Multi-Objective Design Exploration (MODE)

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• Multi-Objective Design Exploration (MODE)
• - Visualization and Mapping of Design Space
• Shigeru Obayashi
• Institute of Fluid Science
• Tohoku University

2
Outline

• Background
• Flow Visualization
• Multidisciplinary Design Optimization (MDO)
• Self-Organizing Map (SOM)
• Rough Set
• Multi-Objective Design Exploration (MODE)
• Application to Regional Jet Design
• Wing-Nacelle-Pylon-Body Configuration
• Analysis of Sweet-Spot Cluster
• Conclusion

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Flow Visualization -1
Flow transition Reynolds number
4
Flow Visualization -2
Stall boundary layer separation
5
Flow Visualization -3
Karman Votex
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Flow Visualization -4
Flow visualization Seeing is believing (Seeing
is understanding) (Picture is worth a thousand
words)
Drag divergence shock wave
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Aircraft Design
Aerodynamics

• Compromise of all disciplines
• Multidisciplinary Design Optimization (MDO) as
  Multi-Objective Optimization (MOP)

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How to Solve MOP

• Collection of non-dominated solutions that
  form trade-offs between multiple objectives
• Gradient-based method with weights between
  objectives
• Utility function f ??f1 ??f2
• Other analytical methods
• Normal-Boundary Intersection Method
• Aspiration Level Method
• Multi-Objective Evolutionary Algorithms (MOEAs)
• Population-based search

Gradient-based method
MOEAs
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How to Understand MOP
Extreme Pareto Solution
f1
X Arithmatic Average
Improvement
Extreme Pareto Solution
Pareto front
f2

• Global optimization is needed
• Visualization is essential!
• Data mining is required
• Design optimization?Design exploration

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Visualization of Tradeoffs
2 objectives
Minimization problems
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Self-Organizing Map(SOM)

• Neural network model proposed by Kohonen
• Unsupervised, competitive learning
• High-dimensional data ? 2D map
• Qualitative description of data

SOM provides design visualization Seeing is
understanding (Essential design tool)
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How to understand SOM better?

• Colored SOMs identify the global structure of the
  design space
• Resulting clusters classify possible designs
• If 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

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Rough Set - Pawlak(1982) -

• Granulation of information
• Reduction of information
• Extraction of rules (knowledge acquisition)

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Rough Set and Attribute
U Condition attribute C Condition attribute C 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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U
x1,x2,x3,x4,x5,x6,x7,x8
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U
Gasoline
x5,x6,x8,x7
U Condition attribute C Condition attribute C Condition attribute C Decision attribute 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
Upper approximation
Gasoline
x5,x6,x8,x7
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U
Lower approximation
Gasoline
x5,x6,x8,x7
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U
Lower approximation
Propane
x1
Gasoline
x5,x6,x8,x7
Rule extraction by lower approximationif propane
then good
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U
Engine Size
Diesel Medium
x2,x4
Propane Compact
Diesel full
x1
x3
Gasoline Medium
x6
Gasoline Compact
Gasoline full
x7
x5,x8
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U
Engine Color
Diesel Gold
x2
Diesel White
x3
Propane Black
x1
Diesel Red
x4
Gasoline Black
Gasoline Silver
x5
x6,x8
Gasoline White
x7
Two attributes out of thee are sufficient ?
reduct (reduced set of attributes)
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What is MODE?
Multi-Objective Design Exploration (MODE)
Step 1 Multi-objective Shape Optimization
Multi-objective Genetic Algorithm
Computational Fluid Dynamics
Step 2 Knowledge Mining
Data mining maps, patterns, models, rules
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Small Jet Aircraft RD Project
FSW (Friction Stir Welding)
New Light Composite Material
Advanced Human-Centered Cockpit
Advanced Higher L/D Wing
Health Monitoring System for LRU
Optimized High Lift Device
More Electric
Aero-Structure Multi-Disciplinary Design
Optimization
RD Organization
New Energy and Industrial Technology
Development Organization (NEDO)
Research Collaboration
Japan Aerospace Exploration Agency (JAXA)
Mitsubishi Heavy Industries
Tohoku University
RD Activities
Fuji Heavy Industries
Japan Aircraft Development Corporation (JADC)
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Present MODE System
START
Latin Hypercube Sampling
Design variables
NURBS airfoil
END
3D wing
Data mining
Wing-body configuration
Kriging model optimization module
Definition of Design Space
Initial Kriging model
CFD (FP/Euler)
No
Yes
MOGA (maximization of EIs)
Pressure distribution
Continue ?
Load condition
FLEXCFD
Selection of additional sample points
Update of Kriging model
Strength flutter requirements
Static analysis model
Flutter analysis model
Aerodynamic structural performance
Structural optimization code NASTRAN
Aerodynamic structural performance
Design variables
CFDCSD
Mesh generation
CFDCSD module
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Optimization of Wing-Nacelle-Pylon-Body
Configuration
Shock wave
Shock wave occuring at inboard of pylon may lead
to separation and buffeting
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Definition of Optimization Problem -1 -
Objective Functions -
Minimize

1. Drag at the cruising condition (CD)
2. Shock strength near wing-pylon junction (-Cp,max)
3. Structural weight of main wing (wing weight)

• Function evaluation tools

CFD Euler code (TAS-code) CSD/Flutter
analysis MSC. NASTRAN
Cp,max
Cp
x/c
-CP distribution of lower surface _at_?0.29
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Definition of Optimization Problem -2 - Design
Variables -
Lower surface of Airfoil shapes at 2 spanwise
sections (? 0.12, 0.29)
? 13 variables (NURBS) 2 sections 26
variables Twist angles at 4 sections 4
variables
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variables in total
NURBS control points
? 0.12
? 0.29
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Performances of baseline shape and sample points
CD vs. Cp,max
Cp,max vs. wing weight
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
CD vs. wing weight
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Definition of Configuration Variables for Data
Mining

• XmaxL
• maxL
• XmaxTC
• maxTC
• sparTC
• At wing root and pylon locations
• ?
• 10 variables

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Visualization of Design Space
SOM with 9 clusters
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Analysis of SweetSpot Cluster

• Handpick
• Parallel coordinates
• Extraction of design rules by discretization of
  configuration variables
• Visualization
• Rough set

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Handpick -Cp,max and dv6 (XmaxTC at pylon)
Others
Analysis of Variance (ANOVA)
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Visualization of SOM Clusters by Parallel
Coordinates
4
1
7
5
2
8
6
9
3
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Discretization of Configuration Variablesby
Equal Frequency Binning
Index
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Finding Design Rules by Visualization
Sweet-spot cluster
Airfoil parameters
dv2 XmaxL _at_ ? 0.29
dv6 XmaxTC _at_ ? 0.29
dv9 sparTC _at_ ? 0.12
dv10 sparTC _at_ ? 0.29
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Flowchart of Data Mining Using Rough Set
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Generated rules to belong to sweet spot cluster
with support of more than eight occurrence
Rule 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)) gt 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)) gt 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)) gt 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)) gt 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)) gt 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)) gt 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)) gt 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)) gt 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)) gt 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)) gt 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)) gt 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)) gt 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)) gt 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)) gt 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)) gt 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)) gt 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)) gt Cluster(C6) 8
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Statistics of rule conditions and comparison with
previous results
Number Airfoil parameters
dv1 XmaxL _at_ ? 0.12
dv2 XmaxL _at_ ? 0.29
dv3 maxL _at_ ? 0.12
dv4 maxL _at_ ? 0.29
dv5 XmaxTC _at_ ? 0.12
dv6 XmaxTC _at_ ? 0.29
dv7 maxTC _at_ ? 0.12
dv8 maxTC _at_ ? 0.29
dv9 sparTC _at_ ? 0.12
dv10 sparTC _at_ ? 0.29
Sweet
dv1 11
dv2 9
dv3 8
dv4 10
dv5 13
dv6 7
dv7 9
dv8 2
dv9 9
dv10 14
large small
XmaxTC
maxTC
sparTC
XmaxL
maxL
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Statistics of rule conditions for all objectives
Number Airfoil parameters
dv1 XmaxL _at_ ? 0.12
dv2 XmaxL _at_ ? 0.29
dv3 maxL _at_ ? 0.12
dv4 maxL _at_ ? 0.29
dv5 XmaxTC _at_ ? 0.12
dv6 XmaxTC _at_ ? 0.29
dv7 maxTC _at_ ? 0.12
dv8 maxTC _at_ ? 0.29
dv9 sparTC _at_ ? 0.12
dv10 sparTC _at_ ? 0.29
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
large small No large dv10
XmaxTC
maxTC
sparTC
XmaxL
maxL
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Conclusions

• Multi-Objective Design Exploration (MODE) has
  been proposed
• Visualization and data mining based on SOM
• Regional-jet design has been demonstrated
• Wing-nacelle-pylon-body configuration
• SOM reveals the structure of design space and
  visualizes it
• Analysis of the sweet-spot cluster leads to
  design rules

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Acknowledgements

• Prof. Shinkyu Jeong and Dr. Takayasu Kumano
• Mitsubishi Heavy Industries
• Supercomputer NEC SX-8 at Institute of Fluid
  Science
• Prof. 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 Jet (MRJ)

• First flight due 2011
• Let me know if you are interested in a special
  offer!