Research on ATT-BiLSTM-Based Restoration Method for Deflection Monitoring Data of a Steel Truss Bridge

Abstract

Given the intricate operating environment of steel truss bridges, data anomalies are frequently initiated by faults in the sensor monitoring system itself during the monitoring process. This paper utilizes a steel truss bridge as a case study in engineering, with a primary focus on the deflection of the main girder. The paper establishes an Attention Mechanism-based Bidirectional Long Short-Term Memory Neural Network (ATT-BiLSTM) model, with the objective of accurately repairing abnormal monitoring data. Firstly, correlation heat maps and Gray correlation are employed to detect anomalies in key measurement point data. Subsequently, the ATT-BiLSTM and Support Vector Machine (SVR) models are established to repair the anomalous monitoring data. Finally, various evaluation indexes, including Pearson’s correlation coefficient, mean squared error, and coefficient of determination, are utilized to validate the repairing accuracy of the ATT-BiLSTM model. The findings indicate that the repair efficacy of ATT-BiLSTM on anomalous data surpasses that of SVR. The repaired data exhibited a tendency to decrease in amplitude at the anomalous position, while maintaining the prominence of the data at abrupt deflection change points, thereby preserving the characteristics of the data. The repair rate of anomalous data attained 93.88%, and the mean square error of the actual complete data was only 0.0226, leading to substantial enhancement in the integrity and reliability of the data.

1. Introduction

The advent of innovative materials, design methodologies, and construction technologies has led to the widespread adoption of steel truss bridges, which possess the capacity to bear substantial loads, span considerable distances, and exhibit aesthetic appeal [1,2,3]. However, steel truss bridges are susceptible to component failure during long-term service. In the absence of timely notification regarding local damage, a chain reaction may be initiated, potentially resulting in significant impairment to the structural system in its entirety [4]. Therefore, the implementation of an effective structural health monitoring (SHM) system is imperative to ensure the safe operation of steel truss bridges in service [5,6]. The reliability of the monitoring data directly correlates with the effectiveness of the structural health monitoring system. The optimal arrangement of sensors is a pivotal technology for ensuring data integrity. Research has demonstrated that a reasonable sensor arrangement design can enhance the quality of data acquisition [7,8].

However, under the influence of complex natural environments, anomalies in the collected monitoring data are often observed [9,10,11]. These anomalies can be categorized into two distinct groups. The first category is attributed to the structural integrity of the bridge itself, influenced by its performance and the progressive deterioration of the materials used. This results in anomalies in the monitoring data. The second category is associated with errors in the sensor monitoring system itself, leading to data anomalies [12]. The latter type of anomalous data, caused by objective factors, is not reflective of the actual state of the structure to which the anomalies relate. This type of anomaly is referred to as a monitoring data anomaly. The necessity arises to employ effective methods to locate the abnormal monitoring data, as well as to troubleshoot and repair the data [13,14,15].

In the extant research on the monitoring of data from steel truss bridges, the majority of scholars employ conventional methods, such as the moving average and interpolation, to rectify anomalous data. However, these methods frequently neglect the correlation between abnormal data points, which hinders the precise identification of complex abnormalities and consequently reduces the accuracy of repairs. Additionally, their data simulation capabilities are constrained, impeding the capture of intricate relationships within time-series information and failing to accurately mirror the dynamic alterations in steel truss bridge structures [16,17,18].

In order to address the intricacies and nonlinear properties inherent in the monitoring data of steel truss girder bridges, and to ensure the precision and dependability of the rectification of anomalous monitoring data, this paper proposes the implementation of an Attention Mechanism-based Bidirectional Long Short-Term Memory Neural Network (ATT-BiLSTM) model, which integrates the Attention Mechanism (Attention) and the Bidirectional Long Short-Term Memory (BiLSTM) network. This method has been demonstrated to be more adaptive in the context of bridge monitoring data, with the capacity to more accurately identify and rectify anomalous data, thereby enhancing the efficacy of the overall repair process. BiLSTM is a model that emphasizes the temporal relationships present in the entirety of the sequence. The Attention Mechanism enables the model to dynamically adjust the level of attention allocated to different time steps, thereby facilitating more effective handling of anomalies at various points in time [19,20].

Therefore, the present paper integrates a range of theoretical frameworks to collectively address the restoration of deflection monitoring data for primary girders of steel truss bridges. The detection of abnormalities is facilitated by the utilization of correlation heat maps and Gray correlation for pivotal measurement point data. Subsequently, the ATT-BiLSTM model is employed to rectify the abnormal data. Various evaluation metrics are employed to assess and substantiate the efficacy of the rectification process. The objective of this initiative is to establish a reference point for the processing of analogous bridge monitoring data, thereby enhancing the reliability and accuracy of the monitoring system.

2. Project Examples

The research object is a steel truss bridge in Fujian Province, China. The bridge is a double-deck variable-height public-rail dual-use steel truss bridge with a span composition of 121 + 276 + 121 = 518 m. Its main span adopts a 276 m variable-height prestressed steel truss combined with girders, the upper deck of the bridge is designed as a 31 m wide highway line, and the lower deck is designed as a bidirectional subway line [21]. The main truss cross-section consists of two main trusses, with a truss width of 15 m, a standard truss height of 9.5 m in the middle of the span, and an intersection length of 12 m, adopting a triangular truss with no vertical rod; at the main pier, the truss height gradually increases to 23 m through five intersections; the main girder is equipped with bearings at both the main pier and the side piers, among which, pier 1# is a fixed bearing, the rest of the bearings can be moved in a longitudinal direction, and the transversal direction has a fixed bearing at one side and movable bearings at the other side. The transverse side is a fixed bearing, and the other side is a movable bearing [22]. The structural elevation of the bridge is shown in Figure 1.

3. Monitoring Point Selection and Anomalous DATA Detection

3.1. Selection of Monitoring Points

A comprehensive analysis of the substantial monitoring data concerning main girder deflection obtained from the monitoring system of a real bridge was conducted. A portion of the data was selected for further study. The remainder of the paper enumerates the primary girder deflection monitoring data of the aforementioned bridge from 4:00 on 11 October 2023 to 10:00 on 12 October 2023, along with the results of the ensuing analysis.

Main girder deflection is a visual manifestation of the structural mechanical behavior characteristics of large-span steel truss girder bridges. It is also an important index that affects the normal use of steel truss girder bridges. In the monitoring process, specific correlations in deflection are evident between measurement points at varying locations. When the relative distance between measurement points falls within the optimal range, the correlation is pronounced, and the data reconstruction accuracy is enhanced [23].

To ensure the accuracy and reliability of the deflection data repair, the six deflection monitoring points shown in Figure 2 and Figure 3 were selected for the study. Specifically, measurement points 1 and 2 are situated within the same cross-section in the primary girder span, while measurement points 3, 4, 5, and 6 are positioned in the 3/8 and 5/8 cross-sections of the main span, adjacent to the measurement points in the main girder span.

The employment of correlation heat maps as a pivotal instrument for the preliminary analysis of deflection monitoring data facilitates the expeditious identification of sensor monitoring data at pivotal locations of steel truss bridges (e.g., in the middle of the main girder spans), which are indispensable for the evaluation of the bridge’s overall performance [24]. Figure 4 shows the correlation heat map for the six measurement points.

As demonstrated in Figure 4, the correlation coefficient of the two-by-two cross cells of points 1, 2, and 3 is 0.98, which is nearly 1, suggesting a high degree of linear correlation. From a color perspective, the right side of the color scale indicates that the closer the value is to 1, the deeper the color. The color of the corresponding cells of the three points is consistent with the color scale of the area near 1, which intuitively reflects the strong correlation. A close examination reveals a high degree of correlation among these three monitoring points, with a notable synchronization in the trend of their data changes.

Consequently, guided by the correlation heat map, three deflection monitoring points (point 1, point 2, and point 3) with high correlation were selected for focused analysis, thereby establishing a data foundation for the subsequent exclusion and localization of anomalous data, as well as the assessment of the repair effect. Given that monitoring point 2 is located in the middle of the main girder span of the bridge and has the most significant structural response to the bridge’s deflection, point 2 was selected as the target repair point.

3.2. Abnormal Data Detection

A thorough examination of the deflection monitoring data reveals that the characteristics exhibited by the steel truss girder bridge in Fujian can be categorized into four distinct types: missing, jumping point, drift, and trend anomaly. In the context of real-time monitoring data, anomalous data types frequently coexist, and the situation is more complex and diverse. The initial step in this process is the identification of anomalous data points, which includes such phenomena as jumps, drifts, and trend anomalies.

Gray correlation has been demonstrated to be applicable in the domains of data preprocessing and anomaly detection. The accuracy requirements for Gray correlation data are modest, even in the presence of noise or uncertainty. Gray correlation can yield valuable insights into the relationships between data, even when faced with limited sample sizes. Its effectiveness remains consistent, making it a suitable approach for scenarios with limited data.

Gray correlation is a methodological approach employed for analysis of the degree of correlation between two time series. This methodology is particularly suited to application in the context of nonlinear data [25,26]. Calculation of Gray correlation is based on the correlation coefficient between sample points. It has been demonstrated that the larger the coefficient, the more similar the two series are, and the stronger the correlation is. The calculation process is meticulously delineated as follows: firstly, standardization of the original sequence is implemented; secondly, calculation of the correlation coefficient sequence ensues; and finally, calculation of the Gray correlation is conducted. Among them, the standardization is to eliminate the influence of different scales, while the correlation coefficient reflects the degree of difference or similarity between the elements in the sequence, and the mean value of the Gray correlation quantifies the degree of correlation of the overall data. By following these three steps, a quantitative indicator of the overall correlation can be obtained. The mathematical formulas are as follows:

• Original sequence:

Initially, two original sequences, $X$ and $Y$, are established, each possessing a length of $n$.

$$X=\left[x_1,x_2,\dots ,x_n\right]$$

(1)

$$Y=[y_1,y_2,\dots ,y_n]$$

(2)

2.

Sequence normalization:

$$X^{*}={\displaystyle \frac{X-\mathit{min}(X)}{max\left(X\right)-\mathit{min}(X)}}$$

(3)

$$Y^{*}={\displaystyle \frac{Y-\mathit{min}(Y)}{\mathit{max}(Y)-\mathit{min}(Y)}}$$

(4)

Normalize the original sequence to $X^{*}$and$Y^{*}$.

3.

Calculate the sequence of association coefficients:

Calculate the association coefficient sequences $C_X$ and $C_Y$, denoting the association coefficients of $X$ and $Y$, respectively.

$$C_X=\sum _{i=1}^n|x_i-x|$$

(5)

$$C_Y=\sum _{i=1}^n|y_i-y|$$

(6)

where$x$denotes the mean value of the$X$sequence and$y$denotes the mean value of the$Y$sequence.

4.

Gray correlation calculation:

Calculate the Gray correlation$GR$. The overall correlation is represented by the mean of the correlation coefficients [27].

$$GR=\exp \left[-\rho \sqrt{{\left({\displaystyle \frac{C_X}{C_{Xmax}}}\right)}^2+{\left({\displaystyle \frac{C_Y}{C_{Ymax}}}\right)}^2}\right]$$

(7)

where$\rho$is the correlation coefficient weight, generally taken as 0.5, and $C_{Xmax}$ and $C_{Ymax}$ are the maximum values in$C_X$and$C_Y$, respectively.

The empirical value-taking method was employed to set the correlation threshold at 0.8. The correlation coefficient weight, denoted by ρ, was set to a constant of 0.5, thereby indicating the weight of the correlation coefficient. This coefficient was employed to adjust the influence degree of exponential decay. The robustness of the system was verified through a parameter sensitivity analysis, which revealed that the optimal balance between the detection rate and the false alarm rate was achieved at a threshold of 0.8 and a correlation coefficient weight of 0.5. This outcome meets the requirements of engineering practice. gr1_2, gr2_3, and gr3_1 are the correlation of deflection data between deflection measurement points 1 and 2, 2 and 3, and 3 and 1, respectively, as shown in

Table 1. Correlation of deflection data at measurement points 1, 2, and 3.

Data Point	Gr1_2	Gr2_3	Gr3_1
0	0.884405	0.868338	0.870946
1	0.876814	0.857433	0.864177
2	0.849149	0.843059	0.845116
3	0.818202	0.810212	0.806560
4	0.803600	0.798713	0.788723
5	0.809120	0.807189	0.803115
6	0.797163	0.785178	0.805654
…	…	…	…
99,995	0.929417	0.929678	0.929959
99,996	0.929417	0.929678	0.929959
99,997	0.931791	0.929678	0.932353
99,998	0.932966	0.931992	0.933562
99,999	0.934044	0.931992	0.934650
Total: 100,000

and Figure 5.

In typical circumstances, the deflection data between disparate monitoring points is expected to demonstrate a high degree of correlation, while the time trend is anticipated to exhibit consistency. In the event that the correlation coefficient falls below the predetermined threshold of 0.8, it is indicative of a substantial discrepancy in the deflection data between the designated monitoring points. This discrepancy typically signifies the presence of anomalous conditions.

The Gray correlation method, as previously outlined, was employed to calculate the correlation coefficients of gr1-2 and gr2-3. This calculation was conducted separately using the deflection data between monitoring points 1, 3, and 2. Calculation of the correlation coefficient sequence is contingent upon the pre-established threshold of 0.8, which serves as the criterion for determining whether the correlation coefficient falls below this threshold. When gr1-2 and gr2-3 are both lower than 0.8, it is indicative of a greater inconsistency in the deflection data between monitoring points 2 and 3, and between points 1 and 2. This inconsistency is greater than the established threshold, which is identified as the anomalous data from monitoring point 2. As illustrated in Table 1, data point 6 corresponds to the abnormal data from monitoring point 2. As illustrated in Figure 5d, for gr1-2 and gr2-3, both values below 0.8 are identified as anomalous data points for monitoring point 2.

According to the aforementioned methodology, a total of 4061 anomalous data points were derived for deflection measurement point 2, exhibiting a data anomaly rate of 4.06%. The specific locations and values of these anomalous data points are enumerated in

Table 2. Deflection point 2 anomaly monitoring data (mm).

Abnormal Data Point	Abnormal Data Values	Abnormal Data Point	Abnormal Data Values
6	11.8750	99,199	15.6875
311	3.9375	99,200	15.5000
312	3.5000	99,201	15.5625
313	3.0625	99,202	15.3125
314	2.9375	99,203	14.5625
…	…	Total: 4061

.

4. ATT-BiLSTM Anomaly Data Processing

Given that data integrity and accuracy are fundamental to the reliability of bridge monitoring systems, effective repair of abnormal monitoring data is imperative. Consequently, in this paper, the anomalous data at measurement point 2 will be rectified using the ATT-BiLSTM model, as illustrated in Figure 6. The specific steps in this process include data preprocessing, model construction and training, and repair and validation of anomalous data.

Attention Mechanisms play a critical role in enabling the model to focus on key areas during the process of data monitoring and repair. In this regard, the model has the capacity to dynamically adjust its weights on input sequences, thereby emphasizing data points that are particularly salient for the repair task at hand. This, in turn, contributes to enhancing the model’s repair accuracy with each iteration, thus ensuring the model’s enhanced ability to accurately identify the locations and patterns of anomalous data.

The role of the Long Short-Term Memory (LSTM) neural network is twofold. Firstly, it is employed to capture long-term dependencies in time-series data. Secondly, it is utilized to retain information from past moments. Given that bridge monitoring data are typically characterized by the temporal sequence of events, the utilization of LSTM proves advantageous in facilitating the comprehension and anticipation of evolving patterns within the monitoring data. This approach enables the preservation of historical data through its memory units, thereby facilitating the consideration of potential temporal correlations during the repair process. The technology has been demonstrated to have significant applicability in the domains of structural health monitoring, deformation reconstruction, and response prediction for bridges with small deformations.

4.1. ATT-BiLSTM Data Preprocessing

In order to ensure the stability and accuracy of the model, it is imperative to implement rigorous preprocessing of the raw data. The primary preprocessing steps entail data standardization and dataset division.

(1)

Data standardization

The Z-score standardization method is employed to transform the data into a standard normal distribution with a mean of 0 and a standard deviation of 1. This transformation facilitates the convergence of the model and enhances its performance [28]. Standardization of the deflection monitoring data was achieved through the implementation of the StandardScaler class, a component of the Scikit-Learn library. Initially, the training set data were fitted to calculate the mean and standard deviation. Subsequently, these parameters were applied to normalize the training and test sets to ensure that they had the same normalized form.

The mathematical formulas are as follows:

• Dataset organization: according to the deflection monitoring data, organized into the original feature dataset:

  $$X={\left[x_1,x_2,\dots ,x_n\right]}^T$$

  (8)
• Z-score normalization:

  $$z_i={\displaystyle \frac{x_i-\mu }{\sigma }}$$

  (9)

  where$z_i$is the normalized eigenvalue, $x_i$is the original eigenvalue, $\mu$ is the mean of the feature, and$\sigma$ is the standard deviation of the feature.

In the StandardScaler class, the fit_transform method is employed to fit the data, calculate the mean and standard deviation, and subsequently perform a normalization transformation to obtain the normalized dataset$X$.

(2)

Division of the dataset

The objective of the dataset division is to furnish the ATT-BiLSTM repair model with patterns and features that have been learned to correlate between the deflection monitoring data and to validate the learning effect. The repair of the abnormal deflection data at measurement point 2 served as the guiding principle, with all of the normal data from measurement point 2 being utilized as the model training output set. Meanwhile, the data from measurement points 1 and 3 were employed as the model training input set. The model focused on learning the structural features of the bridge under normal conditions through an all-data training strategy.

The primary rationale for not establishing a distinct test set is to guarantee that the model can leverage the entirety of the available data to discern the characteristics of the bridge structure in its normal state. This approach enables the model to concentrate on acquiring knowledge about the normal state, which may enhance its capacity to predict abnormal data more effectively.

Subsequent to the training phase, the model can be utilized for the purpose of predicting anomalous data. Given the absence of a test set designed to evaluate the model’s performance on unseen data, traditional verification methods for assessing the model’s generalization ability are not applicable. However, this paper employs a comparative analysis of abnormal and predicted data, and also compares the correlation between the original data and the normal data plus the predicted data as a means of verifying the accuracy of the model in predicting abnormal data, as well as verifying the model’s sensitivity to and ability to recognize changes in the structural state of the bridge.

4.2. ATT-BiLSTM Model Setup and Training

In the ATT-BiLSTM model construction and training process, the two core components—the BiLSTM layer and the Attention Mechanism—are fully utilized. For the bridge deflection data anomalies, based on experience and experimental results, after many iterations of parameter tuning, we finally obtained the optimal model parameters and structural settings. The following is a detailed introduction of the model hyperparameters and the network structure design.

(1)

Hyperparameterization

• Learning Rate: The learning rate is a pivotal hyperparameter that dictates the step size of the model during parameter updates, thereby influencing the rate of model convergence. A modest learning rate was selected to guarantee the model’s steady convergence during the training process. The learning rate was established at 0.001, as specified by learning_rate = 0.001. Through a series of experiments and research studies, it was ascertained that this specific learning rate facilitated rapid convergence of the model while ensuring that the optimal solution was not bypassed during the training process, thereby yielding favorable outcomes.
• Dropout Rate: The dropout rate is employed to regulate the random disconnection of neurons during the training process. It is set to 0.01 to maximize the model’s expressive capacity during training while mitigating the risk of overfitting, as specified by dropout_rate = 0.01.
• Number of Layers: The number of network layers refers to the number of LSTM layers in the model. According to related studies, a two-layer bidirectional LSTM is beneficial for the model to capture long-term dependencies in the input sequences. Therefore, the number of network layers in this model is set to two, which is specified by num_layers = 2 [29].
• Hidden Size: The quantity of hidden layer nodes is contingent upon the number of neurons in each LSTM layer, constituting a pivotal parameter within the model. In order to guarantee that the model does not become excessively complex while simultaneously acquiring knowledge of the task features, subsequent to parameter tuning, the number of hidden layer nodes is configured to 128, as specified by the hidden_size parameter set to 128.

(2)

Model structure setup

• BiLSTM Layer: A bidirectional LSTM layer is employed for the purpose of bi-directional modeling of input sequences. The number of input features is designated as input_size, while the number of output features is calculated as hidden_size multiplied by two (bidirectional) with num_layers layer, created by nn.LSTM.
• Attention Mechanism: The Attention Mechanism is employed to enhance the model’s attention to the input sequence. Attention inputs are of size hidden_size × 2, and outputs are of size hidden_size × 2. Two linear layers were created by nn.Linear.
• Full Connectivity Layer: The Attention output was mapped to the final output dimension, with an input feature count of hidden_size × 2 and an output feature count of 1. This mapping was created by nn.Linear.

(3)

Loss function and optimizer selection

• Loss Function: The primary objective of this model is to predict the value of deflection, a process often referred to as regression. The mean square error, a statistical measure of the average squared difference between predicted and actual values, is employed in regression analysis. The formula for the mean square error is as follows:
  $$MSE={\displaystyle \frac{1}{n}}\sum _{i=1}^n(y_i-{\widehat{y}}_i{)}^2$$

  (10)

  where$n$is the number of samples,$y_i$is the actual label, and ${\widehat{y}}_i$ is the predicted output of the model.
• Optimizer: The Adam optimizer (torch.optim.Adam) is an adaptive learning rate optimization algorithm that automatically adjusts the learning rate for each parameter, with different learning rates for different parameters, so that this training process converges more efficiently.

(4)

Training Process

• Number of Iterations: The selection of the number of iterations is contingent upon factors such as the size of the training set, the complexity of the model, and the constraints imposed by computational resources. An excess of iterations may result in overfitting, whereas an insufficient number of iterations may hinder the model’s learning process. Through a series of experiments and adjustments, the optimal number of iterations was determined to be three.
• Batch Size: The selection of batch size is constrained by computational resources. A larger batch size may necessitate more memory but can enhance the training speed. A smaller batch size may yield more precise gradient estimation but may result in a noisier training process. Following numerous experiments and adjustments, the batch size is set to 128.
• Loss Curve: The loss curve is a graphical representation of the loss function, the objective of which is to minimize the squared difference between the predicted value and the actual value. This enables the model to better fit the training data. During the training process, the model parameters are adjusted through the back propagation algorithm according to the loss function. This process enables the gradual improvement of the model’s prediction accuracy and ultimately leads to the generation of the model’s loss curve. It is evident that the model’s fit to the training data is optimized when the loss value is minimal.

As illustrated in Figure 7, the loss curve demonstrates the relationship between the number of training batches (horizontal axis) and the model’s loss (vertical axis). At the onset of the training process, the loss value is typically substantial (approximately 1.2), and as the training progresses, the loss value undergoes a rapid decrease, ultimately converging at approximately 0.02. This convergence signifies that the model has effectively learned the pattern of the data, exhibits a good fit, and demonstrates a rapid enhancement in performance on the training set. Furthermore, the model loss stabilizes at approximately 0.02, suggesting that there is an absence of overfitting. Furthermore, the loss function exhibits a rapid decrease, with a low fluctuation rate that remains within the range of 0.01. This observation suggests that the model has been set at an appropriate learning rate.

4.3. ATT-BiLSTM Anomaly Data Repair

In order to verify the practicality of the model, the trained model was used to predict the anomalous data at measurement point 2 (the mid-span section, which better reflects the structural response state of the bridge) and analyze the fit with the actual data.

The data at measurement points 1 and 3, corresponding to the anomalous location of measurement point 2, are utilized as the input set for the ATT-BiLSTM data repair model that was trained in the previous section. The prediction input set is delineated in

Table 3. ATT-BiLSTM model predicts input set and repair set (mm).

Data Point	Measurement Point 1 Input Data	Actual Anomaly Data for Measurement Point 2	Measurement Point 3 Input Data	Measurement Point 2 ATT-BiLSTM Repair Data
6	12.2500	11.8750	11.6875	12.450481
311	3.8750	3.9375	2.3125	4.201364
312	3.5000	3.5000	2.0625	3.868597
313	3.1875	3.0625	1.6875	3.577300
314	2.8750	2.9375	1.3750	3.414109
…	…	…	…	…
99,199	16.1250	15.6875	15.8750	16.220303
99,200	15.8750	15.5000	15.8750	16.057016
99,201	15.6250	15.5625	15.5625	15.795417
99,202	14.9375	15.3125	15.3750	15.320224
99,203	13.9375	14.5625	15.0000	14.631486
Total: 4061

. Following the precise predictions made by the ATT-BiLSTM data repair model, it was determined that the anomalies had been successfully rectified, thereby enhancing the continuity and smoothness of the data series. This observation is substantiated by examination of the model-repaired data Table 3.

In order to demonstrate the impact of model repair in a more intuitive manner, the abnormal data repair results are represented in Figure 8. A comparison of the original anomalous data with the model repair data reveals that the repaired data and the original data remain consistent in trend, yet there is a significant improvement in outliers. The abnormal fluctuation points in the original data are clearly discernible, as illustrated in Figure 9.

As illustrated in Figure 8 and Figure 9, the data post-repair demonstrates a tendency of amplitude diminution at the anomaly, thereby effectively mitigating the likelihood of false alarms. Concurrently, at the deflection jump point, the rectified data did not fully eliminate the prominence of the jump point, thereby ensuring the thoroughness of the warning information and averting the occurrence of underreporting. This finding suggests that the model not only learns the internal correlation of the data during the repair process, but also pays particular attention to the associated deflection of the main girder mid-span section and its neighboring parts. Consequently, this data repair method can provide more reliable data support for deflection monitoring of steel truss bridges.

5. SVR Exception Data Handling

The objective of this section is to compare the effectiveness of different methods for data repair. To this end, the Support Vector Machine (SVR) model is employed for training. The SVR model has been demonstrated to possess excellent regression analysis capabilities [30]. It captures the complex relationships in the data and repairs abnormal data.

5.1. SVR Data Preprocessing

In the data preprocessing stage, the data were standardized in strict accordance with the methods described in Section 4.1, and the dataset was reasonably divided, with the aim of ensuring the consistency of the SVR and ATT-BiLSTM models in the data. This laid a solid foundation for the subsequent comparative assessment of the two models and ensured the objectivity and validity of the assessment results.

5.2. SVR Model Setup and Training

(1)

Model Setup

• Kernel Function Selection: Given the evident nonlinear characteristics exhibited by the deflection monitoring data, the radial basis function (RBF) was selected as the kernel function for this model (kernel = ‘rbf’).
• Hyperparameterization: The regularization parameter, which governs the severity of penalty imposed for errors, is intended to avert the model from overfitting on the training set, over-adapting to noise, and losing the capacity to generalize to novel data. In light of the prevailing circumstances and the temporal demands associated with model training, it is advisable to establish a moderate degree of regularization, denoted by $C$= 1.0. The epsilon parameter serves to delineate the model’s tolerance threshold for outliers during the training phase. It further determines the extent to which the model accommodates samples that do not adhere to the constraints imposed by the loss function. The formulation of this model is informed by tuning experiments and heuristic rules. In this context, the epsilon parameter is set to 0.2.
• Optimization Algorithm: The SMO algorithm is employed to address the data anomaly problem, which is essentially the dyadic problem in regression. This algorithm is utilized to solve the convex optimization problem with constraints and to identify the optimal function [30].

(2)

Model training

Termination Conditions: It is imperative to ascertain whether the optimization problem satisfies the termination condition. In the event that it does not, the process must return to the second step. The SVR model is executed by the SMO algorithm, whose algorithmic termination condition primarily depends on the convergence of the model. The convergence discrimination of this model is achieved through the implementation of a variable updating mode, which is evaluated by assessing the difference between updates and a predefined threshold (set at tol = 1 × 10⁻³). When the change in the objective function falls below tol, indicating that the optimization problem has converged, the algorithm is terminated, and the training of the model is considered complete.

5.3. SVR Exception Data Repair

The utilization of a trained SVR model, which operates in a manner analogous to that delineated in Section 4.3, results in the generation of the data shown in

Table 4. SVR model predicts input set and repair set (mm).

Data Point	Measurement Point 1 Input Data	Measurement Point 3 Input Data	Measurement Point 2 SVR Restoration Data
6	12.2500	11.6875	12.414220
311	3.8750	2.3125	3.614474
312	3.5000	2.0625	2.768712
313	3.1875	1.6875	2.438040
314	2.8750	1.3750	2.078867
…	…	…	…
99,199	16.1250	15.8750	16.027738
99,200	15.8750	15.8750	15.763535
99,201	15.6250	15.5625	15.206753
99,202	14.9375	15.3750	14.994968
99,203	13.9375	15.0000	14.723242
Total: 4061

following the implementation of the SVR model repair.

6. ATT-BiLSTM and SVR Repair Accuracy Evaluation

Performance evaluation constitutes a pivotal phase in validating the restoration efficacy of the model. This section employs a multifaceted approach to evaluate the linear correlation between the restoration data and the actual monitoring data. First, the Pearson correlation coefficient is calculated to quantify the linear relationship between the two sets of data. Then, error assessment indicators and model validation are utilized to objectively assess the degree of deviation between the restoration data and the actual monitoring data.

6.1. ATT-BiLSTM and SVR Accuracy Validation

In the evaluation of the ATT-BiLSTM model and the SVR model’s anomaly data repair accuracy, the correlation matrix is constructed using Pearson’s correlation coefficient. This coefficient helps us to understand the relationship between the two sets of data features and is used to evaluate feature selection, data preprocessing, and model interpretation.

The correlation matrix is defined as a square matrix in which the elements represent the correlation between the corresponding features. In the upper and lower triangles, the elements on the diagonal are assigned a value of 1. This is due to the fact that each feature is maximally correlated with itself, indicating a perfect positive correlation. The Pearson correlation coefficient, in contrast, is a statistical measure of the degree of linear relationship between two variables. This coefficient ranges from −1 to 1, with 1 indicating a perfect positive correlation between the two variables [31,32].

The deflection monitoring data were calculated before and after the integration of the restoration. The correlation matrix between the columns of the original and restored data was obtained, and clearly demonstrated the linear relationship between different features in the data, as shown in

Table 5. Original, ATT-BiLSTM-repaired, and SVR-repaired correlation matrix for anomalous data.

Data Type	Deflection Monitoring Point	Point1_Data	Point2_Data	Point3_Data
Original anomaly data	Point1_data	1.000000	0.962409	0.954059
	Point2_data	0.962409	1.000000	0.960798
	Point3_data	0.954059	0.960798	1.000000
Anomalous data repaired by ATT-BiLSTM	Point1_data	1.000000	0.989927	0.954059
	Point2_data	0.989927	1.000000	0.985518
	Point3_data	0.954059	0.985518	1.000000
Anomalous data repaired by SVR	Point1_data	1.000000	0.985372	0.954059
	Point2_data	0.985372	1.000000	0.985186
	Point3_data	0.954059	0.985186	1.000000

and

Table 6. Correlation matrix for all original data and all data after ATT-BiLSTM repair and SVR repair.

Data Type	Deflection Monitoring Point	Point1_Data	Point2_Data	Point3_Data
All original data	Point1_data	1.000000	0.983706	0.978996
	Point2_data	0.983706	1.000000	0.982825
	Point3_data	0.978996	0.982825	1.000000
All data after ATT-BiLSTM repair	Point1_data	1.000000	0.986342	0.978996
	Point2_data	0.986342	1.000000	0.985148
	Point3_data	0.978996	0.985148	1.000000
All data after SVR repair	Point1_data	1.000000	0.984546	0.978996
	Point2_data	0.984546	1.000000	0.983359
	Point3_data	0.978996	0.983359	1.000000

.

As illustrated in the above table, the original anomaly data exhibited a high degree of correlation. When the model selects the training data, the three deflection measurement points with the highest correlation are selected as inputs to ensure that the anomaly data in deflection measurement point 2 can be accurately recognized. A comparison of the repair effects of SVR and ATT-BiLSTM reveals the following findings:

(1) The ATT-BiLSTM and SVR models are demonstrated to enhance the correlations of the corr-colf1-colf2 and corr-colf2-colf3 datasets following data repair. This outcome indicates that the correlations of the repaired deflection monitoring data on the entire dataset are further enhanced, thereby substantiating the rationality and feasibility of data repair.

(2) The ATT-BiLSTM model enhances the correlation between colf1_data and colf2_data from 0.983706 to 0.986342, while the SVR model elevates it to 0.984546. This enhancement is more substantial for the ATT-BiLSTM model compared to the SVR model. For the correlation between colf3_data and colf2_data, the ATT-BiLSTM model enhances the correlation from 0. The range of values is from 982,825 to 0.985148, while the SVR model improves it to 0.983359, which is also larger than that of the SVR model. This indicates that, compared to the SVR model, the ATT-BiLSTM model, in terms of the overall data correlation after repairing the anomalous data, is capable of more accurately recovering the correlation between colf1_data and colf2_data and between colf3_data and colf2_data.

(3) To further quantify this advantage, the score_SVR and score_ATT-BiLSTM scores were calculated. The two scores under consideration represent the SVR and ATT-BiLSTM model scores, respectively. These scores are obtained by comparing the correlation coefficients of the repaired data and the corresponding features in the anomalous (or raw) data and accumulating the differences. The mathematical formulas for score_SVR and score_ATT-BiLSTM can be expressed as follows:

$$score\_SVR={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{i=1}^n(corr\_SVR[i,j]-corr[i,j])}}$$

(11)

$$score\_ATT-BiLSTM={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{i=1}^n(corr\_ATT-BiLSTM[i,j]-corr[i,j])}}$$

(12)

where$n$is the number of features,$corr$is the correlation matrix between the features of the original data,$corr\_SVR$is the correlation matrix between the features of the predicted results of the SVR model, and$corr\_ATT-BiLSTM$is the correlation matrix between the features of the ATT-BiLSTM repaired data.

The discrepancy between the correlation matrix of the SVR predictions and the correlation matrix of the original data was calculated, and these differences were summed up to obtain$score\_SVR$= 0.0477. In a similar manner, for the ATT-BiLSTM-repaired data, the discrepancy between the repaired correlation matrix and the correlation matrix of the original data was calculated. These discrepancies were then summed to obtain$score\_ATT-BiLSTM$= 0.052. The specific scores are displayed in Figure 10.

The calculation of these two scores is performed in a manner that quantifies the discrepancy between the repair effects of SVR and LSTM. The results of this calculation clearly demonstrate that the repair of anomalous data by ATT-BiLSTM is superior to that of the SVR model. Therefore, the ATT-BiLSTM model proposed in this paper has been demonstrated to possess both reliability and high accuracy when utilized for data repair.

6.2. Evaluation of ATT-BiLSTM Error Metrics

In order to further validate the repair accuracy of the model, three evaluation metrics—MSE (mean square error), RMSE (root mean square error), and R² (coefficient of determination)—were introduced. Error evaluation metrics, global performance analysis, and local performance analysis were used for specific description [33].

• Mean Square Error (MSE): A statistical measure of the discrepancy between the restoration value and the true value. A low MSE indicates a high degree of accuracy in the restoration, with smaller values approaching 0. The formula for calculating MSE is shown in Formula (10). Where $n$ denotes the sample size, $y_i$denotes the actual observations, and ${\widehat{y}}_i$denotes the model predictions.
• Root Mean Square Error (RMSE): The square root of the mean square error (MSE), which is a metric used to quantify the discrepancy between the values predicted by a model and the actual values [34].
  $$RMSE=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n(y_i-\widehat{y_i}{)}^2}$$

  (13)
• Coefficient of Determination (R²): A statistical measure of how well a model aligns with observed data. A value of R² close to 1 indicates a stronger match between the model and the data, suggesting a higher degree of model fit.

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n(y_i-\widehat{y_i}{)}^2}{{\sum }_{i=1}^n(y_i-\overline{y_i}{)}^2}}$$

(14)

(1)

Global performance analysis

The repair performance of the ATT-BiLSTM model for the global deflection dataset (including the repaired data as well as the normal data) is analyzed as follows:

• The MSE is calculated to be 0.0226, indicating that the mean squared error between the predicted and true values of the model in the entire dataset is minimal. This finding reflects the model’s strong predictive ability in the global range and its ability to accurately fit the overall distribution of the data.
• The RMSE is 0.1505, which further confirms that the absolute value of the model’s prediction error is small, indicating that the model’s prediction accuracy in the whole dataset is high.
• R² is 0.9943, which is close to 1. This indicates that the model has a good fit to the global dataset and that it is also predictive.

Based on the aforementioned calculations, the ATT-BiLSTM model demonstrates remarkably high levels of prediction accuracy and goodness of fit on the global dataset. Furthermore, the model is capable of effectively capturing the overall trend and characteristics of the data. A comparison plot of the original data with all the data following ATT-BiLSTM repair is shown in Figure 11. In this figure, the vertical coordinate is the deflection data (mm), and the horizontal coordinates are the deflection data points.

(2)

Local performance analysis

The repair performance of the ATT-BiLSTM model for the anomalous deflection dataset is analyzed as follows:

• The MSE was calculated to be 0.5576, which is high relative to the global MSE value. However, the error value is still in the acceptable range due to the fact that anomalous data usually has higher uncertainty and complexity [35].
• The RMSE is 0.7467, which is marginally higher than the global RMSE due to the nature of the anomalous data. However, the accuracy generally meets the requirements.
• The R² value of 0.9388 indicates a slight decrease compared to the global R² value, yet it remains close to 1, suggesting that the model continues to adequately fit the anomalous data and effectively identify and repair most anomalous data while maintaining high prediction accuracy. The comparison graph of the original anomalous data and the repaired anomalous data is shown in Figure 12.

The ATT-BiLSTM model demonstrates a high degree of prediction accuracy and goodness of fit on the global deflection dataset, as evidenced by its ability to accurately fit the overall distribution and trend of the data. Despite the presence of some errors in predicting the anomalous data, the error value is deemed acceptable when taking into account the complexity and uncertainty of the anomalous data, as well as the reasonableness of the data comparison plot. Concurrently, the R² value of the model on the anomalous deflection data remains elevated, signifying its capacity to effectively identify and rectify the majority of anomalous data. The ATT-BiLSTM model, which integrates global and local performance analyses, demonstrates high accuracy and a robust capacity for anomalous data repair. This capability can markedly enhance the quality and reliability of the data.

7. Conclusions and Prospects

7.1. Conclusions

The present study utilizes a steel truss bridge in Fujian Province, China, as its engineering background and conducts a comprehensive technical analysis based on the bridge’s actual main beam deflection monitoring data. This analysis includes anomaly detection, anomaly data processing, and data accuracy assessment. The ensuing conclusions are hereby summarized:

(1) The efficacy of the screening process for anomaly detection was substantiated by the implementation of data selection, correlation heat map, and Gray correlation calculation theories. The anomaly data at the pivotal measurement point 2 (mid-span of the main girder) was localized and investigated, yielding an anomaly rate of 4.06%.

(2) The ATT-BiLSTM model has been established to address the anomalous monitoring data, with the repair results presented in graphical and correlation coefficient calculation formats. The results indicate that the repaired data at the anomalous location exhibit a trend of amplitude reduction. At the deflection jump point, the repaired data do not fully eliminate the prominence of the jump point, which effectively ensures the characteristics of the data.

(3) In terms of correlation performance, a comparison of the data restoration results of the ATT-BiLSTM model and the SVR analysis method reveals that the restoration effect of the ATT-BiLSTM model is superior to that of the SVR model.

(4) The efficacy of the ATT-BiLSTM model was assessed by employing various evaluation metrics, including mean square error, root mean square error, and coefficient of determination. The ATT-BiLSTM model was demonstrated to exhibit superiority in the realm of data monitoring and processing. The efficacy of this model is evidenced by its ability to repair 93.88% of abnormal data, while concurrently exhibiting an RMS error of 0.0226 with actual complete data. This outcome signifies the model’s capacity to effectively rectify abnormal data, thereby enhancing the reliability of the data.

The findings of this paper offer a robust scientific foundation for the analysis and evaluation of deflection monitoring data from analogous bridges. Conversely, by modifying the parameters of the ATT-BiLSTM model (e.g., the number of hidden layers, the design of the Attention Mechanism, and the selection of hyperparameters, etc.), the model could be applied to the analysis of other bridges of different types and environmental conditions, and longer monitoring cycles. It is evident that the methodology delineated in this paper exhibits extensive applicability in the domains of data analysis and the evaluation of structural health monitoring.

7.2. Prospects

The deflection monitoring data repair method for steel truss bridges, as outlined in this paper, has yielded specific outcomes. However, there is still potential for enhancement and optimization, which will be realized through further development and integration of monitoring data processing and visualization technologies. Future research could be initiated in the following areas:

(1) Bridge deflection values are constrained by the laws of physics and structural limits; however, the prediction process in the paper lacks physical constraints, such as the imposition of allowable deflection limits. This may lead to prediction bias in extreme cases, and this will be improved in subsequent studies.

(2) The primary objective of this paper was to examine the deflection monitoring data of specific sections of the bridge to ensure its overall integrity. To this end, future research initiatives should be pursued that encompass diverse monitoring types and extend to the entire bridge. This comprehensive approach will ensure the comprehensiveness of the bridge monitoring data.

(3) A more thorough examination of data repair and anomaly localization techniques could facilitate the optimization of neural network model design, enhancing the accuracy and efficiency of anomalous data repair.