Damage Detection in Bridge Structure Using Vibration Data under Random Travelling Vehicle Loads

Transcription

1 Journal of Physcs: Conference Seres PAPER OPEN ACCESS Damage Detecton n Brdge Structure Usng Vbraton Data under Random ravellng Vehcle Loads o cte ths artcle: C H Loh et al 2015 J. Phys.: Conf. Ser Related content - Damage localzaton from vbraton data usng herarchcal a pror assumptons A Huhtala and S Bossuyt - Energy dsspaton and absorpton capacty nfluence on expermental modal parameters of a PC grder O S Luna Vera, C W Km and Y Oshma - A proposal applcaton based on stran energy for damage detecton and quantfcaton of beam composte structure usng vbraton data S achacht, A Bouazzoun, S Khatr et al. Vew the artcle onlne for updates and enhancements. hs content was downloaded from IP address on 04/12/2017 at 03:40

2 11th Internatonal Conference on Damage Assessment of Structures (DAMAS 2015) Journal of Physcs: Conference Seres 628 (2015) do: / /628/1/ Damage Detecton n Brdge Structure Usng Vbraton Data under Random ravellng Vehcle Loads C H Loh 1, Y Hung 1, S F Chen 1 and W Hsu 1 Department of Cvl Engneerng, Natonal awan Unversty ape 10617, awan E-mal: lohc0220@ccms.ntu.edu.tw Abstract. Due to the random nature of the road exctaton and the nherent uncertantes n brdge-vehcle system, damage dentfcaton of brdge structure through contnuous montorng under operatng stuaton become a challenge problem. Methods for system dentfcaton and damage detecton of a contnuous two-span concrete brdge structure n tme doman s presented usng nteracton forces from random movng vehcles as exctaton. he sgnals recorded n dfferent locatons of the nstrumented brdge are mxed wth sgnals from dfferent nternal and external (road roughness) vbraton sources. he damage structure s also modelled as the stffness reducton n one of the beam element. For the purpose of system dentfcaton and damage detecton three dfferent output-only modal analyss technques are proposed: he covarance-drven stochastc subspace dentfcaton (SSI-COV), the blnd source separaton algorthms (called Second Order Blnd Identfcaton) and the multvarate AR model. he advantages and dsadvantages of the three algorthms are dscussed. Fnally, the null-space damage ndex, subspace damage ndces and mode shape slope change are used to detect and locate the damage. he proposed approaches has been tested n smulaton and proved to be effectve for structural health montorng. 1. Introducton One of questons n research attenton s the use of structural response from operatonal dynamc loads n the damage detecton procedures. In the long servce lfe and contnuous operaton process, brdge may suffer resstance and damage accumulaton under the comprehensve effect of random vehcle loads and envronmental effects such as wnd load and ran load. By placng sensors on brdges, the brdge health status can be montored onlne through health montorng system n order to determne the degree of damage. For brdge montorng the vehcle-brdge structure nteracton effect needs to be consdered n the modal parameter dentfcaton. Generally, the modal parameters of the vehclebrdge system are changng when the random vehcles are movng on top of the brdge (nclude the road roughness). For such a system, system dentfcaton tools must be developed and tested usng numercally generated tme hstores so as to verfy the methodologes. For dentfcaton, usng tmefrequency tools, whch are non-parametrc methods for processng responses of non-lnear or nonstatonary system, had been studed [1, 2]. A lnear approach derved from the stochastc subspace dentfcaton (SSI) method, together wth the movng wndow SSI to examne the tme-varyng system, has also been adopted for vbraton-based system dentfcaton [3]. 1 CH Loh, Professor, Dept. of Cvl Engneerng, Natonal awan Unversty, ape 10617, awan Y Hong, SF Chen, W Hsu, graduate student, Cvl Eng. Dept., Natonal awan Unversty Content from ths work may be used under the terms of the Creatve Commons Attrbuton 3.0 lcence. Any further dstrbuton of ths work must mantan attrbuton to the author(s) and the ttle of the work, journal ctaton and DOI. Publshed under lcence by Ltd 1

3 11th Internatonal Conference on Damage Assessment of Structures (DAMAS 2015) Journal of Physcs: Conference Seres 628 (2015) do: / /628/1/ In ths study, comparson of three dfferent tme-doman dentfcaton and damage detecton methods are proposed to dentfy the brdge model propertes by usng the smulaton data of a vehcle-brdge structural nteracton under random travellng loads and wth consderaton of surface roughness. Frst, the automatc covarance-drve stochastc subspace dentfcaton (SSI-COV) s proposed to extract the system poles through stablty dagram. In cooperated wth the wavelet packet transform (WP) sftng process for modal phase consstency, spurous modes can be removed from usng SSI. For wellseparated modes, the blnd source separaton (called Second-order Blnd Identfcaton, SOBI) algorthm can also be used for dentfcaton and damage detecton. Advantages and dsadvantages of the two methods are dscussed. Fnally, a parametrc dentfcaton method, usng multvarate ARmodel, s adopted to enhance the damage detecton and compare the result wth other methods. 2. Smulaton of brdge-vehcle nteracton system A two span brdge model s proposed n ths study, as shown n Fg.1. It shows a brdge carryng a seres of random movng vehcles whch are modelled as a sprung-mass system. he brdge s modelled as a Bernoull-Euler beam by fnte element method. he nformaton for the brdge and vehcles are provded n able 1. he traffc loads are assumed as random and to be movng as a group from both sdes (two ways) of the brdge wth random velocty. he prescrbed velocty of each car s random generated and shown n the travel tme across the brdge wth span length of total 200 m, as shown n Fg.2. A total of 16 cars are on the brdge durng the measurement. From Fg.2 one can see that durng the recorded tme wndow (.e. 30. sec) some cars are stll on the brdge and some cars may just enter/leave the brdge. In ths paper, the smulaton of road roughness n vehcle brdge nteracton s also consdered [4, 5]. he random road surface roughness of the brdge can be descrbed by a knd of zero-mean, real-valued, statonary Gaussan process defned by ISO 8608 [6]. he movng vehcle s also modelled as a movng mass wth sprng-mass system. Based on the fnte element method a total of 10 beam elements (Bernoull-Euler beam) are used and the nodal ponts are consdered as measurements. Frst, the system equaton of moton s formed, then the equatons of moton of the brdge-vehcle nteracton system can be solved by Newmark-βmethod. Acceleraton responses from each nodal pont (smlar to measurement pont) are collected wth duraton of 30. sec. Both ntact and damaged stuaton of the brdge structure are smulated. For damaged case a 50% of stffness reducton at element 7 (between measurement pont 5 and 6) s assumed Fgure 1. Brdge model wth two-way travellng vehcles and the locaton of measurement ponts. Brdge Data Vehcle Data Brdge Freq. (Hz) able 1. Natural frequences of brdge model and vehcle nformaton. 1 st mode 2 nd mode 3 rd mode 4 th mode 5 th mode 6 th mode 7 th mode 8 th mode Vehcle system natural frequency: 1.96 Hz ~ 6.5 Hz Vehcle Weght (ton) : 1.5 ~ Identfcaton of brdge-vehcle nteracton system o dentfy the dynamc characterstcs of the brdge drectly from the vbraton measurement durng random travellng vehcles, two dfferent approaches are employed: the covarance-drve stochastc subspace dentfcaton (SSI-COV) and the second-order blnd dentfcaton (SOBI). Damage detecton wll also be studed from the extracted vbraton features and system modal propertes. 2

4 11th Internatonal Conference on Damage Assessment of Structures (DAMAS 2015) Journal of Physcs: Conference Seres 628 (2015) do: / /628/1/ Dscusson on the dentfcaton of damage locaton usng parametrc Multvarate-AR model s also presented for comparson. Fgure 2. Plot the relatonshp between the recorded tme wndow (30. sec) and the locaton of vehcles (8 cars from rght and another 8 cars from left) travellng wth dfferent speed Automatc covarance-drve stochastc subspace dentfcaton (SSI-COV) A fully automatc dentfcaton scheme of reference-base SSI-COV algorthm s developed to extract the dynamc characterstcs of the montorng structure. echnque to remove the spurous modes s ncluded n the automatc dentfcaton scheme and the calculaton of uncertanty on the dentfed modal parameters s to confrm the accuracy of the dentfed modes. he followng 4 stages are developed to provde a good qualty of the stablty dagram from usng SSI-COV [13]: a. Conduct down-samplng on the recorded data (from 200. Hz to 50 Hz), and then adopt sngular spectrum analyss (SSA) on the data oepltz matrx so as to construct the stablty dagram (fx number of rows n data Hankel matrx and change number of order n Sngular Value Decomposton). b. Select output modal ampltude crtera (OMAC) and mode phase co-lnearty (MPC) to remove the spurous modes from stablty dagram. he hard crtera, such as threshold values on mode assurance crtera, system natural frequency and dampng rato are also employed. c. Use the 4-means clusterng algorthm to mnmze the sum of the squared Eucldean dstance between the extracted poles, and determne the sutable poles satsfy the crtera. d. Groupng of poles wth each ndvdual mode and dentfy the physcal modal parameters of each mode by usng uncertanty bounds of modal frequency and dampng rato as weghtng factor for each pole n each specfc group of poles. hrough the proposed 4 stages n SSI-COV analyss, one can sgnfcantly ncrease the autonomous ablty to remove the spurous modes and create a clear and dentfable stablty dagram. he system dynamc characterstcs can also be dentfed Second-order blnd dentfcaton (SOBI) In applyng SSI-COV some parameters need to be determned, such as the number of row n data Hankel matrx and the number of order, whch depends on the dynamc characterstcs of the system. Dfferent from the SSI-COV algorthm, blnd source separaton (BSS) s also a sgnal processng technque, whch attempts to recover ndvdual unknown but statstcally ndependent components wth only knowledge of measurements [7]. here s no need to provde parameters n usng BSS algorthm. he smple model for BSS assumes the exstence of n ndependent sgnals S [s1(t),, sn(t)] and m measurements X [x1(t),, xm(t)]. hs s completely represented by the mxng equaton X(t) AS(t) (1) 3

5 11th Internatonal Conference on Damage Assessment of Structures (DAMAS 2015) Journal of Physcs: Conference Seres 628 (2015) do: / /628/1/ A R mxn where. If the number of measurements and the exctaton sources are reman the same, then the source vector S can be obtaned once the mxng matrx A s estmated. But the physcal meanng of the mxng equaton needs to be establshed. Now consder a lnear tme-nvarant system wth n degree-of-freedom (DOF). he system response can be formulated as the product of mode shapes Φ ] [,,, ] and modal coordnates U(t): [ 1 2 n X(t) [ Φ] U(t) (2) Compare Eqs.(1) and (2), under the condtons where the modal coordnates are mutually uncorrelated wth non-smlar spectra for dynamc system whch s smlar to the assumpton of BSS that provded a one-to-one mappng between the mxng matrces (sources) and the vbraton modes (modal responses) of the system, therefore, the BSS can be nterpreted as the modal expanson. Snce most BSS technques are based on a model n whch the sources are mutually ndependent, however, the second order blnd dentfcaton (SOBI) belongs to a BSS technque that makes use of the temporal structure. It means that the sources have dfferent autocorrelaton functon (or power spectra) and are mutually uncorrelated [8, 9]. o perform SOBI two computaton steps are requred: whtng process and determnng the matrx U that approxmately dagonal the whtened covarance matrx. For whtng process, frst, conduct the egenvalue decomposton of the sgnal covarance matrx: [ RX(0)] EDE (3) From whch the weghtng matrx s defned: Addtonally, the whtenng observed data Z can be expressed as: 2 W D 1 E (4) Z WX (5) he covarance matrx of the whtenng data becomes: E [ ZZ ] WAE[ SS ] A W WAA W UU I (6) where E[ SS ] I and U WA. Because sources are statonary and uncorrelated, therefore, the tmedelayed covarance matrx of sources s dagonal. From ths one can easly determne the U matrx through an egenvalue decomposton of the tme-delayed covarance matrx of whtened data. For dfferent tme-delayed, the whtened covarance matrx s also dfferent. SOBI algorthm employs the jont approxmaton dagonalzaton (JAD) technque to determne the matrx U that approxmately dagonalzed the whtened covarance matrx wth dfferent tme-delayed value [10]. Procedures of usng SOBI for modal dentfcaton are lsted as follows: 1. Pre-Processng: Zero-mean can remove the offset and slope of the measured sgnals. Whtenng makes the measured sgnals uncorrelated and have unt varance. 2. JAD Analyss : After applyng jont approxmaton dagonalzaton, the U matrx whch dagonalzed the whtened covarance matrces wth dfferent tme-delayed value can be obtaned. 3. Modal Analyss: When mxng matrx A s obtaned; the source vector S can be determned and apply Fourer transform to the source vector to determne the system natural frequences. 4. Vbraton-based system dentfcaton of brdge under travellng vehcle loads Acceleraton response data (vertcal vbraton) of the vehcle-brdge structure nteracton through numercal smulaton was used for analyss. he orgnal samplng rate was 500 Hz. Before adoptng the SSI-COV algorthm to extract the system dynamc characterstcs, the data was down-sampled to 125 Hz for the analyss (through Butterworth low-pass flter). In ths smulaton a total of 16 cars (both ways) travelled on the brdge wth dfferent speed smultaneously. Fgs. 3a and 3b shows the stablty dagram developed from SSI-COV. he sze of the data Hankel matrx s (500x500). Fg. 3a used the OMAC crtera of 99.99% to remove the spurous mode whle Fg. 3b used both OMAC (99.99%) and MPC (99.9%) crtera. It s clear that wth addng extra MPC crtera some spurous modes near 4

6 11th Internatonal Conference on Damage Assessment of Structures (DAMAS 2015) Journal of Physcs: Conference Seres 628 (2015) do: / /628/1/ frequency 4.5 Hz and 6.4 Hz can be removed from the stablty dagram, but stll has some poles whch stll stay n the stablty dagram. hs s the phenomenon of complex modes (the effect of travellng waves). o check poles under such ambguty, wavelet packet transform (WP) s appled to extract sgnal near the frequency where ambguty poles are located. As shown n Fg. 4, the response (from WP) from each measurement s plotted at frequency of 4.28 Hz and 5.26 Hz (from the locaton of ambguty poles) [14]. It s observed that the phase dfference among the measurement at frequency of 4.28 s not consstent even though the dentfed poles are satsfy both the OMAC and MPC crtera. hrough such an observaton these ambguty poles can be also be removed from the stablty dagram.. b Fgure 3a. Stablty dagram wth usng OMPC crtera to remove the spurous modes. Fgure 3b. Stablty dagram wth usng both OMPC and MPC crtera to remove the spurous modes. (a) (b) Fgure 4: (a) Extract vbraton sgnal at frequency of 4.28 Hz, (b) Extract vbraton sgnal at frequency of 5.26 Hz. As dscuss before, n usng the SSI-COV to dentfy the system dynamc characterstcs there s stll have some hard crtera, such as the sze of data Hankel matrx or threshold of dampng rato, that need to be determned (cannot automatcally setup). On the contrary, n applyng BSS less pre-determned parameters s requred, therefore, the BBS technque s used to mnmze of usng model parametersfor system dentfcaton. Fg. 5 shows the Fourer ampltude spectrum of the dentfed source sgnals (a total of 8 modes whch are equvalent to the system modal responses). here s no spurous mode needs to be removed. It s confrmed that the modal frequency from each dentfed source s consstent wth the result from SSI-COV, as shown n able 2. he result s very consstence. Results of dentfcaton from SSI-COV and BSS-SOBI algorthms can also be also appled to the damage case (a 50% reducton of flexble stffness between measurment pont 5~6). able 2 also lsts the dentfed 5

7 11th Internatonal Conference on Damage Assessment of Structures (DAMAS 2015) Journal of Physcs: Conference Seres 628 (2015) do: / /628/1/ system natural frequences for comparson. It s observed that the change of natural frequences of the damage case s obvous and partculary focus on the hgher modes. he dentfed mode shapes from the mxng matrc A of BSS for both damaged and undamaged case s shown n Fg. 6. It s observed that there s no sgnfcant dfference among them, so the dentfed mode shapes are not a good ndcator for damage detecton even though there have obvous chang on the dentfed modal frequences. o perform damage detecton further analyss s requred. Fgure 5. fourer ampltude spectrum of each dentfed source sgnal usng SOBI able 2. Comparson on the dentfed natural frequences between damaged and udamafged case. Fgure 6. Comparson on the dentfed mode shapes between undamaged and damaged cases(sobi method) 5. Damage detecton usng reponse measurement o dentfy the damage locaton of the beam-lke structure, three dfferent approaches are used. Frst, takng the advantage of constructng the data Hankel matrx, a method based on null subspace and subspace damage detecton s used [11]. It s defned the null-space damage ndex (DI n) as: DI n meanu s U n0 (7) 6

8 11th Internatonal Conference on Damage Assessment of Structures (DAMAS 2015) Journal of Physcs: Conference Seres 628 (2015) do: / /628/1/ where U s s the subspace of the target analyss matrx Y (multplcaton of the transpose of data Hankel matrx) and U n0 s the null-space of the reference analyss matrx Y 0. Dfferent from the null-space damage ndex, the subspace damage ndex, DIs, s also defned as [11]: DI S K 1 ( y y y K 1 (8) where y s the th column of matrx Y. he term n the denomnator s used to normalze the damage ndex DI s so as to have DI s ranges from 0 to 1. he reference data (undamaged data) s needed to calculate the damage ndces. Larger DI s or DI n means the montor structure s dfferent from the reference structure. It s also beleved that data collected from near damage locaton may record sgnfcant response sgnals due to the occurrence of damage n the structural member. Damage ndex usng the dfference of Hlbert ampltude spectrum of the damaged data and the reference (undamaged) data can be used for locatng the damage. It s now defned the Hlbert ampltude assurance crtera (HAAC) between the damage case and reference case of the Hlbert ampltude spectrum at sensor locaton as : e t,f e j t, f ( t Η f Ref ( H d j (t,f) y (t,f) H t f t f 2 Large value of ndcated the smlarty s hgher at meaurement locaton. As shown n Fg. 7a, at node 5 and node 6 the HAAC value s much lower whch ndcate the damage locaton. Fnally, to verfy the accuracy of the proposed method n damage locaton dentfcaton, the the multvarate AR model wth order of 3 was used to dentfy the model parameters [12]. he analyss of multvarate AR model s conducted usng all the measurement data. By usng the dentfed model parameter from undamaged data, and adopt the damaged data for one step predcton for all measurement node, predct error can determned. Fg. 8 shows the error norm ncreases sgnfcanrtly near the locaton where element stffness reduced. Comparson wth the estmated damage locaton usng the change of mode shape curvature s als shown n the same plot. he result shows the U y Ref H s0 d j U (t,f)) s0 (t,f) dentfed damage locaton s almost the same from three dfferent approaches. (a) (b) Hlbert Ampltude Assurance Crtera undamaged vs. undamaged undamaged vs. damaged 2 y ) 1 2 ) e t,f (9) Fgure 7. (a) Calculate HAAC between undamaged and damaged cases to estmate the damage locaton; (b) Plot the change of mode shape curvature change (open crcle) and the predcton error norm (close crcle) wth respect to measurement locaton. 6. Conclusons hs study presented three dfferent system dentfcaton methods to extract the dynamc characterstcs and damage detecton by usng output-only measurement of the brdge-vehcle nteracton system. hrough numercal smulaton the dynamc response of a 2-span brdge subject to 7

9 11th Internatonal Conference on Damage Assessment of Structures (DAMAS 2015) Journal of Physcs: Conference Seres 628 (2015) do: / /628/1/ random travellng vehcle loads and wth the consderaton of surface roughness was generated for ths study. A new developed automatc covarance-drve stochastc subspace dentfcaton (SSI-COV) algorthm, the second-order blnd dentfcaton (SOBI) and multvarate AR-model are used to extract the dynamc characterstcs of the brdge system. echnque to remove the spurous modes n developng the stablty dagram of usng SSI-COV s dscussed. It s demonstrated that both methods can exactly dentfy the system natual frequences and mode shapes. Wth the mplemeaton of reducton n element stffness to smulate the damage of the brdge, through the proposed dentfcaton merthods, one can also detect the damage and dentfy the damage locaton by consderng the mode shape curvature change, norm of the predcton error and Hlbert ampltude assurance crtera. It demonstrated that each proposed dentyfcaton method has t goodness as well as the drawback n system dentfcton. For system wth well separate modes ether one of the method can detect the damage locaton well. Acknowlefgement he support from Monstry of Scence & echnology under grant No. MOS M s acknowledged. References [1] A.G.Poulmenos, S.D.Fassos, Parametrc tme-doman methods for non-statonary random vbraton modelng and analyss a crtcal survey and comparson, Mechancal Systems and Sgnal Processng, 20(4) (2006) [2] P.Argoul,.-P.Le, Instantaneous ndcators of structural behavor based on the contnuous Cauchy wavelet analyss, Mechancal Systems and Sgnal Processng,17(1) (2003) [3] Bart Peeters and Gudo De Roeck, Reference-based stochastc subspace dentfcaton for output-only modal analyss. Mechancal Systems and Sgnal Processng 13(6) (1999) [4] Yang, Y. B., and Ln, B. H. (1995). Vehcle-brdge nteracton analyss by dynamc condensaton method, J. Struct. Engrg., ASCE. 121(11) (1995) [5] Y.B. Yang, Y.S. Wu, A versatle element for analyzng vehcle brdge nteracton response, Engneerng Structures 23 (2001) [6] Internatonal Organzaton for Standardzaton (ISO), Mechancal vbraton road surface profles, reportng of measured data, ISO8608:1995(E). [7] Chaojun Huang and Satsh Nagarajaah, Expermental study on brdge structural health montorng usng blnd source separaton method: arch brdge, Structural Montorng and Mantenance, Vol. 1, No. 1 (2014) [8] B. Swamnathan, B. Sharma, S. Chauhan, Utlzaton of blnd source separaton technques for modal analyss, Proceedngs of the IMAC-XXVIII February 1 4, Jacksonvlle, Florda USA 2010 Socety for Expermental Mechancs Inc, [9] F. Poncelet, G. Kerschen, J.-C. Golnval, D. Verhelst, Output-only modal analyss usng blnd source separaton technques, Mechancal Systems and Sgnal Processng 21 (2007) [10] Adel Belouchran, A Blnd Source Separaton echnque Usng Second-Order Statstcs, IEEE transacton on Sgnal Proceedngs, Vol. 45, No. 2, February [11] Yan, A-Mn and Jean-Claude Golnval, Null subspace-based damage detecton of structures usng vbraton measurements, Mechancal Systems and Sgnal Processng, Vol: 20, (2006) [12] Vu, V. H., et al.. Operatonal modal analyss by updatng autoregressve model. Mechancal Systems and Sgnal Processng, 25(3), (2011) [13] We-ng Hsu, Chn-Hsung Loh and Shu-Hsen Chao,, Uncertanty Calculaton for Modal Parameters Used wth Stochastc Subspace Identfcaton: An Applcaton to a Brdge Structure, Paper ID , SPIE Smart Structures/NDE 2015 conference, San Dego, March 9-12, [14] Sheng-Fu Chen, zu-yun Hung and Chn-Hsung Loh, Analyss of traffc-nduced vbraton and damage detecton by blnd source separaton wth applcaton to brdge montorng, Paper ID , SPIE Smart Structures/NDE 2015 conference, San Dego, March 9-12,