# Automated Modal Analysis Using Stochastic Subspace Identification and Field Monitoring Data
## 4 Examples of Field Applications
### Verification Result Using Four-Story RC Frame in Hualien  
The second dataset includes 30 channels of accelerometers connected to the conventional SHM system, and it was collected from the RC building in Hualien, Taiwan. Figure 4b shows the sensor locations. Similar to the first dataset, only the structural responses in the longitudinal and transverse directions are exploited to identify the modal parameters, and the channels 4, 5, 10, 11, 13, 14, 16, 17, 18, 19, 22, and 23 are therefore used in the following verification. To discriminate nonstationary excitations, regarding the basic assumption, ground motions are measured through free-field sensors, although these channels are not shown in the figure. As a result, the structural responses from the ambient excitations, rather than the earthquake excitations, can be separated and analyzed by SSI. Again, in the first step, waveforms that were clearly distorted or exhibited dropouts or glitches were excluded from the measurements. Then, the normalized Arias intensity and AIC were implemented to exclude nonstationary parts. FFT was applied to the acceleration responses before down-sampling, so that an overview of the structure's modal information could be reviewed. Notably, this RC frame was also damaged by the Chi-Chi earthquake in 1999. After careful examination, the fundamental frequency of the four-story RC building was about 3.1 Hz before the Chi-Chi earthquake and 2.6 Hz after the destructive earthquake. Moreover, the structure's highest mode of interest is less than 20 Hz, so acceleration responses can be down-sampled to 50 Hz--which corresponds to the Nyquist frequency of 25 Hz--to reduce the computational effect. Due to a high similarity  
Figure 9: The identified frequencies of the first dataset through the automated SSI-based OMA. (**a**) without the proposed procedure; (**b**) with the proposed procedure. with previous results and limited space, the results in the data preprocessing step are not demonstrated herein. Figure 10 shows the identified frequencies across the ten-year dataset. Unfortunately, the results are more complicated than those in the first dataset due to several reasons, including smaller signals, stiffer behaviors, and more complex compartments. Some modes are not stimulated or identified in some measurements, such as the frequencies located at approximately 1.1-1.2 Hz, 5 Hz, and 8 Hz. Generally, two modes can be consistently observed from this figure, represented by the red lines in the figure. According to the reconnaissance report of the destructive earthquake, this frame was identified as having some damage by senior engineers, so an obvious drop can be found prior to 22 September 1999. The report also pointed out that the four-story RC frame underwent subsequent repairs around 2000. As a result, the fundamental frequency increased after 2001. The frame also underwent a further retrofit around 2010, in accordance with the nationwide school building enhancement program, although the measurements are not included in this dataset. Lastly, the estimated system orders, using four approaches through singular values, are illustrated in Figure 11. From the first dataset, the proposed (fourth) approach shows more stable results over a decade, ranging from 8 to 18. In contrast, the first approach has the largest variation in both datasets because of its high dependency on the measured signals. The second approach seems more reliable compared to the first one; however, it kept advancing after the destructive earthquake and the structural repairs in the second dataset. This indicates that the second approach is difficult to update the results if the structural responses display increasing uncertainties. Typically, the third approach tends to underestimate the system order, although the estimated system orders are very similar to the proposed approach in the first dataset. The identified results may therefore lose many modes. Considering the identified frequencies in Figures 9 and 10, the fourth approach is clearly the most highly recommended one.