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Multi-Objective Design Exploration Multi-Objective Design Exploration (MODE)(MODE)
- - Visualization and Mapping of Design Visualization and Mapping of Design SpaceSpace
ShigeruShigeru ObayashiObayashi
Institute of Fluid ScienceInstitute of Fluid ScienceTohoku UniversityTohoku University
2
BackgroundBackground
Flow VisualizationFlow Visualization
Multidisciplinary Design Optimization (MDO) Multidisciplinary Design Optimization (MDO)
Self-Organizing Map (SOM)Self-Organizing Map (SOM)
Rough SetRough Set
Multi-Objective Design Exploration (MODE)Multi-Objective Design Exploration (MODE)
Application to Regional Jet DesignApplication to Regional Jet Design
Wing-Nacelle-Pylon-Body ConfigurationWing-Nacelle-Pylon-Body Configuration
Analysis of Sweet-Spot ClusterAnalysis of Sweet-Spot Cluster
ConclusionConclusion
OutlineOutline
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Flow Visualization -1 Flow Visualization -1
Flow transition:Reynolds number
4
Flow Visualization -2 Flow Visualization -2
Stall: boundary layer separation
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Flow Visualization -3 Flow Visualization -3
Karman Votex
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Flow Visualization -4 Flow Visualization -4
Drag divergence:shock wave
Flow visualization: Seeing is believing (Seeing is understanding)
(Picture is worth a thousand words)
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Aircraft DesignAircraft Design
Aerodynamics Propulsion Structure
•Compromise of all disciplines•Multidisciplinary Design Optimization (MDO) Multidisciplinary Design Optimization (MDO) as Multi-Objective Optimization (MOP) as Multi-Objective Optimization (MOP)
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Collection of non-dominated solutions that form trade-offs between multiple objectives
Gradient-based method with weights between objectivesUtility function: f = f1 + f2
Other analytical methodsNormal-Boundary Intersection MethodAspiration Level Method
Multi-Objective Evolutionary Algorithms (MOEAs)Population-based search
f1
f2
Gradient-based methodf1
f2
MOEAs
How to Solve MOPHow to Solve MOP
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X Arithmatic Average
Improvement
Pareto front
f1
f2
Extreme Pareto Solution
Extreme Pareto SolutionPareto Front
f1
f2
Pareto front
f1
f2
Pareto front
f1
f2
Global optimization is neededVisualization is essential!Data mining is requiredDesign optimization→Design exploration
How to Understand MOPHow to Understand MOP
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Visualization of TradeoffsVisualization of Tradeoffs
2 objectives 3 objectives
?4 objectives
Pro
ject
ion
Minimization problems
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Self-Organizing MapSelf-Organizing Map (( SOMSOM ))
Neural network model proposed by KohonenUnsupervised, competitive learning
High-dimensional data → 2D map
Qualitative description of data
•Node represents a neuron.-Neuron is a three-dimensional vector (Obj.1, Obj.2, Obj.3)-Each neuron corresponds to a design.
•Neuron is self-organized so that similar neurons are neighbored to each other. •Similar neurons form a cluster
SOM provides design visualization: Seeing is understanding(Essential design tool)
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Colored SOMs identify the global structure of the design space
Resulting clusters classify possible designsIf a cluster has all objectives near optimal, it is called as sweet-spot cluster
If the sweet-spot cluster exists, it should be analyzed in detail
Visualization of design variables
Data mining, such as decision tree and rough set
How to understand SOM better?How to understand SOM better?
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Rough SetRough Set - Pawlak(1982) -- Pawlak(1982) -
Granulation of informationReduction of informationExtraction of rules
(knowledge acquisition)
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Rough Set and AttributeRough Set and Attribute
U Condition attribute C Decision attribute D
Vehicle type
Engine Size Color Preference
x1 propane compact black good
x2 diesel medium gold bad
x3 diesel full white bad
x4 diesel medium red bad
x5 gasoline compact black good
x6 gasoline medium silver good
x7 gasoline full white bad
x8 gasoline compact silver good
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x1 , x2 , x3 , x4 , x5 , x6 , x7 ,x8
U
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U
x5 , x6 , x8 , x7
x1Propane x2 , x3 , x4
Diesel
Gasoline
Good
U Condition attribute C Decision attribut
e D
Vehicle
Engine Size Color Preference
x1 propane
compact
black good
x2 diesel medium gold bad
x3 diesel full white bad
x4 diesel medium red bad
x5 gasoline
compact
black good
x6 gasoline
medium silver good
x7 gasoline
full white bad
x8 gasoline
compact
silver good
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U
x5 , x6 , x8 , x7
x1Propane x2 , x3 , x4
Diesel
Gasoline
Good
Upper approximation
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U
x5 , x6 , x8 , x7
x1Propane x2 , x3 , x4
Diesel
Gasoline
Good
Lower approximation
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U
x5 , x6 , x8 , x7
x1Propane x2 , x3 , x4
Diesel
Gasoline
Good
Lower approximation
Rule extraction by lower approximation : if propane then good
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x 5 , x8
x1PropaneCompact
x 2 , x4DieselMedium
GasolineCompact
Good
Engine +Size
x 3Dieselfull
x 7Gasolinefull
x6GasolineMedium
U
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x 6 , x8
x1PropaneBlack
GasolineSilver
x 3DieselWhite
x 7GasolineWhite
x5
GasolineBlack
x 2DieselGold
x 4DieselRed
Engine +Color
Good
U
Two attributes out of thee are sufficient→ reduct (reduced set of attributes)
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What is MODE?What is MODE?
Multi-objective Genetic
Algorithm
Computational Fluid Dynamics
Design Database
Design Knowledge
Visualization and Data Mining
Multi-Objective Design Exploration (MODE)
Step 1Multi-objective
Shape Optimization
Step 2Knowledge Mining
Data mining:maps, patterns,models, rules
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Small Jet Aircraft R&D ProjectSmall Jet Aircraft R&D Project
More Electric
Advanced Human-Centered Cockpit
Health Monitoring System for
LRU
FSW(Friction Stir Welding)
Aero-Structure Multi-Disciplinary Design Optimization
New Light Composite Material
Optimized High Lift Device
Advanced Higher L/D Wing
New Energy and Industrial Technology Development Organization (NEDO)
Mitsubishi Heavy Industries
Fuji Heavy IndustriesTohoku University
R&D Organization
Research Collaboration
R&DActivities
Japan Aircraft Development Corporation (JADC)
Japan Aerospace Exploration Agency (JAXA)
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Present MODE SystemPresent MODE System
FEM mesh
CFD mesh
START
END
Latin Hypercube Sampling
Design variables
NURBS airfoil
3D wing
Wing-body configuration
Definition of Design Space
CFD (FP/Euler)
Pressure distribution Load condition
FLEXCFD
Strength & flutter requirements
Static analysis modelFlutter analysis model
Structural optimization code + NASTRAN
Aerodynamic & structural performance
CFD&CSD moduleCFD&CSD module
Initial Kriging model
MOGA(maximization of EIs)
Selection of additional sample points
Design variables
Mesh generation CFD&CSDCFD&CSD
Update of Kriging model
Continue ?
Kriging model & Kriging model & optimization moduleoptimization module
Aerodynamic & structural performance
No
Yes
Data mining
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Optimization of Wing-Nacelle-Pylon-Body Optimization of Wing-Nacelle-Pylon-Body ConfigurationConfiguration
Shock wave
Shock wave occuring at inboard of pylon may lead Shock wave occuring at inboard of pylon may lead to to separationseparation and and buffetingbuffeting
26= 0.29
Definition of Optimization Problem -1Definition of Optimization Problem -1 - Objective Functions - - Objective Functions -
MinimizeMinimize
Function evaluation toolsFunction evaluation tools
1.1. Drag at the cruising condition (CDrag at the cruising condition (CDD))
2.2. Shock strength near wing-pylon junction (-CShock strength near wing-pylon junction (-Cp,maxp,max))
3.3. Structural weight of main wing (wing weight)Structural weight of main wing (wing weight)
・ ・ CFDCFD :: Euler code (TAS-code)Euler code (TAS-code)・ ・ CSD/Flutter analysisCSD/Flutter analysis : : MSC. NASTRANMSC. NASTRAN
0.00 0.20 0.40 0.60 0.80 1.00 1.20
x/c
-Cp
-CP distribution of lower surface @η=0.29
–Cp,max
–Cp
x/c
27= 0.29 = 0.12
・ ・ Lower surface of Airfoil shapes at 2 spanwise sections Lower surface of Airfoil shapes at 2 spanwise sections (η= 0.12, 0.29) (η= 0.12, 0.29)
→ → 13 variables (NURBS) × 2 sections = 26 variables13 variables (NURBS) × 2 sections = 26 variables ・ ・ Twist angles at 4 sections = 4 variables Twist angles at 4 sections = 4 variables 30 30 variables in totalvariables in total
(0, dv1)
(dv2, dv3)
(dv4, dv5) (dv6, dv7)
(dv8, dv9)
(dv10, dv11)
(dv12, dv13)
NURBS control pointsNURBS control points
Definition of Optimization Problem -2Definition of Optimization Problem -2 - Design Variables - - Design Variables -
28CD
Win
g w
eig
ht
[kg
]
Initial sample points
Additinal sample points
Baseline
-Cpmax
Win
g w
eig
ht
[kg
]
Initial sample points
Additional sample points
Baseline
CD
-Cp
ma
x
Initial sample points
Additional sample points
Baseline
Performances of baseline shape and sample pointsPerformances of baseline shape and sample points
Optimum Direction
Optimum Direction
Optimum Direction
0.2
20 counts
20 kg
0.5
20 kg
20 counts
CD vs. –Cp,max –Cp,max vs. wing weight
CD vs. wing weight
Point APoint A
Point A
Point A is improved by 6.7 counts in CD, 0.61 in –Cp,max, and 12.2 kg in wing weight compared with the baseline
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Definition of Configuration Variables for Data MiningDefinition of Configuration Variables for Data Mining
XmaxLmaxLXmaxTCmaxTCsparTC
At wing root and pylon locations↓10 variables
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obj1
0.018 0.022
obj2
0.4 1.0 1.7
obj3
758 827 895
dv1
13 28 42 56
dv2
19 31 44 56
dv3
8 9 10 12
dv4
6.3 7.3 8.3
dv5
14 24 34 44
dv6
23 32 42 51
dv7
14 15 16 18
dv8
12 13 13 14
dv9
12 14 16 18
dv10
10 11 12 13
Visualization of Design Space Visualization of Design Space
SOM with 9 clusters
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Analysis of Sweet–Spot ClusterAnalysis of Sweet–Spot Cluster
HandpickParallel coordinatesExtraction of design rules by
discretization of configuration variablesVisualizationRough set
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- Cpmax
dv632%
dv1016%
dv4- dv69%
dv29%
dv48%
dv4- dv107%
dv15%
その他14%
obj2
0.4 0.5 0.7 0.8 0.9 1.1 1.2 1.4 1.5 1.7
dv6
23 26 29 32 36 39 42 45 48 51
XmaxTC@η=0.29
HandpickHandpick-C-Cp,maxp,max and dv6 (XmaxTC at pylon) and dv6 (XmaxTC at pylon)
Analysis of Variance (ANOVA)
Others
0.00 0.20 0.40 0.60 0.80 1.00 1.20
x/c
-Cp
Airfoil-Cp
Large Large dv6dv6
0.00 0.20 0.40 0.60 0.80 1.00 1.20
x/c
-Cp
Airfoil
-Cp
Small Small dv6dv6
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Visualization of SOM Clusters by Parallel Coordinates Visualization of SOM Clusters by Parallel Coordinates
䢢 SOM clustering (x value) - 0
䢢 SOM clustering (x value) - 1
䢢 SOM clustering (x value) - 2
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Discretization of Configuration VariablesDiscretization of Configuration Variablesby Equal Frequency Binningby Equal Frequency Binning
Index
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Finding Design Rules by VisualizationFinding Design Rules by Visualization
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dv08
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dv09
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Binned
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dv10
Sweet-spot cluster
Airfoil parameters
dv2 XmaxL @ = 0.29
dv6 XmaxTC @ = 0.29
dv9 sparTC @ = 0.12
dv10 sparTC @ = 0.29
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Flowchart of Data Mining Using Rough Set Flowchart of Data Mining Using Rough Set
Discretization of numerical data
Reduction
Generation of rules
Filtering
Interpretation of rules
Preparation of data
Free softwareROSETTA
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Generated rules to belong to sweet spot Generated rules to belong to sweet spot cluster with support of more than eight cluster with support of more than eight
occurrenceoccurrenceRule Count
dv1([33.08, 39.30)) AND dv2([40.69, *)) AND dv5([29.65, 33.61)) AND dv7([15.09, 15.83)) AND dv9([*, 12.62)) AND dv10([*, 10.58)) => Cluster(C6) 10
dv1([33.08, 39.30)) AND dv2([40.69, *)) AND dv3([8.88, 9.57)) AND dv5([29.65, 33.61)) AND dv9([*, 12.62)) AND dv10([*, 10.58)) => Cluster(C6) 10
dv1([33.08, 39.30)) AND dv3([8.88, 9.57)) AND dv5([29.65, 33.61)) AND dv6([39.25, *)) AND dv9([*, 12.62)) AND dv10([*, 10.58)) => Cluster(C6) 10
dv1([33.08, 39.30)) AND dv5([29.65, 33.61)) AND dv6([39.25, *)) AND dv7([15.09, 15.83)) AND dv9([*, 12.62)) AND dv10([*, 10.58)) => Cluster(C6) 10
dv1([33.08, 39.30)) AND dv2([40.69, *)) AND dv5([29.65, 33.61)) AND dv6([39.25, *)) AND dv7([15.09, 15.83)) AND dv9([*, 12.62)) AND dv10([*, 10.58)) => Cluster(C6) 10
dv1([33.08, 39.30)) AND dv3([8.88, 9.57)) AND dv4([7.54, *)) AND dv6([39.25, *)) AND dv10([*, 10.58)) => Cluster(C6) 9
dv1([33.08, 39.30)) AND dv2([40.69, *)) AND dv3([8.88, 9.57)) AND dv4([7.54, *)) AND dv10([*, 10.58)) => Cluster(C6) 9
dv3([8.88, 9.57)) AND dv4([7.54, *)) AND dv5([29.65, 33.61)) AND dv6([39.25, *)) AND dv10([*, 10.58)) => Cluster(C6) 8
dv2([40.69, *)) AND dv3([8.88, 9.57)) AND dv5([29.65, 33.61)) AND dv8([12.82, 13.32)) AND dv9([*, 12.62)) => Cluster(C6) 8
dv2([40.69, *)) AND dv5([29.65, 33.61)) AND dv7([15.09, 15.83)) AND dv8([12.82, 13.32)) AND dv9([*, 12.62)) => Cluster(C6) 8
dv1([33.08, 39.30)) AND dv4([7.54, *)) AND dv5([29.65, 33.61)) AND dv7([15.09, 15.83)) AND dv10([*, 10.58)) => Cluster(C6) 8
dv1([33.08, 39.30)) AND dv3([8.88, 9.57)) AND dv4([7.54, *)) AND dv5([29.65, 33.61)) AND dv10([*, 10.58)) => Cluster(C6) 8
dv1([33.08, 39.30)) AND dv4([7.54, *)) AND dv6([39.25, *)) AND dv7([15.09, 15.83)) AND dv9([*, 12.62)) AND dv10([*, 10.58)) => Cluster(C6) 8
dv1([33.08, 39.30)) AND dv2([40.69, *)) AND dv4([7.54, *)) AND dv7([15.09, 15.83)) AND dv9([*, 12.62)) AND dv10([*, 10.58)) => Cluster(C6) 8
dv2([40.69, *)) AND dv3([8.88, 9.57)) AND dv4([7.54, *)) AND dv5([29.65, 33.61)) AND dv10([*, 10.58)) => Cluster(C6) 8
dv2([40.69, *)) AND dv4([7.54, *)) AND dv5([29.65, 33.61)) AND dv7([15.09, 15.83)) AND dv10([*, 10.58)) => Cluster(C6) 8
dv4([7.54, *)) AND dv5([29.65, 33.61)) AND dv6([39.25, *)) AND dv7([15.09, 15.83)) AND dv10([*, 10.58)) => Cluster(C6) 8
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Statistics of rule conditions and Statistics of rule conditions and comparison with previous resultscomparison with previous results
Sweet
dv1 11
dv2 9
dv3 8
dv4 10
dv5 13
dv6 7
dv7 9
dv8 2
dv9 9
dv10 14
large small
Number Airfoil parameters
dv1 XmaxL @ = 0.12
dv2 XmaxL @ = 0.29
dv3 maxL @ = 0.12
dv4 maxL @ = 0.29
dv5 XmaxTC @ = 0.12
dv6 XmaxTC @ = 0.29
dv7 maxTC @ = 0.12
dv8 maxTC @ = 0.29
dv9 sparTC @ = 0.12
dv10 sparTC @ = 0.29
maxL
maxTCXmaxTC
XmaxL
sparTC
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Statistics of rule conditions Statistics of rule conditions for all objectivesfor all objectives
Sweet Cd Cp WW
dv1 11 1 1 5
dv2 9 2 6 3
dv3 8 5 6 4
dv4 10 3 5 11
dv5 13 8 1 7
dv6 7 6 3 3
dv7 9 5 6 5
dv8 2 4 3 2
dv9 9 2 2 3
dv10 14 9 8 8
Number Airfoil parameters
dv1 XmaxL @ = 0.12
dv2 XmaxL @ = 0.29
dv3 maxL @ = 0.12
dv4 maxL @ = 0.29
dv5 XmaxTC @ = 0.12
dv6 XmaxTC @ = 0.29
dv7 maxTC @ = 0.12
dv8 maxTC @ = 0.29
dv9 sparTC @ = 0.12
dv10 sparTC @ = 0.29
maxL
maxTCXmaxTC
XmaxL
sparTC
large smallNo large dv10
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ConclusionsConclusions
Multi-Objective Design Exploration (MODE) has Multi-Objective Design Exploration (MODE) has been proposedbeen proposed
Visualization and data mining based on SOMVisualization and data mining based on SOM
Regional-jet design has been demonstratedRegional-jet design has been demonstrated
Wing-nacelle-pylon-body configurationWing-nacelle-pylon-body configurationSOM reveals the structure of design space SOM reveals the structure of design space
and visualizes it and visualizes it Analysis of the sweet-spot cluster leads to Analysis of the sweet-spot cluster leads to
design rulesdesign rules
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AcknowledgementsAcknowledgements
Prof. Shinkyu Jeong and Dr. Takayasu KumanoMitsubishi Heavy IndustriesSupercomputer NEC SX-8 at Institute of Fluid
ScienceProf. Yasushi Ito, University of Alabama at
Birmingham, for EdgeEditor (mesh generator)Prof. Kazuhiro Nakahashi, Tohoku University,
for TAS (unstructured-mesh flow solver)Mr. Hiroyuki Sakai, TIBCO Software Japan, Inc.,
for DecisionSite (data visualization)
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Mitsubishi Regional JetMitsubishi Regional Jet ( (MRJ)MRJ)
First flight due 2011
Let me know if you are interested in a special offer!
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