# A Fast Wavelet-Based Bridge Condition Assessment Approach Using Only Moving Vehicle Measurements
## 4 Numerically Verification
### The Effect of Road Roughness  
Road roughness is one of the main challenges in the application of the drive-by bridge SHM [4]. To investigate this effect, the road profile is first not considered in the VBI system. Figure 5 shows the accelerations of the axle and the vehicle body for the healthy bridge conditions, as well as their spectrums with FFT. As described in the theoretical background of drive-by bridge SHM, the vehicle responses contain the bridge's modal information. Both accelerations are dominated by the 1 st natural frequency of the bridge, as well as the vehicle's vibration frequencies. Based on the power spectral density-curve, as shown in ISO 8608 [45], a road profile with a 'class A' is then randomly generated. The corresponding results are illustrated in Figure 6 when this road profile is considered in the VBI system. As shown, the axle acceleration is more sensitive to road roughness, where the undesirable frequencies caused by road roughness cover the frequencies of the VBI system. No useful information can be found from it directly. For the vehicle responses of the vehicle body, the road profile excites the vibration of the vehicle itself and the spectrum is dominated by the \(f_{\rm{v1}}\), but without a clue for the 1 st natural frequency of the bridge, \(f_{\rm{b1}}\). It is demonstrated that road roughness has an intensively negative effect on the drive-by bridge SHM. The response of the vehicle body may be more suitable for implementing the drive-by bridge SHM than the axle response, as it is less negatively affected by road roughness. Figure 5: Vehicle responses and its spectrums without road roughness. (**a**) the axle acceleration \(\tilde{u}_{a}\); (**b**) spectrum for \(\tilde{u}_{a}\); (**c**) the vehicle body acceleration \(\tilde{u}_{s}\); (**d**) spectrum for \(\tilde{u}_{s}\). To further present the effect of road roughness in drive-by bridge SHM, another related study is introduced. [PERSON], [PERSON], and [PERSON] [9] proposed a wavelet-based approach to estimate the bridge damage and its location when the road profile is not considered. For example, the bridge damage is assumed at 13 m from the left end with a damage level of 40%. The acceleration of the axle is subjected to the wavelet transform with a wavelet function of 'Mexican hat', and the wavelet scalogram is shown in Figure 7a. The wavelet function of 'Mexican hat' is selected because it has been verified as one of the suitable functions to detect the bridge defect [40]. Besides the edge effect, there is an \"anomaly\" at the location of the bridge damage. In addition, the wavelet coefficient at a particular scale is illustrated in Figure 7b. As can be seen, a clear peak can be observed to indicate the damage location. However, when the previous road surface profile is considered in the VBI system, the corresponding results are shown in Figure 7c,d, where there is no way to identify the damage and the damage location. It is again demonstrated that road roughness has a negative effect on damage estimation using indirect measurements. Because the vehicle body acceleration is more robust to the road roughness, this signal is used as input for the proposed approach instead of the axle acceleration of the vehicle. Regarding the previous cases, Figure 8 shows the accelerations of the vehicle axle at different bridge conditions. As shown, although the bridge has been damaged, there are no clear changes in the moving vehicle responses. Figure 9 plots the wavelet scalogram (with 'Mexican hat') on the acceleration of the vehicle under damaged bridge conditions. As shown, no resource of information can be obtained to indicate the bridge damage. The proposed approach is then used to detect the bridge damage and localize the identified damage.