Vehicle-bridge Interaction Research Articles

Dynamic Intelligent Analysis of Single-Column Pier Bridges Considering Vehicle–Bridge Interaction

With its advantages of low engineering cost, minimal space occupancy, and aesthetically pleasing shape, the single-column pier bridge is frequently utilized in urban viaducts and interchange ramps. Due to structural peculiarities, the bridge subjected to eccentric loading, flexural and torsional interaction, and centrifugal force may undergo tipping accidents. To better comprehend the overturning resistance of the bridge, the vibration governing equation of the bridge (idealized as an orthotropic thin plate with point supports in the domain model) is established considering vehicle–bridge interaction. An approximate dynamic analysis formula is subsequently derived via a hybrid method using the grey wolf optimizer. Compared with the outcomes of finite element analysis, the maximal deviation arising from this derived analytical formula is approximately [Formula: see text]% with the greater discrepancy being observed in scenarios featuring minimal support reactions. Compared with the finite element method, the proposed method in this study has higher computational efficiency with precision. This analytical solution is then utilized in the parametric study to scrutinize the influences of span, road surface roughness, and vehicle velocity on a single-column pier bridge under four vehicles. The analysis findings indicate that the proposed approach is reasonably precise, remarkably efficient, and efficacious.

Compressed sensing with smooth L0 constraints for moving force identification from bridge response measurements

Abstract Compressed sensing (CS), as an emerging information sampling technique, has been successfully applied in the field of moving force identification (MFI). However, existing MFI CS models often fail to obtain the optimal sparse solutions and frequently underestimate the amplitude of local impact forces. To effectively address this issue, a new CS method is proposed for MFI based on smooth L0 norm constraints and bridge response measurements. Firstly, a smooth function is used to approximate the L0 norm, establishing a noise CS reconstruction model for MFI. The introduction of the smoothing function can locally convexify the original MFI problem and enhance the smoothness and differentiability of the objective function, making the optimization problem easier to solve. Subsequently, the Polak–Ribiere–Polyak formula is adopted to point the descent direction of the new objective function, and the sparse solution is iteratively advanced through the conjugate gradient algorithm. Finally, the applicability and feasibility of the proposed method is confirmed by numerical simulations and vehicle–bridge interaction tests, respectively. The results show that the proposed method can accurately identify moving forces from limited measurements of bridge responses. Compared with existing methods, it can provide more precise sparse solutions with higher robustness to measurement noises, and address the issue of underestimating on the amplitude of local impact forces, which is expected to enhance the performance and in-situ applicability of MFI.

Physically Guided Estimation of Vehicle Loading-Induced Low-Frequency Bridge Responses with BP-ANN

The intersectional relationship in bridge health monitoring refers to the mapping function that correlates bridge responses across different locations. This relationship is pivotal for estimating structural responses, which are then instrumental in assessing a bridge’s service status and identifying potential damage. The current research landscape is heavily focused on high-frequency responses, especially those associated with single-mode vibration. When it comes to low-frequency responses triggered by multi-mode vehicle loading, a prevalent strategy is to regard these low-frequency responses as “quasi-static” and subsequently apply time-series prediction techniques to simulate the intersectional relationship. However, these methods are contingent upon data regarding external loading, such as traffic conditions and air temperatures. This necessitates the collection of long-term monitoring data to account for fluctuations in traffic and temperature, a task that can be quite daunting in real-world engineering contexts. To address this challenge, our study shifts the analytical perspective from a static analysis to a dynamic analysis. By delving into the physical features of bridge responses of the vehicle–bridge interaction (VBI) system, we identify that the intersectional relationship should be inherently time-independent. The perceived time lag in quasi-static responses is, in essence, a result of low-frequency vibrations that are aligned with driving force modes. We specifically derive the intersectional relationship for low-frequency bridge responses within the VBI system and determine it to be a time-invariant transfer matrix associated with multiple mode shapes. Drawing on these physical insights, we adopt a time-independent machine learning method, the backpropagation–artificial neural network (BP-ANN), to simulate the intersectional relationship. To train the network, monitoring data from various cross-sections were input, with the responses at a particular section designated as the output. The trained network is now capable of estimating responses even in scenarios where time-related traffic conditions and temperatures deviate from those present in the training data set. To substantiate the time-independent nature of the derived intersectional relationship, finite element models were developed. The proposed method was further validated through the in-field monitoring of a continuous highway bridge. We anticipate that this method will be highly effective in estimating low-frequency responses under a variety of unknown traffic and air temperature conditions, offering significant convenience for practical engineering applications.

Characterization of dynamic coupling induced shifts of frequencies in vehicle-scanning method

A comprehensive strategy combining theory and experiment is proposed to characterize the dynamic coupling induced shifts of vehicle and bridge frequencies through both experimental investigation and numerical validation, in which the effect of vehicle-bridge interaction is theoretically incorporated in the vehicle-scanning method based on the experimental model. It is known that the measurement of bridge frequencies plays an important role in structural health monitoring as the shift of frequency can be served as an indicator of possible damage occurring in a bridge. Nevertheless, the attention has been mainly drawn on the accuracy improvement in developing the vehicle-scanning method so far, with limited discussion of dynamic coupling effect on the frequency shifts. As such, a combined theoretical–experimental approach is presented to show that the influence of vehicle-bridge interaction results in the coupled frequencies of a vehicle-beam system using the vehicle-scanning method, and adopting a heavy lumped test vehicle can lead to the underestimated bridge frequency and overestimated vehicle frequency. As a new finding, the effect of rolling frequency is experimentally observed in the vehicle spectrum for the first time.

Bridge damage location and quantification under the moving vehicle loads based on deep learning multi-objective regression

The extraction of damage-sensitive features based on deep learning for the vibration response caused by vehicle-bridge interaction (VBI) has become a mainstream method in damage identification. However, most studies remain at the stage of qualitative damage assessment, not achieving precise numerical quantification of damage. They also typically involve multiple frequent runs using only a single dedicated vehicle. In this study, utilizing a deep neural network designed for multi-objective regression tasks, a novel method for bridge damage localization and quantification is presented with a multi-objective regressor designed to create a direct mapping between the curve of bridge deflection in time domain and the damage information matrix. The final quantitative damage values are obtained through statistical analysis. The method is evaluated on a simulated data set generated from VBI simulation using various 3D heavy vehicle models. The results demonstrate that this method can accurately locate and quantify damage even with unseen vehicle load conditions, damage scenarios, and measurement noise. The structure and depth affect the effectiveness of extracting damage-sensitive features from time-domain deflection during training. The study shows potential for real-time damage identification under normal operating conditions of real bridges in the rapid development of intelligent transportation systems.

A visual measurement method of vibration displacement of railway bridge bearings based on phase correlation

Currently, contact displacement meters for bearing displacement measurement are prone to fatigue failure. Non-contact visual measurement has become a more effective technique. In this study, an innovative model based on phase correlation is established for the visual measurement of vibration displacement of railway bridge bearings. Firstly, it is suggested to extract the vehicle–bridge interaction time using the sliding window average detection and K-means methods. Secondly, to circumvent the limited measurement accuracy of the existing methods, the phase correlation technique is applied to efficiently calculate the displacement of bearings within a two-dimensional plane. Thirdly, an image sharpness estimation method based on the Tenengrad function is proposed, and then a line segment detector is used for updating the measurement parameters. Through comparative experiments, the measurement error of presented method is within 0.04 mm. In the process of long-term service, the proposed method exhibits no fatigue failure issues, highlighting its good technical advantage.

Utilizing on-board sensing of passing train vehicles for virtual sensing of bridges

This study proposes a bridge response reconstruction approach using exclusively measurements obtained from instrumented train vehicles with known properties. The approach relies on an Augmented Kalman Filter (AKF) technique to estimate contact forces without prior knowledge of rail profile irregularities. Furthermore, the proposed methodology addresses the challenge of accurate vehicle-bridge interaction (VBI) contact force estimation in the presence of rigid-body modes in the train model, by separating rigid-body from flexible modes, and establishing a state-space formulation that incorporates the vehicle dynamics of solely flexible modes. The study examines, by means of numerical simulations, the impact of measurement and model errors, vehicle speed, and rail irregularities on both contact force estimation and bridge response reconstruction. It also investigates sensor configurations that minimize the number of sensors required on the train and shows that acceleration at all wheels and strain of at least one primary suspension per bogie are necessary for accurate force estimation. The results emphasize the significant role of VBI in achieving accurate bridge response reconstruction. The estimated contact forces in combination with a bridge model allow the reconstruction of the bridge response through virtual sensing, providing valuable information on the bridge’s health status.

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

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

Extended Modified Bridge System (EMBS) method for decoupling seismic vehicle‐bridge interaction

AbstractSeismic vehicle‐bridge interaction (SVBI) is the study of vehicle‐bridge interaction (VBI) in the presence of earthquake excitation. SVBI is an interdisciplinary problem of increasing importance to the design and safety of railways. This study deploys a consistent methodology to decouple the vehicle‐bridge system and solve independently the bridge and vehicle subsystems, bypassing multiple challenges the seismic response analysis of a coupled vehicle‐bridge system entails. The proposed approach builds upon the previously established Extended Modified Bridge System (EMBS) method for decoupling vehicle‐bridge systems (in the absence of earthquake excitation). Its premise is to first characterize and then assess the relative importance of the VBI effect on the bridge and vehicle responses and replicate it by modifying the pertinent uncoupled equations of motion (EOMs). The formulation deployed accommodates multi‐degree of freedom models for both the vehicle and bridge and can thus tackle complex systems. The analysis examines the ability of the proposed decoupling approach to predict the response of a realistic system vehicle‐bridge system under a suit of historical earthquake records. The decoupled results are in excellent agreement with the coupled solutions for all earthquake records and scenarios (i.e., earthquake excitation solely in the transverse direction of the bridge, as well as in both the transverse and vertical directions simultaneously).

A Generative adversarial network model for estimating temporal frequency variation of vehicle-bridge interaction using modified Stockwell transform

The presence of massive and directional vehicles moving on a railroad bridge causes temporal fluctuations in the fundamental frequencies of both bridge and vehicle systems, making traditional structural inspections difficult to employ effectively. Thus, this paper proposes an image-to-image Generative Adversarial Network (GAN) that estimates temporal frequency variation for the vehicle-bridge interaction system. To address the challenges associated with conventional approaches, eigenvalue analysis, numerical substitution, and Fourier series approximations are examined using a simple degree of freedom and a more complex model. Thus, the GAN model is proposed to overcome those limitations. In the framework, based on the properties of a real bridge and vehicle model, the modified Stockwell transform of bridge acceleration from the dynamic simulation is used as input data with the paired data from the numerical substitution approach. Then, the model is validated through quantitative measures and laboratory scale experiments. Results showed that the model has strong performances across the various scenarios, demonstrating the potential for bridge condition assessment under operational conditions.

Free Vibration Response Studies on Bridges

Abstract Bridges are essential components of the transportation network. These are unique constructions that serve as a transportation link between regions separated by physical barrier. Because of their critical role in ensuring passenger safety, these structures require constant maintenance. When vehicle cross a bridge, the structural components vibrate, which over time may cause damage to these components. The preferred method of maintaining structural health is currently seeing a rise in the use of Structural Health Monitoring (SHM) systems on infrastructure, especially bridges. In order to overcome the drawbacks of visual inspection methods, it is crucial to continuously monitor the integrity and analyse the dynamic properties of bridges. This work provides a comprehensive analysis of bridge health monitoring, emphasizing three key elements: vibration-based structural health monitoring (SHM), vehicle-bridge interaction analysis, and machine learning integration. The work improves monitoring, maintenance, and safety protocols by expanding our knowledge of structural integrity assessment for bridges by a detailed examination of the convergence of these domains. Notably, the work uses a condensed 2D model to forecast bridge natural frequencies Understanding the dynamic behaviour and structural integrity of the vital infrastructures is greatly aided by free vibration response research on bridges. The results, insights, and new directions in the subject of bridge free vibration analysis are summarized in this review paper. The uses and drawbacks of several analytical, numerical, and experimental techniques are covered. The research on the free vibration response of bridges is also reviewed in this review paper, with an emphasis on new developments incorporating machine learning principles.

Bridge damage identification based on synchronous statistical moment theory of vehicle–bridge interaction

AbstractConsidering the weak noise resistance and low identification efficiency of traditional bridge damage identification methods, a data‐driven approach based on synchronous statistical moment theory and vehicle–bridge interaction vibration theory is proposed. This method involves two main steps. First, a two‐axle test vehicle is used to collect acceleration response signals synchronously from adjacent designated measurement points while stationary. This operation is repeated to calculate the second‐order statistical moment curvature (SOSMC) difference of entire bridge points corresponding signals in different states. By comparing with the reference value, the preliminary damage location of the bridge can be obtained. Second, the first‐order modal shape curve is constructed using the second‐order statistical moment (SOSM). The refined identification of bridge damage is then based on an improved direct stiffness back calculation of the bridge's stiffness. This article proposes the synchronization theory for the first time and combines it with the statistical moment clustering method, forming an innovative approach to obtaining structural vibration modes. The effectiveness of this method has been well validated through numerical simulations with different parameters and on‐site bridge tests. The research results indicate that SOSMC indicators have better noise resistance and higher recognition efficiency in identifying damage locations, compared to modal curvature and flexibility curvature indicators. Additionally, compared to transfer rate and random subspace methods, the SOSM method results in smaller error and higher identification efficiency.

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.

Toward Indirect Real-Time Prediction of Bridge Vibration Responses Under Traffic Flow Through a Population of Connected Sensing Vehicles

Condition monitoring of bridge structures as the lifelines of smart cities is high of importance. While indirect vehicle scanning techniques have shown promising results and have less cost compared to mounting fixed sensors on the bridge, they have limitations in predicting response under traffic flow since the crossing time of one vehicle is very short. This paper presents a novel crowsensing-based framework for predicting bridge acceleration responses and identifying the modal characteristics. This method utilizes smartphone data from a diverse population of sensing vehicles as they traverse the bridge to predict bridge acceleration response at various virtual sensing locations. Subsequently, the predicted acceleration is used to identify the mode shapes and natural frequencies of the bridge. The principal innovation in this practical and cost-effective monitoring solution is the utilization of a randomly selected set of sensing vehicles at each timestamp. These selections may differ from one timestamp to the next, reflecting the real-world conditions where certain vehicles may intermittently lose or disconnect their internet connectivity. By consistently updating the set of sensing agents while other vehicles cross the bridge, the proposed framework overcomes the data length limitations of conventional vehicle-based methods by leveraging multiple vehicles and continuous data collection. Comprehensive numerical studies are conducted to evaluate the performance of the method. In the numerical investigations, a three-span bridge is subjected to the continuous passing of a large number of half-car vehicle models with random speeds and initial locations. Vehicle-bridge interaction is considered in the analysis. Utilizing a single randomly selected sensing agent at each timestamp, the results demonstrate the effectiveness of the framework in predicting bridge acceleration response with a relative error of less than 5%. Additionally, the method achieves an accuracy level of 95% in identifying the bridge's initial three mode shapes.

Drive-by bridge damage detection by vehicle-bridge interaction neural operator

Drive-by bridge damage detection using vibrations of vehicles for damage detection of bridges has been studied since it needs no instrumentation on bridges. However, it is still a challenge to be able to extract features that are sensitive to bridge damage and relevant to the responses of the bridge. To address the challenges of drive-by bridge damage detection, machine learning-based approaches have also been actively investigated in recent research. With supervised learning methods, it is almost impossible to obtain training data on the damage state of a bridge. On the other hand, unsupervised learning approaches have been considered, but they only provide changes in relative features rather than physical properties that are useful for estimating the structural performance. To address the above issues, this study aims to propose and investigate the feasibility of drive-by bridge damage detection using a vehicle-bridge interaction neural operator (VINO). In the proposed method, numerical simulations of vehicle-bridge interactions considering the damage field of the bridge are first carried out to generate physically informed training data. The VINO is then constructed using the physically informed training data. However, VINOs are still insufficient to model real bridges. Therefore, in order to improve the practicality of the physically-informed VINO, data-informed fine-tuning is carried out using available data from real bridges. It is noted that no damage data is required in the fine-tuning stage. The feasibility of the drive-by bridge damage detection using VINO is discussed using an in-house experiment on a model bridge under a moving vehicle.

Hybrid vehicle scanning techniques for detection of damaged hangers in tied-arch railway bridges

Regular monitoring of the hanger system is essential for preserving structural integrity in tied-arch bridges. This proactive monitoring enables preventive maintenance and early detection of hanger damage. To confront this issue, we propose a novel scanning method for assessing the impact of damaged hangers on the dynamic behaviour of single-span tied-arch railway bridges. Using each hanger as a positional reference, this method employs an instrumented vehicle as a mobile scanner to indirectly acquire vibration data from the traversed bridge deck. The hybrid approach integrates vehicle-bridge interaction (VBI) dynamics, vehicle scanning method (VSM), and moving windowed Fourier transform (mw-FT) technique to generate time–frequency spectrograms from the collected signals. In this representation, the time axis indicates the duration of the inspection vehicle traversing the bridge deck. By analysing frequency shifts within the spectrogram, we can identify damaged hangers through observed variations in frequency content over time. Numerical studies demonstrate the efficacy of the proposed hybrid vehicle scanning technique in detecting potential hanger damage in tied-arch railway bridges.

Running safety control performance of high-speed trains on bridges under seismic excitation utilizing tuned mass damper

The safety of high-speed trains on bridges during seismic conditions is of paramount concern, especially for high-pier bridges characterized by lower lateral stiffness. The risk of train derailment during earthquakes can increase due to heightened low-frequency excitation. While Tuned Mass Dampers (TMDs) have proven effective in mitigating structural responses, their influence on time-varying vehicle-bridge interactions under earthquakes remains an unexplored area of study. In this research, a 1:10 scale model of a high-speed train-track-bridge coupling system, incorporating a nonlinear wheel-rail interface, was subjected to testing using a four-shaking-table system. This system exhibited good control accuracy and synchronization rates. The experimental results were used to validate the accuracy of the numerical model for the train-track-bridge coupled system under various train speeds. Subsequently, the seismic control performance of TMDs on high-speed trains was assessed through a combination of experimental tests and numerical simulations. Both sets of results, from the experimental and numerical approaches, confirmed the effectiveness of TMDs in controlling acceleration and force-related parameters for both moving and stationary trains. Notably, the control performance is most pronounced when vibrations closely align with the TMD's operating frequency. Additionally, this study delved into the mechanism of train vibration control and conducted a comprehensive parametric investigation, considering factors like pier heights (24 m–50 m), train speeds (0–300 km/h), ground motion intensities (0.04 g–0.21 g), and TMD mass ratios (0.03–0.08). The findings revealed that TMDs have a more significant impact on enhancing the safety index of trains for high-pier bridges characterized by lower frequencies. For instance, in the case of a 50 m pier, the running train's derailment coefficient can be reduced by 34.94 %. However, the control action is narrowband, effectively mitigating train vibrations near the bridge's natural frequency but less effective outside the working frequency range and absolute base acceleration.

Coupled Vibration of a Vehicle Group–Bridge System and Its Application in the Optimal Strategy for Bridge Health Monitoring

The accuracy of bridge performance monitoring and evaluation is easily affected by unfavorable factors such as vehicle coupling and test noise. In order to accurately evaluate the dynamic response and health monitoring threshold of the bridge under different operating conditions, a time-varying dynamic vehicle group model including the main uniform mass and the coupling mass was established, and the influence of road roughness was considered in the coupling equation. A bridge monitoring strategy considering signal noise ratio and vehicle–bridge interaction was proposed, and the effectiveness of the monitoring strategy was verified by taking a simple supported beam as an example. The results showed that the proposed time-varying dynamic vehicle group model could accurately consider the influence of road roughness and estimate the threshold of health monitoring, and the proposed bridge monitoring strategy could filter out a large amount of low signal-to-noise ratio or meaningless data, thus saving computing resources and realizing the lightweight safety monitoring of bridges.

Fatigue life prediction of corroded hangers with parallel steel wire in a network arch bridge under vehicle-bridge interaction based on a novel noniterative simplified method

Fatigue damage is a main concern during the life-cycle maintenance of bridges with corroded hangers under vehicle-bridge interaction (VBI). In this study, a novel noniterative simplified method for VBI is proposed to analyze the responses of hangers in a network arch bridge, considering the effects of vehicle types, driving lanes, and road surface roughness. Furthermore, the fatigue life of corroded hangers is investigated, considering the actual traffic flow and uneven distribution of stress in the hanger’s cross-section. The results show that longitudinal and transverse bending moments of the hanger significantly affect the stress of steel wires in one hanger but have limited influence on stress amplitudes. The fatigue lives of steel wires are considerably reduced when subjected to both uniform and pitting corrosion. The fatigue life of steel wires is reduced under deteriorating road surface conditions. Moreover, as the fatigue life of steel wires in the hangers declines, the variations in fatigue life among individual steel wires within a single hanger gradually decrease. Consequently, this trend leads to a heightened likelihood of continuous wire breakage.

Numerical assessment of the dynamic load allowance on long-span modular steel bridges considering vehicle-bridge interaction

Numerical assessment of the dynamic load allowance on long-span modular steel bridges considering vehicle-bridge interaction