Vehicle-bridge System Research Articles

Evolution of modal properties in the non-proportionally damped coupled vehicle-bridge system

Evolution of modal properties in the non-proportionally damped coupled vehicle-bridge system

Dynamic Analysis of a Vehicle–Bridge System Under Excitation of Random Road Irregularities

This paper presents a comprehensive study of the dynamic response analysis of vehicle–bridge coupled systems, with detailed simulation methods for the vehicles, bridges, and wheel–road coupling relationships. The simulation of the entire vehicle–bridge coupling system is carried out using the open-source finite element analysis platform OpenSees. A novel three-dimensional wheel–road coupling element is introduced to model the interactions between the wheel and road nodes. This element facilitates precise computation of the dynamic responses within the vehicle–bridge coupled system, including both vehicle and bridge behaviors, along with the interaction forces between the wheels and the bridge surface. The coupling element consists of a wheel node and all potential road nodes on the bridge surface that the wheel may traverse. This configuration preserves the finite element model of the entire vehicle–bridge coupled system throughout the vehicle’s movement, thereby improving the efficiency of numerical simulations of vehicle–road interactions. The study accounts for the impact of random road irregularities on the dynamic responses of both the vehicle and the bridge. These irregularities are treated as input parameters for the wheel–road coupling element rather than being accounted for through the wheel–road interaction constraint equations, thereby improving the convenience of simulating random road irregularities.

An efficient dynamic reliability method for maglev vehicle-bridge systems and its application in random controller parameters analysis

This article presents an efficient method for analyzing the dynamic reliability of maglev vehicle-bridge coupled systems by combining a theoretical model with an adaptive surrogate model and the probability density evolution method (PDEM). First, a refined theoretical model of a maglev vehicle-bridge coupling system is established. Next, an adaptive surrogate model of the equivalent extreme value of the system dynamic response is established by combining an adaptive sampling method with radial basis functions. Finally, the adaptive surrogate model and PDEM are combined to further improve the efficiency of the dynamic reliability analysis. In the numerical example, the theoretical model of the maglev vehicle-guideway system was first validated by comparing with the measured data from the Shanghai high-speed maglev line. Then, by treating the controller parameters as normally distributed random variables, the accuracy and efficiency of the proposed reliability method were verified through comparison with the Monte Carlo method and the one-stage sampling surrogate model. Additionally, the impact of the randomness of each controller parameter and the coefficient of variation of the controller parameters on the system’s dynamic reliability was discussed.

A Fast Multi-Objective Optimization Method for Control Parameters of High-Speed Maglev Vehicle-Bridge System

A fast multi-objective optimization method (FMOOM) is proposed by optimizing control parameters to improve the dynamic performance of a high-speed maglev vehicle–bridge system. This approach involves generating the corresponding dynamic response to the sampled control parameters using a theoretical model of a high-speed maglev vehicle–bridge system, followed by establishing an adaptive surrogate model for the relationship between the control parameters and the dynamic response extrema. In the second step, we combine the adaptive surrogate model and the multi-objective gradient-based optimizer (MOGBO) algorithm to obtain the Pareto solution set satisfying different performance indexes. Additionally, the control parameters are optimized using the fuzzy comprehensive evaluation method. In the numerical simulation, we investigate five maglev trains and ten-span simply supported beam bridges and the theoretical model is verified by comparing the calculations with the measured results. The optimization effect of FMOOM is analyzed under different working conditions. The results show that the adaptive surrogate model has good prediction accuracy based on the radial basis function. Furthermore, the Pareto solution distribution of different schemes using FMOOM is reasonable, and the optimization results are as expected. Compared with the reference scheme, the dynamic response of the maglev vehicle–bridge system is smaller after being subjected to FMOOM optimization, and the six performance indexes are dramatically improved.

Directional effects on the nonlinear response of vehicle-bridge system under correlated wind and waves

Long-span railway sea-crossing bridges are subjected to strong winds and high waves. Due to variations in structural features, including stiffness and size across diverse orientations, the dynamic response of vehicles and bridges can exhibit significant differences under distinct wind and wave directions. Consequently, a novel approach for analyzing bridge and vehicle dynamic performance called the directional wind-wave-vehicle-bridge (DWWVB) model has been developed. To acquire the statistical characterization of the correlation between wind and wave conditions, a three-dimensional joint probability distribution of wind and wave characteristics derived from collected data at the bridge site is established. The wind loads are derived from wind tunnel tests and computational fluid dynamics simulations. The nonlinear wave loads are solved utilizing the hydrodynamic solver ANSYS-AQWA. Based on the finite element bridge model and a 23-degree-of-freedom mass-spring-damper vehicle model, the aerodynamic nonlinearity and initial geometric nonlinearity are considered during the iteration process. The Newmark-β method is employed to solve the dynamic response of bridges and vehicles. The calculation results reveal that the most unfavorable response occurs when the wind direction is 45° and the wave direction is 90°. The directional analysis provides valuable insights for selecting optimal bridge locations and reasonable design environmental parameters.

Time-varying characteristics analysis of bridge under moving vehicle using a modified time-frequency method with limited sensors

Investigating the bridge dynamic characteristics under operational traffic load is critical for bridge health monitoring. As vehicles traverse the bridge, the bridge frequencies present time-varying characteristics owing to the effect of vehicle-bridge dynamic interaction. The recently introduced variational nonlinear chirp mode decomposition (VNCMD) demonstrates significant benefits in identifying structural instantaneous frequencies (IFs) from the measured responses. However, its practical application is limited by the requirement for artificially setting priori parameters (i.e., upper bound of noise level and number of modal components). In this study, a modified VNCMD (MVNCMD) is proposed to overcome this limitation and is employed to identify the IFs of the bridge under moving vehicle using single sensor data. First, by modifying the optimization function, the proposed MVNCMD adopts a novel algorithm framework that eliminates the necessity for presetting the upper bound of noise level. An autoregressive spectrum-based method is then introduced to preset the number of modal components. The proposed MVNCMD is evaluated using a synthetic non-stationary signal, demonstrating its effectiveness in identifying IFs and overcoming the limitations of the original VNCMD. Furthermore, the numerical simulation involving different parameter analysis and laboratory experiments of the coupled vehicle-bridge system are conducted to validate the effectiveness of the proposed method. It is to be shown that the proposed MVNCMD method is capable of identifying the IFs of the bridge under moving vehicle using single sensor data and outperforms other time-frequency methods in terms of identification accuracy, which provides a robust tool for analyzing the time-varying characteristics of the vehicle-bridge interaction system.

Effect of Amplifier on Vehicle Scanning Method Concerning Pitching Responses

A vehicle–bridge system with a tunable amplifier is proposed to enhance the resolution of frequency identification in the vehicle scanning method (VSM), with a particular interest in the wheel-center spectra to account for pitching responses. Both semi-analytical and finite element formulations are established. The viability of the proposed amplifier–vehicle–bridge system is demonstrated in consideration of bridge types and boundary conditions, damping effect, and pavement irregularity. The major findings include the following: (1) The tunable feature of the amplifier enhances the visibility of higher-order bridge frequencies in its spectrum. (2) The vehicle responses can be removed in the cancellation conditions of the amplifier while the resonance conditions of the amplifier are not affected by vehicle damping under harmonic excitation. (3) The shifted higher-order bridge frequencies are distinctly shown in the wheel-center spectra, indicating the potential use of pitching responses in VSM. (4) The pitching responses have shown that the front-wheel spectrum has a higher resolution than the rear one, as influenced by the driving direction.

An attention-based deep learning method for safety of uncertain vehicle-bridge system with random near fault earthquakes

In this paper, a novel approach, based on the principle of the deep learning method, is proposed to study the stochastic responses of vehicle-bridge system (VBS) subjected to near fault earthquakes (NFEs), which also considers the effects of uncertain parameters. To generate the training data as the input of the proposed deep learning model, the dynamic formulas of the VBS are deduced by Newmark-β method. The proposed analysis model comprises three modules: the CNN module for seismic data feature extraction, the Attention Mechanism module for enhancing the selection for information between time series to improve the accuracy and efficiency of the final prediction, and the Bidirectional Gated Recurrent Unit (BiGRU) for predicting VBS responses. The mapping connection between earthquake action and the system response is established. The BiGRU model is capable of conveying both the excitation's randomness and the system's uncertain parameters. An actual railway cable-stayed bridge subjected to the running railway vehicle and NFEs is utilized to verify the proposed model. The uncertain train weight, bridge damping ratio and the randomness of NFEs are incorporated into the dynamic responses analysis of VBS. As a result, the time-varying responses obtained by the proposed model show significant agreement with results from a validated dynamic VBS framework. The mean value and standard deviation (STD) of the responses obtained by the proposed method are also compared with those by the Monte Carlo method and probability density evolution method. Therefore, both the individual sample of the dynamic response and the statistical data from diverse stochastic responses are chosen to validate the model's accuracy and efficiency in the VBS analysis under NFEs. In addition, the effects of the stochastic characteristics on the system's random vibrations are also explored through the time-histories of statistical data and the probability density function of the absolute maximum of responses.

Influence of wind barrier on aerodynamic characteristics of vehicle on railway–highway combined bridge

Wind barriers with different parameters will change the aerodynamic force of the car on the bridge as well as the stability of the vehicle–bridge system, affecting the vehicle’s safety and comfort. A numerical simulation test was conducted on the bridge-deck with three different air permeability wind barriers under three distinct vehicles of varying sizes and wind directions, with a large-span road–rail asymmetric cable-stayed bridge serving as the engineering foundation. The results show that the roll force of the bridge is proportional to the width of the body and inversely related to the height of the train. The roll force of a vehicle is inversely proportional to its height and width. The type of vehicle and the properties of the bridge deck exert minimal influence on the stability of the bridge when a single vehicle is positioned upstream. When a single vehicle is situated downstream, the tri-component force coefficient of the bridge undergoes significant changes, and the vehicle’s impact on the bridge’s stability becomes more pronounced. When the bridge deck’s ventilation rate is at 50%, the drag coefficient of the bridge deck doubles compared to that of a bare bridge deck, and the wind pressure coefficient of the vehicle surface on the bridge approaches zero. In scenarios involving two vehicles, the shielding effect caused by the vehicles positioned upstream and downstream results in a substantial shift in the aerodynamic forces acting on the two vehicles. This increases the wake width of the bridge and generates a visible vortex in the wake.

Detecting deck damage in concrete box girder bridges using mode shapes constructed from a moving vehicle

Longitudinal cracks at the bottom of the deck are a common form of hidden damage in box girder bridges. Timely detection of deck cracking is critical to ensure the safe operation of box girder bridges. This paper proposes a damage detection method for the deck of box girder bridges using mode shapes constructed from a moving vehicle. One stationary excitation vehicle excites the local bending modes of the deck, and the other vehicle moves along the planned path. The moving vehicle acceleration is collected to construct mode shapes on the driving path. First, generalized beam theory is used to analyze the dynamic behavior of the box girder bridge. The theoretical model of the proposed approach is built to analyze the response of the vehicle-bridge system under shaker excitation, and mapping relationship between the instantaneous amplitude of the vehicle response and the local bending mode of the deck is deduced. The damage indicator based on the mode curvature is used to determine the crack position. Then, a damage detection process for field testing is proposed. Technical details such as excitation parameters, driving path, and narrowband filtering are explained. Finally, factors that affect damage detection, including road roughness, crack length, and crack height are investigated via numerical analysis. Results show that the proposed method can detect medium damage.

Vehicle suspension tuning for bridge-friendliness and influence on coupled vehicle-bridge system frequency

A novel study on the mitigation of bridge response via tuning of vehicle suspension parameters is presented. The coupled vehicle-bridge interaction (VBI) system consists of a quarter car model with a semi-active skyhook suspension. Transmissibility functions of the time-varying VBI system are derived and an extended fixed points principle is applied to obtain optimally tuned values of the vehicle suspension parameters for bridge-friendliness. Performances of both the optimally tuned passive and semi-active suspensions are assessed in terms of the dynamic responses, energetics and interacting force of the VBI system, and are shown to achieve excellent bridge-friendliness. Effects of vehicle suspension parameters on the temporal variation of the coupled bridge frequency are also studied. It is found that the bridge frequency depends strongly on two key physical parameters: vehicle-bridge frequency ratio and vehicle damping ratio. Moreover, variations of the bridge frequency during the vehicle passage are small when the tuned suspensions are used. This new finding may have critical implications in future research in bridge frequency identification using a moving vehicle.

Study on the aerodynamic performances and the operational safety of the vehicle-bridge system under the crosswind

The train operates in special environments such as large bridges and elevated viaducts. The fluctuations of the aerodynamic loads of the high-speed train (HST) are more intense and the possibility of the train derailment and overturning will increase when the train is running on the bridge under the crosswind. Thus, it is of utmost importance to study both the aerodynamic characteristics and the running safety of the train in this situation. This study uses the IDDES method to investigate the aerodynamic characteristics of the train running on the double track bridge in both up and down train directions at different speeds. The differences in the impact of aerodynamic loads on the train’s dynamic response indicators are discussed using the wind-vehicle coupling dynamic response calculation method. Based on these researches, the operational safety of the train under different operating conditions is evaluated from both flow field and dynamic perspectives. The results show that large-scale vortices fall off from the nose of the train and form a larger vortex structure on the leeward side and when the train is running under the crosswind. Its aerodynamic loads fluctuate intensely with time due to the complex wake flow of the train. The dominant frequencies of the unsteady aerodynamic loads are mostly concentrated in the range of 0–5Hz, which is close to the natural modal frequencies of the train. This will lead to the overturning of the train due to vehicle resonance. The derailment coefficient and wheel load reduction rate of the train increase with the speed. Their peak values exceed the limit of 0.8 while the peak duration of the derailment coefficient is less than 0.05s, which means the state of the leeward wheel will recover from a short derailment. However, the duration of derailment increases with speed. Therefore, appropriate measures should be taken to prevent accidents when the train is running at higher speed on the bridge to guarantee the operational safety of the HST.

Impact of Variable Parameters of Expansion Joints and Bearing Supports on the Vehicle-Induced Vibration of Curved Girder Bridges

To study how varying the parameters of expansion joints and bearing supports (E-B parameters) affects the dynamic response of a coupled vehicle–bridge system for curved girder bridges, a dynamic response analysis method for the coupled vehicle–joint (bearing)–bridge system, which takes into account centrifugal forces, was proposed and verified. Subsequently, taking a continuous curved box girder bridge as the prototype, the influence of the E-B parameters on the vehicle-induced dynamic response of the curved girder bridge was explored. The results showed that the dynamic amplification factor (DAF) of the middle beam of the expansion joint (DAF-EJ) and the main girder of the curved bridge (DAF-MG) were both significantly influenced by the E-B parameters. When there were height differences between the middle beam and side beam in the EJ, the DAF-EJ obviously varied, and the DAF-MG increased. When the EJ was damaged, the impact effect of the vehicle on the bearing support increased. The DAF-EJ and DAF-MG both increased with the decrease of the vertical support stiffness of the bearing support. The DAF-EJ was greatly affected by the single-support void at the near-slit end of the lane. The DAF-MGs at the beam end, the 1/4 point and 1/2 point of the first span, and the 1/2 point of the second span, were significantly affected by the single-support void near the measuring point. Compared with the single-support void, the DAF-EJ and DAF-MG more significantly increased under the double-support void. Variation in the height difference of the EJ had a more significant effect on the DAF-EJ and DAF-MG at the beam end, while a vertical stiffness reduction in the bearing support had a more significant effect on the DAF-MG.

A Bayesian Kalman filter algorithm for quantifying estimation uncertainty of track irregularity on bridges with randomness in system parameters

Vehicle on-board monitoring methods use responses of running vehicles to identify track irregularity in real time. But the parameters of both the bridges and the vehicles in such processes may have a non-negligible degree of uncertainty or randomness that will inevitably lead to uncertainty in the track irregularity identification. Quantifying such uncertainty is a great challenge as the vehicle-bridge system (VBS) to be treated with is time-dependent and random. This paper proposes an on-board track irregularity identification algorithm that realizes an inverse random dynamic analysis of the VBS to quantify estimation uncertainty by using a Bayesian Kalman filter technology. The proposed algorithm utilizes sigma point sets to simulate the random parameters and the noises, and is therefore capable of implementing high-fidelity probability density propagation in the nonlinear state transfer and observation functions describing the VBS. The proposed algorithm is validated by numerical examples with various running states and parameter uncertainty levels.

Reliability analysis of the vehicle-bridge system with uncertain parameters by SPEM integrating deep leaning method

The dynamic response of the vehicle-bridge (VB) system was the key problem in the assessment of railway vehicle running safety on bridges, which performed random vibration analysis due to the necessary uncertain parameter arising from either vehicle or bridge structure. Traditional random analysis methods usually required complete time-history calculated data and modal information to obtain the time-dominate statistics for evaluating the reliability of the vehicle running safety, whose computing was difficult and costs too much. This paper proposed a hybrid approach, which integrated the stochastic pseudo excitation method (SPEM) to optimized deep learning method (OLDM), to study the random vibration of uncertain VB system. The dynamic formulas of the uncertain system were produced by the SPEM, depending on which a neural network was established to construct the numerical model consisting of two functional modules, i.e., convolutional neural network (CNN) training with input rail irregularities and Bi-directional long short-term memory (BiLSTM) layer for the VB system response time-history prediction, i.e., CNN-BiLSTM. Due to the characteristics of calculated responses by SPEM, the BiLSTM cell was simulated by introducing the randomness of excitation and uncertain characteristics of parameters of the system into a portion of the cell, enabling the numerical model to convey the uncertainties of the VB system and obtained its stochastic response. For the proposed method, a vehicle running through a simply-supported railway bridge was applied to verify its accuracy and efficiency. According to the computed dynamic responses of VB system by the SPEM, a deep neural network was optimized for the investigated VB dynamic system. The dynamic statistics and reliability of vehicle were conducted through the optimized deep learning model and compared with the results from the conventional VB model by the Monte Carlo Method (MCM). The influence of training epoch, learn rate drop factor and vehicle running speed were investigated to examine the robustness of the deep learning approach.

Dynamic Factor of Suburban Railway Bridge Considering Random Vibration

The focus of this paper is to examine the dynamic factor of the suburban railway by utilizing the random vibration approach. Breaking through the previous methods of relying on huge amounts of measured data, herein, the dynamic factor essentially results from two major parts: the dynamic effect caused by moving train loads and that generated by track irregularity, which has clear physical significance. As the internal excitation of the vehicle–bridge system, track irregularity has strong randomness. Based on the dimension reduction method, the spatial domain power spectral density (PSD) of the track irregularity is transformed into the time-domain PSD. Therefore, the randomness of the random process is reduced by exploiting the constraint form of a random function, and then, the typical samples of the track irregularity considering randomness are constructed. Using the vehicle–bridge coupled vibration model, the standard deviation of the dynamic factor is evaluated accounting for the random track irregularity and 99.7% guarantee rate. Finally, the impact coefficient of the track irregularity on the bridge is methodically obtained. The sensitivity of the standard deviation of the dynamic factor to vehicle speed and bridge frequency is analyzed. The given solution methodology can fully take into account the randomness of the track irregularity. Thereby, it provides the dynamic factor formulas as a reference for the dynamic performance evaluation of suburban railway bridges and possible revision of current design specifications.

Prediction of stochastic responses of vehicle running through the multi-spans bridge based on an optimized method

The dynamic response of a vehicle-bridge system (VBS) has been a key problem in assessments of train-running safety on bridges, ultimately requiring reliability analyses owing to uncertain parameters and random rail irregularities. To improve the computational efficiency and promote the development of a reliability analysis for VBS, this paper proposes a novel approach incorporating a stochastic pseudo-excitation method (SPEM) to optimize a deep learning approach. This approach can more efficiently calculate the dynamic responses of a VBS than the traditional methods. In this study, the dynamic responses of the uncertain system produced by the SPEM were utilized as the training datasets for the deep learning approach. Based on the training datasets, a neural network was established to construct a numerical model consisting of two functional modules: a full convolutional network (FCN) training for the input rail irregularities and gated recurrent unit (GRU) layer for the VBS response prediction, i.e., a SPEM–FCN–GRU (SFG). The GRU cell was simulated by introducing the randomness of the excitation and uncertain parameters of the system into a portion of the cell, thereby enabling the numerical model to convey the randomness of the VBS and to obtain its stochastic response. Addition, long-time-domain samples of the VBS responses were predicted based on the short-time-domain samples. To verify the accuracy and applicability of the proposed method, a train running through a multi-span simply supported railway bridge was investigated. The dynamic responses of the train were analyzed using the training set data and Monte Carlo method (MCM) and the results showed good agreement with each other. Next, by introducing an algorithm combining a convolutional neural network (CNN) with the MCM and GRU (an MCM–CNN–GRU) and comparing it with the method proposed herein, it was verified that the proposed method has better predictions and higher efficiency than those of a traditional neural network. The prediction efficiency of the SFG was analyzed. Based on the shortcomings of the SFG, we proposed an optimized SFG algorithm. The short-time-domain results predicted by the proposed method were input into the training datasets for the deep learning architecture to enhance the number of training data for the prediction of long-time-domain responses. The efficiency and accuracy of the proposed method were verified by comparing them with those of traditional neural networks. As an example, the dynamic responses of a train running through a three-span bridge were computed by the SPEM; these could be adopted to predict those of a train running through a 10-span bridge. Finally, based on the simulated and predicted results, the reliability of the VBS was studied using a first-order reliability method.

Vehicle-bridge dynamic response analysis under copula-coupled wind and wave actions

In the service period, coastal bridges are suffered from wind, wave, and environmental actions, which is a high-risk meteorological environment. To investigate the safety and comfort of vehicle-bridge subjected to the combined wind and wave, Copula-coupled theory is employed to discriminate the statistical correlation from wind speed (Uw) to wave height (Hs). According to the measured data, the combined values in different bivariate return period (BRP) are obtained by the optimal joint distribution (e.g., Clayton Copula). Wind forces on vehicle-bridge system involved buffeting and statical are considered. The wave forces of substructure are derived by Morison and MacCamy-Fuchs equation. A presentative double pylon cable-stayed bridge is employed to explore the effect of wind and wave loads. The vehicle-bridge dynamic response increases as the increase of BRP, especially the lateral displacement of mid-span, which is mainly affected by the first-order transverse bending fundamental frequency of the bridge. All dynamic response indexes meet the standard value.

Analysis of Vehicle–Bridge Coupling System Under the Wind and Waves Combined Condition During Two Trains’ Meeting

Based on the theories of computational fluid dynamics, aerodynamics, bridge dynamics and vehicle dynamics, a sea-crossing cable-stayed bridge with a main span of 532 m is taken as the research object in this study to explore the characteristics of dynamic response when two CRH3 high-speed trains pass each other under the context of wind–wave combination. Firstly, the CFD method is used to construct an aerodynamic calculation model of the vehicle–bridge system under the context of wind–wave combination. Also, the first wind tunnel and wave flume tests are conducted to verify the numerical results of aerodynamic coefficients. Then, the bridge dynamics model and vehicle dynamics model are established by using both the finite element method and the multi-body dynamics method. Finally, a three-dimension vehicle–bridge coupled model is constructed by using the multi-body dynamic software SIMPACK to explore the effects of average wind and regular waves. It is demonstrated that the dynamic characteristics of the vehicle–bridge coupling system under the condition of wind–wave combination are different than under the context of average wind alone. According to the research result, wave effect can affect or make a difference to the aerodynamic characteristics of the vehicle–bridge coupling system. In general, there is only a slight increase in the dynamic responses of bridge structure including mid-span displacement when compared with the condition of average wind alone, including mid-span displacement. Meanwhile, the wind and waves combined condition also has a negative effect on the dynamic responses and running safety of high-speed trains. Especially for the leeward vehicle, the dynamic responses of the leeward train change more abruptly than under the single static wind condition with the increase of running speed.

Analytical Formulations for Amplifier-Enhanced VBI Systems

In the vehicle scanning method, using the amplifier as the tuned mass damper in the vehicle–bridge system has been shown to be able to scan the higher bridge frequencies clearly in the amplifier spectrum recently. To design a test vehicle enhanced by one or two amplifiers in practice, the analytical approach undoubtedly serves as the guideline. For this purpose, this study is aimed at deriving the analytical formulation for one amplifier-enhanced vehicle–bridge system and the semi-analytical formulation for two amplifier-enhanced vehicle–bridge system, while a miniature three-mass vehicle model is adopted. The correctness of the analytical formulations is verified by the finite element formulations through the dynamic responses of the amplifier, vehicle body, and bridge; good agreement is observed for all responses. The amplifier spectra are further provided to show the distinctly scanned bridge frequencies.