1 Multi-Objective Design Exploration Multi-Objective Design Exploration (MODE) (MODE) - - Visualization and Mapping of Design Visualization and Mapping of Design Space Space Shigeru Shigeru Obayashi Obayashi Institute of Fluid Science Institute of Fluid Science Tohoku University Tohoku University
42
Embed
Multi-Objective Design Exploration (MODE) - Visualization and Mapping of Design Space
Multi-Objective Design Exploration (MODE) - Visualization and Mapping of Design Space Shigeru Obayashi Institute of Fluid Science Tohoku University. Outline. Background Flow Visualization Multidisciplinary Design Optimization (MDO) Self-Organizing Map (SOM) Rough Set - PowerPoint PPT Presentation
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Analysis of Sweet-Spot ClusterAnalysis of Sweet-Spot Cluster
ConclusionConclusion
OutlineOutline
3
Flow Visualization -1 Flow Visualization -1
Flow transition:Reynolds number
4
Flow Visualization -2 Flow Visualization -2
Stall: boundary layer separation
5
Flow Visualization -3 Flow Visualization -3
Karman Votex
6
Flow Visualization -4 Flow Visualization -4
Drag divergence:shock wave
Flow visualization: Seeing is believing (Seeing is understanding)
(Picture is worth a thousand words)
7
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)
8
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
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)
24
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
25
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)
・ ・ 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
29
Definition of Configuration Variables for Data MiningDefinition of Configuration Variables for Data Mining
XmaxLmaxLXmaxTCmaxTCsparTC
At wing root and pylon locations↓10 variables
30
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
31
Analysis of Sweet–Spot ClusterAnalysis of Sweet–Spot Cluster
HandpickParallel coordinatesExtraction of design rules by
discretization of configuration variablesVisualizationRough set
32
- 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
33
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
䢢
0%
䢢
10%
䢢
20%
䢢
30%
䢢
40%
䢢
50%
䢢
60%
䢢
70%
䢢
80%
䢢
90%
䢢
100%
䢢
0%
䢢
10%
䢢
20%
䢢
30%
䢢
40%
䢢
50%
䢢
60%
䢢
70%
䢢
80%
䢢
90%
䢢
100%
䢢
0%
䢢
10%
䢢
20%
䢢
30%
䢢
40%
䢢
50%
䢢
60%
䢢
70%
䢢
80%
䢢
90%
䢢
100%
䢢
obj1
䢢
obj2
䢢
obj3
䢢
obj1
䢢
obj2
䢢
obj3
䢢
obj1
䢢
obj2
䢢
obj3
1
2
3
4
5
6
7
8
9
34
Discretization of Configuration VariablesDiscretization of Configuration Variablesby Equal Frequency Binningby Equal Frequency Binning
Index
35
Finding Design Rules by VisualizationFinding Design Rules by Visualization
䢢
Bin
䢢
0%
䢢
50%
䢢
100%
䢢
0%
䢢
50%
䢢
100%
䢢
0%
䢢
50%
䢢
100%
䢢
0%
䢢
50%
䢢
100%
䢢
0%
䢢
50%
䢢
100%
䢢
0%
䢢
50%
䢢
100%
䢢
0%
䢢
50%
䢢
100%
䢢
0%
䢢
50%
䢢
100%
䢢
0%
䢢
50%
䢢
100%
䢢
Binned
䢢
dv01
䢢
Binned
䢢
dv02
䢢
Binned
䢢
dv03
䢢
Binned
䢢
dv04
䢢
Binned
䢢
dv05
䢢
Binned
䢢
dv06
䢢
Binned
䢢
dv07
䢢
Binned
䢢
dv08
䢢
Binned
䢢
dv09
䢢
Binned
䢢
dv10
Sweet-spot cluster
Airfoil parameters
dv2 XmaxL @ = 0.29
dv6 XmaxTC @ = 0.29
dv9 sparTC @ = 0.12
dv10 sparTC @ = 0.29
36
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
37
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
38
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
39
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
40
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
41
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.,