14/01/20 "engineering optimization in aircraft design" aerodynamic design at univ. of...
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Special lecture fot "Aerodynamic Design of Aircraft" at Univ. Tokyo, "Engineering Optimization in Aircraft Design."TRANSCRIPT
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)
9
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
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-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
Optimization Methods based on Heuristic Approach
14
Ranking of multi-objective problem~ Pareto Ranking
Pareto ranking method by Prof. Deb → Non-dominated Sorting
Lets consider minimization f1, f2
Optimization Methods based on Heuristic Approach
15
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
Optimization Methods based on Heuristic Approach
16
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.)
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 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
Optimization Methods based on Heuristic Approach
Co-variance
Space
19
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 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
Optimization Methods based on Heuristic Approach
22Optimization 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
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
24Optimization 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
25
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 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
27
28
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.
29
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
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)
Ex-i: Exhaust manifold design for car engines 33
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
34
Ex-ii) Airfoil design for Mars airplane Image of MELOS
35
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*
36
*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
37
** 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.
38
+
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)
41
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
42
Better solutions could be acquired.
Ex-ii: Airfoil design for Mars airplane Optimum designs and their pressure distributions
43
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
l/d>45.0
Visualization of design space by PCP (sorted by max l/d)
Ex-ii: Airfoil design for Mars airplane 46
Cd0<0.0010
Visualization of design space by PCP(sorted by Cd0)
Ex-ii: Airfoil design for Mars airplane 47
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
48
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
49
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
53Ex-iii: Wing design for supersonic transport
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.
54Ex-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
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.
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
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)
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 samples105CFD run×60min.=105hours (about 4-5days)
58
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
59
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
Ex-vi: Design exploration for nacelle chine installation 6262
# of design variables: 2 Radius θ Longitudinal length: χ
Objective function (1) maximize: CLmax
0.4cnacelle ≤ χ ≤ 0.8cnacelle30 (deg.) ≤ θ ≤ 90 (deg.)
Ex-vi: Design exploration for nacelle chine installation 63
Initial samples
Additional samples
Sampling result
χ
Ex-vi: Design exploration for nacelle chine installation 64
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)
65
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.