Fast, parametric, reduced models for biomechanics design ......2016/06/17 · Fast, parametric,...

Kambiz Kayvantash Scientific Director of CADLMMassy, [email protected]

1

Sandrine Le CorreModeling specialistMassy, [email protected]

Dorian SalinManager Engineering and biomechanicsMarseille, [email protected]

Amadou-Tidiane ThiamData scientistMassy, [email protected]

www.cadlm.com

Fast, parametric, reduced models for biomechanics

design applications

mailto:[email protected]




Initial velocity: 56 km/h = 15,56 m/s = 1.556 E+4mm/s

Vehicle mass + dummy = 600Kg = 0.6T

United system: T / mm / s / MPa / mJ / °c

TARGET:

Reduce an FE model to a real-time function

HOW?

Use Reduced modelling technique based on POD (Proper Orthogonal Decomposition)

WHY?

Allows for fast, parametric reduced models for optimization single-click evaluations, on-board computing, etc.

Fast, parametric, reduced models for biomechanics design applications»

CONTEXT – Model reduction for parametric or real-time studies

2

Test with of FEmodel of sled with a

dummy

• Model Reduction Techniques (MRT) are algebraic approximation solutions allowing for fast (real-time) interpolations (reconstructions) or extrapolations (predictions), based on previously existing DOE-type results, obtained either from FE computations, or from constructions of reduced FE solutions or directly from experimental data.

POD (Proper Orthogonal Decomposition):

• Unlike response surface methods where smoothed solutions on certain criteria are obtained, MRT's provide complete solutions (reconstructions) of the space-time response of the original differential equation. They are based on a decomposition of spatial and time domains:

F(x , t) = G(x) . H(t)

3


Model reduction for parametric or real-time studies

4


CREATE THE DATABASE : INPUT DATA PRESENTED

Parameters 1 & 2 : the slopes represent decreasing speed of the vehicle

Parameter 3 : variation of multiplier generating different airbag mass flow rate

slope A = parameter 1

slope B = parameter 2Coefficient = parameter 3

INPUT DATASlope A of the speed

parameter 1Slope B of the speed

parameter 2multiplier of the flow rate

parameter 3

Modele M1 122285 83559 0.9

Modele M2 122285 83559 1

Modele M3 122285 83559 1.1

Modele M4 179679 88704 0.9

Modele M5 179679 88704 1

Modele M6 179679 88704 1.1

Modele M7 296105 118272 0.9

Modele M8 296105 118272 1

Modele M9 296105 118272 1.1

M1/M2/M3M4/M5/M6

M7/M8/M9

0

20000

40000

60000

80000

100000

120000

140000

0 50000 100000 150000 200000 250000 300000 350000

Slo

pe

B =

par

ame

ter

2

Slope A = parameter 1

-60

-50

-40

-30

-20

-10

0

10

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17

Ch

est

def

lect

ion

(m

m)

Time (s)

y chest_deflection_v1 y chest_deflection_v2 y chest_deflection_v3 y chest_deflection_v4 y chest_deflection_v5 y chest_deflection_v6 y chest_deflection_v7 y chest_deflection_v8 y chest_deflection_v9

0.11s

0.11s

0.11s

30 points to keep 10 points 10 points to keep

M4/M5/M6

M7/M8/M9

M1/M2/M3

0.07s

0.07s

0.07s

0.09s

0.09s

0.09s 5

Fast, parametric, reduced models for biomechanics design applications

CREATE THE DATABASE : OUTPUT DATA PRESENTED

50 points from orignal LSDYNA curve

original LSDYNA curve

Chest deflection (mm) 50 Points kept at strategic time

0.0E+00

2.0E+05

4.0E+05

6.0E+05

8.0E+05

1.0E+06

1.2E+06

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17

Hea

d a

ccel

erat

ion

(m

m/s

²)

Time (s)

y head_acc_v1 y head_acc_v2 y head_acc_v3 y head_acc_v4 y head_acc_v5 y head_acc_v6 y head_acc_v7 y head_acc_v8 y head_acc_v9

10 points to keep

30 points to keep

10 points to keep

0.04s

0.04s

0.04s

M1/M2/M3

M4/M5/M6

M7/M8/M9

0.12s

0.12s

0.12s

6



Head acceleration (mm/s²) 50 Points kept at strategic time



0.0E+00

1.0E+05

2.0E+05

3.0E+05

4.0E+05

5.0E+05

6.0E+05

7.0E+05

8.0E+05

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17

Pelv

is a

ccel

erat

ion

(m

m/s

²)

Time (s)

y pelvis_acc_v1 y pelvis_acc_v2 y pelvis_acc_v3 y pelvis_acc_v4 y pelvis_acc_v5 y pelvis_acc_v6 y pelvis_acc_v7 y pelvis_acc_v8 y pelvis_acc_v9

10 points to keep

10 points to keep

30 points to keep

M7/M8/M9

M4/M5/M6

M 1/M2 /M30.02s

0.02s

0.02s

0.10s

0.10s

0.10s

7



Pelvis acceleration (mm/s²) 50 Points kept at strategic time



Target of the POD decomposition module: Reduce a DOE to modes

8


POD – METHOD

Decomposition POD executable

obtainUsed byData base with

9 FE models Eigen modes

X i F( X i )

Re-buildNew

databasere-built

X ’ i

Predicted Results

Prediction step

Decomposition step

Prediction POD executable

Compare Results

with LSDYNA model

with the same

parameters X ’ i

Test phase

Binary DB

From LSDYNA curve Reconstructed response at 50points from the modal base

9


POD – COMPARE RECONSTRUCTION vs LSDYNA FE

Chest deflection

Pelvis Acceleration

Head Acceleration

10


POD – PREDICTION

test1

test2

test3

M1/M2/M2M4/M5/M6

M7/M8/M9

0

35000

70000

105000

140000

175000

210000

245000

280000

315000

350000

0 35000 70000 105000 140000 175000 210000 245000 280000 315000

Slo

pe

B =

par

amet

er 2


INPUT DATA Slope A of the speed Slope B of the speedmultiplier of the flow

rate

M1 122285 83559 0.9

M2 122285 83559 1

M3 122285 83559 1.1

M4 179679 88704 0.9

M5 179679 88704 1

M6 179679 88704 1.1

M7 296105 118272 0.9

M8 296105 118272 1

M9 296105 118272 1.1

Test INPUT DATA Slope A of the speed Slope B of the speedmultiplier of the flow

rate

Test1 140000 140000 1.08

Test2 114667 300800 0.96

Test3 250000 65000 1.02

SlopeB

SlopeA

-50

-40

-30

-20

-10

0

0 0.05 0.1 0.15

Ch

est

def

lect

ion

(m

m)

Time (s)

Test 3 chest deflection

(mm)

LSDYNA curve with 50 points

Approximated curve withdatabase at 9 runs

-50

-40

-30

-20

-10

0

0 0.05 0.1 0.15

Ch

est

def

lect

ion

(m

m)

Time (s)


(mm)

11


POD – COMPARE PREDICTION vs LSDYNA

-110-100

-90-80-70-60-50-40-30-20-10

0

0 0.05 0.1 0.15

Ch

est

def

lect

ion

(m

m)

Time (s)


(mm)

0

200000

400000

600000

800000

1000000

0 0.05 0.1 0.15

Fem

ur

forc

e (N

)

Time (s)

test 3Head acceleration

(mm/s²)

12


POD – COMPARE PREDICTION vs LSDYNA FE

0

200000

400000

600000

800000

1000000

0 0.05 0.1 0.15

hea

d a

ccel

erat

ion

(m

m/s

²)

Time (s)

test 1 Head acceleration

(mm/s²)

0

500000

1000000

1500000

2000000

0 0.05 0.1 0.15

Fem

ur

forc

e (N

)

Time (s)

test 2Head acceleration

(mm/s²)LSDYNA curve with 50 points

Approximated curve with database at 9 runs

0

200000

400000

600000

800000

0 0.05 0.1 0.15

Pelv

is a

ccel

erat

ion

(m

m/s

²)

Time (s)

test 3

Pelvis acceleration (mm/s²)

13


POD – COMPARE APROXIMATION vs LSDYNA FE

0

200000

400000

600000

800000

1000000

0 0.05 0.1 0.15

Pelv

is a

ccel

erat

ion

(m

m/s

²)

Time (s)

test 1

Pelvis acceleration (mm/s²)

0

500000

1000000

1500000

0 0.05 0.1 0.15

Pelv

is a

ccel

erat

ion

(m

m/s

²)

Time (s)

test 2

Pelvis acceleration (mm/s²)LSDYNA curve with 50 points

Approximated curve withdatabase at 9 runs

Why test2 is not good ?

The test 2 has the slope B too far from the database

14


POD – THINKING !

test1

test2

test3

M1/M2/M2M4/M5/M6

M7/M8/M9

0

35000

70000

105000

140000

175000

210000

245000

280000

315000

350000

0 35000 70000 105000 140000 175000 210000 245000 280000 315000

Slo

pe

B =

par

amet

er 2


SlopeB

SlopeA

INPUT DATA Slope A of the speed Slope B of the speed multiplier of the flow rate

M1 122285 83559 0.9

M2 122285 83559 1

M3 122285 83559 1.1

M4 179679 88704 0.9

M5 179679 88704 1

M6 179679 88704 1.1

M7 296105 118272 0.9

M8 296105 118272 1

M9 296105 118272 1.1

M10 98048 189184 1.04

M 11 150000 310000 0.93

M 12 160800 62000 0.85

M 13 230000 230000 0.8

M14 116170 114475 0.902

M 15 189541 69353 0.84

Test INPUT DATA Slope A of the speed Slope B of the speed multiplier of the flow rate

Test1 140000 140000 1.08

Test2 114667 300800 0.96

Test3 250000 65000 1.02 15


POD – THINKING!

Slope B

Slope A

test1

test2

test3M1/M2/M

M4/M5/M6 M7/M8/M9

M10

M11

M12

M13

M14

M1545000

95000

145000

195000

245000

295000

345000

0 50000 100000 150000 200000 250000 300000 350000

Pen

te B

= p

aram

eter

2

Pente A = parameter 1

Increase the database at 15 runs

Target of the POD decomposition module: Reduce a DOE to modes

16


POD – METHOD

Decomposition POD executable

obtainUsed byData base with 15 FE models Eigen modes

X i F( X i )

Re-buildNew

databasere-built

X ’ i

Predicted Results

Prediction step

Decomposition step

Prediction POD executable

Compare Results

with LSDYNA model

with the same

parameters X ’ i

Test phase

Binary DB

-55

-35

-15

0 0.05 0.1 0.15

Ch

est

def

lect

ion

(m

m) Time (s)

Test 3chest deflection

(mm)

17



-55

-45

-35

-25

-15

-5 0 0.05 0.1 0.15

Ch

est

def

lect

ion

(m

m)

Time (s)


(mm)

-120

-100

-80

-60

-40

-20

0

0 0.05 0.1 0.15

Ch

est

def

lect

ion

(m

m)

Time (s)


(mm)




0

200000

400000

600000

800000

1000000

0 0.05 0.1 0.15

he

ad a

cc (

mm

/s²)

Time (s)


(mm/s²)

18



0

200000

400000

600000

800000

1000000

0 0.05 0.1 0.15

hea

d a

ccel

erat

ion

(m

m/s

²)

Time (s)


(mm/s²)

0

500000

1000000

1500000

2000000

0 0.05 0.1 0.15

Hea

d a

ccel

erat

ion

(mm

/s²

Time (s)


(mm/s²)




0

200000

400000

600000

800000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Pelv

is a

ccel

erat

ion

(m

m/s

²)

Time (s)

test 3 Pelvis acceleration

(mm/s²)

19



0

200000

400000

600000

800000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Pelv

is a

ccel

erat

ion

(m

m/s

²)

Time (s)

test 1 Pelvis acceleration

(mm/s²)

0

500000

1000000

1500000

2000000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Pelv

is a

ccel

erat

ion

(m

m/s

²)

Time (s)

test 2Pelvis acceleration

(mm/s²)




-20

-15

-10

-5

0

5

10

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Finite Element vs ReducedModel

Série1 Série2

L1

L2

L3

L4

SIMBIO-M – 2016, ENSAM, Paris – CADLM, www.cadlm.com



HUDYNI-Model

L1 / Réponse

-60

-40

-20

0

20

1 4 7 10 13 16 19 22 25 28

60/540

-40

-20

0

20

1 4 7 10 13 16 19 22 25 28

60/470-20

-10

0

10

1 4 7 10 13 16 19 22 25 28

60/420

Impact velocity Impact position1 0.20000000E+02; 0.42000000E+03;2 0.20000000E+02; 0.47000000E+03;3 0.20000000E+02; 0.54000000E+03;4 0.40000000E+02; 0.42000000E+03;5 0.40000000E+02; 0.47000000E+03;6 0.40000000E+02; 0.54000000E+03;7 0.60000000E+02; 0.42000000E+03;8 0.60000000E+02; 0.47000000E+03;9 0.60000000E+02; 0.54000000E+03;

-40

-20

0

20

1 4 7 10 13 16 19 22 25 28

40/540-30

-20

-10

0

10

1 4 7 10 13 16 19 22 25 28

40/470-10

-5

0

5

10

1 4 7 10 13 16 19 22 25 28

40/420

-20

-10

0

10

1 4 7 10 13 16 19 22 25 28

20/540-10

-5

0

5

1 4 7 10 13 16 19 22 25 28

20/470-5

0

5

1 4 7 10 13 16 19 22 25 28

20/420

540

470

420

Finite Elements Reduced Model

SIMBIO-M – 2016, ENSAM, Paris – CADLM, www.cadlm.com

• Good reconstruction with 9 runs (modes) – problem with test 2

• Good improvement of test 2 with 15 runs with additional runs selected at « strategic » points.

• The More the database is densified, the more we reach the perfect model.

• No need to use all modes for reconstruction (but this has little cost anyway), but may be used as filtering

------------------------------------------------------------------------------------------------------------------• A reduced model, can provide satisfactory results for an industrial process requiring real-time

response (on-board, active safety, ADAS, personalized deployment of safety devices, etc.)

• A reduced model can be used in many simulation domains (in a RSM you need to know something about the nature of the response in order to select the best surface reconstruction but not in POD) : Biomechanics, plastic Injection process, Cost estimation, Concept design, Machining process, etc.

• Run time for FE model ~30 minutes (c.f. 1 sec for reduced model) => Optimization, DOE, Robustness, population (statistical) response reconstruction from DOE, …..

• Encapsulation of confidential models

• Coupling of FE car modes with POD Human models (or vice-versa)

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« Obtain a reduced model biomechanical close to the numerical model »

CONCLUSION

Fast, parametric, reduced models for biomechanics design ......2016/06/17 · Fast, parametric,...

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