# A Hybrid Data-Fusion System by Integrating CFD and PNN for Structural Damage Identification
## 3 Simulation Validation
### Single PNN Damage Detection Model  
The effects of input features on damage detection were investigated for the above arch bridge model. Before constructing the single PNN classifier model, some work such as extracting feature parameters and producing training and test samples had to be done in advance [24]. Here, PNN classifier 1 was chosen as an example to elaborate the process of damage detection.  
Before constructing a PNN classifier, calculating the correlation dimension was necessary. Equation (5) was chosen to calculate the correlation dimension. From the raw measurement, the following 6-dimensional feature vector was formed, whose elements were related to the CD, then they were divided into three groups, i.e., NC1, NC2 and NC3, as input vectors for classifier 1, 2 and 3, respectively, which then made PNN decisions respectively.  
For classifier 1, when the noise level \(\varepsilon\) = 1%, the NC1, which contains two groups of correlation dimensions, were taken to the input vectors of classifier 1. Each training sample was set as one neuron in the pattern layer; thus, the number of neurons was 400 in the pattern layer. Neurons in the summation layer corresponded to four damage patterns, thus the number of neurons was four. The structure of classifier 1 was represented with 2-400-4. Here the \(\sigma\)-parameter was set to 0.25. Then the PNN was configured or trained. When presenting on the PNN new input vectors (testing samples), each neuron in the summation layer outputted the PDF estimates for each pattern at the testing sample point. The pattern class with the largest PDF indicated the damage class of the current testing sample.  
Allowing for the effect of noise on identification accuracy of classifier, training and testing samples noise-polluted with \(\varepsilon\) = 2% and 3% were also produced in the same way as those with \(\varepsilon\) = 1%, and the structure of the classifier was also represented with 2-400-4. It should be noted that in each classifier, testing samples were with the same noise level as training samples, respectively. Table 2 shown the identification results of total of 400 testing samples by use of classifiers for the noise levels \(\varepsilon\) = 1%, 2% and 3%, respectively. It is noted that the IAs (Identification Accuracy) of the training phase are 100% for all four classifiers.  
As predicted, the total IA decreases with the increase of the noise level for the same input feature vector; when \(\varepsilon\) = 1%, the detection results were more than 80% of all three classifiers (input features vectors were different). This indicates that the damage identification  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Noise** & & & & **IA of Testing Samples for Each Pattern (\%)** & & & **Average** \\
**Level** & **PNNClassifier** & & & & & **of Total** \\ \(\varepsilon\) (\%) & & & **Pattern 1** & **Pattern 2** & **Pattern 3** & **Pattern 4** & **(\%)** & **IA (\%)** \\ \hline \multirow{3}{*}{1} & 1 (NC1) & 82 & 95 & 87 & 68 & 83 & \\  & 2 (NC2) & 79 & 93 & 86 & 68 & 81.5 & \\  & 3 (NC3) & 83 & 91 & 89 & 81 & 86 & \\  & 1 (NC1) & 85 & 91 & 75 & 83 & 83.5 & \\ \multirow{3}{*}{2} & 2 (NC2) & 70 & 82 & 77 & 65 & 73.5 & \\  & 3 (NC3) & 74 & 78 & 79 & 71 & 75.5 & \\ \multirow{3}{*}{3} & 1 (NC1) & 53 & 71 & 70 & 75 & 67.25 & \\  & 2 (NC2) & 37 & 71 & 67 & 82 & 64.25 & \\ \cline{1-1}  & 3 (NC3) & 48 & 79 & 65 & 87 & 69.75 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Single PNN classifier identification results.  
using the correlation dimension as the eigenvector can obtain a better recognition effect, and it was proven that correlation dimension is sensitive to the damage of the structure.