applied research laboratory approaches to ... · approaches to multidisciplinary design...

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: [email protected]://edog.me.psu.edu/

Acknowledge support from the Office of Naval Researchunder ASSERT Grant# N00014-98-1-0525.

Report Documentation Page

Report Date 15052001

Report Type N/A

Dates Covered (from... to) -

Title and Subtitle Approaches to Multidisciplinary Design Optimization

Contract Number

Grant Number

Program Element Number

Author(s) Simpson, Timothy W.

Project Number

Task Number

Work Unit Number

Performing Organization Name(s) and Address(es) The Pennsylvania State University University Park, PA 16802

Performing Organization Report Number

Sponsoring/Monitoring Agency Name(s) and Address(es) NDIA (National Defense Industrial Association 2111Wilson Blvd., Ste. 400 Arlington, VA 22201-3061

Sponsor/Monitor’s Acronym(s)

Sponsor/Monitor’s Report Number(s)

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


System Level Coordinator

Subsystem 2Simulation

Subsystem nSimulation



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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


s.t. Analysis 2constraints

Analysis 2


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


Power

Sonar

Guidance & Control


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 2Simulator


System Level Coordinator


Subsystem nSimulation


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

1

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.

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