# Damage Identification in Warren Truss Bridges by Two Different Time-Frequency Algorithms
## 4 Results
### Damage between Cross Girders and the Lower Chord  
This section presents the simulation results corresponding to the second kind of bridge damage simulated, affecting the connection between the cross girders and the lower chord. This kind of defect was found to be more easily detectable by the proposed algorithm, being closer to the train wheel and therefore to the actual interaction point between the bridge structure and the vehicle. It was also detected in the case of mild defect, when changing the track irregularity between healthy and damaged cases.  
Figure 17 illustrates the trend identified by the CWT and HHT algorithms in terms of damage-related frequency. The results refer to the CSA train travelling at 100 km/h, in the absence of track irregularity. Again, it is possible to state that the two time-frequency methods led to similar results in terms of frequency identification. The damage-related frequency is similar to the one identified for the previous kind of defect (Figure 13), meaning that the zones of influence of the two defects are rather similar. Moreover, the effect of the bridge damage on the first bending mode of vibration occurring at 16 Hz, is not large enough to be detected by the passing train.  
Figure 18 is intended to investigate a possible dependence of the diagnostic indexes on the position of the damage along the bridge span. Compared to the previous damage scenario in Figure 15, it is possible to notice that for this defect the peak values seem to be less sensitive to damage position. On the other hand, the index magnitudes are generally higher, due to the fact that a defect affecting the cross-girder and the lower chord is closer to the points of interaction between the train and the bridge structure.  
Finally, Figure 19 illustrates the identification performances of the CWT method as a function of the travelling speed and damage position rail vehicle. Since this type of defect is more local than the previous one, the _relative identification error_ is re  
Figure 17: Damage-related frequency identified by HHT and CWT, respectively, as a function of damage position, in the case of severe damage affecting the cross-girder connection.  
as the difference in the estimated defect position and the actual deteriorated cross-girder position, over the length of the bridge:  
\[Error\%=\frac{|Estimated\ damage\ position-Actual\ damage\ position|}{\text{Bridge\ Length}}\cdot 100 \tag{3}\]  
The _relative identification error_ identified in the case of damage between the cross girders and the lower chord is less dependent on the damage position, compared to the case of a defect affecting a diagonal element in the bridge side wall (see Figure 16). This may be due to the more direct coupling existing between what is sensed by the vehicle travelling on the bridge and the damage occurring on the cross-girder, rather than on the diagonal chord.  
Before moving to conclusions section, it is important to remark that the _relative identification error_ performances were computed differently due to the diverse nature of the two  
Figure 19: _Relative identification error_ as a function of damage position and travelling speed With the CSA train, severe cross-girder damage and mild change of irregularity between the two runs.  
Figure 18: Trend of coefficients maximum magnitudes as function of damage position. CSA train travelling at 100 km/h, and no track irregularity.  
damages, in the sense that, while the diagonal element extends longitudinally (across the bridge span), the cross-girder, instead, is transverse to the bridge's longitudinal axis.