# Structural Responses of a Superall Building Subjected to a Severe Typhoon at Landfall
## 4 Results and Discussion
### Identification of Modal Parameters  
#### 4.3.1 Natural Frequency and Damping Ratio  
Figure 9 shows the PSD results based on the acceleration response at the 56 th and the 58 th floors during 15:00-19:00/16. In this study, both the Welch approach and the Yule-Walker technique are adopted to estimate the PSD. The block length for the Fast Fourier Transform (FFT) analysis involved in the Welch method was set as \(2^{14}=16384\) to provide a frequency resolution finer than 0.001 Hz (actually 0.000977 Hz), and the order for the Yule-Walker method was taken as 1000. From Figure 9, the results estimated via the two methods show good agreement, which indicates that the estimation processes were conducted effectively. The results at the 56 th floor show that there exist three evident PSD peaks in the frequency range below 0.8 Hz. However, the sharp peak around 0.430 Hz at the 56 th floor turned out to be considerably subtle for the case at the 58 th floor. From Table 1, the accelerometer at the 58 th floor was placed around the centroid of the cross section, while the one at the 56 th floor was placed far away from it. Thus, the accelerometer at the 58 th floor was hardly able to measure response components of the torsional modes. Based on the above discussions, it is clear that the mode associated with 0.430 Hz belongs to a torsional type, while others belong to a swaying type. Figure 8: Comparison of measured maximum acceleration responses with those recommended by different comfort criteria. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Dir.**} & \multicolumn{2}{c}{**Approaching Period**} & \multicolumn{2}{c}{**Nearest Period**} & \multicolumn{2}{c}{**Leaving Period**} \\ \cline{2-7}  & **Measured** & **Calculated** & **Measured** & **Calculated** & **Measured** & **Calculated** \\ \hline X & 2.99 & 3.26 & 3.03 & 3.26 & 3.03 & 3.28 \\ Y & 3.09 & 3.26 & 2.97 & 3.25 & 3.25 & 3.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Peak factors from measurement and calculation during different periods. The RDT method is then utilized to estimate the damping ratio for different modes based on SDOF response components that are separated from the acceleration signals via band-pass filtering. Figure 10 exhibits associated results for the first swaying mode at the 56 th floor. The damping ratios for the modes along the two measurement directions are estimated to be 1.03% and 1.02%, respectively. The SSI method is further adopted to estimate the modal parameters of Leatop Plaza. As discussed previously, the stability diagram method is used to evaluate the computational mode order with the involved critical values determined through a trial-and-error method as follows: 0.01 for natural frequency, 0.05 for damping ratio, and 0.90 for mode shape. Figure 11 shows the stability diagram overlaid by associated PSD results at the 56 th floor. As reflected, there are three robust stable-axes in the range below 0.8 Hz, and the corresponding frequencies agree well with the natural frequencies  
Figure 10: Typical random decrement (RD) signatures and estimation of natural frequency and damping ratio for first swaying mode at the 56 th floor (N: sample number involved in RD signature). (**a**) Along X; (**b**) Along Y.  
Figure 9: Comparison of power spectral density curves by the Welch and the Yule–Walker methods. (**a**) Along X; (**b**) Along Y.  
obtained via the peak-picking method based on the PSD results. The computational mode order can be then selected as six, which is half of the nominal mode order as marked in the figure. Table 4 compares the identification results of the natural frequencies and the damping ratios via both the SSI method and the RDT method. Basically, the two kinds of results show acceptable agreement. It is noted that it is very different to estimate the damping ratios accurately based on output-only records, and large fluctuation may exist even for the case by using the same method but based on different episodes of records.