## 6 Results  
Figures 7 and 8 show the wavelet energy as a function of frequency for one I-section of the ground floor of specimens FD and SD, respectively. The baseline values for calculation of the RWEE were considered to be the C100 values, after seismic simulation applied 100% times the acceleration of the original earthquake. Peaks of this plot correspond with the natural frequencies of the I-sections. Few differences are visually observed as the level of damage of the damper increases, although some changes are perceived around the resonance at 25 kHz, approximately. For a better view, the Figure also shows a zoomed in version of Figures 7 and 8 around this resonance. Evident in this case is a clear increase of the wavelet energy magnitude as the damage level increases. Damage to the I-sections produces a change in their mechanical properties, in turn producing a change in the vibrational response. It is very well known that as the order of the resonance frequency increases, the change in the vibrational response becomes greater. This is why the differences are more evident around 25 kHz.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multirow{2}{*}{**Location of WPDs**} & \multicolumn{6}{c}{**Damage Level**} \\ \cline{2-7}  & & **d0** & **d1** & **d2** & **d3** & **d4** & **d5** \\ \hline FD & Ground floor & 0.00 & 0.17 & 0.45 & 0.77 & & \\ SD & First floor & 0.00 & 0.02 & 0.05 & 0.15 & 0.27 & 0.40 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Values of index \(ID_{i}\) at different levels of damage to the WPDs.  
Figure 7: Wavelet energy of one I-section of the ground floor of specimen FD. (**a**) Complete frequency range; (**b**) Zoom around the 25 kHz natural frequency.  
Given the wavelet energy, the WE and the damage index RWEE were calculated as explained in Section 4. In order to establish the reliability of the proposed index, a comparison with the mechanical damage index ID was carried out [3,4]. Firstly, a comparison was made for each repetition of the vibration test (T1, T2, T3, T4) at each level of damage of the I-section steel segments of specimen FD, and for T1, T2 and T3 of the I-section steel segment of specimen SD. Results are shown in Figures 9 and 10. It can be seen that the RWEE index follows the behavior of the ID index as the level of damage increases. No important differences exist between the repetitions of the vibration tests.  
Figure 8: Wavelet energy of one I-section of the ground floor of specimen SD. (**a**) Complete frequency range; (**b**) Zoom around the 25 kHz natural frequency.  
Figure 9: The relative wavelet energy entropy index (RWEE) vs. mechanical damage index (ID) for each I-section of the dampers of FD.  
Figure 11 presents the RWEE versus ID plots grouping the four I-sections of each specimen. Each point in this plot is an average of the repetitions of the vibration test. Linear fitting and correlation coefficients are given in each case. Results are generally very satisfactory. In view of the good correlation between the ID and RWEE indices, ID can be indirectly obtained from the RWEE index, thus providing a quantification of damage to the I-section. This affords two important advantages: (i) no real-time data recordings during the earthquake are required; and (ii) the instrumentation needed is simpler and cheaper.