Multi-Disciplinary Optimization with Minamo · optimization Shape optimization Material...

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


Obj

ectiv

e

Design Variable

Initial Accurate Results

Approximate model

PredictedOptimum Artificial Neural Networks

Radial Basis Functions Kriging

Surrogate Based Optimization ONLINE modeling


Adaptive Sampling Capability


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


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


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


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


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


CAD-based Wing MDO

CAD : CATIAV5

AutomaticMesh Generation

Parallel Aeroelastic Computation

Argo + Samcef


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


MS1-0313 Airfoil Mesh


Lift-over-drag Maximization (constrained Cm)


Convergence (from DOE with 30 samples)


Hierarchical blade shape parameterization

Stagger Angle Camber

Sweep

Lean

Chord

Lean Sweep


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%


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


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


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


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)


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)


Total relative pressure just downstream the blade

Marked losses decrease almost until 50%

Axisymmetric referenceOptimized design

Local (low mass flow BL zone) losses increase


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


Aero(-acoustic) open rotor optimization

Multi-point aerodynamic blade shape optimization for cruise/take-off – fixed or variable blade restaggering


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


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


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


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


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


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.

Multi-Disciplinary Optimization with Minamo · optimization Shape optimization Material...

Documents

Transcript of Multi-Disciplinary Optimization with Minamo · optimization Shape optimization Material...