遺伝的アルゴリズムを援用した構造物の振動応答予測モデル構築

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(1)社団法人情報処理学会研究報告 IPSJ SIG Technical Report. 2003−MPS−47 （14） 2003／12／12.

(2) !"#%$&' () * + , ,- .0/ , 12 34 , 5 6 78 9;:=<?>=@=>=@BA=C=@?D=E=F 9G:?<B>=@=C=@=H IKKJMLO~KNQQPS QRMMTQKUWVYhX[Z] Z\_^a`Kv bdc eYfhgKikjSl RQvOmQPQnkVYkoM pqZsMrMtQuQKvwMQc eSxzy|Q{~} KKMQh ZWxzPyqRSY±Q²M sh³¡£¢JK}Q´R¤ ¥Kf¦QYR k{~xzQyqKQYs]§|~¨ Z¡©¢ªl«W} ¬]S®Y¯YhMxzMy[¥KY¦hxh}MM°sW¡a{ ¢ªl l R±Y² |K¾ V x M Z xzf~yq}QYYhs}Q{[ ¡©v ¢z£l ¿MÀ j R Mys¾ µ[xh¶¸ÁY·Ms¹Q{[º ÂQÃ ÄYÅÇÆ f»É»OÈÊl¢k½lh¼ †. ††. ††. †. ††. ††. GA. SEA. GA. Genetic Algorithm Aided Modeling for Structures’ Vibration Response Prediction Hirosuke HORII†, Mitsunori MIKI†† , Takayuki KOIZUMI†† , and Nobutaka TSUJIUCHI†† †. Graduate School of Engineering, Doshisha University †† Faculty of Engineering, Doshisha University. In this research, a genetic algorithm (GA) aided modeling for structures’ vibration response prediction by the statistical energy analysis (SEA) is proposed. The proposed method was evaluated by vibration response prediction of test structures and a real structure. As the result, the SEA prediction model which consisted of parameters identified by the GA obtained more precise prediction result than the current SEA prediction model constructed by theoretical formulas. Furthermore, the loads of experiments for construting the prediction model are reduced than those of current experimental approach.. ÑOÒËÍÓÌÏÔÎ?ÕÖªÐ ×ØOÙOÚÛ Úíì]î Ü Y Ý Ç Þ k ß s à W á W â ½ ã K ä ª å s æ W ç s è W é W ê ë ï ïOôÉõ÷ö©øúù ázâªãðñGØzòkÙ ó ñ ÉÜ

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(19) âã ñä û $. k6=j. 1. Baseplate element 1. 2. Side board element 2. 2‘. Side board element 4. 3. Side board element 3. 4. Side board element 5. 5. Rubber board. ýý. Pi. 3. þ. 0≤η≤1. GA. SEA.   η21 L= ..   . ηN 1. η12. . . . η1N. .  η2 . . . η2N  .. . . ..   . . .  . . . . . . ηN. (3). Ö Þ],Ü N ×N á ä 0 á À º ö¸î ø SEA É. ä- 2ηâãì η ì ä BÑ å ø;Þsª Ü B½ηðB2N4 = Üη N 0 Ï ! ðÄæ öqø ä 0 Ü +À ì,;î 0 Bå ø7ª BÏ3 ðB;4 é À ½ Þçl (Üè ä ï HI ø7J ª 0 Ü iê ï ä ,« ) 0 ( û òªìó û ÞsÜ2è 3 äDÃÅ Æ ¦ ôsõ Ú SEA Ö á2½ O ñ Ü ë ñ 3 å Ö O ê ñ"

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(30) ÿ 9 # ñzÓ ÞsÜ Ú ; 1Ü 5 å bd4 û ë ñ;ò Ö 798;:=<>?@A SEA á 9 ½ ª ñ Þ Ü 5 6 BCDE FHGIJK0L)M @ *NO;PQ 7RTS):VUXW YZ[ R8]\<>^ Z[ 7_8` Gacb D opqrd;eK f KTgh 1U 2U 3 i gh 5 KkjKTlmnSEA s @UFt 2 7u_v E G)ab D SEA de f 7w8": x)y)z{|)} K~ i b U g)h 3 @ x b D i K0gh 1 K xyz{ K |} s i } s @t 3 70u E =D gh q))_ K |)} s } s v i K")U @UU0W YZ[ 78i ` G)arb D iSEA db eD f 7k C f t 4C 7U <>_^ Z[ 7w8_` G)a E 7 t 7;urv LcM"SEA @d0 e N)O ghj x5yc ) : UW YZ[ 798_z `¢¡T£ D s l)m)no)pq U LM=cK"¤)¥ 7T¦ b D0§¨© @0ª C : E =D U<>^ Z)[ 7w8_` Gca_b D SEA de f U LcM" @ ©kC;« m i¬® b U |)})¯° )± 7²³ b C : UW YZ[ U LcM" 4. L. η1. 4. v uN uX Ei − Xi 2 F itness = t Ei i=1. GA. . 5. ÿ û 2B 3ÇÜ 2 2 » ä Þ #$ 0« ) î ù ^ cbd24 . GA. N. 2. : Welding Welding. SEA SEA. GA. 2. : Bolt Connection Volt combination. E. GA. ûû üü ûû üü û ü ú. 1. 2 −54−. 2).

(31) Frequency [Hz]. (a) Simple Structure. Coupling Loss Factor. 0.07. 1_5 (GA Calculation) 2_5 (GA Calculation) 3_5 (GA Calculation) 1_5 (Theoretical Value) 2_5 (Theoretical Value) 3_5 (Theoretical Value). 0.06 0.05 0.04 0.03 0.02 0.01 0.00 31.5. 63. 125. 250. 500. 23. ´. Frequency [Hz]. (b) Simple Structure. 25. 24. 1000. with the Rubber board. 2: Fig.4.37 Value of Comparison Coupling Loss FactorLoss at Test Strucof Coupling Factor between Theoretical Value and. ture with Rubber Board. Estimate Value by GA 15. Acceleration [dBG]. 5 -5 -15 -25. 26. -35. Experimental Value. -45. Theoretical Value. -55. GA Calculation. -65 31.5. 63. 125. 250. 500. 1000. ´. Fig.5.2. Frequency [Hz]. ´. (a) Element 1 (Ele.3 Excitation). -5 -15 -25 -35. 2. 4:. 63. 125. 250. 1000 31.5 63 125 Frequency [Hz] 250 (b) Element 2 (Ele.3 Excitation) 500 1000 between 1 Comparison 2 3 4 of AL 5. [H. Experimental Value,Theoretical Value Element Number and GA Calculation in Simple Structure Averagewith Difference Vibration Response the Rubberofboard. between Fig.4.35(b) SEA Model by GA and Experimental Average Differences of AL Experimental Value Value with Rubberbetween Board. and GA Calculation in Simple Structure with the Rubber board. 8. z]. cy. [H. 63 125 250 500 1000. 4. qu. en. 2 0. ´. 31.5. 6. 1. 2. 3. 4. 5. Fr e. Difference [dBG]. 10. Element Number. 5: Average Difference of Vibration Response. between Fig.4.35(a) SEA Model by Theoretical Value and Average Differences of AL between Value Experimental Value withExperimental Rubber Board. and Theoretical Value in Simple Structure with the Rubber board. 3 −55−. Modeling of the Building. 6: System of Real Structure.. µ0¶¸·¹)º=»¼9½¾0¿ À"¹ºVÁÂÃÄkµ0ÅÆºÇ;È ÉTÊÉ ½;ËÀÌÍ)ÎÏ)ÐcÑÒ)ÓÃÄ ÊÔ º"ÕÖ× ØcÙ º)Æ9Ú¢ÛÜr¹ SEA ÝÞß µÕàFá9â;Çr½Vã ä À]å¸Ç;È ìíïî ð ñ ò ó ô æ5ç õ è Ê0éëöê ÷¸øùúüûþý_ÿ ÕÖ)Ö× Ê 1 µÁÂ Ê ½

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(34) È Õ)à /0 Ø87 Ç"9)ÁÂ Ê 5 0 Ý Þ ß : Ì øùúïû]SEA < ½ ö Ü á Ê ÁÂ ýÿ; = ½;>Â = µ ´ 7Ì 8 Ø 6

(35) È·?0TÌ 23 Ì"@AB CDE ½ Ê ÁÂ = ½<>Â = ½ Ê FGHI µÌÍ)Î ÏÐ Ø87J ÕkàK/0 SEA ÝÞß ØML º)Æ)Ñ ´ 9 Ø ÌNOQP;Ï)Ð Ø87J ÕàK/0 SEA ÝÞß ØRL ºÆÑ ´ 10 ØS åT;å 6

(36) È øùúïû]ýÿU ØkÙ º)ÆÑÌNOKP;ÏÐ Ø87VJ Õ)à /0 SEA ÝÞß Ê Á)Â = ÚUWXR>)Â = ½ZY [ /ÆºÇ\Ì 250[Hz] CD á ]^ 8[dBG/N] Ê HI \_ `Æ)ºÇTÈYaÌÍ)Î)ÏÐ Ø87bJ Õà/ 0 SEA ÝÞß Ê Á)Â = Ê >)Â = ½ Ê-HI ÑÌ F G á 3 [dBG/N] cVd Øe · J Ì fcº=ÁÂÃÄ\Å Àþå Æ)º)Ç0È ö Ü ØÙ ºÆ)ÑÌNO 5. 500. z]. 31.5. cy. 4. GA Calculation. en. 6. Theoretical Value. qu. 10 -55 8 -65. Fig.4.320. ´. Experimental Value. -45. Fr e. Difference [dBG]. Acceleration [dBG]. 3: Vibration Response of Element 1 at Ham15 5 mering Element 3 with Rubber Board.. Structural Element Acoustical Element.

(37) -60. Accelerance Accelerance [dBG/N] [dBG/N]. -70 -60 -80 -70 -90 -80 -100 -90 -110 -100 -120 -110 -130 -120. Experimental Value Theoretical Value GA Calculation Experimental Value Theoretical Value. 31.5. 63. 31.5. 63. 125. -130. Frequency [Hz] 125. 250. 500. 1000. (a) Concrete Wall Frequency [Hz]. -60 7: Vibration Response of Wall Concrete Wall. (a) Concrete -70 -60 -80 -70 -90 -80 -100 -90 -110 -100 -120 -110 -130 -120. Accelerance Accelerance [dBG/N] [dBG/N]. ´. 250 GA 500 1000 Calculation. Experimental Value Theoretical Value GA Calculation Experimental Value Theoretical Value. 31.5. 63. 31.5. 63. 125. -130. 250 GA Calculation 500 1000. Frequency [Hz] 125. 250. 500. 1000. (b) Wall. ´. Frequency [Hz]. Fig.5.13. Comparison of(b)AL between Wall Experimental Value,Theoretical Value 8:Fig.5.13 Vibration Responseofof Partition Wall. Comparison ALSteel between and GA Calculation in Real Structure Experimental Value,Theoretical Value Element : Concrete Wall Element 3in : Wall (entrance) and1 GA Calculation Real Structure Element 4 : Wall (window). 10. ue. 4 2 0. 31.5. nc y[. 63 125 250 500 1000. ]. 6. Hz. 8. 1. 2. 3. Fr eq. Difference [dBG/N]. Element 2 : Wall. 4. ´. Element Number. 9: Average Difference of Vibration Response. between Fig.5.14(b) SEA Model byDifferences GA andof AL Experimental Average between Experimental Value Value at Real Structure. and GA Calculation in Real Structure. ´. Element 3 : Wall (entrance) Element 4 : Wall (window). 20 16. 8. ]. ue. 4 0. 31.5. nc y[. 63 125 250 500 1000. Hz. 12. 1. 2. 3. 4. Fr eq. Difference [dBG/N]. Element 1 : Concrete Wall Element 2 : Wall. Element Number. P;Ï)Ð Ø87J Õàg% åh0 Ý0Þß ÌÊ ]Á^Â á = Ê >Â = ½ Ê HI ÑÌ FG á SEA ½ ÁÂÃÄ\ Ô º"8È [dBG/N] É åÑÌ ½;21 [dBG/N] ö " Ü ½ Ê i ¼jk9\ÌN,jkálkÇ"m n i ¼ Ø op Çr½<qrº i ¼ Ø ¹ rVÆºkÇ0sál Ç½ã ä Àþå¸ÇTÈYaÌÍ)ÎÏ)Ð ØQ7J Õà /0 Ê ÁÂ = Ñ >Â = µÚ½ ØtVuMv ýbw SEA Ý0Þ;ß ÊMx .µ 4&rVÆºÇ0s0Ìy Ê i ¼jk Ø ËË ¿üÀ z"Ì{rÆ Ê @AB CD áÃ)Ä|~}HÁ)Âcáwâ=Æ ºÇTÈ ´ Ì ´ ËrÀÚXÌ0ÍÎÏÐ Ø 7RJ Õàh% å 0 SEA9Ý=Þ0ß 10\Ì<NObPVÏÐ Ø7RJ Õàh% åQ0 7bJ Ì9

(38) p Æ Ê23 Ø)Ù ºÆ fÃÄ Ê SEA ÝTÞ0ß ÁÂ = µÅÆºÇ É ½Z\cáâTÇ"È áÑÌ ÕÖ)× Ê 1 ØÙ Ç 4 23 Ê á-Á)ÂFµ-4&rVÆºÇ\Ì x Õ)Ö Ê álå9Ì x Y Ê SEA Ý;ÞTß \0Ûá_â"Ç=ÈF· 0Ì>)Â = µwÚ½ Ø SEA t uVv ýKw"ÊMx .µ4 5<0s0ÌNO\VcÀ;Ëá)¹ºÌF¹-y i ¼jkcµÚ L ÕÖ× Ø)Ù ºÆ_Ú Ì SEA ÝTÞß µTÕ àcá9â;Ç"\ÌÍÎÏÐ Ê cálÇF½Tº ä ÇTÈ K áÑ Ì GA µV/0TÌ SEA Ø 7 Ç" ÁÂ ÝTÞVß ÕàÐµ"ÍÎR/-0;È ÍÎÏÐÑ0ÌUN ORPVÏÐ Ø 7RJV %åK0 SEA tbu9v ýMw ½Ì Õ)Ö× Ø

(39) Ç;Ò> ØQ7 r=Æ )Â% åh0 Þ ýVw µ /Æ0Ì>B = GA ØK7 rVÆ f Ã)Ä Ê SEA tuKv ýw µ

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(41) )Ç Á)Â Ý Þf);ß Ã)ÕÄ à Ê ØÁÛÂ bi/ 0 \iÅ¸ À Ìå¡N0ObÈ P=·¢Ï0ÐwÌ½ £Fo¹k º />ÆT Ì Ë9À?¤¹Á)Â ÝÞ0ß \Õàá9âTÇ É ½"Ë Þ ÀVÌý>w P;ÏÐw½ o /Æ0ÌÒ> Ø 2

(42) )Ç¥ ¦ Ê0Ô§ \ÅwÀ åQ0È ¨ª© Ñ «¬®Ë_À Ê-¯° µ ± 0 x²³ ^´bµ¶ ù b· ¸ ¹ ¶º9» úÿ ØcÙ Ç Ê Y¼w½-/Æ-4&r<0È ÉÉ Ø ½¾ µ-¿V

(43) Ç0È ÀªÁÃÂQÄ 6. 1) Lyon, R.H. and DeJong, R.G. Theory and Applications of Statistical Energy Analysis, 1995. 2). 10: Average Difference of Vibration Response between Fig.5.14(a) SEA Model byDifferences Theoretical Average of AL Value and between Experimental Value. Experimental Value at Real Structure. and Theoretical Value in Real Structure. 4 −56−. Å-| ÆÈ SEA Ð ØV7 Ç Ç<È-É Ê-Ë Ì ÍÈ Î ËÏ- Ð-ÑÌ Vol.48, No.6Ì pp.433–444Ì 1992È.

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