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Special lecture fot "Aerodynamic Design of Aircraft" at Univ. Tokyo, "Engineering Optimization in...

Special lecture fot "Aerodynamic Design of Aircraft" at Univ. Tokyo, "Engineering Optimization in Aircraft Design."

- Lecture “Aerodynamic design of Aircraft” in University of Tokyo 20th January, 2014

Engineering Optimization in Aircraft Design

Masahiro Kanazaki

Tokyo Metropolitan University

Faculty of System Design

Division of Aerospace Engineering

kana@sd.tmu.ac.jp

Follow me!: @Kanazaki_M - Resume ~ Masahiro Kanazaki

March, 2001 Finish my master course at

April, 2004-March, 2008 Invited researcher at

Graduated school of Mechanical and Aerospace

Japan Aerospace Exploration Agency

Engineering, Tohoku university

April, 2008- , Associate Professor at Division of

March, 2004 Finish my Ph.D. at Faculty at

Graduated school of Information Science, Tohoku

Aerospace Engineering, Faculty of Engineering,

university

Tokyo Metropolitan University

Dr. information science

Experimental

Multi-

evaluation

disciprinaly

based design design

optimization

optimization

Aerodynamic

Aerodynamic

design

for

design of high-

complex

lift

airfoil

geometry

deployment

using

genetic

using

high-

algorithm

fidelity solver - Contents(1/2)

1. What is engineering optimization? ~ Optimization,

Exploration, Inovization

2. Optimization Methods based on Heuristic Approach

i.

How to evaluate the optimality of the multi-objective

problem. ~ Pareto ranking method

ii. Genetic algorithm (GA)

iii. Surrogate model，Kriging method

iv. Knowledge discovery – Data mining，Multi-variate

analysis

3. Aircraft Design Problem

i.

Fundamental constraints

ii. Evaluation of aircraft performance

iii. Computer aided design - Contents(1/2)

4. Examples

i.

Exhaust manifold design for car engines ~ automated

design of complex geometry and application of MOGA

ii. Airfoil design for Mars airplane ~ airfoil representation/

parameterization

iii. Wing design for supersonic transport ~ multi-

disciplinary design

iv. Design exploration for nacelle chine installation - 5

What is engineering optimization? ~

Optimization, Exploration, Inovization - What is optimization？(1/4)

6

Acquire the minimum/ maximum/ ideal solution of a function

Such point can be acquired by searching zero gradient

Multi-point will shows zero gradient, if the function is multi-modal.

Are only such points the practical optimum for real-world

problem?

Optimization is not automatic

Proper problem definition

decision making tool.

Knowledge regarding the design problem

Objective function

Objective function

Design variable(s)

Design variable(s) - What is optimization？(2/4)

7

Mathematical approach

Finding the point which function’s gradient=0

→Deterministic approach

Local optimums

Assurance of optimality

Gradient method (GM)

Population based searching (=exploration)

→Heuristic method

Global exploration and global optimums

Approximate optimum but knowledge can acquired

based on the data set in the population

Evolutionary strategy (ES) - What is optimization？(3/4)

8

Real-world design problem/ system integration

（Aerodynamic, Stricture, Control）

Importance of design problem definition

Efficient optimization method

Post process, visualization（similar to numerical

simulation）

In my opinion,

Engineering optimization is a tool to help every

engineers.

We (designers) need useful opinion from veterans.

Significance of pre/post process

Consider interesting and useful design problem! - What is optimization？(4/4)

9

Recent history of “optimization”

Finding single optimum (max. or min.) point

（Classical idea）

“Design exploration” which includes the

optimization and the data-mining

Multi-Objective Design Exploration: MODE:

Prof. Obayashi）

Innovation by the global design optimization

(Inovization: Prof. Deb)

Principle of design problem(Prof. Wu) - 10

Optimization Methods based on

Heuristic Approach - 11

Optimization Methods based on Heuristic Approach

Example which show the importance of knowledge Since 2002,,,

Development of new aircraft…

Innovative ideas

Efficient methods

are required.

Mitsubishi Regional Jet（MRJ）

In Boeing

Boeing767

Announcement of development

“sonic cruiser” in 2001

Sonic Cruiser

Market

shrink due

to 9.11

Boeing787

Because they have been had much knowledge

Reconsider their plan to 787

regarding aircraft development, it was easy for

them to change the plan. - Optimization Methods based on Heuristic Approach 12

Aerodynamic Design of Civil Transport

Design Considering Many Requirement

High fuel efficiency

Low emission

Low noise around airport

Conformability

Computer Aided Design

For higher aerodynamic performance

For noise reduction

↔ Time consuming computational

fluid dynamics (CFD)

Efficient and global optimization is

desirable. - 13

Optimization Methods based on Heuristic Approach

Multi-objective → Pareto ranking

Real-world problem generally has multi-objective.

If a lecture is interesting but its examination is very

difficult, what do you think?

Multi-objective problem

・・・・ などなど

The optimality is decided based on multi-phase

Example) How do you get to Osaka from Tokyo?

Pareto-solutions

Non-dominated solutions

e

In engineering problem

Far

ex.) Performance vs. Cost

Aerodynamics vs. Structure

Pareto optimum

Performance vs. Environment

Time

→ Trade-off - 14

Optimization Methods based on Heuristic Approach

Ranking of multi-objective problem

～ Pareto Ranking

Lets consider minimization f1, f2

Pareto ranking method by Prof. Deb

→ Non-dominated Sorting - 15

Optimization Methods based on Heuristic Approach

Heuristic search：Multi-objective

genetic algorithm (MOGA)

Inspired by evolution of life

Selection, crossover, mutation

Many evaluations ⇒High cost

x

x

x

x

x

1

2

3

4

5

Parent

Child

Blended Cross Over - α - 16

Optimization Methods based on Heuristic Approach

For high efficiency and high the diversity

GA is suitable for parallel computation

（ex: One PE uses for one design evaluation.）

Distributed environment scheme/ Island mode

（ex: One PE uses for one set of design evaluations.） - Optimization Methods based on Heuristic Approach 17

Island model is similar to

something which is important

factor for the evolution of life.

Continental drift theory

What do you think about it? - 18

Optimization Methods based on Heuristic Approach

Surrogate model

Polynomial response surface

Identification coefficients whose existent

fanction

Kriging method

Interpolation based on sampling data

Model of objective function

Standard error estimation (uncertainty)

Co-variance

( i

y x ) ( i

x )

Space

global model

localized deviation

from the global model - 19

Optimization Methods based on Heuristic Approach

Sampling and Evaluation

Initial designs

Simulation

Surrogate model construction

Initial model

Kriging model

Exact

Evaluation of

Multi-objective optimization

Additional designs

additional samples

and Selection of additional samples

Genetic Algorithms

Termination?

No

Yes

Improved model

Knowledge discovery

Image of additional sampling based on

Knowledge based design

EI for minimization problem.

, ：standard distribution,

normal density

s

：standard error

DR Jones, “Efficient Global Optimization of Expensive Black-Box Functions,” 1998. - Optimization Methods based on Heuristic Approach 20

Heuristic search：Genetic algorithm (GA)

Inspired by evolution of life

Selection, crossover, mutation

BLX-0.5

EI maximization → Multi-modal problem

Island GA which divide the population into

subpopulations

Maintain high diversity - 21

Optimization Methods based on Heuristic Approach

We can obtain huge number of data set.

What should we do next?

Visualization to understand design problem

→Datamining, Multivariate analysis

To understand the design problem visually

Three kind of techniques regarding knowledge

discovery

Graphs in Statistical Analysis → Application of

conventional graph method

Machine learning

→ Abductive reasoning

Analysis of variance→Multi-validate analysis - 22

Optimization Methods based on Heuristic Approach

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. - Optimization Methods based on Heuristic Approach 23

Analysis of Variance

One of multivariate analysis for quantitative information

Integrate

The main effect of design variable xi:

(x ) yˆ(x ,.....,x dx

)

,..., dx , dx ,.., dx

i

i

1

n

1

i 1

i 1

n

variance

where:

yˆ(x ,.....,x dx

)

,.....,dx

μ 1

1

n

1

n

Total proportion to the total variance:

2

i ix

p

i

dx

i

2

yˆ( x ,....,x )

1

n

dx ...dx

1

n

where, εis the variance due to design variable xi.

Proportion (Main effect) - 24

Optimization Methods based on Heuristic Approach

Self-organizing map for qualititative information

Proposed by Prof. Kohonen

Unsupervised learning

Nonlinear projection algorithm from high to two dimensional map

Design-objective

Two-dimensional map

（Colored by an component, N

component plane, for N

Multi-objective

dimensional input.） - 25

Optimization Methods based on Heuristic Approach

How SOM is working.

Input data, (X1, X2, …., XN), Xi: vector (objective functions) : Designs

i=1, 2,…..N

Xi

W

1.Preparation

2.Search similar

3.Learning1

4.Learning2

Prototype vector

vector W that

W is moved toward X .i

W’s neighbors are

is randomized.

looks like X

W = W +α(X - W)

i

i

moved toward X .i

Each prototype vector

is compared with one

input vector Xi.

Map can be visualized by circle grid, square grid, Hexagonal grid, … - 26

How to apply to the aircraft design

Several constraints should be considered.

In aircraft design, following constraints are required.

Lift=Weight

Trim balance

Evaluation

High-fidelity solver, Low-fidelity solver

Experiment

CAD

How to represent the geometry.

NURBS, B-spline

PARSEC airfoil representation - 27

Ex-i： Exhaust manifold design for

car engines - 28

Ex-i: Exhaust manifold design for car engines

Engine cycle and exhaust manifold

Air

Air cleaner

Muffler

Catalysis

Intake manifold

Remove Nox/Cox

排気マニホールド

Exhaust manifold

Higher temperature

Smoothness of

Intake port

Exhaust port

exhaust gas

Higher charging

Intake valve

Exhaust valve

efficiency

燃焼室

charging efficiency(%)=100×

Volume of intake flow/Volume of cylinder - Ex-i: Exhaust manifold design for car engines

29

Exhaust manifold

Lead exhaust air from several camber

to one catalysis

Merging geometry effect to the power

Chemical reaction in the catalysis is

promoted at high temperature. - Ex-i: Exhaust manifold design for car engines

30

Evaluations

Engine cycle: Empirical one dimensional code

Exhaust manifold : Unstructured based three-dimensional Euler code - Ex-i: Exhaust manifold design for car engines

31

Geometry generation for manifold

1. Definition of each pipe

2. Detection the merging line

3. Merge pipes - Ex-i: Exhaust manifold design for car engines

32

Objective function

排気マニホールドの最適設計

Minimize Charging efficiency

Maximize Temperature of

merging3

merging1, 2

exhaust gas

Design variables

Merging point and radius

distribution of pipes

p2

p2

p1

p2

Definition of off-spring for merging point and radius - Ex-i: Exhaust manifold design for car engines

33

A

C

B (Maximum temperature)

A (Maximum charging efficiency)

D

)

90

％

B

ficiency ( 87.5

Initial

ging ef

Char

85

C

1490

1500

1510

1520

D

Temperature (K) - 34

Ex-ii) Airfoil design for Mars airplane

~ airfoil representation/ parameterization - Ex-ii) Airfoil design for Mars airplane

35

Image of MELOS

Exploration by winged vehicle

Ikeshita/JAXA

Propulsion

Aerodynamics

Structural dyanamics

・Atmosphere density: 1% that of

the earth

・Requirement of airfoil which has

higher aerodynamic performance - Ex-ii: Airfoil design for Mars airplane

36

Airfoil representation for unknown design problem

B-spline curve, NURBS

High degree of freedom

Parameterization which dose not considered aerodynamics

PARSEC(PARametric SECtion) method*

Parameterization based on the

knowledge of transonic flow

Define upper surface and lower surface,

respectively

Suitable for automated optimization and

data mining

Camber is not define directly.

→ It is not good for the airfoil design

which has large camber.

*Sobieczky, H., “Parametric Airfoils and Wings,” Notes on Numerical Fluid Mechanics, pp. 71-88, Vieweg 1998. - Ex-ii: Airfoil design for Mars airplane

37

Modification of PARSEC representation**

Thickness distribution and camber are defined,

respectively.

Theory of wing section

Maintain beneficial features of original PARSEC

Same number of design variables.

Easy to understand by visualization because the parameterization is in

theory of wing section

** K. Matsushima, Application of PARSEC Geometry Representation to High-Fidelity Aircraft Design by CFD,

proceedings of 5th WCCM/ ECCOMAS2008, Venice, CAS1.8-4 (MS106), 2008. - Ex-ii: Airfoil design for Mars airplane

38

Parameterization of modified PARSEC method

The center of LE radius should be on the camber line, because

thickness distribution and camber are defined, respectively.

Thickness distribution is same as symmetrical airfoil by original

PARSEC.

Camber is defined by polynomial function.

Square root term is for design of LE radius.

Thickness

Camber

6

2 n 1

5

2

z

z b x

n

b

x

c

0

t

a x

n

n

n 1

n 1

＋ - Ex-ii: Airfoil design for Mars airplane

Formulation

Objective functions

Maximize maximum l/d

Minimize C （

d0 zero-lift drag）

subject to t/c=target t/c (t/c=0.07c)

Evaluation

Structured mesh based flow solver

Baldwin-Lomax turbulent model

Flow condition (same as Martian atmosphere)

Density=0.0118kg/m3

Temperature=241.0K

Speed of sound=258.0m/s

Design condition

Velocity=60m/s

Reynolds number：20,823.53

Mach number：0.233 - Ex-ii: Airfoil design for Mars airplane

Design variables

Upper bound Lower bound

dv1

LE radius

0.0020

0.0090

dv2

x-coord. of maximum thickness

0.2000

0.6000

dv3

z-coord. of maximum thickness

0.0350

0.0350

0.35 for t/c=0.07c

dv4

curvature at maximum thickness

-0.9000

-0.4000

dv5

angle of TE

5.0000

10.0000

dv6

camber radius at LE

0.0000

0.0060

dv7

x-coord. of maximum camber

0.3000

0.4000

dv8

z-coord. of maximum camber

0.0000

0.0800

dv9

curvature at maximum camber

-0.2500

0.0100

dv10 z-coordinate of TE

-0.0400

0.0100

dv11 angle of camber at TE

4.0000

14.0000 - Ex-ii: Airfoil design for Mars airplane

41

Design result (objective space)

Multi-Objective Genetic Algorithm: (MOGA)

Des_moga#3

Baseline

Des_moga#1

Des_moga#2

Trade-off can be found out. - Ex-ii: Airfoil design for Mars airplane

42

α vs. l/d, α vs. Cd, α vs. Cl

Better solutions could

be acquired. - Ex-ii: Airfoil design for Mars airplane

43

Optimum designs and their pressure distributions

Des_moga#1

Des_moga#2

Des_moga#3 - Ex-ii: Airfoil design for Mars airplane

44

Visualization of design space by PCP - Ex-ii: Airfoil design for Mars airplane

45

Visualization of design space by PCP (sorted by max l/d)

l/d>45.0 - Ex-ii: Airfoil design for Mars airplane

46

Visualization of design space by PCP(sorted by C )

d0

Cd0<0.0010 - Ex-ii: Airfoil design for Mars airplane

47

SOGA

MOGA

maxl/d

th25

th75

maxl/d

Cd0

th25

th75

max

54.2988

0.0700

0.1046

49.3560

0.0335

0.0700

0.0539

min

23.1859

0.0102

0.0035

25.7858

0.0091

0.0677

0.0214

Cd0<0.0010

l/d>45.0

Larger LE thickness (th25)→same trend compared with baseline

Larger maxl/d should be smaller (dv4(zxx)) (Larger curvature)→TE thickness (th75)

becomes smaller，

Smaller Cd0should be larger (dv5)，dv4(zxx)→ thickness of TE (th75) becomes

larger. - 48

Ex-iii) Wing design for supersonic

transport ~ multi-disciplinary design - Ex-iii: Wing design for supersonic transport

49

Supersonic Transport (SST)

Concord(retired)

One of SST for civil transport

Flying across the Atlantic

Silent Supersonic T

about three

ransport Demonstrator (S3TD)

Silent Supersonic Transport Demonstrator (S3TD)

hours

High-cost because of bad fuel economy

Noise around airport

Sonic-boom in super cruise

Next generation SST

SAI: Supersonic Aerospace International LLC.

For trans/intercontinental travel

With high aerodynamic performance

Without noise, environmental impact,

SAI’s QSST

Aerion

and sonic-boom

Development of small aircraft for

personal use.

JAXA

Concept of SST for commercial airline is desirable. - Ex-iii: Wing design for supersonic transport

50

Development and research of SST in Japan (conducted by JAXA)

NEXST1

Silent Supersonic Transport Demonstrator (S3TD)

Flight of unpowered experimental model in 2005.

Low drag design using CFD

Low boom airframe concept

multi-fidelity CFD

Exploration using genetic algorithm

Conceptual design of supersonic business jet.

Requirement of high efficient design process - 51

Ex-iii: Wing design for supersonic transport

Design method

Efficient Global Optimization (EGO)

Genetic , Kriging model

Analysis of variance (ANOVA)

Self-organizing map (SOM)

Evaluations

Full potential solver，MSC.NASTRAN

Design problem for JAXA’s silent SST demonstrator

# of design variables(14)

# of objective functions(3)

Aerodynamic performance

Sonic boom

Structural weight - 52

Ex-iii: Wing design for supersonic transport

Design variables

Table 1 Design space.

Design variable

Upper bound Lower bound

dv1

Sweepback angle at inboard section

57 (°)

69 (°)

dv2

Sweepback angle at outboard section

40 (°)

50 (°)

dv3

Twist angle at wing root

0 (°)

2(°)

dv4

Twist angle at wing kink

–1 (°)

0 (°)

dv5

Twist angle at wing tip

–2 (°)

–1 (°)

dv6

Maximum thickness at wing root

3%c

5%c

dv7

Maximum thickness at wing kink

3%c

5%c

dv8

Maximum thickness at wing tip

3%c

5%c

dv9

Aspect ratio

2

3

dv10

Wing root camber at 25%c

–1%c

2%c

dv11

Wing root camber at 75%c

–2%c

1%c

dv12

Wing kink camber at 25%c

–1%c

2%c

dv13

Wing kink camber at 25%c

–2%c

1%c

dv14

Wing tip camber at 25%c

–2%c

2%c - 53

Ex-iii: Wing design for supersonic transport

Objective functions

center

Maximize L/D

C. G.

aerodynamic

Minimize ΔP

Angle of horizontal tail

Minimize W

Location of

w

at M=1.6, CL =0.105

lC

Trim balance

target Cl

Decision of angle of horizontal tail

Cd

(HT) ⇒ total of 12 CFD evaluations

Setting aerodynamic center same

location with center of gravity

Realistic aircraft’s layout

x - 54

Ex-iii: Wing design for supersonic transport

Design exploration results by EGO

DesA

DesA

DesB

DesB

DesC

DesC

Many additional samples around non-dominated solutions

Extreme Pareto solutions (to be discussed later):

DesA achieves the higest L/D, DesB achieves the lowest ΔP, and DesC achieves the lowest W

⇒ Why they are optimum solutions?

w. - Ex-iii: Wing design for supersonic transport

ANOVA: effect of dvs

L/D

ΔP

Effect of root camber

Effect of sweep back angle at wing root

Effect of root camber ⇒ influence on

aerodynamic performance of inboard wing

at supersonic cruise

W

Sweep back is effective to boom intensity.

wing - 56

Ex-iii: Wing design for supersonic transport

Trade-off between objective function

(size of square represents BMU(Beat Matching Unit))

L/D

ΔP

Compromised solution

W

Angle of HT

wing

Trade-off

Compromised solution can be observed.

L/D↓, W

↓, and Angle of HT↑ ⇒Lift of the wing is relative small.

wing

14 Colored component plane for design variables ⇒ Which dvs are important? - 57

Ex-iii: Wing design for supersonic transport

Comparison of component planes

L/D ΔP Wwing

Angle of HT

Larger sweep back

⇒ Low boom, high L/D (low drag)

Sweep back@Inboard

Camber@Kink25%c Camber@Root25%c

Small camber at LE and large camber at TE

⇒ Low boom, high L/D (high lift)

Sweep back@Outboard

Camber@Kink75%c

Blue box: Chosen by similarity of color map, Green box: Chosen by ANOVA result - Ex-iii: Wing design for supersonic transport

58

Computational efficiency

・CAPAS evaluation in 60min./case (including

decision of angle of HT)

75 initial samples + 30 additional samples

= total of 105 samples

105CFD run×60min.=105hours (about 4-5days)

If we use direct GA search with 30population and 100 generation, total of

3000CFD run is needed.

If we use only high-fidelity solver (ex. 10hours/case), it takes total of about 40-

50days. - 59

ex-iv) Design exploration of optimum

installation for nacelle chine - Ex-vi: Design exploration for nacelle chine installation 60

Nacelle chine:

For improve the stall due to the interaction of

the vortex from the nacelle/ pylon and the

wing at landing.

Nacelle installation problem:

It is difficult to evaluate

complex flow interaction by

CFD.

⇒ Introduction of experiment

based optimization - 61

Ex-vi: Design exploration for nacelle chine installation

Design method

Efficient Global Optimization(EGO)

Experiment

Model’s half-span: 2.3m

Flow speed: 60m/s - 62

Ex-vi: Design exploration for nacelle chine installation 62

# of design variables: 2

Radius θ

Longitudinal length: χ

0.4c

≤ χ ≤ 0.8c

nacelle

nacelle

30 (deg.) ≤ θ ≤ 90 (deg.)

Objective function (1)

maximize: CLmax - Ex-vi: Design exploration for nacelle chine installation 63

Sampling result

Initial samples

Additional samples

χ - Ex-vi: Design exploration for nacelle chine installation 64

Sampling result (w/ additional samples)

Initial samples

Additional samples

Improvement of accuracy around optimum region

χ - Ex-vi: Design exploration for nacelle chine installation 65

Projection of surrogate model to the CAD data

15 wind tunnel testing(approximately 7hours) - Conclusion

Today’s lecture is engineering optimization.

“Optimization” is mathematical techniques to

acquire minimum/ maximum point.

Formulation/ visualization are important → How to

formulate interesting and useful design problem. Design

methods for real-world problem

Evolutionary algorithm is useful for multi-objective problem

Surrogate model to reduce the design cost

Application to aircraft design

Proper objectives, constraints and evaluation method (It is

most difficult issue for designers!)