## 4 Application to an Eight-Story Building  
In order to evaluate the performance of the proposed methodology under real-life conditions, the eight-story steel frame experimental data are used to estimate its natural frequencies and damping ratios. A graphical illustration of the structure is shown in Figure 10. The building has H-shaped columns with dimensions of 1.5 m \(\times\) 1.1 m \(\times\) 9.44 m (width, length, and height). Additionally, lead plates of 250 kg are piled on each floor; hence, each floor has a total mass of 325 kg. The base of the building was subjected to white noise excitation in the long-span direction. This structure is located in the National Center for Research on Earthquake Engineering, Taiwan, and is also used by [PERSON] et al. [53]. The responses were measured using eight velocity sensors distributed on the eight stories and located at the center of each floor. The sensor employs a sampling rate of 200 Hz during 100 s, thus each signal contains 20,000 samples. The measured vibration response of sensor 4 is used indistinctly to estimate the modal parameters of the structure. Figure 11 depicts the signal measured by sensor 4. Using the proposal, the acquired vibration data are transformed to the to free-damped vibration form using NExT method. In an analogous way to the previous example, sensor 8 is used as the reference signal to estimate the free-decay response, since this sensor is far away from selected sensor 4 to estimate the modal parameters of structure. In this case, sensor 8 satisfies this specification recommended by [PERSON] [52]. In this example, 1000 samples signal are selected to estimate the free-damped vibration form. This means that the original signal is converted to a new signal of 5.0 s, as shown in Figure 12. This number of samples is sufficient to estimate the free-damped form. Then,  
Figure 11: Sensor used for estimating the modal parameters of the eight-story building. Figure 10: General overview of the eight-story building analyzed. once obtained the free-damped response, it is processed by SWT in order to extract the individual modes contained in the signal, which are illustrated in Figure 13.  
Finally, the micro-GA approach is used to obtain the natural frequencies and damping ratios of extracted modes, obtained in the previous step, of the analyzed building. Table 3 presents the values of estimated natural frequencies and damping ratios values using the proposal and FEA. Further, the estimated modal parameters of eight-story steel frame using the methodologies proposed by [PERSON] et al. [53] and [PERSON] et al. [11] are also presented. It is observed that these methodologies present similar results to the estimated by FEA model, which indicates that they can be considered as accurate; however, it is important to mention that the methodology proposed by [PERSON] et al. [53] requires calibration for each structure analyzed, limiting an automatic estimation of the parameters. On the other hand, it is also seen a slightly difference between the estimated DR values using the methodologies proposed by [PERSON] et al. [53], [PERSON] et al. [11], and the values obtained with the proposal. It should be noticed that for this case, there are no reference values for the DR; thus, the comparison is performed in a qualitative way, that is, how similar are the values obtained with the different methodologies. In general, it can be seen that the proposal obtains similar values compared with those obtained by [PERSON] et al. [53]. The difference between the values obtained by [PERSON] et al. [11] and the proposal is due to that the KF still delivers a signal with some spikes that affect its quality, deteriorating the estimated results by HT, as the mathematical operations used for obtaining the value (a derivative) can be affected by the spikes, even a slightly one. On the contrary, the proposed methodology demonstrates to be efficient to perform the MPI of automatic manner,  
Figure 12: Free-damped response estimated for the eight-story building.