# Drive-by Bridge Damage Detection Using Continuous Wavelet Transform
## 4 Parametric Study
### Road Roughness Level  
As discussed above, road roughness is one of the parameters that adversely affect the success of drive-by monitoring methods in estimating bridge modal parameters and detecting damage. We also demonstrated in Section 3 that using residual accelerations, which are computed as the difference between the accelerations recorded on the front-axle and the rear-axle, eliminates these adverse effects. However, so far, we only tested the efficacy of this approach for one roughness level. This section investigates the effect of four distinct Class A roads on damage estimation of the bridge utilizing the proposed method. The roughness profiles were generated using Equations (1)-(3). The \(G(n_{0})\) value was specified as 0.01 \(\times\) 10\({}^{-6}\) m\({}^{3}\), 0.1 \(\times\) 10\({}^{-6}\) m\({}^{3}\), 1 \(\times\) 10\({}^{-6}\) m\({}^{3}\), and 10 \(\times\) 10\({}^{-6}\) m\({}^{3}\) for _very low_, _low_, _moderate_, and _high_ roughness levels, respectively.  
Figure 15 depicts the wavelet coefficients at a scale of 600 obtained from the residual accelerations for the different roughness levels. Different levels of damage is introduced between 10 m and 11 m. The speed of the vehicle was kept constant at 2 m/s. The results indicate that, despite the remedies taken to reduce its effect, road roughness still plays a significant role in detecting damage. For very low and low levels of road roughness, its effects are very limited and we can clearly detect the lowest levels of damage investigated in this study. However, once we reach the moderate roughness level, it becomes very difficult to distinguish the wavelet coefficients from the undamaged case and 20% damaged case.  
Figure 14: Wavelet coefficients at for different vehicle speeds.  
As such, only damage levels of 50% and above can be clearly identified for this roughness level. Finally, for the high roughness level, the fluctuations in the wavelet coefficients of the damaged case due to the road roughness become so significant that it is not possible to ascertain whether they are created by the damage or by the road roughness. Further for the moderate and high levels of road roughness, the wavelet coefficients for the undamaged bridge do not remain as stable as they do for the lower roughness levels, making it difficult for the proposed method to detect and locate the damage.  
One question that needs to be considered here is: \"If we do not know the road roughness level, how do we understand if the fluctuations are due to damage (e.g., Figure 15a) or due to road roughness (e.g., Figure 15d)\". This is a crucial question for the success of the practical applications of the proposed method. Focusing on Figure 15a,d, which depict the wavelet coefficients for very low and high roughness levels, respectively, we can observe that the fluctuations due to damage have mainly low frequency. On the other hand, fluctuations due to road roughness have significant high frequency components as can be observed from Figure 15d, and to a certain extent, Figure 15c. Therefore, the frequency content of the fluctuations in the wavelet coefficients should be examined to determine the source of the fluctuations in the wavelet coefficients to ascertain whether they are caused by road roughness or damage.