aerodynamic design of aircraft”
TRANSCRIPT
Engineering Optimization in Aircraft Design
Masahiro Kanazaki
Tokyo Metropolitan UniversityFaculty of System Design
Division of Aerospace Engineering
Follow me!: @Kanazaki_M
Lecture “Aerodynamic design of Aircraft” in University of Tokyo 21st December, 2015
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
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
What is engineering optimization? ~
Optimization, Exploration, Inovization
5
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)
Ob
jecti
ve f
un
cti
on
Optimization is not automatic
decision making tool.
Ob
jecti
ve f
un
cti
on
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
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
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
Optimization Methods based on
Heuristic Approach
10
Development of new aircraft…
Innovative ideas
Efficient 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）
Boeing787
Reconsider their plan to 787
Since 2002,,,
In Boeing
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
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
Fa
re
In engineering problem
ex.) Performance vs. CostAerodynamics vs. Structure
Performance vs. Environment
→ Trade-off
Optimization Methods based on Heuristic Approach
14Optimization 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
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
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
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
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
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
Surrogate modelPolynomial 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
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.
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
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
24Optimization 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 25
niinii dxdxdxdxxxyx ,..,,,...,),.....,(ˆ)( 1111
nn dxdxxxy ,.....,),.....,(ˆ11
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
Inte
gra
te
μ1
Proportion (Main effect)
Analysis of Variance
One of multivariate analysis for quantitative information
26Optimization 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
i=1, 2,…..NXi
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.PreparationPrototype vector
is randomized.
2.Search similar
vector W that
looks like Xi
Each 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.
28How 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
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.
Ex-i： Exhaust manifold design for
car engines
30
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
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
Ex-i: Exhaust manifold design for car engines 33
Evaluations
Engine cycle: Empirical one dimensional code
Exhaust manifold : Unstructured based three-dimensional Euler code
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
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
D
B (Maximum temperature)
Ex-i: Exhaust manifold design for car engines 36
1490 1500 1510 1520
85
87.5
90
Ch
arg
ing
eff
icie
ncy
(％
)
Temperature (K)
Initial
A
B
CDA (Maximum charging efficiency)
C
Ex-ii) Airfoil design for Mars airplane
~ airfoil representation/ parameterization
37
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
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.
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.
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
xazn
nt
5
1
0
n
n
nc xbxbz
CamberThickness
Ex-ii: Airfoil design for Mars airplane FormulationObjective 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 conditionVelocity=60m/s
Reynolds number：20,823.53
Mach 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)
44
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
45
Better solutions could
be acquired.
Ex-ii: Airfoil design for Mars airplane Optimum designs and their pressure distributions
46
Des_moga#1 Des_moga#2
Des_moga#3
Ex-ii: Airfoil design for Mars airplane 47
Visualization of design space by PCP
Ex-ii: Airfoil design for Mars airplane 48
l/d>45.0
Visualization of design space by PCP (sorted by max l/d)
Ex-ii: Airfoil design for Mars airplane 49
Cd0<0.0010
Visualization of design space by PCP(sorted by Cd0)
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 0.0539min 23.1859 0.0102 0.0035 25.7858 0.0091 0.0677 0.0214
SOGA MOGA
l/d>45.0
Cd0<0.0010
Ex-iii) Wing design for supersonic
transport ~ multi-disciplinary design
51
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)
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
54Ex-iii: Wing design for supersonic transportDesign 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
55Ex-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
56Ex-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
Loca
tion o
f aer
odyn
am
ic c
ente
r
Angle of horizontal tail
x
C. G.
57Ex-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.
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
59Ex-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
60Ex-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)
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.
ex-iv) Design exploration of optimum
installation for nacelle chine
62
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
64Ex-vi: Design exploration for nacelle chine installation
Design method
Efficient Global Optimization(EGO)
Experiment
Model’s half-span: 2.3m
Flow speed: 60m/s
Ex-vi: Design exploration for nacelle chine installation 65
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.)
Ex-vi: Design exploration for nacelle chine installation 66
Initial samples
Additional samples
Sampling result
χ
Ex-vi: Design exploration for nacelle chine installation 67
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 data
15 wind tunnel testing(approximately 7hours)
68
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.