## 5 Conclusions  
Due to the advantage of the high-distance resolution of the GBSAR technique, the obtained time-series displacements of the adjacent monitoring points had a similar noise. Therefore, in this study, to improve the accuracy of the obtained dynamic time-series displacement of bridges using GBSAR, an improved SOBI signal de-noising method was proposed to reduce the influence of noise. This was achieved by using the obtained dynamic time-series displacements of three adjacent monitoring points in the same time domain. In addition, the de-noised signal of the middle point among the three adjacent monitoring points was obtained. This was done to address the noise caused by instantaneous vibrations of the equipment itself and noise caused by passing vehicles. More specifically, the results presented in the study clearly highlight the following: \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **EMD** & **EEMD** & **SOBI** \\ \hline NRR (db) & \(-2.3393\) & 3.2862 & 6.7116 \\ NM (mm) & 2.5066 & 0.7211 & 3.7622 \\ SER & 0.9870 & 0.9947 & 1.0012 \\ RMSE (mm) & 0.0264 & 0.0073 & 0.0120 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the four evaluation indexes among the three de-noised methods. Figure 11: De-noised time-series displacement of the mid-span point of the Fengbei Bridge. 1. A simulation experiment was performed to validate the feasibility of the improved SOBI signal de-noising method where three mixed signals were linearly mixed using three sets of simulation source signals with different frequency scales. The obtained correlation coefficients between each simulated source signal and the corresponding separated signal component were all greater than 0.99. The results showed that the improved SOBI signal de-noising method effectively distinguished the useful signals and noise signals from the mixed signals, which can be useful for signal de-noising of time-series displacements obtained using GBSAR. 2. By fully considering the characteristics of the high-distance resolution GBSAR technique, the obtained dynamic time-series displacements of three adjacent monitoring points in the same time domain were selected as input signals. This was done in order to obtain the de-noised time-series displacement of the middle point among three adjacent monitoring points by using the improved SOBI signal de-noising method. Using a spectrum analysis, the separated noise components were effectively determined from the separated signals, and the original amplitude of the de-noised signal was recovered using an inverse reconstruction with a mixing matrix. The results showed that the improved SOBI signal de-noising method not only reduced the noise caused by the surrounding environment, but also reduced the noise caused by vibrations of the monitoring instrument. 3. Compared with the EDM and EEMD signal de-noising methods, the improved SOBI signal de-noising method displayed a greater improvement in the indexes of NRR, NM, and SER for the obtained time-series displacement of a bridge using GBSAR. The results indicate that the improved SOBI signal de-noising method has a powerful signal de-noising ability. Conceptualization, X.L. and M.H. ; methodology, H.W., W.Y. and X.L. ; formal analysis, H.W. ; data curation, H.W. ; writing--original draft preparation, X.L., and H.W. ; writing--review and editing, X.L. This study was sponsored by the National Natural Science Foundation of China (grant no. 41871367), the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions (grant no. CIT&TCD201704053), the Science and Technology Project of Ministry of Housing and Urban-Rural Development of the People's Republic of China (grant no. 2017-K4-002), the Scientific Research Project of Beijing Educational Committee (grant no. KM201910016005), the Major Projects of Beijing Advanced innovation center for future urban design (grant no.