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宇宙航空研究開発機構特別資料

JAXA Special Publication

第 3 回 EFD/CFD 融合ワークショップ

The 3rd Workshop on Integration of EFD and CFD

開  催  日:平成 22 年 1 月 25 日

開催場所:秋葉原コンベンションホール

2010 年 8 月

August 2010

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2.実行委員会 委員名簿 ...2 3.プログラム ...3 4.発表資料

1.JAXA デジタル / アナログ・ハイブリッド風洞の開発状況について

Status Report on the Development of JAXA Digital/Analog Hybrid Wind Tunnel ...5 口石 茂(JAXA)

2.逐次データ同化入門:数理的基礎と最新の動向

Introduction to Sequential Data Assimilation Methods: Their Mathematical Basis and Recent Development ...17 樋口 知之(統計数理研)

3.EFD と飛行シミュレーション ―次世代動的風洞実験法の開発に向けて

EFD and Flight Simulation ―Towards the Development of the Next-Generation Dynamic Wind-Tunnel Testing ...41 浅井 圭介(東北大)

4.ターボ機械における内部流動現象の EFD/CFD ハイブリッド解析

EFD/CFD Hybrid Analysis of Internal Flow Phenomena in Turbomachinery ...63 山田 和豊(九州大)

5.自動車の開発における CFD と EFD の利用について

Application of CFD and EFD on Vehicle Development ...83 橋爪 祥光(スズキ株式会社)

6.Unifi ed Data Visualization using the Virtual Diagnostics Interface (ViDI)...91 Richard J. Schwartz(ATK at NASA LaRC)

5.パネルディスカッション「Can EFD/CFD Integration Maximize Productivity?」 ...121

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The 3rd Workshop on Integration of EFD and CFD

➨ᅇEFD/CFD⼥ྜ࣮࣡ࢡࢩࣙࢵࣉ

㛤ദ㊃ព᭩

ᚑ᮶ࠊᩘ್ὶయຊᏛ㸦Computational Fluid Dynamics, CFD㸧࡜ᐇ㦂ὶయຊᏛ㸦Experimental Fluid Dynamics, EFD㸧࡜ࡣࠊ኱ᆺࡢ㢼Ὕ➼ࢆᣢࡘ◊✲ᶵᵓ࡛ࡣ࡝ࡕࡽ࠿࡜࠸࠼ࡤูಶࡢศ㔝

࡜ࡳ࡞ࡉࢀࠊࡑࢀࡒࢀேᮦࡶࣜࢯ࣮ࢫࡶ⊂❧࡟ࠊ⊂⮬ࡢ❧ሙ࡛⾜ࢃࢀ࡚ࡁࡲࡋࡓࠋࡋ࠿ࡋ࡞ࡀ

ࡽࠊCFDࡣ≀⌮⌧㇟ࢆࣔࢹࣝ໬ࡋ࡚ᩘ್ⓗ࡟ゎࢆồࡵ࡚࠸ࡿ௨ୖࠊ⤖ᯝࡢጇᙜᛶࢆᐇ㦂ࢹ࣮ࢱ

ࢆ⏝࠸᳨࡚ドࡍࡿᚲせࡀ࠶ࡾࠊࡑࡢព࿡࡛CFDࡣEFD࡟୍᪉ⓗ࡟౫Ꮡࡋ࡚࠸ࡓ࡜ゝ࠼ࡲࡍࠋ EFDࡶࡇࢀࡲ࡛CFD࡟ᑐࡋ࡚ഐほ⪅ⓗ࡞❧ሙ࡟⤊ጞࡋ࡚ࡁࡓࡇ࡜ࡣྰࡵ࡞࠸୍᪉ࠊEFD࡟ࡣ EFDᅛ᭷ࡢ୙☜࠿ࡉࡀ࠶ࡾࠊࡲࡓᚓࡽࢀࡿ᝟ሗ࡟ࡶไ㝈ࡀ⏕ࡌࡲࡍࠋ☜ᐇ࡟ゝ࠼ࡿࡇ࡜ࡣࠊ EFD/CFD༢⊂࡛ᚓࡽࢀࡿࢹ࣮ࢱࡢ⢭ᗘࡸಙ㢗ᛶ࡟ࡣ⮬ࡎ࠿ࡽ㝈⏺ࡀ⏕ࡌࡿ࡜࠸࠺ࡇ࡜࡛ࡋࡻ

࠺ࠋ

୍᪉ࠊ኱Ꮫࡢ◊✲ᐊ➼࡟࠾࠸࡚ࡣࠊᐇ㦂࡜ィ⟬ࡢ୧㠃࠿ࡽࡢ࢔ࣉ࣮ࣟࢳࡣ᪥ᖖⓗ࡞ᡭẁ࡛࠶

ࡾࠊᐇ㦂࡜ィ⟬ࡢ༢⣧࡞ẚ㍑࠿ࡽ⪃ᐹࢆࡋ࡚⾜ࡃ࡜࠸࠺ព࿡࡛ࡣEFD࡜CFDࡣᖖ࡟ᐦ᥋࡞㛵ಀ

࡟࠶ࡾࡲࡍࠋ

ࡇࡢࡼ࠺࡞⌧≧࡟㚷ࡳࠊ◊✲ᶵᵓ࡟࠾࠸࡚ࡣࠊ஧ඖㄽⓗ࡞⪃࠼᪉ࢆᨵࡵ཮᪉ࡢಙ㢗ᛶࢆྥୖ

ࡉࡏ┿࡟ᐇ⏝࡟౪ࡍࡿࢶ࣮ࣝ࡜࡞ࡍࡓࡵ࡟ࠊࡲࡓࠊ኱Ꮫ➼࡟࠾࠸࡚ࡣࠊ༢⣧ẚ㍑ࢆ㉸࠼ࡓࡼࡾ

῝࠸Ὕᐹ࣭▱ぢࢆᚓࡽࢀࡿࡼ࠺࡟ࡍࡿࡓࡵࠊEFD/CFDࡢ஫࠸ࡢၥ㢟Ⅼࡢ⿵᏶ࡸ᪂ࡓ࡞ᯟ⤌ࡳ

ࡢᵓ⠏࡟ࡼࡗ࡚ᚓࡽࢀࡿࢩࢼࢪ࣮ຠᯝࢆぢ࠸ࡔࡍࡇ࡜ࡀ㔜せ࡛ࡣ࡞࠸࡛ࡋࡻ࠺࠿ࠋ

ᮏ࣮࣡ࢡࢩࣙࢵࣉࡣࡇࡢࡼ࠺࡞EFD࡜CFDࡢ⼥ྜࢆࢸ࣮࣐࡜ࡋࠊὶయຊᏛ࡟ᦠࢃࡿ◊✲⪅ࡸ

ᢏ⾡⪅ࡀㅮ₇ࡸࢹ࢕ࢫ࢝ࢵࢩࣙࣥࢆ㏻ࡋ࡚ࡑࡢᚲせᛶ࣭㔜せᛶ࡟ࡘ࠸࡚ㄆ㆑ࢆ῝ࡵࠊ࠿ࡘ▱ぢ

ࢆᗈࡆࡿࡇ࡜ࢆ┠ⓗ࡜ࡋ࡚࠾ࡾࡲࡍࠋ

ࡇࡢ࣮࣡ࢡࢩࣙࢵࣉࡀࠊEFD/CFD⼥ྜ࡜࠸࠺ྂࡃ࡚᪂ࡋ࠸ࢸ࣮࣐࡟㛵ࡋ࡚᝟ሗ஺᥮ࢆࡍࡿ

ࡼ࠸ᶵ఍࡜࡞ࡾࠊ᪂ࡓ࡞Ⓨ᝿࡟ࡼࡿ◊✲㛤Ⓨάືࡀᅜෆእ࡛ࡼࡾ୍ᒙᒎ㛤ࡉࢀࡿࡼ࠺࡟࡞ࢀࡤࠊ

୺ദ⪅࡜ࡋ࡚ఱࡼࡾࡢ႐ࡧ࡛ࡍࠋࡲࡓࠊᮏ࣮࣡ࢡࢩࣙࢵࣉࡣ௒ᚋࡶ⥅⥆ࡉࡏ࡚࠸ࡃணᐃ࡛ࡍࡢ

࡛ࠊෆᐜ࡟ࡘ࠸࡚ࡈពぢࡸࡈᥦ᱌➼ࡈࡊ࠸ࡲࡋࡓࡽࡐࡦ࡜ࡶ࠾▱ࡽࡏ࠸ࡓࡔࡁࡓࡃࠊᐅࡋࡃ࠾

㢪࠸⏦ࡋୖࡆࡲࡍࠋ

ᖹᡂ22125

3EFD/CFD⼥ྜ࣮࣡ࢡࢩࣙࢵࣉᐇ⾜ጤဨ఍ ጤဨ㛗 Ᏹᐂ⯟✵◊✲㛤Ⓨᶵᵓ ◊✲㛤Ⓨᮏ㒊 ᯇᑿ ⿱୍

ᮾ໭኱Ꮫὶయ⛉Ꮫ◊✲ᡤ ኱ᯘⱱ

(4)

3EFD/CFD⼥ྜ࣮࣡ࢡࢩࣙࢵࣉ ᐇ⾜ጤဨ఍ ጤဨྡ⡙

ጤဨ㛗 ᯇᑿ ⿱୍ JAXA◊✲㛤Ⓨᮏ㒊 ᩘ್ゎᯒࢢ࣮ࣝࣉ

኱ᯘ ⱱ ᮾ໭኱Ꮫ ὶయ⛉Ꮫ◊✲ᡤ 㝃ᒓὶయ⼥ྜ◊✲ࢭࣥࢱ࣮

ጤဨ 㟷ᒣ ๛ྐ JAXA◊✲㛤Ⓨᮏ㒊 ᩘ್ゎᯒࢢ࣮ࣝࣉ

ὸ஭ ᆂ௓ ᮾ໭኱Ꮫ኱Ꮫ㝔 ᕤᏛ◊✲⛉ ⯟✵ᏱᐂᕤᏛᑓᨷ

ఀ⸨ ㈗அ ࠾ⲔࡢỈዪᏊ኱Ꮫ኱Ꮫ㝔 ⌮Ꮫ㒊᝟ሗ⛉Ꮫ⛉

ఀ⸨ ೺ JAXA◊✲㛤Ⓨᮏ㒊 㢼Ὕᢏ⾡㛤Ⓨࢭࣥࢱ࣮

ᕝῧ ༤ග 㫽ྲྀ኱Ꮫ ኱Ꮫ㝔ᕤᏛ◊✲⛉ ᶵᲔᏱᐂᕤᏛᑓᨷ బ᐀ ❶ᘯ ྡྂᒇ኱Ꮫ኱Ꮫ㝔 ᕤᏛ◊✲⛉ ⯟✵ᏱᐂᕤᏛᑓᨷ

⃝⏣ ᜨ௓ ᮾ໭኱Ꮫ኱Ꮫ㝔 ᕤᏛ◊✲⛉ ⯟✵ᏱᐂᕤᏛᑓᨷ 㕥ᮌ ᏹ஧㑻 ᮾி኱Ꮫ኱Ꮫ㝔 ᪂㡿ᇦ๰ᡂ⛉Ꮫ◊✲⛉

㕥ᮌ ಇஅ JAXA◊✲㛤Ⓨᮏ㒊 ᮍ㋃ᢏ⾡◊✲ࢭࣥࢱ࣮

ᆤ಴ ㄔ ໭ᾏ㐨኱ᏛᕤᏛ㒊 ᶵᲔ▱⬟ᕤᏛ⛉

ᮧୖ ᱇୍ JAXA◊✲㛤Ⓨᮏ㒊 ᩘ್ゎᯒࢢ࣮ࣝࣉ

ᒣᮏ ୍⮧ JAXA⯟✵ࣉࣟࢢ࣒ࣛࢢ࣮ࣝࣉ ᅜ⏘᪑ᐈᶵࢳ࣮࣒

ྜྷ⏣ ᠇ྖ JAXA⯟✵ࣉࣟࢢ࣒ࣛࢢ࣮ࣝࣉ ㉸㡢㏿ᶵࢳ࣮࣒

Ώ㎶ 㔜ဢ JAXA◊✲㛤Ⓨᮏ㒊 ὶయࢢ࣮ࣝࣉ

஦ົᒁ ┦᭮ ⚽᫛ JAXA◊✲㛤Ⓨᮏ㒊 ᩘ್ゎᯒࢢ࣮ࣝࣉ

ཱྀ▼ ⱱ JAXA◊✲㛤Ⓨᮏ㒊 ὶయࢢ࣮ࣝࣉ

(5)

㼀㼔㼑㻌㻟㼞㼐㻌㼃㼛㼞㼗㼟㼔㼛㼜㻌㼛㼚㻌㻵㼚㼠㼑㼓㼞㼍㼠㼕㼛㼚㻌㼛㼒㻌㻱㻲㻰㻌㼍㼚㼐㻌㻯㻲㻰㻌

⛅ⴥཎ䝁䞁䝧䞁䝅䝵䞁䝩䞊䝹㻌 㻡㻮 ఍㆟ᐊ㻌 㻭㻷㻵㻴㻭㻮㻭㻾㻭㻌㻯㼛㼚㼢㼑㼚㼠㼕㼛㼚㻌㻴㼍㼘㼘㻦㻌㻾㼛㼛㼙㻌㻡㻮㻌

㻼㼞㼛㼓㼞㼍㼙㻌

㻶㼍㼚㻚㻌㻞㻡㻌㻔㻹㼛㼚㻚㻕㻘㻌㻞㻜㻝㻜㻌

㻥㻦㻟㻜㻙㻥㻦㻟㻡㻌 ኱ᯘ㻌 ⱱ㻌 㻔ᮾ໭኱ὶయ◊㻕㻌

㻿㼔㼕㼓㼑㼞㼡㻌㻻㼎㼍㼥㼍㼟㼔㼕㻌㻔㼀㼛㼔㼛㼗㼡㻌㼁㼚㼕㼢㻚㻕㻌 㻻㼜㼑㼚㼕㼚㼓㻌㻭㼐㼐㼞㼑㼟㼟㻌

㻿㼑㼟㼟㼕㼛㼚㻌㻝㻌㻨㻶㻭㼄㻭㻌㻷㼑㼥㼚㼛㼠㼑㻌㻿㼜㼑㼑㼏㼔㻪㻌 ྖ఍㻦㻌 ኱ᯘ㻌 ⱱ㻌 㻔ᮾ໭኱ὶయ◊㻕

㻯㼔㼍㼕㼞㼜㼑㼞㼟㼛㼚㻦㻌 㻿㼔㼕㼓㼑㼞㼡㻌 㻻㼎㼍㼥㼍㼟㼔㼕㻌 㻔㼀㼛㼔㼛㼗㼡㻌 㼁㼚㼕㼢㻚㻕 㻥㻦㻟㻡㻙㻝㻜㻦㻝㻜㻌 ཱྀ▼㻌 ⱱ㻌 㻔㻶㻭㼄㻭㻕㻌

㻿㼔㼕㼓㼑㼞㼡㻌㻷㼡㼏㼔㼕㻙㻵㼟㼔㼕㻌㻔㻶㻭㼄㻭㻕㻌

㻶㻭㼄㻭 䝕䝆䝍䝹㻛䜰䝘䝻䜾䞉䝝䜲䝤䝸䝑䝗㢼Ὕ䝅䝇䝔䝮䛾㛤Ⓨ≧ἣ䛻䛴䛔䛶㻌 㻿㼠㼍㼠㼡㼟㻌㻾㼑㼜㼛㼞㼠㻌㼛㼚㻌㼠㼔㼑㻌㻰㼑㼢㼑㼘㼛㼜㼙㼑㼚㼠㻌㼛㼒㻌㻶㻭㼄㻭㻌㻰㼕㼓㼕㼠㼍㼘㻛㻭㼚㼍㼘㼛㼓㻌㻴㼥㼎㼞㼕㼐㻌㼃㼕㼚㼐㻌㼀㼡㼚㼚㼑㼘㻌

㻿㼑㼟㼟㼕㼛㼚㻌㻞㻌㻨㻵㼚㼢㼕㼠㼑㼐㻌㻸㼑㼏㼠㼡㼞㼑㻏㻝㻪㻌 ྖ఍㻦㻌 బ᐀㻌 ❶ᘯ㻌 㻔ྡ኱㻕

㻯㼔㼍㼕㼞㼜㼑㼞㼟㼛㼚㻦㻌 㻭㼗㼕㼔㼕㼞㼛㻌 㻿㼍㼟㼛㼔㻌 㻔㻺㼍㼓㼛㼥㼍㻌 㼁㼚㼕㼢㻚㻕

㻝㻜㻦㻝㻜㻙㻝㻝㻦㻝㻜㻌

ᵽཱྀ㻌 ▱அ㻌 㻔⤫ィᩘ⌮◊㻕㻌 㼀㼛㼙㼛㼥㼡㼗㼕㻌㻴㼕㼓㼡㼏㼔㼕㻌

㻌 㻔㻵㼚㼟㼠㼕㼠㼡㼠㼑㻌㼛㼒㻌㻿㼠㼍㼠㼕㼟㼠㼕㼏㼍㼘㻌㻹㼍㼠㼔㼑㼙㼍㼠㼕㼏㼟㻕㻌

㏲ḟ䝕䞊䝍ྠ໬ධ㛛䠖ᩘ⌮ⓗᇶ♏䛸᭱᪂䛾ືྥ㻌 㻵㼚㼠㼞㼛㼐㼡㼏㼠㼕㼛㼚㻌㼠㼛㻌㻿㼑㼝㼡㼑㼚㼠㼕㼍㼘㻌㻰㼍㼠㼍㻌㻭㼟㼟㼕㼙㼕㼘㼍㼠㼕㼛㼚㻌㻹㼑㼠㼔㼛㼐㼟㻦㻌 㼀㼔㼑㼕㼞㻌㻹㼍㼠㼔㼑㼙㼍㼠㼕㼏㼍㼘㻌㻮㼍㼟㼕㼟㻌㼍㼚㼐㻌㻾㼑㼏㼑㼚㼠㻌㻰㼑㼢㼑㼘㼛㼜㼙㼑㼚㼠

㻝㻝㻦㻝㻜㻙㻝㻝㻦㻠㻡㻌 ὸ஭㻌 ᆂ௓㻌 㻔ᮾ໭኱㻕㻌 㻷㼑㼕㼟㼡㼗㼑㻌㻭㼟㼍㼕㻌㻔㼀㼛㼔㼛㼗㼡㻌㼁㼚㼕㼢㻚㻕㻌

㻱㻲㻰䛸㣕⾜䝅䝭䝳䝺䞊䝅䝵䞁㻌 㻙㻌 ḟୡ௦ືⓗ㢼Ὕᐇ㦂ἲ䛾㛤Ⓨ䛻ྥ䛡䛶㻌 㻱㻲㻰㻌㼍㼚㼐㻌㻲㼘㼕㼓㼔㼠㻌㻿㼕㼙㼡㼘㼍㼠㼕㼛㼚㻌㻙㻌㼀㼛㼣㼍㼞㼐㼟㻌㼠㼔㼑㻌㻰㼑㼢㼑㼘㼛㼜㼙㼑㼚㼠㻌㼛㼒㻌㼠㼔㼑㻌㻺㼑㼤㼠㻙㻳㼑㼚㼑㼞㼍㼠㼕㼛㼚㻌 㻰㼥㼚㼍㼙㼕㼏㻌㼃㼕㼚㼐㻙㼀㼡㼚㼚㼑㼘㻌㼀㼑㼟㼠㼕㼚㼓㻌

㻸㼡㼚㼏㼔㻌

㻿㼑㼟㼟㼕㼛㼚㻌㻟㻌㻨㻵㼚㼢㼕㼠㼑㼐㻌㻸㼑㼏㼠㼡㼞㼑㻏㻞㻪㻌 ྖ఍㻦㻌 ᆤ಴㻌 ㄔ㻌 㻔໭኱㻕

㻯㼔㼍㼕㼞㼜㼑㼞㼟㼛㼚㻦㻌 㻹㼍㼗㼛㼠㼛㻌 㼀㼟㼡㼎㼛㼗㼡㼞㼍㻌 㻔㻴㼛㼗㼗㼍㼕㼐㼛㻌 㼁㼚㼕㼢㻚㻕 㻝㻟㻦㻜㻜㻙㻝㻟㻦㻟㻡㻌 ᒣ⏣㻌 ࿴㇏㻌 㻔஑ᕞ኱㻕㻌

㻷㼍㼦㼡㼠㼛㼥㼛㻌㼅㼍㼙㼍㼐㼍㻌㻔㻷㼥㼡㼟㼔㼡㻌㼁㼚㼕㼢㻚㻕㻌

䝍䞊䝪ᶵᲔ䛻䛚䛡䜛ෆ㒊ὶື⌧㇟䛾 㻱㻲㻰㻛㻯㻲㻰 䝝䜲䝤䝸䝑䝗ゎᯒ㻌

㻱㻲㻰㻛㻯㻲㻰㻌㻴㼥㼎㼞㼕㼐㻌㻭㼚㼍㼘㼥㼟㼕㼟㻌㼛㼒㻌㻵㼚㼠㼑㼞㼚㼍㼘㻌㻲㼘㼛㼣㻌㻼㼔㼑㼚㼛㼙㼑㼚㼍㻌㼕㼚㻌㼀㼡㼞㼎㼛㼙㼍㼏㼔㼕㼚㼑㼞㼥㻌

㻝㻟㻦㻟㻡㻙㻝㻠㻦㻝㻜㻌

ᶫ∎㻌 ⚈ග㻌 㻔䝇䝈䜻ᰴᘧ఍♫㻕㻌

㼅㼛㼟㼔㼕㼙㼕㼠㼟㼡㻌 㻴㼍㼟㼔㼕㼦㼡㼙㼑㻌 㻔㻿㼡㼦㼡㼗㼕㻌 㻹㼛㼠㼛㼞㻌 㻯㼛㼞㼜㻚㻕㻌

⮬ື㌴䛾㛤Ⓨ䛻䛚䛡䜛 㻯㻲㻰 䛸 㻱㻲㻰 䛾฼⏝䛻䛴䛔䛶㻌 㻭㼜㼜㼘㼕㼏㼍㼠㼕㼛㼚㻌㼛㼒㻌㻯㻲㻰㻌㼍㼚㼐㻌㻱㻲㻰㻌㼛㼚㻌㼂㼑㼔㼕㼏㼘㼑㻌㻰㼑㼢㼑㼘㼛㼜㼙㼑㼚㼠㻌

㻿㼑㼟㼟㼕㼛㼚㻌㻠㻌㻨㻵㼚㼢㼕㼠㼑㼐㻌㻸㼑㼏㼠㼡㼞㼑㻏㻟㻪㻌 ྖ఍㻦㻌 ᯇᑿ㻌 ⿱୍㻌 㻔㻶㻭㼄㻭㻕

㻯㼔㼍㼕㼞㼜㼑㼞㼟㼛㼚㻦㻌 㼅㼡㼕㼏㼔㼕㻌 㻹㼍㼠㼟㼡㼛㻌 㻔㻶㻭㼄㻭㻕

㻝㻠㻦㻞㻜㻙㻝㻡㻦㻞㻜㻌 㻾㼕㼏㼔㼍㼞㼐㻌 㻶㻚㻌 㻿㼏㼔㼣㼍㼞㼠㼦㻌 㻔㻭㼀㻷㻌 㼍㼠㻌 㻺㻭㻿㻭㻌

㻸㼍㻾㻯㻕㻌 㼁㼚㼕㼒㼕㼑㼐㻌㻰㼍㼠㼍㻌㼂㼕㼟㼡㼍㼘㼕㼦㼍㼠㼕㼛㼚㻌㼡㼟㼕㼚㼓㻌㼠㼔㼑㻌㼂㼕㼞㼠㼡㼍㼘㻌㻰㼕㼍㼓㼚㼛㼟㼠㼕㼏㼟㻌㻵㼚㼠㼑㼞㼒㼍㼏㼑㻌㻔㼂㼕㻰㻵㻕㻌

㻿㼑㼟㼟㼕㼛㼚㻌㻡㻌㻨㻼㼍㼚㼑㼘㻌㻰㼕㼟㼏㼡㼟㼟㼕㼛㼚㼟㻪㻌 䝁䞊䝕䜱䝛䞊䝍㻦㻌 ⃝⏣㻌 ᜨ௓㻌 㻔ᮾ໭኱㻕

㻯㼛㼛㼞㼐㼕㼚㼍㼠㼛㼞㻦㻌 㻷㼑㼕㼟㼡㼗㼑㻌 㻿㼍㼣㼍㼐㼍㻌 㻔㼀㼛㼔㼛㼗㼡㻌 㼁㼚㼕㼢㻚㻕

㻝㻡㻦㻟㻜㻙㻝㻣㻦㻟㻜㻌

㼀㼕㼠㼘㼑㻦㻌㻯㼍㼚㻌㻱㻲㻰㻛㻯㻲㻰㻌㻵㼚㼠㼑㼓㼞㼍㼠㼕㼛㼚㻌㻹㼍㼤㼕㼙㼕㼦㼑㻌㻼㼞㼛㼐㼡㼏㼠㼕㼢㼕㼠㼥㻫㻌

䝟䝛䝸䝇䝖㻔㻼㼍㼚㼑㼘㼕㼟㼠㼟㻕㻦㻌

㻾㼕㼏㼔㼍㼞㼐㻌㻶㻚㻌㻿㼏㼔㼣㼍㼞㼠㼦㻌㻔㻭㼀㻷㻌㼍㼠㻌㻺㻭㻿㻭㻌㻸㼍㻾㻯㻕㻌

ᕝῧ㻌 ༤ග㻌 㻔㫽ྲྀ኱㻕㻌 㻌 㻌 㻌 㻌 㻌 㻴㼕㼞㼛㼙㼕㼠㼟㼡㻌㻷㼍㼣㼍㼦㼛㼑㻌㻔㼀㼛㼠㼠㼛㼞㼕㻌㼁㼚㼕㼢㻚㻕㻌

(6)

JAXA

䝕䝆䝍䝹

/

䜰䝘䝻䜾䞉䝝䜲䝤䝸䝑䝗㢼Ὕ䛾㛤Ⓨ≧ἣ䛻䛴䛔䛶

Status Report on the Development of

Status Report on the Development of JAXA Digital/Analog Hybrid Wind Tunnel

ཱྀ▼ ⱱ,, Ώ㎶ 㔜ဢ 䠄JAXA ◊✲㛤Ⓨᮏ㒊䠅 Shigeru KUCHI-ISHI and Shigeya WATANBE Aerospace Research and Development Directorate

Japan Aerospace Exploration Agency (JAXA) Japan Aerospace Exploration Agency (JAXA)

➨3ᅇEFD/CFD⼥ྜ䝽䞊䜽䝅䝵䝑䝥

The 3rd Workshop on Integration of EFD and CFD Jan. 25, 2010

AKIHABARA Convention Hall Tokyo Japan AKIHABARA Convention Hall, Tokyo Japan

Contents

„JAXA Digital/Analog Hybrid Wind Tunnel (HWT)

• Motivation

• Concept

• Wind Tunnel/Computer

• System ArchitectureSystem Architecture

• Functional Components

„Status on Subsystem Development

Digital Wind Tunnel

• Digital Wind Tunnel

• Acceleration of Analog Wind Tunnel

„Status on Main System Development

• Web-System Development Using RCM System Software

• Unified WT/CFD Data Management

• Unified WT/CFD Data Visualization/Analysis

• WT Setting Simulation

„JAXA 2m㽢2m Transonic Wind Tunnel Test

„Schedule

1

„Schedule

„Summary

(7)

Motivation (1/2)

„Enhance efficiency and user-friendliness: WT

• Model design and test planningModel design and test planning

• Data check/analysis during run time

• Data check from remote location

• Speed-up of data acquisition/reduction process

Real-time data processing for balance/pressure port data

PIV d t i i ithi 10 i t ft i iti

PIV data image processing within 10 minutes after acquisition

„Enhance efficiency and user-friendliness: CFD

• High-speed and simple grid generation

Within 1 hour for 1,000,000 grid points (unstructured grid) High speed and simple CFD analysis

• High-speed and simple CFD analysis

Within 1 hour for 1,000,000 grid points (unstructured grid) Two major methods for aerodynamic

characteristics prediction

2

From “EFD and CFD” to Integrated EFD/CFD

„Integration of EFD/CFD 䠖 䠄or fusion, synergy䠅

䞉More than simple collaboration 䞉

Aiming a new world where 1 + 1 > 2

„EFD:

Experimental Fluid Dynamics (Wind tunnel test)

Pressure measurement by PSP JAXA 2mx2m

Transonic WT

Analog, Real Analog, Real

Digital, Virtual Digital, Virtual

Nakahashi (2004)

„CFD:

Computational Fluid Dynamics

(8)

Motivation (2/2)

„Improve WT/CFD data accuracy/reliability

• WT wall/support interference correctionpp

• Detailed CFD analysis

Model deformation effects

T b l d l h i

Turbulence model choice

• High-fidelity model design and test planning Model deformation effects

• WT/CFD data uncertainty estimation

• Maximum-likelihood estimation of WT/CFD data

• Flight prediction

„Unified platform for WT/CFD data managementUnified platform for WT/CFD data management

• Common data format/data base

4

5

Expanding the technology integrating experiment and numerical simulation to other fields

Expanding the technology integrating experiment and numerical simulation to other fields

Concept

EFD (Analog WT)

Automatic/adaptive grid generation Automatic/adaptive

grid generation Fast CFD solver Fast CFD solver

Wind Tunnel

Test Wind Tunnel

High-Speed Reduction Test

of WT Data High-Speed Reduction

of WT Data

Database of both EFD and CFD Database of both EFD and CFD Virtual participation in

WTT via internet Virtual participation in

WTT via internet

Optimization of test planning, technique, and model Optimization of test planning,

technique, and model

WT wall&sting correction WT wall&sting correction

CFD Parameter Tuning (Turb. model, grid, etc.) CFD Parameter Tuning

(Turb. model, grid, etc.)

•Quasi-real-time WT/CFD comparison

•Validation data

CFD considering both test model and wind tunnel

(wall, model support) CFD considering both test

model and wind tunnel (wall, model support)

CFD (Digital WT)

Data fusion considering advantages and reliability of

EFD and CFD

(9)

6

Wind Tunnel/Computer

„JAXA 2m2m Transonic Wind Tunnel (JTWT)

„ JAXA Super Computer System (JSS)

9 Built 1960 (1994 refinement) 9 Continuous, circulation type 9 M = 0.1 – 1.4

9 Built 2009

9 3008CPU, 120Tflops, 94TB Memory (M-System)

ᵠᵿᶁᶉᶓᶎᴾᵱᶃᶐᶔᶃᶐ ᵴᶇᶑᶓᵿᶊᶇᶘᵿᶒᶇᶍᶌᴾᵱᶃᶐᶔᶃᶐ

ᵱᵟᵬ ᵱᶃᶐᶔᶃᶐ

ᵡᵟᵢᴾᵱᶃᶐᶔᶃᶐ ᵵᵲᴾᵱᶃᶐᶔᶃᶐ

ᵵᶃᶀ ᵱᶃᶐᶔᶃᶐ

ᵭᵱᾉ ᵰᶃᶂᴾᵦᵿᶒᴾᵣᶌᶒᶃᶐᶎᶐᶇᶑᶃᴾᵪᶇᶌᶓᶖ ᵡᵮᵳᾉ ᵏᵡᵮᵳᴾᵆᵐᵌᵗᵑᵥᵦΈᵍᵒᵡᶍᶐᶃ ᶖᴾᵏᵇ ᵫᶃᶋᶍᶐᶗᾉ ᵒᵥᵠ

ᵦᵢᵢᾉ ᵑᵎᵎᵥᵠᴾᶖᴾᵐᴾᵆᵰᵟᵧᵢᵏᵇ

ᵭᵱᾉ ᵰᶃᶂᴾᵦᵿᶒᴾᵣᶌᶒᶃᶐᶎᶐᶇᶑᶃᴾᵪᶇᶌᶓᶖ ᵡᵮᵳᾉ ᵐᵡᵮᵳᴾᵆᵐᵌᵗᵑᵥᵦΈᵍᵒᵡᶍᶐᶃ ᶖᴾᵐᵇ ᵫᶃᶋᶍᶐᶗᾉ ᵖᵥᵠ

ᵦᵢᵢᾉ ᵒᵓᵎᵥᵠᴾᶖᴾᵐᴾᵆᵰᵟᵧᵢᵏᵇ ᵡᶍᶌᶒᶐᶍᶊᴾᵱᶃᶐᶔᶃᶐ ᵰᶍᶓᶒᶃᶐ

ᵭᵱᵘᴾᴾᴾᴾᴾᵰᶃᶂᴾᵦᵿᶒᴾᵣᶌᶒᶃᶐᶎᶐᶇᶑᶃᴾᵪᶇᶌᶓᶖ ᵡᵮᵳᵘᴾᴾᴾᵐᵡᵮᵳᴾᵆᵐᵌᵗᵑᵥᵦΈᵍᵒᵡᶍᶐᶃ ᶖᴾᵐᵇ ᵫᶃᶋᶍᶐᶗᵘᴾᵏᵔᵥᵠ

ᵦᵢᵢᵘᴾᴾᴾᵒᵓᵎᵥᵠᴾᶖᴾᵐᴾᵆᵰᵟᵧᵢᵏᵇ

ᵏᵥᴾᵠᵟᵱᵣᴾᵣᶒᶆᶃᶐᶌᶃᶒ

System Architecture

ᵵᶃᶀ

ᵳᶑᶃᶐ

ᵨᵱᵱ

ᵭᵱᾉ ᵱᵳᵱᵣᵋᵠᵿᶑᶃ

ᵡᵮᵳᾉ ᵐᵡᵮᵳᴾᵆᵏᵌᵖᵔᵥᵦΈᵍᵒᵡᶍᶐᶃ ᶖᴾᵐᵇ ᵫᶃᶋᶍᶐᶗᾉ ᵐᵒᵥᵠ

ᵦᵢᵢᾉ ᵏᵒᵔᵥᵠᴾᶖᴾᵐᴾᵆᵰᵟᵧᵢᵏᵇ ᵤᵡ

ᵨᵲᵵᵲ

(10)

8

Functional Componetns (1/4)

WT Pre-Setting Simulation

Check model support system size and/or PIV/PSP camera-system setting location shorten WT preparation time

Pre-CFD

High-Speed CFD analysis for 1/5 of all WT test conditions Model deformation

CFD including WT wall/support system help model design and test planning

㻹㼛㼐㼑㼘㻌㻸㼛㼏㼍㼠㼕㼛㼚㻌㻯㼔㼑㼏㼗㻌 㼒㼞㼛㼙㻌㼃㼕㼚㼐㼛㼣㼟

㻹㼛㼐㼑㼘㻌㻿㼡㼜㼜㼛㼞㼠㻌 㻿㼥㼟㼠㼑㼙㻌㻯㼔㼑㼏㼗

9

Functional Componetns (2/4)

Model Deformation Analysis

Pre-Estimate by fluid/structure coupling analysis

Model Pressure Port Location/Test Planning Support Optimize by pre-CFD

Reaction Surface for Pressure/Aerodynamic Coefficient

Reaction Surface for Pressure/Aerodynamic Coefficient

Optimization Model Design Test Planning Pre-CFD

㏻㢼୰

↓㢼᫬

㏻㢼୰

↓㢼᫬

Wind-on Wind-off

(11)

Functional Componetns (4/4)

Real Time WT Test Monitoring

Monitoring WT data form remote locations via Internet WT-Aided CFD

Model optimization by WT data (turbulence model, grid locations)

Enhance WT data accuracy by optimized CFD (wall/support interference) Enhance WT data accuracy by optimized CFD (wall/support interference) WT/CFD Data Uncertainty Anasysis

Estimate error bar of WT data by traditional WT uncertainty analysis Estimate error bar of WT data by traditional WT uncertainty analysis Estimate error bar of CFD data by newly developed approach Maximum-Likelihood Estimation

Maximum Likelihood Estimation

Estimate maximum-likelihood force/pressure data by integrating WT and CFD

10

Functional Componetns (3/4)

WT Wall/Support Interference Correction

Estimate wall/support effects on aerodynamic coefficients by pre-CFD Unified WT/CFD Data Visualization/Analysis

Real-time visualization during WT blow time Auto-Check WT data using pre-CFD data

䞉Solid/Perforated Wall 䞉Model Sting/Strut

㼃㼀㼃㼀 㻼㼞㼑㻙㻯㻲㻰㻼㼞㼑㻙㻯㻲㻰

Check

OK NG

(12)

12

Development of Digital Wind Tunnel (1/2)

„Automatic grid generator: HexaGrid

9Automatic grid generator based on hexahedral grid 9Unstructured mesh based on Cartesian mesh

„New fast CFD solver: FaSTAR(FaST Aerodynamic Routines) 9Target: 300 cases/20days

(300 cases = 1/5 of a WT test campaign) 1hour/case (100CPU, 10,000,000 grid points)

13

Development of Digital Wind Tunnel (2/2)

„Transonic Wind Tunnel Simulation

Challenges: treatment of complex geometry (e.g. control surface) Challenges: treatment of complex geometry (e.g. control surface)

Test section

Porous wall Intake model

sting strut

(13)

14

„Objective:to improve data productivity of Analog WT by accelerating data reduction for PIV and PSP images.

High-speed data reduction of imaging techniques

Ex)

Acceleration of PIV data reduction

Cell/B.E.(High performance CPU developed by IBM / Toshiba / Sony) is the most promising candidate.

Accelerationsystem(PC cluster) Camera

PresentPIVsystem

Several hours for data reduction

CommercialPIVdataprocessingsoftware Issues

Imageacquisition computer

Acceleration of PIV processing

Celll/B.E.

Accelerator

Several minutes for data reduction Goal

7.88s / frame

by x8 CPUs(Pentium D 2.8GHz)

0.32s / frame by x2 Cell/B.E.

Accelerators

x 25 faster

at StereoPIV case

(2k x 2k CCD, 2 cameras)

PIV processing PC

•XML-Based Data Base (DB)

-> Flexible for the change of data structure/relation

•Data/Flow Control (Command/DB/Input/Output) by workflow template

•Coding/DB design-free

Listoftemplates

WorkflowTemplate

Web-System Development Using RCM System Software

RCM®: R&D Chain Management Quatre-i Science Co., Ltd.

(14)

16

Unified WT/CFD Data Management

¾ HDF5 type common data format

Easy to handle WT/CFD data in the same manner

¾WT/CFD common data base Easy to find a set of WT/CFD data at the same condition

㻿㼑㼍㼞㼏㼔㻌㼃㼀㻌㼠㼑㼟㼠㻌 㼕㼚㼒㼛㼞㼙㼍㼠㼕㼛㼚

㻿㼑㼘㼑㼏㼠㻌㼣㼛㼞㼗㼒㼘㼛㼣

㻹㼛㼚㼕㼠㼛㼞㻌㼃㼀㻌㼐㼍㼠㼍㻌㼟㼑㼞㼢㼑㼞㻌 㼍㼚㼐㻌㼍㼡㼠㼛㼙㼍㼠㼕㼏㼍㼘㼘㼥㻌㼒㼛㼞㼣㼍㼞㼐㻌 㼚㼑㼣㻌㼐㼍㼠㼍㻌㼕㼚㼠㼛㻌㼠㼔㼑㻌㼟㼥㼟㼠㼑㼙

㻯㼛㼚㼢㼑㼞㼠㻌㼃㼀㻌㼐㼍㼠㼍㻌㼠㼛㻌 㼏㼛㼙㼙㼛㼚㻌㼒㼛㼞㼙㼍㼠㻌㼍㼚㼐㻌 㼑㼚㼠㼞㼥㻌㼠㼛㻌㻰㻮 㼃㼛㼞㼗㼒㼘㼛㼣

17

Unified Data Visualization/Analysis

¾Simple and rapid WT/CFD data visualization by accessing WT/CFD common data base

¾Support FieldView and Tecplot

㻯㻲㻰㻌㻰㼍㼠㼍 㻾㼑㼍㼘㼕㼦㼑㻌㼡㼚㼕㼒㼕㼑㼐㻌㼢㼕㼟㼡㼍㼘㼕㼦㼍㼠㼕㼛㼚㻌㼎㼥㻌

㼟㼜㼑㼏㼕㼒㼥㼕㼚㼓㻌㼃㼀㻛㻯㻲㻰㻌㼐㼍㼠㼍㻌㼕㼚㻌㻰㻮

㼂㼕㼟㼡㼍㼘㼕㼦㼍㼠㼕㼛㼚㻌㼕㼙㼍㼓㼑㻌㼟㼠㼛㼞㼑㼐㻌㼕㼚㻌㻰㻮 㼁㼚㼕㼒㼕㼑㼐㻌㼂㼕㼟㼡㼍㼘㼕㼦㼍㼠㼕㼛㼚

㼃㼀

䠄㻼㻿㻼䠅 㻯㻲㻰

㻼㻿㻼㻦㻌㻼㼞㼑㼟㼟㼡㼞㼑㻌㻿㼑㼚㼟㼕㼠㼕㼢㼑㻌㻼㼍㼕㼚㼠

㻯㻸

㻼㼞㼑㼟㼟㼡㼞㼑㻌 㼐㼕㼟㼠㼞㼕㼎㼡㼠㼕㼛㼚㻌

㼃㼀㻌㻰㼍㼠㼍

(15)

18

WT Setting Simulation

㼂㼕㼟㼡㼍㼘㼕㼦㼑㻌㼢㼕㼑㼣㻙㼍㼞㼑㼍㻌㼛㼒㻌㼙㼡㼘㼠㼕㻙㼏㼍㼙㼑㼞㼍㻌㼟㼥㼟㼠㼑㼙㻧㻌 㼜㼞㼑㻙㼏㼔㼑㼏㼗㻌㼏㼍㼙㼑㼞㼍㻛㼃㼀㻌㼕㼚㼠㼑㼞㼒㼑㼞㼑㼚㼏㼑

¾Handle model/WT CAD data by high-end CAD software (CATIA V. 5) via Excel Possible to use without the knowledge of CATIA manipulation

¾Pre-Check model/WT interference

Possible to check safety before WT tests

¾Pre-Check of optical system setting (camera, laser, etc.) for PIV/PSP measurements Possible to shorten WT

preparation works

㻿㼜㼑㼏㼕㼒㼥㻌㼏㼍㼙㼑㼞㼍㻌㼘㼛㼏㼍㼠㼕㼛㼚㻛㼍㼚㼓㼘㼑

㻼㼞㼑㻙㼏㼔㼑㼏㼗㻌㼙㼛㼐㼑㼘㻛㼃㼀㻌㼕㼚㼠㼑㼞㼒㼑㼞㼑㼚㼏㼑㻌㼎㼥㻌 㼏㼔㼍㼚㼓㼕㼚㼓㻌㼍㼚㼓㼘㼑㻌㼛㼒㻌㼍㼠㼠㼍㼏㼗

㻾㼑㼏㼛㼞㼐㻌㼏㼍㼙㼑㼞㼍㻌㼟㼑㼠㼠㼕㼚㼓㻌㼜㼍㼞㼍㼙㼑㼠㼑㼞㻌 㻔㼘㼛㼏㼍㼠㼕㼛㼚㻘㻌㼍㼚㼓㼘㼑㻘㻌㼑㼠㼏㻚㻕

JAXA 2m 㽢 2m Transonic WT Test

9 Two support types evaluate support interference

9 Porous wall pressure measurement

Used for CFD wall interference correction DLR-F6 Model (90% scale)

Direct-Sting Support Blade-Support

9 Pressure measurements at downstream of WT 䊻Used for CFD boundary conditions

„2009/12/22 – 2010/1/15

„17 run, 3777 points

(16)

Summary

„ JAXA has started the development of “Digital/Analog Hybrid Wind

T l” t t li i EFD/CFD i t ti Th i iti l

Tunnel” as a prototype realizing EFD/CFD integration. The initial system will be completed in 2011.

„ Main technical development items

„ Main technical development items

9WT/CFD data integration systems (unified WT/CFD data management/Visualization, WT test pre-setting simulation).g p g ) 9Automatic grid generation and high-speed solver for Digital WT.

9Acceleration of image data reduction for aerodynamicg y measurement such as PIV.

„ Future components to be developed include WT wall/support interference correction, WT-aided CFD, maximum-likelihood estimation, etc.

21

㻿㼏㼔㼑㼐㼡㼘㼑

20

㻲㼅㻞㻜㻜㻤 㻲㼅㻞㻜㻜㻥 㻲㼅㻞㻜㻝㻜 㻲㼅㻞㻜㻝㻝 㻲㼅㻞㻜㻝㻞 㻼㼞㼑㻙㻰㼑㼟㼕㼓㼚

㻰㼑㼟㼕㼓㼚 㻰㼑㼢㼑㼘㼛㼜㼙㼑㼚㼠

㼂㼍㼘㼕㼐㼍㼠㼕㼛㼚 㻱㼢㼍㼘㼡㼍㼠㼕㼛㼚 㻭㼐㼢㼍㼚㼏㼕㼚㼓

Initial System Complete

Advanced System Complete

Wall/Support interference correction Real time WT test monitoring Pressure port/test planning Support

Model deformation analysis WT-aided CFD

WT/CFD uncertainty analysis Maximum-likelihood estimation

(17)

Acknowledgements

JAXA EFD Group:

Y Ijima H Kato S Koike T Hirotani and M Kohzai

JAXA CFD Group:

Y. Ijima, H. Kato, S. Koike, T. Hirotani, and M. Kohzai

T. Aoyama, K. Murakami, A. Hashimoto, N. Fujita, and Y. Matsuo Ryoyu Systems Co., Ltd.

QUATRE-i Science Co., Ltd.,

22

(18)

Introduction to Sequential Data assimilation methods:

Their mathematical basis and recent development

Tomoyuki Higuchi

Research Organization of Information and Systems The Institute of Statistical Mathematics/JST CREST

1/42

Deductive Approach

Inductive Approach

TESD: Four Kinds of Methodology of Science

T:Theory E:Experiment

S:Simulation D 䠖 Massive

Data Analysis

(Axle)

Data Assimilation

Drive Force for Science

2/42 Red colorindicates a slide used in the last year’s presentation (2nd. Workshop on Integration of EFD and CFD)

(19)

3

What is Data Assimilation?

• Emerging subject in meteorology and oceanography.

• Methodology to synthesize numerical simulation model and observed data

– Simulation model can not reflect real physics accurately.

e.g.Accurate weather forecast needs good initial conditions.

• Uncertainty in the model (boundary condition, initial condition, unknown parameters, unknown dynamics...) exists.

– Observation data have some physical/budgetary restrictions.

Correct variables in numerical simulation model using observation data. = Data Assimilation

Simulation model Observation data

3/42

Objects of Data Assimilation from a viewpoint of Meteorology and Oceanography

[1] To produce the best (better) initial condition for forecasting. It is actually realized in the real weather forecast (ex., Japan Meteorological Agency).

[2] To find the best (better) boundary condition in constructing a simulation model. This procedure includes a setting of appropriate boundary conditions necessary for dealing with a coupled phenomena.

[3] To attain an optimal parametervector that appears in an empirical law (scheme) employed for describing complicated phenomena with the different time and spatial scales. A validationof the empirically given values is

regarded as this problem.

[4] To inter/extrapolate (estimate) an physical quantity at times and locations without observations based on a numerical simulation model. This procedure is called “a generation of re-analysis dataset (product)”. This dataset is used to discover a new scientific findings by general geophysical researchers.

(20)

5

Outline

• Mathematical basis and Bayesian computation

• Sequential data assimilation

• Ensemble-based nonlinear filtering method

Particle filter (PF)

• Advanced methods for PF

Merging PF

Meta PF

PF with GPGPU

• Conclusions

5/42

Construction of Simulation Model

Observation points and observed variables are limited.

) , , ( i i i

i T U V

[

i 1 i

physical variable vector is assigned at each grid point. temperature

Wind vector

1

[i

[i

) , ( t 1 t

t F x v

x

) ( t1

t F x

x

vt

w

w 2 t cx x

䠄simplified meteorological model around Japan䠅

PDE : Partial differential equation

(time varying)

6/42

(21)

777

Past and

Present Present

and Future State

x t

State Vector 䠖 Contact point between past and future

) ( t 1

t F x

x

Simulation Model

State of time t-1

State of timet

7/42

From one path to PDF (=Probability Distribution Function)

Simulation model

1 t t

t F x

x

1

| t t

t F x

x

Simulation model with uncertainty

x

t

x

t

t t1

t F x

x

p G

xt

p

t t

t h x

y |

Relation to observed data yt

xt yy

p |

1 t

t x

F

)

| (

p x y

Conditional distribution

Next slide

(22)

999

Conditional and Joint Probabilities

9/42

B

A ˆ

{ ) A (

p Probability of A

) { B A, (

p Probability of A and B

{ ) B

| A (

p Probability of B given A

Conditional Probability Joint Probability

Total: 100

# of consumers to buy a bag of coffee grounds : 30

# of consumers to buy milk: 60

# of consumers to buy a coffee bag and milk: 10

A=1: Buy a bag of coffee grounds

=0: Not buy B=1: Buy milk

=0: Not buy

A ‰ B

20 10 50

30 60

20 )

10 20 (

10 30

) 10 1 A

| 1 B ( 100, ) 10 1 B , 1 A ( 100, ) 30 1 A

( p p

p

¦¦

4

1 6

1

1 ) B , A (

i j

j i

p

10 10 10

Marginalization

10/42

¦

6

1

) B

, 3 A ( )

3 A (

j

j p

p p ( A i , B j )

Joint probability

A=3

B=1 B=6

A

A=1: Yahoo

=2: Google

=3: Microsoft

=4: Others

B=1: NEC, =2: Fujitsu, =3: Dell

=4: Toshiba, =5: Apple , =6: Others Others

B

possible

¦

B '

) B B , A ( )

A A (

j j

j i

i p

p

PC Web Search Engine

³ ( A, B ) B

) A

( p d

p

(23)

11 11 11

Bayes’ Theorem

11/42

B

B A ‰

20 10 50

30 60

20

¦

¦

Ÿ



) A ( A)

| (B

) A ( A)

| (B )

B A, (

) B A, ( )

B (

B) , ) (A

B

| A (

) A ( ) A

| B ( B) , ) (A

A (

B) , ) (A

A

| B (

A A

p p

p p

p p p

p p

p p

p p p p

䚷䚷 䚷䚷䚷䚷

䛾䛸䜛ྍ⬟ᛶ

50 10

10 100

70 70 50 100

30 30

10 100 30 30 10

0) (A 0) A

| 1 (B 1) (A 1) A

| 1 (B

1) (A 1) A

| 1 (B ) 1 B

| 1 A (

˜

˜

˜

p p

p p

p p

p

It is

easy

to

calculate.

A=1: Buy a bag of coffee grounds (Search Engine type) B=1: Buy milk (PC type)

Generative Model, Inversion with Bayes’ theorem, and Data Assimilation

y x x y p( | )

Data distribution :Forward Posterior distribution:

Inverse

y x y x p( | ) x

x p( )

Prior distribution :Forward

Build a generative model and Use Bayes’ theorem Simulation Fitness of Simulation to Data

) , (

) ( )

| (

) (

) ( )

| ) (

| (

y x p

x p x y p

y p

x p x y y p

x p

˜ v

{ ˜

䚷䚷䚷䚷

Bayes’ Theorem

䚷䚷䚷䚷

x

simulation variables

y

data

Prior dist.

Data dist.likelihood function

Posterior dist.

(24)

) ,

(

) ,

( 1

t t

t

t t

t

w x

h y

v x

f

x

Data Assimilation in Generalized State Space Model

State VectorSimulation variables

Stochastic simulation model

Observation model

Measurement model

map nonlinear :

L LŸ

t t

t t

G G

!!

' '

1 step time simulation :

ns observatio of

time sampling :

14/42

G t

' t

Missing value (Outlier)

time integration

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Prior Belief about values of x Posterior

Improved knowledge about values of x

13 Likelihood

Feasibility of realization of y for given x

) ( )

| ( )

|

( x y p y x p x

p v ˜

13/42

Cyclical structure

(25)

x

1

x

2

x

3

) ( x

1

x p

x

x

t

) (

t

x p x

x

T

State Vector and Concatenated State Vectors

15 15

Chain Structure Graphical Model

x

0

y

2

y

t

x

2

x

t

Latent Vector

Observable Vector

y

1

Observation model

x

1

System model

^ `

^

x0,yx11,,,,yxtt,,,,yxTT

`

)

| (

]) ,

, , [

| (

]) ,

, , [

| (

]) ,

, , [

| (

: 1 :

1

2 1 :

1

2 1 :

1

1 2

1 1

: 1

T T

T T

t

t t

t

t t

t

p

y y

y p

y y

y p

y y

y p

y x

y x

y x

y x

{

{

{

Today’s economic situation given

yesterday’s stock market data Today’s economic situation estimated by the stock market data up to today Today’s economic situation analyzed by

using all available data when we look back on the today in future

Suppose a statistical inference problem on a daily economic status given daily stock market data

15/42

(26)

Find X=[x1, …, xT ] that maximize

y

T

p X |

1:

For t= 1, …,T :

estimate p

xt | y1:T

x1 xt1 xt xt1 xT

y1 yt1 yt yt1 yT

x1 xt1 xt xt1 xT

y1 yt1 yt yt1 yT

Variational DA method Sequential DA method

•Adjoint method (4DVar)

•Representer method

•Kalman filter (KF), smoother

•Extended KF (EKF)

•Ensemble KF (EnKF)

•Particle filter (PF)

Two ways of DA method

Smoothing dist.

17/42

Optimization and Statistical Inference

x

t

t t t

t

t t

d p

p f

x x x

x

x x

˜

Ÿ

³ ( )

ˆ

) ( )

(

^ ( ) `

ˆ max ) (

X X

X

f f

Dimension of Xis huge

^ `

^ ` ^

f T

`

T f

T

h f exp ( )/

/ ) ( exp

/ ) ( ) exp

( ș

ș

ș ș v

¦

18/42

(27)

Recursive formula

)

|

di ti d it (

Conditional Distribution

)

| (

)

|

(

t 1t: 1

x

p x p

y y

predictive density:

filter density:

Today’s economic situation given yesterday’s stock market data Today’s economic situation

)

| (

)

| (

: 1

: 1

T t

t t

x p

x p

y y

filter density:

smoother density:

estimated by the stock market data up to today

Today’s economic situation analyzed by using all available data when we

)

| (

t 1T:

p y

y

)

| ( x

j 1:k

p y j

y g

look back on the today in future

)

| ( x

t 1

y

1:t 1

p (

t1

| y

1:tprediction1

) p ( x

t

| y

1t: 1

) y

1:t

{ { y

1

, , y

t

} p

k p ( x

t1

| y

1:t

)

)

| (

t

y

1:t1

p

)

| ( x

t

y

1t:

p

filtering

)

| ( x

n1

y

1:n1

p

19 19

smoothing 19

)

| ( x

t 1

y

1:T

p

)

| ( x

t

y

1T:

p p ( x

T

| y

1T:

)

19/42

Prediction

1 :

1

)

| ( x

t

y

t

p

1 1

: 1 1 1

: 1

)

| ,

(

|

³

t t t t

t t

dx y

x x p y

1 1

: 1 1 1

: 1

1

, ) ( | )

|

(

³ p x

t

x

t

y

t

p x

t

y

t

dx

t

³

)

| ( ) ,

|

(xt xt1 y1:t1 p xt xt1

p Markov property䠄䠍䠅

1 1

: 1 1

1

) ( | )

|

(

³ p x

t

x

t

p x

t

y

t

dx

t

参照

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