## 2 The Building, Temporary Instrumentation and Methodology
### Analysis Procedure of the Nonparametric Method  
Considering the concepts explained above, this subsection details the use of the nonparametric approach and the criteria applied to obtain the dynamic parameters. To better understand the problem under study, a diagram with sensors ordered by floor is presented in Figure 8.  
With the acceleration records sorted by floor, we proceed to obtain the Welch power spectra (\(G_{xx}\)). The first criterion is that only the first six frequencies (i.e., the six frequencies with the highest amplitudes) are identified due to the fact that for structural dynamic analysis, we are interested only in a certain range of frequencies for analysis. Outside that range, for this study case, the frequencies have no physical importance.  
The next step is to analyze whether the identified frequencies correspond to the frequencies of the floor or of the structure. To this end, the cross-power correlation between the signal of the first floor and that of the last floor (\(G_{xy}\)) is calculated. With the obtained correlation and the Welch power spectrum, it is possible to obtain the transfer functions \(H_{1}(f)\) and \(H_{2}(f)\), and with these values, the coherence function between floor \(-3\) and floor \(16\) can be acquired. Here, a second criterion is applied to the analysis of the result of  
Figure 8: Graphical scheme of the nonparametric process.  
the coherence function (\(\gamma^{2}{}_{xy}\)). If the value of this variable is greater than 0.9, frequency corresponds to the soil (\(f_{s}\)). This is due to the fact that having a coherence greater than 0.9 means that the movement of the last floor is mostly a product of the movement of floor \(-3\), i.e., the floor in direct contact with the ground. Nevertheless, an analysis of the soil frequencies is beyond the scope of this article.  
Once the frequencies of the structure have been identified, only whether they correspond to translational or torsional frequencies remains to be checked. For this purpose, the registers on opposite corners of the same floor are correlated. The phase angle between these signals on the same floor is verified, and the last criterion is used, to verify whether the result of the phase angle is less than 1. If so, the relative movement is in the same direction, which is interpreted as a translational movement.  
With the translational frequencies of the structure, we proceed to identify the modal shapes by performing three types of correlations. The first is to correlate all floors with the \(-3\) and obtain the relative displacements with the phase angles. The second option is to take continuous correlations between floors and likewise obtain relative displacements with the phase angles. A third correlation is performed. This is created after appreciating the results between the parametric and non-parametric method in which a way to improve the results is sought, where it is correlated up to floor 3 with -3 and then correlated floor with floor up to 16.  
Finally, following these three calculations, the amplitudes of the modes can be obtained through the Welch power spectrum, and the vibration shapes can be normalized. These three ways of correlating the signals are discussed in detail in the results.