## 4 Examples
### Three-Bay Two-Story Framework
#### 4.1.1 Parameter Tuning in PFAM for the Three-Bay Two-Story Framework
With rigid connections and constant values \(\beta_{0}=1\), \(nt=30\), \(k_{max}=100\), \(\gamma_{0}=10\), and \(\alpha_{0}=1\), the values of the \(t_{c}\) and \(m\) parameters were modified. As previously carried out with \(nt\) and \(k_{max}\), and because it was the first sensitivity calculation performed with parameters \(t_{c}\) and \(m\), wide ranges of both parameters were considered. The accuracy results are shown in Table 18, and the standard deviation results are shown in Table 19.  
In Table 18, the maximum accuracy values have been highlighted in bold, as have the minimum values of standard deviation in Table 19. Figures 14-17 include the graphs of the accuracy and standard deviation means. These graphs show the sensitivity of both metrics to parameters \(m\) and \(t_{c}\). Some of the graphs also include linear regression analyses of the data, which helps detect trends in both metrics against changes in the value of the parameters. Tables 18 and 19 show that good and similar results were obtained for the metrics of parameter values \(t_{c}=0.1\) to 0.7 and \(m=1\) to 4. However, Figures 14-17 show that the means of the metrics improve for high values of parameter \(m\) and low values of parameter \(t_{c}\), the latter having the most influence on the results. For this reason, two sensitivity analyses were performed: (i) with parameter values \(t_{c}=0.3\) and \(m=2\), and (ii) with parameter values \(t_{c}=0.1\) and \(m=4\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & & \multicolumn{3}{c}{\(m\)} & \multicolumn{1}{c}{**Mean**} \\ \cline{3-8}  & & **0.1** & **1** & **2** & **3** & **4** & \\ \hline \multirow{4}{*}{\(t_{c}\)} & 0.1 & 0.939981 & 0.952263 & 0.907926 & 0.906337 & 0.997757 & 0.940853 \\ \cline{2-8}  & 0.3 & 0.892027 & 0.952263 & **1.000000** & **1.000000** & 0.972434 & **0.963345** \\ \cline{2-8}  & 0.5 & 0.991727 & 0.968677 & 0.991667 & 0.949523 & **0.865564** & 0.953432 \\ \cline{2-8}  & 0.7 & 0.849647 & 0.989311 & 0.962938 & 0.930684 & 0.935820 & 0.933680 \\ \cline{2-8}  & 0.9 & 0.773004 & 0.783040 & 0.802276 & 0.852616 & 0.928368 & 0.827861 \\ \hline \multicolumn{2}{c}{**mean**} & 0.889277 & 0.929111 & 0.932961 & 0.927832 & **0.939988** & \\ \hline \hline \end{tabular}
\end{table} 
Table 18: Three-bay two-story framework with rigid connections. Sensitivity analysis for \(t_{c}\) and \(m\). Accuracy. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{\(m\)} & \multicolumn{1}{c}{**Mean**} \\ \cline{3-8}  & & **0.1** & **1** & **2** & **3** & **4** & \\ \hline \multirow{4}{*}{\(t_{c}\)} & 0.1 & 1706.55 & 1326.28 & 2747.97 & 1933.51 & 62.20 & 1555.30 \\ \cline{2-8}  & 0.3 & 3168.78 & 3407.01 & **0.00** & **0.00** & 672.47 & 1449.65 \\ \cline{2-8}  & 0.5 & 106.54 & 896.74 & 107.80 & 1357.73 & 2315.51 & **956.86** \\ \cline{2-8}  & 0.7 & 2880.12 & 119.48 & 813.47 & 1813.61 & 1268.89 & 1379.11 \\ \cline{2-8}  & 0.9 & 2499.57 & 2696.02 & 2340.14 & 2202.24 & 405.41 & 2028.68 \\ \hline \multicolumn{2}{c}{**mean**} & 2072.31 & 1689.11 & 1201.87 & 1461.42 & **944.90** & \\ \hline \hline \end{tabular}
\end{table} 
Table 19: Three-bay two-story framework with rigid connections. Sensitivity analysis for \(t_{c}\) and \(m\). Standard deviation. Figure 14: Three-bay two-story framework with rigid connections. Accuracy vs. \(m\). Figure 15: Three-bay two-story framework with rigid connections. Accuracy vs. \(t_{c}\). * First sensitivity analysis: with rigid connections and constant values \(\beta_{0}=1\), \(nt=30\), \(k_{max}=100\), \(t_{c}=0.3\), and \(m=2\), the values of the \(\alpha_{0}\) and \(\gamma_{0}\) parameters were modified. As previously carried out, and because it was the first sensitivity calculation performed with parameters \(\alpha_{0}\) and \(\gamma_{0}\), wide ranges of both parameters were considered. The accuracy results are shown in Table 20, and the standard deviation results are shown in Table 21.  
Figure 16: Three-bay two-story framework with rigid connections. Standard deviation vs. \(m\).