# Data Fusion-Based Structural Damage Identification Approach Integrating Fractal and RCPN
## 4 Damage Identification of ASCE Benchmark Structure [41]
### Damage Detection Results of Single RCPN Classifier
The damage identification results of a single RCPN classifier under various noise levels are shown in Table 2.  
It can be seen from Table 2, when the noise levels are 30%, 50% and 70%, respectively, the total average IA of a single RCPN classifier is 91.6%, 87.25% and 78.3%, respectively, with the total average IA all exceeding 78%. This indicates that the correlation dimension as the feature vector for damage identification can receive better recognition effect, and also indicates that the damage feature vector is more sensitive to structural damage. When the noise level is 30%, the comparison of damage identification results of each damage feature vector is shown in Figure 4a. As can be seen from Figure 4a, IA of damage patterns 1 and 2 is relatively high, while that of damage patterns 3 and 4 is slightly lower. The same phenomenon is also observed when the noise level is 50% and 70%, as shown in Figure 4b,c. This is mainly because damage patterns 1 and 2 are both more severe, so are easier to distinguish compared with the other two kinds of damage, so the IA is better. It can also be seen from Table 2 that when the noise level is 30%, the average IA of feature vectors NC1, NC2 and NC3 is 92.75%, 92% and 90%, respectively. When the noise level is 50%, the average IA of feature vectors NC1, NC2 and NC3 is 87%, 86.75% and 88%, respectively. When the noise level is 70%, the average IA of feature vectors NC1, NC2 and NC3 is 78%, 78.25% and 78.75%, respectively. On the whole, there is little difference in the accuracy of damage identification among the three feature vectors, which also indicates that the RCPN network model has good noise resistance and robustness. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Noise Level** \\ \(\varepsilon\) **(\%)** \\ \end{tabular} } & \multirow{2}{*}{**Classifier**} & \multicolumn{3}{c}{**IA of Damage Patterns (\%)**} & \multirow{2}{*}{\begin{tabular}{c} **Average** \\ **Pattern 1** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Total** \\ **Pattern 2** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Pattern 4** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Pattern 4** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Pattern 4** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Pattern 4** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **IA(\%)** \\ \end{tabular} } \\ \hline \multirow{3}{*}{30} & NC1 & 96 & 94 & 91 & 90 & 92.75 & \multirow{3}{*}{91.6} \\  & NC2 & 91 & 95 & 89 & 93 & 92 & \\  & NC3 & 94 & 91 & 83 & 88 & 90 & \\ \hline \multirow{3}{*}{50} & NC1 & 93 & 89 & 85 & 81 & 87 & \multirow{3}{*}{87.25} \\  & NC2 & 90 & 95 & 80 & 82 & 86.75 & & \\ \cline{1-1}  & NC3 & 89 & 91 & 84 & 88 & 88 & \\ \hline \multirow{3}{*}{70} & NC1 & 83 & 85 & 71 & 73 & 78 & \multirow{3}{*}{78.3} \\  & NC2 & 81 & 87 & 74 & 71 & 78.25 & & \\ \cline{1-1}  & NC3 & 82 & 85 & 73 & 75 & 78.75 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Damage identification results of a single RCPN classifier. Figure 4: Comparison of the accuracy of damage pattern recognition when the noise level is 30%, 50% and 70% respectively. (**a**) Noise level \(\epsilon=30\%\). (**b**) Noise level \(\epsilon=50\%\). (**c**) Noise level \(\epsilon=70\%\).