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Student Research Symposium Student Research Symposium 2018

May 2nd, 11:00 AM - 1:00 PM

Radiation Source Localization by using Radiation Source Localization by using

Backpropagation Neural Network Backpropagation Neural Network

Jian Meng Portland State University

Christof Teuscher Portland State University

Walt Woods Portland State University

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Meng, Jian; Teuscher, Christof; and Woods, Walt, "Radiation Source Localization by using Backpropagation Neural Network" (2018). Student Research Symposium. 1. https://pdxscholar.library.pdx.edu/studentsymposium/2018/Poster/1

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Themostdifficultpartoftheradiationlocalizationisthatwecannotusethetraditionalacousticlocalizationmethodtodeterminewheretheradiationsourceis.It’smainlybecausetheelectromagneticwavesaretotallydifferentwiththesoundwave.Asweallknow,soundwavehascertainwavevelocityindifferentmedia,sowecandeterminethedistancebyanalyzingthetimedifferencebetweentheincidentandthereflectedwave,orwecanalsoanalyzetheenergyofthewave.Besides,multiplesensorarrayscanalsotelluswherethesoundsourceisbasedonmaximumlikelihoodalgorithm.Nuclearradiationbasicallyisatypeofelectromagneticradiation,anditishardtomeasurethevelocityoftheradiationandthetimedifference.Besides,differenttypesofnuclidehavedifferentintensities.Therelationshipbetweentheradiationintensityanddistancecanbedescribedas:

𝐴 = 𝐾%𝑅' 𝐴(

A istotalradioactiveactivity;Kr istheradioactiveconstant;R isthedistancefromtheradioactivesource.Inthisproject,wedon’tconsiderthedecayofthenuclidebecausethehalf-lifeofcommonradioactiveelementsarelongenoughthatwecanignorethat(Table.1)Sincetheradioactivenuclideisextremelydangerous,soitisnecessarytofindawaythatcanlocatetheradioactivesourceefficiently.Notethatradioactiverateconstantisameasureoftherateofionizationof air dueto ionizingradiation from photons.

Background

FixedsourceandlinearlymovingsensorSincethesensorismovinglinearly,thenetworkwastrainedbythechangingoftheradiationateachtimepointplusthevelocityofthesensorineachdirection:

Algorithm&Methods

Results:WiththebeststructurethatdepictsinTable2,theaverageaccuracyofthepredictedintensityoftheradioactivesourceis99.7%.Theaveragedifferencebetweenthepredictedlocationofthesourceandtheactuallocationofthesourceis5.6m,whichisaprettybigportionofa20𝑚 × 20𝑚 × 20𝑚 space.Inthisversion,thenetworkcancorrectlypredicttheintensityoftheradioactivesource,thepredictionofthelocationofthesourcehasapproximately80%accuracy.Fromallthepreviousanalysisandresults,wecanconcludethatourmodelcanpredictthelocationoftheradiationsourceeffectively.Mathematically,imaginetheinputmeasurementsasavector,whatneuralnetworkdoingismappingtheinputvectorintothespacethatweexpected(Fig.4).

FutureResearch:Chasingthesource:Iftheradiationsourceisinmotion,thelocationoftheradioactivesourceisentirelydifferentateachsecond,insomecomplexcases,thesourceisevenmovingrandomly,soitisalmostimpossibletopredictthefuturecoordinateofthemovementofthesource.Besides,thenoisesignalcanalsoreducetheaccuracyofthemeasurement.Iftheneuralnetworkcan“drive”thesensorflyingtothesourcetomakethedistancebetweenthesourceandthesensorascloseaspossible,thesensorcaneasilymeasuredtheactualradiationofthesource,andthatcanalsoreducetheeffectofthenoisesignal.

Conclusion&FutureResearchInput features Number of layers Number of nodes Output features Learning rate Framework

23 4 20 4 1E-03 Full-connection

Fig.5Effectofdifferentlearningrate(Coordinateerrorvsepoch)Fig.1:Radiationintensityvsthelocationofaverticallymovingsensor

Table2:Structureofneuralnetwork

Effectoflearningrate:Learningrateisthe”Steplength”ofgradientdescent.Forcomplexneuralnetworkmodel,thelossfunctionmighthavemultiplelocalminima,soifthelearningrateistoosmall,it’seasytofallintothelocalminimumpointratherthantheglobaloptima.Minimizethelossthroughtrainingprocesscanminimizethepercentageoferrorintesting.Table.3showsthelossanderrorchangeineachexperiment,toosmalllearningratewillslowdownthespeedofgradientdescent,aswecanseefromFig.5,theerrorwon’tconvergetominimaafter1000iterationsandthetrainingprocessisalsounstable.Thebestlearningrateforthegradientdescentinthismodelis1E-03,whichiswhatweusedintheneuralnetwork.Anotherthingthatcanaffectthespeedofgradientdescentisthebatchsize(thenumberoftrainingexamplesinoneforward/backwardpass),ifthebatchsizeistoosmall,thedirectionofgradientdescentwillchangebackandforthfrequently,sothefinalestimationwillalsobelessaccurate.

Fig.3:Blockdiagramofneuralnetwork

Fig.4:Ifwecanthinktheinputfeaturesoftheneuralasavectorthatcontainscertaininformation,thentheneuralworkworkingasafunctionthatmappingtheinputvectortothetargetoutput.

RadiationSourceLocalizationbyusingBackpropagationNeuralNetworkJianMeng,WaltWoods,ChristofTeuscher

Fig.2:Thefixedsourceandmovingsensor.Thegreenstaristheradioactivesourcefixedattheorigin.Reddotsrepresentthetrace,eachdothasasetofmeasurements.

Batchsize Learning rate Number of nodes Final Loss Intensityerror Coordinateerror32 0.0001 10 19.17 1.5% 8.7m32 0.0001 15 17.19 1.7% 7.6m32 0.0005 15 12.17 0.98% 6.5m32 0.001 20 10.11 0.66% 4.9m64 0.001 20 9.22 0.23% 4.3m

Table.3:Resultsummary

IntroductionFromtheexpressionoftheradioactiveintensity,wecantellthattheintensityofradiationnotonlydependonthedistancefromtheradiationbutalsorelatedtothetypeofthenuclide.Ingeneral,therelationshipbetweentheintensityandthedistancesatisfytheinverse-squarelaw,whichisanon-linearrelationship.Inotherwords,ifwecanusethemeasurementanddynamicparametersofthemovingsensortotrainaneuralnetwork.Thetrainednetworkcanpredictthelocationandtheintensityofthesourcebasedonanymovementofthesensor.

Fixedsourceandlinearlymovingsensor:Sofartheresearchfocusonthesituationthattheradioactivesourcewasfixedatacertainpoint,andthesensorismovinglinearlywiththerandominitiallocationina20𝑚 × 20𝑚 × 20𝑚 space.

Movingsource+movingsensor:Thefinalgoalofthissituationisthatthealgorithmiscapabletolocatethelocationofthesensor.Sincethesensorisinmotion,sothealgorithmshouldupdatethelocationandtheintensityofthesourceateachtimepoint,nomatterwhatthemovingpatternis.

Whylinearlymovingsensor?Inordertotrainthenetworkeffectively,ourtrainingsetcannotbeentirelyrandom,ithastofollowsomeorder.Oneimportantfactis:Wecancontrolthemovementofthesensor.Thus,ifthemovementofthesensorfollowsacertainpattern,itiseasytoanalyzeandtrainthenetwork.Forexample,ifthesensormovingvertically,asthedistancebetweenthesensorandthesourcedecreasing,themeasuredintensityincreasing,andthemeasurementwilldecreasewhenthesensormovingawayfromthesource(Fig.1)Aswecanseefromthepicture,ifthemovementofthesensorhascertainpattern,thechangingofradioactivereadingwillalsofollowthecertainpattern.Anotheradvantageofthelinearlymovingsensoris,onceweknowtheinitiallocationandthevelocityofthesensor,wecancomputethecoordinatesofthesensoratanytimepoint,whichmeansthelocationofthesourcecanbedeterminedbythedistancebetweenthecoordinatesofthesourceandthecoordinatesoftheinitiallocationofthesensor.

High-levelalgorithm&Backpropagation:ThestructureoftheneuralnetworkisdepictedinFig.3.Thedatageneratorgeneratestracesandcorrespondingmeasurementsateachtimepoint.Eachtraceconsistsof20datapoints(Fig.2),whichmeansthedatageneratoractuallyintroducethechangingofmeasuredintensitiestotheneuralnetwork.Timeisnottheactualinputoftheneuralnetwork,buttrainthenetworkwithtime-varyingpatterncanmakethenetworkget“familiar”withthevariation.Inthehigh-levelalgorithm,theneuralnetworkisatypicalsupervisedlearning.Thebackpropagationprocesscomputesthelossbetweenthepredictedoutputandthetargetoutput,thenusethelosstoupdatetheweightvaluesateachneuronbydoingthegradientdescent.TheobjectiveoftheSGDistofindasetofweightsthatcanminimizethevalueoferror.

Training:Thenetworkwastrainedby5,000tracesover1,000iterations.Theaccuracylocalizationwasrepresentedbythedistancedifferencebetweenthepredictedcoordinatesandtheactualcoordinateofthesource.Theintensityaccuracywasrepresentedbythedifferencebetweenthepredictedradioactiveintensityandtheactualintensity.Theentiredatasetwassplitintotwoparts:Using80%ofthetracesasthetrainingsettotrainthenetwork,andtherest20%isthetestsettoverifythepredictionoftheneuralnetworkmodel.

Optimization

Table1:Halflifeofcommonradioactiveelements

Elements Half-life(years) Kr(𝑹 + 𝒄𝒎𝟐)

Cs137 30 3.4Co60 5 12.8Ra226 1600 8.25

The authors acknowledge the support of the Semiconductor Research Corporation (SRC) Education Alliance (award # 2009-UR-2032G) and of the Maseeh College of Engineering and Computer Science (MCECS) through the Undergraduate Research and Mentoring Program (URMP)

Acknowledgment

1. Xiaohong ShengandYu-HenHu,"Maximumlikelihoodmultiple-sourcelocalizationusingacousticenergymeasurementswithwirelesssensornetworks,"in IEEETransactionsonSignalProcessing,vol.53,no.1,pp.44-53,Jan.2005.

2. SimonHaykin, SimonS.Haykin,NeuralNetworksandLearningMachines,Volume10.3. Yuan,Ya-xiang."Step-sizesforthegradientmethod." AMSIPStudiesinAdvancedMathematics 42.2(2008):785.

ReferencesName:JianMengTeuscherLabMaseehCollegeofEngineeringandComputerScience(MCECS),PortlandStateUniversityEmail:mengjian@pdx.edu

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