A Depth-Scalable Inversion Method and System for 3D Ground Penetrating Radar Data

Abstract

This invention provides a depth-scalable inversion method and system for 3D ground-penetrating radar (GPR) data. The method includes: spatially mapping the 3D GPR volume data of the area to be inverted point by point according to spatial coordinate points based on a 3D reservoir computing network to obtain waveform dynamic features characterizing the electromagnetic response variation law of the underground medium; extracting global spatial features of the 3D GPR volume data based on a convolutional neural network; predicting the target category of the 3D GPR volume data based on the waveform dynamic features and global spatial features; determining the inversion network depth based on the target category; constructing an encoder-decoder inversion network with corresponding layers based on the inversion network depth; using the encoder-decoder inversion network to extract multi-scale spatial features and texture structure features of the 3D GPR volume data; and predicting the 3D distribution of the underground dielectric constant corresponding to the 3D GPR volume data based on the multi-scale spatial features and texture structure features.

Description

Technical Field

[0001] This invention relates to the fields of ground-penetrating radar data processing and geophysical remote sensing technology, and in particular to a depth-scalable inversion method and system for three-dimensional ground-penetrating radar data. Background Technology

[0002] Ground penetrating radar (GPR) is a non-destructive electromagnetic detection technology widely used in civil engineering, infrastructure inspection, geotechnical investigation, underground target identification, and environmental monitoring. With the increasing demand for detailed underground exploration, achieving high-precision inversion of the underground dielectric constant distribution based on 3D GPR data has become an important research direction in the fields of remote sensing and geophysics.

[0003] Existing deep learning-based methods for 3D ground-penetrating radar (GPR) data inversion mainly fall into two categories. The first category involves extracting single-channel 2D slices from the 3D GPR volume data, processing them slice by slice using a 2D inversion model, and finally stitching them together to obtain the 3D reconstruction result. While this method is relatively easy to implement, it often fails to accurately restore the continuity of underground structures in 3D space due to neglecting important correlation information between adjacent channels, easily leading to problems such as structural fragmentation and inconsistent boundaries. The second category directly performs a unified inversion on the entire 3D GPR volume data, typically using a fixed-depth 3D convolutional neural network to establish a nonlinear mapping relationship from GPR data to dielectric constant distribution. This method can preserve 3D spatial context information to some extent, but to ensure inversion accuracy in complex target scenarios, it usually requires constructing a deep network structure, resulting in significant computational costs and inference overhead, limiting its application in engineering scenarios with high timeliness requirements.

[0004] Furthermore, existing underground target classification methods typically focus on modeling single features. One type of method primarily focuses on spatial features such as geometric shape and boundary texture, while another type focuses on the dynamic waveform changes exhibited during electromagnetic wave propagation. However, spatial features and dynamic features reflect different attributes of underground targets, and the two are clearly complementary. Relying solely on a single feature for classification can easily lead to the inaccurate differentiation of targets with similar shapes but significantly different dielectric responses, thus affecting the subsequent inversion network's reasonable modeling of different targets.

[0005] In real-world underground scenarios, many areas constitute normal backgrounds without significant targets, requiring only shallow networks for effective inversion. However, for complex underground targets such as cracks, cavities, and pipelines, deeper feature extraction and structural reconstruction capabilities are needed. Existing deep networks fail to adaptively adjust based on target category and structural complexity, leading to redundant computations in ordinary background areas and potentially insufficient inversion accuracy in complex target areas. Therefore, there is an urgent need to propose a 3D ground-penetrating radar inversion method that can integrate multiple discriminative features and adaptively adjust the network depth according to the underground target category, thus balancing computational efficiency and inversion accuracy. Summary of the Invention

[0006] In view of the above problems, the present invention is proposed to provide a depth-scalable inversion method and system for three-dimensional ground-penetrating radar data that overcomes the above problems.

[0007] This invention provides a depth-scalable inversion method for three-dimensional ground-penetrating radar data, the method comprising:

[0008] Based on the pre-set three-dimensional reservoir computing network, the target three-dimensional ground-penetrating radar volume data to be inverted is spatially mapped point by point according to the spatial coordinate points to obtain the waveform dynamic characteristics that characterize the electromagnetic response variation law of the underground medium.

[0009] A pre-defined convolutional neural network is used to extract global spatial features from the target's three-dimensional ground-penetrating radar volume data;

[0010] Predict the target category to which the target's three-dimensional ground-penetrating radar data belongs based on the waveform dynamic characteristics and global spatial characteristics;

[0011] The inversion network depth is adaptively determined based on the target category;

[0012] Based on the depth of the inversion network, an encoder-decoder inversion network with corresponding layers is constructed. The encoder-decoder inversion network is used to extract multi-scale spatial features and texture structure features from the target 3D ground-penetrating radar volume data. Based on the multi-scale spatial features and texture structure features, the three-dimensional distribution of the underground dielectric constant corresponding to the target 3D ground-penetrating radar volume data is predicted.

[0013] Another aspect of the present invention provides a depth-scalable inversion system for three-dimensional ground-penetrating radar data, the system comprising:

[0014] The dynamic feature extraction module is used to perform spatial mapping on the target three-dimensional ground-penetrating radar data to be inverted according to the spatial coordinate points in sequence based on the preset three-dimensional reservoir computing network, so as to obtain the waveform dynamic features that characterize the electromagnetic response change law of the underground medium.

[0015] The spatial feature extraction module is used to extract global spatial features of the target's three-dimensional ground-penetrating radar volume data using a preset convolutional neural network;

[0016] The target category prediction module is used to predict the target category to which the three-dimensional ground-penetrating radar data belongs based on the waveform dynamic features and global spatial features.

[0017] The depth adaptive module is used to adaptively determine the depth of the inversion network based on the target category;

[0018] The inversion prediction module is used to construct an encoder-decoder inversion network with corresponding layers based on the depth of the inversion network. The encoder-decoder inversion network is used to extract multi-scale spatial features and texture structure features from the target 3D ground-penetrating radar volume data, and predict the 3D distribution of the underground dielectric constant corresponding to the target 3D ground-penetrating radar volume data based on the multi-scale spatial features and texture structure features.

[0019] The depth-scalable inversion method and system for three-dimensional ground-penetrating radar data provided by this invention achieves accurate identification of underground target categories by jointly extracting waveform dynamic features and local spatial features of three-dimensional ground-penetrating radar volume data; and uses the predicted category information to adaptively control the depth configuration of the inversion network, thereby improving the prediction accuracy and structural consistency of the three-dimensional distribution of underground dielectric constant while reducing computational complexity.

[0020] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0021] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. In the drawings:

[0022] Figure 1 This is a flowchart of a depth scalable inversion method for three-dimensional ground-penetrating radar data according to an embodiment of the present invention;

[0023] Figure 2 This is a structural block diagram of a depth-scalable inversion system for three-dimensional ground-penetrating radar data according to an embodiment of the present invention. Detailed Implementation

[0024] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0025] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art and should not be interpreted in an idealized or overly formal sense unless specifically defined.

[0026] To overcome the problems of redundant computation and insufficient ability to reconstruct complex targets caused by the uniform use of fixed-depth network structures in existing 3D ground-penetrating radar (GPR) inversion methods, and to address the issue of insufficient accuracy in identifying underground targets due to existing classification methods relying solely on single spatial or dynamic features, this invention proposes a depth-scalable inversion method for 3D GPR data. This method achieves accurate identification of underground target categories by jointly extracting waveform dynamic features and local spatial features from 3D GPR data; and it adaptively controls the depth configuration of the inversion network using predicted category information, thereby reducing computational complexity while improving the accuracy and structural consistency of the 3D reconstruction of underground dielectric constant distribution.

[0027] like Figure 1 As shown, the depth scalable inversion method for three-dimensional ground-penetrating radar data proposed in this invention includes the following steps:

[0028] S11. Based on the preset three-dimensional reservoir computing network, the target three-dimensional ground-penetrating radar volume data to be inverted is spatially mapped point by point according to the spatial coordinate points to obtain the waveform dynamic characteristics that characterize the electromagnetic response change law of the underground medium.

[0029] In this embodiment, before extracting the waveform dynamic features, preprocessing operations are also performed on the target three-dimensional ground-penetrating radar volume data to be inverted, including data cropping, normalization, noise suppression, and the division of training set, validation set, and test set.

[0030] S12. Use a pre-set convolutional neural network to extract the global spatial features of the target's three-dimensional ground-penetrating radar volume data.

[0031] S13. Predict the target category of the target's three-dimensional ground-penetrating radar data based on the waveform dynamic characteristics and global spatial characteristics.

[0032] S14. Adaptively determine the inversion network depth based on the target category.

[0033] S15. Construct an encoder-decoder inversion network with corresponding layers based on the inversion network depth. Use the encoder-decoder inversion network to extract multi-scale spatial features and texture structure features from the target 3D ground-penetrating radar volume data. Based on the multi-scale spatial features and texture structure features, predict the 3D distribution of the underground dielectric constant corresponding to the target 3D ground-penetrating radar volume data.

[0034] The depth-scalable inversion method for three-dimensional ground-penetrating radar data provided in this invention achieves accurate identification of underground target categories by jointly extracting waveform dynamic features and local spatial features of three-dimensional ground-penetrating radar volume data; and uses the predicted category information to adaptively control the depth configuration of the inversion network, thereby reducing computational complexity while improving the prediction accuracy and structural consistency of the three-dimensional distribution of underground dielectric constant.

[0035] In this embodiment of the invention, step S11, based on a preset three-dimensional reservoir computing network, performs spatial mapping point-by-point on the target three-dimensional ground-penetrating radar volume data to be inverted according to the spatial coordinate points. Specifically, this includes the following steps (not shown in the accompanying drawings):

[0036] S111. A preset three-dimensional reservoir computing network is used to iterate the target three-dimensional ground-penetrating radar volume data point by point according to the spatial coordinate points to calculate the hidden state of each coordinate point. The hidden state is obtained by coupling the historical hidden state of the previous coordinate point in three dimensions and the voxel value of the current coordinate point.

[0037] S112. The output weight matrix of the three-dimensional reservoir computing network is estimated using a training paradigm based on the prediction of the next data point, and the output weight matrix is ​​used as the waveform dynamic feature vector of the target three-dimensional ground-penetrating radar volume data.

[0038] In this embodiment, the preprocessed target 3D ground-penetrating radar volume data is input into a 3D reservoir computing network. It is processed point-by-point according to spatial coordinates. Utilizing the hidden states of the previous data point in three spatial directions, the current input data, and a preset weight matrix, the hidden state of the current data point is iteratively updated to establish multi-directional dependencies in 3D space, extracting waveform dynamic features reflecting the changing electromagnetic response of the underground medium. Subsequently, a training paradigm based on prediction of the next data point is adopted. The output weight matrix is ​​obtained by solving a ridge regression problem, and this output weight matrix is ​​used as the dynamic feature vector of the input sample.

[0039] In this embodiment of the invention, step S12, which involves using a preset convolutional neural network to extract the global spatial features of the target's three-dimensional ground-penetrating radar volume data, specifically includes the following steps (not shown in the accompanying drawings):

[0040] S121. Divide the target's three-dimensional ground-penetrating radar volume data into several non-overlapping three-dimensional data blocks;

[0041] S122. Input each three-dimensional data block into a preset three-dimensional convolutional neural network to extract the local spatial structure features of each three-dimensional data block.

[0042] S123. The local spatial structure features corresponding to each three-dimensional data block are spliced ​​together along the feature dimension to form a global spatial feature that represents the global spatial structure information.

[0043] In this embodiment, the target 3D ground-penetrating radar volume data is first divided into multiple non-overlapping 3D data blocks, each with a selectable size of 16×16×16. A convolutional neural network containing multiple 3D convolutional layers is then used to process each non-overlapping data block, with a selectable kernel size of 3×3×3 and a stride of 2. Local spatial structure features are extracted layer by layer using activation functions. Subsequently, the local spatial structure feature vectors corresponding to each 3D data block are concatenated along the feature dimension to obtain a spatial feature vector representing the global spatial structure information.

[0044] In this embodiment of the invention, step S13, which involves predicting the target category of the target's three-dimensional ground-penetrating radar volume data based on the waveform dynamic features and global spatial features, specifically includes the following steps (not shown in the accompanying drawings):

[0045] S131. A cross-attention mechanism is used to fuse and enhance waveform dynamic features and global spatial features to obtain fused features;

[0046] S132. Input the fused features into a preset multilayer perceptron classifier to output the target category probability distribution corresponding to the target's three-dimensional ground-penetrating radar volume data.

[0047] In this embodiment, the waveform dynamic feature vector extracted in step S11 and the spatial feature vector extracted in step S12 are input into a preset cross-attention fusion module. The cross-attention mechanism enables information interaction and enhancement between the two feature vectors, resulting in a fused feature representation. The fused feature is then input into a multilayer perceptron classifier to output the probability distribution of underground target categories, thus obtaining the target category information of the current target's 3D ground-penetrating radar volume data. The target category may include categories such as normal background, cracks, cavities, and pipelines.

[0048] Furthermore, in this embodiment, step S14, adaptively determining the inversion network depth based on the target category, specifically includes:

[0049] The target category probability distribution is input into a preset network depth controller, which is a multilayer perceptron. To output the candidate depth set The probability distribution on:

[0050]

[0051] in, This represents the probability of selecting each candidate depth from the candidate depth set. The probability distribution of the target category;

[0052] According to the probability distribution Alternatively, the candidate depth with the highest probability can be selected as the inversion network depth, or a random sampling strategy based on probability distribution can be used to select the inversion network depth.

[0053] This invention inputs the target category information obtained in step S13 into a pre-trained network depth controller, which adaptively selects the depth configuration of the subsequent inversion network based on the structural complexity corresponding to different categories. A shallower network structure is used for normal background areas, while a deeper network structure is used for samples with complex underground targets, in order to reduce invalid computation and enhance the representation ability for complex structures.

[0054] In this embodiment of the invention, step S15, which involves constructing an encoder-decoder inversion network with the corresponding number of layers based on the inversion network depth, specifically includes: determining the number of layers of the encoder and decoder participating in the feature extraction task in the preset inversion network based on the inversion network depth, thus forming an encoder-decoder inversion network. In this invention, the inversion network is implemented using an encoder-decoder structure, and its depth is determined by the target category to which the target 3D ground-penetrating radar volume data belongs. During the encoding stage, spatial features under different receptive fields are extracted through multi-scale convolution to simultaneously capture fine-grained texture information and large-scale contextual information; during the decoding stage, spatial resolution and structural details are gradually restored through layer-by-layer upsampling and skip connections, ultimately outputting a 3D distribution of the underground dielectric constant corresponding to the input 3D ground-penetrating radar volume data.

[0055] Specifically, the encoder network in the encoder-decoder inversion network is the first... Layer features are represented as:

[0056]

[0057] in, This represents a combination of batch normalization and activation operations. This indicates a feature concatenation operation. This indicates a pooling operation. , , These represent 3D convolution operations of 3×3×3, 5×5×5, and 7×7×7, respectively, used to process features from the previous layer. Perform multi-scale feature extraction;

[0058] The first decoder network in the encoder-decoder inversion network Layer decoding features are represented as follows:

[0059]

[0060] in, This indicates a trilinear upsampling operation. The feature concatenation operation represents a skip connection. Represents a 3D convolution operation;

[0061] The output features of the output convolutional layer in the encoder-decoder inversion network are represented as follows:

[0062]

[0063] in, This represents a 3D convolution operation. The predicted three-dimensional distribution of the underground dielectric constant corresponding to the three-dimensional ground-penetrating radar volume data of the target.

[0064] Furthermore, in the encoder-decoder inversion network, a residual bridging block is set between the encoder and decoder to refine high-level latent features and stabilize feature propagation. The residual output is represented as:

[0065]

[0066] in, This represents the bottleneck residual mapping consisting of a 1×1×1 dimensionality-reduced convolution, a 3×3×3 convolution, and a 1×1×1 recovery convolution, where B is the input of the residual bridging block.

[0067] The depth-scalable inversion method for 3D ground-penetrating radar data proposed in this invention also includes a step of pre-training a model for the entire inversion framework, specifically including:

[0068] A training set is constructed by simulating 3D ground-penetrating radar (GPR) scenarios for different types of underground targets to obtain 3D GPR volume data and their corresponding true dielectric constant distribution maps. These two data are then paired to form training samples, forming the training set. In this embodiment, the training samples are obtained by simulating scenarios corresponding to different underground target categories using gprMax simulation software. Furthermore, during the training phase, after collecting 3D GPR volume data for different underground target categories, necessary preprocessing operations are required according to the actual task requirements. These operations include data cropping, normalization, noise suppression, and the division of the training, validation, and test sets to ensure stable training and inference of the subsequent network model.

[0069] The entire inversion framework is trained based on training samples. The training process includes: spatially mapping each training sample point by point according to spatial coordinates using a pre-set three-dimensional reservoir computing network to obtain waveform dynamic feature samples that characterize the electromagnetic response variation law of the underground medium of each training sample; extracting global spatial feature samples of each training sample using a pre-set convolutional neural network; predicting the target category of the current training sample based on the waveform dynamic feature samples and global spatial feature samples of each training sample; adaptively determining the depth of the second inversion network based on the target category of the current training sample; constructing an encoder-decoder inversion network with corresponding layers based on the depth of the second inversion network; using the obtained encoder-decoder inversion network to extract multi-scale spatial features and texture structure features of the training samples; and outputting the three-dimensional distribution of the underground dielectric constant corresponding to the training samples based on the multi-scale spatial features and texture structure features.

[0070] During the training phase, a composite objective function is constructed that includes reconstruction loss and network depth regularization loss. Based on the composite objective function, the joint optimization training of the entire inversion framework is achieved.

[0071] The model training process of the entire inversion framework of this invention includes underground target classification, category-driven depth configuration, depth scalable inversion, and joint optimization training. By constructing an integrated framework consisting of a target classification module and a depth scalable inversion module, efficient and high-precision three-dimensional inversion of complex underground targets can be achieved.

[0072] Furthermore, during the training phase, a composite objective function is constructed that includes reconstruction loss and network depth regularization loss, specifically including:

[0073] A reconstruction loss is constructed to measure the error between the predicted 3D distribution of underground dielectric constants of the training samples and the true dielectric constant distribution. ;

[0074] Construct a network depth regularization loss to measure the model complexity corresponding to the selected network depth. The network depth regularization loss is expressed as:

[0075]

[0076] in, For the first Layer parameter quantity, This represents the maximum number of selectable network parameters. For dynamic weighting coefficients, The currently selected network depth;

[0077] A dynamic weight optimization strategy is introduced to adaptively adjust the dynamic weight coefficients of the network depth regularization loss based on the relative rate of change of the reconstruction loss and the network depth regularization loss during continuous training iterations.

[0078] The following example of 3D ground-penetrating radar (GPR) underground target inversion further illustrates the implementation of the present invention, but the scope of protection of the present invention is not limited thereto. In this embodiment, the input is 3D GPR volume data. The output is the three-dimensional distribution of the corresponding underground dielectric constant. The entire process includes steps such as data preprocessing, dynamic feature extraction, spatial feature extraction, joint classification, category-driven deep configuration, deep scalable inversion, and loss optimization.

[0079] Step 1: Acquisition and preprocessing of 3D ground-penetrating radar data.

[0080] Acquire 3D ground-penetrating radar volume data of the area to be inverted Then, normalization, pruning, and dataset partitioning are performed. Let the value of any voxel in the original volume data be... Then, the min-max normalization method can be used for normalization:

[0081]

[0082] in, and These represent the minimum and maximum values ​​in the current sample data, respectively. This represents the normalized voxel values. Normalization helps to accelerate model convergence and improve training stability.

[0083] Step 2: Extraction of dynamic waveform features.

[0084] The preprocessed 3D ground-penetrating radar volume data is input into the 3D reservoir computing network, and then sorted by spatial location. Update the hidden state sequentially. Let the input at the current position be... Hidden state is Then the hidden state update formula can be written as:

[0085]

[0086] in, For the input weight matrix, , , These are the state transition weight matrices for the three spatial directions, respectively. For bias terms, The activation function is hyperbolic tangent. Through the above update method, a multi-directional dependency relationship of the volumetric data in three spatial directions can be established, thereby extracting waveform dynamic features reflecting the electromagnetic propagation variation law of the underground medium.

[0087] Furthermore, the output weight matrix is ​​estimated using a training paradigm based on the prediction of the next data point. Assume that the matrix is ​​obtained by stacking all hidden states column-wise. The monitoring target is the data matrix at the next position. Then the output weight matrix It can be obtained through ridge regression:

[0088]

[0089] in, The regularization coefficient is . It is an identity matrix. Ultimately, it will... The dynamic feature vector representation of the current sample is denoted as:

[0090]

[0091] Step 3: Global spatial feature extraction.

[0092] Input data Divide into several non-overlapping three-dimensional data blocks, denoted as the first... One data block is The preferred block size is Each data block is input into a three-dimensional convolutional neural network for processing. The output of a convolutional layer can be represented as:

[0093]

[0094] Specifically, when calculating the output of the first convolutional layer, The value is 1. , and They represent the first Layer convolution kernel parameters and bias terms, The activation function is preferably the ReLU function.

[0095]

[0096] After multiple convolutions, the local spatial feature vector of each data block is obtained. Then, the features are concatenated along the feature dimension to form a global spatial feature vector representation:

[0097]

[0098] in, This represents the total number of non-overlapping data blocks.

[0099] Step 4: Joint classification and category prediction.

[0100] Dynamic feature vectors and global space feature vectors The input is fused using a cross-attention module. First, query, key, and value vectors are generated through a learnable mapping matrix:

[0101]

[0102] in, , , This is a learnable parameter matrix. Further, scaled dot product attention is used to compute the fused representation:

[0103]

[0104]

[0105] in, Represents the dimension of the key vector. Represents the attention weight matrix. This represents the fused features. The fused features are then input into the classification head, which outputs the target class probability distribution:

[0106]

[0107] in, express The probability distribution of each category and These represent the classification layer weights and bias terms, respectively. The final target category can be represented as:

[0108]

[0109] in, The prediction category is indicated, preferably including normal background, cracks, cavities, and pipelines.

[0110] Step 5: Category-driven deep configuration.

[0111] The target category probability vector obtained in step four Input the network depth controller to output a candidate depth set. The probability distribution on the surface. Let the depth controller be a multilayer perceptron. Then we have:

[0112]

[0113] in, This represents the probability of selecting each candidate depth. The final network depth is then sampled or selected based on this probability distribution.

[0114]

[0115] Alternatively, a probability-distribution-based random sampling strategy can be used for depth selection during training. To address the issue of discrete depth not being differentiable, the REINFORCE reinforcement learning strategy can be used to optimize the depth controller, and its policy gradient can be written as:

[0116]

[0117] in, For depth controller parameters, For the reward signal corresponding to the depth configuration, the reward can be composed of inversion accuracy-related indicators.

[0118] Step 6: Depth-Scalable Inversion.

[0119] Based on the network depth determined in step five Construct the encoder-decoder inversion network for the corresponding number of layers. Encoding stage... Layer features can be represented as:

[0120]

[0121] in, This represents a combination of batch normalization and activation operations. .

[0122] A residual bridging block is set between the encoder and decoder to refine high-level features. Let the bridging input be... Then the residual output can be written as:

[0123]

[0124] in, Indicates by Dimensionality reduction convolution, Convolution and Recover the bottleneck residual mapping formed by convolution.

[0125] The decoding stage employs trilinear upsampling and skip connections to recover spatial resolution layer by layer. Layer decoding features can be represented as:

[0126]

[0127] in, This indicates a trilinear upsampling operation.

[0128] Finally, the predicted dielectric constant volume data is obtained through the output convolutional layer:

[0129]

[0130] Step 7: Loss function calculation and model optimization.

[0131] During the training phase, the predicted dielectric constant distribution is first calculated. Compared with the true dielectric constant distribution The reconstruction loss between the two. The mean absolute error loss is preferred.

[0132]

[0133] Where H, W, and D represent the height, width, and depth dimensions of the dielectric constant volume data, respectively.

[0134] Secondly, a network depth regularization loss is constructed to measure the model complexity corresponding to the selected depth. Let the... The number of layer parameters is The maximum number of selectable network parameters is Then the complexity regularization term can be expressed as:

[0135]

[0136] in, This is a dynamic weighting coefficient, and its initial value can be set to 1.0.

[0137] Furthermore, the relative rates of change of the two types of losses are dynamically adjusted based on consecutive training rounds. Let the first... The time-based reconstruction loss and the regularization loss are respectively and Then its relative rate of change can be expressed as:

[0138]

[0139]

[0140] in, To prevent the use of tiny constants with a denominator of zero, SoftMax is used to map both to adaptive weights.

[0141]

[0142] in, This is a smoothing factor. The dynamic coefficients are updated based on the above weights. :

[0143]

[0144] The final total loss function is:

[0145]

[0146] Then, backpropagation and parameter updates are performed based on this total loss until the model converges.

[0147] Step 8: Output the results.

[0148] During the inference phase, the 3D ground-penetrating radar volume data to be inverted is input into the trained model, which sequentially performs dynamic feature extraction, spatial feature extraction, cross-attention fusion classification, category-driven depth selection, and depth-scalable inversion, ultimately outputting the 3D distribution of the subsurface dielectric constant. The results can be further applied to tasks such as underground cavity identification, crack detection, buried pipeline detection, and engineering safety assessment.

[0149] The depth-scalable inversion method for three-dimensional ground-penetrating radar data provided in this invention has the following beneficial effects:

[0150] 1. This invention extracts the waveform dynamic features and local spatial features of three-dimensional ground-penetrating radar data simultaneously and performs deep fusion using a cross-attention mechanism, which can more comprehensively characterize the physical attributes and spatial morphology of underground targets and improve the accuracy of underground target category identification.

[0151] 2. This invention adaptively adjusts the depth of the inversion network according to the category of underground targets, so that a shallower network is used for ordinary background areas and a deeper network is used for complex target areas, thereby reducing redundant calculations in non-target areas and improving the overall inversion efficiency.

[0152] 3. This invention adopts a deep scalable encoder-decoder inversion architecture, which can perform category-specific modeling for underground targets with different structural complexities, thereby improving the accuracy, structural integrity and boundary continuity of the three-dimensional reconstruction of underground dielectric constant.

[0153] 4. This invention introduces residual bridging and multi-scale feature extraction mechanisms between the encoder and decoder, which enhances the network's ability to jointly model complex underground structural details and large-scale contextual information, thus improving the high fidelity of the inversion results.

[0154] 5. This invention constructs a joint optimization objective that includes reconstruction loss and complexity regularization loss, and adaptively balances inversion accuracy and network complexity through a dynamic weight optimization strategy. It can reduce computing power consumption while ensuring high-quality reconstruction, and has good engineering application value.

[0155] For the sake of simplicity, the method embodiments are described as a series of actions. However, those skilled in the art should understand that the embodiments of the present invention are not limited to the described order of actions, because according to the embodiments of the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions involved are not necessarily essential to the embodiments of the present invention.

[0156] This invention provides a depth-scalable inversion system for three-dimensional ground-penetrating radar data, the system including functional modules for implementing the depth-scalable inversion method for three-dimensional ground-penetrating radar data as described in any of the preceding claims. Figure 2 The schematic diagram illustrates the structure of a depth-scalable inversion system for three-dimensional ground-penetrating radar data provided in an embodiment of the present invention, with reference to... Figure 2 The system described in this embodiment of the invention includes:

[0157] The dynamic feature extraction module 201 is used to perform spatial mapping on the target three-dimensional ground-penetrating radar data to be inverted according to the spatial coordinate points in sequence based on the preset three-dimensional reservoir computing network, so as to obtain the waveform dynamic features that characterize the electromagnetic response change law of the underground medium.

[0158] The spatial feature extraction module 202 is used to extract the global spatial features of the target's three-dimensional ground-penetrating radar volume data using a preset convolutional neural network;

[0159] Target category prediction module 203 is used to predict the target category of the target's three-dimensional ground-penetrating radar data based on the waveform dynamic features and global spatial features;

[0160] Depth adaptation module 204 is used to adaptively determine the depth of the inversion network according to the target category;

[0161] The inversion prediction module 205 is used to construct an encoder-decoder inversion network with corresponding layers based on the depth of the inversion network. The encoder-decoder inversion network is used to extract multi-scale spatial features and texture structure features of the target three-dimensional ground-penetrating radar volume data, and predict the three-dimensional distribution of the underground dielectric constant corresponding to the target three-dimensional ground-penetrating radar volume data based on the multi-scale spatial features and texture structure features.

[0162] In this embodiment of the invention, the system further includes: a dataset construction module, a model training module, and an optimization module.

[0163] The dataset construction module is used to build a training set. It labels the 3D ground-penetrating radar volume data belonging to different underground target categories in the training set with the true dielectric constant distribution to obtain training samples.

[0164] The model training module is used to train the entire inversion framework model based on training samples. The training process includes: spatially mapping each training sample point by point according to the spatial coordinate points based on a preset three-dimensional reservoir computing network to obtain waveform dynamic feature samples that characterize the electromagnetic response variation law of the underground medium of each training sample; extracting global spatial feature samples of each training sample using a preset convolutional neural network; predicting the target category of the current training sample based on the waveform dynamic feature samples and global spatial feature samples of each training sample; adaptively determining the depth of the second inversion network based on the target category of the current training sample; constructing an encoder-decoder inversion network with corresponding layers based on the depth of the second inversion network; using the obtained encoder-decoder inversion network to extract multi-scale spatial features and texture structure features of the training samples; and outputting the three-dimensional distribution of the underground dielectric constant corresponding to the training samples based on the multi-scale spatial features and texture structure features.

[0165] The optimization module is used to construct a composite objective function that includes reconstruction loss and network depth regularization loss, and to achieve joint optimization training of the entire inversion framework based on the composite objective function.

[0166] Furthermore, the optimization module is specifically used to construct a reconstruction loss that measures the error between the predicted three-dimensional distribution of the underground dielectric constant of the training samples and the true dielectric constant distribution. Construct a network depth regularization loss to measure the model complexity corresponding to the selected network depth. The network depth regularization loss is expressed as:

[0167]

[0168] in, For the first Layer parameter quantity, This represents the maximum number of selectable network parameters. For dynamic weighting coefficients, The currently selected network depth;

[0169] A dynamic weight optimization strategy is introduced to adaptively adjust the dynamic weight coefficients of the network depth regularization loss based on the relative rate of change of the reconstruction loss and the network depth regularization loss during continuous training iterations. The joint optimization training of the entire framework is achieved through backpropagation and parameter updates.

[0170] As the system implementation is basically similar to the method implementation, the description is relatively simple, and relevant parts can be found in the description of the method implementation.

[0171] Furthermore, another embodiment of the present invention provides a computer program product on which a computer program is stored, and when the computer program is executed by a processor, it implements the steps described above in the embodiment of the depth scalable inversion method for three-dimensional ground penetrating radar data.

[0172] Furthermore, another embodiment of the present invention provides a computer device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps described above in the embodiment of the depth scalable inversion method for three-dimensional ground-penetrating radar data.

[0173] Furthermore, those skilled in the art will understand that although some embodiments herein include certain features included in other embodiments but not others, combinations of features from different embodiments are intended to be within the scope of the invention and form different embodiments. For example, any of the claimed embodiments can be used in any combination.

[0174] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A depth-scalable inversion method for three-dimensional ground-penetrating radar data, characterized in that, The method includes: Based on the pre-set three-dimensional reservoir computing network, the target three-dimensional ground-penetrating radar volume data to be inverted is spatially mapped point by point according to the spatial coordinate points to obtain the waveform dynamic characteristics that characterize the electromagnetic response variation law of the underground medium. A pre-defined convolutional neural network is used to extract global spatial features from the target's three-dimensional ground-penetrating radar volume data; Predict the target category to which the target's three-dimensional ground-penetrating radar data belongs based on the waveform dynamic characteristics and global spatial characteristics; The inversion network depth is adaptively determined based on the target category; Based on the depth of the inversion network, an encoder-decoder inversion network with corresponding layers is constructed. The encoder-decoder inversion network is used to extract multi-scale spatial features and texture structure features from the target 3D ground-penetrating radar volume data. Based on the multi-scale spatial features and texture structure features, the three-dimensional distribution of the underground dielectric constant corresponding to the target 3D ground-penetrating radar volume data is predicted.

2. The method according to claim 1, characterized in that, Based on a pre-defined three-dimensional reservoir computing network, the target three-dimensional ground-penetrating radar volume data to be inverted is spatially mapped point-by-point according to spatial coordinates, including: A pre-defined three-dimensional reservoir computing network is used to iterate the target three-dimensional ground-penetrating radar volume data point by point according to the spatial coordinate points to calculate the hidden state of each coordinate point. The hidden state is obtained by coupling the historical hidden state of the previous coordinate point in three dimensions and the voxel value of the current coordinate point. The output weight matrix of the three-dimensional reservoir computing network is estimated using a training paradigm based on next data point prediction, and the output weight matrix is ​​used as the waveform dynamic feature vector of the target three-dimensional ground-penetrating radar volume data.

3. The method according to claim 1, characterized in that, A pre-defined convolutional neural network is used to extract global spatial features from the target's 3D ground-penetrating radar volume data, including: The target's three-dimensional ground-penetrating radar volume data is divided into several non-overlapping three-dimensional data blocks; Each 3D data block is input into a pre-defined 3D convolutional neural network to extract the local spatial structure features of each 3D data block. The local spatial structure features corresponding to each three-dimensional data block are spliced ​​together along the feature dimension to form a global spatial feature that represents the global spatial structure information.

4. The method according to claim 1, characterized in that, Based on the waveform dynamic characteristics and global spatial characteristics, the target category of the target's three-dimensional ground-penetrating radar volume data is predicted, including: A cross-attention mechanism is used to fuse and enhance waveform dynamic features and global spatial features to obtain fused features. The fused features are input into a pre-defined multilayer perceptron classifier to output the target category probability distribution corresponding to the target's 3D ground-penetrating radar volume data.

5. The method according to claim 4, characterized in that, The inversion network depth is adaptively determined based on the target category, including: The target category probability distribution is input into a preset network depth controller, which is a multilayer perceptron. To output the candidate depth set The probability distribution on: in, This represents the probability of selecting each candidate depth from the candidate depth set. The probability distribution of the target category; According to the probability distribution Alternatively, the candidate depth with the highest probability can be selected as the inversion network depth, or a random sampling strategy based on probability distribution can be used to select the inversion network depth.

6. The method according to claim 1, characterized in that, Construct an encoder-decoder inversion network with corresponding layers based on the inversion network depth, including: The number of layers of the encoder and decoder participating in the feature extraction task in the preset inversion network is determined based on the depth of the inversion network, thus forming the encoder-decoder inversion network; The encoder network in the encoder-decoder inversion network Layer features are represented as: in, This represents a combination of batch normalization and activation operations. This indicates a feature concatenation operation. This indicates a pooling operation. , , These represent 3D convolution operations of 3×3×3, 5×5×5, and 7×7×7, respectively, used to process features from the previous layer. Perform multi-scale feature extraction; The first decoder network in the encoder-decoder inversion network Layer decoding features are represented as follows: in, This indicates a trilinear upsampling operation. The feature concatenation operation represents a skip connection. Represents a 3D convolution operation; The output features of the output convolutional layer in the encoder-decoder inversion network are represented as follows: in, This represents a 3D convolution operation. The predicted three-dimensional distribution of the underground dielectric constant corresponding to the three-dimensional ground-penetrating radar volume data of the target.

7. The method according to claim 6, characterized in that, In the encoder-decoder inversion network, a residual bridging block is set between the encoder and the decoder, and the residual output is represented as: in, This represents the bottleneck residual mapping consisting of a 1×1×1 dimensionality-reduced convolution, a 3×3×3 convolution, and a 1×1×1 recovery convolution, where B is the input of the residual bridging block.

8. The method according to any one of claims 1-7, characterized in that, The method further includes: A training set is constructed to simulate three-dimensional ground-penetrating radar scenarios for different types of underground targets, obtain three-dimensional ground-penetrating radar volume data and their corresponding real dielectric constant distribution maps, and pair the two to form training samples, thus forming a training set. The entire inversion framework is trained based on training samples. The training process includes: spatially mapping each training sample point by point according to spatial coordinates using a pre-set three-dimensional reservoir computing network to obtain waveform dynamic feature samples that characterize the electromagnetic response variation law of the underground medium of each training sample; extracting global spatial feature samples of each training sample using a pre-set convolutional neural network; predicting the target category of the current training sample based on the waveform dynamic feature samples and global spatial feature samples of each training sample; adaptively determining the depth of the second inversion network based on the target category of the current training sample; constructing an encoder-decoder inversion network with corresponding layers based on the depth of the second inversion network; using the obtained encoder-decoder inversion network to extract multi-scale spatial features and texture structure features of the training samples; and outputting the three-dimensional distribution of the underground dielectric constant corresponding to the training samples based on the multi-scale spatial features and texture structure features. During the training phase, a composite objective function is constructed that includes reconstruction loss and network depth regularization loss. Based on the composite objective function, the joint optimization training of the entire inversion framework is achieved.

9. The method according to claim 8, characterized in that, During the training phase, a composite objective function is constructed that includes reconstruction loss and network depth regularization loss, including: A reconstruction loss is constructed to measure the error between the predicted 3D distribution of underground dielectric constants of the training samples and the true dielectric constant distribution. ; Construct a network depth regularization loss to measure the model complexity corresponding to the selected network depth. The network depth regularization loss is expressed as: in, For the first Layer parameter quantity, This represents the maximum number of selectable network parameters. For dynamic weighting coefficients, The currently selected network depth; A dynamic weight optimization strategy is introduced to adaptively adjust the dynamic weight coefficients of the network depth regularization loss based on the relative rate of change of the reconstruction loss and the network depth regularization loss during continuous training iterations.

10. A depth-scalable inversion system for three-dimensional ground-penetrating radar data, characterized in that, The system includes: The dynamic feature extraction module is used to perform spatial mapping on the target three-dimensional ground-penetrating radar data to be inverted according to the spatial coordinate points in sequence based on the preset three-dimensional reservoir computing network, so as to obtain the waveform dynamic features that characterize the electromagnetic response change law of the underground medium. The spatial feature extraction module is used to extract global spatial features of the target's three-dimensional ground-penetrating radar volume data using a preset convolutional neural network; The target category prediction module is used to predict the target category to which the three-dimensional ground-penetrating radar data belongs based on the waveform dynamic features and global spatial features. The depth adaptive module is used to adaptively determine the depth of the inversion network based on the target category; The inversion prediction module is used to construct an encoder-decoder inversion network with corresponding layers based on the depth of the inversion network. The encoder-decoder inversion network is used to extract multi-scale spatial features and texture structure features from the target 3D ground-penetrating radar volume data, and predict the 3D distribution of the underground dielectric constant corresponding to the target 3D ground-penetrating radar volume data based on the multi-scale spatial features and texture structure features.

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