# A Hybrid Data-Fusion System by Integrating CFD and PNN for Structural Damage Identification
## 3 Simulation Validation  
### Structural Model and Damage Simulation  
In order to prove the proposed hybrid system, a two-span concrete-filled steel tubular arch bridge in service as shown in Figure 4 was employed. Here, ANSYS 10.0 (Finite Element Software) was used to build this arch bridge model (as shown in Figure 5). First of all, we inputted the health condition command flow of this bridge to ANSYS software, then used complete method to calculate dynamic response of this bridge under given loads. Considering that noise is inevitable, we then added noise to dynamic response, and this mixed-signal model is used to simulate the real dynamic response of the bridge. Figure 4: Hong Fu bridge in Dong Wan. Figure 5: The element model of the arch bridge. Then, we inputted the damage condition command flow with different damage location and different damage degree respectively based on the health condition of bridge model. Finally, transient dynamic analysis of ANSYS was used to calculate the structural response under arbitrary change of load with time, namely, time-history of structural response. Transient dynamic analysis was used to determine the change rule of structural displacement, stress and strain under steady-state load, composite action of transient load and harmonic load. A weight of 10 t vehicle load was used as dynamic load, and the car went through the bridge with a speed of 12.5 m/s, and then we calculated the displacement response of the arch rib nodes of the arch bridge. Considering the symmetry of the bridge, we used a rib of the arch bridge for research (as shown in Figure 6), hollow digital stands for rib element, solid digital stands for rib node, and the rib is divided into 18 elements and 19 nodes (as shown in Figure 6); 1-8 are the number of elements and 1-19 are the node numbers. In general, there are two ways to simulate element damage: changing the cross-section and reducing the element stiffness. In reality, the stability problems of arch bridge are quite conspicuous; the arch rib mainly bears axial force, the stiffness decline of it can reduce directly the stability of the local components even overall structure. In fact, the damage of structure, such as cracks, and reducing of material elastic modulus all can cause the decline of the structural stiffness. On the contrary, the impact on quality is little. So, during the analysis process, the quality was assumed constant, and the decline of elastic modulus was used to simulate the decline of element stiffness. In this paper, there were four damage cases, i.e., a single damage, multiple damage, different damage locations and degrees. The damages were located in the arch rib elements. Considering the complexity of this large bridge, relatively big damage was chosen in the simulating the four damage conditions. It is shown in the Table 1.  
In the actual signal measurement, there is a lot of noise. In order to simulate measured data, each set of the analytical computed correlation dimension added by a random sequence for each damage, i.e.,  
\[y_{i}=y_{i}^{a}\times(1+\varepsilon R)\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Damage Conditions** & **Damage Location** & **Damage Levels** \\ \hline
1 & Arch rib element 5 & 50\% \\
2 & Arch rib element 5 & 80\% \\
3 & Arch rib element 5 and 13 & 50\% \\
4 & Arch rib element 5 and 13 & 80\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Four damage conditions of arch bridge. Figure 6: The number of an arch rib element. where \(y_{i}\) and \(y_{i}{}^{a}\) stand for the noise-polluted measured correlation dimension and the analytically computed values for each damage simulation respectively; \(R\) is a normally distributed random variable with zero mean and deviated with 1; \(\varepsilon\) is an index representing the noise degree, here \(\varepsilon\) is set 1%, 2%, and 3%, respectively [25]. Here, 200 sets of damage case were produced at every noise level, namely, 200 sets of measured data.