## 6 Conclusions  
In this paper, a new vibration data-based hybrid ML using SVM and MU using CSO for the SHM of joints in planer steel frame structures was presented in order to overcome the problems of ML and model updating based techniques. The study was carried out to localize localization and quantification of joint damage with a lesser number of data sets compared to the data sets required if only either the ML-based technique or model updating technique is employed for the same purpose. Further, the effectiveness of three entropy-based features, namely, approximate entropy, Shannon entropy, and Renyi's entropy along with statistical features, namely, mean absolute deviation, standard deviation, variance, kurtosis, and skewness were examined for the identification of probable joint damage locations. Assuming the fixity factors of these identified probable locations as the updating variables, FE model updating using CSO was carried out to identify the exact damage location and its severity. The method was applied to an experimental single-story and one pseudo-experimental four-story planer frame structure. Based on our observations, the following conclusions can be drawn:  
* The hybrid ML and MU method considered damaged data collected from the sensors surrounding the damage for two loosened cases only and the undamaged data collected from all the sensors for healthy/un-loosened conditions along with data obtained from the sensors are far from the loosened locations for the same two loosened conditions.
* The testing was carried out with the data for different locations of loosening of bolts and different levels of damage to produce uncorrelated data. The confusion matrices thus identify the damaged joints.
* The average training and validation accuracy for the experimental and numerical models were found to be 92.5%, 88.75% and 91.50%, 85.40%, respectively, and the testing results show 79.00% and 77.00% accuracy, respectively.
* The FE model updating technique successfully detects the actual damage (loosening of bolts) location by calculating the fixity factors.
* The method needs only strain gauge data for finding out the differentiable features in order to monitor the connections of planer steel frame structures, hence, it reduces the involvement of skilled labor.  
Conceptualization, J.P. and S.S.; methodology, J.P. and S.S.; software, J.P.; validation, J.P.; formal analysis, S.S. and J.P.; investigation, J.P. and S.S.; resources, S.B. and P.B.; data curation, J.P.; writing--original draft preparation, J.P. and S.S.; writing--review and editing, J.P., S.S., S.B. and P.B.; visualization, J.P.; supervision, S.B. and P.B.; project administration, J.P.; funding acquisition, S.B. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Authors are humbly acknowledging the support of the Laboratory staff of Experimental Mechanics Lab, IIT Bombay.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Type** & \multicolumn{2}{c}{**Probable Locations**} & \multicolumn{2}{c}{**Actual Fixity Factor**} & \multicolumn{2}{c}{**Estimated Fixity Factor**} \\ \hline NLB1 & S20 & S21 & - & 0.75 & 0.891 & - & 0.743 & 0.890 & - \\ NLB2 & S14 & S15 & S19 & 0.891 & 0.891 & 0.75 & 0.881 & 0.890 & 0.694 \\ NLB3 & S8 & S9 & S13 & 0.891 & 0.891 & 0.70 & 0.889 & 0.889 & 0.688 \\ NLB4 & S2 & S3 & S7 & 0.891 & 0.891 & 0.70 & 0.885 & 0.887 & 0.699 \\ NLB5 & S2 & S3 & S7 & 0.891 & 0.891 & 0.70 & 0.887 & 0.889 & 0.689 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Estimated fixity factors for four storey numerical model.