Lecture on “Aerodynamic design of Aircraft” in University of Tokyo 21st December, 2015. Optimization techniques, data-visualization and their applications are inclusive.

1. 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
Lecture “Aerodynamic design of Aircraft” in University of Tokyo 21st December, 2015

2. Resume ~ Masahiro Kanazaki
March, 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 Agency
April, 2008- , Associate Professor at Division of
Aerospace Engineering, Faculty of Engineering,
Tokyo Metropolitan University
Aerodynamic
design for
complex
geometry
using genetic
algorithm
Aerodynamic
design of high-
lift airfoil
deployment
using high-
fidelity solver
Experimental
evaluation
based design
optimization
Multi-
disciprinaly
design
optimization

3. 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

4. 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
5

6. What is optimization？(1/4)
 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?
Proper problem definition
Knowledge regarding the design problem
6
Design variable(s) Design variable(s)
Objectivefunction
Optimization is not automatic
decision making tool.
Objectivefunction

7. What is optimization？(2/4)
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)
7

8. What is optimization？(3/4)
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!
8

9. 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-mining
Multi-Objective Design Exploration: MODE:
Prof. Obayashi）
Innovation by the global design optimization
(Inovization: Prof. Deb)
Principle of design problem(Prof. Wu)
9

10. Optimization Methods based on
Heuristic Approach
10

11. Development of new aircraft…
 Innovative ideas
 Efficient methods
are required.
11
Optimization 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）
Boeing787
Reconsider their plan to 787
Since 2002,,,
In Boeing

12. Optimization Methods based on Heuristic Approach
 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.

13. 13
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-solutions
Non-dominated solutions
The optimality is decided based on multi-phase
Multi-objective problem
Time
Fare
In engineering problem
ex.) Performance vs. Cost
Aerodynamics vs. Structure
Performance vs. Environment
→ Trade-off
Optimization Methods based on Heuristic Approach

14. 14
Optimization Methods based on Heuristic Approach
 Multi-objective GA (MOGA)
 Pareto-ranking method
 Ranking of designs for multi-objective function
 Parents are selected based on the ranking.
Non-dominated solutions
Dominated solutions
 A rectangle by yellow point includes one individual. ⇒ rank=2
 A rectangle by blue point includes two individuals. ⇒ rank=3
 Rectangles by Red points do not include any other individual. ⇒ non-dominated solutions
Definition 1: Dominance
A vector u = (u1,….,u n) dominates v = (v1,….,vm) if u ≤ v and at least a set of ui ≤ vi.
Definition 2: Pareto-optimal
A solution x∈X is Pareto-optimal if there is no x’∈X for which f(x’) = (f1(x’),….,fn(x’))
dominates f(x) = (f1(x),….,fn(x)).
Minimize f1
Minimize f2
Optimum direction

15. 15
Heuristic search：Multi-objective
genetic algorithm (MOGA)
Inspired by evolution of life
Selection, crossover, mutation
Many evaluations ⇒High cost
Blended Cross Over - α
Parent
Child
x2 x4x3x1 x5
Optimization Methods based on Heuristic Approach

16. Optimization Methods based on Heuristic Approach
Two-objective case
Maximize f1=rcosθ
Maximize f2=rsinθ
subject to
0≦r ≦1, 0≦θ≦π/2
16
Pareto-optimal set must
foam a circle.
Non-dominated solutions

17. Optimization Methods based on Heuristic Approach
Three-objective case
Maximize f1=rsinθcosγ
Maximize f2=rsinθsinγ
Maximize f3=rcosθ
subject to
0≦r ≦1
0≦θ≦π/2, 0≦γ≦π/2
17
Pareto-optimal set must
foam a sphere.
Non-dominated solutions
It is hard to observe multi-dimensional
data (solution and design space.)

18. 18
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

19. Optimization Methods based on Heuristic Approach
Island model is similar to
something which is important
factor for the evolution of life.
Continental drift theory
 What do you think about it?
19

20. 20
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)
)()( ii
y xx  
global model localized deviation
from the global model
Optimization Methods based on Heuristic Approach
Co-variance
Space

21. 21
DR Jones, “Efficient Global Optimization of Expensive Black-Box Functions,” 1998.
Optimization Methods based on Heuristic Approach
, ：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.

22. Optimization Methods based on Heuristic Approach 22
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

23. 23
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
Optimization Methods based on Heuristic Approach

24. 24
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.

25. Optimization Methods based on Heuristic Approach 25
    niinii dxdxdxdxxxyx ,..,,,...,),.....,(ˆ)( 1111
nn dxdxxxy ,.....,),.....,(ˆ 11  
  
  

 nn
iii
dxdxxxy
dxx
ip
...),....,(ˆ 1
2
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
Integrate
μ1
Proportion (Main effect)
Analysis of Variance
One of multivariate analysis for quantitative information

26. 26
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
Two-dimensional map
（Colored by an component, N
component plane, for N
dimensional input.）
Design-objective
Multi-objective

27. 27
i=1, 2,…..N
Xi
W
Optimization Methods based on Heuristic Approach
Input data, (X1, X2, …., XN), Xi: vector (objective functions) : Designs
Map can be visualized by circle grid, square grid, Hexagonal grid, …
1.Preparation
Prototype vector
is randomized.
2.Search similar
vector W that
looks like Xi
Each prototype vector
is compared with one
input vector Xi.
3.Learning1
W is moved toward Xi.
W = W +α(Xi- W)
4.Learning2
W’s neighbors are
moved toward Xi.
How SOM is working.

28. 28
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

29. 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 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!)
Today’s lecture is engineering optimization.

30. Ex-i： Exhaust manifold design for
car engines
30

31. 31
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 manifold
Remove 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

32. Ex-i: Exhaust manifold design for car engines
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.
32

33. Ex-i: Exhaust manifold design for car engines 33
Evaluations
 Engine cycle: Empirical one dimensional code
 Exhaust manifold : Unstructured based three-dimensional Euler code

34. Ex-i: Exhaust manifold design for car engines 34
Geometry generation for manifold
1. Definition of each pipe
2. Detection the merging line
3. Merge pipes

35. Ex-i: Exhaust manifold design for car engines 35
排気マニホールドの最適設計
 Objective function
 Minimize Charging efficiency
 Maximize Temperature of
exhaust gas
 Design variables
 Merging point and radius
distribution of pipes
merging3 merging1, 2
Definition of off-spring for merging point and radius
p1 p2
p2 p2

36. D
B (Maximum temperature)
Ex-i: Exhaust manifold design for car engines 36
1490 1500 1510 1520
85
87.5
90
Chargingefficiency(％)
Temperature (K)
Initial
A
B
C
DA (Maximum charging efficiency)
C

37. Ex-ii) Airfoil design for Mars airplane
~ airfoil representation/ parameterization
37

38. Ex-ii) Airfoil design for Mars airplane
Image of MELOS
38
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

39. Ex-ii: Airfoil design for Mars airplane
Airfoil representation for unknown design problem
 B-spline curve, NURBS
High degree of freedom
Parameterization which dose not considered aerodynamics
 PARSEC(PARametric SECtion) method*
39
*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.

40. 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
40
** 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.

41. 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.
41
＋
2
126
1

 
n
xaz
n
nt 

5
1
0
n
n
nc xbxbz
CamberThickness

42. Ex-ii: Airfoil design for Mars airplane
Formulation
 Objective functions
Maximize maximum l/d
Minimize Cd0（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

43. 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 0.6000
dv3 z-coord. of maximum thickness 0.0350 0.0350
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

44. Ex-ii: Airfoil design for Mars airplane
Design result (objective space)
 Multi-Objective Genetic Algorithm: (MOGA)
44
Des_moga#2
Des_moga#1
Des_moga#3
 Trade-off can be found out.
Baseline

45. Ex-ii: Airfoil design for Mars airplane
α vs. l/d, α vs. Cd, α vs. Cl
45
Better solutions could
be acquired.

46. Ex-ii: Airfoil design for Mars airplane
Optimum designs and their pressure distributions
46
Des_moga#1 Des_moga#2
Des_moga#3

47. Ex-ii: Airfoil design for Mars airplane 47
Visualization of design space by PCP

48. Ex-ii: Airfoil design for Mars airplane 48
l/d>45.0
Visualization of design space by PCP (sorted by max l/d)

49. Ex-ii: Airfoil design for Mars airplane 49
Cd0<0.0010
Visualization of design space by PCP(sorted by Cd0)

50. Ex-ii: Airfoil design for Mars airplane 50
 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 0.0539
min 23.1859 0.0102 0.0035 25.7858 0.0091 0.0677 0.0214
SOGA MOGA
l/d>45.0
Cd0<0.0010

51. Ex-iii) Wing design for supersonic
transport ~ multi-disciplinary design
51

52. 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
52
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)

53. Ex-iii: Wing design for supersonic transport 53
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 CFD
Low boom airframe concept
multi-fidelity CFD
Exploration using genetic algorithm
Requirement of high efficient design process
Silent Supersonic Transport Demonstrator (S3TD)
NEXST1

54. 54
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

55. 55
Ex-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

56. 56
Ex-iii: Wing design for supersonic transport
Objective functions
Maximize L/D
Minimize ΔP
Minimize Ww
at M=1.6, CL =0.105
Trim balance
Decision of angle of horizontal tail
(HT) ⇒ total of 12 CFD evaluations
Setting aerodynamic center same
location with center of gravity
Realistic aircraft’s layout
target Cl
Cl
Cd
Locationofaerodynamiccenter
Angle of horizontal tail
x
C. G.

57. 57
Ex-iii: Wing design for supersonic transport
Design exploration results by EGO
Many additional samples around non-dominated solutions
⇒ Why they are optimum solutions?
DesB
DesA
DesCDesC
DesA 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.

58. Ex-iii: Wing design for supersonic transport
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

59. 59
Ex-iii: Wing design for supersonic transport
Trade-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

60. 60
Ex-iii: Wing design for supersonic transport
Comparison 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)

61. Ex-iii: Wing design for supersonic transport
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)
61
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.

62. ex-iv) Design exploration of optimum
installation for nacelle chine
62

63. Ex-vi: Design exploration for nacelle chine installation 63
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

64. 64
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

65. Ex-vi: Design exploration for nacelle chine installation65
65
 # of design variables: 2
 Radius θ
 Longitudinal length: χ
 Objective function (1)
 maximize: CLmax
0.4cnacelle ≤ χ ≤ 0.8cnacelle
30 (deg.) ≤ θ ≤ 90 (deg.)

66. Ex-vi: Design exploration for nacelle chine installation66
Initial samples
Additional samples
Sampling result
χ

67. Ex-vi: Design exploration for nacelle chine installation67
χ
Improvement of accuracy around optimum region
Sampling result (w/ additional samples)
Initial samples
Additional samples

68. Ex-vi: Design exploration for nacelle chine installation
Projection of surrogate model to the CAD data
15 wind tunnel testing(approximately 7hours)
68

69. 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 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!)
Today’s lecture is engineering optimization.