressureregulation3，4）orasthetotalamountof leakedwaterfromthenetwork5）．Themaindrawbackofuslngthiscategoryofmodelsisits COmputationaltime．Theobjectivefunctionofal1availablemodelsofthatclassdealdirectly withthepressureregulationproblemfrom anoptimizationpoint ofviewwhichrequireda computationaltime depending on the water network size，the number of variables to be optimizedandtheusedoptimizationmethodandinmostcasesrequiredanetworksimplifica− tionmethodwhichisconsiderasanotheroptimizationproblem． Thesecondcategoryofthepressureregulationmodelsarebasedonextractingseveral usefuloperationalrulesbased on the previous knowledge and experience，analyzing past recordeddataandthepresentexperienceandskillsofoperators．Existingvalveoperation supportfunctionsappliedinFukuokaCityarefromthistype．Themainadvantageofthis kindofmodelsthatitcouldbeusedason−1ineoperationalmodelprovidinguswiththemost recommendedvaluesforelectricmotorvalvessetandprovidinguswiththesystemresponse for those recommended values． InthisstudyananalysisoftheexistingmotorvalveoperationsofBlock120fFukuoka Citywater supplynetworkispresented．We start to classify the different operations of electric motor valves attached to the plpeS Of Block12．This classification has been performedusingthreeyearsofcontinuoustelemetrydatawithonehourinterval．Thenwe tried to use an unsupervised class of ArtificialNeuralNetworks（ANN）named Self− OrganizingMaps（SOM）inordertoexpandtheanalysisofexistingvalveoperationsusedin this block． ANN are already quite commonly usedin severalapplications of water resources englneerlngaSanalternativeforconventionalcomputationalmodels．ANNusedanensem− bleofinput−OutputpatternStOmOdelamapfromaninputlayertoanoutputlayer，Whichis consideredinthiscaseasupervisedtypeofANN．SOMareconsideredalsoaclassofANN buttrainedinanunsupervisedway．ThatmeansSOMdonotrequireanassociatedoutput （target）for eachinput pattern during training．The process of SOM classify theinput patternstodifferentgroupsbasedonmeasuringsimilaritybetweeninputpatterns，Withnoor littleknowledgeaboutthestructure ofuseddata． ThepurposeofusingSOMinthisstudyistotestitsabilityofclusteringthedifferent complicatedoperationalgroups ofvalves，Visualizingthehugeamount oftelemetryvalve dataanddetectingthegroupswhichneedfutureimprovement．Finally，uSingtheresults obtainedfromtheSOM，WeCOuldsuggestgoodalternativesolutionsforimprovingfuture Valve operations． 66 H．AwAD，A．KAWAMURA，K．JINNOand Y．KuNO 2．Self−OrganizingMaps（SOM） TheSOMisrelativelyasimpleunsupervisedneuralnetworkusedforthecategorization Ofinputpatternsintoafinitenumberofclasses．SOMconsistsoftwolayersunits，theinput unitsare a one−dimensionalarraywhichprovides simulationto a usuallytwo−dimensional arrayofmapspaceunits（outputunits）anda11unitsintheinputlayerarefullyconnected With the unitsin the outputlayer（Fig．1）．The neurons of the outputlayer whichis preferabletobearrangedintwodimensionalgridsforbettervisualizationareconnectedto adjacent neurons by a neighborhood relation dictating the structure of the map．The arrangementoftheoutputlayerneuronsareusuallydistributedinrectangularorhexagonal arrangement．Genera11yitispreferabletousethehexagonallattice，becauseitdoesnotfavor horizontalandverticaldirectionsasmuchasrectangulararray6）． When aninput vector xis sent throughthe network，eaCh neuron k of the output network，Whichisalsocalledcompetitivelayercomputesthedistancebetweentheweight VeCtOr W andtheinputvectorx．Amongalltheoutputneurons，theso−Calledwinningunit OrBesトMatchingUnit（BMU）isdeterminedbythesimilaritybetweentheweightvectorw Onthatunitandtheinputvectorx．Foraninputvectorx，theBMUisdeterminedby li∬一抄。Il＝min（llJ一粧購（1） inwhichthesubscriptcreferstothewinningunit（BMU），Il…l‡isthedistancemeasureand ireferstoallunitsinthecompetitionlayer，inEq．1eachunitinthetwo−dimensionaloutput layerisidentifiedbyasinglesubscriptforsimplicity．Accordingly，aSeCOndwinningunitwill bedeterminedwithrespecttothesecondinputvector，andsoforth．Attheendofcompetition OnlyoneunitinthecompetitivelayerwinsincorrespondingtoonelnputVeCtOr． FortheBMUanditsneighborhoodneurons，theweightvectors w areupdatedbythe SOMlearningrule．ル勅1）＝（十α（佃）（抽卜刷） e （2） Whereαisthelearningrateattimet；hciSO−Calledneighborhoodfunctionthatisvalidforthe neighborhoodNc・ThevalueofαVariesfromO．Otol．0，anditcontroIstherateoflearning AnαOfl・Omeansitlearnsanewexampleassoonasitispresented・However，itforgets Fig・．1StructureofSOMnetwork． AnalysisofMotorValveOperationsinFukuokaCityWaterSupplyNetworkUsingSelf−OrganizingMap 67 allpreviousexamplesofthatclass．Similarly，anαOfO．Omeansthatthenetworkdoesno learnatall，butclassifiesnewexamplesbasedonpreviousexperiencesonly．Theneighbor− hoodfunctionhci（t）isatime−Variableandadecreasingfunction［hci（t）→Owhent→∞］．It isoftenrepresentedbyaGaussianfunctionasfollow ゐ。f（オ）＝e￣ dき〟2鞘）2 （3） where6istheneighborhoodradiusattimetanddci＝llr。−rillisthedistancebetweenmap units c andionthemapgrid． Thetrainingisusuallyperformedintwophases．Inthefirstphase，relativelylargeinitia learningrateandneighborhoodradiusareused．Inthesecondphasebothlearningrateand neighborhoodradiusaresmallrightfromthebeginnlng．Thisprocedurecorrespondstofirst tuningtheSOMapproximatelytothesamespaceastheinputdataandthenfine−tuningthe map． Therearetwodifferentstylesoftrainingstrategies．Insequentialtrainlngtheweights areupdatedeachtimewhenaninputvectorispresented．Inbatchtrainingtheweightsare Onlyupdatedafterthepresentationofallinputvectors．Inmanyapplications，batchtraining typeis the preferred option，aSit forces the search to movein the direction of the true gradientateachweightupdate．However，SeVeralresearcherssuggestusingthesequenti type，aSitrequireslessstorageand“…makesthesearchpathintheweightspacestochastic… Which allowsfor a wider exploration ofthe searchspace and，pOtentially，1eadstobetter qualitysolutions”7・8） Aftersometrainingsteps，theSOMwillarrangehigh−dimensionalinputdataalongit twoqdimensionaloutputspacesuchthatsimilarinputsaremappedontoneighboringregions Of the map which means that the similarity of theinput datais preserved within the representationspaceoftheSOM．Usually，intheSOMapplication，inordertoensur allvariablesofanylnputVeCtOrXreCeiveequalattentionduringthetrainingprocess，itis importanttonormalizetheinputvectortounitlengthbeforethetrainingsteps． To measure the ability of SOM to arrange the differentinput vectors throughits two−dimensiongrid，uSuallytwoevaluationcriteriacouldbeappliedtomeasurethequality OfSOM；reSOlutionandtopologypreservation．Foridentifyingandmeasuringtheresolution OftheSOM，WeCOmputethequantizationerror6）whichistheaveragedistancebetweeneach datavectoranditswinningunit（BMU）．Thetopographicerrorwhichusedtopresentthe accuracy of the training mapin the preserving topologyis also calculated．This error representstheproportionofallinputdatavectorsforwhichfirstandsecondBMUsarenot adjacent for the measurement of topology preservation．The topographic error can be calculated as follows9）：どf＝去鼻“（∬た）（4） whereNisthenumberofinputvectors；u（xk）isO．OifthefirstandsecondBMU’sofxkare nexttoeachother，Otherwise u（xk）isl．0． Inrecenttimes，aVarietyofapplicationshaveusedtheSOMinseveralwaterresources managementproblems．TheFollowingrepresentsomesuccessfulapplicationsinthisfield （i）Evaluation of water qualityin reservoirslO），（ii）Data division for water resources modelsll），（iii）Optimizationofwaterapplicationundertrickleirrigation12），（iv）Riverflow forecasting13）；and（Ⅴ）Classification of flood datainto classes defined by representative regionalcatchments14）．ReviewtheliteratureshowalsothatSOMhasneverbeenusedinth field of water distribution network which provide a rich future area of researchin the 68 H．AwAD，A．KAWAMURA，K．JINNOandY．KuNO applicationofSOMinthisfield． InthispaperweusedSOMtoclassifydifferentelectricmotor valve operations，eaCh represented by one vector representing the actualrecorded set of valves setting．After Classification we usedtwo methods to cluster the obtained SOM to severalmain groups． First，We applied the method of unified distance matrix6）（U−matrix）whichis based on CalculatingthedistancebetweenadjacentSOMunits．Aftercalculatedthe U−matrixitcould bevisualizedonaspecialcolormapsizeandthenwecoulddetectthedifferentclustersusing acolorscaledisplayonthemap． Anothermethodthatwehaveappliedtoselectthebestnumberofgroupsiscomputing theDavies−BouldinIndex（DBI）15）．ThesmallestvalueofDBIrepresentsthebestnumberof groupswhichindicatethebestclustering．SmallDBIvalues occurfor asolutionwithlow Variancewithingroups（Clusters）andhighvariancebetweenclusters．Therefore，aChoice ismadeconcerningthenumber ofclusters atwhichtheDBIattainsitsminimumvalue． After clustering the different groups of motor valve operations with the methods of U−matrix and DBI，We make a comparative analysis of the characteristics of different Operationgroups and their effect on the realmeasured pressure at the different pressure gauges．Withtheresultsobtainedwecoulddetectthewelloperatedgroupsandthegroups thatneedfutureimprovement． 3．Case StudyandI）ata Used ThewatersupplynetworkofFukuokacityisdividedinto21blocksandtheareaserved byeachblocktakesintoconsiderationseparatewaterdistributionareas，differencesinland elevation，location of rivers and railroads，aS Wellaslocaldifferencesinwater usage． FukuokaCityisthefirstJapanese Citythathasestablished a Water DistributionControI Centerin1981．InthissystemmotorvalvesareoperatedbyremotecontroIwhilepressure gaugesandflowmetersattachedtodistributionpipesaremonitored．Thevaluesofflowrate passlng eaCh flow meter，the openlng perCentage Of each motor valve and the pressure intensityateachpressuregauge arerecordedeveryminute．AsinApri12001，thesystem includes120water pressure gauges，68flow meters，and149electric motor valves at all importantpointsalongthewaterdistributionpipes． Block12asoneofthemainblocksofthecitynetworkisselectedasacasestudydue toitslocationinthecenterofthecity．Ourcasestudy（Block12）issurroundedfromthe northbyHakataBay，fromtheeastbytheNakaRiverandBlock9，fromthewestbythe HiiRiverandBlock15；andfromthesouthbyanelevatedarea（Block50）andalsobyBlock 13．In Block12the originalnumber of nodes and pipes arel133and1645，reSPeCtively， COnSidering pipes with diameters more thanlOO mm．A skeletonized figure of Block12 COntainlng57nodesand83pipesisshowninFig．2．Inthisblock，thereare20motorvalves， 7flowmeters，andllpressuregauges．Itisnoticedfromthefigurethatflowmetersare COnneCtedtothemaininletsandoutletsandavalveisconnectedadjacenttoeachflowmeter inordertocontroltheflowenteringorleavingtheblock（e．g．，Ml，Vl；M4，V6；…）． remainingmotorvalvesareconnectedtothemainjunctionsofthisnetwork（e．g．，V3；V5；V7； …）tomakewaterdistributionmoreefficientandalsoplayanimportantroletochangethe directionofwaterflowatanypipeinordertopreventtheoccurrenceofredwater．Pressure gauges arelocated at different zonesin theimportant end flow points to maintain an acceptablevalueofpressureandgetagoodideaaboutthewaterpressurestatusinthiszone． Theanalyzeddatainthisstudyarebasedonhourlydataforallflowmeters，preSSure gauges，and motor valves sincelSt April1998to31St March2001．This makes the total AnalysisofMotorValveOperationsinFukuokaCityWaterSupplyNetworkUsingSelf−OrganizingMap 69 Fig．2 Block120ftheFukuokaCitywatersupply． numberofdataforeachtelemeter26304（totalnumberofhoursduringthisperiod）．The analysisofmotorvalveoperationsisbasedon24799vectorsoutofthe26304vectorsbecause thereare1505vectorsofvalvesdatasetwhicharecompletelymissing． 4．Correlation Analysis EachmotorvalveofBlock12hasitsowntimeseriesoperationduringwhichthevalve Openingvariesbetweenaminimumandmaximumvalues．Togetanideaaboutthedifferent Valvesoperationweplotthebox−Whiskerplotforthedifferent20motorvalvesofBlock12 （seeFig．3）．Inthisfigure，thebox−Whiskerplotshowsthemedian，upperandlowerquart upperandlower5％ofeventsandthemaximumandlowermotorvalveopeningrecordedfor thethreeyearsofvalvestelemetrydataset．Inthisfigure，SOmemOtOrValvesarecontinually 1 2 3 4 5 6 7 8 910111213141516171819 20 MotorvaJve number Fig．3 Box−Whiskerplotsforthe20electricmotorvalveofBlock12． 70 H．AwAD，A．KAWAMURA，K．JINNOand Y．KuNO 00 80 0 6 8 ︵U 10 12 14 16 18 20 22 24 8 96 6 84 4 72 La9time（l℃U「S） 4 60 2 48 2 36 40 24 60 乳首じ苫J￠d 0 12 Time（hours）（C） 5 2 ￠切望u￠2￠d 0 5 1 ︵U 1 監豆∪申P芯d 0 2 00 64 10 12 14 16 18 2 Time（hou「S） 0 10 12 14 16 18 20 22 24 2 4 6 8 10 20 22 24 Time（hours） Fig．4（A）statisticallyclassificationofelectricmotorvalvesusingautocorrelationfunc− tion，（B）Valve17asanexampleoftypel，（C）Valve16asanexampleoftype2； and（D）Valve6asanexampleoftype3． Operated（e．g．，V2，V3andV4）whileothermotorvalvesareoperatedoccasiona11y（see V8andV9）． Toclassifythedifferentoperationaltypesofmotorvalves，WeCOmputeaCOllectionof COrrelationcoefficientcalculatedforvariouslagswhichisnamedautocorrelationfunction （ACF）foreachmotorvalveofBlock12．Figure4AshowsanexampleofACFplottedfor thetypicalthreetypesofvalveoperationsinthisnetworkwhileFigs．4B，4Cand4Dshow abox−Whiskerplot ofthestatisticaldistributionofhourlydegreeofvalve openingfor the Classified three types of valve operationsin Block12．The box−Whisker plot shows the median，upper andlower quartiles and also the maximum and minimum valve opening recordedforeachtypeofthemotorvalves．V17，V16andV6areselectedasrepresentative Oftypel，type2andtype3respectively． ThefollowlngSarethemaincharacteristicsofthethreetypesofvalves． −Tbpel：SixvalvesofthisnetworkfallsinthistypeandtheyareValvesl，4，8，9，11 and17．Allthese valves are connected to the main entrances of the network and have approximatelyconstantpercentage of openingduringthedifferenthours ofthe day（Fig． 4B）． −2bpe2：Valves13，15，16and20areclassifiedunderthistype．Thosevalveshaveonly Onemainchangeduringdailyoperation；theyarecompletelyclosedduringnighttime（from lO，00p．m．to6．00a．m．）andtheyhaveapproximatelyconstantpercentageofopeningdu theremalnlnghoursoftheday．ThistypeisconnectedtotheinternalplpeSOftheblockto reducepipe−1eakagethroughthenetwork；andalsotodecreasethepressureduringthenight AnalysisofMotorValveOperationsinFukuokaCityWaterSupplyNetworkUsingSelf−OrganizingMap 71 timewhenthewaterdemandisatminimum（Fig．4C）．一物e3：TheremaininglOvalvesareconsideredofthistype．Thistypeofvalveshas twomainchangesduringdailyoperationandtheyareusedtomaintainthepressurevalue between24mand32m．Thereforethosevalvesareslightlyopenedaroundtherush−hou （at7．00a．m．and8．00p．m．）andtheyarecompletelyclosedduringthelatenighthours（F 4D）． Theclassificationofvalvesisimportantforfutureimprovementofmotorvalveopera− tionsaccordingtothetimehorizononwhichtheyareconsidered．Forlong−termOperation， thevalvesof7う少elareresponsibleforsupplyingthedifferentnodesofBlock12withthe requiredwaterdemand．Anyfutureimprovementsofthosevalvesettingsshouldbedonein COnjunctionwithothervalves connectedtothemaininlets and outlets of adjacentblocks． Forexample，anyChange occursinmotorvalve（Vl）willaffectdirectlythe operationo Block15whichislocatedinthewestofthestudiedBlock12．Fromanotherpointofview electricmotorvalve（Vl）couldbeconsideredasacommonvalvebetweenbothblocks12and 15． Formiddle−termOperationordailymanagement，thefourvalvesof乃少e2iscompletely affectthistimehorizonmanagementandinalesserdegreethelOvalvesof乃少e3．Those Valvestakeintoconsiderationthemaindailychangeinconsumption．Therefore，theyare COmpletelyclosedduringthenighttimewhenthewaterdemandatdifferentnetworknodes isatitsminimum．Ontheotherhand，theyarepartiallyopenedduringtheremaininghours Ofdailyoperation．Whenconsideringtheroughtuningofpressureregulationproblemboth Valvesof7Weland2shouldbeinvoIvedinthisoperationtoregulatepressureatdifferent networknodesbetweenthedesiredupperandlowertargetvalues． For short−term Operation or hourly management，734）e3valves take the complete responsibilityofregulatingthepressureatdifferentnetworknodes．Thosevalveshaveno effect on the adjacent blocks and could be considered as fine−tuning operationalvalves． Accordingtothetypeoftimehorizonoperation，thevalveoperationscouldbedividedinto threeoperationterms． 5．Self・OrganlZlng MapsAnalysis InputvectorstotheSOMareallsetsofelectricmotorvalvesforthestudiedthreeyears Ofavailablehourlydata．ConsideringthatthesizeofSOMwillaffectdirectlytheclassifica− tionofinputvectorstothedifferentSOMcompetitivelayerunits，thereforeasuitablesize Of SOM shouldbe used．Different map size has been evaluated by calculating the above mentionedtopographicandquantizationerrors．Figure5showscontourmapforbothkinds Oferrorsusedinthisstudyforallpossibletwo−dimensionalmapsizeswhichvariesfrom2to 30neurons． Itisclearfrombotherrorcontourmapsthatthesizeofthemaphasastrongeffecton the distribution efficiency ofinput data vectors to the different neurons of the map．In general，increasingthemapsizewillincreasethetopographicerrorwhichiscalculatedusing Eq．4andrepresentedinpercentage（Fig．5A）whileinFig．5Bbringsmoreresolutioni mapping when the quantization error decreases．Itis not recommended regarding both figurestoselectarectangularSOMshape，thetopographicerrorincreaserapidlynearboth horizontalandverticalaxisandthequantizationerrorcontourlineshasconcaveshapenear thediagonallinewhichstartsfromtheorigin． Itisimportanttoselectanoptimalmapsizethereforewedecidetoselectasquareshape andalsoamiddlemapsize．Themapsizeselectedtopresentthedifferentclassificationof 72 H．AwAD，A．KAWAMURA，K．JINNOandY．KuNO 3 （B）QuantizationErrorContourMap （A）Topog「aphicErrorContourMap UO竜聖篭ゝ∪芯UO﹂コ2−O﹂むq∈﹁一Z 2 2 uO膏聖壱ゝ∪芯UO﹂コぎー〇﹂むq∈コZ 5 10 15 20 25 30 5 10 15 20 25 30 Numberofneuronsinxdirection Numberofneuronsinxdirection Fig．5 Contourmap oftopographic and quantizationerrors，SelectedSOM sizelOXlO （Topographicandquantizationerrorsequa12．9541and2．3456，reSpeCtively）． motorvalveoperationsis．Atthatsizethetopographicandquantizationerrorsequa12．9541 and2．3456，reSpeCtively．That’smeanthatoutofthe24799vectorusedinthetrainingofSOM thereisonly733vectorinwhichthefirstandsecondBMUaren’tadjacent． After selecting a map size oflOxlO the mapis trained with the valve opening data Subjectedto Eq．1and2．Figure6shows a representationof a11data components onthe trainedSOM．AsshowninFig．6SOMcouldbeconsideredasagoodtooltovisualizeahigh dimensionaldata．InFig．6，24799vectorsarepresentedwhereeachvectorcontains20moto Valveopening．OneofthegoodadvantagesuponclassifyingdifferentinputvectorsbySOM thatif any vector contains missing data the SOM could dealwith this vector during the training process；eaCh corresponding weight for the missing datain the vector wi11be neglectedtemporallyfromthecalculation．Focusingonanyunitofthemap（forexamplethe upperleft one），WeWillsee that Vlrepresents an opening oflO％，V2correspondto an Openingof2％uptoV20whichiscompletelyclosed．Thesameprocedurecouldbecarried OnOtherunits．ThegooddistributionofcolorsinSOMfora11componentsoffersasuitable representationofanyvalvesettingandalsoglVeSagOOdideaabouttheoperationruleofthis valve and the relation with other valves． Forallthethreetypesofvalveoperationsmentionedinthecorrelationanalysissection， relativelyhighcrosscorrelationsexistbetweenallvalveslocatedinthesametype．For7We 2valves（V13，V15，V16andV20）theupperareainthecomponentanalysismap（Fig．6） indicatesthatthosevalvesarecompletelyclosedwhilethelowerunitsshowthatthefour Valvesarepartiallyopenedattheirmaximumvaluesduringthethreeyearsofoperation． TocomparethepresentationofSOMcomponentswiththebox−Whiskerplotofmotor Valvesshownin Fig．3．Bothpresentationsgive a goodindication about different valves Operation．When presenting an operation ruleitis difficult for the box−Whisker plot to efficientlyrepresentthecomplicatedelectricmotorvalveoperationslikethepresentationof the SOM shownin Fig．6in which any unit represent an operationalrule while each COmpOnentrepreSentthecharacteristicsofthecorrespondingmotorvalve． AnalysisofMotorValveOperationsinFukuokaCityWaterSupplyNetworkUsingSelf−OrganizingMap Va付e2 −12．9 Valve3 0 1 5 Va付e9 7 5 只V 5 5 7 ∩︶ l門⊆⊆：L■匝仁．．トl 12 5 5 つ‘ 4 1 八U て 0 0 5 5 8 6 1 7 ÷÷十十 ∧U 0 1 1 小＋小十 5 5 7 5 5 〓．︰“∵ ＝V 1 4 ︵U ※十小つエ︵U 0 1 2 ∵十∴※ 甲．卜︰い．．、．．hi 2 1 鹿 a 1 Valvell 11 VaLve4 t68 Valve5 1 34 Va付el 73 6 8 1 府逐斗 VaNe18 9 5 7 91 8 ∩︶・i ︵U ナ︸十十 ∵ 9 ︹ノー 6 8 0 網凪−四一 l Fig・．6VisualizationofallelectricmotorvalvesopeningsofBlock12calculatedinthetrainedSOM． Fig．7 UnifieddistancematrixoftrainedSOMoftheelectricmotorvalves（U−Matrix）． ToclusterthedifferentlOOunitsofthetrainedSOMtoitsmaingroups，the U−matrix techniquehasbeenapplied．Fig11re7showstheunifieddistancematrixofsize19×19where SCalecolorbarontherightrepresentsthedifferencesbetweenSOMunits；eaChunitinthe U−matrixmaprepresentsweightdifferencebetweentwoadjacentneuronsofthecompetitive 74 H．AwAD，A．KAWAMURA，K．JINNO and Y．KuNO SOMlayer．Highestvaluerepresentsbigdifferenceandthentheboundarybetweengroups； ifseveraladjacentunitshavesamecolors（lowestvalues）thentheyarelocatedinthesame group．Rough1ywecoulddeterminefromthe U−matrixmapthemaingroupsofthevalves SuppOrtfunctionbutto accuratelyestimatethenumber ofgroupswecompute theDavies− BouldinIndex（DBI）for clusters number varies from2to20．The minimum DBIis O．61 recordedatlOclusters（Fig．8）．Clustersdefinedby U−matrixandtheDBIagreedwitheach Other．Thus，ValvesdatawereclassifiedintotengroupsmentioninLatinnumbers（I，II，III，．．．，Ⅹ）whereeachgrouprepresentaunionofSOMneurons． Figure9showstheclustersofthetrainedSOMunits．Thenumberwritteninsideeach 1 9 0∩︶O nO 7 XむPリー∪叫P一⊃Om・Sのち田口 2 4 6 8 10 12 14 Numberofc［usters 16 18 20 Fig．8 Davies−BouldinIndex（DBI）atdifferentnumberofclustersonthetrainedSOM． Fig．9 ClustersofthetrainedSOMunits．Theboundariesofdifferentgroupsmentionedin LatinnumbersaresetuslngtheDBIand U−matrixmethods．Thenumberwritten insideeachunitindicatesthetotalnumberofhitsassociatedwiththoseunits（Total numberofhitsis24799） AnalysisofMotorValveOperationsinFukuokaCityWaterSupplyNetworkUsingSelf−OrganizingMap 75 unitindicates the totalnumber of hits associated with those units or thelocation of BMU eachvectorofinputdata．BoundariesofdifferentgroupsmentionedinLatinnumbersareset using the DBIand U−matrix methods．Distribution of the24799hit varies between a minimumvalueof628hitrecordedatgroupIIto5256hitrecordedatgroupIII． SOMcouldbeconsideredasgoodtoolforthepresentationofhigh1ydimensionaldata． Itpresentsthecharacteristicsofeachdatacomponentandalsopresentstherelationbetween differentcomponents．For timeseries analysisSOM couldpresentsalsothetrajectory of data occurrence in which the movement of events from one unit to another on the map indicatesimportantinformationaboutthestudiedproblem．Afterthe clustering ofmotor valveoperationstoitsmaingroups，inFig．10weplotthethreeyearshourlydatadistribution 周Group1日GroupL［ロGroupl”田GroupIV国GroupVIヨGroupVlロGroupVJI田GroupV川EaGroupIXロGroupX 1100 1000 900 800 0 0 7・ 0 0 ∩︶ 6 0 ∽l王−OL心q∈⊃Z 0 0 5 0 ︵ 4U O n 3︶ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6 7 8 9 10 Time（Hours） 2 Fig．10 Three years hourly data distribution of the trained SOM classifiedinto ten CategOriesaccordingtothetotalnumberofhitsrecordedateachgroup． 50 嶋 40 ︵∈︶巴⊃SS2d 35 30 1 2 3 4 5 6 7 8 9 10 25 Group Fig．11Box−WhiskerplotsforpressuregaugeP3classifiedtothedifferentlOgroupsofthe trained SOM． 76 H．AwAD，A．KAWAMURA，K．JINNOandY∴KuHO OfthetrainedSOMintothetenclassifiedcategoriesaccordingtothetotalnumber ofhits recordedateachgroup．The occurrenceofeventsforalltengroups arepresentedinthis figureinwhicheachgroupislocatedat aspecifiedtimeinterval．Duringthenighttime Operation，bothgroupsIandIIIarethedominategroupswith1299hitand5256hit，reSpeCtive− 1y．GroupIXwhichpresentabignumberofhits（4263hit）occursduringdailyoperationwith its maximum number of hits at6．00p．m．Group Vwith3145hit occurs mainlyin the afternoonperiodwhileGroupXpresentedwith3047eventhasitsbiggest effect afterthe nightrush−hourat9．00p．m．andbeforethemainchangeofvalvesoperationinthenighttim A11detaileddistributionofthedifferenttengroupsisplottedinFig．10． Inorderto detectthewaterpressurevarianceinthedifferentgroupswithrespect to PreSSuregaugeS，Fig．1loutlinesthepressuremonitoredinalltengroupswithrespecttoa Selected pressure gauge（P3）．The box−Whisker plot shows the median，upPer andlower quartiles，upPerandlower5％ofeventsandalsothemaximumandlowerpressurerecorded for each group ofthe trained SOM．From this chartitis seen that the median value of pressureatallgroupsvariedfrom24mto32m，Whilefortheupper5％ofallevents，the PreSSureeXCeedsthevalueof32mandthemaximumpressurevaluecouldreachthevalue Of55m．Ontheotherhandforlessthan5％ofallevents，thepressureapproximatelyequal totheminimumtargetvalue（24m）andtheminimumpressurevaluereached17m．When relatively comparing the groups，both groupsland3which the majority of their events OCCurredduringnighttimeshowanincreaseinpressurecomparedtotheremaining8groups． In GroupIandIII，41％and50％of events exceed the permissible upper target value， respectively．Therefore a futureimprovement of motor valve operationsin both groups Shouldbedoneinordertopreventtherelativelyhighpercentageofeventsthatexceedthe uppertargetvalue． SOM could be used for improving the existing valve operation support functions by trainingamapwiththeflowmeterreadingswhichrepresentanembeddedrepresentationof therealwaterdemandofthenetwork．Thetrainingdataforflowmetersshouldbeselected fromwellregulatedpressurecases．InthismapanyunitintheSOMwillpresentacasein Whichthe pressureiswellregulated andthisunit contains also the correspondingvalves Openingset．AftertrainingtheSOM，aSimulationstepisusedtoclassifytheunregulated pressurecasestothedifferentSOMunitsaccordingtotheirflowmetersreading．Basedon those classifications the appropriate electricalmotor valves setting for the wellpressure regulationeventsareusedfortheunregulatedones．Thismethodologyoffersgoodalterna− tivesolutionsforimprovlngfuturevalveoperationalsupportfunctions． 6．Conclusions ThispaperpresentsananalysISOfmotorvalveoperationsinBlock120ftheFukuoka City water distribution networks．The analysis has been performed on three years of telemetrydatabyuslngCOrrelationanalysIS andanunSuperVised class of artificialneural networksnamedSelf−OrganizingMaps（SOM）．Correlationanalysishassuccessfullyclassi− fiedthe different motorvalve operations of Block12into three categoriesin which each CategOryisresponsibleofatermofoperation．Thosecategorieshavebeendefinedupontheir effect on the studied block and the adjacent blocks．The SOM has been applied for understanding the motor valve operationalrules．It has shown a high performancein Visualization andabstraction ofmotorvalvedata comparlngtOtraditionalmethods．The trained SOM efficiently classified the different operational rules and displayed all data AnalysisofMotorValveOperationsinFukuokaCityWaterSupplyNetworkUsingSelf−OrganizingMap 77 COmPOnentSCharacteristics．Withtheassistanceoftheunifieddistancematrix（U−matrix） and the Davies−BouldinIndex（DBI）the trained SOM has been clusteredinto ten main groups．Thecharacteristics of eachgroup havebeen analyzedto determineits effect on PreSSureValuesrecordedatobservednodes．Ananalysisofdifferentoperationalruleshas beenperformedandanapplicationofSOMforimprovingfuturemotorvalveoperationhas beensuggested． References l）Onizuka，Y．：Renewalofwater distributionregulationsystemleadstoimprovedoper− ability and reliability，Proceedings of the12thIWSA−ASPAC regionalconference， Chiangmai，Thailand，522−528，2000． 2）FukuokaCityWaterworksBureau：WaterdistributioncontroIcenter，Publicationofthe 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