Mashiro KanazakiTokyo Metropolitan University

Efficient Design Exploration for Civil AircraftUsing a Kriging-Based Genetic Algorithm

Eurogen 2013 October 7–9, 2013, Las Palmas de Gran Canaria, Spain

Contents

IntroductionAerodynamic Design of Civil Transport

Optimization methodEfficient Global OptimizationData miningFlow solver

Case1: Optimization of wing integrated engine nacelle

Case2: Multi-disciplinary design of wing tipConclusions

2

Introductino1

Design Considering Many Requirement High fuel efficiency Low emission Low noise around airport Conformability

3

Aerodynamic Design of Civil Transport

Computer Aided Development For higher aerodynamic performance For noise reduction

Time consuming computational fluid dynamics (CFD)

Efficient and global optimization is desirable.

Many requirements for real world problem: cost, efficiency, emission, noise..

Many constraint, such astarget lift, minimization of bending and torsion moments → several evaluations for one case(10-30hours)

4Introduction2

Genetic algorithm with surrogate model is realistic method for aerodynamic design in aeronautical engineering

Efficient design

target Cl

Cl

Cdx

Introduction3

Several efficient and global optimizationCombination of heuristic optimization and

surrogate model Efficient Global Optimization(Jones, D. R., 1998)

Analysis design problem using data miningMulti-Objective Design Exploration (Obayashi, S. and

Jeong, S., 2005)

5

6ObjectivesIntroduction of efficient global optimization with high

fidelity flow solver (such as Navier-Stokes solver)Kriging modelGenetic AlgorithmKnowledge discovery using ANOVA and SOM

Application of realistic design problemWing design for an engine nacelle installed under

the wing (Case1)Multi-disciplinary design of wing let (Case2)

7Optimization Method(1/5) Surrogate model：Kriging model

Interpolation based on sampling data Standard error estimation (uncertainty)

)()( iiy xx

global model localized deviationfrom the global model

EI(Expected Improvement) The balance between optimality and uncertainty EI maximum point has possibility to improve the model.

Improvement at a point x is I=max(fmin-Y,0) Expected improvement E[I(x))]=E[max(fmin-Y,0)]To calculate EI,

Jones, D. R., “Efficient Global Optimization of Expensive Black-Box Functions,” J. Glob. Opt., Vol. 13, pp.455-492 1998.

8Optimization Method(2/5)

, ：standard distribution, normal density

：standard errors

Surrogate model construction

Multi-objective optimization

and Selection of additional samples

Sampling and Evaluation

Evaluation of additional samples

Termination?

Yes

Knowledge discovery

Knowledge based design

No

Kriging model

Genetic Algorithms

Simulation

Exact

Initial model

Initial designs

Additional designs

Improved model

Image of additional sampling based on EI for minimization problem.

9Optimization Method(3/5) Heuristic search：Genetic algorithm (GA)

Inspired by evolution of life Selection, crossover, mutation

BLX-0.5EI maximization → Multi-modal problem Island GA which divide the population into

subpopulationsMaintain high diversity

Design Methods (4/5) 10

Parallel Coordinate Plot (PCP) One of statistical visualization techniques from high-

dimensional data into two dimensional graph. Normalized design variables and objective functions are

set parallel in the normalized axis. Global trends of design variables can be visualized using

PCP.

niinii dxdxdxdxxxyx ,..,,,...,),.....,(ˆ)( 1111

nn dxdxxxy ,.....,),.....,(ˆ 11

nn

iii

dxdxxxy

dxxip

...),....,(ˆ 12

1

2

The main effect of design variable xi:

where:

Total proportion to the total variance:

where, εis the variance due to design variable xi.

variance

Inte

grat

e

μ 1

Proportion (Main effect)

11Optimization Method(5/5)

Analysis of VarianceOne of multi-valiate analysis for quantitative information

Knowledge management1

Aerodynamic evaluation 12

Navier-Stockes Solver for complex geometryGoverning equation: Reynolds Averaged Navier-Stokes

solverTurbulent model: Spalart-Allmaras modelTime integration: LU-SGSFlux evaluation HLLEW

Computational GridTetra based Unstructured GridTotal number of grid about 7 million.

Case１

Wing design for an engine nacelle installed under the wing

13

Engine integration problem 14

Purposes of this case Finding optimum wing integrated

engine Investigation of difference between

flow through engine and intake/exhaust simulation Flow through model: often use in wind

tunnel testing

Evaluation of Boundary Condition 15

IntakeNeumann condition

according to the flow in front of intake

ExhaustCalculate by / 0 , / 0

, : total pressure and temperature at boundary.0, 0: total pressure and temperature of main stream.

16Formulations

Design Variables Design rangedv1 Camber (Wing root) 0.00~1.00dv2 Camber (Wing kink) 0.00~1.00dv3 Camber (Wing tip) 0.00~1.00dv4 Twist angle at kink 0.01~0.50dv5 Twist angle at tip 0.50~2.00

Minimize CD (Drag coefficient)Subject to CL = 0.3

Optimization for two casesWith flow through engineWith simulating of intake/exhaust flow

Objective functions

Design variables

Design Exploration Result 17

With intake /exhaust flowFlow through

21 initial samples and six additional samples are calculated. In each case, additional samples carried out lower CD than the initial

samples.→Next interest is the difference of the design space.

Visualization by PCP 18

With intake /exhaust flowFlow through

Picking up five lowest CD design, higher kink camber and larger twist at kink and root in the case with intake/exhaust flow than those of flow through nacelle.

→ The engine driving condition remarkably effects to the design of inboard wing.

Visualization by ANOVA

Parameters effect to the difference (⊿Drag=Dragin/ex-Dragflowthrough)

19

Kink camber, dv2, showspredominant effect.

Root camber, dv1 and tipcamber dv1 also shows effect.

Twist angle has small effect.(Because the longitudinal angleof engine is changed accordingto wing twist.)

CFD-EFD integrationThese knowledge will be useful for

simulation/experiment integration.

20

DAHWIN system developed in JAXAVisit: http://integration2012.jaxa.jp/

http://www.aero.jaxa.jp/eng/

CFD-EFD integration 21

CFD EFD

Flow thorough

w/ in/ex flow w/ in/ex flow

Comparison

Comparison Prediction

Flow thorough

Case2Wing tip design considering the bending moment

22

Wing Tip Design Universal representation

23

Parameterization for global design exploration. Additional swept angle, twist and cant angle, taper ratio

Cant angle

Add. sweep

ctip

croot

TR=ctip/croot

・Blended winglet・Raked wingtip・Downward-facing winglet・Forward swept wingtip

Twist angle

Formulations 24

Minimize CD at M=0.85Minimize C_Mbend

Objective functions

Design variables

Base model: NASA’s common research model (CRM)

MO Design exploration result 25

Des20

Des21

Des20 is typical raked wing tip.→ It achieves lower drag.

Des21 is forward swept wing tip.→ It achieves low moment.

26Flow visualizations M=0.85 Impact of swept angle to flowfield

Smaller vortex with raked wing tip (Des20) Diffused vortex with forward swept wing tip (Des21)

des21des1 des20

27Conclusions High-efficient design procedure for aerodynamic design.Employment of EGO’s efficient global search

Genetic algorithm, and Kriging surrogate model

Knowledge discovery techniques, such as ANOVA and PCPDesign knowledge management

Two cases could successfully solved.Effect of the difference to the wing design due engine

driving conditionMulti-disciprinaly design of wing tip.