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Model order reduction. A new paradigm for efficient design of materials, structures and processes Francisco (Paco) Chinesta ESI/EADS Chairs @ Ecole Centrale Nantes Institut Universitaire de France Francisco.Chinesta @ec-nantes.fr Real Academia de la Ingeniería de España, 28 Octubre 2014

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Page 1: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Model order reduction. A new paradigm for efficient design of

materials, structures and processes

Francisco (Paco) ChinestaESI/EADS Chairs @ Ecole Centrale Nantes

Institut Universitaire de France [email protected]

Real Academia de la Ingeniería de España, 28 Octubre 2014

mailto:[email protected]
Page 2: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

The present

The dream

Page 3: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Model

• Material parameters:• Geometrical parameters:• Applied loads:

Quantities of interest:

Offline static simulation …

U(x,t)

Page 4: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

When all “possible” solutions have been pre-calculated !!

Page 5: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 6: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Towards modern vademecum …

Page 7: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Model

• Material parameters:• Geometrical parameters:• Applied loads:

U(x,t;M1,L ,Mm,G1,L ,Gg,L1,L ,Ll )

Parametric solution

Page 8: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

It’s nice BUT

we cannot pre-compute the solution for any possible scenario

because the number of them increases exponentially !!!

Page 9: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Alternative route :

Advanced Model Order Reduction

Page 10: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

u

t k

2u

x2 S

u(t,x;k)

Parametric modeling

The issue: u(t,x,k) 3D

2D

u

t k

2u

x2 S

PGD : parameters as

extra-coordinates

Page 11: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Optimization & Inverse identification

u(t,x,k)

du

dk(t,x,k) is explicitly available

Page 12: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Stochastic modeling becomes a simple

matter

u(t

g,x

g,k)

k

u x

g,t

g

k

n

u(t,x,k)

Page 13: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

It’s nice, BUT parametric problems becomes highly

multidimensional

u(x,t,k) Xi(x) T

i(t) K

i(k)

i1

N

Page 14: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

u1(x,t,k) X

1(x) T

1(t) K

1(k)

X

1(x)T

1(t), K

1(k)

T

1(t) X

1(x), K

1(k)

K

1(k) X

1(x),T

1(t)

u2(x,t,k) X

1(x) T

1(t) K

1(k) X

2(x) T

2(t) K

2(k)

Page 15: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 16: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Applications

Page 17: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

y

u x,y,p

p

x9D

uj

x,y,p Xi

jx

i1

iN

Yi

jy Pi

jp

Real time in haptic devices

Page 18: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

u x,y,p

Page 19: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 20: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 21: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

21

Cutting

Page 22: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Real time contact

u(x,p,y)

(x; (p,y))

Page 23: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 24: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Process optimization : ATPAutomated tape placement

ARIANE 6 cryogenic tank

Page 25: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

u(x,y,z,t,h1,h2,h3,Q,v,o1,o2,L )

Page 26: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 27: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 28: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Process simulation : Welding

Page 29: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Process control : Machining

Page 30: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 31: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

um(x,a

ij,b

ij,L ) X

k

m(x) Ak

m,ij (aij)

ij

k1

n

Bk

m,ij (bij)

ij

K

ij

0 aij b

ij z c

ij z2 L

Page 32: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

LaserTool

Page 33: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 34: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

The main ingredients of our approach

I – Parameters are considered as extra-

coordinates:

Model parameters

Initial conditions

Boundary conditions

Geometrical parameters …

II – The offline solution of the multidimensional

model by using the PGD (separation of variables)

defines the computational “vademecum”

III – The vademecum can be used online for real

time simulation, optimization and control purposes.

Page 35: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Breve trayectoria y

agradecimientos

Page 36: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 37: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 38: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 39: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 40: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 41: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 42: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Hombre de ciencia

Page 43: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Co

no

cim

ien

tos

Page 44: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

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Page 45: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

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Page 46: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Co

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Hu

mild

ad

Page 47: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Co

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Esfu

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oyo

Hu

mild

ad

Page 48: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Med

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Page 49: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Med

ios

Page 50: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Med

ios

Page 51: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 52: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Co

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Ap

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Med

ios

Creatividad, originalidad, innovación, inspiración, ….

Page 53: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 54: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 55: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 56: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 57: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 58: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible
Page 59: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Gracias

Page 60: Model order reduction. A new paradigm for efficient design ...1,L , M m, G 1,L , G g, L 1,L , L l) Parametric solution. It’s nice BUT we cannot pre-compute the solution for any possible

Merci

par ce moment


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