A Neural Network-Based Structural Parameter Assessment Method for Prefabricated Concrete Pavement

Abstract

Due to their construction efficiency, prefabricated concrete pavements are becoming a good choice for airport construction or refreshing. However, as a new type of pavement structure, their structural analysis theory and actual structural performance have not been determined. Therefore, a new method based on a neural network is applied to implement a long-term structural assessment, with the input being monitored strain data; it is named the jellyfish search algorithm-optimized BP neural network (JS-BP) model. Considering the structural characteristics, three key parameters are selected as the key parameters to implement the assessment, namely, the bending and tensile modulus, reaction modulus at top of the subgrade, and seam equivalent modulus. To implement the method, the databases are established first with the simulation results from some finite element models of prefabricated concrete pavement. Then, the proposed JS-BP neural network model is trained and checked with the established database. The simulation results verify an excellent accuracy of the proposed method as the difference between the predicted value and the true value is smaller than 1%. Moreover, the aircraft loads show some influence on the prediction results, in which the prediction error is about 5% for most cases, while it is up to 15% for assessing the top surface reaction modulus of the subgrade. Compared with the proposed JS-BP model, the accuracy of the traditional BP model is not so high, as the largest error can be up to 25%. Lastly, the proposed method is verified with some experiments using laboratory models. From the test results it is indicated that the prediction accuracy of the proposed method for the three parameters is still good enough, as the prediction error is within 5%.

1. Introduction

Prefabricated concrete pavement has significant advantages over traditional pavement cast on site, particularly in terms of rapid repair and large-scale renewal, and is increasingly being adopted by various countries [1,2,3,4]. However, prefabricated pavements are composed of multiple panels assembled on site, with the surface and base layers often disconnected, weakening the overall structural integrity of the pavement. Under the influence of cyclic aircraft loads and environmental factors, the base layer, surface layer, and joints between surface panels are prone to significant damage, which significantly reduces the structural load-bearing capacity of the pavement. The reaction modulus at the top of the subgrade, bending and tensile modulus, and seam equivalent modulus are critical parameters influencing the performance of the pavement panels, such as horizontal load transfer between panels, and vertical load transfer between the surface layer and subgrade. Therefore, obtaining these key structural parameters is of critical importance for evaluating the structural performance of pavement.

The structural parameters of the pavement cannot be directly obtained from monitoring and inspection data; they are generally analyzed with structural response indexes (e.g., strain, displacement). The traditional method for inverting pavement structural parameters mainly uses deflection data obtained from the falling weight deflectometer (FWD) test along with the input of the loads, panel thickness, and structural layer parameters to perform an inversion based on the theory of panels on elastic foundations. This includes methods such as the deflection basin area index method [5,6], the deflection basin center-of-gravity distance method [7,8], and the average distance method [9,10], with the deflection basin area index method being the mainstream approach used in both domestic and international standards. However, prefabricated pavements, composed of multiple panels, exhibit relatively weak inter-panel interactions compared to traditional pavements, and the application of infinite panel theory leads to significant estimation errors. Consequently, these standardized methods are not suitable for the structural analysis of prefabricated pavements. Due to the lack of adequate panel and shell theories specific to prefabricated pavements, an effective theoretical calculation-based inversion method for determining the structural parameters of these pavements has not been fully developed.

With the rapid development of theories related to artificial intelligence and machine learning, many researchers have combined finite element analysis with machine learning to address the limitations of traditional methods, providing new approaches and solutions for the inversion of structural parameters of prefabricated pavements. Currently, extensive research has been conducted both domestically and internationally on the inversion of roadway structural parameters [11,12]. Amin et al. [13] utilized the generalized delta rule learning algorithm to optimize and adjust connection weights in a BP neural network, significantly improving the inversion accuracy of pavement parameters. Fan et al. [14] developed an artificial neural network (ANN)-based inverse algorithm for determining pavement structural parameters using finite element model analysis results. The results provide a reference for the characteristic analysis of high-speed deflection basins and the back-calculation of pavement structural parameters. Li et al. [15] developed an ANN-GA algorithm to back-calculate the pavement modulus under FWD testing with viscoelastic and nonlinear parameters. Compared to traditional iteration-based inverse calculation methods, the ANN-GA approach offers advantages such as removing the need for an initial seed modulus and considering complex material properties. Li et al. [16] obtained sufficient theoretical deflection basin data of asphalt pavement structures as training samples through mechanical theory and program calculations, training a BP neural network model to predict the structural layer modulus with high accuracy and efficiency. Zhou et al. [17] proposed using strain indices for the inversion of pavement parameters and established a corresponding mathematical model, greatly improving the inversion efficiency and accuracy. This approach is feasible for determining structural parameters of prefabricated pavements using strain as a fundamental index. However, the classical BP model is sensitive to the initial value of the model parameters and the values of the network’s layer thresholds. Variations in these parameters can easily decrease the prediction accuracy of the BP model. Due to its excellent performance, with a fast convergence speed and high accuracy, the application of the jellyfish search (JS) algorithm will improve the performance of the BP model [18].

Therefore, first a BP neural network model is developed in this paper, which is then optimized by the jellyfish search (JS) algorithm, known for its fast convergence speed and high accuracy. Then, a finite element model of nine prefabricated pavement panels is constructed to implement the simulation to form the database to train the neural network. The input of strain is the key parameter, which is used to assess the other three parameters; namely, the concrete’s bending and tensile modulus, reaction modulus at the top of the subgrade, and seam equivalent modulus. Finally, the trained JS-BP neural network is verified with some simulations and static experiments of a laboratory model.

2. JS-BP Neural Network Model Construction

2.1. BP Neural Network

A BP neural network, also known as a backpropagation neural network, learns and predicts complex patterns by iteratively adjusting weights and biases to minimize the error between its predicted output and the actual values. A BP neural network typically consists of an input layer, one or more hidden layers, and an output layer. Each neuron is connected to neurons in the previous layer and is associated with weights and biases. Outputs are computed through forward propagation, and weights and biases are adjusted during backpropagation to reduce error. Figure 1 schematically illustrates the structure of a BP neural network.

2.2. JS-BP Neural Network

The artificial jellyfish search (AJS) optimizer is a novel optimization algorithm proposed by Taiwanese researcher Chou et al. [18] in 2020. The basic principle of the algorithm is based on mimicking the foraging behavior of jellyfish in the ocean. This includes the movement of jellyfish with ocean currents and their collaborative behavior, along with a time control mechanism that adjusts movement patterns. The algorithm exhibits strong search and optimization capabilities and achieves fast convergence.

The artificial jellyfish search algorithm includes the following processes.

Jellyfish move with ocean currents that lead to abundant food, and their movement direction is influenced by the positions of all jellyfish in the environment to ensure successful access to food resources, with the average position of the jellyfish given by

$$u={\displaystyle \frac{\overrightarrow{pop}}{n}}$$

(1)

where u is the average position of the jellyfish and n represents the number of jellyfish.

The current formula for the mean positional difference between an individual and the whole jellyfish population is

$$\Delta u=eu$$

(2)

In the above equation, e is the factor controlling the attractiveness. e is expressed mathematically as follows:

$$e=\beta \ast rand$$

(3)

where $\beta$ is the distribution coefficient, with a value of 3.

It follows from Equations (2) and (3) above that

$$\Delta u=\beta \ast rand\ast u$$

(4)

The trends in the position of each jellyfish are given by

$$\overrightarrow{tre}=X^{\ast }-\Delta u$$

(5)

In the above equation, $X^{\ast }$ is the optimal location of the jellyfish population. $\overrightarrow{tre}$ refers to the changing trend in the position of each jellyfish.

The formula for updating the location of each jellyfish is

$$X_i(t+1)=X_i(t)+rand\ast \overrightarrow{tre}$$

(6)

$$X_i(i+1)=X_i(t)+rand\ast (X^{\ast }-\beta \ast rand\ast u)$$

(7)

where $X_i(i+1)$ refers to the updated position of each jellyfish.

Jellyfish within a jellyfish colony have two types of operation: A and B, which are passive and active motions, respectively. Among them, type A motion is the passive motion of jellyfish floating in the water, and its position update equation is

$$X_i(t+1)=X_i(t)+\gamma \ast rand(0,1)\ast (U_b-L_b)$$

(8)

where $U_b$ and $L_b$ are the upper and lower bounds of the search space, and γ is the coefficient of motion, taken as 0.1.

Type B movement, on the other hand, is the position of an individual jellyfish actively approaching other jellyfish that have more food, and is calculated by the following formula:

$$\overrightarrow{step}=X_i(t+1)-X_i(t)$$

(9)

$$X_i(t+1)=\overrightarrow{step}+X_i(t)$$

(10)

$$\overrightarrow{step}=rand(0,1)\ast \overrightarrow{Dir}$$

(11)

$$\overrightarrow{Dir}=\left\{\begin{array}{cc}{X}_j(t)-X_i(t)& f(X_i)\ge f(X_j)\\ X_i(t)-X_j(t)& else\end{array}\right.$$

(12)

This formula shows that when the amount of food at jellyfish i is greater than at jellyfish j, jellyfish j moves towards jellyfish i and vice versa.

A total of three modes of motion exist as described above, and a temporal control mechanism is designed to mediate the three modes of motion, which is formulated as follows:

$$c(t)=\left|(1-{\displaystyle \frac{t}{Max\_iter}})\ast (2\ast rand(0,1)-1)\right|$$

(13)

where $t$ is the number of iterations and Max_iter is the maximum number of iterations.

The specific realization steps are as follows:

Step 1. Set initialization parameters. These include the number of individual jellyfish, the selection of the maximum number of generations, etc.

Step 2. Randomly initialize jellyfish positions. According to the range of the search space, randomly generate the initial positions of jellyfish.

Step 3. Evaluate the fitness. According to the objective function of the problem, calculate the fitness value of each jellyfish individual.

Step 4. The search process is as follows:

(1)

Calculate the new position using the current jellyfish position and the search radius. For the case of exceeding the search space, a boundary processing strategy is adopted to limit the position to the search range;

(2)

Calculate the fitness value of the new position and update the global optimal solution;

(3)

With each iteration, the search radius is gradually reduced. When the maximum number of iterations is achieved or the termination condition is met, the search process ends; otherwise, return to step 2.

In this paper, the jellyfish search algorithm is used to optimize the BP neural network and establish a prediction model for the structural parameters of the pavement. It aims to solve the problem of insufficient precise positioning of weights and thresholds in the training process of BP neural network, which leads to a decrease in the prediction accuracy of the model. The specific steps are as follows:

(1)

Establish a BP neural network model; determine the network structure, transfer function, and learning rules; and input the database into the model for training.

(2)

Optimize the weights and thresholds of the BP neural network using the jellyfish search algorithm. If the training results reach the set parameters, stop the calculation and obtain the optimal network weights and thresholds; otherwise, recalculate.

(3)

After obtaining the optimal network weights and thresholds, use the BP neural network model to train and output the results.

To minimize the overfitting issue of the JS-BP network model, this study increases the amount of training data for each condition to reduce the impact of noise; simultaneously, it reduces the number of features by eliminating non-common features to enhance the model’s generalization ability; dropout is used in the neural network to remove a certain proportion of neurons in the hidden layers, simplifying the structure of the neural network and thereby reducing overfitting. In the later stages, the model’s parameters and hyperparameters can also be adjusted based on the prediction results.

2.3. Parameter Selection for JS-BP Neural Network Model

The primary purpose of this study is to utilize optimization algorithms to predict pavement parameters. Although the selection of hyperparameters in optimization algorithms is important, it is not the core content of this research. Therefore, this study first determines the values of hyperparameters based on the content of references [19,20], and then determines whether it is necessary to adjust the values of hyperparameters based on the results of parameter prediction.

For the sake of efficient and convenient neural network computation, in this study the BP neural network was set to 3 layers, with 10 neurons in the input layer, 21 neurons in the hidden layer, and 1 neuron in the output layer. The maximum number of training iterations was set to not exceed 1000, the neural network learning rate was 0.01, the minimum error during the training process was set to not exceed 0.00001, the momentum factor was 0.01, and the minimum performance gradient was 0.000001.

In the JS algorithm, the number of jellyfish is set to 50, the maximum number of iterations is set to 1000, and the time control parameter is set to 0.5. When the value of the time control function exceeds 0.5, the jellyfish follow the ocean currents. When its value is below 0.5, the jellyfish move within the jellyfish population. The upper limit of the optimization parameter is set to 1, and the lower limit is set to −1. The above parameters were substituted into the model for calculation.

3. Database Construction and Training of the Neural Network

3.1. Finite Element Model

The finite element (FE) software ABAQUS 2020 was applied to implement the simulation in this paper. A finite element model of a prefabricated pavement consisting of nine panels was established. Each pavement panel had a thickness of 300 mm and dimensions of 2500 mm × 5000 mm, as shown in Figure 2. There were 3 connection areas to connect the panels, made of small steel plates. A steel rebar was used as structural reinforcement, with upper and lower layers of bi-directional reinforcement, and a protective layer thickness of 50 mm. The pavement panels were modeled with three-dimensional solid elements, the element type employed a C3D20R reduced integration element, while the concrete’s Poisson ratio was set to 0.15. The steel reinforcement had an elastic modulus of 200 GPa and a Poisson ratio of 0.33, and it was embedded within the concrete panel. The reinforcement was modeled with truss elements.

In the models, the Winkler foundation model was used to represent the pavement subgrade and soil base as composite springs, defining the corresponding foundation reaction coefficients. The main difference this and the continuum-based foundation model is that there is no bonding between the pavement plate and foundation for the proposed prefabricated pavement in this paper, but they are bonded together for the common cast-in-place pavement. Therefore, compared with the continuum-based foundation model, the Winkler foundation model is considered more similar to the actual structure. The foundation simulation was performed using the “Elastic Foundation” feature in the Abaqus Interaction Module, specifying the foundation surface in contact with the pavement panels. The inter-slab joint connection is crucial for the load transfer between prefabricated pavement panels, achieved by establishing a virtual surface layer. The element type C3D20R was applied to reduce element integration. The elastic modulus of this virtual surface layer in the connection areas between pavement panels was defined as the joint equivalent modulus, and a Tie connection was used between the virtual surface layer and the concrete slab. The aircraft B-737-800 was selected as the typical load from the specification in [21]. The load distribution in the model can be found in Figure 2.

The values of some key parameters, namely, the concrete’s bending and tensile modulus, the reaction modulus at top of the subgrade, and the seam equivalent modulus, were changed within a reasonable range, as shown in

Table 1. Parameter values and combinations.

Structural Parameters	Bending and Tensile Modulus (MPa)	Reaction Modulus at Top of the Subgrade (MN/m3)	Seam Equivalent Modulus (MPa)
Range of values	30,000–60,000	20–200	60–160
Step value	2000	5	10
Step number	16	37	11
Combination number	16 × 37 × 11 = 6512

. Then, these values were combined to input the FE model to implement the simulation to form the database for training the proposed neural network. The total number of combinations in the database was 6512.

Moreover, to implement the proposed method, the strain was acquired along the length of the 5th panel, as shown in Figure 2. The strain here means the average strain within the 500 mm length of the panel, which is considered more accurate than the traditional point strain for representing the structural performance of concrete structures. In fact, long-gauge fiber Bragg grating (FBG) sensors can implement the measurement of averaged strain with a gauge from 100 mm to 1000 mm [22,23]. The strain location here is the location where the maximum strain often happens. In fact, one or more strain sensors were installed to obtain the strain response under aircraft loads. However, the model should include all the locations in the training process to implement the parameter assessment for the actual needs.

3.2. Database Construction

Some secondary development of ABAQUS was performed with Python, developing programs for batch modification of structural parameters, automatic job generation and submission, batch extraction of results, and database storage. Firstly, finite element models of prefabricated pavement with various parameter combinations were generated, as detailed in Table 1. Secondly, the finite element models were submitted in batches. Finally, the files of results were used to acquire the concerned strain data. Then, the data were stored to build the parameter database. There are a total of 6512 sets of data in the database, which has been uploaded as a separate attachment. The database was used for training the neural networks. The BP and JS-BP neural network models were built on the MATLAB R2018a simulation platform, and the database was incorporated into the neural network models for training.

3.3. Neural Network Training

3.3.1. Evaluation Indexes

To comprehensively evaluate the training effect of the BP and JS-BP neural network models, several indexes are used in this study: Mean absolute error (MAE), mean absolute percentage error (MAPE), mean squared error (MSE), root mean squared error (RMSE), and coefficient of determination (R²). The detailed calculation formulas of these indexes are shown in

Table 2. Formulas of evaluation indexes.

Index	MAE	MAPE	MSE	RMSE	R2
Formula	${\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|\Delta y_i\right|}$	${\displaystyle \frac{100\%}{n}}{\displaystyle \sum _{i=1}^n\left|\frac{\Delta y_i}{y_i}\right|}$	${\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\Delta y_i^2}$	$\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\Delta y_i^2}}$	$1-{\displaystyle \frac{{\displaystyle \sum _{i=1}^n\Delta y_i^2}}{{\displaystyle \sum _{i=1}^n{(y_i-{\overline{y}}_i)}^2}}}$

In the formulas, n is the number of samples; $y_i$ is the true value of the sample point of the test set; ${\widehat{y}}_i$ is the predicted value; ${\overline{y}}_i$ is the average of all true values; $\Delta y_i=y_i-{\widehat{y}}_i$.

.

3.3.2. Training Results

The size of the test set was chosen to ensure a robust evaluation of the model’s generalization performance while maintaining enough data for training. For each of the three parameters, about 20% of the database, about 1000 samples, was selected as the test set, while the remaining samples were used as the training set. For having a clear look at the variation of the results, 30 of 1000 results were randomly taken to draw in the figures. This split was determined based on a trade-off between model training stability and reliable performance evaluation. The parameter database was then imported into the BP and JS-BP neural network models for training to develop a prediction model for the prefabricated pavement parameters.

As clearly shown in Figure 3, after the JS-BP neural network reaches the thousandth iteration, where training is terminated, the mean squared error of the training process has basically converged to a fixed value of 0.02. The test values and training values are basically consistent during the training process, and there is no occurrence of overfitting. This fully proves that the optimized algorithm has strong stability and good generalization performance.

The training results of the JS-BP and BP neural network models for the three structural parameters are shown in Figure 4. There is nearly no deviation between the actual values and the predicted values as the difference is smaller than 1%, indicating that the accuracy of the trained network models is high.

The values of the evaluation indexes are also calculated, as shown in Figure 5. In the figures, the values of the coefficient of determination R² from the two neural network models are close to each other, greater than 0.99, indicating a very small deviation between the actual value and the predicted value. For the other four indexes, the values obtained from the JS-BP neural network model are smaller than those from the BP neural network model, which means that the JS-BP neural network model has a better prediction effect than the BP neural network model.

3.4. Analysis of Influence from Aircraft Loads

3.4.1. Aircraft Load Location

Aircraft operating on the runway do not always align with the centerline, and their trajectories may deviate, resulting in varying strains recorded by the sensors due to different aircraft trajectories, which can lead to significant errors in parameter prediction. Therefore, it is essential to include the effect of aircraft load position to create a comprehensive database for parameter prediction analysis. As shown in Figure 6, the range of movement for the main landing gear of the B-737-800 model spans from 3200 mm to 5200 mm, with a step size of 100 mm for each condition. A corresponding parameter database was created. For each of the three parameters, about 20% of the database, about 1000 samples, was selected as the test set, while the remaining samples were used as the training set. For having a clear look at the variation of the results, 30 of 1000 results were randomly taken to draw in the figures.

The training results of the JS-BP and BP neural network models for the top surface reaction modulus of the subgrade are shown in Figure 7. It can be observed that both models, JS-BP and BP, can predict the structural parameters of the pavement based on their respective databases. Among these, the JS-BP model provides a slightly better prediction accuracy for the top surface reaction modulus of the subgrade compared to the BP model. The maximum deviation of the JS-BP model from the actual value is 16 MN/m³, with a relative error within 15% and a correlation coefficient of 0.967. In contrast, the BP neural network model shows a maximum deviation of 36.5 MN/m³ from the actual value, with a relative error within 25% and a correlation coefficient of 0.858. The inversion results for other parameters are also influenced by the position of the aircraft load, but the relative error remains within 5%, with correlation coefficients close to 1. Comparing with the results in Figure 5, it is evident that the results of MAE, MAPE, RMSE, and MSE in Figure 8 for each structural parameter have increased, indicating a decrease in inversion accuracy when accounting for the influence of aircraft load position. However, the JS-BP neural network model outperforms the BP neural network model, as it more effectively reduces the impact of aircraft load position on the prediction of structural parameters.

3.4.2. Aircraft Load Size

The load exerted on the pavement by aircraft varies due to factors such as flight speed and fuel load. Given that the empty weight of the aircraft is approximately 0.5 times the maximum taxiing weight, tire pressures of 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 times the maximum value were chosen for analysis. For each of the three parameters, about 20% of the database, about 1000 samples, was selected as the test set, while the remaining samples were used as the training set. For having a clear look at the variation in the results, 30 of the 1000 results were randomly taken to draw in the figures.

The training results of the JS-BP and BP neural network models for the top surface reaction modulus of the subgrade are shown in Figure 9. Both models can predict the structural parameters of the pavement, with the JS-BP neural network achieving relative errors for structural parameter predictions of less than 5%, and load magnitude predictions with relative errors within 10%, and a correlation coefficient greater than 0.97. In contrast, the BP neural network achieves relative errors of up to 10% for structural parameter predictions, and load magnitude predictions with errors reaching up to 57.5%, with a correlation coefficient of 0.938, indicating poorer prediction performance. As shown in Figure 10, the evaluation metrics MAE, MAPE, RMSE, and MSE indicate that the accuracy of the JS-BP neural network is significantly better than that of the BP neural network. The JS-BP neural network effectively mitigates the influence of aircraft load size on the pavement’s structural parameters, enabling high-precision predictions of these parameters.

The above results demonstrate that the optimization process using the JS algorithm has improved the performance of the traditional BP neural network. The optimized model achieves lower error metrics (MAE, MAPE, MSE, RMSE) compared to the traditional BP model, validating the effectiveness of the optimization. Overall, the JS-BP model shows better generalization capabilities and more accurate predictions, which has verified the efficiency of incorporating optimization techniques into traditional neural network training.

4. Verification with Experiments of Prefabricated Pavement Models

4.1. Introduction of Experiments

4.1.1. Prefabricated Pavement Panel

Nine reinforced concrete (RC) prefabricated pavement panels were prepared with a thickness of 120 mm and a plane dimension of 750 mm × 1500 mm, as shown in Figure 11. The geometric scale factor is 3:10 compared with the actual panel size. The diameter of the reinforcement bars is 8 mm, with a yielding strength of 400 MPa. These bars are arranged in a double-layer bi-directional configuration with a spacing of 90 mm. The depth of the protective concrete layer is 15 mm.

There are three steel bar connections with a diameter of 8 mm installed on each side of the panel specimen. These steel bars are welded together with the steel bars from the adjacent panel to connect the panels together as a whole pavement, as shown in Figure 2.

4.1.2. Strain Sensor and Its Deployment

Over the past decade, distributed fiber optic monitoring technology has been widely applied to implement structural health monitoring (SHM) due to its high accuracy and excellent durability. Long-gauge fiber Bragg grating (FBG) strain sensors, developed by the authors’ research group, have been proposed to implement the long-term monitoring of concrete structures due to their measurement style of average strain within a gauge from 0.1 m to 1 m, which matches the material non-uniformity of concrete’s structure.

As shown in Figure 2, the maximum strain occurs at the side when the aircraft load is applied at the middle side of the panel, as per the specification, namely, Specification for the Design of Cement Concrete Pavement at Civilian Airports of China. For embedding the FBG sensors into the concrete, the sensors are embedded into one steel bar at first, named the self-sensing bar. Then, the self-sensing bar is directly tied together with the other common steel bars and embedded into the concrete. In the experiments, the gauge length of the FBG sensors is 150 mm. In total, five sensors are installed in one bar, as shown in Figure 12. Theses sensors are numbered S1 to S5. The panel with the self-sensing bar embedded is in the middle part of the pavement model, namely, the fifth panel, as shown in Figure 2.

The strain-sensing performance of the self-sensing bar is verified with some static tension tests before its actual application. Three strain cases are set, namely, a small-strain case, medium-strain case, and large-strain case. The small-strain case represents the case before concrete cracking. The large-strain case represents a large-damage case, namely, after concrete cracking. The typical test results are as shown in Figure 13. From the results, a linear relationship can easily be found between the wavelength change and strain, with no influence of the strain cases, indicating that the proposed sensing method can implement the strain monitoring of the whole mechanical life of an RC panel. Meanwhile, an excellent measurement repeatability is evident in the figures, ensuring long-term monitoring accuracy.

4.1.3. Pavement Base and Loading

The panels are usually installed on the surface of the base. However, for the prefabricated pavement, the demand for base evenness is higher than that for common pavement. Therefore, a special function layer composed of rubber cloth and cement mortar was used in the experiments. The total depth was about 30 mm. In the function layer, the rubber cloth was installed on the top side of the cement mortar. Below the function layer, there was a thick soil layer with a depth of 400 mm, which was used to simulate the common pavement base. During the model construction, tamper and vibration instruments were applied to make the soil layer dense.

The B-737-800 aircraft was also selected as the typical load from the specification. The ground size of the tire was 610 mm × 420 mm, with a pressure of 1.47 MPa. Considering the reduced scale, in the experiments the loading size was 183 mm × 126 mm, while the pressure was kept the same as the actual aircraft loading. The loading method was as shown in Figure 14.

4.2. Measurement of Structural Parameters

Bending and tensile modulus. The bending test on small beams is the standard method to measure the concrete’s bending and tensile modulus. The results of the three concrete beams were 40,496 MPa, 39,388 MPa, and 39,904 MPa, respectively. Here, the average value of 39,929 MPa was applied as the value of the bending and tensile modulus.

Reaction modulus at top of the subgrade. The load is applied upon a plate on the top surface of the base to implement the reaction modulus tests. From the test results the reaction modulus at the top of the subgrade was determined to be 85 MN/m³.

Seam equivalent modulus. According to the specification, loads were applied at the middle of the longitudinal edge and the middle of the transverse edge of the fifth panel, with each test repeated three times. The seam equivalent modulus was determined to be 50 MPa.

4.3. Inversion Results for Structural Parameters

The strain results obtained from each strain sensor under the three loading cycles are listed in

Table 3. Strain results under different loading cycles.

Sensor No.	Strain (με)
	Cycle 1	Cycle 2	Cycle 3	Average Value
S1	25	27	28	27
S2	57	58	58	58
S3	81	82	82	82
S4	54	57	55	55
S5	21	21	24	22

, revealing that the FBG sensor has a good strain measurement accuracy, as the largest deviation between the three tests is about 3 με. The average strain is also calculated as the strain input to implement the inversion with the trained JS-BP neural network model.

The JS-BP neural network has already been trained with the FE simulation results. The average strain in Table 3 is input into the JS-BP neural network to obtain the predicted values of the three parameters. The results of the inversion are listed and compared with the measured values in

Table 4. Predicted results of structural parameters of pavement panels.

Parameter	Measured Value	Predicted Value	Absolute Error (MPa)	Relative Error (%)
Bending and tensile modulus (MPa)	39,929	40,243	314	0.8
Reaction modulus at top of the subgrade (MN/m3)	85	88.9	3.9	4.6
Seam equivalent modulus (MPa)	50	50.4	0.4	0.8

. From the results it can be found that the predicted values are close to the measured values, among which the largest error is 4.6%, for the reaction modulus at the top of the subgrade. The reason may be that the accuracy of the measurement method for the reaction modulus at the top of the subgrade is not as high as that for the other two parameters. However, the relative error for the inversion of all parameters is within 5%, demonstrating that the JS-BP neural network effectively realizes the inversion analysis of pavement structural parameters.

5. Conclusions

In this paper, a JS-BP neural network-based inversion method for determining the structural parameters of airport prefabricated concrete pavement is proposed, and the following main conclusions are drawn from FE simulations and small-scale model tests:

(1)

The JS-BP neural network model can be constructed and trained for assessing the key parameters of prefabricated concrete pavement with a database obtained from the FE simulations; namely, the bending and tensile modulus, reaction modulus at the top of the subgrade, and seam equivalent modulus. The prediction accuracy is good enough as the difference between the predicted value and the true value for the three parameters is smaller than 1%.

(2)

The aircraft loads show some influence on the prediction results, in which the prediction error is about 5% for most cases, while it is up to 15% for assessing the top surface reaction modulus of the subgrade. Compared with the load size, the load location presents a larger influence on the results.

(3)

Compared with a BP network model, the JS-BP network model has a higher accuracy for parameter assessment for prefabricated concrete pavement, especially in the case of changing the aircraft loads. When the aircraft load location is changed, the largest error in parameter prediction is 15% for the JS-BP network model, while it is 25% for the BP network model. When the aircraft load size is changed, the largest error in parameter prediction is 5% for the JS-BP network model, while it is 10% for the BP network model.

(4)

The excellent performance of the trained JS-BP neural network model is verified with experiments on a small-scale model, as the relative errors between the predicted values and the measured values are smaller than 5% for all the three parameters of the prefabricated concrete pavement.

Considering the efficiency, the proposed method is a good choice for assessing the structural parameters of prefabricated concrete pavement, as the structural analysis theory is not already constructed. In future applications, the actual monitoring data should be selected to refresh the trained model, as all the data in this paper used to train the JS-BP network model are from a simulation, which is considered likely to be different to data obtained from actual structures.