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EXCELLENCE IN SIMULATION TECHNOLOGIES
Multi-Disciplinary Optimization with Minamo
Ingrid Lepot Numerical Methods and Optimization Group, Cenaero
CESAR Training Workshop, Mar 18, 2009
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Surrogate Based Optimization
Approximate model
Obj
ectiv
e
PredictedOptimum
Design Variable
Initial Accurate Results
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Obj
ectiv
e
Design Variable
Initial Accurate Results
Approximate model
PredictedOptimum Artificial Neural Networks
Radial Basis Functions Kriging
Surrogate Based Optimization ONLINE modeling
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Adaptive Sampling Capability
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
UserUserSpecifications
Approximate ModelANN, RBF, Kriging, …
OptimizationOptimizationEA, gradient-based, …
Performance Check
DATABASEDATABASE
Accurate Model Accurate Model CFD / Structure / Exp. / ...
END
ONLINE modeling
Surrogate Assisted Optimization Workflow
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Derivative Free Optimization with Minamo
Less than 100 iterations
4 design variables
Multi-modal function
Local Minima
Minamo Software FunctionalitiesSpace filling DoE techniques: LHS,
Voronoï tessellations, Latinized Voronoï tesselations
Auto-adaptive DoESingle Objective Algorithms: GAs,
GAs/Gradient methods with surrogate models
Multiple Objectives Algorithms: Objective summation, Pareto GA, Pareto GA with surrogate model
Constraints: Transformed into penalties, handled directly by GA
Parallel: Any queuing systemUncomputable objective functionsEasy simulation CouplingQuantitative Variance Analysis CAD:
Efficient shape parameterization, Direct CAD access
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Monitoring/steering/analysis peripheral tools
• Response surfaces reliability through leave-k-out cross-validation
• Constraints activity monitoring• Quantitative Variance Analysis tool (ANOVA):
Sobol sensitivity indices estimation• Data mining utilities for high-dimensional output,
self organizing maps
Base mono-objective optimization capabilities integrated and available as Useropt
Minamo as Optimus Plug-in with Online Modeling
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Master script (Python or C++, called by Minamo)
CAPRI client
CA
D M
od
el
Ref
. mes
h
Linux
WindowsCAPRI server
CATIA V5 – UG – Pro/E …
TC
P/I
P
Mo
difi
ed
C
AD
mo
de
l
Simmetrix
IGG/AutoGrid 5
Mo
difi
ed
CA
D M
od
el
Mes
h
Ref
. m
esh
Direct CAD Access
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
import CAPRI
session = CAPRI.Session.Instance(“CatiaV5”)
session.Start()
model = session.LoadModel(“Wing”)
volume = model.VolumeAt(1)
volume.Retesselate(0, 0, 2.0, 178.0, 0.0, 0.0)
volume.ExportGMSH(“ref.msh”)
session.Stop()
import Simmetrix
Simmetrix.Session.Instance().Start()
model = Simmetrix.DiscreteModel(“ref.msh”)
mesh = Simmetrix.Mesh(model)
mesh.SetGlobalMeshSize(200.0)
for face in [1, 5, 7, 8, 9]:
mesh.SetLocalMeshSize(face, 20.0)
mesh.ModifySurfaceMesh()
mesh.GenerateVolumeMesh()
mesh.ExportGMSH(“mesh.msh”)
Simmetrix.Session.Instance().Stop()
CATIA V5 to 3D Unstructured CFD Mesh
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
CAD-based Wing MDO
CAD : CATIAV5
AutomaticMesh Generation
Parallel Aeroelastic Computation
Argo + Samcef
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
MS1-0313 Airfoil Optimization
• AC1 wing tip section• Bernstein third order polynomial parameterization
(7 parameters)– Leading edge radius– Trailing edge angle– Maximum thickness– Maximum thickness location– Camber at the leading edge– Camber at the trailing edge– Camber at the middle of the airfoil
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
MS1-0313 Airfoil Mesh
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Lift-over-drag Maximization (constrained Cm)
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Convergence (from DOE with 30 samples)
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Hierarchical blade shape parameterization
Stagger Angle Camber
Sweep
Lean
Chord
Lean Sweep
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Comparison of both geometries
2 gap values/2 operating points
Initial geometry
Optimal geometry
Efficiency - Mass flow
0,83
0,84
0,85
0,86
0,87
0,88
0,89
0,9
0,91
0,92
28,6 28,8 29 29,2 29,4 29,6 29,8 30 30,2
Mass flow
Isen
tro
pic
eff
icie
ncy
Optimal geometry with open gap
Optimal geometry with nominal gap
Initial geometry with nominal gap
Initial geometry with open gap
TE
TE
HP Compressor Rotor design (engine wear)
TE 0.4 kg/s
Mass Flow
Isentropic E
fficiency
0.2%
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
ANOVA – Sobol indices
Relative Importance of Parameters
0
0,05
0,1
0,15
0,2
0,25
0,3
cambe
r_S1_
1
cambe
r_S1_
3
cambe
r_S2_
2
cambe
r_S3_
1
cambe
r_S3_
3
cambe
r_S4_
2
cambe
r_S5_
1
cambe
r_S5_
3
cambe
r_S6_
2
stack
ing_S
1_X
stack
ing_S
3_X
stack
ing_S
5_X
stack
ing_S
1_Y
stack
ing_S
3_Y
stack
ing_S
5_Y
stagg
er_S
1
stagg
er_S
3
Stagge
r_S5
Shift_S
1
Shift_S
3
Shift_S
5
Axial_C
hord
_S1
Axial_C
hord
_S3
Axial_C
hord
_S5
Inter
actio
n
So
bo
l In
dic
es Isent_Eff_Large_Gap_1.10
Isent_Eff_Small_Gap_1.10
Isent_Eff_Large_Gap_1.13
Isent_Eff_Small_Gap_1.13
Section 5 first camber parameter
Illustration on NEWAC optimization accounting for engine wear
First order sensitivities and interaction volume (if required higher order sensitivities) quantification
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Geometry (Fixed) single mobile row – CATIA v5 parameterized hub endwall
Per individual 2 operating points computed: 1 close to peak efficiency and 1 close to the stability limit (elsA simulation / ≈ 2.2 M. grid points / tip clearance modeling / RANS k-l Smith turbulence model)
Objective
1st Mono-point optimization to freely search the design space
Maximize isentropic efficiency (free of constraint)
Two-point optimization
Maximize isentropic efficiency at design point
Constraint on Total-to-Total pressure ratio at close to stall point
Manufacturing constraints - Mass flow/Outlet angle monitoring
HP Compressor Rotor Hub Design
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Parameterization
CATIA v5 R17
16 parameters
Series of B-spline curves
Design between LE and TE
6 main control points in the blade channel that can move radially, axially and/or circumferentially
3D surfaces that follow the blade curvature
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Design Convergence History
Large DoE scatter - Stabilization after about 50 design iterations: 2 different promising design families pointed out, satisfying the manufacturing constraints
LOO Reliability Assessment:
Isentropic efficiency correlation coefficient
0.915502 (DoE) 0.9685 (optimization)
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Overall Performance Results
First mono-point optimization highlighted a marked total pressure drop close to stall
Need for robust multi-point design
Two-point design: Performance gain at the design point Efficiency increase by 0.4 % Mass flow increase only by 0.4% (DoE scatter > 1%) Total-to-total pressure ratio preserved close to stall Very moderate outlet flow angle alteration
Gain should be preserved in a stage environment Checked and confirmed (3D RANS simulations)
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Total relative pressure just downstream the blade
Marked losses decrease almost until 50%
Axisymmetric referenceOptimized design
Local (low mass flow BL zone) losses increase
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Relative Mach number in the B2B plane (23.6% span)
Marked decrease of the relative Mach number downstream the shock, in the region of flow acceleration
Optimized design Axisymmetric reference
Visible reduction of the wake
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Aero(-acoustic) open rotor optimization
Multi-point aerodynamic blade shape optimization for cruise/take-off – fixed or variable blade restaggering
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
SuMo/AutoGrid/elsA/Minamo chain
Reference geometryModified geometry
Maximization of propulsive efficiency@ CR while retaining thrust for both operating points 96 parameters
Farfield handled as a meridian technological effect
Key player in noise generation: Rotor 1 tip vortex trajectory/ Rotor 2 LE
Acoustic cost function implemented to be handled for noise minimization @ TO multi-objective optimization
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Techno-economical composite door optimization
Shapeoptimization
Materialoptimization
Manufacturingcost minimization
GeometryAngles & dimensionsAddition or removal of stiffeners or structural partsPosition changes
MaterialsLaminate definition (number of plies, stacking sequence, ply orientation, fibre volume fraction, nature of constituents)
Cost parametersMaterials, process, complexity, dimensions, manpower, tooling cost …Materials, process, complexity, Materials, process, complexity, dimensions, manpower, tooling cost …dimensions, manpower, tooling cost …
Shape & materials are linked to the manufacturing process which defines conditions of feasibility
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Numerical framework - Software
Optimization Minamo CAD Catia V5, Solidworks Direct access to CAD CADNexus CAPRI Meshing Simmetrix Materials database In-house FE Solver Samcef, Nastran Dedicated cost model Gallorath SEER-DFMTM In-house libraries CADMesh, Composites Optimization
Tool
• Multi-objective, multi-constraint optimization • with a large number of discrete, integer & continuous variables
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Connections and workflow
Excel
CATIA V5
SOLVER : SAMCEF
Post-processing
In-housetools
Material properties
modification
CAD Master Model modification
Material properties modification
CADConnexion
software
Material properties
Composite structure optimization with direct CAD access, mixed integer/real design variables
Minamo
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Pareto frontFront de Pareto
800
900
1000
1100
1200
1300
1400
11 11.5 12 12.5 13 13.5 14
Max Displacement Skin (mm)
Cos
t F
unct
ion
(eur
os)
ZONE de conception avec respect de masse < 45 kg.
SOLUTION 1
SOLUTION 2
SOLUTION 3
CESAR Workshop – March 18, 2009 © Copyright Cenaero 2009 – All rights reserved
Development Perspectives
Sampling and meta-modeling Further development of auto-adaptive sampling Kriging + Expected Improvement Criterion Surrogate models coupling: local/global - weighted average RBFN adaptive fine tuning Support Vector Machines
Optimization - Hybridization: Investigation of adequate GA – gradient based method (surrogate
based) switching. Exploitation of collective knowledge with multi-parent crossovers
(UNDX). Gradient knowledge (SPSA, FDSA, …) to be incorporated in
genetic operators, e.g. gradient-based mutation.