Bridge Displacement Research Articles

Design and Seismic Performance Study of Multistage Controllable Isolation Bearing for High-Speed Railway Simply Supported Beam

The high-speed railway (HSR) system imposes stringent requirements for track smoothness. However, conventional seismic isolation bearings frequently fail to meet these demands. To address this challenge, a novel seismic isolation bearing was developed based on the principle of functional separation design. This innovative bearing effectively achieves the multistage control objectives, including amplitude limitation to ensure track smoothness during frequent earthquakes, energy dissipation to guarantee train running safety during design earthquakes, and structural integrity maintenance to prevent beam collapse during rare earthquakes. Firstly, an overview of the novel isolation bearing’s structural design and operational principle is provided. Subsequently, a corresponding mechanical model is formulated, with the parameters of the new bearing determined through finite element analysis. The study then compares the seismic performance of the general rubber bearing and the new bearing, using an HSR simply supported bridge as an engineering background. The dynamic response of the bridge under varying seismic waves, pier heights, and bridge spans is meticulously analyzed. The results indicate that the new bearing can achieve multistage control. Compared to general bearings, it reduces bridge displacement vibration by over 46.4% under frequent, design, and rare earthquakes. The bridge deformation under frequent earthquakes remains below 3 mm, thus meeting the track smoothness requirements for normal HSR operations. Additionally, the study reveals that higher pier heights increase the seismic response, peaking at 15 m. The vibration reduction provided by the new bearing varies but remains effective in most earthquake scenarios, with maximum reductions of 92.9% for displacement and 74.17% for bending moment. Furthermore, larger bridge spans also increase the seismic response, with the 24 m span bridge outperforming the 32 m span bridge. In conclusion, the novel seismic isolation bearing significantly enhances the seismic performance of HSR bridges, ensuring train running safety and operational reliability.

High-rate bridge displacement monitoring with low-rate virtual reference station data

We present a new Global Navigation Satellite Systems (GNSS) positioning approach that utilizes low-rate Virtual Reference Station (VRS) data to achieve high-rate displacement monitoring. The method integrates tightly the VRS technology with asynchronous Real-Time Kinematic (RTK) method to overcome the limitation of VRS in high-rate structural health monitoring (SHM) applications. When this approach is used, no local reference station is required so that the efforts and cost of setting up reference stations can be avoided. Experiments with datasets from a controlled shaking platform and a long-span bridge in Hong Kong with both temperature and typhoon excitations have indicated that the proposed approach worked effectively. The results demonstrated that when a baseline exceeded about 3 km, the vertical errors of RTK GNSS positioning could be up to about 15.9 mm (standard deviations), insufficient for most SHM applications. In this case, the proposed method enhanced the accuracy by about 60% to 6.0 mm when using VRS data openly available in Hong Kong. The accuracy achieved was equivalent to that of RTK positioning using a 1.2 km baseline. The shaking platform trial demonstrated that the monitoring station could be up-sampled to 100 Hz without a noticeable loss in accuracy. The proposed method could capture precisely the peak frequencies and amplitudes of vibrations, with errors as low as 0.001 Hz and 0.1 mm. This method broadens the applicability of GNSS positioning in SHM applications.

Data-based feature representation of traffic flow for predicting bridge displacement responses with ensemble learning model

Data-based feature representation of traffic flow for predicting bridge displacement responses with ensemble learning model

Deflections and frequencies of long-span steel railroad truss bridges under passenger train excitation using laser Doppler vibrometer

ABSTRACT Given the critical challenge of aging infrastructure, it is imperative to adopt novel techniques that utilize modern technology to assess the structural integrity of existing bridges. This study presents a methodology to estimate the loading frequency of the train passing over the bridge and bridge dynamic responses, such as the acceleration and displacement response of long-span open-deck steel railroad truss-type bridge under the passenger train excitation using a Laser Doppler Vibrometer. The selected bridges for this study were the Cos Cob and Devon Railroad bridges in southern Connecticut, both in the Northeast Corridor. The structural response of the bridge floor system was collected during the field test using a single-point laser Doppler vibrometer and uniaxial accelerometers for reference under passenger trains, such as Metro-North M8, Amtrak Regional, and Amtrak Acela. The recorded data were analyzed using the moving load theory, interpreted, and discussed in the time and frequency domain. The study findings indicate that the bridge response and displacement align with the theoretical and vehicle axle loads. Also, it should provide valuable information about the behavior of the considered bridges under typical operating conditions.

An image-based bridge displacement field measurement method with self-vibration elimination

Displacement is a critical indicator that reflects the degeneration of overall stiffness for bridges. However, for most bridges, contact displacement measurement is difficult to achieve due to the lack of reference points and technical limitations. In this paper, a unique dual-camera visual sensor system for the whole field displacement measurement of bridge undersurfaces was developed. The visual sensor system relies on feature point algorithm and several algorithms are involved to improve the accuracy and efficiency. The dual-camera equipment can independently eliminate the impact of the camera vibration, thereby solving the problem of camera vibration caused by ground vibrations and wind loads at outdoor inspection sites when measuring bridge displacement. In a laboratory testing environment, a steel plate simulated a bridge and different experiments were conducted to test the visual system in situations with and without vibration disturbances to the camera. The results verify the accuracy of the developed visual sensor, especially the effectiveness of the vibration reduction method.

LAVOLUTION: Tunable structured light for bridge displacement measurement

Assessing bridge conditions is critical, but field measurements often face challenges like sensor installation and accuracy requirements. This paper introduces a novel approach using structured light (SL) for non-target-based measurements, eliminating the need for physical markers. A tunable SL system, featuring four laser pointers aligned with a commercial camera, was developed to estimate the relative angle between the camera and the target structure, and to accurately calculate the scale factor. The proposed method involves three main processes: (1) laser alignment, (2) angle estimation, and (3) real-time displacement measurement. By precisely aligning the SL system and minimizing discrepancies between projected SL points and an ideal numerical model, the method achieves accurate results. Validation through numerical simulations, lab-scale tests, and full-scale bridge tests demonstrated a maximum error of 2.69% in scale and 2.53% in displacement, confirming the method’s effectiveness and applicability.

The thermal responses of composite box girder bridges with corrugated steel webs under solar radiation

Owing to the direct exposure to complex atmospheric environments, the temperature field of composite box girder bridge with corrugated steel webs (CBGB-CSW) is likely non-uniformly distributed. Whereas, the current researches regarding the thermal responses of CBGB-CSW are insufficient, and the thermal responses of CBGB-CSW under solar radiation are still unknown. Therefore, this paper conducted a long-term temperature experiment on a scaled model to explore the temperature distribution characteristics in CBGB-CSW. Meanwhile, a three-dimensional thermal–mechanical coupling Finite Element (FE) model is established to simulate the temperature field in the experiment girder. The accuracy and effectiveness of the developed FE model has been verified by the measured temperature data. Therewith, the thermal responses (i.e., stress and displacement) of a full-scale continuous CBGB-CSW with a span of 150 m are numerically investigated. The results indicate that the maximum stresses always occur at the midspan section (with a depth of 5 m) of the continuous CBGB-CSW, and considerable concentrations of stress are observed in the steel-concrete junction. The maximum longitudinal tensile and compressive normal stresses within 0.4 m of the upper junction can reach 5.55 MPa and −8.46 MPa respectively, and those of the lower junction can reach 6.96 MPa and −7.05 MPa respectively. Besides, owing to the impacts of vertical and horizontal temperature gradients, significant displacements of the whole bridge can also be observed. The maximum vertical displacement (5.33 mm) of the CBGB-CSW is estimated at the top plate in the midspan, while the maximum horizontal displacement (0.74 mm) is estimated at the trough of the southern corrugated steel web in the midspan. Notably, the outcomes of this paper can provide some useful references for engineers and scholars to understand the thermal responses of the CBGB-CSW.

Analytical solutions for static longitudinal displacements of suspension bridges under a moving vertical concentrated load

The longitudinal displacement at the girder ends of long-span suspension bridges is a crucial issue that affects structural safety, durability, as well as traffic safety and ride comfort. The primary cause of these reciprocating displacements is the action of moving live loads, which induces quasi-static displacements in the longitudinal direction. This paper theoretically investigates the static longitudinal displacements of suspension bridges under a moving vertical concentrated load and elucidates the underlying deformation mechanisms. Considering geometrical nonlinearity, analytical equations are established for the longitudinal deformations of the main cable and stiffening girder under a vertical concentrated load. By analyzing the geometrical deformation conditions of the suspenders, the relationship between the longitudinal displacements of the stiffening girder and the main cable is derived. Due to the coupling between longitudinal and vertical displacements, the vertical displacement of the stiffening girder must be solved to obtain its longitudinal displacement. Based on deflection theory and considering the bending stiffness of the stiffening girder, this paper derives the vertical deformations of the stiffening girder for single-span suspension bridges and those with short continuous side spans under a vertical concentrated load, which is then used to calculate the longitudinal displacement. Finite element models are used to verify the accuracy of the analytical solutions. Differences between the proposed solutions and previous solutions neglecting the bending stiffness of the stiffening girder are compared and analyzed. The effects of neglecting the longitudinal displacement at the bridge tower top and the presence of short continuous side spans on the longitudinal displacement of stiffening girder are also investigated. The results demonstrate the high accuracy of the proposed analytical solution for the longitudinal displacement at the girder ends of suspension bridges. Importantly, the bending stiffness of the stiffening girder cannot be neglected in calculating the longitudinal displacement. The longitudinal displacement at the girder ends is primarily caused by the longitudinal deformation of the main cable, while the contribution from the flexural deformation of the girder is negligible. Furthermore, the longitudinal displacement at the bridge tower top has a negligible effect on the longitudinal displacement of the girder, and the presence of short continuous side spans is beneficial for reducing the longitudinal displacement of the stiffening girder. The proposed analytical solution method provides a rapid approach for calculating the static longitudinal displacement at the girder ends of suspension bridges under passing live loads and reveals the deformation mechanism. This is beneficial for preliminary design and structural optimization, as it avoids the complex finite element modeling and solution process.

Accelerometer-aided millimeter-wave radar interferometry for uninterrupted bridge displacement estimation considering intermittent radar target occlusion

Monitoring bridge displacement is necessary to detect early signs of damage, prevent catastrophic failures, and maintain public confidence in the safety of critical transportation infrastructure. Radar interferometry is attractive for long-term continuous monitoring of bridge displacements, given its resilience to weather and lighting conditions. However, intermittent radar target occlusions caused by moving vehicles beneath bridges pose challenges during extended continuous monitoring periods. In this study, accelerometer-aided millimeter-wave radar interferometry was explored with an explicit consideration of intermittent radar target occlusion. Radar and accelerometer measurements were first recorded over a short period. Multiple good targets were selected among all radar-detected targets, and their direction-converting factors were estimated using short-period measurements. Subsequently, bridge displacement was continuously estimated by overcoming intermittent radar target occlusions. A displacement reconstruction algorithm was proposed for target occlusion periods, and a multitarget-based phase-unwrapping algorithm was proposed to remove the displacement drift caused by radar target occlusion. The proposed technique was experimentally validated through laboratory tests on a 10-meter-long bridge structure and field tests on two different spans of a footbridge. The technique accurately estimated displacements with overall errors below 0.1 mm, allowing it to be widely applied to bridges with millimeter-scale displacements.

UAS-based bridge displacement measurement using two cameras with non-overlapping fields of view

Traditionally, when a bridge fails an assessment, information required for bridge load capacity may be obtained by fitting a bridge with sensors and measuring the bridge's response to a load of known weight being driven across. Unfortunately, fixing sensors to the bridge is cumbersome and time-consuming, requiring erection of scaffolds and platforms and so can be expensive. Camera-based measurements using Unmanned Aerial System (UAS) promise an alternative non-contact approach that is safe, affordable, and fast. However, the lack of stationary locations near bridge mid-span makes it difficult to both measure displacements and stabilise the ego motion of a UAS. To overcome this challenge, this paper therefore presents the experimental validation of a method that uses two different cameras mounted on a UAS. One camera is focused on taking measurements near the midspan while another camera is used to stabilise the UAS using stationary locations at the bridge supports. The method does not require that the stationary object is in the field of view of the measurement camera. The method only uses video feed from two cameras viewing different parts of the bridge and no additional sensor information. The significance of this paper to the field of UAS bridge displacement measurements is that the method opens up the ability to measure displacements in locations such as midspans where stationary objects are rare. Submillimetre accuracy was achieved indoors on a model bridge setup and outdoors on a 5 m bridge analogue.

Time-varying Multivariate Linear Regression Modeling of Temperature-induced Bearing Displacements of A Single Tower Cable-Stayed Bridge

Time-varying Multivariate Linear Regression Modeling of Temperature-induced Bearing Displacements of A Single Tower Cable-Stayed Bridge

A Novel Method for Heat Haze-Induced Error Mitigation in Vision-Based Bridge Displacement Measurement.

Vision-based techniques have become widely applied in structural displacement monitoring. However, heat haze poses a great threat to the precision of vision systems by creating distortions in the images. This paper proposes a vision-based bridge displacement measurement technique with heat haze mitigation capability. The properties of heat haze-induced errors are illustrated. A dual-tree complex wavelet transform (DT-CWT) is used to mitigate the heat haze in images, and the speeded-up robust features (SURF) algorithm is employed to extract the displacement. The proposed method is validated through indoor experiments on a bridge model. The designed vision system achieves high measurement accuracy in a heat haze-free condition. The proposed mitigation method successfully corrects 61.05% of heat haze-induced errors in static experiments and 95.31% in dynamic experiments.

Drive-By Identification of Joint Bridge Damage and Surface Roughness Based on Sensitivity Analysis of Residual Contact Point Deflections

Drive-by inspection of bridge damage using a passing vehicle’s dynamic response has great potential in bridge damage identification. Among the current drive-by methodologies, the methods based on bridge modeling have been proposed for the quantitative identification of bridge damage and bridge surface roughness. However, the coupling of bridge damage and unknown surface roughness increases the difficulty of the identification problem and most previous studies conduct the identification task of bridge damage or bridge surface roughness separately. In this paper, a novel method is proposed for the identification of joint bridge damage and bridge surface roughness based on the residual bridge deflections from the front and rear wheels contact points of an instrumented passing vehicle. The vehicle–bridge interaction is analyzed using a half-car model of a four degrees of freedom (4-DOF) with front and rear vehicle wheels. First, the vehicle–bridge unknown forces and displacement of the vehicle axles are identified by the generalized Kalman filter under unknown input (GKF-UI) proposed by the authors. The sensors can be installed conveniently on the vehicle body due to GKF-UI. Then, the residual bridge deflections from the front and rear vehicle wheels contact points are utilized to eliminate the effect of road surface roughness. Afterward, bridge structural damage is identified based on the sensitivity analysis of residual bridge deflections from the front and rear contact points with [Formula: see text]1-norm regularization. Finally, bridge road surface roughness is estimated based on the identified unknown forces and updated bridge model with damage. The results of numerical identification examples demonstrate the effectiveness of the proposed method for the identification of joint bridge damage and surface roughness.

A systematic correlation analysis for regression model selection: Application to bridge response prediction using contact and remote sensor systems

Correlation analysis is a crucial step prior to any regression modeling for data prediction, as it can unveil the relationship between predictors and responses, particularly in terms of linearity and nonlinearity. This step is often mandatory for selecting the most suitable regression model. The major challenge is that linear correlation measures are only appropriate for linear cases and there are limited nonlinear measures for nonlinearity assessment. Apart from these challenges, the demanding issue relates to the influence of unknown and unmeasured predictor data in regression model selection thereby yielding unrealistic and inaccurate outputs from both linear and nonlinear correlation measures. To tackle these challenges, this paper proposes a hierarchical correlation analysis method that initially indicates the influence of unknown predictors and then assists in selecting the best regressor for modeling and forecasting. The proposed method utilizes a linear measure known as canonical correlation analysis and a nonlinear measure known as the maximal information criterion. Based on the correlation values derived from these measures, it is possible to classify them into three levels of correlation: low, moderate, and high. In the first and second scenarios, it is inferred that the response data is linearly or nonlinearly influenced by the measured predictors, respectively. In the third scenario, three conditions are derived from the correlation levels, suggesting that the response data is not influenced by the measured predictors. To validate the proposed hierarchical correlation analysis method's applicability and effectiveness, it is tested with predictor and response data related to real-world long-span bridges. The only measured predictor is air temperature, while the response data comprises limited bridge displacements obtained from synthetic aperture radar images, in line with remote sensing technology. The results indicate that the proposed method is highly effective and applicable for selecting the best regression model for prediction.

Bayesian Data Fusion for Enhanced Monitoring of Bridge Displacements Using Satellite InSAR and Topographic Techniques

This paper investigates the effectiveness of satellite Interferometric Synthetic Aperture Radar (InSAR) technology to remotely monitor the structural health of road bridges and detect possible unexpected behaviours. The study is based on an Italian multi-span prestressed concrete bridge and a dataset of eight years of X-band SAR images collected by the COSMO-SkyMed satellite constellation. The method implemented for this study is as follows. First, SAR images are analysed using the Multi-Temporal InSAR technique to extract displacement time series of reflective targets on the bridge decks. Then, the extracted displacements are interpreted to validate their consistency with the bridge's expected responses to environmental loads, such as air temperature and river water flow variations, and detect possible unexpected behaviours. Eventually, the correlation with the air temperature is investigated to identify different bridge spans based only on monitoring data. The findings from this study advance the knowledge on using satellite InSAR-based monitoring for early detection of anomalous bridge behaviours on a large scale, providing valuable insights for the maintenance and safety of critical infrastructure.

Structural displacement measurement using deep optical flow and uncertainty analysis

Displacement serves as a crucial indicator in the field of structure health monitoring for assessing the condition of civil engineering structures. Computer vision is commonly employed for this purpose due to its cost-effectiveness and convenience. Traditional non-contact computer vision methods, such as optical flow, have been applied to obtain the displacement of bridges. However, real-time monitoring remains challenging due to the computational complexity involved. Therefore, optical flow based on deep learning (referred to as deep optical flow) has gained significant attention. Its main advantage lies in its ability to achieve real-time displacement monitoring, which is of great significance. Furthermore, the accuracy of deep optical flow is comparable to that of traditional optical flow methods for displacement measurement. In this paper, the deep optical flow, RAFT-GOCor, is proposed and applied to extract the displacement of structures, then Bayesian RAFT-GOCor based on Monte Carlo dropout is also presented and applied to analyze the uncertainty of the displacement. The algorithms are verified by laboratory simulated experiments and field bridge loading test. The results indicate that both deep optical flow and uncertainty analysis are feasible methods for measuring structural displacement.

Preliminary field estimation of vertical displacements of prestressed concrete bridges under construction based on measured strains and inclinations

The development of continuous and automatic quantitative monitoring methods will improve bridge construction. This paper proposes a method for estimating vertical bridge displacement during construction based on the Bayesian inverse problem. The proposed method is applied to a bridge under construction in Japan. Case studies suggest that the observed rotation angle is more important than the observed strain for the estimation of vertical displacement. Based on strain and rotation angle measurements, vertical bridge displacement was estimated with an accuracy of less than 2 mm, as determined from a comparison with displacements obtained in a leveling survey. The 95 % confidence interval of the estimation error is consistent with the scatter of measured data of displacement, rotation angle, and strain.

Machine Learning Approaches for Vehicle Counting on Bridges Based on Global Ground-Based Radar Data

Abstract. This study introduces a novel data-driven approach for classifying and estimating the number of vehicles crossing a bridge solely on non-invasive ground-based radar time series data (GBR data). GBR is used to measure the bridge displacement remotely. It has recently been investigated for remote bridge weigh-in-motion (BWIM). BWIM mainly focuses on single-vehicle events. However, events with several vehicles should be exploited to increase the amount of data. Therefore, extracting the number of involved vehicles in the first step would be beneficial. Acquiring such information from global bridge responses such as displacement can be challenging. This study indicates that a data-driven machine learning approach can extract the vehicle count from GBR time series data. When classifying events according to the number of vehicles, we achieve a balanced accuracy of up to 80 % on an imbalanced dataset. We also try to estimate the number of cars and trucks separately via regression and acquire a R2 of 0.8. Finally, we show the impact of the data augmentation methods we apply to the GBR data to tackle the skew in the dataset using the feature importance of Random Forests.

Measurement Refinements of Ground-Based Radar Interferometry in Bridge Load Test Monitoring: Comprehensive Analysis on a Multi-Span Cable-Stayed Bridge

This paper presents three refinements in ground-based radar interferometer (GB-radar) measurement for bridge load testing: (1) GB-radar phase jumps were detected for the first time on bridge tower displacement monitoring, and a recovery method is presented to obtain the correct unwrapped value; (2) a precise displacement projection method considering target deformation was exploited, and a case study of the Fifth Nanjing Yangtze River Bridge (FNYRB) GB-radar campaign shows that a centimeter-level compensation can be achieved; (3) a post-construction settlement phenomenon was found during the FNYRB static load tests, characterized by 0.31 mm/min, which accumulated up to 25 mm. In addition, the dynamic monitoring capabilities of GB-radar for the bridge tower and girder were verified, highlighting its potential for bridge structural health monitoring (SHM). The insights gained from this study offer valuable recommendations for future GB-radar bridge displacement monitoring.

Thermography measurement for bridge displacement in the darkness using power-free target

Vision-based displacement measurement has become increasingly popular in bridge health assessment. However, this technology faces challenge that a complicated power-consuming supply system must be installed in the darkness, making it unable to meet the needs of low energy consumption and low cost. This paper proposes a bridge displacement measurement method using power-free target and thermography to address it. First, a thermography measurement system for bridge displacement in the darkness is developed. The power-free target with a hollowed-out circular feature is adopted to form the contrast to the background, and graphene is coated on the target surface to enhance the infrared emissivity and contrast further. Second, a sub-pixel elliptic center positioning algorithm based on thermography enhancement and data optimization is proposed to improve the accuracy and the ability to resist occlusion. The feasibility of the method is verified by laboratory tests and bridge field tests. When the measurement distance is within 15 m, the results meet the engineering error requirements of 5%, with the prospect of popularization in small and medium-sized bridges displacement measurement.