12/17/98

Multidisciplinary Optimization Methods for Preliminary Design

J. J. Korte, R. P. Weston, and T. A. Zang

Multidisciplinary Optimization Branch, MS 159,

NASA Langley Research Center,

Hampton, Virginia 23681 USA

AGARD Interpanel (FDP+PEP) Symposium "Future Aerospace Technology in the Service of the Alliance”

April 1997, Paris, France.

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Outline

• Definitions

• Requirements for using MDO in Preliminary Design

• Preliminary Design MDO Examples

• Summary

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MDO Definition

Multidisciplinary Design Optimization (MDO) is a methodology for the design of complex engineering systems

and subsystems that coherently exploits the synergism of mutually interacting phenomena

“∆MDO”

∆Design = (∑i ∆Discipline i) + ∆MDO

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OptimizationProcedures

Decomposition

SensitivityAnalysis

MDO Conceptual Elements

Information Science& Technology

Design-OrientedMD Analysis MD Optimization

Data & S/WStandards

Product DataModels

Approximations

MathematicalModeling

Cost vs. AccuracyTrade-off

SmartReanalysis

Design SpaceSearch

HumanInterface

Data Management,Storage & Visualization

S/W EngineeringPractices

DisciplineOptimization

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Product Data Model Example(CAD Parametric Geometry Model)

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Sensitivity Analysis

• Computing derivatives of objective with respect to the design variables

• Methods– Finite differences

• time consuming

• difficult to pick ∆– Analytic

• hard to code

• changes with each application

• fast

– Automatic differentation• easy to use

• accurate

• can be time consuming

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Automatic Differentiation of 3-Dimensional Navier-Stokes Flow Code (CFL3D)

BC

RC

TC

OS

IS

Wing Planform Design Variables

(DV)

Aerodynamic CoefficientsCL LiftCD DragCY Side ForceCMY Pitching Moment

Sensitivity Derivatives - Derivatives of Aerodynamic Coefficients With Respect to Wing Planform Variables

Time to Compute Sensitivity Derivatives (for 4 digits of Accuracy) Automatic Differentiation (Residual reduced 4 orders) = 10.75 unitsFinite Difference Method (Residual reduced 11 orders) = 15.00 units

∂CD

∂DV

∂CL

∂DV

∂Cy

∂DV

∂CMy

∂DV

High Speed Civil TransportMach Number = 2.4, α = 1°

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Optimization Procedures

analysis

optimizer

analysis

sensitivity

local approx

cycl

eoptimizer

Direct InterfaceIndirect Interface Using

Approximations

sensitivity

itera

tion

itera

tion

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Decomposition

System Level Optimization (Coordinates Subproblems)

AerodynamicsOptimization Subproblem

Structures OptimizationSubproblem

Other DisciplineOptimizationSubproblem

. . .

Information Flow

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Preliminary Design• Conventional Process

– CAD-based geometry• surface

• internal layout

– Higher-order analysis• CFD

• Finite Element

– Discipline analysis & optimization• sequential or loosely coupled

• discipline-based figure of merits ( i.e., weight, thrust, drag, lift, etc. )

• Emerging MD Enhancements– Parametric CAD definition

– Fully coupled multidiscipline analysis

– Multidisciplinary optimization• Figures of merit

– system performance and cost

– multi-objective

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Requirements for MDO Enhancements of Preliminary Design

• Information Science & Technology– heavy duty hardware; fast CPU(s), large memory & disk space

– common parametric geometry model– software support

• integration of proprietary, legacy, commercial, and research codes– code robustness, compatibility, & low algorithm noise

• configuration control and data management

• collaborative work environment; person-person/machine

• Design-Oriented MD Analysis– well posed interfaces for disciplines

• automated grid generation (CFD, FEM)

– discipline & MD sensitivities

• MD Optimization– MDO problem definition

• design variables, objective(s), constraints

– MDO strategy

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Preliminary MDO Examples

• Aerospike Rocket Nozzle– Direct Optimization Approach

• High-Speed Civil Transport (HSCT)– Approximation Optimization Approach

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MDO Applied to Aerospike Nozzle Design

Multidisciplinary Optimization BranchNASA Langley Research Center

Aerospike Engine

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Aerospike MDO Problem

• Objective• minimize Vehicle Gross-Lift-Off Weight

• Design Parameters• 5 geometry variables• 13 structural variables

• Constraints• Stresses < allowable

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Aerospike MDO Domain Decomposition

CFD-96-OPTIMIZATION DISK/WWF

CFD DOMAIN

BASEFLOW MODEL DOMAIN

BASE BLEED

FEM STRUCTURES DOMAIN

T/W

Isp

GLOW Contours

TRAJECTORY DOMAIN

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Aerospike Nozzle Structural Design Parameters

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Aerospike Nozzle Optimization

Sequential Optimization

(Single Discipline Only)

Aerodynamics

Maximize Thrust

Structural

Minimize Weight

Base-line Solution

Multidisciplinary Optimization

Integrated

Aerodynamics and Structures

Minimize Gross-Lift-Off Weight

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0.94

0.96

0.98

1.00

1.02

Gro

ss

-Lif

t-O

ff-W

eig

ht

Ra

tio

0 5 10 15 20

Iteration Number

MDO∆MDO

Optimized Single Discipline Result

Aerospike Objective Function

202/17/98 Framework for Interdisciplinary Design Optimization (FIDO)

MDO Applied to High-Speed Civil Transport (HSCT) Using FIDO

Mach 2.4 at 55,000 ft 6000-mile range 250 passengers

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HSCT MDO Problem Diagram

EoC = End of Cruise

SoC = Start of Cruise

= Program

= Data

Aero GridUpdate

FEM NodeUpdate

WeightsRigid AeroAnalysis

SoCAero/Struc

Rigid Analysis

EoCAeroelastic

Static Analysis

SoCProp Analysis

EoCProp Analysis

Performance

OptimizerTotal Weight

EoC WeightsSoC Weights Sensitivity

Derivatives

UpdatedValues

Design VariablesBase GeometryFlight Conditions

UnloadedShape

Stresses

Range

Fuel FlowRate

SoC CL, CD

CLα, α0

EoC CL, CD

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COMET

Has Structural DeformationConverged?

TRN3D

ADVMOD

SURFACEVOLUME

ISAAC

Initial Shape from Design Variables

Surface Shape Modifications

Aerodynamic Grid Generation

Euler CFD

Loads Transfer :Aero to Structures

FEM Structural Analysis

Structural ResponseSTOP

No

Yes

“Converged Shape”

Key Steps in FIDO Aeroelastic Loop

Surface Pressures

15,000 cells

FEM Deflections

7300 Degrees of Freedom

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HSCT Design Optimization

t outbd

t inbd

β = 0

β = 1.0

C1, C2, C3, C 4

DEPENDENT DESIGN VARIABLES:

t inbd = C0 +C1 (1- β) + C2 (1- β)2

t outbd = C0 +C3(1- β) + C 4 (1- β)2

IND EPENDENT DESIGN VARIABLES:

ginbd = f(K-S)goutbd = f(K-S)

CONSTRAINTS

OBJECTIVE FUNCTIONWeight

:

:

3.0E+05

3.2E+05

3.5E+05

3.8E+05

4.0E+05A

ircr

aft W

eigh

t, lb

s.

5 10 15 20

Cycle Number

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Concluding Remarks

• MDO is much broader than just MD-Analysis; it contains elements from information sciences, design-oriented analysis and optimization methods

• The “∆MDO” is the improvement in design obtained from multidisciplinary synergy of the disciplines as demonstrated by the Aerospike nozzle application

• Application of MDO to preliminary design requires sophistication in the computational infrastructure and MDO algorithms

• Adoption of MDO in industry design process requires demonstrations which quantify– “∆MDO” improvement in design

– reduction in time and effort in the design process