# Automated Modal Analysis Using Stochastic Subspace Identification and Field Monitoring Data
## 4 Examples of Field Applications
### Verification Result Using Seven-Story RC Frame in Taichung
(**a**) \(i\) selected via conventional procedure; (**b**) \(i\) selected via proposed procedure. Figure 7: The results of the four approaches for selecting system orders through singular values. (**a**) \(C_{1}\) = 0.05; (**b**) \(C_{2}\) = 0.01; (**c**) \(C_{3}\) = 0.7; (**d**) \(C_{4}\) = 5.  
correlated with those observed in the Fourier spectrum. Five modes can be identified, including 2.27 Hz, 2.47 Hz, 3.19 Hz, 7.09 Hz, and 7.7 Hz. The consistency of the stability diagram also suggests that the proposed procedure provides clearer decomposition by designating the lagged vectors with complete cycles. The spurious mode can be further identified by applying the criterion of assured modes, which is represented as a cross in the stability diagram (unstable poles in Figure 8). This example generally illustrates the proposed three-step procedure for complex structures or field applications, and demonstrates the ability to produce reliable identification results. Finally, the identified frequencies across the ten-year dataset are shown in Figure 9. It can be seen that the identification results with the proposed procedure are better than those without a carefully selected SSI matrix size and an adaptive estimation of system order, as shown in Figure 9a. With the proposed procedure, two more frequencies represent secondary modes, ranging from 5 Hz to 10 Hz, although some modes are not stimulated or identified in some measurements. Generally, this figure can be divided into three sections: the first seven sets of measurements represent the RC frame before the destructive earthquake, the eighth to thirteenth sets represent the frame after the earthquake, and the last three sets of measurements represent the last section, as separated by the red lines in the figure. According to the reconnaissance report by senior engineers, the destructive earthquake was identified as having caused moderate damage. The second section presents the damaged RC frame, which generates a 15% to 20% reduction in modal frequencies. Moreover, the report also indicated that the seven-story RC frame underwent repairs, representing the retrofitted RC frame, increasing the modal frequencies by about 5% to 10% in the results. In the first two modal frequencies identified from the 16 sets of measurements, the average and the standard deviation of the overall error after applying the proposed procedure are around 1.99% and 1.89%, respectively. The error percentages range from 0.06% to 7.22%. On the other hand, the average and the standard deviation of the overall error before applying the proposed procedure are around 2.24% and 2.06%, respectively, while the error percentages range from 0.08% to 7.93%. Upon comparing these two cases, with and without a carefully selected SSI matrix size and an adaptive estimation of system order, it can be noted that the proposed procedure improved all the statistical indexes by approximately 10%. Most importantly, seven out of thirty-two modal frequencies are missed in the conventional SSI-based OMA; however, with the help of the proposed procedure, only  
Figure 8: The stability diagram of the selected \(i\), together with the Fourier spectrum. two are missed, indicating three to four times superior performance in terms of identifying the structure's mode in complex field applications.