## 5 The Seismic Vulnerability of an \(\pm\)800 kV Suspended Filter Capacitor  
### Material Parameter Combination and Ground Motion Sampling  
As a case study, the suspended filter capacitor was utilized as the object to illustrate the proposed method. Section 2 exhibits the structures and parameters of the filter capacitor whereas they are certain values that cannot reflect the actual situation. To consider the uncertainty of material parameters, the distributions of some key parameters of the filter capacitor are given in Table 4. At first, the pre-tension force is set as 20 kN, as is true. The parameters include the elastic modulus \(E_{in}\), density \(\rho_{in}\), and damping ratio \(\eta_{in}\) of the insulators, and the elastic modulus \(E_{g}\) of the steel gantry. In this study, these parameters are regarded as independent of each other. Table 4 also exhibits the distribution of PGA to represent the uncertainty of ground motion intensity. To get the calculation samples, LHS was utilized to randomly select parameter combinations from the distributions given in Table 4, thereby 50 groups of samples (M = 50) were obtained. In each samples group, there are five parameters that represent one engineering situation.  
On the other hand, the uncertainty of ground motions should be considered. Twenty (\(N=20\)) natural ground motion recordings were selected as the input of the simulation model during the time history computations. The selection of the ground motions is based on the recommendation of the FEMA/SAC project [60]. The response spectra of the twenty ground motions are shown in Figure 12. This type of uncertainty also includes the variety of PGA while it has been considered in Table 4.  
The 50 groups of parameter combinations and 20 ground motions would be combined one to one, thereby 50 \(\times\) 20 = 1000 time history computations should be completed, with which 50 \(\times\) 20 = 1000 responses can be obtained. Here, the response is the maximum axial stress response of the top insulators of the filter capacitor, since the maximum stress of the filter appears on the top insulators, as mentioned before. For each parameter combination, there are 20 response values that respond to the 20 ground motions, so their mean \(\mu\) and standard deviation \(\sigma\) can be calculated, as listed in Figure 13. It can be seen that the mean values of the responses vary from near 0 to 150 MPa, which indicates the effect of LHS. In addition, each parameter combination provides one certain PGA for the different ground motions, therefore the responses can be plotted on the basis of PGA as an independent variable, as shown in Figure 14. In Figure 14, the mean \(\mu\), \(\mu-\sigma\), and \(\mu+\sigma\) of the responses under each PGA are also given. Overall, the responses increase with the growth of the PGA whereas the amplitude of fluctuation is also gradually increasing.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Parameter** & **Unit** & **Mean** & **(Logarithmic) Std. dev.** & **Distribution** \\ \hline \(E_{\text{in}}\) & GPa & 40 & 5 & Normal distribution \\ \(\rho_{\text{in}}\) & kg/m\({}^{3}\) & 2160 & 200 & Normal distribution \\ \(\eta_{\text{in}}\) & — & 0.02 & 0.005 & Log-normal distribution \\ \(E_{\text{g}}\) & GPa & 206 & 50 & Log-normal distribution \\ PGA & g & 0.60 & 0.346 & Uniform distribution \\ \hline \end{tabular}
\end{table}
Table 4: Distributions of material parameters and PGA.  
Figure 12: Response spectra of the selected ground motions and average spectrum.