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In the actual structural health monitoring system of suspension bridges, only part of suspenders tension can be monitored, but not all the suspenders tension can be obtained. To solve this problem, a method for suspenders tension identification of bridges based on the spatio‐temporal correlation between the girder strain and suspenders tension is proposed. By using actual monitoring data of vehicle loads, a spatio‐temporal correlation model of the girder strain and tension forces of all suspenders is constructed based on the combined application of stacked denoising autoencoder and convolutional neural networks‐long short‐term memory model, so as to realize the preliminary identification of suspenders tension. On this basis, by using the actual monitoring data of suspenders tension and the strain monitoring data obtained through the distributed optical fiber sensors, the delicate identification of tension forces of all suspenders is realized based on the error interpolation of preliminary identification results. The results of the example bridge show that the method in this paper can effectively identify tension forces of all suspenders of the suspension bridge, and identification results are more accurate than the method using only the monitoring data of suspenders. [ABSTRACT FROM AUTHOR]

High-speed railway suspension bridges (HSRSBs) have been constructed with the new advancements in technology. The deformation prediction for HSRSBs is essential to their safety and maintenance. The conventional prediction methods are developed for bridges without high-speed railway. Different factors, including temperature (TEMP), time delay compensation (TDC), train live load (TLL), are considered in these methods. However, the train side (TS) and train instantaneous position (TIP) have a significant impact on deformation for HSRSBs, and they are not used in the prediction. More importantly, the coupling issue among different factors is so significant that it cannot be neglected. In this study, we propose a deformation prediction model based on a backpropagation (BP) neural network. This model uses different factors as model input, including TEMP, TDC, TLL, TS, and TIP. The coupling issue is addressed by using the new model. The new model was evaluated using a dataset of 10-day field measurements. It achieves a mean absolute error (MAE) of 8.81 mm, a mean relative error (MRE) of 9.82%, and coefficient of determination (R2) of 0.94. The new model will provide high-precision prediction for deformation and will be used in the development of an early warning system. [ABSTRACT FROM AUTHOR]

This paper introduces a new accelerating algorithm, efficient match slimmer (EMS), specifically designed to lighten computational loads of sophisticated template matching algorithms, enabling these algorithms to be effectively run on single‐board computers. Utilizing EMS in conjunction with a robust template matching algorithm, we have developed Raspberry Vision—a compact, cost‐effective, and real‐time vision‐based system. Its compactness and portability facilitate a practical measurement strategy that not only minimizes the camera‐to‐target distance but also simplifies the camera calibration process in bridge displacement monitoring, thereby enhancing measurement accuracy. The performance of the system is estimated on two operational suspension bridges. The results demonstrate that Raspberry Vision, equipped with the measurement strategy, can significantly improve the measurement accuracy in the long‐span bridge test and is also suitable for cross‐sea bridge measurements. [ABSTRACT FROM AUTHOR]

The First Egongyan Bridge in Chongqing, China was opened to traffic on December 27, 2000. It carries six-lanes of city traffic and two pedestrian paths, one on each side. It is a 600 m span suspension bridge. It was planned that the two pedestrian paths might eventually be converted to transit tracks in the future. However, with the rapid increase in urban traffic, the deck was transformed into an 8-lane bridge instead. Therefore, a new bridge parallel and adjacent to the old bridge was built for the rail transit. For aesthetic reasons, the city decided that the new bridge should also be a suspension bridge, with the same span length and tower height as the first bridge. The First Egongyan Bridge was a true suspension bridge with main cables anchored to ground anchors. However, the new bridge bridge's proximity to the first bridge necessitated the construction of a self-anchored suspension bridge that did away with a second set of ground anchors. This 600 m span happened to be the world's longest span for a self-anchored suspension bridge. [ABSTRACT FROM AUTHOR]

Suspenders play a crucial role in transmitting loads from the bridge deck to the main cable in a suspension bridge. They are susceptible to fatigue due to repeated dynamic loads, particularly traffic loads. Traffic Load Models (TLMs), typically created using Monte–Carlo simulation and Weigh-In-Motion (WIM) data, are employed to evaluate this fatigue. However, these models often overlook practical vehicle trajectories and spatio-temporal distribution, which compromises the precision of fatigue assessments. In this study, we introduce a novel 2D Intelligent Driver Model (2D-IDM) that incorporates actual vehicle trajectories, with a particular focus on transverse vehicle movement. This enhancement aims to improve the fidelity of existing TLMs. To provide a clear, qualitative, and quantitative understanding of the effects of fatigue evaluation with or without actual trajectory characteristics, we have structured this paper as a comparative study. We compare our proposed model, denoted as TLM S-3, with two observation-based models (O-1 and O-2) and two simulation-based models (S-1 and S-2). We conducted an experimental case study on a long-span suspension bridge, where the actual traffic load trajectory was obtained using a WIM-Vision integrated system. To calculate fatigue damage considering both longitudinal and transverse directions, we established a multi-scale Finite Element Model (FEM) using solid element types to simulate the bridge girder. This model can generate the stress influence surface of the bridge and has been verified in both static and dynamic aspects. Our detailed comparative analysis demonstrates the consistency of the proposed 2D-IDM with the actual measured traffic load trajectories. This indicates that our approach can enhance the fidelity and precision of fatigue evaluations for bridge suspenders. [ABSTRACT FROM AUTHOR]

The Eddy Current Damper (ECD) is a velocity-based passive energy dissipation device that can be used for structural vibration control. This study aims to reveal the damper behavior and determine the optimal parameters of the ECDs applied to a suspension bridge suffering from bi-directional earthquakes. The influence of the bi-directional vibration interaction on the damping force is theoretically investigated. An optimization method is proposed combining the Sobol Sequence sampling method, the Coefficient of Variation (COV) method, and the Backpropagation neural network (BPNN) algorithm. A numerical model of a long-span suspension bridge with bi-directional ECDs is established and taken as a case study to verify the feasibility of the proposed optimization method. The results indicate that the ECD system with bi-directional interaction will produce a larger maximum force and less energy dissipation than one without bi-directional interaction. The proposed optimization method possesses the characteristics of objectivity, accuracy, and effectiveness. The obtained optimal bi-directional ECDs can significantly reduce the longitudinal and transverse vibration. Failing to consider bi-directional effects will lead to an overestimation of longitudinal damper parameters and an underestimation to transverse ones, as well as ignoring the influence of damper length on its mechanical performance. [ABSTRACT FROM AUTHOR]

Recent seismic events have unequivocally highlighted the susceptibility of fault-crossing bridges to the synergistic effects of ground surface vibrations on either side of the fault plane and the tectonic dislocations arising from fault-induced surface ruptures. This study delineates both seismic and parametric response analyses of fault-crossing suspension bridges, employing a straightforward yet efficacious method for simulating desired ground motions near fault-rupture zones. Herein, we introduce a user-friendly method to incorporate predicted fault-induced displacements, accounting for both fling-step and directivity effects, into processed ground motion chronologies, enabling the generation of dip-slip fault ground motions. The accuracy and efficacy of the proposed method are affirmed by juxtaposing the generated ground motions with the observed ones (MGM). An exhaustive parametric analysis, addressing factors like fault-crossing location, fault-crossing angle, and frequency components of fault-crossing ground motions, of a suspension bridge over a rupture fault, is executed using the fashionable ANSYS software. This study provides clear and specific guidelines for the seismic design of suspension bridges traversing rupture faults. [ABSTRACT FROM AUTHOR]

Fire accidents often pose severe threats to the safety of steel bridges. This paper presents the numerical study of the Runyang Suspension Bridge (RSB) fire accident with an emphasis on its in-fire thermal effect on the hangers. This fire accident was caused by the collision of two heavy-goods vehicles (HGVs) on March 4, 2017, and lasted for 1.5 h. Based on the simulated temperature, the structural safety of four burned hangers during and after the fire accident was evaluated and compared. In general, the simulation results are consistent with the actual situation, and the evidence for the replacement of the hangers is sufficient. The influence of wind parameters and cooling actions on the hanger safety is also discussed. It is found that the wind parameters affect the directions and tilts of the flame, so that the highest temperature and the corresponding height are influenced accordingly. Also, the efficiency of the water-cooling method is influenced by the intervention time of fire engines. If water spraying is conducted within 30 min from fire initiation, the safety of the hangers during and after the fire could be improved, as compared with air cooling. [ABSTRACT FROM AUTHOR]

The present work offers a comprehensive overview of methods related to condition assessment of bridges through Structural Health Monitoring (SHM) procedures, with a particular interest on aspects of seismic assessment. Established techniques pertaining to different levels of the SHM hierarchy, reflecting increasing detail and complexity, are first outlined. A significant portion of this review work is then devoted to the overview of computational intelligence schemes across various aspects of bridge condition assessment, including sensor placement and health tracking. The paper concludes with illustrative examples of two long-span suspension bridges, in which several instrumentation aspects and assessments of seismic response issues are discussed. [ABSTRACT FROM AUTHOR]

The present paper combined the natural environment excitation technology (NExT) with the eigen system realization algorithm (ERA) to identify the modal parameters of a suspension bridge. Firstly, the critical parameters in NExt–ERA, such as record length, window length, and ranks of the Hankel matrix, and their influence on identification accuracy have been discussed. Subsequently, based on the acceleration series obtained from the Xihoumen Bridge Health Monitoring System, 3015 sets of modal frequencies and modal damping ratios of the Xihoumen Bridge were identified under 7 sets of wind speeds by the NExt–ERA. Finally, the probability distribution and confidence interval of the structural modal damping ratios were analyzed. Besides, the dependence of identified frequencies damping ratios on wind speed was also discussed. The results show that at the same wind speed, the mean value, and variance of the torsional and lateral mode damping ratios are larger than those of the vertical mode, but this difference gradually decreases with the increment of wind speed. The modal damping ratios along three directions under different wind speeds all follow the generalized extreme value distribution, but wind speed affects the tailing properties of probability distribution of the vertical and torsional mode damping ratios. The estimated damping ratios could provide references for structural design and vibration control of similar long-span bridges. [ABSTRACT FROM AUTHOR]

In the complex mountain wind environment, especially in the strong wind, fluctuating wind speed is a non-stationary and non-Gaussian random process. With the increase of suspension bridges' span, they are more sensitive to wind-induced vibration response. In this paper, a non-stationary and non-Gaussian buffeting reliability analysis method for long-span bridges is presented. Firstly, the non-stationary wind speed is simulated by the modulation function based on the stationary wind speed model. Secondly, the load is obtained by simulated wind speed, the obtained loads are loaded on the finite element model by ANSYS and the whole bridge time-domain analysis is performed, the time history of displacement response is obtained. Thirdly, based on the first excursion failure criterion of random vibration, the samples of the non-stationary and non-Gaussian displacement time history are transformed into a standard Gaussian process through a modified Fleishman approximation method, and then the non-stationary Poisson distribution method is used for structural reliability analysis. Finally, a mountainous long-span suspension bridge is used as the engineering background, and the proposed reliability analysis method is applied to analyze the reliability of the bridge. The influence of different wind attack angles and modulation functions on the dynamic reliability of the bridge is further studied. The results indicate that the displacement response obtained by the transformation of non-stationary and non-Gaussian random process is less reliable than that obtained by traditional analysis method. Its dynamic reliability is maximum at 1 ∘ wind attack angle, the reliability of negative wind attack angle is lower than that of positive wind attack angle, and decreases with the increase of wind attack angle. The reliability obtained by using different modulation functions is lower than that of traditional method. If the traditional analysis method is still used for reliability analysis, it will produce unsafe consequences and reduce the engineering safety reserve. [ABSTRACT FROM AUTHOR]

Closely spaced modes commonly observed in long-span suspension bridges can greatly increase the difficulty of identifying and tracking modal parameters. Most existing studies generally focus on identifying the closely spaced modes and quantifying the uncertainties based on numerical and experimental models. Further research focusing on full-scale long-span bridges is still required. A case study on identifying the closely spaced modes of the Qixiashan Yangtze River Bridge, a long-span suspension bridge with a main span of 1 418 m, is conducted in this paper. The effectiveness of the generalized fast Bayesian fast Fourier transform (GFBFFT) method is verified by both the simulated and monitoring data. The results show that a larger coefficient of variation (COV) and higher uncertainty is typically contained in the closely spaced modes than the separated modes. Compared with the FDD and SSI methods, the GFBFFT method guarantees higher identification accuracy of modal parameters and can serve as a reliable tool to identify the closely spaced modes. [ABSTRACT FROM AUTHOR]

Vortex-induced force (VIF) identification and modelling of a long-span bridge are often conducted in terms of aeroelastic sectional model tests in wind tunnels. However, there are uncertainties inherent in wind tunnel model tests so that vortex-induced vibration (VIV) still occurs in real long-span bridges designed according to wind tunnel test results. This paper presents a framework for VIF identification of a long-span bridge based on field-measured wind and acceleration data. The framework is composed of the four steps: (1) decompose field-measured acceleration response time histories using variational mode decomposition (VMD) method; (2) obtain velocity and displacement response time histories using frequency domain integration (FDI) method; (3) establish and update the finite element model and identify the generalized VIF time histories of the bridge; and (4) identify the parameters in the polynomial VIF models and decide the most suitable VIF model. The proposed framework is finally applied to a real suspension bridge with a recent VIV event. The results show that the proposed framework can accurately identify the generalized VIF acting on the bridge from the field-measured acceleration and wind data, and the derived most suitable VIF model can produce almost the same vortex-induced response (VIR) as the measured ones. [ABSTRACT FROM AUTHOR]

The Gordie Howe International Bridge project is providing a new modern border crossing between Windsor, ON, Canada and Detroit, MI, USA. The centrepiece of the project is a 2.5 km long cable-stayed bridge with 853 m main span over the Detroit River and 220 m tall towers on both sides of the river. In addition to the bridge, the project includes ports of entry on both sides of the border and a new freeway interchange with Interstate-75 in Detroit. The project was procured as a public–private partnership that allowed the proponents to propose either a suspension or cable-stayed bridge, with the ultimate selection creating the longest cable-stayed bridge in North America. The paper outlines the need for the new border crossing and results of the environmental assessment process, as well as describing the project evolution from planning through procurement and into detailed design. The scoping of the bridge design parameters is discussed, including: comprehensive geotechnical investigation; load study to develop project-specific live loading; the approach for durability requirements to achieve a service life of 125 years; special considerations for security; wind engineering; and compliance with both Canadian and US design codes. The paper also discusses the approach to achieving an aesthetically pleasing bridge design. [ABSTRACT FROM AUTHOR]

Hybrid cable-stayed suspension bridges combine the advantages of cable-stayed and suspension bridges, mitigating their deficiencies. Due to its super spanning ability, this novel form of bridge enjoys a bright application prospect as a large-span structure. This study introduces an analytical algorithm to estimate the full-bridge response of a hybrid cable-stayed suspension bridge with a vertical uniformly distributed load applied to the main beam. This method is based on the assumption that all parameters, such as the geometric configuration, internal force distribution, and material properties, of the whole bridge under a dead load are known; then, it analyzes the full-bridge response under a live load. First, the minimum and independent basic unknown parameters of the full-bridge response are determined. Next, the governing equations are derived and solved based on the conservation of unstressed length of each section of cable, closure of span lengths and elevation difference in different spans, and conditions for stress balance of the main beam. Thus, the values of basic unknown parameters are obtained. Finally, they are substituted into the governing equations to estimate the full-bridge response, including each bridge component's internal forces and deflections. The proposed analytical method involves no iterative procedures when dealing with nonlinear problems but only focuses on the bridge's state with and without loading. The results are obtained directly by solving the equations, which have the advantages of high efficiency, simplicity, and clear physical meaning. Finally, the feasibility and effectiveness of the proposed method are verified by a finite-element-based calculation of an exemplary asymmetric cable-stayed suspension cooperation system bridge with a main span of 1400 m. [ABSTRACT FROM AUTHOR]

This paper presents a dynamic modal identification of the Fatih Sultan Mehmet (FSM) Bridge utilizing structural health monitoring (SHM) data recorded during a recent extreme wind event (maximum wind speed: 130 km/h) that occurred on November 29–30, 2021, to provide a preliminary report for future posthazard health assessments for similar long-span suspension bridges. First, four different operational modal analysis (OMA) techniques are performed to identify the bridge's modal parameters (modal frequencies, damping ratios, and modal shapes). The analysis results are compared with each estimator and those of an experimental investigation published in the literature to verify the bridge's modal parameters. Secondly, natural frequency history and damage indicators are determined using the modal parameters and estimated standard deviations obtained from the stochastic subspace identification with extended unweighted principal component (SSI-UPCX) technique. The result of modal damage indicators reveals a healthy structure after this extreme wind event; onsite visual inspections also support this finding. In conclusion, it is believed that these significant findings will lend invaluable knowledge to stakeholders. [ABSTRACT FROM AUTHOR]

The rapid growth of suspension bridges' span makes vortex-induced vibration (VIV) appears more and more frequently, and once it occurs the closure of the bridge results in considerable economic losses. Investigating the dynamic behavior of the bridge experiencing VIV and the vehicles running on it is thus imperative for providing a reliable guidance for the managers to make operation decisions. Nevertheless, most of the existing studies focus on VIV of bridges subjected to smooth winds, but a certain level of turbulence always exists in reality. The effects of turbulence on vortex-induced dynamic response of the bridge and ride comfort of the vehicles are not clear. This study thus develops a coupled vortex-vehicle-bridge system applicable to the multi-mode lock-in regions of a twin-box deck subjected to both vortex-induced forces and buffeting forces in a turbulent flow. The system is then applied to a real long suspension bridge with three types of vehicles subjected to either smooth or turbulent winds. The results from the case study show that the increasing turbulence mitigates vortex-induced responses of both the bridge and the vehicles and reasonably improves the vehicles' ride comfort. However, the buffeting forces induced by turbulent wind component should not be ignored when turbulence intensity becomes high. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to investigate the equivalent relationship between accelerated corrosion tests and real environmental spectrum of suspenders in long-span suspension bridge considering multiple factors action. Design/methodology/approach: Based on Faraday's law, corrosion current was used as a measure of metal corrosion, and the equivalent conversion relationship between laboratory environment and real service environment was established. The equivalent conversion method for bridge structural steel had been determined under different temperature, humidity, pH value and NaCl concentration conditions. The compilation of environmental spectra for large span bridges considering multiple factors and the principle of equivalent conversion have been proposed. Findings: Environmental factors, including temperature, humidity, pH value and NaCl concentration, have significant impact on the corrosion degree of suspension steel wires, and only considering these two factors for equivalent conversion cannot accurately reflect the true service environment of the bridge. The 33.8-h salt spray accelerated corrosion test using the standard conditions can be equivalent to one year of suspenders corrosion in a real service environment. Originality/value: The equivalent accelerated corrosion method for steel wires proposed in this study can effectively predict the corrosion degree of the suspenders, which has been verified to be correct and can provide theoretical guidance for the development of corrosion test plans for steel wires and engineering technical basis for anti-corrosion control and calendar life research of suspension bridge suspenders. [ABSTRACT FROM AUTHOR]

Structural displacement monitoring is one of the major tasks of structural health monitoring and it is a significant challenge for research and engineering practices relating to large-scale civil structures. While computer vision-based structural monitoring has gained traction, current practices largely focus on laboratory experiments, small-scale structures, or close-range applications. This paper demonstrates its applications on three landmark long-span suspension bridges in Turkey: the First Bosphorus Bridge, the Second Bosphorus Bridge, and the Osman Gazi Bridge, among the longest landmark bridges in the world, with main spans of 1074 m, 1090 m, and 1550 m, respectively. The presented studies achieved non-contact displacement monitoring from a distance of 600 m, 755 m, and 1350 m for the respective bridges. The presented concepts, analysis, and results provide an overview of long-span bridge monitoring using computer vision-based monitoring. The results are assessed with conventional monitoring approaches and finite element analysis based on observed traffic conditions. Both displacements and dynamic frequencies align well with these conventional techniques and finite element analyses. This study also highlights the challenges of computer vision-based structural monitoring of long-span bridges and presents considerations such as the encountered adverse environmental factors, target and algorithm selection, and potential directions of future studies. [ABSTRACT FROM AUTHOR]

This paper proposes a vision monitoring system for multipoint deflection of a large‐span bridge that can well compensate the camera motion–induced errors. The camera network system (CNS) consists of a series of dual‐camera stations that are linked with the cooperative markers. The infrared illumination supplement device is integrated in the camera station and the regular double‐sided prism is selected as the cooperative marker to realize 24‐h continuous monitoring. The feasibility and efficiency of CNS are verified by conducting a field test inside the steel box girders of a suspension bridge with a length of 1038 m. The results show that the proposed camera networking method can well solve the problem of the large‐scale high‐precision monitoring under unstable measuring platform. For the kilometer‐level flexible bridge, CNS can meet submillimeter precision in quasi‐static measurement, and can also provide deflection data similar to the conventional robotic total station and connecting pipe system in long‐term monitoring. The geometric alignment of large‐span bridges with dense multimeasuring points can be automatically monitored and recorded by CNS. The observed deflections of the studied suspension bridge are dominated with the vehicle load and wind load in the short term and are correlated with the temperature change in the long term. The proposed CNS can provide a new option for the bridge deflection monitoring and provide new parameters for bridge safety evaluation. [ABSTRACT FROM AUTHOR]

Using structural health monitoring (SHM) techniques, Brillouin optical time-domain analysis (BOTDA) sensors can be mounted along the main box girder entire length of a long-span suspension bridge, and the high-density measured points strain monitoring data can be obtained. However, insufficient research has been conducted on accurately diagnosing the structural condition of a long-span suspension bridge by using the abovementioned strain monitoring data. To address this issue, a cross-diagnosis method that determines the structural condition of long-span suspension bridges based on the distributed strain data spatial window is proposed in this study. First, the distributed strain data spatial window based on a long-span suspension bridge structural symmetry is defined. Then, a method that divides the distributed strain data of the bridge main box girder into different spatial windows using mutual information between the strain data from BOTDA sensors is presented. The special symmetry of the environmental temperature effect on the spatial window structural performance is carried out to separate the temperature effect from the strain monitoring data; this process can effectively reduce the interference of ambient temperature on the results of the structural condition diagnosis. Second, using a convolutional neural network, a diagnosis index of the structural condition is generated by using the correlation model between the high-density measured points and the distributed strain data belonging to one whole spatial window. Regarding one spatial window, the proposed diagnosis index can effectively reflect the variation in the distributed strain correlation model caused by the damaged condition of the long-span suspension bridge to achieve cross-diagnosis of the structural condition of the bridge. Finally, the effectiveness of the proposed method is demonstrated through a numerical simulation using strain monitoring data obtained from a real bridge. [ABSTRACT FROM AUTHOR]

The nonlinear characteristics of bridge aerodynamics preclude a closed‐form solution of limit‐cycle oscillation (LCO) amplitude and frequency in the post‐flutter stage. To address this issue, a long short‐term memory (LSTM) network is utilized as the reduced‐order modeling of nonlinear aeroelastic forces on the bridge deck section, and it is repeatedly employed to generate force inputs at spanwise nodes of a three‐dimensional (3D) finite element model (FEM) of the long‐span bridge (using spatial beam elements). All LSTM networks are dynamically coupled through FEM, and the 3D nonlinear flutter response is accordingly obtained. To improve the simulation accuracy and reduce the required training data of the standard LSTM network, both general knowledge (motivated by the gating mechanism and mathematical models for information processing) and domain knowledge (resulting from the basic understanding of bridge aerodynamics) are leveraged to, respectively, customize the LSTM cell and network architecture. In addition, a fast‐training algorithm effectively combining the linear convergence of stochastic gradient descent and superlinear convergence of modified Broyden–Fletcher–Goldfarb–Shanno is developed to improve the training efficiency of the obtained knowledge‐enhanced LSTM network. To further advance the computational efficiency of the coupled LSTM‐FEM nonlinear flutter analysis, the convolution‐based numerical integration is adopted in the finite element modeling of long‐span bridge dynamics. A case study of a long‐span suspension bridge under strong winds demonstrates the proposed 3D nonlinear flutter analysis presents high simulation efficiency and accuracy and can be utilized to effectively obtain the nonlinear LCO characteristics in a wide range of post‐flutter wind speeds. [ABSTRACT FROM AUTHOR]

The caisson-bored pile composite anchorage (CBPCA) foundation, as a new form of gravity-type foundation for long-span suspension bridges, has been recently proposed and numerically studied by the authors. In this paper, the bearing performance of the CBPCA foundation under different working loads is further investigated by performing a series of 1-g model tests. Taking into consideration the traditional caisson foundation (CA foundation) and the CBPCA foundations with different pile diameters (i.e., d = 20 mm, 30 mm), pile spacing (i.e., S = 3.5 d, 4.5 d, 5.5 d) and pile lengths (i.e., l = 270 mm, 360 mm, 450 mm), seven working conditions were considered. The horizontal displacement, vertical displacement, earth pressures on the front surface and the bottom of caisson, as well as the induced bending moments in the piles, were analyzed to illustrate the bearing capacity of the CBPCA foundation. The test results show that compared to traditional CA foundation, the CBPCA foundation is feasible for long-span suspension bridges considering its smaller displacements and inclination angles under certain circumstances (i.e., pile diameter d ≥ 20 mm, pile length l ≥ 450 mm, and pile spacing S ≤ 4.5 d). Moreover, the bending moments in piles of different locations were also discussed, and the corner pile and edge pile located under the front caisson subject to the greatest bending moment. [ABSTRACT FROM AUTHOR]

Different from the condition rating system for bridges, the criticality and vulnerability rating system for long-span suspension bridges is used to determine the time intervals for routine general inspection of key structural components of the bridge. In consideration of uncertainties involved in the current rating system for long-span suspension bridges, this study presents a cloud-based analytic hierarchical process (C-AHP) rating system to determine inspection intervals. A three-level hierarchical structure is first introduced in terms of criticality and vulnerability, and the relative weights for the hierarchical structure are determined by AHP. The Gaussian cloud model is then introduced to the AHP rating system to form a C-AHP rating system for long-span suspension bridges. Finally, the feasibility and effectiveness of the proposed C-AHP rating system are calibrated by using the Tsing Ma Bridge in Hong Kong as a case study. The case study results show that the proposed C-AHP rating system could take into consideration not only fuzziness but also randomness in the AHP rating system and provide stricter time intervals than the F-AHP rating system for routine general inspection of long-span suspension bridges. [ABSTRACT FROM AUTHOR]

To mitigate longitudinal vibration of long-span railway suspension bridges, a Combined Viscous-Steel Damping System (CVSDS) is put forward in this paper. In the CVSDS, the viscous damper is expected to work under train braking and frequent earthquakes, while the steel damper can resist rare earthquakes. Moreover, a fuse-lock device is proposed to work as the switch between the aforementioned two dampers. The working mechanism of the CVSDS was introduced. The locking function was verified by static test, and the vibration reduction efficiency of the proposed system was validated through numerical method. The results show that the combined system is efficient. [ABSTRACT FROM AUTHOR]

The cables of the long-span bridge are usually featured as ultra-low frequency, hence making the acceleration unable to accurately capture the information, e.g. damping ratios, for assessing the cable state assessment and mitigating the excessive structural vibration. The displacement was approved to be more sensitive to the low-frequency vibration than the acceleration. However, there is still a lack of effective method to accurately monitor the long-term displacements of bridge cables using reference-free methods. To address this issue, this paper develops a novel acceleration-based approach for monitoring the long-term displacements of the cables of long-span bridges. In the monitoring scheme, recursive least squares method is utilized to conduct baseline correction in the time domain integration of acceleration. An adaptive band-pass filtering method considering cable vibration characteristics is used to eliminate noise, thus avoiding the difficulty of selecting the cut-off frequency by experience in traditional methods. A numerical test of an analytical cable model and a field experiment of the hanger of a full-scale suspension bridge are applied to the applicability and robustness of the developed method. Result shows that adaptive band-pass filter considering the vibration characteristics is suitable for estimating the displacements of the cables. The estimated displacements using the developed method agree well with the background truth in both time and frequency domains. [ABSTRACT FROM AUTHOR]

Flexible suspension bridges are susceptible to aerodynamic instability phenomena. In this paper, the torsional divergence is addressed in terms of underlying mechanism, 3D and turbulence effects. A 3D generalized analytical model is first established by reasonable simplification of the model. Comparisons among results from different models are performed. The mechanisms of symmetric and asymmetric torsional divergence are explored. Finally, the 3D and turbulence effects are investigated. The results show that the proposed 3D generalized model is feasible for estimating the critical wind speed of asymmetric torsional divergence, and its computational accuracy is higher than the method provided by the code. The effects of turbulence on torsional divergence are multifaceted: the buffeting response due to wind fluctuations can significantly reduce the aerostatic stability of the bridge, resulting in a much lower critical wind speed than that in a smooth flow; the threshold of divergence is ambiguous and the instability is intermittent; further, the left and right quarter span sections largely vibrate in opposite directions during asymmetric torsional divergence. [ABSTRACT FROM AUTHOR]

Historically, monitoring possible deformations in suspension bridges has been a crucial issue for structural engineers. Therefore, to understand and calibrate models of the "load-structure-response", it is essential to implement suspension bridge monitoring programs. In this work, due to increasing GNSS technology development, we study the movement of a long-span bridge structure using differenced carrier phases in adjacent epochs. Many measurement errors can be decreased by a single difference between consecutive epochs, especially from receivers operating at 10 Hz. Another advantage is not requiring two receivers to observe simultaneously. In assessing the results obtained, to avoid unexpected large errors, the outlier and cycle-slip exclusion are indispensable. The final goal of this paper is to obtain the relative positioning and associated standard deviations of a stand-alone geodetic receiver. Short-term movements generated by traffic, tidal current, wind, or earthquakes must be recoverable deformations, as evidenced by the vertical displacement graphs obtained through this approach. For comparison studies, three geodetic receivers were positioned on the Assut de l'Or Bridge in València, Spain. The associated standard deviation for the north, east, and vertical positioning values was approximately 0.01 m. [ABSTRACT FROM AUTHOR]

The boundary conditions of the main girder are complicated for suspension bridges. And they have a significant impact on the static and dynamic response of the structure. This study proposes a model updating method based on influence lines considering boundary conditions. First, rotational and translational spring elements are used to simulate the boundary conditions of the main girder. Then, rotational spring stiffness is estimated by constructing a sensitive objective function based on the influence lines. Translational spring stiffness is estimated by constructing a sensitive objective function based on the temperature-induced displacements at both ends of the girder. To improve calculation efficiency, a Gaussian process model is used instead of the finite element model (FEM). The estimation of boundary conditions is expressed as an optimization whose main goal is to iteratively estimate the boundary conditions to minimize the objective functions. After the boundary conditions are determined, the influence lines-based model updating is carried out by using the adaptive metamodel global optimization method. To validate the proposed method, a long-span suspension bridge is taken as a case study. The results show that the boundary conditions of the main girder have been successfully estimated. The accuracy of the model updating is improved after the boundary conditions are considered. The updated FEM with accurate boundary conditions can be a benchmark model for bridge damage identification or condition assessment. [ABSTRACT FROM AUTHOR]

Long‐span bridges are susceptible to vortex‐induced vibration (VIV), which affects the serviceability and safety of bridges when the vibration amplitude is too large and lasts for a long time. Traditional contact‐type sensing technologies (i.e., accelerometers and linear variable differential transformer) are inconvenient and dangerous to be installed on long‐span bridges for monitoring VIV events. To address this limitation, this article focuses on the VIV measurement of a long‐span suspension bridge through noncontact sensing strategies. The contribution of this article lies in (1) noncontact sensing technologies including microwave radar, optical camera and video equipment were employed to measure multiple‐point displacements of the studied bridge under VIV events; (2) dynamic properties of the bridge (i.e., natural frequency, damping ratio, mode shapes) and characteristics of the VIV event (i.e., single‐mode vibration and dominant vibration mode switch) were identified by analyzing monitoring data; (3) an early warning framework for VIV event of long‐span suspension bridges was proposed based on monitored dynamic responses and wind fields; specifically, two indicators, the dominant vibration frequency and the similarity between bridge shape and vibration mode shape, were proposed to identify the VIV event, and then the root mean square (RMS) of measured response was further calculated to determine whether there is a need to trigger the warning system or not. The proposed noncontact VIV measurement strategy has the advantage of rapid measurement of vibration magnitude, rapid identification of dynamic properties of the studied bridge and characteristics of the VIV event, which are helpful for the government and bridge owners to make decisions on vibration mitigation measures and to avoid safety issues. [ABSTRACT FROM AUTHOR]

This paper reviews various active control measures used for controlling the wind-induced vibration, which is a problem of great concern for long-span suspension bridges. Firstly, a brief discussion of passive control measures and their limitations is presented. Then, the development of active aerodynamic control and active mechanical control is comprehensively reviewed to present the characteristics and limitations of numerous control devices with emphasis on the control surfaces adopted for active aerodynamic control. Particularly, the existing challenges and suggestions for future studies are proposed for various countermeasures, especially for the control surfaces used in active control. It is expected that the information provided in this article will facilitate further research in the area of vibration control for long-span suspension bridges under various wind conditions. [ABSTRACT FROM AUTHOR]

The local wind environment above the bridge deck affects the aerodynamic characteristics of vehicles, thus affecting the driving safety of the bridge deck. Influenced by the mountain topography and the bridge deck's ancillary facilities, the local wind environment above the bridge deck is complex and changeable, and its impact on the bridge deck traffic can not be ignored. In order to accurately evaluate the local wind field parameters, a monitoring system of the local wind environment is developed. Utilizing the monitoring system, wind parameters above the approach deck of a long-span suspension bridge in a mountain area are measured. The relationship of wind characteristics between the incoming flow and the wind above the bridge deck is investigated. Results show the significant difference between the local wind environment above the bridge deck and the incoming flow's characteristics; the wind profile above the bridge deck does not follow the exponential distribution; the equivalent height of the wind load on the vehicle is higher than the vehicle's gravity centre. This study is relevant for studying the local wind environment, driving safety, and serviceability of long-span bridges in mountainous areas. [ABSTRACT FROM AUTHOR]

Based on the aerostatic force model under skew wind, considering the nonlinear and three-dimensional effects of aerostatic forces and also structural geometric nonlinearity, a method of three-dimensional nonlinear aerostatic stability analysis under skew wind is presented, and the corresponding computational procedure (SNAA-SW) is developed. By taking a suspension bridge- the Runyang suspension bridge over the Yangtze River as example, 3D nonlinear aerostatic stability analysis of the bridge under skew wind is conducted, and the skew wind effect on the aerostatic stability of long-span suspension bridges is ascertained. The results show that the skew wind effect does not change the aerostatic instability mode of suspension bridges, which shows a spatial bending-torsion coupled instability mode as the same as normal wind case. The skew wind has positive and negative effects on the aerostatic stability of suspension bridge under different wind attack angles, and the evolutions of critical wind speed of aerostatic instability with wind yaw angle are completely different from the cosine rule as proposed by the skew wind decomposition method, for most cases, the lowest critical wind speed of aerostatic instability occurs under skew wind. With the increase of wind yaw angle, the skew wind effect on the critical wind speed of aerostatic instability becomes more prominent, and the influence is between −10.7% and 8.1%. Therefore, the skew wind effect needs to be accurately considered in the aerostatic stability analysis of long-span suspension bridges in particular at large wind yaw angles. [ABSTRACT FROM AUTHOR]

Summary: In long‐span suspension bridges, fatigue is a significant concern for steel members as they are continuously under multiple effects such as wind, temperature, and traffic loads. Therefore, it is important to quantify the fatigue damage at critical details for effective maintenance countermeasures. This paper proposes an ensemble machine‐learning‐based method with physical interpretation, which predicts fatigue damage with monitored parameters of temperature, wind, train, and roadway loads. Interpretation of the machine learning model is achieved regarding the different contributions of the monitored parameters to the fatigue damage. Datasets from the structural health monitoring (SHM) system of a long‐span rail‐road suspension bridge are utilized to verify the proposed method. They are divided into 80% of training datasets and 20% of testing datasets. The ensemble machine learning model is established with Gradient Boosting Regression Tree (GBRT), and the fatigue damage for top chords on the upstream and downstream sides is predicted. The results are compared with other state‐of‐the‐art machine learning algorithms, namely, artificial neural network (ANN), support vector machine (SVM), decision tree (DT), and random forest (RF). It is found that GBRT demonstrates the highest accuracy for fatigue damage prediction with R2 of 0.9016 and 0.9180, respectively. Furthermore, interpretation of the results is carried out with feature importance estimates (FIE) and individual conditional expectation (ICE). FIE results indicate that the train load has the most significant influence on fatigue damage of the suspension bridge, and ICE results can provide insights on better maintenance plans to avoid severe fatigue damage. [ABSTRACT FROM AUTHOR]

Structural health monitoring (SHM) systems have been widely applied in long-span bridges and a large amount of SHM data is continually collected. The harsh environment of sensors installed at structures causes multiple types of anomalies such as outlier, minor, missing, trend, drift, and break in the SHM data, which seriously hinders the further analysis of SHM data. In order to achieve anomaly detection from a large amount of SHM data, this paper proposes a long-short term memory (LSTM) network-based anomaly detection method. Firstly, the proposed method reduces the workload for preparing training sets. Secondly, the purpose of real-time anomaly detection can be met. Thirdly, the problem of high alarm rate can be avoided by utilizing double thresholds. To validate the effectiveness of the proposed method, a case study of finite element model simulation is firstly introduced, which illustrates the detailed implementation process. Finally, acceleration data from the SHM system of a long-span suspension bridge located in Jiangyin, China is employed. The results show that the proposed method can detect anomaly with high accuracy and identify abnormal accidents such as a ship collision quickly. [ABSTRACT FROM AUTHOR]

Bridges are a popular topic in this journal, because they are a very visual display of static and dynamic physical principles. In this paper, we provide an intuitive derivation of the equations associated with suspension bridge cables and load-bearing arches, which is of pedagogical interest in illustrating the consequences of Newton's laws for familiar and visually striking objects. [ABSTRACT FROM AUTHOR]

This paper investigates the influence of an explosive load, due to a terrorist action, on the behavior of a long or a suspension bridge, and studies the explosion characteristics and their effect on the bridge. The purpose of this paper is not to investigate the consequences of the loss of structural elements. The main subject is to determine the critical magnitudes of the explosions that a bridge could suffer, to indicate the possible points where the explosives can be placed, the combination of positions and also the simultaneous action or the action with time hysteresis of the explosions. The theoretical formulation is based on a continuum approach which has been used in literature to analyze such long or suspension bridges. The analysis is carried out with the modal superposition method, and the resulting differential equations are solved using the second Duhamel's integral. [ABSTRACT FROM AUTHOR]

The kilometer scale rail-road suspension bridge is subjected to environmental thermal actions, causing significant temperature-induced effects on the rail track alignment and the rail-track vertical irregularity exceeding the threshold during operation. This paper investigates the temperature distribution and associated responses of a rail-road suspension bridge through a combination of structural health monitoring (SHM), on-site tests, and numerical analysis. Based on the SHM, a strong linear relationship between the ambient temperature and the temperature-induced effects on the girder was observed. It is concluded that the long-term temperature-induced effects can cause an overall temperature variation in the structure with the main factor being the girder deflection. Then, the long-term temperature-induced deflection of the mid-span can reach up to 30 mm/°C. The on-site test results also indicate that the absolute elevation of the rail track has good followability relative to the girder, and dramatic temperature fluctuations can significantly influence rail-track irregularity. Based on measurements of the ambient temperatures and the adoption of a solar radiation model, the time-dependent temperature distribution and the temperature-induced deflections were calculated through a coupled thermo-mechanical method. Moreover, the dramatical variations of ambient temperature were then put into the numerical model to obtain the deflections of girder and chord offset values of the rail track. Results show that the dramatic variations of ambient temperature have exerted significant impacts on the rail-track irregularity on the bridge. These findings can provide an improved recommendation for maintaining rail-track operating performance during operation. • The long-term temperature-induced effects is the main factor for the deflection of the girder. • The absolute elevation of the rail track has good followability relative to the girder. • The ambient temperatures dramatical variation have a impact on the rail track irregularity on suspension bridges. [ABSTRACT FROM AUTHOR]

The presence of rigid central clamps (RCCs) minimises the damage potential of short suspenders and expansion joints in in-service long-span suspension bridges. The study presented in this paper evaluated the impact of the presence of RCCs on the longitudinal deformation of a long-span suspension bridge under live load with vehicle braking and random traffic flow excitations. Two finite element (FE) models of the bridge were developed – one with RCCs and the other with a traditional suspender (TS) at mid-span. The impact of RCCs and TS on the structural system response was evaluated by comparing the dynamic characteristics of the models. The exceeding probabilities of longitudinal deformation under different traffic flow levels during the design reference period were obtained. The simulation results show that the RCCs are capable of reducing the longitudinal deformation by 35% to 45%. The unfavourable exceeding probabilities of longitudinal deformation over the design threshold decreased from 1.0 to 0.0002, showing that the RCCs could be an effective measure to enhance the service life of the shortest suspender and expansion joints of long-span suspension bridges. [ABSTRACT FROM AUTHOR]

Although long-span suspension bridges play a vital role in the transportation infrastructure, their resistance to disproportionate collapse resulting from locally induced damage has not yet been adequately investigated. In this study, computational simulation is used to shed light on how a prototype long-span suspension bridge responds to sudden loss of suspenders. Several scenarios were considered, with a focus on the total number of suspenders lost, their locations, and mode of removal. An increasing number of suspenders were removed either sequentially (i.e., one at a time) or simultaneously (i.e., multiple suspenders removed at the same time) until progressive collapse of the bridge was triggered. The simulation results showed that the bridge exhibited increasing levels of damage as the number of removed suspenders increased, and that the most critical location for suspender removal was near the middle of the bridge. It is shown that the sequential loss of a group of suspenders led to bridge responses that are almost identical with the simultaneous loss of the same group of suspenders. It is also argued that suspension bridges like the prototype system under consideration are highly robust. [ABSTRACT FROM AUTHOR]

Summary: Vortex‐induced vibrations (VIVs) are a serious problem in suspension bridges and other long‐span bridges during their service periods. It can cause excessive amplitudes of the structure under low wind speeds, not only affecting driving comfort and safety but also increasing the risk of fatigue failure. Previous research on the identification and evaluation of bridge VIV events during their service periods was based on offline batch processing and analyses of monitoring data, which cannot realize real‐time perception, calculation, and early warning online. This paper proposes an intelligent monitoring and warning method for VIVs of suspension bridges based on the recursive Hilbert transform according to the vibration characteristics of single‐mode sinusoidal‐like vibrations of engineering structures during VIVs. First, the real‐time acceleration integral algorithm is used to realize the real‐time calculation from the acceleration monitoring data to the dynamic displacement of the stiffening beam. Then, the recursive Hilbert transform is used to obtain real‐time analytical signals of the structural displacement during VIVs. Based on its single‐mode near‐circular trajectory characteristic, the VIV index and the real‐time analysis method are proposed to characterize the development trend of VIV events. This online extraction algorithm can realize the first warning and whole‐process tracking and perception of VIV events. Furthermore, this paper presents a real‐time online identification method for key motion parameters such as the instantaneous frequency, phase, and amplitude of the structure during VIV, laying the foundation for the real‐time monitoring of the entire VIV process and further evaluation and management decision making. The accuracy, reliability, and engineering feasibility of the proposed method are verified by performing numerical simulations and monitoring VIV data of a real bridge. [ABSTRACT FROM AUTHOR]

Hangers are primary load-carrying members in suspension bridges, connecting the girder to the main cable, and in case of fire accident, the bridge safety may be affected due to the deteriorated performance of hangers. In this study, a number of 160-wire specimens were tested to obtain their strengths after being heated to various temperatures and cooled down. Then the Weibull distribution was used to describe the randomness of the results. Thereafter, a statistical model was established to estimate the capacity of postfire hanger consisting of parallel steel wires. Subsequently, static tensile tests were carried out on three steel wire bundles, with each consisting of 19 parallel steel wires, to verify the model, where two bundles were heated. Based on the predicted residual capacities and field measured hanger forces, the reliabilities of postfire hangers of the Runyang Suspension Bridge were assessed. It was found that the tensile strength of hangers degraded after exposure to high temperatures, and their residual strength and reliability were highly dependent on the highest exposure temperature. Finally, the repair and replacement of the four postfire hangers on the bridge was conducted according to the assessment. [ABSTRACT FROM AUTHOR]

This paper investigates the track–bridge interactions of the Wufengshan Yangtze Bridge, the longest high-speed railway suspension bridge in China. A finite element model of the track and bridge is built using the commercial software ANSYS. The longitudinal additional forces of the track under a single effect and combination effects of temperature rising load, bending load, and braking load are calculated. The numerical results show that strong additional forces appear in the continuously welded rail of the Wufengshan Yangtze Bridge. Temperature effect is the dominant factor for the residual internal forces. The maximum tensile stress is 115.5 MPa and the extreme compressive stress reaches 329.9 MPa. Rail expansion joints are needed for this long-span suspension bridge. [ABSTRACT FROM AUTHOR]

As flexible structures, suspension bridges usually undergo significant deformation under live load when carrying rail traffic, jeopardizing the safety of passing trains. In engineering practice, suspension bridges with short extended spans have been applied to reduce the beam-end rotation angle under live load. However, the extended span layout is still determined empirically, and optimizing the span layout of such bridges to reduce maximum deformation under live load requires further investigation. This study proposes an analytical method for solving the maximum deformation responses of suspension bridges with extended spans under live load based on deflection theory and the extreme value analysis method. The proposed method can accurately solve the deformation responses of suspension bridges with extended spans caused by live load. It also allows one to analyze the most unfavorable live load distribution and the maximum deformation under live load, avoiding the redundant search process of the finite element method. Furthermore, the proposed method is applied to analyze the influence of the extended span layout on the maximum deformation responses under live load. The results show that adequately increasing the length of the first extended span and decreasing the length of the second extended span is beneficial to reduce the maximum beam-end rotation angle and the maximum curvature of the main beam. • The method can effectively solve the deformation responses in extended-spans suspension bridges under specific live load. • The method can determine the most unfavorable live load distribution and the maximum deformation responses under live load. • An in-depth analysis is conducted on how the extended span layout influences maximum deformation responses under live loads. • The method merges the deflection theory with extreme value analysis method, laying the groundwork for structural design. [ABSTRACT FROM AUTHOR]

This study provides a theoretical explanation for a perplexing experimental phenomenon observed frequently in suspension bridge flutter testing, where the flutter critical wind speed (U cr) predicted by two-dimensional (2D) section model testing is higher than that predicted by three-dimensional (3D) full aeroelastic model testing. Six long-span suspension bridges with either a single simply supported span or multiple continuously supported spans were taken as research examples, then the comparative studies on the flutter critical wind speeds, flutter frequencies, modal energy ratios and aerodynamic damping corresponding to 2D and 3D coupled flutter states were carried out to illustrate the flutter modal effects. The research findings indicate that the U cr of 2D testing being higher than that of 3D testing is an inherent characteristic for single-span simply-supported suspension bridges, which can be attributed to the prominent aerodynamic negative damping associated with 2nd-order vertical bending mode. However, due to the aerodynamic positive damping associated with 3rd-order vertical bending mode, the U cr of 2D testing is consistently lower than that of 3D testing in the cases of multi-spans continuously-supported suspension bridges. Additionally, to eliminate unsafe 2D evaluations, a reasonable modal matching principle is recommended for section model testing of single-span simply-supported suspension bridges. • The modal effects of span-layout types on coupled flutter of suspension bridges are clarified. • The reasons for the unsafe 2D flutter evaluations compared to 3D evaluations are revealed. • An improved modal matching suggestion is proposed to eliminate unsafe 2D evaluations. [ABSTRACT FROM AUTHOR]

Fault dislocations may lead to permanent ground rupture displacements, causing significant damage to bridges spanning fault lines. Accurate prediction of permanent displacement due to fault dislocations is essential for assessing the seismic resilience of bridges across faults. This study introduces a highly precise BPNN (Backpropagation Neural Network)-based model for predicting permanent fault rupture displacements at the ground surface. The model produces artificial ground motion, known as 'fault-crossing ground motion', through the integration of low-frequency (LF) and high-frequency (HF) components. The research centers on a 538-m long-span steel truss suspension bridge, employing a comprehensive finite element (FE) model developed with ABAQUS software. The study methodically investigates the impact of permanent fault rupture displacement, fault-crossing effects, and angles on the seismic behavior of the suspension bridge. Research findings indicate that the BPNN-based approach precisely predicts permanent fault rupture displacements due to fault movements. The position of the fault line relative to the bridge, along with the fault-crossing angle and permanent fault rupture displacement, significantly influences the bridge's seismic responses. Notably, as permanent fault rupture displacements increase, the magnitudes of dynamic responses vary considerably. Longitudinally, the amplification of displacement, shear force, and moment in the towers is more pronounced than transversely. Furthermore, a gradual increase in shear force at the tower base poses a significant risk of shear failure. LF components predominantly determine the requirements for internal forces and displacements. This study presents a direct and dependable method for artificially synthesizing ground motion for the seismic analysis of fault-crossing suspension bridges, underscoring the influence of fault-crossing angles and locations on seismic responses. • The model for predicting ground rupture dislocation based on BPNN is proposed. • The proposed model is used to generate fault-crossing ground motion by a superposition method. • The FE model of a suspension bridge is established and parameter analyses are performed. • Recommendations for the seismic design of suspension bridges subjected to faulting are drawn. [ABSTRACT FROM AUTHOR]

Accurate vehicle-induced deflection prediction is critical to bridge structural management and maintenance. However, most existing studies use finite element models and weigh-in-motion (WIM) system to predict the deflection of bridges, the cost of building finite element models is expensive. An accurate and low-cost vehicle-induced deflection prediction framework is developed in this study. In this framework, the calculation method of the spatio-temporal distribution matrix of the vehicle loads is proposed. A fusion attention mechanism bidirectional long short-term memory (ATT-BiLSTM) model is used to predict vehicle-induced deflection. Taking a suspension bridge in China as an example, the accuracy of short- and long-term vehicle-induced deflection prediction is tested, and different deep learning models are used for comparison. The results show that the proposed framework can predict short-term vehicle-induced deflection with a mean absolute error (MAE) of less than 2 mm, which can also accurately predict the extrema of vehicle-induced deflection within a certain time window. The proposed framework is independent of finite element models and lowers the cost of bridge deflection prediction. • An accurate and low-cost vehicle-induced deflection prediction framework is developed in this study. • The calculation method of the spatio-temporal distribution matrix of the vehicle loads is proposed. By using a fusion attention mechanism bidirectional long short-term memory (ATT-BiLSTM) model, the vehicle-induced deflection of the bridge is predicted. • Taking a suspension bridge in China as an example, the accuracy of short- and long-term vehicle-induced deflection prediction is investigated. [ABSTRACT FROM AUTHOR]

The functionality of expansion joints, bearings, and dampers in suspension bridges is directly impacted by the longitudinal movement of the girder ends. The complex longitudinal resistance of the girder significantly influences this movement in railway suspension bridges. This study develops an analytical model of a railway suspension bridge using measured displacement. The model encompasses various longitudinal nonlinear resistances, including girder-rail interaction, bearing friction, and viscous dampers, enabling a detailed analysis of longitudinal motion characteristics and deformation patterns of girder ends under train loads. This study investigates the effects of various longitudinal resistances on the movement of the girder and stress within the connecting components. A novel central buckle design is proposed to reduce the stress amplitude of the central buckles in railway suspension bridges. Results show that the innovative analysis model can accurately assess the longitudinal movement of girder ends in railway suspension bridges, aligning closely with the measured. The girder displays minimal longitudinal movement under train loads, owing to the longitudinal nonlinear resistances. However, there is a significant relative longitudinal displacement between the cable and girder in short hangers, leading to a considerable increase in bending stress and vast stress in the central buckle. Consequently, when studying the longitudinal movement in railway suspension bridges, it is critical to comprehensively analyze the longitudinal displacement of girder ends and the stress across various bridge components. The novel central buckle effectively mitigates excessive stress on the central buckle during train passage and simultaneously alleviates bending stresses of the short hangers. The findings of this study offer invaluable theoretical direction and practical engineering insights for the rational design of railway suspension bridges. • Developed a novel analytical model for railway suspension bridges to precise evaluation of girder ends' movement under train loads. • Revealed minimal girder longitudinal movement due to nonlinear resistances, with notable relative displacement in short hangers. • Proposed a new central buckle design to reduce component stress, providing practical engineering insights for bridge design. [ABSTRACT FROM AUTHOR]

Finite element model updating (FEMU) is a frequent method for minimizing the differences between actual and predicted bridge structural behavior. However, static model updating for long-span bridges usually requires load tests to obtain the response under known static loads, which is costly due to long traffic interruptions. To offset this disadvantage, a static FEMU method based on long-term monitoring data is proposed to update the model in real-time by taking stochastic traffic loads with certain statistical characteristics as known static loads. First, the theoretical relationship between stochastic traffic flow statistical characteristics, static response statistical characteristics, and structural stiffness parameters is established. An objective function based on the probability characteristics of the long-term vehicle-induced response is constructed. Then, the FEMU process based on monitoring data is introduced, including the acquisition of the finite element model vehicle-induced response, the extraction of the actual vehicle-induced response based on the monitoring data, the selection of model updating parameters, and the application of the global-local parameter updating optimization method. Finally, the effectiveness of the proposed method is verified by applying numerical examples and real bridge examples to a long-span suspension bridge. It can be concluded that the proposed method can achieve FEMU based on long-term monitoring data, avoiding the inconvenience and large cost caused by load tests. The accuracy and efficiency of the model updating can meet the engineering requirements well through comparison with the result of the traditional load test method. • This paper presents a static finite element model updating method based on the statistical characteristics of long-term monitoring data during normal operation, avoiding the inconvenience and large cost caused by the previous model updating method based on the load test. • The proposed method takes stochastic traffic load with known probability characteristics as known static load, and can realize model updating well by reducing the error of the actual response probability characteristics and finite element model prediction response probability characteristics. • The probabilistic characteristics of long-term vehicle-induced static response are related to structural stiffness parameters and probabilistic characteristics of stochastic traffic flow. When the probabilistic characteristics of stochastic traffic flow are the same, the static response probabilistic characteristics are related to only the structural stiffness parameters. [ABSTRACT FROM AUTHOR]