# Data Fusion-Based Structural Damage Identification Approach Integrating Fractal and RCPN
## 4 Damage Identification of ASCE Benchmark Structure [41]
### Damage Detection Results of Feature-Level Fusion Model  
Feature-level fusion refers to the feature-level fusion of input vectors of the above single RCPN network model. Then, the fused correlation dimension groups were used as a new feature vector and input into the input layer of the RCPN network model for RCPN calculation, and eventually output the damage recognition results, which were shown in Table 3.  
It can be seen from Table 3, after the feature-level fusion, when the noise level is 30%, 50% and 70%, the total average IA of the feature-level fusion damage recognition model is 95.2%, 88.7% and 81.0%, respectively. Moreover, with the increase of noise level, the recognition accuracy of the model decreases correspondingly, which is completely consistent with the reality. Taking a noise level of 30% as an example, the recognition results of a single RCPN classifier and a feature-level fusion model are compared, as shown in Figure 5.  
It can also be seen from Table 3 and Figure 5, comparing with single RCPN classifiers, the classifier of feature-level fusion has better improved IA. When the noise level is 30%,  
Figure 5: Comparison of the accuracy of damage between feature-level and single RCPN when the noise level is 30%.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Noise Level**} & \multirow{2}{*}{**Feature-Level Fusion Methods**} & \multicolumn{3}{c}{**IA of Damage Patterns (\%)**} & \multirow{2}{*}{**Average**} & \multirow{2}{*}{**Total** \\ \cline{3-6}  & & & **Pattern 1** & **Pattern 2** & **Pattern 3** & **Pattern 4** & **IA(\%)** \\ \hline \multirow{4}{*}{30} & Classifier 1 (NC1 + NC2) & 99 & 99 & 97 & 96 & 97 & \\  & Classifier 2 (NC2 + NC3) & 97 & 97 & 91 & 93 & 94.5 & \\  & Classifier 3 (NC1+NC3) & 98 & 96 & 94 & 94 & 95.5 & \\  & Classifier 4 (NC1 + NC2 + NC3) & 96 & 98 & 91 & 90 & 93.75 & \\ \hline \multirow{4}{*}{50} & Classifier 1 (NC1 + NC2) & 94 & 97 & 82 & 81 & 88.5 & \\  & Classifier 2 (NC2 + NC3) & 96 & 92 & 80 & 82 & 87.5 & \\  & Classifier 3 (NC1 + NC3) & 95 & 95 & 85 & 87 & 90.5 & \\  & Classifier 4 (NC1 + NC2 + NC3) & 93 & 94 & 81 & 85 & 88.25 & \\ \hline \multirow{4}{*}{70} & Classifier 1 (NC1 + NC2) & 87 & 85 & 76 & 75 & 80.75 & \\  & Classifier 2 (NC2 + NC3) & 87 & 89 & 75 & 74 & 81.25 & \\ \cline{1-1}  & Classifier 3 (NC1 + NC3) & 84 & 88 & 76 & 79 & 81.75 & \\ \cline{1-1}  & Classifier 4 (NC1 + NC2 + NC3) & 83 & 86 & 78 & 74 & 80.25 & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Feature level fusion damage identification results of RCPN.  
the total recognition accuracy of the four feature-level fusion methods is 97%, 94.5%, 95.5% and 93.75%, respectively, with the total average IA exceeding 93%, which is significantly improved compared with the single RCPN network model. Among them, fusion method 1 had the highest damage identification accuracy. This is mainly because, in the identification of a single RCPN model, the total identification accuracy of single feature vectors NC1 and NC2 is high, and these two feature vectors are more sensitive to structural damage. Therefore, after feature-level fusion, the damage identification result is bound to be higher than that of other combination methods. When the noise level is 50%, this phenomenon is also reflected. The damage recognition results of the RCPN model with single feature vectors NC1 and NC3 are better. Therefore, after the feature-level fusion, the damage recognition results after the fusion of two feature vectors are further improved.