## 3 Extraction of the Ground Vibration Components
### Comparison of EMD and MEEMD Based Long Period Component Extraction
#### 3.3.1 Extraction and Reconstruction of Long-Period Ground Vibration Components  
In the following, we study three long-period ground shocks, ILA056, TCU068, and CHY025, and take TCU068 as an example to be decomposed by the two methods, EMD and MEEMD, respectively. As shown in Figure 8, ten IMF components and one residual component were obtained after EMD decomposition; eleven IMF components and one residual component were obtained after MEEMD decomposition, and as the decomposition proceeded, the frequency of the obtained components also gradually decreased. According to Equation (9) [24], the IMF components and residual components of the three long-period seismic waves are calculated as shown in Table 3.  
\[T_{r}=\frac{\sum_{i}T_{i}\big{(}\frac{S_{a}(T_{i})}{PGA}\big{)}^{2}}{\sum_{i} \big{(}\frac{S_{a}(T_{i})}{PGA}\big{)}^{2}}\qquad\qquad 0.05\,s\leq T_{i}\leq 10\,s \tag{9}\]  
It is shown in [11] that after \(\text{Tr}\geq 2\) s, the amplitude of the high-frequency part of the Fourier spectrum above 1 Hz is greatly attenuated, and the region of the velocity spectrum with a larger amplitude is distributed in the longer-period section. The components (including residual components) obtained after the decomposition of the EMD and MEEMD methods were divided by \(\text{Tr}=2\) s; the components with \(\text{Tr}<2\) s were reconstructed as short-period components (SPC), and the components with \(\rm{Tr}\geq 2\) s were reconstructed as long-period components (LPC). The reconstructed component \(\rm{Tr}\) is shown in Table 4. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Ground Motion** & **Tr/s** & **IMF1** & **IMF2** & **IMF3** & **IMF4** & **IMF5** & **IMF6** & **IMF7** & **IMF8** & **IMF9** & **IMF10** & **IMF11** \\ \hline ILA056 & EMD & 1.126 & 1.004 & 1.326 & 2.022 & 5.169 & 6.215 & 7.11 & 5.95 & 5.168 & 5.124 & - \\ ILA056 & MEEMD & 0.966 & 1.519 & 2.338 & 5.233 & 7.427 & 6.407 & 5.115 & - & - & - & - \\  & EMD & 0.282 & 0.536 & 0.432 & 0.831 & 1.54 & 2.405 & 4.18 & 7.445 & 7.058 & 5.08 & - \\ TCU068 & MEEMD & 0.415 & 0.492 & 0.817 & 2.647 & 3.19 & 7.321 & 6.88 & 7.519 & 5.383 & 5.39 & 5.45 \\  & EMD & 0.271 & 0.5 & 0.762 & 1.31 & 3.101 & 4.01 & 5.268 & 6.901 & 7.698 & 5.29 & 5.109 \\ CHY025 & MEEMD & 0.557 & 1.39 & 1.70 & 2.256 & 4.099 & 6.711 & 7.856 & 6.224 & 5.126 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The parameters of each IMF component \(\rm{Tr}\) (s). Figure 8: Decomposition of TCU068: (**a**) EMD method; (**b**) MEEMD method. However, the reconstructed components have a large baseline drift in the velocity time course and need to be baseline corrected. The baseline-corrected signal is used as the long-period component of the ground shaking. Figure 9 shows the comparison of the acceleration, velocity, and displacement of the long-period component of TCU068 before and after the baseline correction based on the MEEMD method. Figure 10 shows the time-range curves of the TCU068 long- and short-period components after the baseline correction, based on the two methods of decomposition and reconstruction. The time-range curves of component acceleration were similar in the two methods of reconstruction; however, the velocity and displacement curves were quite different. 3.2 Validation of the Correlation between the Long-Period Ground Shaking and the Effect of the Long-Period Components on the Structural Response  
In the previous section, the extraction method of the long-period component of ground shaking was proposed based on the EMD and MEEMD; therefore, it was necessary to verify the validity of this component separation method. In this section, we describe the verification of its validity using the correlation between the components extracted from the two methods and the response characteristics of the original ground shaking to the structure. In addition, we compare the two methods.