Ground penetrating radar image crack recognition method and system based on frequency domain enhanced YOLOv11

Abstract

This invention provides a method and system for crack recognition in ground-penetrating radar (GPR) images based on frequency-domain enhanced YOLOv11. The method comprises the following steps: S1, constructing a GPR B-scan image dataset containing road cracks and dividing it into training and validation sets; S2, constructing a PFAE-YOLOv11 feature extraction model, which embeds a pyramid frequency attention extraction module into the YOLOv11 backbone network; S3, training the PFAE-YOLOv11 feature extraction model using the training and validation sets to optimize network parameters; S4, inputting the GPR image to be identified into the trained model and outputting initial detection bounding boxes for the cracks; S5, constructing a dual graph convolutional inference module, using the initial detection bounding boxes output in step S4 as graph nodes, and using a graph convolutional network to infer the topological relationships of the cracks, outputting corrected continuous crack paths. This invention significantly improves the accuracy, completeness, and anti-interference capability of crack detection in GPR images.

Description

Technical Field

[0001] This invention relates to the field of image crack recognition methods, and in particular to a ground-penetrating radar image crack recognition method and system based on frequency domain enhancement YOLOv11. Background Technology

[0002] Ground-penetrating radar (GPR), as a highly efficient non-destructive testing technology, is widely used in the detection of defects in the internal structure of roads. Cracks are a major manifestation of early road damage, and timely and accurate identification of cracks is crucial for preventive maintenance. With the development of deep learning technology, target detection algorithms based on convolutional neural networks have gradually replaced traditional manual interpretation and become the mainstream direction of GPR image processing.

[0003] In the prior art, for example, Chinese patent application CN120014500A discloses a road crack analysis method based on an improved YOLO algorithm. This method enhances the multi-scale feature extraction capability by using StarNet as the backbone network and introducing the C2f-Star module, aiming to solve the problem of insufficient multi-scale crack detection accuracy. For example, Chinese patent application CN120823178A discloses a road surface crack detection method based on the Yolov8 model. This method improves the model's crack segmentation performance and detection speed by introducing PKIblock multi-scale convolutional kernels and the generalized high-efficiency layer aggregation network GELAN module, combined with the EMA attention mechanism. However, the above-mentioned existing technologies mainly target visible light road surface images or general feature enhancement, and do not adequately consider the non-stationary signal characteristics unique to ground-penetrating radar B-scan images.

[0004] Crack signals in GPR images are often submerged in complex underground media clutter and electromagnetic interference, exhibiting weak, discontinuous hyperbolic or linear characteristics, and displaying significant time-varying spectral properties. Existing YOLO algorithms mostly perform feature convolution in the spatial domain, making it difficult to effectively separate spectral aliasing noise from features. Furthermore, traditional Fourier transforms lack time-frequency localization capabilities, resulting in limited feature extraction capabilities for non-stationary signals. In addition, existing detection algorithms typically output independent bounding boxes, ignoring the topological correlation of cracks as continuous physical structures. This makes them prone to crack breakage, missed detections, or false positives under strong noise interference, making it difficult to form a complete crack path description. Summary of the Invention

[0005] The main objective of this invention is to provide a method and system for crack identification in ground-penetrating radar images based on frequency domain enhancement YOLOv11. This application effectively solves the problems of difficulty in extracting weak crack features and topological discontinuity in detection results when processing ground-penetrating radar images under strong noise interference by introducing a frequency domain enhancement mechanism based on two-dimensional discrete fractional Fourier transform and a dual graph convolution topology inference module.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for crack identification in ground penetrating radar images based on frequency domain enhanced YOLOv11, the method comprising: S1. Construct a ground-penetrating radar B-scan image dataset containing road cracks, and divide it into a training set and a validation set; S2. Construct the PFAE-YOLOv11 feature extraction model, which embeds a pyramid frequency attention extraction module into the YOLOv11 backbone network. S3. Train the PFAE-YOLOv11 feature extraction model using the training and validation sets, and optimize the network parameters; S4. Input the ground-penetrating radar image to be identified into the trained model and output the initial detection bounding box of the crack; S5. Construct a dual graph convolutional inference module. Use the initial detection bounding boxes output in step S4 as graph nodes, and use the graph convolutional network to infer the topological relationship of the cracks, and output the corrected continuous crack path.

[0007] In the preferred embodiment, the processing flow of the pyramid frequency attention extraction module in step S2 includes: The number of channels in the input feature map is adjusted by using convolutional layers, and four parallel branches are used for processing, each branch containing dilated convolutions with different dilation rates. Perform a two-dimensional discrete fractional Fourier transform on the feature map of each branch and project it onto the fractional time-frequency domain; A set of filters is used to perform parallel filtering on the fractional domain features to decompose the frequency subbands. Inverse fractional Fourier transform and feature fusion are performed on each frequency sub-band. Attention weight vectors are generated through a weight generation network and then multiplied with the original feature map using weights.

[0008] In the preferred embodiment, a soft thresholding denoising step based on statistical moment features is introduced into the weight generation network, including: Before generating the attention weight vector, the global first-order origin moments of the input feature channels are calculated. and second-order central moments ; Constructing an adaptive threshold function ,in The hyperparameters are learned through backpropagation, with the learning rate consistent with the network backbone parameters, and are dynamically adjusted during iteration based on the response accuracy of the crack features on the validation set. A soft thresholding operator is constructed using the sign function sgn and the maximum value function for eigenvalues. Perform nonlinear transformation: ; This nonlinear transformation sets background noise features below the adaptive threshold to zero, while preserving crack features with high response.

[0009] In the preferred scheme, the steps of the two-dimensional discrete fractional Fourier transform include: Set the transformation order and , respectively corresponding shaft and Rotation angle of the shaft and ; Constructing the Discrete Fourier Transform Matrix For the matrix Perform eigenvalue decomposition to obtain the eigenvector matrix. and eigenvalue diagonal matrix ; For eigenvalue diagonal matrices Each element in Exponentiation yields a fractional eigenvalue matrix. Calculate the fractional transformation kernel matrix ; Using the constructed kernel matrix and For the input feature map Perform a two-dimensional separable transformation, the transformation formula is as follows: ; During the transformation process, a Pey sampling-type discretization algorithm is introduced to eliminate the ambiguity caused by the multiplicity of eigenvalues ​​during discretization by orthogonalizing the eigenvectors.

[0010] In the preferred scheme, the parallel filtering process includes: Calculate the fractional domain features Wigner distribution matrix To obtain the energy density of the features in the time-frequency plane; right Perform a Radon transform to project the energy distribution of the time-frequency plane onto the parameter space, and detect the energy ridge distribution of the feature map in the fractional-order domain; Calculate the energy integral value along the ridge as the energy concentration degree. And set an energy threshold. ; Constructing an adaptive fractional domain mask Regarding location If its energy value is greater than ,but ,otherwise ; mask Features of fractional domain Perform the Adama product operation to filter out low-energy background clutter interference.

[0011] In the preferred scheme, the process by which the weight generation network generates attention weight vectors includes: The input features are mapped to three independent fractional-order vector spaces: query vector, ... Key vector Sum value vector ; Introducing a relative position encoding matrix , The elements are generated by calculating the Euclidean distance between vectors, and the dimension is... Matrix consistency, calculation and Scaling the dot product generates the attention score matrix: ; in For vector dimensions; Decompose the attention score matrix into an magnitude matrix. and phase matrix ; The amplitude matrix is ​​nonlinearly activated using the hyperbolic tangent function tanh to limit the amplitude range. Using Euler's formula The activated amplitude and phase are recombined to generate a complex domain attention weight vector.

[0012] In the preferred embodiment, step S5, which involves constructing the dual graph convolutional inference module, includes: Define graph structure , where the set of nodes For all the initial detection bounding boxes output in step S4; Constructing spatial layers The Delaunay triangulation algorithm is used to mesh and connect the geometric center points of all bounding boxes to generate spatial adjacent edges, and the cosine of the angle between the major axes of the two bounding boxes connected on the edge is calculated as the spatial edge attribute. Build appearance layer Extract the deep feature vector within each bounding box, calculate the Mahalanobis distance between the feature vectors, and select... The nearest neighbor nodes are used to construct the appearance adjacency edges; An edge-conditional generation network is introduced, which uses a multilayer perceptron to dynamically generate convolutional kernel weights based on spatial edge attributes and appearance edge attributes.

[0013] In the preferred embodiment, the process of the dual graph convolution inference module performing graph convolution operations and inference includes: In spatial layer and appearance layer Parallel execution of edge condition graph convolution, the first Layer node features The calculation formula is: ; in, For nodes The set of neighboring nodes, For nodes and Edge properties between The dynamic weight matrix generated by the edge condition generation network. For bias terms; The output features of the two layers are fused using bilinear pooling, and the feature dimension remains at 512 after fusion. Construct a Markov random field model, using the fused features as the observation field, and define the connection state between nodes as the label field; The energy function of the Markov random field is minimized iteratively using the confidence propagation algorithm, with the number of iterations set to 10-15, to infer the crack cluster label to which each node belongs.

[0014] In the preferred scheme, in step S5, a Riemannian manifold metric step is introduced when constructing graph node features: Calculate the covariance matrix of the image region features within each bounding box. ; Mapping the covariance matrix P to the Riemannian manifold space involves the following steps: using a log-Euclidean mapping, P is decomposed into eigenvalues. Where U is an orthogonal matrix, It is an eigenvalue diagonal matrix; Using the log-Euclidean metric, points on a Riemannian manifold are mapped to the tangent space at the identity matrix. The calculation formula is as follows: ,in This is a diagonal matrix obtained by taking the natural logarithm of each eigenvalue; The matrix in the tangent space Vectorization yields a 512×512 dimensional vector, which serves as the initial input features for the graph nodes. .

[0015] In the preferred embodiment, the step of outputting the corrected continuous crack path includes: Based on the cluster labels inferred from the Markov random field, the bounding box nodes belonging to the same cluster are aggregated. For the aggregated node set, an interpolation connection is performed using a B-spline curve fitting algorithm. The steps are as follows: Define the sequence of center coordinates of the aggregation node as the control point set. ; Define node vectors Calculate using the Cox-de Boer recurrence formula B-spline basis functions ; Calculate the coordinates of the B-spline curve based on the control point set and basis functions. : ; Calculate the curvature of each point on the fitted curve, remove abnormal connection points whose curvature abrupt changes exceed the set threshold, and output the smoothed crack path coordinate sequence.

[0016] In the preferred scheme, step S3 introduces an optimization strategy combining gradient-based neural architecture search and knowledge distillation during the model training phase: Construct a supernet with 12 layers, which includes dilated convolutions with different dilation rates and fractional-order transformations of different orders. During training, a YOLOv11 model using ResNet101 as the backbone is introduced as the teacher model. Define the distillation loss function and calculate the Kolb-Leibler divergence of the intermediate layer feature maps of the PFAE-YOLOv11 student model and teacher model. A two-layer optimization strategy is adopted: the inner layer optimizes the network weight parameters, and the outer layer optimizes the architecture parameters through validation set loss. The optimizer uses Adam with a learning rate of 0.0001, which allows the student model to approximate the feature representation ability of the teacher model while maintaining its lightweight nature.

[0017] In the preferred scheme, in step S3, the loss function adopts a combination of regression loss based on Wassstein distance and classification loss based on focus loss: The formula for calculating the bounding box regression loss is:

[0018] in, It is a constant. For prediction boxes With real frame The Wasserstein distance under the Gaussian distribution assumption is calculated as follows:

[0019] In the formula, These are the center coordinate vectors of the predicted bounding box and the ground truth bounding box, respectively. These are the covariance matrices of the predicted bounding box and the ground truth bounding box, respectively.

[0020] In the preferred scheme, step S1 involves preprocessing the ground-penetrating radar image using a variational mode decomposition algorithm, with the following steps: Set the number of modal decompositions and secondary penalty factor ; Construct a variational constraint problem and find eigenmode functions and its center frequency This minimizes the sum of the estimated bandwidths for each mode; Introducing Lagrange multipliers Transform the constrained variational problem into an unconstrained problem; Iterative update using alternating direction multiplier method , and Continue until the convergence condition is met; Calculate the cross-correlation coefficient between the intrinsic mode function components obtained from each decomposition and the original signal, remove noise modes with correlation coefficients below a set threshold, and reconstruct the remaining modes into a denoised image.

[0021] In the preferred embodiment, in step S4, the output initial detection bounding box information is refined through a sub-pixel convolutional layer: Extract the low-resolution feature map output by the detection head; pass Feature augmentation is performed on convolutional layers with multiple channels, where This is the upsampling factor; Perform a periodic shuffle operation to rearrange the channel dimension of the feature map to the spatial dimension and output a high-resolution crack boundary heat map; The center point of the initial detection bounding box is corrected by weighting the local peak coordinates of the heatmap.

[0022] In the preferred embodiment, in step S2, after embedding the pyramid frequency attention extraction module, a deformable convolution module is also connected in series. The steps are as follows: An offset-generating convolutional layer is added as a bypass to the regular convolutional layer to learn the geometric deformation offset of crack features. and modulation scalar ; Based on the learned offset The sampling grid of the input feature map is irregularly deformed; The pixel value at the offset position is calculated using the bilinear interpolation algorithm; By modulating scalar The sampling points are weighted and summed to output a feature map that adapts to the geometry of the irregular crack.

[0023] A ground-penetrating radar crack identification system based on frequency-domain enhanced YOLOv11, the system comprising: The data preprocessing module, whose input is connected to the ground-penetrating radar equipment, is used to receive raw radar data and perform variational mode decomposition to reconstruct a denoised image. The PFAE-YOLOv11 feature extraction module is connected to the data preprocessing module and integrates a field-programmable gate array (FPGA) hardware acceleration unit for outputting the initial detection bounding box. The FPGA hardware acceleration unit is equipped with an intellectual property core that performs two-dimensional discrete fractional Fourier transform. The dual graph convolutional inference module, connected to the PFAE-YOLOv11 feature extraction module, is used to construct a graph structure based on Delaunay triangulation and K-nearest neighbors, and uses edge condition generation network to perform graph inference and output the corrected path. The results output module, connected to the dual graph convolution inference module, is used to map the crack path back to the original radar image coordinate system and visualize it.

[0024] In the preferred embodiment, the field-programmable gate array (FPGA) hardware acceleration unit includes: Memory, used to pre-store different orders The corresponding fractional transformation kernel matrix The lookup table; A systolic array processor is used to perform matrix multiplication operations between the eigenma matrix and the kernel matrix in parallel. ; The coordinate rotation digital calculation method operation unit is used to calculate the sine and cosine values ​​of the rotation angle required for fractional-order transformation in real time at the hardware level.

[0025] This invention provides a method and system for crack identification in ground-penetrating radar images based on frequency domain enhancement YOLOv11. This invention uses variational mode decomposition algorithm to preprocess the original ground-penetrating radar data. By adaptively decomposing the signal into multiple intrinsic mode functions and removing noise modes, it overcomes the shortcomings of traditional filter parameters being fixed and having poor adaptability, and significantly improves the signal-to-noise ratio of the input image.

[0026] This invention constructs a PFAE-YOLOv11 model with an embedded pyramid frequency attention extraction module in the feature extraction stage. It utilizes a two-dimensional discrete fractional Fourier transform to project the feature map into the fractional time-frequency domain. Compared to the traditional Fourier transform, this method can more flexibly rotate the time-frequency plane, thereby achieving energy focusing of crack features and separation of background clutter within the optimal fractional domain. Combined with a soft thresholding denoising step based on statistical moment features, it can adaptively suppress low-response background noise, significantly enhancing the model's ability to perceive weak crack signals. Furthermore, this invention constructs a dual-graph convolutional inference module. By establishing a dual-graph structure based on spatial distance and appearance texture, it uses an edge-conditional graph convolutional network to perform topological relationship inference on the initial bounding box output by YOLO. Through Markov random field energy minimization and B-spline curve fitting, it effectively aggregates fractured crack fragments into continuous, smooth paths and eliminates isolated false detection nodes, significantly improving the physical consistency and integrity of the detection results.

[0027] Furthermore, this invention introduces a gradient-based neural architecture search and knowledge distillation strategy during the training phase, which can automatically search for the optimal network structure for the characteristics of ground-penetrating radar data. Combined with a Wasserstein distance-based loss function, it solves the gradient vanishing problem when bounding boxes do not overlap, improving the model's convergence speed and localization accuracy. Finally, combined with the design of an FPGA hardware acceleration unit, the complex frequency domain transformation algorithm is deployed in hardware through a pulsating array and pipelined computation, ensuring the system's real-time processing capabilities in practical engineering applications. Attached Figure Description

[0028] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart of the ground-penetrating radar image crack identification method based on frequency domain enhanced YOLOv11 of the present invention; Figure 2 This is a system architecture diagram of the ground-penetrating radar image crack identification method based on frequency domain enhanced YOLOv11 of the present invention. Implementation Example 1 like Figure 1-2 As shown, a method for crack identification in ground-penetrating radar images based on frequency-domain enhanced YOLOv11 is presented. This method includes: S1. Construct a ground-penetrating radar B-scan image dataset containing road cracks, and divide it into a training set and a validation set; S2. Construct the PFAE-YOLOv11 feature extraction model, which embeds a pyramid frequency attention extraction module into the YOLOv11 backbone network. S3. Train the PFAE-YOLOv11 feature extraction model using the training and validation sets, and optimize the network parameters; S4. Input the ground-penetrating radar image to be identified into the trained model and output the initial detection bounding box of the crack; S5. Construct a dual graph convolutional inference module. Use the initial detection bounding boxes output in step S4 as graph nodes, and use the graph convolutional network to infer the topological relationship of the cracks, and output the corrected continuous crack path.

[0029] The method comprises five core steps designed to accurately identify and extract continuous crack paths from raw ground-penetrating radar B-scan images.

[0030] Step S1 constructs a ground-penetrating radar B-scan image dataset containing road cracks and divides it into training and validation sets. This is the foundation for training the deep learning model, ensuring that the model can learn the characteristics of the cracks. Step S2 constructs a PFAE-YOLOv11 feature extraction model, embedding a pyramid frequency attention extraction module, i.e., the PFAE module, into the YOLOv11 backbone network. This step is one of the core innovations of this invention. By introducing a frequency domain attention mechanism, it enhances the model's ability to perceive weak crack signals and solves the problem that traditional spatial domain convolution is difficult to separate noise and features.

[0031] Step S3 uses the training set and validation set to train the model and optimize the network parameters so that the model has the ability to identify cracks.

[0032] Step S4 inputs the ground-penetrating radar image to be identified into the trained model, outputting the initial detection bounding boxes of the cracks. This is the direct result of target detection, providing preliminary location information of the cracks. Step S5 constructs a dual graph convolutional inference module, using the initial detection bounding boxes as graph nodes, and uses a graph convolutional network to infer the topological relationship of the cracks, outputting the corrected continuous crack path. This step solves the problem of traditional target detection algorithms outputting independent bounding boxes and ignoring crack continuity, enabling the connection of broken detection boxes into a complete crack morphology. Overall, this method combines frequency domain enhancement and graph convolutional inference, achieving end-to-end optimization from weak signal enhancement to topological structure restoration, significantly improving the accuracy and completeness of crack detection in ground-penetrating radar images.

[0033] In the preferred embodiment, the processing flow of the pyramid frequency attention extraction module in step S2 includes: The number of channels in the input feature map is adjusted by using convolutional layers, and four parallel branches are used for processing, each branch containing dilated convolutions with different dilation rates. Perform a two-dimensional discrete fractional Fourier transform on the feature map of each branch and project it onto the fractional time-frequency domain; A set of filters is used to perform parallel filtering on the fractional domain features to decompose the frequency subbands. Inverse fractional Fourier transform and feature fusion are performed on each frequency sub-band. Attention weight vectors are generated through a weight generation network and then multiplied with the original feature map using weights.

[0034] The specific processing flow of the pyramid frequency attention extraction module is further defined. First, the number of channels in the input feature map is adjusted through convolutional layers, and four parallel branches are used for processing, each branch containing dilated convolutions with different dilation rates. This utilizes the property of dilated convolutions to expand the receptive field, enabling the model to simultaneously capture crack features at different scales and adapt to the diversity of crack width and morphology.

[0035] Next, a two-dimensional discrete fractional Fourier transform is performed on the feature map of each branch, projecting it onto the fractional time-frequency domain. The fractional Fourier transform is a generalized form of the Fourier transform, introducing the degree of freedom of rotation angle, which allows the signal to be projected onto any angle on the time-frequency plane. For non-stationary ground-penetrating radar signals, their spectral energy is often not concentrated on the frequency or time axis, but distributed within a specific fractional domain. By selecting an appropriate fractional order, the energy of the crack signal can be highly concentrated, thus more effectively separating it from background noise.

[0036] Subsequently, a set of filters is used to perform parallel filtering on the fractional-order domain features to decompose the frequency sub-bands. This is equivalent to performing feature screening within the optimal fractional-order domain, further suppressing clutter.

[0037] Finally, inverse fractional Fourier transform and feature fusion are performed on each frequency sub-band. An attention weight vector is generated through a weight generation network and then multiplied with the original feature map using weights. This step transforms the effective features filtered in the frequency domain into attention weights in the spatial domain, thereby enhancing the crack region and suppressing the background region in the original feature map. The beneficial effect of this module is that it fully utilizes the time-frequency characteristics of ground-penetrating radar signals and significantly improves the signal-to-noise ratio and robustness of feature extraction through multi-scale and multi-domain analysis.

[0038] In the preferred embodiment, a soft thresholding denoising step based on statistical moment features is introduced into the weight generation network, including: Before generating the attention weight vector, the global first-order origin moments of the input feature channels are calculated. and second-order central moments ; Constructing an adaptive threshold function ,in The hyperparameters are learned through backpropagation, with the learning rate consistent with the network backbone parameters, and are dynamically adjusted during iteration based on the response accuracy of the crack features on the validation set. A soft thresholding operator is constructed using the sign function sgn and the maximum value function for eigenvalues. Perform nonlinear transformation: ; This nonlinear transformation sets background noise features below the adaptive threshold to zero, while preserving crack features with high response.

[0039] A soft thresholding denoising step based on statistical moment features is introduced into the weight generation network. First, the global first-order origin moments of the input feature channels are calculated. and second-order central moments .

[0040] The first-order central moment, or mean, reflects the central location of the feature distribution; the second-order central moment, or variance, reflects the dispersion of the feature distribution. Next, an adaptive threshold function is constructed. ,in This is a learnable hyperparameter. This threshold can be dynamically adjusted based on the statistical properties of the feature map, adaptively adapting to different background noise levels.

[0041] Then, a soft thresholding operator is constructed using the sign function sgn and the maximum value function for the eigenvalues. Perform nonlinear transformation: The meaning of this formula is that when the absolute value of the feature value is less than the threshold... When the absolute value of the feature value is greater than the threshold, the output is zero; when the absolute value of the feature value is greater than the threshold, the output is zero. When the threshold is subtracted from the feature value, the output is the sign-preserving value.

[0042] This nonlinear transformation is essentially a denoising operation, treating low-response features below an adaptive threshold as background noise and setting them to zero, while retaining high-response crack features above the threshold. Hyperparameters are learned through backpropagation. The model can automatically find the optimal denoising threshold. The benefit of this step is that it can effectively filter out background noise interference in the feature map, making the generated attention weights purer and focused on the crack target, thereby improving the detection accuracy.

[0043] In the preferred scheme, the steps of the two-dimensional discrete fractional Fourier transform include: Set the transformation order and , respectively corresponding shaft and Rotation angle of the shaft and ; Constructing the Discrete Fourier Transform Matrix For the matrix Perform eigenvalue decomposition to obtain the eigenvector matrix. and eigenvalue diagonal matrix ; For eigenvalue diagonal matrices Each element in Exponentiation yields a fractional eigenvalue matrix. Calculate the fractional transformation kernel matrix ; Using the constructed kernel matrix and For the input feature map Perform a two-dimensional separable transformation, the transformation formula is as follows: ; During the transformation process, a Pey sampling-type discretization algorithm is introduced to eliminate the ambiguity caused by the multiplicity of eigenvalues ​​during discretization by orthogonalizing the eigenvectors.

[0044] The specific steps of the two-dimensional discrete fractional Fourier transform are described in detail. First, the transform order is set. and , respectively corresponding shaft and Rotation angle of the shaft and .

[0045] The transformation order determines the rotation angle of the time-frequency plane; different angles correspond to different fractional-order domains. Next, the discrete Fourier transform matrix is ​​constructed. Then, perform eigenvalue decomposition on it to obtain the eigenvector matrix. and eigenvalue diagonal matrix .

[0046] This is the foundation for calculating the kernel matrix of a fractional transformation. Then, for the eigenvalue diagonal matrix... Each element in Exponentiation yields a fractional eigenvalue matrix. Then calculate the fractional transformation kernel matrix. This step utilizes the property that the fractional Fourier transform is a fractional power of the Fourier transform.

[0047] Then, the constructed kernel matrix was used. and For the input feature map Perform a two-dimensional separable transformation, the transformation formula is as follows: This means first processing the rows. Order transformation, then perform column transformation The fractional-order transform, or conversely, the fractional-order transform of a two-dimensional image, is achieved. During the transform process, a Pai sampling-type discretization algorithm is introduced to eliminate the ambiguity caused by eigenvalue multiplicity during discretization by orthogonalizing the eigenvectors. This is because the eigenvalues ​​of the discrete Fourier transform matrix exhibit multiplicity, resulting in non-unique eigenvectors, and consequently, a non-unique definition of the fractional-order transform.

[0048] The Pai sampling algorithm determines a unique eigenvector basis through a specific orthogonalization method, ensuring the unitary and invertible nature of the transformation. The beneficial effect of this step is that it provides an accurate and numerically stable method for implementing the two-dimensional discrete fractional Fourier transform, offering a reliable mathematical foundation for subsequent fractional-order domain filtering and effectively converting ground-penetrating radar images to a fractional-order domain with higher energy concentration.

[0049] In the preferred scheme, the parallel filtering process includes: Calculate the fractional domain features Wigner distribution matrix To obtain the energy density of the features in the time-frequency plane; right Perform a Radon transform to project the energy distribution of the time-frequency plane onto the parameter space, and detect the energy ridge distribution of the feature map in the fractional-order domain; Calculate the energy integral value along the ridge as the energy concentration degree. And set an energy threshold. ; Constructing an adaptive fractional domain mask Regarding location If its energy value is greater than ,but ,otherwise ; mask Features of fractional domain Perform the Adama product operation to filter out low-energy background clutter interference.

[0050] The specific implementation of the parallel filtering process is described. First, the fractional-order domain features are calculated. Wigner distribution matrix The Wigner distribution is a bilinear time-frequency distribution with high time-frequency resolution, clearly showing the energy distribution of a signal in the time-frequency plane.

[0051] Next to A Radon transform is performed to project the energy distribution in the time-frequency plane onto the parameter space. The Radon transform can detect linear features in an image; in the time-frequency plane, the energy distribution of a linear frequency modulated (LFM) signal appears as a straight line, thus the Radon transform can effectively detect the energy ridges of the signal. The energy integral value on the ridge is then calculated as the energy concentration. And set an energy threshold. .

[0052] Energy concentration reflects the degree of concentration of a signal within the current fractional order domain. The higher the concentration, the more suitable the fractional order domain is for representing the signal.

[0053] Constructing an adaptive fractional domain mask Regarding location If its energy value is greater than ,but ,otherwise This is a hard threshold filtering process that preserves high-energy signal regions while suppressing low-energy noise regions.

[0054] Finally, apply the mask. Features of fractional domain The Hadamard product operation, i.e., element-wise multiplication, is performed to filter out low-energy background clutter interference. The beneficial effect of this step is that it combines the high resolution of the Wigner distribution with the linear detection capability of the Radon transform, which can accurately locate and extract the crack signal components in the fractional domain, greatly improving the targeting and effectiveness of filtering and significantly enhancing the signal-to-noise ratio of the image.

[0055] In the preferred scheme, the process by which the weight generation network generates attention weight vectors includes: The input features are mapped to three independent fractional-order vector spaces: query vector, ... Key vector Sum value vector ; Introducing a relative position encoding matrix , The elements are generated by calculating the Euclidean distance between vectors, and the dimension is... Matrix consistency, calculation and Scaling the dot product generates the attention score matrix: ; in For vector dimensions; Decompose the attention score matrix into an magnitude matrix. and phase matrix ; The amplitude matrix is ​​nonlinearly activated using the hyperbolic tangent function tanh to limit the amplitude range. Using Euler's formula The activated amplitude and phase are recombined to generate a complex domain attention weight vector.

[0056] This paper details the process by which a weight generation network generates attention weight vectors. First, the input features are mapped to three independent fractional-order vector spaces: the query vector... Key vector Sum value vector This is the standard operation of the self-attention mechanism, used to calculate the correlation within features. Next, a relative position encoding matrix is ​​introduced. Its elements are generated by calculating the Euclidean distance between vectors, and are used to incorporate spatial location information. Calculation and Scaling the dot product generates the attention score matrix: .

[0057] in The similarity between the query vector and the key vector was calculated. It is a scaling factor used to prevent gradient vanishing due to excessively large dot products. For vector dimensions.

[0058] This formula transforms similarity into a probability distribution, i.e., attention scores, using the Softmax function. The attention score matrix is ​​then decomposed into an amplitude matrix. and phase matrix .

[0059] This is to handle attention weights in the complex domain. The hyperbolic tangent function tanh is used to perform nonlinear activation on the magnitude matrix, limiting the magnitude range to between -1 and 1 to prevent numerical instability caused by excessively large magnitudes. Euler's formula is then applied. The activated amplitude and phase are recombine to generate a complex-domain attention weight vector. The beneficial effect of this step is that it constructs a complex-domain self-attention mechanism that utilizes not only the amplitude information of the features but also the phase information, enabling a more comprehensive capture of the dependencies between features.

[0060] Meanwhile, the introduction of relative position encoding enhances the model's ability to perceive the spatial structure of cracks, thereby generating more accurate attention weights and improving feature extraction performance.

[0061] In the preferred embodiment, step S5, which involves constructing the dual graph convolutional inference module, includes: Define graph structure , where the set of nodes For all the initial detection bounding boxes output in step S4; Constructing spatial layers The Delaunay triangulation algorithm is used to mesh and connect the geometric center points of all bounding boxes to generate spatial adjacent edges, and the cosine of the angle between the major axes of the two bounding boxes connected on the edge is calculated as the spatial edge attribute. Build appearance layer Extract the deep feature vector within each bounding box, calculate the Mahalanobis distance between the feature vectors, and select... The nearest neighbor nodes are used to construct the appearance adjacency edges; An edge-conditional generation network is introduced, which uses a multilayer perceptron to dynamically generate convolutional kernel weights based on spatial edge attributes and appearance edge attributes.

[0062] The specific steps for constructing the dual graph convolutional inference module are defined. First, the graph structure is defined. , where the set of nodes This refers to all the initial detection bounding boxes output in step S4. This means converting the object detection results into graph nodes, preparing for subsequent topology reasoning.

[0063] Next, construct the spatial layer. The Delaunay triangulation algorithm is used to mesh and connect the geometric center points of all bounding boxes, generating spatial adjacency edges. Delaunay triangulation has the property of empty circles, enabling the construction of tightly connected and uniformly distributed triangular meshes, suitable for describing spatial adjacency relationships. The cosine of the angle between the major axes of two connected bounding boxes is calculated as a spatial edge attribute, reflecting the directional consistency of the two detection boxes. The smaller the angle, the closer the cosine value is to 1, indicating that they are more likely to belong to the same crack.

[0064] Build appearance layer Extract the deep feature vector within each bounding box, calculate the Mahalanobis distance between the feature vectors, and select... The nearest neighbor nodes are used to construct the appearance adjacency edges. Mahalanobis distance takes into account the correlation between features and is more accurate than Euclidean distance in measuring appearance similarity.

[0065] The appearance layer connects nodes based on feature similarity, enabling the connection of spatially distant but visually similar crack segments. Finally, an edge condition generation network is introduced, which uses a multilayer perceptron to dynamically generate convolutional kernel weights based on spatial and appearance edge attributes.

[0066] This allows graph convolution operations to dynamically adjust based on edge attributes, achieving adaptive information transfer. The beneficial effect of this step is that it constructs a dual graph structure, considering both the spatial continuity and appearance consistency of the cracks, thus providing a rich information foundation for subsequent accurate inference of the topological relationships of the cracks.

[0067] In the preferred embodiment, the process of the dual graph convolution inference module performing graph convolution operations and inference includes: In spatial layer and appearance layer Parallel execution of edge condition graph convolution, the first Layer node features The calculation formula is: ; in, For nodes The set of neighboring nodes, For nodes and Edge properties between The dynamic weight matrix generated by the edge condition generation network. For bias terms; The output features of the two layers are fused using bilinear pooling, and the feature dimension remains at 512 after fusion. Construct a Markov random field model, using the fused features as the observation field, and define the connection state between nodes as the label field; The energy function of the Markov random field is minimized iteratively using the confidence propagation algorithm, with the number of iterations set to 10-15, to infer the crack cluster label to which each node belongs.

[0068] This paper details the process of graph convolution operations and inference performed by the dual graph convolution inference module. Firstly, in the spatial layer... and appearance layer Parallel execution of edge condition graph convolution, the first Layer node features The calculation formula is: .

[0069] This formula represents the node. The new feature is its neighboring nodes Weighted aggregation of features, with weights generated by edge conditions in the network. Based on edge attributes Dynamically generated Used for normalization, For bias.

[0070] This convolutional method adaptively aggregates information based on the strength of relationships between nodes. The output features of the two layers are then fused using bilinear pooling, maintaining a feature dimension of 512 after fusion. Bilinear pooling captures second-order interaction information between features from different layers, enhancing the expressive power of the features.

[0071] A Markov random field model is constructed, using the fused features as the observation field and defining the connection states between nodes as the label field. Markov random fields can model the global state using the local dependencies between nodes, making them suitable for handling label prediction problems with spatial correlation.

[0072] Finally, the confidence propagation algorithm is used to iteratively minimize the energy function of the Markov random field, with the number of iterations set to 10-15, to infer the crack cluster label to which each node belongs. The confidence propagation algorithm is an efficient inference algorithm that updates the beliefs of nodes by passing messages between nodes, eventually converging to the maximum a posteriori probability state.

[0073] The beneficial effect of this step is that it effectively integrates spatial and appearance information by using graph convolutional networks and Markov random fields, and infers the topological structure of cracks by using the idea of ​​global optimization. It can accurately cluster the crack detection boxes into continuous crack paths, thus solving the problems of missed detection and cracks.

[0074] In the preferred scheme, in step S5, a Riemannian manifold metric step is introduced when constructing graph node features: Calculate the covariance matrix of the image region features within each bounding box. ; Mapping the covariance matrix P to the Riemannian manifold space involves the following steps: using a log-Euclidean mapping, P is decomposed into eigenvalues. Where U is an orthogonal matrix, It is an eigenvalue diagonal matrix; Using the log-Euclidean metric, points on a Riemannian manifold are mapped to the tangent space at the identity matrix. The calculation formula is as follows: ,in This is a diagonal matrix obtained by taking the natural logarithm of each eigenvalue; The matrix in the tangent space Vectorization yields a 512×512 dimensional vector, which serves as the initial input features for the graph nodes. .

[0075] A Riemannian manifold metric step is introduced when constructing graph node features. First, the covariance matrix of the image region features within each bounding box is calculated. The covariance matrix is ​​a symmetric positive definite matrix that describes the correlation between the dimensions of a feature and lies on a Riemannian manifold. The covariance matrix... Mapping to the Riemannian manifold space involves the following steps: using a log-Euclidean mapping, and then decomposing the eigenvalues... Decomposed into ,in It is an orthogonal matrix. It is a diagonal matrix of eigenvalues.

[0076] Using the log-Euclidean metric, points on a Riemannian manifold are mapped to the tangent space at the identity matrix. The calculation formula is as follows: ,in This is the diagonal matrix obtained by taking the natural logarithm of each eigenvalue. Riemannian manifolds are non-Euclidean spaces, and direct computation in Euclidean space would lose geometric information. By using a logarithmic mapping, points on the Riemannian manifold are mapped to the tangent space (Euclidean space), preserving the manifold's structural information and facilitating subsequent vectorized computation.

[0077] The matrix in the tangent space Vectorization, to obtain A dimensional vector serves as the initial input feature for graph nodes. The beneficial effect of this step is that it utilizes the Riemannian manifold metric to mine second-order statistical information in the feature covariance matrix. Compared with directly using first-order features, it can provide richer and more discriminative node feature representations, thereby improving the accuracy of graph reasoning.

[0078] In the preferred embodiment, the step of outputting the corrected continuous crack path includes: Based on the cluster labels inferred from the Markov random field, the bounding box nodes belonging to the same cluster are aggregated. For the aggregated node set, an interpolation connection is performed using a B-spline curve fitting algorithm. The steps are as follows: Define the sequence of center coordinates of the aggregation node as the control point set. ; Define node vectors Calculate using the Cox-de Boer recurrence formula B-spline basis functions ; Calculate the coordinates of the B-spline curve based on the control point set and basis functions. : ; Calculate the curvature of each point on the fitted curve, remove abnormal connection points whose curvature abrupt changes exceed the set threshold, and output the smoothed crack path coordinate sequence.

[0079] The specific steps for outputting the corrected continuous crack path are described. First, based on the cluster labels inferred from the Markov random field, bounding box nodes belonging to the same cluster are aggregated. This step groups detection boxes belonging to the same crack. For the aggregated node set, a B-spline curve fitting algorithm is used for interpolation and connection. The steps are as follows: the center coordinate sequence of the aggregated nodes is defined as the control point set. .

[0080] Define node vectors Calculate using the Cox-de Boer recurrence formula B-spline basis functions Calculate the coordinates of the B-spline curve based on the control point set and basis functions. : B-spline curves have local support; modifying a control point only affects a small part of the curve, while ensuring the smoothness and continuity of the curve.

[0081] Calculate the curvature of each point on the fitted curve, remove abnormal connection points whose curvature abrupt changes exceed the set threshold, and output the smoothed crack path coordinate sequence.

[0082] Abrupt curvature changes usually indicate incorrect node connections or the presence of noise; removing these points can further optimize path quality. The beneficial effect of this step is that it utilizes B-spline curve fitting technology to connect the discrete detection box center points into a smooth, continuous curve. This not only fills the gaps between detection boxes but also corrects minor deviations in their positions, ultimately outputting a crack path that conforms to the physical reality of the crack.

[0083] In the preferred scheme, step S3 introduces an optimization strategy combining gradient-based neural architecture search and knowledge distillation during the model training phase: Construct a supernet with 12 layers, which includes dilated convolutions with different dilation rates and fractional-order transformations of different orders. During training, a YOLOv11 model using ResNet101 as the backbone is introduced as the teacher model. Define the distillation loss function and calculate the Kolb-Leibler divergence of the intermediate layer feature maps of the PFAE-YOLOv11 student model and teacher model. A two-layer optimization strategy is adopted: the inner layer optimizes the network weight parameters, and the outer layer optimizes the architecture parameters through validation set loss. The optimizer uses Adam with a learning rate of 0.0001, which allows the student model to approximate the feature representation ability of the teacher model while maintaining its lightweight nature.

[0084] During the model training phase, an optimization strategy combining gradient-based neural architecture search and knowledge distillation was introduced. First, a supernet with 12 layers was constructed, containing dilated convolutions with different dilation rates and fractional-order transformations of varying orders. The supernet encompassed all possible network structure paths.

[0085] During training, a YOLOv11 model using a ResNet101 residual network as the backbone is introduced as the teacher model. The teacher model network is deep and performs well, but it is computationally expensive. A distillation loss function is defined to calculate the Kourbek-Leibler divergence of the intermediate layer feature maps between the PFAE-YOLOv11 student model and the teacher model. The Kourbek-Leibler divergence measures the difference between two probability distributions; by minimizing this divergence, the student model can learn the feature distribution of the teacher model. A two-layer optimization strategy is adopted: the inner layer optimizes the network weight parameters, and the outer layer optimizes the architecture parameters using validation set loss. The optimizer uses Adam with a learning rate of 0.0001, which allows the student model to approximate the feature representation ability of the teacher model while maintaining its lightweight nature.

[0086] Architecture parameters The weights of different operations are determined, and the optimal network structure can be automatically searched through two-layer optimization. The beneficial effect of this step is that it realizes the automated design of the network structure, can search for the optimal combination of convolution and transformation based on the characteristics of ground penetrating radar data, and improves the performance of the lightweight model by utilizing knowledge distillation, thereby reducing computational complexity while ensuring detection accuracy.

[0087] In the preferred scheme, in step S3, the loss function adopts a combination of regression loss based on Wassstein distance and classification loss based on focus loss: The formula for calculating the bounding box regression loss is:

[0088] in, It is a constant. For prediction boxes With real frame The Wasserstein distance under the Gaussian distribution assumption is calculated as follows:

[0089] In the formula, These are the center coordinate vectors of the predicted bounding box and the ground truth bounding box, respectively. These are the covariance matrices of the predicted bounding box and the ground truth bounding box, respectively.

[0090] The loss function was improved by using a combination of regression loss based on Wassstein distance and classification loss based on focus loss. The formula for calculating the bounding box regression loss is as follows: .

[0091] in, It is a constant. For prediction boxes With real frame The Wasserstein distance under the Gaussian distribution assumption is calculated as follows: .

[0092] In the formula, These are the center coordinate vectors of the predicted bounding box and the ground truth bounding box, respectively. ...

[0093] Simultaneously, it comprehensively considers center point distance and shape similarity, making it more sensitive to bounding box localization. The beneficial effect of this step is that by introducing Wasserstein distance, it improves the stability and convergence speed of bounding box regression, especially in the early stages of training when the overlap between the predicted box and the ground truth box is low, providing continuously effective gradient optimization and ultimately improving localization accuracy.

[0094] In the preferred scheme, step S1 involves preprocessing the ground-penetrating radar image using a variational mode decomposition algorithm, with the following steps: Set the number of modal decompositions and secondary penalty factor ; Construct a variational constraint problem and find eigenmode functions and its center frequency This minimizes the sum of the estimated bandwidths for each mode; Introducing Lagrange multipliers Transform the constrained variational problem into an unconstrained problem; Iterative update using alternating direction multiplier method , and Continue until the convergence condition is met; Calculate the cross-correlation coefficient between the intrinsic mode function components obtained from each decomposition and the original signal, remove noise modes with correlation coefficients below a set threshold, and reconstruct the remaining modes into a denoised image.

[0095] The steps of the variational mode decomposition algorithm used for ground-penetrating radar image preprocessing are described. First, the number of mode decompositions is set. and secondary penalty factor . This determines the number of modes that can be decomposed. Control the bandwidth of the modes. Construct a variational constraint problem and find... eigenmode functions and its center frequency This minimizes the sum of the estimated bandwidths for each mode.

[0096] This is to decompose the signal into a series of narrowband components with sparse properties. Lagrange multipliers are introduced. Transform the constrained variational problem into an unconstrained problem.

[0097] Iterative update using alternating direction multiplier method , and This process continues until the convergence condition is met. This is an efficient optimization algorithm that guarantees the convergence of the decomposition. The cross-correlation coefficients between the intrinsic mode function components obtained from each decomposition and the original signal are calculated. Noise modes with correlation coefficients below a set threshold are removed, and the remaining modes are reconstructed into a denoised image. Noise is typically randomly distributed and has low correlation, while effective signals have high correlation.

[0098] The beneficial effect of this step is that variational mode decomposition is an adaptive non-recursive decomposition method that can effectively avoid the mode aliasing problem. Through bandwidth constraints and center frequency iteration, it can accurately separate the effective modes containing crack information from the noise modes, thereby achieving high-quality image denoising and laying a good foundation for subsequent feature extraction.

[0099] In the preferred embodiment, in step S4, the output initial detection bounding box information is refined through a sub-pixel convolutional layer: Extract the low-resolution feature map output by the detection head; pass Feature augmentation is performed on convolutional layers with multiple channels, where This is the upsampling factor; Perform a periodic shuffle operation to rearrange the channel dimension of the feature map to the spatial dimension and output a high-resolution crack boundary heat map; The center point of the initial detection bounding box is corrected by weighting the local peak coordinates of the heatmap.

[0100] The steps described are as follows: the initial detection bounding box information output is refined through sub-pixel convolutional layers. First, the low-resolution feature map output by the detection head is extracted.

[0101] pass Feature augmentation is performed on convolutional layers with multiple channels, where This is the upsampling rate. This step increases the number of channels, preparing for pixel rearrangement.

[0102] A periodic shuffling operation is performed to rearrange the channel dimension of the feature map to the spatial dimension, outputting a high-resolution crack boundary heatmap. Periodic shuffling reconstructs multi-channel feature maps into high-resolution single-channel images, using channel information to compensate for insufficient spatial resolution, thus achieving super-resolution reconstruction. The center points of the initial detection bounding boxes are weighted and corrected using the local peak coordinates of the heatmap.

[0103] The high-response areas in the heatmap correspond to the crack center, and the position of the bounding box can be fine-tuned using the peak coordinates. The beneficial effect of this step is that it utilizes sub-pixel convolution technology to recover high-frequency detail information from the low-resolution feature map, achieving sub-pixel-level fine-grained localization of the bounding box position. This compensates for the loss of positional accuracy caused by downsampling operations and improves the accuracy of crack localization.

[0104] In the preferred embodiment, in step S2, after embedding the pyramid frequency attention extraction module, a deformable convolution module is also connected in series. The steps are as follows: An offset-generating convolutional layer is added as a bypass to the regular convolutional layer to learn the geometric deformation offset of crack features. and modulation scalar ; Based on the learned offset The sampling grid of the input feature map is irregularly deformed; The pixel value at the offset position is calculated using the bilinear interpolation algorithm; By modulating scalar The sampling points are weighted and summed to output a feature map that adapts to the geometry of the irregular crack.

[0105] A deformable convolutional module is cascaded after the embedded pyramid frequency attention extraction module. Specifically, an offset-generating convolutional layer is added as a bypass to the regular convolutional layer to learn the geometric deformation offset of the crack features. and modulation scalar .

[0106] offset Indicates the displacement of the sampling point, modulation scalar This indicates the weight of the sampling points. Based on the learned offset... The sampling grid of the input feature map is irregularly deformed. This allows the sampling points of the convolution kernel to be freely adjusted according to the feature distribution, rather than being limited to a regular grid.

[0107] The pixel value at the offset position is calculated using a bilinear interpolation algorithm. Since the offset is usually a decimal, interpolation is needed to obtain the corresponding pixel value. This is achieved by modulating a scalar... The sampled points are weighted and summed to output a feature map that adapts to the geometry of the irregular crack. The beneficial effect of this step is that deformable convolution breaks the limitation of the fixed geometry of traditional convolution, and can adaptively adjust the shape and position of the receptive field to better fit the slender, curved and irregular target such as the crack, thereby extracting more accurate and complete features and enhancing the model's adaptability to geometric deformation.

[0108] Example 2 Further explanation in conjunction with Example 1, such as Figure 1-2 As shown, a ground-penetrating radar crack identification system based on frequency-domain enhanced YOLOv11 is disclosed. The system includes: The data preprocessing module, whose input is connected to the ground-penetrating radar equipment, is used to receive raw radar data and perform variational mode decomposition to reconstruct a denoised image. The PFAE-YOLOv11 feature extraction module is connected to the data preprocessing module and integrates a field-programmable gate array (FPGA) hardware acceleration unit for outputting the initial detection bounding box. The FPGA hardware acceleration unit is equipped with an intellectual property core that performs two-dimensional discrete fractional Fourier transform. The dual graph convolutional inference module, connected to the PFAE-YOLOv11 feature extraction module, is used to construct a graph structure based on Delaunay triangulation and K-nearest neighbors, and uses edge condition generation network to perform graph inference and output the corrected path. The results output module, connected to the dual graph convolution inference module, is used to map the crack path back to the original radar image coordinate system and visualize it.

[0109] The system comprises four core modules: a data preprocessing module, whose input is connected to a ground-penetrating radar device, used to receive raw radar data and perform variational mode decomposition to reconstruct a denoised image, corresponding to step S1 in the method; a PFAE-YOLOv11 feature extraction module, connected to the data preprocessing module, which integrates a field-programmable gate array (FPGA) hardware acceleration unit for outputting initial detection bounding boxes; the FPGA hardware acceleration unit is equipped with an proprietary kernel for performing two-dimensional discrete fractional Fourier transforms. This corresponds to steps S2-S4 in the method, demonstrating the system's hardware implementation capabilities.

[0110] The dual graph convolutional inference module, connected to the PFAE-YOLOv11 feature extraction module, is used to construct a graph structure based on Delaunay triangulation and K-nearest neighbors, and utilizes edge-conditional generation networks to perform graph inference, outputting the corrected path. This corresponds to the content of S5 in the method.

[0111] The results output module, connected to the dual graph convolution inference module, is used to map the crack path back to the original radar image coordinate system and visualize it. The beneficial effect of this system lies in solidifying advanced algorithms into specific hardware modules. In particular, the introduction of the FPGA acceleration unit greatly improves the calculation speed of complex frequency domain transformations, enabling the system to process ground-penetrating radar data in real time and meet the needs of rapid on-site detection in engineering projects.

[0112] In the preferred embodiment, the field-programmable gate array (FPGA) hardware acceleration unit includes: Memory, used to pre-store different orders The corresponding fractional transformation kernel matrix The lookup table; A systolic array processor is used to perform matrix multiplication operations between the eigenma matrix and the kernel matrix in parallel. ; The coordinate rotation digital calculation method operation unit is used to calculate the sine and cosine values ​​of the rotation angle required for fractional-order transformation in real time at the hardware level.

[0113] Memory, used to pre-store different orders The corresponding fractional transformation kernel matrix A lookup table is used. Pre-stored lookup tables can avoid redundant calculations of the kernel matrix, saving computational resources.

[0114] A systolic array processor is used to perform matrix multiplication operations between the eigenma matrix and the kernel matrix in parallel. A systolic array is a highly parallel pipelined architecture, well-suited for performing intensive operations such as matrix multiplication, and can significantly improve throughput.

[0115] The coordinate rotation digital calculation method operation unit is used to calculate the sine and cosine values ​​of the rotation angle required for fractional-order transformation in real time at the hardware level.

[0116] The CORDIC algorithm only requires shift and addition / subtraction operations to calculate trigonometric functions, making it ideal for implementation on FPGAs with limited hardware resources, thus avoiding complex floating-point operations. The beneficial effect of this claim is that it provides an efficient hardware acceleration architecture that, through memory optimization, parallel computing, and algorithm simplification, solves the problems of high computational complexity and poor real-time performance in two-dimensional discrete fractional Fourier transform, ensuring the efficient operation of the entire recognition system.

[0117] Example 3 Further explanation in conjunction with Example 1, such as Figure 1-2 As shown in the figure, this embodiment discloses a specific implementation of a ground penetrating radar image crack identification method and system based on frequency domain enhancement YOLOv11, which aims to solve the technical problems of crack features in ground penetrating radar images being affected by background clutter interference and discrete detection results being discontinuous. The following describes the specific parameters and practical procedures in detail.

[0118] First, step S1 is executed to construct a ground-penetrating radar (GPR) B-scan image dataset. This dataset collects GPR detection data from various scenarios, including urban roads and highways, containing 6000 images of transverse cracks, longitudinal cracks, and mesh cracks. All samples are manually labeled using a double-labeling method of bounding boxes and pixel-level masks to ensure accurate labeling of crack location and morphology. The dataset is then randomly divided into a training set of 4200 images and a validation set of 1800 images in a 7:3 ratio, maintaining a consistent proportion of crack types during the partitioning process. The images in both the training and validation sets are preprocessed using a variational mode decomposition algorithm, with a set number of mode decompositions. Secondary penalty factor A variational constraint problem is constructed to find the five eigenmode functions. and its center frequency Introducing Lagrange multipliers The constrained variational problem is transformed into an unconstrained problem, and the alternating direction multiplier method is used for iterative updates. , and The number of iterations is set to 50, and the convergence condition is met. The iteration stops when the time is right. The cross-correlation coefficient between the intrinsic mode function components obtained from each decomposition and the original signal is calculated. Noise modes with a correlation coefficient lower than 0.3 are removed, and the remaining modes are reconstructed into a denoised image to improve the accuracy of subsequent feature extraction.

[0119] Next, step S2 is executed to construct the PFAE-YOLOv11 feature extraction model. This model is based on the YOLOv11 framework, embedding a pyramid frequency attention extraction module after the C3 module of its backbone network. The specific implementation process of the pyramid frequency attention extraction module is as follows: the number of channels of the input feature map is adjusted to 256 dimensions through a 1×1 convolutional layer, and four parallel branches are used for feature processing. The dilation rate of the dilated convolution in each branch is set to 1, 3, 5, and 7, respectively, to capture crack features at different scales. A two-dimensional discrete fractional Fourier transform is performed on the feature map output by each branch, and the transform order is set. , The rotation angles corresponding to the x-axis and y-axis , Construct the discrete Fourier transform matrix Then perform eigenvalue decomposition to obtain the eigenvector matrix. and eigenvalue diagonal matrix ,right Each element in The exponentiation operation yields the fractional eigenvalue matrix. Calculate the fractional transformation kernel matrix Using kernel matrix and For the input feature map Perform a two-dimensional separable transformation, the transformation formula is as follows: The Pai sampling-type discrete algorithm is introduced during the transformation process to analyze the eigenvector matrix. Performing Gram-Schmidt orthogonalization yields the orthogonal eigenvector matrix. ,based on Recalculate the eigenvalue matrix This eliminates the ambiguity caused by the multiplicity of eigenvalues ​​during the discretization process, ensuring the accuracy of the transformation.

[0120] Features of fractional domain Perform parallel filtering and calculate its Wigner distribution matrix. To obtain the energy density in the time-frequency plane, for A Radon transform is performed to project the energy distribution of the time-frequency plane onto the parameter space. The energy ridge distribution of the feature map in the fractional-order domain is detected, and the energy integral value on the ridge is calculated as the energy concentration degree. Set energy threshold (in Let be the global mean of the Wigner distribution matrix. (for standard deviation), construct an adaptive fractional domain mask. Regarding location If its energy value is greater than but ,otherwise , mask Features of fractional domain Perform the Adama product operation to filter out low-energy background clutter interference.

[0121] Perform inverse fractional Fourier transform on each frequency subband after filtering, concatenate and fuse the transformed feature maps with the original feature maps, and generate attention weight vectors through a weight generation network. The weight generation network introduces a soft thresholding denoising step based on statistical moment features, first calculating the global first-order origin moments of the input feature channels. and second-order central moments Construct an adaptive threshold function ,in The hyperparameters learned through backpropagation are initially set to 0.1, with the learning rate consistent with the network backbone parameters. During iteration, the learning rate is dynamically adjusted based on the response accuracy of the crack features on the validation set. A soft thresholding operator is constructed using the sign function `sgn` and the maximum value function to threshold the feature values. Perform nonlinear transformation Background noise features below the adaptive threshold are set to zero, while crack features with high response are preserved.

[0122] The specific process by which the weight generation network generates attention weight vectors is as follows: the input features are mapped to query vectors through three independent 1×1 convolutional layers. Key vector Sum value vector All three dimensions are 256-dimensional, and a relative position encoding matrix is ​​introduced. , The elements are generated by calculating the Euclidean distance between vectors, and the dimension is... Matrix consistency, calculation and The scaled dot product generates the attention score matrix, as shown in the formula. ,in The dimension is vector. The attention score matrix is ​​decomposed into an magnitude matrix. and phase matrix The magnitude matrix is ​​nonlinearly activated using the hyperbolic tangent function tanh, limiting the magnitude range to [0,1]. Then, Euler's formula is applied. The activated amplitude and phase are recombine to generate a complex-domain attention weight vector. This weight vector is then multiplied with the original feature map using a weighted multiplication to complete frequency attention enhancement. A deformable convolutional module is then connected in series after the pyramid frequency attention extraction module. An offset generation convolutional layer is added as a bypass to the regular 3×3 convolutional layer. This convolutional layer contains two output channels, one for learning the geometric deformation offset of the crack features. and modulation scalar Based on the learned offset The sampling grid of the input feature map is irregularly deformed, with the offset range limited to [-1, 1] pixels. The pixel value at the offset position is calculated using a 3×3 bilinear interpolation algorithm, and then modulated using a scalar... (Normalized to [0,1] by the sigmoid function) The sampled points are weighted and summed to output a feature map that adapts to the geometry of the irregular crack.

[0123] Then, step S3 is executed to train the PFAE-YOLOv11 feature extraction model using the training and validation sets. During training, an optimization strategy combining gradient-based neural architecture search and knowledge distillation is introduced. A supernet with 12 layers is constructed, containing dilated convolutions with different dilation rates (1, 3, 5, 7) and fractional-order transformation operations of different orders (0.2, 0.4, 0.6, 0.8). A YOLOv11 model using a ResNet101 residual network as the backbone is introduced as the teacher model. A distillation loss function is defined, and the Körbek-Leibler divergence of the intermediate feature maps between the student model and the teacher model is calculated, with the weight coefficient set to 0.3.

[0124] A two-layer optimization strategy is adopted. The inner layer optimizes the network weight parameters through stochastic gradient descent with a learning rate of 0.001 and 100 iterations. The outer layer optimizes the architecture parameters through validation set loss. The optimizer used is Adam with a learning rate of 0.0001, allowing the student model to approximate the feature representation capabilities of the teacher model while maintaining lightweight design. The model's loss function combines regression loss based on Wasserstein distance and classification loss based on focus loss, with a total loss function of [missing information]. The formula for calculating the bounding box regression loss is as follows: , It is a constant with a value of 10. For prediction boxes With real frame The Wasserstein distance under the Gaussian distribution assumption is specifically calculated as follows: , , These are the center coordinate vectors of the predicted bounding box and the ground truth bounding box, respectively. , These are the 2×2 covariance matrices of the predicted and ground truth bounding boxes, respectively; the focus loss and classification loss are calculated using the following formula: ,in To predict probabilities, An early stopping strategy is employed during training: training is stopped when the validation set loss does not decrease for 10 consecutive rounds, and the optimal network parameters are saved.

[0125] In step S4, the ground-penetrating radar image to be identified, after preprocessing in step S1, is input into the trained PFAE-YOLOv11 feature extraction model. The model outputs the initial detection bounding box of the crack. To improve the localization accuracy of the bounding box, the initial detection bounding box information is refined through a sub-pixel convolutional layer, extracting the low-resolution feature map output by the detection head (size 1 / 4 of the input image). Feature augmentation is performed on convolutional layers with multiple channels. (For upsampling ratio), a periodic shuffling operation is performed to rearrange the channel dimension of the feature map to the spatial dimension, and a high-resolution crack boundary heatmap with the same size as the input image is output. The center point of the initial detection bounding box is weighted and corrected using the local peak coordinates of the heatmap. The weight coefficient is positively correlated with the peak response intensity, and finally a high-precision initial detection bounding box is obtained.

[0126] Finally, step S5 is executed to construct a dual graph convolutional inference module to correct the crack path. First, the graph structure is defined. , where the set of nodes For all the initial detection bounding boxes output in step S4, construct a spatial layer. The Delaunay triangulation algorithm is used to mesh and connect the geometric center points of all bounding boxes, generating spatial adjacent edges. The cosine of the angle between the major axes of the two bounding boxes connected by the edge is calculated as the spatial edge attribute, with a value range of [-1, 1]. An appearance layer is then constructed. Extract a 512-dimensional deep feature vector from each bounding box, calculate the Mahalanobis distance between the feature vectors, and select... The appearance adjacency edges are constructed using the nearest neighbor nodes. An edge-conditional generation network is introduced, which is a 3-layer perceptron with ReLU activation function in the hidden layers. The 512×512-dimensional convolutional kernel weights are dynamically generated based on the spatial edge attributes and appearance edge attributes.

[0127] In spatial layer and appearance layer Parallel execution of edge condition graph convolution, the first Layer node features The calculation formula is ,in For nodes The set of neighboring nodes, For nodes and Edge properties between The dynamic weight matrix generated by the edge condition generation network. The bias term is used. The output features of the two layers are fused using bilinear pooling, maintaining a feature dimension of 512 after fusion. A Markov random field model is constructed, and the fused features are used as the observation field. The connection states between nodes are defined as the label field, with labels taking values ​​of 0 or 1, representing non-connection and connection, respectively. The energy function of the Markov random field is iteratively minimized using the confidence propagation algorithm, with 12 iterations, to infer the crack cluster label to which each node belongs.

[0128] When constructing graph node features, a Riemannian manifold metric step is introduced: the 512×512 covariance matrix of the image region features within each bounding box is calculated. The covariance matrix is ​​transformed using a log-Euclidean mapping. Mapped to the Riemannian manifold space, and then decomposed by eigenvalues. Decomposed into , It is an orthogonal matrix. Given an eigenvalue diagonal matrix, the log-Euclidean metric is used to map points on the Riemannian manifold to the tangent space at the identity matrix. The calculation formula is as follows: , To obtain the diagonal matrix by taking the natural logarithm of each eigenvalue, the matrix in the tangent space... Vectorization yields a 512×512 dimensional vector, which serves as the initial input features for the graph nodes. .

[0129] Based on the cluster labels inferred from Markov random fields, bounding box nodes belonging to the same cluster are aggregated. The aggregated node set is then interpolated using a B-spline curve fitting algorithm. The center coordinates of the aggregated nodes are sorted according to the detection order and defined as a control point set. Define node vectors ,in cubic B-spline, the node vectors satisfy , The intermediate nodes are allocated according to the principle of equal interval; the cubic B-spline basis functions are calculated using the Cox-de Bohr recursive formula. Calculate the coordinates of the B-spline curve based on the control point set and basis functions. ; Calculate the curvature of each point on the fitted curve Set curvature threshold (Calibrated by minimizing validation set error), values ​​exceeding curvature mutation limits are removed. The abnormal connection points are identified, and the smoothed crack path coordinate sequence is output.

[0130] This embodiment also provides a ground-penetrating radar crack identification system based on frequency domain enhanced YOLOv11. The system applies the above-mentioned identification method and includes a data preprocessing module, a PFAE-YOLOv11 feature extraction module, a dual graph convolution inference module, and a result output module.

[0131] The input of the data preprocessing module is connected to the ground-penetrating radar equipment to receive raw radar data and execute the aforementioned variational mode decomposition algorithm to reconstruct the denoised image, with processing latency controlled within 50ms. The PFAE-YOLOv11 feature extraction module is connected to the data preprocessing module and integrates an FPGA hardware acceleration unit. This acceleration unit is equipped with an intellectual property core for performing two-dimensional discrete fractional Fourier transforms, including a memory, a 16×16 pulsating array processor, and a coordinate rotation digital computation method operation unit. The memory pre-stores different orders. The corresponding fractional transformation kernel matrix The lookup table is for the transformation order. (Step size 0.1) Pre-compute the kernel matrix, stored in 32-bit floating-point format, addressed by order index, supporting reading the complete kernel matrix in a single clock cycle. The systolic array processor uses row-first data flow, and the feature matrix... Divided into 16×16 blocks, and related to the kernel matrix. Parallel matrix multiplication is performed with a computational latency controlled within 100ns. The coordinate rotation digital calculation method's computational unit is used to calculate the sine and cosine values ​​of the rotation angle in real time, with a calculation accuracy of [missing information]. The computational latency is no more than 10ns, enabling parallel acceleration of the two-dimensional discrete fractional Fourier transform and rapid output of high-precision initial detection bounding boxes. The dual graph convolutional inference module is connected to the PFAE-YOLOv11 feature extraction module to construct a graph structure based on Delaunay triangulation and K-nearest neighbors, and uses edge condition generation network to perform graph inference and output the corrected path. The result output module is connected to the dual graph convolutional inference module to map the crack path back to the original radar image coordinate system and perform visualization. It supports real-time calculation of crack length and width parameters, making it convenient for staff to intuitively obtain crack information.

[0132] Through the above implementation methods, this method and system can effectively enhance the crack features in ground penetrating radar images, suppress background clutter interference, and improve the accuracy and path continuity of crack identification. According to the test, the crack identification accuracy can reach 95.2%, and the average error of path continuity correction is less than 2 pixels, which meets the needs of practical engineering applications.

[0133] Example 4 Further explanation in conjunction with Example 1, such as Figure 1-2 As shown, in actual deployment, the first step is to build a suitable hardware and software environment. On the software side, Python 3.9 is chosen as the development language, and PyTorch 2.1, which supports custom modules and hardware acceleration interfaces, is used as the deep learning framework. This is accompanied by OpenCV 4.8 for image reading, writing, and preprocessing; NumPy 1.26 for matrix operations; SciPy 1.11 for Fourier transform and interpolation tools; and PyTorchGeometric 2.3 for graph convolution operations. The FPGA development tool chosen is Xilinx Vivado 2023.1 for hardware acceleration unit IP core design and logic synthesis. On the hardware side, a server equipped with an NVIDIA RTX 4090 graphics card is configured for model inference acceleration; a Xilinx Zynq UltraScale+ FPGA chip with integrated PFAE module hardware acceleration unit is used; and a ground-penetrating radar data acquisition device and display terminal support real-time B-scan image output are also included.

[0134] During the deployment preparation phase, the trained PFAE-YOLOv11 model is exported to ONNX format via PyTorch's torch.onnx.export interface. TensorRT 8.6 is used for inference optimization to generate an acceleration engine adapted to the GPU. Core operators such as kernel matrix calculation and parallel filtering for two-dimensional discrete fractional Fourier transform are designed as proprietary cores using Vivado, burned into the FPGA chip, and adapted to the PCIe interface of the server. 32-bit floating-point format fractional transform kernel matrix lookup tables corresponding to different orders are pre-stored. At the same time, the variational mode decomposition algorithm required for preprocessing, the Delaunay triangulation of the graph convolution inference module, and the Markov random field confidence propagation logic are encapsulated into Python calling interfaces to ensure data flow compatibility between modules.

[0135] In practical use, the first step is to start the ground-penetrating radar equipment to collect road detection data. The raw B-scan image is transmitted to the server in real time via the equipment's built-in data transmission interface. The server calls the OpenCV `imread` function to read the image data, converts the image format to RGB three-channel, and normalizes the pixel values ​​to the [0,1] range. The second step is to execute the preprocessing flow, calling the custom variational mode decomposition module according to parameters. , The image modalities are decomposed, and after 50 iterations, noisy modalities with a correlation coefficient lower than 0.3 are removed, and the denoised image is reconstructed. The third step is to start the PFAE-YOLOv11 feature extraction module. First, the TensorRT-optimized model engine is loaded through the GPU. After the denoised image is input, the backbone network of the model and the embedded pyramid frequency attention extraction module work together. Fractional Fourier transform, parallel filtering and other operations are performed by FPGA hardware acceleration units, and the operation latency is controlled within 100ns. The initial detection bounding box coordinates of the crack are output.

[0136] The fourth step refines the initial bounding box. The sub-pixel convolution module extracts the low-resolution feature map output by the detection head. A 16-channel convolutional layer expands the feature dimension, and a periodic shuffling operation upsamples the image to its original size, generating a crack boundary heatmap. SciPy's `signal.find_peaks` function detects local peaks in the heatmap, and the bounding box center point coordinates are corrected by weighting the peak response intensity, resulting in a high-precision initial detection result. The fifth step starts the dual graph convolution inference module, calling the PyTorch Geometric interface to construct the graph structure. Using the corrected bounding box as nodes, the Delaunay triangulation of the spatial layer is performed using SciPy's `spatial.Delaunay` function. The cosine of the major axis angle of the bounding box is calculated as the spatial edge attribute. 512-dimensional deep features within the bounding box are extracted, and Mahalanobis distance is calculated. Five nearest neighbor nodes are selected to construct the appearance layer. An edge conditional generation network composed of three ReLU activation perceptrons dynamically generates convolutional kernel weights, and graph convolution operations of the spatial layer and appearance layer are performed in parallel, outputting the fused node features.

[0137] The sixth step involves inferring crack cluster labels. A Markov random field model is constructed, using fused features as the observation field and node connection states as the label field. A custom confidence propagation algorithm is called to iterate 12 times to minimize the energy function, obtaining the crack cluster affiliation label for each node. Simultaneously, a log-Euclidean mapping is performed on the feature covariance matrix of each bounding box, and the vectorized feature is used as the initial feature for graph node inference. The seventh step involves crack path fitting. Bounding box nodes are aggregated according to cluster labels, and the center coordinates are sorted into a control point set according to the detection order. The SciPy interpolate.BSpline function is called to construct a cubic B-spline curve, with node vectors distributed at equal intervals, and the curvature of each point on the curve is calculated. Remove outliers with curvature abrupt changes exceeding 0.8 and output a smoothed crack path coordinate sequence.

[0138] Finally, the results output module maps the crack path coordinates back to the original radar image coordinate system. It draws the crack path on the original image with a solid red line using OpenCV's polylines function, calls a custom length and width calculation function based on the coordinate distance formula to calculate the crack parameters in real time, and synchronously transmits the labeled image and parameter data to the display terminal to complete the visualization and result storage. It supports exporting crack coordinate and size data in CSV format. The end-to-end latency of the entire deployment process from data acquisition to result output is controlled within 200ms, which meets the requirements of real-time detection.

[0139] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for crack identification in ground-penetrating radar images based on frequency-domain enhanced YOLOv11, characterized by: The method includes: S1. Construct a ground-penetrating radar B-scan image dataset containing road cracks, and divide it into a training set and a validation set; S2. Construct the PFAE-YOLOv11 feature extraction model, which embeds a pyramid frequency attention extraction module into the YOLOv11 backbone network. S3. Train the PFAE-YOLOv11 feature extraction model using the training and validation sets, and optimize the network parameters; S4. Input the ground-penetrating radar image to be identified into the trained model and output the initial detection bounding box of the crack; S5. Construct a dual graph convolutional inference module. Use the initial detection bounding boxes output in step S4 as graph nodes, and use the graph convolutional network to infer the topological relationship of the cracks, and output the corrected continuous crack path. Step S5, the steps for constructing the dual graph convolutional inference module include: Define graph structure , where the set of nodes For all the initial detection bounding boxes output in step S4; Constructing spatial layers The Delaunay triangulation algorithm is used to mesh and connect the geometric center points of all bounding boxes to generate spatial adjacent edges, and the cosine of the angle between the major axes of the two bounding boxes connected on the edge is calculated as the spatial edge attribute. Build appearance layer Extract the deep feature vector within each bounding box, calculate the Mahalanobis distance between the feature vectors, and select... The nearest neighbor nodes are used to construct the appearance adjacency edges; An edge condition generation network is introduced, and a multilayer perceptron is used to dynamically generate convolutional kernel weights based on spatial edge attributes and appearance edge attributes. The dual graph convolution inference module performs graph convolution operations and inference, including the following processes: In spatial layer and appearance layer Parallel execution of edge condition graph convolution, the first Layer node features The calculation formula is: ； in, For nodes The set of neighboring nodes, For nodes and Edge properties between The dynamic weight matrix generated by the edge condition generation network. For bias terms; The output features of the two layers are fused using bilinear pooling, and the feature dimension remains at 512 after fusion. Construct a Markov random field model, using the fused features as the observation field, and define the connection state between nodes as the label field; The energy function of the Markov random field is minimized iteratively using the confidence propagation algorithm, with the number of iterations set to 10-15, to infer the crack cluster label to which each node belongs; The steps for outputting the corrected continuous crack path include: Based on the cluster labels inferred from the Markov random field, the bounding box nodes belonging to the same cluster are aggregated. For the aggregated node set, an interpolation connection is performed using a B-spline curve fitting algorithm. The steps are as follows: Define the sequence of center coordinates of the aggregation node as the control point set. ; Define node vectors Calculate using the Cox-de Boer recurrence formula B-spline basis functions ; Calculate the coordinates of the B-spline curve based on the control point set and basis functions. : ； Calculate the curvature of each point on the fitted curve, remove abnormal connection points whose curvature abrupt changes exceed the set threshold, and output the smoothed crack path coordinate sequence.

2. The method for crack identification in ground-penetrating radar images based on frequency-domain enhanced YOLOv11 as described in claim 1, characterized in that: In step S2, the processing flow of the pyramid frequency attention extraction module includes: The number of channels in the input feature map is adjusted by using convolutional layers, and four parallel branches are used for processing, each branch containing dilated convolutions with different dilation rates. Perform a two-dimensional discrete fractional Fourier transform on the feature map of each branch and project it onto the fractional time-frequency domain; A set of filters is used to perform parallel filtering on the fractional domain features to decompose the frequency subbands. Inverse fractional Fourier transform and feature fusion are performed on each frequency sub-band. Attention weight vectors are generated through a weight generation network and then multiplied with the original feature map using weights.

3. The method for crack identification in ground-penetrating radar images based on frequency-domain enhanced YOLOv11 as described in claim 2, characterized in that: The weight generation network incorporates a soft thresholding denoising step based on statistical moment features, including: Before generating the attention weight vector, the global first-order origin moments of the input feature channels are calculated. and second-order central moments ; Constructing an adaptive threshold function ,in The hyperparameters are learned through backpropagation, with the learning rate consistent with the network backbone parameters, and are dynamically adjusted during iteration based on the response accuracy of the crack features on the validation set. A soft thresholding operator is constructed using the sign function sgn and the maximum value function for eigenvalues. Perform nonlinear transformation: ； This nonlinear transformation sets background noise features below the adaptive threshold to zero, while preserving crack features with high response.

4. The method for crack identification in ground-penetrating radar images based on frequency-domain enhanced YOLOv11 as described in claim 2, characterized in that: The steps of a two-dimensional discrete fractional Fourier transform include: Set the transformation order and , respectively corresponding shaft and Rotation angle of the shaft and ; Constructing the Discrete Fourier Transform Matrix For the matrix Perform eigenvalue decomposition to obtain the eigenvector matrix. and eigenvalue diagonal matrix ; For eigenvalue diagonal matrices Each element in Exponentiation yields a fractional eigenvalue matrix. Calculate the fractional transformation kernel matrix ; Using the constructed kernel matrix and For the input feature map Perform a two-dimensional separable transformation, the transformation formula is as follows: ; During the transformation process, a Pey sampling-type discretization algorithm is introduced to eliminate the ambiguity caused by the multiplicity of eigenvalues ​​during discretization by orthogonalizing the eigenvectors.

5. The method for crack identification in ground-penetrating radar images based on frequency-domain enhanced YOLOv11 as described in claim 4, characterized in that: The parallel filtering process includes: Calculate the fractional domain features Wigner distribution matrix To obtain the energy density of the features in the time-frequency plane; right Perform a Radon transform to project the energy distribution of the time-frequency plane onto the parameter space, and detect the energy ridge distribution of the feature map in the fractional-order domain; Calculate the energy integral value along the ridge as the energy concentration degree. And set an energy threshold. ; Constructing an adaptive fractional domain mask Regarding location If its energy value is greater than ,but ,otherwise ; mask Features of fractional domain Perform the Adama product operation to filter out low-energy background clutter interference.

6. The method for crack identification in ground-penetrating radar images based on frequency-domain enhanced YOLOv11 as described in claim 2, characterized in that: The process by which a weight generation network generates attention weight vectors includes: The input features are mapped to three independent fractional-order vector spaces: query vector, ... Key vector Sum value vector ; Introducing a relative position encoding matrix , The elements are generated by calculating the Euclidean distance between vectors, and the dimension is... Matrix consistency, calculation and Scaling the dot product generates the attention score matrix: ； in For vector dimensions; Decompose the attention score matrix into an magnitude matrix. and phase matrix ; The amplitude matrix is ​​nonlinearly activated using the hyperbolic tangent function tanh to limit the amplitude range. Using Euler's formula The activated amplitude and phase are recombined to generate a complex domain attention weight vector.

7. The method for crack identification in ground-penetrating radar images based on frequency-domain enhanced YOLOv11 as described in claim 6, characterized in that: In step S5, a Riemannian manifold metric step is introduced when constructing graph node features: Calculate the covariance matrix of the image region features within each bounding box. ; Mapping the covariance matrix P to the Riemannian manifold space involves the following steps: using a log-Euclidean mapping, P is decomposed into eigenvalues. Where U is an orthogonal matrix, It is an eigenvalue diagonal matrix; Using the log-Euclidean metric, points on a Riemannian manifold are mapped to the tangent space at the identity matrix. The calculation formula is as follows: ,in This is a diagonal matrix obtained by taking the natural logarithm of each eigenvalue; The matrix in the tangent space Vectorization yields a 512×512 dimensional vector, which serves as the initial input features for the graph nodes. .

8. The method for crack identification in ground-penetrating radar images based on frequency-domain enhanced YOLOv11 as described in claim 1, characterized in that: In step S3, an optimization strategy combining gradient-based neural architecture search and knowledge distillation is introduced during the model training phase: Construct a supernet with 12 layers, which includes dilated convolutions with different dilation rates and fractional-order transformations of different orders. During training, a YOLOv11 model using ResNet101 as the backbone is introduced as the teacher model. Define the distillation loss function and calculate the Kolb-Leibler divergence of the intermediate layer feature maps of the PFAE-YOLOv11 student model and teacher model. A two-layer optimization strategy is adopted: the inner layer optimizes the network weight parameters, and the outer layer optimizes the architecture parameters through validation set loss. The optimizer uses Adam with a learning rate of 0.0001, which allows the student model to approximate the feature representation ability of the teacher model while maintaining its lightweight nature.

9. The method for crack identification in ground-penetrating radar images based on frequency-domain enhanced YOLOv11 as described in claim 1, characterized in that: In step S3, the loss function is a combination of regression loss based on Wasselstein distance and classification loss based on focus loss: The formula for calculating the bounding box regression loss is: in, It is a constant. For prediction boxes With real frame The Wasserstein distance under the Gaussian distribution assumption is calculated as follows: In the formula, These are the center coordinate vectors of the predicted bounding box and the ground truth bounding box, respectively. These are the covariance matrices of the predicted bounding box and the ground truth bounding box, respectively.

10. The method for crack identification in ground-penetrating radar images based on frequency-domain enhanced YOLOv11 according to claim 1, characterized in that: In step S1, the preprocessing of the ground-penetrating radar image employs a variational mode decomposition algorithm. The steps are as follows: Set the number of modal decompositions and secondary penalty factor ; Construct a variational constraint problem and find eigenmode functions and its center frequency This minimizes the sum of the estimated bandwidths for each mode; Introducing Lagrange multipliers Transform the constrained variational problem into an unconstrained problem; Iterative update using alternating direction multiplier method , and Continue until the convergence condition is met; Calculate the cross-correlation coefficient between the intrinsic mode function components obtained from each decomposition and the original signal, remove noise modes with correlation coefficients below a set threshold, and reconstruct the remaining modes into a denoised image.

11. The method for crack identification in ground-penetrating radar images based on frequency-domain enhanced YOLOv11 as described in claim 1, characterized in that: In step S4, the output initial detection bounding box information is refined through a sub-pixel convolutional layer: Extract the low-resolution feature map output by the detection head; pass Feature augmentation is performed on convolutional layers with multiple channels, where This is the upsampling factor; Perform a periodic shuffle operation to rearrange the channel dimension of the feature map to the spatial dimension and output a high-resolution crack boundary heat map; The center point of the initial detection bounding box is corrected by weighting the local peak coordinates of the heatmap.

12. The method for crack identification in ground-penetrating radar images based on frequency-domain enhanced YOLOv11 as described in claim 1, characterized in that: In step S2, after embedding the pyramid frequency attention extraction module, a deformable convolution module is also connected in series. The steps are as follows: An offset-generating convolutional layer is added as a bypass to the regular convolutional layer to learn the geometric deformation offset of crack features. and modulation scalar ; Based on the learned offset The sampling grid of the input feature map is irregularly deformed; The pixel value at the offset position is calculated using the bilinear interpolation algorithm; By modulating scalar The sampling points are weighted and summed to output a feature map that adapts to the geometry of the irregular crack.

13. A ground-penetrating radar crack identification system based on frequency-domain enhanced YOLOv11, characterized in that: The system, applicable to the method described in any one of claims 1-12, comprises: The data preprocessing module, whose input is connected to the ground-penetrating radar equipment, is used to receive raw radar data and perform variational mode decomposition to reconstruct a denoised image. The PFAE-YOLOv11 feature extraction module is connected to the data preprocessing module and integrates a field-programmable gate array (FPGA) hardware acceleration unit for outputting the initial detection bounding box. The FPGA hardware acceleration unit is equipped with an intellectual property core that performs two-dimensional discrete fractional Fourier transform. The dual graph convolutional inference module, connected to the PFAE-YOLOv11 feature extraction module, is used to construct a graph structure based on Delaunay triangulation and K-nearest neighbors, and uses edge condition generation network to perform graph inference and output the corrected path. The results output module, connected to the dual graph convolution inference module, is used to map the crack path back to the original radar image coordinate system and visualize it.

14. A ground-penetrating radar crack identification system based on frequency-domain enhanced YOLOv11 according to claim 13, characterized in that: on-site... The programmable gate array hardware acceleration unit includes: Memory, used to pre-store different orders The corresponding fractional transformation kernel matrix The lookup table; A systolic array processor is used to perform matrix multiplication operations between the eigenma matrix and the kernel matrix in parallel. ; The coordinate rotation digital calculation method operation unit is used to calculate the sine and cosine values ​​of the rotation angle required for fractional-order transformation in real time at the hardware level.

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