14/01/20 "Engineering Optimization in Aircraft Design" Aerodynamic Design at Univ. of Tokyo

Engineering Optimization in Aircraft Design

Masahiro KanazakiTokyo Metropolitan University

Faculty of System DesignDivision of Aerospace Engineering

[email protected] me!: @Kanazaki_M

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

Resume ~ Masahiro KanazakiMarch, 2001 Finish my master course at Graduated school of Mechanical and Aerospace Engineering, Tohoku university March, 2004 Finish my Ph.D. at Faculty at Graduated school of Information Science, Tohoku university

Dr. information science

April, 2004-March, 2008 Invited researcher at Japan Aerospace Exploration AgencyApril, 2008- , Associate Professor at Division of Aerospace Engineering, Faculty of Engineering, Tokyo Metropolitan University

Aerodynamicdesign forcomplexgeometryusing geneticalgorithm

Aerodynamicdesign of high-lift airfoildeploymentusing high-fidelity solver

Experimentalevaluationbased designoptimization

Multi-disciprinalydesignoptimization

Contents(1/2)1. What is engineering optimization? ~ Optimization,

Exploration, Inovization2. 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 methodiv. Knowledge discovery – Data mining，Multi-variate

analysis3. Aircraft Design Problem

i. Fundamental constraintsii. Evaluation of aircraft performanceiii. 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

What is engineering optimization? ~ Optimization, Exploration, Inovization

5

What is optimization？(1/4) Acquire the minimum/ maximum/ ideal solution of a functionSuch 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?Proper problem definitionKnowledge regarding the design problem

6

Design variable(s) Design variable(s)

Obj

ectiv

e fu

nctio

n

Optimization is not automatic decision making tool.

Obj

ectiv

e fu

nctio

n

What is optimization？(2/4)Mathematical approach Finding the point which function’s gradient=0

→Deterministic approachLocal optimums Assurance of optimalityGradient method (GM)

Population based searching (=exploration)→Heuristic method

Global exploration and global optimumsApproximate optimum but knowledge can acquired

based on the data set in the populationEvolutionary strategy (ES)

7

What is optimization？(3/4)Real-world design problem/ system integration

（Aerodynamic, Stricture, Control）Importance of design problem definitionEfficient optimization methodPost 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 processConsider interesting and useful design problem!

8

What is optimization？(4/4)Recent history of “optimization”Finding single optimum (max. or min.) point

（Classical idea）

“Design exploration” which includes the optimization and the data-miningMulti-Objective Design Exploration: MODE:

Prof. Obayashi）Innovation by the global design optimization

(Inovization: Prof. Deb)Principle of design problem(Prof. Wu)

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Optimization Methods based on Heuristic Approach

10

Development of new aircraft… Innovative ideasEfficient methods

are required.

11Optimization Methods based on Heuristic Approach

Because they have been had much knowledge regarding aircraft development, it was easy for them to change the plan.

Example which show the importance of knowledge

Boeing767

Sonic Cruiser

Announcement of development “sonic cruiser” in 2001

Market shrink due to 9.11

Mitsubishi Regional Jet（MRJ）

Boeing787Reconsider their plan to 787

Since 2002,,,

In Boeing


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

12

Aerodynamic Design of Civil Transport

Computer Aided Design For higher aerodynamic performance For noise reduction

↔ Time consuming computational fluid dynamics (CFD)

Efficient and global optimization is desirable.

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Pareto optimum

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?・・・・などなど

Example) How do you get to Osaka from Tokyo?

Pareto-solutionsNon-dominated solutions

The optimality is decided based on multi-phaseMulti-objective problem

Time

Fare In engineering problem

ex.) Performance vs. CostAerodynamics vs. StructurePerformance vs. Environment

→ Trade-off


14

Ranking of multi-objective problem～ Pareto Ranking

Pareto ranking method by Prof. Deb → Non-dominated Sorting

Lets consider minimization f1, f2


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Heuristic search：Multi-objective genetic algorithm (MOGA)Inspired by evolution of lifeSelection, crossover, mutationMany evaluations ⇒High cost

Blended Cross Over - α

Parent

Child

x2 x4x3x1 x5


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For high efficiency and high the diversityGA 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.）



Island model is similar to something which is important factor for the evolution of life.Continental drift theoryWhat do you think about it?

17

18

Surrogate modelPolynomial response surfaceIdentification coefficients whose existent

fanctionKriging methodInterpolation based on sampling dataModel of objective functionStandard error estimation (uncertainty)

)()( iiy xx

global model localized deviationfrom the global model


Co-variance

Space

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DR Jones, “Efficient Global Optimization of Expensive Black-Box Functions,” 1998.


, ：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.

Optimization Methods based on Heuristic Approach 20

Heuristic search：Genetic algorithm (GA)Inspired by evolution of lifeSelection, crossover, mutationBLX-0.5

EI maximization → Multi-modal problemIsland GA which divide the population into

subpopulationsMaintain high diversity

21

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 visuallyThree kind of techniques regarding knowledge

discoveryGraphs in Statistical Analysis → Application of

conventional graph method Machine learning → Abductive reasoningAnalysis of variance→Multi-validate analysis



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

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)

Analysis of VarianceOne of multivariate analysis for quantitative information


Self-organizing map for qualititative information Proposed by Prof. Kohonen Unsupervised learning Nonlinear projection algorithm from high to two dimensional map

Two-dimensional map （Colored by an component, N component plane, for N dimensional input.）

Design-objective

Multi-objective

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i=1, 2,…..NXi

W


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

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

1.PreparationPrototype vector is randomized.

2.Search similar vector W that looks like XiEach prototype vector is compared with one input vector Xi.

3.Learning1W is moved toward Xi.W = W +α(Xi- W)

4.Learning2W’s neighbors are moved toward Xi.

How SOM is working.

26How to apply to the aircraft designSeveral constraints should be considered.In aircraft design, following constraints are required. Lift=WeightTrim balance

Evaluation High-fidelity solver, Low-fidelity solverExperiment

CADHow to represent the geometry.NURBS, B-splinePARSEC airfoil representation

Ex-i： Exhaust manifold design for car engines

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Air cleaner

Intake manifold

Intake port

Intake valve

Air

燃焼室

Muffler

排気マニホールド

Exhaust port

Exhaust valve

Catalysis

Smoothness of exhaust gas

Higher temperatureExhaust manifoldRemove Nox/Cox

Higher charging efficiency

Engine cycle and exhaust manifold

charging efficiency(%)=100×Volume of intake flow/Volume of cylinder

Ex-i: Exhaust manifold design for car engines

Ex-i: Exhaust manifold design for car engines

Exhaust manifoldLead exhaust air from several camber

to one catalysisMerging geometry effect to the powerChemical reaction in the catalysis is

promoted at high temperature.

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Ex-i: Exhaust manifold design for car engines 30

Evaluations Engine cycle: Empirical one dimensional code Exhaust manifold : Unstructured based three-dimensional Euler code


Geometry generation for manifold

1. Definition of each pipe

2. Detection the merging line

3. Merge pipes


排気マニホールドの最適設計 Objective functionMinimize Charging efficiencyMaximize Temperature of

exhaust gas Design variablesMerging point and radius

distribution of pipes

merging3 merging1, 2

Definition of off-spring for merging point and radius

p1 p2

p2 p2

D

B (Maximum temperature)


1490 1500 1510 1520

85

87.5

90

Cha

rgin

g ef

ficie

ncy

(％)

Temperature (K)

Initial

A

B

CDA (Maximum charging efficiency)

C

Ex-ii) Airfoil design for Mars airplane

~ airfoil representation/ parameterization

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Ex-ii) Airfoil design for Mars airplane Image of MELOS

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Ikeshita/JAXA Exploration by winged vehicle

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 Airfoil representation for unknown design problemB-spline curve, NURBS

High degree of freedomParameterization which dose not considered aerodynamics

PARSEC(PARametric SECtion) method*

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*Sobieczky, H., “Parametric Airfoils and Wings,” Notes on Numerical Fluid Mechanics, pp. 71-88, Vieweg 1998.

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.

Ex-ii: Airfoil design for Mars airplane 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

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** 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 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.

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＋

2126

1

n

xazn

nt

5

10

n

nnc xbxbz

CamberThickness

Ex-ii: Airfoil design for Mars airplane Formulation Objective functions

Maximize maximum l/dMinimize Cd0（zero-lift drag）

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

EvaluationStructured mesh based flow solver

Baldwin-Lomax turbulent modelFlow condition (same as Martian atmosphere)

Density=0.0118kg/m3

Temperature=241.0KSpeed of sound=258.0m/s

Design conditionVelocity=60m/sReynolds number：20,823.53Mach number：0.233

Ex-ii: Airfoil design for Mars airplane

Design variables

0.35 for t/c=0.07c

Upper bound Lower bound

dv1 LE radius 0.0020 0.0090

dv2 x-coord. of maximum thickness 0.2000 0.6000dv3 z-coord. of maximum thickness 0.0350 0.0350dv4 curvature at maximum thickness -0.9000 -0.4000dv5 angle of TE 5.0000 10.0000dv6 camber radius at LE 0.0000 0.0060dv7 x-coord. of maximum camber 0.3000 0.4000dv8 z-coord. of maximum camber 0.0000 0.0800dv9 curvature at maximum camber -0.2500 0.0100dv10 z-coordinate of TE -0.0400 0.0100dv11 angle of camber at TE 4.0000 14.0000

Ex-ii: Airfoil design for Mars airplane Design result (objective space) Multi-Objective Genetic Algorithm: (MOGA)

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Des_moga#2

Des_moga#1

Des_moga#3

Trade-off can be found out.

Baseline

Ex-ii: Airfoil design for Mars airplane α vs. l/d, α vs. Cd, α vs. Cl

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Better solutions could be acquired.

Ex-ii: Airfoil design for Mars airplane Optimum designs and their pressure distributions

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Des_moga#1 Des_moga#2

Des_moga#3

Ex-ii: Airfoil design for Mars airplane 44

Visualization of design space by PCP


l/d>45.0

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


Cd0<0.0010

Visualization of design space by PCP(sorted by Cd0)


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.

maxl/d th25 th75 maxl/d Cd0 th25 th75

max 54.2988 0.0700 0.1046 49.3560 0.0335 0.0700 0.0539min 23.1859 0.0102 0.0035 25.7858 0.0091 0.0677 0.0214

SOGA MOGA

l/d>45.0Cd0<0.0010

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

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Ex-iii: Wing design for supersonic transport

Concord(retired) One of SST for civil transport Flying across the Atlantic about three

hours High-cost because of bad fuel economy Noise around airport Sonic-boom in super cruise

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Supersonic Transport (SST)

Next generation SST For trans/intercontinental travel With high aerodynamic performance Without noise, environmental impact,

and sonic-boom Development of small aircraft for

personal use.Concept of SST for commercial airline is desirable.

AerionSAI’s QSST

SAI: Supersonic Aerospace International LLC.

JAXA

Silent Supersonic Transport Demonstrator (S3TD)Silent Supersonic Transport Demonstrator (S3TD)

Ex-iii: Wing design for supersonic transport 50

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

Flight of unpowered experimental model in 2005.

Conceptual design of supersonic business jet.

Low drag design using CFDLow boom airframe concept

multi-fidelity CFDExploration using genetic algorithm

Requirement of high efficient design process

Silent Supersonic Transport Demonstrator (S3TD)

NEXST1

51Ex-iii: Wing design for supersonic transportDesign method

Efficient Global Optimization (EGO)Genetic , Kriging modelAnalysis of variance (ANOVA)Self-organizing map (SOM)

EvaluationsFull 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

52Ex-iii: Wing design for supersonic transport

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

Table 1 Design space.Design variables


Objective functionsMaximize L/DMinimize ΔPMinimize Ww

at M=1.6, CL =0.105Trim balanceDecision of angle of horizontal tail

(HT) ⇒ total of 12 CFD evaluationsSetting aerodynamic center same

location with center of gravityRealistic aircraft’s layout

target Cl

Cl

Cd

Loca

tion

of a

erod

ynam

ic c

ente

r

Angle of horizontal tail

x

C. G.


Design exploration results by EGO

Many additional samples around non-dominated solutions

⇒ Why they are optimum solutions?

DesB

DesA

DesCDesCDesA DesB

Extreme Pareto solutions (to be discussed later):DesA achieves the higest L/D, DesB achieves the lowest ΔP, and DesC achieves the lowest Ww.


Effect of root camber ⇒ influence on aerodynamic performance of inboard wing at supersonic cruise

Sweep back is effective to boom intensity.

ANOVA: effect of dvs

L/D ΔP

Wwing

Effect of root camber

Effect of sweep back angle at wing root

56Ex-iii: Wing design for supersonic transportTrade-off between objective function

(size of square represents BMU(Beat Matching Unit))L/D

Compromised solution

Compromised solution can be observed.

L/D↓, Wwing↓, and Angle of HT↑ ⇒Lift of the wing is relative small.

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

ΔP

Angle of HTWwing Trade-off

57Ex-iii: Wing design for supersonic transportComparison of component planes

L/D ΔP Wwing Angle of HT

Sweep back@Inboard Camber@Kink25%c Camber@Root25%c

Blue box: Chosen by similarity of color map, Green box: Chosen by ANOVA result

Larger sweep back

⇒ Low boom, high L/D (low drag)

Sweep back@Outboard Camber@Kink75%c

Small camber at LE and large camber at TE

⇒ Low boom, high L/D (high lift)


Computational efficiency・CAPAS evaluation in 60min./case (including

decision of angle of HT)75 initial samples + 30 additional samples

= total of 105 samples105CFD run×60min.=105hours (about 4-5days)

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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.

ex-iv) Design exploration of optimum installation for nacelle chine

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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

61Ex-vi: Design exploration for nacelle chine installation

Design methodEfficient Global Optimization(EGO)

ExperimentModel’s half-span: 2.3mFlow speed: 60m/s


# of design variables: 2 Radius θ Longitudinal length: χ

Objective function (1) maximize: CLmax

0.4cnacelle ≤ χ ≤ 0.8cnacelle30 (deg.) ≤ θ ≤ 90 (deg.)


Initial samples

Additional samples

Sampling result

χ


χ

Improvement of accuracy around optimum region

Sampling result (w/ additional samples)Initial samples

Additional samples

Ex-vi: Design exploration for nacelle chine installation

Projection of surrogate model to the CAD data15 wind tunnel testing(approximately 7hours)

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Conclusion

“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 problemSurrogate model to reduce the design cost

Application to aircraft designProper objectives, constraints and evaluation method (It is

most difficult issue for designers!)

Today’s lecture is engineering optimization.

14/01/20 "Engineering Optimization in Aircraft Design" Aerodynamic Design at Univ. of Tokyo

Design

Transcript of 14/01/20 "Engineering Optimization in Aircraft Design" Aerodynamic Design at Univ. of Tokyo