## 2 Methodology of SSI-COV
### Implementation of SSI-COV
If the relative difference is within the tolerance prescribed by the parameter, it is considered stable. In this work, the SSI-COV method was applied following a series of detailed steps. Initially, and as a first exploratory step, the method was applied directly to the original raw data that were sampled at 400 Hz. The output is presented in Section 5 and it shows values in frequencies up to 70 Hz, but no noticeable frequencies of interest show up. Subsequently, time series were downsampled to 30 Hz using MATLAB's resample function. This has two consequences: the data are considerably reduced, and high-frequency information is eliminated; but, these high-frequency components are not physically significant for this type of structure. Then, the downsampled time series were analyzed with the method. Here, two frequency ranges are visible, one is at 2.5 Hz and the other is at 9.7 Hz. This procedure is presented in Section 5. Both values are used as inputs for the SSI-COV method in MATLAB (MATLAB v.2024a), namely, as the center frequency of optional band-pass filters. Specifically, this filtering process was configured as a band-pass filter with a central frequency \(f_{0}\), allowing signals within a certain frequency range to pass while attenuating those outside of it. The filter uses a flat top bandwidth B1 (the range around the central frequency \(f_{0}\), where the signal passes unattenuated) and tapering bandwidths B2 on each side, providing gradual attenuation outside the flat top range. The selections of 2.5 Hz and 9.7 Hz were complementarily confirmed as frequencies of interest based on the results of a modal analysis calculated using a structural model exported from Revit to ETABS. This analysis identifies frequencies with significant modal participation, indicating their prominent contributions to the overall dynamic response of the structure. Modal participation, in this context, refers to the relative influence of each mode on the vibrational behavior of the structure, highlighting the importance of these frequencies in capturing its dynamic characteristics. In Table 1, the results of the modal analysis from the numerical model are presented. These steps, along with the filter configurations used, are presented in the methodology diagram depicted in Figure 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mode** & **Frequency HZ** & **UX \%** & **UY\%** \\ \hline
1 & 1.94 & 1.94 & 0.01 \\
2 & 2.24 & 63.07 & 0.61 \\
3 & 2.74 & 0.36 & 66.31 \\
4 & 7.30 & 1.87 & 0 \\
5 & 9.34 & 14.38 & 1.32 \\
6 & 10.10 & 1.19 & 17.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of the modal analysis from the ETABS model. In this stage, records from various sensors are integrated, which must be synchronized with each other. These records may correspond to three specific types of vibrations: ambient, generated by adjacent construction, and seismic events. Before applying the main method, preliminary signal treatments such as downsampling or filtering can be performed. These treatments allow the analysis to focus on specific frequency ranges that may be relevant for assessing the dynamic response and reducing the computational effort. In this stage, the SSI-COV method implemented in MATLAB is applied. The parameters required for the analysis include the model order, the number of blocks, and the corresponding tolerances. The stabilization diagram displays the singular values derived from the power spectral density (PSD) matrix across different frequencies. The blue, orange, and yellow lines represent the first three singular values, which indicate the energy levels of the dominant modes in the system at each frequency. The results focus on modes considered stable based on the stabilization diagram and the established tolerance values, allowing for the identification of the structure's dynamic characteristics based on these stability criteria. The example graph shown below corresponds to the case of the band-pass filter applied at 2.5 Hz, serving as an illustrative representation of the method's application.