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ARESEARCHONDATAPROCESSINGMODELOFGPSDAMDEFORMATIONMONITORINGNETWORKABSTRACTCONSIDERINGTHEPARTICULARITYOFTHEGPSDAMDEFORMATIONMONITORINGNETWORK,ADATAPROCESSINGMODELBASEDONTHESTATIONORTHOGONALCOORDINATESYSTEMFORTHREEDIMENSIONGPSDAMDEFORMATIONMONITORINGNETWORK,WASPUTFORWARDALSO,AMATHEMATICALMODELOFUSINGTHECLUSTERINGANALYSISMETHODINFUZZYMATHEMATICSTOTESTTHERELATIVESTABILITYOFQUASISTABLEPOINTSORDATUMMARKSWASSUCCESSFULLYBROUGHTFORWARDTHEADJUSTMENTMETHODDURINGTHECOURSEOFDATAPROCESSINGWASQUASISTABLEADJUSTMENTATLAST,ASOFTWARESYSTEMOFTHREEDIMENSIONGPSDAMDEFORMATIONMONITORINGNETWORKWASDESIGNEDANDOPENEDUPWITHTHEHELPOFVISUALBASICLANGUAGEWITHTHREEPERIODSOBSERVATIONDATAFROMTHEGPSDEFORMATIONMONITORINGNETWORKOFADAM,ANADJUSTMENTCALCULATIONWASDONEBYTHESOFTWARETHECALCULATIONRESULTSHOWSTHATTHEMATHEMATICALMODELSCANBEMORESUITABLEFORTHEDATAPROCESSINGINGPSDAMDEFORMATIONMONITORINGNETWORKKEYWORDSGPS,DAMDEFORMATIONMONITORING,QUASISTABLEADJUSTMENT,CLUSTERINGANALYSIS1INTRODUCTIONWGS84COORDINATESYSTEMISGENERALLYUSEDINGPSBUTLOCALORINDEPENDENTCOORDINATESYSTEMSAREUSUALLYCHOSENINDAMDEFORMATIONMONITORINGNETWORKSFORTHEIRSMALLAREASDURINGTHECOURSEOFPASTDATAPROCESSING,THEADJUSTMENTUNDERWGS84COORDINATESYSTEMFORINDEPENDENTNETWORKSORNETWORKSWITHSEVERALFIXEDPOINTSISOFTENFIRSTLYMADETHEN,THETRANSFORMATIONFROMWGS84COORDINATESYSTEMTOLOCALORINDEPENDENTCOORDINATESYSTEMSISDONEFORGPSDEFORMATIONMONITORINGNETWORKSWITHREPETITIVEOBSERVATIONDATA,THEOBVIOUSCHANGEOFDATUMMARKSCOORDINATESUNDERTHETWODIFFERENTCOORDINATESYSTEMSCANBEBROUGHTBYTHETINYDEFORMATIONOFDATUMMARKSAMONGDIFFERENTPERIODSOFOBSERVATIONANDTHEGREATERERRORCANBEMADEDURINGTHECOORDINATETRANSFORMATIONIFALOCALGAUSSCOORDINATESYSTEMISCHOSEN,THEPROJECTIONDISTORTIONSCANALSOBEPRODUCEDBYTHETRANSFORMATIONITSELFFORTHEREASONSABOVE,THESTATIONORTHOGONALCOORDINATESYSTEMISCHOSENASTHEREFERENCECOORDINATESYSTEMFORDATAPROCESSINGOFGPSDAMDEFORMATIONNETWORKSANDTHEMATHEMATICALMODELISPUTFORWARDANDDEDUCED2DATAPROCESSINGMODELBASEDONTHESTATIONORTHOGONALCOORDINATESYSTEMFORTHREEDIMENSIONGPSDEFORMATIONMONITORINGNETWORKS21COORDINATESYSTEMTHESTATIONORTHOGONALCOORDINATESYSTEMISALEFTHANDCOORDINATESYSTEMITSORIGINISSETATONEOFTHEGPSMONITORINGPOINTSTHEEXAXISPOINTSATTHEMERIDIANPASSINGTHEORIGINITISONTHETANGENTPLANEOFTHEORIGINANDTHERIGHTNORTHISTAKENASFORWARDDIRECTIONTHEHZAXISISONTHENORMALLINEOFWGS84ELLIPSOIDATTHEPOINTANDTAKESOUTWARDASFORWARDDIRECTIONTHEEYAXISISALSOONTHETANGENTPLANEOFTHEORIGINANDUSESEASTFORFORWARDDIRECTIONIFTHEPOSITIONVECTOROFTHESTATIONORTHOGONALCOORDINATESYSTEMORIGINP0INWGS84ISEXPRESSEDAS,ACCORDINGTOTHE0RZYX0TGEODETICLATITUDEANDLONGITUDE（，）,THEPOSITIONVECTORBL0RIINTHESTATIONORTHOGONALCOORDINATESYSTEMORIGINOFARANDOMPOINTPICANBEGOTTHROUGHTHETRANSLATIONANDROTATIONOFITSWGS84POSITIONVECTORRIH（）（1）II0INTHEABOVEEQUATION,HCANBEWRITTENASHBLB000SINICOSCOSINCOIN（2）IFTHEBASELINEVECTORSOFTHETWORANDOMPOINTSANDINWGS84COORDINATESYSTEMANDTHETHESTATIONORTHOGONALPIJCOORDINATESYSTEMAREWRITTENASRESPECTIVELY,THEEXPRESSIONCANBEEASILYGAINEDASFOLLOWSTHEN,THERELATIONEQUATIONBETWEENTHETWOBASELINEVECTORSISEXPRESSEDASTHEREARETWOSTEPSINTHEGPSOBSERVATIONDATAPROCESSINGCOURSETHEYAREBASELINECALCULATIONANDNETWORKADJUSTMENTTHEBASELINEVECTORSINWGS84CANBEFIRSTLYGOTUSINGBASELINECALCULATIONSECONDLY,THEBASELINEVECTORTRANSFORMATIONFROMWGS84TOTHESTATIONORTHOGONALCOORDINATESYSTEMCANBEDONEWITH3ATLAST,THEADJUSTMENTOFGPSDEFORMATIONMONITORINGNETWORKSINTHESTATIONORTHOGONALCOORDINATESYSTEMCANBESUCCESSFULLYFINISHED22ADJUSTMENTMETHODANDMATHEMATICALMODELDEFORMATIONMONITORINGNETWORKSUSUALLYREQUIREHIGHERPRECISIONANDIFSEVERALFIXEDPOINTSAREADOPTEDFORDATUM,THEOBSERVATIONPRECISIONCANBEGREATLYREDUCED,BECAUSETHEKNOWNDATASPRECISIONISOFTENLOWERTHANTHEREQUIREDPRECISIONANDTHEBEGINNINGPOINTSDISPLACEMENTCANMAKEANNEXEEFFECTTOOBSERVATIONDATAESPECIALLYDURINGTHECOURSEOFREPETITIVEOBSERVATIONSOTHECLASSICALADJUSTMENTMETHOD,WHICHHASSOMEGIVENPOINTS,ISGENERALLYNOTUSEDBUTITISIMPORTANTTOCHOOSETHEREFERENCEPOINTSWITHSTABLEPHYSICALSTATUSASDATUMOFDEFORMATIONMONITORINGNETWORKSCONSIDERINGTHEABOVETWOCASES,THEQUASISTABLEADJUSTMENTCANBEEMPLOYEDTOMAKETHEMORESTABLEUNKNOWNDATATHECOORDINATESOFRELATIVELYSTABLEPOINTSAWAYFROMTHEDAMMATCHTHEIRSTABLEVALUESTHEN,THEREARENODISTORTIONOFSURVEYINGRESULTANDRELATIVELYSTABLEDATUMANDTHEGOALTOMONITORTHEDEFORMATIONCANBEREACHEDWELLTHEADJUSTMENTMODELOFGPSRANKDEFICIENTNETWORKSCANBEWRITTENASWITHTHELEASTSQUAREMETHOD,THENORMALEQUATIONISEXPRESSEDASNXW（5）WHERENEQUALSPAANDWEQUALSPLATATANDTHEEQUATIONCANBEGOTASFOLLOWSRNRARWHEREADENOTESTHERANKDEFICIENTMATRIX，WHOSERANKDEFICIENTNUMBERDISNRIFSISASETOFRADICALOFZEROSPACENAANDRSDENOTESD,THEEQUATIONISWRITTENASAS0（6）WHENTHEINNERPRODUCTSPACEISDEFINEDASX,YRYANDRRD,XTUNDERTHECONSTRAINTCONDITIONRXMIN,THEFOLLOWINGEQUATIONCANTBEGOTRX07STWITH5AND7,THESOLUTIONEQUATIONOFWEIGHTINGRANKDEFICIENTNETWORKSCANBEEXPRESSEDASWHEREDENOTESQRWHENRISADIAGONALMATRIXANDITSVALUEIS1OR0,（8）CANBECOMETHEMODELOFQUASISTABLEADJUSTMENTTHESMATRIXCANBEGIVENACCORDINGTOTHECONDITIONAS0ANDTHESMATRIXOFGPS3DIMENSIONALDEFORMATIONMONITORINGNETWORKSISWRITTENAS23MATHEMATICALMODELOFCALCULATINGQUASISTABLEPOINTSRELATIVESTABILITYWITHCLUSTERINGANALYSISFORGPSDAMDEFORMATIONMONITORINGNETWORKS,THESTABILITYOFDATUMMARKSMUSTBEFIRSTLYTESTEDINTHEOBSERVATIONDATAPROCESSINGTHOUGHTHERELATIVELYSTABLEAREAISCHOSENFORBUILDINGDATUMMARKSWHENGPSDAMDEFORMATIONMONITORINGNETWORKSAREDESIGNED,THEDEFORMATIONOFDATUMMARKSCANCOMEINTOBEINGEVENIFTHEQUASISTABLEADJUSTMENTMETHODISUSED,THESTABILITYTESTNEEDSTOBEMADE,TOOTHEQUASISTABLEPOINTSQUASISTABLEPOINTSORDATUMMARKSINDESIGNSCHEMEWITHMARKEDDEFORMATIONSHOULDBEELIMINATEDTHEMATHEMATICALMODELOFCALCULATINGQUASISTABLEPOINTSORDATUMMARKSRELATIVESTABILITYWITHCLUSTERINGANALYSISINFUZZYMATHEMATICSISPUTFORWARDTOENSURETHESTABLEQUASISTABLEPOINTSORDATUMMARKSINGPSOBSERVATIONDATAPROCESSINGONECHARACTERISTICOFQUASISTABLEADJUSTMENTISTHATTHECORRECTIONVALUEVOFOBSERVATIONDATAAFTERADJUSTMENTISINVARIABLESOTHEADJUSTEDVALUELOFOBSERVATIONDATAISALSOINVARIABLEANDITISSHOWNTHATTHENETWORKSHAPEAFTERADJUSTMENTISUNCHANGEDTHEOBSERVATIONDATAOFGPSNETWORKSADJUSTMENTISBASELINEVECTORSCOORDINATEDIFFERENCESIN3COORDINATEAXISDIRECTIONSTHEN,AFTERTHEQUASISTABLEADJUSTMENTOFTWOPERIODSOFOBSERVATIONDATA,THEDIFFERENCESOFCOORDINATEDIFFERENCESOFTWORANDOMQUASISTABLEPOINTSIN3COORDINATEAXISDIRECTIONSBETWEENTHETWOPERIODSAREINVARIABLESO,THESEVALUESCANTBECHANGEDWITHDIFFERENTCHOICESANDWORKCANBEFINISHEDONCEFORADOTOAVOIDTHETROUBLEOFSOMEMETHODSCALCULATINGSTEPBYSTEPANDDENOTETHECOORDINATEDIFFERENCESOFTWOL1IJ2IJRANDOMQUASISTABLEPOINTSIANDJAFTERTWOPERIODSOBSERVATIONDATAADJUSTMENTISTHEDIFFERENCEOFCOORDINATEDIFFERENCESBETWEENL1IJTWOPERIODSANDEQUATIONSAREASFOLLOWSSTATISTICISWRITTENASIFTHECHANGEOFBETWEENTWOPERIODSISCAUSEDBYTHEACCIDENTALERRORL1IJOFGPSOBSERVATION,ITISEXPRESSEDASTHEFUZZYMEMBERSHIPGRADEOFTHERELATIVESTABILITYOFTHETWORANDOMQUASISTABLEPOINTSIANDJISDEFINEDASTHATISTOSAY,THEFUZZYRELATIONOFTHERELATIVESTABILITYOFQUASISTABLEPOINTSISTHEPROBABILITYDENSITYVALUEOFSTANDARDNORMALDISTRIBUTIONABOUTTO,ITCANBEDEFINEDASUIJRIJ0FORSUPPLEMENTITISALSOASFOLLOWSUIANDTHEFUZZYRELATIONOFRELATIVESTABILITYOFQUASISTABLEPOINTSDEFINEDBY12AND13ONLYSATISFIESTHESYMMETRYOFEQUIVALENCEFUZZYRELATIONTHEREFLEXIVITYCANBESTANDARDIZEDAND,ISREDEFINEDASRIJTHEFUZZYRELATIONRHASMETTHEFIRSTTWOCONDITIONSOFFUZZYEQUIVALENCERELATIONTHENRISAFUZZYSIMILARMATRIXTOTRANSITIVITY,THEFUZZYSIMILARMATRIXCANBECHANGEDTOAFUZZYEQUIVALENCEMATRIXWITHTHEHELPOFTHETRANSITIVECLOSEDPACKAGETRANDTHEFUZZYANALYSISCANBEDONETHESORTEDINDEXPARAMETEROFCLUSTERINGANALYSISISCOMPUTEDWITHTHESTATISTICHYPOTHESISMETHODIFTHECHANGEOFBETWEENTWOPERIODSISL1IJCAUSEDBYTHEACCIDENTALERROROFGPSOBSERVATION,ITISEXPRESSEDASFORTHEGIVENCONSPICUOUSLEVEL,THEREISACRITICALVALUEWITH,KTHECORRESPONDINGVALUECANBEGOTFROM14ANDISTHESORTEDRRINDEXPARAMETEROFCLUSTERINGANALYSISOFQUASISTABLEPOINTSRELATIVESTABILITYTAB1BELOWSHOWSTHEVALUESOFANDOBVIOUSLYSHOULDBECHANGEDINTHEPRACTICEITISCONCLUDEDTHATALARGERSHOULDBECHOSENACCORDINGTOTHEOPERATIONRULEINCLUSTERINGANALYSISANDITCANBERECOMMENDEDTHATANDSHOULDUSE5AND01465RESPECTIVELY3ACOMPUTATIONEXAMPLEANDRESULTANALYSISTHECOMPUTATIONEXAMPLEWASCHOSENFROMTHEGPSDEFORMATIONMONITORINGNETWORKOFSOMEROCKANDSOILGRAVITYDAMTHEREWERE3PERIODSOFOBSERVATIONDATAINTOTALTHEOBSERVATIONDATESWEREMAR4TO7,JUN4TO11,ANDAUG31TOSEPT4IN2001THEREWERE75GPSMONITORINGPOINTSINTHISNETWORKAND6OFTHETOTALWEREINTHERELATIVELYSTABLEAREAOFTHELOWERRIVEROFTHEDAMTHEOTHER69POINTSWEREATTHEDAMBODYALLTHEMONITORINGPOINTSWEREBUILTONOBSERVATIONPIERSANDHADCOMPULSIVECENTERINGEQUIPMENTANDALLTHEOBSERVATIONWASFINISHEDBY6ASHTECHZSURVEYORDUALFREQUENCYRECEIVERSTHEPERIODSOFALLTHEPOINTSWEREMORETHANANHOURTHEBASELINESOLUTIONOFGPSOBSERVATIONDATAWASGAINEDBYTHEASHTECHASSOCIATEDSOFTWARESOLUTION25FOREVERYPERIOD,EVERYDAYOBSERVATIONDATAWASPROCESSEDSINGLYTHEPERIODSOFTIMEWITHBADSIGNALSWEREFIRSTELIMINATEDIFTHEYWERESTILLNOTELIGIBLE,THEOBSERVATIONDATAWASDELETEDTHEN,WITHEVERYDAYQUALIFIEDBASELINES,THENETWORKADJUSTMENTWASPREPAREDTHEBASELINESOLUTIONPRECISIONISLISTEDINTAB16MONITORINGPOINTSINTHERELATIVELYSTABLEAREAOFDAMLOWERRIVERBANKSWEREUSEDASFIXEDINITIALDATUMANDTHEADJUSTMENTWITHFIXEDPOINTSWASDONEWITHTHEADJUSTMENTRESULTBEINGANALYZED,ITWASSHOWNTHATTHEDISPLACEMENTAMONG6INITIALPOINTSCOULDREACHABOUT23MMANDTHEMONITORINGPOINTSPRECISIONAFTERTHEADJUSTMENTWITH6FIXEDPOINTSWAS12TIMESLARGERTHANTHEPRECISIONUSINGQUASISTABLEADJUSTMENTTHERESULTALSOEXPLAINEDTHEDISPLACEMENTOFINITIALPOINTSBECAUSEFIXEDINITIALDATUMCOULDREACTONOBSERVATIONDATAFORCOMPULSIVEFIXING,THEPRECISIONWASBADINORDERTOTESTTHESTABILITYOFQUASISTABLEPOINTS,THEMATHEMATICALMODELOFCLUSTERINGANALYSISMETHODWASEMPLOYEDITWASFOUNDTHATTHEQUASISTABLEPOINTKL3INYDIRECTIONWASOBVIOUSLYDIFFERENTFROMTHEOTHER5POINTSWHENTHESECONDPERIODOFOBSERVATIONWASCOMPAREDWITHTHEFIRSTANDKL3INYANDZDIRECTIONSWASDISTINCTLYDIFFERENTFROMTHEOTHERSWHENTHETHIRDWASCOMPAREDWITHTHEFIRSTTHEN,KL3WASELIMINATEDAFTERINTEGRATINGTHECLUSTERINGANALYSISRESULTOFTHESECONDANDTHETHIRDPERIODSATLAST,KL1、KL2、KL7、KR1ANDKR3WERETAKENASQUASISTABLEPOINTSBECAUSETHEREWASNOQUASISTABLEADJUSTMENTFUNCTIONINGPSASSOCIATEDSOFTWAREOFGPSMANUFACTURERSATHOMEORINFOREIGNCOUNTRIES,THENETWORKADJUSTMENTSOFTWAREWASDESIGNEDFORGPSDEFORMATIONMONITORINGNETWORKSUSINGV
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