## 4 On-Site Experiment and Analysis
### Results Analysis and Discussion  
Three separate signal components were obtained using the improved SOBI signal de-noising method, namely S1, S2, and S3, as shown in Figure 8. The inspection of curves of the separated signal components shown in this figure clearly highlight that: (1) as shown in Figure 8a, the separated signal, S1, with an inverted displacement is consistent with the original time-series displacement, X1, of the mid-span point of the Fengbei Bridge, which can be regarded as actual monitored data, and; (2) as shown in Figure 8b,c, there are some sudden changes in these two curves of the separate S2 and S3 signals, which can be regarded as noise signals. These may have been caused by the passing vehicles near the IBIS-S instrument, which led to several vibrations of the IBIS-S instrument. Moreover, there are some smaller fluctuations in these two curves, which may have been caused by the surrounding environment, such as wind thrusts and ground motions. Moreover, as shown in Figure 9, the spectra of the three observed signals are basically the same, with a similar first order frequency of 2.46 Hz. In the spectrum of the separated signal, S1, found using the improved SOBI method, the first order frequency is the same as that of the three observed signals as shown in Figure 10a. This indicates that the separated signal, S1, is the useful signal. However, for the spectra of the separated signals--S2 and S3--found using the improved SOBI method, the frequencies are disorderly and irregular as shown in Figure 10b,c. This indicates that the separated signals--S2 and S3--are noise signals. By zero processing the separated noise signal, the de-noised time-series displacement of the mid-span point was obtained by inversely reconstructing the separated signal using a mixing matrix, as shown in Figure 11. The red curve is the original signal of the obtained time-series displacement of the mid-span point, and the blue curve is the de-noised signal. Compared with the original time-series displacement, the de-noised time-series displacement is more stable and smooth. Moreover, as the six black boxes show in Figure 11, there are greater changes between the original signal and the de-noised signal. Furthermore, these six time ranges are the same as the time ranges of the sudden changes in the curves of the separated signals--S2 and S3--as shown in Figure 8b,c. The results show that the noise information caused by the passing vehicles near the IBIS-S instrument was effectively eliminated. Figure 8: Three separated signal components found using the improved SOBI method. (**a**) Separated signal S1, (**b**) separated signal S2, and (**c**) separated signal S3. Figure 10: Spectra of the three separated signals found using the improved SOBI method. (**a**) Spectrum of the separated signal S1, (**b**) spectrum of the separated signal S2, and (**c**) spectrum of the separated signal S3. Figure 9: Spectra of the three original observation signals. (**a**) Spectrum of the observed signal X1, (**b**) spectrum of the observed signal X2, and (**c**) spectrum of observed signal X3. To validate the accuracy of the improved SOBI signal de-noising method for dynamic deflection measurements using GBSAR, two de-noising methods--EMD [20] and EEMD [22]--were selected to be compared with the improved SOBI signal de-noising method. The comparison results are shown in Table 2. The inspection from this table highlights that: (1) The NRR and NM are 6.7116 db and 3.7622 mm for the improved SOBI signal de-noising method, which are much better than that of the EMD and EEMD methods. Moreover, the SER is 1.0012 for the improved SOBI signal de-noising method, which is closer to one than the other two methods. Therefore, according to these three indexes, the improved SOBI signal de-noising method had a more powerful ability than the EMD and EEMD methods for dynamic deflection measurements using GBSAR.