On the Fundamental Tautology of Validating Data-Driven ... · electric field, and magnetic induction of the material points of a body are self-evident and observable in any thermoelectromechanical

5/18/2005 ICCS-05 1

On the Fundamental Tautology of ValidatingData-Driven Models and Simulations

John Michopoulos & Sam Lambrakos Naval Research Laboratory

Materials Science and Technology DivisionWashington DC, 20375, USA

[email protected]

International Conference on Computational Sciences 2005 Atlanta, GA USA,, 22-25 May 2005

This material is based upon work supported by the National Science Foundation under Grant No. ITR-0205663

5/18/2005 ICCS-05 2

OUTLINE

• Motivational Aspects• Qualification Verification Validation In general• “Embedded Validation”• Epistemological Aspects• Example• Conclusions

5/18/2005 ICCS-05 3

Motivational Aspects

Answer Some Questions for systems where BOTH input and output are measurable:

Are data-driven modeling and simulation practices equivalent to the non data-driven (or model driven) practices the same from the QV&V perspective?

Do data-driven models require validation in the model-driven modeling sense?

5/18/2005 ICCS-05 4

Term Definitions

Modeling: Establishing, a conceptual (analytical, mathematical) and computational (discretization, algorithmic, programmatic, visualization) representation of the system such that its behavior is the same with that of the actual physical system.Simulation: Generating predictive behavior of the system through exercising the a previously established model of the system.Model-Driven: Modeling uses some a priori concept of how the system works from an inside-out perspective (Bottom-Up)Data-Driven: Modeling uses only behavioral data and ignores internal composition (Top-Down)

5/18/2005 ICCS-05 5

System-Model-Behavior

System External Appearance Behavior AppearanceInternal Appearance

Phys

ical

Wor

ldCo

ncep

tual

Wor

ld

Hybrid 10 Load versus StrokeOpen Hole, Net Tension

-20

0

20

40

60

80

100

120

140

160

180

200

0 1 2 3 4 5 6

Stroke (mm)

Load

(kN)

Modeled System

?

P

P

δ

Physical System

Hybrid 10 Load versus StrokeOpen Hole, Net Tension

-20

0

20

40

60

80

100

120

140

160

180

200

0 1 2 3 4 5 6

Stroke (mm)

Load

(kN)

)(PδP δ )(δP

0),( =δPRPδ

5/18/2005 ICCS-05 6

MODELING A MULTIPHYSICS SYSTEM

Homogeneous SystemHomogeneous Fieldsi.e. Deformable Media

Multiple SystemHomogeneous Fieldsi.e. Deformable Media

In contact

Homogeneous System

Multiple Fieldsi.e. Electro-Thermo-

elastic Media

Multiple SystemMultiple Fields

i.e. Thermoelasticmedia

In Fluids

FieldCardinality

Multiple DomainsOne Domain

One

Fie

ldM

ultip

le F

ield

s

DomainCardinality

aV∂

aV

bV∂

bV

2aΓ

3aΓ

1bΓ

1aΓ

2bΓ

kp

lp

kq

lq

bkp

nI mOPhysical system

Analytical model

mFnJ mP

Obs.-Math. Op. Obs.-Math. Op.

nJ mPComputational

model

mCF

Math.+Coding. Op. Math.+ Coding. Op.

nJ mPVisualization

model

mDF

Discr.+Coding Op. Discr.+Coding Op.

MO

DELIN

G

SIMU

LATIO

N

5/18/2005 ICCS-05 7


I O

mmnnmn

OIOI ℜ⊆ℜ⊆→ ,,:~ F Behavior Functional relating the output to the inputs of the system.

p r

0)~,~,~( =pq ξR Relational restriction over dependent, independent, parameter variables.

)~,~ ~ ~ pq p ξ(Ξ∇= Vector Function Storage Mechanism:Potential or Energy Density function.

0,...)~ ,~( =

∂∂

∇ℵ qt

q mm

n

i Composition Behavior through Conservation Law Relations: Dependence, of dependent variables on position in the structure, and time.

Structuralstate

engine

)~,~~~ pq ξ(C= Bulk Constitutive Relations:Functional dependence, of dependentvariables on independent variablesand parameters.

Bulkstate

engine q

~ )~,~~~ εεξσ ⋅= (C

5/18/2005 ICCS-05 8


Methodologies for Developing Potential Functions

Potential Function

Lagrangean/Hamiltonian Thermodynamic

Equilibrium Non-Equilibrium

Compensating Fields Internal Variables

5/18/2005 ICCS-05 9


Model driven coupled field methodology

Is # of equations >from # of variable pairs

Consider theoretical physicalsystem characteristics

& define state parameters

Define dependent &independent variable pairs

Employ conservation laws

Postulate constitutiveequations

Employ additional axioms

Rewrite previous restrictions to field eqtns.

Define BV problem forgiven structure

Solve field equations

Evaluate & Display resultsSimulate system response

Determine material properties constants

yes

no

Keep and Stop

Validated?

yes

no

5/18/2005 ICCS-05 10


AXIOMS OF CONSTITUTIVE BEHAVIOR DERIVATION PROCESSAxiom (I) Causality: The motion, temperature, electric field, and magnetic induction of the material points of a body are self-evident and observable in any thermoelectromechanical behavior of a body. The remaining quantities (other than those derivable from the motion, temperature, electric field, and magnetic induction) excluding the body force, energy supply, and free charge density that enter the balance laws and the entropy inequality, are the dependent variables.

Axiom (II) Determinism: The value of any depen-dent variable, at material point X of the body B at time t, is determined by the history of all material points of B.

Axiom (III) Equipresence: At the outset, all constitutive response functionals are to be considered to depend on the same list of constitutive variables, until the contrary is deduced.

Axiom (IV) Objectivity: The constitutive response functionals are form-invariant under arbitrary rigid motions of the spatial frame of reference and a constant shift of the origin of time.

Axiom (V) Time Reversal: The entropy product-ion must be nonnegative under time reversal.

Axiom (VI) Material Invariance: The constitutive response functionals must be form-invariant with respect to a group of transformations of the material frame of reference {X ---> X } and "microscopic time reversal" as {t ---> -t } representing the material symmetry conditions. These transformations must leave the density and charge at { X, t } unchanged.

Axiom (VII) Neighborhood: The values of the response functionals at X are not affected appreciably by the values of the independent constitutive variables at distant points from X.

Axiom (VIII) Memory: The values of the constitutive variables, at a distant past from the present, do not affect appreciably the values of the constitutive response functionals at present.

Axiom (IX) Admissibility: Constitutive equations must be consistent with the balance laws and the entropy inequality.

5/18/2005 ICCS-05 11


MAIN SCIENTIFIC CHALLENGES OF MODEL DRIVEN APPROACH• Impossible Uncoupled Experiments for Coupling coefficients

Determination?EXAMPLE: Isotropic Nonlinear Electromagnetic Solids. Two of the 20 apriori

derived constitutive relations for the spatial vectors for heat and current define some of the known “effects”:

• Potentially NON TERMINATING

Thermal conductivity

Ohm’s effect

Peltier’s effect

Seebeck’s effect

Anisotropic Peltier’s effect

Righi-Leduc’s effect Ettinghaussen’seffect

Anisotropic Seebeck’s effect

Hall’s effect Nerst’s effect

]~)~()~(~[]~)~~()~~(~[

~)~(~)~~(~~~

~~~~~~~~

1112

1111

1092

82

7

651

41

321

BTeBTeBEeBEe

BTBBEBTeEe

BTBETeEeTEJ

×∇−×∇+×−×+

∇⋅+⋅+∇++

×∇+×+∇++∇+=

−−−−

−−

−−

λλ

λλλλ

λλλλλλ

]~)~~()~~(~[]~)~()~(~[

~)~~(~)~(~~~

~~~~~~~~

1112

1111

1092

82

7

651

41

321

BEeBEeBTeBTe

BEBBTBEeTe

BEBTEeTeETq

×−×+×∇−×∇+

⋅+∇⋅++∇+

×+×∇++∇++∇=

−−−−

−−

−−

κκ

κκκκ

κκκκκκ

5/18/2005 ICCS-05 12


Data driven Modeling methodology

Consider state parameters

Define dependent &independent variable sets

Add detail by employing conservation laws

Generate constitutive lawsand field equations

Define BV problem forgiven structure

Solve field equations

Evaluate & Display resultsSimulate system response

Keep and Stop

Experimentally Collectinput/output pairs

Define relation between i/o pairs trough potential

function(s) with free coefficients

Construct & solve over-determined system of equations

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QV&V Definitions

Intersecting definitions according to AIAA, DMSO, ASME, DOE/DP-ASCI

• Qualification: determination that a conceptual model implementation represents correctly a real physical system.

• Verification: determination that a computational model implementation represents correctly a conceptual model of the physical system.

• Validation: determination of the degree to which a computer model is an accurate representation of the real physical system from the perspective of the intended uses of the model.

5/18/2005 ICCS-05 14

Model-Driven Approach for Q&VV

Expe

rim

enta

tion

Physical Behavior

(data)

ACTUAL PHYSICAL SYSTEM

ANALYTICAL SYSTEM MODEL

COMPUTATIONAL SYSTEM MODEL

Programming

PrototypingAnalysis

Simulated Behavior

(data)Simulation

verification test

no: -> readjust

qualification test (=) no: -

>adapt

validation test (=)no: -

>adapt

Simulated Behavior

(data)Simulation

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General Optimization Approach

EXPERIMENTATION

SIMULATION

System Model

Physical System

OPTIMIZATION

PhysicalBehavior

SimulatedBehavior

closeenough?

Modify designvariables

Final designvariables

yes

no

5/18/2005 ICCS-05 16

Data-Driven Approach for Q&VV

Expe

rim

enta

tion

Physical Behavior

(data)




Programming

PrototypingAnalysis

Simulated Behavior

(data)Simulation

verification test

no: -> readjust

qualification test (=) no: -

>adapt

Simulated Behavior

(data)Simulation

5/18/2005 ICCS-05 17

EPISTEMOLOGICAL BACKGROUND

Identify Observables

Collect Control andBehavior Facts

Formulate Theory T torepresent these facts

inductively

Use T to predictunobserved behavior with

certainty

Industrialized-InductiveScientific Method

PhysicalWorld

ConceptualWorldfrom from

in

Make some observations

Make Hypothesis H

Formulate Theory T

Use logic to deducepredicted observation O

Do experiment to observeO or ~O

~O isobserved

H or T is falsified(Popper)

O isobserved

true

H under T is confirmed(Hempel)

false

OR

true

Use T with noconfidence

Use T with lowconfidence

Strong Approach Weak Approach

Hypothetico-deductive Scientific Method

false

Hypothetico-deductive(rationalist)

inductive(empiricist)

Hypothetico-deductive

Industrializedinductive

LogicalPositivism

1800s 1920-30 Today

Scientific Method Evolution

5/18/2005 ICCS-05 18

EXAMPLE: IONIC POLYMER COMPOSITE ARTIFICIAL MUSCLES

5/18/2005 ICCS-05 19

Ionic Polymer Metal Composite (IPMC) Large Deflection PlatesNon-linear electro-elasto-dynamic field PDEs:

For Electric and Mechanical activation onlywithout mass transport:

2 2 2,22 ,11 ,12 ,12 ,11 ,22

2 2 2 2,12 ,11 ,22

2 20

(1 ) ( 2 ),

[( ) ]1 2{ }

k k

k k

i k k c

h qw p E F w F w F wN h

F Ep E E w w w

V p F p EEh

ν

νε ρ

∇ ∇ − + ∇ = + − +

∇ ∇ − ∇ = −

−∇ + ∇ − =

or equivalently:2 2 2

1 ,22 ,11 ,12 ,12 ,11 ,22

2 2 2 22 ,12 ,11 ,22

2 2 23 4 5

( 2 ),

[( ) ]

0

h qw c V F w F w F wN h

F c V E w w w

V c F c V c

∇ ∇ − ∇ = + − +

∇ ∇ − ∇ = −

∇ + ∇ ∇ + + =

5/18/2005 ICCS-05 20

IPMC Large Deflection Plates: Parameter Identification

Multi-Objective Function Optimization2 2 2

1 1 1min ( ) min{ [ ( ) ] [ ( ) ] [ ( ) ] }

subject to constrains:

where: , , are the experimentally observed state variables a

n n no s e s e s e

j i j i i j i i j ii i i

u lj j j

e e ei i i

f c w c w F c F V c V

t c t

w F V

= = =

= − + − + −

≥ ≥

∑ ∑ ∑

t each point

( ), ( ), ( ) are the simulated state variables at each point

are the uknown constants to be identified

, are the upper and lowe

s s si j i j i j

j

u lj j

i

w c F c V c i

c

t t r limits constraining each uknown j

To fully characterize ci we need a family of experiments that sweeps across boundary values of w, F, V and measuresthem on a grid superimposed on the domain of the plate

5/18/2005 ICCS-05 21

IPMC Large Deflection Plates: Experimental Results (M. Shahinpoor UNM)

Voltage, Displacement vs. Time of IPMC plate

-0.1

0

0.1

0 2 4 6

Time (s)

Volta

ge (1

00v)

, D

ispl

acem

ent

(mm

)

Voltage Displacement

Voltage vs. Displacement of an IPMC plate (40mm x 40mm x 0.21mm)

012345678

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Displacement (mm)

Vol

tage

(v)

5/18/2005 ICCS-05 22

IPMC Large Deflection Plates: Biharmonic Single-Field Bases

4 41

6 2 2 2 2 21 1

16 (2 ) (2 )( , ) sin sin( ) 2 2

s

m n

q a b m x a m y bw x yD mn b m a n a b

π ππ

∞ ∞

= =

+ +=

+∑∑4 ( 1) / 2

25 5

1,3,5,...

tanh 24 ( 1)( , ) cos (1 cosh2cosh

1 sinh )2cosh

2

ms m m

m m

m

m

qa m x m yw x yD m a a

m y m ya a

m ba

α απ ππ α

π πα

πα

−∞

=

+−= − +

+

=

∑

(1,2)where: ( , ) single-field plate deflection at point ( , ) ( , ) mechanical load distribution on the plate Flexural rigility of the plate , length and wi

sw x y x yq q x yDa b

==

dth of the plate along x and y axes

5/18/2005 ICCS-05 23

IPMC Large Deflection Plates: Comparison (1)

Deflection Time Histories in 3D carpet plots

EXPERIMENT COMPUTED

5/18/2005 ICCS-05 24

IPMC Large Deflection Plates: Comparison (2)

Deflection Time Histories in Contour plots

EXPERIMENT COMPUTED

5/18/2005 ICCS-05 25

Conclusions

• Data driven models and simulations contain validation

• Model-driven models have epistemologicorigins

• When data exist “data-driven” is preferable

5/18/2005 ICCS-05 26

THANK YOU FOR YOUR ATTENTIONQUESTIONS?

5/18/2005 ICCS-05 27

Data-Driven Approach: ExampleIdentify material from small specimens to predict behavior of large system

Data Driven Composite Materials & Structures WorkbenchData Driven Composite Materials & Structures Workbench

1.0”

0.5”

0.5”

0.5”

0.6”

0.04”

0.1”

grip area

grip area

?

MaterialCharacterization

MaterialCharacterization

Material/StructuralComposition

Material/StructuralComposition

Material/StructuralBehavior Simulation

Material/StructuralBehavior Simulation

SpecimenTesting

SpecimenTesting

5/18/2005 ICCS-05 28

MECHATRONICALLY AUTOMATED APPROACH: Overview

General Case:3 displacements + 3 rotations + 3 forces + 3 moments + Np x 3 strains + Np x Nf = 12+ (3+Nf)xNp Datastreams

u0

u1

u2

u0

u1

u2

p1

p2

p3

p4

p5

p6

p7

p8

p9

p10

p11

p12

p13

p14

p15

u0

u1

u2

p1

p2

p3

p4

p5

p6

p7

p8

p9

p10

p11

p12

p13

p14

p15

p1

p2

p3

p4

p5

p6

p7

p8

p9

p10

p11

p12

p13

p14

p15

u0

u1

u2

p1

p2

p3

p4

p5

p6

p7

p8

p9

p10

p11

p12

p13

p14

p15p11

Θ2

Θ1

NRL’s Automated 6-D Loader

Specimen Special Case:2 displacements + 1 rotation=3DOFs=6Datastreams

5/18/2005 ICCS-05 29

Approach

Data driven methodology for PMCs: Data Collection

Hexcel Rd5129, (+/-15), path 2Pure Opening

HexcelRd5129pc 815,- 15<, Load case ;2

-0.002-0.001 00.001d1

-0.03

-0.02

-0.01

0

d2

00.00050.001

0.00150.002d3

-0.002-0.001 00.001d1

u0u1

u2

HexcelRd5129pc 815,- 15<, Load case ;2

-1001020

f1

-1500

-1000

-500

0

f2

0

200

400

f3

-1001020

f1

-1500

-1000

-500

0

f2

f0f1

f2

0.005 0.01 0.015 0.02 0.025 0.03 0.035disp

250

500

750

1000

1250

1500

f HexcelRd5129pc 815,- 15<, Load case ;2

u

f

5/18/2005 ICCS-05 30

Approach

-2

0

2

0 0.005 0.01 0.015 0.02-500050010001500

-500050010001500

1350-1350-1800 1800

Θ2

Θ1

r

900

900

-900

-900 450

450

-450

-450

00

2 5 8 11 1458 811

Data driven methodology for PMCs: Data Reduction

r

f

Θ1

5/18/2005 ICCS-05 31

Approach

Data driven methodology for PMCs: Data Reduction

-0.01

0

0.01 x

-0.01

0

0.01

y0

1000

2000

3000

4000

f@x, yD0

1000

2000

3000

4000

f@x, yD

u0

u1

f-0.02

-0.01

0

0.01

0.02

-0.02-0.01

00.01

0.02

-500050010001500

-0.02

-0.01

0

0.01

0.02u1

u0

Load

-0.02

-0.01

0

0.01

0.02

-0.02-0.01

00.01

0.02

0

50000

100000

-0.02

-0.01

0

0.01

0.02u1

u0

Stiffness

-0.02

-0.01

0

0.01

0.02

-0.02-0.01

00.01

0.02

0510

15

-0.02

-0.01

0

0.01

0.02u1

u0

Dissipated energy

5/18/2005 ICCS-05 32

MECHATRONICALLY AUTOMATED APPROACH: Inverse Model

u0

u1

u2

t0

t1

t2n discrete elements

)~()())~(~( ~~)~,~ εχεχεφ ii mcxcc =⋅=(

Energy Balance: jjV

iv

tsv

v

u

u dxxuutdqqtr ))(( 21

0 ∫∫ =−∂

εφ

General Problem: Build a function out of knowing some of its values trough a collocation method

kkk VD φ=Total DE in

element k of n

∑ ∫=

=n

kjj

Vikk dxxV

1

))(( ∂

εφφ

Total DE inwhole structure

εr

εθ

εφ

Strain Space125,,2,1,for

,0 ,1

)~( …=

⎭⎬⎫

⎩⎨⎧

≠=

= ji

jiji

ji εχ

εθ εφ

χ

εθ εφ

χ

εθ εφ

χ

εθ εφ

χ

εθ εφ

χ)(0)(0)~

)~()(1)()~()()~ 11

mcmc

mcmcmc

iii

immiii

=++++=

++++=

……

……

εφ

εχεχεφ(

(

5/18/2005 ICCS-05 33

MECHATRONICALLY AUTOMATED APPROACH:Optimization

jjV

iv

tsv

v

u

u dxxuutdqqtr ))(( 21

0 ∫∫ =−∂

εφ

[ ] 0~ ≥cM

DED monotonicity: 100 additional constrains

pp

e

ep

ep

ii DeVmc =+∑=110

1

)~()( εχFor a loading point p:

Final Problem: Minimize subject to

e~ [ ] 0~ ≥cMUsing 17 points per loading pathgenerates 255 loading points leading to 255 equations for 125 unknowns

[ ] decX ~~~ =+For all selected loading points:

Solution Method: Least Squares with Linear Constrains

5/18/2005 ICCS-05 34

MECHATRONICALLY AUTOMATED APPROACH:Simulation Synthesis

Pr. JGM 13

UTILIZATION OF BASIS LOADING CASES RESPONSE THROUGH LINEAR COMBINATION OF RESULTING STRAIN FIELDS

a a axx

yy

xy sliding

xx

yy

xy open close

xx

yy

xy bending

0 1 2

~~~

~~~

~~~

/

εεε

εεε

εεε

⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪

+

⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪

+

⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪

u0

u1

u2

a1

a2

a0

~ ~ ~ ~u a u a u a up = + +0 0 1 1 2 2

~up

Compute Dissipated EnergyDensity Distribution

bending basis case

opening/sliding basis case

sliding basis case

u0

~~~

εεε

xx

yy

xy sliding

⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪

u1~~~

/

εεε

xx

yy

xy open close

⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪

~~~

εεε

xx

yy

xy bending

⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪

u2

5/18/2005 ICCS-05 35

MECHATRONICALLY AUTOMATED APPROACH:Simulation Synthesis

u0

u1

u2

(opening)

(bending)

(shearing)

5/18/2005 ICCS-05 36

Approach

Data driven methodology for PMCs: Material Characterization

SpecimenManufacturing

SpecimenManufacturing

Material, Geometry,Loading Spec.

Material, Geometry,Loading Spec.

Strain FieldDetermination

Strain FieldDetermination

SpecimenSpecimen

Strain FieldsStrain Fields

Multi-dTesting

Multi-dTesting

Analytic DEDDetermination

Analytic DEDDetermination

Minimize Difference|Meas.-Anal.|DE

Minimize Difference|Meas.-Anal.|DE

Derivation ofMeasured DED

Derivation ofMeasured DEDMeasured Boundary

Displ. & Loads

Measured BoundaryDispl. & Loads

Measured DEMeasured DE

Set of Analytic DEsSet of Analytic DEs

Actual DEDActual DED

5/18/2005 ICCS-05 37

How - ApproachSTRUCTURAL SYSTEM IDENTIFICATION-CHARACTERIZATION

)()()()( .. δψδδδδ +=+== mPPPP irecrec

)~(~~)~( ucu χψ ⋅=

∫∫∂

⋅+=V

kjjkiii uducmduuPi ~)~(~)(21)(

0χδδ

δ

iiij bcA =

)()()( .. δδ

δδ

δδ irecrectotal W

ddW

ddW

dd

+=

1-D Load Space Partitioned Model of Behavior

∫∫∂

+=V

kjjkiii udumduuPi ~)~()(21)(

0ψδδ

δ

n-D Load Space Partitioned Model of Behavior

duumduuP ∫∫ +=δδψδδ

00)()(

21)(

)()()( .. δδδ irecrectotal WWW +=

5/18/2005 ICCS-05 38

How - Approach:GENERAL CONTINUOUM SYSTEMS MODELING

Data driven methodology for PMCs

AXIOMS OF ENRICHMENT

• All state variables are varying in a locally flat fashion both in space and time (continuity)

• The behavior of the whole structure is equivalent to the composition of the behaviors of structural discretization units (composition behavior)

• The observed behavior is repeatable when observed under identical conditions in various times (first order of reality)

ASSUMPTIONS

• Loading is either static or slowly varying• The material behavior will be non-viscous, and independent of rate and load history• The constitutive relation is continuous both in input and output variables• Deformations are sufficiently small so that the infinitesimal stress and strain tensors may be

employed

5/18/2005 ICCS-05 39


I O

mmnnmn

OIOI ℜ⊆ℜ⊆→ ,,:~ F Behavior Functional relating the output to the inputs of the system.

p r

0)~,~,~( =pq ξR Relational restriction over dependent, independent, parameter variables.

0,...)~ ,~( =

∂∂

∇ℵ qt

q mm

n

i Composition Behavior through Conservation Law Relations: Dependence, of dependent variables on position in the structure, and time.

Structuralstate

engine

)~,~~~ pq ξ(C= Bulk Constitutive Relations:Functional dependence, of dependentvariables on independent variablesand parameters.

Bulkstate

engine q

~ )~,~~~ εεξσ ⋅= (C


5/18/2005 ICCS-05 40


Data driven Modeling methodology


)~,~ )~,~)~,~ ppp ξϕξξ ((( +Φ=Ξ Additivity of recoverable and non-recoverable components.

ppqp ~)~(~2

1)~,~ ⋅=Φ ξ(

Recoverable energy definition.

))~(~,~( ~~)~,~ xpcp ξχξϕ ⋅=(

Non-recoverable energy definition.

5/18/2005 ICCS-05 41

Expe

rim

enta

tion

Traditional vs. Data-Driven Approach of Q&VV




Programming

PrototypingAnalysis

Physical Behavior

(data)

Simulated Behavior

(data)

Simulated Behavior

(data)

validation test (=)

verification test

qualification test (=)

Simulation

no: -> readjustno: -

>adapt

no: ->

adapt

Simulation

DATA DRIVEN INVERSEMODELING ENCAPSULATION

DATA DRIVEN CODEGENERATION

5/18/2005 ICCS-05 42

Data-Driven System Identification and Simulation

Simulator

Physical system

System Model

Optimizer

ExperimentalFRAME

System Model

Sensor or DesignFRAME

5/18/2005 ICCS-05 43


CONCEPTUAL SYSTEM MODEL


Programming

SimulationAnalysis

Physical Behavior

(data)

Simulated Behavior

(data)

Simulated Behavior

(data)

validation test (=)

Experimentation

Pred

ictio

n

Prediction

no: ->

adapt

DATA DRIVEN CONCEPTUAL SYSTEM MODEL

Documents

On the Fundamental Tautology of Validating Data-Driven ... · electric field, and magnetic induction of the material points of a body are self-evident and observable in any thermoelectromechanical