Calibration transfer in temperature modulated gas sensor arrays

ContentslistsavailableatScienceDirect

Sensors

and

Actuators

B:

Chemical

j ourn a l h o m e pa g e :w w w . e l s e v i e r . c o m / l o c a t e / s n b

Calibration

transfer

in

temperature

modulated

gas

sensor

arrays

L.

Fernandez

_,

_S.

_Guney

_,

_A.

_{Gutierrez-Galvez}

_,

_S.

_Marco

b_{UniversityofBarcelona,Barcelona,Spain} c_{BaskentUniversity,Ankara,Turkey}

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received27July2015

Receivedinrevisedform11February2016 Accepted26February2016

Availableonline10March2016 Keywords:

Calibrationtransfer Gassensorarray MOX

Temperaturemodulation

a

b

s

t

r

a

c

t

Shiftsinworkingtemperatureareanimportantissuethatpreventsthesuccessfultransferofcalibration modelsfromonechemicalinstrumenttoanother.Thiseffectisofspecialrelevancewhenworkingwith gassensorarraysmodulatedintemperature.Inthispaper,westudytheuseofmultivariatetechniques totransferthecalibrationmodelfromatemperaturemodulatedgassensorarraytoanotherwhena globalchangeoftemperatureoccurs.Todoso,webuilt12identicalmastersensorarrayscomposedof threedifferenttypesofcommercialFigarosensorsandacquiredadatasetofsensorresponsestothree puresubstances(ethanol,acetoneandbutanone)dosedat7concentrations.Themasterarraysarethen shiftedintemperature(from−50to50◦_C,T=10◦_{C)andconsideredasslavearrays.Datacorrectionis}

performedforanincreasingnumberoftransfersampleswith4differentcalibrationtransfertechniques: DirectStandardization,Piece-wiseDirectStandardization,OrthogonalSignalCorrectionandGeneralized LeastSquaresWeighting.Inordertoevaluatetheperformanceofthecalibrationtransfer,wecomparethe RootMeanSquareErrorofPrediction(RMSEP)ofmasterandslavearrays,foreachinstrumentcorrection. BestresultsareobtainedfromPiece-wiseDirectstandardization,whichexhibitsthelowerRMSEPvalues aftercorrectionforthesmallernumberoftransfersamples.

©2016ElsevierB.V.Allrightsreserved.

1. Introduction

Shiftsinworkingtemperaturepreventdirectcalibration

trans-ferbetweenchemical measuringinstruments[1].Thatistosay

thatcalibrationmodelsbuiltforinstrumentI1workingata

tem-peratureT1 experienceanimportant degradationonprediction

whenappliedtodatasamplesofinstrument I2 atT2 (T2 /=T1).

Thisisamatteroftheutmostimportancefortemperature

modu-latedmetaloxidegassensorarrays[2],wheretolerancesinheater

resistancesvalues,variationsontheworkingflowconditions,and

environmentalfluctuations cangiverisetoaglobalshiftT of

thesensornominaltemperatureprofile,andthereforeofthe

sen-sorresponse waveform. A naïveapproach toovercome invalid

calibrationtransferis tocreate independentcalibrationmodels

foreach ofthearrays. However,this isanimpracticalsolution,

sinceitimpliescostlyandlabor-intensivemeasurementperiods.A

preferablemethodologyistheuseofinstrumentstandardization

techniques[3]tocorrectthetemperatureshiftinsensor arrays

ascomparedtoareferencearray(fromnowonwewillreferto

∗ Corresponding authorat: Institute of Bioengineering of Catalonia (IBEC), Barcelona,Spain.Tel.:+34934034804;fax:+34934021148.

E-mailaddresses:lfernandez@el.ub.es,lfernrom@gmail.com(L.Fernandez).

thesearraysasslaveandmasterarraysrespectively)calibratedfora

completesetofexperimentalconditionsandapropertemperature

profile.Thecalibrationtransferthenreliesonthemeasurementof

onlyasmallsubsetofexperimentalpointsintheslavearray(herein

calledtransfersamples).

AccordingtoMarcoandGutierrez-Galvez[4],calibration

trans-fer can be realized following three different strategies: (i) by

transformingtheslaveinstrumentreadingstokeepthecalibration

modelofthemasterinstrumentstillvalidontheslaveinstrument,

(ii)bymodifyingthetargetlabelsofthesamplesfromtheslave

instrumentsoastomatchthoseobtainedfromthemaster

instru-ment,and (iii) byforcingmasterand slavereadingstobecome

moresimilarbeforecreatingthecalibrationmodel.Direct

Stan-dardization(DS)andPiecewiseDirectStandardization(PDS)arethe

morepopularmethodstostandardizeslaveinstrumentresponse

[5,6]. Withrespectto thesecond strategy, themostfrequently

usedmethodisunivariateMultiplicativeSignalCorrection(MSC)

[7].Finally,ComponentCorrection(CC),OrthogonalSignal

Correc-tion(OSC)andGeneralizedLeastSquaresWeighting(GLSW)are

commonlyusedtoremoveinstrument-to-instrument variability

[8–10].

Alargenumberofstudiesoninstrumentstandardizationhave

beenappliedtoNearInfraredSpectroscopy(NIRS).However,there

isanoticeablelackofstudiesaboutthestandardizationofgas

sen-http://dx.doi.org/10.1016/j.snb.2016.02.131

sorarrays,withtheexceptionof threeimportantcontributions.

Balabanetal.[11]builtacalibrationmodeltoidentifytheageof

milksampleswithachemicalsensorarrayof12conductive

poly-mers.Theytransferredthismodeltoadifferentarraywiththesame

sensors.Todoso,theytransformedtheslavearrayresponseinto

masterarrayreadingsbyapplyingthreedifferenttypesof

correc-tions:UnivariateRegression,MultivariateRegression(MLR)and

MultilayerPerceptrons(MLP).Thesecalibrationtransfermethods

wereevaluatedcomparingtheclassificationratesof themaster

andthetransformedmasterarrays.Multivariateregressionshowed

thebestperformanceinstandardizingtheinstruments.Ina

sim-ilarstudy,Tomicetal.[12] aimedatcompensatingtheeffectof

sensorreplacementinahybridsensorarraycomposedof12MOS

(metal-oxidesemiconductor)sensorsand5MOSFET(metal-oxide

semiconductorfield-effecttransistor).Theproblemtosolvewasto

distinguishbetweenmilkingoodconditionfromoff-flavormilk.

Theyacquiredtwicethe completeset ofmeasurements, before

and afterthe sensorreplacement. Thentheymodeled thedata

oftheoldsensorarray,whichwasselectedasthemaster

instru-ment.Measurementsobtainedfromthenewarraywereadapted

tobeusedinthemasterclassificationmodelwithtwodifferent

techniques:ComponentCorrection(CC) andMultiplicative Drift

Correction(MDC).Thelaterwasshowntobeslightlymoreefficient

inrectifyingtheslaveinstrumentresponseusingtheclassification

rateobtainedforthetestasafigureofmerit.Inamorerecentpaper,

Carmelet al. [13] showedthe possibility of buildingmappings

betweentwodifferentsensortechnologyarrays,a32conducting

polymerarray(CP)andan8sensorquartzmicrobalancemodule

(QMB),which wereexposed toasetof 23purechemicals.The

authorsbuiltaPCAmodelforeachinstrumentandtriedtoclassify

testsamplesaccordingtothedistancetothecentroidofthenearest

class.Afterthat,theytransformedtheprojecteddatafromone

sen-sorarraytotheotherinbothdirections.Toperformthistask,they

investigatedthreedifferentapproaches:MultivariateRegression

(MLR,PCR,PLS),NeuralNetworks(NN)andTesselation-based

Lin-earInterpolation(TLI).Again,theclassificationratewasthefigure

ofmeritusedtocomparemasterandthestandardizedslave

instru-ments.Theirresultsshowedthattheperformanceofthedifferent

standardizationmethodswasdependentonthemappingdirection,

obtainingthebestresultsfortheconversionfromCPtoQMBusing

NN,andapplyingTLIinthereversemapping.Inalltheseprevious

worksthecompletesetoftrainingsamplesusedtocreatethedata

modelswastransferredfromthemastertotheslaveinstrument.

Beyondthesevaluablecontributions,wehaveidentifiedthree

importantopenquestionsforcalibrationtransferine-noses.(i)

E-nosearrayscantunetheiroperationalparameterssoastoenhance

theirsensitivitytodifferentcompounds[14].Therefore,instrument

dissimilaritiesdue to tolerances ontheoperational parameters

mustbecorrectedaccordingly.(ii)Inordertomakeanefficient

cal-ibrationtransfer,alimitedsubsetofexperimentsshouldberunin

theslaveinstruments.Tothebestofourknowledge,nosystematic

studycomparingtheperformanceofdifferentcalibrationtransfer

techniqueswithrespecttothenumberoftransfersamplesisfound

intheliteraturefor e-noses.(iii)Continuouscalibrationmodels

(regressors)provideamoresensitivemeasureofthecalibration

transferperformancethandiscretecalibrationmodels(classifiers).

However,intheliteratureyoucanonlyfindclassificationmodels

transferredfromoneinstrumenttoanother.

Inthispaper,weaddressthesethreeopenquestionswiththe

followingstudy.Wehaveexploredthecalibrationtransfer

prob-lemfortemperaturemodulatedmetaloxidesensorarrayswhena

globalshiftoftemperatureoccurs(i).Inanexhaustivestudythat

includes132master-slaveinstrumentcombinations,wewill

eval-uatethequalityofthecalibrationtransferobtainedfromseveral

instrumentstandardizationtechniques.Wewillcomparemaster

andslaveerrors(RMSEP)fordifferenttemperatureshiftsandsizes

ofthetransfersampleset(ii)andonconcentrationprediction(iii).

2. Theory

In this paper, we follow two of the three different

strate-giesproposedintheliteratureforcalibrationtransfer[Marcoand

Gutierrez-Galvez[4]].Thefirstone consistsin transformingthe

sensorresponsesoftheslaveinstrumentsotheyresemblethoseof

themasterinstrument.Inthisway,wecandirectlyusethe

calibra-tionmodelbuiltonthesensorresponsesofthemasterinstrument

withthetransformedslavesensorresponses.Inthisstrategy,we

workonthespaceofresponsesofthemasterinstrument.To

trans-formthesensorresponsesoftheslaveinstrument,weusedDirect

Standardization(DS)andPiece-wiseDirectStandardization(PDS).

Thesecondstrategyconsistsoftransformingnotonlythesensor

responsesof theslave instrumentbut alsothose ofthe master

instrument to a joint master-slave space. Thus, the calibration

modelisbuiltinthisjointspace.Thesensorresponse

transforma-tionmethodsusedinthisstrategyareGeneralizedLeastSquares

Weighting(GLSW)andOrthogonalSignalCorrection(OSC).Fig.1

illustratesbothstrategies.

Inadditiontothis,werealizedasamplesubsetselectiontosort

outthesamplesusedtostudytheperformanceofthecalibration

transferintermsofthenumberofsamplesconsideredfromthe

slaveinstrument.We testtwodifferentapproaches:select

sam-plesbeforeoraftercreatingthecalibrationmodelofthemaster

instrument.Next,wedescribethemainfeaturesofthedifferent

calibrationtransfertechniquesusedinthispaper,aswellasthe

twomethodologiesusedtoperformsamplesubsetselection.

2.1. Calibrationtransfertechniques

Thepurposeofcalibrationtransferistocorrectinstrumental

dif-ferencessothatthereadingsoftheslaveinstrument(XS)become

similartothereadingsofthemasterinstrument(XM).Eachofthe

calibrationtransfertechniquesemployedinthis workhasbeen

trainedtoperformthistaskusingasubsetofsamplesofthe

train-ingsetofmasterandslaveinstruments.Thesesamplesareusually

calledtransfersamplesS.Thisnotationisemployedinthe

descrip-tionofthefollowingfourcalibrationtransfertechniques.

2.1.1. DirectStandardization(DS)

DirectStandardization[15]isacalibrationtransfertechnique

thatrelatesthereadingsoftheslaveinstrumenttothoseofthe

masteraccordingtothefollowinglineartransformation:

¯SM= ¯SS×F (1)

where ¯SM and ¯SS are the mean-centered response matrices of

transfersamplesofmasterandslaveinstrumentsandFthe

slave-to-mastertransformationmatrix,whichisestimatedastheproduct

¯SMandthepseudo-inverseof ¯SS:

F= ¯S+

S × ¯SM (2)

Inthisway,newsamplesfromtheslaveinstrumentXScanbe

projectedontothemasterinstrumentresponsespaceXM:

XT_M=XT_S×F (3)

2.1.2. Piece-wiseDirectStandardization(PDS)

TheDSmethodhasthelimitationofnotproperlytransformthe

responsesfromslavetomasterinstrumentswhenthenumberof

variablespersampleisgreaterthanthenumberofsamples.Thus,

thetransformationmatrixF(Eq.(2))becomesunderdetermined[7].

Piece-wiseDirectStandardization[16]avoidsthisproblemusing

a)

_b)

Fig.1. Blockdiagramofthecalibrationtransferprocess(a)totransformtheresponsesoftheslaveinstrumentsoastoworkonthespaceofresponsesofthemasterinstrument (DSandPDS),and(b)totransformtheresponsesofthemasterandslaveinstrumentinordertoworkonajointmaster-slavespace(OSC,GLSW).

responseofthemasterinstrumentvariableswithinawindowof

sizewcenteredatthej-thvariabletothej-thvariableontheslave

array.TheresultingtransformationmatrixforthemethodFhasa

diagonalstructure:

F=diag





wherekisthenumberofvariablesonbothinstruments.The

projec-tionofdatafromthemasterontotheslaveinstrumentisperformed

followingEq.(3).

2.1.3. OrthogonalSignalCorrection(OSC)

OrthogonalSignalCorrection[17]aimstoremovethesourcesof

varianceoftheslaveinstrumentthatareorthogonaltothemaster

array.TheOSCalgorithmstartscalculatingthescoresvectort1of

thefirstPrincipalcomponentoftheslavearraymatrixoftransfer

samples,SS.Thatvectoristhenorthogonalizedagainstthemaster

instrumentresponsematrixoftransfersamplesSM,givingraiseto

t1 t₁ =









Afterthat,theweightsw1oftheproductSSw1arecalculatedfor

themaximumprojectionontotheorthogonalscoresvectort1:

w1= ¯S+S ×t



1 (6)

SS+beingthepseudo-inverseofSS.Thescoresvectort1isthen

updated:

t1=SS×w1 (7)

Next,thealgorithmreturnstoEq.(5),wherethedetermination

oftheorthogonalscorevectorisrepeateduntilconvergence.At

thispoint,theloadingvectorcorrespondingtothefirstorthogonal

scoreiscomputedas:

p1=STS×t1





andthefirstOSCcomponentcanberemovedfromtheoriginal

SSmatrixobtainingthedeflateddatamatrixSS,1:

SS,1=SS,1−t1pT1 (9)

Finally,thecomplete processcanberepeateduntiltheN-th

OrthogonalSignalComponentasfollows:

SS,N=SS−

i=N



i=1

tipT1 (10)

2.1.4. GeneralizedLeastSquaresWeighting(GLSW)

Generalized Least Squares Weighting [18] method identifies

anddown-weightstheinstrumentchannels(features)

responsi-bleforthemajorsourcesofvariancebetweenmasterandslave

instruments.Tobuildthefilter,thecovariancematrixCfromthe

differencebetweenthemean-centeredmasterandslavematrixof

transfersamplesiscomputed:

C=







¯SM− ¯SS



(11)

Next,Cisfactorizedastheproductofthreematricesthrough

singularvaluedecomposition(SVD):

C=VD2VT (12)

whereVandDare,respectively,theeigenvectorandthesingular

valuematrices.Afterthat,theSmatrixisweightedinthefollowing

way:

W=



D2

˛ +I (13)

BeingWthematrixoftheweightedeigenvalues,␣the

weight-ingparameterandItheidentitymatrix.Theparameter␣controls

thedegreeofdissimilarityallowedtotheinstruments.Whilehigh

valuesof␣increasethedownweighting,lowervaluesof␣reduce

itseffect.ThefilteringmatrixGisthencalculatedusingtheinverse

oftheweightedeigenvalues:

G₌VW−1VT (14)

2.2. Samplesubsetselection

Samplesubsetselectioncanbeconductedintwomanners:(a)

multivariatemean)onthemasterinstrumentmatrix ¯XMthrough

thecalculusoftheleveragematrixH[19]:

H= ¯XM¯XMT (15)

And(b)byseekingforthemostinfluentialsamplesofthe

mas-ter’sinstrumentcalibrationmodel,approachingHastheleverage

matrixfortheinversecalibrationmodel ¯X_M+,alsomean-centered:

H= ¯XM¯XM+ (16)

Inbothcases,themaximumdiagonalelementofHcorresponds

tothemostrelevantsampleinthetrainingset.Oncethefirstsample

isobtained,therestofthedatasetisorthogonalizedagainstit,anew

leveragematrixHiscreated,andthenextmostinfluentialsample

canbeselected.Table1showsthefirst12samplesselectedusing

bothmethods.

3. Methods

3.1. Experimental

Toperformthisstudy,weusedasetofthreedifferenttypesof

Figarometaloxidesemiconductorsensors(TGS-2600,TGS-2610,

TGS-2620)replicated12timeseach.Inallexperiments,onegroup

ofthreedifferentsensorswasusedasamasterinstrumenttofind

acalibrationmodelandtheresttreatedasslavearraystostudy

thecalibrationtransfer.Thereadoutofthesensorsisperformed

throughaloadresistor(RL=6.1K)inahalfbridgeconfiguration.

Wemodulatedthesensortemperatureswitharampprofile

rang-ingfrom ambienttemperature to495◦C_±5◦C [20] in a period

of90s. The36 sensorswereexposedduring900sto3analytes

(ethanol,acetone,butanone)at7differentconcentrations(0,20,40,

60,80,100,120),givingriseto21differentexperiments.Detailed

information ontheodordeliverysystemand theestimation of

sample concentrationcan be foundin our previouswork [21].

Aftereachmeasurementblock,thesensorchamberwascleaned

insyntheticairoveraperiodof1800s.Usingthissetof

experi-ments,webuiltcalibrationmodelsofthemasterinstrumentsfor

thepredictionofethanol,acetoneandbutanoneconcentration.We

acquiredadifferentnumberofrepetitionsperexperimentfor

train-ing(7) andtesting(3)thecalibrationmodels.Experiments with

concentrationlevelsof0,40,80and120ppmwereacquiredand

usedasatrainingset(3pureanalytes_×4concentrations_×7

rep-etitions=84samples).Similarly,experimentswithconcentrations

of20,60, 100ppm wereacquiredand employedfortestingthe

calibrationmodels(3pureanalytes×3concentrations×3

repeti-tions=27samples).Theselectedtemperaturewindowusedforthe

calibrationofthemasterinstrumentswas[200–300]◦C.

3.2. Calibrationmodel

Wehave approachedthecalibrationofourinstrumentsasa

regressionproblemtoprovidemoresensitivitywhentransferring

thecalibrationmodeltoanotherinstrument.Inparticular,wehave

usedpartialleastsquaresregression(PLSR).WenotethatthePLSR

modelofthemasterinstrument providessimultaneouslya

pre-dictionfortheconcentrationofethanol,acetoneandbutanoneof

gassamples.Weemployedthesetoftrainingsamplestogenerate

thecalibrationmodels,whoselevelofcomplexity(i.e.,the

num-beroflatentvariables)wassetthrougha cross-validationstage

basedontheLeaveOneBlockOut(LOBO)approach.More

specifi-cally,eachblockofsamplesusedforcross-validationbelongedto

oneexperimenttypeofthetrainingset.Therefore,weemployed

12blocksofexperiments,with7sampleseach.Basically,theLOBO

methodcomputestheRootMeanSquareErrorinCross-Validation

(RMSECVM)astheaverageRMSEobtainedfrompredictingeachof

thedifferentblocksofexperimentsusingaPLSRmodelbuiltfrom

thecomplementaryblocksofexperiments:

RMSECVM= 1 C C







˜yi,j,k−yi,j,k



NV×M

(17)

where ˜yi,j,kandvi,j,k are,respectively,theobservedandthe

pre-dicted concentration values for the i-th sample, the j-th pure

substanceandthek-thdatapartition,NVisthenumberofsamples

fortestingeachpartitionofthevalidationset(7),Mthenumber

ofpureanalytespresentinthedataset(3)andCthenumberof

blocksofexperimentsofthetrainingset(12).Thenumberoflatent

variablesofthecalibrationmodelwasdeterminedcalculatingthe

RMSECVM(lv)foranincreasingnumberoflatentvariables(lvfrom

1to10).WhenthecurrentRMSECVM (lv=r)didnotreducethe

previousRMSECVM(lv=r−1)valuemorethana1%,theselected

numberoflatentvariableswasdeterminedlv=r−1.

Themeasureofthemodel’sperformancefittingthetestdatafor

themasterarraywastheRootMeanSquaredErrorofPrediction

(RMSEPM): RMSEPM=





˜yi,j−yi,j



NT×M

(18)

where ˜yi,jandyi,jwere,respectively,theobservedandthepredicted

concentrationvaluesforthesamplei-thsample,thej-thpure

ana-lyte,NTisthenumberofsamplesoftestset(27),Mthenumberof

pureanalytespresentinthedataset(3).TheRMSEPwasalsoused

asameasureofgoodnessoffitforthetransformedslavereadings

(RMSEPS).

3.3. Calibrationtransfer

Inthisstudy,wehaveevaluatedtheabilityoffourtechniques

(DS,PDS,OSC,GLSW)tocounteracttheeffectoftemperatureshift

oncalibrationtransfer.Aseriesof experimentswereconducted

wherethetemperatureoftheslaveswasshiftedaccordingtothe

following temperaturevalues:T=0◦C, ±10◦_C,±20◦_{C, ±30}◦_C,

±40◦_C,±50◦_{C.Fig.2showsthedramaticchangeonMOXsensor}

waveformsduetotemperatureshifting(T=−50◦_C),fora

temper-aturemodulatedTGS-2620sensorexposedtothe3testsetethanol

concentrations.Theeffectofthenumberoftransfersamples(from

1upto12)onthecalibrationtransferqualitywasstudied,giving

risetoatotalof17424differentcalibrationmodelstransferred(12

masters×11slaves×11temperatureshifts×12transfersamples)

perinstrumentstandardizationtechnique.Anexampleofthe

cali-brationtransferprocessisshowninfigure(Fig.3a–c)usingDirect

Standardization,foratemperatureshiftingofT=−50◦_Cand12

transfersamples.ThesefiguresshowthescoresplotofaPCAmodel

for themasterarray (3a),theuncorrected slave array(3b)and

correctedslavearray(3c).Calibrationtransferallowsplacingtest

samplesbacktoitsoriginalpositionornearby.

3.3.1. Calibrationtransfermodels

Weoptimizedthe4calibrationtransfermethodsminimizing

thedifferencebetweenthemasterandthecorrectedslavearray

readings.Thisprocedureoptimizedtheparametersofthe

differ-entcalibrationtransferalgorithmsselectingthemamongasetof

possiblevalues.Therangeofparametervaluesdependedonthe

particulartechniqueemployed.Thewindowsizewwasselected

fromalistof1–31channelsforPDS.Themaximumvalueforwwas

limitedto31sothatallowedtemperatureshiftcorrectionbetween

instrumentswithoutmixingfeaturesfromdifferentsensorsofthe

masterarray.Therangeoftheweightingparameter␣inGLSWwas

dis-Table1

First12transfersamplesofthecalibrationdatasetselectedusingmethods1and2.

Method1 Method2

TransferSamples SampleReplicate Concentration(ppm) SampleReplicate Concentration(ppm)

Eth Acet But Eth Acet But

1 9 0 120 0 10 120 0 0 2 10 0 0 0 2 0 120 0 3 6 120 0 0 5 0 0 120 4 1 0 0 120 7 0 0 40 5 8 40 0 0 10 80 0 0 6 10 80 0 0 10 0 40 0 7 6 0 0 40 3 0 0 80 8 9 0 0 120 2 40 0 0 9 2 0 120 0 7 0 80 0 10 7 40 0 0 7 0 0 120 11 5 0 0 120 4 120 0 0 12 5 0 0 40 8 0 80 0 200 225 250 275 300 4 5 6 7 8 9 10 11 Reference Temperature (ºC) Sensor Response (V) Non shifted −50 ºC Shift TGS−2620 Ethanol 20 ppm Ethanol 60 ppm Ethanol 100 ppm

Fig.2.ResponseofaTGS2620sensorunitto20,60,100ppmofethanolwithin anominaltemperaturewindowof200–300◦_{Cfora)notemperatureshift}

(gray-dashedcorves)andb)foratemperatureshiftofT=−50◦_{C(redcorves).(For}

interpretationofthereferencestocolourinthisfigurelegend,thereaderisreferred tothewebversionofthisarticle).

similaritybetweenmasterandslaveinstruments.Largevaluesfor ␣(closeto1)areneededforcorrectinginstrumentaldissimilarities whoseimpactintheoverallvarianceofthedataiscomparableto theusefulvarianceofthemeasurement.Inpractice,weselected␣ fromthecollectionofvalues1,0.5,0.01,0.05,0.001,0.005.Finally, thenumberofOrthogonalComponents,ncomp,inOSCwassetin therangefrom2to12.Thereasonforthatwasthatthemaximum valueofthisparameterwaslimitedbynumberoftransfer sam-plesusedtoperformthecalibrationtransferbetweenmasterand slaveinstruments(from2to12).Thevalidationstarted perform-ingdatacorrectionforeachtechniqueandsetofparametervalues. Thecalibrationmodelofthemasterinstrumentwasthenapplied onthetransformedtrainingsetoftheslaveinstrumentandthe pre-dictionsofbothinstrumentswerecompared.Thecomparisonwas performedthroughthecalculationoftheRootMeanSquaredError ofCalibration(RMSECM-S): RMSECM−S=









i,jandySi,jarethepredictedconcentrationvaluesofthe masterandslaveinstrumentsforthesamplei-thsampleandthe j-thpuresubstances,NC (84)isthenumberoftrainingsamples andMthenumberofsubstancespresentinthedataset(3).Theset

−20

−10

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20

−10

−5

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Scores on PC 1 (89.79%)

Scores on PC 2 (8.86%)

Train

Test

−20

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−10

−5

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Scores on PC 1 (89.79%)

Scores on PC 2 (8.86%)

Train

S.Test

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−10

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−10

−5

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Scores on PC 1 (89.79%)

Scores on PC 2 (8.86%)

Train

C.Test

a)

b)

c)

Fig.3. (a–c)PCAplotofthesensorresponseforthetraining(blackcircles)andtest setswithinterleavedconcentrationsfor:a)themasterexperiments(bluesquares), (b)theuncorrectedslaves(reddiamonds)and(c)thecorrectedslavesafter perform-ingaDirectStandardization(greentriangles),(T=−50◦_{C).(Forinterpretationof}

thereferencestocolourinthisfigurelegend,thereaderisreferredtothewebversion ofthisarticle).

ofparametervalueswhoseRMSECM-Swasnotabletobereduced inmorethan1%byanyothersetwasselectedtobuildthe cali-brationtransfermodel,foreachcalibrationtransferalgorithm.The

−50 −30 −10 10 30 50 0 20 40 60 80 100 120 140 160 180 200 Temperature Shift (ºC) RMSEP (ppm)

Average RMSEP vs Temperature Shift Slave Master

Fig.4.AveragedRMSEPSasfunctionofthetemperatureshiftforthenon-corrected

slaveinstruments.Noteastheworstpredictionsarebiasedtowardpositive tem-peratureshifts.

RMSEwasalsoemployedasameasureofgoodnessoffitforthe transformedslavereadingsofthetestset(RMSEPM-S).

4. Results

Togainsomeinsightontheeffectoftemperatureshifton cal-ibrationmodeltransfer,wewillshowfirstresultsofthemaster calibrationmodel applieddirectlyonthe slavewithout correc-tion. This will provide a baseline performance from where to improve.Then,wewillpresenttheresultsoftheslaveRMSEPfor anincreasingnumber oftransfersamplesand alsoas tempera-tureshiftsvariesintherangeof[–50,50]◦C.Finally,theresultsfor theRMSEPM-Sacrossalltemperatureshiftsandnumberoftransfer sampleswillprovideacomprehensivepictureoftheperformance ofthedifferentcalibrationtransfertechniques.

Inthisstudy,eachofthearrayreplicateswasusedbothasmaster instrumentfortheotherreplicatesorasslavearraytobecorrected byanothermasterarray.Whenactingasmasterinstruments,the arrayreplicatesproducedsimilarcalibrationmodelsintermsof complexityandmodelperformance.Mostofthearrayreplicates builta 4 latentvariablePLSR model (9out of12) whereasthe remaining(3)needed5latentvariablestoachievethe specifica-tionssetforcross-validation.TheaverageRMSEPMforthesetof masterinstrumentswas(4.7±1.1)ppm.

Thedirectapplicationofthemastercalibrationmodelinthe slave arrays led, as anticipated, to high RMSEPS. Fig. 4 shows

theaveragepredictionerrorofuncorrectedslavearrays(RMSEPS)

along temperature shift, for all possiblemaster-slave

combina-tions.TheRMSEPSwassubstantiallyhigherthantheRMSEPM.The

minimum differencebetweeninstruments wasfound when no

temperatureshiftwasproduced(RMSEPS|T=0=29.1±18.9ppm).

As canbe expected, theRMSEPS increased as thetemperature

shiftbetweeninstrumentsincreased.Though,thiseffectwasnot

symmetric:shiftstowardhighertemperaturesexhibitedagreater

penalty on the RMSEPS than shifts in the opposite direction.

Comparingthe mostextremetemperature shifts inboth

direc-tionswe found that theerror of prediction at T=+50◦C was

RMSEPS|T=+50◦C=128.2±41.4ppm,whereas at T=−50◦C was

RMSEP_S|T=−50◦C=40.6±6.1ppm.

Afterdatacorrection,theRMSEPSoftheslavearrayswas

con-siderablyreduced.Thedegreeoferrorreductiondependedonthe

amountoftransfersamplesandtheshiftoftemperature.Asa

gen-eraltrend,theRMSEPSdecreasedgraduallyuntilsaturationasthe

numberoftransfersamplesincreased,foranytemperatureshift

andcalibrationtransfertechnique.Theinfluenceof thetransfer

samplesubsetsizeonthequalityofthecalibrationtransferis

illus-tratedinFig.5(a–d).ThefigureshowstheaverageRMSEPSofthe

corrected slaveinstrumentsof thedifferentcalibrationtransfer

techniques,foranincreasingnumber oftransfer samplesand a

fixedtemperatureshiftofT=−20◦_{C.DSandPDSobtainedthe}

lowest RMSEPS levels (6.3±2.1ppm, and 6.1±1.4ppm,

respec-tively)althoughPDSneededafewernumberofsamplestoreach

errorsaturation(fiveinsteadofeleven).OSCandGLSW showed

higher RMSEPS values (around8ppm, for bothtechniques) and

slowertransitionstosaturation.Concerningtheinfluenceof

tem-perature shift, we found that the lowest RMSEPS were biased

toward negativeshifts,foranynumber oftransfersamplesand

calibrationtransfertechnique.However,PDSdemonstratedtobe

themostrobusttechniqueagainstthisdirection-dependenteffect.

Anexample ofthis behavior canbeseenonFig.6(a–d),where

weshowtheaverageRMSEPSofthecorrectedslavearraysusing

thefourinstrumentstandardizationmethods,forthecompleteset

ofthetemperatureshifts,fixingto5thenumberoftransfer

sam-ples.TheminimumRMSEPSvalueforDSandPDSisobtainedfora

temperatureshiftofT=−30◦_{C(9.4±4.0ppm,and6.2±1.6ppm,}

respectively).Ontheotherhand,OSCandGLSWpresentedtheir

minimumRMSEPSvalueforT=0◦C(8.7±2.8ppmforOSCand

9.1±3.3ppmforGLSW).

Fig.7(a–d)showsthecolormapsplotsfortheaverageRMSEPM-S

ofthetransformedslaves,for eachnumber oftransfersamples,

temperature shiftand calibrationtransfer technique.Dark/light

tonesdenotegood/badperformancesincorrectinginstrument

dis-similarities.Toenhancethecontrastofplots,thepredictionerrors

below5ppmand above20ppmweresaturated,respectively,to

black andwhite colors.To comparethequalityof thedifferent

instrumentstandardizationmethodsweevaluatedthepercentage

ofslavearrayswitherrorsofpredictionbelow5ppminFig.7(a–d).

Accordingtothiscriterion,DSwasabletocorrectproperlyaround

the23%oftheseslavearrays.However,DSneededatleast5

trans-fersamplestoobtainpredictionerrorsbelow20ppm,andtended

topresentbettercorrectionsforslavearraysbiasedtoward

nega-tivetemperatureshifts.RegardingOSCandGLSW,theyexhibited

asimilarbehaviorinthesensethattheyexperienceddifficulties

tocorrecttheeffectoftemperatureshifting.Notethatboth

tech-niquesneededatleast8transfersamplestoreducetheprediction

errorbelow5ppm,forthenearesttemperatureshift(T=−10◦_C).

Inanycase,noneofthemproperlycorrectedmorethana15%ofthe

slavearrays.Again,PDSpresentedthebestperformance,sincethe

techniquecouldcopebetterwiththeRMSEPerrorcontributiondue

tothetemperatureshiftdirection.Forinstance,PDSonlyneeded

5transfersamplestocorrectslavearraysintherangeof

tempera-tureshiftsthatgoesfromT=−20◦_CtoT=20◦_{C.Consequently,}

providedthehighestnumberofproperlyslavecorrections(60%of

theslavearrays).

5. Discussion

ThereasonwhyPDSperformedbettercorrectionsthanDSis

thatPDScreateslocalcorrectivemodelsforeachofthechannels

oftheslavearray,whereasDSgeneratesasingleglobalmodel,less

flexibleandmorecomplex.ThisseemstobesoalsoforOSCand

GLSW.Inadditiontothis,PDSdetectedwhichchannelsofthe

mas-terarray(withinawindow)weremorecorrelatedtotheparticular

channelontheslavearray,down-weightingthecontributionto

thecorrectionofthenon-importantchannels.Asaconsequence,

thenumberoftransfersamplesbetweenmasterandslavearrays

2

4

6

8

10

12

0

10

20

30

40

Transfer Samples

RMSEP (ppm)

DS

Slaves

Masters

2

4

6

8

10

12

0

10

20

30

40

RMSEP (ppm)

Transfer Samples

PDS

Slaves

Masters

2

4

6

8

10

12

0

10

20

30

40

Transfer Samples

RMSEP (ppm)

OSC

Slaves

Masters

2

4

6

8

10

12

0

10

20

30

40

Transfer Samples

RMSEP (ppm)

GLSW

Slaves

Masters

c)

d)

a)

b)

Fig.5.(a–d)AverageRMSEPSofthecorrectedslaveinstrumentsasfunctionofthenumberoftransfersamples,forafixedtemperatureshiftofT=−20◦C.Datacorrection

wasperformedusinga)DirectStandardization(blue-dottedline),b)Piece-wiseDirectStandardizationred-dottedline),(c)OrthogonalSignalCorrection(green-dottedline), and(d)GeneralizedLeastSquaresWeighting(black-dottedline).TheaveragedRMSEPMisincludedineachoftheplotswithcomparativepurposes.(Forinterpretationofthe

referencestocolourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle).

−50 −30 −10 10 30 50

0

10

20

30

40

Temperature Shift (ºC)

RMSEP (ppm)

DS

Slaves

Masters

−50 −30 −10 10 30 50

0

10

20

30

40

RMSEP (ppm)

Temperature Shift (ºC)

PDS

Slaves

Masters

−50 −30 −10 10 30 50

0

10

20

30

40

Temperature Shift (ºC)

RMSEP (ppm)

OSC

Slaves

Masters

−50 −30 −10 10 30 50

0

10

20

30

40

Temperature Shift (ºC)

RMSEP (ppm)

GLSW

Slaves

Masters

c)

b)

a)

d)

Fig.6. (a–d)AverageRMSEPSofthecorrectedslaveinstrumentsasfunctionofthetemperatureshift,foranumberof5transfersamples.Datacorrectionwasperformedusing

(a)DirectStandardization(blue-dottedline),(b)Piece-wiseDirectStandardizationred-dottedline),(c)OrthogonalSignalCorrection(green-dottedline),and(d)Generalized LeastSquaresWeighting(black-dottedline).TheaverageRMSEPMisincludedineachoftheplotswithcomparativepurposes.(Forinterpretationofthereferencestocolour

inthisfigurelegend,thereaderisreferredtothewebversionofthisarticle).

Thatsuggeststhatthepiece-wisedextensionsofOSCandGLSW

mayoutperformtheresultsobtainedfromtheglobalversionsof

thealgorithms,althoughthisdiscussionisbeyondthescopeofthis

paper.

The performance of a calibrationmodel with a highdegree

ofcomplexity is directlyrelated withtheavailabilityof a large

numberofsamples.Effectively,asweknowfromFig.5(a–d),an

incrementonthenumberoftransfersamplesprovides, uptoa

improve-Fig.7.(a–d)AverageRMSEPM-Softhecorrectedslaveinstrumentsasfunctionofthetemperatureshift,foreachtemperatureshiftandnumberoftransfersamples.Data

correctionwasperformedusing(a)DirectStandardization,(b)Piece-wiseDirectStandardization,(c)OrthogonalSignalCorrection,and(d)GeneralizedLeastSquares Weighting.

Table2a

Median,firstquartileandthirdquartileoftheoptimizedsetofparametersused compensateforatemperatureshiftof−20◦_{Cintheslavearrays,foradifferent}

numberoftransfersampleandcalibrationtransfertechnique.

TransferSamples PDS(w) OSC(ncomp) GLSW(␣) Q1 Median Q3 Q1 Median Q3 Q1 Median Q3 2 1 9 11 2 2 2 0.1 0.1 0.1 3 3 9 12 3 3 3 0.1 0.1 0.1 4 5 9 17 2 4 4 0.01 0.1 0.1 5 8 12 19 2 5 5 0.01 0.05 0.1 6 7 13 21 2 6 6 0.01 0.05 0.05 7 7 15 23 3 5 7 0.01 0.01 0.05 8 9 15 23 3 5 8 0.005 0.01 0.05 9 9 15 27 3 6 9 0.005 0.01 0.01 10 11 17 27 3 6 8 0.005 0.01 0.01 11 13 21 27 3 6 8 0.005 0.01 0.01 12 13 21 27 3 6 8 0.003 0.01 0.01

mentisreflectedonthestructureofthecalibrationtransfermodels (Table2a),wheretheparametersthatgovernthesample

trans-formationsaregraduallymodifieduntilreachingsaturation.The

reasonforerrorsaturationonthecorrectedslavearrays canbe

deducedfromtheselectionofthecalibrationtransfersample

sub-set,showninTable1.Basically,foracertainnumberofselected

samples we start to find samples that belong to a previously

acquiredcategory(substanceandconcentration).Inconsequence,

nonewinformationisaddedtothetransfermodelsandtheerror

ofpredictionforthecorrectedslavearrayscannotdecrease

signif-icantly.Thetransitiontoerrorsaturationisfasterwhentheoption

forselectingthetransfersamplesisMethod2.Thatoccursbecause

itincludesarepresentativeofeachofthecategoriespresent on

thetraining set (with theexception of the air samples) before

addingsamplereplicates,whileMethod1discardsthreesample

categories.Inreferencetothecalibrationtransfermodels,those

methodsthatperformeddatacorrectionbeforetobuildthe

calibra-tionmodel(GLSWandOSC)exhibitedtheirbestresultsemploying

thesamplesubsetMethod1,whereasthosemethodsthatapplied

data correctionafter the creation of thecalibration model (DS

Table2b

Median,firstquartileandthirdquartileoftheoptimizedsetofparametersusedto correctthereadingsslavearrays,forthedifferenttemperatureshiftsandcalibration transfertechniqueandfixingto5thenumberoftransfersamples.

Temp.Shift(◦_{C) PDS(w) OSC(ncomp) GLSW(␣)}

Q1 Median Q3 Q1 Median Q3 Q1 Median Q3 −50 17 19 29 5 5 5 0.01 0.05 0.1 −40 13 21 31 5 5 5 0.01 0.05 0.1 −30 9 21 27 5 5 5 0.01 0.05 0.1 −20 8 13 22 3 5 5 0.01 0.05 0.1 −10 7 11 20 2 4 5 0.01 0.05 0.1 0 5 9 13 2 3 5 0.01 0.01 0.05 10 5 7 13 3 5 5 0.01 0.05 0.1 20 7 9 11 2.5 5 5 0.01 0.1 0.1 30 11 13 15 3 5 5 0.01 0.1 0.1 40 11 13 16 5 5 5 0.01 0.1 0.1 50 15 13 19 5 5 5 0.01 0.1 0.1

andPDS)showedtheirbestperformanceforthesamplingsubset Method2.

Aspecialcommentdeservestheasymmetryinsensorresponse with respect to temperature shift. Revisiting the results of

Fig.6(a–d)weobservethatanincreaseonthetemperatureshift

forcesanincrementonthemodel’sspecifications(seeTable2b).

Interestingly,theasymmetryshowedbytheRMSEPSforopposite

temperatureshiftpositionsisalsopresentontheparameter

val-uesofallthecalibrationtransfertechniques.Thisisinagreement

withtheresultsobtainedinFig.4foradirectcalibrationtransfer

betweeninstrumentsshiftedintemperature,wherethehigher

pre-dictionerrorswerefoundtowardpositivetemperatureshifts.The

asymmetryontheerrorduetotemperatureshiftingwasproduced

becausetheuncorrectedslavearrayresponsetendstosaturateto

thehighestvoltagelevel(10V)foranysubstanceand

concentra-tion,asreviewinFig.2.Projectingtheresponseoftestsetsamples

ofaslavearrayshiftedtowardnegativesincrementsoftemperature

(T=–50◦C)onaPCAmodelbuiltfromthetrainingsetofamaster

array(Fig.3b)weseethatthesesamplesapproximatetothemaster

arrayresponsetoair.Takingthatresultasareferencewecan

theslavearraysamplesbyairmeasurementsofthemasterarray.

Thatgivesrisetoalowererrorboundaroundthe68ppm.Toward

positivetemperatureshifts,nosaturationontheuncorrectedslave

arrayresponseisproduced,sothetestsamplestendtospreadon

thePCAspaceandtheerroriscontinuouslyincreasing.

6. Conclusions

Inthepresentstudy,weshowedthattheeffectoftemperature

shiftsbetweenhomologousMOXsensorarraysleadstoinvalid

cal-ibrationtransfersfeaturedwithlowpredictiveperformanceand

direction-dependenterrormagnitudes.Toovercomeinstrument

dissimilaritiestheuseofcalibrationtransfertechniquesisrequired.

Amongthefourdifferentcalibrationtechniquesusedinthispaper,

thePiece-wiseDirectStandardizationprocedureshowedthebest

performanceinreducingtheslavearraypredictionerrorforany

temperatureshiftdirectionandusingfewertransfersamples.The

mainadvantageofthePDSmethodliedinitsabilitytocorrect

indi-viduallyeachoneoftheslaveinstrumentschannelsthroughtheuse

ofmultivariatelocalmodels.Thisresultsinacalibrationtransfer

modelwithlesscomplexityandmoreflexibility.

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LuisFernandezisaPh.D.studentattheDepartmentofElectronicsoftheUniversity ofBarcelona.HereceivedaB.S.inPhysics(2005)andaB.S.inElectricalEngineering (2011)fromtheUniversityofBarcelona.Hiscurrentresearchtopicisbio-inspired largesensorarraysbasedonmetaloxidesensors.

SeldaGuneyreceivedtheM.Sc.andPh.D.degreeinelectricalandelectronics engi-neeringfromKaradenizTechnicalUniversityofTrabzon,Turkeyin2007and2013 respectively.Currently,sheisanAssistantProfessorwiththeDepartmentof Elec-tricalandElectronics,BaskentUniversity.Herresearchinterestsinclude,control systems,patternrecognitionandsignalprocessingofgassensorarrays.

AgustinGutierrez-GalvezreceivedtheB.E.degreeinphysicsandelectrical engi-neeringfromtheUniversityofBarcelona,Catalonia,Spain,in1995and2000, respectively.HereceivedthePh.D.degreeincomputersciencefromTexasA&M Uni-versity,CollegeStation,in2005.HewasaJSPSPost-DoctoralFellowwiththeTokyo InstituteofTechnology,Tokyo,Japan,in2006,andcamebacktotheUniversityof BarcelonawithaMarieCurieFellowship.Currently,heisanAssistantProfessorwith theDepartmentofElectronics,UniversityofBarcelona.Hiscurrentresearch inter-estsincludebiologicallyinspiredprocessingforgassensorarrays,computational modelsoftheolfactorysystems,patternrecognition,anddynamicalsystems.

SantiagoMarcoreceivedtheDegreeinappliedphysicsandthePh.D.degreein microsystemtechnologyfromtheUniversityofBarcelona,Catalonia,Spain,in1988 and1993,respectively.HeheldaHumanCapitalMobilityGrantforapost-doctoral positionattheDepartmentofElectronicEngineering,UniversityofRome“Tor Ver-gata,”Rome,Italy,in1994.Since1995,hehasbeenanAssociateProfessorwiththe DepartmentofElectronics,UniversityofBarcelona.In2004,hehadasabbaticalleave atEADS-CorporateResearch,Munich,Germany,wherehewasinvolvedinion mobil-ityspectrometry.HehasrecentlybeenappointedleaderoftheArtificialOlfaction Laboratory,InstituteofBioengineeringofCatalonia,Barcelona,Spain.Hiscurrent researchinterestsincludethedevelopmentofsignal/dataprocessingalgorithmic solutionsforsmartchemicalsensingbasedinsensorarraysormicrospectrometers integratedtypicallyusingmicrosystemtechnologies.