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1、INTRODUCTIONPedestrian protection has been drawing attention for morethan two decades.In 2008,pedestrian fatalities made up12%-33%of all road fatalities in the US,European Union,and Japan 1.Statistics show that the lower limb is the mostfrequently injured body part in car-to-pedestrian accidents2,an
2、d that more than 30%of all pedestrians involved incar-to-pedestrian accidents suffer knee injuries 3.In impacts with the vehicle front-end,pedestrian lowerlimbs will contact with the bumper system first,which willcreate a turning moment about the center of gravity of thepedestrian and cause the uppe
3、r body to arc downwards.Theupper leg,pelvis,chest and head will contact with the bonnetleading edge,bonnet and windshield successively 4,asshown in Figure 1.In regulatory tests,legform impactors are used to evaluatelower limb injuries of pedestrians when laterally impacted bya vehicle.Popular legfor
4、m impactors include the EEVCpedestrian legform impactor(EEVC-PLI)and the Flexlegforms 5,7,6.Due to the repeatability and reusabilityrequirement for testing,simplified structures are usuallypreferred in the design of the impactors.They are usuallyunable to completely reflect real lower limb injurymec
5、hanisms and kinematics due to their design limitations7-8.Figure 1.Kinematics of pedestrian impacts with vehiclefront-end 9.In order to enhance the real-life protection of pedestrians,a validated finite element full-body pedestrian human bodymodel(HBM)is used as an effective tool for the study oflow
6、er limb injuries.It can provide realistic kinematic lowerlimb response in real-world accidents and can be used toassess pedestrian injuries at the bone and tissue level.To evaluate the vehicle protection performance,it isnecessary to give a quick prediction on human bodykinematics and injury levels
7、under different impact loadingconditions.Response surface(RS)methodology is taken asthe approach to construct global approximations to systembehavior based on results calculated at various points in thedesign space 10.It explores the relationships between inputdesign variables and one or more respon
8、ses 11.The mainideal is to use a sequence of design experiments to obtain the2013-01-0216Published 04/08/2013Copyright 2013 SAE Internationaldoi:10.4271/2013-01-0216saetransaf.saejournals.orgResponse Surface Generation for Kinematics and InjuryPrediction in Pedestrian Impact SimulationsBingbing Nie,
9、Yong Xia,Qing Zhou and Jun HuangTsinghua Univ.Bing Deng and Mark NealGeneral Motors CompanyABSTRACTThis study concerns the generation of response surfaces for kinematics and injury prediction in pedestrian impactsimulations using human body model.A 1000-case DOE(Design of Experiments)study with a La
10、tin Hypercube samplingscheme is conducted using a finite element pedestrian human body model and a simplified parametric vehicle front-endmodel.The Kriging method is taken as the approach to construct global approximations to system behavior based onresults calculated at various points in the design
11、 space.Using the response surface models,human lower limb kinematicsand injuries,including impact posture,lateral bending angle,ligament elongation and bone fractures,can be quicklyassessed when either the structural dimensions or the structural behavior of the vehicle front-end design change.This w
12、illaid in vehicle front-end design to enhance protection of pedestrian lower limbs.CITATION:Nie,B.,Xia,Y.,Zhou,Q.,Huang,J.et al.,Response Surface Generation for Kinematics and Injury Predictionin Pedestrian Impact Simulations,SAE Int.J.Trans.Safety 1(2):2013,doi:10.4271/2013-01-0216._THIS DOCUMENT I
13、S PROTECTED BY U.S.AND INTERNATIONAL COPYRIGHT.It may not be reproduced,stored in a retrieval system,distributed or transmitted,in whole or in part,in any form or by any means.Downloaded from SAE International by Bingbing Nie,Sunday,March 24,2013 09:19:36 PMresponse of a new design.Global approximat
14、ions are oftenutilized in multidisciplinary optimization 12 or in reliabilitycalculations 13.Response surface modeling approaches arewidely used in aerospace engineering 14,structural design15,and mechanical engineering 16.To deal with the highly nonlinear responses in car-pedestrian impacts,Kriging
15、 models are used since they cangive global approximations with relatively good accuracy17-18.In recent years,the Kriging method has found widerapplication as a spatial prediction method in engineeringdesign.Design of experiment(data sampling)plays animportant role,especially when building Kriging mo
16、dels19.Latin Hypercube sampling,or other space fillingmethods,are typically used as the data sampling strategy incombination with the Kriging method 20-21.This paper documents the generation of response surfacesfor kinematics and injury prediction in pedestrian impactsimulations using human body mod
17、el.A computationallyefficient,parametric vehicle model with adjustable geometricand stiffness variables to represent different vehicle front endconfigurations has been developed.This model has beenvalidated by performing impact simulations with a humanbody model in a standing posture and comparing t
18、o similarsimulations with a detailed finite element model of a vehiclefront structure.Impact simulations between simplifiedvehicle models with different stiffness or geometry designvariable values and a standing finite element human bodymodel have been performed.Several response surfaces for pedestr
19、ian human lowerlimb kinematics and injury predictions are generated usingthe numerical DOE(Design of Experiments)study.Theaccuracy of the RS models is validated with additional checkpoints which are not in the DOE matrix.Using the RSmodels,human lower limb injuries,including ligamentelongation and b
20、one fractures,can be quickly assessed wheneither the structural dimensions or the structural behavior ofthe vehicle front-end design changes.This will aid in vehiclefront-end design to enhance pedestrian protection of lowerlimbs.MODEL SETUPTo assess the protection performance of various vehiclefront
21、-end designs,simulations of the finite element humanbody model in a standing posture impacted by the simplifiedvehicle model with different design variable values werecarried out(Figure 2).The impact speed of the vehicle was40 kpm,and the pedestrian was struck laterally,at thecenterline of the vehic
22、le.The trailing lower limb on the rightside was the first contact with the vehicle.Human Body Model(HBM)The full-body mid-size pedestrian model(HBM)in thispaper was first developed by General Motors(GM)and theUniversity of Virginia(UVA)in 2007(Figure 2)22.Themodel is 177 cm high and weighs 77 kg,whi
23、ch represents a50th percentile male pedestrian in a standing posture.It is anLS-DYNA based finite element model,containing about 370parts and 130,000 elements,including 83,900 solid elementsand 45,000 shell elements.It consists of FE lower limbmodels,rigid foot and shoe models,a rigid pelvis,a FE pe
24、lvicflesh model and other upper body part models.Thebiofidelity of the lower limbs has been validated atcomponent level 23,24,25.The kinematics of the HBMhas been validated at full-scale level,using the data from 7full-scale Post Mortem Human Subjects(PMHS)impact tests26.The HBM can therefore be use
25、d to evaluate the injuriesand kinematics of human lower limbs under different impactloading conditions more realistically.Figure 2.FE modeling of HBM impacts with simplifiedvehicle front-end model.Kinematics DescriptionKinematics of the first-struck right lower limb is assessedusing five markers;the
26、ir locations are shown in Figure 3.Time histories of the corresponding nodal coordinates in theglobal coordinate system are output to give their spatialposition during impact.This could provide reference pointsfor drawing the lower limb posture at a specified moment,e.g.the right lower limb posture
27、at maximum bending angle.Figure 3.Kinematics markers on the right lower limb.Considering the typical lateral impact situation forpedestrians,the lateral bending angle is taken as an importantoutput parameter.A knee joint coordinate system was definedin order to describe the three rotational motions
28、of the kneejoint 27,with the lateral bending angle taken as globalNie et al/SAE Int.J.Trans.Safety/Volume 1,Issue 2(August 2013)THIS DOCUMENT IS PROTECTED BY U.S.AND INTERNATIONAL COPYRIGHT.It may not be reproduced,stored in a retrieval system,distributed or transmitted,in whole or in part,in any fo
29、rm or by any means.Downloaded from SAE International by Bingbing Nie,Sunday,March 24,2013 09:19:36 PMkinematic parameter that predicts the risk of knee ligamentinjury.Injury Parameter DefinitionLigament rupture and bone fracture are the most commoninjury patterns in the lower limb 2,28.To evaluate t
30、hehuman body injuries,several parameters are output in theHBM simulations.The ligament elongation,defined as theratio of the change in length to the original ligament length,istaken to predict ligament injury in the HBM.It is calculatedfrom columns of nodes selected along the length of each ofthe fo
31、ur knee joint ligaments.It has been found that fractureof the femur and/or tibia shaft usually results fromacceleration of the lower limb during contact with the vehicle29.Therefore,maximum accelerations measured at tibia arealso output.Maximum bending moments at possible bonefracture locations are
32、also recorded,and will be used toevaluate bone fracture risk.Typical impact responses of theHBM impacted with one detailed vehicle model are shown inFigure 4 30.(a).Lateral bending angle(right lower limb)(b).Knee ligament elongation(right lower limb)(c).Trajectory of the kinematics markers(right low
33、erlimb)Figure 4.Typical time histories of the HBM response inimpact with vehicle front-end.Parametric Vehicle Front-End ModelThe simplified parametric vehicle model used in the DOEstudy is shown in Figure 5.It consists of five parts,representing the front faces of the bonnet leading edge(BLE)(Part 1
34、),upper grill(Part 2),main bumper(Part 3),lower grill(Part 4)and spoiler(Part 5).Five geometry variables andseven stiffness variables are included.Figure 5.The simplified parametric vehicle model forDOE and RS generation 30.To reflect the local deformation on the vehicle inpedestrian-vehicle impact,
35、Part 3 and Part 5 are modeled bydeformable shell elements to provide a deformable contactsurface.An array of uniformly distributed beam elements areused to model the dynamic stiffness of the bumper andspoiler structures.When impacting with pedestrian legs,sucha structure can have a more realistic re
36、sponse in terms ofdifferent contact time and contact location of the two lowerlimbs.Proper ranges of the upper and lower grill stiffness arealso determined to provide continuous contact with the HBMduring impact.These two parts do not contribute much to thelocal deformation due to the relatively low
37、 stiffness.Sincethey usually do not have significant displacement in thevertical direction during impact,only the structural stiffnessin the horizontal direction is defined.This parametric model is validated by comparingsimulations with the parametric vehicle model and with adetailed vehicle model,a
38、nd good correlations have beenobtained.Using the simplified vehicle model,thecomputation time of each HBM-to-vehicle impact simulationis reduced from 5.8 h to 1.3 h(6 CPUs on the MassivelyParallel Processing)30.The reduction is necessary forresponse surface generation due to the need of a large numb
39、erof simulation runs.Nie et al/SAE Int.J.Trans.Safety/Volume 1,Issue 2(August 2013)THIS DOCUMENT IS PROTECTED BY U.S.AND INTERNATIONAL COPYRIGHT.It may not be reproduced,stored in a retrieval system,distributed or transmitted,in whole or in part,in any form or by any means.Downloaded from SAE Intern
40、ational by Bingbing Nie,Sunday,March 24,2013 09:19:36 PMDESIGN OF EXPERIMENT&RESPONSE SURFACE GENERATIONDescription of the Kriging Model andSampling StrategyThe Kriging model is named after D.G.Krige,whoapplied empirical methods for determining true ore gradedistributions from distributions based on
41、 sampled ore grades31.A detailed mathematical formulation of Kriging is givenby Simpson 32.Kriging models combine a regression termfor the global portion of the model in conjunction with acorrelation function for local departures and can providesuccess in approximation of highly nonlinear computersi
42、mulations 33.The basic postulate of this formulation 32 is:(1)where y is the unknown function of interest,f(x)is a knownapproximation(usually polynomial)function and Z(x)is thestochastic component with mean zero and covariance:(2)With L the number of sampling points,R is the L Lcorrelation matrix,an
43、d R(xi,xj)is the correlation functionbetween any two of the L sampled data points xi and xj.R issymmetric positive definite with ones along the diagonal.Thecorrelation function R(xi,xj)has different forms and theGaussian correlation function is used in this study:(3)where n is the number of variable
44、s and,thedistance between the kth components of sample points xi andxj.There are n unknown k-values to be determined as thecorrelation parameters.The predicted estimate of the response(x)is given by:(4)where rT(x)is the correlation vector(length L)between aprediction point x and the L sampling point
45、s,y represents theresponses at the L points and f is a L-vector from the basisapproximation function f(x)in equation(1).The vector rT(x)and scalar are given by:(5)The estimate of variance from the underlying globalmodel is:(6)The maximum likelihood estimates for k,k=1,n,inequation(3),which is used t
46、o establish the Kriging model canbe found by solving the following constrained maximizationproblem:(7)Therefore,the construction problem of Kriging model isturned into a nonlinear and unconstrained optimizationproblem.After k is solved,the Kriging approximation modelis established and estimate of th
47、e response(x)can beobtained from equation(3),(4),(5).In addition to being flexible due to the wide range of thecorrelation functions,the Kriging method can also provide abasis for a stepwise algorithm to determine the importantfactors for screening and building the predictor model 34.To conduct the
48、numerical experiments for the Krigingresponse surface models,the Latin Hypercube(LH)waschosen as the sampling scheme for the DOE study.It is firstintroduced by McKay in 1979 35,as a statistical method forgenerating a stratified sample of parameter values frommultidimensional distributions.Assume tha
49、t N sample points are to be determined for a k-vector variable X=(x1,xk).Then the range of each xi(i=1,k)will be divided into N equally probable intervals andsampled once from each interval.Let this sample be xij(j=1,N).For the xi(i=1,k)component in Xj(j=1,N),the components of the various xis are ma
50、tched at random.Adetailed computer code and manual has been given by Iman36.As a structured quasi-random sampling strategy,the LatinHypercube can generate random sample points ensuring thatall portions of the vector space are sampled 35,andpotentially nonlinear input and output relationships 37-38ca