# A Hybrid Data-Fusion System by Integrating CFD and PNN for Structural Damage Identification
## 4 Experimental Validation
### Results Analysis  
Similar to the numerical simulation, calculating the correlation dimension is the first step. Equation (5) was employed to calculate the correlation dimension. Here, each storey raw measurement was used to extract the correlation dimension, so that it can obtain 200 correlation dimensions for each storey and each damage pattern, and in total obtain 1200 data sets for each damage pattern. Then 200 samples were produced (200 \(\times\) 6); the first 100 sets were used to create training samples, and the others were used to create test samples, with each sample containing a six-column correlation fractal dimension. So, three PNN input vectors were obtained through dividing the six-column correlation fractal dimension into three groups, named NC1, NC2 and NC3, where each of them contains two columns, as inputs for classifier 1, 2 and 3, respectively. The process of damage identification was the same as in Section 3, so it will not be reiterated here. The identification results of the hybrid system which contains three damage identification models are shown in Tables 6-8.  
Comparing Tables 6-8, it can be found that average IA was remarkably improved with the different damage identification models, which proved that the proposed hybrid system can identify the damage successfully. The total IAs have no apparent change when using four different classifiers fusion in the decision-level model. This is also proves again that, for the different feature vectors, the proposed model was insensitive. Namely, the proposed model has better robustness.  
It also can be found that the IA of the three models in the hybrid system are all not very high, which may be because of the influence of noise in the measurement and measurement  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**PNN Classifier**} & \multicolumn{3}{c}{**IA of Testing Samples for Each Pattern (\%)**} & \multirow{2}{*}{**Total IA (\%)**} & \multirow{2}{*}{**Average of Total IA (\%)**} \\ \cline{2-2} \cline{4-6}  & **Pattern 1** & **Pattern 2** & **Pattern 3** & **Pattern 4** & \\ \hline
1 (NC1) & 69 & 74 & 83 & 94 & 80 \\
2 (NC2) & 71 & 71 & 81 & 93 & 79 \\
3 (NC3) & 68 & 73 & 82 & 91 & 78.5 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Identification results of using single PNN classifier model.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Eigen Fusion Method**} & \multicolumn{3}{c}{**IA of Testing Samples for Each Pattern (\%)**} & \multirow{2}{*}{**Total IA (\%)**} & \multirow{2}{*}{**Average of Total IA (\%)**} \\ \cline{2-2} \cline{4-6}  & **Pattern 1** & **Pattern 2** & **Pattern 3** & **Pattern 4** & \\ \hline
1 (NC1 + NC2) & 77 & 79 & 89 & 97 & 85.5 & \\
2 (NC2 + NC3) & 75 & 77 & 89 & 93 & 83.5 & 84.0 \\
3 (NC1 + NC3) & 76 & 77 & 84 & 95 & 83 & \\ \hline \hline \end{tabular}
\end{table}
Table 7: Identification results of eigen-level fusion model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Pattern Class**} & \multirow{2}{*}{**Small Damage**} & \multirow{2}{*}{**Large Damage**} \\ \hline Pattern 1 & 4 th storey & \\ Pattern 2 & 6 th storey & 4 th storey \\ Pattern 3 & 3 rd and 6 th storeys & 4 th storey \\ Pattern 4 & & 3 rd, 4 th and 6 th storeys \\ \hline \hline \end{tabular}
\end{table}
Table 5: Magnitudes and locations of damage.  
error, the error in the process of obtaining the correlation fractal dimension and so on. Therefore, in future study, it also needs to be improved the method of damage identification, and decrease the influence the error may have on the measurement and calculation and so on. Another study direction should be on how to eliminate the measurement noise, how to improve the IA and so on. Through these studies, good identification results will be obtained.