## 3 Experimental Study
Therefore, by training the algorithm with a lesser number of classes and with limited data, the loosened joint can be identified which may not precisely localize the loosened connection. However, it is found that if the connection is fully loosened, the joint could be identified with higher accuracy compared to hand tight case. For the hand tight joints, bias toward the healthy class is observed. Four bolts are hand-tight and placed in a small area which allows very little movement between the members, causing bias to the healthy class. Again, another case BL7 was studied in which two bolts on the left column side were fully loosened and the remaining two bolts were fully tight. Table 5 indicates that the same trained network fails to identify the loosened location. The relative movement between the members at the loosened location is very small, and the case is classified as unloosed. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multicolumn{3}{c}{**Training**} & \multicolumn{3}{c}{**Validation**} \\ \cline{2-7}  & & **Healthy** & **Loosened** & & **Healthy** & **Loosened** \\ \hline \multirow{2}{*}{UL} & Healthy & 40 & 0 & \multirow{2}{*}{UL} & Healthy & 80 & 0 \\  & Loosened & 0 & 0 & & Loosened & 0 & 0 \\ \hline \multirow{2}{*}{BL1} & Healthy & 30 & 0 & \multirow{2}{*}{BL1} & Healthy & 40 & 10 \\  & Loosened & 15 & 35 & & Loosened & 11 & 19 \\ \hline \multirow{2}{*}{BL2} & Healthy & 30 & 0 & \multirow{2}{*}{BL2} & Healthy & 44 & 6 \\  & Loosened & 0 & 50 & & Loosened & 0 & 30 \\ \hline \multicolumn{7}{c}{Av. Accuracy:} & 92.5\% & \multicolumn{3}{c}{88.75\%} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Confusion charts show the average training and validation accuracy for experimental models. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Cases**} & \multicolumn{2}{c}{**Healthy**} & **Loosened** \\ \hline \multirow{2}{*}{BL3} & Healthy & 67 & 13 \\  & Loosened & 19 & 21 \\  & Healthy & 72 & 8 \\  & Loosened & 8 & 32 \\  & Healthy & 65 & 15 \\  & Loosened & 18 & 22 \\  & Healthy & 70 & 10 \\  & Loosened & 10 & 30 \\ \hline \multicolumn{3}{c}{Accuracy} & 79.0\% \\ \hline \multirow{2}{*}{BL7} & Healthy & 80 & 0 \\  & Loosened & 36 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Classification results show the average testing accuracy for experimental models. Now, at each joint, there are two connections. Therefore, two probable locations of the loosening of bolts may be assumed. Considering the fixity factors of these two connections as updating parameters, the FE model updating operation was performed to exactly localize the loosening of bolts and their severity. The fixity factors are directly proportional to joint stiffness, and it is assumed that the members do not have any material or geometrical degradation. Hence the changes in natural frequencies are because of joint stiffness only. Finally, it has been found that with the change in the fixity factor, the natural frequencies are changing significantly and can be considered as a parameter. After trial and error, the optimum population size was found to be 15 and the values of the remaining parameters were chosen based on [PERSON] et al. (2011) [48]. Table 6 shows the FE model updating results. Initially, the unloosened fixity factors of the springs were estimated. Finally, considering only the fixity factors of the probable locations of the loosening of bolts as the updating variables and the exact location of the loosening of bolts and its severity was estimated. Table 6 represents the values of fixity factors at the different connections and the percentage reduction compared to the UL condition. It is relevant to mention here that initially, an FE model updating operation was performed to estimate the fixity factors at different connections for the full-tight condition to get the baseline values. It was found that the fixity factors corresponding to S1 and S6 were 0.57 and 0.59, respectively.