APPLICATION OF CROSS SPECTRUM BASED MODAL IDENTIFICATION TO OUTPUT-ONLY RECORDS OF AMBIENT VIBRATION

Transcription

1 3 h World Cofrc o Erhqu Egrg Vcouvr,.C., Cd ugus -6, 4 Ppr No. 368 PPLICTION OF CRO PECTRUM ED MODL IDENTIFICTION TO OUTPUT-ONLY RECORD OF MIENT VIRTION K KNZW UMMRY cross spcru bsd odl dfco chqu, whch hs b dvlopd b h uhors, s d o h pplcbl o b vbro rcords of buldgs, d s horcl bcgroud s lso rvwd. Th odl dfco chqu s dd fro h spcrl so sch bsd o uorgrssv ovg-vrg d ovg-vrg RMM odl, whch hs followg dvgs: Owg o cross spcru bsd chqu, s o cssr o prsu rloshps bw pus d oupus; Modl chrcrscs of buldg c b dfd ccurl, v usg rcords cod wh locl oss du o chcl vbro or locl br vbro. INTRODUCTION Vbro ss of sg buldgs hv b coducd o ol o vsg hr dc bhvor bu o cofr h vld of hr dsg, cosruco d c schs, d h rsuls hv b rflcd o h prov of srucurl dsg gs lrg rhqus. Of vbro ss, b vbro s VT s o sur vr sll srucurl dc rspos drv b vrous d of vbro sourcs orl opro, d o c s h dc chrcrscs of h buldg lsc rg. Th dvg of VT s h c b coducd low cos d d c b obd or frqul coprd o ohr vbro ss:.g. forc-ducd s or dc rspos obsrvo gs rhqu d wd lods. I ccordc wh rc dvlops of surg chqu d qup, h dvg of VT s wdl sprdg h bfor. To dvg of h surg opro, h VT wll b hopfull ppld for srucurl hlh oorg o vlu sg srucurl cpbl of buldgs.g.: Rr[], Frrr l. [], Housr l. [3]. I vlug dc chrcrscs of h buldg, odl prr dfco d srucurl odl dfco r powrful ools o dr h hcl odl or h phscl prrs of h buldg fro surd rcords. I h rhqu grg fld, h ss dfco chqus bsd o pu-oupu rlos hv so fr b dvlopd for rhqu obsrvo rcords of buldg udr h ssupo h h rcords h groud floor or r h groud surfc r Rsrch Egr, Crl Rsrch Isu of Elcrc Powr Idusr, Jp. El: w@crp.d.or.p

2 cosdrd s h srucurl pus o h buldg.g.: Hosh d o[4], f[5]. For h VT rcords, howvr, hs ssupo s o lws vld, bcus h b vbro of h buldg s cd b wd forcs s wll s groud oo Iu l.[6], d bcus h copl rcords of h wd forcs co b surd prcc. Furhror, s dffcul o sur v h pus fro h groud o h buldg ccurl, spcll wh h ffc of sol-srucur rco co b gord Tob l.[7]. Thus h ss dfco chqus bsd o pu-oupu rlos hv lo for usg h VT rcord. o lrv pprochs hv b proposd rcl, whch s prsd o usg ol oupu rcords whou h us of h pu rcords.g.: Prs d D Roc[8]. Of h oupu-ol odl dfco, o pproch s o cosdr surd corrlo fucos s h fr vbro sgur of h buldg, d o plo h odl dfco chqus for fr vbro:.g. Ibrh do hodibrh[9], Ibrh l.[][], gss rlo lgorhjug d Ppp[]. ohr pproch s o ssu h h pu of h buldg s odld s sochsc procss osl wh os procss, d o plo h odl dfco schs bsd o pu-oupu rlos:.g. subspc-bsd lgorh or sochsc subspc dfco Lror[3], V Ovrsch d Moor[4], frquc do dcoposorcr l.[5]. Th uhors hv proposd oupu-ol odl dfco chqus whch dffr fro h forod pprochs, h h r bsd o cross- d uo-powr spcrl dsspds of lr dffrc odlskw l.[6][7], Kw[8]. I h proposd chqus h crossd uo-pds c b odld s uorgrssv ovg-vrg odl RM odl, Kw l.[6] or uorgrssv ovg-vrg d ovg-vrg odl RMM odl, Kw l.[7]. Espcll, h RMM odl s rd h ppr, s w lr dffrc odl coposd of M rs ddd o RM odl. usg h spcrl lss of h RMM odls, o c clrl spr corrld d ucorrld copos of h vbro rcords of h buldg[9]. Morovr, bcus of h dvg of h spcrl lss, h proposd oupu-ol odl dfco chqu gvs ccur odl prrs fro h corrld copos of h vbro rcords. I hs ppr, h uhor ss h horcl bcgroud of h oupu-ol odl dfco chqu bsd o h cross spcru of h RMM odl. d, o vsg h pplcbl of h odl dfco chqu, b vbro rcords of lrg col slos r ld. THEORETICL CKGROUND OF CRO PECTRUM ED MODL IDENTIFICTION Th cross spcrl bsd odl dfco chqu s coposd of cross spcru so d s pplco o odl dfco. I h blow dscrpo of h horcl bcgroud, frs, h spcrl so sch usg h RMM odl s rvwd brfl. Th dl of h spcrl so hor s foud rfrcs[7][9]. Th, fr drvg h cross spcru prsso for dc rsposs h grl phscl odl, h uhor wll prs h hor of h odl dfco chqu b usg rlo of cross spcru bw h RMM odl d h phscl odl. Cross spcru for of RMM odl[7][9] L d b surd rsposs o sor procss, h RMM odls r dfd dscr s

3 C D + C D + whr, d r uull dpd wh os squcs wh u vrcs; s h u-dl opror;,, C d C r h R oprors s,, c C, c C ; 3,, c, c ; 4,, D d D r h M oprors s b, b, d D, d D. 5 I quos d, d r drv b h coo pu, hrfor, h frs rs of h rgh-hd sds ch quo c rprs corrld copos bw d. O h ohr hd, h scod rs of h rgh-hd sds ch quo rl ucorrld copos bw d. Equos d c b rwr h lr dffrc fors s + d b c c 6 + d b c c 7 Ech odl quos 6 d 7 cosss of o R r d wo M rs, hrfor, h uhors proposd o cll h "uo-rgrssv Movg-vrg d Movg-vrg RMM" odls. Th cross-pd bw d, d h uo-pd of whch corrspod o quos d c b obd s follows: 8 + C C D D 9

4 I s od h h uo-pd of s slrl prssd quo 9. Th cross- d uo-pd fors quos 8 d 9 c b splfd s follows l Rrs l l l Rww l l C C whr R R rs ww l R l +, h l c c h R l + + h ; 3 R l s h cross-corrlo fuco of d ; R l s h uo-corrlo fuco of. Th bov drvo fro quos 8 d 9 o d s slr o h uo-pd for of RM odl proposd b Kl l.[] d Kvh[]. I quos hrough 3, h PDs r prssd whou h us of h M coffcs. clculg h R coffcs d h corrlo fucos fro h surd rsposs d, o c s h cross- d uo-pds gv b quos hrough 3. Hr, h R coffcs c b clculd b usg h Yul-Wlr quos blow: d R l R l; l + 4 R l R l; l + 5 R + l c R l; l + 6 Th R coffcs d c b clculd b suffc ss of quos 4 d 5, rspcvl. fr h R coffcs r obd, h R coffcs c c b lso clculd b suffc s of quo 6. I h blow pls, h uhor solvd h ss of quos 4 hrough 6 b h sgulr vlu dcoposo[3].

5 Cross spcru for of MDOF srucurs[6] Th dc bhvor of ul-dgr-of-frdomdof srucur cossg of sss cocd hrough sprgs d dprs s dscrbd b followg r dffrl quo: [ M ]{& } + [ C]{ & } + [ K]{ } { f } 7 whr [M ], [C] d [K] r h ss, dpg d sffss rcs; { } d { f } r h dsplc d rl forc vcors. Hr, h gvcors r of h lf-hd sd quo T 7 s dod b [ ], d l us ssu h proporol dpg; l, [ ] [ C][ ] s dgol r. Th quo 7 c b rwr s h dpd s of quos o odl coords: & Γ ξ + ς ω & ξ + ω ξ ;,,..., 8 whr ξ s h -h odl dsplc; ς d frquc ssocd wh ξ ; ω r h odl dpg fcor d h odl crculr Γ s h -h odl forc gv b s h odl ss of h -h od; Γ f 9 L h b h -h puls cclro rspos quo 8, wo cclro rsposs & l d & h -h d l -h ods of h MDOF srucur bco l & l h η Γ η dη d & h η Γ & η dη. g h pco of h produc of & l d & gv b quo, d b pplg h Wr-Khch hor, h cross-pd l s c b obd for h wo cclro rsposs: l s l H s H s ΓΓ s whr H s s h puls rsfr fuco ssocd wh, whch s gv b h H s s ; s + ς ω s + ω Γ Γ s s h cross-pd of h odl forcs Γ d copl coug opror. Hr, h pols of H s c b show s Γ ; s dos h Lplc prr; dos h sˆ ς ω + ω ς d sˆ ς ω ω ς 3

6 ssug h boh Γ Γ s d H s H s hv o coo pols, h h cross-pds quos c b rwr h blow prl frco for: ˆ l ˆ l l l s s sˆ ˆ s sˆ + s + s s sˆ l + l s 4 whr s + sˆ H s H s ΓΓ s s sˆ l l, ˆ s sˆ H s H s ΓΓ s s sˆ 5 d l s s h rdr fuco. s show quo 4, h cross PD of h cclro rsposs of h MDOF chcl srucur c b prssd s frcol fucos r of s gvlus ŝ. lg l quo 4, h uo-pd c b lso obd. I h bov drvo, h uhor drvd h cross- PD of h rlv cclro rsposs of h srucur wh proporol dpg. I h cs of bsolu cclro rsposs of srucur wh o-proporol dpg, h cross-pd c b prssd s h slr for quo 4[7]. Modl dfco chqu To rl h cross-pd of h RMM odl o h of phscl odl, quo s rsld o h Lplc pl: + s β β γ γ β γ s s s s s s s s s s s s + 6 whr s d s r h pols h Lplc pl, whch r clculd b solvg d, d b rslg h soluos fro h -pl o h Lplc pl; β d γ r h rsdus ssocd wh h pols s d s gv b β d γ 7 whch d r h soluos d, rspcvl; dos h cos r. I quo 6, h frs suo dos prs of copl coug copos, h s, h frs suo c b ssocd wh vbro chrcrscs, bcus h pols of ch odl chrcrscs ppr s pr of copl cougs. L us rl h frs suo quo 6 o

7 h cross-pd for of h phscl odl quo 4. ccordg o quo 4, v wh rsposs o h phscl odl r slcd s h wo rcords, h cross-pds lws hv coo pols corrspodg o h gvlus such s ŝ, sˆ, ŝ d s ˆ. O h ohr hd, quo 6 h frs suo of h cross-pds co hv coo pols v wh d r slcd o h rsposs h buldg. To ovrco h dscrpc, s ssud h h R oprors d r rplcd b h s R oprors h cross-pd so, d lso ssud h h R opror s coo og ll cross-pds of h rsposs of h obcv buldg. Ths ssupos us b rsobl bcus h R oprors for h corrld copos r rprsd s chrcrscs of gvlus.g.: url frquc, dpg fcor of chcl srucur, d lso bcus h gvlus r coo ll h odl pos of h srucur. roducg hs ssupos, l s b h pols, h cross- PD of h RMM odl c b rwr s + s β β γ γ β γ s s s s s s s s s s s s + 8 lrl h uo-pd quo c b rrrgd h prsso s s β β γ γ s s s s s s s s β s s γ + s s + + s 9 whr s s h rdr fuco of s, whch cos h copos for h pols C. Hr, l us suppos h s fd o rspos h od l s rfrc rcord d s rspos h od,,...,, h - cross-pds d uo-pd c b obd s h fors quos 8 d 9. qug quos 8 d 9 wh quo 4, h blow rlo of h rsdus c b foud: l γ l γ M γ l ˆ l M 3 whr l γ dos h rsdu for h h od h PD bw h od l d. s show quo 3 h -h rsdu vcors r proporol o h -h od vcors phscl l odl, hrfor, h odl vcors phscl odl c b sd fro h ros of h rsdu γ. I should b od h such odl vcors r dpd of rl forcs cg o h obcv buldg. Thus h odl proprs c b drd whou h us of pu rcords. Th url

8 crculr frquc d dpg fcor ssocd wh h odl vcors γ } c b drvd fro usg quo 3: ω s 3 ς cos rg s 3 { l PPLICTION TO MIENT VIRTION RECORD pcs of h slos Th slos r cosrucd col-ful powr so, whch c sor h col up o 7, os. Fgur shows ovrvw of h slos, whch h VTs wr coducd h wo slos. s show h fgur, h wo slos r clld lo d lo, rspcvl. Th slos r rforcd cocr RC cldrcl shll srucurs wh h wll hgh of 65 rs d r dr of 46 rs. Th hcss of h RC wll chgs lrl wh hgh, whch s.3 rs h boo, d s.5 rs h op. b vbro s To vlu chgs of odl proprs wh h ou of h sord col, h VTs of h wo slos wr coducd dffr col sorg ss. For lo, wo VTs wr coducd.., h p d full-sord s. For lo, hr VTs wr coducd h p s, h o-hrd sorg s d h full-sord s. Fgur shows h dplo of hr-copo cclrors. Th ssors for lo wr s o h boo d op floors vr 3 dgrs uhll log wh h crcufrc of h shll wll. I ddo o h rrg slr o lo, for lo cclrors wr s o h s-sd wll of h RC shll log flgh of srs. I boh css, bcus h surg pos wr or h h ssors vlbl, h b vbro rcords of ll surg pos wr obd b wo succssv surs wh rplcg svrl cclrors. I dl, wo surs wr coducd h souh-sd d h orh-sd for lo, or h s-sd d h ws-sd for lo, rspcvl, d h rcord of ch sur ws obd for o hour wh h splg H. Ts rsuls d dscusso Th odl proprs of h wo slos would b dfd b pplg h proposd cross spcru bsd odl dfco o h b vbro rcords. Fgur 3 shows h rsuls of h od shps o h roof d h ssocd url frqucs d dpg fcors for lo h full-sord s. s show h fgur, s odl proprs wr obd d so url frqucs of h r closl spcd. Th s d d ods show Fg. 3 d b r h rslol os o h N d EW drcos, whr h shll l dforo s do log h hgh of h slo. Th 3rd d 4h ods show Fg. 3c d d r boh h d ovl shps whr h rdl dforo s do o h roof, whrs boh s of h ovl shp cross h gl of 45 dgr. Th 5h od show Fg. 3 s h 3rd ovl shp. d h 6h od show Fg. 3f s h rslol o N drco, whch s slr o h s od shp, howvr, h oos of r col wll b oppos phs. s obsrvd bov, h proposd odl dfco chqu gvs ccur odl propr ss v wh h closl spcd ods s. Fgur 4 lso shows 3D spl od shps of h s d 3rd ods, whr h dspld pluds h bs r gfd s. s show h fgurs, h oos of h bs c b clrl cpurd wh h dforos of sol-srucur dc rco ffc pho.

9 c h od shps c b clrl dsgushd fro o ohr bov ws, o c dscuss h dc chrcrscs or dl. Fgur 5 s o of h pl, whch shows rloshps bw gvlus d h ou of sord col. s show h fgur, h url frquc vr od shp dcrss wh h crs of h ou of h sord col, whrs h dcs of dcrsg ros r clrl dffr fro ch ohr. Furhror, h vlu of dpg fcors h rslol od crs wh h crs of h ou of h sord col, bu hos ovl od dcrs. CONCLUION Th proposd cross spcru bsd odl dfco chqu hv b show o s odl proprs of buldg fro h oupu-ol rcords such s hos b b vbro s VT. Th proposd chqu hs hr or dvgs s follows:. Owg o cross spcru bsd chqu, s o cssr o prsu rloshps bw pus d oupus bfor odl dfco.. Dc chrcrscs of buldg c b dfd ccurl, v usg d cod wh locl oss such s hos b chcl vbro or locl brs vbro. 3. Ech odl propr c b wll dfd v wh h clos-spcd ods s. Espcll, h frs dvg of rg uow pus s ffcv o l h b vbro rcords. Ths ffcvss s provd hroughou h os o h VTs of h wo lrg col slos. Furhror, covol odl dfco chqus usg srucurl oupu ol roduc h ssupo h h srucurl pus r wh os or wd-bd procss squcs:.g., [9]-[5]. O h ohr hd, h proposd chqu rqurs h ssupo h ll pols gvlus h vbro odl d h pus.g.: rl forcs or groud cclros r dffr fro ch ohr. Ths ssupo s lss rsrcv. Th uhor lso blvs h proposd chqu s ffcv o rhqu rspos rcords of chcl srucurs, whr h pu-oupu bsd odl dfco hv b of plod. Epso of h pplcbl o h rhqu grg fld wll b o of h fuur wor. CKNOWLEDGMENT Th uhors r grful o Mr. Ksuho Mu of hou Elcrc Powr Co. Ic. for surg sssc of h b vbro s of h lrg col slos. d h uhor grfull hs Dr. Ku Hr of CRIEPI for dscussg h drf of h ppr. REFERENCE. Rr. "Vbrol bsd spco of cvl grg srucurs," Ph.D. Thss Dpr of buldg cholog d srucurl grg, Uvrs of lborg, Dr, pr Frrr CR, cr WE l. "Dc chrcrscs d dg dco h -4 brdg ovr h Ro Grd", Los los Nol Lboror rpor L-767-M, Ju Housr GW, l. "pcl ssu: rucurl corol: Ps, prs, d fuur," Jourl of Egrg Mchcs, CE, Nov. 997, 39: Hosh M d o E. "rucurl dfco b dd Kl flr," Jourl Egrg Mchcs, CE, Dc. 984, : f E. "Idfco of lr srucurs usg dscr- flrs," Jourl of Egrg Mchcs, CE, Oc. 99, 7:

10 6. Iu M, Kuur H d Tob J. "Proprs of b vbro ss of srucur," Jourl of rucurl d Cosruco Egrg, IJ, Mr. 99, 49: Jps. 7. Tob J, Fuuw N d Yg. "Eprl vluo of dc chrcrscs of low d du-rs buldgs wh sol-srucur rco", Proc. of h h World Cofrc o Erhqu Egrg, NZ. Ppr o.44, Fb.. 8. Prs d D Roc G. "ochsc ss dfco for oprol odl lss: rvw," Jourl of Dc s, Msur, d Corol, ME, Dc., 3: Ibrh R. "Rdo dcr chqu for odl dfco of srucurs," Jourl of pccrf d Rocs, I, J. 977, 4: Ibrh R d Mulc EC. " hod for h drc dfco of vbro prr fro h fr rspos, " hoc d Vbro ull, 977, 47: Ibrh R, rcr R d suss JC. "Modl prr dfco fro rspos of grl uow rdo pus," Proc. of h 4h Irol Modl lss Cofrc,996: Jug JN d Ppp R. " gss rlo lgorh for odl prr dfco d odl rduco," Jourl of Gudc, Corol d Dcs, I, p. 985, 85: Lror WE. "s dfco, rducd ordr flrs d odlg v cocl vr lss," Proc. of h 983 rc Corol Cofrc, 983, : V Ovrsch P d Moor D. "ubspc lgorhs for h sochsc dfco probl," uoc, 993, 33: rcr R, Zhg L d drs P. "Modl dfco fro b rsposs usg frquc do dcoposo," Proc, of h 8h Irol Modl lss Cofrc, Fb., oo, TX: Kw K. d Hr K. "Modl dfco for ul dgr of frdo ss usg cross spcru hod," Jourl of rucurl d Cosruco Egrg, IJ, Mr., 59: Jps 7. Kw K. d Msu T. "RMM odl for spcrl lss d odl dfco," Jourl of rucurl d Cosruco Egrg, IJ, pr., 554: 7-78 Jps. 8. Kw K. "pplco of odl dfco chqu usg RMM odl o b vbro rcords," Proc. of h h Jp Erhqu Egrg posu, Nov. : Jps. 9. Kw K d Hr K "Prrc so of h cross powr spcrl ds," Jourl of oud d Vbro o ppr.. Kl JF, Prl J, chrf LL d ubbrud R. " o o covrc-vr dgl flr dsg d uorgrssv ovg-vrg spcrl so," IEEE Trs. cous., pch., gl Procssg, 979, P-7: -.. Kvh M. "Hgh rsoluo spcrl so for os sgls," IEEE Trs. cous., pch., gl Procssg, 979, P-7: Cdow J, sgh d Hsu T. "gulr-vlu dcoposo pproch o srs odlg," Proc. of IEEE, 983, 33: -.

11 Fgur Ovrvw of col slos. Fgur sor locos. Fgur 3 Rsuls of h od shps o h roof of lo h full-sord s.

12 h s od corrspodd wh Fg.4 b h 3rd od corrspodd wh Fg.4c Fgur 4 Th od shps of lo h full-sord s. Fgur 5 Dpdc of g-proprs upo h ou of sord col, drd b h proposd chqu.