LITERATURE REVIEW
2.2. LITERATURE REVIEW
2.2.3. Identification of modal parameters
estimated from the ambient vibration responses using the random decrement technique (RDT) (Ibrahim 1977) and this makes possible for the techniques like ITD to identify the modal parameters using ambient vibration data. The data-driven stochastic subspace identification (SSI-DATA) technique (Van Overschee and De Moor 1996) identifies the structural system in the form of state space matrices directly from the ambient response data.
Some of the important inherent steps / measures of SSI-DATA are orthogonal or oblique projection, estimation of Kalman states, least-square, singular value decomposition (SVD) etc. Finally the modal parameters are obtained using the identified state space model.
Covariance-driven stochastic subspace identification (SSI-COR) technique (Peeters and De Roeck 1999) is another technique based on the framework of SSI. The block Toeplitz matrix is decomposed using SVD to obtain the observability matrix and the stochastic controllability matrix. Subsequently the modal parameters are obtained. Further, auto regressive (AR) as well as auto regressive moving average (ARMA) based identification techniques have been implemented (Pandit 1991; Huang 2001; Pakzad and Fenves 2009; Loh and Wu 1996; He and De Roeck 1997; Kirkegaard el al. 1996) for modal parameter identification using ambient responses. It may be mentioned that Smail et al. (1999a; 1999b) proposed a new approach for modal analysis using the autoregressive moving average (ARMA) model and further presented the effect of model order and sampling frequency in modal analysis using ARMA model. Pakzad and Fenves (2009) identified the modal parameters in terms of central tendency and dispersion for better acceptability of the identified modal parameters. In many cases, it becomes difficult to measure from all the degrees of freedom (DOFs) in a single attempt while carrying out the ambient testing of large structures. All these DOFs are considered in multiple set-ups with overlapping reference sensors. A novel approach based on SSI named as SSI-ref (Peeters and De Roeck 1999; Peeters and De Roeck 2008) is developed to consider the multiple set-ups in the identification stage itself.
The simplest method in frequency domain is the peak-picking (PP) method (Bishop and Gladwell 1963). It provides reasonably good results under the assumption that the modes are well separated and the damping is lower. To avoid such limitations, frequency domain decomposition (FDD) method (Brincker et al. 2001) was presented based on the SVD of the power spectral density (PSD) matrix at every discrete frequency. First singular vector becomes an estimate of mode shape associated to a modal frequency and nearby PSD function helps to identify natural frequency and damping ratio. FDD method is further improved as frequency-spatial domain decomposition (FSDD) method (Zhang et al. 2005;
Zhang et al. 2010) considering similarity establishment with the well-accepted complex mode indicator function (CMIF) method (Shih et al. 1988). FSDD identifies natural frequency and damping ratio using curve fitting with enhanced PSD. Enhanced PSD may be viewed as similar entity as enhanced FRF which was proposed by Shih et al. (1988). A frequency domain based maximum likelihood (ML) identification technique (Hermans et al. 1998) was proposed to extract the modal parameters from output-only response data. Rational fraction orthogonal polynomial (RFOP) method (Richardson and Formenti 1985; Richardson 1986) was presented to obtain the modal parameters using the output-only data, where frequency response function (FRF) is expressed in rational fraction form (orthogonal Forsythe polynomials) instead of partial fraction form. Further, a different version of ERA, in frequency domain, was presented by Juang and Suzuki (1988) along with demonstration of its good performance. Polyreference least-squares complex frequency (PolyMAX) technique was proposed by Peeters et al. (2004). In the first phase a stabilization diagram is constructed and frequencies along with damping ratios are evaluated. Secondly, the mode shapes, associated to the stable poles, are estimated using the least-squares frequency-domain (LSFD) method. In the recent time, output-only system identification in the framework of Bayesian statistics is observed to be carried out in the works of Yuen (2003); Au S-K (2012a, 2012b);
Au S-K et al. (2013). Finally, various OMA applications along with the employed OMA techniques are presented in Table 2.1 helping to understand popularity of various OMA techniques.
Table 2.1. Various OMA applications along with the employed OMA techniques
SL no. Investigated structure
(reference) Employed techniques
1 Tsing Ma bridge (Qin et al. 2001) An improved version of ERA (FERA) 2 North Grand Island Bridge (Shama et
al. 2001) Peak picking
3 Cumberland River Bridge (Ren et al.
2004) Peak picking, SSI
4 FRP composite pedestrian truss bridge
(Bai and Keller 2008) Peak picking, SSI 5 Hakucho Suspension Bridge
(Siringoringo and Fujino 2008) ITD, NExT-ERA
6 Gi-Lu Bridge (Weng el at 2008) SSI, FDD
7 Alfred Zampa Memorial Bridge (He et
al. 2009) NExT-ERA, SSI, EFDD
8
Concrete arch bridge, over the Douro River, North Portugal (Magalhães et al.
2009)
SSI
9 Golden Gate Bridge (Pakzad and Fenves 2009)
Autoregressive with moving average models (ARMA) based identification 10
Eynel Highway Bridge, an arch type steel highway bridges, located in
Turkey (Altunişik et al. 2011a)
EFDD, SSI
11
Gülburnu Highway Bridge, a post- tensioned segmental concrete highway bridge, situated in Turkey (Altunişik et
al. 2011b)
EFDD, SSI
12
A cable-stayed bridge over the river Oglio in Italy (Benedettini and Gentile
2011)
EFDD, SSI
13
A stress-ribbon footbridge situated in the Faculty of Engineering of University of Porto (Hu et al. 2012)
SSI
14 Shanghai World Financial Center (Shi
et al. 2012) PP, RDT, Hilbert-Huang transform 15
Tamar Bridge - a long-span suspension in Southwest England (Cross et al.
2013)
SSI
16
The San Michele Bridge and A13 highway overpass in Bologna (Ubertini
et al. 2013)
FDD, SSI
Although many case studies are observed in the literature for various existing bridges as well as building structures, no large and complex bridge structure like the Saraighat Bridge is found to be investigated for modal parameters. Various strategies are found in literature for efficient modal identification against various unfavourable conditions, which are usually involved in OMA exercises. There are (a) implementation of multiple techniques, usually, both in time and frequency domains (b) identification of modal parameters in statistical way (central tendency, dispersion, confidence interval). Combined effort based on these major approaches is likely to have better acceptance of the identified modal parameters. Further, detailed study is not reported in the literature to find out the suitable size of Hankel Matrix, which is an important factor for efficient modal identification.