Transformer-Enhanced Traffic Load Simulation for Wear Evaluation of Bridge Expansion Joint

. Timely wear evaluation is crucial in maintaining the functionality of bridge expansion joints (BEJs), ultimately ensuring the safety of bridges. Despite the signifcance of trafc load simulation (TLS) in simulation-based evaluation methods, existing TLS approaches face challenges in accurately modeling in situ trafc fow at a high fdelity. Tis paper presents a novel methodology and its application for evaluating the wear performance of BEJs, employing a Transformer-enhanced TLS approach. Initially, a tailored dataset is crafted for data-driven car-following modeling, leveraging an established spatial-temporal trafc load monitoring system. High-fdelity TLS with a mean absolute error (MAE) of 0.1738m/s is then achieved using Transformer modules equipped with an attention mechanism. To evaluate the fnal wear life of BEJs, transient dynamic analysis and a calibrated fnite element model of the bridge are employed to extract cumulative displacement. Additionally, a surrogate model is developed to depict the relationship between the hourly trafc weight on the entire bridge deck and the cumulative displacement of BEJs, yielding an impressive R-squared value of 0.96619. Comparative results demonstrate the superior performance of our proposed TLS approach over other data-driven approaches, with the linear model derived from our TLS approach outperforming the model generated by the conventional Monte Carlo-based TLS approach. To conclude, our proposed TLS emerges as a comprehensive and precise methodology for the wear evaluation of BEJs.


Introduction
Bridge expansion joints (BEJs) constitute integral structural components designed to enable bridges to accommodate thermal movements and vibrations induced by trafc loads, wind forces, and seismic activities.However, the wear of slide bearings has emerged as one of the most frequent failure incidents for BEJs in long-span bridges, resulting in a service lifespan for BEJs that is considerably shorter than that of the bridge itself.Terefore, it is imperative to employ efective and predictive wear evaluation methodologies for BEJs to prevent structural damage and minimize additional maintenance costs [1,2].
Although factors such as severe climatic conditions and unsuitable material components can infuence the wear state, it has been confrmed that the primary cause of wear damage in BEJs is the cumulative displacement at the end of the girder [3][4][5][6].Data analysis research, based on displacement gauges from structural health monitoring (SHM) systems, has been conducted.A variety of methods, including correlation ftting [3,[7][8][9][10][11], mechanical performance analysis of bridge structures [12][13][14][15], Bayesian approaches [16,17], statistical machine learning [18], and data reconstruction [19,20], have been utilized to examine the displacement patterns of BEJs for damage evaluation.Te fndings indicate that the wear damage of BEJs is primarily due to large cumulative displacements, which are signifcantly infuenced by temperature and trafc loading.Te temperature factor imparts a consistent trend to cumulative displacements and exhibits a linear relationship [9].
Conversely, trafc loading contributes signifcantly to the cumulative displacements of BEJs [3,21].However, trafc patterns are more spatially and temporally random, complicating the establishment of a relationship between trafc loads and cumulative displacements.
Despite the importance of SHM systems, the costs associated with their real-time installation and maintenance can be substantial.Moreover, wide-range gauges situated at the girder's end may operate at a low frequency (i.e., 2 Hz [7]), which presents difculties in detecting displacement peaks and valleys, particularly when vehicles are entering or exiting the bridge.To address this issue, numerical simulation techniques have been introduced and applied for the wear evaluation of BEJs.Tese techniques integrate trafc loads with mechanical analysis.Considering the signifcance of trafc loads in the evaluation of BEJs, trafc load simulation (TLS) methods are vital as they ofer substantial inputs for the analysis procedure.A commonly used TLS method is the Monte Carlo sampling of vehicle loads, which leverages data from the practical weigh-in-motion (WIM) system [22][23][24].Te recorded trafc load data undergo statistical analysis, and distribution equations of vehicle parameters are derived for subsequent TLS [25,26].Consequently, vehicles are generated based on statistical arrival times and traverse the lanes at constant speeds.Utilizing a fnite element model (FEM) of the bridge structure, displacement histories and corresponding cumulative displacements are calculated to assess the wear performance of BEJs [3,27].To enhance the accuracy of displacement calculations, vehicle-bridge dynamic analysis has been incorporated into TLS [21].
However, the precision of TLS in these studies is somewhat compromised.Tis is primarily due to the inability of the Monte Carlo sampling-based method to consider vehicle interactions [28,29].Such interactions can induce speed fuctuations among vehicles, which in turn infuence the distribution of trafc loads.Terefore, while these methods are widely accepted and utilized, they may not provide the high precision required for certain comprehensive bridge evaluations.
In recent years, microscopic trafc simulation approaches have been proposed, with a focus on the detailed description of each vehicle's movement on the road [30,31].Tese approaches aim to enhance the fdelity of trafc simulations, thereby improving the accuracy of structural evaluation procedures [32].A key concept in microscopic trafc simulation is the car-following model, which takes into account the interactions between each pair of leading and following vehicles, thereby facilitating the simulation of comprehensive trafc fows on the road.Data-driven car-following models have gained increasing popularity in recent decades [33].Tese models leverage trafc surveillance data to establish trafc fow characteristics.A multitude of studies have been conducted using a specifc dataset known as the Next Generation SIMulation (NGSIM), provided by the Federal Highway Administration [34].
In terms of algorithms, to enhance the feature extraction capability of traditional models such as K-neighbouring [35], support vector machine (SVM) [36], and artifcial neural networks (ANNs) [37], deep learning-based methods have been introduced and employed for the car-following prediction problem.Te recurrent neural network (RNN) model, which takes into account the historical status of leading and subject vehicles, has been validated to simulate typical trafc phenomena [38].Following this, models based on long short-term memory (LSTM) and gated recurrent unit (GRU) have been applied to the car-following prediction problem [39,40] and have shown superior performance compared to the basic RNN model due to their more efcient memory cells [41].Additionally, the Sequence-to-Sequence (Seq2Seq) and Encoder-Decoder architecture have demonstrated their advantages in multistep input and output performance [42,43].
However, several challenges remain in the current TLSbased wear evaluation of BEJs, as detailed below.(1) Gaps exist between the microscopic TLS method and its practical application in the wear evaluation of BEJs and other bridge components.(2) Tere is an absence of a specifc benchmarking dataset for data-driven TLS research related to long-span bridges.(3) Present data-driven vehicle trajectory prediction models encounter challenges in modeling longterm dependencies.
To address the challenges identifed, this study presents a comprehensive methodology for evaluating the wear performance of BEJs using a Transformer-enhanced deep learning TLS approach.Specifcally, a unique benchmarking dataset for data-driven TLS research is established, derived from a large-feld trafc load monitoring system that employs machine vision and WIM data fusion.Furthermore, we propose a time-sequence model for predicting vehicle speed histories, which leverages Transformer modules to incorporate the attention mechanism, thereby recognizing long-term serial signal dependencies.Ultimately, precise wear evaluation of BEJs is achieved through transient dynamic analysis of the FEM of the long-span bridge.Te primary contributions of this paper are four-fold.(1) We propose a data-driven methodology that facilitates a more precise wear evaluation of BEJs.(2) We provide a unique, frst-of-its-kind dataset for benchmarking full-bridge TLS.(3) We develop a vehicle speed prediction car-following model for TLS, enhanced with Transformer modules within a deep learning framework, which achieves a low MAE.(4) We demonstrate that the linear surrogate model for BEJ wear evaluation, calibrated from the proposed TLS loading, outperforms conventional methods.
Tis paper is organized as follows.Section 2 introduces our proposed framework for the wear evaluation of BEJs, detailing the methods employed within the framework.In Section 3, we provide comprehensive information on benchmarking data collection and FEM verifcation for the bridge under study.Te performance and feasibility of our model for high-fdelity wear evaluation of BEJs are presented in Section 4, along with discussions on comparative studies with existing models.Finally, Section 5 provides a conclusion, summarizing the key fndings and implications of our research.

2
Structural Control and Health Monitoring

Methodology
2.1.Overview.Tis paper presents a methodology for evaluating the wear performance of BEJs using a Transformer-enhanced deep learning TLS approach.Te methodology consists of three primary components, as depicted in Figure 1.
Initially, a spatial-temporal trafc load monitoring process is implemented using both visual and weighing sensors.A computer vision system, comprising multiple visual sensors, ensures complete coverage of the entire bridge deck.Identifcation algorithms are utilized to collect vehicle trajectory data.Te WIM system, incorporating weighing sensors and induction coil sensors embedded within the pavement, is used to capture specifc parameters of each passing vehicle, including its length, axle weight, and axle spacing.
Subsequently, a TLS approach, enhanced with deep learning and incorporating Transformer modules, is implemented.Following the initial phase, the vehicle trajectory data undergo a smoothing process and are segmented into car-following pairs.Tese pairs serve as the training data for the deep learning model for the prediction of the subject vehicle's speed.Concurrently, the vehicle weighing data are processed to determine the distribution of key parameters, such as vehicle arrival frequencies and axle weights.Tese distributions are then utilized to calibrate the Monte Carlo simulators for random sampling.Te Monte Carlo simulators, in conjunction with the deep learning model, are then deployed for the generation of vehicles and the evolution of trafc on the bridge deck, respectively.Tis process results in the production of microscopic TLS data over a designated time.
Finally, the TLS data are sequentially incorporated into the FEM.Trough the execution of a transient dynamic analysis, the displacement time histories of the girder's end are extracted.Ultimately, the cumulative displacements are computed to estimate the wear life of the BEJs.

Full-Span Trafc Load Acquisition. To complete the
Transformer-enhanced data-driven TLS, the frst requirement is the precise acquisition of on-deck trafc load, both spatially and temporally.Our previous studies [44,45], which focused on a large-feld trafc load monitoring system that utilizes the fusion of multivision and WIM sensing, have enabled us to acquire full-span trafc load fow.Briefy, as shown in Figure 2, our approach to trafc load acquisition incorporates both the WIM system and the computer vision system.Within the WIM system, signals from both the induction coils and weighing sensors are processed.Tis involves the identifcation of impulse signals and the integration of time-sequence signals, respectively.As a result, we can determine the dimensions and axle weights of each vehicle.Te WIM system, which is commercially available, has been actively collecting vehicle weight data since its installation.
In the case of the computer vision system, multiple highdefnition cameras are mounted on the pylons to ensure complete coverage of the entire bridge deck.Te video streams captured by these cameras are fetched, rectifed, and stitched to generate a panoramic image fow of the bridge deck.Tese images are then processed using a trained YOLO-v4 object detector and a Kalman flter.Te former is utilized to detect vehicles within the image fow and to obtain their respective coordinates and types.Te latter is applied to track these vehicles based on the detections, thereby enabling the acquisition of their trajectories.For a more comprehensive understanding of the algorithms employed, readers are encouraged to refer to our previous studies [44,45].

Microscopic TLS Scenario.
Car-following phenomena are widely acknowledged as efective models for the observation and simulation of microscopic trafc fow.As illustrated in Figure 3, a car-following pair is composed of the subject vehicle and the vehicle leading it.In this context, v i , Δv, and Δx denote the speed of the subject vehicle, the speed diference, and the gap distance, respectively.Consequently, a car-following model serves to illustrate the interactions between adjacent vehicles.Te primary objective of a car-following model is to predict the speeds of the subject vehicle based on these crucial parameters.

Transformer-Enhanced Deep Learning Model for Speed
Prediction.Deep learning techniques have gained signifcant popularity, leading to the emergence of numerous data-driven approaches that exhibit greater fdelity and robustness compared to conventional methods [46].Te attention mechanism and Transformer module, innovative architectures in the feld of deep learning, have inspired research in computer vision and natural language processing since their introduction in 2017 [47].Te Transformer module typically combines an Encoder-Decoder structure with an improved self-attention mechanism.Recently, the application of the Transformer module to timesequence forecasting problems [48,49] has shown superior performance compared to other sequence models.
As shown in Figure 4(a), the self-attention mechanism is realized through the scaled dot-product operation.Initially, the input sequence, denoted as X, is mapped into three vectors: the query vector Q, key vector K, and value vector V. Tis mapping is computed as per the following equation: ( In their work [47], Vaswani discovered the benefts of linearly projecting vectors of varying dimensions, which led to the proposition of the multihead self-attention (MHSA) approach, as illustrated in Figure 4(b).MHSA allows the model to attend to information from diferent representation subspaces at diverse positions simultaneously.Consequently, MHSA constitutes a critical component of the Transformer layer, as defned by the following equation: where h denotes the number of heads.All W are linear weight matrices that are learned from the data.
In this study, we specifcally employ Transformer modules for the time-sequence speed prediction of each vehicle traversing the bridge deck, thereby achieving the trafc evolution prediction within the TLS procedure.As depicted in Figure 5, the input sequences are time series data of three key parameters derived from the car-following pair data, namely, (v i , Δv, Δx).Te dimension of the input sequence is 3 × T, where T denotes the number of historical data steps.
Tese vectors are subsequently passed through the Encoder-Decoder structure, which is composed of N stacked Transformer modules and feed-forward layers.
Here N represents the number of identical layers that constitute the Encoder and Decoder.Following this, a fully connected layer is applied to generate the fnal output.Te dimension of this output sequence is 1 × L, where L denotes the number of predicted steps.Consequently, the Transformer-enhanced model maps the input sequence to the output sequence, as demonstrated in the following equation:  Structural Control and Health Monitoring

Transient Dynamic Analysis for Displacement
Calculation.Te transient dynamic analysis (TDA) approach is required to compute the displacement history of the bridge under trafc loads, utilizing the following dynamic equation: where Linear Linear Linear    Structural Control and Health Monitoring the node displacement vector, and F(t) is the dynamic load vector.
Te direct integration method, based on the Newmark-β method proposed by Newmark in 1959, is an efcient approach to solving the dynamic equation.Tis method utilizes the following iterative formulas: where β and c are integration constants that determine the method's precision and stability.Te Newmark-β method remains stable if the time step satisfes the following condition: Continuing to rearrange equation ( 6), we obtain By substituting ( 8) into ( 5), we derive an equation that contains only the unknown u i+1 , which can be solved to obtain u i+1 .Further substituting u i+1 into equation ( 8), we can determine _ u i+1 and € u i+1 , thereby accomplishing the computation for a single time step.
To utilize the Newmark-β method for evaluating the wear damage of BEJs, a sequential approach is established.Tis approach, based on the proposed Transformerenhanced vehicle speed prediction model and TDA, comprises four major steps:   6 provides a depiction of the overall layout of the RSB.

Vehicle Trajectory Reconstruction.
Upon the installation of the trafc load monitoring system, vehicle trajectory data can be collected across the entire bridge deck at each time point.However, due to factors such as perspective distortion, occlusion, and other imaging inaccuracies, positional measurement errors may arise.Tese errors can adversely afect the modeling performance of data-driven approaches [50].To mitigate this, we employ four processing steps to reconstruct the raw speeds captured by the monitoring system, based on previous research by Montanino [51].
Firstly, extreme positional errors, referred to as "outliers," are eliminated by substituting these data points with synthetic ones.Secondly, random noise, which manifests as excessive peaks and valleys, is mitigated by applying a lowpass digital flter.Tirdly, unreasonable local trajectories are examined and reconstructed using the physically consistent rule of the vehicle.Lastly, residual noise is eradicated by reapplying the low-pass flter.
An example of trajectory reconstruction is illustrated in Figure 7(a), with the corresponding accelerations of the vehicle shown in Figure 7(c).Simultaneously, the relative speeds and gaps between the vehicle and its leading vehicle are displayed in Figures 7(b) and 7(d).Te reconstructed speeds exhibit enhanced consistency and reasonableness compared to the raw data, thereby contributing to the improved performance of subsequent training of datadriven TLS models.

Finite Element Modeling and Verifcation.
Upon acquiring the TLS data, a precise FEM of the RSB is required to compute the time-sequence displacements and further evaluate the BEJ.A FEM of the RSB is constructed using ANSYS software, as depicted in Figure 8. Concretely, the Beam4 element type is employed for modeling the girder, pylons, and central buckles.Te Link10 element type is used for the main cables and suspenders, while the Mass21 element type represents the weights from the pavements and diaphragms.Lastly, the Combin37 element type is utilized for the BEJs at both ends of the girder.
Specifcally, the Combin37 element type is designed to simulate a nonlinear spring with force-speed characteristics, with the damping force calculated using equation (9).Based on prior research [52], we set c � 3750 kN • (m • s) − α and α � 0.4.Structural Control and Health Monitoring where c represents the damping factor, α is a constant exponent, sgn is a sign function indicating the direction of the damping force, and v denotes the relative speed between the two nodes of the element.Te FEM of the RSB is validated in both static and dynamic aspects.Initially, the longitudinal stifness of the FEM is compared with data from an early static test [52].Te static test contains two static loading cases, achieved by positioning 52 identical trucks, each weighing 30.0 t.As listed in Table 1, the longitudinal displacements of BEJs calculated by the FEM align well with those from the static test.
In addition, the dynamic behavior of the established FEM has been computed, with the results presented in Table 2. Te in situ testing results from a previous study [53] serve as the measured frequencies for error evaluation.Te results indicate that the modal parameters of the FEM align well with the measured values, including both the nature of modes and their corresponding frequencies.

Transformer-Enhanced Model Training and Evaluation.
For model training, the PyTorch framework is utilized to conduct all deep learning-based experiments.Te experiments are performed on a desktop PC equipped with an Intel® Core(TM) i7-6700k CPU, 32 GB RAM, and an NVIDIA GeForce GTX 1080Ti GPU, with the support of CUDA v10.2 and cuDNN v7.6.5.
In terms of setting training parameters, we set the learning rate to 0.001.Te batch size for each update is set to 128, considering memory cost.As speed prediction is a regression problem, the dropout rate is set to 0. Te total number of epochs for the training process is initially set to 100, with early stopping of model training occurring if the validation loss does not decrease after 10 epochs.Furthermore, by splitting the car-following pairs, we allocate the training set, validation set, and test set in a ratio of 0.70 : 0.15 : 0.15.
Subsequently, for evaluation, we employ the mean square error (MSE) and mean absolute error (MAE) metrics, defned in equation (10).MSE is used to visualize the trend of loss value during training, while MAE is applied to the test set to evaluate the precision of the model after training.
where N represents the number of samples and  v j and v j denote the predicted and actual speed of the j-th vehicle, respectively.
To optimize the performance of the Transformerenhanced model, we implement hyperparameter optimization.In this study, we select the number of layers, historical inputs, and predicted outputs for optimization, as they are the primary factors constituting the deep learning model.Tus, training and evaluation are conducted for each combination of hyperparameters, with the results depicted in Figure 9. Te fnal selected parameters are listed below, and the model achieved a minimum MAE of 0.1738 m/s.During the training and evaluation phase, the chosen hyperparameters are utilized to monitor the model's performance.Te loss curve, as illustrated in Figure 10, demonstrates a consistent decrease and convergence of loss values for both the training and validation sets.Tis trend signifes an enhancement in the model's ability to predict speed.Notably, the fnal loss values for the training and validation sets are remarkably similar, suggesting that the model is not overftting.

Performance Comparison for Single-Step Prediction.
Previous studies have utilized machine learning and deep learning models such as SVM [54], ANN [55], LSTM [56], GRU [57], and Seq2Seq [58] to tackle the time-sequence prediction problem of subject vehicles.
To evaluate the performance of various data-driven models, we conduct a comparison of the prediction errors on the test set between these models and the Transformerenhanced model.Tese comparative models are trained on the same training and validation set as the Transformerenhanced model, with their hyperparameters optimized to ensure the best possible results.Te MAE of all models is detailed in Table 3.
As indicated by the table, the Transformer-enhanced model achieves a lower error rate compared to the other Prediction outputs (time steps) Structural Control and Health Monitoring models.Moreover, due to their ability to extract more profound features from sequences, deep learning-based time-sequence models outperform machine learningbased models.At the same time, the Seq2Seq model demonstrates superior performance over the original GRU and LSTM models.

Performance Comparison for Full-Bridge Evolution
Prediction.Prior to its application in TLS, the trained Transformer-enhanced model undergoes further validation by comparing its trajectory prediction with the observed data.Specifcally, for the tested subject vehicle, the positions of its leading vehicle are maintained identical to the actual observed data.Meanwhile, the speeds of the subject vehicle are predicted by the Transformer-enhanced model at each time step, with the latest vector (v i , Δv, Δx) T being updated after each prediction.Tus, the updated positions of the subject vehicle can be computed recursively by using the following equation: Te trained deep learning models are employed for predicting the trajectory of each subject vehicle in the test set.Concurrently, the MAE of the vehicle speed at each step for each subject vehicle is calculated and presented in Table 4. Te results revealed that the errors of the entire trajectory profles are larger than the errors of scattered samples from Table 3, considering the cumulative efect.Nevertheless, the trained Transformer-enhanced model outperforms the others and achieves the lowest error at 0.4376 m/s.
To provide a visual representation of the model evaluation process, an example with errors similar to the MAE in Table 4 is selected.As a result, the trajectory profle of vehicle ID 1401 is chosen and depicted in Figure 11, which includes the speed, speed diference, acceleration, and gap curves of the car-following pair.As observed from Figures 11(a), 11(b), and 11(d), all trained deep learning models are capable of reconstructing the time-sequence trends of the subject vehicle.Furthermore, by examining the acceleration values in Figure 11(c), it is evident that the Seq2Seq and Transformer-enhanced models exhibit less oscillation than the LSTM and GRU models.Te Transformer-enhanced model provides a smoother and more consistent output with the observed data compared to other models.

TLS Based on Transformer-Enhanced Model and Monte
Carlo Sampling.Figure 1 illustrates the process following the calibration of the Monte Carlo simulators and the training of the Transformer-enhanced model, which enables the implementation of the microscopic TLS for subsequent applications.
In this study, a one-hour TLS is conducted, producing spatial-temporal trafc load data for the entire bridge.Specifcally, the Monte Carlo simulators generate vehicles for each lane through random sampling, based on statistical features extracted from the WIM data.Te Transformerenhanced model then predicts the speeds of each generated vehicle in a step-by-step manner until they eventually exit the bridge deck.
Figure 12 displays three frames of the simulated trafc loads, with the gross weights of the vehicles indicated for better understanding.Te trafc loads consist of all carfollowing pairs across the entire bridge deck.Te proposed TLS has demonstrated its capability for high-precision modeling and simulation of the actual observed trafc load fow.For instance, the pair highlighted in the blue box accurately emulates the deceleration behavior of the subject vehicle.
In addition to the microscopic behaviors of carfollowing pairs, the macroscopic characteristics of the TLS method have been validated through a comparison of vehicle speeds derived from the TLS data and the observed data.For  Structural Control and Health Monitoring is designed to be 133 km [8].By applying the cumulative damage rule, the wear damage incurred during this hour can be quantifed as 0.0028%.Furthermore, 24-hour TLS and FEM loading are performed, based on the recorded trafc volume of the RSB on a specifc day [59].Te hourly trafc weight is also documented, as shown in Figure 14(a).It can be observed that the trend of cumulative displacement of the BEJ and the hourly trafc weight are highly consistent, both exhibiting peak values during morning and evening rush hours and low values during the early morning of-peak hours.Te hourly cumulative wear damage curve is also illustrated in Figure 14(b).It is evident that, considering this trafc load fow as the average level, the PTFE plate of the BEJ has a typical usage time of 1/(6.48571× 10 − 4 ) � 1542 days.

Relationship Analysis between Trafc Weight and Cumulative Displacement.
While the TDA based on TLS and FEM ofers an accurate evaluation of the wear performance of the BEJ, this procedure can be time-intensive.For more predictive and efective maintenance of BEJs, it is essential to examine the relationships between cumulative displacement and key parameters, necessitating a simplifed surrogate model designed for engineering applications.Conventionally, only Monte Carlo sampling is employed in the TLS procedure, which assumes that the generated vehicles move at a uniform speed along the road centerline to form TLS results.Tis method has been widely applied in previous studies [8,21].For comparison purposes, we also implemented an experiment involving hundreds of simulations based on this method.Te results are shown in the scatter plot in Figure 16, indicating that the linear relationship still holds.However, the goodness of ft for the model is R 2 � 0.86463, and the slope is less than that of the surrogate model obtained from the deep learning model proposed in this paper.
In conclusion, our proposed Transformer-enhanced deep learning model takes into account the interactions between vehicles, thereby refecting the actual spatialtemporal trafc load with high fdelity.Terefore, the surrogate model based on our proposed Transformer-enhanced   Structural Control and Health Monitoring method outperforms the conventional Monte Carlo sampling method with a consistent speed assumption and exhibits more conservative damage results in this study.

Conclusions
High-fdelity TLS is crucial for the precise evaluation of BEJs and other components of long-span bridges.Tis study introduces a novel methodology for a more accurate evaluation of BEJ wear due to trafc loads, employing a deep learning-based TLS approach.A deep learning timesequence model, constructed using Transformer modules, is designed to predict microscopic trafc evolution, thus generating high-accuracy trafc loads on the bridge deck for wear evaluation.Subsequently, the cumulative displacements of BEJs are determined through FEM loading, facilitating the assessment of BEJ wear damage.Additionally, an experimental investigation on an in situ bridge has been conducted, leading to the following conclusions: (1) By utilizing a large-feld trafc load monitoring system, we gathered comprehensive bridge trafc load data and reconstructed vehicle trajectories, thereby minimizing systematic measurement inaccuracies.As a result, a custom benchmark dataset for trafc load evolution was created for the frst time.(2) A deep learning model incorporating the attention mechanism and Transformer modules is developed.Tis time-sequenced model predicts the speed histories of a vehicle in trafc fow, enabling the prediction of the entire trafc evolution in TLS.Te trained model achieved an MAE of 0.1738 m/s and 0.4376 m/s for single-instance and full-bridge speed prediction, respectively.Te performance of our model surpasses previous models such as GRU [57], LSTM [39,40], and Seq2Seq [42].
(3) Our model was integrated with a Monte Carlo sampling simulator for vehicle generation, establishing a TLS method for high-fdelity spatialtemporal trafc loading.Transient dynamic analysis was utilized to derive accurate time histories of BEJ displacement.Te cumulative displacement over 24 hours was computed as 6.48571 × 10 − 4 .Subsequently, a surrogate model was ftted to represent the linear relationship between hourly trafc weight and cumulative displacement.Tis model achieved an R-squared value of 0.96619, indicating superior performance compared to previous methods, which had an R-squared value of 0.86463.
Te methodology proposed in this study provides a comprehensive and precise approach for evaluating the wear of BEJs.Looking ahead, our future work will focus on expanding the TLS dataset to encompass a variety of environmental and trafc conditions.We also plan to make this dataset publicly accessible to facilitate further research in this feld.Additionally, we aim to further enhance the accuracy of the deep learning TLS method for the performance evaluation of other bridge components, such as suspenders and cables.
×d v are linear matrices.Here, T and d x denote the length and dimensions of X, respectively, while d k , d k , and d v represent the dimensions of Q, K, and V, respectively.Further, as per equation (2), Q and K are aggregated using the dot-product operation.Te resultant values are then normalized by the scale factor �� d k  and subjected to the Structural Control and Health Monitoring Softmax operation.Ultimately, the outcome is multiplied by V to yield the fnal output vector Z.

Figure 1 :
Figure 1: Overview of Transformer-enhanced TLS for wear evaluation of BEJs.

Figure 3 :
Figure 3: A car-following pair in the microscopic TLS scenario.

Figure 5 :
Figure 5: Transformer-enhanced deep learning model for speed prediction.

(i) Step 1 .
Calibrate the Monte Carlo simulators and train the Transformer-enhanced model using observed data.Ten, obtain TLS results for the specifed time range.(ii) Step 2. Load the TLS results onto the nodes of the FEM according to the loading steps and locations.If there are no nodes at the loading location, distribute the load between the two adjacent nodes in inverse proportion.(iii) Step 3. Import the loading data into the ANSYS software in a step-by-step manner and initiate TDA starting from the frst step.(iv) Step 4. Extract the longitudinal displacement of the expansion joint at each step.Ten, calculate cumulative displacements to evaluate the wear damage of the BEJ.

Figure 12 :
Figure 12: TLS on the entire bridge deck.

14
Structural Control and Health MonitoringConsequently, we conduct hundreds of simulations with varying trafc volumes.Specifcally, Monte Carlo sampling and the Transformer-enhanced deep learning model are utilized for vehicle generation and trafc evolution prediction, respectively, as depicted in Figure1.Cumulative displacements of the BEJ are then obtained through comprehensive TDA.Te scatter plot, displayed in Figure15, reveals a robust linear relationship between the two variables.Te goodness of ft for the linear model, represented by R-squared, achieved a value of R 2 � 0.96619.Tis ftted model can act as an accurate surrogate model, facilitating rapid evaluation of BEJs' long-term performance in real-world engineering scenarios.

Figure 14 :
Figure 14: 24-hour analysis of cumulative displacement and wear damage of BEJ.(a) Hourly trafc weight and cumulative displacement.(b) Cumulative wear damage by cumulative displacement.

Figure 15 :
Figure 15: Relationship between hourly trafc weight and BEJ cumulative displacement (trafc evolution by deep learning).
shaped reinforced concrete pylons.Te bridge includes a central span of 1,490 m, two side spans of 470 m, and two pylons with a height of 207 m.Te design incorporates 180 suspenders and 2 central buckles to connect the main cable with the bridge deck.Additionally, the typical cross section of the girder measures 38.7 m in width and 3 m in height.Te deck accommodates six standard lanes and two emergency lanes, with widths of 3.75 m and 3 m, respectively.Figure 3.1.BridgeInformation.An on-site experiment was conducted on the Runyang Suspension Bridge (RSB), a bridge that spans the Yangtze River in China.Te RSB is a longspan suspension bridge, featuring a fat steel box girder and two H-

Table 1 :
Verifcation of the static behavior of the established FEM.

Table 2 :
Verifcation of the dynamic behavior of the established FEM.

Table 3 :
Comparative performance of data-driven models for speed prediction.

Table 4 :
Performance comparison of deep learning models for full-bridge trajectory prediction.

Table 5 .
Overall, the vehicle speeds generated by the TLS method show a strong alignment with the observed data, especially in Lane #3, where the errors are less than 4%.Te maximum error observed is 11.1% of the 25% quantile value in Lane #5.Considering the signifcantly lower number of vehicles and samples in Lane #5 used for model training compared to Lane #3, it is expected that these errors could be substantially minimized by enlarging the dataset in future studies.

Table 5 :
Quantitative comparison of speed distribution between TLS data and observed data.