Local Damage Detection using Incomplete Modal Data

Transcription

1 Loal Damag Dtton usng Inomplt Modal Data Km, B.-H., Stubbs, N., and Skorsky, C. xas A&M Unvrsty, Cvl Engnrng Dpt., MS 6, Collg Staton, X 778, USA. Stat of Calforna, Dpt. of ransportaton, P. O. Box 987, Saramnto, CA 97, USA. ABSRAC. hs papr ntrodus a nw mthod that an dntfy th loaton and stmat th svrty of damag n a strutur usng lmtd modal data suh as: () fw of th lowr natural frquns and mod shaps, () lmtd masurmnts of dgrs of frdom, and () spatally nomplt masurmnts of mod shaps. h mthod s basd on th physal ntrprtaton of modal flxblty and an assumpton that a small damag vnt wll hav an nsgnfant fft on th ntrnal for of a strutur undr rtan loadng ondtons. h mthod s applabl to nomplt modal data masurd from thr a ford vbraton tst or an ambnt vbraton tst. On of th attratv advantags of th mthod s th loalzaton of som faults usng mod shaps. h mthod s blvd to b ffnt n th followng stuatons: () f an nspton of th ntr strutur s not nssary, and () f only loal masurmnts of modal data ar avalabl. h fftvnss, fasblty, and pratablty of th mthod ar nvstgatd through modal data xtratd from vbratonal masurmnts from th Swss Z Brdg.. INRODUCION It s ssntal to montor prodally th load arryng apaty of a strutur, sn th aumulaton of damag n a strutural mmbr may rsult n atastroph strutural falur. For suh applatons, urrnt nondstrutv damag valuaton (NDE) mthods nlud vsual nspton, aoust msson, ultrason, radography, ddy urrnt, magnt partl nspton [], and vbraton-basd nsptons []. In partular, th vbraton-basd NDE mthods hav rvd nrasng attnton n vl ngnrng struturs, baus th most urrntly usd vsual or loalzd mthods ar lmtd not only wth rspt to a pror knowldg of th loaton of damag, but also lmtd to assblty to th vnty of damag []. Modal tst and analyss of a strutur s a prrqust for th vbraton-basd NDE mthods. Wth th ntroduton of th dsrt Fast Fourr ransformaton (FF), many thnqus to xtrat th dynam haratrsts of a strutur hav bn studd sn arly 970s. Rntly, ambnt modal analyss thnqus hav fousd on vl ngnrng struturs, sn th so-alld output-only modal tstng mthods nd no qupmnt to xt a strutur (partularly larg struturs). h thnqus that us ambnt xtaton utlz xtrnal fors rsultng from wnd loadng, traff loadng, wavs, t. Consquntly, ompard to ford xtaton mthods, output-only mthods ar lss ntrusv and nxpnsv. Rntly avalabl mthods for ambnt modal analyss nlud smpl pak-pkng [], th random drmnt mthod [], th gnsystm ralzaton algorthm wth data orrlaton [], and th Frquny Doman Domposton (FDD) thnqu [6]. Assumng that th modal paramtrs of a strutur an b mad avalabl to th damag dtton analyst, numrous rsarh studs n th flds of th vbraton-basd NDE [] hav bn ondutd durng th past two dads. Intal studs stmmd from th onpt that hangs n loal stffnss ar rfltd by hangs n gnfrquns [7]. Rprsntatv studs oftn td n th ltratur nlud a frquny-stffnss snstvty mthod [8], th mod shap urvatur mthod [9], th damag ndx mthod [0], th dynam stffnss dntfaton thnqu [], th stat stffnss dntfaton mthod [], th modal flxblty mthod [], and th stat flxblty mthod []. Dspt ths rsarh fforts, at last two problms rman to b solvd n ordr to montor th halth ondton of struturs n ral-tm usng ambnt xtaton. Frst, a nd xsts to dvlop an outputonly modal analyss that s apabl of dalng wth nosy sgnals, larg omputaton tm, and xssv mmory rqurmnt on th omputr. Sond, a nd xsts to dvlop a unfd mthod that an rumvnt th lmtatons of th xstng damag dtton mthods suh as th stmaton of damag svrty. h objtv of ths papr s to dmonstrat how to valuat nondstrutvly th damag n a strutur usng th nos-ontamnatd output-only masurd sgnals. o ahv th objtv, w prform th

2 followng thr tasks. Frst, w outln a nw approah to xtrat modal paramtrs usng tmdoman data. Sond, w propos a nw approah to loalz damag n a strutur usng th modal data dntfd n th prvous task. hrd, w dmonstrat th fasblty and pratablty of th mthod usng alraton-tm hstors provdd for varous damag snaros nfltd n th Z brdg nar Zurh, Swtzrland.. A HEORY OF IME DOMAIN DECOMPOSIION. Mod Shap It s wll stablshd n lnar algbra that any vtor an b spannd by ts bass []. h bass for th output of a lnar strutural dynamal systm onssts of ts undrlyng mod shaps. Consdr th smpl bam shown n Fg.. p- p h p output dsplamnt profl vtor ausd by an ambnt load at tm t, y (t), an b dsrbd as y( t) = φ () = wth y = [ y y ] p,and φ [ ] = φ φp s th th mod shap. h salar valu (t) dnots th th modal ontrbuton fator at tm t. h subsrpt, p, dnots th numbr of snsors. hn th output alraton tm hstory an b obtand as y = φ () = hs ontnuous-tm dsrpton n dsrt spa an b masurd wth a unform samplng tm t. h masurd alraton rsponss (whh ar th dsrt-tm, dsrt-spa dynam dsrpton) rprsnt mult-output rsponss for a mult dgr of frdom systm. Lt an arbtrary tm, t = k t, b dnotd by k. hn th masurd alraton sgnal an b approxmatd as n y ( k) ( k) φ () = Fg. Loaton of Snsors whr n dnots th numbr of mods rsolvd n th masurd alraton sgnals. hus ah masurd tm sgnal ontans n domnant pols wthn th Nyqust frquny. Although th frquny loaton of th pols an not b xatly dntfd du to nos and dampng of a strutur, nformaton about th frquny band of ah pol an radly b obtand by vsual nspton of auto sptrums of th masurd sgnals. For ah vsually dntfd frquny band, on an radly dsgn a band pass fltr wth a proprly hosn fltr ordr. On th band pass fltrs ar dsgnd for th domnant n pols, th fltrd tm srs ontanng only th th mod an b ratd from th masurd tm sgnals usng lnar systm thory []. hn th targtd systm to b dntfd boms a mult-output, sngl dgr of frdom systm. h rommndd typ of a fltr for ths purpos s th Buttrworth fltr that has no rppl n pass band. Consdr a fltrd alraton tm hstory that ontans only th th mod: y ( k) = ( k) φ () If th N sampls ar masurd, th matrx form of Eq. () an b dsrbd as y () y ( N) φ = [ () p( N) ] () yp () yp( N) φp In a mor onvnnt form, th quaton an b rwrttn as [ Y ] = φ (6) whr th p N matrx, [Y ], dnots an fltrd output alraton tm hstory that ontans only th th mod. Dfn a p p matrx, [E ], dnotng th output nrgy orrlaton of th th mod wth rspt to loaton of snsors. [ E ] [ ][ ] Y Y (7) hs output nrgy orrlaton matrx an radly b omputd from th masurd alraton sgnals through a smpl matrx multplaton. Substtuton of Eq. (6) nto Eq. (7) ylds [ E ] = φ φ = φ q φ (8) whr th salar, q s dfnd as q =. h p p ral sm-postv symmtr matrx, [E ], n th lft sd of Eq. (8) an b also domposd as [6] [ E] = UΣU (9) wth U = [ u u p ], and Σ = dag[ σ σ p ]. h postv numbrs, σ σ p, ar th sngular valus of [E ]. h p p ral orthonormal matrx, U, s th sngular vtor matrx of [E ], and th olumns of U onsst of orthogonal vtors, u,, up. Equaton (9) an b domposd th sngular valus, baus th p p sngular valu matrx, Σ, s a dagonal. [ E ] = u σu + + upσpup (0) Comparng Eq. (8) and Eq.(0) rvals that th sngular vtors also form a bass of th matrx [Y ]. hrfor, th mod shap, φ, th frst sngular vtor, u, and th sngular valus, σ,, σ p, should b zros n th as of nos fr sgnals. For nosy sgnals, th sngular valus, σ,, σ p may b nonzro but small ompard to σ. For th dal ass, th frst sngular valu s largst and th orrspondng frst sngular vtor, u, rprsnts th th dsrd un-dampd mod shap, φ. h thnqu dsrbd hr to xtrat mod shaps s subsquntly rfrd to as tm doman domposton (DD). In summary, th DD thnqu prsntd hr has thr stps. Frst, a dgtal band pass fltr to solat ah targt mod must b dsgnd, and th fltrd tm hstors ontanng th solatd mod must b gnratd. Sond, th output nrgy orrlaton matrx, [E ] n 6

3 Eq.(7), usng fltrd tm hstors, s onstrutd. A Sngular Valu Domposton (SVD) of [E ], usng Eq. (9), s nxt prformd. h frst olumn of th sngular vtor, u, s th dsrd mod shap for ah fltrd mod.. Natural Frquny Pr-multplaton of th transpos of th dntfd th mod shap on Eq. (6) ylds φ [ Y ] = φ φ () Nxt a tm hstory of th th modal ontrbuton fator an b obtand by = φ [ Y ] () φ φ hs sgnal ontans a sngl-output, sngl dgr of frdom systm that s a rprsntaton of th th modal bhavor for th ntr st of p sgnals. hrfor, th auto sptrum of ċ ontans on pak, and th frquny loaton of th pak s th dsrd natural frquny of th th mod.. Faturs of DD h prsntd DD thnqu xtrats mod shaps as th frst stp, thn obtans th orrspondng natural frquns as th sond stp. Although th DD nd frquny nformaton for fltr dsgn and natural frquny, th major omputatonal part of th mthod dos not nvolv th dsrt Fourr transformaton. In addton, th omputatonally xpnsv SVD pross rqurs only n tms for th p p matrx from a st of p sgnals ontanng n mods. hus, w an sgnfantly sav omputng tm and rdu rqurd mmory n th as of n << p. Furthrmor, for th dal ass, th auray dos not dpnd on th numbr of sampl ponts or th frquny rsoluton. hus th dntfd mod shaps onvrg vry fast wth rspt to th numbr of sampl ponts. Also, th DD thnqu may b mplmntd n ral-tm applaton. Morovr, th DD s abl to xtrat th unbasd mod shaps from losly plad mods by adjustng th pass band rang of a fltr.. A HEORY OF LOCAL DAMAGE DEECION. Small Damag Assumpton h small dflton thory rqurs that th hang n shap of a strutur du to a for must not afft th ln of aton of th appld loads [7]. hs ngnrng approxmaton maks t possbl to us ntal onfguraton for th omputaton of ntrnal fors ausd by th appld loads. Basd on suh onsdraton, th addtonal hang n shap of a strutur du to small damag vnt undr a gvn loadng ondton may also not afft th ln of aton of th appld loads. hus w assum that a small damag vnt wll hav an nsgnfant fft on th ntrnal fors of a statstally dtrmnat lnar strutur or a statally ndtrmnat lnar strutur.. Modal Flxblty Usng th DD thnqu, modal paramtrs suh as mod shaps and natural frquns of a strutur an radly b xtratd usng th ambnt vbraton tm hstors. h flxblty matrx s th nvrs of th stffnss matrx. h physal ntrprtaton of th jth olumn of th flxblty matrx s a dsplamnt vtor du to a unt load at th jth dgr of frdom. h modal approxmaton of th jth olumn of th stat flxblty matrx an b alld th jth modal flxblty. h jth modal flxblty vtor, w j, an b obtand n trms of th modal paramtrs [8] usng th followng quaton: φ = n j w j φ () = λ m whr th p vtor, φ, dnots th th dsplamnt normalzd mod shap whos maxmum s unty, and th salar valu, φ, dnots th jth omponnt of th φ. h salar, n, dnots th numbr of mod onsdrd. h salar valus, λ, and m, dnot th th gnvalu and modal mass. h attnton to th modal flxblty hr s du to th followng fats. Frst, th flxblty matrx an b auratly synthszd from a fw of th lowr frquns and mod shaps [8]. Sond, th flxblty matrx s lss snstv to hangs of mass than th stffnss matrx [8]. hrd, th dttablty of hangs on strutural proprts s ndpndnt of th probng dgr of frdom du to a matrx nvrson proprty. Howvr, a shortomng of modal flxblty s th omputaton of th modal mass. For output-only masurmnts, thr s no way to fnd th modal mass n Eq.(). Howvr, f w assum that th dnsty of a strutur s not hangd durng a damag vnt, th th modal mass for a unform bam an b obtand auratly by a numral ntgraton of th followng formula: m = ρa φ φ L dx () whr th ρ and A dnot th dnsty and ross stonal ara of th bam, rsptvly. In addton, th absolut valu of th dnsty of th strutur turns out to b unnssary n th fnal damag dtton shm as wll b shown subsquntly. In th as of oars snsor ntrvals, Cub Spln-ntrpolaton of φ s rommndd bfor th numral ntgraton. A losr xamnaton of th physal ntrprtaton of th jth modal flxblty rvals that th appld for at th jth nod and th orrspondng dflton shap an b stmatd from th masurd modal paramtrs, and th unknowns ar th matral proprts whh rprsnt th damagd ondton for a gvn gomtry. hs ntrprtaton radly mpls that th damag dtton problm usng th vbraton masurmnts an b transformd nto a damag dtton problm usng th stat masurmnts, and on an maks full us of th wll stablshd mhanal onpts and mthodologs. j 7

4 . Flxural Damag Indx Equaton hs ston s rstrtd to th damag analyss of an Eulr-Brnoull bam. Assum that th modal paramtrs for th only transvrs dgrs of frdom of a bam ar masurd, baus th masurmnts of th rotatonal dgrs of frdom ar not pratal n th fld ondton wth urrnt stat-of-th-art snsors. h jth modal flxblty an b synthszd utlzng Eq. (). h rsult s th transvrs dflton vtor of th bam du to a unt load at th jth nod. Consdr a fnt lmnt of th bam shown n Fg.. hn, th slop-dflton formula for th bam lmnt ar gvn by th systm of quatons: L L θ = EI 6EI M + L L w θ () L L M w 6EI EI L L whr th symbols θ and w dnot rotatonal and transvrs dgrs of frdom at nod, rsptvly. h symbols M, EI, and L dnot th bndng momnt, th flxural rgdty, and th lngth of th bam lmnt, rsptvly. Fnally, subsrpts dnot th orrspondng nod numbrs n th loal oordnat systm. From Fg. for th th lmnt, Eq. () n global oordnat boms L L θ 6 M = + L L w (6) θ L L M w 6EI L L For th +th lmnt, Eq. () n global oordnat boms L L + θ + 6+ = M + L L w + (7) θ L L M+ w+ 6EI + + L L Sn th slop s th sam at th th nod, w hav a ontnuty quaton as + θ = θ (8) Global Coordnats w w θ L, EI θ Loal Coordnats w + w + + θ + L, EI + θ + Fg. Engnrng Bam Elmnts Aftr substtutng Eq. (6) and Eq. (7) nto Eq. (8), th rarrangmnt wth rspt to th flxural rgdty of ah lmnt ylds w w + w + ( M + M ) + (M + M + ) = 6 (9) + L For a damagd strutur, Eq. (9) boms w w + w + ( M + M ) + (M M + + ) = 6 (0) + L whr th suprsrpt,, dnots th damagd systm. h applaton of th assumpton, that M M, gvs w w + w + ( M + M ) + (M M + + ) = 6 () + L h rght hand sd of Eq.() s a fnt dffrn approxmaton of th urvatur of damagd strutur at th th nod. ( M + M ) + (M + M+ ) = 6κ () + whr κ dnots th urvatur of damagd strutur at th th nod. It s wll known fat that th fnt dffrn approxmaton of th onsttutv law s as follows M = EI κ () Assumng th flxural rgdty of an ntat strutur s unform, (EI =EI +=EI =EI +), a substtuton of Eq. () nto Eq. () ylds th Flxural Damag Indx Equaton (FDIE) ( κ + κ) β + (κ + κ+ ) β+ = 6κ () whr β / dnots a flxural damag ndx of th th lmnt. It s notd that dttabl sz of damag dpnds on masurmnt spang sn th ntral dffrn approxmaton s usd n th both sds of th damag ndx quaton. o ahv good urvatur profl from oars masurmnt spang, Cub Spln ntrpolaton of modal flxblty s rommndd bfor applyng th dffrn formula. Not also that th damag ndx s rlatd to th urvatur of a strutur rathr than modal flxblty tslf. hus, th assumd dnsty of a strutur usd for salng modal flxblty wll b anld out n both sds n th FDIE f th dnsty of strutur s nvarant durng small damag vnts. If th numbr of th ntrpolatd masurmnt poston s q, th numbr of th FDIE s q- for th jth modal flxblty. In addtons, a st of th damag ndx quatons s also vald for th j+ th modal flxblty. hrfor, total possbl numbr of th quatons s (q-) (q-). Howvr, th numbr of unknown damag nds, β, s only q-. hrfor, substtutng nto quaton (), an ovr-dtrmnd systm of lnar quatons s avalabl. Howvr, th rsultng matrx quaton may not b drtly solvd by a smpl psudo nvrs thnqu, baus th sngularts ars nar th nflton ponts spally for th statally ndtrmnat struturs. hs sngularty problm an asly b rsolvd by gnralzd psudo nvrs thnqu by SVD. Consdr an ovr-dtrmnd damag ndx matrx quaton produd from Eq. () [ κ] β = κ () whr th (q-) vtor, β, dnots th damag ndx vtor supposd to b valuatd, and (q-) vtor, κ, dnots a urvatur vtor of damagd 8

5 strutur. h (q-) (q-) matrx, [κ] rprsnts a urvatur st of undamagd strutur. Aftr prmultplyng [κ] on both sds n Eq. (), multplaton of th SVD psudo nvrs of [κ] [κ] on both sds ylds β = [ ρ] κ (6) whr [ ρ] U Σ U [ κ] s a (q-) (q-) radus matrx r r of urvatur f th rank of [ κ] [ κ] r s r (q- r). Not that th radus matrx of urvatur dnots th lnar rlatonshp btwn th unknown damag ndx, β, and th masurd urvatur of damagd strutur, κ. hrfor, th dsrd damag ndx vtor an radly b obtand by a smpl matrx multplaton wth κ, on th radus matrx of urvatur s omputd from ntat strutur.. Faturs of FDIE hr ar many faturs n ths approah. Frst, on rprsntatv soluton an b found from mor than on mod, baus of th faturs of modal flxblty. Sond, both natural frquns and mod shaps ar usd to valuat modal flxblty. hrd, th damag ndator s a rato of flxural rgdty btwn ntat strutur and damagd strutur. hus th physal ntrprtaton of th stmatd damag ndator s lar. Fourth, th sngularty problm nar nflton ponts s systmatally dalt wth SVD n onjunton wth FDIE. Ffth, unlk dffult stat dflton masurmnt task, th dflton profl an radly b obtand wth a good auray by th vbraton tsts du to th faturs of modal flxblty. hus, a vsual nspton of th jth modal flxblty allows dttng th faults on mod shap f any physally unrasonabl knk xsts, ompard to th dflton profl du to a unt load at th jth nod. Sxth, th omputatonally xpnsv SVD produr nds only on tm for an ntat strutur as shown n Eq. (6). hus th damag ndx an radly b obtand for many progrssv damag snaros by a smpl matrx multplaton, on th radus matrx of urvatur, [ρ], s known. Svnth, ths potntal soluton produr an radly b xtndd to th othr typs of struturs, sn bas strutural onpt and th small damag assumpton usd n th prvous drvaton of FDIE for a bam an b xtndd to mor omplx systms.. APPLICAION. Dsrpton of Strutur h Z Brdg was an ovrpass on th Swss Natonal Hghway A btwn Brn and Zurh. h Z s a slghtly skwd thr-span onrt brdg. It s a post-tnsond, onrt box grdr wth a man span of 0m and two m sd spans. Abutmnts onsstd of onrt olumns onntd of onrt hngs and ntrmdat supports onsstd of onrt prs lampd to th grdr. h brdg was onstrutd n 96 and dmolshd at th nd of 998 to mak way for a nw brdg wth a longr sd span. No sgnfant damag or dtroraton was notd n th strutur bfor ntaton of th squntal damag snaros..7m m 0m m.7m Utznstorf Koppgn.m.0m 8. o Zurh m.m.m Fg. Elvaton Brn 0m Fg. Plan 6.0m. Progrssv Damag sts On th bass of th Europan Brt Euram Projt B 96-7 SIMCES ( Systm Idntfaton to Montor Cvl Engnrng Struturs ), a srs of Progrssv Damag sts (PD s) wr prformd on th Z brdg, and th ambnt alraton tm hstors of th brdg wr rordd for ah as [9]. In ths papr th damag snaros of th sttlmnt of a sngl pr ar onsdrd for th purpos of omparson wth a st of prvous damag dtton rsults [0]. o smulat th sttlmnt of th Z, th pr of Koppgn sd was ut. Som part of th onrt was rmovd and rplad by stl fll plats and thr hydraul jaks [0]. h appld squntal damag snaros ar as follows. PD: basln for strutur PD: m sttlmnt of pr PD: m sttlmnt of pr PD: 8m sttlmnt of pr PD6: 9.m sttlmnt of pr m.m Fg. Cross Ston of Supr Strutur. Ambnt Modal st and Data Aquston For ah damag snaro, th full-sal D xprmnt ontand a total of probng postons that onssts of lans ponts = ponts for th brdg dk and prs 8 pont = 6 ponts on th prs. Consdrng th larg numbr of snsor postons, th rovng snsor thnqu was shduld wth rfrn ponts and 9 data sts for ah damag snaro. Eah data st onsstd of 0.97 mnuts long alraton tm hstors sampld smultanously at 00 Hz. Howvr, th data usd n ths papr s a modfd D vrson onsstng of total 9 probng poston aftr dsardng a larg part of th masurmnt ponts. h total numbr of probng postons on th modfd D vrson onssts of lans 0 ponts = 0 ponts for th brdg dk, prs 8 pont = 6 ponts on th prs, and rfrn postons. h modfd D 9

6 vrson data s fltrd so that th samplng tm s 0.0 s and th duraton of rordng s 0.87mn. (76 sampls).. Modal Analyss Usng DD Usng a vrtal rfrn pont loatd on th mddl of a man span of 0m, th mods for th brdg dk ar stmatd by DD thnqu. h dntfd natural frquns ar lstd n abl. abl. Idntfd Natural Frquns PD Mods (Hz) Not: Frquny rsoluton = 0.08Hz h frst and sond mods rprsnt th pur st transvrsal bndng and torsonal mod, rsptvly. hrd and fourth mods ar oupld by th nd transvrsal bndng and st torson mods. h ffth mod dnots th pur rd transvrsal bndng mod. At th sond and ffth mods, th ohrn funtons and ross sptrums of th rfrn sgnals wth th othr sgnals ar vry wak. It was thn onludd that th appld ambnt nput was not nough to xt th sond and ffth mods. o solat ah mod, th rd ordr dgtal Buttrworth fltr was dsgnd for ah mod. h rason of ths slton s du to th fat that th Buttrworth fltr has no rppl n th pass band zon. A typal frquny rspons funton of th dsgnd dgtal Buttrworth band pass fltr for th frst mod wghs ts frquny band (.Hz ~.Hz) up to a unty, and wghs th othr frquny omponnts down to zro. On a fltr s dsgnd for ah mod usng fltr thory, th fltrd tm sgnals an b omputd by lnar systm thory. h dntfd mod shaps for damag snaros, PD and PD6, ar ompard n Fg. 6, 7, and 8. For th omparson purpos only, th Modal Assuran Crtra (MAC) valus btwn th DD and th FDD rsults of PD ar shown n abl and. It s notd that mod shaps xtratd by DD thnqu ar un-dampd mod shaps whl th mod shaps xtratd by FDD ar slghtly dampd mod shaps. h appld rovng snsor thnqu to ollt data hghly dpnds upon th qualty of rfrn sgnals. If a rtan mod of a rfrn poston s not xtd by ambnt sour, t affts rsultng ntr mod shaps ourrd at th th mod n PD (S abl ). abl. MAC Valus of PD : DD & FDD Mod abl. MAC Valus of PD6 : DD & FDD Mod φ PD PD Dstan X (m) Fg. 6. h st Mod Shap from Brn Sd (s Fg.) n PD and PD PD 0. φ PD Dstan X (m) Fg. 7. h rd Mod Shap from Brn Sd (S Fg.) n PD and PD PD φ 0 PD Dstan X (m) Fg. 8. h th Mod Shap from Brn Sd (S Fg. ) n PD and PD6. Loal Damag Dtton Usng th FDIE As an b sn n abl, th natural frquns n damag snaros, PD and PD6, ar sgnfantly hangd ompard to th rsults n th undamagd snaro PD. Consdrng th oars snsor ntrvals and qualts of sgnals, th damag snaro PD6 s hosn for ths dmonstraton of th FDIE mthod. o mphasz th fasblty of loal damag dtton, loal mod shaps on a man span of 0m at th Brn sd s only onsdrd hr. For th omputaton of th modal flxblty, th only thr mods (th frst, thrd, and fourth mods) ar only usd for ths dmonstraton. Sn th undamagd modal data ar avalabl, th damag snaro PD 0 6

7 s sltd as a basln strutur for a onvnn wthout modlng any numral modl. h rsult of damag dtton s shown n Fg β Damagd Loaton Utznstorf Pr Koppgn Pr Dstan X(m) Fg. 9. Estmatd Flxural Damag Indx of Mddl Span on Brn Sd (S Fg. ) n PD6 From th stmatd flxural damag ndx of PD6, th followng two obsrvatons an b mad: () Du to th 9.m sttlmnt on th Koppgn pr, flxural damag s th most svr nar m lft from th Koppgn pr. () At m lft from th Koppgn pr, th flxural rgdty of th brdg s rdud to about tms. A prvous damag dtton study ndatd that a rakd zon s about 0m lft and rght of th Koppgn pr was notabl [0].. CONCLUSIONS Basd on th rsults, th followng thr onlusons an b mad. Frst, th prsntd DD thnqu s pratal and ffnt to xtrat modal paramtrs from th output-only nosy tm srs. Sond, th proposd approah of loal damag dtton an loat and stmat th svrty of damag n a strutur from th followng nomplt modal data: () fw of th lowr natural frquns and mod shaps, () lmtd masurmnts of dgrs of frdom, and () spatally nomplt masurmnts of mod shaps. hrd, th ombnaton of th DD and th FDIE mthod s fasbl and pratal for a ral-tm applaton of damag dtton. 6. REFERENCE [] Bray, D. E. and MBrd, D. Nondstrutv tstng thnqus. John Wly & Sons, NY, NY, 99. [] Doblng, S. W., Farrar, C.R., and Prm, M. B. A Summary Rvw of Vbraton-Basd Damag Idntfaton Mthods. h Shok and Vbraton Dgst, 0(), 9-0, 998. [] Bndat, J. S. and Prsol, A. G. Engnrng Applatons of Corrlaton and Sptral Analyss. John Wly & Sons, NY, NY, p.8-86, 980. [] Asmussn, J. C., Ibrahm, S. R., and Brnkr, R. Random Drmnt: Idntfaton of Struturs Subjtd to Ambnt Extaton. Pro. of 6th IMAC, 9-9, 998. [] Juang, J.-N. Appld Systm Idntfaton. Prnt-Hall, Englwood Clffs,Nw Jrsy, 99. [6] Brnkr, R., Zhang, L., and Andrsn, P. Modal Idntfaton from Ambnt Rsponss usng Frquny Doman Domposton. Pro. of 8th IMAC, San Antono, xas, 6-60, 000. [7] Cawly, P., and Adams, A. D. h Loaton of Dfts n Struturs from Masurmnts of Natural Frquns. J. of Stran Analyss, (), 9-7, 979. [8] Stubbs, N. A Gnral hory of Non-dstrutv Damag Dtton n Struturs. Strutural Control: Pro. of th nd Intrnatonal Symposum on Strutural ontrol, Unvrsty of Watrloo, Ontaro, Canada, H. H. H. Lpholz, d., Martnus Njhoff Publshrs, Dordrht, Nthrlands, 69-7, 98. [9] Pandy, A. K., Bswas, M., and Samman, M. M. Damag Dtton from Changs n Curvatur Mod Shaps. J. of Sound and Vbraton, (), -, 99. [0] Stubbs, N., and Km, J.-. Fld Vrfaton of a Nondstrutv Damag Loalzaton and Svrty Estmaton Algorthm. Pro. of th IMAC, Nashvll, N, I, 0-8, 99. [] Chn, J.-C, and Gaba, J. A. On-orbt Damag Assssmnt for Larg Spa Struturs. AIAA J., 6(9), 9-6, 988. [] Sanay, M., and Saltnk, M. J. Paramtr Estmaton of Struturs from Stat Stran Masurmnts. I: Formulaton. J. of strutural ngnrng, ASCE, (), -6, 996. [] Pandy, A. K., and Bswas, M. Damag Dtton n Struturs Usng Changs n Flxblty. J. of Sound and Vbraton, 69(), - 7, 99. [] Dnoyr, K. K., and Ptrson, L. D. Mthod for Strutural Modl Updat Usng Dynamally Masurd Stat Flxblty Matrs. AIAA J., (), 6-68, 997. [] Chn, C.-. Lnar Systm hory and Dgn. rd Ed. Oxford Unvrsty Prss, Nw York, Nw York, 999. [6] Golub, G. H. and Van Loan, C. F. Matrx Computatons. rd Ed. h Jhons Hopkns Unvrsty Prss, Baltmor, Maryland, p. 70, 996. [7] moshnko, S. P., and Gr, J. M. hory of Elast Stablty, nd Ed. MGRAW-HILL, In., Nw York, Nw York, p., 96. [8] Brman, A., and Flannlly, W, G. hory of Inomplt Modls of Dynam Struturs. AIAA J., 9(8), 8-87,97. [9] Kramr, C, Smt, C. A. M., and Rok, G. Z Brdg Damag Dtton sts., Pro. of 7th IMAC, Kssm, FL, 999. [0] Wahab, M. M. A., and Rok, G. Damag Dtton n Brdgs Usng Modal Curvaturs: Applaton to a Ral Damag Snaro. J. of Sound and Vbraton, 6(), 7-,999. 7