Damage detection of frames using the increment of lateral displacement change

Transcription

1 0 Wang e al. / J Zheiang Univ SCI 005 6A():0- Journal of Zheiang Universiy SCIENCE ISSN hp:// zus@zu.edu.cn Damage deecion of frames using he incremen of laeral displacemen change WANG Jian-min ( 王建民 ), CHEN ong-zhu ( 陈龙珠 ) (School of Civil Engineering and Mechanics, Shanghai Jiao Tong Universiy, Shanghai 0040, China) wangianmin@su.edu.cn; lzchen@su.edu.cn Received Jan. 4, 004; revision acceped Mar. 5, 004 Asrac: The mehod proposed in his paper is ased on he fac ha he damage in differen ypes of srucural memers has disincive influence on he srucural siffness. The inrinsic mechanical propery of he srucure is apped and fully uilized for damage deecion. The simplified model of he flexiiliy of frames reas he individual soreys as springs in series and he frame as an equivalen column. I fully considers he main deformaion of all eams and columns in he frame. The deformaion propery of he simplified model accorded well wih ha of he acual frame model. The oained incremen of laeral displacemen change (IODC) a he sorey level was found o e very sensiive o he local damage in he frame. A damage deecion mehod is proposed using he IODCs as he damage idenificaion parameers. Numerical examples demonsrae he poenial applicailiy of his mehod. ey words: Damage deecion, Incremen of laeral displacemen change, Saic es, Frame, Equivalen column doi:0.6/zus.005.a00 Documen code: A CC numer: TU;O4 INTRODUCTION Damage deecion of srucures is very imporan for ensuring and evaluaing he safey of srucure sysems during heir lifeime. The approaches developed in his field may e generally classified ino dynamic idenificaion approach using dynamic es daa and saic idenificaion approach using saic es daa (Wang e al., 00). The dynamic idenificaion approach has een highly developed, alhough several inheren drawacks and prolems handicap he full uilizaion of his approach: () The necessary exciaion response is generally difficul o e oained saisfacorily, especially for pracical srucures in he field; () The polluion of he measuremen noise grealy affecs he precision of es daa, which is more serious in he high-order modal daa, such as he srain mode, curvaure mode; () Damage in srucures will cause changes in heir siffness, mass and damping. In some dynamic idenificaion mehods, i is assumed ha here is no damping or ha he damage does no cause changes of he mass and/or damping. How o make he analyical mehod reasonaly applicale o acual damage deecion is a key prolem; (4) The change in dynamic response of he srucure is generally a macro reflecion of he damage siuaion, and is insensiive o he local elemen damage. Compared wih dynamic idenificaion mehods, he saic idenificaion mehods are usually simple and easily implemened. The saic idenificaion mehod has pracical value, paricularly in he laoraory where saic es daa can e oained wih relaively high accuracy. The prolems in he saic idenificaion mehods are ha he usale informaion is relaively less, and ha he idenificaion resul is more influenced y he seleced loading cases. In oh he dynamic and saic idenificaion mehods, he incompleeness of he es daa and he finieness of he oainale damage informaion are wo grea osacles. arious model condensaion echniques were developed (Guyan, 965; oh e al.,

2 Wang e al. / J Zheiang Univ SCI 005 6A(): ) o resolve he incompleeness of he es daa. For many large or complex srucure sysems, various simplified models were developed, e.g., lumped-mass models or shear-uilding models. A prolem arising from he oversimplificaion of models is ha he change in siffness induced y he local damage ends o spread ou or diffuse ino oher adacen elemens. This siffness diffusion prolem makes he damage deecion uncerain and inaccurae (oh e al., 995; Nake and Yao, 988). By inroducing an improved condensaion mehod o idenify he local damage in muli-sorey frame uildings, oh e al. presened a mehod ha can idenify he siffness reducion a he sorey level only due o he column damage, in which, he eam was assumed o e rigid. To correlae well he experimen model wih he assumed siuaion, he floor siffness of he model was inensified y race ars. In realiy, eams in many momen-resising frame-ype srucures are no rigid. The deformaion and possile damage in eams are exisen. The assumpion of rigid eams will undouedly susanially overesimae he frame siffness. To make he heoreical analysis have pracical applicaion meaning, he simulaion model should e possily correlaed wih real srucures. The model canno e oversimplified, and he main deformaion of all memers in srucures should e considered. Many advanced compuing mehods have een developed for srucural damage deecion as an inverse prolem, e.g. geneic algorihm (Chou and Ghaoussi, 00), arificial neural nework (Pandey and Barai, 995; Yun and Bahng, 000; Waszczyszyn and Ziemiański, 00; o e al., 00) and various minimizaion opimizaion algorihms (oh e al., 995; Helmsad and Shin, 997). There are several mehods for solving he damage deecion prolems only hrough purely numerical opimizaion algorihms. These mehods exhausively searched he damaged memers from all memers in he srucure solely according o he errors eween he calculaed and measured resuls. This scheme will work ineffecively as damage cases are complicaed and he srucure scale is large and complex. In fac, o ap and uilize he inrinsic mechanical characerisics of he srucure is mos essenial, whichever echnique or mehod is developed for damage deecion. Alhough he deerioraion in srengh or he accumulaion of plasic srain is sensiive o damage, he changes in hese parameers are mainly concenraed on he local damaged memers. The measuremen of hese parameers is relaively difficul and inconvenien, especially for large srucure sysems. Wih respec o hese parameers, he change in he displacemen of he srucure due o he damage is relaively easily o e measured, and i direcly reflecs he change in he srucural flexiiliy. Therefore, o analyze he flexiiliy change for damage deecion has more pracical meaning. According o he aove-menioned analysis, he auhors fully considered he main deformaion of eams ogeher wih ha of columns when formulaing he laeral flexiiliy of muli-sorey frame srucures. By reasonaly simplifying he model and formulaing he laeral flexiiliy of he frame, he oained incremen of laeral displacemen change (IODC) a he sorey level was found o e very sensiive o he local damage. A he same ime, he rules on he damage in differen ypes of srucural memers has is disincive influence on he IODCs of he srucure were oained. A las, a damage deecion mehod is proposed. The disinguishing characerisic of he mehod is ha, i can effecively idenify he damage in differen memers (e.g. he column and/or eam) a he sorey level in he frame srucure. Even hough for complicaed damage siuaions wih many damaged memers, using he IODCs and he disincive rules of he damage in differen memer ypes on he IODCs can approximaely idenify he damage a he sorey level. FEXIBIITY FORMUATION OF FRAME STRUCTURES The mehod simplifying he muli-sorey frame srucure model and formulaing he laeral flexiiliy used for damage deecion is ased on he work of Sameer and Jain (99; 994), Dua e al.(000a; 000). To faciliae inroducion, a one-ay, muli-sorey sandard plane frame model was adoped, as shown in Fig.. All eams and columns are similar and have idenical cross-secion dimensions, respecively. All sorey heighs are equal. The formulaion analysis is ased on he following assumpions (Dua e al., 000a; 000):

3 04 Wang e al. / J Zheiang Univ SCI 005 6A():0-. The srucure ehavior is elasic and linear;. Cener-line dimensions are used, neglecing he siffness conriuion of finie-sized oin zones a he uncions of eams and columns;. The columns in he oom sorey are fixed agains ranslaion and roaion on he ase; oher nodes are free; 4. The shear deformaion in he columns is negligile, and he laeral displacemen due o he axial deformaion in columns is no considered. To formulae he laeral flexiiliy of he frame, he frame is firs divided ino individual soreys, and he flexiiliy of he individual sorey is analyzed. The analyical uni is isolaed y making cus a each eam. For generalizaion of analysis, he isolaed analyical uni model in Green (978) was used and shown in Fig.. I is assumed ha he poins of inflecion for all eams and columns excep columns in he oom sorey occur a he mid span; and ha he locaion of inflecion poins of columns in he oom sorey is deermined y Eq.(40) in Sameer and Jain (994). The laeral deformaion of a column consiss of wo pars: one is due o he roaion of he op and oom ends of he column, and he oher is he deflecion of he column acing as a canilever suppored a he oins (Sameer and Jain, 99), as shown in Fig.. aeral flexiiliy of inermediae soreys For he column in he inermediae soreys, he laeral deflecion can e expressed as in Sameer and Jain (99): he curren sorey respecively;, θ θ roaion siffness of op and oom ends respecively. 6 N θ N 6 θ 6 6 () here, lengh of he eam; E Young s modulus of he eam; N numer of eams meeing he column a he end. N i i N i i, (4) i i I, I ineria momens of he eams meeing he column a he op and oom ends, respecively. Susiuing Eqs.() (4) ino Eq.() yields P000 N h θ h θ h () m c c c Fig. Plane frame model c m where c laeral relaive displacemen eween he ends of he column; E c Young s modulus of he column; I c he ineria momen of he column; shear force applied on he column; hhe sorey heigh; θ, θ roaion angles of op and oom ends respecively. h/ h/ θ ( h + h ) ( h + h ) a, θ () θ θ in which, h a, h heighs of soreys aove and elow / Fig. Isolaed uni of inermediae soreys for analyzing deformaion due o ending of eams and columns /

4 Wang e al. / J Zheiang Univ SCI 005 6A():0-05 h ( h + h) h ( h + h) h + + m a c c c 4 4 (5) h + c c col c (0) For he plane frame, he roaion siffness of he op and oom ends of he column is he conriuion of he ending siffness of eams lying in he ending plane of he frame and meeing he end. I is assumed ha he axial deformaion of he eams is negligile. The compaiiliy requires equal laeral displacemen of all columns in he same sorey. The laeral siffness of a single column in he inermediae sorey of he frame is expressed as h h + h h + h h (6) m c c col m c c c a For sandard frames wih idenical eams, idenical columns and equal sorey heighs, Eq.(6) may e furher simplified as h + m c c col c c c / c (7) where, E I h. A las, he siffness of individual columns in an inermediae sorey is summed o form he siffness of he sorey, m Nc (8) m col in which, N c is he numer of columns in he sorey. The laeral flexiiliy of he inermediae sorey is as follows, f m / m (9) aeral flexiiliy of he op sorey The formulaion of he laeral siffness of he op sorey is similar o ha of he inermediae sorey. The only difference is ha here is nohing aove he op sorey. Therefore, he erm h a in Eq.(5) equals zero for he op sorey, and he siffness of individual columns is deduced as The laeral siffness of he op sorey is formulaed as Nc () col The laeral flexiiliy of he op sorey is as follows, f / () aeral flexiiliy of he oom sorey For he oom sorey, ecause he columns are fixed agains ranslaion and roaion on he ase, he resrains on wo ends of he columns are no idenical. The poin of inflecion will have a shif owards he end where he momen-resising siffness is smaller, as shown in Fig.. The column has is poin of inflecion deermined y Eq.(40) in Sameer and Jain (994). For he sandard frame, y, y may e approximaely calculaed as follows c c c c + y h h, y h h () 6 6 The laeral relaive displacemen eween he ends of he column in he oom sorey is expressed as ( y ) ( y ) (4) c θy c c c c / c y / y Fig. Isolaed uni of oom sorey for analyzing deformaion due o ending of eams and columns

5 06 Wang e al. / J Zheiang Univ SCI 005 6A():0- And he laeral siffness of he individual column is expressed as follows The following is used o verify he accuracy of his mehod o formulae he flexiiliy of he frame. h c c col 6( ) ( ) ( + c) + ( c) ( c ) 8 (5) The laeral siffness of he oom sorey is formulaed y summing he siffness of individual columns Nc (6) col The laeral flexiiliy of he oom sorey is f / (7) aeral flexiiliy of he frame srucure Afer he analysis for all individual soreys, he laeral flexiiliy of he frame can e oained y reaing he soreys as springs in series, n n i + m + i F f f f (8) The laeral flexiiliy a he h sorey heigh of he frame is formulaed as i m i F f + f, n (9a) F, f (9) In his way, he enire frame is simplified and modeled as a single equivalen column o formulae he laeral flexiiliy. The simplified model is shown in Fig.4a. Firs, he siffness of individual columns in a sorey is summed o oain he siffness of he individual sorey; and hen, he overall flexiiliy of he frame is oained y reaing all individual soreys as a andem springs sysem. When he frame srucure is sueced o a laeral poin load a he op end, he oal laeral deformaion of he frame equals he summaion of he inersorey deformaion of all individual soreys. (a) Fig.4 Simplified frame model and real column (a) Simplified model; () The real column erificaion of he flexiiliy simplificaion mehod The physical dimension of he frame model in Fig. is, span widh W500 mm, frame heigh H500 mm, sorey heigh h500 mm, cross-secion of eams and columns is 500 mm, Young s modulus of maerial E06 GPa, Poisson s raio υ0.. Under he laeral poin force P000 N, he laeral displacemen of he frame a he sorey level calculaed from he simplified mehod and ha from he finie elemen mehod (FEM) are shown in Fig.5. I is clear ha he resul calculaed from he simplified mehod is saisfacory and agrees well wih ha from FEM. Sory numer FEM resul Simplified mehod To make he simplified mehod eing more accurae, Eqs.(8) and (9) are furher modified as n n i + i m + n i F w f w f w f () aeral displacemen (mm) Fig.5 aeral displacemen of he frame

6 Wang e al. / J Zheiang Univ SCI 005 6A():0-07 i i m i F w f + w f, n F w f, (0) where w i is he weigh corresponding o he ih sorey. Under he loading case of a laeral poin force P applied on he op end of he frame column, he laeral displacemen a each sorey heigh of he frame is approximaely expressed as D PF ( n) () The inersorey relaive displacemen of he frame is as follows, f R D D Pf ( D 0; n) () 0 is he laeral flexiiliy of he h individual sorey. ANAYSIS OF THE DAMAGE DETECTION According o he mehod of formulaing he flexiiliy in he las secion, he damage in differen ypes of memers (he eam and column) in he frame will have disincive influence on he laeral displacemen. A he same ime, a new damage idenificaion parameer, he oained incremen of laeral displacemen change (IODC) a he sorey level of he frame is found o e very sensiive o he local damage. The following gives he deailed analysis. Definiion of he IODC I is assumed some memer in he h sorey of he frame is damaged. The inersorey relaive displacemen of he frame afer he memer damage in he h sorey is expressed as ( R ) ( D ) ( D ) P( f ) ( D 0, n) 0 () Here, he IODC of he h sorey in he frame is defined as I ( R ) R [( D ) D ] [( D ) D ] d D D P[( f ) f ] P f ( n, D 0) (4) in which, D, D are he laeral displacemen changes a he h and ( )h sorey heighs of he frame efore and afer damage; f is he flexiiliy change of he h sorey due o he memer damage. Eqs.() (4) show ha a definie relaion exiss eween he IODC and he change in he laeral flexiiliy of he individual sorey. Taking he inermediae sorey in he sandard frame as an example, i can e seen from Eq.(7) ha he laeral siffness of he individual sorey is influenced y he flexure rigidiy of he columns in he sorey and ha of he eams meeing he columns a he op and oom ends. The flexiiliy formula of he individual sorey shows ha he damage in eams and columns has differen influence characerisics on he siffness of he individual sorey: The damage of he column only reduces he siffness of is own sorey (when i is individually analyzed). Differen from he column, he eam lies eween wo adacen soreys. Is damage will simulaneously induce reducion in he siffness oh of he soreys aove and under he eam. In paricular cases, he reducion of siffness in soreys aove and under he damaged eam are approximaely equal in he sandard frame. Fig.6 shows he IODCs of he frame model in Fig. due o he damage in differen memer ypes. I is clear ha he damage in differen ypes of memers follows disincive rules of he IODCs a he sorey level. When column 4 (which lies in he second sorey) in he frame is damaged y simulaing 0% reducion of he Young s modulus, he IODCs in oher soreys excep he second sorey are very small. Beam 6 lies eween he second and hird soreys; is damage causes approximaely equivalen IODCs in he second and hird soreys, and he IODCs in oher soreys are exremely small. Influence of he damage in eams and columns on he laeral displacemen Afer simplificaion of he frame model and formulaion of he overall laeral flexiiliy, Eqs.(8) (0) show ha, when here is damage in he ih sorey column, he laeral flexiiliies a he sorey heighs aove he ih sorey all increase. The incremen approximaely equals ha of he ih sorey 0

7 08 Wang e al. / J Zheiang Univ SCI 005 6A():0- IODC (mm) Column 4 in frame is damaged y 0% Beam 6 in frame is damaged y 0% Columns 4,5,7,8 in frame are damaged y 0% 4 Elemen in real column is damaged y 0% Fig.6 IODC a he sorey level of he frame and real column F ( F ) F f ( i n) (5) D ( D ) D D ( i n) (6) i i where, F,( F ), D,( D) are he flexiiliies and he laeral displacemens a he h sorey heigh of he frame efore and afer he damage; f i is he flexiiliy change of he damaged sorey when i is individually analyzed. For he damage in eams, he flexiiliy changes a he heighs of soreys aove he damaged eam approximaely equal he sum of he flexiiliy changes of he wo soreys aove and under he damaged eam when hey are individually analyzed. F F F f + f i n (7) i i ( ) ( ) i i D ( D ) D D + D ( i n) (8) f i, f i are flexiiliy changes of he wo soreys aove and under he damaged eam during he individual analysis. The changes in he laeral displacemen due o he damage in differen memer ypes are shown in Fig.7. In addiion, he change in he laeral displacemen of he frame due o he memer damage is differen from ha of he real column, which is also shown in Fig.7. The real column model in Fig.4 is used for comparison. Is physical dimensions are: he heigh H000 mm, cross-secion is 500 mm, Young s modulus E06 GPa, Poisson s raio υ0.. Under a laeral poin force P500 N applying on he op end, is displacemen change due o he damage in elemen is shown. Fig.7 shows ha when here is damage in he real column, he displacemen changes a he node heighs aove he damaged elemen all have a relaively large incremen. However, he siuaion is differen in he frame srucure. Changes in laeral displacemen (mm) Column 4 in frame is damaged y 0% Beam 6 in frame is damaged y 0% Elemen in real column is damaged y 0% 0 Fig.7 Displacemen change due o elemen damage in frame and real column Scheme using he IODCs for damage deecion According o aove-menioned analysis, he IODC of each sorey in he frame is a parameer very sensiive o he local damage; and he damage in differen memer ypes follows disincive rules of he IODC a he sorey level. A damage deecion mehod is developed ased on hese characerisics. Due o he physical symmeric propery of he frame, he damage in differen columns in he same sorey has he same influence on he displacemen. I is assumed in he following analysis ha he damage in he column means ha all columns in he same sorey have same exen of damage. The columns in he same sorey are seen as a uni o e deeced. From Fig.6, oh Cases and have approximaely he same influence characerisics on IODCs of frame. In his siuaion, only he IODCs mighily work ineffecively in disinguishing he differen damage paerns. Therefore, he naural frequency changes of he frame are comined ogeher wih he IODCs for damage deecion y designing a BP neural nework. The IODCs a he sorey level and he frequency change raes of he firs several modes are normalized respecively, and hen are comined ogeher as he inpu vecor of he neural nework; he oupu of he nework is he damage exen of memers. A deailed illusraion for his mehod is given

8 Wang e al. / J Zheiang Univ SCI 005 6A():0-09 hrough numerical examples in he nex secion. NUMERICA EXAMPES The effeciveness of he presened mehod is verified y wo numerical examples. In his paper, all he possile damage paerns when here are wo damaged memers a mos are considered. Example The plane frame model in Fig. is adoped. The frequency change raes of he firs hree laeral free-viraion modes are comined wih he IODCs as he inpu vecor of he neural nework. The oupu of he nework is assumed o have en unis, i.e. a eam and a column uni in each sorey of frame. The numer of all possile damage paerns considered is Np C5 + C5 + C5 C5 55. Of which, fify paerns are seleced o rain he nework, and he oher five paerns are used as he esing paerns. Two damage exens are considered during generaion of he damage samples, 0% and 40% reducion in he Young s modulus. One hundred raining samples are generaed. The hree-layer BP neural nework srucure is adoped; he acivaion funcions on he hidden and oupu layers of he BP nework are aken as he log-sigmoid and linear ransfer funcions, respecively. The improved ack-propagaion algorihm is employed o rain he nework. Afer successful raining, he srucure of he nework is The eigh esing samples lised in Tale are divided ino wo groups, he firs four samples are no included in he raining paern se; he las four are included in he raining paern se, u he damage exen is differen from ha in he raining samples. The IODCs of he esing samples are shown in Fig.8, and he esing resuls from he nework are shown in Fig.9. Damage exens of less han 5% are ignored in he idenificaion resuls. I can e seen ha he nework generally can give saisfacory idenificaion oh of he damaged memers and damage exen. For he las four cases, he deecion resuls are relaively more saisfacory. In Case 6, he column in he hird sorey is idenified as having rivial damage ogeher wih he eam in he second sorey. By furher comining wih he corresponding IODC rule in Fig.8, i can e concluded ha only he eam in he second sorey is damaged. Comining wih he rules of IODCs in Fig.8, he idenificaion resuls of he firs four esing samples direcly from he nework can e furher correcly modified. In Case, i is very clear ha only he column(s) in he second sorey is (are) damaged. Therefore, he eam in he firs sorey can e eliminaed from he damaged elemens. In he same way, he eam of he firs sorey can also e eliminaed from he damaged elemens in Case ; and eams of he firs and fourh soreys can e eliminaed from he damaged elemens in Case 4. Comparison of he idenificaion resuls of all he esing samples showed ha he resuling errors of Cases and are relaively larger. In Case, he column in he second sorey of he frame is misudged wih rivial damage; and in Case, eams in he second and he fifh soreys are misudged wih rivial damage. This is mainly ecause he assumed damage exens in hese wo cases are relaively smaller. Example Fig.0 shows a space frame designed o furher verify he proposed mehod. The physical dimension of he frame is: frame heigh H500 mm, sorey heigh h500 mm, span widhs in X and Y direcions are W x 500 mm, W y 400 mm, Young s modulus E000 MPa, cross-secion of columns and eams is mm. A laeral poin force P 000 N is applied on he op end of he frame in X direcion. The damage in columns and eams in X direcion is considered. The same mehods as ha in Example are used o design and rain he neural nework. A las, four damage samples are presened o es he successfully rained BPNN. The esing resuls are ploed in Fig.. I is clear ha he proposed mehod gives relaively saisfacory idenificaion resuls for he damage siuaion in he complex frame. CONCUSION By simplifying he model and formulaing he laeral flexiiliy of he frame, he IODC a he sorey level of he frame was found o e very sensiive o he local damage. A he same ime, i was found ha he damage in differen ypes of memers follow-

9 0 Wang e al. / J Zheiang Univ SCI 005 6A():0- Examples Tale Tesing damage samples Damage Damage descripion samples Damage locaion (%) Case Columns in he second sorey 40 Case Beams in he firs and fourh soreys 0 Case Columns in he second sorey and eam in he hird sorey 0 Case 4 Columns in he second and fourh soreys 40 Case 5 Columns in he second and hird soreys 0 Case 6 Beam in he second sorey 0 Case 7 Columns and eam in he second sorey 0 Case 8 Columns in he second sorey and eam in he fourh sorey 0 Case Columns in he hird sorey 0 Case Beams in X direcion in he second soreys 0 Case Columns in he firs and fourh soreys 0 Case 4 Beams in X direcion in he firs and hird soreys 0 IODC (mm) IODC (mm) IODC (mm) IODC (mm) (a) (c) (e) (e) (g) IODC (mm) IODC (mm) IODC (mm) IODC (mm) () (d) (f) (h) Fig.8 IODCs of esing samples in Example (a) Case ; () Case ; (c) Case ; (d) Case 4; (e) Case 5; (f) Case 6; (g) Case 7; (h) Case 8

10 Wang e al. / J Zheiang Univ SCI 005 6A(): C B C B C B C4 B4 C5 B5 (a) C B C B C B C4 B4 C5 B5 (c) C B C B C B C4 B4 C5 B5 (e) C B C B C B C4 B4 C5 B5 (g) C B C B C B C4 B4 C5 B5 () C B C B C B C4 B4 C5 B5 (d) C B C B C B C4 B4 C5 B5 (f) C B C B C B C4 B4 C5 B5 (h) Fig.9 Idenificaion resuls of esing samples in example (C-Column; B-Beam) (a) Case ; () Case ; (c) Case ; (d) Case 4; (e) Case 5; (f) Case 6; (g) Case 7; (h) Case 8 P P Y X Fig.0 Space frame model ed disincive rules of IODCs. A damage deecion mehod is proposed ased on he aforemenioned analysis. Numerical examples demonsrae he poenial applicailiy of he mehod. The mehod can effecively idenify he damage in differen ypes of memers a he sorey level of he frame. Even for more complicaed damage paerns, he IODCs a he sorey level of he frame can approximaely indicae which soreys are damaged. The deecion of

11 Wang e al. / J Zheiang Univ SCI 005 6A(): C B C B C B C4 B4 C5 B5 (a) C B C B C B C4 B4 C5 B5 (c) C B C B C B C4 B4 C5 B5 () C B C B C B C4 B4 C5 B5 (d) Fig. Idenificaion resuls of esing samples in example (C-Column; B-Beam) (a) Case ; () Case ; (c) Case ; (d) Case 4 more complicaed damage paerns in large-scale srucures needs furher sudy in fuure research o deermine how his mehod scales up. References Chou, J.H., Ghaoussi, J., 00. Geneic algorihm in srucural damage deecion. Compuers and Srucures, 79(4): 5-5. Dua, S.C., Jain, S.., Mury, C..R., 000a. Alernae ank saging configuraions wih reduced orsional vulnerailiy. Soil Dynamics and Earhquake Engineering, 9(): Dua, S.C., Jain, S.., Mury, C..R., 000. Assessing he seismic orsional vulnerailiy of elevaed anks wih RC frame-ype saging. Soil Dynamics and Earhquake Engineering, 9():8-97. Green, N.B., 978. Earhquake Resisan Building Design and Consrucion. an Nosrand Reinhold Company, New York. Guyan, R.J., 965. Reducion of siffness and mass marices. AIAA Journal, ():80. Helmsad,.D., Shin, S., 997. Damage deecion and assessmen of srucures from saic response. Journal of Engineering Mechanics, (6): o, J.M., Sun, Z.G., Ni, Y.Q., 00. Muli-sage idenificaion scheme for deecing damage in cale-sayed ap Shui Mun Bridge. Engineering Srucures, 4(7): oh, C.G., See,.M., Balendra, T., 995. Damage deecion of uildings: numerical and experimenal sudies. Journal of Srucural Engineering, (8): Nake, H.G., Yao, J.T.P., 988. Sysem Idenificaion Approaches in Srucural Safey Evaluaion. In: Nake, H.G., Yao, J.T.P.(Eds.), Srucural Safey Evaluaion Based on Sysem Idenificaion Approaches. Wiesaden, Germany, p Pandey, P.C., Barai, S.., 995. Mulilayer percepron in damage deecion of ridge srucures. Compuers & Srucures, 54(4): Sameer, S., Jain, S.., 99. Approximae mehods for deerminaion of ime period of waer ank sagings. The Indian Concree Journal, 66(): Sameer, S., Jain, S.., 994. aeral-load analysis of frame sagings for elevaed waer anks. Journal of Srucural Engineering, 0(5): Wang, X., Hu, N., Fukunaga, H., Yao, Z.H., 00. Srucural damage idenificaion using saic es daa and changes in frequencies. Engineering Srucures, (6):60-6. Waszczyszyn, Z., Ziemiański,., 00. Neural neworks in mechanics of srucures and maerials new resuls and prospecs of applicaions. Compuers & Srucures, 79(6-8):6-76. Yun, C.B., Bahng, E.Y., 000. Susrucural idenificaion using neural neworks. Compuers & Srucures, 77():4-5.