Earthquake collapse building dielectric constant inversion method based on improved neural network

Abstract

The invention discloses an earthquake collapse building dielectric constant inversion method based on an improved neural network, and aims to improve the inversion precision of ground penetrating radar (GPR) data and the recognition capability of an internal structure. The method comprises the following steps: firstly, acquiring a radar data set for simulating a collapsed building structure, and preprocessing the radar data set, including background interference removal, median filtering and time gain enhancement, so as to improve the signal-to-noise ratio; on the basis, a UKAN neural network introducing an attention mechanism and depth separable convolution is constructed, and a KAN module is combined to strengthen the nonlinear modeling capability. The GPR image is inverted through the model, dielectric constant distribution in a collapse structure is reconstructed, and automatic recognition of key areas such as survival gaps is achieved. The method can provide efficient and accurate structural analysis and rescue decision support in a complex post-disaster environment, and has practical application value.

Description

Technical Field

[0001] The present invention relates to a ground penetrating radar data inversion technology, belonging to the field of non-destructive testing technology, and specifically to a dielectric constant inversion method for earthquake-collapsed buildings based on an improved neural network. Background Art

[0002] Ground Penetrating Radar (GPR) is a nondestructive electromagnetic detection technology that can be used to identify targets such as cavities, pipelines, and cracks in underground structures or buildings. It is widely used in geological surveys, structural inspections, and disaster rescue. In the event of a building collapse caused by an earthquake or explosion, GPR can assist in analyzing the internal structure and dielectric constant distribution of the rubble, thereby locating possible survival gaps and providing technical support for rescue decisions.

[0003] Traditional GPR inversion relies primarily on numerical calculation methods based on physical models, such as the finite-difference time-domain (FDTD) method, which reconstructs the dielectric constant distribution by simulating electromagnetic wave propagation. This method offers high accuracy but high computational complexity, making it difficult to meet the needs of real-time rescue. Empirical methods based on reflected waves rely on the manual extraction of features such as amplitude and phase, which are highly subjective and lack generalization capabilities. In recent years, full waveform inversion (FWI) has improved inversion accuracy by iteratively optimizing the matching of observed and simulated data. However, it is highly sensitive to the initial model, prone to falling into local optimality, and has a low tolerance for noise, limiting its application in complex collapse environments.

[0004] To overcome the limitations of traditional methods, machine learning and deep learning techniques have been introduced to GPR inversion. Early methods such as support vector machines (SVM) and random forests (RF) relied on artificial feature design and struggled to capture the complex nonlinear relationships in GPR data. The rise of deep learning has brought breakthroughs in inversion. Models such as convolutional neural networks (CNNs) and U-Nets have significantly improved feature extraction and inversion accuracy through end-to-end learning. However, standard deep learning models still have shortcomings when processing GPR data, such as insufficient attention to key areas (such as survival gaps), poor training stability, and numerical learning difficulties caused by the large range of dielectric constant distribution. Recent research has improved performance by refining neural network architecture (such as introducing attention mechanisms) or optimizing data preprocessing (such as logarithmic normalization), but generalization and real-time performance in complex environments still need improvement.

[0005] During earthquake rescue operations, quickly and accurately locating survival gaps in collapsed buildings is crucial for improving rescue success rates. Traditional GPR inversion methods, due to their low computational efficiency, sensitivity to noise, and strong reliance on prior information, struggle to meet practical needs. Deep learning offers new avenues for GPR inversion, but existing technologies lack accuracy and stability in complex scenarios. There is an urgent need to develop more efficient and stable inversion methods to enhance the application value of GPR in disaster relief.

[0006] To address these issues, this paper proposes a method for inverting the dielectric constant of earthquake-collapsed buildings based on an improved neural network. This method integrates an encoder-decoder framework with a multi-layer KAN nonlinear modeling module within the overall network structure. By introducing learnable functions within the network instead of traditional fixed activation functions, the method significantly improves the modeling capability of nonlinear relationships in complex structures. Furthermore, a convolutional attention mechanism is introduced within the shallow convolutional module to enhance the model's focus on key regional features. Furthermore, signal preprocessing strategies such as time gain compensation and mean filtering are designed, taking into account the noise characteristics of radar images. This optimizes the input data quality from the source, ultimately achieving higher-precision and more robust inversion and reconstruction of collapsed structures, providing reliable support for emergency search and rescue in building disaster scenarios.

[0007] First, a search revealed that Chinese invention patent publication number CN118709524A proposes a ground-penetrating radar (GPR) data inversion method based on a multi-scale supervised generative adversarial network. This method improves the deep learning framework based on pix2pixGan by incorporating a multi-scale convolution module and an EMA attention module to more accurately capture multiple hyperbolic waveforms and clutter features in B-scan images. Taking into account the imbalance between background pixels and inversion target pixels in the subsurface dielectric constant distribution image in the dataset, the original L1 error loss function is modified to a focal-weighted mean square error function, and a SSIM loss function is also incorporated. Simulated GPR B-scan waveform images and corresponding subsurface dielectric constant distribution images are generated using GPRMax+ParaView simulation software to establish a paired B-scan-dielectric constant distribution dataset for training. The method then trains pix2pixGan, and the trained U-net generator inverts the B-scan images to obtain a subsurface dielectric constant distribution map, ultimately achieving GPR data inversion.

[0008] The technical comparison between the above-mentioned reference documents and this application is as follows:

[0009] 1. The aforementioned reference document improves upon the Pix2Pix GAN framework, employing multi-scale convolution and attention modules for GPR image inversion, focusing on improving the quality of B-scan image generation. This paper, however, focuses on dielectric constant inversion and survivor space identification in collapsed buildings after disasters. By integrating KAN nonlinear modeling, CBAM attention mechanisms, and depthwise separable convolutions, a new UKAN network is constructed to restore the distribution of physical properties in complex structures.

[0010] 2. The aforementioned comparative document used gprMax and ParaView to generate data, employed a multi-scale GAN architecture to optimize image inversion, and used focally weighted MSE and SSIM losses to optimize generation quality. However, its output primarily consisted of image translations, with limited physical interpretation of the inversion. This present invention not only focuses on structural restoration but also emphasizes continuous modeling and numerical precision control of physical quantities such as the dielectric constant. It also employs SmoothLoss, regularization, and gradient penalty terms to enhance inversion reliability.

[0011] 3. The aforementioned comparative documents emphasize inversion image clarity and multi-scale structural information modeling, and are suitable for engineering scenarios such as underground target detection. The present invention, on the other hand, targets post-disaster emergency rescue and uses deep inversion of GPR data to identify surviving void areas and cavity structures after building collapse. The two differ fundamentally in their application scenarios, core objectives, and technical approaches.

[0012] Second, a search revealed a Chinese invention patent, publication number CN119723279A, that proposes a U-Net network construction method based on dual-input and image-separable convolution. This improved dual-input U-Net (DIWSUnet) based on image-separable convolution enables ground-penetrating radar (GPR) data imaging and inversion of subsurface objects. First, a B-scan image is generated from GPR data. Frequency-wavenumber shift (FK) processing is then performed on the GPR data, achieving a dual-input inversion of the B-scan image and the FK-shifted image to obtain the final object image. Dual color input (6 channels) and color output (3 channels) are used to distinguish objects, inverting their subsurface location and classifying them. Inspired by the deep separable convolution model, the original input module is modified to an image-wise separable convolution (IWS) module, significantly improving performance with only a small parameter increase.

[0013] The technical comparison between this application and the above-mentioned reference documents is as follows:

[0014] 1. The aforementioned reference document proposes the DIWS-Unet network, based on an improved U-Net structure. It uses a B-scan image and a FK offset map as dual inputs to detect and classify objects in RGB color images, outputting object categories and locations. This network is suitable for identifying and segmenting small underground objects. However, the present invention focuses on inverting complex dielectric constant distributions and detecting cavities in collapsed buildings, aiming to support lifesaving and disaster analysis, rather than focusing on object category segmentation.

[0015] 2. The aforementioned reference document uses an image separable convolutional module (IWS) in its network structure, improving receptive field and feature extraction capabilities through multi-channel input, but does not involve nonlinear modeling or attention mechanisms. The present invention, on the other hand, introduces a KAN module to perform nonlinear mapping of input features, supplemented by CBAM attention to enhance channel and spatial focusing capabilities. This enables more accurate reconstruction of dielectric constant maps in complex environments and captures fine-grained structural changes.

[0016] 3. The aforementioned reference document uses BCELoss as a loss function, suitable for pixel classification tasks. The present invention employs SmoothLoss with gradient regularization and L2 decay, making it more suitable for continuous-valued regression tasks. The two methods differ significantly in their loss design, output targets, and evaluation metrics. The present invention focuses on cavity recovery and electromagnetic property reconstruction in real-world scenarios, rather than object detection and semantic segmentation. Summary of the Invention

[0017] To solve the above technical problems, the present invention proposes an inversion method for the dielectric constant of earthquake-collapsed buildings based on an improved neural network, which can achieve higher-precision and higher-robust inversion reconstruction of collapsed structures, providing reliable support for emergency search and rescue in building disaster scenarios.

[0018] To achieve the above object, the technical solution adopted by the present invention is:

[0019] The dielectric constant inversion method of earthquake collapsed buildings based on an improved neural network is characterized by comprising the following steps:

[0020] S1. Data Collection

[0021] The simulation data was generated by Python random script to simulate the dielectric constant cross-section of the real building collapse, and the Blender plug-in was used to capture the collapse interface data;

[0022] S2. Dataset Construction

[0023] The simulation data and collapsed interface data were simulated using the GPRMAX tool to obtain the corresponding dielectric constant-Bscean data set;

[0024] S3, dataset preprocessing

[0025] Apply time gain to the radar signal to compensate for signal attenuation due to propagation loss, and use a median filter algorithm to suppress background noise;

[0026] S4. Training the improved UKAN neural network

[0027] Input the preprocessed simulation data set into the improved UKAN neural network for pre-training;

[0028] S5. Get the inversion result

[0029] After the pre-training of the improved UKAN neural network is completed, the measured data set is input for training to obtain the final inversion result.

[0030] As a preferred technical solution of the present invention: Step S1 is specifically as follows:

[0031] S11. Generate dielectric constant map

[0032] A simulated dielectric constant map was generated using a Python random algorithm to simulate the collapsed cross-section of a building, forming a layered and block-like structure with a width of 2.5 meters and a depth of 6 meters. Each layer was randomly divided into 4–12 sublayers, which were further subdivided into subblocks. 1–4 polygonal or triangular air voids were randomly set with a dielectric constant of 1, and the dielectric constants of other areas were randomly set to 3–25. This simulated the electromagnetic properties of real building materials. The dielectric constant distribution map showed a layered structure, with air voids displayed in dark purple and building materials displayed in green, yellow, or red.

[0033] S12. Building Modeling

[0034] Blender software was used to construct a 3D building model based on the measured building structural parameters, and a modular design was used to divide the building into multiple independent structural units;

[0035] S13. Collapse simulation

[0036] The 3D building model was imported into Blender and preprocessed using the BCB plug-in, including model grouping, mesh discretization, and material property definition. Physical properties were set based on actual material parameters, and independent structural units were connected through the BCB constraint builder. The collapse scenario was simulated to generate a collapsed cross-section model and a dielectric constant distribution map.

[0037] As a preferred technical solution of the present invention: Step S2 is specifically as follows:

[0038] The GPRMAX tool was used to input the collapsed section model and perform electromagnetic wave propagation simulation with a 350 MHz Ricker pulse source. The B-scan radar image and dielectric constant distribution matrix were generated based on the finite-difference time-domain method to form the training, validation, and test data sets.

[0039] As a preferred technical solution of the present invention: Step S3 is as follows:

[0040] During the dataset construction phase, the simulation data and field-measured GPR data were combined to establish a dataset that shows the correspondence between GPR signals and the underground dielectric constant distribution. The raw radar data were preprocessed and enhanced as follows:

[0041] S31. To address the direct wave interference and background offset in the original B-scan image, a method for removing direct waves based on lateral channel mean subtraction is used. The processing process is as follows: for each time sampling point, the mean value along the channel direction is calculated and subtracted from the original data. The mathematical expression is as follows:

[0042] (1)

[0043] in, For the Rank Columns of raw radar data, is the total number of channels;

[0044] S32. Apply median filtering to suppress local isolated noise. Specifically, take the median of each time line signal and deduct the correction. The expression is as follows:

[0045] (2)

[0046] In order to compensate for the energy attenuation of radar signals during propagation, an exponential time gain strategy is adopted to weight the signal amplitude according to the time depth. The gain function is defined as:

[0047] (3);

[0048] S33, the final enhanced signal is:

[0049] (4)

[0050] in, For the The maximum gain is limited to 50 times.

[0051] As a preferred technical solution of the present invention: in step S4,

[0052] S41. Construct an improved UKAN neural network. The specific steps are as follows:

[0053] S411: The preprocessed radar image is input into the improved KAN deep neural network model. The overall structure of this model adopts the "encoder-bottleneck-decoder" form. In the encoder part, the input data size is set to 256×256. First, feature extraction is performed through three groups of convolution modules. Each convolution module contains two 3×3 convolution kernels with a stride of 1 and a padding of 1. The activation function uses the ReLU function. After applying the InstanceNorm layer to each convolution layer, the local dimension is equalized by specifying each kernel. After the convolution module, the custom KANBlock module is introduced as the network core enhancement unit.

[0054] S412: A convolutional attention module is embedded in the three-layer convolutional structure. The convolutional attention module consists of two submodules in series, namely the channel attention module and the spatial attention module, which jointly model the semantic information and spatial layout information of the convolutional feature map. The details are as follows:

[0055] First, the channel attention module performs global average pooling and global maximum pooling on the input feature map along the spatial dimension to generate two channel description vectors respectively. After transformation through a shared multi-layer perceptron, the two are added and fused. The channel attention weight map is then obtained through the Sigmoid activation function, which is expressed as:

[0056] (5)

[0057] in, represents the input feature map, represents the Sigmoid function, Represents the channel attention weight map, which is element-wise multiplied with the input feature map along the channel dimension to form an enhanced feature map:

[0058] (6)

[0059] Then, the spatial attention module treats the above output Average pooling and maximum pooling are performed along the channel dimension to generate two single-channel spatial feature maps, which are concatenated by channel and sent to a 7×7 convolution operation, and the spatial attention map is output through the Sigmoid function:

[0060] (7)

[0061] in, represents the spatial attention map, represents a 7×7 convolution operation, represents a feature concatenation operation,

[0062] The final output feature map is:

[0063] (8);

[0064] S413: Tokenized KAN stage

[0065] In the tokenized KAN module, we first transform the output features of the convolutional stage into Reshape into a series of flattened 2D patches for tokenization, where each patch is of size ,N= is the number of feature patches, and then a trainable linear projection is used The vectorized patches are mapped into a latent D-dimensional embedding space, specifically expressed as:

[0066] (9)

[0067] Linear projection This is achieved through a convolutional layer with a kernel size of 3;

[0068] S414: KAN layer embedding

[0069] Based on the Kolmogorov–Arnold representation theorem, the KAN layer is designed to perform deep mapping of image embedding features as follows:

[0070] The KAN layer construction methods include:

[0071] Node simplification: neurons only perform weighted summation of inputs without performing nonlinear transformations;

[0072] Edge function replacement: each connection is represented by a learnable B-spline basis function ;

[0073] Parameterization: Each connection function It is parameterized as a combination of spline coefficients and grid nodes, where the grid nodes are statically or dynamically adjustable point sets and the spline coefficients are learnable parameters;

[0074] Enhanced adjustability: The KAN network introduces a grid node adaptive update mechanism that can dynamically adjust the domain division of the spline function based on the distribution of training data;

[0075] Regularization term constraint: L1 regularization and entropy regularization are introduced during training to control the complexity of the spline function;

[0076] The forward propagation process of the KAN layer includes the following steps:

[0077] Input feature vector Enter each KANLinear unit;

[0078] Each feature component One-dimensional spline function Mapping is an intermediate result;

[0079] The mapping result is multiplied by the corresponding weight and summed in the output dimension direction to obtain the final output, which is formulated as follows:

[0080] (10)

[0081] in, For input Channels are mapped to output The spline function of channels is defined by a set of spline coefficients and mesh nodes.

[0082] After the KAN layer, the features are further input into the depthwise separable convolution module and sequentially undergo batch normalization, ReLU activation, residual connection, and layer normalization.

[0083] The KAN layer improves the modeling and expression capabilities of nonlinear features in complex and noisy GPR images:

[0084] (11)

[0085] in, represents the output feature map of the kth layer, represents the above parameterized KAN nonlinear mapping function;

[0086] S415: Decoder structure and skip connection

[0087] The decoder structure is symmetrical with the encoder, gradually restoring the feature map from low resolution to high resolution. The decoder structure consists of five levels of decoding modules, each of which includes upsampling operations, skip connections, and decoding convolution modules.

[0088] S416: Upsampling operation

[0089] The deepest feature map is obtained from the end of the encoder structure. It is first upsampled by bilinear interpolation with a scaling factor of 2 to expand the feature map size to 1 / 2 of the original image. After upsampling, the feature map is input to the decoding convolution module decoder1, which consists of two convolutional layers with a convolution kernel size of 3×3, a ReLU activation function, and an InstanceNorm2d normalization layer.

[0090] S417: Skip Connection and Splicing

[0091] A skip connection mechanism is introduced in each decoder level, which is implemented as follows:

[0092] First, take the encoder output feature map corresponding to the current decoding level;

[0093] Then, the encoder output is concatenated with the current upsampled decoder feature map in the channel dimension;

[0094] Finally, the concatenated feature map is input into the decoding convolution module of the next layer for processing;

[0095] The splicing operation is implemented as follows:

[0096] (12)

[0097] in, represents the upsampled feature map, represents the encoder feature map corresponding to the jump connection, Indicates channel dimension splicing;

[0098] S418: Decoding convolution module processing

[0099] The concatenated feature maps are input to the corresponding decoding modules decoder2 to decoder5. Each decoding module has the same structure, consisting of two convolutional layers with a convolution kernel size of 3×3, a padding of 1, a stride of 1, and a ReLU activation and InstanceNorm2d normalization operation. The decoder restores the feature map size to 1 / 2, 1 / 4, 1 / 8, and 1 / 1 of the original image input, and fuses the feature maps of the same scale of the encoder through skip connections at each level.

[0100] S419: Final output generation

[0101] After processing by decoder5, the output feature map size is restored to the original input map size, and the feature map is integrated into a single-channel output through a 1×1 convolution layer. Each pixel value of this channel corresponds to the predicted dielectric constant value, and finally the dielectric constant distribution map predicted by the model is output.

[0102] As a preferred technical solution of the present invention: in step S4,

[0103] S42. Pre-train the improved UKAN neural network as follows:

[0104] S421. When the improved UKAN neural network is used to train the training set, SmoothLoss is used for training, where the formula is as follows

[0105] (13)

[0106] in, is the real dielectric constant, is the predicted value, is the smoothing coefficient, and its value is 0.05;

[0107] S422, use Adam optimizer to perform gradient update on the parameters of the improved UKAN neural network, and introduce L2 regularization term into it, and set the weight decay coefficient to , which is used to control model complexity and prevent overfitting. The complete training process is iterated for 150 rounds.

[0108] Compared with the prior art, the present invention has the following beneficial effects:

[0109] This invention provides a method for inverting the dielectric constant of earthquake-collapsed buildings based on an improved neural network. This method can quickly and accurately reconstruct the internal dielectric constant distribution of complex collapsed structures, assisting in identifying potential survival gaps. Compared to traditional physical modeling or shallow neural network methods, this method incorporates a multi-scale feature extraction mechanism and a learnable nonlinear modeling module (KAN) into the network structure, effectively enhancing the model's ability to perceive complex signals and structural changes. Furthermore, by embedding a CBAM attention mechanism, the network's focus on key features is enhanced. Combined with the temporal gain and mean filtering strategies used in signal preprocessing, this method effectively improves input data quality and training efficiency. This method enables intelligent inversion of building internal structural features without requiring a precise prior model. It boasts high inversion accuracy, fast inference speed, and strong adaptability, providing technical support for emergency search and rescue in disaster scenarios such as earthquakes and explosions. It has promising practical application prospects and social value. BRIEF DESCRIPTION OF THE DRAWINGS

[0110] Figure 1 This is the overall flow chart of the dielectric constant inversion method for earthquake collapsed buildings based on the improved neural network;

[0111] Figure 2 It is a schematic diagram of the improved UKAN neural network model;

[0112] Figure 3 It is the inversion result obtained after training the improved UKAN neural network model. DETAILED DESCRIPTION

[0113] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0114] like Figure 1-3 As shown, the dielectric constant inversion method of earthquake collapsed buildings based on the improved neural network proposed in the present invention includes the following steps:

[0115] S1. Data Collection

[0116] The simulation data was generated by Python random script to simulate the dielectric constant cross-section of the real building collapse, and the Blender plug-in was used to capture the collapse interface data;

[0117] Step S1 is specifically as follows:

[0118] S11. Generate dielectric constant map

[0119] A simulated dielectric constant map was generated using a Python randomized algorithm to simulate a collapsed building cross-section, resulting in a complex multi-layered, multi-block structure. The model was 2.5 meters wide and 6 meters deep, with each layer randomly divided into 4–12 sublayers, further subdivided into several subblocks. One to four polygonal or triangular air voids (with a dielectric constant of 1) were randomly placed, while the dielectric constants of other areas were randomly set between 3 and 25 to simulate the electromagnetic properties of real building materials. The dielectric constant distribution map shows a layered structure, with air voids displayed in dark purple and building materials (with dielectric constants of 3–25) in green, yellow, or red.

[0120] S12. Building Modeling

[0121] A three-dimensional model was constructed using Blender software based on the measured building structural parameters, and a modular design was used to divide the building into multiple independent structural units, providing a basis for generating real cross-sectional data for the subsequent BCB plug-in collapse simulation.

[0122] S13. Collapse simulation

[0123] Import the 3D building model into Blender and perform preprocessing using the BCB plugin, including model grouping, mesh discretization, and material property definition. Physical properties are set based on actual material parameters, and structural elements are connected using the BCB constraint builder. Simulating collapse scenarios (such as removing supports or applying external forces) generates collapsed cross-section layouts and dielectric constant distribution maps.

[0124] S2. Dataset Construction

[0125] The simulation data and collapsed interface data were simulated using the GPRMAX tool to obtain the corresponding dielectric constant-Bscean data set;

[0126] Step S2 specifically includes: using the gprMax tool, inputting the collapsed section model, performing electromagnetic wave propagation simulation with a 350 MHz Ricker pulse source, generating B-scan radar images and dielectric constant distribution matrices based on the finite-difference time-domain method (FDTD), and forming training, validation, and test data sets.

[0127] S3, dataset preprocessing

[0128] Apply time gain to the radar signal to compensate for signal attenuation due to propagation loss, and use a median filter algorithm to suppress background noise;

[0129] Step S3 is as follows:

[0130] During the dataset construction phase, simulation data and field-measured ground-penetrating radar (GPR) data were combined to establish a dataset that correlates GPR signals with the distribution of underground dielectric constants. To improve the training stability and generalization capabilities of the neural network model, the raw radar data required multi-step preprocessing and enhancement, including the following operations:

[0131] S31. To address the direct wave interference and background offset present in the original B-scan image, a method for removing direct waves based on lateral channel mean subtraction is used. The processing process is as follows: for each time sampling point, the mean value along the channel direction (number of channels) is calculated and subtracted from the original data. The mathematical expression is as follows:

[0132] (1)

[0133] in, For the Rank Columns of raw radar data, is the total number of channels.

[0134] S32. Further apply median filtering to suppress local isolated noise. Specifically, take the median of each time line signal and deduct the correction. The expression is as follows:

[0135] (2)

[0136] Through the above steps, high-amplitude direct waves and random noise components can be effectively eliminated, and the signal-to-noise ratio of the target signal can be improved.

[0137] In addition, to compensate for the energy attenuation of radar signals during propagation, an exponential time gain (TimeGain) strategy is adopted. The signal amplitude is weighted according to the time depth, and the gain function is defined as:

[0138] (3)

[0139] S33, the final enhanced signal is:

[0140] (4)

[0141] in, For the The maximum gain is limited to 50 times to prevent excessive amplification of deep noise.

[0142] After completing the above preprocessing operations, radar signal data with optimized signal-to-noise ratio and normalized dynamic range is obtained, laying the foundation for subsequent network training and inversion modeling

[0143] S4. Training the improved UKAN neural network

[0144] Input the preprocessed simulation data set into the improved UKAN neural network for pre-training;

[0145] In step S4,

[0146] S41. First, build the improved UKAN neural network. The specific steps are as follows:

[0147] S411: The preprocessed radar image is input into the improved KAN deep neural network model. The overall structure of the model adopts the form of "encoder-bottleneck-decoder". In the encoder part, the input data size is set to 256×256. First, feature extraction is performed through three groups of convolution modules. Each group of convolution modules contains two 3×3 convolution kernels, with a step size of 1, a padding of 1, and an activation function using the ReLU function. Unlike traditional networks, the present invention applies the InstanceNorm layer to each layer of convolution, and then realizes the local dimension equation by specifying each kernel. It not only improves the model convergence speed, but also significantly enhances the generalization ability of the model when processing GPR high-noise data. After the convolution module, a custom KANBlock module is introduced as the network core enhancement unit to replace the traditional linear layer and enhance the ability to express nonlinear relationships.

[0148] S412: To further enhance the model's ability to identify fine-grained features in key areas of collapsed structures, such as surviving voids, a convolutional attention module is embedded within the three-layer convolutional architecture to enhance the saliency of feature maps in both the channel and spatial dimensions. This module is lightweight and computationally inexpensive, making it suitable for embedding within existing convolutional modules to enhance representation capabilities and improve defect recognition accuracy.

[0149] More specifically, the CBAM module consists of two sub-modules in series, namely the channel attention module and the spatial attention module, which jointly model the semantic information and spatial layout information of the convolutional feature map.

[0150] First, the channel attention module performs global average pooling and global maximum pooling on the input feature map along the spatial dimension to generate two channel description vectors, which are then transformed and fused by a shared multi-layer perceptron (MLP). The channel attention weight map is then obtained by the Sigmoid activation function. It can be expressed as:

[0151] (5)

[0152] in, represents the input feature map, represents the Sigmoid function, Represents the channel attention weight map. This weight map is element-wise multiplied with the input feature map along the channel dimension to form an enhanced feature map:

[0153] (6)

[0154] Then, the spatial attention module treats the above output Average pooling and maximum pooling are performed along the channel dimension to generate two single-channel spatial feature maps; they are concatenated by channel and sent to a 7×7 convolution operation, and the spatial attention map is output through the Sigmoid function:

[0155] (7)

[0156] in, represents the spatial attention map, represents a 7×7 convolution operation, and represents a feature concatenation operation. The final output feature map is:

[0157] (8)

[0158] The CBAM module, as part of the convolutional block in the residual module, is embedded between three layers of convolutional structures. Combined with the residual connection and normalized activation mechanism, it enables the network to automatically focus on areas in the image that are highly correlated with tunnel lining defects while suppressing background redundant information, significantly improving the model's performance in tunnel lining radar image classification tasks.

[0159] S413: Tokenized KAN stage

[0160] Tokenization In the tokenized KAN module, we first transform the output features of the convolutional stage into Reshape into a series of flattened 2D patches for tokenization, where each patch is of size ,N= is the number of feature patches. We then use a trainable linear projection The vectorized patches are mapped into a latent D-dimensional embedding space, specifically expressed as:

[0161] (9)

[0162] Linear projection This is achieved through a convolutional layer with a kernel size of 3

[0163] S414: KAN layer embedding

[0164] In order to improve the network's ability to model nonlinear relationships, this paper designs a KAN (Kolmogorov-Arnold Network) layer based on the Kolmogorov–Arnold representation theorem to perform deep mapping of image embedding features.

[0165] The KAN layer abandons traditional activation functions and uses learnable one-dimensional functions instead of connection weights, improving the approximation of complex functions and model interpretability. Its construction method includes: node simplification: neurons no longer perform nonlinear activation operations, but are only used for weighted summation of inputs;

[0166] Node simplification: neurons only perform weighted summation of inputs without performing nonlinear transformations;

[0167] Edge function replacement: Each connection is represented by a learnable B-spline basis function,

[0168] Parameterization: Each connection function It is parameterized as a combination of spline coefficients and grid nodes, where the grid nodes are statically or dynamically adjustable point sets and the spline coefficients are learnable parameters;

[0169] Enhanced adjustability: The KAN network introduces a grid node adaptive update mechanism that can dynamically adjust the domain division of the spline function based on the distribution of training data, thereby improving local fitting accuracy.

[0170] Regularization term constraint: L1 regularization and entropy regularization are introduced during the training process to control the complexity of the spline function and ensure generalization ability.

[0171] The forward propagation process of the KAN layer includes the following steps:

[0172] Input feature vector Enter each KANLinear unit;

[0173] Each feature component One-dimensional spline function Mapping is an intermediate result;

[0174] The mapping result is multiplied by the corresponding weight and summed in the output dimension direction to obtain the final output.

[0175] The formula is as follows:

[0176] (10)

[0177] in, For input Channels are mapped to output A spline function with 1 channel, defined by a set of spline coefficients and mesh nodes.

[0178] After the KAN layer, the features are further input into the depthwise separable convolution module and sequentially undergo batch normalization (BatchNorm); ReLU activation; residual connection; and layer normalization (LayerNorm).

[0179] Through the above structure, KAN effectively improves the ability to model and express nonlinear features in high-noise complex GPR images.

[0180] (11)

[0181] in, represents the output feature map of the kth layer, represents the above parameterized KAN nonlinear mapping function.

[0182] In this example, each KANBlock is embedded with L = 3 KAN layers, resulting in a network structure with a total of K = 2 KANBlock modules. Each KAN layer uses a B-spline kernel function with 5 nodes and a spline order of 3. An adaptive grid node update mechanism is also enabled to enhance the model's adaptability to changes in the input spatial distribution.

[0183] Through this structural design, the KAN module can improve the model's nonlinear modeling capabilities for the dielectric constant characteristic map of underground structures while maintaining a low parameter count. It is particularly suitable for inversion and identification tasks in radar images with high noise and heterogeneous geological conditions.

[0184] S415: Decoder structure and jump connection.

[0185] In this embodiment of the present invention, the decoder structure is symmetrical to the encoder structure, gradually restoring the feature map from low resolution to high resolution. The structure consists of five levels of decoding modules, each of which includes upsampling operations, skip connections, and decoding convolution modules.

[0186] S416: Upsampling operation.

[0187] The deepest feature map obtained from the encoder is first upsampled using bilinear interpolation with a scaling factor of 2 to expand the feature map size to half the original image. After upsampling, the feature map is fed into the decoder convolution module decoder1, which consists of two convolutional layers with a 3×3 kernel size, a ReLU activation function, and InstanceNorm2d normalization.

[0188] S417: Skip connection and splicing method.

[0189] In order to fuse shallow details in the encoding stage with deep semantic information in the decoding stage, a skip connection mechanism is introduced in each decoder level. The specific implementation is as follows:

[0190] Get the encoder output feature map corresponding to the current decoding level

[0191] Concatenate the encoder output with the current upsampled decoder feature map in the channel dimension;

[0192] The concatenated feature map is input into the decoding convolution module of the next layer for processing.

[0193] The splicing operation is implemented as follows:

[0194] (12)

[0195] in, represents the upsampled feature map, represents the encoder feature map corresponding to the jump connection, Indicates channel dimension splicing.

[0196] S418: Decoding convolution module processing.

[0197] The concatenated feature maps are fed into the corresponding decoding modules decoder2 through decoder5. Each decoding module has a consistent structure, consisting of two convolutional layers with a 3×3 kernel size, 1 padding, and a stride of 1. ReLU activation and InstanceNorm2d normalization are also applied. The decoder resizes the feature maps to 1 / 2, 1 / 4, 1 / 8, and 1 / 1 of the original input image, and fuses feature maps of the same scale from the encoder using skip connections at each level.

[0198] S419: Final output is generated.

[0199] After processing in decoder5, the output feature map is restored to its original input size. A 1×1 convolutional layer then integrates the feature map into a single-channel output. Each pixel in this channel corresponds to a predicted dielectric constant value, ultimately outputting the model's predicted dielectric constant distribution map. Through this multi-stage decoding and skip connection mechanism, the decoder architecture of the present invention effectively preserves shallow edge and texture details from the encoder while incorporating deeper semantic features. The result is a radar image inversion with high spatial resolution and strong expressiveness, effectively improving the recognition and location accuracy of targets such as underground cavities.

[0200] In step S4,

[0201] S42. Pre-train the improved UKAN neural network model. The specific steps are as follows:

[0202] S421: When the model trains the training set, SmoothLoss is used for training, where the formula is as follows

[0203] (13)

[0204] in, is the real dielectric constant, is the predicted value, is the smoothing coefficient, which is 0.05 in this example.

[0205] S422: Adam optimizer is used to perform gradient update on neural network parameters, and L2 regularization term (weight decay) is introduced into it. The weight decay coefficient is set to , used to control model complexity and prevent overfitting. The complete training process is iterated for 150 rounds.

[0206] S5. Get the inversion result

[0207] After the pre-training of the improved UKAN neural network is completed, the measured data set is input for training to obtain the final inversion result.

[0208] Based on the above-mentioned method, the present invention can quickly and accurately reconstruct the internal dielectric constant distribution map of complex collapsed structures, assisting in the identification of potential survival gaps. Compared to traditional physical modeling or shallow neural network methods, the present invention introduces a multi-scale feature extraction mechanism and a learnable nonlinear modeling module (KAN) into the network structure, effectively enhancing the model's perception of complex signals and structural changes. Furthermore, by embedding the CBAM attention mechanism, the network's focus on key features is enhanced. Combined with the time gain and median filtering strategies used in signal preprocessing, this method effectively improves input data quality and training efficiency. This method enables intelligent inversion of building internal structural features without the need for a precise prior model. It boasts high inversion accuracy, fast inference speed, and strong adaptability, providing technical support for emergency search and rescue in disaster scenarios such as earthquakes and explosions, and possesses promising practical application prospects and social value.

[0209] The above description is merely a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent variation based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. The dielectric constant inversion method of earthquake collapsed buildings based on improved neural network is characterized by: The steps include: S1. Data Collection The simulation data was generated by Python random script to simulate the dielectric constant cross-section of the real building collapse, and the Blender plug-in was used to capture the collapse interface data; S2. Dataset Construction The simulation data and collapsed interface data were simulated using the GPRMAX tool to obtain the corresponding dielectric constant-Bscean data set; S3, dataset preprocessing Apply time gain to the radar signal to compensate for signal attenuation due to propagation loss, and use a median filter algorithm to suppress background noise; S4. Training the improved UKAN neural network Input the preprocessed simulation data set into the improved UKAN neural network for pre-training; S5. Get the inversion result After the pre-training of the improved UKAN neural network is completed, the measured data set is input for training to obtain the final inversion result.

2. The method for inverting the dielectric constant of earthquake-collapsed buildings based on an improved neural network according to claim 1, characterized in that: Step S1 is specifically as follows: S11. Generate dielectric constant map A simulated dielectric constant map was generated using a Python random algorithm to simulate the collapsed cross-section of a building, forming a layered and block-like structure with a width of 2.5 meters and a depth of 6 meters. Each layer was randomly divided into 4–12 sublayers, which were further subdivided into subblocks. 1–4 polygonal or triangular air voids were randomly set with a dielectric constant of 1, and the dielectric constants of other areas were randomly set to 3–25. This simulated the electromagnetic properties of real building materials. The dielectric constant distribution map showed a layered structure, with air voids displayed in dark purple and building materials displayed in green, yellow, or red. S12. Building Modeling Blender software was used to construct a 3D building model based on the measured building structural parameters, and a modular design was used to divide the building into multiple independent structural units; S13. Collapse simulation The 3D building model was imported into Blender and preprocessed using the BCB plug-in, including model grouping, mesh discretization, and material property definition. Physical properties were set based on actual material parameters, and independent structural units were connected through the BCB constraint builder. The collapse scenario was simulated to generate a collapsed cross-section model and a dielectric constant distribution map.

3. The method for inverting the dielectric constant of earthquake-collapsed buildings based on an improved neural network according to claim 1 or 2, characterized in that: Step S2 is specifically as follows: The GPRMAX tool was used to input the collapsed section model and perform electromagnetic wave propagation simulation with a 350 MHz Ricker pulse source. The B-scan radar image and dielectric constant distribution matrix were generated based on the finite-difference time-domain method to form the training, validation, and test data sets.

4. The method for inverting the dielectric constant of earthquake-collapsed buildings based on an improved neural network according to claim 1, characterized in that: Step S3 is as follows: During the dataset construction phase, the simulation data and field-measured GPR data were combined to establish a dataset that shows the correspondence between GPR signals and the underground dielectric constant distribution. The raw radar data were preprocessed and enhanced as follows: S31. To address the direct wave interference and background offset in the original B-scan image, a method for removing direct waves based on lateral channel mean subtraction is used. The processing process is as follows: for each time sampling point, the mean value along the channel direction is calculated and subtracted from the original data. The mathematical expression is as follows: （1） in, For the Rank Columns of raw radar data, is the total number of channels; S32. Apply median filtering to suppress local isolated noise. Specifically, take the median of each time line signal and deduct the correction. The expression is as follows: （2） In order to compensate for the energy attenuation of radar signals during propagation, an exponential time gain strategy is adopted to weight the signal amplitude according to the time depth. The gain function is defined as: （3）； S33, the final enhanced signal is: （4） in, For the The maximum gain is limited to 50 times.

5. The method for inverting the dielectric constant of earthquake-collapsed buildings based on an improved neural network according to claim 1, characterized in that: In step S4, S41. Construct an improved UKAN neural network. The specific steps are as follows: S411: The preprocessed radar image is input into the improved KAN deep neural network model. The overall structure of this model adopts the "encoder-bottleneck-decoder" form. In the encoder part, the input data size is set to 256×256. First, feature extraction is performed through three groups of convolution modules. Each convolution module contains two 3×3 convolution kernels with a stride of 1 and a padding of 1. The activation function is the ReLU function. After applying the InstanceNorm layer to each convolution layer, the local dimension is equalized by specifying each kernel. After the convolution module, the custom KANBlock module is introduced as the network core enhancement unit. S412: A convolutional attention module is embedded in the three-layer convolutional structure. The convolutional attention module consists of two submodules in series, namely the channel attention module and the spatial attention module, which jointly model the semantic information and spatial layout information of the convolutional feature map. The details are as follows: First, the channel attention module performs global average pooling and global maximum pooling on the input feature map along the spatial dimension to generate two channel description vectors respectively. After transformation through a shared multi-layer perceptron, the two are added and fused. The channel attention weight map is then obtained through the Sigmoid activation function, which is expressed as: （5） in, represents the input feature map, represents the Sigmoid function, Represents the channel attention weight map, which is element-wise multiplied with the input feature map along the channel dimension to form an enhanced feature map: （6） Then, the spatial attention module treats the above output Average pooling and maximum pooling are performed along the channel dimension to generate two single-channel spatial feature maps, which are concatenated by channel and sent to a 7×7 convolution operation, and the spatial attention map is output through the Sigmoid function: （7） in, represents the spatial attention map, represents a 7×7 convolution operation, represents a feature concatenation operation, The final output feature map is: （8）； S413: Tokenized KAN stage In the tokenized KAN module, we first transform the output features of the convolutional stage into Reshape into a series of flattened 2D patches for tokenization, where each patch is of size ,N= is the number of feature patches, and then a trainable linear projection is used The vectorized patches are mapped into a latent D-dimensional embedding space, specifically expressed as: （9） Linear projection This is achieved through a convolutional layer with a kernel size of 3; S414: KAN layer embedding Based on the Kolmogorov–Arnold representation theorem, the KAN layer is designed to perform deep mapping of image embedding features as follows: The KAN layer construction methods include: Node simplification: neurons only perform weighted summation of inputs without performing nonlinear transformations; Edge function replacement: each connection is represented by a learnable B-spline basis function ; Parameterization: Each connection function It is parameterized as a combination of spline coefficients and grid nodes, where the grid nodes are statically or dynamically adjustable point sets and the spline coefficients are learnable parameters; Enhanced adjustability: The KAN network introduces a grid node adaptive update mechanism that can dynamically adjust the domain division of the spline function based on the distribution of training data; Regularization term constraint: L1 regularization and entropy regularization are introduced during the training process to control the complexity of the spline function; The forward propagation process of the KAN layer includes the following steps: Input feature vector Enter each KANLinear unit; Each feature component One-dimensional spline function Mapping is an intermediate result; The mapping result is multiplied by the corresponding weight and summed in the output dimension direction to obtain the final output, which is formulated as follows: （10） in, For input Channels are mapped to output The spline function of channels is defined by a set of spline coefficients and mesh nodes. After the KAN layer, the features are further input into the depthwise separable convolution module and sequentially undergo batch normalization, ReLU activation, residual connection, and layer normalization. The KAN layer improves the modeling and expression capabilities of nonlinear features in noisy and complex GPR images: （11） in, represents the output feature map of the kth layer, represents the above parameterized KAN nonlinear mapping function; S415: Decoder structure and skip connection The decoder structure is symmetrical with the encoder, gradually restoring the feature map from low resolution to high resolution. The decoder structure consists of five levels of decoding modules, each of which includes upsampling operations, skip connections, and decoding convolution modules. S416: Upsampling operation The deepest feature map is obtained from the end of the encoder structure. It is first upsampled by bilinear interpolation with a scaling factor of 2 to expand the feature map size to 1 / 2 of the original image. After upsampling, the feature map is input to the decoding convolution module decoder1, which consists of two convolutional layers with a convolution kernel size of 3×3, a ReLU activation function, and an InstanceNorm2d normalization layer. S417: Skip Connection and Splicing A skip connection mechanism is introduced in each decoder level, which is implemented as follows: First, take the encoder output feature map corresponding to the current decoding level; Then, the encoder output is concatenated with the current upsampled decoder feature map in the channel dimension; Finally, the concatenated feature map is input into the decoding convolution module of the next layer for processing; The splicing operation is implemented as follows: （12） in, represents the upsampled feature map, represents the encoder feature map corresponding to the jump connection, Indicates channel dimension splicing; S418: Decoding convolution module processing The concatenated feature maps are input to the corresponding decoding modules decoder2 to decoder5. Each decoding module has the same structure, consisting of two convolutional layers with a convolution kernel size of 3×3, a padding of 1, a stride of 1, and a ReLU activation and InstanceNorm2d normalization operation. The decoder restores the feature map size to 1 / 2, 1 / 4, 1 / 8, and 1 / 1 of the original image input, and fuses the feature maps of the same scale of the encoder through skip connections at each level. S419: Final output generation After processing by decoder5, the output feature map size is restored to the original input map size, and the feature map is integrated into a single-channel output through a 1×1 convolution layer. Each pixel value of this channel corresponds to the predicted dielectric constant value, and finally the dielectric constant distribution map predicted by the model is output.

6. The method for inverting the dielectric constant of earthquake-collapsed buildings based on an improved neural network according to claim 1, characterized in that: In step S4, S42. Pre-train the improved UKAN neural network as follows: S421. When the improved UKAN neural network is used to train the training set, SmoothLoss is used for training, where the formula is as follows （13） in, is the real dielectric constant, is the predicted value, is the smoothing coefficient, and its value is 0.05; S422, use Adam optimizer to perform gradient update on the parameters of the improved UKAN neural network, and introduce L2 regularization term into it, and set the weight decay coefficient to , which is used to control model complexity and prevent overfitting. The complete training process is iterated for 150 rounds.

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