Multi-Objective Design Exploration (MODE) - Visualization and Mapping of Design Space

1

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

3

Flow Visualization -1 Flow Visualization -1

Flow transition:Reynolds number

4


Stall: boundary layer separation

5


Karman Votex

6


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

Multi-Objective Evolutionary Algorithms (MOEAs)Population-based search

f1

f2

Gradient-based methodf1

f2

MOEAs

How to Solve MOPHow to Solve MOP

9

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

10

Visualization of TradeoffsVisualization of Tradeoffs

2 objectives 3 objectives

?4 objectives

Pro

ject

ion

Minimization problems

11

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)

12

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?

13

Rough SetRough Set 　　- Pawlak(1982) -- Pawlak(1982) -

Granulation of informationReduction of informationExtraction of rules

(knowledge acquisition)

14

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

15

x1 ， x2 ， x3 ， x4 ， x5 ， x6 ， x7 ，ｘ８

U

16

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

17

U

x5 ， x6 ， x8 ， x7


Diesel

Gasoline

Good

Upper approximation

18

U

x5 ， x6 ， x8 ， x7


Diesel

Gasoline

Good

Lower approximation

19

U

x5 ， x6 ， x8 ， x7


Diesel

Gasoline

Good

Lower approximation

Rule extraction by lower approximation ： if propane then good

20

ｘ 5 ， x8

x1PropaneCompact

ｘ 2 ， x4DieselMedium

GasolineCompact

Good

Engine +Size

ｘ 3Dieselfull

ｘ 7Gasolinefull

x6GasolineMedium

U

21

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)

22

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

23

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)

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)

・・ 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

]


Additional sample points

Baseline

CD

-Cp

ma

x


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

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


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


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.,

for DecisionSite (data visualization)

42

Mitsubishi Regional JetMitsubishi Regional Jet ( (MRJ)MRJ)

First flight due 2011

Let me know if you are interested in a special offer!

Multi-Objective Design Exploration (MODE) - Visualization and Mapping of Design Space

Documents

Transcript of Multi-Objective Design Exploration (MODE) - Visualization and Mapping of Design Space