## 4 Examples
### Three-Bay Two-Story Framework
#### 4.1.1 Parameter Tuning in PFAM for the Three-Bay Two-Story Framework
To better understand the behavior of the metrics with more detailed variations of parameters \(\alpha_{0}\) and \(\gamma_{0}\), an additional sensitivity analysis was performed with the constant values of the parameters \(\beta_{0}\) = 1, \(nt\) = 250, \(k_{max}\) = 100, \(t_{c}\) = 0.1, and \(m\) = 1. The accuracy results are shown in Table 11, and the standard deviation results are shown in Table 12.  
Table 11 shows the values of the accuracy metric, and its mean values calculated, using rows and columns. The maximum values have been highlighted in bold. Table 12 shows the standard deviation metric, and its mean values calculated, using rows and columns. The minimum values have been highlighted in bold. The metric values included in the tables are good and very similar to each other, except for those corresponding to the values of parameters \(\gamma_{0}\) = 1 and \(\alpha_{0}\) belonging to the range [0.3, 0.6]. Figures 10-13 include the graphs of the accuracy and standard deviation means. These graphs show the sensitivity of both metrics against parameters \(\gamma_{0}\) and \(\alpha_{0}\). Some of the graphs also include linear regression analysis on the data, which helps detect trends in both metrics against changes in the parameter values. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number of Independent Runs** & **Accuracy** & **Standard Deviation** \\ \hline
10 & 0.999274 & 1.39 \\ \hline
20 & 0.999326 & 1.91 \\ \hline
30 & 0.999280 & 1.37 \\ \hline
40 & 0.999139 & 1.77 \\ \hline
50 & 0.999263 & 1.55 \\ \hline
60 & 0.999248 & 1.41 \\ \hline
70 & 0.999234 & 1.97 \\ \hline
80 & 0.999204 & 1.77 \\ \hline
90 & 0.999263 & 1.69 \\ \hline
100 & 0.999225 & 1.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Three-bay two-story framework with EEP2 semi-rigid connections. Influence of the number of independent runs on the metrics. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{\(\gamma_{0}\)} & \multicolumn{2}{c}{Mean} \\ \cline{3-8}  & & **1** & **26** & **51** & **76** & **101** & \\ \hline
0.3 & & 43.83 & 1.69 & 1.65 & 1.68 & 1.86 & 1.72 \\ \hline
0.4 & & 34.53 & 1.79 & 1.63 & 1.89 & 1.97 & 1.82 \\ \hline
0.5 & & 25.59 & 1.67 & 1.76 & 1.83 & 1.77 & 1.76 \\ \hline
0.6 & & 25.90 & 1.71 & 1.57 & 1.82 & 1.84 & 1.73 \\ \hline
0.7 & & 2.06 & 1.68 & 1.84 & 1.87 & 1.82 & 1.80 \\ \hline
0.8 & & 1.75 & 1.73 & **1.44** & 1.97 & 1.86 & 1.75 \\ \hline
0.9 & & 1.96 & 1.59 & 1.61 & 1.68 & 1.79 & **1.67** \\ \hline
1.0 & & 1.81 & 1.88 & 1.63 & 1.89 & 1.73 & 1.78 \\ \hline
**mean** & & 17.18 & 1.72 & **1.64** & 1.83 & 1.83 & \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Three-by two-story framework with EEP2 semi-rigid connections. Second sensitivity analysis for \(\alpha_{0}\) and \(\gamma_{0}\). Standard deviation. Figure 10: Three-bay two-story framework with EEP2 semi-rigid connections. Accuracy vs. \(\alpha_{0}\). Figure 10 shows how the accuracy metric improves slightly when parameter \(\alpha_{0}\) decreases. Figure 12 shows something similar occurring with the standard deviation metric, which does not exceed values of 1.83. Therefore, the PFAM is efficient and robust for values of \(\alpha_{0}\) between 0.3 and 1.0. Figures 11 and 13 show that, for values of parameter \(\gamma_{0}\) above unity, the accuracy and standard deviation metrics give good and very similar values. Tables 8 and 9 show that this effect appears with \(\gamma_{0}\) values above 10. Therefore, PFAM is efficient and robust for \(\gamma_{0}\) values between 10 and 100. Figure 11: Three-bay two-story framework with EEP2 semi-rigid connections. Accuracy vs. \(\gamma_{0}\). Figure 12: Three-bay two-story framework with EEP2 semi-rigid connections. Standard deviation vs. \(\alpha_{0}\). interdependence among the parameters. Therefore, any sensitivity study needs to take this effect into account.