# Bridge Model Updating Based on Wavelet Neural Network and Wind-Driven Optimization
## 5 Finite Element Model Updating of Ningbo Bund Bridge
### Selection of Updating Parameters  
The selection of correction parameters is mainly based on engineering and modeling experience and sensitivity analysis methods. The Ningbo Bund Bridge has a novel structure and complex form and has many structural design parameters. When establishing the initial finite element model, the physical parameters of the structure, such as the elastic modulus of the material, mass density, geometric parameters, boundary conditions, and others, were mainly determined based on the construction design drawings, and these physical parameters are often different from the actual situation. The Ningbo Bund Bridge is a steel bridge, and most components were prefabricated and assembled. Assembly may adversely affect the structural rigidity, and some detailed components may contribute to the structural rigidity to a certain extent. The influence of assembly and the contribution of detailed components to structural rigidity should be considered when establishing the model. Therefore, based on engineering experience, the elastic modulus of the main beam \(E_{1}\), the elastic modulus of the front tower column \(E_{2}\), the elastic modulus of the rear-inclined rod \(E_{3}\), the elastic modulus of the horizontal rod \(E_{4}\), the elastic modulus of the stay cable \(E_{5}\), and the elastic modulus of the cross-beam \(E_{6}\) were selected as updating parameters. Meanwhile, the equivalent density method was used in the modeling to equalize the mass of the detailed components, bridge deck pavement, and bridge deck auxiliary structures to the main structure, and there may be deviations in the mass conversion process. Therefore, the girder density \(\rho_{1}\), the front tower column density \(\rho_{2}\), the rear-inclined rod density \(\rho_{3}\), the horizontal rod density \(\rho_{4}\), the stay cable density \(\rho_{5}\), and the cross-beam density \(\rho_{6}\) were also selected as updating parameters. Additionally, the cable force of the bridge was adjusted according to the construction acceptance standard of the cable-stayed bridge, and a small cable force error was obtained; the error between the cable force of the completed bridge and the designed cable force is within 5% [48; 49]. The whole bridge has a total of 64 cables, and to simplify the model updating process, as the cable force error is small, the actual measured cable force of the bridge was used as the input rather than selected as updating parameters. Furthermore, the error between the actual size and the design size of the prefabricated components of the bridge is very small, and the element section of the finite element model was established according to design drawings; thus, the geometric parameters of the sections were not considered. The boundary constraints of the bridge are few and all controlled in an ideal state, and the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Order of Natural** & **Measured Value** & **Calculated Value** & **Difference (\%)** & **Description of Mode Shape** \\
**Frequency** & **(Hz)** & **(Hz)** & **(Hz)** & **(\%)** & **(\%)** \\ \hline
1 & 0.55 & 0.49 & \(-\)10.9\% & 225 m span main girder vertical \\  & 0.73 & 0.78 & 6.8\% & Lateral vibration of the bridge tower \\  & 0.86 & 0.88 & 2.3\% & 225 m span main girder vertical \\  & 0.88 & 0.88 & 2.3\% & bending vibration \\  & 0.88 & 0.88 & 2.3\% & Lateral bending vibration of the \\  & 0.88 & 0.88 & 2.3\% & main beam \\  & 0.88 & 0.88 & 2.3\% & Torsional vibration of the \\  & 0.88 & 0.88 & 2.3\% & Vertical bending vibration of the \\  & 0.88 & 0.88 & 2.3\% & main beam \\  & 0.88 & 0.88 & 2.3\% & Lateral vibration of the \\  & 0.88 & 0.88 & 2.3\% & Torsional vibration of the \\  & 0.88 & 0.88 & 2.  
partially consolidated piers have little effect on the natural frequencies of the structure; hence, the boundary conditions were also not considered.