## 3 Experimental Results
### Analysis of Structural Response Using FDD  
The Frequency Domain Decomposition (FDD) algorithm serves as a convenient and accessible method for structural parameter identification. In our experiment, we initiate the process by organizing the aligned signals, obtained through the DTW algorithm, into a matrix structure, as outlined in Equation (8). Each row of the matrix corresponds to a specific data point, while the columns represent the number of sensor nodes employed, which, in our case, is three.  
Once the matrix is constructed, the subsequent step involves computing the PSD using the matrix data. This computation provides valuable insights into the frequency content of the signals. Subsequently, we apply SVD to decompose the PSD matrix at discrete frequencies, as described in Equation (12). Through the SVD, we obtain the singular values, which highlight the significance of each frequency component within the signal. To facilitate comprehension and interpretation, we visually represent these singular values using graphical plots. This graphical representation offers an intuitive visualization of the frequency characteristics exhibited by the system.  
Figure 14 illustrates the plot of singular values in dB versus frequency obtained through the FDD algorithm applied to the DTW-aligned signals. In this plot, the topmost line represents the first singular value, followed by the second singular value in the middle, and the third singular value at the bottom. Figure 14a corresponds to the singular values plot of the responses from Structure 1, providing insights into its frequency characteristics. Similarly, Figure 14b showcases the singular values plot of the responses from Structure 2, offering a visual representation of its distinct frequency characteristics.  
Figure 14: Plot of the first singular value obtained through the FDD algorithm applied to the DTW-aligned signals in linear scale (m\({}^{2}\)/s\({}^{4}\)/Hz). (**a**) Singular values plot of the responses from Structure 1, providing insights into its frequency characteristics. (**b**) Singular values plot of the responses from Structure 2, offering a visual representation of its distinct frequency characteristics.  
Additionally, it is important to highlight that the natural frequencies of the first mode obtained from the FDD analysis for Structure 1 and Structure 2 are 1.30 Hz and 0.90 Hz, respectively. However, the magnitude spectra analysis indicates that the natural frequencies of the first mode for Structure 1 and Structure 2 are 1.50 Hz and 1.25 Hz, respectively. This discrepancy arises due to the difference in frequency resolution between the two analysis techniques.  
The presence of a structural imbalance in Structure 2 leads to the manifestation of a torsional mode when subjected to excitation. The dissipation of vibrations associated with the torsional mode can potentially disrupt the higher modes of natural frequency. This influence of the torsional mode is reflected in the singular value results, which indicate the presence of higher mode natural frequencies in Structure 2.  
Nevertheless, it is noteworthy that even with low-cost, off-the-shelf sensors, the natural frequencies of the two distinct structures can still be distinguished. This emphasizes the capability of these sensors to capture and differentiate the unique frequency characteristics of structural responses, despite potential limitations in frequency resolution.