# Novel Method for Bridge Structural Full-Field Displacement Monitoring and Damage Identification
## 3 Damage Identification Method Based on FFDV Monitoring
### Damage Identification Index for the FFDV of the Structure  
As shown in Figure 29, before damage occurred, the structural system was complete, and the rotation angle of the structure's FFDV changed only slightly, thus satisfying the structure's deformation coordination under load conditions. After the nos. 13-14 vertical member was damaged (Figure 29), the rotation angle of the no. 13 gusset plate (as shown by the red arrow in Figure 29) changed significantly. Since the lower section of gusset plate no. 13 could not maintain its vertical support under the load conditions, gusset plate no. 13 flipped abnormally under the inclined member (nos. 12-13) support, resulting in  
Figure 28: Relative displacement of nos. 13-14 damaged member under load condition D03.  
Figure 29: FFDV extraction results for test beams above and below steel plates under D03 400 kN  
an abnormal rotation angle of the displacement vector on gusset plate no. 13. The nos. 12-13 inclined member was subjected to further damage (Figure 1(c)); consequently, gusset plate no. 13 could not maintain its support. At this time, the rotation of gusset plate no. 13 was restrained only by the transverse steel plates at both ends. Compared with the gusset plate, the transverse steel plate features a smaller section, lower stiffness, and limited restraint capacity. Therefore, gusset plate no. 13 cannot effectively coordinate with the main structure during deformation. Under load conditions, it only deformed downward, showing an abnormal displacement vector distribution under the deformation law of the structure system (as indicated by the red arrow in Figure 1(c)).  
The essence of the structure's FFDV abnormal angle, as shown in Figure 29, is that damage destroys the structure's deformation coordination and expresses damage information via the FFDV's abnormal rotation angle. This property can be used to analyze the FFDV's rotation-angle change rate before and after damage. Figure 30 shows the solution model for the vector's rotation-angle change rate, and Equation (1) shows the equation to calculate the vector's rotation-angle change rate.  
\[K=\frac{{\theta_{n}}^{\prime}-\theta_{n}}{\theta_{n}} \tag{1}\]  
To validate the proposed damage identification index, the rotation-angle distribution of the upper chord steel plate edge was extracted. Figure 31 shows the rotation-angle distribution curve of the upper chord steel plate edge.  
Figure 31: Upper chord steel plate edge’s rotation-angle distribution under conditions D01–D03.  
Figure 30: Schematic diagram of displacement vector’s rotation-angle change rate.  
Subsequently, the \(K\) value for the two damage conditions was calculated, as shown in Figure 32.  
Figure 32a shows the peak value of the rotation-angle change rate under condition D02 on the no. 13 gusset plate, which was situated above the nos. 13-14 damaged member. Figure 32b shows that the abnormal distribution area of the rotation-angle change rate under condition D03 was wider than that under condition D02. The peak value was near the no. 12 gusset plate, and the abnormal distribution area of the rotation-angle change rate was consistent with the position of the two damaged members, i.e., the nos. 12-13 and 13-14 members.