## 4 Results and Validation
### Small-Scale Testing
#### 4.1.2 Flexible Structure Monitoring  
The modal identification of the dominant natural frequencies and mode shapes of the two-story structure provided five ambient vibration records. All ambient vibration datasets were post-processed to determine the best fitting time windows that would enable confident modal identification and MAC evaluation according to the information gathered. Figure 19 presents the dynamic response of the flexible structure in the frequency domain by the SHM systems in comparison. The SVD spectrum outlines the dominant vibration modes; the natural frequencies are identified from the representative singular value peaks, and the singular vectors associated with these peaks represent the mode shapes for the S1 values' frequency line. Otherwise, the S2 values' frequency line may include noise or  
Figure 16: Spectrograms for the 0.25 cm displacement frequency chirp: (**a**) PCB L74 spectrogram. (**b**) ADXL355 RBP1 spectrogram. (**c**) ADXL355 RBP4 spectrogram. Figure 17: Spectrograms for the 0.50 cm displacement frequency chirp: (**a**) PCB L74 spectrogram. (**b**) ADXL355 RBP1 spectrogram. (**c**) ADXL355 RBP4 spectrogram. Figure 18: Spectrograms for the 0.75 cm displacement frequency chirp: (**a**) PCB L74 spectrogram. (**b**) ADXL355 RBP1 spectrogram. (**c**) ADXL355 RBP4 spectrogram. information about vibration modes less representative behind the natural dynamic response in the bandwidth. Thus, the S2 values' frequency line is neglected in this approach [34]. Both monitoring systems identified the first and second singular value peaks at 1.95 and 7.81 Hz, respectively. The mode shape vector related to each frequency notably represents the dynamic system response. Therefore, the 1.95 Hz natural frequency was adopted as the first dominant vibration mode, and the 7.81 Hz natural frequency was assumed as the second dominant vibration mode of the two-story structure. The modal identification results considering the measured dynamic response are shown in Table 7. Furthermore, the mode shapes detected from the SHM systems are depicted in Figure 20.  
For the dynamic characterization results of the flexible structure, the modal identification performed through the low-cost SHM system demonstrates an accurate estimation. The natural frequencies reported from the low-cost SHM system were exactly equal considering the approach of the reference SHM system. For the mode shape validation of the WSN monitoring system, the MAC values were calculated to compare mode shapes estimated by the WSN and wired monitoring system. Figure 21 shows the MAC values calculated for the mode shapes' validation; the target vibration mode indicates the modal vectors determined by the reference SHM system, whereas the calculated vibration mode represents the modal vectors obtained from the low-cost SHM system. It was observed that the diagonal values of the MAC matrix were very close to the unity, demonstrating a high significant vibration mode correlation between mode shapes. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Vibration Mode 1**} \\ \hline \multirow{2}{*}{**Channel**} & \multicolumn{2}{c}{**Frequency (Hz)**} & \multicolumn{2}{c}{**Modal Coordinate**} \\ \cline{2-5}  & **Reference System** & **Low-Cost System** & **Reference System** & **Low-Cost System** \\ \hline
1 & \multirow{2}{*}{1.95} & \multirow{2}{*}{1.95} & \multirow{2}{*}{1.00} & 0.588 & 0.445 \\
2 & & & & 1.000 & 1.000 \\ \hline \multicolumn{5}{c}{**Vibration Mode 2**} \\ \hline \multirow{2}{*}{**Channel**} & \multicolumn{2}{c}{**Frequency (Hz)**} & \multicolumn{2}{c}{**Modal Coordinate**} \\ \cline{2-5}  & **Reference System** & **Low-Cost System** & **Reference System** & **Low-Cost System** \\ \hline
1 & \multirow{2}{*}{7.81} & \multirow{2}{*}{7.81} & 1.000 & 1.000 \\
2 & & & \(-\)0.759 & \(-\)0.536 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Natural frequencies and mode shapes identified of the flexible structure from both monitoring systems.