# Damage Detection in Beam Bridges Using Quasi-static Displacement Influence Lines
## 3 Numerical Example
### Comparison of the Performance Between the Proposed Method and the Traditional Approach
#### 3.3.3 Damage Detection Considering Different Loading Conditions before and after Damage  
Based on the results acquired in Section 3.3.2, we evaluate the effect of measurement noise on the inconsistency in the quasi-static loading conditions before and after damage. As discussed in Section 3.2, the traditional method--that is, analyzing the difference in the displacement ILs--does not work when the weight of the quasi-static loading vehicle is inconsistent before and after bridge damage occurs. To assess the effectiveness of the proposed method, the damage case described in Section 3.3.2 is taken as an example and the inconsistency in the loading condition is achieved by  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Case Conditions** & & & & & & & & & & & \\ \hline Damage extent & 5\% & 5\% & 5\% & 5\% & 5\% & 5\% & 5\% & 5\% & 5\% & 5\% & 5\% \\ Noise level & 1.2\% & 1.6\% & 2.0\% & 2.4\% & 2.8\% & 3.2\% & 3.6\% & 4.0\% & 4.4\% & 4.8\% & 5.2\% \\ Traditional method & Yes & No & No & No & No & No & No & No & No & No \\ Proposed method & Yes & Yes & Yes & Yes & Yes & Yes & Yes & Yes & Yes & Yes & No \\ \hline Extent of damage & 10\% & 10\% & 10\% & 10\% & 10\% & 10\% & 10\% & 10\% & 10\% & 10\% \\ Noise level & 2.4\% & 3.2\% & 4.0\% & 4.8\% & 5.6\% & 6.4\% & 7.2\% & 8.0\% & 8.8\% & 9.6\% & 10.4\% \\ Traditional method & Yes & No & No & No & No & No & No & No & No & No \\ Proposed method & Yes & Yes & Yes & Yes & Yes & Yes & Yes & Yes & Yes & Yes & No \\ \hline Extent of damage & 15\% & 15\% & 15\% & 15\% & 15\% & 15\% & 15\% & 15\% & 15\% & 15\% & 15\% \\ Noise level & 3.6\% & 4.8\% & 6.0\% & 7.2\% & 8.4\% & 9.6\% & 10.4\% & 12.0\% & 13.2\% & 14.4\% & 15.6\% \\ Traditional method & Yes & No & No & No & No & No & No & No & No & No & No \\ Proposed method & Yes & Yes & Yes & Yes & Yes & Yes & Yes & Yes & Yes & Yes & No \\ \hline \hline \end{tabular}
\end{table}
Table 3: Description of all cases for the quasi-static load test of the model bridge.  
Figure 7: Comparison of the damage detection performance between the traditional method and the proposed method before and after damage with a 1.6% noise level: (**a**) displacement ILs; (**b**) difference between two displacement ILs obtained by the traditional method; (**c**) metric of the damage feature obtained by the proposed method.  
using quasi-static loading vehicles with weights of 100 kN and 50 kN for healthy and damaged bridges, respectively. As shown in Figure 8a,b, there is an obvious difference in the displacement ILs for the healthy bridge acted upon by the two different quasi-static loads; however, under the above two loading conditions, the difference in the displacement ILs before and after damage does not exhibit any discrepancy. Unlike the traditional approach, the proposed method works effectively under the influence of measurement noise, as shown in Figure 8c. Therefore, the large difference in the weight of the loading vehicle is used in this section to evaluate the performance of the proposed method. For practical applications, the weight of the loading vehicle before and after damage should be as consistent as possible and should be sufficiently heavy to obtain precise data on the damage experienced by the bridge, as described in Section 2.1.