Practical issues in signal processing for structural flexibility identification

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1 See dicuion, tat, and author profile for thi publication at: Practical iue in ignal proceing for tructural flexibility identification Article in SMART STRUCTURES AND SYSTEMS January 2015 DOI: / CITATION 1 READS 47 3 author, including: J. Zhang Southeat Univerity (China) 40 PUBLICATIONS 193 CITATIONS Yun Zhou Hunan Univerity 27 PUBLICATIONS 50 CITATIONS SEE PROFILE SEE PROFILE Some of the author of thi publication are alo working on thee related project: CNSF, China View project All content following thi page wa uploaded by J. Zhang on 02 April The uer ha requeted enhancement of the downloaded file.

2 Smart Structure and Sytem, Vol. 15, No. 1 (2015) DOI: Practical iue in ignal proceing for tructural flexibility identification J. Zhang 1,3, Y. Zhou 2 and P.J. Li 3 1 Key Laboratory of C&RC Structure of the Minitry of Education, Southeat Univerity, Nanjing , China 2 College of Civil Engineering, Hunan Univerity, , China 3 International Intitute for Urban Sytem Engineering, Southeat Univerity, Nanjing , China (Received January 10, 2014, Revied May 17, 2014, Accepted May 28, 2014) Abtract. Compared to ambient vibration teting, impact teting ha the merit to extract not only tructural modal parameter but alo tructural flexibility. Therefore, tructural deflection under any tatic load can be predicted from the identified reult of the impact tet data. In thi article, a ignal proceing procedure for tructural flexibility identification i firt preented. Epecially, practical iue in applying the propoed procedure for tructural flexibility identification are invetigated, which include enitivity analye of three pre-defined parameter required in the data pre-proceing tage to invetigate how they affect the accuracy of the identified tructural flexibility. Finally, multiple-reference impact tet data of a three-pan reinforced concrete T-beam bridge are imulated by the FE analyi, and they are ued a a benchmark tructure to invetigate the practical iue in the propoed ignal proceing procedure for tructural flexibility identification. Keyword: impact tet; ignal proceing; flexibility identification; parameter enitivity 1. Introduction Variou kind of enor have been developed and applied for tructural health monitoring (SHM). The mot frequently ued enor for SHM probably are train gauge and accelerometer. The train gauge i widely adopted becaue it provide train data with very clear phyical meaning which are eay for bridge engineer and owner to ue for afety evaluation of key tructural element. The dynamic train meaurement i uitable for long-term SHM, and it can alo be ued for tructural modal analye (Adewuyi and Wu 2011). Even though the train gauge ha irreplaceable ue value in SHM, it ha the drawback that it i enitive to local tructural damage thu it i not uitable for global tructural parameter identification. In contrat, the acceleration-baed SHM are powerful to identify tructural global parameter. It ha been progreively becoming a maintream way for health monitoring of civil infratructure after over thirty year development (Yu et al. 2010, Chen et al. 2011, Lei et al. 2012a, Lei et al. 2012b, ASCE 2011). The ambient vibration teting i one of the mot widely adopted way for tructural field tet, Correponding author, Profeor, jianzhang.civil@gmail.com Copyright 2015 Techno-Pre, Ltd. ISSN: (Print), (Online)

3 J. Zhang, Y. Zhou and P.J. Li epecially for large-cale tructure like high-rie building and long-pan bridge, becaue they are not eay to excite by human-made force while the ambient vibration tet take the natural force like traffic and wind a excitation. Structural dynamic repone (e.g., acceleration) meaured during the ambient vibration tet are the bai of the well developed vibration-baed SHM mythologie. Modal analyi ha been developed for a long hitory ince the Fat Fourier Tranform (FFT) technology developed to tranform the acceleration in the time domain to the frequency domain. A number of modal analyi method have been developed in the literature, like peak picking, ERA (Eigenytem Realization Algorithm), CMIF (Complex Mode Indication Function), PolyMAX, and PPT (Poly Reference Time-domain) method, to identify tructural modal parameter including frequencie, damping ratio and mode hape from meaured acceleration (Catba et al. 2004, Peeter 2004). Almot all large-cale tructural health monitoring ytem employ the ambient vibration tet and modal analyi a the main tool, upplemented by train gauge and other kind of enor. For intance, the ASCE tructural identification committee recently publihed a tate-of-the-art tructural health monitoring report (ASCE 2011). It collected 5 cae tudie for building health monitoring and 10 cae tudie for bridge health monitoring, almot all of which performed ambient vibration tet and modal analye (Grimmelman et al. 2007, Carden and Brownjohn 2008, Zhang et al. 2009). However, there i till a wide gap between modal analyi reult and tructural afety evaluation in engineering practice. Structure owner generally want to know whether their tructure are damaged and where are the damage, but modal analyi reult are difficult to directly provide uch kind of information. Thi gap ignificantly prohibit the application of the vibration-baed SHM technologie in engineering practice, and it ha become the bottleneck problem in the SHM technology development. Even though a few method uing meaured acceleration for tructural damage detection have been developed, e.g., uing genetic algorithm to earch optimum tructural parameter by minimizing the error between the imulated and meaured acceleration, there i till a far way to apply them in engineering practice. The mot practical way uing ambient vibration tet for tructural health monitoring by far probably i the ix-tep procedure propoed by ASCE tructural identification committee (ASCE 2011). It include field inpection, prior FE modeling, vibration tet, ignal proceing, FE modal calibration, and FE prediction for tructural afety evaluation. Thi ix tep procedure tried to connect the modal analyi reult with tructural afety evaluation through the FE calibration, and it ha been uccefully applied for health monitoring of everal long-pan bridge, like the Henry Hadon bridge and the Throg Neck bridge (Grimmelman et al. 2007, Zhang et al. 2009). Thi ix-tep procedure greatly improve the progre of the tructural health monitoring technology, but it drawback i alo clear. For intance, due to variou kind of uncertainty exit in experiment, data proceing and FE modeling, there may be more than one calibrated FE model perfectly matching the experiment reult (Friwell and Motterhead 1995). Unlike the ambient vibration tet only providing tructural modal parameter, the impact tet i potential to produce not only modal parameter but alo tructural flexibility. By meauring both tructural repone and impacting force, tructural flexibility identification become poible, from which tructural deflection under any tatic load can be predicted. It i known that tructural deflection meaurement from the truck tatic load tet have been defined to be a tandard tructural afety evaluation index in many bridge deign or maintenance code (AASHTO 2007). The impact tet i able to predict tructural deflection under any tatic load, thu it i potential to replace the expenive truck tatic tet and become an effective way for practical bridge afety evaluation. Due to thi merit, the impact tet ha aborbed reearcher interet for bridge health monitoring in

4 Practical iue in ignal proceing for tructural flexibility identification recent year. Dr. Aktan and hi group member have uccefully performed the impact tet on a few bridge (Catba et al. 2005). The reult how that the deflection predicted from the identified flexibility matrix agreed well with thoe from the correponding truck tatic tet. However, the current technology need expert experience to carefully identify tructural flexibility from the impact tet data due to variou kind of uncertainty exiting in experiment and ignal proceing tage. How to quickly and tably identify tructural flexibility and from impact tet data i till a challenging problem. Effort from the following two area are potential to improve the reliability for tructural flexibility identification and deflection prediction: (a) improving the impacting device; Hammer impacting adopted in traditional impact tet generally produce weak impacting force, and the excited repone are greatly affected by traffic noie. Developing advanced impacting device to provide tronger impacting force with a wide frequency range will be much helpful to improve the data quality from the point of view of experiment. (b). developing robut ignal proceing method; The meaured data are unavoidably polluted by noie and other kind of uncertainty, thu robut ignal proceing method are neceary for accurate modal parameter identification epecially for flexibility identification becaue it i much more enitive to uncertainty. A few reearcher are working on the firt apect to develop advanced impacting device. For intance, Moon and hi colleague are developing a drop hammer device for bridge impact teting which i potential to provide a much tronger impact force for bridge excitation (Zhou et al. 2011). In thi article, the focu i put on the econd apect: how to accurately and tably identify tructural flexibility from impact tet data by developing an advanced ignal proceing method and invetigating practical iue in applying the propoed ignal proceing method. For thi purpoe, a ignal proceing procedure identifying tructural flexibility from impact tet data, which include a uit of data pre-proceing trategie and a Sub-PolyMax data pot-proceing method, i firt propoed. Then, Senitivity tudie of three pre-defined parameter required in the ignal proceing procedure will be performed to invetigate how they affect the identification reult through a 3-pan concrete reinforced bridge example. 2. A ignal proceing procedure for tructural flexibility identification 2.1 The ignal proceing framework For a typical bridge impact tet, N 0 enor are mounted to key node of the monitored bridge. N i node are elected a reference node. The impacting device (for intance, the ledge hammer) will hit the reference node one by one, until all referenced node are hit. During each hitting, the impact force and tructure repone at N 0 node will be meaured. Baed on the number of the reference node elected, the impact tet i called the ingle-reference (N i =1) or the multiple-reference ( N i 1) impact tet. Generally the multi-reference impact tet produce better identification reult than the ingle-reference tet, becaue the tructural modal repone epecially thoe in high mode are prone to be well excited by multiple-point hammer hitting. In general the impacting device repeatedly hit a reference node a few time, then the averaging technique i ued to average thee repeated meaurement in the data proceing tage for random uncertainty reduction. After multi-reference impact tet data are meaured, a procedure including a uit of data pre-proceing trategie and a data pot-proceing method a hown in Fig. 1 i propoed to identify tructural modal parameter and flexibility matrix. The data pre-proceing trategie

5 J. Zhang, Y. Zhou and P.J. Li reduce variou kind of uncertainty involved in the tet data, while the Sub-PolyMax method i employed a the data pot-proceing method to identify tructural characteritic. Both the data pre-proceing and pot-proceing technique are preented below. 2.2 Data pre-proceing trategie for uncertainty reduction Due to traffic noie, environment affect, enor enitivity and other reaon, impact tet data are unavoidably involve variou kind of uncertainty. Special attention are required to reduce the noie level and improve the data quality in the data pre-proceing tage for ubequent tructural identification. A uit of data pre-proceing technique are firt developed to clean the data (Fig. 1). Force and acceleration record are firt inpected to identify any malfunctioning enor or pike. If an acceleration time erie contained repetitive pronounced error uch a bia or large pike, or the impact force ha clear rebound force or double click, the channel i tagged and diregarded from further proceing. Subequently, the ampling rate i caled up/down under the tradeoff between the computation time and frequency reolution. The affect of the ampling rate on the tructural flexibility identification will be invetigated later. Thirdly, a digital Butterworth band pa filter with certain cut-off frequencie i deigned to remove the low and high frequency component. Following that, the exponential window i ued to artificially force the repone data to decay to zero at the end of meaurement thu minimizing leakage. The mathematical form of the exponential window i defined a ω(t) = e βt where β = 1 τ (1) Fig. 1 The framework of the propoed ignal proceing method

6 Practical iue in ignal proceing for tructural flexibility identification where τ i a parameter determining how fat the repone data decay to zero at the end of meaurement. Thi parameter affect the accuracy of the identified flexibility, and it will be invetigated in next ection. While the exponential window i applied to the tructural repone, the rectangular window i added to the impact force record to et all the force time erie to be zero except the hort time window when the impact device hit the tructure. After the windowing, the impact force and acceleration are ued to generate pectra. The equation for pectra generation are not provided here for brevity, but it worth to note that the data averaging technique can be ued here to reduce random uncertainty. A preented earlier, the impacting device may repeatedly hit the ame reference node a few time in the experiment tage. Thee repeated force and acceleration are averaged in thi tep to produce averaged pectra. The average technique i a imple but very effective way to improve the data quality. From the generated pectra, frequency repone function (FRF) are etimated by uing the H1, H2 or Hv method. A the lat tep of the data pre-proceing, a data reliability evaluation procedure i neceary to guarantee the cleaned data have adequate quality. The FRF reciprocity and the coherence function plot are ueful to evaluate the quality of the generated FRF, which are the bai for ubequent data pot-proceing for tructural modal parameter and flexibility identification. In thi propoed pre-proceing tage, everal pre-defined parameter are required and their variation affect the flexibility identification reult. They are (a) the parameter,, in the exponential window technology, which affect how fat the acceleration decay to zero at the end of the meaurement; (b) the fft point number, N fft, which determine the frequency reolution ( f=f/n fft ) of the etimated FRF, where F= 1 dt i ampling frequency and dt i the time interval; (c) decimation number, which adjut the ampling rate of both the recorded impacting force and acceleration thu affect the frequency reolution. 2.3 The ub-polymax method for flexibility identification A number of modal analyi method have been developed to identify tructural modal parameter from impact tet data, e.g., the peak picking method, the CMIF method, and the PolyMax method. However, there are few method developed for tructural flexibility identification. In the author known, only the CMIF method i available in the literature for flexibility identification (Catba et al. 2004). In thi ection, a Sub-PolyMAX method i employed, which not only extend the PolyMax method from modal identification to flexibility identification, but alo improve the efficiency and accuracy of the PolyMax method. The baic idea of the Sub-PolyMax method i dividing the whole frequency range to everal narrow frequency band, and performing parameter etimation in each frequency band, finally aembling identification reult from all frequency band for tructural flexibility identification. Compared to the PolyMax method identifying tructural parameter in the whole frequency range, the Sub-PolyMax method ha the merit that computation time i much reduced and the accuracy of the identified reult i greatly improved. Intead of invetigating the FRF data in the wide frequency range in the traditional PolyMax method, only a narrow frequency band, ω ka ~ω kb, involving only the rth tructural mode, ω r, i tudied in the Sub-PolyMax method. The partial fraction of the FRF for the rth mode, H p (ω k ), i written a H p (ω k ) = i=n B i i=1 pi zk i=n A i i z k i=1 (2)

7 J. Zhang, Y. Zhou and P.J. Li where the upercript,, denote that the invetigation i performed in a ubpace of the whole frequency range; k i the kth frequencie line from ka to kb; n i model order; A i and B pi are unknown polynomial coefficient, repectively. By writing the FRF partial fraction in the rth mode a a numerator polynomial divided by a denominator polynomial, modal parameter of the rth mode can be etimated by olving the root of the denominator polynomial. Due to the frequency band conidered i narrow and only the rth mode i involved, the required model order i low. From Eq. (2), the Jacobean LS implementation can be written to olve the polynomial coefficient where, θ = [ β 1 β No α ], β p = [ n 1 z ka z ka 1 z Z p = ka+1 n [ 1 z kb z ka+1 n z kb ], ℵ p = B p0 B pn [ A 0 ], α = [ J θ = 0 (3) Z ], 0 Z J = 1 0 [ 0 0 Z No n H p (ω ka ) A n H p (ω ka ) z ka H p (ω ka ) H p (ω ka+1 ) z ka H p (ω ka+1 ) H p (ω kb ) z kb H p (ω kb ) z ka z ka ℵ 1 ℵ 2 ], ℵ No n H p (ω ka+1 ). n H p (ω kb ) ] It i een that only part of FRF data within the frequency band ω ka ~ω kb are ued in Eq. (3) to identify modal parameter in a pecific tructural mode, thu it ignificantly reduce the Jacobean matrix ize by reducing the number of frequency line. Moreover, the required model order n i very low due to only one mode i included in the invetigated narrow frequency band, thu it further reduce the ize of the Jacobean matrix. In addition, Eq. (2) etimate each mode eparately by uing FRF value in narrow frequency band, the identified modal parameter will not be influenced by FRF data outide the invetigated the frequency band thu they will be more accurate. Even Eq. (3) wa derived on the aumption that only one mode i involved in the invetigated narrow frequency band, it i eay to be extended to the cae when a narrow frequency band involve more mode. After denominator polynomial coefficient, α, are olved from Eq. (3), tructural modal parameter are extracted from the root of the polynomial. The eigen value and the eigen vector of the matrix α can be produced from the eigen analyi, which ha the following relationhip with tructural modal parameter where γ r, γ r = r ω r ± j 1 r 2 ω r, z kb r = e jγ r t (4) r i the number of tructure mode. From the calculated eigen-value, tructural frequency and damping ratio are identified a ω r = imag( log ( r) ), and r = real(log ( r) ) t. Modal participation factor, L imag( log ( r) r Ni 1, i identified from eigen-vector, V. It ) t hould be noted that the length of L r i the number of input N i, not the number of output N o, thu it need to be extended to be a matrix with the length of N o which will be preented later. After frequencie, damping ratio, and model participation factor, L r, have been etimated in t

8 Practical iue in ignal proceing for tructural flexibility identification narrow frequency band, mode hape, r, modal caling factor, reidual, and flexibility matrix can be etimated a preented below. The FRF for each output i written a Note that here H p 1 ( k ) Lr pr (5) j k r pr include the line of the rth mode hape and it conjugate. Solving pr from Eq. (5) i till performed in each narrow frequency band. After pr for all output and all mode are calculated, they are aembled to the tructural mode hape matrix,. It hould be known that dimenion of both the modal participation factor, L, and the mode hape, identified o far are not full matrixe. To overcome thi limit, the caling factor can be ued to extend their dimenion to be N 0 N 0. The caling factor of the rth mode i calculated by Q / (6) r L ir where i denote the ith input location. By uing the identified caling factor, the modal participate e factor i extended to be Lr Qr r, where N 0 L e 1 r R. By uing thi extended modal participate factor, the dimenion of the etimated mode hape matrix from Eq. (6) i extended to be N 0 N 0. Through thi extenion, tructural flexibility matrix identified below will alo be a full matrix, thu tructural deflection when the tatic load locate at any output node can be predicted. Since caling factor ha been etimated, it i eay to derive tructural flexibility in the following way: m R r Rr f H( k 0) r (7) 1 r ir where f i tructural flexibility matrix, and Rr L r r i the reidue of the rth mode. After tructural flexibility matrix i identified, tructural deflection under any tatic load can be predicted. It i een from the equation preented above that the Sub-PolyMAx method identifie tructural parameter in narrow frequency band, thu the Jacobin matrix dimenion i ignificantly reduced by adopting le frequency line and a much maller modal order. Thi make computation time be much reduced. Furthermore, tructural identification reult in a narrow frequency band i not affected by FRF data in other band, thu it i potential to accurately identify tructural parameter in the frequency band with much lower FRF peak. Epecially, the Sub-PolyMax method not only identifie tructural modal parameter, but alo identifie tructural flexibility. 3. Practical iue in tructural flexibility identification 3.1 The benchmark tructure A procedure including a uit of data pre-proceing trategie and the Sub-PolyMax method ha been developed in lat ection. Due to the complex of tructural flexibility identification, it i neceary to ue a benchmark tructure to invetigate how the pre-defined parameter required in the data pre-proceing tage affect the identification reult and how robut of the propoed T ir

9 J. Zhang, Y. Zhou and P.J. Li Sub-PolyMax method work for tructural flexibility identification. For thi purpoe, the flexibility of the tudied tructure hould be beforehand known, in order to provide a baeline to compare with the identified reult. Due to thi reaon, the FE model of a real reinforced concrete bridge i developed to erve a the benchmark tructure. Impact tet data from field tet of real bridge are not appropriate for enitivity analyi performed in thi article, becaue the flexibility of real tructure i unknown and there i no way to evaluate the correctne of the identified flexibility. The prototype of the FE model i a three pan reinforced concrete T-beam bridge located in Wet Virginal. It i a imply upported concrete tructure with a kew of approximately 18 (Fig. 2). Each pan of thi bridge i approximately 14.6 m long; with a width along the kew i 14.6 m a well. The FE model of thi bridge i contructed in the SAP2000 oftware. Becaue the purpoe the FE modeling i for parameter enitivity invetigation and method verification, only the longitudinal and tranveral beam and the pier are modeled for implicity. The bridge deck can be eaily modeled by uing the hell element but it i excluded in the developed FE model becaue it make the computation time be much longer in the multi-reference impact tet imulation. The beam and pier are modeled by uing the frame element. The beam and the pier cap are connected uing rigid link, forcing the component to act compoitely. The upport condition at the abutment are pin, while the bae of the pier i fixed. In total, the model i compried of 1408 frame element, and 336 rigid link. The multiple reference impact tet data of the Smither Bridge i imulated by uing the developed FE model. The dynamic analyi of the whole FE model i performed, but only the repone of the left pan with the intrumentation plan preented below i ued for tructural identification becaue thee three pan have very weak coupling and each pan can be een a an individual tructure. 18 node a hown in Fig. 3 are elected a output node (N 0 =18) whoe tructural acceleration under each impacting are recorded. Four input node (N i =4) a hown in Fig. 3 are elected a reference node. Namely, the impacting force i applied on one of the reference node each time until all reference node are impacted. The impacting force ued in the FE imulation are from the recorded hammer hitting force in a real bridge impact tet. To imulate the obervation noie and other kind of uncertainty exiting in the experiment tage, the imulated data are polluted by noie in the way a decribed below. It i known that traffic noie i one of the main uncertainty ource. Therefore, a erie of traffic vibration induced acceleration recorded in a bridge ambient vibration tet are added into the imulated tructural repone a the traffic noie. The magnitude of the added traffic noie i 15%, which mean that the tandard deviation of the added traffic noie i 15% of that of the imulated acceleration (Zhang et al. 2008). Furthermore, to imulate other kind of uncertainty epecially to imulate the noie involved in the impact force, 3% Gauian noie are alo added to both the tructural repone and impacting force, where the magnitude of the noie i defined in the ame way a decribed above. It i een that extremely trong noie (15% traffic noie plu 3% Gauian noie) are added into the imulated data aiming at invetigating the enitivity of the pre-defined parameter of the data pre-proceing algorithm and the robutne of the propoed procedure for tructural flexibility identification. 3.2 Sentivity analyi After the multi-reference impact data are imulated, the propoed ignal proceing procedure a illutrated in Fig. 1 i employed for tructural flexibility identification and deflection prediction.

10 Practical iue in ignal proceing for tructural flexibility identification (a) Fig. 2 The bridge model; (a) The bridge prototype, and (b) The FE model (b) Fig. 3 Impact tet enor layout In the data pre-proceing tage, data checking, filtering, windowing (rectangular and exp window for force and acceleration, repectively) technologie are employed to clean the data, and FRF reciprocity and coherence function plot are ued to check the quality of the cleaned data. In the data pot-proceing, the Sub-PolyMax method i executed to identify tructural flexibility matrix. A pointed out in Section 2, 3 pre-defined parameter required in the data pre-proceing tage affect the flexibility identification reult, like the parameter,, in the exponential window technology, the FFT point number, N fft, and the ampling rate, F = 1/dt. To invetigate how thee parameter affect tructural identification reult, enitivity analye of thee three parameter are performed by employing tructural identification with the variation of thee parameter. The averaged error between the deflection predicted from the identified flexibility matrix and thoe from FE imulation are calculated a an index to evaluate the parameter enitivity. Fig. 4(a) illutrate how the parameter,, affect the predicted deflection. Fig. 4(b) and 4(c) provide other way to evaluate the parameter enitivity. In Fig. 4(b), the FRF denote the error between the FRF directly etimated from the tet data and thoe recontructed from the etimated tructural modal parameter uing Eq. (2). The FRF reciprocity denote the error between the FRF when the location of force and repone are exchanged. Theoretically the FRF data from a

11 Error Error (%) Error (%) J. Zhang, Y. Zhou and P.J. Li meaurement hould be identical if we exchange the location of force and repone for a linear and time invariant tructure in the ingle input cae, thu reciprocity check the FRF i a imple but ueful index to check the parameter enitivity. The FRF reciprocity check for H(1,13) and H(13,1) are hown in Fig. 5, which are for the cae uing 0.1%, and 1 in the exponential window, repectively. In Fig. 4(c), the Frequency denote the averaged error of the identified frequencie in the firt 6 mode and thoe from the FE imulation, and the MAC mean the averaged MAC error between the identified modal hape and thoe from the FE model. It i een that Fig. 4(a)-4(c) ue the identified deflection, the recontructed FRF, the FRF reciprocity, the frequency, and the MAC, repectively, a indexe to evaluate how the parameter,, affect tructural identification reult. It i found that better identification reult are produced while employing a maller. The optimum exponential window parameter i elected a 0.1% for tructural modal parameter and flexibility identification. The enitivity of the FFT point number, N fft, i alo tudied and it reult are hown in Fig. 6(a). Generally, the FFT i implemented to tranform the time domain tet data to the frequency p p domain by uing a tandard blockize of N 2, where p i the firt value uch that 2 i fft larger than the time erie length. The normalized FFT point in Fig. 6(a) mean how many time the fft point number i the tandard blockize, N. The FFT point number affect frequency reolution. It doe affect tructural identification reult, but a higher frequency reolution for the FRF doen t guarantee better deflection prediction reult. The optimum value for the FFT point number i elected a the tandard FFT blockize, N, which yielded a frequency reolution of Hz. fft fft 12 8 (a) Deflection 4 3.0E-9 2.0E-9 1.0E-9 (b) FRF reciprocity FRF (%) (c) Frequency MAC value 0.0E (%) (%) Fig. 4 Senitivity analyi of the parameter

12 Error (%) Error (%) Practical iue in ignal proceing for tructural flexibility identification (a) Fig. 5 Reciprocity check with (a) 0.1%, and (b) 1 (b) 12 8 Deflection Deflection Normalized FFT Point Normalized Sampling Rate (a) (b) Fig. 6 Senitivity analye of (a) FFT point number, and (b) Sampling rate Senitivity analyi of the ampling rate i performed a well a hown in Fig. 6(b) to tudy how the ampling rate affect the deflection prediction reult. The normalized ampling rate in Fig. 6(b) mean how many time to cale up the ampling rate which i in thi tudy correponding with a ampling frequency of 2400 Hz. In the impact tet, a ampling rate need to be etup before recoding the data. The meaurement of both the impact force and the acceleration are recorded with the ame apling rate. It i een from Fig. 6(b) that the ampling rate greatly influence the deflection identification reult. The reaon i that a very high ampling frequency i required to recorder the impact force peak during the impacting device contact the bridge urface which occur in a very hort time window. It i learning from here that a much higher ampling frequency hould be et in impact tet for flexibility identification, which generally hould be at leat 10 time of that in uual ambient vibration tet. 3.3 Flexibility identification reult Practical iue in applying the propoed ignal proceing method for tructural flexibility identification have been invetigated by performing enitivity analye of everal pre-defined parameter required in data proceing. Thi ection illutrate the detailed flexibility identification reult from the propoed Sub-PolyMax method. A preented earlier, the Sub-PolyMax method perform parameter identification in ubpace of the whole frequency range, to achieve efficiency and accurate flexibility identification. In thi example, two frequency egment, 4.25 Hz ~18.92

13 J. Zhang, Y. Zhou and P.J. Li Hz, and Hz ~ 33.6 Hz, are elected from the whole frequency range, each egment with 100 frequency line. The Sub-PolyMAX method wa implemented in each egment independently to identify denominator polynomial coefficient by Eq. (3) and ubequent tructural modal parameter by Eq. (4). It hould be noted that the model order n hould be elected in Eq. (2), and it hould be larger than the number of tructural mode involved in the invetigated narrow i n n i frequency band. Thi induce that part of polynomial root of i A 1 1 zk are ytem root involving tructural mode, while other are puriou root due to uncertainty. Stabilization diagram are ued to eparate ytem pole from puriou pole. The pole atifying the criteria ( r 0, r 0.1, r 0.2, MAC 0.96), where mean frequency or damping ratio change with model order increaing, and MAC denote model aurance criterion) are elected a table ytem pole. The tabilization diagram i alo helpful to elect the appropriate mode order. Fig. 7 how the tabilization diagram in two elected frequency band, from which the model order i elected to be n = 20. From the identified tructural modal parameter, FRF are yntheized a hown in Fig. 8. It i een that for the tudied tructure, it FRF curve ha much larger peak value at the low frequency range than thoe in the high frequency range. In the un-weighted PolyMAX method, the leat quare error at all frequency line are equally weighted, thu tructural modal parameter in high mode are very difficult to accurately identify. By dividing the whole frequency range to narrow frequency band which only involve a few tructural mode, only FRF data in a narrow frequency band are ued thu the identified tructural modal parameter are not affected by FRF value in other frequency band. A hown in Fig. 8, the yntheized FRF are comparable to the FRF identified directly from input/output tet data, even in the high frequency range. Thi i the merit of the propoed SubPolyMax method. Fig. 7 Stabilization diagram (circle denote table pole, triangle denote untable pole, the blue line in the figure denote CMIF plot)

14 Practical iue in ignal proceing for tructural flexibility identification Fig. 8 Syntheized FRF After tructural frequencie, damping ratio and modal participation factor are extracted from the identified polynomial coefficient from Eq. (4), tructural modal hape are etimated by caling the modal participation factor from Eq. (5). It hould be known that the number of reference node (N i =4) i lower than the number of the output node (N 0 =18), thu the modal hape identified o far i only a partial part of the full modal hape matrix, thu it need to extend to a full matrix by uing the caling factor a calculated from Eq. (6). Identified frequencie and mode hape of the tudied tructure are plotted in Fig. 9, and the frequencie and mode hape calculated from FE imulation are alo provided in Fig. 9 for comparion. The MAC value calculated from the identified and imulated mode hape are alo plotted in Fig. 10. It i een that identified tructural modal parameter from the propoed ignal proceing procedure are very accurate, even though the imulated data are polluted by trong noie (15% traffic noie plu 3% Gauian noie a preented earlier). After that, reidual and flexibility matrix are etimated. A hown in Eq. (7), the flexibility i calculated by uing the identified modal parameter in the firt m mode. The identified flexibilitie uing different mode combination are ued to predict deflection, and they are compared with the tatic reult from FE imulation. In the tatic load cae, point tatic load with the magnitude of 1000 KN are applied on node 2, 3, 8, and 9, and the imulated diplacenet on node 1 to 18 are imulated. Structural deflection under the tatic load from the tatic tet and thoe calculated from the identified flexibility matrix were plotted in Fig. 11(a) for comparion. Similarly, Fig 11(b) plot the predicted deflection and the one from the tatic tet when 1000 KN tatic load are on the 7 th to 12 th node. It i een that tructural flexibility identified by uing modal parameter in the firt 6 mode produce very accurate deflection.

15 J. Zhang, Y. Zhou and P.J. Li Fig. 9 Identified modal parameter

16 Diplacement (m) Diplacement (m) Practical iue in ignal proceing for tructural flexibility identification Fig. 10 MAC value between the identified and imulated modal hape 0 Node Number mode 3 mode 6 mode FEM Node Number mode 3 mode 6 mode FEM Fig. 11 Deflection prediction from the identified flexibility

17 J. Zhang, Y. Zhou and P.J. Li 4. Concluion The following concluion have been drawn baed on the reearch o far: (1) A ignal proceing procedure ha been preented for tructural flexibility from the multi-reference impact tet data. It include a uit of data pre-proceing trategie to improve the data quality, and a Sub-PolyMax method for tructural identification in narrow frequency band. (2) Practical iue in uing the ignal proceing procedure for tructural flexibility identification have been invetigated. How the pre-defined parameter affect the identified flexibility reult have been revealed. (3) The invetigation throughout thi paper take the FE model of a real three-pan reinforced concrete T-beam bridge a the benchmark tructure, in which extremely trong noie including 15% traffic noie and 3% Gauian noie have been added into the imulated impact tet data. Impact tet data from field tet of real bridge are not appropriate for enitivity analyi performed in thi article, becaue the flexibility of real tructure i unknown and it i difficult to evaluate the correctne of the identified flexibility. Acknowledgement Thi work wa ponored by the National Science Foundation of China ( ) and the Supporting Program of the Twelve Five-year Plan for Science & Technology Reearch of China (2011BAK02B03). The firt author would particularly like to acknowledge the upport from Dr. F. Moon and A.E. Aktan of the Drexel Univerity. Reference Adewuyi, A.P. and Wu, Z. (2011), Vibration-baed damage localization in flexural tructure uing normalized modal macrotrain technique from limited meaurement, Comput.-Aided Civil Infratruct. Eng., 26(3), American Aociation of State Highway and Tranportation Official (AASHTO) (2007), AASHTO Maintenance Manual: The Maintenance and Management of Roadway and Bridge, 4th Ed.. ASCE (2011), Structural Identification of Contructed Facilitie: Approache, Method and Technologie for Effective Practice of St-Id, A State-of-the-Art Report, ASCE SEI Committee on Structural Identification of Contructed Sytem, In Pre. Catba, F.N., Brown, D.L. and Aktan, A.E. (2004), Parameter etimation for multiple-input multiple-output modal analyi of large tructure, J. Eng. Mech. - ASCE, 130(8), Catba, F.N., Ciloglu, S.K. and Aktan, A.E. (2005), Strategie for condition aement of infratructure population: a cae tudy on T-beam bridge, Struct. Infratruct. E., 1(3), Carden, E.P. and Brownjohn, J.M.W. (2008), Fuzzy clutering of tability diagram for vibration-baed tructural health monitoring, Comput.-Aided Civil Infratruct. Eng., 23(5), Chen, Z.W., Xu, Y.L., Li, Q. and Wu, D.J. (2011), Dynamic tre analyi of long upenion bridge under wind, railway and highway loading, J. Bridge Eng. - ASCE, 16(3), Friwell, M.I. and Motterhead, J.E. (1995), Finite Element Model Updating in Structural Dynamic, Kluwer Academic Publiher. Grimmelman, K.A., Pan, Q. and Aktan, A.E. (2007), Analyi of data quality for ambient vibration teting of the Henry Hudon Bridge, J. Intel. Mat. Syt. Str., 18, Lei, Y., Jiang, Y. and Zhang, X. (2012), Structural damage detection with limited input and output

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