# Damage Identification in Warren Truss Bridges by Two Different Time-Frequency Algorithms
## 4 Results
### Influence of Damage Position  
This section investigates the influence of the damage position on the results of the CWT and HHT diagnostic algorithms, without track irregularity. Figure 13 reports the damage-related frequencies as a function of the position of the defect along the bridge span. The results refer to the case of total damage of the diagonal chord. The trends representing the damage-related frequency obtained from CWT and HHT show almost total agreement, enough to infer that the position of the damage along the bridge does not affect the coherence in terms of frequency information provided by the two different methods. The damage-related frequency does not change significantly with the defect position, being in all cases close to the frequency values already given in Figures 8, 10 and 11. An exception was found in the points corresponding to the case in which the damage is located in the first module of the bridge (positioned at about 3 m), in which a dominant peak is visible at about 9 Hz. In this occurrence, the lower frequency peak is still present  
Figure 12: CWT damage detection results in the presence of different track irregularities in the healthy-bridge and damaged-bridge simulations and measuring noise. (represented with thinner circles), but it becomes a secondary peak compared to the main one at 9 Hz. Modal analysis showed that a local mode of vibration at around 9 Hz, caused by the inefficiency of the diagonal chord, appears only in the cases in which the damage affects the first or last module in the bridge. On the other hand, it is not present when the damage is located along the other bridge modules; this may be due to the higher elastic energy which would occur for the local mode shape. This mode shape is represented in Figure 14.  
The 9 Hz frequency peak is indeed also found in the CWT when the defect affects the last module, but in this case the dominant peak is the one at low frequency, which is therefore represented in Figure 13 (at the \(x\)-axis position of about 18 m): again, the secondary peaks (in terms of magnitudes) are represented with thinner circles. The above-made observations point out that the damage-related frequency is generally due to the area of influence of the defect (being therefore dependent on train speed), but in some circumstances it can also be related to a mode of vibration of the structure, being therefore independent of train speed. With the view to applying the drive-by method to a real bridge case, a preliminary modal analysis of the structure should therefore be carried out through FEM simulation of possible damaged configurations. This would allow estimation of the possible frequencies involved in the damaged structure, setting of a frequency range in the results of the CWT algorithm to maintain monitoring during the operation of the diagnostic system. Figure 15 illustrates the magnitudes of the diagnostic indexes (i.e., CWT and HHT output) as a function of the location of the damage along the bridge span. It is possible to notice that defects occurring at the extremes of the bridge lead to higher magnitudes, if compared to the cases in which the damage affects the structure closer to mid-span. This is clearly visible in both the cases of damage affecting the first and the last module, and therefore not only in the case in which the 9 Hz normal frequency is involved. The reason is due to the fact that at the ends of the bridge the diagonal elements face higher shear  
Figure 14: Local mode shape arising when the damaged diagonal member is positioned in the first module of the truss bridge (the missing AB diagonal member represent the damaged element). Figure 13: Damage-related frequency identified through CWT and HHT as a function of damage position. forces, so the damage under analysis, involving a diagonal element of the side wall, leads to a more intense difference in the behavior of the bridge under the train passage. This is in agreement to what was observed by the authors in [31; 32].