## 3 Results
### Continuous Wavelet Transform (CWT)  
#### 3.2.1 Scalogram Images  
One of the principal differences between CWT and PSD is the analysis of the signal in the time-frequency domain, which enables the identification of frequency components, their energy density, and the behavior of the vibration signal over time. Figures 19-25 illustrate the scalogram images of each sensor for all excitation scenarios mentioned in this article. Figure 19 presents a representative difference in the energy density of frequency components in the 3-DoF structure between the healthy condition (AV) and damaged condition (AVD) under ambient vibration excitations. The energy density of each \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Frequency [Hz]** & \(f_{\text{rd}}\)**Case [dB/Hz]** & \(f_{\text{rd}}\)**Case [dB/Hz]** & \(f_{\text{rd}}\)**Case [dB/Hz]** \\ \hline \multirow{3}{*}{1.76} & - & \(-44.83\), \((53)\) & - \\  & - & \(-47.15\), \((54)\) & - \\  & - & \(-48.89\), \((52)\) & - \\ \hline \multirow{3}{*}{1.78} & \(-40.15\), \((53)\) & - & - \\  & \(-40.40\), \((54)\) & - & - \\  & \(-44.12\), \((52)\) & - & - \\ \hline \multirow{3}{*}{1.80} & - & - & \(-30.57\), \((53)\) \\  & - & - & \(-31.77\), \((54)\) \\  & - & - & \(-36.19\), \((52)\) \\ \hline \multirow{3}{*}{2.11} & \(19.60\), \((53)\) & - & - \\  & \(19.01\), \((54)\) & - & - \\  & \(12.92\), \((52)\) & - & - \\ \hline \multirow{3}{*}{5.71} & - & - & \(-33.93\), \((52)\) \\  & - & - & \(-38.98\), \((54)\) \\  & - & - & \(-51.80\), \((53)\) \\ \hline \multirow{3}{*}{5.76} & \(-28.82\), \((52)\) & - & - \\  & \(-33.74\), \((54)\) & - & - \\  & \(-46.61\), \((53)\) & - & - \\ \hline \multirow{3}{*}{5.78} & - & \(-27.71\), \((52)\) & - \\  & - & \(-32.90\), \((54)\) & - \\  & - & \(-47.26\), \((53)\) & - \\ \hline \multirow{3}{*}{6.41} & - & \(23.02\), \((52)\) & - \\  & - & \(16.84\), \((54)\) & - \\  & - & \(-27.79\), \((53)\) & - \\ \hline \multirow{3}{*}{9.32} & \(-29.22\), \((53)\) & - & \(-29.60\), \((53)\) \\  & \(-30.86\), \((54)\) & \(-35.53\), \((54)\) & \(-31.13\), \((54)\) \\  & \(-39.75\), \((52)\) & \(-44.79\), \((52)\) & \(-39.44\), \((52)\) \\ \hline \multirow{3}{*}{9.68} & - & - & \(0.83\), \((53)\) \\  & - & - & \(-1.02\), \((52)\) \\ \cline{1-1}  & - & - & \(-1.86\), \((54)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental natural frequencies and excitation frequencies of the power spectral density using a shaker in the 3-DoF structure. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(f_{\text{rd}}\)**[Hz]** & **Cases** & \(f_{\text{rd}}\)**[Hz]** & \(\text{RE}=\frac{\left|f_{\text{rd}}-f_{\text{rd}}\right|}{f_{\text{rd}}}\)\(\times\)**100\%** \\ \hline \multirow{3}{*}{\(f_{\text{rd}1}=1.93\)} & 6 & 1.76 & 8.89\% \\  & 5 & 1.78 & 7.77\% \\  & 2,\(3,4,7\) & 1.80 & 6.74\% \\  & 1 & 1.86 & 3.71\% \\ \hline \multirow{3}{*}{\(f_{\text{rd}2}=5.87\)} & 7 & 5.71 & 2.75\% \\  & 2,\(3,4\) & 5.72 & 2.61\% \\  & 5 & 5.76 & 1.90\% \\  & 6 & 5.78 & 1.62\% \\  & 1 & 5.87 & 0.00\% \\ \hline \multirow{3}{*}{\(f_{\text{rd}3}=8.86\)} & 2,\(3,4,5,6,7\) & 9.32 & 5.15\% \\  & 1 & 9.33 & 5.34\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of theoretical and experimental natural frequencies of the 3 DoF structure determined based on PSD. frequency component varies over time in response to changes in vibration signals. In addition, the AVD case shows notably higher energy in several narrow bands compared to the AV case. The scalogram analysis, together with the four statistical descriptors (mean \(\mu\), standard deviation \(\sigma\), coefficient of variation \(CV\), and maximum energy \(MaxEp\)), provides a quantitative comparison of the vibration response in the undamaged (AV) and damaged (AVD) states under ambient vibration excitation. It should be noted that, for frequencies below 1 Hz, the energy peaks are exceedingly weak and the mean energy density approaches zero, which disproportionately increases the coefficient of variation.