## 4 Full-Scale Measurement of the Canton Tower
Figures 12 and 13 show the time histories and the associated Hilbert spectrum of 7 th-10 th IMFs. It can be seen that the main frequency ranges from 0.07 Hz to 0.1 Hz. With the aid of power spectrum analysis, it can be inferred that the IMF8 and IMF10 are corresponding to the second and the first vibration mode of the X direction, respectively. Figure 10: View of Canton Tower and monitoring system. Figure 11: Acceleration response measured atop Canton Tower during the earthquake. Figure 12: 7 th–10 th IMFs of X-direction response of Canton Tower. Then, the modal parameters are mainly identified by the SSI and FBFFT methods. Due to the close and multiple vibration modes of the Canton Tower, it is still difficult to determine the exact system order in SSI methods using the singular spectrum and stabilization diagram as displayed in Figures 14a and 15a. [PERSON] et al. [29] adapted the system orders of 90 and 120 in the SSI method after reducing the noise with the singular spectrum analysis; nonetheless, the drawbacks that spurious modes cannot be avoided and some actual modes may be improperly filtered out still exist. Figures 14b and 15b show the singular value and stabilization diagram of IMF10, the first vibration mode of X direction. It is obviously observed that, in Figure 14b, there is a significant gap in the distribution of singular value when N = 2 and in Figure 15b the frequency of stable poles almost indicates the same frequency, which is the only one peak in the figure of PSD function of the reference point. Therefore, for the decomposed signal, the system order can be set clearly as two. As mentioned before, the row of the Toeplitz matrix plays a significant role in discriminating between the noise and true vibration signal, so the effect between the various Toeplitz matrix row numbers with the modal parameters is taken into consideration as shown in Figure 16, in which each mode is identified separately with the system orders of two, except that the Mode4 and Mode5 are extracted synchronously from the 8 th IMF of Y-direction so the system order is decided as four. It can be seen that the frequencies are quite stable with the increasing of the rows of the Toeplitz matrix in the stability diagram. Figure 13: Hilbert spectrum of the 7 th–10 th IMFs of X-direction. (**a**) IMF7; (**b**) IMF8; (**c**) IMF9; (**d**) IMF10. Figure 14: Singular spectrum from SVD of Toeplitz matrix. (**a**) Original data; (**b**) IMF10. Figure 15: Stabilization diagram of original and decomposed acceleration response for the Canton Tower. (**a**) Original data; (**b**) IMF10. The modal parameters of Canton Tower under earthquake excitation are identified by the MEMD-based SSI and FBFFT methods. In the FBFFT method, the initial frequencies are picked up from the power spectrum density function directly and frequency bands are manually selected approximately with a length of 10 percent of the initial frequency, as listed in Table 6. The identified frequencies and damping ratios together with other results by the HHT combined with the RDT method and HPBW are summarized in Tables 7 and 8, respectively. In addition, for comparison, the modal parameters under the Shenzhen earthquake by the frequency decomposition method are listed together as well [44]. Similar to previous illustrations, the frequencies identified by various methods are consistent with each other, while damping ratios display great discreteness. The COVs of the frequencies in the Bayesian are less than 1%, showing high confidence, and associated COVs of the damping ratios of the first two modes are as much as 50%. Figure 17 shows the comparison of the identified mode shapes of Canton Tower. It can be seen that the mode shapes can be effectively identified by two methods that are consistent with each other, especially for the first two modes.