Dynamic Load Identification on Prefabricated Girder Bridges Based on a CNN and Dynamic Strain Data

Abstract

The vehicle load on a bridge is a critical and dynamic variable. It adversely affects bridges, especially when overloading occurs. Bridges are prone to fatigue damage or collapse. Therefore, identifying the size and type of dynamic vehicle loads on bridges is critical for theoretical studies and practical applications, such as health monitoring, daily maintenance, safety assessment, and traffic planning. The paper proposes a method for identifying the dynamic load parameters based on a convolutional neural network (CNN) and dynamic strain data. The model is implemented in MATLAB. An initial finite-element model of a three-span precast beam bridge is established in the software ABAQUS and modified by combining the modal and experimental data derived from a segmental girder bridge. The dynamic strain response of the bridge under a moving vehicle load is simulated under different working conditions. The results are used as the training data of the CNN to identify the vehicle’s position, speed, and load on the bridge. The high prediction accuracy indicates the proposed model’s suitability for identifying the dynamic load parameters.

1. Introduction

Bridges are critical components of the national road network. Concrete bridges are the most widely used bridge type. However, advances in science and technology have resulted in the application of new construction technologies, such as precast beam bridges. They have many advantages over other bridge types, such as fast construction speed, wide spans, lower cost, and environmental protection. Therefore, precast beam bridges will be extensively used in future bridge construction [1,2]. The number of prefabricated girder bridges in China has increased, and the threat of collapses cannot be ignored [3,4]. Therefore, it is critical to determine vehicle parameters efficiently and accurately, especially dynamic vehicle loads, to perform safety assessments of bridges and obtain traffic statistics [5,6].

Structural health monitoring of long-span bridges is typically conducted by installing a dynamic weigh-in-motion (WIM) system [7,8]. It uses sensors and data processing instruments to calculate vehicle weight, speed, and other information as the vehicle passes through the measurement site. Research on dynamic weighing started only recently in China. Due to the high installation and maintenance costs of the WIM equipment and monitoring system and complex factors affecting the working performance of bridges, these systems are typically only installed on service bridges and rarely on conventional beam bridges [9]. Using a WIM system to obtain vehicle parameter information has the advantages of low cost, convenient use, and simultaneous monitoring of the bridge’s utilization [10]. Zhou et al. [11] proposed an integral time-domain method to discretize the time-domain integral equation of the load response. They replaced the unit impulse response function with an integral form to obtain the load inversion matrix and transformed the load identification problem into a linear equation problem. Chan et al. [12] performed a Fourier transform of the equation of motion represented by modal coordinates. The relationship between the structural response and the moving force was established, and the least squares method was used to calculate the force spectrum in the frequency range. The time history of the moving force was obtained by performing an inverse Fourier transform. Qian et al. [13] used the influence line to establish a relationship between the moving load and the bending moment. They proposed a method for identifying the moving load using the bending moment influence line. Law et al. [14] simplified the bridge as a simply supported Euler beam model and expressed the time-varying interaction force between the vehicle and the bridge as a step function in a short time interval, expressing the vibration equation in modal coordinates. The moving load identification equation was derived using the modal superposition in the time domain. Au et al. [15] used a multi-stage genetic algorithm to select the optimum parameters by minimizing the error between the measured acceleration and the acceleration reconstructed from the identification parameters. The variable search domain was reduced step by step to identify the moving vehicle parameters and vehicle loads on the beam.

Although the theory of moving load identification on bridges is relatively mature [16,17,18], several problems remain in the practical application due to the complex and dynamic interactions between vehicles and bridges, such as low identification accuracy and noise pollution. In addition, the mathematical model of the identified structure should be established before identifying the load. It is difficult to determine the exact parameters for most structures, complicating the establishment of the theoretical model because the parameters affect the accuracy of moving load identification.

With the rapid development of artificial intelligence and computer technology, some scholars have used artificial neural networks to identify moving loads [19,20]. Kromanis et al. [21] proposed a vector regression prediction model to predict the thermal response of the bridge based on distributed temperature measurements. Six years of temperature and strain monitoring data of a concrete bridge were used as samples for the model. The results demonstrated the model’s effectiveness, but large amounts of historical monitoring data were required. Kim et al. [22] used an artificial neural network and data from a bridge WIM (BWIM) system to extract the parameters of heavy vehicles from the strain time-domain data. Numerous vehicle driving tests were conducted on simply supported prestressed concrete girder bridges and cable-stayed bridges to verify the model’s feasibility. However, the identification error of individual factors was large. Li et al. [23] proposed a phased identification method based on a backpropagation (BP) neural network for identifying moving loads on bridges. This method accurately identified the vehicle speed and dynamic loads in real time. However, it does not consider the interaction between moving load parameters, which is unrealistic. Chen et al. [24] analyzed the basic principle and implementation steps of a neural network to identify moving loads. They used an improved particle swarm optimization algorithm to obtain the deviation and weight of the neural network, but its effectiveness was not verified by experiments. Yang et al. [25] used an artificial neural network to identify the load, position, speed, and wheelbase of vehicles crossing a simply supported beam bridge based on the dynamic strain response. The feasibility of the neural network method was verified by a model test but not by a case study.

In summary, artificial neural networks have strong logical reasoning ability and are suitable for inverse problems such as structural load identification. They are less expensive than the installation and maintenance of bridge health monitoring systems. However, neural networks may have difficulty converging, and many training samples are required. Moreover, current neural network recognition methods are mainly aimed at simple and continuous girder bridges, whereas few studies have been conducted on prefabricated girder bridges. In this context, finite-element analysis (FEA), as a powerful numerical computation tool, can effectively complement the methods of artificial neural networks. By conducting finite-element modeling and analysis of bridge structures, FEA can provide a wealth of simulated data for the neural networks, therefore overcoming the issue of insufficient real training samples.

Therefore, we propose a method for identifying moving load parameters of vehicles on prefabricated girder bridges using a convolutional neural network (CNN) implemented in MATLAB. An initial finite-element model of a three-span segmental assembled bridge is established using the software ABAQUS 2021 and modified using modal test data obtained from a case study. The dynamic strain response of the bridge under a moving vehicle load is simulated under different working conditions, and the results are utilized as the training data for the CNN to identify the position, speed, and load of vehicles crossing the segmental girder bridge.

2. Moving Load Parameter Identification Based on CNN

A CNN can have various structures [26] but consists of several convolution, pooling, fully connected, input, and output layers. The convolution layer is the core of the CNN. The architecture is shown in Figure 1 [27].

The objective is to convolve the input data using the convolution kernel and introduce the activation function to obtain the output feature map. This operation generally increases the number of extracted features. The pooling layer is another critical layer. Its function is to downsample the input feature map, reduce the dimensions of the feature map and the number of parameters to prevent overfitting and ensure the stability of the network while reducing the computational complexity. The convolution and pooling layers alternate in the network and are used for feature extraction. The fully connected layer performs classification, i.e., the features are integrated to enable the classifier to provide an output.

2.1. Identification Method of Moving Load Parameters

It is necessary to extract the dynamic strain response of the main girder at different positions, vehicle speeds, and load combinations to identify the moving load of segmental girder bridges using a CNN. The strain signal, which is sensitive to the load identification parameters, is selected as the input vector, and the identification parameters of the moving vehicle on the bridge are output to obtain the pre-processed data set. A sample library for neural network identification is created based on feature changes. An appropriate network structure and training method are selected. Known samples are used as the training set to train the network, and test samples are used to test the recognition accuracy of the network. This process is used to adjust the network’s nonlinear mapping relationship. The method for the moving load identification of prefabricated bridges based on a CNN and dynamic strain is illustrated in Figure 2.

2.2. Structural Analysis and Network Design

The strain response data of the measuring point under specific working conditions is used as the network input, and the CNN is implemented in MATLAB 2021 software. The moving load parameter identification problem is a regression prediction problem with multiple outputs. After repeated network adjustment, a CNN with 11 layers is obtained [28].

The CNN structure is shown in Figure 3. The CNN is trained with the strain response data for different moving load parameters and used to establish a mapping relationship between the strain response and the moving vehicle parameters [29] to identify and output unknown moving vehicle parameters. The details of the different layers of the CNN are as follows:

(1) Input Layer. This layer receives a two-dimensional numerical matrix composed of the strain response data of segmented assembled beam bridges under the action of moving loads. The size of the matrix is A1 × A2 with one channel, where A1 is the number of strain measurement points under a single working condition, and A2 represents the number of collected data for a single strain gauge corresponding to the output indicators.

(2) Convolution layer 1. The size of the convolution kernel is B1 × B2, the number is 32, the convolution step size is 1, and the Padding method is valid. B1 and B2 correspond to the length and width of the convolution kernel layer. The convolution layer is used with a batch normalization layer and the ReLU layer. The former normalizes the output data of the previous layer in batches and passes it to the next layer to accelerate the convergence speed during network training. Common activation functions are Sigmoid, Tanh, and ReLU. The ReLU nonlinear activation function is more suitable for backpropagation and parameter updating of the network and prevents gradient disappearance. Therefore, the ReLU activation layer was used.

(3) Pooling layer. Maximum pooling is used to extract the background features. The size of the pooling area is C1 × C2, and the pooling step size is 1.

(4) Convolution layer 2. The size of the convolution kernel is D1 × D2, the number is 64, the convolution step size is 1, and the convolution method is valid. The convolution layer is also used with a batch normalization layer and a ReLU layer.

(5) Dropout layer. Due to the small training data set, the CNN has a deep structure with many parameters. A random deactivation layer is used to prevent overfitting. This layer randomly sets the input elements to zero according to a predetermined probability, and the remaining elements remain unchanged. This method improves the network’s generalization ability. The random zero probability is 20%.

(6) Fully connected layer. The fully connected layer reduces the dimensions of the learned features, integrates the local feature information extracted from the convolution layer or the pooling layer, and assigns sample labels. The number of neurons in the fully connected layer in the last stage is equal to the number of output target indicators.

(7) Output layer. Since this paper performs regression prediction, this layer is a regression layer that outputs the regression prediction results.

2.3. Hyperparameter Settings

In a deep network, hyperparameters refer to parameters that must be determined before network training. They control the model’s structure, function, and efficiency. The purpose is to obtain the optimal mapping relationship. While referring to existing design codes [30], after repeated network adjustment, the training batch size is 25, the maximum number of training epochs is 500, the initial learning rate is 0.001, the learning rate decline factor is 0.1, the learning rate decline cycle is 300, and the data are disorganized after each training round. We employ the commonly used learning algorithm Adam [31], an adaptive learning rate optimizer, which combines the characteristics of stochastic gradient descent (SGD) and root mean square propagation (RMSProp). Although the Adam optimizer is more complex than the SGD optimizers, it automatically adjusts the learning rate, has high computational efficiency, and is not prone to falling into a locally optimal solution. Thus, it is widely used in training neural networks.

2.4. Network Evaluation Index

The coefficient of determination ($R^2$) [32] is used to assess the CNN’s performance. It is calculated as follows:

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

(1)

where n is the number of samples, ${\widehat{y}}_i$ is the calculated value, $y_i$ is the true value, and ${\overline{y}}_i$ is the average value of the true value.

The smaller the $R^2$ value, the worse the performance of the CNN and vice versa. In addition, aiming at the recognition effect of the network on the moving vehicle load position, the gap between the recognition position and the real position is measured. In addition, the correct recognition rate of the network is calculated. It is the proportion of samples with a relative error of less than or equal to 10% [33]. The relative output error of the network is the ratio of the distance between the output vector of the network and the ideal output vector to the norm of the ideal output vector:

$$\mathrm{R}\mathrm{e}={\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}}||{\widehat{\mathrm{y}}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}}||/{\displaystyle \frac{1}{\mathrm{n}}}{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}}||{\mathrm{y}}_{\mathrm{i}}||$$

(2)

where: n is the number of samples, ${\widehat{y}}_i$ is the calculated value, and $y_i$ is the true value.

3. Simulation of Precast Beam Bridge

3.1. Target Bridge

Determining the input and output parameters is crucial in load identification using neural networks. A 3 × 43 m prefabricated segmental bridge was used as a case study. The bridge has a three-span continuous beam, with a 43 m length for each span. The layout diagram is shown in Figure 4. The prestressed concrete single-box single-compartment segmental girder bridge is adopted in this joint, and the mid-span cross-section of the main beam is shown in Figure 5. The numerical simulation model of the bridge was established in ABAQUS, and the moving load conditions were applied using the DLOAD subroutine to calculate the response data of the bridge’s control section under different working conditions. Based on specific vehicle parameters, internal functions such as time, travel speed V, and vehicle load F are written and adjusted in Fortran, enabling the representation of various load effects of different vehicles [34,35]. The influence of the initial displacement and strain caused by prestressing was eliminated in the initial data processing.

3.2. Numerical Simulation

A finite-element model of the entire segmental assembly bridge was established using ABAQUS software, with the main girder and prestressing tendons modeled using C3D8R and T3D2 elements, respectively [36]. The mesh utilized a structured partitioning type; however, due to the complexity of the finite-element model, a direct structured mesh could not be implemented. Therefore, the partition tool was used to segment the irregular areas of the model before proceeding with the mesh division, resulting in a more optimized mesh. Ultimately, the entire bridge consisted of 301,820 nodes and 204,635 elements. The finite-element mesh model of the main girder section is shown in Figure 6, and the lane layout is depicted in Figure 7.

The cohesive finite-element method with finite interface thickness was used to model the adhesive joints [37]. A cohesive element consisting of epoxy resin with a thickness of 1 mm was inserted between the prefabricated sections. The material parameters of the components are listed in

Table 1. Concrete material characteristics.

Material Type	Modulus of Elasticity (MPa)	Poisson’s Ratio	Weight Capacity (kN·m−3)	Compressive Strength (MPa)	Tensile Strength (MPa)
C60	3.6 × 104	0.2	26.5	27.5	2.04

,

Table 2. Material properties of steel strand.

Material Type	Modulus of Elasticity (MPa)	Compressive Strength (MPa)	Tension Control Stress (MPa)	Coefficient of Thermal Expansion (°C−1)	Weight Capacity (kN·m−3)
Prestressed bar	1.95 × 104	1860.0	1395.0 (1305.0)	27.5	78.5

and

Table 3. Performance index of segmental assembly epoxy resin adhesive.

Colloidal properties	Tensile strength (MPa)	40.0
	Tensile modulus of elasticity (MPa)	3200.0
	Flexural Strength (MPa)	50.0
	Compressive strength (MPa)	80.0
	Elongation (%)	1.5
bonding ability	Steel-Steel T Impact Stripping Capacity (mm)	20.0
	Standard value of steel-steel tensile shear strength (MPa)	15.0
	Positive tensile bond strength of steel as base material (MPa)	15.0
	Tensile bond strength to concrete (MPa)	2.5

.

Embedded elements were used to simulate the interaction between the prestressed tendons and the concrete to ensure convergence and high computational efficiency [38]. The bottom of the No.0 cast-in-place block in the middle span was attached to the pier using a full constraint. The remaining bearings were one-way movable bearings to limit the displacement in the x and y directions and the rotation in the x and z directions [34]. The three-dimensional model of the bridge is shown in Figure 8. The unit length in the longitudinal direction of the bridge is 0.2 m

3.3. Sensor Layout

The model was validated by monitoring the vehicle load on the target bridge. The maximum positive bending moment and the maximum vertical displacement occurred in the main girder span of the bridge. The maximum negative bending moment and shear stress were generated near the main pier fulcrum. Therefore, three sections in the middle of the main beam span, the adjacent joints of the 1/4 beam segment, and the 3/4 beam segment were selected as monitoring and control sections. One-third points at the bottom of the beam in each control section were selected to measure the strain. The measurement point configuration is shown in Figure 6. The dynamic strain acquisition was carried out using the DHDAS strain acquisition system. Strain gauge sensors were used to measure the strain in the control section. The specific equipment is illustrated in Figure 9. The parameters of the sensors are listed in

Table 4. Sensor parameter.

Model Number	120-50AA
resistance	120 ± 0.5 Ω
Sensitivity coefficient	2.11 ± 1%
Strain limit	20,000 μm/m
Operating temperature	−20–80 °C

.

3.4. Model Validation

To process the strain data from the field test in a targeted manner, it is first necessary to do a statistical analysis of the traffic volume during the field test. The total traffic volume in one month is selected for statistical analysis, and the statistical results of the monthly average daily traffic volume are shown in Figure 10.

The daily maximum hourly traffic volume basically appears in the morning and evening peaks, while in the evening, the traffic volume is smaller, but through the monitoring records the general heavy vehicles can be seen basically appearing in the evening. Therefore, the vehicle load and speed information at night were screened, and it ultimately found that the load of 300 KN vehicles accounted for 42% of the total number of vehicles, vehicle speed distribution peak more in 40–100 km/h, the night due to fewer vehicles, so the speed will be relatively large, so in the verification of the results of the analysis of the vehicle conditions selected the interval of the driving parameter values.

A modal comparison analysis of the segmental girder bridge model was conducted. The first-order frequency of the bridge was 2.615 Hz through simulation calculation. The first-order frequency of the bridge was 2.637 Hz through measurement, and the ratio of the measured to the simulated value of the first-order natural frequency was 1.01. It shows that the finite-element model established in this paper can simulate the real structure of the bridge well. Its damping ratio is 0.03.

Based on the aforementioned actual operational statistical analysis of the bridge, two sets of control conditions were established. In the second lane, a 300 kN heavy vehicle was allowed to travel at uniform speeds of 15 m/s and 20 m/s without any obstruction. After applying the moving load, the maximum strain values were extracted from the central measurement points at the bottom of the cross-sections along the bridge at 1/4 L, 1/2 L, and 3/4 L. The fitted curves comparing the measured strains near the bottom edge of the beam slab corresponding to the traffic lanes with the simulation results obtained from ABAQUS are shown in Figure 11 and

Table 5. The maximum strain error is calculated by field measurement and ABAQUS.

Machine Speed (m/s)	Location of Cross-Section	Measured Value		Calculated Value		Relative Error %
		Time of Arrival (s)	$\mathbf{Maximum}\mathbf{Strain}\mathbf{Value}(\mathit{\mu }\mathit{\epsilon }$)	Time of Arrival (s)	$\mathbf{Maximum}\mathbf{Strain}\mathbf{Value}(\mathit{\mu }\mathit{\epsilon }$)
15	1/4 L	3.60	7.88	3.56	8.10	2.8
	1/2 L	4.20	13.96	4.29	14.27	2.2
	3/4 L	4.95	7.96	4.99	8.12	2.0
20	1/4 L	2.55	8.14	2.67	8.37	2.8
	1/2 L	3.20	14.90	3.23	15.14	1.6
	3/4 L	3.75	8.23	3.74	8.42	2.3

Note: Relative error = |Maximum measured dynamic strain − Maximum simulated dynamic strain|/Maximum measured dynamic strain.

.

The measured and calculated values of the dynamic strain were in good agreement. A slight difference was observed when the vehicle reached the control section of the main beam under each working condition, indicating that the vehicle did not travel at the design average speed. However, the difference in the peak value of the dynamic strain between the measured and calculated results was only about 1 s, demonstrating a good agreement.

The relative error of the maximum strain for the 1/4 L, 1/2 L, and 3/4 L sections was within 5%, verifying the accuracy of the finite-element model. The maximum strain was smaller than the calculated value, indicating that the mechanical performance of the segmental assembled beam bridge was consistent with the theoretical results.

4. CNN Training Test

4.1. Analysis of Network Input Parameters

A sufficient number of strain data were obtained from the ABAQUS numerical simulation. Nonlinear mapping was performed from the input to the output parameters using the CNN. The significant eigenvalues of the bridge responses were selected as input variables to improve the accuracy and efficiency of network learning. Figure 12 and Figure 13 show the strain time history curves for the bottom center of the main beam’s control section and the four points at the bottom of the mid-span cross-section (the configuration of the measuring points is shown in Figure 6) as a vehicle with a standard axle load of 200 kN traveled on the third lane of the target bridge.

As shown in Figure 12, the vehicle load significantly affected the dynamic strain response of the segmental girder bridge. The regularity trend of the dynamic strain time history curve at 1/8 and 7/8 sections of the middle span is not as strong as that of other sections. The dynamic strain time history curves were similar in the 1/4, 3/4, and 1/2 sections. Therefore, only the strain time history curves in these sections were used to identify the vehicle parameters.

The vehicle position substantially influenced the strain response. As shown in Figure 13, the No. 4 measuring point was the closest to the lane’s center. The strain value of this measuring point was the highest in this section when the vehicle traveled in lane 3. Therefore, the strain time history curve of the measuring points in the same section must be considered in the load identification.

4.2. Dynamic Vehicle Parameter Identification

4.2.1. Dynamic Vehicle Load Category Identification

The strain time history data obtained from the 9 measuring points at the bottom of the 1/4, 1/2, and 3/4 sections of the mid-span of the bridge were used as input to the CNN. The sampling frequency was the ratio of the maximum design speed to the length of the two longitudinal cells; thus, 9 × 356 data points were extracted under one working condition. The travel time differed for different speeds. Therefore, the same number of data points were used to compare the results for different working conditions. The strain was 0 when there was no load on the bridge.

The vehicle load, driving speed, and lane were considered and simplified. According to the “Code for Design of Urban Bridges” [39], the plan dimensions of a standard heavy vehicle are shown in Figure 14. The factors and the design of the load conditions for a single vehicle are listed in

Table 6. Vehicle loading type.

Vehicle Type	Standard Load (B1) (kN)	Overload 50% (B2) (kN)	Overload 100% (B3) (kN)
Two-axle vehicle (A1)	200 (I)	/	/
Tri-axle vehicle (A2)	300 (II)	450 (III)	600 (IV)
Four-axle vehicle (A3)	400 (V)	600 (VI)	800 (VII)
Five-axle vehicle (A4)	500 (VIII)	750 (IX)	1000 (X)

,

Table 7. Single-lane traffic lanes.

	Lane
Traffic lanes	First lane	Second lane	Third lane	Fourth lane
Lane type numbering	C1	C2	C3	C4

and

Table 8. Vehicle speed (m/s).

	Vehicle Speed(m/s)
	10	13	16	19	22	25
Speed type numbering	D1	D2	D3	D4	D5	D6

. A total of 240 samples were used (240 × 9 × 356); 70% of the samples were used as training data, and 30% were used as test data. The number of levels increased or decreased according to the test results and training conditions. The strain caused by the self-weight of the bridge and the prestress was ignored. The training data to obtain the optimal parameters of the neural network are listed in

Table 9. Vehicle load category identification network structure parameter setting table.

Layer Name	Parameter Setting
Input layer	9 × 356 × 1
Convolution layer 1	(2 × 2 × 16) [2 × 2]
Convolution layer 2	(2 × 2 × 32) [1 × 1]
Fully connected layer	3
Output layer	1 × 1 × 3

Note: In the convolutional layer, “16” in “(2 × 2 × 16) [2 × 2]” represents the number of convolutional nuclei; “(2 × 2)” represents the size of the convolution kernel; “[2 × 2]” represents the size of the core used for the maximum pooling operation. The parameter settings for the fully connected layer represent the number of neurons.

.

4.2.2. Identification of Moving Vehicle Position

The vehicle positions must be known to assess the strain responses at the measuring points. Therefore, it is necessary to change the features of the input layer sample dataset in Section 4.2.1. Since the distance between the front and rear axles of the same vehicle type is constant, the position of the front axle relative to the main span was determined, and the input data were filtered accordingly. The number of samples after reclassification was 30,240. One working condition was selected as the test data, and the other working conditions for the same vehicle type were used as the training data, resulting in 6 × 10 groups of working conditions. The number of training sets for each working condition was 378, the number of test sets was 126, and the ratio was 75%:25%. The training set was used to train the CNN, and the test set was used to assess the model’s performance to determine the vehicle’s position on the bridge.

After repeated debugging, the hidden layer of the model was used to fit the complex relationship between the feature matrix and the position information after the input signal was pooled by the convolution kernel. Its structure was similar to that of the neural network. The number of hidden layer neurons was 16, and the training batch size was changed to 30 in the hyperparameter setting of the deep learning model. The remaining settings were the same as described in Section 2.3 to obtain the optimal parameters of the CNN (

Table 10. Vehicle Position identification network structure parameter setting table.

Layer Name	Parameter Setting
Input layer	9 × 1 × 1
Convolution layer 1	(3 × 1 × 16) [2 × 1]
Convolution layer 2	(3 × 1 × 32) [1 × 1]
Fully connected layer 1	16
Fully connected layer 2	1
Output layer	1 × 1 × 1

Note: As shown in Table 9.

). Increasing the number of convolutional or fully connected layers did not significantly increase the recognition accuracy, whereas reducing the number of layers decreased it.

5. Results and Discussion

5.1. Model Performance

The model results for the training and test sets are shown in Figure 15, Figure 16 and Figure 17. To facilitate subsequent analysis, we define the output variables—namely the lane in which the vehicle operates, the vehicle load type, and the vehicle speed—as index 1 to 3, respectively. The following is observed:

(1) The predicted lane position, vehicle type, and vehicle speed obtained from the CNN model were very close to the actual values. The fitting degree of the CNN model was high, indicating that it had high training performance.

(2) The results for the test set demonstrated the high generalization ability of the neural network. The difference between the predicted and actual values for the indices was very small, indicating that the neural network could accurately identify and predict the moving load parameters. In addition, the output parameters were suitable for characterizing the traffic on the bridge.

The $R^2$ values are listed in

Table 11. The prediction effect of each output index of the convolutional neural network ($R^2$ value).

Data Set	Index 1	Index 2	Index 3
Training sets	0.9406	0.9632	0.9845
Testing set	0.9068	0.9564	0.9433

.

The following is observed in Table 11:

(1)

The $R^2$ values for the training set exceeded 0.9, indicating high model performance. Those for the test set differed but were greater than 0.9. The minimum $R^2$ value was 0.9068 for index 1, and the maximum was 0.9564 for index 2. The model had a high fit for the three moving load parameter indices, with the best performance for index 2.

(2)

The ranking of the indices based on the $R^2$ value in the test set was index 2 > index 3 > index 1. The CNN exhibited different fitting degrees for various types of moving loads, showing a better performance for vehicle load identification and a worse performance for lane identification.

5.2. Recognition Accuracy

Figure 18 shows the model’s recognition accuracy for identifying the front axle position of a class I vehicle passing through the middle span of the bridge at a speed of 10 m/s. Errors occurred when the vehicle entered and left the mid-span. When the vehicle was traveling on the bridge, the identified position was very close to the actual position.

Table 12. Qualified rate of vehicle load position identification under different vehicle types and speeds.

Qualified Rate/%		Speed (m/s)
		10	13	16	19	22	25
Vehicle loading type	I	84.83	80.27	90.64	91.73	88.18	83.65
	II	86.09	85.93	91.23	91.23	92.11	86.76
	III	85.21	89.44	89.47	89.47	89.47	86.76
	IV	85.23	88.57	90.35	92.11	90.35	85.89
	V	89.91	89.79	88.33	90.01	92.5	90.62
	VI	89.24	89.29	94.17	88.33	85.83	85.62
	VII	90.74	89.79	93.33	94.17	91.67	88.96
	VIII	90.31	91.81	93.94	93.37	93.79	89.09
	IX	91.86	92.58	94.50	95.70	95.02	91.26
	X	90.31	92.58	94.16	93.17	94.56	90.42

lists the correct recognition rates of the CNN for the vehicle’s position under different working conditions. The rates exceeded 80% [40], indicating a high accuracy in identifying the vehicle’s position. The lowest recognition rate was 80.27% for a two-axle vehicle traveling at 13 m/s, and the highest rate was 95.70% for a five-axle vehicle moving at 19 m/s.

The recognition rates for the vehicle speed and load type were similar, and good recognition results can be obtained for both small and large wheelbases. This is attributed to the permutation and method to select samples, resulting in uniform samples and high similarity in the vehicle conditions.

As the vehicle speed increased, the recognition rate of the vehicle’s position increased, reaching the maximum at 19 m/s, followed by a decrease in the recognition rate. After the vehicle reached the mid-span at a given speed, the recognition rate increased with the number of axles and the axle load of the vehicle. The reason for this is that the strain increases with an increase in the spacing between the front and rear axles [41]. The position recognition accuracy increased with the number of axles and the axle load and with the vehicle speed in a certain speed range. Subsequently, the recognition rate decreased slightly, but it met the engineering needs.

5.3. Effect of Noise on CNN Network Load Identification

During the data acquisition process, environmental factors and instrument noise will introduce certain levels of noise to the strain signals. Since these noise influences are challenging to eliminate, it is crucial to consider the impact of noise on the test signals. In this section, we first simulate actual measurement samples by adding 1%, 5%, and 10% random noise to simulated data [42]. Next, we train a CNN network following the training scheme in Section 4.2. Finally, 60 sets of representative strain signals were randomly selected under three different working conditions, namely the lane affected by vehicles, the type of vehicle load, and the vehicle running speed, to evaluate the recognition accuracy of the mobile vehicle parameters detected by the CNN network. The recognition prediction results for each category are shown in Figure 19 and

Table 13. The impact of different noise levels on identification effectiveness.

Pass Rate	1% Noise Level	5%1% Noise Level	10%1% Noise Level
Vehicle lane	94.16%	87.55%	81.71%
Vehicle loading type	96.37%	89.36%	76.18%
Vehicle speed	96.95%	84.71%	78.52%

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The above results indicate that noise has a certain impact on the recognition of load parameters. As the level of noise increases, the recognition accuracy of the network gradually decreases. Among them, the addition of noise has the greatest impact on the identification of vehicle load categories, with a decrease in recognition accuracy of 20.19%. However, even when 10% of noise is added, the recognition accuracy of the network is still above 75%, indicating that the network remains effective under these conditions.

6. Conclusions

This paper establishes a single-vehicle moving load identification model for precast beam bridges based on convolutional neural networks (CNN) and dynamic strain data, performing regression predictions under various working conditions. The model demonstrated the highest performance in predicting vehicle load types, achieving an R² value of 0.9564, while it showed the lowest performance in lane identification, with an R² value of 0.9068. The recognition accuracy of vehicle position improved with the number of axles and axle loads. Within the speed range of 10 m/s to 19 m/s, the recognition accuracy increased with speed, reaching a maximum of 95.70% for a five-axle vehicle traveling at 19 m/s. Subsequently, the model’s accuracy slightly decreased but remained above 80%, meeting the engineering accuracy requirements.

This study only considered the effects of different vehicle speeds, weights, and lane positions of a single vehicle on the dynamic response of bridges. Future research should also take into account the impact of different vehicle fleets on dynamic performance. In summary, the segmental assembly beam bridge single-vehicle moving load parameter identification model based on CNN and dynamic strain exhibits good predictive performance, indicating that it is feasible to identify single-vehicle moving load parameters by measuring the strain response of segmental assembly beam bridges under vehicle traffic. This provides a technical reference for the operation, maintenance, and performance evaluation of segmental beam bridges.