1 Real world implementation of belief function theory to Detect Dislocation of Materials in Construction Saiedeh N. Razavi Civil Engineering Department University of Waterloo Waterloo, ON, Canada snavabza@engmail.uwaterloo.ca Carl T. Haas Civil Engineering Department University of Waterloo Waterloo, ON, Canada chaas@civmail.uwaterloo.ca Philippe Vanheeghe LAGIS UMR 8146, Ecole Centrale de Lille, Cite Scientifique, BP 48, 59651 Villeneuve dAscq Cedex, FRANCE philippe.vanheeghe@ec-lille.fr Emmanuel Duflos LAGIS UMR 8146, Ecole Centrale de Lille, Cite Scientifique, BP 48, 59651 Villeneuve dAscq Cedex, FRANCE emmanuel.duflos@ec-lille.fr AbstractDislocationsofconstructionmaterialson largesitesrepresentcriticalstatechanges.Theabilityto detectdislocationsautomaticallyfortensofthousandsof itemscanultimatelyimproveprojectperformance significantly.ABelief_function-baseddatafusion algorithmwasdevelopedtoestimatematerialslocations anddetectdislocations.Dislocationisdefinedasthe changebetweendiscretesequentiallocationsofcritical materials such as special valves or fabricated items, on a large construction project. Detecting these dislocations in anoisyinformationenvironmentwherelowcostRadio FrequencyIdentificationtagsareattachedtoeachpiece ofmaterial,andthematerialismovedsometimesonlya few meters, is the main focus of this study. This work is a continuationofpreviousresearch,inwhichwetackled the location estimation problem by fusing the data from a simulation model. The results indicate the potential of the Belief_functionbasedalgorithmtodetectobject dislocation. Keywords:Locating,dislocationdetection,belief function theory, construction materials. 1Introduction Materialtrackingisakeyelementinaconstruction materialsmanagementsystem.Theunavailabilityof constructionmaterialsattherightplaceandattheright timehasbeenrecognizedashavingamajornegative impactonconstructionproductivity.Moreover,poorsite materialsmanagementpotentiallydelaysconstruction activities,andthusthreatensprojectcompletiondatesand stands to raise total installed costs [9].Whileautomatedcontrolsareoftenestablishedfor engineeredandothercriticalmaterialsduringthedesign and procurement stages of large industrial projects, on-site controlpracticesarestillbasedonnecessarilyfallible directhumanobservation,manualdataentry,and adherencetoprocesses.Theseareinadequatefor overcomingthedynamicandunpredictablenatureof construction sites.Nodelocationapproachesusingsignalstrengthand basedontriangulationorrelaxationalgorithms[3,4,8, 10]arelimitedbecauseofthecostofrequirednode electronics(nocurrenthighvolumedemandexists),and becausetheanisotropic,dynamictransmissionspaceona construction site, for example, can not feasibly be mapped atthetemporalorspatialresolutionrequired.Inaddition, evensophisticatedandexpensivesolutionsexperience multipath,deadspace,andenvironmentally-related interference to some extent. For example, the Wi-Fi RTLS (real time location systems), such as commercial solutions fromAeroScout,Ubisense,Ekahau,andthePanGo Network,requireextensivecalibrationtomaptheWi-Fi signalstolocationsthroughoutabuildingwhilethe existence of 802.11 access points is not guaranteed for any facilitybeingbuilt.Thuswehaveselectedamorecost-effectiveapproachthatisapplicabletoconstructionjob sitespecifications.However,developingamethodfor location estimation that is robust to measurement noise but still has a reasonable implementation cost is a challenge. Wirelesssensornetwork-baseddatacollection technologiessuchasGPSandRFID(RadioFrequency Identification) are being developed for a wide spectrum of applications.Specifically,morerecentresearchis demonstratingthat,coupledwithmobilecomputers,data collectiontechnologiesandsensorscanprovideacost-effective,scalable,andeasy-to-implementmaterials location sensing system in real world construction sites [1, 5, 9, 11, 15, and 16].The evident drawback of the current 12th International Conference on Information FusionSeattle, WA, USA, July 6-9, 2009978-0-9824438-0-4 2009 ISIF 7482 cost-effectiveandscalablesystemsislackofaccuracy, precision, and robustness. Thisstudypresentsanimprovedformulationfor robustlyprocessinguncertaintyandimprecisionin proximitymethodsandisbasedontheBelieffunction theory [7, 12, 14]. By proximity we mean a binary spatial-constraint-basedmethod[16].Theapproachpresented heregracefullymanagestheissueofdislocatedtags,and results are presented graphically in an intuitive format.Forthepurposeofthisresearch,anintegratedsolution forautomatedidentificationandlocalizationof constructionmaterialswasincorporatedforalarge industrial construction project. The main focus of the field trialwastodevelopadatafusionmethodforlocation estimationthatisrobusttomeasurementnoiseandhasa reasonableimplementationcost.Thefieldtrialinvolveda continuous site presence over 16 months by three graduate and three undergraduate students. Forthesubsetofdatausedinthispaper,thetags location data were logged by GPS-enabled readers for 109 tags,threetimesperday,forfourconsequentdays.RFID readratesweresporadic,rangingfromtenreadsofatag per minute to periods of hours without reads.Thispaperisorganizedintothefollowingsections.A briefintroductionprovidesbackgroundtooccupancycell frameworkandproximitylocalizationmethods.Then,a practical elaboration on formulating belief function theory forlocatingmaterialsanddetectingdislocateditemsis presented.Abriefdescriptionoftheconstructionfield experimentandtheacquireddatasetfollows.Theresults indicatingthepotentialoftheBelieffunctiontheoryto detectmaterialsdislocationmakeupthenextsection. Finally,theconclusionsummarizesthefindingsofthis research study, and suggests additional further works. 2Background In general, there are two approaches to localization. One is finegrainedlocalizationusingdetailedinformation,and theotheriscoarse-grainedlocalizationusingminimal information.Thetradeoffbetweenthetwoapproachesis obvious:minimaltechniquesareeasiertoimplementand morelikelytoconsumefewerresourcesandincurlower equipmentcosts,buttheyprovidelessaccuracythan detailed information techniques. Fine-grainednodelocalizationmethodsarebasedon specificdetailedinformationandcanbecategorizedinto these measurement techniques: Time of Flight Received Signal Strength (RSS) Lateration and AngulationDistance-estimationusingtimedifference (TDoA)Pattern Matching (RADAR)RF sequence decoding.Coarse-grainednodelocalizationorconnectivity-based localizationalgorithmsarethosewhichdonotuseanyof themeasurementtechniquesdescribedabove.Inthis category,somesensorscalledanchorshaveapriori informationabouttheirlocation.Thelocationsofother sensorsareestimatedbasedonconnectivityinformation, such as who is within communication range of whom. Proximity is the basis of another localization model that doesnotattempttoactuallymeasureanobjectsdistance fromreferencepoints,butratherdetermineswhetheran object isnear one ormoreknown locations. The presence ofanobjectwithinacertainrangeisusuallydetermined bymonitoringofphysicalphenomenawithalimited range,e.g.,physicalcontacttoamagneticscanner,or communication connectivity to access points in awireless cellularnetwork.Someoftheproximity-basedmethods introducedinthissectionmakeupapartoftheproposed solution for this research. Inproximitymodels,forreductionofcomputational complexity,adiscreterepresentationin2Disemployed insteadofamorerealisticcontinuousmodel.Inthe discrete view, a rover (any reader carrier) moves around in a square region, Q, with sides of length s; Q is partitioned into n2 congruent squares called cells of area (sn)2.The RF communication region of a read is modeled as a square centeredatthereadandcontaining(p + )2cells, instead of a disk of radius r.Thus, the position of reads as well as tags is represented by a cell withgrid coordinates, ratherthanapointwithCartesiancoordinates,andoneis onlyinterestedinfindingthecell(s)thatcontainseach RFIDtag(Figure1).Thisparadigmisappliedinthe proximity approaches in particular. Figure 1: Modeling the RF communication region under the occupancy cell framework [17] SimicandSastry[13]presentedadistributedalgorithm for locatingnodes in a discrete model of a random ad hoc communication network and introduced a bounding model foralgorithmcomplexity.Songetal[17]adaptedthis discreteframework,basedontheconceptthatafield supervisororpieceofmaterialshandlingequipmentis equippedwithanRFIDreaderandaGPSreceiver,and serves as a rover (a platform for effortless reading).The position of the reader at any time is known since the rover isequippedwithaGPSreceiver,andmanyreadscanbe generatedbytemporalsamplingofasinglerovermoving around the site. If the reader reads an RFID tag fixed at an unknownlocation,thenRFcommunicationsconnectivity exists between the reader and the tag, contributing exactly oneproximityconstrainttotheproblemofestimatingthe taglocation.Astherovercomesintocommunication rangewiththetagtimeandtimeagain,morereadsform suchproximityconstraintsforthetag.Combiningthese 7493 proximityconstraintsrestrictsthefeasibleregionforthe unknownpositionofthetagtotheregioninwhichthe squarescenteredatthereadsintersectwithoneanother (Figure 2). Figure 2: An illustration on how proximity methods work Songetal[16]alsoimplementedSimicandSastrys algorithminlarge-scalefieldexperiments,includingas parameters(1)RFpowertransmittedfromanRFID reader,(2)thenumberoftagsplaced,(3)patternsoftag placement, and (4) the number of reads generated based on randomreaderpaths.Analyzingdatacollectedshowsthat in51%ofthetotal4,200instances,thetruelocationofa tag was expected to be within +/3 cells from the center of theregionestimatedtocontainthattag.Althoughthis approachwas proven adequate (3-4m accuracy)for static distributionsoftags,itisnoteasilyextendedtotracking moving or moved tags. 3 Belief function theory for locating materials Thetheoryofbelieffunctionisageneralizationof Bayesiantheory.Thistheoryhasbeeninitiallydeveloped by Dempster [7] and mathematically formalized by Shafer [12].Belieffunctiontheoryisapopularmethodtodeal withuncertaintyandimprecisionwithatheoretically attractiveevidentialreasoningframework[2].Caronetal [6]showedthatitcanalsomanagetheissueofmoving tags while it is scalable and the granularity of the frame of evidence can shift in real-time. Inthistheorythesourceofinformationiscalled evidenceandthepossiblebasichypothesesarecalledthe frame of discernment (E). The frame of discernment is our problemworldthatwearetryingtoobserveand understand. Forthepresentapplication,thehypothesesforeachtag will be of the form It is in location ] [Formula (1)]. A setofmutuallyexclusivepropositionsbasedonthese hypothesesshouldbedefinedtobuildtheframeof discernment. So,for each tag, the frame of discernment is thesetofnonoverlappingsquarecellsoftheregion (Figure3).Acircularareabasedontheidealreading rangeofanRFIDreaderistheclosestshapetothe antennasreadingzone,buttheycannotcoverthewhole areaofinterestwithoutoverlappingandaddingalotof computationalcomplexitytotheproblem.Inaddition,the actualrangeofanyreadpositioninthefieldissohighly dependentonantennaorientation,multipathinterference, and other factors such as RFID tag signal strength that it is highlyill-formedandisthusnotmoreunreasonably modeledasasquarethananyothershape.Moreover,the squareiscomputationallyattractive.Iftheconstruction siteisvirtuallypartitionedinto m n squarecellsof ], i=1,..., n, j=1,,m, then the frame of discernment for each tag is { } m j n i C Eij,..., 1 , ,..., 1 | = = = (1) Forthemodelproposedhere,theRFcommunication regionofareadismodeledasasquare,centeredatthe read and containing ( )21 2 + R cells while R is the ideal read rangeforthedefinedframework.Thus,thepositionof readsaswellastagsisrepresentedbyacellwithgrid coordinates, rather than a point with Cartesian coordinates, and only the cell(s) that contains each RFID tag are of our interests.Tolowertheerrorrateofthesolution,cellsare definedasm 1 1 squares.Theideaisadoptedfromthe discrete framework presented in section 2. Figure 3:Discrete frame of discernment and modeling the RF communication region AnyobservationoftheGPS/RFIDsensor ,willbe presented by assigning its beliefs over E. This is called the mass function of the sensors , and is denoted by . Thus according to the sensors observation of locationI , the probability that the specific tag is in locationI can not be lower than the belief confidence ( )i iL Belief .( )i iL Beliefisthebeliefconfidenceonalltheevidences kthatsupportsthegivenproposition.Totakeinto considerationthewholebeliefthatisinthegiven proposition,weneed to include all the subsets of Ewhich imply I. The belief is calculated as: ( ) ( )=i kL Ek i i iE m L Belief(2) Forthecurrentpurpose,whenanRFIDreaderreadsa tag,thecombinationofGPS/RFIDdatagivesinformation aboutthelocationofthetag,whichisahypothesis.This informationcanbemodeledbyabasicbeliefassignment becauseoftheuncertaintyinRFIDreadrangeduetothe surrounding environment.To deal with this uncertain read rangeweassigndifferentbeliefstodifferentsubsetsof cellscenteredontheGPS/RFIDsensorsetofsuch that the sum of the all beliefs are equal to one. Let j be the indexforpnestedsquareareascenteredontheRFID reader such that 1 c 2 c 3 c 4 [6].RFID tag Rover path Virtual reader that reads tag Virtual reader that did Not read tag 750 ( ) 11==jpjiE m

For the solution proposed here, we assume fortheareawithhalfareadrange,and therestoftheareawithinreadrange(Figure valuesinbeliefassignmentaresetupbasedonlocation errordistributionofthesampledata(Figure10distributionshowsthattherecouldbeahigherbeliefforthe area closer to the tag.Figure 4: The proposed solution mass allocationForfusingthedataofmorethanonesensor, functiontheoryprovidesameanstocombinethese observations.Inthissensorfusionwesupposethatthe sensorsareindependent.Fortheapplicationproposed here,wecanhavemultipleRFIDreaderscoupledwith GPS or multiple GPS chips with RFID interrogators or any other upcoming related technology.Inthesimplestscenario,duetotheenvotherfactors,GPSandRFIDarehavingdifferent reliabilitiesforeacheventofread.Thereforedifferent readeventscanbeconsideredastheindependent observationsthatcanbefusedbythe theory.Foreachpossibleproposition(e.g.,ItisatlocationBelieffunctiontheorygivesaruleforcombiningthe sensorssobservationwiththesensors observation: ( )( )(kE EikE Eii j iE mm E mL m mk kiL k k= = = 1) (TheDempstersruleofcombination(Formula4reallocatestheconflict.Thisruleiscommutativeand associativeandcanbeusedinasequentialmode,to combine more that two acquired reads. Thesystemneedstodecideatwhichcellthetagis located.Thereforeitneedstocomparethemasses allocatedtoeachcellafterthefusionprocess.Thecenter of gravity of the cells that have the maximum mass will be chosen as the location of the tag. 4Detecting dislocation Fordifferentessentialcausesconflictmayexist:sourcesmaynotbereliable,orthebasicbelief assignments may be modeled incorrectly.(3) For the solution proposed here, we assumefor eawithinreadrange(Figure4).Thetwo valuesinbeliefassignmentaresetupbasedonlocation nofthesampledata(Figure10).The eahigherbelieffor : The proposed solution mass allocation Forfusingthedataofmorethanonesensor,Belief providesameanstocombinethese upposethatthe sensorsareindependent.Fortheapplicationproposed here,wecanhavemultipleRFIDreaderscoupledwith GPS or multiple GPS chips with RFID interrogators or any Inthesimplestscenario,duetotheenvironmentaland otherfactors,GPSandRFIDarehavingdifferent reliabilitiesforeacheventofread.Thereforedifferent readeventscanbeconsideredastheindependent observationsthatcanbefusedbytheBelieffunction oposition(e.g.,Itisatlocation) theorygivesaruleforcombiningthe withthesensorss ( )) ( )k j kk jE mE m(4) nation(Formula4) .Thisruleiscommutativeand associativeandcanbeusedinasequentialmode,to Thesystemneedstodecideatwhichcellthetagis mparethemasses allocatedtoeachcellafterthefusionprocess.Thecenter of gravity of the cells that have the maximum mass will be Fordifferentessentialcausesconflictmayexist:the maynotbereliable,orthebasicbelief Whenatagisdislocated,anewreadingmaybemadewhoseassociatedbasicbeliefassignments pastmeasurements.Conflictvalueisusedheretodetect thiscontradictionandsothemovementsoftagsinthe field. Figure 5: Detecting dislocation with Theconflictmanagementcanbehandledinfour different ways: Discounting of previous basic belief assignments at each time step to favor the latestReject the old basic belief assignments when the conflict is over the thresholdDecrease conflict by enlarging the focal setsDevelop a new method in the frame of the Dezert-Smarandache TheoryUse other combination rulesPrades rule (DP), Dezert-(DSmT), or some others. Todealwithconflictinthisstudy,oldbasicbelief assignments are rejected when the conflict is beyond a predefinedthreshold.Thisapproachwaschosenduetothe simplicityofcomputationand method. Figure5illustratesasamplecasestudyinwhicha dislocated tag is detected. In this case study, 6 read events ofanRFIDtaghavebeenintroducedsequentiallytothe fusionalgorithm.Thefinalestimatedlocationisequalto thecenterofthedarkestblueareathatcorrespondsthighest allocated mass. 4 anewreadingmaybemade whoseassociatedbasicbeliefassignmentscontradictthe pastmeasurements.Conflictvalueisusedheretodetect movementsoftagsinthe ing dislocation with conflict ratioTheconflictmanagementcanbehandledinfour Discounting of previous basic belief assignments the latest Reject the old basic belief assignments when the conflict is over the threshold Decrease conflict by enlarging the focal sets Develop a new method in the frame of the Smarandache Theory (DSmT). Use other combination rules such as Dubois--Smarandache Theory Todealwithconflictinthisstudy,oldbasicbelief assignments are rejected when the conflict is beyond a pre-definedthreshold.Thisapproachwaschosenduetothe simplicityofcomputationandthescalabilityofthe lecasestudyinwhicha dislocated tag is detected. In this case study, 6 read events ofanRFIDtaghavebeenintroducedsequentiallytothe fusionalgorithm.Thefinalestimatedlocationisequalto thecenterofthedarkestblueareathatcorrespondstothe 751 5Field experiments Fieldtrialswereconductedtoobtainexperimental datato validatethedatafusionmodelandtodemonstratethe feasibilityofemployingthecomponents,methodstechnologiesdeveloped.Alargeindustriproject in Toronto hosted one field trial.EthernetFigure 6: System network diagramAnRFID-GPS-basedlocationestimationprototypewas usedinacomprehensiveseriesofexperiments technologyforthisresearchcombinesGlobalPositioning System (GPS) and Radio Frequency Identification (RFID) technologytoautomaticallylocatematerialsonthejob site.EachRFIDtagisassignedtoacriticalcomponent. Then, a person traveling around the site with GPSreadersdetectsthepresenceoftagsaround position (Figure 6). Figure 7: Sample map, including several RFID tag locations Figure 8: Sample tagged items Fieldtrialswereconductedtoobtainexperimental datato validatethedatafusionmodelandtodemonstratethe feasibilityofemployingthecomponents,methods,and technologiesdeveloped.Alargeindustrialconstruction ServerPDAEthernetServerLaptop computerUserPrinterTablet computerComm-linkSymbol DescriptionLegend SubtitleLegendDatabase: System network diagram basedlocationestimationprototypewas acomprehensiveseriesofexperimentsThe inesGlobalPositioning System (GPS) and Radio Frequency Identification (RFID) technologytoautomaticallylocatematerialsonthejob site.EachRFIDtagisassignedtoacriticalcomponent. round the site with GPS-enabled gsaroundhis/herown Figure 7: Sample map, including several RFID tag Figure 8: Sample tagged items Duringthewholecourseoftheexperiment,375wereusedtotestthefeasibilityoftcertaincriticalcomponentsonaconstructionsiteandits supplychain.Thedatafortestingthemodelarethe coordinatesofeachtagIDonthelaydownyardshavebeenloggedonadailybasisforestimatedsizeofthedatasetis94multipliedby,onaverage,110tagson multiplied by, typically a dozen reads per tag per day [11]The daily location data is saved in the it can be opened in the Google Earth map environment the location information visualized. An AutoCAD drawing ofthesiteoverlaidontheGoogleEarthaerialphoto providedmorelandmarkreferencedetails locationsonthesite.Mapswere granularity and various scales to allow proper visualizabyfieldworkers.Thefigures7and8item and a sample map. 6Results Outputs of the used RFID-GPS-based prototype were used astheinputsforthedeveloped algorithm. The prototype outputs were estimated locations of the tags, based on the observed read events for each tag. Theseestimatedlocationswerecalculatedinthecentroid model. The figure 9 illustrates the hierarchical amongtagreadevents,estimatedlocationsofthe prototype, and the Belief-function-based fused estimationFigure 9: Hierarchical relationship representation among read events, estimated locations, and the estimations of the belief_function_based fusiA case study of a sample data subset is presented in this section.Thissubsetwascapturedatareaoverfoursequentialdays andis cyclesofreadingandestimatinglocationscyclemightresultinatypicalnumberof readspertag.Thefollowingtablerepresentsthedata specificationswithrespecttothedistancebetweenthe estimated location of the prototype and the real location of a tag.Tag read eventsPrototype 's estimated locations in time (Centroid)belief_function basedfusion levelfused estimated time1read event 1read event n5 hewholecourseoftheexperiment,375tags testthefeasibilityoftrackingandlocating criticalcomponentsonaconstructionsiteandits supplychain.Thedatafortestingthemodelarethe coordinatesofeachtagIDonthelaydownyards,which havebeenloggedonadailybasisforfivemonths.The atedsizeofthedatasetis94daysofdatalogging tagsonthesiteperday dozen reads per tag per day [11]. The daily location data is saved in the kml format so that be opened in the Google Earth map environment and . An AutoCAD drawing ofthesiteoverlaidontheGoogleEarthaerialphoto providedmorelandmarkreferencedetailsaboutthe werecreatedindifferent granularity and various scales to allow proper visualization 7and8presentatagged based prototype were used astheinputsforthedevelopedBelief-function-based algorithm. The prototype outputs were estimated locations based on the observed read events for each tag. Theseestimatedlocationswerecalculatedinthecentroid illustrates the hierarchical relationship tagreadevents,estimatedlocationsofthe based fused estimation. : Hierarchical relationship representation among and the estimations of the fusion level A case study of a sample data subset is presented in this wascapturedatthesitewarehouse andisbasedonthreedaily locations.Eachreading tinatypicalnumberoftentofifteen readspertag.Thefollowingtablerepresentsthedata specificationswithrespecttothedistancebetweenthe prototype based on the reads fused estimated locationread event ntime nread event 1read event n. 7526 Figure 10: Location error distribution in the data subset Atotalnumberof57dislocationswerecreatedinthe sampledatasubset,amongwhichmorethanone dislocationmaybeassignedtosomeofthetags. Benchmark measurements in the sample data subset with sub-foot accuracy GPS shows only a few dislocations for theperiodofobservationinthesampledatasubset.To provideagreaternumberofdislocatedsamplesina controlledmanner,57sampleswerecreatedby transposingasequenceofestimatesandtheirassociated benchmarksfortwostationarytags.Thefigure11 illustrates this method of creating dislocation samples.

Figure 11: Creating dislocated samples by transposing a subset of estimates sequence and the corresponding benchmarks for two tags Thealgorithmwasrunthroughthewholesampledata subset to allow the observation of the dislocation detection rate with respect to the conflict threshold and the assumed read range in the frame of discernment. The results show a real potential for using the Belief function theory to detect the dislocated materials. Dislocationdetectionrateswithrespecttotheconflict thresholdareshowninTable1.Figure12presentsthe ReceiverOperatingCharacteristiccurve(ROC).Results indicatethatalowconflictthresholdcauseshigh sensitivityandmayresultinfalsedislocation-detections. Conversely,withahighconflictthreshold,some dislocations may not be detected. Table 1: Dislocation detection rate with respect to conflict threshold Conflict threshold True-positive (TP) False-positive (FP) True-negative (TN) False-negative (FN) 057116000 0.23939112118 0.43734112620 0.63533112722 0.83534112620 12229113135 2000116057 Figure 12: Receiver Operating Characteristic Curve (ROC) for different conflict thresholds Table2presentsthedislocationdetectionratesfor differenthypotheticalreadrangesintheframeof discernment(Figure4).Figure13alsoshowstheROC diagramforthedatashownintable2.Theresultsare obtained for the conflict threshold of 0.4 and indicate that a hypothetical range similar to that experienced on the site works best. Table 2: Dislocation detection rate with respect to the hypothetical read range (Conflict threshold = 0.4) Hypothetical read range (m) True-positive(TP) False-positive (FP) True-negative (TN) False-negative (FN) 0569811871 2543478133 64687109114 84040112017 103734112620 143533112722 163130113026 182732112730 01002003001611162126313641465156FrequencyDistancebetween the estimated and real tag location Sample Data SubsetLocation Error Distribution00.20.60.80.412000.20.40.60.811 0.034 0.029 0.029 0.028 0.025 0True-positive rateFalse-positive rateReceiver Operating Characteristic Curve (ROC)Tag 1: sequence of estimatesTag 2: sequence of estimates7537 Figure 13: Receiver Operating Characteristic Curve (ROC) for different hypothetical read ranges Figure 14: Distribution of the distance between benchmark locations of all dislocated sample as opposed to true-positive detections, for conflict-threshold = 0.8 and hypothetical read range=16m Figure 14 presents a histogramfor the distance between benchmarklocationsofthetrue-positivedetections comparabletothesamedistributionfortheentire dislocatedsamplespopulation.Thetrue-positive detectionratesshowninthisfigurearebasedonthe conflict-threshold of 0.8 and the hypothetical read range of 16m.Acomparisonofthesetwohistogramsshowsthat theprobabilityofdetectionincreaseswhendislocations distances are higher. 7ConclusionThe targeted application described in this paper is to detect dislocationofmaterialsonaconstructionsite.Each materialtodetectisequippedwithaRFIDtag.Arover equippedwithaRFIDreceiverandaGPSreceiveris movingontheconstruction.TheRFIDreceiverallows detectionsandtheGPSlocalizations.Imprecisionand uncertaintyarethetwomaincharacteristicsofthis process. Belief function theory is therefore well adapted to proposeasolutiontoimprovethedetectionespeciallyin caseofdislocation.Themaincontributionofthiswork hasbeentoshowthatalargeandrealworldapplication based on the belief theory framework has been technically possible and has allowed saving money. The detection process is based on a discretization of the search space. Each element of few nested subsets are then characterizedbyabasicbeliefassignmentcorresponding tothebeliefthatanRFIDtagbelongstothissubsetand therefore that a material is present within the border of the subset.Thelocationofthesubsetisdeterminedusinga GPS receiver. When several readings are made, a fusion is madetoobtainanewbasicbeliefassignment.A dislocationisdetectedwhentheconflictresultingofthe fusionprocessisgreaterthanaknowngiventhreshold. Thismethodhasbeenimplementedonareallarge construction site in Toronto. The estimated size of the data setis94daysofdataloggingmultipliedby,onaverage, 110tagsperdays.Adozenreadspertagperdaywere logged. The work focused on dislocations detections.The resultsobtainedshowedquitegooddetectionratesand ROC curves have been plotted. As awaited the false alarm rateincreasesasthethresholdusedtodetecttheconflict and therefore the dislocation. The conflict management is the heart of this method and the ROC curves show a rather high sensitivity to the value ofthethreshold.Adeeperstudymustthereforenowbe carriedoutonthispoint.Thismaybedoneinfour different ways: Discounting of previous basic belief assignments at each time step to favor the latest Reject the old basic belief assignments when the conflict is over the threshold Decrease conflict by enlarging the focal sets Develop a new method in the frame of the Dezert-Smarandache Theory. Use other combination rules such as Dubois-Prades rule (DP), Dezert-Smarandache Theory (DSmT), or some others. Finally, we can notice that the results presented here can beeasilyreproducedintheframeofalargesensors network where the aim is to detect the moving of sensors. Acknowledgement Theauthorsgratefullyacknowledgethecollaborationand helpful advice of Dr. Francois Caron. 0m2m14m6m10m8m18m16m00.20.40.60.81True_possitive rateFalse-positive rateReceiver Operating Characteristic Curve (ROC)051015201 5 10 15 20 25 30 35 40 45 50Actual distance between benchmark locationsDistribution of the distance between benchmark locations True-positive detections of dislocationNumber of dislocation samples7548 References [1]Akinci,B.,Patton,M.,andErgen,E.."Utilizing RadioFrequencyIdentificationonPrecastConcrete Components-Supplier'sPerspective."theNineteenth InternationalSymposiumonAutomationandRoboticsin Construction(ISARC2002),Washington,DCUSA,September 2002, pp. 381-386 [2]BasirO,KarrayF,ZhuHW.,Connectionist-based Dempster-Shaferevidentialreasoningfordata fusion.IEEETransactionsonNeuralNetworks,16(6), pp. 1513_1530. 2005 [3]Boyd,S.,andVandenberghe,L.Convex Optimization,CambridgeUniversityPress,Cambridge, UK., 2004. [4]Bulusu, N., Heidemann, J., and Estrin, D. 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