Train-bridge Interaction Research Articles

A Machine Learning-Based Algorithm for the Prediction of Eigenfrequencies of Railway Bridges

As part of the development of advanced, data-driven methods for predictive maintenance of railway infrastructure, this paper analyzes and evaluates more realistic predictions of eigenfrequencies of railway bridges, also referred to as natural frequencies, based on a population of already assessed, measured existing bridges using regression techniques. For this purpose, Machine Learning (ML) techniques such as Polynomial Regression (PR), ANN and XGBoost are consistently evaluated and the application of the XGBoost algorithm is identified as the most suitable prediction model for these eigenfrequencies, usable for dynamic train-bridge interactions. The results of the post-processing are incorporated into the safety architecture for bridge verification (risk management). The presented data-based techniques are a steppingstone towards digitalization of structural health monitoring and offer safety and longevity of the railway bridges. Furthermore, the use of these methods can save costs that would be incurred by physical in-situ measurements. The types of bridges analyzed with ML are Filler Beam Bridges (FBE), which outnumber other construction types of bridges in Germany (DB InfraGO AG). This methodology is applicable to any bridge type as long as sufficient data are gathered for training, validation and testing.

Fatigue life prediction for high-speed railway bridges by reconstructing monitoring-based dynamic stress

Abstract Bridge responses that are excited by high-speed trains have the characteristics of high amplitude, high cycle, and large dynamic effects, which greatly affect the fatigue bearing capacity of affected bridges. To achieve reliable analysis of the fatigue performance of high-speed railway bridges, this study developed a bridge fatigue life prediction method based on the reconstruction of the train-induced dynamic stress time history. First, the equations for solving the static stress time history under influence line virtual loading are derived, and then the dynamic stress time history reconstruction method based on two types of dynamic correction factors is proposed. The statistical characteristics of the train loads and dynamic correction factors are fit according to monitoring data, and bridge fatigue life prediction is realized by use of the reliability theory. Finally, the applicability and effectiveness of the proposed method are verified by using a train-bridge interaction model and monitoring data from a long-span high-speed railway bridge. The results show that the proposed method can greatly improve the accuracy of fatigue performance analysis and can effectively predict the fatigue life of high-speed railway bridges under complex loads. These results can provide an important reference for fatigue evaluation of high-speed railway bridges.

Development of corrosion-fatigue analysis method of cable hangers in tied-arch bridges considering train-bridge interaction

This study proposes an integrated corrosion-fatigue analysis method for bridge hangers by combining the dynamic bridge-train interaction analysis for random train arrivals with various speeds and the linear elastic fracture mechanics (LEFM)-based crack propagation analysis considering the corrosion-fatigue effects. Accordingly, a three-stage process, namely, zinc coating corrosion, pit-crack transition, and corrosion-fatigue crack propagation for wires in hangers, was proposed to simulate the total service life. A train-bridge-interaction analysis was conducted on a tied-arch bridge with multiple cable hangers using the vector form intrinsic finite element method, where the stresses in the hangers were generated under high-speed train loads. The pit-crack transition was analyzed based on the pit growth and fatigue growth; whose rates compete to dominate the transition phenomenon. The fatigue crack growth rate was estimated using a LEFM approach considering the equivalent stress ranges and number of stress cycles. The effects of reducing the cable cross-section and updating the internal stress of the multi-layered wires were investigated. The present method was compared with the continuum damage mechanics model for validation. A relatively short remaining corrosion-fatigue life was found in the cables under the train loads, after corrosion of the zinc coating and pit-crack transition in the steel wires were developed.

A meshless computational framework for a modified dynamic system of vehicle coupled with plate structure

In previous simulations of train–bridge interaction systems (TBIS), the supporting system for the train are commonly treated as beam structures, leading to less accurate results, particularly for small-span cases. To address this limitation, a modified vertical TBIS is proposed. In the presented TBIS, the supporting system is considered as a Reissner–Mindlin plate, and the displacement field is described by first-order shear deformation theory (FSDT). To establish the model, radial point interpolation method (RPIM), a meshless method, is employed. Finally, a coupled dynamic equation is established to calculate various responses of the system. Several numerical examples are presented to illustrate the disparities between the system based on plate model and traditional beam model. The results indicate that the beam model yields higher estimates of the mid-span vertical displacement of the bridge, while the peak of the mid-span vertical acceleration is smaller compared to the plate model; additionally, it is observed that the carbody is primarily influenced by rail irregularities. Consequently, the proposed plate model offers distinct advantages over the beam model in providing comprehensive structural response information, thereby offering novel insights into bridge design and analysis. Additionally, this marks the inaugural application of the meshless method in the field of TBIS, which further extends the application scope of meshless methods.

Displacement response waveform restoration of simply supported bridge during train passage using measured acceleration integration based on linear vibration theory

This study proposes a method for restoring the displacement waveform during train passage using the acceleration integration based on linear vibration theory and noise cancellation techniques. This method replaces the low-frequency region affected by noise with a linear theoretical solution; however, this method uses the actual measurement data around the natural frequency, where nonlinearities (such as concrete member cracks and the train–bridge interaction) can be observed. The method identifies only the ratio of single axle weight to modal stiffness. Numerical experiments clarify that the method can estimate the maximum displacement of a bridge from acceleration with an error of approximately 5% or less. Improved prediction accuracy can be achieved using the proposed noise cancellation technique not only in the high-speed range but also into the lower-speed ranges as well. Furthermore, the proposed method is applied to acceleration monitoring data, and results show that the displacement waveform can be restored from the acceleration waveform.

Dynamic analysis of the hangers in high-speed railway arch bridge based on train-bridge interaction simulation and field measurement

Dynamic analysis of the hangers in high-speed railway arch bridge based on train-bridge interaction simulation and field measurement

A novel train–bridge interaction computational framework based on a meshless box girder model

In traditional train–bridge coupled system (TBCS), simply supported box girder bridges are often modeled using Euler beam elements, neglecting their spatial structure. This simplification may yield inaccurate results, impacting the running safety analysis of high-speed railway. To address this issue, a novel train–bridge interaction computational framework based on first-order shear deformation theory (FSDT) and radial point interpolation method (RPIM) for the box girder bridge model is proposed. In this model, the displacement fields of top, bottom, and web plates are represented using FSDT and numerically discretized by RPIM. The traditional TBCS is upgraded by replacing the Euler beam model with the novel model. This is the first time that the framework has been applied to TBCS field. Several numerical examples are presented to highlight the accuracy of this novel model, and illustrate the differences, and advantages of it over the traditional model. The results indicate that the proposed model closely matches the accuracy of the solid element (C3D20) model; it can provide a comprehensive bridge response compared to traditional TBCS, and the latter may underestimate the dynamic response of the structure. The proposed model holds significant potential for the simulation of box structures and widespread application in the field of TBCS.

Phase shift-based resonance assessment for in-service high-speed railway bridges

Resonance in high-speed railway bridges can deteriorate the structural integrity and running safety of a train; thus, the resonant speed needs to be identified. Previous studies have proposed resonant conditions analytically, but their applications to in-service bridges are limited. Free vibration after the passage of a train was utilized to assess resonance, but it could not capture the natural frequency of the coupled system because the train-bridge interaction was neglected. This study proposed a practical framework for quantifying the resonance in a high-speed railway bridge using a phase shift. The static displacement of the railway bridge was numerically reconstructed using the train loading history. Phase angles were extracted by comparing the static and dynamic displacements, which were directly utilized to develop a novel resonance indicator in this study. Numerical simulations and field demonstrations validated the applicability of the proposed method for understanding the resonance behavior of full-scale railway bridges.

Railway Bridge Runability Safety Analysis in a Vessel Collision Event

Bridges connecting islands close to the coast and crossing the sea have been attracting the attention of several researchers working in the field of train–bridge interactions. A runability analysis of a bridge during the event of a ship impact with a pier is one of the most interesting and challenging scenarios to simulate. The objective of the present paper is to study the impact on the running safety of a train crossing a sea bridge as a function of different operational factors, such as the train travelling speed, the type of impacting ship, and the impact force magnitude. Considering train–bridge interactions, a focus is also placed on wheel–rail geometrical contact profiles, considering new and worn wheel–rail profiles. This work is developed considering a representative continuous deck bridge with pier foundations located on the sea bed composed of six spans of 80 m. Time-domain simulations of trains running on the bridge during ship impact events were carried out to quantify the effect of different operating parameters on the train running safety. For this purpose, derailment and unloading coefficients, according to railway standards, were calculated from wheel–rail vertical and lateral contact forces. Maps of the safety coefficients were finally built to assess the combined effect of the impact force magnitude and train speed. The present investigation also showed that new wheel–rail contact geometrical profiles represent the most critical case compared to moderately worn wheel–rail profiles.

Dynamic Amplification of Railway Bridges under Varying Wagon Pass Frequencies

Train configurations give rise to a primary wagon pass forcing frequency and their multiples. When any one of these frequencies coincides with the natural frequency of vibration of the bridge, a resonant response can occur. This condition can amplify the dynamic response of the bridge, leading to increased levels of displacement, stresses and acceleration. Increased stress levels on critical bridge structural elements increases the rate at which fatigue damage accumulates. Increased bridge acceleration levels can affect passenger comfort, noise levels, and can also compromise train safety. For older bridges the effects of fatigue, and being able to predict the remaining life, has become a primary concern for bridge engineers. Better understanding of the sensitivity of fatigue damage to the characteristics of the passing train will lead to more accurate remaining life predictions and can also help to identify optimal train speeds for a given train–bridge configuration. In this paper, a mathematical model which enables the dynamic response of railway bridges to be assessed for different train configurations is presented. The model is based on the well established closed from solution of the Euler–Bernoulli Beam (EBB) model, for a series of moving loads, using the inverse Laplace–Carson transform. In this work the methodology is adapted to allow different train configurations to be easily implemented into the formulation in a generalised form. A generalised equation, which captures the primary wagon pass frequency for any train configuration, is developed and verified by presenting the results of the bridge response in the frequency domain. The model, and the accuracy of the equation for predicting the primary wagon pass frequency, is verified using independently obtained measured field train–bridge response data. The main emphasis of this work is to enable the practicing engineer, railway operators and bridge asset owners, to easily and efficiently make an initial assessment of dynamic amplification, and the optimal train speeds, for a given bridge and train configuration. This is visually presented in this work using a Campbell diagram, which shows dynamic amplification and compares this with those calculated based on the design code, across a range of train speeds. The diagram is able to identify train speeds at which a resonance response can occur, and the wagon pass frequency, or its multiples, which are causing the increased dynamic amplification. The model is implemented in Matlab and demonstrated by analysing a range of short- to medium-single span simply supported plate girder railway bridges, typically found on the UK railway network, using the standard BS-5400 train configurations. The model does not consider the effects of the train mass and suspension system as this would require a non-closed form numerical solution of the problem which is not practical for the purposes of an initial assessment of the train–bridge interaction problem.

A novel 3D train–bridge interaction model for monorail system considering nonlinear wheel-track slipping behavior

Variable speed operation of the train cause easily the wheel-track slipping phenomenon, inducing strong nonlinear dynamic behavior of the suspended monorail train and bridge system (SMTBS), especially under an insufficient wheel-track friction coefficient. To investigate the coupled vibration features of the SMTBS under variable speed conditions, a novel 3D train–bridge interaction model for the monorail system considering nonlinear wheel-track slipping behavior is developed. Firstly, based on the D’Alembert principle, the vibration equations of the vehicle subsystem are derived by adequately considering the nonlinear interactive behavior among the vehicle components. Then, a high-efficiency modeling method for the large-scale bridge subsystem is proposed based on the component mode synthesis (CMS) method. The vehicle and bridge subsystems are coupled with a spatial wheel-track interaction model considering the nonlinear wheel-track sliding behavior. Furtherly, by a comprehensive comparison with the field test data, the effectiveness of the proposed method is verified, as well as the reasonable modal truncation frequencies of the bridge subsystem are determined. On this basis, the dynamics performances of the SMTBS are evaluated under different initial braking speeds and wheel-track interfacial adhesion conditions; besides, the nonlinear wheel-track slipping characteristics and their influences on the vehicle–bridge interaction are also revealed. The analysis results indicate that the proposed model is reliable for investigating the time-varying dynamic features of SMTBS under variable train speeds. Both the axle load transfer phenomenon and longitudinal slip of the driving tire would be easy to appear under the braking condition, which would significantly increase the longitudinal vehicle–bridge dynamic responses. To ensure a good vehicle–bridge dynamics performance, it is suggested that the wheel-track interfacial friction coefficient is larger than 0.35.

A new methodology for pre-camber design of a long-span bridge considering dynamic train load and complex environmental effects

This work aims to develop a reasonable pre-camber design method for long-span cable-stayed bridges by investigating the high-speed train-bridge interaction under complex environmental loads, including ambient temperature, concrete creep, and concrete shrinkage (CCCS). First, an integrated dynamic model of the train-track-cable stayed bridge system (TTCSBS) is established using multibody dynamics and finite element theory and validated through field test. Then, the temperature change features at several key positions on the long-span bridge are investigated using long-term monitoring data. Temperature-induced bridge deformation is calculated by applying the established bridge finite element model (FEM) and compared with test results. CCCS-induced bridge deformation is determined through numerical calculations that consider the bridge's structural and material properties. On this basis, the effects of bridge deformation caused by environmental loads on vehicle-bridge dynamic interaction are investigated in detail, and a new bridge pre-camber design method is proposed to counteract the effects of both environmental and train dynamic loads. Results indicate that the proposed model's simulations align well with field test data. The long-span bridge deformation induced by the environmental loads intensifies the dynamic responses of a running vehicle, particularly the wheel-rail vertical force and car-body vertical vibration. However, it has slight influence on train-induced bridge vibration. The proposed pre-camber design method for long-span bridges, which accounts for long-term environmental load action, effectively ensures good vehicle service performance. The research results could provide useful guidance for the design of long-span bridge systems.

Prediction of extreme response of an innovative HSR integral bridge subjected to crosswind and high-speed train

The randomness of responses in a train-bridge interaction (TBI) system induced by stochastic track irregularity and crosswind has been addressed. However, the extreme value distribution (EVD) and reliability prediction of TBI system are little known. Due to the complexity of TBI system, the prediction approach is critical to the issues of extreme value and reliability evaluation, involving the computational accuracy and efficiency. Thus, the Monto Carlo-based global maximum method, probability density evolution-based virtual time process method (VPM), and average conditional exceeding rate method (ACERM) are considered in this study. The optimal approach for the EVD prediction of bridge buffeting responses and the TBI system with or without the consideration of crosswinds is identified. An innovative 3 × 70 m integral bridge is chosen as the study case, which is an emerging type of bridge structures used in the Chinese high-speed railway lines. Its extreme responses under the single and dual stochastic excitations of track irregularity and wind turbulence are fully investigated in this study. The study results show that the VPM and ACERM are efficient and accurate to evaluate the extreme responses of a TBI system. The ACERM is recommended in assessing the train running safety due to its high computational efficiency and reasonable accuracy. When the crosswind is not a consideration, the high-speed train running safety can be ensured with high probability if the train travels on the integral bridge below the design speed of 350 km/h. However, the failure probability of wheel-rail lateral contact forces reaches 51% if predicted under the mean wind speed of 30 m/s and train speed of 120 km/h. Finally, the advantages of the integral bridge over conventional bridges (e.g., continuous girder bridge) are discussed.

Stochastic response analysis of uncertain train–bridge interaction system by stochastic pseudo excitation method

The stochastic pseudo-excitation method (SPEM) is applied to improve the efficiency of the random vibration analysis of an uncertain train–bridge interaction (TBI) system. This method is combined with the first-order reliability method to handle the reliability analysis of the system. It is characterized by the introduction of a random variable of the amplitude coefficient based on the principle of the PEM, establishing stochastic excitation at each selected frequency point. Unlike the traditional PEM, the calculation results by the SPEM can consider the random characteristics of external loads and also reflect the effect of uncertain parameters. Two comparisons were conducted to verify the accuracy and efficiency of the proposed method for the dynamic analysis of an uncertain TBI system. First, the results calculated using the SPEM were compared with those calculated using the PEM, indicating that the SPEM can calculate the dynamic responses of the TBI system without uncertainties. Second, the stochastic responses of the uncertain TBI system obtained by the SPEM were compared with those obtained by the MCM, which exhibited good agreement and verified the efficiency of the proposed method. Third, the system response of the simplified TBI model was analyzed to determine the parametric sensitivity. Finally, the reliability of the TBI model was studied based on the selected sensitive parameters. These results indicated that the uncertain mass of the train played an essential role in the random vibration of the system. In addition, the safety index of the structure became more accurate with increasing number of samples, and the probabilistic distribution of the dynamic responses of the uncertain TBI system followed a Gaussian distribution extremely well, further verifying the appropriateness of the selected amplitude coefficient in the SPEM.

Resonance reduction for linked train cars moving on multiple simply supported bridges

The dynamic interaction of a moving train over a series of railway bridges with equal spans can result in a coupled vibration problem of wave transmission between two periodic structures. Dual resonance occurs when both systems vibrate in phase and the train travels at a resonant speed. The objectives of this paper are to (1) develop an active pitching resonator (APR) to attenuate resonance waves in a train; (2) study the dispersion relation for pitching motion control of periodically linked train cars; (3) investigate the key parameters that affect the dispersion band gaps of wave attenuation in a train; (4) present an active vibration cancellation method to enhance the control performance of the APR; and (5) demonstrate the effectiveness of using the optimal APRs to reduce resonance of a moving train. Through dispersion analysis, the optimum APR can not only shift the target frequency level away from resonance of a moving train, but also create a wide resonance band gap to reduce wave transmission in the train. Finally, the effectiveness of the optimum APR unit in reducing the resonance and attenuating the waves of a train travelling over multiple-span simple beams is demonstrated by dynamic finite element analysis of the train-bridge interaction.

Dynamic Analysis of Coupled Train and Cracked Bridge Systems Using Multiscale Finite Element Modeling

Cracking frequently encountered in railway bridges can lead to significant changes in bridge dynamic characteristics and further dynamic performance of train–bridge interaction (TBI) system. It is desirable to develop an effective method to understand the dynamic behavior of coupled train and cracked bridge systems. This paper proposes a framework for coupled vibration analysis of train and cracked bridge systems using multiscale finite element modeling. A multiscale bridge model adopting frictional surface–surface contact to characterize nonlinear breathing phenomenon of the crack is incorporated into the three-dimensional coupled TBI model. Subsequently, a multiloop numerical solution strategy is formulated to solve the established dynamic equation of coupled train and cracked bridge systems. The proposed framework is used to analyze the cracked beams presented in the literature, and the obtained and literature data are compared. Moreover, an actual heavy-haul railway bridge is taken as an illustrative example, in which vehicle dynamic response, bridge vibration, and train running safety index are calculated considering various crack types, train speeds, and track conditions. The results show that apart from the bridge displacement and acceleration, the presence of crack can have a large influence on the vehicle acceleration response, derailment factor, and offload factor. Differences larger than ±10% in the maximum dynamic indices associated with the intact and cracked bridges are observed, indicating the necessity of considering the crack damage in train–bridge coupled dynamic analysis.

Vibration Control of the Steel-Concrete Composite Box Girder Bridge with Slip and Shear-Lag Effects by MTMDs under the Train-Bridge Interaction

Steel-concrete composite girder bridges, in essence, are thin-walled structures, the dynamic responses of which will be greater than those of a typical Euler–Bernoulli beam under the train-bridge interaction because of the shear lag and interface slip. Thus, in this study, the dynamic analysis model of a train-composite box girder bridge-multiple tuned mass damper (MTMD) coupling system is proposed, with the derived dynamic equations of this time-varying system. Meanwhile, the program is compiled using the Newmark-β method for the solution, combined with the optimization toolbox to solve the complex optimization design problems of MTMDs involved. Finally, factors affecting the vibration-damping effect are studied, such as the mass ratio of MTMDs, the number of trains, and the slip and shear lag of the composite box girder bridge.

New Contributions for Damping Assessment on Filler-Beam Railway Bridges Framed on In2Track EU Projects

Structural damping is an important characteristic in railway bridges, which affects the performance of the structure, especially for bridges with train speeds higher than 200 km/h. The accurate evaluation of damping must be performed properly to correctly assess the structural performance of the bridge under dynamic loading conditions. The present article introduces an alternative methodology that contributes to the assessment of damping coefficients with application to railway bridges. The methodology is based in the Prony method with an energy-sorting technique for the identification of dominant frequencies of a free vibration signal of a passing train. The numerical validation of the method is based on a sensitivity analysis of the free vibration periods of signals through the evaluation of influence lines of displacement and numerically simulated receptance tests, and in the estimation of the damping coefficient from the free vibration period obtained in a train-bridge interaction dynamic analysis with a known imposed value. Finally, and in the scope of the In2Track2 and In2Track3 projects, the experimental assessment of damping coefficients using this methodology was carried out, considering four filler-beam bridges from the Portuguese Railway Network. The ambient vibration tests allowed the evaluation of the main frequencies and damping in these bridges, and the dynamic tests under railway traffic allowed the definition of the dynamic response of these bridges and subsequent application of the Prony method for two types of trains. The results of this work allow a new update of the database for damping coefficients of filler-beam railway bridges, contributing to future revisions of EN1991-2.

Efficient model-correction-based reliability analysis of uncertain dynamical systems

The scope of this paper is to apply a model-correction-based strategy for efficient reliability analysis of uncertain dynamical systems based on a low-fidelity (LF) model whose outcomes are corrected in a probabilistic sense to represent the more realistic outcomes of a high-fidelity (HF) model. In the model-correction approach utilized, the LF model is calibrated to the HF model close to the so-called most probable point in standard normal space, which allows a more realistic assessment of the considered complex dynamical system. Since only few expensive limit state function evaluations of the HF model are required, an efficient reliability analysis is enabled. In an application example, the LF model describes an existing single-span railway bridge modelled as simply supported Euler–Bernoulli beam subjected to moving single forces representing the axle loads of a moving train. The HF modelling approach accounts for the bridge–train interaction by modelling the passing train as mass-spring-damper system, however increasing the computational effort of the limit state function evaluations. Failure probabilities evaluated with the model-correction approach are contrasted and discussed with failure probabilities of the sophisticated bridge–train interaction model evaluated with the first-order reliability method (FORM). It is demonstrated that the efficiency of the method depends on the correlation between the LF and the HF model. A comparison of the results of FORM and the model-correction-based approach shows that the latter provides reliable failure probability prediction of the HF model while leading to a significant reduction in computational effort.

Train–Track–Bridge Dynamic Interaction on a Bowstring-Arch Railway Bridge: Advanced Modeling and Experimental Validation

This article describes the validation of a 3D dynamic interaction model of the train-track-bridge system on a bowstring-arch railway bridge based on experimental tests. The train, track, and bridge subsystems were modeled on the basis of large-scale and highly complex finite elements models previously calibrated on the basis of experimental modal parameters. The train-bridge dynamic interaction problem, in the vertical direction, was efficiently solved using a dedicated computational application (TBI software). This software resorts to an uncoupled methodology that considers the two subsystems, bridge and train, as two independent structures and uses an iterative procedure to guarantee the compatibility of the forces and displacements at the contact points at each timestep. The bridge subsystem is solved by the mode superposition method, while the train subsystem is solved by a direct integration method. The track irregularities were included in the dynamic problem based on real measurements performed by a track inspection vehicle. A dynamic test under traffic actions allowed measuring the responses in the bridge, track, and vehicles, which were synchronized by GPS systems. The test results demonstrated the occurrence of upward displacements on the deck, which is a characteristic of structures with an arch structural behavior, as well as an alternation of tensile/compressive stresses between the rail and deck due to the deck-track composite effect. Furthermore, the acceleration response of the bridge proved to be significantly influenced by the train operating speed. The validation procedure involved comparing the dynamic responses obtained from the train-bridge interaction model, including track irregularities, and the responses obtained experimentally, through the test under traffic actions. A very good correlation was obtained between numerical and experimental results in terms of accelerations, displacements, and strains. The contributions derived from the parametric excitation of the train, the global/local dynamic behavior of the bridge, and the excitation derived from the track irregularities were decisive to accurately reproduce the complex behavior of the train-track-bridge system.