## 4 Examples
### Three-Bay Two-Story Framework
#### 4.1.1 Parameter Tuning in PFAM for the Three-Bay Two-Story Framework
* Second sensitivity analysis: with rigid connections and constant values \(\beta_{0}=1\), \(nt=30\), \(k_{max}=100\), \(t_{c}=0.1\), and \(m=4\), the values of the \(\alpha_{0}\) and \(\gamma_{0}\) parameters were modified. As previously carried out, wide ranges of parameters \(\alpha_{0}\) and \(\gamma_{0}\) were considered. The accuracy results are shown in Table 22, and the standard deviation results are shown in Table 23.  
Figure 21: Three-bay two-story framework with rigid connections. First sensitivity analysis. Standard deviation vs. \(\gamma_{0}\). Figure 20: Three-bay two-story framework with rigid connections. First sensitivity analysis. Standard deviation vs. \(\alpha_{0}\). Figure 23: Three-bay two-story framework with rigid connections. Second sensitivity analysis. Accuracy vs. \(\gamma_{0}\). Figure 22: Three-bay two-story framework with rigid connections. Second sensitivity analysis. Accuracy vs. \(\alpha_{0}\). Comparing Figures 18, 20, 22 and 24, showing the evolution of the accuracy and standard deviation metrics with \(\alpha_{0}\), we can see that the sensitivity of both metrics with \(\alpha_{0}\) increases when the value of \(t_{c}\) is reduced. Better results are also obtained from the metrics for values of \(t_{c}\) = 0.1. Finally, the best results are obtained for \(\alpha_{0}\) values in the range [0.3, 0.5] for both \(t_{c}\) = 0.1 and \(t_{c}\) = 0.3. Comparing Figures 19, 21, 23 and 25, showing the evolution of the accuracy and standard deviation metrics with \(\gamma_{0}\), we can see that the sensitivity of both metrics with \(\gamma_{0}\) increases when the value of \(t_{c}\) is reduced. Better results are also obtained from the metrics for values of \(t_{c}\) = 0.1. Finally, the best results are obtained for \(\gamma_{0}\) values in the range [1,25] for \(t_{c}\) = 0.1 and for \(\gamma_{0}\) values in the range [0.1, 10] for \(t_{c}\) = 0.3. To better understand the behavior of the metrics with more detailed variations of parameters \(t_{c}\) and \(m\), an additional sensitivity analysis was conducted with constant values  
Figure 24: Three-bay two-story framework with rigid connections. Second sensitivity analysis. Standard deviation vs. \(\alpha_{0}\). Figure 25: Three-bay two-story framework with rigid connections. Second sensitivity analysis. Standard deviation vs. \(\gamma_{0}\). for parameters \(\beta_{0}=1\), \(nt=30\), \(k_{max}=100\), \(\alpha_{0}=0.3\), and \(\gamma_{0}=0.1\). The accuracy results are shown in Table 24, and the standard deviation results are shown in Figure 19:0  
If Tables 18 and 19 (obtained with \(\alpha_{0}=1.0\), \(\gamma_{0}=10\)) are compared with Tables 24 and 25 (obtained with \(\alpha_{0}=0.3\), \(\gamma_{0}=0.1\)), we can see that the shaded areas, corresponding to poor values of efficiency and robustness, are more extensive in Tables 18 and 19. This, again, demonstrates the interdependence among the parameters. As a result of the sensitivity analyses performed in this example, PFAM initially seems efficient and robust for the parameter values in Figure 19:1  
If we take into account the parameter values included in Table 15 (EEP2 semi-rigid connections) and Table 26 (rigid connections) and look for the intersection or common values in these tables for a three-bay two-story framework, PFAM seems efficient and robust for the parameter values included in Figure 19:2 \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{\(\beta_{0}\)} & \multirow{2}{*}{\(t_{c}\)} & \multirow{2}{*}{\(\alpha_{0}\)} & \multirow{2}{*}{\(\gamma_{0}\)} & \multirow{2}{*}{\(m\)} & \multirow{2}{*}{\(nt\)} & \multirow{2}{*}{\(k_{max}\)} \\ \hline
**Values** & 1 & [0.1, 0.5] & [0.3, 0.5] & [0.1, 25] & [1, 4] & 30 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 26: Three-bay two-story framework with rigid connections. Optimum values of PFAM parameters.