Optimization of the impact performance of
a metal/polyurea composite plate via
coupling of a genetic algorithm and a finite
element code
Kiran Narayanana
in collaboration with
Angel Moraa, Nicholas Allsoppa,b, Tamer El Sayeda
a Physical
Sciences and Engineering Division
King Abdullah University of Science and Technology (KAUST)
Building 4, 4700 KAUST
Thuwal 23955-6900, KSA
b Cray
Computing Deutschland GmbH
University of Stuttgart, HLRS
Nobelstrasse 19
D-70569 Stuttgart, Germany
High velocity impact : Scenarios
Space shuttle window pit
from orbital debris impact
Extra-vehicular activities in
space
Composite materials are used for
Micrometeoroid Orbital Debris
(MOD) ballistic-shielding
Low
High
International Space Station: Impact Risk
K Narayanan, ECCOMAS 2012
Picture credits: NASA
2
Problem specification
Composite
Plate
X
Impactor Z
(
Find Vz-0 that minimizes Vz- final Vz-0 , a,G,Y, h
)
such that Vz- final < 0 and 100 m/s £ Vz-0 £ 500 m/s
Vz-0
Y
Steel (HSS)
Vzero Velocity
Polyurea
Large No. of Function
Evaluations
Impact mass (g)
145
Steel target plate mass (g)
692.2
Steel target plate diameter (mm)
154.2
Steel target plate average thickness (mm) 4.75
Polymer diameter (mm)
154.2
Polymer/steel thickness ratio
2.335
Finite Element model adapted from El Sayed et al (2009)
3
K Narayanan, ECCOMAS 2012
Computational Resources
Master: Single x86 node on a cluster
Workers: BG/P
Rack
Blue Gene/P
Cabled 8x8x16
32 Node Cards
Node Card
222 TFlop/s
64TB
(32 chips 4x4x2)
32 compute, 0-2 IO cards
13.9 TFlop/s
4 TB
Compute Card
1 chip, 20
DRAMs
435 GF/s
128GB
Chip
4 processors
16 Racks, 32x32x16
With permission from KAUST Supercomputing Laboratory
13.6 GF/s
4.0 GB DDR2
13.6 GF/s
8 MB EDRAM
K Narayanan, ECCOMAS 2012
4
Parallelization
Strategy
START
Initialization
Write
parameter
cycle file
Function evaluation
Crossover
Mutation
n=n+1
Function evaluation
Write
parameter
cycle file
Fitness assessment
Replacement
Single Objective Genetic Algorithm (SOGA) iterator
from DAKOTAa is used to compute optimal value of
velocity V0 that is used as input to the FE simulation.
The fitness function for the GA is |Vz-final|.
Convergence
NO
YES
Write results
file
a Adams et al (2009)
STOP
Flowchart - GA
5
K Narayanan, ECCOMAS 2012
Computational Steering
(GA/FE Coupling)
GA parameter file
Create FE input
Submit to LL on
BG/P
Return value to GA
Submission
successful
NO
Set velocity to
5.555e-6 m/s
NO
Return value to GA
YES
Simulation
complete
Set velocity to
6.666e-6 m/s
YES
NO
Clean
termination
YES
Write results
K Narayanan, ECCOMAS 2012
NO
Wall
clock
limit
YES
Write results
6
Results
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K Narayanan, ECCOMAS 2012
Simulation run time T(p’) [secs]
Strong Scaling of FE code
Simulation times of the dynamic problem
reached at wall clock limit of 24 hrs
T ( p' ) = A + B
p'
p =128
'
opt
No. of processors (p’)
Computational time to reach a predetermined
dynamic simulation time
Optimal number of MPI-enabled jobs for each objective function evaluation was determined to be 128
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K Narayanan, ECCOMAS 2012
Relative Efficiency of hybrid parallelization
T(1)
Efficiency h p =
pT(p)
()
()
E p
( )
E p =
h ( pmin )
(p
E ( p) =
'
min
Relative Efficiency b
p
Total No. of processors
'
pmin
Min no. of processors for function evaluation
k
bp
h ( p)
bp =
No. of evaluations per GA iteration
Max. no of evaluations any worker performs in each GA iteration
=
( )
pT ( p )
pminT p min
) (
)
'
+1 T pmin
+1
( )
(2)
pT p
k
(3)
é p -1ù
ê
ú
ë p û
(p
E ( p) »
) ( )
pb T ( p )
( p +1) k p T ( p )
E ( p) »
(1+ k p ) p T ( p )
'
min
(1)
'
+1 kT pmin
'
(4)
p
b Eldred
and Hart (1998)
'
min
'
opt
'
opt
'
'
min
'
(5)
Number of processors (p) vs Relative Efficiency E(p)
Concurrency=5
Concurrency=16
K Narayanan, ECCOMAS 2012
Concurrency=32
9
Optimal impact velocity of projectile
opt
Vz-init
= 302 m/s
Max. Concurrency=5, Total Evaluations=25
Max. Concurrency=16, Total Evaluations=32
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K Narayanan, ECCOMAS 2012
Performance of Genetic Algorithm
Projectile impact velocity
(m/s)
Impact velocities closest to optimal value
500
450
400
350
300
250
200
150
100
50
0
"Kappa=5, Max. Eval=25"
Kappa=16, Max. Eval = 32
Optimal Impact Velocity
0
2
4
6
8
Generation No.
10
12
14
16
Computational Time (sec)
Computational time to calculate optimal impact velocity
800000
700000
55.6 hrs
600000
500000
400000
300000
Kappa=5, Max. Eval = 25
200000
Kappa=16, Max. Eval = 32
100000
0
0
K Narayanan, ECCOMAS 2012
2
4
6
8
Generation No.
10
12
14
16
11
Conclusions
• GA/FE coupling was used to facilitate guided
computation of optimal impact velocity with
reduced computational time
• The methodology of coupling and selection of
parameters is applicable to simulation-based
optimizations in general and is scalable
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K Narayanan, ECCOMAS 2012
Acknowledgements
• For computer time, this research used the
resources of the Supercomputing Laboratory at
King Abdullah University of Science & Technology
(KAUST) in Thuwal, Saudi Arabia
• This work was fully funded by the KAUST baseline
fund
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K Narayanan, ECCOMAS 2012
References
Narayanan K, Mora A, Allsopp N, El Sayed T, A hybrid massively parallel implementation of a genetic
algorithm for optimization of the impact performance of a metal/polymer composite plate, International
Journal of High Performance Computing Applications, Published online before print July 17, 2012, DOI:
10.1177/1094342012451474
El Sayed T, Willis M Jr., Mota A, Fraternalli F, Ortiz M, Computational Assessment of ballistic impact on a
high strength structural steel/polyurea composite plate, Computational Mechanics, 43, 525-534 (2009)
Adams BM, Bohnhoff WJ, Dalbey KR, Eddy JP, Eldred MS, Gay DM, Haskell K, Hough PD, Swiler LP, DAKOTA,
A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation,
Uncertainty Quantification, and Sensitivity Analysis: Version 5.0 User's Manual, Sandia Technical Report
SAND2010-2183 (2009)
Eldred MS, Hart WE, Design and implementation of multilevel parallel optimization on the Intel teraflops,
Paper AIAA-98-4707 in Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary
Analysis and Optimization, 44-54 (1998)
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K Narayanan, ECCOMAS 2012