Vehicle-bridge Interaction System Research Articles

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.

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.

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.

Study on driving safety of vehicle-bridge interaction system based on ultra-high-dimensional point-selected extremum methods

ABSTRACT The driving safety indexes involve the geometric nonlinear contact relationship of the wheel and rail and the high-frequency vibration of the wheel-set. The calculation of their probability characteristic parameters requires very precise selection of random excitation samples. Track irregularity is an essential external excitation force in the vehicle-bridge interaction system (VBIS). Besides, many random phase angles must be considered when using the harmonic superposition method to simulate VBIS, leading to the ultra-high-dimensional random variables problem. Thus, this paper proposes a square power point method and a pseudo-random sequence (Sobol sequence) based on a number theoretic approach to model ultra-high dimensional random variables accurately. This strategy reduces the deviation between the representative track irregularity samples (TIS) and can be applied to fields of strongly nonlinear and high-frequency vibration. Then, by increasing the number of representative TIS, the deviation between response samples caused by non-linear factors can be significantly reduced. Finally, this paper proposes a threshold method for driving safety indexes that determines the service life of bridges, which can quickly obtain the threshold of its extreme value distribution through the cumulative distribution function, and establish the relationship between the threshold and the number of trains travelled. The above theories are verified by calculation examples, and some engineering suggestions are obtained.

Theoretical and Experimental Investigations of Identifying Bridge Damage Using Instantaneous Amplitude Squared Extracted from Vibration Responses of a Two-Axle Passing Vehicle

Identifying bridge damage using a movable test vehicle is highly regarded for its mobility, cost-effectiveness, and broad monitoring coverage. Previous studies have shown that the residual contact-point (CP) response between connected vehicles is free of the impact of vehicle self-vibrations and road roughness, making it particularly suitable for the indirect extraction of bridge modal properties. However, most experimental campaigns regarding contact-point (CP) responses focus on a single-axle testing vehicle within a non-moving state. This study aims to theoretically and experimentally identify bridge damage using the instantaneous amplitude squared (IAS) extracted from the residual CP response of a two-axle passing vehicle. First, the closed-form solution of the residual CP acceleration was derived for a two-axle vehicle interacting with a simply supported beam. The IAS index was constructed from the driving frequency of the residual CP acceleration. Then, numerical investigations using finite element simulation were conducted to validate using the IAS index for indirect bridge damage identification. The application scope of the approach under various vehicle speeds and road roughness grades was examined. Finally, a laboratory vehicle–bridge interaction system was tested to validate the approach. Numerical studies demonstrated that bridge damage could be directly determined by observing the IAS abnormalities, which were baseline-free. The IAS from the residual CP response outperformed the IAS from CP responses in identifying bridge damage. However, it was better to use the IAS when the vehicle speed was no greater than 2 m/s and the grade of the road surface roughness was not high. Laboratory tests showed that it was possible to identify bridge damage using the IAS extracted from the residual CP acceleration under perfect road surfaces. However, it fell short under rough road surfaces. Hence, further experiments are required to fully examine the capacity of the IAS for bridge damage identification in practical applications.

Contact-point response reconstruction for indirect bridge monitoring via Bayesian expectation-maximization based augmented Kalman filter

The drive-by bridge dynamic measurement using an instrumented vehicle during its passage over the bridge can be an indirect bridge structural health monitoring system. The identification of the contact-point (CP) responses between vehicle wheels and bridge structure from vehicle responses offers an efficient and economical way for the modal identification and condition assessment of short- to mid-span road bridges. This paper proposes a novel method for the contact-point displacement response reconstruction of the vehicle-bridge interaction (VBI) system in a joint input-state estimation manner based on Bayesian Expectation-Maximization (BEM). An analytical model of VBI including the road approach in front of a simply-supported bridge is presented firstly. Then the augmented state-space model of the vehicle with the contact-point responses included as variables along with vehicle states is established. A new method by integrating the augmented Kalman filter (AKF) with a BEM strategy is proposed to solve the state estimation problem without knowing the vehicle axle responses. The vehicle states and CP displacement responses are identified simultaneously. The effects of the measurement noise, road surface roughness and vehicle speed on the identified results are investigated using numerical simulations. The experimental tests are used to further verify the feasibility and accuracy of the proposed method. The results show that the proposed method has potential for drive-by bridge condition assessment using on-board vehicle response measurements for a large population of short- to mid-span bridges.

Subspace Identification of Bridge Frequencies Based on the Dimensionless Response of a Two-Axle Vehicle.

As an essential reference to bridge dynamic characteristics, the identification of bridge frequencies has far-reaching consequences for the health monitoring and damage evaluation of bridges. This study proposes a uniform scheme to identify bridge frequencies with two different subspace-based methodologies, i.e., an improved Short-Time Stochastic Subspace Identification (ST-SSI) method and an improved Multivariable Output Error State Space (MOESP) method, by simply adjusting the signal inputs. One of the key features of the proposed scheme is the dimensionless description of the vehicle-bridge interaction system and the employment of the dimensionless response of a two-axle vehicle as the state input, which enhances the robustness of the vehicle properties and speed. Additionally, it establishes the equation of the vehicle biaxial response difference considering the time shift between the front and the rear wheels, theoretically eliminating the road roughness information in the state equation and output signal effectively. The numerical examples discuss the effects of vehicle speeds, road roughness conditions, and ongoing traffic on the bridge identification. According to the dimensionless speed parameter Sv1 of the vehicle, the ST-SSI (Sv1 < 0.1) or MOESP (Sv1 ≥ 0.1) algorithm is applied to extract the frequencies of a simply supported bridge from the dimensionless response of a two-axle vehicle on a single passage. In addition, the proposed methodology is applied to two types of long-span complex bridges. The results show that the proposed approaches exhibit good performance in identifying multi-order frequencies of the bridges, even considering high vehicle speeds, high levels of road surface roughness, and random traffic flows.

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.

Dynamic Analysis and Optimization of Vehicle-Bridge Interaction System under Road Roughness and Time Variability of Element Interpolation Function

Vehicle-induced load, as one of the main excitation factors to bridge vibration and fatigue damage, plays a vital role in the analyzing of the vehicle-bridge interaction (VBI) system, but is still limited in both spatial location and numerical value. This paper presents an improved VBI system to investigate bridge vibration and vehicle vibration considering the coherent roughness and multiple lanes excitation. The vehicle and bridge subsystems and coherent roughness road are developed and are further integrated to form the VBI system based on the displacement relationship between wheels and the bridge. Further, the solution method of the VBI system is given, and the calculation platform is constructed. Meanwhile, the natural frequencies and mode shapes, as well as the mid-span displacement of the bridge, are verified with the results calculated in commercial software. Subsequently, the responses of the VBI system are investigated under different degrees of freedom of vehicle vibration, bridge damping ratio, road roughness class, multiple lanes, and velocity. It can be concluded that road roughness and velocity have a complex nonlinear relationship with the vibration of the VBI system. Finally, the Pareto strategy is applied to find the optimized value of suspension stiffness and damping, and the depth, unit mass, and elastic modulus of the bridge to minimize the system vibration. The results show an obvious improvement in the vibration of the VBI system.

Moving force identification based on the nonnegative flexible conjugate gradient least square method and experimental verification

Moving force identification (MFI) is an approach aimed at acquiring the time history of unknown moving loads acting on a bridge, which is actually an inverse problem. The accuracy and efficiency of MFI are significantly influenced by the ill-posedness problem during the process of solving the vehicle-bridge interaction system, especially when the vehicle axles getting on or getting off the bridge. The objective of the study is thus to reduce the effect of ill-posedness problem on the accuracy and efficiency of MFI through numerical and experimental methods. A nonnegative flexible conjugate gradient least square (NN-FCGLS) method is first developed through enriching the conjugate gradient least square method with the flexible Krylov subspace technique and nonnegative constraint conditions. Then, the solution of the NN-FCGLS method is continuously updated with the Krylov subspace technique and the Karush-Kuhn-Tucker conditions at each iteration to obtain a stable solution for ill-posed dynamic force identification. Finally, laboratory experiments were carried out with a simply supported aluminum alloy beam. Numerical simulation results show that the NN-FCGLS method is insensitive to vehicle speed and vehicle wheelbase, and has better accuracy, stronger robustness and higher computational efficiency than the time domain method and the conjugate gradient least square method. The relative percent errors of all ten cases do not exceed 7.8 % under the interference of 20 % noise level. The experimental results shows that the correlation coefficients between measured responses and reconstructed responses are larger than 0.92 in all cases. Experimental studies demonstrate the accuracy and efficiency of the proposed NN-FCGLS method in the practice of MFI.

Bridge Frequency Identification Using Cross-Power Spectra of Vehicle Vibrations from Multiple Moving Speeds

In recent years, a rapid bridge health monitoring technology has been developed using an instrumental moving vehicle. Using recorded vehicle vibration data, bridge frequencies are identified for bridge health monitoring or finite element model updating. Target bridge frequencies with significant amplitudes in the vehicle’s vibration frequency spectra are expected to be found. However, in the coupled vehicle–bridge interaction (VBI) system, bridge vibration-relevant vehicle dynamics might not be noticeable. The bridge frequency would be difficult to identify because of the potential influence of road roughness. To resolve this difficulty, a novel bridge frequency identification method is proposed to mitigate the negative effects of road roughness. First, theoretical derivations are done to ascertain the VBI system dynamic characteristics considering road surface roughness. Our findings showed that the road roughness-relevant vehicle dynamics are closely related with the traveling speed, whereas the bridge frequency remains approximately constant. Theoretical investigations indicated that cross-power spectra between vehicle dynamics at multiple moving speeds are effective to mitigate the negative effects of road roughness. Presumably, it is feasible to identify the target bridge frequency from the cross-power spectra. Both the dynamic characteristics of the VBI system and the effectiveness of the proposed method for bridge frequency identification were examined using finite element simulations and laboratory experiments. Compared to existing methods, the proposed method is widely applicable to real-world situations and difficulties.

Comparative study of damage modeling techniques for beam-like structures and their application in vehicle-bridge-interaction-based structural health monitoring

Damage modeling techniques are essential tools for revealing the impact pattern of damage on structural responses. Currently, different damage level parameters are defined for different damage modeling techniques, but there is no established equivalence among them. This might plague researchers in their selection of damage modeling techniques for theoretical and numerical studies. To address this challenge, comparative studies of different damage modeling techniques for beam-like structures were conducted, and their impact on vehicle-bridge-interaction (VBI)-based structural health monitoring was analyzed. First, the theoretical basis of four damage modeling techniques, that is, element stiffness loss, element mass increase, cracked beam element, and crack spring element, were analyzed, and equivalent damage level relationships were established based on beam frequencies. Then, a finite element simulation of the VBI system consisting of a two-axle vehicle and a beam-like structure with damage was formulated and verified. Finally, the impacts of different damage modeling techniques with unified damage levels on the dynamic responses were studied, and the feasibilities of damage identification using vehicle and bridge responses under different damage modeling techniques were compared. The results indicated that the dynamic responses generated by different damage modeling techniques varied under the same damage level. The damage modeling technique using the crack spring element posed the most significant impact on the VBI responses, the cracked beam element and element stiffness loss techniques had the equivalent impact, but the element mass increase technique showed a negligible impact. Damage location and severity could be well detected by the cracked beam element and element stiffness loss techniques. However, the dynamic responses generated by the element mass increase technique could not be used to identify the damage. Vehicle responses were more useful than bridge responses for damage identification, demonstrating the advancement of indirect monitoring of bridge health conditions using an instrumented passing vehicle.

A Novel Split-Type Two-Axle Vehicle Model for Bridge Indirect Measurement

A split-type two-axle vehicle for bridge indirect measurement is proposed to address the deficiencies of single-axle and conventional two-axle vehicles. At first, the conceptual design of the split-type two-axle vehicle is put forth, and the analytical solution for the vehicle-bridge interaction (VBI) system response is derived. After that, the regularity of the vehicle frequency response function is studied, and the numerical analysis method is utilized to validate the analytical solution. Based on the theoretical findings, the vehicle frequency and speed are studied to investigate their impacts on extracting bridge frequencies from vehicle responses. The results indicate that a peak will form in the frequency response function (FRF) curves when the input frequency is near to the vehicle frequency. The single peak phenomenon will occur when the zero-point condition of the FRF from the contact point to the vehicle body is remarkably close to the second vibration frequency of the vehicle. It is preferable for the first frequency of the vehicle to be higher than that of the bridge since this helps to extract the bridge frequency. On the other hand, at low speeds ([Formula: see text] 43.2km/h), higher vehicle speeds will result in a greater distance between the peaks of the left- and right-shifted frequencies of the bridge, wider frequency bands, and lower spectral resolution, which is not conducive to bridge frequency identification.

Dynamic Reliability Analysis of Running Safety and Stability of a High-Speed Maglev Train on a Guideway Bridge

The dynamic performance of high-speed maglev trains, a next-generation rapid transit system, has received continuous attention in recent years. In this study, a dynamic reliability analysis method for a high-speed maglev train–guideway coupled system was proposed. First, a refined model of the maglev vehicle–bridge interaction system was established, where the vehicle subsystem was simulated as a rigid body-spring-damper model with 101 degrees of freedom. The guideway subsystem was simulated as a finite element model, and these two subsystems were coupled as an entire system through a magnet–rail interaction model with a proportional-derivative (PD) controller. Second, a dimension-reduction method for the simulation of representative samples of track irregularities was developed, and thus the number of random variables in the system was reduced to four. Finally, an efficient method for the calculation of the dynamic reliability of a maglev train–guideway coupled system was proposed using the probability density evolution method-based equivalent extreme value principle. With numerical examples, the accuracy of the maglev train–guideway interaction model was verified by comparing it with field measurement data from the Shanghai high-speed maglev line. The accuracy of the proposed dynamic reliability analysis method was confirmed by comparing three types of results, that is, the mean value time-history curve, the probability density function, and the cumulative distribution function of extreme values, obtained by the Monte Carlo method. Finally, the dynamic reliability of the running safety and stability of the maglev vehicle at a speed of 430 km/h and the variation laws of the dynamic reliabilities with train speed were examined in detail.

Exploring Time-Varying Characteristics in Drive-By Bridge Frequency Extraction with the Second-Order Synchrosqueezing Transform

Recently, due to low cost and convenience, the concept of estimating the bridge’s first natural frequency through indirect measurements of a passing vehicle has gained increasing attention—known as drive-by bridge structural health monitoring. As the vehicle acts as a moving mass added to the bridge, this system is nonstationary with time-varying characteristics. Most related studies assume constant bridge and vehicle frequencies of vehicle–bridge interaction (VBI), which is only appropriate when the VBI effect is negligible. When the vehicle mass is significant compared with the bridge mass, often a feature of railway bridges, the interaction effect cannot be ignored. Therefore, this paper presents a nonlinear time–frequency analysis approach to examine the time-varying nature of frequencies in the VBI system using the second-order synchrosqueezing transform. In comparison to the classical linear approaches, such as wavelet transform and short-time Fourier transform, the proposed method can significantly improve the energy concentration of the time–frequency representations, resulting in a clear pattern to show how the frequencies change. In addition, an indicator is proposed to automatically select the parameters with the proposed approach to obtain suitable results. Both numerical simulation and laboratory experiments are carried out to investigate the feasibility of the proposed approach. It is found that due to the time-varying nature of VBI, the frequencies of both vehicles and bridges are time-varying. Therefore, the extracted drive-by bridge frequency should be distinguished from that found using direct (on-bridge free vibration) measurements.

A co-simulation approach for straddle monorail vehicle–bridge interaction subjected to nonlinear excitation

Straddle monorail systems, a lightweight rail transit mode, are being increasingly used for developing infrastructures in medium-sized cities. Vehicle–bridge interaction (VBI) is a critical issue in the design of straddle monorail systems. However, existing straddle monorail VBI studies have not simultaneously considered nonlinear excitations, structural nonlinearities, and bridge alignment defects. Therefore, this study proposes a co-simulation approach that combines MATLAB and ANSYS software packages to analyze the dynamic responses of a straddle monorail VBI system. The equations of motion of the monorail train are formulated following D'Alembert's principle and are solved by self-programming on the MATLAB platform. A finite element model of the bridge is established and solved using the ANSYS programming. The bridge and vehicle subsystems are coupled through global iteration with the exchange of wheel–rail contact forces calculated using MATLAB and bridge responses calculated using ANSYS. The co-simulation approach is validated by the dynamic responses of the monorail train and bridge reported in the relevant literature. To demonstrate further the effectiveness and high efficiency of the proposed approach, the dynamic responses of the VBI system with a monorail train crossing a three-span continuous rigid-frame prestressed concrete-girder bridge are analyzed, and three investigated cases of sole earthquake, sole moving-train, and combined earthquake and moving-train excitations are compared. These results demonstrated that the proposed co-simulation approach can provide an effective tool for nonlinear dynamic responses of straddle monorail VBI systems subjected to nonlinear excitation and other nonlinear-coupled dynamic issues.

Selection of design parameters of straddle monorail system considering vehicle–bridge interaction

Vehicle–bridge interaction (VBI) is an essential focal point in the design of straddle monorail systems. Existing studies on them primarily use multibody dynamics software, however, it is disadvantageous as several important factors such as nonlinear excitations, structural nonlinearity, and bridge alignment defects cannot be analyzed. Therefore, a co-simulation approach is proposed in this paper to investigate the dynamic responses of the straddle monorail VBI system where various factors can be easily considered. The proposed approach couples bridge and vehicle subsystems through global iterations with the exchange of wheel-rail contact forces and bridge responses calculated using MATLAB and ANSYS, respectively. The accuracy of the proposed approach is validated using numerical and experimental data reported in existing literature. Further, the effect of design parameters on the dynamic responses of the straddle monorail VBI system is analyzed using the proposed approach. The analysis results indicate that a single-axle straddle monorail train outperforms the conventional two-axle train with reduced dynamic responses and lighter mass. Recommendations are provided for the stiffness and damping of the guiding, stabilizing, and riding wheelsets, as well as for the vertical and lateral stiffness and damping of the air springs. The radius of a girder curve should be at least 150 m over regular operation sections to ensure riding safety; it can be less at special entrance and exit sections where the train speed is low. The findings of these parametric analyses provide guidelines to select proper design parameters for straddle monorail systems to mitigate dynamic responses.

Coupled Vibration Analysis of Ice–Wind–Vehicle–Bridge Interaction System

Bridges built in ice-covered water regions are mostly in complex marine environments, they not only need to withstand strong wind but also resist the impact of drift ice. However, at present, there is a lack of vehicle–bridge coupling vibration analysis and driving safety assessment under combined ice and wind. Therefore, this study constructs a complete analysis framework of ice–wind–vehicle–bridge interaction to investigate the dynamic responses of the coupled system. Ice load is simulated by a linearized ice–structure interaction model, which is based on the self-excited vibration theory. Wind load on the bridge deck includes steady-state force and buffeting force. Wind load on the vehicle is simulated based on the quasi-steady model. Subsequently, ice load, wind load, soil–structure interaction (SSI), and additional water mass are all integrated into a full bridge model based on a sea-crossing bridge with running vehicles in the Bohai Sea. The results indicate that ice load has a greater impact on the lateral dynamic response of the bridge, the combined action of ice and wind has no superimposed effect on the movement of the bridge but has a restraining effect. Wind load presents a more significant influence on the lateral dynamic response of the vehicle, the coupled dynamic responses of the vehicle cannot be combined by the superposition under separate ice and wind. The combined effect of ice and wind obviously increases the sideslip risk of running vehicles and reduces driving safety.

A Rapid Identification Technique of Moving Loads Based on MobileNetV2 and Transfer Learning

Rapid and accurate identification of moving load is crucial for bridge operation management and early warning of overload events. However, it is hard to obtain them rapidly via traditional machine learning methods, due to their massive model parameters and complex network structure. To this end, this paper proposes a novel method to perform moving loads identification using MobileNetV2 and transfer learning. Specifically, the dynamic responses of a vehicle–bridge interaction system are firstly transformed into a two-dimensional time-frequency image by continuous wavelet transform to construct the database. Secondly, a pre-trained MobileNetV2 model based on ImageNet is transferred to the moving load identification task by transfer learning strategy for describing the mapping relationship between structural response and these specified moving loads. Then, load identification can be performed through inputting bridge responses into the established relationship. Finally, the effectiveness of the method is verified by numerical simulation. The results show that it can accurately identify the vehicle weight, vehicle speed information, and presents excellent strong robustness. In addition, MobileNetV2 has faster identification speed and requires less computational resources than several traditional deep convolutional neural network models in moving load identification, which can provide a novel idea for the rapid identification of moving loads.

Investigation of Spatial-Varying Frequencies Concerning Effects of Moving Mass on a Beam

The spatial-varying frequency of a vehicle-bridge interaction (VBI) system subjected to a moving mass is theoretically derived and numerically investigated through a three-dimensional VBI model, in which the effects of moving mass are introduced through the inertial force and centrifugal force in the equation of motion of the bridge. For a large vehicle-to-bridge mass ratio, it has been known that the frequency of a VBI system could change with respect to the location of a moving vehicle. As such, this study derives the analytical solution based on a moving mass-beam system to account for frequency variation and further builds the numerical model with detailed implementation for practical applications. The numerical results show the following findings: (1) The frequency of a VBI system is a function of velocity and location of a moving vehicle. (2) The reduction of spatial-varying frequency ratio for a particular mode decreases with respect to the mode of higher order. (3) The maximum reduction of spatial-varying frequency ratio of the first mode in a moving mass-beam system occurs in the location where the bridge has the maximum deflection as a result of local mode excitation. (4) For the VBI system with high suspension stiffness and large vehicle-to-bridge mass ratio, the absolute variation of spatial-varying frequency ratio of the first mode can be up to 30–40%.