GB-RAR Deformation Information Estimation of High-Speed Railway Bridge in Consideration of the Effects of Colored Noise

Abstract

Safety assessment must accurately grasp deformation information of a high-speed railway bridge. When the ground-based radar collected high-frequency data, white and colored noises will be present in the radar signal due to the influence of environment and instrument errors. The existence of the above-mentioned two kinds of noises will affect the accurate estimation of deformation information. Based on the above situation, a ground-based real aperture radar (GB-RAR) deformation information estimation method considering the effect of colored noise was proposed in this work. The proposed method was applied to the safety monitoring and analysis of East Lake High-tech Bridge during the Wuhan Metro Line 11 shield tunnel crossing underneath this bridge. First, the settlement deformation time series of the bridge was derived based on GB-RAR, and it was verified by leveling at an accuracy better than 0.27 mm. Second, white, and colored noises were detected in the denoised settlement deformation time series through a power spectral analysis and maximum likelihood estimation, and the colored noise spectral indexes were approximately −1. Finally, according to the proposed method, the estimated settlement rates of No. 7 and 8 piers were 0.0112 ± 0.0026 and −0.0046 ± 0.0053 mm/h, and the accumulative settlement values were −0.40 and −0.16 mm, respectively. The results were in good agreement with the results of leveling measurement and more accurate than those of the deformation information estimation method without considering the effect of colored noise. The research results showed the reliability and effectiveness of the method in this work, and the bridge was stable and safe during the monitoring period.

1. Introduction

The deformation monitoring and analysis of high-speed railway bridges are of great significance for early safety assessment and effective protection measures [1,2,3]. Dynamic behavior evaluation of bridge helps to explain the factors causing bridge deformation and provides guidance for bridge construction and operation [4,5]. Various traditional deformation monitoring methods have been widely used in bridge safety assessment and early warning, including leveling, GNSS, sensor measurement, and acceleration measurement [6,7,8,9,10,11,12]. Traditional monitoring methods are accurate and reliable, but they usually assess the safety of a bridge by obtaining and analyzing the deformation of certain characteristic points on the bridge. Therefore, it is difficult to realize the overall deformation monitoring and analysis of bridges [13,14].

Interferometry Synthetic Aperture Radar (InSAR), which is a non-contact measurement method, can effectively monitor and analyze bridge deformation [15,16,17]. Huang et al. [18] established an InSAR time series analysis method suitable for longitudinal displacement monitoring of long-span bridges, which was successfully applied to Nanjing Dashengguan Bridge. Lazecky et al. [19] used TerrasSAR-X images and InSAR technology to monitor the Radotin Bridge in Prague, Czech Republic, and obtained the displacement. Qin et al. [20] proposed a structure knowledge-InSAR integration method. The method has been successfully applied to high-precision deformation monitoring and risk identification of sea-crossing bridges. Xiong et al. [21] used time-series methods to post-process the PS-InSAR-derived time-series displacements of the Hong Kong–Zhuhai–Macao Bridge based on Sentinel-1A TOPS SAR images spanning from 2018 to 2020. The results showed that the continuous subsidence of about 17 mm/year were detected at the east man-made island. The InSAR technology can overcome the limitations of traditional deformation monitoring methods because of its advantages of non-contact, high spatial resolution, and low cost [22,23,24,25]. However, high precision dynamic deformation monitoring of bridges is difficult to achieve due to the limitations of InSAR technology satellite platform (such as low time resolution and geometric distortion) [26,27].

To overcome the disadvantages of InSAR, a ground-based radar interferometry technique was proposed, which can monitor a small line of sight deformation of the monitored object within a few thousand meters from the real time radar sensor (about 0.01 mm) [28,29,30]. Based on the different imaging principles and systems of ground-based radar, ground-based radars are divided into two types: ground-based real aperture radar (GB-RAR) and ground-based synthetic aperture radar (GB-SAR). The GB-RAR technology has the advantages of high precision measurement, high data sampling frequency, and simultaneous response at multiple points [31,32,33]. According to the monitoring requirements, the most favorable monitoring orientation can be selected for the bridge to be monitored to install the ground-based interference radar [34,35]. Since the GB-RAR technology was put forward, it is widely used in bridge deformation monitoring and analysis. Stabile et al. [36] analyzed the dynamic characteristics of Italy’s Musmeci bridge by GB-RAR and verified it with accelerometer and microseismometer data. The results of the three technologies showed high consistency. Xu et al. [37] proposed a method for analyzing local relative deformation of bridge body based on the characteristics of ground-based interferometric radar monitoring data and used IBIS-S to monitor the dynamic deformation of a Yangtze River bridge, verifying the feasibility of GB-RAR technology in dynamic health monitoring of actual Bridges. Pieraccini et al. [38] used GB-RAR technology to obtain the information of dynamic influencing factors of railway bridges and provide data for bridge evaluation.

Most previous studies assume that only white noise exists in the deformation time series. When extracting deformation information from high-frequency data of ground-based interferometric radar, white (time-independent) and colored (time-dependent) noises exist in the radar signal. When ground-based interferometric radar used a high-frequency mode to monitor deformation, the radar signal will be affected by white and colored noises at the same time. A GB-RAR deformation information estimation method considering the influence of colored noise was proposed in this work. The GB-RAR technology was used in this work to monitor the settlement deformation change of the East Lake High-tech (ELH) Bridge during the crossing of the Wuhan Metro Line 11 shield tunnel underneath this bridge. The time series deformation of the main piers during the monitoring period were extracted. Moreover, the settlement time series results derived by GB-RAR data were verified by leveling monitoring data. The noise characteristics in the settlement time series derived based on radar data were analyzed by using power spectral density (PSD) analysis and maximum likelihood estimation (MLE) methods to accurately extract the deformation information of the ELH Bridge during the underpass of Metro Line 11 and provide a reliable basis for the safety assessment of the bridge. Furthermore, we can estimate the white noise and colored noise components in the deformed time series.

According to each noise component, a GB-RAR deformation information estimation method that can consider the influence of white and colored noises was proposed to estimate the settlement rate, uncertainty of settlement rate, and cumulative settlement of the ELH Bridge in the monitoring process and evaluate the deformation state of the bridge.

2. Project Example Overview

2.1. Overview of the ELH Bridge

ELH Bridge is a bridge on the Wuhan–Guangzhou high-speed railway in Wuhan, China, located in the ELH Development Zone. The ELH Bridge crosses High-tech Avenue and Wuhan Metro Line 11 under construction, as shown in Figure 1. The bridge has 10 piers and is a simple-supported girder bridge with a length of 293.4 m and a span of 32.6 m. The pile top of the bridge is about 2.5 m from the ground. Each pile-top of the No. 7 and 8 piers is composed of eight bored piles with a diameter of 1 m, and the pile lengths are 18.5 and 19.0 m, respectively. The bottom diameters of the tunnel are 1.0 and 0.5 m lower than the bridge pile. The horizontal distances between the bridge pile of the No. 7 and 8 piers and the metro section structure are 10.2 and 13.5 m, respectively. From 17 to 18 November 2016, the shield tunnel of Wuhan Metro Line 11 passed under the ELH Bridge. Wuhan Metro Line 11 is the first metro line crossing the high-speed railway in Wuhan, and it is also the first metro in China where the shield tunnel passes through the high-speed railway with a speed of 300 km/h. During the metro tunnel crossing, the high-speed rail trains are limited to 120 km/h through the construction section to ensure that the shield tunneling machine can safely and stably cross the ELH bridge.

2.2. Monitoring Scheme and Actual Measurement

Two kinds of monitoring methods (i.e., GB-RAR and precision leveling) were used to monitor the settlement deformation and evaluate the safety of Wuhan Metro Line 11 as it crossed the ELH bridge. The GB-RAR deformation monitoring adopted the IBIS-S system, and the interferometric radar was installed at a stable position near the No. 5 pier (Figure 1). During the monitoring period, the interferometric radar adopted the real-time monitoring mode, the maximum monitoring distance was set to 200 m, and the sampling frequency was set to 20 Hz. The main configuration parameters for IBIS-S system monitoring are shown in

Table 1. IBIS-S system parameter setting.

Parameter	Description
Radar type	FMCW
Bandwidth	200 MHz
Frequency range	17.1–17.3 GHz (Ku band)
Radar antenna inclination	10°
Observation distance	200 m
Range resolution	0.5 m
Sampling frequency	20 Hz
Start time	17 November 2016 06:00
End time	18 November 2016 18:00

. Figure 2 shows the IBIS-S interferometric radar monitoring scene and the monitoring scene in the direction of radar line-of-sight taken from the installation position of the IBIS-S system.

The second-order leveling was adopted to monitor the settlement of the bridge. Figure 3 shows the leveling monitoring site and the layout position of the leveling monitoring points on No. 7 pier. We arranged four leveling monitoring points on each pier. The bar code of precise invar leveling rod for leveling is directly pasted at the monitoring point on the pier to reduce the measurement error as much as possible and protect the pier from damage (Figure 3b). The monitoring time of leveling is the same as that of radar monitoring, but the time interval of leveling was 2 h.

3. GB-RAR Deformation Information Estimation Method Considering the Influence of Colored Noise

The ground-based radar image contains amplitude and phase information, and the phase information in ground-based radar images reflects the geometric distance between radar and target. According to the phase changes between the radar images obtained at different times, the displacement changes between the radar and the target can be inverted by using interferometry technology.

Assuming that two radar images ($t_B>t_A$) are obtained at different times $t_A$ and $t_B$, ${\varphi }_A$ and ${\varphi }_B$ are the phase values of the same pixel on the radar image at $t_A$ and $t_B$, respectively. The interference phase $\Delta {\varphi }_{BA}$ with the radar images at $t_A$ and $t_B$ can be derived after image interference processing [39,40]:

$$\begin{array}{ll}\Delta {\varphi }_{BA}& ={\varphi }_B-{\varphi }_A\\ & =\frac{4\pi (R_B-R_A)}{\lambda }+({\varphi }_{scatter,B}-{\varphi }_{scatter,A})\\ & +({\varphi }_{atm,B}-{\varphi }_{atm,A})+{\varphi }_{noise}\end{array}$$

(1)

where $\lambda$ is the wavelength of the radar signal; $R_A$ and $R_B$ are the geometric distance between the radar and the target at $t_A$ and $t_B$, respectively; ${\varphi }_{scatter}$ represents the phase shift caused by the interaction between the microwave and the monitoring target; ${\varphi }_{atm}$ denotes the phase produced by the influence of atmospheric disturbance; and ${\varphi }_{noise}$ refers to the random noise phase.

The phase component ${\varphi }_{scatter}$ of the radar image obtained at times $t_A$ and $t_B$ are assumed to be constant. Then, Equation (1) can be reduced as follows:

$$\begin{array}{ll}\Delta {\varphi }_{BA}& ={\varphi }_B-{\varphi }_A\\ & =\frac{4\pi d_{LOS}}{\lambda }+({\varphi }_{atm,B}-{\varphi }_{atm,A})+{\varphi }_{noise}\end{array}$$

(2)

where $d_{LOS}=R_B-R_A$ is the displacement change of the target in the radar line-of-sight (LOS) direction between $t_A$ and $t_B$. When the phase component $({\varphi }_{atm,B}-{\varphi }_{atm,A})$ and noise phase component ${\varphi }_{noise}$ produced by atmospheric effect are removed, the deformation occurring in the radar LOS direction can be obtained:

$$d_{LOS}=\frac{\Delta {{\varphi }^{\prime }}_{BA}\lambda }{4\pi }$$

(3)

where $\Delta {{\varphi }^{\prime }}_{BA}$ denotes the interference phase of the radar images between $t_A$ and $t_B$ after removing the phase errors of atmospheric effect phase component and other corresponding noise. The vertical deformation (i.e., settlement) of the target monitoring point can be solved according to the radar monitoring angle $\theta$ (the angle between the horizontal direction and the radar LOS direction):

$$y=d_{LOS}/\sin (\theta )$$

(4)

The settlement deformation time series obtained based on GB-RAR may contain colored noise due to the influence of several factors (such as systematic errors related to the GB-RAR technology). When analyzing the settlement deformation time series, only considering white noise will affect the accurate estimation of the uncertainty of settlement rate. Accordingly, the noise properties of settlement deformation time series must be analyzed. Then, the settlement model of the monitoring point can be expressed as follows:

$$y(t_i)=t_{i}x+v_{t_i}$$

(5)

where $y(t_i)$ represents the settlement deformation time series of monitoring piers; $x$ refers to the settlement rate; and $v_{t_i}$ is the linear combination of white noise $\alpha$ and colored noise $\beta$, and its manifestations are as follows:

$$v_i={\sigma }_w{\alpha }_{t_i}+{\sigma }_K{\beta }_{t_i}$$

(6)

where ${\sigma }_w$ and ${\sigma }_K$ are the amplitudes of the white and colored noises with spectral index $K$, respectively. The matrix form and stochastic model of Equation (5) can be expressed as follows:

$$y=Ax+\epsilon$$

(7)

$$D(y)=Q_y={\sigma }_w^{2}I+{\sigma }_K^2{Q}_K$$

(8)

where $A$ denotes the design matrix, $\epsilon$ is the error, $Q_y=D(y)$ represents the covariance matrix, $I$ refers to the identity matrix, and $Q_K$ is the covariance matrix of colored noise. Under the combination model of white noise and power law noise, the MLE criterion was used to analyze the settlement deformation time series and determine the estimation of each noise amplitude in the sequence, which can maximize the joint probability density of the residual and covariance of the deformation time series.

The joint probability density of the residual $v$ series and covariance matrix of the settlement deformation time series is expressed as follows:

$$\mathrm{lik}(v,Q_y)=\frac{1}{{(2\pi )}^{N/2}{\left(\det Q_y\right)}^{1/2}}\exp \left(-0.5v^{\mathrm{T}}{Q}_{{}_y}^{-1}v\right)$$

(9)

where $\det$ denotes the determinant of the matrix, and $N$ is the amount of data in the time series.

After taking logarithms on both sides of Equation (9), it is equivalent to:

$$\ln \left[\mathrm{lik}(v,Q_y)\right]=-0.5\left[\ln \left(\det Q_y\right)+v^{\mathrm{T}}{Q}_{{}_y}^{-1}v+N\ln (2\pi )\right]$$

(10)

When the spectral index $K$ of colored noise is adjusted, the covariance matrix $Q_y$ continuously changes until the maximum likelihood function value of Equation (10) reaches the maximum. The parameter estimation $\widehat{x}=\left(A^{\mathrm{T}}{Q}_{{}_y}^{-1}A\right)A^{\mathrm{T}}{Q}_{{}_y}^{-1}y$ is obtained by weighted least squares estimation, and the covariance matrix $Q_{\widehat{x}}={\left(A^{\mathrm{T}}{Q}_{{}_y}^{-1}A\right)}^{-1}$ of the parameter can be finally obtained.

4. The Settlement Monitoring Results of the ELH Bridge

4.1. Settlement Time Series Obtained Based on GB-RAR

Figure 4 shows the power profile of the IBIS-S interferometer radar line-of-sight direction. In Figure 4, multiple peaks are within the radar monitoring range, and these peaks correspond to the position of monitoring points (such as piers) with good electromagnetic reflectivity. In order to evaluate the safety condition of shield when crossing the ELH bridge, the settlement time series and settlement rate of No. 7 and 8 were monitored and analyzed. The thermal signal-to-noise ratios (SNR) of No. 7 and 8 piers were 71.5 and 54.2 dB, respectively, indicating a high phase stability of the monitored bridge piers.

We used the geometric projection method to obtain the settlement deformation of piers (namely, the vertical deformation component of line-of-sight deformation) because the GB-RAR technology can only obtain the deformation in the direction of the radar line of sight. Given that the ELH Bridge is an important high-speed railway bridge, a train passes through it at high speed every 10 min during the monitoring period. Therefore, the pier was affected by the vertical load of high-speed train operation and the vibration generated by shield tunneling machine. The atmospheric variation and other random noises also have an impact on radar signals. The settlement observation value sequence obtained based on the GB-RAR technology was seriously affected by various noises due to the above-mentioned reasons. In this work, sym4 wavelet was used to denoise the GB-RAR-derived settlement time series.

Figure 5 shows the settlement time series of No. 7 and 8 piers obtained based on the GB-RAR technology. During the monitoring period, the settlement changes were essentially within 1 mm. The vibration generated by the shield tunneling machine will have a certain impact on the deformation monitoring of No. 7 and 8 piers because the shield tunneling machine passes through between No. 7 and 8 piers (as shown in Figure 1). In addition, the noise in the radar signal will increase with the increase in the radar monitoring distance. Because of the above reasons, the wavelet analysis method used to reduce the noise of the settlement time series of No. 7 and 8 piers. After wavelet denoising, the SNR of the settlement time series of No. 7 and 8 piers was increased from 9.7/4.4 to 19.5/9.6, and the change law of settlement time series was clearer. The settlement time series of No. 7 and 8 piers showed a nonlinear downward trend. The standard deviations of the settlement time series of No. 7 and 8 piers obtained based on the GB-RAR technology were 0.19 and 0.18 mm, respectively. The settlement monitoring accuracy of GB-RAR technology was typically high.

4.2. Comparative Analysis of the GB-RAR Settlement Results and Leveling Data

This section compared and analyzed the leveling results with the GB-RAR results to prove the reliability of the settlement time series results obtained using the GB-RAR technology. Considering that GB-RAR obtained high-frequency radar data, and the sampling interval of leveling was 2 h, the data should be processed as follows before the comparative analysis: (1) Select the monitoring data with overlapping time of the two methods; (2) Extract the same settlement as the leveling sampling time from the settlement time series obtained by GB-RAR.

Figure 6a,b show the settlement time series of No. 7 and 8 piers, respectively. The results obtained by leveling and GB-RAR technology had good consistency. During the shield tunnel of the Metro Line 11 crossing the bridge, the settlement changes of No. 7 and 8 piers showed a slight downward trend. Figure 6c,d show the residual distribution of the GB-RAR results relative to the leveling results. The residual was basically distributed in the range of −0.5–0.5 mm. The settlement time series obtained by the GB-RAR technology and leveling have good consistency. The difference between the two methods was statistically analyzed. In the No. 7 pier, the average error between the GB-RAR and the leveling results was −0.05 mm, the root mean square error was 0.20 mm, the maximum difference was 0.40 mm, and the minimum difference was 0.01 mm. The average error, root mean square error, maximum difference, and minimum difference of the No. 8 pier were −0.12, 0.27, 0.55, and 0.01 mm, respectively. In conclusion, the settlement results obtained by using the GB-RAR technology consistent with the leveling results. In addition, the safety monitoring requirements of the ELH Bridge can be met by the use of GB-RAR and the leveling technology under the shield tunnel of Metro Line 11.

4.3. 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.

Table 2. Settlement deformation rates and rate uncertainties of the piers estimated by the three methods.

Method	Time Span	Settlement Rates and Uncertainties (mm/h)
		No. 7 Pier	No. 8 Pier
GB-RAR Deformation Information Estimation Method Considering the Influence of Colored Noise	2016.11.17	−0.0315 ± 0.0053	−0.0210 ± 0.0085
	2016.11.18	−0.0145 ± 0.0059	−0.0000 ± 0.0125
	2016.11.17–18	−0.0112 ± 0.0026	−0.0046 ± 0.0053
GB-RAR Deformation Information Estimation Method without Considering the Influence of Colored Noise	2016.11.17	−0.0270 ± 0.0007	−0.0197 ± 0.0007
	2016.11.18	−0.0099 ± 0.0007	−0.0007 ± 0.0007
	2016.11.17–18	−0.0145 ± ≪10−4	−0.0013 ± ≪10−4
Leveling	2016.11.17	−0.0055 ± 0.0650	−0.0140 ± 0.0360
	2016.11.18	0.0108 ± 0.0755	0.0079 ± 0.0408
	2016.11.17–18	−0.0107 ± 0.0110	−0.0089 ± 0.0641

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 ± 0.0026 and −0.0046 ± 0.0053 mm/h, respectively. Based on the leveling data, the settlement rates of No. 7 and 8 piers were −0.0107 ± 0.0110 and −0.0089 ± 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 pier was closer to the metro tunnel than the No. 8 pier, which may be one of the main reasons why No. 7 pier accumulates more settlement than the No. 8 pier. In conclusion, the settlement rates of the No. 7 and 8 piers were small during the shield tunnel of the Metro Line 11 passing through the ELH Bridge, and the cumulative settlement of both piers was within 1 mm, which satisfied the safety assessment requirements of China Railway Corporation. During the shield tunnel passing through the ELH Bridge, the cumulative settlement of the piers of the ELH Bridge was controlled within 1 mm.

5. Conclusions

This work studied the safety monitoring of the ELH Bridge by using the GB-RAR technology during the crossing of the shield tunnel of Wuhan Metro Line 11 underneath the bridge. A GB-RAR deformation information estimation method considering the influence of colored noise was proposed. The accurate settlement monitoring results of the ELH Bridge during the monitoring period are derived by using the proposed estimation method. The main results are as follows:

(1)

White and colored noises were detected in the settlement deformation time series of the No. 7 and 8 piers after denoising by wavelet analysis algorithm, and the colored noise spectral index of each series was estimated to be approximately −1 according to the settlement time series of the No. 7 and 8 piers.

(2)

The standard deviations of the settlement time series of the No. 7 and 8 piers of the ELH Bridge were 0.19 and 0.18 mm, respectively, indicating that the monitoring accuracy of ground-based interferometric radar was high. The leveling results were used to verify the settlement results obtained by the GB-RAR technology. The root mean square errors of the No. 7 and 8 piers were 0.20 and 0.27 mm, respectively. The results indicate that the GB-RAR technology can effectively and accurately realize the bridge safety monitoring.

(3)

Affected by various noises, the settlement changes of piers obtained based on the GB-RAR technology show nonlinear settlement. Based on the GB-RAR deformation information estimation method considering the influence of colored noise, the estimated settlement rates of the No. 7 and 8 piers were −0.0112 ± 0.0026 and −0.0046 ± 0.0053 mm/h, respectively. The corresponding cumulative settlements were −0.40 mm and −0.16 mm. The cumulative settlements of the No. 7 and 8 piers obtained by the leveling method were −0.39 and −0.32 mm, respectively. The results of the two methods were consistent and satisfied the requirements of safety assessment. During the shield tunneling machine crossing under the ELH Bridge, the cumulative settlement of piers must be less than 1 mm.

The method proposed in this paper can be used not only for deformation monitoring and analysis of bridges, but also for deformation monitoring and analysis of other monitoring objects (e.g., super high-rise buildings, dam, and landslide). In the following research work, we will analyze the relationship between GB-RAR deformation time series noise and deformation information, study relevant filtering methods to weaken colored noise, and further improve the reliability of deformation results.