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Multidisciplinary Optimization p y pfor Industrial Aeronautical Applications
M Delanaye F Lani I LepotM. Delanaye, F. Lani, I. Lepot
Dr. Michel DelanayeGeneral Manager
Contact: michel delanaye@cenaero be
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Contact: [email protected]
Aim & Outline
• Aim– Present some “real” applications of multi-objective– Present some real applications of multi-objective
multidisciplinary optimization for complex design problems in aeronautics
• Outline– Quick presentation of Minamo platform
E l 1 d i f t t ti t– Example 1: design of counter rotating open rotors (aeroacoustics)
– Example 2: design of composite structural parts– Example 2: design of composite structural parts (cost, manufacturing)
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Who we are ?
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
R&T private company focused on simulation and modelling
process modelingprocess modeling
integrity analysis
structure design
On demand
flow analysis
Multidisciplinaryanalysis
d d
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
aerodynamic design
Minamo basics
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Surrogate assisted Genetic Algorithm workflow
UserUserSpecifications
Gradients for complex objectives usually non available !
Specifications
Approximate ModelANN RBFANN, RBF, …
OptimizationOptimizationppGA, SA, … DATABASEDATABASE
Accurate Model Accurate Model CFD / Structure / Exp. / ...
Performance CheckEND
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Surrogate based optimization
ectiv
e
Actual Optimum
Approximate
Obj
e
PredictedOptimum
p
Approximate model
Initial Accurate Results
Design Variable
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Surrogate based optimization
PredictedOptimum
Actual Optimum Artificial Neural Networksec
tive
OptimumRadial Basis FunctionsKriging
Obj
e
Appro imate
...
Approximate model
Initial Accurate Results
Design Variable
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Key issues
• Efficient design exploration techniques– Reduce the number of samplings (high fidelity– Reduce the number of samplings (high fidelity
simulation)
• Accuracy of response surfaces (models)
• Methodologies to assess the quality and reliability of the modelsy
• Efficient multi-objective GAEfficient multi objective GA
• …
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
…
Derivative free optimization with Minamo
Illustration of adaptive sampling capability
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Efficient Design Exploration
Candle functionGlobal optimum
Misplaced optimum
Exact solution
Standard LHSsampling
Auto‐adaptive LCVT sampling
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Monitoring/ReliabilityLeave-One-Out (Open gap/Stall point)
DOE
Optimization
Large DoE scatter - Stabilization afterLOO Reliability Assessment:
Large DoE scatter Stabilization after about 50 design iterations: 2 different promising design families pointed out, satisfying the manufacturing constraints
Isentropic efficiency correlation coefficient
0.915502 (DoE) 0.9685 (optimization)
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
satisfying the manufacturing constraints
ANOVA – Sobol indices
First order sensitivities and interaction volume (if required higher order sensitivities) quantification
0 3
Relative Importance of Parameters
sensitivities) quantification
0,2
0,25
0,3
s
Section 5 first camber parameter
0,1
0,15
Sobo
l Indi
ces
Isent_Eff_Large_Gap_1.10Isent_Eff_Small_Gap_1.10Isent_Eff_Large_Gap_1.13Isent_Eff_Small_Gap_1.13
p
0
0,05
Illustration on NEWAC optimization accounting for engine wear
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Illustration on NEWAC optimization accounting for engine wear
Direct CAD access CATIA – CAPRI – mesher
Master script (Python or C++, called by Minamo)p ( y , y )
D M
odel
mes
h
difie
d m
odel
Mod
ified
D M
odel
esh
ef. m
esh
CAPRI client
CA
Ref
.
Mod
CAD
GeomSim Discrete, MeshSim
M CA M
e
Re
Linux/Windows
SOAP IGG/AutoGrid 5/Samcef/Abaqus CAE, etc
TCP/IP
Windows/Linux
CAPRI server
CATIA V5 – SolidWorks – UG NX – Pro/Engineer ‐ OpenCASCADE …
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Summary of Minamo Features
• Mono- and multi-objective evolutionary algorithms, including memetic approaches
• Online surrogates approach• Online surrogates approach • Space fill and auto-adaptive DoE (LHS, CVT,
LCVT, …)• Efficient adaptive nonlinear global and local• Efficient adaptive nonlinear global and local
models (ANN, RBFN, Kriging, SVM, …)• Response surfaces reliability through leave-k-out
cross validationcross-validation• Constraints activity interactive monitoring• Quantitative Variance Analysis tool (ANOVA):
Sobol sensitivity indices estimation• Data mining capabilities for efficient multi-criteria
decision making (self organizing maps, …)• Simulation coupling through Python scripting• Native and neutral CAD access• Available in standalone version or as engine
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
gplug-in in other software (Optimus)
Example 1: Design of Counter-Rotating Open Rotors
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Aeromechanical Optimization of a Counter-Rotating Open Rotor (CROR)
• Open Rotor Advanced Concept Studies
• Potential to meet drastic fuel burn decrease for future passengersdecrease for future passengers aircraft at horizon > 2020
• Challenges:• Noise mitigation while ensuring g g
high efficiency
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved 1717
Optimization Specification
• Objective function:• Maximization of global efficiency @ TOC• Minimization of acoustic level @ TO
• Constraints:• Aerodynamic constraints:
• Thrust requirements @ TOC and TO• Torque split @ TOC and TO (DD architecture)• Streamlines contraction/R1 tip vortex
• Mechanical constraints• Max VM stress/ linear FE, rig-scale• Simplified flutter criterion
• Geometric constraints/feasibilitiy: • LE/TE thickness, max thickness, reverse mode,• LE curvature change criterion, curvilinear length of TE, CG position
RPM RPM• RPMR1= RPMR2• Variable blade re-staggering (including between both OPs)• Clipping of rotor 2 is fixed, no contouring modification
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved 18
pp g , g• Failed or unstable simulations handled by a success switch
In-house Cenaero blade modeler
• Profile shape (6 equidistant sections along blade height)• Maximum thickness• Maximum thickness position• Chord lengthChord length• Stagger angle• Skeleton angle at LE/TE
St ki• Stacking (6 equidistant sections along blade height + 2 additional sections at 90 and 95%)
• CG axial position • CG tangential position
• Blade pitch anglesi l di i bl d lt t iincluding variable delta restaggering between TOC and TO
102 parameters conception space
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved 19
102 parameters conception space
CROR Optimization Chain Setup
Maximize efficiency @TOCMinimize acoustics @TOAero /Mech constraintsAero./Mech. constraints
Approximate ModelsAuto adaptive RBF
Design of Auto-adaptive RBF
networks
E l ti MO O ti i ti
Experiments
Evolutionary MO OptimizationDATABASE
l A RANSMinamo elsA RANS FE SAMCEF
Post treatment utilities
Minamo
Performance check
ONLINE modelingInfill criteria
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Success switchEND
CROR CFD Setup
• elsA (ONERA) RANS simulations with mixing plane• Absolute velocity formulation
N fl ti f fi ld BC• Non reflecting farfield BCs• k-ω Wilcox turbulence model• Jameson's scheme• Full Multigrid (2 levels)
• Mesh convergenceMesh convergence analysis (~ 3 106 nodes)• Cost functions convergence• Farfield boundaries positioning• Regeneration robustness
assesssed through dedicated DoEassesssed through dedicated DoE
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Lessons Learned Phase 2Acoustic cost function behaviour
A ti it i bAcoustic criterion may be seen as “minimization of R1 wake, up to the height of R2”
REFERENCE OPTIMIZEDŵ = projection of relative speed fluctuation on the normal to the mean flow
R2”
Wake of R1 reduced up toWake of R1 reduced up to the height of R2
R1 tip vortex strengthenedR1 tip vortex strengthened, but above R2 tip
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Pareto front (MM+CFD): acoustic cost function @TO vs global efficiency @TOC – Phase 3
V 1.2
Phase 2
V 2.0
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Pareto front: Acoustic cost function @TO vs global efficiency @TOC g y @
V 1.2
Phase 2 Gain: >10 dB
V 2.0
Phase 2A
coevel
Gain: >10 dBEffi: > 1.5 %
oustic cos
AeromechanicalOptimization Phase 3
Mechanical constraints most stringentA
cous
tic l
st functio
p
102 dimensions~ 500 function calls
Aon @
TO
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Global efficiency @ TOCGlobal efficiciency
Promising case (selected V2.2)Rotor 1 SS Pressure Distribution
OPTIMIZED REFERENCEOPTIMIZED REFERENCE
Non dimensional static pressure
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Example 2: Design of composite structures
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Structural preliminary design and optimization of composite structures
1. Objectives– Multi-disciplinary / multi-physics technical objectives:
• Maximize the stiffness• Minimize the mass• Maximize the buckling resistance• Minimize the max / average shear angle of plies due to draping onto complex
areas• Minimize drag (Fluid-structure interaction and CFD computations))•• …
– Economical objective:• Minimize the manufacturing cost (provided a realistic cost model)
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Structural preliminary design and optimization of composite structures
1. Constraints– Design rules– Manufacturing constraints– Maximum allowable mass– Damage criterion & modelsg– Technological (eg: problematic vibration, water ingress, flame retardant,
buckling, …) and geometrical constraints
2. Design space– Materials
• Constituents of the plies (fibres and matrix)• Constituents of the plies (fibres and matrix) • Ply thickness and orientation• Stacking sequence• Draping seed point curve splits orderDraping seed point, curve, splits, order
– Geometry• Position, angles, dimensions• Addition or removal of elements (quasi topological approach)Constraints
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
• Addition or removal of elements (quasi topological approach)Constraints
Structural preliminary design and optimization of composite structures
• Multi-objective, multi-constraint optimisation with a discrete & continuous variables– appropriate & efficient genetic algorithm enhanced with meta-
models (neural network, radial basis functions) for accelerated convergenceconvergence
• Direct access to CAD required for shape optimisation • CAD – Mesh – BCs – Materials associativityy• Materials database with appropriate formalism• Finite element solver with appropriate features (multi-layer shell
elements, failure criteria, …)• Other solvers for the technical objectives• Dedicated cost model introducing manufacturing constraints• In-house libraries & software interfaces
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Typical optimization workflows for composite structures
• Minamo – Catia CPD – Simulayt CompositeMinamo Catia CPD Simulayt Composite Link – Abaqus Link in Catia – Simulayt Composite Modeler – Abaqus – Seer DFMp q
• Minamo – Catia – FMS-FMD – CAPRI –vel Minamo Catia FMS FMD CAPRI
Simmetrix – CADMesh – Mecamesh –Samcef (also Samcef Gateway) – Seer DFMat
ion Lev
( y)
• Minamo – Catia – FMS-FMD – CAPRI –Autom
a
Simmetrix – CADMesh – MSC Nastran –Seer DFM
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Design and optimization of a satellites dispenser
Initial metallic design design violated constraints => composite
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Initial metallic design design violated constraints => composite
Design and optimization of a satellites dispenser
2 Objectives:• minimum massminimum mass• minimization of the frequency margin of the fi t l t l ib tifirst lateral vibration mode
352 Constraints:• Maximum allowed cost• Static dynamic• Static, dynamic• Buckling
Design space: laminates & geometry(25 design variables
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
reduced to 13 after ANOVA)
Optimization Loop Based on Samcef
Minamo.dat
MinamoTMopti.prjDetailed view:
cost.out response.out
Client (LINUX)
Serveur (Windows)
parameter_modification.pyScript Python
model.stlcost.out
Client (LINUX)
Serveur (Windows)
parameter_modification.pyScript Python
model.stl
- client‐server ops
- I/O operationsSEER
geometry_modification.ccGeometry_modification.ccCatia V5
model_reconstruction.pyScript Python
Serveur (Windows)
Client (LINUX) Catia V5
model_reconstruction.pyScript Python
Serveur (Windows)
Client (LINUX)
CADMeshPackagepost.cc
- meshing
- Functioning of in‐h lib i
SEERDFM
Simmetrix
mesh_translationmesh.dat
pli.datSimmetrix
mesh_translationmesh.dat
house libraries
...!parameter definitionINPUT “pli dat”
model.dattsai.txt mass.dat
...
INPUT “pli dat”
model.dat
disp.txt
mass.dat
Samcef V12.1-3
INPUT “pli.dat”INPUT “mesh.dat”
...model.res
INPUT “pli.dat”INPUT “mesh.dat”
!end of the definition ...
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Design and optimization of a satellites dispenser
1. A slight increase of Target mass
2. 7% improvement of the margin on thethe margin on the frequency
3. Cost reduced by 12%
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
y
Sensitivity of structural integrity to draping
• Nacelle subjected to pressure and with clamping conditions at the interface with theclamping conditions at the interface with the pylon
• Quasi-isotropic CFRP laminates with 10 pliesQuasi isotropic CFRP laminates with 10 plies
• Design space:• Design space:– Seed point for plies 1-5
• SM = static margin basedon the Tsaï Hill (th) criterionon the Tsaï-Hill (th) criterion
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Sensitivity of structural integrity to draping
Computational chainMinamo + Catia CPD –Simulayt Composite Link –Abaqus Link in Catia –Simulayt Composite
Flatpattern
Modeler – Abaqus
Shear
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Sensitivity of structural integrity to draping
Variable: Seed PointVariable: Seed Point
Ply 1 Ply 2 Ply 3 Ply 4 Ply 5
SM Region 1 12% 2% 2% 0% 4%
SM Region 2 8% 1% 9% 3% 3%
SM Region 3 2% 12% 6% 2% 2%
SM Region 4 1% 7% 0% 1% 5%
SM Region 5 8% 2% 0% 1% 1%
SM R i 6 7% 1% 14% 1% 2%SM Region 6 7% 1% 14% 1% 2%
SM Region 7 6% 23% 2% 22% 7%
SM Region 8 3% 0% 1% 8% 4% Coupled optimization of SM Region 8 3% 0% 1% 8% 4% Coup ed opt at o oplies orientations and manufacturing (automatedfiber placement
Orientation of plies + draping seed points position influence the behavior of the structural integraty
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
fiber placement.influence the behavior of the structural integraty.
Ongoing developments
Sampling and meta-modelingFurther development of auto adaptive samplingFurther development of auto-adaptive samplingKriging + Expected Improvement CriterionSurrogate models coupling: local/global - weighted averageRBFN (auto-)adaptive fine tuningSupport Vector Machines
Optimization - Hybridization:Memetic approaches / efficient global-local couplingExploitation of collective knowledge with multi parent crossoversExploitation of collective knowledge with multi-parent crossovers (UNDX).Gradient knowledge (SPSA, FDSA, …) to be incorporated in genetic
t di t b d t tioperators, e.g. gradient-based mutation.
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved
Conclusion
• Multiobjective, multidisciplinary optimization for complex design problems is not a dream ! Butcomplex design problems is not a dream ! But requires:
– Efficient and powerful optimization engines– Careful accuracy, steering and reliability ad-hocCareful accuracy, steering and reliability ad hoc
methodologies– Fully automated CAD to objective functions
icomputations– Enough computing power
Thank you for your attention
Teratec Forum 2010 – 16/06/2010 © 2010 Cenaero – All rights reserved