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.
22/17/98
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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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
112/17/98
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 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
192/17/98
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
262/17/98
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