# Drive-by Bridge Damage Detection Using Continuous Wavelet Transform
## 5 Concluding Remarks  
This article summarizes a drive-by monitoring method that is based on the continuous wavelet transform of the residual accelerations recorded on a vehicle crossing the bridge. First, we demonstrated that, using the residual accelerations, which are computed by the accelerations recorded at the back axle from those recorded at the front axle, eliminates the adverse effects of road roughness on the wavelet coefficient maps. Once these effects are eliminated, the wavelet coefficients at a scale far away from the bridge, vehicle and driving frequencies, are shown to be stable around zero in the absence of damage. On the other hand, flexural damage leads to disturbances in the wavelet coefficients around the damage location. Leveraging this observation, the proposed method can detect and locate damage even in the absence of data from the undamaged bridge. We also conducted a parametric study to investigate the effect of different parameters on the efficacy of the proposed method. Through this parametric study, we observed that:  
* The proposed method can successfully detect damage as low as 20% at different locations of the bridge even in the presence of road roughness. * The proposed method illustrated that, as the damage level increases, perturbations in the wavelet coefficient maps also increase, potentially facilitating the quantification of damage. However, the proposed method cannot quantify the damage level in its current form when the damage is detected for the first time. However, as the damage propagates with time, repeated application of the proposed method enables the detection of the escalating damage levels. * The vehicle speed has a negative impact on damage detection using the proposed method because, as the vehicle speed increases the driving frequency becomes closer to the vehicle and bridge frequencies, minimizing the window that we select the scale  
Figure 17: Wavelet coefficients at scale 600 for 20% damage at multiple locations. (**a**) Multiple damages between 7–8 m and between 12–13 m, (**b**) Multiple damages between 7–8 m and between 16–17 m.  
used for damage detection. Hence, the proposed method should be used with low vehicle speeds to ensure successful damage detection. * Although using the residual accelerations largely eliminates the negative impacts of road roughness when road roughness is limited to low levels, for higher levels of road roughness, only higher levels of damage can be detected successfully. * Owing to the edge effects encountered in CWT, the proposed method is constrained to identifying and locating damage in regions where these edge effects are less pronounced. * When the bridge is seated on relatively soft bearings, the edge effects associated with continuous wavelet transform, is amplified and extends to a longer section of the bridge at the ends. As such, the segment of the bridge where damage can be detected becomes shorter. However, when the damage is close to the middle of the span and sufficiently away from the supports, the proposed method can successfully detect and locate damage. * The proposed method was also shown to detect and locate presence of multiple damaged sections. In the numerical analysis where we introduced damage in two separate sections of the bridge, we can clearly observe two peaks, both negative and positive, close to the damage locations, while we could only observe a single peak when only one bridge section was damaged. Further, as in the case of single damage, the wavelet coefficients reach a negative peak just before the damage location, increase after this peak, and cross the time axis at the middle of the bridge location before attaining a positive peak. Thus, using the proposed method, we can locate both damaged sections successfully. One parameter that we did not include in the parametric study is the measurement noise. The main reason for omitting this parameter lies in the underlying principle of the proposed framework, which aims to capture the static response of the structure at low frequencies.