6 Mode Shape Identification Using Drive-by Monitoring: A Comparative Study 59 Fig . 6. 2 (a ) Vehicle response; (b ) CP response; (c ) FFT spectrum of vehicle response; (d ) FFT spectrum of CP response Regarding the slight differences observed between the identified and numerical bridge frequencies, it should be noted that the actual modal frequencies of bridges can be obtained under ambient vibrations. However, the dynamic response of the vehicle-bridge interaction (VBI) system is a nonstationary problem due to the moving vehicle that causes the bridge to behave under the forced vibrations [22]. Therefore, observing the variation between the identified bridge frequencies extracted from the nonstationary response and the theoretical ones is reasonable. The configurations used to describe the system and the moving vehicle analysis, which are explained above, are referred to as the benchmark model in the rest of this chapter. In the following sections, various simulations are carried out with the same bridge and vehicle properties to investigate the effects of vehicle speeds, sampling rates, and road surface roughness on mode shape identification using two approaches proposed by Yang et al. [9, 16] and Li et al. [19], respectively. These two methods are briefly introduced in the following sections. For further details, the readers are recommended to refer to the Refs. [9, 16, 19]. 6.2.1 Method 1 Method 1 proposed by Yang et al. [9, 16] utilizes the same VBI system as presented in Fig. 6.1. This method is principally based on signal decomposition to identify the modal information of the bridge and processing the decomposed signals to construct the mode shapes. First, the vertical acceleration response of CP recorded during the passage of the vehicle over the bridge at a constant velocity is used to filter the vehicle frequency out as described [16] and depicted in Fig. 6.2d. Second, the component responses associated with the modal frequencies of the bridge can be extracted by implementing a feasible signal decomposition tool to the recorded signal, such as the band-pass filter, singular spectrum analysis, and empirical modal decomposition. In this study, the variational mode decomposition (VMD) method is applied as a signal decomposition tool to extract the first three modal components [23]. Finally, the obtained components are processed by the Hilbert transform (HT) to provide the instantaneous amplitude history for constructing the mode shape of the given mode [24]. For instance, when the acceleration response of CP in Fig. 6.2b is processed by VMD and HT, the components related to the first three modes and their amplitude histories are plotted in Fig. 6.3.
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