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Applied Research Laboratory
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Approaches to MultidisciplinaryDesign Optimization
Timothy W. SimpsonAssistant Professor
Mechanical & Nuclear Engineering andIndustrial & Manufacturing Engineering
The Pennsylvania State UniversityUniversity Park, PA 16802
phone: (814) 863-7136email: tws8@psu.eduhttp://edog.me.psu.edu/
Acknowledge support from the Office of Naval Researchunder ASSERT Grant# N00014-98-1-0525.
Report Documentation Page
Report Date 15052001
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Title and Subtitle Approaches to Multidisciplinary Design Optimization
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Author(s) Simpson, Timothy W.
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Performing Organization Name(s) and Address(es) The Pennsylvania State University University Park, PA 16802
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Sponsoring/Monitoring Agency Name(s) and Address(es) NDIA (National Defense Industrial Association 2111Wilson Blvd., Ste. 400 Arlington, VA 22201-3061
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Distribution/Availability Statement Approved for public release, distribution unlimited
Supplementary Notes Proceedings from 3rd Simulation Based Acquisition conference, 15-17 May 2001, sponsored by NDIA,The original document contains color images.
Abstract
Subject Terms
Report Classification unclassified
Classification of this page unclassified
Classification of Abstract unclassified
Limitation of Abstract UU
Number of Pages 26
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Presentation Overview
• What is multidisciplinary design optimization?– Why use it?– How is it used?
• Example MDO application
• Computational challenges in MDO
• Example surrogate modeling application
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What is MDO?
• Multidisciplinary design optimization (MDO):
– is a methodology for the design of systems in whichstrong interactions between disciplines motivatesdesigners to simultaneously manipulate variables inseveral disciplines
– involves the coordination of multiple disciplinary analysesto realize more effective solutions during the design andoptimization of complex systems
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Simulation-Based Design Architecture
Design Servers:• Automated System Synthesis
Java-based GUI Performance Agent
Cost Agent
Undersea Vehicle(torpedo, ATT)
GnC
ADCAPMK48
MK46MK50
Warhead
BULKSHAPED
ADVANCED
Power
HYDROXADSCEPS
MK50ADCAP
SCEPS
MK46ADV ELEX PWR
Propulsor
ADCAPMK50
MK46
Cmd Wire
MK48MK48MOD
GENERIC
DataRepository
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Design Server Interactions
Subsystem nSimulator
Subsystem 2Simulator
Subsystem nSimulator
System Level Coordinator
Subsystem 2Simulation
Subsystem nSimulation
Subsystem 1Simulation
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System-level Objective
Undersea Vehicle(torpedo, ATT)
GnC
ADCAPMK48
MK46MK50
Warhead
BULKSHAPED
ADVANCED
PowerHYDROXADSCEPS
MK50ADCAPSCEPS
MK46ADV ELEX PWR
Propulsor
ADCAPMK50
MK46
Cmd Wire
MK48MK48MOD
GENERIC
TechnologyChoices
CostTargets
PerformanceTargets
EffectivenessEstimate (P)
Estimate Costs ($)
Design Servers Max. f(P,$)s.t. feasibledesigns thatmeet targets
Max. f(P,$)s.t. feasibledesigns thatmeet targets
PerformanceAgent
Cost Agent
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How is it used?
• Using MDO involves:
– decomposing the system into multiple subsystems ordisciplinary analyses
– developing mathematically models and analyses for:
• the “parent” system
• each subsystem and its interactions
– selecting an appropriate MDO formulation andalgorithm
– solving the MDO problem to generate solutions
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Space of feasibledesigns
Initial guess
Nearest feasiblepoint
optimum
Stays feasible
Multiple Discipline Feasible
• Get feasible and stay feasible• Implies each iteration is a two part process:
– move to improve design– re-establish feasibility
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Space of feasibledesigns
Initial guess optimum
Individual Discipline Feasible
• Go straight to optimum• Since optimum usually on boundary, not
feasible until optimal– equivalent to discrepancy = 0
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Collaborative Optimization
Decomposesystem intosmaller unitsthat can beindividuallyoptimizedand thensynthesizedinto a system
Subspace Optimizer nSubspace Optimizer 2
System-Level Optimizer
Goal: Design objective
s.t. Interdisciplinarycompatibilityconstraints
Subspace Optimizer 1
Goal: Interdisciplinarycompatibility
s.t. Analysis 1constraints
Analysis 1
Goal: Interdisciplinarycompatibility
s.t. Analysis 2constraints
Analysis 2
Goal: Interdisciplinarycompatibility
s.t. Analysis nconstraints
Analysis n
…
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Underwater Exploratory Vehicle
• 4 Subsystems:– Guidance & Control– Instrumentation– Power– Propulsion
• Subsystemanalysesdeveloped by Erik Halberg(M.S., ME)
• 7 Design Variables:– Volumes
InitialDesign
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Underwater Vehicle Example
L-V
Void Volume
L-G L-I L-P
d D-V
Guidance and Control
SonarInstrumentation
Package Power
Packaging Penalty
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Underwater Exploratory Vehicle
Min P1(d8- ) + P2(d4
-) + P3(d5- + d6
- + d7-) +
P4(d1- + d2
- + d3-)
stLGC + LP + LI – LV = 0(e0 - dE
- + dE+)*50/(s0 - dS
- + dS+) – R = 0
Guidance & Control
Min Σ(di- + di
+) i = 1,2,3stP(V) + d3
- - d3+ = p0
dB(V) + d2- - d2
+ = dB0
ω(V) + d1- - d1
+ = ω0
Power
Min Σ(dk- + dk
+) k = 5,6,7stE(V) + d6
- - d6+ = e0
HP(V) + d7- - d7
+ = hp0
SP(V) + d5- - d5
+ = sp0
Instrumentation
Min d4- + d4
+
stPn(V) + d4
- - d4+ = pn0
Propulsion
Min d8- + d8
+
stS(SP) + d8
- - d8+ = s0
di- di
+
VGC
dB- dB
+ VI di- di
+ VP dS- dS
+ SP
p0 dB0 ω0
pn0 e0 hp0 sp0 s0
LV, DV, R
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Vehicle Performance
• MDO formulation yieldssuperior performance:– Speed– Endurance– Effectiveness
0
5
10
15
20
25
30
35
40
Spe
ed
En
du
r
Eff
ect
Trad.
Bi-LevGP
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Vehicle Optimization
• Final Design:– Slightly different
configurations
• Solution Time:– 1 minute vs. 3 hours 0
100020003000
40005000
6000
7000
8000
GnC Inst Pw
Trad.
Bi-LevGP
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Vehicle Configurations
TraditionalFormulationFinal Design
CollaborativeOptimizationFinal Design
InitialDesign
Sonar
Guidance & Control
InstrumentationPackage
Power
Sonar
Guidance & Control
InstrumentationPackage
Power
Sonar
Guidance & Control
InstrumentationPackage
Power
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Computational Challenges in MDO
• In MDO, computer simulation codes are:
– often “black-box” in nature
– discipline-specific
– composed in different languages (e.g., Fortran, C, Java)
– distributed, both geographically and on differentcomputer platforms
– computationally expensive due to fidelity of modeling andneed for accurate results
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Surrogate Models for MDO
• Surrogate models are fast, simple approximationsof computationally-expensive computer simulationsand/or analyses
• They provide a “model of a model” which can beused in place of the original computer simulation
• Surrogate modeling can be used to generate “smartobjects” that can be used in place of the originalanalyses and integrated within any SBDinfrastructure
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Overview of Surrogate Modeling
X1
X2
SimulationRoutine
(“black box”) y1
low high
low
high
Use surrogate modelingcapability to constructa “model of the model”
SimulationRoutine
(“black box”)(x1,2,x2,2) y2
(x1,1,x2,1)
Generate simulationdata using design of
experiments capability
Y
X
Z
X1
Y
X2
Design space
• • •
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Surrogate Models in MDO
Subsystem nSimulator
Subsystem 2Simulator
Subsystem nSimulator
System Level Coordinator
Subsystem 2Simulation
Subsystem nSimulation
Subsystem 1Simulation
Cost Estimator
Each sub-system or disciplinary analysis can be replaced by asurrogate model and invoked by the higher-level coordinator
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Aerospike NozzleVenture Star RLV
Application: Rocket Nozzle
• Utilize surrogate models to facilitate multidisciplinarydesign and optimization of an aerospike rocketnozzle for the next generation shuttle
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CFDmodel
Base-flowmodel
Aer
od
ynam
ics S
tructu
resAngle, Height, Length
Nozzleprofile
TrajectoryMap
Pressures
Displacements
Thrust Weight
GLOW
Structuralmodel
Iterate untilconverged
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-1
0
1
heig
h t
-1
0
1
ang le
-1
-0 .5
0
0.5
1
le ngth
2 nd Orde rRS Mo de l
KrigingMode l
Thrus t
- 1
0
1
heig
ht
-1
0
1
ang le
-1
- 0.5
0
0 .5
1
leng th
X
Y
Z
thr10.9990.9980.9970.996
angle
angle
heig
ht
heig
ht
length
length
Thrust
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-1
0
1
he
i gh
t
-1
0
1
ang le
-1
- 0.5
0
0 .5
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le ng th
X
Y
Z
glow10.990.980.970.968
GLOW
2 nd Orde rRS Mode l
Krig ingMo de l
-1
0
1
heig
h t
-1
0
1
ang le
-1
-0.5
0
0.5
1
length
angle
angle
heig
ht
heig
ht
length
length
GLOW
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Closing Remarks
• MDO involves the coordination of multipledisciplinary analyses to realize more effectivesolutions during the design of complex systems
• Surrogate models can be used to address many ofthe computational challenges associated with MDO
• MDO formulations that incorporate uncertainty arecurrently being investigated
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For Further Reading• McAllister, C. D. and Simpson, T. W. Multidisciplinary Robust Design Optimization of an
Internal Combustion Engine, ASME Design Technical Conferences - Design AutomationConference (Diaz, A., ed.), Pittsburgh, PA, September 9-12, ASME, Paper No.DETC2001/DAC-21124.
• McAllister, C. D., Simpson, T. W. and Yukish, M. (2000) Goal Programming Applications inMultidisciplinary Design Optimization, 8th AIAA/NASA/USAF/ISSMO Symposium onMultidisciplinary Analysis and Optimization, Long Beach, CA, September 6-8, AIAA, AIAA-2000-4717.
• Simpson, T. W., Mauery, T. M., Korte, J. J. and Mistree, F., "Comparison of ResponseSurface and Kriging Models for Multidisciplinary Design Optimization," 7thAIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis & Optimization, AIAA,Vol. 1, 1998, pp. 381-391.
• Koch, P. N., Simpson, T. W., Allen, J. K. and Mistree, F., "Statistical Approximations forMultidisciplinary Optimization: The Problem of Size," Special Multidisciplinary DesignOptimization Issue of Journal of Aircraft, Vol. 36, No. 1, 1999, pp. 275-286.
• Jin, R., Chen, W. and Simpson, T. W., "Comparative Studies of Metamodeling Techniquesunder Multiple Modeling Criteria," 8th AIAA/NASA/USAF/ISSMO Symposium onMultidisciplinary Analysis and Optimization, Long Beach, CA, AIAA, 2000, AIAA-2000-4801, to appear in Journal of Structural and Multidisciplinary Optimization.