Keywords

1 Introduction

The twenty-first century is the century of underground engineering development, China’s underground engineering construction into the "blowout" development era, a large number of subway, high-speed rail tunnels are under construction or put into operation [1]. With the increasing number of tunnels put into operation in China's water conservancy, transportation, municipal and other fields, the structural damage of tunnel lining is aggravated year by year, which will threaten the safety of high-speed trains during operation [2]. Therefore, it is necessary to detect the quality of tunnel lining structural disease during tunnel construction or operation to guarantee the quality of tunnel construction.

At present, ground-penetrating radar is one of the main methods for detecting diseases in railway tunnel lining structure. Some scholars have carried out in-depth research on disease numerical simulation, disease identification and detection. Jiang [3] scholars summarized the electromagnetic wave propagation laws and image characteristics of different shapes of cavities in tunnel lining structures in different media, and analyzed the reasons why radar disease images are easy to misjudge. Gao [4] scholars numerically simulated a certain number of radar images of cavity and de hollowing damage, and proposed a recognition method integrating residual network and migration learning. The results show that the method can effectively identify the cavity and dehollowing damage of tunnel lining structure. Yang [5] scholars studied the application of convolutional neural network target detection in disease identification. Typical diseases of tunnel lining structure can be detected to a certain extent. Although the convolutional neural network can identify lining structure diseases, the method still has some limitations. Due to the private nature of real radar disease data of tunnel structures, there are not a large number of real radar image samples for deep learning model training. While the numerical simulation of lining structure disease radar images solves the problem of insufficient number of samples for training, the numerical simulation radar images differ from the real complex and diverse radar images, and there is the problem of poor generalisation ability of the training network in the detection of actual lining structure diseases, which leads to the missed identification or incorrect identification [6].

Aiming at the above problems, based on the foundation of previous research, this paper further investigates the deep migration learning technology for structural diseases of railway tunnel lining [7]. A deep migration intelligent detection method based on radar images is proposed. Among them, migration learning is a learning process that takes advantage of the similarity between numerically simulated radar images and real images, and applies the network weights learned from similar domains to real image detection, which improves the adaptability and generalisation ability of neural networks [8]. The research ideas of this paper are as follows: firstly, gprMax software was used to establish a numerical model of defective body of various geometries, simulate a variety of typical radar images approximating the actual working conditions, and construct a database consisting of numerical simulation and real radar images [9]. Then, a depth migration method for detecting structural diseases of railway tunnel lining is proposed, and a self-learning and self-updating intelligent detection network model for depth migration of structural diseases of tunnel lining is established, which automatically learns the complex disease characteristics and updates the parameters of the network model. Finally, the effectiveness of the intelligent detection network model is further verified by building a concrete test bed [10]. The problem of poor generalisation ability of the training network in the detection of diseases such as dehollowing and cavities in actual lining structures is solved.

2 Numerical Modelling of Typical Diseases of Tunnel Lining Structures

2.1 Numerical Simulation of Ground-Penetrating Radar

In this paper, gprMax software is used to solve the system of Maxwell’s equations for electromagnetic waves of ground-penetrating radar, as shown in Eq. (1). gprMax is a finite-difference time-domain method for solving the system of Maxwell’s equations in 3D, which simulates the propagation process of electromagnetic waves in the tunnel lining structure [10]. The finite difference approach is used to discretize Maxwell's rotational equations in time and space.

$$ \begin{gathered} \nabla \times E = \frac{\partial B}{{\partial {\text{t}}}} \hfill \\ \nabla \times H = J + \frac{\partial D}{{\partial {\text{t}}}} \hfill \\ \nabla \cdot B = 0 \hfill \\ \nabla \cdot D = {\text{p}} \hfill \\ \end{gathered} $$
(1)

where: E is the electric field strength (v/m). b is the magnetic flux density (Wb/m2). h is the magnetic field strength (A/m). j is the current density (A/m2). d is the electric flux density (c/m2); ρ is the charge density (c/m3).

In order to solve the differential Maxwell's system of equations stably, the spatial grid size and time step size need to satisfy the numerical stability condition, which satisfies Eq. (2). At the same time, in order to ensure the accuracy of the calculation results, the time step and spatial grid size also need to take into account the dispersion effect in the electromagnetic wave propagation process, satisfying Eq. (3). Therefore, in this paper, a perfectly matched layer with a finite thickness is used so that the radar incident wave passes through the interfaces without reflection and enters the PML layer.

$$ \Delta {\text{t}} \le \frac{1}{{{\text{c}}\sqrt {\frac{1}{{(\Delta {\text{x}})^{2} }} + \frac{1}{{(\Delta {\text{y}})^{2} }} + \frac{1}{{(\Delta {\text{z}})^{2} }}} }} $$
(2)
$$ \Delta {\text{x}} \le \frac{\lambda }{12},\Delta {\text{y}} \le \frac{\lambda }{12}\Delta {\text{z}} \le \frac{\lambda }{12}\Delta {\text{t}} \le \frac{T}{12} $$
(3)

where: λ is the radar wavelength, which is related to the frequency and relative permittivity of the electromagnetic wave, as shown in Eq. (4).

$$ \lambda = \frac{C}{{{\text{f}}\sqrt {\varepsilon_{{\text{r}}} } }} $$
(4)

where C is the speed of light, f is the excitation frequency, and εr is the relative permittivity.

2.2 Numerical Simulation and Discussion of Results

In this paper, for the common cavity, dehollowing and incompactness lesions in tunnel lining structure, the basic knowledge of ground-penetrating radar numerical simulation in the previous section is utilized to determine the parameters such as excitation type, excitation frequency, spatial and temporal step, and the number of layers of the PML unit required for the simulation calculation. And the numerical models of defective bodies with various geometries were established, and the corresponding ground-penetrating radar images were acquired. To this end, this paper formulates the numerical simulation steps for tunnel lining structural diseases, and the specific simulation parameters are shown in Table 1and Fig. 1.

Table 1 Simulation parameters
Full size table
Fig. 1
Ten graphs of time versus position plot the round hole, rectangular hole, upper triangular cavity, lower triangular cavity, rectangular deflation, densely packed, single row of rebar right angled triangular voids, and double rows of rebar right triangular voids.

Typical disease images

Full size image

3 Intelligent Detection Network for Tunnel Lining Structural Diseases

3.1 Sample Bank

The essence of neural network detection of disease is to construct a neural network classification and logistic regressor, and train the network using a large number of tunnel lining structure disease samples so that its network can accurately detect the disease. Therefore, this paper establishes a sample library based on numerical simulation and real radar images. The finite difference method is applied to simulate the radar images of lining structure without disease and with disease, respectively. Among them, the radar images of hollow, incompact, and dehollowing diseases under different conditions, totaling 1500. At the same time, a number of radar images of tunnel lining structures provided by Zhengwan High Speed Railway, Zhangjihuai, and Qingdao Electric Wave Institute, totaling 149 images, were collated.

3.2 Deep Learning Based Target Detection Network

Currently, deep learning networks for target detection mainly include FasterR-CNN, MaskR-CNN, SSD, YOLOV3, etc. The main drawbacks of FasterR-CNN, MaskR-CNN, SSD are long training time, slow inference speed, and difficulty in detecting small targets. FasterR-CNN, MaskR-CNN, SSD, etc. The main disadvantages of FasterR-CNN, MaskR-CNN, and SSD are long training time, slow inference speed, and difficulty in detecting small targets. YOLOV3 uses a new network architecture, DarkNet53, for feature extraction, and fuses three different sizes of feature maps to predict the bounding box of the target, which realizes the fusion of features at different scales, and enhances the performance of detecting multi-scale small targets. Net53 feature extraction network, the different scaling feature fusion network, and the output composed of convolution. The loss function designed in the model consists of the center coordinate and width-height coordinate error of the target bounding box, the confidence error of the presence or absence of the target in the bounding box, and the classification error.

Aiming at the difficulty of obtaining deep neural networks with generalization due to the small number of real diseases. In this paper, a YOLOV3 network detection idea based on migration learning is proposed to migrate the shared parameters learned from numerical simulation data to the real dataset to further improve the accuracy of disease detection. The YOLOV3 network with migration learning is applied to detect abnormal radar images and identify the corresponding locations. The main ideas for the construction of the detection network structure are: first, the width and height dimensions of the image are scaled to 416, i.e., the shape of the input image to the target detection network is 416 × 416 × 3. Second, the input image is augmented with data enhancement methods such as scaling, translation transformation, flipping, and color transformation. Also the image target frame is changed accordingly. Then, the numerical simulation images are randomly divided into training and testing sets to train the YOLOV3 network according to the ratio of 7:3 to obtain the weights of the simulation network model. Finally, based on the model parameter sharing and knowledge migration method, the target detection network is trained several times based on real radar image data.

In this study, Adam is chosen as the model optimization strategy, which is a more advanced version of stochastic gradient descent. In this experiment, the starting learning rate of the model is 10–4 and 10–6, respectively, and the dynamic reduction strategy is applied to adjust the learning rate of the training process. That is, after 10 iterations of the model, when the loss curve of the validation set does not decrease, the value of the learning rate will be reduced to the original learning rate of 0.1 after the training. At the same time, this paper adopts the early stopping method to prevent the model generalization performance from deteriorating during the training process and avoid overfitting of the deep learning network. In addition, this paper sets the confidence threshold to 0.5, the intersection ratio of the target bounding box to 0.5, and the number of images for batch training to 8.

In this paper, direct, different migration learning strategies (as shown in Table 2) were used to train YOLOV3 network in real radar image data, and the model convergence speed curve was obtained, as shown in Fig. 2. Figure 2 shows that: the number of iterations required to train YOLOV3 network directly, the loss value is greater than the three kinds of migration learning strategy, thus proving the effectiveness of migration learning strategy in intelligent detection. At the same time, the comprehensive consideration of the number of iterations and loss curve of the kind of migration strategy, this paper adopts the network model of the migration learning strategy two for the disease detection of tunnel lining structure.

Table 2 Transfer learning strategy
Full size table
Fig. 2
A dual-line graph plots the declining trends of the training loss and the validation loss versus iteration times. Training loss starts at (0, 6750), passes through (20, 0), and ends at (160, 0). Validation loss begins at (0, 4400) and ends at (15, 40). All values are approximate.

Convergence curve

Full size image

3.3 Analysis of the Test Results of the Test Set

Figure 3 shows the P-R curve of the migration network model in the test set by applying the recall and accuracy assessment. Where, AP is the area of the P-R curve, which indicates the accuracy of detection. The accuracy of the network is 91.15%, which indicates that the network model successfully migrates from the source domain to the target domain, and the migration effect is obvious without negative migration.

Fig. 3
A line graph of precision versus recall. The line starts at (0, 1), goes to (0.6, 1), and raggedly down to around (0.91, 0.9). Class, 91.15% equals abnormal A P.

Test set precision versus recall curves

Full size image

Figure 4 shows the detection results of the numerical simulation radar image, which can detect circular voids, rectangular voids, upper triangular voids, lower triangular voids, rectangular dehollowing, and incompactness, with a confidence level of 0.99, 0.87, 0.88, 0.79, 0.87, and 0.93. Figure 4 shows the detection results of the real radar image, which can detect rectangular voids, triangular voids, rectangular dehollowing, and incompactness, with a confidence level of 0.99, 0.87, 0.88, 0.79, 0.87, and 0.93 respectively. Their confidence levels are 0.87, 0.62, 0.98, 0.97,0.90, 0.53. The results show that the combination of YOLOV3 network and transfer learning can effectively detect various diseases in different shapes of tunnel lining structures.

Fig. 4
Six graphs of time versus position display structures of round hole, rectangular hole, upper triangular cavity, lower triangular cavity, rectangular deflation, and densely packed radar images. The peak of time is highlighted.

Numerical radar image detection results

Full size image

4 Lining Structure Test Bed Validation

In order to further test the effect of the intelligent detection network in this paper, the establishment of a defect-containing tunnel concrete test bed, length, width and height of 5 × 1.4 × 1 m, the construction of the process parameters and the actual tunnel to maintain consistency. The test bench installation location for the casting benchmark, in turn, 4 layers of casting.

After 2 months of maintenance of the test bed, using Qingdao Institute of radio waves 900 MHz ground-penetrating radar antenna testing test bed, the collection of measuring lines for 5. Using the range wheel mode, sampling time window of 20 ns, the number of sampling points is 512, the acquisition speed is 128, the data acquisition process is filtered. Data processing using radar data processing software, processing steps include correction of zero bias, amplitude compensation, adjust the zero point, digital filtering, sliding average, signal gain. Analyzing the ground-penetrating radar images of 5 lines, we can see that the 900 MHz ground-penetrating radar antenna can only detect the defective body at a depth of 0.25–0.3 m (radar image shown in Fig. 5), and fail to detect the defective body at 0.425, 0.78 m, which is mainly due to the fact that there is a small amount of water in the internal environment of the test bench, which greatly attenuates the energy of the electromagnetic wave. In order to verify the effect of this paper's intelligent detection network, the application of the test bench four line of ground-penetrating radar images to verify the detection results in Fig. 5. From Fig. 5, it can be seen that the application of this paper's intelligent detection network detected five defects in the test bench four line of the test bench, and the test bench of the actual location of the defects, the number of coincides with the detection of the five lesions of the confidence level of 0.58, 0.53, 0.76, 0.41, 0.5, 0.5, 0.5 and 0.5, respectively. 5.

Fig. 5
A radar image highlights 2 leakiness and 2 hollow portions.

Image detection results

Full size image

5 Conclusions

  1. (1)

    This paper numerically simulates the propagation law of electromagnetic wave in tunnel lining structure under a variety of working conditions, and summarizes the characteristics of the radar image of hollow, dehollowing, incompact and other diseases. The simulated ground-penetrating radar image database is established, which lays the foundation for the application of ground-penetrating radar in actual lining detection.

  2. (2)

    At present, this paper in the ground-penetrating radar image anomaly detection to do some research work, to a certain extent to identify the tunnel lining structure whether there is a disease and the location, but cannot distinguish between specific types of disease (cavity, dehollowing, not compact). For this reason, we continue to collect data at the tunnel site to further enrich the radar data of the lining structure with cavity, dehollowing and incompactness. At the same time, on the basis of this model, in-depth study of more refined multi-classification intelligent detection model, to solve the problem of target detection of small sample industrial data.