THE ANALYSIS OF INSTRUMENT RESPONSE ERRORS FOR FORCE-BALANCE ACCELEROMETER AND THEIR CORRECTION METHOD

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1 4th Iteatioal Cofeece o Eathquae Egieeig Taipei, Taiwa Octobe 1-13, 006 Pape o. 1 THE AALYSIS OF ISTRUMET RESPOSE ERRORS FOR FORCE-BALACE ACCELEROMETER AD THEIR CORRECTIO METHOD Yu Hai-Yig 1 ABSTRACT The aalysis of istumet espose eos fo foce-balace acceleomete of digital acceleogaph system is caied though i this pape, a method fo coectig istumet espose eos has bee put fowad (the diffeetial-diffeetial method), i.e. the u-coectio acceleatio data ae teated by low-pass filteig, they ae diffeetiated twice with appoximate ideal diffeetiatos to obtai the coected acceleogam. I allusio to the eathquae istumet system (KIS) of Daya bay uclea powe statio, the istumet espose coectio demostatio is give, ad the coespodig compute pocessig softwae ae compiled. The method is applicable fo istumet espose coectio pocessig of acceleogam ecoded by digital acceleogaph of Chia stog motio etwo. Keywods: Digital acceleogaph Foce-balace acceleomete Istumet espose eos coectio Acceleogam Softwae ITRODUCTIO I the ealy 1980s of last cetuy, alog with the developmet of digital obsevatio techique, the digital stog motio acceleogaph system has aleady bee used i Chia stog motio et ad mobile obsevatio.thee ae the acceleometes equipped with this id of system, such as Type FBA-3 ad Type FBA-13 etc. made by Ameica Kiemetices Compay, ad Type SLJ-100 eseached ad made by Istitute of Egieeig Mechaics, Chia Eathquae Admiistatio. The digital stog motio acceleogaph has may advatageous pefomaces which ae ot able to be compaed by theaalog stog motio acceleogaph. The ecods obtaied ae with big dyamic scope, boad fequecy ad absolute time scale, ad the wavefoms ae complete with head. But, the digital stog motio acceleogaph ae geeally applied with foe-balace acceleometes with the aowe fequecy bad scope (fom 0 to 30 Hz), ad the ecods fo this id of istumets should cay out the istumet coectio. Fo the istumet high feguecy eo coectio of the aalog stog motio acceleogaph, Ameica schola Tifuac, M.D. etc. eseached it, ad Chiese schola Xie Li Li etc. also eseached the ampeemete ad diectly photogaphic ecodig field aalog stog motio acceleogaph system. I ecet yeas, oviova, E.I. ad Tifuac,M.D. eseached the istumet fequecy eos fo digital stog motio acceleogaph system. I the pape, though the aalysis fo the foce-balace 1 Pofese, Istitute of Egieeig Mechaics, Chia Eathquae Admiistatio, Habi Chia haiyigyu@16.com

2 acceleomete istumet espose distotio ad eos, a pocessig method fo coectig this id of eos (diffeetia l-diffeetia l method) has bee peseted, i.e. afte the ucoected ecods ae Low-pass filteed, the filte is applied with Buttewoth, they ae diffeetiated twice by appoximately ideal diffeetiato to obtai the coected acceleatio ecods. I allusio to the eathquae istumet system (KIS) of Daya bay uclea powe statio, a demostatio of the istumet coectio has bee give, ad the compute coespodig pocessig softwae have bee compiled. The method is suitable fo the istumet distotio coectio pocessig fo the acceleatio ecods obtaied by Chia stog motio et digital stog motio acceleogaphs. But, it is ecessay to poit out that i ecet yeas, the foce-balace acceleometes (e.g.fba-3, SLJ-100 FBA-T) made by U.S.A ad Chia istumets fequecy bad scope is usua lly fom 0 to 80 Hz, ad both the high fequecy ad low fequecy espose chaacteistics ae moe supeio tha the ealy foce-balace acceleometes. Accodig to the theoy, it is cosideed that without the istumet fequecy espose distotio coectio pocessig, it ca be satisfied with the fequecy scope equiemets of the iteest to the eathquae egieeig. THE AALYSIS FOR THE ISTRUMET RESPOSE DISTORTIO AD ERRORS Fo the woig piciple of the foce balace acceleometes, it shall ot be itoduced i detail. The diffeeces amog it ad othe types of sesos lie i that it has a electoic feedbac closed loop, ad though the feedbac closed loop, it ca supply wide effective fequecy espose scope tha geeal sesos, But it is as same as othe istumets, has the istumet espose eos, i.e. the ecods ca oly i the cetai fequecy segmet epeset the measued vibatio, if beyod this fequecy segmet, the istumet ecods will have seious distotio. Fo FBA-3 Foce-balace acceleomete, ad ea to o beyod the fee fequecy high fequecy vibatig compoets, the istumet ecods will iclude vey big eos. FBA-3 Foce-balace acceleomete tasfe fuctio measued i the vibatio table expeimet is show as Fig1. The esults demostate: the tasfe fuctio cuve fom 0 to 30 Hz is flat. FBA foce-balace acceleato s movemet diffeetial equatio is as the followig: X & + ω ζx& + ω X X& (1) I the equatio: ω ζ ω c m DKGγ + mr0 K m DKG + mr0 g FBA-3 acceleomete fuctio db Figue 1 Seso tasfe fuctio fequecy (Hz) D - vaiable capacitace modulatio facto (volt/mete) K - feedbac closed-loop gai G - electic costat(ewto/ampee)?- speed covesio elatio X epesets elative displacemet of acceleatio seso vibatig cete,? is fo seso iheet vibatig cicle fequecy,? is fo acceleatig seso dampig costat, ad X g is fo the measuig poit place motio acceleatio. Accodig to the seismogaph theoy, afte itoducig the feedbac techique, this id of sesos mae the system fee fequecy icease geatly icease, ad the sesitivity does t dop, ad the system fee fequecy is geatly bigge tha the measued vibatig fequecy. The elative

3 displacemet fo the seso vibatig cete is diectly popotioal to the measued goud acceleatio, i.e. ω X X& g () As show i the tasfe fuctio of FBA-3 foce-balace acceleomete, whe the pedulum fee fequecy Fm51. Hz, ad i the age fom 030 Hz the cuve is flat. Ad oly i the fequecy segmet, ca it epeset pecisely the goud movemet acceleatio. If it is beyod the fequecy segmet, the seso movemet diffeetial equatio caot be established. At this time the obtaied acceleatio ecods may become distoted. So the istumet espose coectio must be caied out fo the distoted ecods. THE ISTRUMET DISTORTIO CORRECTIO METHOD what the digital stog motio acceleogaph system ecods is seso pedulum mass elative displacemet, ad is discetized data seies, ad witte as {X }. I ode to avoid the oise s effect o the digital diffeetial calculatio, Buttewoth digital filte should be Low-pass filteed oce, the cut-off fequecy selected is 50 Hz. Buttewoth digital filte fequecy espose cuve is show i Fig. The seso movemet diffeetial equatio ca be chaged ito: { x & } + W { x& } + ω { x } { X& } ζ (3) Amog them, { X & } is goud movemet acceleatio X & g 's discoetized expessio fom. The distotio ecods (equatio) ae diffeetiated twice, ad the the pedulum mass elative velocity { x& & } ad elative acceleatio { x& } ca be obtaied, ad accodig to the above equatio, afte the combiatio, at oce the ecods afte the istumet espose distotio coectio ca obtai. I ode to eseve may effective high fequecy elemets i the sigals bette, we select the oppoximately ideal diffeetial covesio algoithm, ad apply the opeatio fomula 1 ( X X ) X & b (4) + I the actual diffeetial opeatio, it ca use Limited sum to substitute the above equatio X& 1 C ( X X ) + By applyig the fomula, doig faltug itegal opeatio to obtai fist-ode diffeetial X & H(f) F L F H f(h z ) Figue Fequecy espose cuve of Buttewoth digital filte Figue 3 Appoximately ideal diffeetial opeatio tasfe fuctio

4 Similaly, substitutig X & ito the above equatio, afte that, though adjustmet, obtaiig secod- ode diffeetial X &. I the equatio: C b W b 1 ( 1) K T 1 π W 1 cos 1,, LL, +. Buttewoth ) X & (t X & (t) Figue 4 Digital stog motio acceleogaph distotio coectio bloc diagam I ode to elimiate Gibbs pheomeo poduced because of cut-off Fouie seies, we itoduce widow fuctio w to mae smooth, hee Hoig widow is used. Whe gettig 0, the diffeetial opeatio is caied out,the accodig to the seso movemet diffeetial equatio which has bee chaged, the coected acceleatio ecods ae obtaied. The above give istumet coectio method is called as diffeetial- diffeetial method. Fig.3 is appoximately ideal diffeetial opeatio tasfe fuctio, ad Fig.4 is digital stog motio acceleogaph distotio coectio bloc diagam. THE DEMOSTRATIO OF THE ISTRUMET CORRECTIO By meas of MS Fota advaced desig laguage, i allusio to the istumet coectio method peseted, i the pape, the calculatio pogams have bee compiled, ad it is applied i Daya bay ucla powe statio eathquae istumet system (KIS) stadad data pocessig softwae. Type FBA-3 foce-balace acceleomete made by Ameica Kiemetics compay is applied fo KIS system acceleomete. Because of that sice the system was established, it did t obtai the eathquae ecods, so the atificial simulatio eathquae method is applied fo obtaiig the atificial simulatio eathquae ecods. Fig.5 is the atificial simulatio ecod time-histoies which is that by meas of the istumet coectio method peseted i the pape, befoe ad afte pefomig the istumet distotio coectio calculatio fo a measued poit atificial simulatio eathquae acceleatio ecods of KIS system. a, v, ad d epeset espectively ucoected acceleatio, itegal speed, ad displacemet time-histoies. Ad A, V,ad D epeset espectively coected acceleatio, itegal speed ad displacemet time-histoies.

5 Figue 5 The atificial simulatio ecod time-histoies befoe ad afte the istumet distotio coectio COCLUSIO The esults demostate that by meas of the istumet coectio method peseted i the pape, the acceleatio time-histoies fequecy espose age fo istumet coectio pocessig has bee expaded, ad the fequecy segmet is fom 0 to 50 Hz, ad i the fequecy segmet, the acceleatio ecods ae without high fequecy distotio pheomea. Theefoe it satisfies the fequecy age equiemets fo the eathquae egieeig with geat iteest. The method is suitable fo the acceleatio ecods obtaied by Chia stog motio et digital stog motio acceleogaph distotio coectio pocessig. But it is ecessay to poit out that, i the ecet yeas, the foce-balace acceleometes made by U.S.A. ad Chia may ot do the istumet fequecy espose distotio coectio pocessig. REFERECES [1] OVIKOVA,E.I.,TRIFUAC,M.D., Digital Istumet Respose Coectio fo Foce-Balace Acceleomete, Eathquae Specta, 8(3), 199. [] TRIFUAC, M.D., A ote o Coectio of Stog Motio Acceleogams fo Istumet Respose, Bull. Seism. Soc. Am.,6, 197. [3] XIE LI-LI, The Mai Featues Of Data Pocessig Pocedue Fo Stog Motio Recods I Chia, Physics of the Eath Ad Plaetay Iteios, 38, , Elsevie Sciece Publishes B.V., Amstedam-Pited I the ethelads [4] V.W.LEE, Digitizatio ad Data Pocessig of Stog Motio Eathquae Acceleogams, Poceedigs of the Iteatioal Cofeece o Advaces ad ew Challeges i Eathquae Egieeig Reseach, Hog Kog Volume, 00.8 [7] Aalysis of digitizatio eos fom the pocessig of digitizig stog motio acceleogams ad thei elimiatio method ad softwae