GPS水准测量外文翻译文献.docx
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GPS水准测量外文翻译文献.docx
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GPS水准测量外文翻译文献
GPS水准测量外文翻译文献
(文档含中英文对照即英文原文和中文翻译)
AnalyzingtheDeformationsofaBridge
UsingGPSandLevelingData
Abstract.Theaimofthisstudyisanalyzing1D(invertical)and3Dmovementsofahighwayviaduct,whichcrossesoveralake,usingGPSandlevelingmeasurementdataseparatelyandtheircombinationaswell.ThedataareacquiredfromthemeasurementcampaignswhichincludeGPSsessionsandpreciselevelingmeasurements,performedwithsix–monthintervalsfortwoyears.
In1Danalysisofthe(vertical)deformations,theheightdifferencesderivedfromGPSandlevelingdatawereevaluated.Whilecombiningtheheight–differencesets(GPSderivedandlevelingderived)inthethirdstageof1Danalysis,VarianceComponentEstimation(VCE)techniquesaccordingtoHelmert’sapproachandRao’sMinimumNormQuadraticUnbiasedEstimation(MINQUE)approachhavebeenused.
In3DanalysisofthedeformationswithonlyGPSdataclassicalS–transformationmethodwasemployed.
Thetheoreticalaspectsofeachmethodthatwasusedinthedataanalysesofthisstudyaresummarized.Theanalysisresultsofthedeformationinspectionsofthehighwayviaductarediscussedandfromtheresults,anoptimalwayofcombiningGPSdataandlevelingdatatoprovidereliableinputstodeformationinvestigationsisinvestigatedinthisstudy.
Keywords.GPS,Leveling,DeformationAnalysis,VarianceComponentEstimation,S–Transformation
1Introduction
Ithasaconsiderableimportancetohavethemovementsofanengineeringstructurewithincertainlimitsforthesafetyofthecommunitydependingonit.Todeterminewhetheranengineeringstructureissafetouseornot,theirmovementsaremonitoredandpossibledeformationsaredetectedfromtheanalysisofobservations.Anappropriateobservationtechnique,whichcanbegeodeticornon–geodetic(geotechnical–structural)accordingtoclassificationinChrzanowskiandChrzanowski(1995),ischosenwithconsideringthephysicalconditionsoftheobservedstructure(itsshape,sizelocationandsoon),environmentalconditions(thegeologicpropertiesofthebasedground,tectonicactivitiesoftheregion,commonatmosphericphenomenaaroundthestructureandsoon),thetypeofmonitoring(continuousorstatic)andtherequiredmeasuringaccuracyforbeingabletorecognizethesignificantmovements.Untilthebeginningofthe1980’s,conventionalmeasurementtechniqueshavebeenusedfordetectingthedeformationsinlargeengineeringstructures.Afterthattheadvancesinspacetechnologiesandtheirgeodeticapplicationsprovidedimpetusfortheiruseindeformationmeasurements(ErolandAyan(2003)).GPSpositioningtechniquehasthebiggestbenefitofhighaccuracy3Dpositioning;however,theverticalpositionistheleastaccuratelydeterminedcomponentduetoinherentgeometricweaknessofthesystemandatmosphericerrors(Featherstoneetal.(1998)).
Therefore,usingGPSmeasurementtechniqueindeformationmeasurementsatmillimeterlevelaccuracyrequiressomespecialprecautions,suchasusingforcedcenteringequipment,applyingspecialmeasuringtechniquesliketherapidstaticmethodforshortbaselinesordesigningspecialequipmentforpreciseantennaheightreadings(seeErolandAyan(2003)fortheirusesinpractice).Insomecases,eventhesespecialprecautionsremaininsufficientandhence,theGPSmeasurementsneedtobecombinedwithanothermeasurementtechniquetoimproveitsaccuracyinheightcomponent.
Ingeodeticevaluationofdeformations,staticobservationsobtainedbyterrestrialand/orGPStechniquearesubjecttoatwo–epochanalysis.Thetwo–epochanalysisbasicallyconsistsofindependentLeastSquaresEstimation(LSE)ofthesingleepochsandgeometricaldetectionofdeformationsbetweenepochs.DetailedexplanationsofthemethodsbasedonthisfundamentalideaarefoundinNiemeieretal.(1982),Chen(1983),Gründigetal.(1985),FraserandGründig(1985),ChrzanowskiandChen(1986),Caspary(1987),Cooper(1987),Biacs(1989),TeskeyandBiacs(1990),Chrzanowskietal.(1991).
Here,theaimisanalyzing1Dand3DdeformationsofanengineeringstructureusingGPSandlevelingmeasurementsdata.Duringthe1Ddeformationanalysis,threedifferentapproacheswereperformedseparately.Inthefirstandsecondapproaches,heightdifferencesfrompreciselevelingmeasurementsandGPSmeasurementsrespectivelywereinputintheanalyzingalgorithm.Inthethirdapproachthecombinationofheightdifferencesfrombothtechniqueswereevaluatedforverticaldeformation.Whilecombiningthetwomeasurementsets,HelmertVarianceComponentEstimation(HVCE)andMinimumNormQuadraticUnbiasedEstimation(MINQUE)techniqueswereused.3DdeformationanalysisonlywithGPSmeasurementswasaccomplishedusingS-transformationtechnique.Thetheoriesbehindtheuseddeformationanalysisandvariancecomponentestimationmethodsaresummarizedinthefollowing.ThereaftertheoptimalsolutionforcombiningtheGPSandpreciselevelingdatatoimprovetheGPSderivedheightsandhencetoprovidereliableinputsviatheoptimalsolutionforthedeformationinvestigationsarediscussed.
Thehighwayviaductofwhichdeformationswereinspectedinthisstudyis2160meterlongandcrossesoveralakeon110piers.ItislocatedinactivetectonicregionveryclosetotheNorthAnatolianFault(NAF).Withtheaimofmonitoringitsdeformations,fourmeasurementcampaignsincludingGPSsessionsandpreciselevelingmeasurementswerecarriedoutwithsix–monthintervals.Thesessionplanswerepreparedappropriatelyforeachcampaignonapre–positioneddeformationnetwork.
2DeformationAnalysisUsingHeightDifferences
Ingeneral,theclassical(geometrical)deformationanalysisisevaluatedinthreestepsinageodeticnetwork.Inthefirststep,theobservations,whichwererecordedatepocht1andepocht2,areadjustedseparatelyaccordingtofreenetworkadjustmentapproach.Duringthecomputations,allpointheightsareassumedtobesubjecttochangeandthesamepointheights,whichareapproximatevalues,areusedinadjustmentcomputationofeachepoch.Computationsarerepeateduntilalloutliersareeliminated.
Inthesecondstep,globaltestprocedureisappliedtoensurethestabilityassumptionsofnetworkpointsduringtheinterval.Intheglobaltest,thecombinedfreeadjustmentisappliedtobothepochmeasurements(and).Inthisadjustmentcomputation,thepartial–traceminimumsolutionisappliedonthestablepoints(seeErolandAyan(2003)).
;
(1)
;
(2)
;(3)
wheresignifythedegreeoffreedomafterfirst,secondandthirdadjustmentcomputationsrespectively.Equation
(1)andequation
(2)representfreeadjustmentcomputationsofthefirstandsecondepochsandequation(3)describescombinedfreeadjustment.Fromtheresultsfoundinequation
(1),
(2)and(3),thetestvalueisdeterminedasinthefollowing.
;
;(4)
ThistestvalueisindependentfromthedatumanditisinF–distribution.testvalueiscomparedwiththecriticalvaluewhichisselectedfromtheFisher–distributiontableaccordingtor(rank)and(degreesoffreedom)forS=1-
(0.95)confidencelevel.If,thenullhypothesiswhichimpliesistrueforthepointsofwhichheightswereassumednottobechanged.
Ontheotherhand,if,inthegroupofpointswhichhadbeenassumedasstableintheglobaltestprocedure,thereis/areinstablepoint(s).Thenthenecessityoflocalizationofthedeformationsisunderstoodandthecombinedfreeadjustmentandglobaltestarerepeateduntilonlythestablepointsareleftoutintheset
Inthelaststepoftheanalysis,thefollowingtestingprocedureisappliedtotheheightchanges.Similartoprevioussteps,testvaluesarecalculatedforallnetworkpointsexceptthestableonesandcomparedwiththecriticalvalueofFfromtheFisher–distributiontable.
;
;(5)
If,itisconcludedthatthechangeinheightissignificant.Otherwise,itisconcludedthattheheightchangedisnotsignificantanditiscausedbytherandommeasurementerrors.
2.1VarianceComponentEstimation
InthemethodofLeastSquares(LS),weightsoftheobservationsaretheessentialprerequisiteinordertocorrectlyestimatetheunknownparameters.Thepurposeofvariancecomponentestimation(VCE)isbasicallytofindrealisticandreliablevariancesofthemeasurementsforconstructingtheappropriatea–prioricovariancematrixoftheobservations.Improperstochasticmodelingcanleadtosystematicdeviationsintheresultsandtheseresultsmayappeartoincludesignificantdeformations.Methodsforestimatingvarianceandcovariancecomponents,withinthecontextoftheLSadjustment,havebeenintensivelyinvestigatedinthestatisticalandgeodeticliterature.Themethodsdevelopedsofarcanbecategorizedasfollows(seeCrocettoetal(2000)):
Functionalmodels
Stochasticmodels
Estimationapproaches
Whenthevariancecomponentestimationisconcerned,afirstsolutiontotheproblemwasprovidedbyHelmertin1924,whoproposedamethodforunbiasedvarianceestimates(Helmert(1924)).In1970,anindependentsolutionwasderivedbyRao,whowasunawareofHelmert'smethod,andwascalledtheminimumnormquadraticunbiasedestimation(MINQUE)method(Rao(1970)).Undertheassumptionofnormallydistributedobservations,bothHelmertandRao'sMINQUEapproachesareequivalent.
2.1.1HelmertApproachinVCE
AfullderivationoftheHelmerttechniqueandcomputationalmodelofvariancecomponentestimationisgiveninGrafarend(1984).Asummaryofthemathematicalmodelisgivenbelow(Kızılsu(1998)).TheHelmertequation,
(6)
Thematrixexpressionofequation(6)isgivenin(7)
(7)
where,uisthenumberofmeasurementgroups.
(8)
(9)
(10)
where,
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