# Damage Identification in Warren Truss Bridges by Two Different Time-Frequency Algorithms
## 4 Results
As in the results of Figure 9, the HHT performs less precisely in locating the defect. The better performances of the CWT compared to the HHT becomes more evident when the irregularity profile adopted for the damaged-bridge and the healthy-bridge simulations is slightly changed, to represent the track degradation with time which might occur between two consecutive observations. The difference in the irregularity profiles was of the same order as the ones reported in Figure 4: as stated before, the RMS of the two profiles differs by 8%. Figure 11 reports the results obtained by means of the CWT (Figure 11a) and the HHT (Figure 11b). The CWT is still able to identify the damaged region, whereas the HHT results are affected by the change in the track profile which occurred in the two simulations. In the HHT result of Figure 11b, indeed, the maximum peak of instantaneous energy is detected  
Figure 11: Damage detection results in the presence of different track irregularities in the healthy-bridge and damaged-bridge simulations with the CSA train at 100 km/h and total damage on the fastening between the side wall diagonal element and the lateral chord. (**a**) Module of the difference in wavelet coefficients. (**b**) Hilbert spectrum. Figure 10: Damage detection results in the presence of track irregularity, with the CSA train at 100 km/h showing total damage on the fastening between the side wall diagonal member and the lateral chord. (**a**) Module of the difference in wavelet coefficients. (**b**) Hilbert spectrum. outside the bridge span. The Continuous Wavelet Transform is therefore proven to be more robust to track profile changes. In this case, the damage-related frequency is similar to that presented in the previous cases (i.e., Figures 8a and 10a), which confirms that it is actually related to the damage presence rather than to the track profile. Furthermore, the CWT was also found to be robust to the presence of measuring noise, which was modelled in this work by means of a gaussian variable whose standard deviation is 10% of the RMS of the original signal. In fact, as shown in Figure 12, the CWT is still able to correctly identify the damage position across the bridge span, in the presence of a change in terms of track profile, and with the addition of measuring noise. The results of the entire set of simulations carried out showed that, in the case of the time-invariant profile (and of course without the track irregularity profile), good identification performances are also obtained in the case of lower entity of the damage (i.e., partial damage modeled as described in Section 2.2.1), for both the CWT and HHT methods. However, when modelling a variation of the irregularity profile, even the effectiveness of the CWT method depends on the amount of change in the irregularity profile, and the severity of the damage. Only the total damage, representing a full disconnected joint, was detected for any tested change in track irregularity between the damage and healthy case simulation. Mild damages, on the contrary, are hidden even by low changes in the track profiles.