# Damage Identification in Warren Truss Bridges by Two Different Time-Frequency Algorithms
## 4 Results  
This section illustrates the results obtained by applying the two aforementioned procedures to the acceleration simulated on the leading bogie of the train. The outcomes achieved from the bogie accelerations corresponding to the side of the bridge damage are shown, with an increasing level of complexity of the simulations to evaluate the robustness of the two methods to disturbing factors. As a reference example, the results obtained for the CSA train running at 100 km/h are reported, as well as all the remaining combinations of train and speeds leading to consistent results, as reported in the following sections. The first results presented illustrate the application of the procedures corresponding to the damage affecting the connection between the lower chord and a diagonal member of the bridge, as described in Section 2.2.1. Total damage on the second diagonal member of the third module of the bridge (see Figure 2) is considered, located at around mid-span. For clarity, in this introductory example no track irregularity is included in the simulation. Figure 7 compares the accelerations obtained on the leading bogie of the CSA train in case of a healthy and a damaged bridge, respectively. In the figure, as in all the following ones in this section, the two vertical black lines identify the two extremes of the damaged diagonal chord. The difference between the accelerations corresponding to the healthy and the damaged bridge is clearly visible in an area wider than the one directly affected by the defect. Although the defect is local, it extends its influence to a larger portion of the bridge. Figure 8 reports the position-frequency map of the difference of the CWT coefficients of the damaged and healthy condition, while the results of the HHT are reported in Figure 8. In both the cases, the maxima of the index revealing the presence of the damage can identify the damaged region, although the HHT instantaneous energy peak falls at the right margin of the affected region. The frequencies associated to the peaks detected by the two methods are rather similar (3.68 Hz and 4.2 Hz, respectively), so that the damage-related frequencies can be considered dependent on the nature of the damage itself rather than on the method used to detect its presence. The identified frequencies change proportionally with the train speed, so that they can be related to the extension of the region of influence of the damage on the bridge behavior. The damage-related frequencies identified from the analysis do not change when an irregularity profile is added to the track. Figure 9 shows the accelerations on the leading bogie in case of the healthy and the damaged bridge with the same track profile (i.e., level 3, the highest level adopted). Figure 6: Scheme illustrating the way in which the HHT was used in the present work. Figure 8: Damage detection results in the absence of track irregularity; the CSA train travels at 100 km/h and total damage on the fastening between the diagonal member and the lateral chord is considered (**a**) Module of the difference in wavelet coefficients. (**b**) Hilbert spectrum. Figure 7: Leading bogie accelerations corresponding to the healthy and the damaged bridge. The CSA train travelling at 100 km/h, in the absence of irregularity and total damage affecting the side wall diagonal chord. Figure 9: Leading bogie front right accelerations in the case of the healthy and the damaged bridge, respectively, and the time-invariant irregularity profile. Results are for the CSA train travelling at 100 km/h. Figure 10 reports the results obtained through the CWT (Figure 10a) and the HHT (Figure 10b). Again, the actual damage positions are correctly identified by the CWT and the HHT (the peak falls at the left margin of the damaged region), with damage-related frequencies (i.e., 3.68 Hz and 4.5 Hz, respectively) similar to those observed in Figure 9 without track irregularity. It can be therefore inferred that these appear to be related to the signature of the defect affecting the structure.