14/01/20 "Engineering Optimization in Aircraft Design" Aerodynamic Design at Univ. of Tokyo
1. 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
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
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
Dr. information science
Experimental
evaluation
based design
optimization
Aerodynamic
design
for
complex
geometry
using genetic
algorithm
Aerodynamic
design of highlift
airfoil
deployment
using
highfidelity solver
Multidisciprinaly
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 ~ multidisciplinary design
iv. Design exploration for nacelle chine installation
6. 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
Optimization is not automatic
problem?
Objective function
Objective function
decision making tool.
Proper problem definition
Knowledge regarding the design problem
Design variable(s)
Design variable(s)
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
11. Optimization Methods based on Heuristic Approach
11
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
Market
Sonic Cruiser
shrink due
to 9.11
Because they have been had much knowledge
regarding aircraft development, it was easy for
them to change the plan.
Boeing787
Reconsider their plan to 787
12. Optimization Methods based on Heuristic Approach
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.
12
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?
・・・・ などなど
Multi-objective problem
The optimality is decided based on multi-phase
Example) How do you get to Osaka from Tokyo?
Pareto-solutions
Fare
Non-dominated solutions
Pareto optimum
Time
In engineering problem
ex.) Performance vs. Cost
Aerodynamics vs. Structure
Performance vs. Environment
→ Trade-off
13
14. Optimization Methods based on Heuristic Approach
14
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
x1
x2
x3
x4
x5
Parent
Child
Blended Cross Over - α
15
16. Optimization Methods based on Heuristic Approach
16
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.）
17. 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?
17
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
y (xi ) (xi )
Space
global model
localized deviation
from the global model
18
19. Optimization Methods based on Heuristic Approach
Sampling and Evaluation
Initial designs
Simulation
Surrogate model construction
Initial model
Kriging model
Exact
Additional designs
Evaluation of
additional samples
Multi-objective optimization
and Selection of additional samples
Termination?
No
Yes
Improved model
Image of additional sampling based on
EI for minimization problem.
Genetic Algorithms
Knowledge discovery
Knowledge based design
,
DR Jones, “Efficient Global Optimization of Expensive Black-Box Functions,” 1998.
s
：standard distribution,
normal density
：standard error
19
20. Optimization Methods based on Heuristic Approach
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
20
21. Optimization Methods based on Heuristic Approach
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 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 highdimensional 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.
22
23. Analysis of Variance
One of multivariate analysis for quantitative information
23
Integrate
Optimization Methods based on Heuristic Approach
The main effect of design variable xi:
ˆ
i ( xi ) y( x1 ,....., xn )dx1 ,..., dxi 1 , dxi 1 ,.., dxn
variance
ˆ
y( x1 ,....., xn )dx1 ,....., dxn
μ1
where:
Total proportion to the total variance:
pi
i xi dxi
2
ˆ
y ( x1 ,...., xn ) dx1 ...dxn
2
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
Multi-objective
Two-dimensional map
（Colored by an component, N
component plane, for N
dimensional input.）
24
25. Optimization Methods based on Heuristic Approach
How SOM is working.
Input data, (X1, X2, …., XN), Xi: vector (objective functions) : Designs
Xi
i=1, 2,…..N
W
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.
Map can be visualized by circle grid, square grid, Hexagonal grid, …
25
26. How to apply to the aircraft design
26
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
28. Ex-i: Exhaust manifold design for car engines
Engine cycle and exhaust manifold
Air
Muffler
Air cleaner
Catalysis
Intake manifold
排気マニホールド
Exhaust manifold
Intake port
Exhaust port
Intake valve
Exhaust valve
燃焼室
Remove Nox/Cox
Higher temperature
Smoothness of
exhaust gas
Higher charging
efficiency
charging efficiency(%)=100×
Volume of intake flow/Volume of cylinder
28
29. 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.
29
30. Ex-i: Exhaust manifold design for car engines
Evaluations
Engine cycle: Empirical one dimensional code
Exhaust manifold : Unstructured based three-dimensional Euler code
30
31. Ex-i: Exhaust manifold design for car engines
Geometry generation for manifold
1. Definition of each pipe
2. Detection the merging line
3. Merge pipes
31
32. Ex-i: Exhaust manifold design for car engines
Objective function
排気マニホールドの最適設計
Minimize Charging efficiency
Maximize Temperature of
exhaust gas
Design variables
Merging point and radius
distribution of pipes
merging3
p2
p1
merging1, 2
p2
p2
Definition of off-spring for merging point and radius
32
33. Ex-i: Exhaust manifold design for car engines
A (Maximum charging efficiency)
Charging efficiency (％)
A
C
90
87.5
D
B (Maximum temperature)
B
Initial
85
C
1490
1500
1510
Temperature (K)
1520
D
33
35. Ex-ii) Airfoil design for Mars airplane
Image of MELOS
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
35
36. 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*
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.
36
37. 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
** 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.
37
38. 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
6
z t an x
2 n1
2
n 1
Camber
5
zc b0 x bn x n
n 1
＋
39. 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
40. 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
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
0.35 for t/c=0.07c
41. Ex-ii: Airfoil design for Mars airplane
Design result (objective space)
Multi-Objective Genetic Algorithm: (MOGA)
Baseline
Des_moga#3
Des_moga#1
Des_moga#2
Trade-off can be found out.
41
42. Ex-ii: Airfoil design for Mars airplane
α vs. l/d, α vs. Cd, α vs. Cl
Better solutions could
be acquired.
42
43. Ex-ii: Airfoil design for Mars airplane
Optimum designs and their pressure distributions
Des_moga#1
Des_moga#3
Des_moga#2
43
49. Ex-iii: Wing design for supersonic transport
49
Supersonic Transport (SST)
Concord(retired)
One of SST for civil transport
Silent Supersonic Transport Demonstrator 3TD)
Flying across the Atlantic about three(S(S3TD)
Silent Supersonic Transport Demonstrator
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
SAI’s QSST
Without noise, environmental impact,
and sonic-boom
Development of small aircraft for
personal use.
JAXA
Concept of SST for commercial airline is desirable.
Aerion
50. 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
51
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
52
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. 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
53
C. G.
Angle of horizontal tail
Cl
Objective functions
Maximize L/D
Minimize ΔP
Minimize Ww
at M=1.6, CL =0.105
Trim balance
Location of aerodynamic center
Ex-iii: Wing design for supersonic transport
target Cl
Cd
x
54. Ex-iii: Wing design for supersonic transport
54
Design exploration results by EGO
DesA
DesB
DesA
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 Ww.
⇒ Why they are optimum solutions?
55. 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
Wwing
Sweep back is effective to boom intensity.
56. Ex-iii: Wing design for supersonic transport
56
Trade-off between objective function
L/D
(size of square represents BMU(Beat Matching Unit))
ΔP
Compromised solution
Wwing
Trade-off
Angle of HT
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?
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
Sweep back@Outboard
⇒ Low boom, high L/D (high lift)
Camber@Kink75%c
Blue box: Chosen by similarity of color map, Green box: Chosen by ANOVA result
57
58. 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)
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 4050days.
58
60. 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
63. Ex-vi: Design exploration for nacelle chine installation63
Sampling result
Initial samples
Additional samples
χ
64. Ex-vi: Design exploration for nacelle chine installation64
Sampling result (w/ additional samples)
Initial samples
Additional samples
Improvement of accuracy around optimum region
χ
65. Ex-vi: Design exploration for nacelle chine installation65
Projection of surrogate model to the CAD data
15 wind tunnel testing(approximately 7hours)
66. 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!)
