AbstractNormalisationistheprocessofmodifyingasetofpostmortemhumansubject(PMHS)responsedatatobetterrepresentthatofastandardsizedhuman.Thisimprovedmethodisbasedonthefactthatallplotsofdeflectionenergyversusdeflectionforthethoraxareofconstantslope.Thedeflectionenergyistheintegraloftheappliedimpactforceoverthedeflectionmeasuredbyachestbanduptothepointofmaximumdeflection.Standardsizedhumanthoraxdeflectionenergiesandslopesarefoundfrommultivariateanalysesrelatingenergyandslope,separately,totheanthropometricdataforallsubjects.Forceisthespatialderivativeofthelineardeflectionenergycurveandisaconstant.Theresultingrectangularforceversusdeflectioncurveleadstoscalefactorsforforce,deflection,elasticstiffness,theviscousconstant,andtime,assumingatwoelementsolidviscoelasticmodel.Subjecteffectivemassandpostimpactvelocitywerecalculatedfromconservationofenergyandimpulseequalsmomentum,solvedsimultaneously,providingscalefactorsforeffectivemassandsubjectvelocityatmaximumdeflection.Thetimehistoriesandforceversusdeflectionhavebeenplotted,thestandarddeviationtargetsoverplotted,andcoefficientsofvariationcalculated.Resultshavebeenqualitativelyandquantitativelycomparedtopreviousmethods. Keywords biofidelity,datanormalisation,postmortemhumansubject(PMHS),scaling

I. INTRODUCTIONTheprocessofnormalisingpostmortemhumansubject(PMHS)responsedatafromimpacttestingtoobtain

a representationof the typical,or average,human responsehasbeen an importantpartof anthropometriccrash dummy design and development for many years. Normalisation is the process of mathematicallymodifyingtheresponsedatafromasetofPMHSsubjectstoastandardhumansize.Thisnormalisedresponse isusedasastandardagainstwhichtheresponseofananthropometricdummy is

comparedtoassessthedummybiofidelity.Aquantifiedmeasureofbiofidelityisdesirabletoprovidethebasisforanobjectivedecisionastotheabilityofadummytoassessvehiclecrashprotectionforahumanofsimilarsize.In1984amethodfornormalisingPMHSdatabasedontheratioofthewholebodymassofasubjecttothe

standard totalbodymass (e.g.50thpercentilemale)wasdeveloped [1]. Thismethodologyassumed thatallsubject responseswill be related directly to thewhole bodymass. Clearly force, deflection and kinematicresponses fromwidelyvarying sizesand shapesofhumansarenot likely tobe related solelybywholebodymass. An impulsemomentum and stiffnessbased normalisationmethod [2]was presented in 1984. Scalefactorsweredevelopedfrombothanthropometrymeasuresandratiosofthesolutionforthesingledegreeoffreedom(DOF)differentialequationforalinearelasticsystemwhichrepresentedalargeimpactingmasssuchasasled typeof impact. In1989an improvement to thismethodologywaspresented [3]byexpanding thederivationofscalefactorstothetwoDOFlinearelasticsystemwhichbetterrepresentspendulumtypeimpactswherethestrikingandstruckmassesaremorenearlyequal.Againthescalefactorsweredevelopedfromratiosofthesolutiontothesystemofdifferentialequations.Animprovement[4]wasmadetothetwoDOFmethodusing the integralof the forceversusdeflection curve, thedeflectionenergy, todevelopanelasticeffectivestiffness directly from the force versus deflection response data rather than from characteristic subjectdimensions.Thislatterstudy[4]alsocomparedtheeffectivenessofthevariousnormalisationmethodsinforceversusdeflectionspaceusingthestandarddeviationellipse[5]andamodifiedcoefficientofvariationmeasuretakingonehalfoftheareaoftheellipsedividedbytheproductofforceanddeflectionateachdatapoint.Thisquantitativecomparison indicated thateffectivestiffnesscollapsed the forceversusdeflectioncurves toward BRDonnellyisaPhDatBiomechanicsResearchAssociatesLtd.,USA,(+17406020531/brucedonnellyphd@columbus.rr.com).HHRhuleisaBSandKMMoorhouseandJAStammenarePhDsattheNationalHighwayTrafficSafetyAdministrationVehicleResearchandTestCenter,USA.YSKangisaPhDattheOhioStateUniversityInjuryBiomechanicsResearchCenter,USA.

AnImprovedDeflectionEnergyMethodtoNormalisePMHSThoracicResponseData

BruceR.Donnelly,HeatherH.Rhule,KevinM.Moorhouse,YunSeokKang,JasonA.Stammen

IRC-17-72 IRCOBI Conference 2017

-577-

eachothermoreeffectivelythantheothermethods.MorerecentlytheauthorsofthiscurrentstudypresentedamethodfornormalisingPMHSthoracicimpactdatabasedonthedeflectionenergyandatwoDOFviscoelasticmodel [6]. Thisapproachwasmathematically cumbersomebutdid improve thequantitative results slightlyover the effective stiffness approach [4] asmeasured using a time based average coefficient of variationmeasureandtheellipsecoefficientofvariationmeasureforforceversusdeflection.Thisstudybuildsuponallof thispriorwork todevelopan improved,andsimpler,mechanisticmethod for

normalisingthoracicPMHSdataagainusingatwoDOFviscoelasticmodel. PMHSdatafrom19subjectsfromthreestudies[5][7][8]ofthoracicpendulumtestswereanalysedtoillustratethemethodology.Thedeflectionenergyand theslopeof thedeflectionenergyversusdeflectioncurvewereused todevelopscale factors forenergy,slope,force,deflection,elasticstiffness,theviscousconstant,andtime.Scalefactorsforeffectivemassandsubjectvelocitywerederivedfromconservationofenergyandconservationofmomentum.Of thepreviousnormalisationstudies themassbasedmethodusedsubjectanthropometryand theknown

anthropometryvaluesofstandardsizedhumanstodevelopscalefactorsfornormalisation. Theotherearliermethodsusedchestanthropometryratiosandaveragesoftheresponsesofthesubjectpoolbeinganalysedtoestimate thestandardsizedhumanresponsesused todevelopscale factors. Thecurrentstudymodifies thisapproachbyusing the responsemeasuresofdeflectionenergyand slope fromall19 subjectsasdependentvariablesandthesubjectanthropometrymeasuresasindependentvariablestodevelopstatisticalmultivariaterelationships for energy and slope. The resulting equations can then be used with any standard humananthropometry values to estimate standard human deflection energy and slope values and to calculate thecorrespondingscalefactorsforthestandardforce,deflection,elasticstiffness,viscousconstant,andtime.Results fromnormalisingall19subjectstothe50thpercentilemalearepresented,alongwithmeancurves

andstandarddeviationbiofidelitytargets, inbothtimehistoryplotsand forceversusdeflectionplots. Theseplots have been compared with results from previous methods both qualitatively and quantitatively todemonstrate the improved grouping and smaller standard deviation targets of the deflection energynormalisationresults.

II. METHODSResponsedataandanthropometrydatafrom19PMHStested in lateralandobliquependulumtype impact

tests in three studieswereanalysedusingadeflectionenergymethodanda twoDOFviscoelasticmodel todevelopscalefactorsfornormalisationtothe50thpercentilesizemalehuman. Standardvaluesfordeflectionenergy and the slope of the deflection energy versus deflection curve were estimated using multivariaterelationshipsbetweenanthropometrymeasuresand impactvelocityas independentvariablesanddeflectionenergyandslopeofdeflectionenergyasdependentvariables.Mechanicalvaluesforenergy,force,deflection,stiffness, theviscousconstant,and timewerecalculated from thedatausing the twoDOFmodel. Effectivemassandsubjectvelocityvalueswere foundusing theequations forconservationofenergyandmomentumsolvedsimultaneously.Normalisationscalefactorstaketheform

1 andareappliedtotherelevantparameterateachpointinthetimehistory.Adescriptionof the subjects and the data analysed, thederivationof the subjectmechanical values, the

developmentofthemultivariaterelationshipforthestandardhumanmechanicalvalues,andthedevelopmentofscalefactorsispresentedbelow.

SubjectDataNineteenPMHSfromthreethoracic impactstudieswereanalysed inthisstudy. Reference[6]testedseven

PMHS innominal2.5m/s lateralandobliquethoracic impactsatthefourth intercostalspaceusinga23.86kgimpactorwitha15.24cmdiametercircularface.Reference[7]tested12PMHSin4.5m/sand5.5m/slateralandoblique thoracic impact testsat thexyphoidusinga23.99kg impactorwitha15.24cmhighx30.48cmwiderectangularface.Reference[8]alsotestedfiveadditionalPMHSin2.5and4.5m/sinlateralandobliquethoracic impact tests at either the fourth intercostal space or the xyphoid using either the circular face or

IRC-17-72 IRCOBI Conference 2017

-578-

rectangularfaceimpactors.Ofthese24PMHS,19wereselectedforanalysisinthisstudy.Thefivethatwerenotusedwereeliminated forvarious reasons suchas the impulseandmomentumcalculatedat the timeofmaximum thoracic deflection beingmore than 30% different [5][9]. Many of these subjects were testedmultipletimesbutonlythefirsttestwasusedinthisstudy.The19subjectsincludedwerejudgedtohaveverygoodqualitydataforanalysisandwouldlendconfidencetoademonstrationoftheprocedure.Theappliedforceversustimeandthechestbanddeflectionversustimewerecrossplottedandintegratedup

tothepointofmaximumdeflectiontoobtainthedeflectionenergy.Forreasonsofconsistencytimezerowassetatthepointoffirstcontinuouspositivechestbanddeflectionforeverysubject. Generallytherewassomeappliedforcebeforethechestbandregistereddeflectionduetocontactwiththethoraxskinandsubcutaneousfat. Asaresult, attimezerothereusuallywasan initialpositiveforce. Thealternativewouldbetosettimezeroattheinitialpositiveforcebutinthatcasetherewouldbenomeasureddeflectionatthattime.Thedataused in thisanalysis included lateralandoblique testsaswellas circularand rectangular impact

faces.Reference[8]testedameasureofelasticstiffnessandindicatednosignificantdifferenceinlateralversusoblique responseamong thevarious testsexcept for testswith thecircular impact face. Thestandard ttestprobabilityof=0.05wasused inthatanalysistoprotectagainsttype Ierrorandappropriatelyrejectedthenullhypothesisthatthedifferenceinthemeansofthestiffnesswaszero.Inthisstudyitwasdesirabletohavealargesetofsubjectstodemonstratethemethod.Thestandardforassumingthesubjectsarefromthesamepopulationwaslessstringentthaninastudydevelopingbiomechanicalresponsetargets.Thedatawastestedcomparingthedeflectionenergycurveslopesofthelateralteststotheobliquetestsandcircularimpactorfaceteststotherectangular impactorfacetests inallcombinations(seeAppendixA). Thenullhypothesis ineachcasewas that the difference in the slope valueswas zero. The pvalues for slope varied from 0.4 to 0.9indicatingitwasnotpossibletorejectthenullhypothesisoftheslopesbeingthesame.Itwasfeltthatforthepurposeofdemonstrating themethod itwasacceptable to considerallof the testsasbeing from the samepopulation. This isnotacontradictionofthepreviousresultbutratherpresentsadifferentviewofthedata,examiningadifferentvariable,forthepurposeofdemonstratingthenormalizationmethod. Ifthebiofidelityresponseofadummyinaparticulartestconfigurationwasbeingassessedonemightchoosetouseasubsetofthedata.

TwoDegreeofFreedomViscoelasticModelThemaximumdeflectionenergyistheintegralofappliedforcewithrespecttothoracicdeflection.

2

where E=deflectionenergy F=appliedforce t=time S=thoracicdeflectionfromchestband.Thedeflectionenergyversusdeflectioncurvesforallofthethoracicimpactsexaminedinthisstudyarevirtuallystraight linesofconstantslopeupto,and including,themaximumdeflection. Fig.1showsthreeexamplesofthisphenomenonwhicharetypicalofall19subjects.

(a) (b) (c)

Fig.1.Plotsofintegrateddeflectionenergyversusdeflectiondemonstratingthestraightlineslope.

IRC-17-72 IRCOBI Conference 2017

-579-

In this study the term deflection energy is used indicate the energy absorbed and dissipated during the

thoracicimpacteventuptothepointofmaximumdeflection.Deflectionenergyisaonedimensionalanalogtostrainenergy[10]wherethespatialderivativeofdeflectionenergyisforceratherthanstress.Ifthedeflectionenergyversusdefelctioncurvehasaconstantslopeandappliedforce isthespatialderivativeofenergy,thenappliedforceisconstant.Theslopeofthecurveis

.

andtherefore

. 3

Wehavearelationshipamongenergy,constantforce,anddeflectionthatcanbeusedtodevelopscalefactorsfornormalisation.This relationship also leads directly to a twoDOF viscoelasticmodel that can be used to find the elastic

stiffness,viscousconstant,damped frequencyand theperiod. The forceversusdeflectioncurvewouldhaveconstantforceuptothemaximumdeflectionasseeninFig.2.

Fig.2.Schematicofaconstantforcevs.deflectioncurve

withelasticandviscousenergyareaslabeled.Thetotaldeflectionenergyistheareaunderthecurve,E=Fconstant*Smax.Theelasticenergyportion(stored)of

theenergyisthelowerrighttriangle,*E=*Fconstant*Smax.Theviscousenergyportion(dissipated)istheupperlefttriangleandhasthesamearea.TheequationfortheforceinatwoDOFviscoelasticmodelis

(4) where =elasticstiffness =viscousconstant =timederivativeofdeflection(velocity).Theelasticenergyis (5)and

K= (6)

Theviscousenergyis (7) where =velocityatzerodeflectionor and (8)

ThedampednaturalfrequencyfromthedifferentialequationforatwoDOFviscoelasticsolidis

IRC-17-72 IRCOBI Conference 2017

-580-

(9)

where =dampednaturalfrequency =(mI+ms)/(mI*ms) (10) mI=impactormass ms=subjecteffectivemassand theperiodis 2 / . (11)Itshouldalsobenotedthatbecausetheviscousenergy is linearlydependentontherateofdeflection,the

ratemustbeastraight line in equaltothe impactvelocity, ,whendeflection iszeroandequaltozeroatmaximumdeflection, (12) where =rateofdeflection =impactvelocity =maximumdeflection =deflection.Fora constant force thedifferentialequationabove isequivalent to thedifferentialequation for the two

element viscoelastic solid (Equation 4). Solving the differential equation for deflection, S(t), results in anincreasing exponential function in time [11]. The rate, , is a complementary decreasing exponentialfunction. Whenmultipliedby their respective coefficientsand combined the result isa constant forceas isrequiredbytheconstantslopeofthedeflectionenergyversusdeflectioncurve.Theeffectivemassofthesubjectandthesubjectvelocityatthetimeofmaximumdeflectioncanbefoundby

solving the equations for conservation of energy, including the deflection energy, and conservation ofmomentumsimultaneouslyfromtimezerotothepointofmaximumdeflection.Theresultingequationsare

2 11

and

2 12

where effectivemassofthesubject

impactormass =impactvelocity,V0= deflectionenergy velocityofsubjectatmaximumdeflection.Finally, it shouldbenoted that thisapproach isapplicable toa twodegreeof freedom system (pendulum

impact)ortoonedegreeoffreedomsystemssuchassledordroptestsbymodifyingthesizeoftheimpactingmass,i.e.,aninfinitemassforadroptestandaverylargemassforasledtest.

MultivariateRegressiontoEstimate50thPercentileDeflectionEnergyandSlope Wenowhaveamodelthatprovidesvaluesforenergy,slope,force,deflection,stiffness,theviscousconstant,time, effectivemass, and subject velocity for each subject that can be used to develop scaling ratios tonormalise the response to thatofa standardhuman. The standardhuman responsewasestimated fromamultivariaterelationshipdevelopedusingthedeflectionenergyandtheslopeoftheenergycurve,respectively,asdependentvariablesandtheanthropometrymeasuresforallsubjectsasindependentmeasures.TheMatlabfunction stepwiselm [12]wasused todevelop this relationship. The analysisusing the stepwiselm function

IRC-17-72 IRCOBI Conference 2017

-581-

considered all of the independent anthropometry variables available from the three studies and eliminatedthosevariablesthatwerenotsignificantleavinganequationforthedependentvariablebasedonlyonthemostimportantvariablesandtheinteractions.Thisprocedureisgenerallyreferredtoasstepwiseforwardestimation[13]. The considered variableswere gender, age,height,mass,bodymass indexBMI, chestbreadth, chestdepth,andimpactvelocity.Thetwomultivariateequationsfoundforenergyandslopewerebasedonsubjectage,mass,height,BMI,andimpactvelocity.Theanthropometricdataforthestandardhuman(50thpercentilemale),alongwith thedesired impactvelocity,were then input to themultivariateequation toobtainenergyand slopevalues for the standardhuman. The standardhumanenergyand slopevaluesand theequationsderived above provide the standard human values for force, deflection, stiffness, the viscous constant, andtime. The standardhumanenergy isused in the equations for conservationofenergy and conservationofmomentumtosolveforthestandardeffectivemassandsubjectvelocityatmaximumdeflection.NormalisationFactorsRatios,showninTableI,madeupofthestandardparametervaluesrelativetothesubjectparametervalues

providenormalisationscalingfactorsforeachsubjectthatwereusedtonormalisetheresponsetimehistoriesandforceversusdeflectioncurvestothatofthestandardhuman.ImpactvelocityisalinearcoefficientinthedifferentialequationsforthetwoDOFviscoelasticmodeland,therefore,velocitywasscaledbeforecalculatingthe normalisation factors in Table I, i.e., the applied force, chestband deflection, and the equations forconservationofenergyandmomentumwereallscaledforimpactvelocityofacommonvalue.The19subjectsanalysedherewere testedatnominal impact velocitiesof2.5,4.5and5.5m/s (as shown inTable II in theResultssection).Todemonstratethemethodthenormalisationimpactvelocitywasselectedtobe3.5m/sforall19subjectsinthisanalysis.Themultivariateequationwasdevelopedusingtheactualimpactvelocitiesbutwhenestimatingenergyandslopevaluesforthe50thpercentilemalethenormalisationvalueof3.5m/swasinput.

TableI.Normalisationscalefactors.

Impactvelocity Energy Slope Force Deflection Stiffness

Viscousconstant Time

Effectivemass

Subjectvelocity

ForceVersusDeflectionStandardDeviationEllipsesThestandarddeviationellipsescanbeconstructedfromthestandarddeviationsforforceandfordeflection

calculatedateachpoint in time. Inpreviousstudies [4][14] the timebasedstandarddeviationellipseswereplotted in force versus deflection spacewhich ismisleading since the force versus deflection pairs of eachsubject based on the time point are not colocated in force versus deflection space. The result of thisphenomenon isthatthetimebasedstandarddeviationellipsesdonotaccuratelyrepresentthevariance,andthegrouping,of the forceversusdeflection curves in forceversusdeflection space. Interpolating forceanddeflectiontoacommondeflectionenergybaseresolvesthisproblemandtheellipsescanthenbecalculatedand located accurately in force versus deflection space. However, comparing the effectiveness of thisdeformation energy based normalisation methodology to previous methods using the average ellipsecoefficientofvariationcanonlybedoneaccuratelyifthecoefficientsofvariationarecalculatedthesameway.In order tomake a reasonable comparison among the several normalisationmethods, the coefficients ofvariationwerecalculatedbasedonstandarddeviationscalculatedfromtheforceanddeflectiontimehistorieseven though this is, strictly speaking,not correct. Since thedeformationenergywasnot calculated for thepreviousmethods,therewaslittlechoice.Thecoefficientofvariationforthemoreaccuratemethodwasalsocalculated for the deflection energy normalisationmethod presented in this study and is both plotted andtabulated.

III. RESULTSThetestinformationandtheanthropometricdataforthe19subjectsanalysedinthisstudyarepresentedin

TableIIalongwiththeanthropometricvaluesandimpactvelocityusedforthe50thpercentilemalehuman.

IRC-17-72 IRCOBI Conference 2017

-582-

TableII.Testandsubjectcharacteristics.

Subject#

Ref.Vo

(m/s)SideAngle

Plate(cm)

Impactormass(kg)

GenderAge(yrs)

Height(cm)

Mass(kg)

BMI(kg/m2)

0503 [6] 2.62 left60o circle 23.86 male 79 180.3 65.8 20.20504 [6] 2.43 left90o circle 23.86 male 80 165.1 80.7 29.60505 [6] 2.46 right90o circle 23.86 male 77 177.8 66.2 21.00506 [6] 2.54 right60o circle 23.86 male 87 175.3 65.8 21.40507 [6] 2.45 left60o circle 23.86 male 53 165.1 65.3 24.00601 [6] 2.57 left90o circle 23.86 male 63 185.4 93.0 27.00802 [7] 4.77 left90o rectangle 23.99 male 67 169 81.6 28.60803 [7] 4.58 left60o rectangle 23.99 male 77 178 64 200804 [7] 4.47 left60o rectangle 23.99 male 81 159 52 20.70902 [7] 4.63 left90o rectangle 23.99 male 60 183 89 26.50903 [7] 4.68 left90o rectangle 23.99 female 29 175 79 25.60904 [7] 5.64 left90o rectangle 23.99 female 81 177 79 25.50905 [7] 5.50 left60o rectangle 23.99 male 81 175 93 30.11001 [7] 4.76 left90o rectangle 23.99 male 82 175 72 23.51002 [7] 4.44 left90o rectangle 23.99 male 87 186 71 20.61003 [7] 4.56 left60o rectangle 23.99 male 48 175 78 25.51201 [8] 2.63 right60o rectangle 23.99 male 56 176.0 88.0 28.41202 [8] 2.57 right60o circle 23.99 male 76 183.5 97.5 29.01203 [8] 2.56 right60o rectangle 23.99 male 71 172.0 75.8 25.650th [15] 3.5 45 175 77 25.5

Asmentionedpreviouslytheenergyandslopevaluesestimatedbythemultivariateequationsarefoundfor

thenominal impactvelocityof3.5m/s. Themultivariateregressioncoefficients forenergyand forslopearepresentedinTableIIIandwereentirelydeterminedbytheanthropometricpropertiesofthesubjectandimpactvelocity. The coefficients in Table III, columns two and three, are multiplied by the individual subjectanthropometricvariables listed in columnone (theactual subjectdata ispresented inTable II) toobtainanestimateofthesubjectdeflectionenergyandslope.Table IVpresentsboththe integratedandtheestimatedvalues for energy and for slope for each subject, at the actual impact velocities, aswell as the differencebetweenthetwovalues.

TableIII.Multivariateregressioncoefficientsforenergyandslope.

Variables EnergyCoefficients SlopeCoefficientsconstant 5.0140 352.5938Age 0.1688 2.4432

Height 0.0288 1.8116Mass 0.0095 2.0358BMI 0.1845 8.4510

impactvelocity 2.3992 43.4126age*height 0.0010 0.0132age*mass 0.0009 0.0200age*BMI 0.0029 0.0662

age*impactvelocity 0.0005 0.0031height*mass 0 0height*BMI 0.0012 0

height*impactvelocity 0.0136 0.2389mass*BMI 0 0.0102

mass*impactvelocity 0.0143 0.2464BMI*impactvelocity 0.0451 0.8103

IRC-17-72 IRCOBI Conference 2017

-583-

TableIV.Integratedandestimateddeflectionenergyandslope.

Integratedenergy&slope

Multivariateestimate

Difference

SubjectV0

(m/s)E

(Nm)b

(Nm/mm)Eest(Nm)

best(Nm/mm)

energy(Nm)

%error

slope(Nm/mm)

%error

0503 2.62 32.69 1.16 32.70 1.21 0.01 -0.03 0.05 4.530504 2.58 44.41 1.27 44.84 1.29 0.43 -0.96 0.02 1.500505 2.46 30.00 1.04 25.66 1.04 4.34 14.46 0.00 0.150506 2.54 35.44 1.24 42.55 1.19 7.10 -20.04 0.04 3.470507 2.45 43.27 1.00 41.56 1.01 1.70 3.93 0.02 1.620601 2.57 43.77 1.38 43.89 1.39 0.13 -0.29 0.01 0.800802 4.77 144.71 2.64 137.57 2.58 7.14 4.94 0.05 2.010803 4.58 130.91 2.19 136.47 2.07 5.56 -4.25 0.13 5.730804 4.47 115.44 1.94 113.47 1.93 1.97 1.71 0.01 0.470902 4.63 118.21 1.97 109.48 2.01 8.73 7.38 0.04 2.110903 4.68 85.31 1.74 90.15 1.66 4.84 -5.67 0.08 4.610904 5.64 147.37 2.53 151.52 2.59 4.14 -2.81 0.06 2.530905 5.50 143.94 2.58 149.06 2.55 5.12 -3.55 0.03 1.091001 4.76 126.08 2.76 123.77 2.79 2.31 1.83 0.03 1.161002 4.44 108.33 2.48 104.98 2.52 3.35 3.09 0.04 1.511003 4.56 109.75 2.18 109.17 2.24 0.58 0.52 0.06 2.581201 2.63 41.60 1.75 46.85 1.83 5.25 -12.62 0.08 4.491202 2.57 49.58 1.61 48.73 1.65 0.85 1.72 0.04 2.401203 2.56 46.77 1.65 45.16 1.62 1.60 3.43 0.04 2.1350th 2.5 55.47 1.59 Avg.error 0.38 Avg.error 0.2950th 3.5 81.54 1.88 50th 4.5 107.61 2.18 Deflection energies for each subject were calculated from the test data by integrating the force versus

deflectionfromthepoint intimeofthe initialpositive increase indeflectiontothemaximumdeflection. Theslopesofeachdeflection energy curveweredeterminedbydividing themaximumenergyby themaximumdeflectionwhich occur simultaneously. The remaining valueswere calculated as described in theMethodssection. The calculated values for the scale factors at the impact velocity of 3.5m/s are presented in theAppendix.Plotsoftheoriginalunscaledandnonnormalisedsubjectforceanddeflectionversustimeandforceversus

deflectionarepresentedinFig.3(ac).PlotsofthesameresponsedatascaledforimpactvelocityarepresentedinFig.4(ac). Plotsoftheresponsedatanormalisedusingtheeffectivestiffnessmethod[4]arepresented inFig.5(ac). Plotsofthedeflectionenergynormalisedresponsecurves intimearepresented inFig.6(ac). Aplotof thedeflectionenergynormalisedresponsecurveswith thestandarddeviationellipsesshown in forceversusdeflectionspaceispresentedinFig.7(b)withFig.6(c)repeatedasFig.7(a)forpurposesofcomparison.

For the time history curves the standard deviation and the CVwere calculated at each time point andaveragedovertheentiretimeoftheevent.Thisapproacheliminatesneckingintheplottedstandarddeviationtimeplotswhich isbeneficialwhenqualitativelycomparingPMHStargetstodummyresponses forbiofidelityassessment.TheellipseCVresultswerefoundbydividingonehalfoftheareaofthestandarddeviationellipsebytheproductoftheforceanddeflectionatthatpoint.TheresultswerethenaveragedovertheentireeventtogettheellipseCV. AllCVswerecalculatedfromastartingpointof10%ofthemaximumdeflectiontotheendingpointofmaximumdeflectionanddirectcomparisonsofCVsaremeaningful.ThecoefficientofvariationresultsarepresentedinTablesVandVI.

IRC-17-72 IRCOBI Conference 2017

-584-

(a)

(b)

(c)

Fig.3.O

riginalre

spon

sedataun

scaledandno

nno

rmalise

d.

(a)

(b)

(c)

Fig.4.R

espo

nsedatasc

aled

forimpactvelocity

.

IRC-17-72 IRCOBI Conference 2017

-585-

(a)

(b)

(c)

Fig.5.R

espo

nsedatanormalise

dusingtheeffectivestiffne

ssm

etho

d[4].

(a)

(b)

(c)

Fig.6.Re

spon

sedatano

rmalise

dusingde

flectionen

ergywith

forceversusdeflectionplottedusingtim

ebasedstandarddeviatio

ns.

IRC-17-72 IRCOBI Conference 2017

-586-

(a) (b)

Fig.7.Normalisedresponsedatawith(a)timebasedstandarddeviationellipsesand(b)deflectionbasedstandarddeviationellipses(note:Fig.7(a)isFig.6(c)repeated).

TableV.Comparisonofaveragecoefficientsofvariationcalculatedfromtimehistories.Method ForcevsTime DeflectionvsTime ForcevsDeflection

Original 0.312 0.352 0.176ScaledforImpactVelocity 0.203 0.167 0.056EppingerMethod 0.167 0.203 0.083MertzVianoMethod 0.170 0.170 0.039MoorhouseMethod 0.117 0.143 0.042DeflectionEnergyMethod 0.096 0.119 0.019

TableVI.Averageellipsecoefficientofvariationcalculatedinforceversusdeflectionspace.

Method ForcevsDeflectionNormalisedinForceversusDeflectionSpace 0.011

IV. DISCUSSIONTheobjectiveofnormalisation is todevelopscale factors,basedonsoundmechanicalprinciples, thatare

used toadjust thePMHS response to representa standard sizedhuman: in thisexample the50thpercentileadultmale. It has been generally accepted that reducing the variation in a set of response data curves issuccessful normalisation. Previous normalisation methods assumed that PMHS subjects, and the impactresponses,arenormallydistributedandthatasetofsubjectresponsedatacouldbeusedtocalculateameanresponse to represent a standardhuman (50thpercentilemale). Reference [2]was the first to suggest thisresponse data approachwith the effectivemass approximation and Reference [4] also used it for effectivestiffness. Thisstudydoesnotuse themeanof the responsedata tonormalise the responsedatabut ratheruses the statistical approach of multivariate regression based on the independent variables of subjectanthropometrytoestimatetheresponseofthe50thpercentilemale.Inasensetheapproachusedinthisstudyharkens back to the mass based approach [1] where the response data was normalised based only onanthropometrymeasures.ThisstudythendevelopedsubjectresponsevaluesbasedonatwoDOFviscoelasticmodel and basicmechanical principles, conservation of energy andmomentum, to develop normalisationfactors that reduce the effectofhuman variationon response. Theuseof an elasticmechanicalmodel tonormalise response data has been used by all researchers since themass basedmethod and the use of aviscoelasticmodelisalogicalstepformodellingastructurewithaviscousresponse,i.e.,thehumanbody.Theassumptionofnormalityisstillusedandthenormalisedresponsesareaveragedandthestandarddeviationsintime, or standard deviation ellipses in force vs deflection space, provide a target againstwhich a dummyresponsecanbebothqualitativelyandquantitativelycomparedwhentested inthesameway. Normalisation

IRC-17-72 IRCOBI Conference 2017

-587-

provides the appropriate biofidelity response specification for the design and assessment of standard sizeddummiessuchthatthedummyaccuratelymodelsthehumanresponse.

Thisstudyimprovesseveralaspectsofthedeflectionenergymethodpresentedin[6].Itwasrecognisedthattheslopeoftheenergyversusdeflectioncurve isastraight lineand isequaltoaconstantforce inatwoDOFviscoelastic model. This observation makes the calculation of all necessary values for normalisationstraightforwardandmakes theuseofaviscoelasticmodeleasilyapplied tonormalisationofPMHS responsedata. The use of themultivariate analysis approach for estimating the deflection energy and the slope of thedeflectionenergyversusdeflectioncurveforstandardsizedhumansprovidedanindependentlydeterminedsetofstandardhumanpropertiestobeusedinthescalefactors.Unfortunatelythedatasetof19subjectswasnotlargeenoughor sufficientlywelldistributedenough in termsofanthropometric characteristics toeffectivelymodel the human population. In particular there were only a few smaller subjects and only two femalesubjects.Alsoaproblemwasthepreponderanceofolderagedsubjects.Theresultwasaregressionequationthatdidnotmodelthe5thpercentilefemalesizeverywell. TableVII liststheestimateddeflectionenergyforthe5thpercentile femaleandthe50thand95thpercentilemalesatthreeagesof45,65,and85yearsofage.Clearly the 5th percentile female values are not useful. Fig. 8 shows the same data graphically. However,regressionestimatesforallofthevarioussizedsubjects inthisstudyarereasonableasseen inTable IV. Theaveragedifferencesbetweenthe integrateddataandtheestimatedvaluesforenergyandslopewere 0.38%and 0.29% respectively. Themaximumdifference for slopewas4.61%but forenergy itwas 20.04%. Thislattercasewasasmallersubject,subject0506. Theregressionequationmatchesthemodeledsubjectvaluesfairlywell. There is no indication of outlier subjects in the results. Nonetheless the estimate for the 5thpercentile female is poor. Only the 50th percentile male estimated values were utilized in this study todemonstratethemethod.

TableVII.EstimatedDeflectionEnergyforSeveralSizes

andAgesofPMHSat3.5m/sec.Size/Age 45years 65years 85years

5thpercentilefemale 99.9Nm 58.1Nm 216.1Nm50thpercentilemale 81.4Nm 53.2Nm 25.1Nm95thpercentilemale 62.0Nm 46.5Nm 31.0Nm

Fig.8.EstimatedDeflectionEnergyforSeveralSizesandAgesofPMHSimpactedat3.5m/sec.

Toimprovethemodelalargersampleofthoracicimpactsubjectswithwelldistributedanthropometriccharacteristicswouldberequired,particularlyincludingsmallersubjects.Thoseanthropometriccharacteristicswouldbethevariablesidentifiedbytheregressionmodel:age,height,mass,andBMI.Inadditiontoalinearregressionmodelitwouldbeinterestingtoexaminenonlinearpolynomialmodelstobetterfitthedataalthoughfittingmultiplevariablenonlinearpolynomialmodelscanbeanexercisefraughtwithunexpectedresults.Thisstudywasintendedtoexaminetheuseoftheconstantslopedeflectionenergyversusdeflectioncurveandthedevelopmentofenergyandslopeestimatesofstandardsizedhumansusinganapproachthatisindependentoftheresponsedatathatistobescaled,i.e.,moreindependentthanaveragesoftheanthropometrymeasures.Ofcourse,withalargeanddiversesampleonewouldexpectresultsfromtheregressionmodelandaveragingtoconverge.

Acomparisonamongthepreviousmethodswaspresented in[5]andplotsofallresultsarenotpresentedhere; however, the coefficients of variation were calculated and presented in tabular form. The twodimensionalstandarddeviationellipsemethodologyforquantifyingandplottingvariancewasfirstpresentedin[6]. Thesetofstandarddeviationellipsesplottedateachpointoftheforceversusdeflectioncurvecreatesatargetagainstwhichadummy response curve canbebothqualitativelyandquantitativelyassessed in force

IRC-17-72 IRCOBI Conference 2017

-588-

versusdeflectionspaceinthesamewaythattimehistorieswereevaluatedusingtheBiofidelityRankingSystem[14]. Theuseof the timeaveragedcoefficientofvariation (CV)and theellipseaveragedCV forquantitativecomparisonswerefirstpresentedby[4]andthenusedby[6]tocompareallofthevariousmethods.ThetimeaveragedCVswere againused in this study. It is clear from theplots and from theCVmeasures that thismodifieddeflection energybasednormalisationmethod eliminates a substantial amountof variation in theresponsedatafromthissetofPMHSandtheCVsfordeflectionenergynormalisationaresmallerthanthoseofpreviousmethods.

The effective stiffnessmethod [4] used a singleDOF elasticmodel to develop normalisation factors andfound a stiffness factorby integratingdeflection energy andmodelling that energy as elastic energywith aconstantslope.Althoughthatstudydidnotrecognisetheconstantenergyversusdeflectionslopephenomenoninthoracicimpact,ineffectitwasutilisedinthatstudyandresultedinimprovednormalisation.Therecognitionof the constant energy versus deflection slope and the addition of a viscous response further improvenormalisationasevidencedinbothplotsandtabulatedCVvalues.It can be seen in Fig. 7 and Table VI that calculating the standard deviation accurately in force versus

deflectionspaceratherthanintimespacereducestheellipsesizesandreducestheCVforthedatasetstudiedhere. Thisconceptcanbedifficult tograsp. Consider that forceanddeflectionareparametrically linkedbytime.CrossplottingtheforceanddeflectionfromeachPMHStestprovidesanaccurateforceversusdeflectionplotforeachPMHS.However,thetimepairedsetofforceanddeflectionpointsforasubjectarenotplottedatequaldeflection increments in force versusdeflection spacebecause each subject timepaired setofpointsoccursatdifferentandunequalincrementsofdeflection.Byinterpolatingthetimepairedforceanddeflectionpointsontoacommondeflectionenergybaseanaccuratemeancurveandassociatedstandarddeviationscanbecalculateddirectlyinforceversusdeflectionspace.The essential weakness in the approach of using a relatively small sample size to characterise a large

population isobviousbutuntila large,welldefinedsamplebecomesavailablethedependenceonsmalldatasets is unavoidable. The best knownmodel of a human is currently the PMHS and PMHS response dataprovides thebestbiofidelity target for crashdummy response. The sample sizeof19 subjects tested fairlyrecently, all at the same laboratory (the InjuryBiomechanicsResearchCenterofOhio StateUniversity) is alargersamplethanisoftenavailablebutisstilltoosmallandinsufficientlydiverseinanthropometrytodevelopa robust regressionmodel that proves reasonable accuracy for all sizes of humans. The development of amultivariate regression model based on the independent variables of subject anthropometry and impactvelocity does provide an independent and reasonably accurate estimate of the 50th percentilemale humanresponse. TheapproachhasmeritandshouldbepursuedwithabettersampleofPMHSexposedtothoracicimpact.Thismethodology clearly reduces the variance among the subject response curves asmeasured by the

averaged coefficients of variation for this thoracic side impact test data. Future work will examine themethodologyforotherbodyregionssuchasfrontalthoracicimpact,abdominalimpact,kneethighhipimpact,andshoulderimpact.Allofthesebodyregionshavelargedeflectionsandthemethodmaybeapplicable.Bodyregionswithminimaldeflection,suchasthehead,maynotbeappropriatefordeflectionenergynormalization.It shouldalsobenoted thatanenergyversusdeflection curve thathasa secondorderpolynomial shape,

rather thana constant slope, is stillamenable to thismethodofdevelopingnormalisation factors. The firstderivativeofa secondorderdeflectionenergyversusdeflection curvewillbea straight line,althoughnotaconstant,and the twoelementviscoelastic solidmodel isapplicable. However, theenergyversusdeflectioncurvewillrequiretwocoefficientstodefineitandthemultivariateregressionprocessandthedevelopmentofscalefactorswillbecomemorecomplicated.Itmaybebettertoregressdeflectiondirectlyinthatcaseratherthantheshapeoftheenergycurve.Finally, the kinematics of the impacted subject (acceleration, velocity, and displacement) can also be

normalisedbyusing the scale factors for forceandeffectivemass to finda scale factor foraccelerationandintegratingtofindvelocityanddisplacement.Alternativelythescalefactorforpostimpactsubjectvelocitycanbeusedbydifferentiatingandintegratingthescaledvelocitytofindaccelerationanddisplacement.Notethatwhenintegratingordifferentiatingscaledresponsedatathescalefactorfortimemustalsobeincluded.

IRC-17-72 IRCOBI Conference 2017

-589-

V. CONCLUSIONSThe use of deflection energy provides an improvedmethodology for normalising PMHS thoracic impact

responsedata. Theconstantslopeofthedeflectionenergyvsdeflectioncurve leadstotheuseofatwoDOFviscoelastic model for development of normalisation factors. The energy and slope values for the 50th

percentilemalehumanwereestimatedusingmultivariateregression.Inthedataanalysedherethisimproveddeflectionenergymethodprovides lessvariation (tightergroupingof response curves) thando thepreviousmethodswhencomparedusingtheaveragecoefficientofvariation.

VI. REFERENCES[1] EppingerRH,MarcusJH,MorganRM.Developmentofdummyand injury indexforNHTSA'sthoracicside

impactprotectionresearchprogram.SAETechnicalPaper.1984.No.840885.[2] MertzHJ.Aprocedurefornormalizingimpactresponsedata.SAETechnicalPaper.1984.No.840884.[3] Viano,DC. Biomechanicalresponsesand injuries inblunt lateral impact. SAETechnicalPaper1989.No.

892432.[4] MoorhouseKM. An improvednormalizationmethodologyfordevelopingmeanhumanresponsecurves.

InternationalTechnicalConferenceontheEnhancedSafetyofVehicles,2013,Seoul,Korea.[5] ShawJM,HerriottRG,McFaddenJD,DonnellyBR,BolteJHIV.Obliqueandlateralimpactresponseofthe

PMHSthorax.StappCarCrashJournal.2006. Vol. 50.[6] DonnellyBR,MoorhouseKM,RhuleHH, Stammen JA. ADeformationEnergyApproach toNormalizing

PMHS Response Data and Developing Biofidelity Targets for Dummy Design. Proceedings of IRCOBIConference.2014.Berlin,Germany.

[7] RhuleHH,SuntayB,HerriottR,AmensonT,StricklinJ,BolteJIV.ResponseofPMHStohighandlowspeedobliqueandlateralpneumaticramimpacts.StappCarCrashJourna.2011.Vol.55.

[8] RhuleHH,SuntayB,HerriottR,StricklinJ,KangYS,BolteJH IV. ResponseofthePMHSThorax inLateralandObliquePneumaticRam Impacts Investigationof ImpactSpeed, ImpactLocationand ImpactFace.ProceedingsofIRCOBIConference.2014.Berlin,Germany.

[9] NusholtzGS,HsuTP,ByersLC.AproposedsideimpactATDbiofidelityevaluationschemeusing a crosscorrelation approach. Proceedings of the 20th International Technical Conference on theEnhancedSafetyofVehicles.2007.Lyon,France.

[10] Tschoegl, NW. The Phenomenological Theory of Linear Viscoelastic Behavior. SpringerVerlag, Berlin,Heidelberg,1989.P.14.ISBN0387191739.

[11] Shames,IH,Cozzarelli,FA.ElasticandInelasticStressAnalysis.PrenticeHall,EnglewoodCliffs,NewJersey.1992.pp.119122.ISBN0132454653.

[12] MATLAB6.1.TheMathWorksInc.,Natick,MA,2000.[13] Hair, JF Jr.,Anderson,RE,Tatham,RL. MultivariateDataAnalysis. MacmillanPublishingCompany,New

York,NewYork,USA.1987.P41.ISBN0023489804.[14] RhuleHH,Donnelly BR,Moorhouse KM, Kang YS. Amethodology for generating objective targets for

quantitatively assessing the biofidelity of crash test dummies. Proceedings of the 25th InternationalTechnicalConferenceontheEnhancedSafetyofVehicles.2013.Seoul,Korea.

[15] Robbins,DH. AnthropometricSpecificationsforMidSizedMaleDummy,Vol.2. Finalreport. December1983.UMTRI83532,UniversityofMichiganTransportationResearchInstitute.

VII. APPENDIXAnalysis of Mean Responses from Oblique versus Lateral Impacts and Circular versus Rectangular FaceImpacts Results from testing thehypothesis that themeansof several comparisonsof the slopesof thedeflectionenergyversusdeflection curvesare from the samepopulationare shown inTableAI. Thecomparisonpairswerea rectangular face impacting laterallyandobliquelyat4.5m/sec;acircular face impacting laterallyandobliquely at 2.5m/sec; lateral impactswith circular and rectangular faces scaled to 3.5m/sec; and obliqueimpactswithcircularand rectangular facesscaled to3.5m/sec. Thenullhypothesis ineachcase is that thedifference in the slope values is zero. The pvalues in each case are quite large,well above the generallyaccepted value of 0.05, indicating it is not possible to reject the null hypothesis. Itwas assumed, for thepurposesofdemonstrating thisnormalizationmethod that the subject responsedata comes from the samepopulation.

IRC-17-72 IRCOBI Conference 2017

-590-

TableAIComparisonoftheslopesfromobliqueversuslateralimpactsandcircularversusrectangularfaceimpacts.

testtype reclat4.5 recobl4.5 cirlat2.5 cirobl2.5 reclat3.5 cirlat3.5 recobl3.5 cirobl3.52.64 2.19 1.27 1.16 1.94 1.72 1.67 1.551.97 1.94 1.04 1.24 1.49 1.48 1.52 1.711.74 2.18 1.38 1.00 1.30 1.88 1.64 1.432.76 1.57 1.67 2.192.48 2.03 2.33

1.95 2.26mean 2.32 2.10 1.23 1.13 1.71 1.69 1.85 1.72

stddev 0.44 0.14 0.17 0.12 0.30 0.20 0.35 0.34degreesfreedom v=3.8 v=3.6 v=6 v=6.7

tvalue t=.94 t=0.83 t=0.12 t=.59pvalue p>.4 p >.45 p >.90 p >.55

SubjectResponseValuesandNormalisationFactorsforallSubjectsThevaluesforthe50thpercentilemaleasdeterminedusingthemultivariatepredictionsareshowninthefirst

rowofTableAII.Thefollowingrowscontaintherelevantvaluesforeachsubjectandtheassociatedscalefactorwhich isaratioofthe50thvalueoverthesubjectvalue,exceptforthetimescalefactorwhich isthe invertedfrequencyvalues.

TableAII.Scalevaluesandnormalisationfactorsforallsubjectsat3.5m/simpactvelocity.

SubjectEnergy(Nm)

Slope(Nm/mm)

Force(N)

Deflection(mm)

Stiffness(N/m)

Viscousconstant(Nsec/m)

Time(sec)

EffectiveMass(kg)

Subjectvelocity(m/s)

50th E=81.54 b=1.88 F=1880 S=43.37 K=43346 C=537 =8.50 m=30.88 Vs=1.51

0503 E=58.33E=1.40b=1.56b=1.20

F=2620F=1.20

S=37.33s=1.16

K=41890k=1.03

C=596c=0.90

=10.05t=1.10

m=16.06m=1.92

Vs=2.08vs=0.73

0504 E=81.74E=1.00b=1.72b=1.09

F=6020F=1.09

S=47.52s=0.91

K=36206k=1.20

C=666c=0.81

=10.85t=0.86

m=31.06m=0.99

Vs=1.50vs=1.00

0505 E=60.72E=1.34b=1.48b=1.27

F=6390F=1.27

S=41.09s=1.06

K=35969k=1.21

C=600c=0.89

=10.79t=0.98

m=17.20m=1.80

Vs=2.02vs=0.75

0506 E=67.30E=1.21b=1.67b=1.13

F=0290F=1.13

S=40.41s=1.07

K=41220k=1.05

C=655c=0.82

=11.32t=1.00

m=20.71m=1.49

Vs=1.86vs=0.81

0507 E=88.30E=0.92b=1.41b=1.34

F=9680F=1.34

S=62.77s=0.69

K=22416k=1.93

C=574c=0.94

=11.06t=0.64

m=37.55m=0.82

Vs=1.34vs=1.12

0601 E=81.17E=1.00b=1.91b=0.98

F=6730F=0.98

S=42.44s=1.02

K=45066k=0.96

C=744c=0.72

=9.81t=0.96

m=30.56m=1.01

Vs=1.52vs=0.99

0802 E=77.91E=1.05b=1.91b=0.98

F=15630F=0.98

S=40.70s=1.07

K=47030k=0.92

C=401c=1.34

=9.30t=1.10

m=27.87m=1.11

Vs=1.60vs=0.94

0803 E=76.45E=1.07b=1.65b=1.14

F=7200F=1.14

S=46.40s=0.93

K=35516k=1.22

C=359c=1.49

=7.27t=0.96

m=26.75m=1.15

Vs=1.63vs=0.92

0804 E=70.77E=1.15b=1.49b=1.26

F=4780F=1.26

S =47.51s=0.91

K=31350k=1.38

C=333c=1.61

=8.29t=0.94

m=22.83m=1.35

Vs=1.77vs=0.85

0902 E=67.55E=1.21b=1.50b=1.26

F=6660F=1.26

S=45.15s=0.96

K=33145k=1.31

C=323c=1.66

=8.51t=0.99

m=20.86m=1.48

Vs=1.85vs=0.82

0903 E=47.72E=1.71b=1.26b=1.49

F=4070F=1.49

S=37.81s=1.15

K=33379k=1.30

C=269c=1.99

=5.42t=1.18

m=11.68m=2.64

Vs=2.33vs=0.65

0904 E=56.75E=1.44b=1.60b=1.17

F=9120F=1.17

S=35.43s=1.22

K=45215k=0.96

C=284c=1.89

=8.13t=1.28

m=15.34m=2.01

Vs=2.11vs=0.71

0905 E=58.29E=1.40b=1.64b=1.15

F=9140F=1.15

S=35.56s=1.22

K=46114k=0.94

C=298c=1.80

=9.35t=1.27

m=16.04m=1.93

Vs=2.08vs=0.73

1001 E=68.17E=1.20b=2.03b=0.93

F=6480F=0.93

S=33.59s=1.29

K=60413k=0.72

C=426c=1.26

=8.17t=1.33

m=21.22m=1.46

Vs=1.84vs=0.82

1002 E=67.32E=1.21b=1.97b=0.96

F=4900F=0.96

S=34.21s=1.27

K=57528k=0.75

C=443c=1.21

=7.97t=1.30

m=20.72m=1.49

Vs=1.86vs=0.81

1003 E=64.65E=1.26b=1.67b=1.12

F=4960F=1.12

S=38.65s=1.12

K=43311k=1.00

C=366c=1.46

=8.41t=1.16

m=19.23m=1.61

Vs=1.92vs=0.79

1201 E=73.64E=1.11b=2.44b=0.77

F=4420F=0.77

S=30.16s=1.44

K=80980k=0.54

C=928c=0.58

=11.53t=1.36

m=24.73m=1.25

Vs=1.70vs=0.89

1202 E=91.96E=0.89b=2.22b=0.85

F=2150F=0.85

S=41.52s=1.04

K=53352k=0.81

C=861c=0.62

=8.32t=0.98

m=41.89m=0.74

Vs=1.25vs=1.20

1203 E=87.42E=0.93b=2.34b=0.80

F=3410F=0.80

S=37.34s=1.16

K=62709k=0.69

C=914c=0.59

=9.24t=1.09

m=36.59m=0.84

Vs=1.37vs=1.11

IRC-17-72 IRCOBI Conference 2017

-591-