Statistical Analysis of Online Response Data of a Stadium Structure

Transcription

1 Statistical Analysis f Online Respnse Data f a Stadium Structure Prasenjit Mhanty, Paul Reynlds and Aleksandar Pavic The University f Sheffield Department f Civil and Structural Engineering Sir Frederick Mappin Building Mappin Street, Sheffield, S1 3JD, UK ABSTRACT Crwd behavir plays an imprtant rle in the dynamic excitatin f a stadium structure. Reliability in the designing the dynamic perfrmance f a sprt stadium depends n its accurate dynamic characterizatin, i.e. natural frequencies, mde shapes and damping f the assciated mdes in the presence f a crwd. A Remte Mnitring System (RMS) prvides a cnvenient way f testing the stadium structures. With an RMS system, mnitring can be carried ut in the presence f a crwd, fr a lng duratin withut direct invlvement f the test engineers. In this paper, test data are analysed that were acquired fr the Bradfrd stadium with the help f an RMS system, develped at the University f Sheffield. Seven different types f ambient mdal parameter identificatin methds have been used t analyze RMS data acquired during a ftball match. Six different sets f data have been chsen frm the whle ftball match, which have been prcessed with the varius identificatin methds. It has been shwn in this wrk that crwd structure interactin has a significant effect n the natural frequencies and crrespnding damping ratis f the structure. It is bserved that natural frequencies f the system decreases and crrespnding damping values increases with the crwd cnfiguratins which agree with the past research. 1 INTRODUCTION Crwd-induced vibratin is a majr surce f cncern when cnsidering stadia structures. The actual behavir is very much dependent n the nature f crwd-structure interactin, which is nt well understd in practice. The nature f crwd-structure interactin in a stadium structure des nt remain the same during a match. Crwds behave differently and thereby interact differently with a stadium structure as a match prceeds. The dynamic prperties f the crwd-structure system therefre change thrughut a match. Accurate determinatin f the dynamic perfrmance f a stadium structure depends n the accuracy f its dynamic characterizatin, i.e. natural frequencies, mde shapes and damping f the assciated mdes. Experimental Mdal Analysis (EMA) f a structure prvides an ideal way t cmpute mdal prperties f the existing empty structures. In the EMA prcedure, an artificial frce is applied that is large enugh t prduce measurable respnse at the measuring pints, but yet small enugh t allw the structure t be cnsidered as a linear system. Bth the input frce t the structure and the respnse f the structure at different lcatins are measured accurately. Mdal parameter identificatin methds are then usually applied t the test data t determine the mdal parameters. In the presence f crwd, testing the stadium structure by EMA prcedure is nt feasible as respnse f the structure due t the unknwn crwd excitatins difficult t separated frm the respnse due t the artificial excitatin. Ambient vibratin testing is used as an alternative testing prcedure t perfrm mdal parameter identificatin f the ccupied stadia structures. In ambient vibratin testing, the input excitatin frce is nt measured. Fr ccupied structure the crwd dynamic excitatin is a surce f unmeasured excitatin. An assumptin may be made that it has a brad spectrum, which can be cnsidered as ambient excitatin. Sme advantages f ambient vibratin testing are: testing is cheap since n excitatin equipment is needed, the measurements are dne in the actual peratinal cnditins fr the structure, s the identified mdal parameters represents the dynamic behavir f the structure such as used in reality, and the mnitring des nt interfere with the peratin f the structure. The RMS system prvides an ideal slutin t mnitr the structure in its perating cnditin, where lng duratin measurements are required. A unique RMS system has been develped by the vibratin engineering research sectin at the 1

2 University f Sheffield [12]. The RMS system was used fr mre than a year t acquire respnse data fr a grandstand in Bradfrd, UK. In this paper, mdal parameters f the stadium have been estimated frm data acquired during a typical ftball match. T imprve cnfidence in the identified mdal parameters, seven different identificatin methds have been used. Six different sets f respnse data have been chsen frm the duratin f the match representing varius crwd cnfiguratins. Prir t lng term mnitring, a single-shaker EMA testing had been perfrmed n the stadium structure t identify the mdal parameters. In this paper, natural frequencies and assciated damping frm the RMS data have been cmputed by seven different identificatin methds with six different sets f data. Finally changes in the mdal parameters with respect t crwd cnfiguratins have been cmpared. 2 DESCRIPTION OF THE GRANDSTAND AND RMS SYSTEM The grandstand was built in the early 1990 s. The stadium structure cnsists f 15 steel frames spaced at 7.19m intervals giving a ttal length f 100m in length. The seating deck is frmed frm precast cncrete L-shaped seating deck units that span between the steel frames. Figure 1: Different views f the grandstand: (a) side view f the grandstand, (b) crss-sectin f the grandstand gemetry and (c) frnt view f the grandstand The RMS system cnsists f 12 Endevc mdel piezelectric lw frequency accelermeters cmbined with tw Micrstar Labs idsc1816, 8-channels 16-bit data acquisitin cards. On the tp f this, a Natinal Instruments IMAQ PCI-1408 image acquisitin card was used fr vide data acquisitin fr crwd behavir. The system was cntrlled with Natinal Instruments LabVIEW sftware. Cmmunicatin with the RMS was perfrmed using the PCAnywhere sftware via a permanent ADSL bradband internet cnnectin. Fig. 1 shws the different views f the grandstand and Fig. 2 shws the 2

3 psitin f the CCTV cameras and accelermeters. Figure 2: Plan f the grandstand shwing lcatin f the CCTV vide cameras 3 AMBIENT MODAL ESTIMATION TECHNIQUES Different parameter estimatin techniques can vary in terms f the mdal prperties they identify in the presence f nise. It is beneficial t identify the mdal parameters using different methds, which imprves cnfidence in the results. Fr this same reasn seven different mdal parameter estimatin methds have been used in this paper. The seven identificatin methds can be classified int three different categries, as fllws: methd based n Singular Values Decmpsitin (SVD) f frequency data. 1. Enhanced Frequency Dmain Decmpsitin (EFDD) [6] methds based Stchastic Subspace Identificatin (SSI) 2 Unweighted Principal Cmpnent (UPC) [13] 3 Principal Cmpnent (PC) [13] 4 Cannical Variate Analysis (CVA) [13] methds based n Natural Excitatin Technique (NExT) 5 Least Square Cmplex Expnential methd (LSCE) 6 Eigensystem Realizatin Algrithm (ERA) 7 Single Statin Time Dmain algrithm (SSTD) Frm the RMS data six different data blcks have been chsen accrding t the crwd cnfiguratin. It is intended t estimate the mdal parameters fr different crwd excitatin level. In the Fig. 3 a typical time histry has been prvided fr the respnse f first accelermeter and in Table 1 data blcks spreading have been prvided fr different events during the match. 3.1 Brief Descriptin f the Estimatin Methds Enhanced Frequency Dmain Decmpsitin (EFDD) is a mdified frm f the Frequency Dmain Decmpsitin (FDD) methd. FDD uses Singular Value Decmpsitin (SVD) f Aut Spectral Density (ASD) f the respnse matrix instead f its ASD directly [5]. It has been prved [1] that the peaks f a singular value plt indicate the presence f structural mdes. Pick-picking is perfrmed n the SVD plt, in the same manner as fr the traditinal peak picking methd applied t the ASP plt. The mdal estimatin is divided int tw steps. In the first step FDD Peak-picking is perfrmed and in the secnd step the mde shapes identified by FDD are used t identify the SDOF Spectral Bell functin by emplying in user specified Mdal Assurance Criteria (MAC) value t include the singular values at bth sides f the peak psitin f the SVD diagram. The natural frequency and the damping rati f the mde are estimated by transfrming the SDOF Spectral 3

4 Acceleratin (m/sec 2 ) Time (sec.) Figure 3: Typical time-histry at the first respnse accelermeter sequence crwd cnfiguratin start (sec.) end (sec.) length (sec.) 1 empty stadium crwd leaving crwd seating crwd filling half time gal Table 1: Distributin f data blcks used in the analysis Bell t time dmain. Using a simple regressin analysis as the time dmain functin, the natural frequency and damping rati can be evaluated. Stchastic Subspace Identificatin (SSI) is applied directly t the time dmain acceleratin respnse data. In this methd, a parametric mdel f the system is fitted directly t the respnses f the accelermeters. The parameters in the mdel can vary accrdingly t the way that a parametric mdel is fitted t the raw time-dmain respnse data. In this paper three different prcedures f SSI have been used; Unweighed Principal Cmpnent (UPC), Principal Cmpnent (PC) and Cannical Variate Analysis (CVA). All the three methds are similar, except that they differ n hw the input matrix is weighted [13]. The third set f methds are based n the Natural Excitatin Technique (NExT) [8]. As described in the NExT prcedure, crss-crrelatin and aut-crrelatin f respnse signals in the presence f ambient excitatins are related t the impulse respnse f the system. The LSCE [2], ERA [3] and SSTD [4] methds are all based n curve fitting the impulse respnse functin f the system. The LSCE and ERA methds can prcess multiple signals at nce. Hwever the SSTD methd can nly cnsider ne nly signal at a time. Fr this reasn, the SSTD methd has been applied t the aut-crrelatin f signal frm the first accelermeter t prcess mdal parameters. 3.2 Estimatin f mdal frequencies and damping Shaker-based mdal testing was perfrmed prir t the remte mnitring f the system. A single shaker was used t excite f the structure. Mdal parameters cmputed frm the Frequency Respnse Functins(FRF) btained via the shaker-based testing are presented in the Table 2 Mde Natural frequencies Viscus mdal damping rati (Hz) (%) Table 2: Mdal parameters cmputed by shaker-based mdal testing 4

5 Figure 4: Prcedures f EFDD in ARTeMIS sftware ERA / NExT: Crwd Leaving, secnds 100 damping % 2.40% 4.80% 7.20% 9.60% 10% 2 Mdal Order Pwer Spectral Density (db) Frequency, Hz Figure 5: Stability plt cmputed by NExT/ERA prcedures 5

6 Mde 1 Frequency [Hz] Mde 4 Frequency [Hz] Mde 7 Frequency [Hz] Crwd Cnfiguratin Crwd Cnfiguratin Crwd Cnfiguratin Mde 8 Frequency [Hz] Mde 5 Frequency [Hz] Mde 2 Frequency [Hz] Crwd Cnfiguratin Crwd Cnfiguratin Crwd Cnfiguratin Mde 3 Frequency [Hz] Mde 6 Frequency [Hz] Mde 9 Frequency [Hz] Crwd Cnfiguratin Crwd Cnfiguratin Crwd Cnfiguratin Crwd Cnfiguratins 1: empty 2: leaving 3: seating 4: filling 5: Half time 6: Gal Clr Identificatins FEDD UPS PC CVA LSCE ERA SSTD Figure 6: Natural frequencies cmputed by different parameter estimatin methds at different crwd cnfiguratins Mde 7 Damping [%] Mde 4 Damping [%] Mde 1 Damping [%] Crwd Cnfiguratin Crwd Cnfiguratin Crwd Cnfiguratin Mde 8 Damping [%] Mde 5 Damping [%] Mde 2 Damping [%] Crwd Cnfiguratin Crwd Cnfiguratin Crwd Cnfiguratin Mde 3 Damping [%] Mde 6 Damping [%] Mde 9 Damping [%] Crwd Cnfiguratin Crwd Cnfiguratin Crwd Cnfiguratin Crwd Cnfiguratins 1: empty 2: leaving 3: seating 4: filling 5: Half time 6: Gal Clr Identificatins FEDD UPS PC CVA LSCE ERA SSTD Figure 7: Mdal damping cmputed by different parameter estimatin methds at different crwd cnfiguratins 6

7 During the acquisitin prcess, the respnse data were sampled at 80Hz. Fr a large civil engineering structure like a stadium, natural frequencies f interest are usually lwer than 10Hz. Nyquist frequency fr RMS data being 40Hz, all the respnse signals were filtered with lw-pass filter t 20Hz prir t implementing the EFDD, UPC, PC and CVA methds implemented in ARTeMIS sftware. In all cases the respnse signal frm the first accelermeter, which is at the test pint 1 has been taken as reference signal. Fig. 4 shws the prcedure fr EFDD using ARTeMIS sftware. EFDD methds prvides bth infrmatin fr natural frequencies and damping ratis. Fr the methds based n NExT prcedures, first crss- and aut-crrelatin functins have been cmputed fr all respnse signals taking the first accelermeter signal as the reference signal. In Fig. 5, a stability plt cmputed with ERA methd has been shwn. It can be nted that in rder avid many number f unnecessary mdes, in the stability plt maximum frequency and damping limits have been set t 10Hz and 12% Mdal parameters cmputed by the methds have been presented in the tw blck diagrams. Fig. 6 cntains natural frequencies infrmatin and Fig. 7 cntains crrespnding damping values. Each blck diagram cntains 9 charts assciated with first 9 mdes f the stadium structure. Each chart in a blck cnsists f six results fr six different sets f test data assciated with the crwd cnfiguratins. Seven different mdal parameter identificatins methds are used and mdal parameters frm each methd are assciated with a specific clr. A hrizntal line (red clr) have been marked n each set f the plt fr mdal parameters. This is the average value f all mdal parameters. It can be seen frm Fig. 6 and 7 that the estimated damping values are higher than the values frm the FRF based testing f the empty structure. In sme f the graphs, damping tend t increase and natural frequencies tends t decrease, which agree with the previus findings [9 11]. Hwever the increases f damping are nt the same fr different crwd cnfiguratins. Reductin f the natural frequencies have been relatively cnstant as cmpared t the increasing values f damping. Anther bservatin is that there is a drp f damping values significantly at the time f gal. This might be due t the substantially different behavir f the crwd during a gal event. 4 COMPARISON OF DIFFERENT METHODS Different parameter estimatin techniques vary in terms f the identified mdal parameters. It is smetimes useful t use different methds t enhance cnfidence in the estimated mdal parameters. In this paper three sets f identificatin techniques have been used. Firstly, the EFDD methd is based n SVD f the respnse matrix. Users have quite gd cntrl in chsing natural frequencies and damping which are based n the peaks f SVD plts. Secndly, the UPC, PC and CVA methds are all based n the SSI principle. These three methds have lt in cmmn, which have been reflected in the identified mdal parameters. It can be bserved that damping values cmputed with these methds are typically higher than prduced in ther methds. Again it can be bserved that weak mdes are nt identified prperly with these methds. Finally, the LSCE, ERA and SSTD methds are based n the NExT principle. LSCE and ERA methds have been able t cmpute mdal parameters quite accurately. LSCE methd is able t estimate mdal parameters f the weakly excited mdes quite accurately. Care shuld be taken t separate spurius cmputatinal mdes frm the real mdes. In the LSCE methd, mdal parameters change rapidly as the mdal rder f the system increases. Unlike the LSCE methd, in the ERA methd mdal parameters d nt vary rapidly as the mdal rder increases, which gives mre cnfidence in the ERA-estimated mdal parameters. Unlike LSCE and ERA methds, the SSTD methd is based n a single impulse respnse f the system. Stability diagram assciated with this methd als lks bit nisy as significantly few data are used t prcess mdal parameters. S the SSTD methd shuld nt be used alne but in cnjuctin with ther methds as a quality check. 5 CONCLUSION It has been shwn in this paper that different identificatin methds differ in their cmputatin f mdal parameters, even when the same data have been used fr all the methds. It is imprtant t use mre identificatin methds t estimate mdal parameters t give increased statistical cnfidence in the results. It appears that crwd structure interactin has a significant effect n natural frequencies and damping ratis f the stadium structure cmpared with its empty cnditin. Changes in natural frequencies and damping ratis are directly related t the crwd cnfiguratins. While cnsidering change f natural frequencies, crwd can be cnsidered as an additinal mass t the structure, but while cnsidering damping, nature f crwd behavir (standing, sitting, jumping, etc) is imprtant. It is very imprtant t cnsider crwd cnfiguratin and behavir while designing a stadium. Effect f crwd cnfiguratin and their dynamics shuld be included in the dynamic analysis f the stadium structures during their design. REFERENCES [1] Ibrahim, S.R. and Mikulcik, E.C. A methd fr the direct identificatin f vibratin parameters frm the free respnse. Shck and Vibratin Bulletin, , N. 47, Pt. 4, Sept [2] D. L. Brwn, R. J. Allemang, R. Zimmerman, M. Mergeay. Parameter Extimatin Techniques fr Mdal Analysis. 7 th Internatinal Seminar n Mdal Analysis, Kathlieke Universiteit Leuven, Belgium, [3] J. N. Juang, R. S. Pappa, An Eigensystem Realizatin Algrithm fr Mdal Parameter Identificatin and Mdel Reductin. Jurnal f Guidance, Cntrl, and Dynamics, 8(5): , Sept.-Oct [4] S. A. 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8 [5] R. Brincker and L. Zhang and P. Andersen. Mdal Identificatin frm Ambient Respnses using Frequency Dmain Decmpsitin Prceedings f the 18th Internatinal Mdal Analysis Cnference (IMAC), San Antni, Texas, [6] R. Brincker and C.E. Ventura and P. Andersen. Damping Estimatin by Frequency Dmain Decmpsitin 19th Internatinal Mdal Analysis Cnference (IMAC), Kissimmee, Flrida, [7] R. Brincker and L. Zhang and P. Andersen. Mdal Parameter Estimatin frm Ambient Respnse Data Prceedings f the 19th Internatinal Mdal Analysis Cnference (IMAC), San Antni, Texas, [8] G. H. James, T.G. Carne, J. P. Lauffer, and Sandia Natinal Labratries. The Natural Excitatin Technique (NExT) fr mdal parameter extractin frm perating structures. Jurnal f Analytical and Experimental Mdal Analysis, 10(4): , Octber [9] R. Sachse, The influence human ccupants n the dynamic prperties f slender structure Ph.D. Thesis, The University f Sheffield, UK, April 2002, ISMN: [10] B. R. Ellis and T Ji, Human-structure vibratin in vertical vibratins Prceedings f the Institute f Civil Engineers, Structures and Buildings, Vl. 122(1), pp. 1-9, [11] P. Reynlds, A. Pavic and Z. Ibrahim, Changes f mdal prperties f a stadia structure ccupied by a crwd Prceedings f IMAC-XXII, January 26-29, 2004, Dearbrn, Michigan. [12] P. Reynlds, A. Pavic and Z. Ibrahim, A Remte Mnitring System fr Stadia Dynamics 21st Internatinal Mdal Analysis Cnference (IMAC XXI), February, 2003, Flrida, USA. [13] Overschee, P. van and B. De Mr, Subspace identificatin fr linear systems Thery, Implementatin, Applicatins. Kluwer academic Publishers, ISBN ,