## 4 The Settlement Monitoring Results of the ELH Bridge
### Settlement Rate Estimation and Result Analysis  
Previous studies mostly assumed the presence of white noise in the settlement time series. Time-dependent noise (colored noise) may exist in the settlement time series due to the influence of various factors (such as systematic error). This section used the periodogram method to analyze the PSD of settlement time series to acquire accurate settlement rate estimation and its uncertainty and analyze the influence of noise on settlement rate uncertainty estimation. The results are shown in Figure 7. No. 7 and 8 piers are close to the construction tunnel. Accordingly, the noise has a great influence on the settlement time series of No. 7 and 8 piers. Figure 7 shows that the slopes of the red and black curves do not amount to zero, indicating the presence of colored noise in the settlement time series of No. 7 and 8 piers. In addition, the colored noise spectral indices of the settlement time series of No. 7 and 8 piers were estimated to be about \(-\)1 based on this method, indicating that the colored noise was flicker noise [41]. This section used the settlement monitoring data of No. 7 and 8 piers to estimate the amplitude of white and colored noises through MLE. The GB-RAR deformation information estimation method considering the influence of colored noise is proposed to estimate the settlement rate and uncertainty of piers accurately. Subsequently, the settlement of each pier was calculated according to the monitoring time span, which provided reliable data support for the safety assessment of the bridge. Figure 6: Comparison of the leveling and GB-RAR results. Table 2 lists the settlement rate and uncertainty results of No. 7 and 8 piers estimated by the GB-SAR deformation information estimation method considering the influence of colored noise, GB-SAR deformation information estimation method without considering the influence of colored noise, and leveling method in different time spans (namely, 17 November 2016, 18 November 2016, and 17-18 November 2016). Table 2 shows that the settlement of No. 7 and 8 piers on 17 November 2016 was more serious than that on 18 November 2016, which may be connected with the gradual departure of the tail of the shield tunneling machine from the projection area of the ELH Bridge on November 18. During the period when the shield tunnel of the Metro Line 11 passed through the bridge core protection area (i.e., 17-18 November 2016), the settlement rates of No. 7 and 8 piers estimated by using the GB-RAR deformation information estimation method considering the influence of colored noise were \(-0.0112\)\(\pm\) 0.0026 and \(-0.0046\)\(\pm\) 0.0053 mm/h, respectively. Based on the leveling data, the settlement rates of No. 7 and 8 piers were \(-0.0107\)\(\pm\) 0.0110 and \(-0.0089\)\(\pm\) 0.0641 mm/h, respectively. The results of the two methods were in good agreement. The uncertainty of the settlement rate was smaller and can be almost ignored when only white noise is considered compared with the estimation results of the settlement rate before and after considering colored noise. This result showed that, if the influence of colored noise on the settlement time series is ignored, then the accuracy of the settlement rate is considerably optimistic. The results of the comparison of the three methods demonstrated that the estimation results are more accurate after considering the influence of colored noise. The cumulative settlement of piers was calculated according to the monitoring time span during the shield tunnel crossing the bridge. The cumulative settlement of No. 7 and 8 piers estimated by GB-SAR deformation information estimation method considering the influence of colored noise are \(-0.40\) and \(-0.16\) mm, respectively. The cumulative settlement of No. 7 and 8 piers obtained by leveling method are \(-0.39\) and \(-0.32\) mm, respectively. The No. 7 piers was closer to the metro tunnel than the No. 8 piers, which may be one of the main reasons why No. 7 pier accumulates more settlement than the No. 8 pier.