## 4 Experimental Verification
### Establishment of Neural Network Model  
ETABS was used to construct a numerical model to generate the training data, and the training database comprised the data of structures subjected to different residual stiffness, namely 100%, 70%, 35%, and 0%. The FE model was established with the real experimental size, and its fundamental frequencies were adjusted to fit with the experimental frequency shown in Table 12. Through this tuning process, the FE model can then be numerically and structurally equivalent to the test physical structure. According to the experimental situation, the stiffness reductions were applied in only the one-story, two-story, three-story, and multistory cases. A time history analysis was conducted using ETABS, and the numerical model constructed with the size of the experimental structure was used to extracted velocity responses. The experimental data were then used to verify this neural network.  
According to previous research [12], RCMCSE parameters such as the template length m, threshold r, signal length N, and scale factor were optimized as 4, 0.08 \(\times\) SD of the time series, 20,000 points, and  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Damage Group** & **Damage Floors** & **Frequency (Hz)** \\ \hline Undamaged & None & 3.34 \\ \hline \multirow{6}{*}{One-story damage} & 1F & 2.08 \\ \cline{2-3}  & 2F & 2.13 \\ \cline{2-3}  & 3F & 2.12 \\ \cline{2-3}  & 4F & 2.29 \\ \cline{2-3}  & 5F & 2.61 \\ \cline{2-3}  & 6F & 2.88 \\ \cline{2-3}  & 7F & 3.2 \\ \hline \multirow{2}{*}{Two-story damage} & 1\&2F & 1.64 \\ \cline{2-3}  & 3\&4F & 1.83 \\ \cline{2-3}  & 5\&6F & 2.32 \\ \hline \multirow{2}{*}{Three-story damage} & 1\&2\&3F & 1.44 \\ \cline{2-3}  & 4\&5\&6F & 1.88 \\ \hline \multirow{2}{*}{Multistory damage} & 1\&2\&3\&4F & 1.33 \\ \cline{2-3}  & 4\&5\&6\&6\&7F & 1.86 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Damage cases and modal analysis.  
Figure 16: The damage simulation: (**a**) the healthy condition; (**b**) the damaged condition.  
10, respectively. RCMCSE was applied to calculate entropy values using numerical data, and all entropy values converted into statistics. These statistical values were stored in the training database. The next step was to train the neural network. Because the neural network of the experimental verification was only conducted to identify the structure status as damage or health, it is slightly adjusted from the neural networks developed in the numerical simulation. Reduction of the number of hidden layer neurons was attempted with the same SHM result. After trial and error, the number of hidden layers was 1 and the number of neurons in the hidden layer was 50 (Table 13). This number of neurons can be served as a reference for future research when the monitoring structure is similar; thereby reducing the calculation time and the trial time the target output was the same as that in the numerical simulation. The training and regression processes are presented in Figure 17a,b.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Training Parameters**} \\ \hline Number of neurons & 50 \\ \hline Number of hidden layers & 1 \\ \hline Transfer function & Logsig \\ \hline Epoch & 30,000 \\ \hline Max failure number & 0 \\ \hline Time & Infinite \\ \hline Goal & 0 \\ \hline Min gradient & \(1\times 10^{-7}\) \\ \hline mu & 0.005 \\ \hline mu\_decrement & 0.1 \\ \hline mu\_increment & 10 \\ \hline Max mu & \(1\times 10^{10}\) \\ \hline \hline \end{tabular}
\end{table}
Table 13: Parameters applied for training.  
Figure 17: _Cont._