Actuator Failure Detection Through Interaction Matrix Formulation

Transcription

1 JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS Vol 28, No 5, Septembe Octobe 2005 Actuato Falue Detecton Though Inteacton Matx Fomulaton B H Koh Dongguk Unvesty, Seoul , Republc of Koea Z L, P Dhaap, and S Nagaajaah Rce Unvesty, Houston, Texas and M Q Phan Datmouth College, Hanove, New Hampshe A novel technque s ntoduced to detect and solate the falues of multple actuatos connected to a system The falue of actuato consdeed n ths study could be any type of eoneous nput that s dffeent fom the commanded one The nteacton matx technque allows the development of nput-output equatons that ae only nfluenced by one taget nput These nput-output equatons seve as an effectve tool to monto the ntegty of each actuato egadless of the status of the othe actuatos Although the pocedue eques the knowledge of analytcal model of the system beng tested, the analytcal edundancy can be expementally pedetemned though standad nput-output-based system dentfcaton algothms such as obseve/kalman-flte dentfcaton (OKID) and egensystem ealzaton algothm (ERA) Ths method s capable of eal-tme actuato falue detecton and solaton unde any type of nput exctaton Both numecal smulatons of a spng-mass-dampe system and a laboatoy expement usng eght-bay NASA tuss stuctue vefy the feasblty of the poposed method I Intoducton TO accommodate a fault-toleant contol system, successful detecton and solaton of actuato/senso falue should be guaanteed along wth elable system dentfcaton Thee have been seveal studes to dagnose actuato falue n contol systems, and many of them explot model-based analytcal edundancy stateges 1,2 The analytcal edundancy appoaches became moe popula n many ndustal applcatons because hadwae edundancy, such as a eplcaton of dentcal hadwae components (actuato/senso), s moe expensve, estcted, and sometmes dffcult to mplement n pactce The key element of analytcal edundancy s to dagnose faults n a system by analyzng the geneated esduals between a po analytcal model and avalable system measuements Theoetcally, esdual o eo sgnals should be zeo-valued fo a healthy case, wheeas devated nonzeo values ae consdeed to be an ndcaton of system falue 3 Hence, the fst step fo falue detecton s to develop a mathematcal algothm that accentuates the esdual sgnal when a fault has occued n a system So fa, paty space (consstency checkng 4,5 ) and obseve-based methods 6,7 have been wdely used fo the esdual geneaton Once esdual sgnals ae detected, the next step s to sepaate the souce of the falue, a so-called fault solaton The sgnfcance of the studes elated to actuato falue detecton s attbuted to the effot of developng an adaptve contol system that can compensate fo the consequence of actuato falue n flght, powe, o pocess contol systems Recently, vaous types of stuc- Receved 1 July 2004; evson eceved 11 Novembe 2004; accepted fo publcaton 17 Novembe 2004 Copyght c 2004 by the Amecan Insttute of Aeonautcs and Astonautcs, Inc All ghts eseved Copes of ths pape may be made fo pesonal o ntenal use, on condton that the cope pay the $1000 pe-copy fee to the Copyght Cleaance Cente, Inc, 222 Rosewood Dve, Danves, MA 01923; nclude the code /05 $1000 n coespondence wth the CCC Assstant Pofesso, Depatment of Mechancal Engneeng, 3-26 Pldong, Chung-gu; fomely Reseach Assocate, Depatment of Cvl and Envonmental Engneeng, Rce Unvesty, Houston, TX Membe AIAA Gaduate Student, Depatment of Cvl and Envonmental Engneeng Assocate Pofesso, Depatments of Cvl and Envonmental Engneeng and Mechancal Engneeng and Mateal Scence Assocate Pofesso, Thaye School of Engneeng Membe AIAA 895 tues such as acaft wngs, bdges, space stuctues, and buldngs apdly adopt the smat mateals that nheently ncopoate contol theoy nto the host stuctue A smat stuctue wth a netwok of obust sensos and hgh-pefomance actuatos can elaboately accomplsh ethe vbaton contol o stuctual health montong 8 Accodngly, the pefomance of a smat stuctue eles on the ntegty of embedded sensos and actuatos Fo nstance, unexpected actuato falue, such as debondng of pezoelectc mateal fom ts host stuctue, can destablze the closed-loop system to pose a sgnfcant theat to the safety of stuctue 9 It s thought that actuato falues occu when the nputs to the system ae dffeent fom the command nputs at some unknown actuatos fo some unknown tme nstants In many stuatons when a stuctue has multple actuatos and sensos n dffeent locatons, each output of the stuctue s smultaneously nfluenced by all dffeent nputs Hence, smply compang the esponse of ndvdual measuement pont on the stuctue does not gve us much nfomaton about whch actuato o when t has faled Fo successful dentfcaton of actuato falue, each nput and output elatonshp should be decoupled n a systematc way, that s, nfluences fom all othe actuatos on output measuements should be elmnated except the only actuato beng examned Ths pape povdes a novel technque to dentfy actuato falue n dynamc systems The concept of nteacton matx s ntoduced and employed to acheve ths objectve Pevous studes show that the condton of the exstence of nteacton matx can elmnate state vaables so that only nput-output elatonshp epesents the system s dynamcs The applcaton of nteacton matx spans fom pedctve contol, 10 state estmaton, 11 and dstubance sepaaton n system dentfcaton 12 In the study of dentfyng the system of dstubance-fee dynamcs, the nteacton matx explctly elmnates the dependence of the state vaables so that unknown dstubance nputs can be sepaated fom the system and ts nputoutput model The key dea of ths study s to elmnate the nfluences of unexamned nputs fom measued outputs so that the devaton o falue of specfc actuato can be manfested as a nonzeo esdual sgnal The mposed condton of the exstence of nteacton matx allows fo the elmnaton of the dependence of all othe nputs except the one beng examned Specfcally, the nteacton matx povdes a mathematcal famewok n whch a sees of specal nput-output

2 896 KOH ET AL equatons (o eo functons) can be fomulated to detect and solate each unknown actuato falue Because the undelyng theoy s to decouple the nfluence of specfc nput eo fom the oveall outputs of the system, the method does not eque a bank of falue hypotheses fom an a po model The poposed method successfully dentfes actuato falues n both numecal smulaton of a spngmass-dampe system and expemental tests on eght-bay NASA tuss stuctue Note that ths method s dectly applcable to onlne system montong and allows any type of nput exctaton II Mathematcal Fomulatons Consde an nth-ode, -nput, q-output contollable and obsevable dscete-tme model of a system n state-space fom: x(k + 1) = Ax(k) + Bu(k), y(k) = Cx(k) (1) An actuato falue s consdeed to occu when an actuato poduces an nput to the plant that s dffeent fom a commanded nput In the followng, specal nput-output equatons wll be developed, one fo each actuato Each equaton wll eveal f an actuato s expeencng a falue egadless of the status of any emanng actuatos Ths s possble f thee exsts fo each actuato an nput-output equaton that nvolves the only actuato beng examned, wheeas the output measuements ae nfluenced by nputs fom all actuatos At fst sght, t s not ntutvely obvous f such elatonshp exsts, what stuctue these equatons possess, and how they ae elated to and can be desgned fom the pecedng state-space model The nteacton matx (M-matx) fomulaton povdes a mechansm to answe these questons n a staghtfowad manne The devaton stats fom the state-space model [Eq (1)] as follows By epeated substtuton fo some p 0, x(k + p) = A p x(k) + Cu p (k), y p (k) = Ox(k) + Tu p (k) (2) whee u p (k) and y p (k) ae column vectos of nput and output data gong nto p steps nto the futue statng wth u(k) and y(k), espectvely, u p (k) = u(k) u(k + 1) u(k + p 1), y p(k) = y(k) y(k + 1) y(k + p 1) (3) Fo asuffcently lage value of p to be detemned late, C s an (extended) n p contollablty matx, O s an (extended) pq n obsevablty matx, and T s a pq p Toepltz matx of the system Makov paametes, C = [A p 1 B,,AB, B], O = [C, CA,,CA p 1 ] T CB 0 0 T = CAB CB 0 (4) 0 CA p 2 B CAB CB 0 Because we ae dealng wth actuato falue detecton, t s necessay to expand the pecedng equaton to show the contbuton of each ndvdual nput = 1, 2,,: x(k + p) = A p x(k) + C 1 u (p) 1 (k) + +C u (p) (k) + B 1 u 1 (k + p 1) + + B u (k + p 1) (5) y p (k) = Ox(k) + T 1 u (p) 1 (k) + +T u (p) (k) whee B = [B 1, B 2,B ], C = [ ] A p 1 B,,A 2 B, AB (6) C ends wth AB, not B Also, u (p) u (p) (k) = (k), and T ae u (k) u (k + 1) u (k + p 2) CB 0 0 T = CAB CB 0 0 CA p 2 B CAB CB Compang the defntons n Eq (6) to those n Eq (4), notce that they ae defned fo each nput Futhemoe C ends wth AB (not B ), and T leaves out the last zeo column The eason fo ths wll become clea late An nteacton matx M s ntoduced by addng and subtactng the poduct M y p (k) to Eq (5) as follows: x(k + p) = A p x(k) + C 1 u (p) 1 (k) + +C u (p) (k) + B 1 u 1 (k + p 1) + + B u (k + p 1) + M y p (k) M y p (k) = ( A p + M O ) x(k) + (C 1 + M T 1 )u (p) 1 (k) + +(C + M T )u (p) (k) M y p (k) + B 1 u 1 (k + p 1) + + B u (k + p 1) (7) Pemultplyng the pecedng equaton by C yelds y(k + p) = ( CA p + CM O ) x(k) + (CC 1 + CM T 1 )u (p) 1 (k) + +(CC + CM T )u (p) (k) CM y p (k) + CB 1 u 1 (k + p 1) + +CB u (k + p 1) (8) Fo each nput,wenow mpose condtons fo the poduct CM n the pecedng equaton so that n Eq (8) coeffcents of state x(k) tems and the nput vectos u (p) j (k) vansh dentcally except fo that nput, CA p + CM O = 0 CC j + CM T j = 0, j (9) Fo example, fo the fst nput ( = 1), CM 1 s equed to satsfy CM 1 [O, T 2,,T ] = [ ] CA p, CC 2,,CC (10) Let us examne the condtons fo the exstence of the poduct CM (whch mples the exstence of M fo ndependent outputs) by takng advantage of the fact that Eq (9) s a set of lnea equatons Thee ae q(pq) = pq 2 unknown elements n CM vs a total of qn + ( 1)q(p 1) = qn + q( 1)(p 1) equatons A necessay condton fo the exstence of CM s pq 2 qn + q( 1)(p 1) (11) Theefoe p must be chosen such that p(q + 1) n + 1 (12) The pecedng condton causes the matx and the poduct CM to have at least as many ows as columns An examnaton of the stuctue of ths matx and ts nfomaton content futhe eveals that t s geneally full (column) ank fo ndependent nputs n whch case the exstence of CM s ensued as long as Eq (12) s satsfed Satsfacton of Eq (12) also eques that q + 1 > 0, whch means that the numbe of ndependent sensos must be at least equal to the numbe of ndependent actuatos (q ) so that falues among actuatos can be dstngushed A smla analyss can be pefomed by mposng the condton fo M nstead of CM, and ths leads to the same concluson In othe wods, the mposed condton of nteacton matx M s ndependent fom output matx C

3 KOH ET AL 897 Fo each nput, wehave y(k + p) = (CC + CM T )u (p) (k) CM y p (k) + CB 1 u 1 (k + p 1) + +CB u (k + p 1) (13) To detect whethe the th actuato fals, we ae nteested n obtanng a elatonshp among the nput and output measuements that does not nvolve any othe actuatos except the th actuato Up to ths pont, the nteacton matx M has elmnated all such dependence except fo the emanng tems CB 1, CB 2,,CB fo whch t has no nfluence The emanng tems (except CB ) can be elmnated by pemultplyng Eq (13) wth a ow vecto that s othogonal to all emanng column vectos CB j, j, (CB j ) = 0, j (14) Because q, such a vecto N can be easly found (subject to nomalzaton facto) Pemultplyng Eq (13) by N poduces a scala equaton that nvolves all measued outputs and the th nput alone y(k + p) = (CC + CM T )u (p) (k) CM y p (k) + CB u (k + p 1) (15) To ave at an actuato falue detecton equaton, we eplace the actual nput u (k) to the plant by a sum of commanded (thus known) nput ū (k) and actuato eo z (k) n Eq (15): y(k + p) = (CC + CM T ) [ ū (p) (k) + z (p) (k) ] CM y p (k) + CB [ū (k + p 1) + z (k + p 1)] (16) Fnally, the actuato eo tems ae sepaated fom the est of the equaton by defnng e (k + p) = (CC + CM T )z (p) (k) + CB z (k + p 1) (17) Equaton (16) becomes e (k + p) = y(k + p) + CM y p (k) (CC + CM T )ū (p) (k) CB ū (k + p 1) (18) Falue of the th actuato can be detected by montong e (k) When thee s no actuato falue, z (k) = 0, t follows that e (k) = 0 Thus when e (k) 0, t can be ntepeted that th actuato fals Let us now examne the stuctue of the actuato falue detecton equaton (18) fom the pespectve of desgn and usage Shftng tme ndex back by p esults n e (k) = y(k) + CM y p (k p) (CC + CM T )ū (p) (k p) CB ū (k 1) (19) Fst, t s a scala equaton, one fo each actuato Second, t assumes the geneal fom e (k) = α 0 y(k) + α 1 y(k 1) + +α p y(k p) + β 1 ū (k 1) + β 2 ū (k 2) + +β p ū (k p) (20) Fo an -nput and q-output system (q ), each coeffcent α 0, α 1,,α p sa1 q ow vecto, wheeas each coeffcent β 1, β 2,,β p s a scala Fo the th actuato, these coeffcents ae elated to those of the ognal state-space model by [α p,α p 1,,α 1,α 0 ] = [ ] CM, (21) [β p,β p 1,,β 2,β 1 ] = [ ] (CC + CM T ), CB (22) Thus gven a state-space model A, B, C, D, t s staghtfowad to fom A p, O, C, T, D fom whch the poduct CM s calculated Fg 1 Thee-nput, thee-output spng-mass-dampe system by solvng the set of lnea equatons gven n Eq (9), and N s detemned fom Eq (14) In geneal the poduct CM that satsfes Eq (9) s not unque The pseudonvese soluton va the sngula value decomposton poduces a mnmum-nom soluton fo CM whle satsfyng Eq (9) exactly Such a mnmum-nom soluton s expected to be advantageous because t esults n small gans fo Eq (20) and thus does not amplfy the effect of measuement nose The sngula value decomposton also povdes the oppotunty to elmnate souces of numecal ll-condtonng by tuncatng elatvely small sngula values f desed Once CM and N ae detemned, Eqs (21) and (22) gve the fomulas fo the equed coeffcents of the th actuato falue detecton equaton III Smulaton Results Consde the followng thee-nput, thee-output, sxth-ode dynamcal system (Fg 1): [ ] [ ] 03 3 I A c =, B M 1 K K 1 c = C M 1 C = [I ] (23) whee m 1 = m 2 = m 3 = 1 kg, c 1 = c 2 = c 3 = 005 N s/m, and k 1 = 20, k 2 = 30, k 3 = 50 N/m, m c 1 + c 2 c 2 0 M = 0 m 2 0, C = c 2 c 2 + c 3 c m 3 0 c 3 c 3 k 1 + k 2 k 2 0 K = k 2 k 2 + k 3 k 3 (24) 0 k 3 k 3 The system s sampled wth an nteval t = 01 sfom whch a dscete-tme epesentaton s deved (wth the usual assumpton of a zeo-ode-hold on the nput) fo the subsequent detemnaton of the actuato falue detecton equatons Because n = 6, q = 3, and = 3, the condton p(q + 1) n + 1ssatsfed wth p 4 Although any value of p 4 can be used, let us choose p = 4nths numecal example Fo each actuato, the poduct CM s calculated by solvng Eq (9) and N fom Eq (14) The length of N s nomalzed to one The coeffcents fo the actuato eo equatons gven n Eq (20) ae computed fom Eqs (21) and (22) Dung a 50-s tme nteval, suppose the followng falue pofle occus Actuato numbe 1 fals dung the tme nteval 10 t 15 s and 30 t 35 s, actuato numbe 2 fals dung 10 t 15 s, and actuato numbe 3 fals dung 15 t 35 s An actuato s consdeed to fal when t poduces an nput to the plant that s dffeent fom a commanded nput The commanded nputs ae taken to be andom exctaton n ths case although any othe nput hstoes can be used The actuato eos e 1, e 2, e 3 descbe coectly the pecedng falue pofle as shown n Fg 2 Note that the falue pofle fo each actuato s detemned coectly egadless of whethe any othe actuato fals o not IV Expemental Results Ths secton dscusses the expemental valdaton of afoementoned actuato falue detecton algothm Two key elements of the expement ae system dentfcaton and falue detecton The poton of system dentfcaton povdes a baselne model, whch epesents a healthy state of the system and consttutes the coeffcents of scala functon defned n Eq (20) Falue detecton

4 898 KOH ET AL a) b) c) Fg 2 Eo functon pofle fo a spng-mass-dampe system: a) actuato 1, b) actuato 2, and c) actuato 3 Table 1 Thee senso sets: (A), (B), and (C) n Fg 4b Locaton set Bay (senso) numbe (A) Bay 4 (senso 1), bay 8 (senso 4) (B) Bay 5 (senso 2), bay 6 (senso 3) (C) Bay 5 (senso 2), bay 8 (senso 4) Fg 3 Pctue of eght-bay NASA tuss stuctue pocess begns by feedng the measued outputs nto Eq (20) and montong ts esdual sgnal n eal tme If the esdual sgnal exhbts nonzeo value, the coespondng actuato s consdeed to be malfunctonng A Test Setup Two electomagnetc shakes seve as ndependent actuatos that ae attached to the test stuctue The test bed s a 40-m-long, standad NASA tuss stuctue wth 109 stuts and 32 node balls, whch connect the stuts n tuss assembly 13 Ths cantleveed tuss spans eght squae bays as shown n Fg 3 Each stut s made of hollow alumnum tube havng 05-n oute damete wth 01-n thckness The Young s modulus of stut s E = 703e 10 N/m, and each shake connects wth the stuctue though a flexble stnge od to tansmt the nput foce only n axal decton The fst shake s located at the fee end, and the second one s nstalled n the mddle secton of the tuss Fgue 4 shows a schematc of the tuss stuctue, llustatng the poston of two shakes, bounday condtons, and locatons of sensos Notce that two hanges vetcally suppot the tuss to pevent vetcal motons as shown n Fg 4a Also, both shakes ae placed on the same plane to ensue the exctaton of only hozontal modes In ths expement, acceleometes ae used as output sensos Fo a two-nput system, the mnmum numbe of ndependent sensos to dentfy each actuato falue s two (q ) Hence, a pa of acceleometes s nstalled at thee dffeent sets of locatons, (A), (B), and (C), as shown n Table 1 The locaton (A) s collnea wth two actuatos at bay 4 (senso 1) and 8 (senso 4), wheeas (B) s located at bay 5 (senso 2) and bay 6 (senso 3) so that both acceleometes ae not collnea wth actuatos as shown n Fg 4b The locaton (C) les n bay 5 (senso 2) and bay 8 (senso 4) such that one acceleomete becomes collnea wth actuato, wheeas the othe one does not The expement has been epeated to collect nput-output data fom each dffeent senso locaton In the expement, shakes ae dven by band-lmted whte-nose nputs fom the amplfe, whch s connected to a dspace boadmplemented compute The dvng nputs to the stuctue ae measued fom foce tansduces nstalled between stnge and node-ball jont of tuss stuctue Because Eq (1) does not hold a dect tansmsson tem D, the devaton of eo functon has been slghtly modfed to accommodate acceleaton output The Toepltz matx n Eq (4) can be modfed as D CB D 0 T = CAB CB D 0 CA p 2 B CAB CB D (25)

5 KOH ET AL 899 a) b) Fg 4 Confguaton of thee-dmensonal tuss stuctue: a) schematc of tuss, showng bounday condtons; and b) ovehead vew of tuss, showng the locaton of shakes and acceleometes Smla to Eq (8), we nclude the poduct of M y p (k) and pemultply the equaton wth C such that y(k + p) = ( CA p + CM O ) x(k) + (CC 1 + CM T 1 )u p 1 (k) + +(CC + CM T )u (p) (k) CM y p (k) + D 1 u 1 (k + p) + + D u (k + p) (26) Hee, the necessay condton fo the exstence of CM becomes p(q + 1) n, and the mposed condton elmnates the state tems and nput vectos smla to Eq (9) as follows: y(k + p) = (CC + CM T )u (p) (k) CM y p (k) + D 1 u 1 (k + p) + + D u (k + p) (27) If we pemultply Eq (27) wth a ow vecto N to get d of D 1, D 2,,D except D, the actuato falue detecton equaton wth acceleaton output fnally becomes e (k) = y(k) + CM y p (k p) (CC + CM T )ū (p) (k p) D ū (k) (28) The majo dffeence n developng an eo functon wth acceleaton measuement s the pesence of D tems n dagonal components n the Toepltz matx [see Eq (25)] Also, CB tems ae eplaced wth D n most of the devaton B Results The test stuctue s smultaneously excted by andom nputs fom both shakes Acceleaton measuements ae ecoded wth samplng tme, t = 0001 s up to 50 s Based on collected nputoutput data, obseve/kalman-flte dentfcaton egensystem ealzaton algothm (OKID-ERA) has been employed fo system dentfcaton The ode of the dentfed state-space model has been etaned as 160 states The numbe of etaned states s chosen fom numeous tals havng dffeent numbe of states, and the dentfed model wth 160 states shows the most accuate estmaton and pedcton esult among all othes Fom ths dentfed state-space model, natual fequences of the tuss stuctue fo the fst two modes ae dentfed as 131 and 613 Hz, whch coespond to fst two n-plane bendng modes, espectably The thd global mode s not dstngushable fom ndvdual membe s local modes, whch typcally show up afte 80 Hz (Ref 13) The dentfed state-space model has been fomulated to an nput-output equaton (e, actuato eo functon) fo each ndvdual actuato Havng obtaned baselne nput-output data, falues of actuatos ae smulated, expementally, by tunng off and on the shakes ntemttently Smla to the spng-mass-dampe smulaton, shake 1 tuns off fo the nteval 20 t 40 s, wheeas shake 2 sequentally tuns off dung the nteval 10 t 15 s and 30 t 40 s In othe wods, the actuato falue n ths expement s smulated by tunng off the powe of shakes fo unknown tme ntevals Fgue 5 exhbts test esult n whch the pofle of eo functon e (k) coectly ndcates the nstant of falue of th actuato Each scala functon ndependently geneates nonzeo eo sgnal coespondng to the coect falue nstants, egadless of the condton of othe actuato In Fg 5, two sensos ae collnea wth each actuato, mplyng that nput foces ae dectly tansmttng to the outputs though a stut membe [senso locaton (A)] Fgues 6 and 7 also pesent the test esult of dffeent sets of senso locatons (B) and (C), espectvely

6 900 KOH ET AL Fg 5 Eo functon pofle fom measuements of sensos 1 and 4: locaton (A) Fg 6 Eo functon pofle fom measuements of sensos 2 and 3: locaton (B) Compason of Fgs 5 7 eveals that the locaton of the sensos s not a ctcal facto n tems of qualty of eo sgnal Futhemoe, t appeas that a small numbe of sensos (only two acceleometes) suffcently dentfes actuato falue n a consdeably complcated system Howeve, the dectonal popetes of sensos ae cucal because the unexcted mode of dynamcs such as vetcal moton cannot be measued In ths expement, both shakes and sensos ae algned wth the same hozontal decton Theefoe, two sensos ae enough to dstngush the falue of actuatos It s ntutvely obvous that only the obsevable dynamcs of the system can be attbuted to the fomulaton of nput-output eo functon The poposed method does not eque a mathematcal model of the test stuctue n physcal coodnates such as stffness, mass, and dampng matces The fomulaton of ndvdual actuato eo functon only eques nput-output data, measued fom the healthy state of the system Howeve, as s obvous fom both expement and the fomulaton of nput eo functon, the qualty of dentfed state-space model s a ctcal facto to obtan dstngushable eo sgnals ove the geneal level of measuement nose Because the measuement nose could be sgnfcant n pactcal applcaton, the closed-loop type technque 8 that enhances the senstvty of eo sgnal would be a easonable appoach to mpove the sgnal-tonose ato

7 KOH ET AL 901 Fg 7 Eo functon pofle fom measuements of sensos 2 and 4: locaton (C) V Conclusons Ths poof-of-concept study demonstates the pefomance of newly developed actuato falue detecton algothm Though the concept of nteacton matx n state-space famewok, a sees of decoupled nput-output eo functons have been fomulated Each eo functon povdes an ndcatve measue fo actuato falues by poducng nonzeo esdual sgnal when the actuato fals to poduce command nputs In the NASA eght-bay tuss expement, the poposed algothm successfully dentfes falues of two electomagnetc shakes that ae attached to the tuss stuctue Consdeng the lmted numbe of measuements and the complexty of the stuctue, test esults ae n close ageement wth smulated example, ensung the capablty of the poposed pocedue n detectng and solatng the smultaneously and abtaly occung multple actuato falues Acknowledgments The authos acknowledge the suppot of the Texas Insttute fo the Intellgent Bo-Nano Mateals and Stuctue fo Aeospace Vehcles, funded by NASA Coopeatve Ageement NCC At the tme of the study, B H Koh was afflated wth Rce Unvesty Refeences 1 Menke, T E, and Maybeck, P S, Senso/Actuato Falue Detecton n the Vsta F-16 by Multple Model Adaptve Estmaton, IEEE Tansactons on Aeospace and Electonc Systems, Vol 31, No 4, 1995, pp Fank, P M, Fault Dagnoss n Dynamc Systems Usng Analytcal and Knowledge-Based Redundancy A Suvey and Some New Results, Automatca, Vol 26, No 3, 1990, pp Chen, J, and Patton, R J, Robust Model-Based Fault Dagnoss fo Dynamc Systems, Kluwe Intenatonal Sees on Asan Studes n Compute and Infomaton Scence, Vol 3, Kluwe Academc, 1999, pp Chow, E Y, and Wllsky, A S, Analytcal Redundancy and the Desgn of Robust Falue Detecton Systems, IEEE Tansactons on Automatc Contol, Vol 29, No 7, 1984, pp Lou, X, Wllsky, A S, and Veghese, G C, Optmally Robust Redunancy Relatons fo Falue Detecton n Uncetan Systems, Automatca, Vol 22, No 3, 1986, pp Clak, R N, Fosth, D C, and Walton, V M, Detectng Instument Malfunctons n Contol Systems, IEEE Tansactons on Aeospace Electonc Systems, Vol 11, No 4, 1975, pp Sebold, S, and Wenet, K, A Tme Doman Method fo the Localzaton of Cacks n Rotos, Jounal of Sound and Vbaton, Vol 195, No 11, 1996, pp Koh, B H, Damage Identfcaton of Smat Stuctues Though Senstvty Enhancng Contol, PhD Dssetaton, Thaye School of Engneeng, Datmouth College, NH, Mach Sun, D, and Tong, L, Closed-Loop Based Detecton of Debondng of Pezoelectc Actuato Patches n Contolled Beams, Intenatonal Jounal of Solds and Stuctues, Vol 40, No 10, 2003, pp Phan, M Q, Lm, R K, and Longman, R W, Unfyng Input-Output and State-Space Pespectves of Pedctve Contol, Dept of Mechancal and Aeospace Engneeng, Pnceton Unv, TR 3044, Pnceton, NJ, Sept Lm, R K, Phan, M Q, and Longman, R W, State Estmaton wth ARMakov Models, Dept of Mechancal and Aeospace Engneeng, Pnceton Unv, TR 3046, Pnceton, NJ, Oct Goodzet, N E, and Phan, M Q, System Identfcaton n the Pesence of Completely Unknown Peodc Dstubances, Jounal of Gudance, Contol, and Dynamcs, Vol 23, No 2, 2000, pp Kashangak, T A-L, Gound Vbaton Tests of a Hgh Fdelty Tuss fo Vefcaton of on-obt Damage Localzaton Technques, NASA TM , May Phan, M Q, Hota, L G, Juang, J-N, and Longman, R W, Lnea System Identfcaton va an Asymptotcally Stable Obseve, Jounal of Optmzaton Theoy and Applcatons, Vol 79, No 1, 1993, pp Juang, J-N, Phan, M Q, Hota, L G, and Longman, R W, Identfcaton of Obseve/Kalman Flte Makov Paametes: Theoy and Expements, Jounal of Gudance, Contol, and Dynamcs, Vol 16, No 2, 1993, pp Phan, M Q, Hota, L G, Juang, J-N, and Longman, R W, Impovement of Obseve/Kalman Flte Identfcaton (OKID) by Resdual Whtenng, Jounal of Vbaton and Acoustcs, Vol 117, Apl 1995, pp Juang, J-N, and Pappa, R S, An Egensystem Realzaton Algothm fo Model Paamete Identfcaton and Model Reducton, Jounal of Gudance, Contol, and Dynamcs, Vol 8, No 5, 1985, pp