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SAE TECHNICAL

PAPER SERIES 2004-01-1631

Correlation Grading Methodology for Occupant

Protection System Models

Deren Ma, Jennifer Matlack, Honglu Zhang and John SparkmanDelphi Corporation

Reprinted From: CAE Methods for Vehicle Crashworthiness and Occupant Safetyand Safety-Critical Systems

(SP-1870)

2004 SAE World CongressDetroit, MichiganMarch 8-11, 2004


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2004-01-1631

Correlation Grading Methodology for OccupantProtection System Models

Deren Ma, Jennifer Matlack, Honglu Zhang and John SparkmanDelphi Corporation

Copyright 2004 SAE International

ABSTRACT

Computer modeling and simulation have become one ofthe primary methods for development and design ofautomobile occupant protection systems (OPS). Toensure the accuracy and reliability of a math-based OPSdesign, the correlation quality assessment of

mathematical models is essential for program success.In a typical industrial approach, correlation quality isassessed by comparing chart characteristics and scoredbased on an engineers modeling experience and

judgment. However, due to the complexity of the OPSmodels and their responses, a systematic approach isneeded for accuracy and consistency. In this paper, acorrelation grading methodology for the OPS models ispresented. The grading system evaluates a widespectrum of a computer models performances, includingkinematics, dynamic responses, and dummy injurymeasurements. Statistical analysis is utilized tocompare the time histories of the tested and simulated

dynamic responses. The statistical quantitymeasurements include the average residual, standarddeviation, correlation coefficient, and 0th to 2nd momentrelative differences. The correlation quality of overallkinematics and dynamic responses is scored and color-coded from weak, marginal, adequate, good to excellent.The grading system can clearly distinguish thecorrelation quality for different models. The evaluationof a side curtain airbag component model and a frontalimpact system model is presented as examples todemonstrate the applications of the correlation gradingsystem.

INTRODUCTION

The design of Occupant Protection Systems (OPS)plays an important role in vehicle development.Extensive government regulations for both frontal andside impacts [1] and consumer information programssuch as New Car Assessment Program (NCAP) [2]make the design and optimization of OPS a challengingtask. Pure physical tests are cost prohibitive because ofthe large number of crash scenarios in which the OPShas to be tested to evaluate its performance and ensurecompliance of government requirements. Therefore,computer modeling and simulation have become a

primary means for design and optimization of theadvanced OPS. To ensure the accuracy and reliability oa math-based OPS design, the correlation qualityassessment of the mathematical models is essential foprogram success.

In a typical industrial approach, correlation quality is

assessed by comparing chart characteristics and scoredbased on an engineers modeling experience and

judgment. This approach is often inaccurate, subjectiveand inconsistent. Due to the complexity of the OPSmodels and their responses, it is hard to compare thecharacteristics of several charts simply by reading thecharts directly. An engineers experience rather thanscientific analysis plays a vital role in such a modequality assessment process. Also the same engineermay apply different criteria on different models, anddifferent engineers may have diverse scores on thequality of the same model. The inconsistency makes ithard to implement organization-wide common

development process and mathematical model re-usestrategy.

To address these issues, many efforts have been madeto provide more quantifiable criteria to judge thecorrelation quality of mathematical models. NationaCrash Analysis Center sponsored by Federal Highway

Administration (FHWA) and National Highway TrafficSafety Administration (NHTSA) developed a timedomain validation procedure to compare simulationresults and test data for full vehicle crash simulation [3]M. H. Ray proposed a set of criteria to validate full-scalecrash simulation results using this procedure [4]. TNO

Automotive and MECALOG also introduced acommercial software package ADVISER whichcontains a model quality-rating module with its ownmeasurement criteria [5,6]. All these systems are tryingto answer the following two questions: (1) Whichmeasurement variables should be used to judge themodel correlation quality; (2) What is the criterion foreach measurement variable. Because of the technicalimitations of the OPS simulation models, such asinadequate understanding of the occupanbiomechanical responses in an OPS system, it isunlikely that the simulation results are very similar to thetest data from a purely statistical point of view


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Therefore, the selection of measurement variables andtheir criteria is vital in the application value of thecorrelation evaluation systems.

Based on engineering experience from both physicaltests and simulation models, a correlation gradingsystem specifically tailored for OPS model evaluationwas developed. The system evaluates a wide spectrumof a computer models performance, includingkinematics, dynamic responses and dummy injurymeasurements. The correlation quality of overallkinematics and dynamic responses is scored and color-coded from weak, marginal, adequate, good to excellent.The evaluation of a side curtain airbag componentmodel and a frontal impact system model is presentedas examples to demonstrate the applications of thecorrelation grading system. The grading system clearlydistinguishes the correlation quality for different modelswith accuracy and consistency, and helps to assessconfidence level of the predictive results. Additionally,the correlation grading system provides an easy-to-understand platform for the communication of OPSmodeling results among various divisions of the

organization, among different organizations or betweenCAE analysts and hardware design engineers who donot necessarily have much background in computersimulations.

THE CORRELATION GRADING SYSTEM

Table 1 shows the overall structure of the correlationgrading system. It consists of two major parts, theoverall kinematics evaluation and the dynamic responseassessment. A single overall kinematics score is grantedaccording to multiple criteria of kinematics similaritybetween the model animation and the physical test

videos. At the same time, several variables are gradedindividually for the dynamic responses. The averagescore of all these variables decides the general dynamicresponse score of the model.

The model output variables to be evaluated are selectedbased on the nature of the model. In a component modeof side curtain airbag free motion headform (FMH) topole impact, for example, the head acceleration is themajor variable to be assessed, while in a frontal impactsystem model, many more variables need to beconsidered, depending on the crash conditions, designregulations and customer requirements. The variableselection may also be influenced by design objectives.

OVERALL KINEMATICS

The kinematics is assessed by comparing the modekinematical responses with physical test videos. Thekinematics variables of a typical OPS model include, buare not limited to, vehicle interior intrusions andmovements, restraint system performances and dummykinematical responses.

DYNAMIC RESPONSES

Dynamic responses are evaluated based on thecomplete time history curves of each variable from both

the simulation results and the test data. Among the fulrange of statistical measurements of two curves, severarepresentative measurements are selected in thecorrelation grading system to draw a comprehensivepicture of the relationship between the curves withminimum number of statistical measurement variables.

When the dynamic responses of a computer simulationmodel are considered close enough to those of aphysical test, the following criteria need to be satisfied:

1. The overall shape and trend of the two timehistory curves are similar.

2. The peak values and their timing of theresponse curves and the correspondingoccupant injury measurements are close.

3. The total areas of the curves are alike.

Table 1 Overall Structure of the Correlation Grading System

Peak Value Statistical analysis

Grading system OverallKinematics Timing Magnitude

AvgResidual

StandardDeviationof

Residual

CorrelationCoefficient

0 MomentDiff

1stMoment

Diff

2ndMoment

Diff

DynamicResponse

Excellent x x x x x x x x Excellent

Good x x x x x x x x Good

Adequate x x x x x x x x Adequate

Marginal x x x x x x x x Marginal

Grade Criteria

Weak x x x x x x x x Weak


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To quantify the above three criteria, two key parts areincluded in the dynamic response evaluation section,peak value comparison and statistical analysis. For peakvalues, both the magnitude and the time when the peakvalue is reached are assessed. The statistics analysis isutilized to measure the overall shape and trend of thesimulated model response time histories, as well as thetotal area of the curves. Average residual, standard

deviation, correlation coefficient and 0thto 2ndmoment

relative differences are the major factors considered inthe correlation grading system [7-9].

( ) ( )

= =

=

=N

i

N

i

ii

i

N

i

i

ffss

ffss

r

1 1

22

1

))((

(3)

where ris the correlation coefficient of two time histories

s and fare the mathematical means of the two timehistory curves. The correlation coefficient can rangefrom -1.00 to +1.00. The value of -1.00 represents aperfect negative correlation while a value of +1.00represents a perfect positive correlation and a value of0.00 represents a lack of correlation. A perfeccorrelation indicates that the model output can belinearly transformed to match the reference signal. Fothe purpose of OPS model correlation, this means thathe shapes of the curves are very similar even if themagnitudes are offset. It is possible and common tohave a very good correlation coefficient and still havesignificant scaling and bias errors.

Average Residual

Average Residual is the average difference between themodel outputs and the reference signal, usually the testresults. It is calculated as Equation 1 and is shown as apercentage of the peak value of the reference signal.Because average residual is a mathematical mean ofthe difference of all data points along the curves, thepositive and negative differences at various data pointsmay cancel each other. As a result, it is not unusual tohave a low average residual and a high standarddeviation when comparing curves with oscillatoryresiduals.

0 2nd Relative Difference of Moments

N

fs

Ri

N

i

i )(1

=

= (1)

The relative moments describe the characteristics of the

time history curves. The nth momentn

of discrete

time histories and can be expressed as:is if

tstsM i

N

i

n

ii

n = =1

)( (4)whereR is the average residual, and are the two

time histories being compared and Nis the data samplesize.

is if

tftfM i

N

i

n

ii

n = =1

)( (5)Standard Deviation of Residual

The standard deviation of residual is defined as thesquare root of the variance of the residual. It iscalculated in Equation 2:

where is time duration at sample data point iand t is

the constant time step. Moments for n=0, 1 and 2correspond to the area under the curve, area moment ofthe curve, and area moment of inertia of the curverespectively. The relative nth moments of discrete time

histories and can be expressed as:

it

is if

( )

1

1

2

1

=

=

N

RR

s

N

i

i

N (2)

1

1

1

)( +

=

=

=

nN

i

i

N

i

i

n

i

i

n

r

t

tst

sM (6)

where is the standard deviation of the residual,

is the residual of the two time histories at sample data

point i and

1Ns iR

R is defined in Equation 1. The standarddeviation of residual is also represented as a percentageof the peak value of the reference signal. It describeshow spread out the residual is around its mathematicalmean.

1

1

1)(+

=

=

=

n

N

i

i

N

i

i

n

i

i

n

r

t

tft

fM (7)Correlation Coefficient

The correlation coefficient is a measurement of thedegree of linear relationship between two time histories.It is given by the following expression:


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The main objective of the model is to predict theheadform acceleration under various airbag pressures adifferent impact locations. Several impact locations andairbag pressures were tested physically. The simulationmodel was intended to match the headformaccelerations in all non-bottom-out cases. Here bottomout means the minimum cushion thickness between thetwo layers of the airbag fabric becomes zero. Once theairbag bottoms out, the interaction between the pole andthe headform plays the major role, not the interactionbetween the airbag and the headform.

The relative difference of the moments is calculated inEquation 8:

( ) ( )in

ri

n

r fMsM = (8)

is and are considered very similar if the relative

difference of moments of and is smaller than a pre-

specified value.

if

is if

The statistical analysis of average residual, standard

deviation, correlation coefficient and 0thto 2ndmomentrelative differences, together with the peak valuemagnitude and timing, depicts an overall picture of thesimilarity between the simulation output and thereference data.

In this model, the main criterion for kinematicscorrelation is whether the airbag bottomed out. The chievariable to consider in dynamic responses is theheadform acceleration time history. To evaluate theoverall correlation quality of the model, all non-bottom-out cases were assessed simultaneously with thecorrelation grading system. Figures 2-6 illustrate thecomparison of headform acceleration curves in all thefive non-bottom-out cases (non-bottom-out in thephysical tests). Table 2 contains the actual values of thedynamic response measurements, and Table 3 is the

output of the correlation grading system, with the set ofgrading criteria for component level FMH impacsimulations applied. In Table 3, 5 is the highest gradewhile 1 is the lowest grade based on the evaluationcriteria.

The grading criteria of the measurement variables areanother important component of the correlation gradingsystem. The criteria vary from case to case. Forexample, for a relatively simple component model, the

criteria are more stringent, while for a complex systemmodel, the criteria are looser. Even among systemmodels, the criteria for frontal systems and side systemsare different. A whole set of criteria for each scenariowere developed in the correlation grading system basedon the engineering experience with the reliability andpredictability of each category of models. Once decided,the grading criteria are applied constantly to all themodels in the same category to ensure the consistencyof the methodology.

CASE 1

0

20

40

60

80

100

120

0 0.02 0.04 0.06 0.08 0.1

Time (s)

HeadAccelerat

ion(g)

Test Simulation

EXAMPLE ONE: CORRELATION QUALITY

ASSESSMENT OF SIDE CURTAIN AIRBAG

COMPONENT LEVEL MODEL

The correlation grading system is applicable forsimulation models with various complexity levels. Todemonstrate the usage of the system, the correlationquality assessment of a relatively simple componentlevel model of side curtain airbag FMH to pole impact ispresented as the first example. Figure 1 is a snapshot ofthe model.

Figure 2 Head Acceleration Curves for Case 1

Figure 1 Side Curtain Airbag FMH Pole Impact Model


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To assess the correlation level of kinematics, vehicleand interior intrusions and movements, restraint systemkinematics and dummy kinematical responses areconsidered. A few examples of vehicle interiorintrusions and movements are seat pitching or dropping,steering wheel bending or column collapsing andinstrument panel or knee bolster intrusion. The restraintsystem kinematics consist of the airbag deploymentshape and timing and the seat belt geometry and spoolout characteristics. The dummy kinematical responsecorrelation concentrates on the pelvis, knee, chest andhead motion. Contact timing is also a very importantfactor in the correlation, especially for the contactbetween the knees and the knee bolster, between theairbag and the windshield, and between the head/chestand the airbag.

The next step is to evaluate the dynamic responses ofthe model. The time histories of all the variables ofinterest were analyzed. Figures 8, 9 and 10 representthe occupants head, chest and pelvis resultantaccelerations and accelerations in X direction. Both thetiming and magnitude of the peak value of each variable

were compared with test data and scored.

The statistical analysis of the average residual, standarddeviation, correlation coefficient and 0

th to 2

nd moment

relative differences completes the picture of thecorrelation. The scores of these statistic analyses wereaveraged. The combination of the scores of peak valuesand the statistical analysis decides the overall dynamicresponse score. Table 4 shows the actual values of thedynamic response evaluation variables, and Table 5 liststhe outputs of the correlation grading system for thismodel. Notice that due to the complexity of the systemmodel, the grading criteria in Table 5 are different from

those in Table 3.

The final grade for this frontal impact system model isExcellent, indicating a high quality of model correlation.

CONCLUSION

The correlation grading system has been successfullyused to quantify the correlation quality of OPS modelsand assess confidence level of the predictive results withaccuracy and consistency. It also helps to communicateOPS modeling results in an easy-to-understandplatform. The system has been proved reliable and

efficient for complex system models as well as relativelysimple component models.

-100

-50

0

50

100

0 0.02 0.04 0.06 0.08 0.1

Time (s)

HeadAcceleration(G)

Resultant Sled Data X Sled Data

Resultant Model Data X Model Data

Figure 8 Time History of the Head Acceleration

-100

-60

-20

20

60

100

0 0.02 0.04 0.06 0.08 0.1

Time (s)

ChestAccelerati

on(G)



Figure 9 Time History of the Chest Acceleration

-100

-60

-20

20

60

100

0 0.02 0.04 0.06 0.08 0.1

Time (s)

PelvisAcceleration(G)



Figure 10 Time History of the Pelvis Acceleration


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Table 4 Correlation Evaluation for Frontal Impact System Model


Grading systemOverall

Kinematics Timing MagnitudeAvg

Residual

StandardDeviation

ofResidual


0 MomentDiff

1stMoment

Diff

2ndMoment

Diff

DynamicResponse

Head R Acc 1 ms 3.9% 5.04 % 10.19 % 0.981 0.142 0.135 0.121

Head X Acc 2 ms 0.1% 4.74 % 10.33 % 1 0.154 0.134 0.113

Chest R Acc 8 ms 0.9% 1.17 % 17.13 % 0.927 0.036 0.102 0.171

Chest X Acc 8 ms 0.9% 0.91 % 17.62 % 0.92 0.029 0.105 0.184

Pelvis R Acc 5 ms 3.6% 3.16 % 14.67 % 1 0.109 0.163 0.21Variables

Pelvis X Acc

Excellent

5 ms 12% 2.31 % 18.31 % 1 0.086 0.096 0.077

Table 5 Correlation Grades for Frontal Impact System Model


Grading systemOverall

Kinematics Timing MagnitudeAvg

Residual

StandardDeviation

ofResidual


0 MomentDiff

1st

MomentDiff

2nd

MomentDiff

Dynamic

Response

Excellent x x x x x x x x Excellent

Good x x x x x x x x Good

Adequate x x x x x x x x Adequate

Marginal x x x x x x x x Marginal

Grade Criteria

Weak x x x x x x x x Weak

Head R Acc 5 5 4 5 5 5 5 5

Head X Acc 5 5 4 5 5 5 5 5

Chest R Acc 3 5 5 4 4 5 5 5

Chest X Acc 3 5 5 4 4 5 5 5

Pelvis R Acc 4 5 5 5 5 5 4 3V

ariables

Pelvis X Acc

E

xcellent

4 3 5 4 5 5 5 5

E

xcellent

REFERENCES

1. U.S. Department of Transportation, National

Highway Traffic Safety Administration, Federal

Motor Vehicle Safety Standards and Other

Regulations.

(http://www.nhtsa.dot.gov/cars/rules/standards/)

2. U.S. Department of Transportation, National

Highway Traffic Safety Administration, New CarAssessment Program, 1978.

(http://www.nhtsa.dot.gov/cars/testing/ncap)

3. FHWA/NHTSA National Crash Analysis Center,

FHWA Quantitative Validation Procedure, 1997.

(http://www.ncac.gwu.edu/archives/software/)

4. M. H. Ray, "Repeatability of Full-Scale Crash Tests

and a Criteria for Validating Finite Element

Simulations", Transportation Research Record

No.1528, Transportation Research Board

Washington, D.C., December, 1997.

5. TNO Automotive, Research and Technology

Development News ADVISER, May, 2003.

6. TNO Automotive, Presentation Script, ADVISER

May, 2003.

7. J.L. Devore, Probability and Statistics fo

Engineering and the Sciences, Brooks/Cole

Publishing Company, 1982.8. S. Basu and A. Haghighi, Numerical Analysis o

Roadside Design (NARD): Validation Manual

Volume III, Report FHWA-RD-88-214, Washington

D. C., Federal Highway Administration, September

1988.

9. The Technology Administration of the U.S

Department of Commerce, NIST/SEMATECH, e

Handbook of Statistical Method.

(http://www.itl.nist.gov/div898/handbook/index.htm)
http://www.nhtsa.dot.gov/cars/rules/standards/http://www.nhtsa.dot.gov/cars/testing/ncaphttp://www.ncac.gwu.edu/archives/software/http://www.itl.nist.gov/div898/handbook/index.htmhttp://www.itl.nist.gov/div898/handbook/index.htmhttp://www.ncac.gwu.edu/archives/software/http://www.nhtsa.dot.gov/cars/testing/ncaphttp://www.nhtsa.dot.gov/cars/rules/standards/

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