䝖䝫䝻䝆䞊᭱㐺ゎ䛾᥈⣴

Self-Organizing Map 䜢⏝䛔䛯

䝖䝫 䝆 ᭱㐺ゎ ᥈⣴

䝖䝫䝻䝆䞊᭱㐺ゎ䛾᥈⣴

䕿 ⏦ 㕷┾ 㻔㻴㼥㼡㼚㼖㼕㼚㻌㻿㻴㻵㻺䠖㻳㼞㼍㼐㼡㼍㼠㼑㻌㼟㼏㼔㼛㼛㼘㻌㼛㼒㻌㻌

㼀㼛㼗㼥㼛㻌㻵㼚㼟㼠㼕㼠㼡㼠㼑㻌㼛㼒㻌㼀㼑㼏㼔㼚㼛㼘㼛㼓㼥㻕 ᖹ㔝 ⩏㙟

䕿㎘ ❶

㼥 㼓㼥㻕

㻔㼅㼛㼟㼔㼕㼥㼍㼟㼡㻌㻴㻵㻾㻭㻺㻻䠖㻶㻭㼄㻭䠅

㻔㻭㼗㼕㼞㼍㻌㼀㻻㻰㻻㻾㻻㻷㻵䠖㼀㼛㼗㼥㼛㻌㻵㼚㼟㼠㼕㼠㼡㼠㼑㻌㼛㼒㻌㼀㼑㼏㼔㼚㼛㼘㼛㼓㼥䠅

Dec, 09, 2011 Tokyo�Institute�of�Technology

Tokyo�Institute�of�Technology Todoroki�

Todoroki��� Mizutani�Lab. Mizutani�Lab.

◊✲⫼ᬒ

㉸㡢㏿㣕⾜ᶵ _{⩼⬗⤖ྜ㔠ල}

㧗㏿ᛶ

⤒῭ᛶ

㍍㔞໬

ⷧ⩼ᵓ㐀

⩼⬗⤖ྜ㔠ල

⤒῭ᛶ

⎔ቃ㐺ྜᛶ ⷧ⩼ᵓ㐀

⩼ෆ タィ✵㛫䛜ᑠ䛥 䠄ⷧ⩼ᵓ㐀䠅

㔠ලタィ䛾ၥ㢟Ⅼ 㔠ලタィ䛾ၥ㢟Ⅼ

⩼ෆ䛾タィ✵㛫䛜ᑠ䛥䛔䠄ⷧ⩼ᵓ㐀䠅 㧗๛ᛶ䛜ᚲせ

✵ຊⲴ㔜䛻䜘䜛ᵝ䚻䛺㈇ⲴⲴ㔜

㉸㡢㏿㣕⾜ᶵ䛾౛

Thin wing structure

㍍㔞໬䛜ᚲせ

◊✲⫼ᬒ

䝖䝫䝻䝆䞊᭱㐺໬

䝖䝫䝻䝆䞊᭱㐺໬

୍ᐃ䛾タィ✵㛫䛾୰䛷᭱㐺䛺ᵓ㐀䛾 䝺䜲䜰䜴䝖䜢᥈⣴䛩䜛ᡭἲ

ᵝ䚻䛺せᅉ䛻䜘䜛᭱㐺ゎ䛾ኚື

䝖䝫䝻䝆䞊᭱㐺໬䛾ၥ㢟 䝖䝫䝻䝆䞊᭱㐺໬䛾ၥ㢟

タィ㡿ᇦ⠊ᅖ䠈䝯䝑䝅䝳ศ๭

㈇ⲴⲴ㔜䛜䠎䛴௨ୖ䛾ሙྜ

ᵝ䚻䛺せᅉ䛻䜘䜛᭱㐺ゎ䛾ኚື

䝖䝫䝻䝆䞊᭱㐺໬䛾౛

㈇ⲴⲴ㔜䛜䠎䛴௨ୖ䛾ሙྜ

�

┠ⓗ㛵ᩘ䛾⥺ᙧ⤖ྜ䛾᪉ἲ➼

Tokyo Institute of Technology 3

◊✲⫼ᬒ

䝖䝫䝻䝆䞊᭱㐺ゎᯒ᭱㐺ゎᯒ

ᵝ䚻䛺Ⲵ㔜᮲௳䛻䜘䜛䝖䝫䝻䝆䞊᭱㐺ゎᯒ䛾ኚື

Ⲵ㔜᮲௳䠄ᵝ䚻䛺✵ຊⲴ㔜䜢᝿ᐃ䠅

䝖䝫䝻䝆䞊᭱㐺ゎ⩌⟬ฟ ༢୍┠ⓗ䝖䝫䝻䝆䞊᭱㐺ゎᯒ

䝖䝫䝻䝆䞊᭱㐺ゎ⩌⟬ฟ ከ┠ⓗ䝖䝫䝻䝆䞊᭱㐺ゎᯒ

⮬ᕫ⤌⧊໬䝬䝑䝥䠄

Self-Organizing Map : SOM)

㧗ḟඖ䝕䞊䝍䜢䛭䛾㛫䛻Ꮡᅾ䛩䜛㠀⥺ᙧ䛺⤫ィⓗ㛵ಀ䛻ᚑ䛔䠈ே㛫䛜⌮

ゎ䛧᫆䛔పḟඖ䛾㞳ᩓ໬䛥䜜䛯䝬䝑䝥ୖ䛻ᑕᙳ䛧䛶ศ㢮䛩䜛ᡭἲ

◊✲┠ⓗ

䝖䝫䝻䝆䞊᭱㐺ゎᯒ 䝖䝫䝻䝆䞊᭱㐺ゎ⩌⟬ฟ 䝖䝫䝻䝆 ᭱㐺ゎᯒ 䝖䝫䝻䝆 ᭱㐺ゎ⩌⟬ฟ

䝖䝫䝻䝆䞊᭱㐺⩌ ᙧ≧䜢⾲⌧䛩䜛≉ᚩ䜢ᢳฟ

ᙧ≧䜢⾲⌧䛩䜛ධຊ䝕䞊䝍䜢ᣦᶆ䛸䛧䠈

䝖䝫䝻䝆 ᭱㐺໬䛻䜘䜛ከᩘ䛾᭱㐺ゎ⩌䜢⮬ᕫ⤌⧊໬䝬 䝥㻔㻿㻻㻹㻕䜢⏝

Self Organizing Map

䜢⏝䛔䛶ศ㢮

䝖䝫䝻䝆䞊᭱㐺໬䛻䜘䜛ከᩘ䛾᭱㐺ゎ⩌䜢⮬ᕫ⤌⧊໬䝬䝑䝥㻔㻿㻻㻹㻕䜢⏝

䛔䛶ศ㢮䛧䠈ᙧ≧䛾≉ᚩ䜢⌮ゎ䛩䜛䛣䛸䛷䠈᭱㐺䛺⩼⬗⤖ྜ㔠ල䛾ᙧ≧䛾 ᥈⣴䜢ヨ䜏䜛䠊

Tokyo Institute of Technology 5

୺⩼ᵓ㐀

Condition of the main wing model

•Flight altitude = 15km

୺⩼䝰䝕䝹 Load Condition

•Mach = 1.6

•lift coefficient = 0.1

lif d i 9

y x

•lift-drag ratio = 9

(T800/3630)

•E_L=167 GPa Material Properties

⩼ཌ䛿 䛻䛧 ༢⣧໬

z

(T800/3630)

✚ᒙᵓᡂ䠖

[(0/90)

₂

]

_S ^•E_•G^{T=9 GPa}

LT=5 GPa

• =0 3 ⩼ཌ䛿

16cm

䛻䛧䠈༢⣧໬

᱆䛸䝸䝤䛿䝃䞁䝗䜲䝑䝏ᵓ㐀

ᥭຊC Lift/1 V²S •_L=0.3

ᥭຊ

ᢠຊ

W L Lift V S

C ²

/ 2

W

D Drag V S

C ²

2 / 1

⩼䛾㠃✚䠖S_W

x᪉ྥ y᪉ྥ z᪉ྥ

㔠ල䛾᭱኱཯ຊ

Unit:[kN] 114~128 14~16 5~8

⩼⬗⤖ྜ㔠ල䝰䝕䝹

タィ㡿ᇦ

タィ㡿ᇦ 䝢䞁䠄ᅛᐃ䠅

rigid elements

25 ^{⩼⬗⤖ྜ㔠ල}

5

Unit䠖cm

E=113.8Gpa

䝫䜰䝋䞁ẚ

=0 34

䝏䝍䞁ྜ㔠䠄

䝏䝍䞁ྜ㔠䠄

Ti Ti--6Al 6Al--4V) 4V)

㠀タィ㡿ᇦ

Unit䠖cm 䝫䜰䝋䞁ẚ

=0.34 CHEXA

せ⣲

Tokyo Institute of Technology 7

䝖䝫䝻䝆䞊᭱㐺ゎᯒ

䝖䝫䝻䝆䞊᭱㐺ゎ⩌䛾⏕ᡂ 䝖䝫䝻䝆䞊᭱㐺ゎ⩌䛾⏕ᡂ

༢୍┠ⓗ䝖䝫䝻䝆䞊᭱㐺ゎᯒ

ᙧ≧䛾≉ᚩᢳฟ ᙧ≧䛾≉ᚩᢳฟ

᭱㐺ゎᯒ᮲௳

䝥

SOM SOM

ศ㢮ศ㢮

┠ⓗ㛵ᩘ䠖䝁䞁䝥䝷䜲䜰䞁䝇᭱ᑠ໬

䠄䜂䛪䜏䜶䝛䝹䜼᭱ᑠ໬䠅

ᣊ᮰᮲௳䠖Ⲵ㔜䛾඲タィ㡿ᇦ䛾

40%

௨ୗ

Ⲵ㔜᮲௳

タィኚᩘ䠖ྛせ⣲䛾ᐦᗘ

䛫䜣᩿ຊ

䛽䛨䜚䝰䞊䝯䞁䝖

᭤䛢 䝯 䝖

Ⲵ㔜᮲௳

᭤䛢䝰䞊䝯䞁䝖

༢⊂䛻㈇Ⲵ䛧䛯ሙྜ (3

䜿䞊䝇

)

ྠ᫬䛻㈇Ⲵ䛧䛯ሙྜ (4

䜿 䝇

)

ྠ᫬䛻㈇Ⲵ䛧䛯ሙྜ (4

䜿䞊䝇

)

䝖䝫䝻䝆䞊᭱㐺ゎᯒ

䝖䝫䝻䝆䞊᭱㐺ゎ⩌䛾⏕ᡂ 䝖䝫䝻䝆䞊᭱㐺ゎ⩌䛾⏕ᡂ

ከ┠ⓗ䝖䝫䝻䝆䞊᭱㐺ゎᯒ

ᙧ≧䛾≉ᚩᢳฟ ᙧ≧䛾≉ᚩᢳฟ

䠄

Weighted Min-Max method

䠅

᭱㐺ゎᯒ᮲௳

SOM SOM

ศ㢮ศ㢮

᭱㐺ゎᯒ᮲௳

┠ⓗ㛵ᩘ䠖

�

䛾᭱ᑠ໬

䠄ྛⲴ㔜䜿䞊䝇䛾䜂䛪䜏䜶䝛䝹䜼䛾᭱ᑠ໬䠅

ᣊ᮰᮲௳䠖Ⲵ㔜䛾඲タィ㡿ᇦ䛾

40%

௨ୗ

3 , 2 , 1

; 0 . 0 )

. / .

( s e s e i

w

_{i i i}^o

Ⲵ㔜᮲௳

タィኚᩘ䠖ྛせ⣲䛾ᐦᗘ

: the strain energy of the utopia point

io

e s.

䛫䜣᩿ຊ

䛽䛨䜚䝰䞊䝯䞁䝖

᭤䛢䝰 䝯䞁䝖

Tokyo Institute of Technology 9

᭤䛢䝰䞊䝯䞁䝖

䝖䝫䝻䝆䞊᭱㐺ゎᯒ

䝖䝫䝻䝆䞊᭱㐺ゎ⩌䛾⏕ᡂ 䝖䝫䝻䝆䞊᭱㐺ゎ⩌䛾⏕ᡂ

ከ┠ⓗ䝖䝫䝻䝆䞊᭱㐺ゎᯒ

ᙧ≧䛾≉ᚩᢳฟ ᙧ≧䛾≉ᚩᢳฟ

䠄

Weighted Min-Max method

䠅

᭱㐺ゎᯒ᮲௳

SOM SOM

ศ㢮ศ㢮

᭱㐺ゎᯒ᮲௳

┠ⓗ㛵ᩘ䠖

�

䛾᭱ᑠ໬

䠄ྛⲴ㔜䜿䞊䝇䛾䜂䛪䜏䜶䝛䝹䜼䛾᭱ᑠ໬䠅

ᣊ᮰᮲௳䠖Ⲵ㔜䛾඲タィ㡿ᇦ䛾

40%

௨ୗ

3 , 2 , 1

; 0 . 0 )

. / .

( s e s e i

w

_{i i i}^o

Ⲵ㔜᮲௳

タィኚᩘ䠖ྛせ⣲䛾ᐦᗘ

: the strain energy of the utopia point

io

e s.

䛫䜣᩿ຊ

䛽䛨䜚䝰䞊䝯䞁䝖

᭤䛢䝰 䝯䞁䝖

Latin Hypercube Sampling 20samples

᭤䛢䝰䞊䝯䞁䝖

20samples

䝖䝫䝻䝆䞊᭱㐺ゎ⩌

⏕ᡂ䛧䛯䝖䝫䝻䝆䞊᭱㐺ゎ⩌ 䝖䝫䝻䝆䞊᭱㐺ゎ⩌䛾⏕ᡂ䝖䝫䝻䝆䞊᭱㐺ゎ⩌䛾⏕ᡂ

⏕ᡂ䛧䛯䝖䝫䝻䝆 ᭱㐺ゎ⩌

ᙧ≧䛾≉ᚩᢳฟ ᙧ≧䛾≉ᚩᢳฟ

SOM SOM

ศ㢮ศ㢮

Tokyo Institute of Technology 11

䝖䝫䝻䝆䞊᭱㐺ゎ䛾ᙧ≧≉ᚩᢳฟ

Grid Based

ᡭἲ ᙧ≧ⓗ䛾≉ᚩ

Grid Based

ᡭἲ

⏬ീ䜲䝯䞊䝆䜢⾲⌧䛩䜛᪉ἲ

せ⣲䛜Ꮡᅾ䛩䜛ᡤ䛿

1

ᙧ≧ⓗ䛾≉ᚩ

ྛ䝉䝹䛻Ꮡᅾ䛩䜛

せ⣲䛾ᩘ

䜿䞊䝇1 䜿䞊䝇2

せ⣲䛜Ꮡᅾ䛩䜛ᡤ䛿

1

Ꮡᅾ䛧䛺䛔ᡤ䛿

0 ᐇ⾜䛾⡆༢䛥

ᩘ್ィ⟬䛸䛾㐺ྜᛶ䛜㧗䛔

せ⣲䛾ᩘ䠊

ᩘ್ィ⟬䛸䛾㐺ྜᛶ䛜㧗䛔 3

ḟඖ䛻ᣑᙇ䛩䜛䛯䜑䛻䛿䠈せ⣲

ᩘ䛜ከ䛟䛺䜚䠈㧗ィ⟬䝁䝇䝖䛜ᚲせ

ศ๭ᩘ䛻䜘䜛ᙧ≧䛾ศ㢮⢭ᗘ䛻

ᑐ䛩䜛᳨ド䛜ᚲせ䠊

8

ಶ䝉䝹䛻ศ๭

2400

ಶ䝉䝹䛻ศ๭

8

ಶ䝉䝹䛻ศ๭

2400

ಶ䝉䝹䛻ศ๭

⮬ᕫ⤌⧊໬䝬䝑䝥 (SOM)

㧗ḟඖ䝕䞊䝍䜢䛭䛾㛫䛻Ꮡᅾ䛩䜛㠀⥺ᙧ䛺⤫ィⓗ㛵ಀ䛻ᚑ䛔䠈ே㛫䛜⌮

ゎ䛧᫆䛔పḟඖ䛾㞳ᩓ໬䛥䜜䛯䝬 䝥ୖ䛻ᑕᙳ䛧䛶ศ㢮䛩䜛ᡭἲ ゎ䛧᫆䛔పḟඖ䛾㞳ᩓ໬䛥䜜䛯䝬䝑䝥ୖ䛻ᑕᙳ䛧䛶ศ㢮䛩䜛ᡭἲ

dḟඖཧ↷䝧䜽䝖䝹䠖m=[m1,…,md]

ධຊ䝕䞊䝍✵㛫

Best Matching Unit(BMU)

ධຊ䝧䜽䝖䝹x䛸㢮ఝᛶ䛜㧗䛔ཧ↷䝧䜽䝖䝹 㢮ఝᛶ䛿Euclidian ㊥㞳

ධຊ䝧䜽䝖䝹x䛸㢮ఝᛶ䛜㧗䛔ཧ↷䝧䜽䝖䝹

i

C x m

m

x min

ཧ↷䝧䜽䝖䝹䛾᭦᪂ (t) 䠖Ꮫ⩦⋡

Tokyo Institute of Technology 13

)]

( ) ( )[

( ) ( ) ( ) 1

(t m t t h t xt m t

m_{i i ci i} h_ci(t)^{䠖㏆ഐ༙ᚄ}

MATLAB SOM Toolbox

ศ㢮⤖ᯝ

䜿䞊䝇

1

䠖

8

ಶ䛾䝉䝹䛻ศ๭䛧ሙྜ

SOM

䛾ධຊ䝕䞊䝍

�

䝉䝹䛾୰䛻Ꮡᅾ䛩䜛せ⣲ᩘ

䝖䝫䝻䝆䞊᭱㐺ゎ

27

ಶ 䝖䝫䝻䝆 ᭱㐺ゎ

27

ಶ

ศ㢮⤖ᯝ

䜿䞊䝇

2

䠖

2400

ಶ䛾䝉䝹䛻ศ๭䛧ሙྜ

SOM

䛾ධຊ䝕䞊䝍

�

䝉䝹䛾୰䛻Ꮡᅾ䛩䜛せ⣲ᩘ

䝖䝫䝻䝆䞊᭱㐺ゎ

27

ಶ 䝖䝫䝻䝆 ᭱㐺ゎ

27

ಶ

Tokyo Institute of Technology 15

ศ㢮⤖ᯝ䛾ẚ㍑

䜿䞊䝇

2

䠖

2400

ಶ䛾䝉䝹 䜿䞊䝇

1

䠖

8

ಶ䛾䝉䝹

ศ㢮⤖ᯝ䛾ẚ㍑䠄䠍䠅

䜿䞊䝇

2

䠖

2400

ಶ䛾䝉䝹 䜿䞊䝇

1

䠖

8

ಶ䛾䝉䝹

model 18 model 23

Tokyo Institute of Technology 17

ศ㢮⤖ᯝ䛾ẚ㍑䠄䠎䠅

䜿䞊䝇

2

䠖

2400

ಶ䛾䝉䝹 䜿䞊䝇

1

䠖

8

ಶ䛾䝉䝹

model 2 model 19

ศ㢮⤖ᯝ䛾ẚ㍑䠄䠎䠅

䜿䞊䝇

1

䠖

8

ಶ䛾䝉䝹

Tokyo Institute of Technology 19

ศ㢮⤖ᯝ䛾ẚ㍑䠄䠎䠅

䜿䞊䝇

1

䠖

8

ಶ䛾䝉䝹

M2 M15 M19

䝉䝹

A

䛻䛚䛡䜛せ⣲ᩘ

Model 2 Model 15 Model 19 Density at cell A

[elements/cell] 4280 4421 4476

せ⣲ᩘ

[elements/cell]

ศ㢮⤖ᯝ䛾ẚ㍑䠄䠏䠅

䜿䞊䝇

2

䠖

2400

ಶ䛾䝉䝹 䜿䞊䝇

1

䠖

8

ಶ䛾䝉䝹

Tokyo Institute of Technology 21

ศ㢮⤖ᯝ䛾ẚ㍑䠄䠏䠅

䜿䞊䝇

2

䠖

2400

ಶ䛾䝉䝹 䜿䞊䝇

1

䠖

8

ಶ䛾䝉䝹

model 21 model 22

䝖䝫䝻䝆䞊᭱㐺ゎ᥈⣴䛾ὶ䜜

䝖䝫䝻䝆 ᭱㐺ゎ⩌䛾⏕ᡂ 䝖䝫䝻䝆 ᭱㐺ゎ⩌䛾⏕ᡂ

ᙧ≧䛾≉ᚩᢳฟ ᙧ≧䛾≉ᚩᢳฟ 䝖䝫䝻䝆䞊᭱㐺ゎ⩌䛾⏕ᡂ 䝖䝫䝻䝆䞊᭱㐺ゎ⩌䛾⏕ᡂ

ᙧ≧䛾≉ᚩᢳฟ ᙧ≧䛾≉ᚩᢳฟ

SOM SOM

ศ㢮ศ㢮㢮㢮

ᙧ≧䛾≉ᚩ䛸ᵓ㐀ᛶ⬟䛾㛵ಀ ᙧ≧䛾≉ᚩ䛸ᵓ㐀ᛶ⬟䛾㛵ಀ

䜽䝷䝇䝍 䝸䞁䜾 䜽䝷䝇䝍 䝸䞁䜾

䝖䝫䝻䝆䞊᭱㐺ゎ䛾᥈⣴

䝖䝫䝻䝆䞊᭱㐺ゎ䛾᥈⣴

䜽䝷䝇䝍䞊䝸䞁䜾 䜽䝷䝇䝍䞊䝸䞁䜾

Tokyo Institute of Technology 23

ᙧ≧䛾≉ᚩ䛸ᵓ㐀ᛶ⬟䛾㛵ಀ

䜿䞊䝇

2

䠖

2400

ಶ䛾䝉䝹

䝖䝫䝻䝆䞊᭱㐺ゎ⩌

ධຊ䝕䞊䝍䠖

ྛ䝉䝹䛾せ⣲ᩘ

ྛ䝉䝹䛾せ⣲ᩘ

䝖䝫䝻䝆䞊᭱㐺໬

ྛⲴ㔜䛻ᑐ䛩䜛䜂䛪䜏䜶䝛䝹䜼

ྛⲴ㔜䜿䞊䝇䛻䛚䛡䜛䜂䛪䜏䜶䝛䝹䜼

SOM

䝟䝍䞊䞁

䛫䜣᩿ຊ 䛽䛨䜚䝰䞊䝯䞁䝖 ᭤䛢䝰䞊䝯䞁䝖

ᙧ≧䛾≉ᚩ䛸ᵓ㐀ᛶ⬟䛾㛵ಀ

ධຊ䝕䞊䝍䠖ྛ䝉䝹䛾せ⣲ᩘ䛾䝟䝍䞊䞁

ྛⲴ㔜䜿䞊䝇䛻䛚䛡䜛䜂䛪䜏䜶䝛䝹䜼

SOM

䝟䝍䞊䞁

SOM 䝉䝹

A

䝉䝹

B

Model 18

Model 21

Tokyo Institute of Technology 25

䛫䜣᩿ຊ 䛽䛨䜚䝰䞊䝯䞁䝖 ᭤䛢䝰䞊䝯䞁䝖

⤫ィⓗ䛺ᙧ≧䛾≉ᚩ

せ⣲䛾ศᕸ䛻ᑐ䛩䜛⤫ィⓗ䛺್

せ⣲䛾ศᕸ䛻ᑐ䛩䜛⤫ィⓗ䛺್

ᙧ≧䛾㔜ᚰ 㼄

^㼓㼏㻘㻌㼅㼓㼏㻘㻌㼆㼓㼏

㻔㼄㼕㻙㼄㼓㼏㻕䛾஧஌ᖹᆒ

㻔㼄㼕 㼄㼓㼏㻕䛾஧஌ᖹᆒ

㻔㼄᪉ྥᖹᆒศᩓ䠖㼂㼇㼄㼉㻕䠈 㼂㼇㼅㼉㻌㻘 㼆㼇㼅㼉

㻔㼄㼕㻙㼄㼓㼏㻕㻌䛸㻔㼅㼕㻙㼅㼓㼏㻕䛾 ✚䛾ᖹᆒ

㻔㼄䛸㼅䛾ඹศᩓ䠖㻯㼛㼢㻔㼄 㼅㻕㻕 㻯㼛㼢㻔㼅 㼆㻕 㻔㼄䛸㼅䛾ඹศᩓ䠖㻯㼛㼢㻔㼄㻘㼅㻕㻕㻌䠈㻯㼛㼢㻔㼅㻘㼆㻕㻘㻌 㻯㼛㼢㻔㼆㻘㼄㻕

㻔㼄㼕㻙㼄㼓㼏㻕^㻞䛸㻔㼅㼕㻙㼅㼓㼏㻕䛾✚䜢ᖹᆒ䛧䛯್䠊 㻔㼄䛾ᖹᆒศᩓ䛸㼅䛾ඹศᩓ䠅㻯 㻔㼂㼇㼄㼉 㼅㻕㻕

Y

㻔㼄䛾ᖹᆒศᩓ䛸㼅䛾ඹศᩓ䠅㻯㼛㼢㻔㼂㼇㼄㼉㻘㼅㻕㻕㻘 㻯㼛㼢㻔㼂㼇㼄㼉㻘㼆㻕㻘㻌㻯㼛㼢㻔㼂㼇㼅㼉㻘㼄㻕㻘㻌㻯㼛㼢㻔㼂㼇㼅㼉㻘㼆㻕㻘 㻯㼛㼢㻔㼂㼇㼆㼉㻘㼄㻕㻘㻌㻯㼛㼢㻔㼂㼇㼆㼉㻘㼅㻕

᩿㠃䠎ḟ 䝯䞁䝖

Z XO

䝖䝫䝻䝆䞊᭱㐺ゎ䛾౛

᩿㠃䠎ḟ䝰䞊䝯䞁䝖

Ixx, Iyy, Izz, J

඲యⓗ䛺ᙧ≧䛾≉ᚩ䛜䜟䛛䜛

඲యⓗ䛺ᙧ≧䛾≉ᚩ䛜䜟䛛䜛

ᙧ≧䛾≉ᚩ䛸ᵓ㐀ᛶ⬟䛾㛵ಀ

[Xc] [V(y)] [C (V( ) )] [ J]

⤫ィⓗ䛺せ⣲䛾≉ᚩ䜢⾲⌧䛩䜛್䛾

SOM

䝟䝍䞊䞁䛾౛

[Xc] [V(y)] [Cor(V(y),x)] [Ixx] [ J]

1.0 0.5

0.0

ྛⲴ㔜䜿䞊䝇䛻䛚䛡䜛䜂䛪䜏䜶䝛䝹䜼

SOM

䝟䝍䞊䞁

ẚ㍑䛜䜘䜚ᐜ᫆

ẚ㍑䛜䜘䜚ᐜ᫆

ᙧ≧䜢⾲⌧䛩䜛䝟䝍䞊䞁

ᵓ㐀ᛶ⬟䜢⾲⌧䛩䜛䝟䝍䞊䞁

Tokyo Institute of Technology 27

䛫䜣᩿ຊ 䛽䛨䜚䝰䞊䝯䞁䝖 ᭤䛢䝰䞊䝯䞁䝖

ᙧ≧䛾≉ᚩ䛸ᵓ㐀ᛶ⬟䛾㛵ಀ

SOM

䝟䝍䞊䞁ẚ㍑䛾ၥ㢟Ⅼ

ከᩘ䛾䝟䝍䞊䞁䜢䛭䛾䜎䜎ே㛫䛾ឤぬ䛷㢮ఝᛶ䜢ุ᩿䛩䜛䛣䛸䛿㞴䛧䛔

SO

䝍 䞁ẚ㍑䛾ၥ㢟Ⅼ

SOM

䛾

SOM

ྛ䚻䛾䝟䝍䞊䞁䛻ᑐᛂ䛩䜛䝧䜽䝖䝹䜢⏝䛔䛶ඹศᩓ⾜ิ䜢ィ⟬䛧 䛭䛾ඹศᩓ್䛻ᇶ

ྛ䚻䛾䝟䝍䞊䞁䛻ᑐᛂ䛩䜛䝧䜽䝖䝹䜢⏝䛔䛶ඹศᩓ⾜ิ䜢ィ⟬䛧䠈䛭䛾ඹศᩓ್䛻ᇶ 䛵䛔䛶෌䜃

SOM

䛷ศ㢮䛩䜛ᡭἲ

ᮏ◊✲䛷䛿

SOM

䛾ධຊ䝕䞊䝍

䝟䝍 䞁䛻ᑐᛂ䛩䜛䝧䜽䝖䝹

ᮏ◊✲䛷䛿

�

䝟䝍䞊䞁䛻ᑐᛂ䛩䜛䝧䜽䝖䝹 ศ㢮䛧䛯ᑐ㇟䝟䝍䞊䞁

せ⣲䛾ศᕸ䜢⤫ィⓗ䛻⾲⌧䛧䛯್䛻䛚䛡䜛せ⣲ ศᕸ䜢⤫ィⓗ ⾲⌧ ್ 䛚䛡䜛

SOM

䝟䝍䞊䞁䝍

䠏䛴䛾Ⲵ㔜䜿䞊䝇䛻䛚䛡䜛䜂䛪䜏䜶䝛䝹䜼䝟䝍䞊䞁

䝟䝍䞊䞁䛾 SOM ศ㢮⤖ᯝ

B [ J]

䝟䝍䞊䞁䜢

SOM

ศ㢮䛧䛯⤖ᯝ 1.0

SE_LMX 0.0

0.5 䜂䛪䜏䜶䝛䝹䜼䝟䝍䞊䞁

䠄䛽䛨䜚䝰䞊䝯䞁䝖䠅

䜂䛪䜏䜶䝛䝹䜼䝟䝍䞊䞁 䠄䛫䜣᩿ຊ䠅

䜂䛪䜏䜶䝛䝹䜼䝟䝍䞊䞁 䠄᭤䛢䝰䞊䝯䞁䝖䠅

Cor(x,y) SE_LFY Iyy B V(y) SE_LMZ

A

A

Tokyo Institute of Technology 29

䝖䝫䝻䝆䞊᭱㐺ゎ᥈⣴䛾ὶ䜜

䝖䝫䝻䝆 ᭱㐺ゎ⩌䛾⏕ᡂ 䝖䝫䝻䝆 ᭱㐺ゎ⩌䛾⏕ᡂ

ᙧ≧䛾≉ᚩᢳฟ ᙧ≧䛾≉ᚩᢳฟ 䝖䝫䝻䝆䞊᭱㐺ゎ⩌䛾⏕ᡂ 䝖䝫䝻䝆䞊᭱㐺ゎ⩌䛾⏕ᡂ

ᙧ≧䛾≉ᚩᢳฟ ᙧ≧䛾≉ᚩᢳฟ

SOM SOM

ศ㢮ศ㢮㢮㢮

ᙧ≧䛾≉ᚩ䛸ᵓ㐀ᛶ⬟䛾㛵ಀ ᙧ≧䛾≉ᚩ䛸ᵓ㐀ᛶ⬟䛾㛵ಀ

䜽䝷䝇䝍 䝸䞁䜾 䜽䝷䝇䝍 䝸䞁䜾

䝖䝫䝻䝆䞊᭱㐺ゎ䛾᥈⣴

䝖䝫䝻䝆䞊᭱㐺ゎ䛾᥈⣴

䜽䝷䝇䝍䞊䝸䞁䜾 䜽䝷䝇䝍䞊䝸䞁䜾

䜽䝷䝇䝍䞊䝸䞁䜾

䜽䝷䝇䝍䞊䝸䞁䜾䛿䛒䜛䝰䝕䝹䛾࿘䜚䛻䛒䜛ᙧ≧䛸䛾㊥㞳䛻ᇶ䛵䛔䛶䜾䝹䞊䝢 䜽䝷䝇䝍 䝸䞁䜾䛿䛒䜛䝰䝕䝹䛾࿘䜚䛻䛒䜛ᙧ≧䛸䛾㊥㞳䛻ᇶ 䛔䛶䜾䝹 䝢

䞁䜾䛩䜛ᡭἲ

䜽䝹䞊䝥䛾ᩘ䛸䛭䛾䜾䝹䞊䝥䜢ồ䜑 ௦⾲ⓗ䛺ᙧ≧䜢㑅ฟ

䜽䝹 䝥䛾ᩘ䛸䛭䛾䜾䝹 䝥䜢ồ䜑䠈௦⾲ⓗ䛺ᙧ≧䜢㑅ฟ

k-means

ἲ

k=3

䛾ሙྜ䛾౛

Step1 Step2 Step3 Step4

Tokyo Institute of Technology 31

䜽䝷䝇䝍䞊䝸䞁䜾䛾⤖ᯝ

2400

ಶ䛾䝉䝹䛾ሙྜ 䜽䝷䝇䝍䞊䝸䞁䜾⤖ᯝ

2 3

00

ಶ䛾䝉䝹䛾ሙྜ 䜽䝷䝇䝍 䝸䞁䜾⤖ᯝ

1 3

4 5 5

6 7

8 9

7

8 9

䝖䝫䝻䝆䞊᭱㐺ゎ᥈⣴䛾ὶ䜜

䝖䝫䝻䝆 ᭱㐺ゎ⩌䛾⏕ᡂ 䝖䝫䝻䝆 ᭱㐺ゎ⩌䛾⏕ᡂ

ᙧ≧䛾≉ᚩᢳฟ ᙧ≧䛾≉ᚩᢳฟ 䝖䝫䝻䝆䞊᭱㐺ゎ⩌䛾⏕ᡂ 䝖䝫䝻䝆䞊᭱㐺ゎ⩌䛾⏕ᡂ

ᙧ≧䛾≉ᚩᢳฟ ᙧ≧䛾≉ᚩᢳฟ

SOM SOM

ศ㢮ศ㢮㢮㢮

ᙧ≧䛾≉ᚩ䛸ᵓ㐀ᛶ⬟䛾㛵ಀ ᙧ≧䛾≉ᚩ䛸ᵓ㐀ᛶ⬟䛾㛵ಀ

䜽䝷䝇䝍 䝸䞁䜾 䜽䝷䝇䝍 䝸䞁䜾

䝖䝫䝻䝆䞊᭱㐺ゎ䛾᥈⣴

䝖䝫䝻䝆䞊᭱㐺ゎ䛾᥈⣴

䜽䝷䝇䝍䞊䝸䞁䜾 䜽䝷䝇䝍䞊䝸䞁䜾

Tokyo Institute of Technology 33

䝖䝫䝻䝆䞊᭱㐺ゎ᥈⣴

ྛⲴ㔜䜿䞊䝇䛻䛚䛡䜛䜂䛪䜏䜶䝛䝹䜼

SOM

䝟䝍䞊䞁 䜽䝷䝇䝍䞊䝸䞁䜾⤖ᯝ

䛫䜣᩿ຊ 䛽䛨䜚䝰䞊䝯䞁䝖 ᭤䛢䝰䞊䝯䞁䝖

⤫ィⓗ䛺せ⣲䛾≉ᚩ䜢⾲⌧䛩䜛್䛾

SOM

䝟䝍䞊䞁

Cor(x,y) Iyy V(y) [ J]

䝖䝫䝻䝆䞊᭱㐺ゎ᥈⣴

ྛⲴ㔜䜿䞊䝇䛻䛚䛡䜛䜂䛪䜏䜶䝛䝹䜼

SOM

䝟䝍䞊䞁

䜽䝷䝇䝍䞊

1,2

䜽䝷䝇䝍䞊䝸䞁䜾⤖ᯝ

䛫䜣᩿ຊ 䛽䛨䜚䝰䞊䝯䞁䝖 ᭤䛢䝰䞊䝯䞁䝖

⤫ィⓗ䛺せ⣲䛾≉ᚩ䜢⾲⌧䛩䜛್䛾

SOM

䝟䝍䞊䞁

Cor(x,y) Iyy V(y) [ J]

Tokyo Institute of Technology 35

䝖䝫䝻䝆䞊᭱㐺ゎ᥈⣴

ྛⲴ㔜䜿䞊䝇䛻䛚䛡䜛䜂䛪䜏䜶䝛䝹䜼

SOM

䝟䝍䞊䞁

䜽䝷䝇䝍䞊

8,9

䜽䝷䝇䝍䞊䝸䞁䜾⤖ᯝ

䛫䜣᩿ຊ 䛽䛨䜚䝰䞊䝯䞁䝖 ᭤䛢䝰䞊䝯䞁䝖

⤫ィⓗ䛺せ⣲䛾≉ᚩ䜢⾲⌧䛩䜛್䛾

SOM

䝟䝍䞊䞁

Cor(x,y) Iyy V(y) [ J]

䝖䝫䝻䝆䞊᭱㐺ゎ᥈⣴

ྛⲴ㔜䜿䞊䝇䛻䛚䛡䜛䜂䛪䜏䜶䝛䝹䜼

SOM

䝟䝍䞊䞁

䜽䝷䝇䝍䞊

3,4,5,6,7

䜽䝷䝇䝍䞊䝸䞁䜾⤖ᯝ

䛫䜣᩿ຊ 䛽䛨䜚䝰䞊䝯䞁䝖 ᭤䛢䝰䞊䝯䞁䝖

⤫ィⓗ䛺せ⣲䛾≉ᚩ䜢⾲⌧䛩䜛್䛾

SOM

䝟䝍䞊䞁

Cor(x,y) Iyy V(y) [ J]

Tokyo Institute of Technology 37

䝖䝫䝻䝆䞊᭱㐺ゎ᥈⣴

ྛⲴ㔜䜿䞊䝇䛻䛚䛡䜛䜂䛪䜏䜶䝛䝹䜼

SOM

䝟䝍䞊䞁 䜽䝷䝇䝍䞊䝸䞁䜾⤖ᯝ

A

䛫䜣᩿ຊ 䛽䛨䜚䝰䞊䝯䞁䝖 ᭤䛢䝰䞊䝯䞁䝖

⤫ィⓗ䛺せ⣲䛾≉ᚩ䜢⾲⌧䛩䜛್䛾

SOM

䝟䝍䞊䞁

Cor(x,y) Iyy V(y) [ J]

B

䝖䝫䝻䝆䞊᭱㐺ゎ᥈⣴

䝜䞊䝗A 䝜䞊䝗B 䜽䝷䝇䝍䞊䝸䞁䜾⤖ᯝ

ᙧ≧

A

᩿㠃 ᙧ≧

B

Tokyo Institute of Technology 39

⤖ゝ

䝖䝫 䝆 ᭱㐺ゎ䛾ᙧ≧ⓗ䛺≉ᚩ䜢⾲䛩䛯䜑䛻 タィ✵㛫䜢ศ

䝖䝫䝻䝆䞊᭱㐺ゎ䛾ᙧ≧ⓗ䛺≉ᚩ䜢⾲䛩䛯䜑䛻䠈タィ✵㛫䜢ศ

๭䛧䠈䛭䛾✵㛫䛤䛸䛾せ⣲ᐦᗘ䜢⏝䛔䜛ᡭἲ䜢♧䛧䛯䠊

SOM

䛾⤖ᯝ䜢䜘䜚ຠᯝⓗ䛻ㄪ䜉䜛䛯䜑䛻䠈⤫ィⓗ䛺せ⣲ᐦᗘ 䛾ศᕸ್䜢⏝䛔䜛ᡭἲ䜢ᥦ᱌䛧䛯䠊

ᙧ≧≉ᚩ䛾䝟䝍䞊䞁䛸䜂䛪䜏䜶䝛䝹䜼䝟䝍䞊䞁䜢ẚ㍑䛧䠈ྛ䚻 䛾఩┦ⓗ≉ᚩ䛸䜂䛪䜏䜶䝛䝹䜼䛾㛵ಀ䜢᫂☜䛻䛧䛯䠊䜎䛯䠈䜽 䝷䝇䝍 䝸䞁䜾䜢⏝䛔 ྛ䚻䛾䜽䝷䝇䝍 䛾≉ᚩ䜢᫂☜䛻䛧䛯 䝷䝇䝍䞊䝸䞁䜾䜢⏝䛔䠈ྛ䚻䛾䜽䝷䝇䝍䞊䛾≉ᚩ䜢᫂☜䛻䛧䛯䠊

䛤Ύ⫈䛒䜚䛜䛸䛖䛤䛦䛔䜎䛧䛯䠊

41