## 5 Conclusions  
This study proposes an SHM system based on RCMCSE and BPN and conducted numerical simulations to assess the performance of the system. To evaluate the reliability of the proposed SHM system, an experimental verification involving 15 damage cases in five categories representing different degrees of damage level was performed. RCMCSE was used to conduct the entropy analysis to obtain entropy values. These entropy values were converted into statistical values, namely maximum,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Damaged Floors**} & \multicolumn{4}{c}{**RCMCSE**} \\ \cline{2-5}  & **TP** & **FP** & **TN** & **FN** \\ \hline
1F & 5 & 0 & 1 & 1 \\ \hline
2F & 6 & 0 & 1 & 0 \\ \hline
3F & 4 & 0 & 1 & 2 \\ \hline
4F & 6 & 1 & 0 & 0 \\ \hline
5F & 5 & 0 & 1 & 1 \\ \hline
6F & 5 & 0 & 1 & 1 \\ \hline
7F & 5 & 0 & 1 & 1 \\ \hline
1\&2F & 5 & 0 & 2 & 0 \\ \hline
3\&4F & 5 & 0 & 2 & 0 \\ \hline
5\&6F & 4 & 0 & 2 & 1 \\ \hline
1\&2\&3F & 4 & 1 & 2 & 0 \\ \hline
4\&5\&6F & 4 & 0 & 3 & 0 \\ \hline
1\&2\&3\&3\&4F & 3 & 1 & 3 & 0 \\ \hline
4\&5\&6\&6\&7F & 3 & 0 & 4 & 0 \\ \hline Total & 64 & 3 & 24 & 2 & 7 \\ \hline Accuracy & & & 89.8\% & & & \\ \hline Precision & & & 95.5\% & & & \\ \hline Recall & & & 90\% & & & \\ \hline \hline \end{tabular}
\end{table}
Table 19: The results of confusion matrix for the experimental verification.  
minimum, mean value, geometric mean, and SD which were employed to construct a simplified numerical model. A database with various stiffness reductions was established through the model. A neural network model was constructed with the statistical entropy values serving as the inputs and stiffness reductions serving as the outputs.  
The numerical simulation conducted on the 15 damage cases revealed a high accuracy rate of 91.8% for the proposed system. A precision of 100% was achieved, demonstrating that all healthy floors were successfully detected. Furthermore, a recall of 88% was observed, signifying that a high percentage of actual damage cases could be detected. In the meantime, the results of the experimental verification demonstrate that 89.8% of the floors were correctly classified into the right categories, and 90% of the actually healthy floors were correctly diagnosed.  
Currently, the proposed method is mainly used for framed structures. The damage location and level are determined on specific (finite) points. Accordingly, the proposed entropy-based SHM system has great potential for use in large and complex structures. As for continuum structures such as dams, the proposed SHM system can be used to provide a preliminary screening on the possible damage area and level with the sensors distributed on the continuum structures to reflect the special structural characteristic. Non-destructive evaluation can then be followed to save the labor and cost required for detailed SHM.  
[PERSON]-[PERSON] conceived, put forward the research ideas, and revised the paper. [PERSON] carried out the numerical analysis, experimental validation and wrote the paper. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.