## 2 Materials and Methods
### Accelerometer Instrumentation  
Acceleration-time histories of the response of the building to ambient vibration were simultaneously recorded at five sites on the roof of the building: at a central point (P1) and at the four corners, north (P2), east (P3), south (P4), and west (P5). These locations were chosen in order to capture the first modes of vibration of the structure. At each point, one high-sensitivity accelerometer (Bruel and Kjaer 8340) was placed for each direction, giving a total of ten accelerometers measuring simultaneously. The measurements in the longitudinal direction (L) of the building correspond to the orientation N 28\({}^{\circ}\)E, while the measurements in the transversal direction (T) coincide with the orientation N 62\({}^{\circ}\)W. The arrangement and location of the sensors are shown in Figure 4.  
Acceleration data were recorded, continuously and synchronously, for 25 min at each of the five points on the roof. A sampling frequency of 200 Hz was set for the acceleration records. Baseline correction was performed, and a Butterworth band-pass filter was applied in the frequency range of interest (1-5 Hz). Figure 5 shows six-second sections (0.1 min) of the ten processed signals.  
Figure 4: Layout of the roof of the _“La Vña”_ building including the location of the ten-accelerometer network and the relative position of the RAR device.  
Figure 3: Geometry of the _“La Vña”_ building: (**a**) floor plan view; (**b**) elevation view.  
Natural Frequencies: The Accelerometric Technique  
In order to detect the natural frequencies of a structure, the frequency of the recorded vibration was investigated using the power spectral density (PSD); the Welch method [37] has been used in this case. The signal analysis on the frequency range was focused between 1 and 5 Hz (periods between 0.2 and 1 s); for this, a band-pass Butterworth filter was applied to the measured displacement-time and acceleration-time histories. The natural frequencies that appear as peaks in the PSD can be picked in an easy way. This frequency domain method, also known as the peak picking method (PPM) [38; 39], has been extensively used for its simplicity, showing good results, especially for finding the frequencies of the first modes of vibration.  
Table 1 shows the PSDs for the ten channels. Peaks with similar spectral shapes can be observed in all channels. The first two peaks of approximately 2.49 and 2.79 Hz are clearly identified in both the T and L directions. The presence of the same resonant frequencies in both directions may indicate the existence of flexural-torsional modes. A third peak, minor in most of the channels, is found at a frequency of 3.98 Hz. Figure 6 shows the three frequency peak values with the highest PSD. At this point, it is difficult to assign these values to the modes of vibration of the building.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Direction** & \multicolumn{2}{c}{1} & \multicolumn{2}{c}{2} & \multicolumn{2}{c}{3} \\ \hline  & **f (H2)** & **T (s)** & **f (H2)** & **T (s)** & **f (H2)** & **T (s)** \\ \hline L & 2.49 & 0.40 & 2.79 & 0.36 & 3.98 & 0.25 \\ T & 2.49 & 0.40 & 2.79 & 0.36 & 3.98 & 0.25 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The first three peaks in order of increasing frequencies, picked in the L and T directions.  
Figure 5: Six-second sections (from 10.0 to 10.1 min) of the processed acceleration–time histories.