Structural Optimization Using Metamodels

Transcription

1 Srucural Opmzaon Usng Meamodels 30 Mar. 007 Dep. o Mechancal Engneerng Dong-A Unvers Korea Kwon-Hee Lee

2 Conens. Numercal Opmzaon. Opmzaon Usng Meamodels Impac beam desgn WB Door desgn 3. Robus Opmzaon Usng Krgng Models 4. Applcaon Eamples 5. Concluson

3 . Numercal Opmzaon Graden Based Opmzaon Applcaons o Algorhms 948: Smple mehod 960 s: SLP Sequenal Lnear Programmng SUM Sequenal Unconsraned Mnmzaon echnques Feasble Drecon Mehod 970 s: Moded Feasble Drecon Mehod Reduced graden mehod 980 s: SQP Sequenal Quadrac Programmng Varable Merc Mehod 990 s: Revsed Esng Algorhms Non-Graden Based Opmzaon GA Genec Algorhm SA Smulaed Annealng Algorhm S abu Search s Scenaro OPIMIZER algorhm nd Scenaro OPIMIZER algorhm 3 rd Scenaro OPIMIZER algorhm somemes ANALYZER FE CODE APPROXIMAE MODELSensv In. ANALYZER FE CODE APPROXIMAE MODELMeamodels ANALYZER FE CODE: Black Bo 3

4 . Numercal Opmzaon : Consrans n he s and nd scenaros Shape Opmzaon Nonlnear Analss Opmzaon Usng Meamodels Dscree Desgn Robus Desgn Robus Opmzaon Usng Meamodels Mehods o make meamodel RSM Response Surace Mehod Krgng Radal Bass Mehod Neural Nework 4

5 . Opmzaon Usng Meamodels: RSM β β β ε 0 β β β 0 DOE rue opmum X X Appromae opmum 5

6 . Opmzaon Usng Meamodels: RSM Impac beam desgn Fnd a b a Mamze Ressance orce Subec o w wo b All dos ed b sprng Unorm veloc : 800mm/sec 6

7 . Opmzaon Usng Meamodels: RSM a b a b a ab b.44 0 b a opmum a7.00mm b.0mm.4mm 7

8 . Opmzaon Usng Meamodels: Krgng β r R β q 8

9 . Opmzaon Usng Meamodels: Krgng Hsor o Krgng D.G. Krge95 Souh Arcan geologs Maheron963: Gaussan Krgng Sacks989: Desgn and Analss o Compuer Epermens Cresse993Guna and Wason 998 Krgng model or a response β z Z~N0 Correlaon uncon beween and k 3 Assumpons An esmaor lnear produc : unbased esmaor w n s E[ ] E[ ] BLUP bes lnear unbased predcor Mn. MSE[ ] E[ w ] Mn. Subec n s MSE[ ] E[ w n s o E[ ] E[ ] ] 6 n k R ; Ep [ z z ] k k R ; Corr k 4 5 Predced response β r R β q r [ 7 ns R R... R ] 9

10 0 / ; β β π β q R q R n Ep L s Predced response Lkelhood uncon L. Opmzaon Usng Meamodels: Krgng R r R r R r ] [ MSE 8 R q q R q β n s q R q β β Θ n>0 ] ln ln [ R n s mamze Esmaon o parameers β Mamum he log-lkelhood uncons gves he mamum lkelhood esmae o β 9 0 n n RMSE ]... [ n MAX MAXAE Valdaons o krgng model 3 n n error Ave 00 %. n s s n CV s he -h esmaor o krgng model consruced whou he -h observaon. 4 5

11 . Opmzaon Usng Meamodels: Krgng WB Door Desgn

12 . Opmzaon Usng Meamodels: Krgng Mnmze Wegh l l subec o δ A - δ Ao 0 δ B - δ B0 0 δ C - δ C0 0 δ D - δ D0 0 6 ω 0 - ω mm...5.5mm -5.0mm l 5.0mm [ ] Z {z d : d... } [l l ] R Here Z mm { }. z k neares[ k z z...z ] 7 where he neares uncon plas he role o replacng k wh z k closes one o he dscree se Φ W 6 Ma[ g 0] α 8

13 . Opmzaon Usng Meamodels: Krgng DOE mehod: Lan hpercube desgn o equaon Mnmze - d s he dsance beween pons and. n s n s d 5 % reducon 3

14 3. Robus Opmzaon Usng Krgng Models Obecve Produc perorms conssenl as nended Under a wde range o user s condons hroughou he cusomer le ccle 4

15 3. Robus Opmzaon Usng Krgng Models amonoonc uncon bmul-modal uncon c varance uncon Concep o global robus opmzaon [ b p] b : desgn varables p : desgn parameers b p b z p z 9 5

16 3. Robus Opmzaon Usng Krgng Models Sequenal Samplng predced responses a sample pons β r R β q β β q 0 Addng he ollowng opma o he sample pons Mnmze L U k wh o k... nk Addng he desgn pon mnmzng MSE o he sample pons Mamze X q R r r R r q R q 6

17 7 μ m m μ. m m m... m q R r β... m q R r β ]... [ ns ns A A A r ]... [ A A A ns ns ns r ]... [ A A A ns ns r ].... [ k m m m k k k Ep A 5 s-order sascal appromaon mehod 3 4 nd-order sascal appromaon mehod Robus Opmzaon Usng Krgng Models : Calculaons o Sascs

18 3. Robus Opmzaon Usng Krgng Models : Desgn Process Dene he sample pons. Full combnaons LHD or orhogonal arras Consruc he krgng models o responses. Valdae he krgng models usng several ndees. Or Resample and reconsruc he krgng models o responses. Sequenal samplng Valdae he krgng models usng several ndees. Yes Are he accepable? Solve he ormulaon or robus opmzaon. Smulaed annealng algorhms Use anoher sample pons. No Perorm he conrmaon analses a he predced robus opmum.mone-carlo Smulaon 8

19 4. Applcaons : Brann uncon Mnmze b b b 0.98b.5955b cos b b 5 0 b 5 9 a-π.75 *0.397 Mnmze μ b 3 b b L b b U 30 c0 6 Δb.0 Δb 6 b bπ.75 *0.397 Brann uncon a Orgnal uncon b appromae Model o 9

20 4. Applcaons : -bar desgn Mnmze Subec o V πd [d HBEP] S S S S 0mm d 80mm 00mm H 000mm.5mm B V H ma cr P B H S πdh S cr π Ed 8 B H 3 b[d H] p[b EP]. Δ [3.0mm 60.0mm 60.0mm 30000MPa 30000N] and Δ 6 robus opmzaon Mnmze μ 3 V V Subec o 0mm d μ 3 S μ 3 S S S 80mm S μ ma cr 3 cr 00mm H 000mm.5mm 3 0

21 4. Applcaons : -bar desgn Sample pons : Orhogonal arra

22 4. Applcaons: Srucural Desgn o a Mcrogroscope z Ω nner gmbal Inner mass drvng sprng bendng sprng sensng sprng orsonal sprng A -vew drvng comb ouer rame z drvng-sensng comb nner gmbal cross seconal o A - vew boom sensng elecrode d Mcro groscope: LPCVD Low Pressure Chemcal Vapor Deposon V F e drvng V d V Laeral C volage a sn orce V w 3 4 F C z m εs d g Ω v

23 3 U L o Subec ln ln Mnmze b U L b p b p b p b 33 0 ln ln L U Ma w Mnmze b b L U b Applcaons: Srucural Desgn o a Mcrogroscope Low Pressure Chemcal Vapor Deposon

24 4. Applcaons: Srucural Desgn o a Mcrogroscope Desgn varables and desgn parameer 4 Probabl o success: 3.5% 4

25 5. Concluson s Scenaro nd Scenaro 3 rd Scenaro Manuacurng Desgn Merc! 감사합니다 Maeral. 5