Reference-free Deflection Measurement of General-shape Bridges using Data Fusion

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1 th Internatonal Conference on Advances n Expermental Structural Engneerng 11 th Internatonal Workshop on Advanced Smart Materals and Smart Structures Technology August 1-, 15, Unversty of Illnos, Urbana-Champagn, Unted States Reference-free Deflecton Measurement of General-shape Brdges usng Data Fuson S. Cho 1, C-B. Yun, S-H. Sm 3 1 Research Assstant Professor, School of Urban and Envronmental Engneerng, UNIST, Ulsan, South Korea. E-mal: soojn@unst.ac.kr Professor Emertus, Dept. of Cvl and Envronmental Engneerng, KAIST, Daejeon, South Korea E-mal: ycb@kast.ac.kr 3 Assstant Professor, School of Urban and Envronmental Engneerng, UNIST, Ulsan, South Korea. E-mal: ssm@unst.ac.kr ABSTRACT Recently, an ndrect dsplacement estmaton method usng data fuson of acceleraton and stran (.e., acceleraton-stran-based method) has been developed. Though the method showed good performance on beam-lke structures, t has nherent lmtaton n applyng to more general types of brdges that may have complex shapes, because t uses assumed analytcal (snusodal) mode shapes to map the measured stran nto dsplacement. Ths paper proposes an mproved dsplacement estmaton method that can be appled to more general types of brdges by buldng the mappng usng the fnte element model of the structure rather than usng the assumed snusodal mode shapes. The performance of the proposed method s evaluated by numercal smulaton on a deck arch brdge model whose mode shapes are dffcult to express as analytcal functons. The dsplacements are estmated by acceleraton-based method, stran-based method, acceleraton-stran-based method, and the mproved method. Then the results are compared wth the exact dsplacement. The proposed method s found to provde the best estmate for dynamc dsplacements n the comparson, showng good agreement wth the measurements as well. KEYWORDS: dsplacement, brdge, data fuson, fnte element model, modal mappng 1. INTRODUCTION Structural health montorng (SHM) s an essental procedure to ensure the sustanablty of cvl nfrastructure. For the SHM, a wde varety of responses, such as acceleraton, dsplacement, stran, and nclnaton, are utlzed dependng on structural types and features to be montored. Despte of ts ntutve feature that drectly results from the external loads to the structure, dsplacement has been relatvely less used due to two possble causes: nconvenence n ts measurement and expensve cost of measurement devces. Especally, the usage of the tradtonal contact-type transducers, such as a lnear varable dfferental transformer (LVDT) and a rng-type transducer, was sgnfcantly lmted at the brdges due to unavalablty of fxed reference pont of the dsplacement measurement. To take the hurdle, noncontact-type devces, such as the global postonng system (GPS) and the laser Doppler vbrometer (LDV), have been emerged as alternatves (Nassf et al. 5, Jo et al. 13). However, hgh cost of such noncontact devces up to a few ten thousand dollars per sensng channel lmts ther real-world applcatons that may requre a dense sensor topology. Instead of usng the noncontact-type devces, there have been research efforts to use other responses that can be converted nto the dsplacement. Acceleraton and stran are the most popular responses used to the end. Especally, Park et al. (13) proposed a dsplacement estmaton method usng data fuson of acceleraton and stran by extendng the acceleraton-based method proposed by Lee et al. (1). In the regularzaton term, the dsplacement converted from stran data by the modal mappng s used to prevent the sgnal drft. For the modal mappng, the assumed analytcal (snusodal) mode shapes proposed by Shn et al. (1) are employed. The method by Park et al. (13), however, nherts a lmtaton n applcaton to more general types of brdges wth complex shapes, such as arch and truss brdges, snce the method uses assumed snusodal mode shapes whch may be reasonably obtaned only for the grder brdges. Ths study proposes a reference-free method to measure the dsplacement usng data fuson of acceleraton and stran for general brdge structures. The proposed method s to extend the method by Park et al. (13) to

2 general types of brdges wthout use of the assumed mode shapes. To the end, the mode shapes for the modal mappng are obtaned from the FE model of a structure nstead of assumed snusodal mode shapes. The performance of the proposed method s evaluated by numercal smulatons on a deck arch brdge model whose mode shapes are hard to be assumed as snusodal functons. The dsplacements are estmated by acceleraton-based method, stran-based method, fuson-based method, and the mproved method, and the results are compared wth exact dsplacements to demonstrate the performance of the proposed method. From the comparson of dsplacements estmated by the four methods to the reference values measured by laser dsplacement meters, the accuracy of the proposed method has been nvestgated.. REFERENCE-FREE DEFLECTION MEASUREMENT METHOD Ths secton descrbes the prncples of the dsplacement estmaton method proposed by Park et al. (13) and the modfcaton made n the proposed method..1 Acceleraton-stran-based dsplacement estmaton method Park et al. (13) have proposed the dsplacement estmaton method by fusng the acceleraton and stran. The method uses the basc form of the acceleraton-based method proposed by Lee et al. (1), whle the regularzaton term s replaced by the dfference between estmated dsplacements and dsplacement estmated from the stran by modal mappng method. The method can be formulated for dsplacement u at the locaton of x as: where measured stran; 1 Mn La( Lcu ( t) a) u D (1) u u and a are the estmated dsplacement and measured acceleraton at the locaton x ; s the t s the tme step; L a s a dagonal weghtng matrx havng the frst and last entres as 1/ and the other entres as 1; L c s the second-order dfferental operator matrx of the dscretzed trapezodal rule (Atknson ); s -norm of a vector; s a regularzaton factor; and D s the th row of modal mappng matrx D that converts stran nto dsplacement as: The modal mappng matrx can be calculated as: u D () D (3) where and denote mode shapes and stran mode shapes, respectvely; the superscrpt denotes the pseudo-nverse. s defned by Lee et al. (1) as 1.95 N ().1 d where N d s the number of acceleraton data to be converted nto dsplacements. The soluton of Eq. 1 can be expressed as u L L I L L a t D T 1 T ( λ ) ( a λ ) Cat C a (5) where T 1 C ( L L I) D. The mode shapes and stran mode shapes may be drectly estmated from measurements, whch would be very expensve. Instead, Park et al. (13) employed assumed snusodal mode shapes and correspondng stran mode shapes, proposed by Shn et al. (1).

3 In ths paper, an mproved method s proposed by employng a modal mappng matrx derved from an FE model of the structure as (Foss and Hauge 1995): FE FE D ( ) () FE FE where and are the mode shapes and the stran mode shapes obtaned from the FE model. Note that, the number of used modes must be smaller than the number of stran measurements to avod the under-determned modal mappng matrx. The accuracy of the estmated dsplacement can be quantfed by employng a percentage RMSD (root mean square devaton) as: N N est ref ref (%) ( ) ( ) (7) RMSD u u u est where u and u ref are the estmated and reference dsplacements, respectvely; and N denotes the number of data samples. 3. DECK-ARCH BRIDGE MODEL The example used n ths study s a D open-spandrel deck arch brdge model shown n Fgure 1. The model has a deck whch locates above the arch and the deck s supported by a number of vertcal columns rsng from the arch. The Ranbow Brdge at Nagara Falls and the Cold Sprng Canyon Arch Brdge are the famous examples of the deck arch brdges. The model s composed of 3 members: 1 deck members, 1 arch members, and 1 vertcal columns. All members are modelled as frame elements. N# and A# denote the nodes and supports on the deck, respectvely. The span length of the brdge s 1 m, and the heght of the arch s m. The sectonal propertes of members for deck, arch, and vertcal columns are shown n Table 1. Fgure 1 Deck arch brdge model wth sensor topology. Table 1. Structural propertes of deck arch brdge model. Members Deck Arch Vertcal Column Sectonal area.5 m. m.17 m nd moment of nerta m m m Elastc modulus GPa Mass densty 75 kg/m 3 The dsplacement, acceleraton, and stran of the beam are smulated usng MATLAB Smulnk. A vertcal load movng from left to rght of the deck wth a constant speed ( v =1 m/s), shown n Fgure, s employed to generate non-zero mean dsplacements. The load s the combnaton of a movng statc load of 3. ton (DB truck load specfed n Korean hghway brdge desgn code) and zero-mean Gaussan random load wth a

4 standard devaton of 13 ton smulatng dynamc loadng effect. Acceleraton s assumed to be measured at N, whle strans on the deck are obtaned at the md spans of four deck members between N1-N, N-N5, N7-N, and N1-N11. The smulated acceleraton and strans are made artfcally contamnated by addng 5 % nose n RMS (root mean square) to emulate the practcal measurement. The dsplacement smulated at N s used as the reference to evaluate the accuracy of estmated dsplacements. Note that acceleraton and dsplacement are obtaned n the vertcal drecton, whle the strans are obtaned on the bottom surfaces of the deck n the longtudnal drecton to capture the bendng stran. Snce four stran data are avalable n ths example, the frst four modes are employed to buld the modal mappng relatonshp. Fgure 3 shows the frst four mode shapes of the FE model, compared wth the snusodal shapes based on the assumpton of a smply supported prsmatc beam. The vsual comparson clearly shows the dfference between the two types of mode shapes, partcularly for the frst and thrd mode shapes near the supports. Ther MAC (modal assurance crteron) values are.71,.93,.51, and.9, respectvely. Thus, t can be expected that the dsplacement estmated near the supports may have consderable error when the assumed modes are used. Fgure Vertcal movng load. Fgure 3 Frst four mode shapes of FE model (sold lnes) compared wth assumed ones (dashed lnes).. COMPARISON OF ESTIMATED DISPLACEMENT The mproved method s valdated from numercal smulatons carred out on the example brdge model. The dsplacements excted by a movng load are estmated by four methods:.e., acceleraton-based method (Lee et al. 1), stran-based method (Kang et al. 7), acceleraton-stran-based method (Park et al. 13), and the mproved acceleraton-stran-based method, and the results are compared for the valdaton..1.1 Comparson of dsplacements at N Fgure shows the comparson of the dsplacements estmated by four methods wth exact one smulated from the MATLAB Smulnk. The acceleraton-based method cannot estmate the nonzero-mean pseudo-statc dsplacement component as shown n Fgure (a). The stran-based method can somewhat estmate the statc component as shown n Fgure (b), whle the dynamc component cannot be estmated accurately. The acceleraton-stran-based method gves an ncorrect the dsplacement due to the ncorrect modal mappng as n Fgure (c). Meanwhle, the mproved acceleraton-stran-based method estmates very accurate dsplacement overlapped wth the exact one as n Fgure (d), despte of the complexty of the deck arch model. Ths clarfes the performance of the mproved method for a complex structure whose mode shapes may not be easly assumed as analytcal functons. The accuracy of the estmated dsplacements can be nvestgated n the dfferent aspects by lookng at the frequency doman. Fgure 5 shows the power spectral densty (PSD) of the estmated dsplacements compared wth that of exact one. Fgs. 5(a) and 5(b) show errors of the acceleraton-based and the stran-based methods n low and hgh frequency range, respectvely. The acceleraton-stran-based method shows slghtly larger error n estmatng the pseudo-statc components near Hz than the mproved method (Fgs. 5(c) and 5(d)).

5 Dsplacement (mm) - Acc-only Dsplacement (mm) - Stran-only Tme (s) (a) Acceleraton-based method Tme (s) (b) Stran-based method. Dsplacement (mm) - Acc-Stran Dsplacement (mm) - Acc-Stran-FE Tme (s) Tme (s) (c) Acceleraton-stran-based method. (d) Improved acceleraton-stran-based method. Fgure Comparson of dsplacements estmated at N for deck arch brdge model by four dfferent estmaton methods wth exact one. 1-5 Acc-only 1-5 Stran-only PSD 1-1 Zoom n ( 1Hz) PSD 1-1 Zoom n ( 1Hz) Frequency (Hz) Frequency (Hz).5 1 (a) Acceleraton-based method..5 1 (b) Stran-based method. 1-5 Acc-Stran 1-5 Acc-Stran-FE PSD 1-1 Zoom n ( 1Hz) PSD 1-1 Zoom n ( 1Hz) Frequency (Hz) Frequency (Hz) (c) Acceleraton-stran-based method. (d) Improved acceleraton-stran-based method. Fgure 5 Comparson of PSD of dsplacements estmated at N for deck arch model by four dfferent estmaton methods wth exact one. The accuracy of the estmated dsplacements by the four methods s quantfed usng the percentage RMSD descrbed n Eq. 7. Fgure shows that the acceleraton-based method provdes the largest RMSD of 5.9 % at N. The stran-based method yelds small error of 17.7 %, snce the method uses accurate modal mappng usng the FE mode shapes. The acceleraton-stran-based method gves a larger RMSD value of.5 % than the stran-based method, whch means the error n the assumed mode shapes may brng sgnfcant error n the estmaton due to ncorrect modal mappng. The mproved method has the smallest RMSD value of 1. % owng to accurate modal mappng usng the FE model. The estmated RMSD values quanttatvely show the performance of the mproved method compared wth the other exstng methods for the general types of brdge structures..1. Comparson of dsplacements at other locatons Fgure shows the RMSD values of the dsplacements estmated by four methods at the left half of the deck: N1-N. All methods except the acceleraton-based method show ncreasng RMSD values as the locaton of the estmaton gets closer to the left support due to smaller ampltude of dsplacement. In addton, the ncorrect

6 modal mappng near the support sgnfcantly ncreases the error of the acceleraton-stran-based method. The mproved method has the smallest RMSD values for all ponts. RMSD (%) 1 Acc-only Stran-only Acc-Stran Acc-Stran-FE N1 N N3 N N5 N Fgure RMSD of dsplacements at N1-N..1.3 Effect of FE model naccuracy The FE model may be subjected to modellng errors, whch may cause estmaton errors n the modal propertes. To see the effect of the naccurate FE model to the estmaton, the FE model s perturbed by ntroducng element-level errors n the elastc modulus. Three types of perturbatons wth 11.5, 3.1, and 3. % n RMS (.e., unform perturbaton n the range of ±%, ±%, and ±% of the ntal value) are consdered. Fgure 7 shows the frst four mode shapes of a perturbed FE model wth 3. % errors n RMS n comparson wth those from the orgnal FE model. Fgure 7 shows that the perturbaton caused consderable dscrepancy partcularly on the hgher mode shapes to be used for the modal mappng. 3 5 Stran-only Acc-Stran-FE 1st mode nd mode 3rd mode th mode RMSD (%) MAC values 5.95 Fgure 7 Frst four mode shapes of perturbed FE model wth 11. % errors n RMS (dotted lnes) compared wth those from orgnal model (sold lnes). 11.5% n RMS 3.1% n RMS 3.% n RMS Fgure RMSD of dsplacements estmated at N5 for perturbed deck arch FE models. 1 Fgure shows the RMSDs of the estmated dsplacements at N by the stran-based and the mproved methods when the perturbed FE models are used for the modal mappng. The MAC values of the perturbed models are plotted together to show the effect of perturbaton to the mode shapes. By the ncremental perturbaton, the mode shapes are found to change ncrementally. However, even wth the sgnfcant perturbaton, the RMSD of the estmated dsplacement rarely changes for both the stran-based and the mproved methods. In the case of wth perturbaton of 3. % n RMS, the RMSD by the mproved method s 1. %, whch s much smaller than.5 % by the acceleraton-stran-based method n Secton.1.1. When the exact FE model was used, the RMSDs are 1. and 17.7 % for the stan-based and the mproved methods, respectvely. The slght ncrease by the large perturbaton s because the RMS s sgnfcantly affected by accuracy of the low frequency components, as shown n the result of the acceleraton-based method. The MAC values of Fgure shows that the large perturbaton makes bgger change as the mode order ncreases, and the frst mode whch sgnfcantly affects the RMSDs s barely changed. The naccuracy n hgher modes resulted n naccurate estmaton of dynamc dsplacements that derves the slght ncrease of the RMSDs. Ths llustrates the mproved method usng the mode shapes of the FE model s very effectve when the structure s complex, even wth a somewhat naccurate FE model.

7 .1. Measurement of strans at load carryng members In the case of the deck arch brdge, the arch and vertcal columns are the major load carryng members to resst the dead loads that comprse majorty of the total load appled to the structure, whle the deck s desgned to transfer the lve load to the arch system. Consderng the case wth stran gauges on the members other than deck, another sensor topology shown n Fgure 9 s consdered. Fgure 1 shows the dsplacement estmated at N usng the mproved method. The result s very close to the exact one wth 9.9 % n RMSD, whch s smaller than the value of 1. % by the stran measurements on the deck descrbed n Secton.1.1. The mode shapes cannot be assumed n an analytcal form for the whole structure when the structure has a complex shape. Therefore, the acceleraton-stran-based method usng the assumed snusodal mode shapes s applcable only when the stran gauges are on the deck. Ths example shows that the proposed mproved method based on the FE model has bg advantage when the stran sensors are placed on non-deck members. Fgure 9 Topology for stran measurement at load carryng members. Dsplacement (mm) - Acc-Stran-FE Tme (s) Fgure 1 Dsplacement estmated at N usng stran measurement on load carryng members. 5. CONCLUSIONS In ths paper, an mproved dsplacement estmaton method based on data fuson of acceleraton and stran has been proposed for the applcaton to general types of brdge structures whose mode shapes may not be assumed n analytcal (e.g., snusodal) functon. The mprovement has been made by employng the mode shapes from an FE model n the modal mappng of stran to dsplacement. The performance of the mproved method has been verfed by numercal smulaton on a deck arch brdge model wth complex shape. The estmated dsplacements by four methods, acceleraton-based method, stran-based method, acceleraton-stran-based method, and mproved method, have been compared. The result of ths study can be summarzed as: (1) In the numercal smulatons on the deck arch model, the proposed method estmated dsplacements wth better accuracy than the other methods at all locatons of the structure owng to the accurate modal mappng usng the FE model. () The perturbaton of the FE model has ncreased the naccuracy of the mproved method. However, at the center locatons, large perturbaton (3. % n RMS) resulted n the RMSD errors of 1. %, whch were less than.5 % by the acceleraton-stran-based method usng assumed snusodal mode shapes for the deck, whch shows the effectveness of the proposed method wth somewhat naccurate FE model.

8 (3) The proposed method estmated the dsplacement equvalently well usng the stran data on non-beam type members such as truss and arch, whch shows ts good compatblty of the mproved method to more general types of structures. ACKNOWLEDGEMENT Ths research was supported by a grant (13SCIPA1) from Smart Cvl Infrastructure Research Program funded by Mnstry of Land, Infrastructure and Transport (MOLIT) of Korea government and Korea Agency for Infrastructure Technology Advancement (KAIA). The support s gratefully apprecated. Note that ths paper s taken from a part of the paper (Cho et al. 15) publshed by Techno-press n South Korea. REFERENCE 1. Nassf, H.H., Gndy, M. and Davs, J. (5) Comparson of laser Doppler vbrometer wth contact sensors for montorng brdge deflecton and vbraton, NDT & E Int., 3(3): Jo, H., Sm, S.-H., Tatkowsk, A., Spencer, Jr., B.F., and Nelson, M.E. (13), Feasblty of dsplacement montorng usng low-cost GPS re-cevers, Struct. Control Hlth., (9), Park, J-W., Sm, S-H., and Jung, H-J. (13) Dsplacement estmaton usng multmetrc data fuson, IEEE/ASME Trans. Mechatroncs, 1(), Lee, H.S., Hong, Y.H., and Park, H.W. (1) Desgn of an FIR flter for the dsplacement reconstructon usng measured acceleraton n low-frequency domnant structures, Int. J. Numer. Meth. Eng., (), Shn, S., Lee, S-U., and Km, N-S. (1) Estmaton of brdge dsplacement responses usng FBG sensors and theoretcal mode shapes, Struct. Eng. Mech., (), Foss, G. and Hauge, E. (1995) "Usng modal test results to develop stran to dsplacement transformatons," Proc. 13th Int. Modal Analyss Conf., Kang, L.H., Km, D.K., and Han, J.H. (7) Estmaton of dynamc structural dsplacements usng fber Bragg gratng stran sensors, J. Sound Vb., 35(3), Cho, S., Yun, C-B., and Sm, S-H. (15) Dsplacement estmaton of brdge structures usng data fuson of acceleraton and stran measurement ncorporatng fnte element model, Smart Str. Syst., 15(3): 5-3.