herman van der auweraer scores workshop leuven, 12-10-2004

System Identification: a Cornerstone of System Identification: a Cornerstone of Structural Design in the Aerospace and Structural Design in the Aerospace and

Automotive IndustriesAutomotive Industries

Herman Van der AuweraerHerman Van der AuweraerSCORES WorkshopSCORES WorkshopLeuven, 12-10-2004Leuven, 12-10-2004

SCORES 2004Leuven 12/10/04 2

Overview

Objective: Objective: To discuss the vital importance of System To discuss the vital importance of System Identification in the Mechanical Identification in the Mechanical Design EngineeringDesign Engineering Process Process

To identify the specific challenges for this kind of problems and To identify the specific challenges for this kind of problems and to illustrate the research needsto illustrate the research needs

Illustrate with typical products: Illustrate with typical products: cars,cars, aircraft, satellites, ….aircraft, satellites, …. where where adequate mechanical product behaviour is vitaladequate mechanical product behaviour is vital


Overview

Introduction: the role of Structural Dynamics in Introduction: the role of Structural Dynamics in

Mechanical Design EngineeringMechanical Design Engineering

Approach and methodology for Structural Dynamics Approach and methodology for Structural Dynamics

Analysis: Analysis: Experimental Modal AnalysisExperimental Modal Analysis

Modal Parameter Identification methodsModal Parameter Identification methods

Applications of modal analysisApplications of modal analysis

Recent evolutions and challenges for the futureRecent evolutions and challenges for the future

ConclusionsConclusions


IntroductionMechanical Design Engineering

Market Demand: Delivering products with the required Market Demand: Delivering products with the required mechanical characteristics: mechanical characteristics: Excel in Excel in

Operational quality (performance specifications…)Operational quality (performance specifications…)

Reliability (load tolerance, fatigue, life-time…)Reliability (load tolerance, fatigue, life-time…)

Safety (vehicle crash, aircraft flutter….)Safety (vehicle crash, aircraft flutter….)

Comfort (noise, vibration, harshness)Comfort (noise, vibration, harshness)

Environmental impact (emissions, waste, noise, Environmental impact (emissions, waste, noise, recycling…) recycling…)

Process process challenges: Process process challenges: Excel in Excel in

Time-to-Market: reduce design cycleTime-to-Market: reduce design cycle

Reduce design costs Reduce design costs

Product customizationProduct customization


Introduction Economic Impact: Some Figures

• Typical vehicle development programs require investment Typical vehicle development programs require investment budgets of 1 .. 4 B$ budgets of 1 .. 4 B$

• New Mercedes C-class New Mercedes C-class (Automotive Engineering Intl., Aug. 2000)(Automotive Engineering Intl., Aug. 2000): : • 600 M$ development + 700M$ production facilities600 M$ development + 700M$ production facilities

• Developed in less than 4 years Developed in less than 4 years

• New Mini: 200M£ development costsNew Mini: 200M£ development costs (+ as much in marketing...)(+ as much in marketing...)

• Chrysler minivan Chrysler minivan (“The Critical Path” by Brock Yates)(“The Critical Path” by Brock Yates)::• 2 B$ development budget, of which 250 M$ R&D2 B$ development budget, of which 250 M$ R&D

• 36 different body styles, 2 wheelbases, 4 engines36 different body styles, 2 wheelbases, 4 engines


IntroductionTime Pressure Increases Recall Risks

Warranty costs may explode the overall budgetWarranty costs may explode the overall budget

• 2000 warranty cost (Mercedes-Benz) : 1.5 b$2000 warranty cost (Mercedes-Benz) : 1.5 b$• Warranty cost exceeds R&D costWarranty cost exceeds R&D cost• Warranty cost x 3 in 2 years ...Warranty cost x 3 in 2 years ...

Warranty costs may explode the overall budgetWarranty costs may explode the overall budget

• 2000 warranty cost (Mercedes-Benz) : 1.5 b$2000 warranty cost (Mercedes-Benz) : 1.5 b$• Warranty cost exceeds R&D costWarranty cost exceeds R&D cost• Warranty cost x 3 in 2 years ...Warranty cost x 3 in 2 years ...


IntroductionMechanical Design Engineering

Early Design Optimization is EssentialEarly Design Optimization is Essential

Product design has to go beyond the “Form and Fit”Product design has to go beyond the “Form and Fit”

Focus on “Functional Performance Engineering”Focus on “Functional Performance Engineering”

For mechanical performances: For mechanical performances: structural analysisstructural analysis Static: strength, load analysisStatic: strength, load analysis Kinematic: mechanisms, motionKinematic: mechanisms, motion Dynamic: vibrations, fatigue, noiseDynamic: vibrations, fatigue, noise

Basic approach: is Basic approach: is through the use of structural modelsthrough the use of structural models A priori (Finite Element) and A priori (Finite Element) and experimental (Modal)experimental (Modal) Analyze the effect of dynamic loadsAnalyze the effect of dynamic loads Understand the intrinsic structural dynamics behaviourUnderstand the intrinsic structural dynamics behaviour Derive optimal design modificationsDerive optimal design modifications


System TransferSource Receiver

AccessoriesAccessories

Environmental Environmental SourcesSources

Total Vehicle Total Vehicle SystemSystem

Road InputRoad Input

Wheel & Tire Wheel & Tire UnbalanceUnbalance

Steering Wheel Steering Wheel ShakeShake

Seat VibrationSeat Vibration

Rearview mirror Rearview mirror vibrationvibration

Noise at Driver’s Noise at Driver’s & Passenger’s & Passenger’s

EarsEars

TA

CT

ILE

TA

CT

ILE

VIS

UA

LV

ISU

AL

AC

OU

ST

ICA

CO

US

TIC

EngineEngine

Introduction: A Systems ApproachA Source-Transmitter-Receiver Model

X =


Overview

Introduction: the role of Structural Dynamics in Introduction: the role of Structural Dynamics in


Approach and methodology for Structural Dynamics Approach and methodology for Structural Dynamics

Analysis: Analysis: Experimental Modal AnalysisExperimental Modal Analysis






Experimental Modal AnalysisPrinciples

Structural dynamics modelling: relating force inputs to Structural dynamics modelling: relating force inputs to displacement/acceleration outputs displacement/acceleration outputs

Multiple D.o.F. System:Multiple D.o.F. System:

Continuous structures approximated by discrete number of Continuous structures approximated by discrete number of degrees of freedom -> Finite Element Matrix Formulationdegrees of freedom -> Finite Element Matrix Formulation

Majority of methods and applications: Majority of methods and applications: Linear Linear and and Time-Time-InvariantInvariant models assumed models assumed

( ) ( ) ( ) ( )M x t C x t K x t f t g

rou

nd

m 1

c 1

k 1

f1

(t)

m 2 m n

gro

un

d

k n+1k 2

c 2c n+1

f2

(t) f n (t)

x1

(t) x2

(t) xn

(t)



Modal Analysis: Related to Eigenvalue AnalysisModal Analysis: Related to Eigenvalue Analysis

Time domain equationTime domain equation

Laplace domain equationLaplace domain equation

Eigenvalue analysis -> system poles and EigenvectorsEigenvalue analysis -> system poles and Eigenvectors System pole -> Resonance frequency and damping valueSystem pole -> Resonance frequency and damping value

Eigenvector -> Mode shapeEigenvector -> Mode shape

Transformation vectors to “Modal Space”Transformation vectors to “Modal Space”

( ) ( ) ( ) ( )M x t C x t K x t f t

2( ) ( ) ( )s M sC K X s F s

* 2, 1k k k k k kj



Modal Shape: Eigenvector in the physical space: physical Modal Shape: Eigenvector in the physical space: physical interpretation (Example “Skytruck”)interpretation (Example “Skytruck”)


Modal Analysis Principle;Decomposition in Eigenmodes

Modal Analysis: The modal superpositionModal Analysis: The modal superposition

==

++

++

++

aa11 aa22

aa33 aa44xx xx

xx xx

++

++ ……

……



Modal Analysis: An input/output relationModal Analysis: An input/output relation

Transfer Function Formulation:Transfer Function Formulation:

Model reduction (Finite number of modes):Model reduction (Finite number of modes):

2 1

( ) ( ) ( )

( ) [ ]

X s H s F s

H s s M sC K

*

*1

( )n

k k

k k k

A AH s

s s

{ } Tk k k kA Q

* 2, 1k k k k k kj



Experimental Analysis: using input/output measurementsExperimental Analysis: using input/output measurements

Non-parametric estimates (FRF, IR) -> Data reductionNon-parametric estimates (FRF, IR) -> Data reduction

Black box models (ARX, state-space)Black box models (ARX, state-space)

Modal modelsModal models

Standard experimental modal analysis approach: Standard experimental modal analysis approach: Fitting the Fitting the Transfer Function model by Frequency Response Function Transfer Function model by Frequency Response Function measurementsmeasurements

HHuu((tt))

UU(ω)(ω)

yy((tt))

YY(ω)(ω)

InputInput SystemSystem OutputOutput


Experimental Modal AnalysisTest Procedure

• ExcitationExcitation• Shakers (Random, Sine) Shakers (Random, Sine)

or Hammer (Impulsive)or Hammer (Impulsive)• Load cell for force meas.Load cell for force meas.

• ResponseResponse• AccelerometersAccelerometers• Laser (LDV)Laser (LDV)

• Cross-spectra averaging Cross-spectra averaging to estimate FRFsto estimate FRFs

• Measurement systemMeasurement system• FFT analyzer (2-4 channel)FFT analyzer (2-4 channel)• PC & data-acquisition PC & data-acquisition

front-end (2-1000 front-end (2-1000 channels)channels)

• ““patching” -> non-patching” -> non-simultaneous datasimultaneous data


Experimental Modal Analysis:Aircraft Test Setup Example

F4

F3

F2

F1

Force Inputs

Responses

Ground Vibration Test (GVT) System

44434241

34333231

24232221

14131211

HHHH

HHHH

HHHH

HHHH

InputsInputs

Res

po

nse

sR

esp

on

ses

0.00 80.00Hz

0.00

0.10

Log

( (m/s

2 )/N)

0.00 80.00LinearHz

0.00 80.00Hz

-180.00

180.00

Phase

°

qppq HH

• 1 row or column 1 row or column suffices to determine suffices to determine modal parametersmodal parameters

• Reciprocity Reciprocity


Experimental Modal AnalysisA Typical Experiment

Vehicle Body TestVehicle Body Test

• F F : 2 inputs: 2 inputs• Indicated by arrowsIndicated by arrows

• X X : 240 outputs: 240 outputs• All nodes in pictureAll nodes in picture

HH has 480 elements has 480 elements

HHFF XX

InputInput SystemSystem OutputOutput

Vertical force

Horizontal force

XX = = HH * * FF


Experimental Modal AnalysisTypical FRFs

IndustrialIndustrial

Gear boxGear box

Vehicle Vehicle SubframeSubframe


Experimental Modal AnalysisTypical FRFs

Engine block Engine block driving point FRFdriving point FRF

Engine block Engine block FRFFRF


Experimental Modal AnalysisAmbient Excitation Tests

Many applications do not allow input/output testsMany applications do not allow input/output tests No possibility to apply inputNo possibility to apply input Typical product loading difficult to realise (non-linear effects)Typical product loading difficult to realise (non-linear effects) Large ambient excitation levels presentLarge ambient excitation levels present

Specific approach:Specific approach: Use output-only data (responses)Use output-only data (responses) Assume white noise excitationAssume white noise excitation Reduce output data to covariances or cross-powersReduce output data to covariances or cross-powers


Experimental Modal AnalysisThe Analysis Process

Modal Analysis: identification of modal model parameters Modal Analysis: identification of modal model parameters from the FRF (or Covariances)from the FRF (or Covariances)

Specific problems:Specific problems: Large number of inputs/outputs, long records (noisy data) Large number of inputs/outputs, long records (noisy data)

Non-simultaneous I/O measurementsNon-simultaneous I/O measurements

High system orders, order truncation, modal overlap High system orders, order truncation, modal overlap

Low system damping (0.1 .. 10%), Large dynamic rangeLow system damping (0.1 .. 10%), Large dynamic range

Specific approach:Specific approach: Simultaneous (“global”) analysis of all reduced (FRF) data Simultaneous (“global”) analysis of all reduced (FRF) data

Order problem: Repeated analysis for increasing orders Order problem: Repeated analysis for increasing orders

-> The stabilisation diagram-> The stabilisation diagram



Experimental Modal Analysis: using FRF measurements in Experimental Modal Analysis: using FRF measurements in a reduced set of structural locationsa reduced set of structural locations


Overview

Introduction: the role of structural dynamics in Mechanical Introduction: the role of structural dynamics in Mechanical

Design EngineeringDesign Engineering

Approach and methodology for structural dynamics analysis: Approach and methodology for structural dynamics analysis:

experimental modal analysisexperimental modal analysis

Modal Parameter Identification methodsModal Parameter Identification methods Usually taking into account the physical modelUsually taking into account the physical model

Use of raw time data exceptional -> reduced FRF modelsUse of raw time data exceptional -> reduced FRF models

Time and frequency domain approachesTime and frequency domain approaches

Industrial and societal applications of modal analysisIndustrial and societal applications of modal analysis




Modal Model Parameter Identification Main Methods

Frequency domain methods: rational polynomial FRF modelFrequency domain methods: rational polynomial FRF model

Nonlinear in the unknownsNonlinear in the unknowns Common denominator methodsCommon denominator methods Partial fraction expansion methodsPartial fraction expansion methods Linearized methodsLinearized methods State space formulations (“Eigensystem Realization”)State space formulations (“Eigensystem Realization”)

M

jjj

N

jjj

A).(

B).(

)(H

0

01

00

]).(][).([)(

M

jjj

N

jjj ABH

*

*1

( )n

k k

k k k

A AH

j j



• Linear frequency domain methodLinear frequency domain method

• Weighted or notWeighted or not

• LS, TLSLS, TLS

• Maximum Likelihood: takes data variance into account -> Non-Maximum Likelihood: takes data variance into account -> Non-linear error formulation -> iterative; Error bounds!!linear error formulation -> iterative; Error bounds!!

• Continuous or discrete frequency domainContinuous or discrete frequency domain• Preferred approach: “PolyMAX”, Least Squares Discrete Preferred approach: “PolyMAX”, Least Squares Discrete

Frequency Domain LS/TLS, originating from VUB.Frequency Domain LS/TLS, originating from VUB.

N

j

M

jjjjj A)()(HB)(

0 0

0



• Time domain: Complex damped exponential approach (UC)Time domain: Complex damped exponential approach (UC)

• Impulse responses or correlations are solutions of the Impulse responses or correlations are solutions of the “characteristic equation”“characteristic equation”

• Poles: found as eigenvalues of [WPoles: found as eigenvalues of [Wii] companion matrix] companion matrix

• Modeshapes: Least-squares fit of FRF matrixModeshapes: Least-squares fit of FRF matrix

m

rr

N

r

Tr

tkr

Tr

tkrk LeLeR

1

** }{}{][*

0...11 ttkkk WRWRIR


• Time domain: Discrete time state space model -> Subspace method • In particular used with output-only data: stochastic subspace

• Estimate [A] and [C] from

• output-only data (KUL…)

• covariances (INRIA):

x A x w

y C x v

k k k

k k k

1

1]][][[][ A

rrt

r ie r r rr C ][




Stabilisation diagram: discrimination of physical poles Stabilisation diagram: discrimination of physical poles versus mathematical/spurious poles -> heuristic approachversus mathematical/spurious poles -> heuristic approach


Overview

Introduction: the role of structural dynamics in Introduction: the role of structural dynamics in


Approach and methodology for structural dynamics Approach and methodology for structural dynamics

analysis: analysis: experimental modal analysisexperimental modal analysis






EMA Example: Aircraft Modal Analysis

• Component DevelopmentComponent Development• Engine, landing gear, ….Engine, landing gear, ….

• Aircraft Ground Vibration TestsAircraft Ground Vibration Tests• Low frequency: 0 … 20… 40 HzLow frequency: 0 … 20… 40 Hz

• > 50 orders, > 250 DOF> 50 orders, > 250 DOF

• Model Validation & updatingModel Validation & updating

• Flutter predictionFlutter prediction


EMA Example: Aircraft Modal Analysis (Dash 8)


EMA Example: Aircraft Modal Analysis for Aeroelasticity (Flutter)

Fre

quen

cy (

Hz)

Dam

ping

(%

)

Airspeed (kts)


EMA Example: Aircraft FE Model Correlation and Updating

FEMFEM

GVTGVT

0

1

2

3

4

5

6

0 1 2 3 4 5

Measured Frequencies [Hz]

An

aly

tic

al F

req

ue

nci

es

[Hz]

FEM

GVT

GVT

FEM EigenfrequencyEigenfrequencycorrelationcorrelation

Mode shapeMode shapeCorrelation (MAC)Correlation (MAC)

Courtesy H. Schaak, Airbus France

+ 5%

- 5%


EMA Example:Business Jet, Wing-Vane In-Flight Excitation

• In-flight excitation, 2 wing-tip vanesIn-flight excitation, 2 wing-tip vanes• 9 responses9 responses• 2 min sine sweep2 min sine sweep• Higher order harmonicsHigher order harmonics• Very noisy dataVery noisy data

4.00 20.00Linear

Hz

0.00

0.10

Lo

g

( g/N)

4.00 20.00LinearHz

Hz

-180.00

180.00

Ph

as

e

°

PolyMAXPolyMAX


In-Operation Modal Analysis Example: PZL-Sokol Helicopter Testing

• Flight tests in different conditions (speed, climbing, hover…)Flight tests in different conditions (speed, climbing, hover…)• 3 flights needed, 90 points3 flights needed, 90 points• Correlation lab. / flight resultsCorrelation lab. / flight results• No problem with rotor frequenciesNo problem with rotor frequencies

SNR GROUND TESTMODE 6.40 Hz

CLIMBING FLIGHT TESTMODE 6.37 Hz

MR-I ODSMR-I ODS 6.4 Hz mode6.4 Hz mode


EMA Example: Car Body and Suspension Tests

• Suspension EMA for a Suspension EMA for a rolling-noise problem : rolling-noise problem : Booming noise at 80HzBooming noise at 80Hz

• Main contribution from Main contribution from rear suspension mountsrear suspension mounts

Body EMA for basic Body EMA for basic bending and torsion bending and torsion analysis (vehicle analysis (vehicle stiffness)stiffness)

25.00 75.00Linear

Hz

0.00

0.13

Lo

g

( (m

/s2

)/N)

25.00 75.00LinearHz

25.00 75.00Hz

-179.96

179.98

Ph

as

e

°


EMA Example:Civil Structures Dynamics

Øresund BridgeØresund Bridge

Input-output Input-output testingtesting

Output-only Output-only testingtesting


Example:Civil Structures - The Vasco da Gama Bridge

In-operation Modal AnalysisIn-operation Modal AnalysisCovariance DrivenCovariance DrivenStochastic SubspaceStochastic Subspace


Overview

Introduction: the role of structural dynamics in Introduction: the role of structural dynamics in


Approach and methodology for structural dynamics Approach and methodology for structural dynamics

analysis: analysis: experimental modal analysisexperimental modal analysis






Industrial Model Analysis: What are the issues and challenges?

• Optimizing the Optimizing the Test processTest process• Large structures (> 1000 points, in operating vehicles…)Large structures (> 1000 points, in operating vehicles…)

– Novel transducers (MEMS, TEDS…)Novel transducers (MEMS, TEDS…)

– Optical measurementsOptical measurements

• Complex structures, novel materials, high and distributed damping Complex structures, novel materials, high and distributed damping (uneven energy distribution)(uneven energy distribution)

– Multiple excitation (MIMO Tests)Multiple excitation (MIMO Tests)

– Use of a priori information for experiment designUse of a priori information for experiment design

– Nonlinearity checks, non-linear model detection and Nonlinearity checks, non-linear model detection and identificationidentification

– Excitation Design: Get maximal information in minimal timeExcitation Design: Get maximal information in minimal time



• Optimizing the Optimizing the Analysis processAnalysis process• High model orders, numerical stabilityHigh model orders, numerical stability

• Discrimination between physical and “mathematical” poles Discrimination between physical and “mathematical” poles

• Automated modal analysisAutomated modal analysis

• Test and analysis duration and complexityTest and analysis duration and complexity

• Test-right-first-time Test-right-first-time

• Support user interaction with “smart results”Support user interaction with “smart results”

• Automating as much as possible the whole processAutomating as much as possible the whole process

• Quantifying data and result uncertaintyQuantifying data and result uncertainty

-> -> bring intelligence in the test and analysis processbring intelligence in the test and analysis process


1

x2

x1

hid1 hid2

2

x2

Automatic Assessment and Classification of FRF Quality and PlausibilityAutomatic Assessment and Classification of FRF Quality and Plausibility

Innovation and Challenges:Data Quality Assessment

2.00 30.00Hz

0.00

1.00

Am

plitu

de/

F Coherence lfw :38:-Z/MultipleF Coherence rgw :38:-Z/Multiple

Coherence analysis (225 spectral lines X 540 DOFs)Coherence analysis (225 spectral lines X 540 DOFs)


Uncertainty and Reliability: A Research Context

• Methods to assess uncertainty and variability of CAE models:Methods to assess uncertainty and variability of CAE models:• Input distribution -> response distributionInput distribution -> response distribution

• Fuzzy-FE, transformation method, Monte-Carlo…Fuzzy-FE, transformation method, Monte-Carlo…

• Robust design and reliability considerationsRobust design and reliability considerations

• What about test data confidence limits?What about test data confidence limits?

ININ

OUTOUT

Uncertainty in front craddleUncertainty in front craddle• Young’s modulus (190-210 GPa)Young’s modulus (190-210 GPa)• mass density (7600-8000 kg/mmass density (7600-8000 kg/m33))• shell thickness (1.6-2.4 mm)shell thickness (1.6-2.4 mm)


• Mimic the human operator (rules, implicit -> NN)?Mimic the human operator (rules, implicit -> NN)?• Iterative methods (MLE)Iterative methods (MLE)• Fundamental issue: Fundamental issue: discriminate mathematical and physical polesdiscriminate mathematical and physical poles

• Indicators (damping value, p-z cancellation or correlation…)Indicators (damping value, p-z cancellation or correlation…)• Fast stabilizing estimation methodsFast stabilizing estimation methods• Clustering techniquesClustering techniques

Innovation and Challenges:Automating Modal Parameter Estimation

PolyMAXPolyMAX



• Novel applicationsNovel applications

• Combined Ambient – I/O testing Combined Ambient – I/O testing

• Nonlinear system detection and identificationNonlinear system detection and identification

• Build system-level models combining EMA and FE models Build system-level models combining EMA and FE models

• Vibro-acoustic modal analysis: include cavity modelsVibro-acoustic modal analysis: include cavity models

• Mechatronic and control Mechatronic and control

• End-of-line controlEnd-of-line control

• Model-based monitoringModel-based monitoring

• ……....

Healthy structureHealthy structure Damaged structureDamaged structure

22ndnd mode shape mode shape


HSS

Engine MountsEngine Mounts BushingsBushings

Subframe Subframe & & CrossmemberCrossmember

Body Body Vibro-acousticsVibro-acoustics

Engine Engine & & BracketsBrackets

HybridSystemSynthesis

Innovative Applications: Building Hybrid System Models


• Acoustic resonances, coupled structural-acoustical Acoustic resonances, coupled structural-acoustical behaviour can be modelled by vibro-acoustic modal modelsbehaviour can be modelled by vibro-acoustic modal models

K K

K

x

pj

C

C

x

p

M

M M

x

p

f

pq

S C

f

S

f

S

cf

0

0

0

02

Innovative Applications: Vibro-Acoustic Modal Analysis

• Excitation by shakers and Excitation by shakers and loudspeakers -> Balancing of test loudspeakers -> Balancing of test data needed (p/f, x/f, p/Q, x/Q)data needed (p/f, x/f, p/Q, x/Q)

• Non-symmetrical modal modelNon-symmetrical modal model• Through structural acoustic Through structural acoustic

couplingcoupling

• Different right and left Different right and left eigenvectorseigenvectors


f = 32.9f = 32.9 Hz Hz = 8.5= 8.5%%

Vibro-Acoustic Modal AnalysisExample: Aircraft Interior Noise

f = 78.3f = 78.3 Hz Hz = 7.0= 7.0%%

ATR42ATR42

F100F100


Summary and Outlook

• Early product optimization is essential to meet market demandsEarly product optimization is essential to meet market demands

• Mechanical Design Analysis and Optimization heavily rely on Mechanical Design Analysis and Optimization heavily rely on Structural ModelsStructural Models

• Experimental Modal Analysis is the key approach, it is a de-facto Experimental Modal Analysis is the key approach, it is a de-facto standard in many industriesstandard in many industries

• While EMA is in essence a system identification problem, While EMA is in essence a system identification problem, particular test and analysis issues arise due to model size and particular test and analysis issues arise due to model size and complexitycomplexity

• Important challenges are related to supporting the industrial Important challenges are related to supporting the industrial demands (test time and accuracy) and novel applicationsdemands (test time and accuracy) and novel applications

• Research efforts should Research efforts should alsoalso pay attention to “state-of-the-use” pay attention to “state-of-the-use” breakthroughsbreakthroughs

herman van der auweraer scores workshop leuven, 12-10-2004

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