Research on the Forward Simulation and Intelligent Detection of Defects in Highways Using Ground-Penetrating Radar

Abstract

The increasing variety and frequency of subgrade defects in operational highways have led to a rise in road safety incidents. This study employed ground-penetrating radar (GPR) detection and forward simulation to analyze the characteristic patterns of common subgrade defects, such as looseness, voids, and cavities. Through the integration of instantaneous feature information from different defect patterns with complex signal techniques, the boundary judgment of structural layers and anomalies in GPR images of various subgrade defects was improved. An intelligent recognition platform was established, and a radar image dataset was created and trained to evaluate the recognition performance of the You Only Look Once (YOLO) v3 and Single-Shot Multi-Box Detector (SSD) algorithms. Evaluation metrics such as precision, recall, F1-score, average precision (AP), and mean average precision (mAP) were used to assess the detection efficiency and accuracy for subgrade defect images. The results showed that YOLO v3 achieved an average detection accuracy of 76.69%, while the SSD achieved 75.07%. This study demonstrates that the reliability of the intelligent recognition and classification of highway subgrade defects can be enhanced by using GPR for non-destructive testing.

1. Introduction

Ground-penetrating radar (GPR) technology is a non-destructive testing method that has been widely applied in subgrade safety monitoring. Due to its non-destructive, rapid, and efficient nature, GPR has emerged as a crucial tool for the monitoring of subgrade safety [1,2]. It is primarily utilized in detecting subgrade structures, identifying defects, and assessing stability, enabling the discovery of anomalies such as voids, loose areas, and cracks within the subgrade [3,4].

GPR technology can be used to effectively detect voids and cracks in the subgrade, providing valuable insights for subgrade reinforcement and repair efforts. Furthermore, it can be used to detect defects in urban roads, particularly cracks and loose areas [5,6]. However, the interpretation of GPR data poses challenges due to the varying electromagnetic properties of different media and the complexity of underground structures. Additionally, the detection efficacy is notably influenced by environmental factors, such as groundwater and salinity, which can lead to suboptimal performance in complex environments [7].

Deep learning technology is renowned for its exceptional performance in image and pattern recognition and has progressively been integrated into the intelligent identification of subgrade defects [8]. One of its primary applications in this domain is object detection. By leveraging convolutional neural networks (CNNs), subgrade cracks can be accurately detected through the use of extensive training samples. Moreover, the Faster R-CNN model has been successfully employed to identify diverse types of defects, including potholes and cracks [9,10,11].

The current research on subgrade defect detection using radar and deep learning primarily focuses on enhancing image recognition accuracy and extracting meaningful image feature data. Acquiring and annotating a substantial volume of subgrade defect images is crucial for intelligent defect recognition. Nevertheless, the lack of precisely labeled datasets represents a significant bottleneck in improving the model performance [12,13]. Given the diverse range of subgrade defects and their distinct characteristics, further research is necessary to develop generalized models that are capable of detecting various types of defects [14,15].

This study utilizes GprMax3.0 software to conduct forward simulations of loose, void, and cavity defects in subgrades. By removing direct waves and enhancing the signal gain, we analyze the characteristics of the defect images. Complex signal analysis techniques are applied to extract the instantaneous amplitude, phase, and frequency features of different defects, thereby improving the accuracy of defect image recognition. Additionally, we employ the PyTorch2.0 deep learning framework along with YOLO and SSD models for the intelligent identification of defect images. The recognition results of these two algorithms are compared and evaluated based on metrics such as accuracy and the recall rate. The findings are then applied to test sections to validate the accuracy and rationality of the research outcomes.

2. Test Method

2.1. GPR Detection and Forward Simulation

GPR technology operates by transmitting high-frequency broadband electromagnetic pulses into a subsurface through a transmitting antenna. As shown in Figure 1, upon encountering subsurface structures with differing electrical properties, these electromagnetic waves undergo reflection and refraction at interfaces, subsequently being received by the receiving antenna upon returning to the surface. By analyzing parameters such as the signal waveform, intensity, and two-way travel time, the depth, spatial position, structure size, electrical properties, and geometric shape of subsurface anomalies can be determined, thereby facilitating the detection of hidden subsurface targets [16,17]. The GPR frequency range encompasses the electromagnetic waves emitted by the radar, utilizing scattered echoes from the targets for signal detection and parameter estimation. The center frequency denotes the peak operating frequency of the radar antenna [18,19].

The propagation time of the electromagnetic pulse is described in Equation (1). When the medium’s electrical conductivity is very low, the wave speed can be approximated using Equations (2) and (3) [20]. However, when the medium’s electrical conductivity is non-negligible, the wave speed $v$ depends on both the electrical conductivity and the dielectric constant of the medium, rendering the calculation more complex, and it is typically determined through empirical measurements [21].

(1)$t=\sqrt{4z^2+x^2}/v$

(2)$v=c/\sqrt{{\mu }_r{\epsilon }_r}$

(3)$c=1/\sqrt{{\mu }_0{\epsilon }_0}\approx 3\times {10}^8 \mathrm{m}/\mathrm{s}=0.3 \mathrm{m}/\mathrm{ns}$

In the above equations, $v$ is the propagation speed of the electromagnetic wave in the medium (m/ns); $z$ is the burial depth of the subsurface target (m); $x$ is the horizontal distance between the transmitting and receiving antennas (m); $t$ is the propagation time of the electromagnetic pulse (ns); $c$ is the speed of electromagnetic waves in a vacuum (m/ns); ${\mu }_r$ is the relative magnetic permeability of the medium; ${\mu }_0$ is the magnetic permeability of a vacuum; ε_r is the relative dielectric constant of the medium; and ${\epsilon }_0$ is the dielectric constant of a vacuum.

This study employs the GprMax forward simulation software, based on the Finite Difference Time Domain (FDTD) method, to solve the 3D Maxwell equations and establish a forward simulation of GPR subgrade defects. The model simulates electromagnetic wave propagation in a semi-infinite space, using lossy media at the boundaries to absorb waves, achieving the desired effect within a finite grid. The model uses perfectly matched layer (PML) boundary absorbing conditions, where the electromagnetic waves entering the PML boundary absorption layer are attenuated rapidly, without reflection. Additionally, the model employs Ricker wavelets as the excitation source for the GprMax forward simulation, effectively simulating the detection of subgrade defect models. Ricker wavelets, which have the minimum phase input with positive and negative peak values, closely resemble the field source of the GPR transmitting antenna [22].

2.2. Complex Signal Processing

Complex signal processing decomposes the reflected wave information from electromagnetic recordings into the instantaneous amplitude, phase, and frequency. This technique primarily uses the Hilbert transform to convert real electromagnetic signals into complex ones and decompose them into the above parameters. These parameters are then used to analyze the response characteristics of anomalous bodies. According to the Hilbert transform, a signal’s frequency domain and time domain exhibit an equivalence relationship after undergoing a Fourier transform, which is closely related to the symmetry of the Fourier transform.

The reflected wave signal data obtained through the GprMax forward simulation are real signals (Equation (4)). By applying the Hilbert transform to the real signal $x\left(t\right)$, the imaginary component of its complex signal can be obtained (Equation (5)). The real signal $x\left(t\right)$ and its corresponding complex signal $\widehat{x}\left(t\right)$ can then be combined to form the complex GPR signal (Equation (6)) [23].

(4)$x\left(t\right)=A\left(t\right)\cos \left[{\omega }_{0}t+\phi \left(t\right)\right]$

(5)$\widehat{x}\left(t\right)=x\left(t\right){\displaystyle \frac{1}{\pi t}}={\displaystyle \frac{1}{\pi }}{\displaystyle {\int }_{-\infty }^{+\infty }\frac{x\left(t\right)}{t-\pi }}dt=A\left(t\right)\sin \left[{\omega }_{0}t+\phi \left(t\right)\right]$

(6)$\begin{array}{l}f\left(t\right)=x\left(t\right)+i\widehat{x}\left(t\right)=A\left(t\right)\cos \left[{\omega }_{0}t+\phi \left(t\right)\right]+iA\left(t\right)\sin \left[{\omega }_{0}t+\phi \left(t\right)\right]\\ =A\left(t\right)e^{i\left[{\omega }_{0}t+\phi \left(t\right)\right]}\end{array}$

In the above equations, $\phi (t)$ is the phase function of the real signal; $A\left(t\right)$ is the amplitude function; ${\omega }_0$ is the center frequency; $t$ is the time variable; and $f\left(t\right)$ is the complex signal of the GPR.

As shown in Equation (7), $A\left(t\right)$ represents the amplitude of $f\left(t\right)$, which reflects the strength of the reflected signal. The instantaneous amplitude is proportional to the square root of the energy of the georadar signal at that moment. When there is an abnormality within the roadbed, the magnitude of the electromagnetic wave signal’s instantaneous amplitude exhibits a significant variation. This anomaly is evident in the instantaneous amplitude profile of the roadbed, where distinct changes occur at the locations of the roadbed’s structural interfaces and internal anomalies.

As shown in Equation (8), $\theta \left(t\right)$ denotes the instantaneous phase of $f\left(t\right)$. The instantaneous phase is primarily used to describe the continuity of the phase axis in the georadar profile. In the instantaneous phase profile of the roadbed, both strong and weak reflected waves are represented by their phases. Even weak-amplitude effective waves can be clearly displayed in the instantaneous phase profile. When an anomaly is present within the roadbed structure, the instantaneous phase of the electromagnetic wave will experience irregularities, resulting in discontinuities in the phase axis.

As shown in Equation (9), the instantaneous frequency can be obtained by taking the derivative of $\theta \left(t\right)$ with respect to $t$. The instantaneous frequency is the rate of change in the instantaneous phase over time; it primarily reflects the variations in the physical properties of the subsurface layers. When electromagnetic waves propagate through different media, the frequency of the reflected signals will vary [24].

(7)$A\left(t\right)=\sqrt{x^2\left(t\right)+\widehat{x}\left(t\right)}$

(8)$\theta \left(t\right)={\omega }_{0}t+\phi \left(t\right)={\tan }^{-1}\left[{\displaystyle \frac{\widehat{x}\left(t\right)}{x\left(t\right)}}\right]$

(9)$S\left(t\right)={\displaystyle \frac{d\theta \left(t\right)}{dt}}={\displaystyle \frac{d}{dt}}{\tan }^{-1}\left[{\displaystyle \frac{\widehat{x}\left(t\right)}{x\left(t\right)}}\right]$

2.3. Intelligent Detection Algorithm

As shown in Figure 2, the SSD network architecture is based on the VGG16 backbone, with an additional six convolutional layers to capture more feature maps. By leveraging multi-scale feature detection, the SSD can maintain high detection accuracy even when the input image resolution is relatively low, achieving a good balance between detection speed and accuracy.

The SSD network model converts the object detection problem into a regression problem. It detects larger objects using high-resolution feature maps and smaller objects using low-resolution feature maps. By directly extracting the object image features at different scales during the convolution stage, the SSD network significantly improves the detection speed. Moreover, the SSD uses the anchor box concept from Faster R-CNN, setting different scales in the anchor boxes at each unit to classify and locate objects, thus reducing the computational burden and enhancing the precision of small-object detection. Multi-scale feature detection allows the SSD to maintain high detection accuracy even with a lower input image resolution. The end-to-end design also simplifies the training process. The SSD achieves a detection speed of 59 FPS and an average detection accuracy of 74.3%, obtaining a good balance between speed and accuracy.

YOLO v3 is the third version of the You Only Look Once (YOLO) series and uses the Darknet53 residual network structure. As shown in Figure 3, the YOLO network architecture consists of 24 convolutional layers, 4 pooling layers, and 2 fully connected layers. The convolutional layers are used to extract image features, the pooling layers enhance target feature information, and the fully connected layers predict the position of the target in the image and estimate the probability values of the target’s class attributes.

It performs object detection using pre-selected boxes on feature maps with three different scales, combining deep and shallow image information to obtain semi-rich composite feature maps, thus enhancing the detection accuracy for small objects. YOLO v3 replaces the Softmax layer with multiple independent logistic classifiers for multi-label classification, and it uses a binary cross-entropy loss function to ensure effective object detection under multi-label conditions.

3. GPR Image Characteristics Analysis

Based on complex signal analysis techniques and the forward simulation results of the interlayer cavity model of road structures, the instantaneous amplitude, instantaneous phase, and instantaneous frequency attributes of loose defects, cavity defects, and void defects were extracted to determine the ground-penetrating radar response characteristics of road defects. The 100th signal was extracted from 200 recorded waves, and the instantaneous feature attributes were normalized to obtain the instantaneous features.

3.1. Model Parameters and Validation

A layered highway model, including surface, base, and subgrade layers, was established based on the actual conditions. Different model parameters were set for each layer, as shown in Table 1, and Figure 4 illustrates the subgrade model, which includes loose subgrades, voids, and cavities.

Considering the simulation effect and resolution, the primary model space was set to 6 m × 2 m × 0.002 m, with spatial discretization sizes of 0.002 m × 0.002 m × 0.002 m in the X, Y, and Z directions, respectively, to achieve the simulation of a semi-infinite subgrade space. The model employed a 3 × 10⁻⁸ s time window and a 1000 MHz center frequency Ricker wavelet excitation source. The main parameters are listed in Table 2.

Using the above parameters, a layered structure model of a highway subgrade without defects was established and subjected to forward simulation and rationality verification. The model’s 2D cross-section and simulation results are shown in Figure 5. In the defect-free subgrade structure, only dielectric constant differences existed between the subgrade layers, with no abnormal bodies. Electromagnetic pulse waves passed through the air layer, surface layer, base layer, and subgrade in sequence, with the relative dielectric constants increasing progressively. The electromagnetic waves were reflected and refracted at the interfaces between the subgrade layers due to dielectric property differences, and the layer interfaces were clear. Strong reflection waves were generated at the air–surface layer interface, with an electric field intensity range of −443.1 to 318.62 V/m. After passing through the air layer, an abnormal waveform appeared at a single travel time of 2 ns, with an electric field intensity range of −66.0 to 96.5 V/m. The calculated propagation speed within the surface layer was approximately 0.15 m/ns, matching the 0.3 m surface layer structure. Subsequently, an abnormal reflection wave appeared at a single travel time of 4 ns, with an electric field intensity range of −6.2 to 7.6 V/m. The calculated propagation speed was approximately 0.1 m/ns, consistent with the 0.4 m base layer thickness. The simulation results matched the theoretical calculations, confirming the reliability of the model calculations.

3.2. Characteristics of Loose Defect

In the instantaneous amplitude image (see Figure 6a), at 2 ns, 6 ns, and 12 ns, the electromagnetic waves consistently generated strong reflective signals. The uniform distribution of the reflective signals at 2 ns and 6 ns indicated a subgrade structural interface. However, at 12 ns, divergent reflective signals indicated a significant disparity in the relative permittivity of the filling medium, suggesting the upper boundary of a loose defect region. At 15 ns, the reflective signals continued to display divergence, accompanied by minor fluctuations, which implied the persistence of the loose defects within the area. As shown in Figure 6b, the normalized instantaneous amplitude of the loose defect revealed strong reflections at 2 ns, 6 ns, and 12 ns, with the strongest signal observed at 2 ns, followed by a secondary peak at 6 ns and a weaker signal at 12 ns. These peaks corresponded to the locations of changes in the electrical parameters between the subgrade structural layers and the target anomaly. By analyzing the instantaneous amplitude and the fluctuation amplitude of the reflected wave in the GPR image, information about the subgrade structural layers and the upper interface of the defect could be inferred.

In the instantaneous phase image (see Figure 6a), when the electromagnetic wave traveled at 10 ns, discontinuities in the phase and emission-like patterns were observed at both ends. Between 10 ns and 30 ns, the instantaneous phase image exhibited a downward-diverging wave, characterized by disrupted, intersecting, and discontinuous in-phase axes. This pattern allowed for the estimation of the size and boundary information of the loose defect in the subgrade. As shown in Figure 7b, which presents the normalized single-trace instantaneous phase image, the presence of electrical differences within the subgrade structure could be inferred based on the reversal of the in-phase axis at 2 ns and 6 ns. The areas marked by green circles in the figure indicate where the electromagnetic waves propagated within the pavement surface and the base layer, showing continuous in-phase axes without phase reversal due to the absence of anomalies. Between 10 ns and 30 ns, multiple phase reversals occurred, indicating multiple reflections and refractions within the anomalous region between 10 ns and 30 ns.

In the instantaneous frequency image (see Figure 8a), during the propagation of the electromagnetic waves within the loose defect area, high-frequency reflection waves exhibited random and irregular distributions. The boundary between the subgrade structural layers and the target anomaly, due to electrical differences, led to higher instantaneous frequencies of the reflection waves at travel times of approximately 2 ns, 6 ns, 10 ns, 14 ns, and 18 ns. Outside these intervals, when the electromagnetic waves propagated within the pavement and base layers, no anomalies were present, resulting in the absence of abnormal high-frequency reflections. Based on the characteristics of the instantaneous frequency image, the boundaries of the subgrade structural layers and anomalies could be inferred.

3.3. Characteristics of Cavity Defect

In the instantaneous amplitude image (see Figure 9a), when the travel time of the electromagnetic wave was 12 ns, an anomalous reflection wave was produced by the cavity defect between the 70th and 130th traces, appearing as a “hyperbolic shape”. The second hyperbolic-shaped anomalous reflection wave corresponded to the lower boundary of the cavity defect. Given that the propagation speed of the electromagnetic wave in the air was 0.3 m/ns, the two-way travel time of the upper and lower boundaries was calculated to be 4 ns, resulting in 0.6 m between the upper and lower vertices of the cavity defect, which aligned with the model design. The single-trace waves at around 6 ns and 6.6 ns exhibited two closely spaced, continuous peaks. For subgrade void defects, the upper and lower interfaces of the defect and the subgrade’s structural layers can be deduced based on the instantaneous amplitude and the normalized amplitude of the single-trace wave in the GPR image. In the instantaneous phase image, when the travel time of the electromagnetic wave was approximately 2 to 8 ns, the characteristic of the reflection wave’s instantaneous phase image was manifested as continuous in-phase axes, indicating uniform and well-compacted structural layers.

In the instantaneous phase image (see Figure 10a), when the travel time of the electromagnetic wave was approximately 2 to 8 ns, the characteristic of the reflection wave’s instantaneous phase image was manifested as continuous in-phase axes, indicating uniform and well-compacted structural layers. Due to the electrical differences between the subgrade structural layers and the anomaly, single-trace instantaneous phase reversals occurred at 2 ns and 6 ns, which could be used to identify the upper boundary of the void defect. The boundaries and affected areas of the void defect could be identified through the instantaneous phase image and the single-trace instantaneous phase variation curve in the GPR image.

In the instantaneous frequency image (see Figure 11a), between the travel times of 8 and 30 ns, the cavity defect exhibited a hyperbolic-shaped instantaneous frequency response, with the opening facing downward. High-frequency reflection waves were seen mostly around 1000 MHz. When the electromagnetic wave reached the upper interface of the void, the reflection coefficient was positive. However, due to the minimal electrical difference between the void and the surrounding subgrade, coupled with the high propagation speed of the electromagnetic wave in the air, only low-frequency reflection waves were generated, making it difficult to accurately identify the posterior boundary.

3.4. Characteristics of Void Defect

In the instantaneous amplitude image (see Figure 12a), when the travel time of the electromagnetic wave was 6 ns, an anomalously strong reflection wave appeared between the 70th and 130th traces. At this time, the normalized amplitude of a single-trace wave for the loose defect was approximately 0.41. The middle part of the upper boundary of the cavity defect presented an almost straight-line reflection wave, accompanied by diffraction phenomena at both ends. The reflection wave below it deformed into a “single-hump shape”. The single-trace waves at approximately 2 ns, 6 ns, and 8 ns exhibited peak instantaneous amplitudes, indicating significant electrical differences between the structural layers within the subgrade, resulting in abnormal reflection waves. The peak at 2 ns corresponded to the air–surface interface of the subgrade structural layer, with a normalized amplitude of 1. The peak at 6 ns corresponded to the interface between the surface and base layers, with a normalized amplitude of 0.23. The abrupt change in the reflection wave at 8 ns was attributed to the propagation of the electromagnetic wave to the upper boundary of the void defect, where the instantaneous amplitude reached its maximum at the peak, with a normalized amplitude of 0.145. The amplitude gradually decreased as it extended to both ends. From the fluctuations in the instantaneous amplitude signal of the void defect and the response characteristics of the instantaneous amplitude image, information about the subgrade structural layers and the boundaries of the target anomaly could be deduced.

In the instantaneous phase image (see Figure 13a), at the travel time of 6 ns, discontinuities in the in-phase axis occurred between the 60th and 140th traces. The instantaneous phase image characteristic of the cavity defect showed discontinuities and intersections of the in-phase axes. At an 8 ns travel time, the single-trace instantaneous phase exhibited an anomalous reversal, corresponding to the upper boundary of the void defect. At 12 ns, a second anomalous reversal in the single-trace instantaneous phase was observed; based on the instantaneous amplitude characteristics, this was likely caused by the electrical differences at the lower boundary of the void defect.

In the instantaneous frequency image (see Figure 14a), between the travel times of 6 and 30 ns, the high-frequency reflection waves of the cavity defect were mainly concentrated between the 70th and 130th traces. The high-frequency distribution of the cavity defect was relatively chaotic and irregular. In the single-trace instantaneous frequency variation image, abrupt high-frequency reflection waves were generated when the electromagnetic waves encountered the interface with differing physical properties. The physical changes in the subgrade structural layers could be inferred based on the variations in the instantaneous frequencies of the electromagnetic waves.

3.5. Image Processing and Enhancement

Based on the forward simulation output of GprMax, Figure 15a shows the image of the void defect after direct wave removal. Between the travel times of 2 ns and 5 ns, no anomalous reflection waves were observed, indicating the absence of anomalous defects in this region. Between the travel times of 5 ns and 7 ns, anomalous reflections occurred, with discontinuous in-phase axes and misaligned reflection waves in adjacent traces. Strong anomalous reflection waves occurred at 7 ns, as well as at the upper interface of the void area, exhibiting similar characteristics to a “hyperbola”.

Figure 15b shows the forward simulation after undergoing signal gain processing. The image filtered strong reflection waves such as direct waves, reducing the disparity between strong and weak reflection waves and allowing weak reflection waves to be better visualized. This provides a more detailed representation of the image characteristics of the void defect. According to the radar simulation image after gain processing, the reflection signals from the upper and lower interfaces of the inflated void were strengthened, and it was possible to obtain the interlayer information of the subgrade structures and the boundary information and image characteristics of the target anomalous body. This enabled the estimation of the size, position, and boundaries of the defect.

Comparing the images before and after processing, the original radar image could only clearly identify the upper surface of the defect area, failing to accurately identify the lower surface. As indicated by the red line in the figure, after gain processing, the electromagnetic wave was reflected at the lower boundary at a travel time of 18 ns, allowing the identification of the lower boundary of the loose defect area. Based on the height of the loose area, and assuming that the relative dielectric constant of the filling medium in the loose area was 4, the propagation speed of the electromagnetic wave in the porous loose defect was deduced to be 0.25 m/ns.

By eliminating direct waves and applying a signal gain, the response characteristics of the GPR image of the subgrade defect could be enhanced, improving the accuracy of GPR detection and the interpretation of subgrade defects.

4. Intelligent Detection and Recognition

Convolutional neural networks (CNNs) are widely used for image recognition, speech recognition, and various other applications. These networks are based on deep learning algorithms and are designed to solve object detection problems in computer vision by identifying and classifying objects within images. In this study, we applied single-stage object detection algorithms, including the SSD and YOLO v3, to detect and identify subgrade defects in the GPR images.

4.1. Dataset Creation

The creation of a defect dataset is fundamental in constructing an object detection algorithm. This study combined the extensive GPR subgrade defect detection data accumulated by our research group with the forward simulation image characteristics of highway subgrade defects studied previously to create a standardized dataset. This dataset included GPR images of subgrade defects such as cavities, loose areas, and voids, both as standard samples and real-world samples, for the training of the subgrade defect detection model.

Partial samples from the defect dataset are shown in Figure 16. The dataset prioritized field data with prominent subgrade defect characteristics. The radar images collected in the field were processed with different gain settings and cropped using Radan 7.0 to enrich the defect data images. The resolution of the GPR images was standardized. Using labeling software, we annotated the defect locations, size ranges, and types in the images, resulting in 1018 annotated images. Additionally, by enhancing and cropping the GPR images, the dataset size was expanded to prevent overfitting during the object detection experiments, thereby improving the detection accuracy for subgrade defects.

4.2. Training Parameter Setting

Based on the dataset of roadbed defects obtained from GPR, the data were divided into training, test, and validation sets according to a specified ratio. Image object detection experiments were then conducted on the vs. Code platform using different object detection algorithms. The parameter settings for the comparative experiments of these detection algorithms primarily affect learning accuracy and efficiency. For YOLO v3, the dataset size was set to 416 × 416 pixels, while for the SSD, the size was set to 300 × 300 pixels. Table 3 summarizes the training parameter settings used in this study.

4.3. Programming Environment and Model Training

The intelligent detection platform was established in the PyTorch environment on a Windows system in order to implement the YOLO and SSD object detection algorithms. Python 3.7 and the corresponding Anaconda were installed, followed by CUDA 10.0 and cuDNN 7.4.1.5 to configure the runtime environment. Finally, the vs. Code platform was installed via Anaconda to run the YOLO v3 and SSD object detection algorithms, enabling the intelligent detection and identification of subgrade defects in the GPR images. The computing environment’s configuration is shown in Table 4.

In Figure 17, the changes in the SSD’s loss function and mean average precision (mAP) during training are illustrated. It can be observed that, when training the GPR subgrade defect dataset using the object detection algorithms, the training procedure was divided into 100 nodes. After processing each node, a loss value and an mAP value were generated. The trend graph of the loss during training showed a general downward trend with an increasing number of computational nodes, eventually converging.

The SSD model’s loss value eventually converged at 0.4876, with a minimum value of 0.4652, indicating a small difference and a steady decrease in the loss value. At the 50th node, a sudden change was observed, with the 51st loss value increasing before gradually decreasing again, which was considered a normal occurrence. The YOLO v3 model’s loss value eventually converged at 4.7117, with a maximum value of 442.6985 and a minimum value of 4.5620, indicating a significant difference. After completing the first step of fitting, the loss value dropped sharply and then began to decrease steadily from the second step, approaching convergence. Both algorithms exhibited oscillations in their mAP curves, showing an overall upward trend and eventually converging. The mAP value of the SSD model converged at 75.07%, while that of the YOLO v3 model converged at 76.69%.

5. Subgrade Defect Intelligent Identification

5.1. Intelligent Detection Results

Several randomly selected GPR images of different types of subgrade defects were imported into the trained subgrade defect detection model. The target detection results are shown in Figure 18 and Figure 19, where the output results reflect the types, areas, and predicted probabilities of the subgrade defects. To compare the prediction results of the two algorithms, loose subgrade areas were marked with red boxes, cavities with green boxes, and pipelines with blue boxes. For the loose subgrade, YOLO v3’s prediction boxes were relatively small. For cavities, the SSD’s prediction boxes were the largest, while the two algorithms showed no significant difference in identifying pipelines.

Both algorithms achieved a recognition rate of over 95% for loose subgrade defects, with YOLO v3 reaching a prediction value of 0.99, being significantly higher than the SSD’s value of 0.88. This demonstrates that object detection and recognition algorithms based on the principles of regression analysis are suitable for the intelligent detection and identification of GPR subgrade defects, with YOLO v3 achieving higher recognition rates for both types of defects.

5.2. Recognition Effect Evaluation

After obtaining the intelligent recognition results, we evaluated the algorithm’s matching performance against the target using five indicators: $Precision$, $Recall$, $F1$, average precision ($AP$), and mean average precision ($mAP$). As shown in Equations (10)–(14), the precision is the ratio of true-positive predictions to the total predictions generated; the recall is the ratio of true-positive predictions to the total actual positives in the dataset; the $F1$ is the harmonic mean of the precision and recall; the $AP$ is the area under the precision–recall curve; and the $mAP$ is the average of the $AP$ values for each class [25,26].

(10)$Precision={\displaystyle \frac{TP}{TP+FP}}$

(11)$Recall={\displaystyle \frac{TP}{TP+FN}}$

(12)$F1={\displaystyle \frac{2\times Precision\times Recall}{Precision+Recall}}$

(13)$Ap={\displaystyle {\int }_0^{1}P\left(R\right)}d\left(R\right)$

(14)$mAP={\displaystyle \frac{1}{N}}{\displaystyle {\sum }_{i=1}^N{\displaystyle {\int }_0^{1}P\left(R\right)}d\left(R\right)}$

In the equations, P(R) represents the curve expression in the P–R curve; d(R) is the differential form along the R axis; N is the number of classes in the image dataset; TP (true positive) is the number of actual positive samples that are correctly predicted; FP (false positive) is the number of actual negative samples that are incorrectly predicted as positive; TN (true negative) is the number of actual negative samples that are correctly predicted; and FN (false negative) is the number of actual positive samples that are incorrectly predicted as negative.

The $AP$ results for the SSD and YOLO v3 algorithms and for different subgrade defects are shown in Figure 20. The larger the area covered by the blue shading in the P–R curve, the better the detection and recognition performance of the object detection algorithm for the dataset. The SSD demonstrated balanced recognition performance across the three target categories, with $AP$ values for all three subgrade defects above 71%. YOLO v3 achieved an $AP$ value of 78.95% for cavity defects, while the SSD achieved only 64.22% for the same category.

As shown in Table 5, based on the $F1$ obtained from the combined precision and recall metrics, YOLO v3 outperforms the SSD in detecting pipeline, cavity, and loose subgrade defects, with the highest $F1$ reaching 0.82. Regarding the AP, YOLO v3 performs better for void and cavity targets, whereas the SSD performs better for loose subgrade defects. Overall, on the GPR subgrade defect image dataset constructed in this study, YOLO v3 demonstrates superior detection performance.

5.3. Field Verification

Based on research into GPR signatures and experiments in intelligent target recognition for roadbed defects, an on-site test was conducted on a selected road surface. The purpose was to further apply and test the intelligent defect recognition algorithm system developed in this study. The on-site testing utilized a Swedish MALA-450 GPR with a 450 MHz antenna and a time window of 50 ns. According to the GPR on-site detection results, a suspected case of roadbed-cavity-induced surface subsidence was identified. The on-site test results are shown in Figure 21.

Figure 22 shows the radar image after gain processing. Intelligent recognition experiments were conducted on the on-site radar detection images using the two algorithms, the SSD and YOLO v3, with the results shown in Figure 23. Both algorithms successfully identified the roadbed cavity defect and its extent, with the red boxes in the images indicating the predicted results. The SSD algorithm yielded a prediction probability of 0.96 and a smaller prediction range, while the YOLO v3 algorithm yielded a prediction probability of 0.98 and a larger prediction range. These results demonstrate that the SSD and YOLO v3 target detection algorithms, when trained on the GPR roadbed defect image dataset developed in this study, could effectively identify and classify defects in shallow-layer radar detection images of roadbeds and predict their locations and extents. Compared to the SSD, the YOLO v3 algorithm exhibited superior performance in intelligently recognizing the location, extent, and classification of the roadbed cavity defect in the GPR images.

6. Conclusions

In this study, the image features of loose subgrades, cavities, and voids were studied by means of forward simulation, complex signal analysis, and image processing. The SSD and YOLO, which are both deep learning-based models, were used to quickly detect and identify GPR subgrade defects. The main conclusions are as follows:

• (1). By using the GPR and forward simulation methods, a layered structure model of a highway with surface, base, and subgrade layers was established. The simulation results were consistent with the theoretical calculations in the verification of the rationality of the forward simulation, confirming the reliability of the model’s calculations.

• (2). Using complex signal analysis techniques and the forward simulation results of the subgrade structure layers, we extracted the instantaneous amplitude, phase, and frequency attributes of the loose subgrade, void, and cavity defects. These attributes helped to analyze the GPR response characteristics of the subgrade defects, improving the boundary judgment of the structural layers and abnormalities in the GPR images.

• (3). Techniques such as direct wave removal and signal gain enhancement improved the response characteristics of the GPR images of the subgrade defects, enhancing the accuracy of GPR detection and the interpretation of voids.

• (4). In the PyTorch environment on the vs. Code platform, the SSD and YOLO v3 algorithms were trained and evaluated with a series of metrics, including the $Precision$, $Recall$, $F1$, $AP$ and $mAP$. On the subgrade defect radar image dataset created in this study, the YOLO v3 algorithm performed the best, achieving an mAP value of 76.69% and demonstrating higher prediction accuracy.

• (5). A field test was conducted with the YOLO v3 and SSD object detection algorithms within the intelligent defect identification system. This system was employed to identify and classify defects in radar images, thereby meeting the requirement for rapid defect image recognition. Compared to the SSD, YOLO v3 demonstrated superior performance in the intelligent detection and classification of the defect locations, extents, and types within the radar images of subgrade voids.

This study primarily investigated subgrade defects through methods such as GPR forward simulation, complex signal analysis techniques, and image processing. These approaches provide a basis for the intelligent identification of highway subgrade defects by characterizing the defect features. Additionally, deep learning-based algorithms for defect detection and classification in highway subgrade GPR images were tested and evaluated. The results offer a technical reference for the non-destructive and intelligent detection of highway subgrade defects. Future work could incorporate parameters such as the relative permittivity, magnetic permeability, conductivity, and other physical properties of the subgrade to simulate real-world conditions more accurately and further enhance detection accuracy.

Author Contributions

Methodology, P.L. and C.L.; Software, P.L. and X.L.; Validation, P.L., M.B. and X.L.; Resources, M.B.; Writing—original draft, P.L.; Writing—review & editing, P.L.; Supervision, M.B. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Principle of geological radar detection.

Figure 2. SSD target detection algorithm network architecture.

Figure 3. YOLO target detection network architecture.

Figure 4. Subgrade defect model.

Figure 5. Forward simulation results of non-defect highway base model.

Figure 6. Loose defect instantaneous amplitude features.

Figure 7. Loose defect instantaneous phase features.

Figure 8. Loose defect instantaneous frequency features.

Figure 9. Cavity defect instantaneous amplitude features.

Figure 10. Cavity defect instantaneous phase features.

Figure 11. Cavity defect instantaneous frequency features.

Figure 12. Void defect instantaneous amplitude features.

Figure 13. Void defect instantaneous phase features.

Figure 14. Void defect instantaneous frequency features.

Figure 15. Image processing of void defect.

Figure 16. Partial samples of defect data.

Figure 17. SSD target detection algorithm: training parameter index changes.

Figure 18. SSD target detection algorithm: roadbed defect target prediction results in GPR files.

Figure 19. YOLO v3 target detection algorithm: roadbed defect target prediction results in GPR files.

Figure 20. AP trend charts for different roadbed defects.

Figure 21. Field roadbed defect test.

Figure 22. Geological radar image.

Figure 23. Intelligent detection results for on-site roadbed defects.

Table 1

Spatial parameters of highway subgrade pavement layer model.

Parameter	Left Lower/m	Upper Right/m	Thickness/m	Relative Dielectric Constant	Conductivity (S/m)
Model space	(0, 0, 0)	(6, 2, 0.002)	2	\	\
Surface of pavement	(0, 1.4, 0)	(6, 1.7, 0.00)	0.3	4	0.001
Base course of pavement	(0, 1, 0)	(6, 1.4, 0.00)	0.4	9	0.05
Subgrade	(0, 0, 0)	(6, 1, 0.002)	1	10~30	0.1

Table 2

Forward simulation parameters of GprMax.

Space Size/m	SpatialDiscretization/m	TimeWindow/s	Excitation Source	Frequency/MHz	Emission Source/m	Receiving Source/m	Step Distance/m
10 × 2 × 0.002	(0.002, 0.002, 0.002)	3 × 10−8	Ricker	1000	(1.0, 1.75, 0)	(1.2, 1.75, 0)	(0.02, 0, 0)

Table 3

Training parameter setting.

YOLO v3	Parameter	SSD	Parameter
Batch Size	64	Batch Size	64
Image Size	416	Image Size	300
Learning Rate	0.001	Learning Rate	0.001
Momentum	0.9	Momentum	0.9
Weight Decay	0.0003	Weight Decay	0.0003

Table 4

Computing environment configuration for target detection algorithms.

Performance Structure	Configuration
CPU	Intel(R) Core(TM) i7–8700 CPU @ 3.20 Ghz
GPU	NVIDIA GeForce GTX 3060 12 GB
RAM	16 GB
Operating system	Windows 64-bit

Table 5

Evaluation index results for different target detection and recognition tests.

Detection Algorithm	Defect Type	Precision	Recall	F1	AP	mAP
YOLO v3	Void	81.03%	82.46%	0.82	84.66%	76.69%
	Cavity	74.07%	81.63%	0.78	80.26%
	Loose	76.76%	62.64%	0.69	65.15%
SSD	Void	81.43%	50.00%	0.62	76.66%	75.07%
	Cavity	80.00%	65.31%	0.72	73.00%
	Loose	77.86%	58.62%	0.67	75.54%

References

1. Xiang, Z.M.; Rashidi, A.; Ou, G. States of Practice and Research on Applying GPR Technology for Labeling and Scanning Constructed Facilities. J. Perform. Constr. Facil.; 2019; 33, 03119001. [DOI: https://dx.doi.org/10.1061/(ASCE)CF.1943-5509.0001313]

2. Loizos, A.; Plati, C. Accuracy of ground penetrating radar horn–antenna technique for sensing pavement subsurface. IEEE Sens. J.; 2007; 7, pp. 842-850. [DOI: https://dx.doi.org/10.1109/JSEN.2007.894152]

3. Yu, Y.; Klotzsche, A.; Weihermüller, L. Measuring vertical soil water content profiles by combining horizontal borehole and dispersive surface ground penetrating radar data. Near Surf. Geophys.; 2020; 18, pp. 275-294. [DOI: https://dx.doi.org/10.1002/nsg.12099]

4. Miccinesi, L.; Pieraccini, M. A GPR Able to Detect Its Own Position Using Fixed Corner Reflectors on Surface. IEEE Trans. Geosci. Remote Sens.; 2021; 59, pp. 4725-4732. [DOI: https://dx.doi.org/10.1109/TGRS.2020.3018507]

5. Zuluaga–Ramírez, P.; Frövel, M.; Belenguer, T. Non contact inspection of the fatigue damage state of carbon fiber reinforced polymer by optical surface roughness measurements. Ndt E Int.; 2015; 70, pp. 22-28. [DOI: https://dx.doi.org/10.1016/j.ndteint.2014.12.003]

6. Christina, P.; Andreas, L. Estimation of in–situ density and moisture content in HMA pavements based on GPR trace reflection amplitude using different frequencies. J. Appl. Geophys.; 2013; 97, pp. 3-10.

7. Cassidy, N.J.; Eddies, R.; Dods, S. Void detection beneath reinforced concrete sections: The practical application of ground–penetrating radar and ultrasonic techniques. J. Appl. Geophys.; 2011; 74, pp. 263-276. [DOI: https://dx.doi.org/10.1016/j.jappgeo.2011.06.003]

8. Wang, Y.; Jin, H.; Li, G. Investigation of the freeze–thaw states of foundation soils in permafrost areas along the China–Russia Crude Oil Pipeline (CRCOP) route using ground–penetrating radar (GPR). Cold Reg. Sci. Technol.; 2016; 126, pp. 10-21. [DOI: https://dx.doi.org/10.1016/j.coldregions.2016.02.013]

9. Benedetto, F.; Tosti, F. A signal processing methodology for assessing the performance of ASTM standard test methods for GPR systems. Signal Process.; 2017; 132, pp. 327-337. [DOI: https://dx.doi.org/10.1016/j.sigpro.2016.06.030]

10. Krohn, N.; Stoessel, R.; Busse, G. Acoustic non–linearity for defect selective imaging. Ultrasonics; 2002; 40, pp. 633-637. [DOI: https://dx.doi.org/10.1016/S0041-624X(02)00188-9]

11. Watanabe, T.; Trang, H.T.H.; Harada, K. Evaluation of corrosion–induced crack and rebar corrosion by ultrasonic testing. Constr. Build. Mater.; 2014; 67, pp. 197-201. [DOI: https://dx.doi.org/10.1016/j.conbuildmat.2014.05.013]

12. Kang, M.S.; An, Y.K. Frequency–Wavenumber Analysis of Deep Learning–based Super Resolution 3D GPR Images. Remote Sens.; 2020; 12, 3056. [DOI: https://dx.doi.org/10.3390/rs12183056]

13. Li, F.B.; Wu, X.D.; Feng, K.W. Forward Simulation and Instantaneous Attribute Analysis of Ground Penetrating Radar in Subgrade Disease Detection. Transp. Sci. Technol.; 2019; 2, pp. 56-59.

14. Zhang, X.W.; Gao, Y.Z.; Fang, G.Y. Application of Hilbert spectrum analysis in Ground Penetrating Radar thin layer recognition. Chin. J. Geophys.–Chin. Ed.; 2013; 56, pp. 2790-2798.

15. Yan, G.; Bore, T.; Bhuyan, H.; Schlaeger, S.; Scheuermann, A. The Technical Challenges for Applying Unsaturated Soil Sensors to Conduct Laboratory-Scale Seepage Experiments. Sensors; 2022; 22, 3724. [DOI: https://dx.doi.org/10.3390/s22103724]

16. Shen, H.Y.; Li, X.S.; Duan, R.F. Quality Evaluation of Ground Improvement by Deep Cement Mixing Piles Via Ground–Penetrating Radar. Nat. Commun.; 2023; 14, 3448. [DOI: https://dx.doi.org/10.1038/s41467-023-39236-4]

17. Szymczyk, P.; Szymczyk, M. Non–destructive building investigation through analysis of GPR signal by S–tranform. Autom. Constr.; 2015; 55, pp. 35-46. [DOI: https://dx.doi.org/10.1016/j.autcon.2015.03.022]

18. Benedetto, A. Water content evaluation in unsaturated soil using GPR signal analysis in the frequency domain. J. Appl. Geophys.; 2010; 71, pp. 26-35. [DOI: https://dx.doi.org/10.1016/j.jappgeo.2010.03.001]

19. Zhao, S.; Al–Qadi, I.L. Algorithm development for real–time thin asphalt concrete overlay compaction monitoring using ground–penetrating radar. NDT E Int.; 2019; 104, pp. 114-123. [DOI: https://dx.doi.org/10.1016/j.ndteint.2019.04.008]

20. Guo, C.; Zhao, L.; Chen, Y. Extraction of the Pavement Permittivity and Thickness from Measured Ground–Coupled GPR Data Using a Ground–Wave Technique. IEEE Geosci. Remote Sens. Lett.; 2017; 14, pp. 399-403. [DOI: https://dx.doi.org/10.1109/LGRS.2016.2645605]

21. Zhang, M.H.; Feng, X.; Bano, M. Review of Ground Penetrating Radar Applications for Water Dynamics Studies in Unsaturated Zone. Remote Sens.; 2022; 14, 5993. [DOI: https://dx.doi.org/10.3390/rs14235993]

22. Tregubov, O.D. Experience in Using GPR to Study New Frozen–Ground Formations in Subgrade Structures. Soil Mech. Found. Eng.; 2015; 52, pp. 286-291. [DOI: https://dx.doi.org/10.1007/s11204-015-9343-7]

23. Liu, H.; Shi, Z.; Li, J. Detection of Cavities in Urban Cities by 3D Ground Penetrating Radar. Geophysics; 2021; 86, pp. WA25-WA33. [DOI: https://dx.doi.org/10.1190/geo2020-0384.1]

24. Ristic, M.G.M. Point coordinates extraction from localized hyperbolic reflections in GPR data. J. Appl. Geophys.; 2017; 144, pp. 1-17. [DOI: https://dx.doi.org/10.1016/j.jappgeo.2017.06.003]

25. Long, J.; Shelhamer, E.; Darrell, T. Fully convolutional networks for semantic segmentation. IEEE Trans. Pattern Anal. Mach. Intell.; 2014; 39, pp. 640-651.

26. Liu, Y.; Liu, H.Y.; Fan, J.L.; Darrell, T. A Survey of Research and Application of Small Object Detection Based on Deep Learning. Acta Electron. Sin.; 2020; 48, pp. 590-601.