## 6 Examples
### Frame with Kelvin Models
On the other hand, the vertex method depends on the number of parameters, and its computational cost is similar for each uncertainty case. It can also be noticed that the presented method is more advantageous in terms of computation time. The calculations were performed using a laptop with an Intel Core i7-7500U CPU 2.70 GHz and 16 GB RAM. The main aim of this article is to present a method allowing for the consideration of uncertainties in the parameters of viscoelastic damping elements. However, the presented method is general and can also account for uncertainties in structural parameters. There are no limitations regarding the number of uncertain parameters; however, the convergence and accuracy of the method decrease as the number of parameters increases. At the same time, the efficiency of the comparative method, such as the vertex method, also significantly decreases as the number of uncertain parameters increases, so despite some inconveniences, the presented approach remains advantageous. To demonstrate that it is possible to account for different numbers of parameters and uncertainties, the same frame is considered, but in addition to the uncertainties in dampers parameters, the stiffness of the stories and the mass of the floors are also uncertain. The stiffness of each story and the mass of each floor can change independently, so together with the uncertain damper parameters, the number \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Frequency \(\lambda\)**} & \multicolumn{2}{c}{**Error of Direct Interval Method [\%]**} & \multicolumn{2}{c}{**Error of Presented Method [\%]**} \\ \cline{2-5}  & **Upper Bound** & **Lower Bound** & **Upper Bound** & **Lower Bound** \\ \hline
0.5 & 8.73 & 7.03 & 0.63 & 0.62 \\
1.1 & 3.88 & 1.74 & 0.66 & 0.13 \\
2.0 & 1.87 & 1.41 & 0.71 & 0.60 \\
3.2 & 2.69 & 3.41 & 1.41 & 1.62 \\
5.2 & 3.64 & 3.51 & 2.94 & 2.82 \\
6.4 & 1.75 & 1.67 & 1.66 & 1.59 \\
7.0 & 1.02 & 0.98 & 1.01 & 0.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Errors for uncertainties of 5%. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Frequency \(\lambda\)**} & \multicolumn{2}{c}{**Error of Direct Interval Method [\%]**} & \multicolumn{2}{c}{**Error of Presented Method [\%]**} \\ \cline{2-5}  & **Upper Bound** & **Lower Bound** & **Upper Bound** & **Lower Bound** \\ \hline
0.5 & 1.40 & 1.35 & 0.07 & 0.07 \\
1.1 & 0.26 & 0.11 & 0.05 & 0.04 \\
2.0 & 0.31 & 0.29 & 0.09 & 0.09 \\
3.2 & 0.56 & 0.58 & 0.22 & 0.22 \\
5.2 & 0.67 & 0.66 & 0.44 & 0.44 \\
6.4 & 0.32 & 0.32 & 0.26 & 0.25 \\
7.0 & 0.19 & 0.19 & 0.17 & 0.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Errors for uncertainties of 1%. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Uncertainties of Parameters [\%]**} & **Presented Method [s]** & **Vertex Method [s]** \\ \hline
5 & 4.400 & 7.497 \\
4 & 3.791 & 7.457 \\
3 & 3.252 & 7.382 \\
2 & 2.756 & 7.456 \\
1 & 2.236 & 7.512 \\
0.5 & 1.896 & 7.380 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Solution times. of changing parameters is 14. It is worth noting that in the case of the vertex method, the number of combinations for each considered frequency is now \(2^{14}=16,384\). It was assumed that the uncertainty of the damper parameter is 1%, the uncertainty of the stiffness of the stories is 0.5%, and the uncertainty of the mass of the floors is 0.75%. The intervals of the design parameter values are presented in Table 9.  
The obtained results of \(H_{11}\) are shown in Figure 19. Therefore, it can be observed that the method can also be applied for the prediction of the dynamic response of structures when the number of parameters is large or when the assumed variabilities are different. The results obtained using the presented method were also compared with those obtained by a method based on Taylor series expansion. Predicted values of the frequency response function were computed for the case of considering the first two terms of the Taylor series ([PERSON] and Lewandowski [20]).