# Possibility of Bridge Inspection through Drive-By Vehicles
## 3 2D VBI Model
### Short Time Fourier Transform Results  
Short-Time Fourier Transform (STFT) analysis is an advanced signal processing method that allows the frequency spectrum to change with time. The effect of different window sizes was researched first. Five different window sizes are selected: 10, 20, 50, 100, and 200, respectively. The STFT of vertical accelerations of the vehicle driving on the health bridge is shown for window size of 100 and 200 in Figures 6 and 7. Here window size means how many time data will be processed at each time instant, and STFT will swipe-process the complete data set through FFT analysis of each segmented window. Through STFT, local disturbance in the time history data could be revealed. Figures 6 and 7 show that the STFT results with a larger window will get better resolution. However, the results of STFT will lose some data at the beginning and ending of the signal equal to half the number of the window length. In other words, more data will be lost with a larger window. As for this research, the rest study will use a window size of 100. When damage exists, the STFT results will show that some area's color is changed, which means the frequency energy of indicated areas is changed. Figure 8 presents the results of the 1 m length damage at 5 m location. Figure 6: Short-time Fourier transformation of the healthy bridge accelerations with window size 100. All damaged cases show similar changing patterns: the low-frequency range energy will increase due to the energy leaked from the original frequency bands at different locations. In this way, the energy of frequency ranging from 0.39 to 1.10 Hz was analyzed to find the relationship between the STFT results and different damage cases. To identify the damage location, a basic energy line was set from the healthy bridge results (Figure 6). The average energy of the aimed range frequency is \(-113.08\) dB/Hz, and it could be assumed that if a 5% change to the energy happens, the location could be marked as a damaged area. As for this study, the identified damaged area starts when the average energy becomes constantly larger than \(-107.7\) dB/Hz. The mid locations of damaged areas are compared between real cases and identified results for different damage locations and shown in Table 2.  
Figure 8: Short-time Fourier transformation of the bridge accelerations with damage at 5 m location. Figure 7: Short-time Fourier transformation of the healthy bridge accelerations with window size 200. Table 2 shows that the damage locations identified are close to the real cases at 5 m and 10 m. For the 1 m damage location case, 50 data (2.5 m long) are lost due to the STFT analysis, leading to the not-so-accurate damage identification. The mid locations of damaged areas and damaged lengths are compared between the real sizes and the identified results for different damage sizes. Table 3 shows that for different size damages, damage location identification still works fine. However, the identified damage sizes are not consistent with the real sizes. The chosen basic energy line may cause this. For different damage levels, only the energy zone at the damaged area is analyzed. The damaged area is at the 10 to 11 m location of the bridge. The energy change with respect to different damage levels is summarized and shown in Figure 9.