## 3 Experimental Results
### Evaluation of Synchronization Performance  
To validate the functionality of the proposed framework, a rigorous experimental evaluation was conducted. The responses from three sensor nodes, as depicted in Figure 4, were meticulously examined, following the explanation in Section 2.3.5. In this evaluation, the three RPi0-2W sensor nodes were subjected to identical impulse forces, generated by manually applying an external force to the side panel. Notably, the \(x\)-axis of all RPi0-2W sensor nodes was precisely aligned with the direction of the external force, ensuring that the 3 DOF system predominantly vibrated in the \(x\)-direction. Figure 7 illustrates the preprocessed raw acceleration responses obtained from the three RPi0-2W sensor nodes positioned at the top storey of the 3 DOF structure. These responses were captured after applying a series of impulse forces to the top of the side panel of the 3 DOF structure. In Figure 7a, the preprocessed raw acceleration data is presented, obtained from the three sensor nodes positioned at the top storey of the 3 DOF structure. The preprocessing steps involved detrending and 100 Hz resampling, implemented using Equations (1)-(4). Notably, the figure illustrates a remarkable alignment among the peaks of the impulse  
Figure 7: Experimental results obtained from the synchronization validation: (**a**) the time history of \(x\)-axis accelerations collected from three sensors positioned on the top storey, as illustrated in Figure 4. (**b**) a magnified view of the first 100 s of the recorded data. response, confirming the effectiveness of the synchronization mechanism employed in the study. Additionally, it is noteworthy that the aligned signals exhibit similar amplitudes, which further highlights the efficacy of the low-cost sensor capabilities. However, Figure 7b reveals a persistent milli to continisecond-level clock drift, despite configuring the chrony NTP client to synchronize with the NTP server and perform system clock adjustments for deviations exceeding 0.1 s. These observations emphasize the ongoing necessity for continuous monitoring and adjustment to address temporal inconsistencies, ensuring reliable synchronization over extended periods. Consequently, these findings underscore the importance of considering the complexities of time synchronization and the need for adaptive strategies to mitigate clock drift. In addition to exploring the time domain characteristics, it is imperative to delve into the frequency domain attributes of the preprocessed signals. Figure 8 offers a comprehensive overview of the frequency domain analysis performed on these signals. Each row within the figure presents the time domain signal, the linear magnitude spectrum computed via FFT, and the spectrogram of each sensor, respectively. The magnitude spectrum was derived from the complete record using a Hanning window. Upon meticulous examination, the analysis uncovers that the initial three peaks of all three sensors consistently center around frequencies ranging from 0.8 to 0.9 Hz, 1.26 to 1.28 Hz, and 1.6 to 1.7 Hz. This observation suggests the existence of coherent frequency components across the preprocessed signals. Furthermore, it's noteworthy that the impulse forces exhibit a distinctive trait of being governed by a narrow-band frequency content, characterized by dominant frequencies concentrated within a limited range. When examining the frequency qualities, specifically the magnitude spectrum and spectrogram, within the time interval from 40 s to 100 s with centered around the first five peaks of the record signals, it becomes evident that the consistent detection of the same frequency patterns, as depicted in Figure 9, is observed across the data obtained from three low-cost sensors. By narrowing the analysis to this specific time interval and examining the frequency content, it becomes apparent that the identified frequency patterns exhibit a remarkable level of consistency and display similar characteristics across the low-cost sensors.