A Method and System for Constructing Dense Time-Varying Arrays Based on Controllable Variational Autoencoders

Abstract

This invention discloses a method and system for constructing dense time-varying arrays based on a controllable variational autoencoder, belonging to the field of ground-penetrating radar data processing technology. The invention proposes a constraint-embedded dense time-varying array construction method based on a controllable variational autoencoder. It uses a time-varying data reconstruction network based on a controllable variational autoencoder, and generates pseudo-trace data that approximates the true distribution by fusing latent space sampling interpolation and deep and shallow layer feature information to increase array density. A data registration module based on scale-invariant feature transformation is constructed, extracting inter-trace gradient features and structural symmetry features, enabling data registration in the spatiotemporal domain. Simultaneously, shallow layer features are embedded as constraint information into the data reconstruction network to eliminate the influence of data trace offset on array generation. This solves the problem in existing technologies where "reconstruction errors accumulate continuously during time-varying data interpolation and reconstruction, leading to a decline in the quality of generated data."

Description

Technical Field

[0001] This invention relates to the field of ground-penetrating radar data processing technology, and in particular to a method and system for constructing dense time-varying arrays based on controllable variational autoencoders. Background Technology

[0002] The statements in this section merely refer to the background art related to this invention and do not necessarily constitute prior art.

[0003] Ground penetrating radar (GPR) is an electromagnetic technology that uses electromagnetic waves to detect the distribution of underground media and determine its internal structure or shape. In recent years, it has been widely used in many fields, including underground structure surveying. In large-scale geological surveys, GPR data is used to construct high-density arrays, forming three-dimensional visual models with continuous physical structures. This provides multiple viewing angles and enhances the reliability of the analysis.

[0004] Ground-penetrating radar (GPR) acquires reflection data based on electromagnetic scattering fields, typically in three forms: A-scan, B-scan, and C-scan. In existing applications of three-dimensional subsurface structure analysis, constructing high-density time-varying arrays based on two-dimensional profile data (B-scan) is one of the main methods. However, the following problems remain unresolved when using B-scan to construct three-dimensional time-varying arrays:

[0005] (1) Constructing a dense, time-varying 3D array first requires high-quality time-varying data. Currently, the main strategy is to gradually add new trace data (A-scan) from the registration and reconstruction of a continuous B-scan array until the entire sequence is reconstructed. However, during large-scale geological surveys, variations in topography, survey lines, and survey parameters lead to spatial data sparsity in the acquired B-scan arrays. The irregular tile spacing of the B-scan dataset, and the data density between tiles being much lower than the data density between traces, easily results in missing traces during the construction of the 3D model, causing spatial structural deformation. Therefore, it is necessary to generate data for the spatial areas not covered by the scan lines to improve the data density between tiles.

[0006] (2) The acquisition of B-scan datasets is not synchronous. The different positions of the zero point of time lead to irregular offsets between time-varying data. During the interpolation and reconstruction of time-varying data, the reconstruction error accumulates continuously, resulting in a decrease in the quality of the generated data. Therefore, it is necessary to perform data registration on the measured data to eliminate irregular offsets between data.

[0007] In short, the reconstruction method for dense time-varying GPR arrays involves increasing the spatial data density, interpolating existing data sequences using the spatiotemporal correlation between channel data, and interpolating the sparse array to achieve the goal of constructing a dense array. Currently, the main strategies for time-varying data interpolation algorithms are to use the moving average of two adjacent effective values ​​of sparse spatial data to interpolate the gaps between effective data and to utilize the spatiotemporal correlation of surrounding data in the sparse spatial data for interpolation.

[0008] In existing technologies, some scholars use cubic spline interpolation for time-varying data reconstruction, connecting any two information points with a straight line or smooth curve. However, GPR data is a highly fluctuating nonlinear time-varying data, and this method masks the local feature changes of adjacent interpolation points, thus its effect on GPR time-varying data is not ideal. Some scholars reconstruct time-varying data based on Harmonic Analysis of Time Series (HANTS), employing a least-squares curve fitting method based on harmonic components, which has shown good performance in time series interpolation. Some scholars use singular spectral analysis (SSA) to iteratively estimate data gaps, optimizing the window width and the number of SSA principal modes through cross-validation to fill sparse data gaps. These algorithms are based on mathematical models and have good generalization performance in applications. However, due to the lack of spatial reference information, the global consistency of the interpolation results for large-scale survey data is not high. Some scholars have proposed an analytical method based on sparse representation to reconstruct missing data in time-varying signals, utilizing both spectral and spatial information. Some researchers use DAISY feature descriptors for data registration to generate dense spatial data, and then extract candidate plane sets to construct dense time-varying arrays. Such methods can reference more information from multiple dimensions; however, the time cost of interpolating large areas of missing data based on spatial information is generally high. Furthermore, trace data can vary significantly over short distances, making such methods unable to represent true data.

[0009] In recent years, scholars both domestically and internationally have incorporated emerging deep learning technologies into their research while maintaining existing methods, innovatively optimizing existing models. Recently, deep learning neural networks with different structures for sparse data interpolation, such as GRU, LSTM, GAN, and VAE, have emerged. Both GRU (gate recurrent unit) and LSTM (long short-term memory) neural networks can retain important features in data interpolation applications by using different thresholds, ensuring that important features are not lost during long-term transmission. They can also learn patterns from observed data and further learn from interpolated data, improving interpolation accuracy. However, GRU and LSTM each have their limitations. GRU is only advantageous for long-term time-varying data and small sample sets; LSTM still suffers from gradient vanishing when dealing with sequences exceeding length limits, and LSTM requires strictly time-dependent sequence data, making it unsuitable for GPR data with time zero-point issues. GAN (generative adversarial networks) are used to learn the overall distribution of time-varying data, thereby interpolating gaps in sparse data. However, due to the fixed amount of information, GAN networks perform poorly in terms of spectrum or time spectrum when generating complex data such as GPR time-varying data, resulting in problems such as low interpolation accuracy and model instability. Kingma et al. proposed the Variational Autoencoder (VAE) in 2014. A VAE consists of an encoder and a decoder. The encoder infers a variational probability distribution that conforms to a normal distribution from the input data; the decoder restores the variational probability distribution to approximate the probability distribution of the original data, forcing the learning of a continuous latent space distribution by adding KL divergence to the loss function. However, the divergence increases during data generation in a VAE, leading to a decrease in feature learning ability and making the output blurry. Denton et al. proposed -VAE to address this problem by increasing divergence weights, artificially reducing divergence to improve its learning ability. Compared to VAE, this method, while adjusting divergence through a control system, comes at the cost of higher reconstruction error. Building on -VAE, Shao et al. proposed ControlVAE, which introduces a nonlinear proportional-integral-derivative controller to adaptively adjust hyperparameters, maximizing the mutual information between the reconstructed data and the latent space, thus achieving a balance between reconstruction error and divergence weight allocation. However, as an unsupervised learning method, ControlVAE cannot capture the matching relationship of the input sequence when generating time-varying sequences, thus failing to achieve accurate interpolation of sparse data. Summary of the Invention

[0010] To address the shortcomings of existing technologies, this invention provides a method, system, electronic device, and computer-readable storage medium for constructing a dense time-varying array based on a controllable variational autoencoder. This method can better balance the weight distribution of reconstruction error and KL divergence, improve the network model's ability to learn features and the quality of reconstructed latent space data, eliminate irregular offsets using constraint information, and ultimately generate a dense time-varying array.

[0011] In a first aspect, the present invention provides a method for constructing a dense time-varying array based on a controllable variational autoencoder;

[0012] A method for constructing dense time-varying arrays based on controllable variational autoencoders includes:

[0013] Two-dimensional profile data is acquired, which is collected by ground-penetrating radar;

[0014] Based on regional joint feature constraints, time-varying data registration is performed on trace data in two-dimensional profile data to obtain additional feature information.

[0015] The additional feature information and trace data are input into a preset controllable variational autoencoder for processing to obtain the reconstructed dense time-varying array.

[0016] Among them, the controllable variational autoencoder extracts the deep feature information of the channel data and uses the additional feature information as a shallow feature constraint for iterative iteration to obtain a dense time-varying array.

[0017] Furthermore, the step of performing time-varying data registration on trace data in the two-dimensional profile data based on regional joint feature constraints to obtain additional feature information includes:

[0018] The two-dimensional profile data is divided into blocks according to the displacement direction to obtain one-dimensional trace data;

[0019] Calculate the gradient direction and gradient magnitude of adjacent one-dimensional trace data, and align the corresponding trace data in consecutive one-dimensional trace data according to the gradient direction and gradient magnitude.

[0020] Using a 9×9 square neighborhood as the data gradient statistics range, the feature vector is obtained by calculating the gradient direction and gradient magnitude accumulation value of each point, so as to perform feature matching and obtain a two-dimensional profile data array.

[0021] The correlation coefficients of the reference trace and the registration trace in the two-dimensional profile data array are calculated sequentially. The two one-dimensional trace data corresponding to the maximum value of the coefficient are regarded as the most approximate traces. The position, amplitude and main direction of the most approximate traces are used as additional feature information.

[0022] Furthermore, the step of inputting the additional feature information and trace data into a preset controllable variational autoencoder for processing includes:

[0023] The input channel data is convolved and second-sampled to compress the data into a low-dimensional vector; the additional feature information of the input is normalized and used as a constraint vector.

[0024] The low-dimensional vector and the constraint vector are input into the encoder. The low-dimensional vector and the constraint vector are jointly sampled to generate a latent vector containing shallow information and deep features, which is then projected onto the latent variable space of the constraint approximation.

[0025] Interpolation sampling between latent vectors in two latent spaces forms a time-varying sequence composite vector;

[0026] The time-varying sequence is synthesized into a vector and input into the decoder to generate reconstructed channel data; latent space interpolation is performed on all the remaining latent vectors to reconstruct the complete dense time-varying array.

[0027] Preferably, the joint distribution sampling of the low-dimensional vector and the constraint vector specifically involves: inputting the low-dimensional vector and the constraint vector into the encoder, performing multivariate Gaussian distribution processing on them, decomposing the input vector into a mean vector and a standard deviation vector that conform to the multivariate Gaussian distribution, using the reparameterization technique, multiplying the standard deviation by a random noise that conforms to the standard normal distribution and adding the mean to obtain the normal distribution of the reconstructed parameters; sampling from the reconstructed parameters and concatenating them with the condition vector to obtain a latent vector that simultaneously contains shallow information and deep features.

[0028] Preferably, the step of interpolating and sampling between latent vectors in two latent spaces to form a new time-varying sequence synthesis vector specifically involves: establishing a mapping between a point in a prior distribution region in the latent space and the input, the mapping being achieved through decoder reconstruction loss and latent variable reparameter constraints; and then interpolating and sampling between latent vectors in the two latent spaces to form a time-varying sequence synthesis vector.

[0029] Furthermore, during the training process of the controllable variational autoencoder, the KL divergence of each training step is sampled using the feedback control concept, and the hyperparameter β(t) is adjusted accordingly through an iterative algorithm to stabilize the KL divergence at the expected value.

[0030] Furthermore, the controllable variational autoencoder includes a convolutional layer, a pooling layer, an encoder, and a decoder connected in sequence.

[0031] Secondly, the present invention provides a dense time-varying array construction system based on a controllable variational autoencoder;

[0032] The first acquisition module is used to acquire two-dimensional profile data, which is collected by ground penetrating radar.

[0033] The second acquisition module is used to perform time-varying data registration on trace data in two-dimensional profile data based on regional joint feature constraints, and to acquire additional feature information.

[0034] The dense time-varying array acquisition module is used to input additional feature information and trace data into a preset controllable variational autoencoder for processing to obtain the reconstructed dense time-varying array.

[0035] Among them, the controllable variational autoencoder extracts deep feature information from the channel data and uses the additional feature information as a shallow feature constraint for iterative iteration to obtain a dense time-varying array. Thirdly, this invention provides an electronic device;

[0036] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When the processor executes the computer instructions, the computer instructions complete the steps of the above-described method for constructing a dense time-varying array based on a controllable variational autoencoder.

[0037] Fourthly, the present invention provides a computer-readable storage medium;

[0038] A computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps of the above-described method for constructing a dense time-varying array based on a controllable variational autoencoder.

[0039] Compared with the prior art, the beneficial effects of the present invention are:

[0040] This invention proposes a method for constructing a constraint-embedded dense time-varying array based on a controllable variational autoencoder (GPR). It leverages the continuous latent space features of the GPR to sample and interpolate latent space data, performing data interpolation in sparse regions to increase spatial data density. A controller dynamically adjusts the loss weights to balance the decoder's generation quality and feature learning ability until the generated accuracy approximates the real data. Then, an improved PSO-SIFT algorithm is used for data registration. Joint registration of the time-varying data is performed in both the spatial and temporal domains. By designing feature descriptors that conform to the GPR time-varying data structure and gradient changes, constraint information is extracted, effectively eliminating the impact of irregular offsets on data reconstruction.

[0041] Experimental results show that the method provided by this invention has higher robustness compared with mainstream algorithms, the generated dense time-varying array has a natural transition, and it can effectively characterize the real underground environment when faced with complex and multi-interference real data. Attached Figure Description

[0042] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0043] Figure 1 This is a flowchart illustrating the method for constructing a dense time-varying array based on a controllable variational autoencoder provided in an embodiment of the present invention.

[0044] Figure 2 A schematic diagram of a three-dimensional GPR time-varying data array field provided in an embodiment of the present invention;

[0045] Figure 3 This is a schematic diagram of a loop-shaped feature descriptor provided in an embodiment of the present invention;

[0046] Figure 4 This is a schematic diagram of the B-scan spatial domain registration result provided in an embodiment of the present invention;

[0047] Figure 5 This is a schematic diagram of the A-scan time-domain registration result provided in an embodiment of the present invention;

[0048] Figure 6 This is a schematic diagram of the controller dynamic feedback calculation process provided in an embodiment of the present invention;

[0049] Figure 7 This is a schematic diagram of the input data and condition vector processing procedure provided in an embodiment of the present invention;

[0050] Figure 8 This is a schematic diagram of the implicit space interpolation reconstruction process provided in an embodiment of the present invention;

[0051] Figure 9 This is a schematic diagram showing the interpolation results of different methods and the magnified comparison of regions a and b arrays provided in the embodiments of the present invention;

[0052] Figure 10 This is a magnified comparison diagram of region c before and after GAN interpolation, provided in an embodiment of the present invention.

[0053] Figure 11 This is a schematic diagram of the generation result of the GPR dense time-varying array provided in an embodiment of the present invention;

[0054] Figure 12 This is a schematic diagram showing the original sparse time-varying array three-dimensional reconstruction result and cross-section provided in an embodiment of the present invention;

[0055] Figure 13 This is a schematic diagram showing the three-dimensional reconstruction results and cross-section of a dense time-varying array provided in an embodiment of the present invention;

[0056] Figure 14 This is a schematic diagram of the three-dimensional reconstruction results of the constraint embedding ablation experiment provided in an embodiment of the present invention;

[0057] Figure 15This is a schematic diagram of the hyperbolic peak calibration visualization results provided in an embodiment of the present invention. Detailed Implementation

[0058] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0059] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments of the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. Furthermore, it should be understood that the terms “comprising” and “having”, and any variations thereof, are intended to cover non-exclusive inclusion, for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0060] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0061] Example 1

[0062] This embodiment provides a method for constructing dense time-varying arrays based on a controllable variational autoencoder (CVE), aiming to solve the problems of low spatial data density and irregular data offset in the construction process of dense time-varying arrays. It employs a region partitioning and multi-domain joint approach to register channel data and generate feature descriptors, constraining the embedded data reconstruction algorithm to effectively eliminate the cumulative error caused by irregular data offset. The loss function of ControlVAE is dynamically adjusted to achieve a balance between reconstruction error and KL divergence weight allocation, improving the quality of generated data. Sampling and interpolation reconstruction are performed in the latent space, fusing multi-level feature information to generate reconstructed data with continuous features.

[0063] Next, combined Figures 1-15 The method for constructing a dense time-varying array based on a controllable variational autoencoder disclosed in this embodiment is described in detail. The specific steps are as follows:

[0064] S1. Acquire two-dimensional profile data, which is collected by ground-penetrating radar. Based on regional joint feature constraints, perform time-varying data registration on the trace data in the two-dimensional profile data to obtain additional feature information. This includes the following steps;

[0065] (1) Divide the two-dimensional profile data into blocks according to the displacement direction to obtain one-dimensional trace data;

[0066] (2) Calculate the gradient direction and gradient magnitude of adjacent one-dimensional channel data, and align the corresponding channel data in the continuous one-dimensional channel data according to the gradient direction and gradient magnitude.

[0067] (3) Using a 9×9 square neighborhood as the data gradient statistics range, the feature vector is obtained by calculating the gradient direction and gradient magnitude accumulation value of each point respectively, so as to perform feature matching and obtain a two-dimensional profile data array.

[0068] (4) Calculate the correlation coefficients of the reference trace and the registration trace in the two-dimensional profile data array in sequence. Take the two one-dimensional trace data corresponding to the maximum value of the coefficient as the most approximate trace, and take the position, amplitude and main direction of the most approximate trace as additional feature information.

[0069] Specifically, the imaging principle of GPR involves transmitting electromagnetic pulses into the ground and receiving corresponding time-varying echo signals. From the perspective of time-varying array analysis, a C-scan array composed of multiple parallel time-varying signals is considered a three-dimensional time-varying array, such as... Figure 2 As shown.

[0070] When the probe pulse encounters a target object, the echo changes significantly, appearing as a hyperbolic wave in the B-scan data. Due to factors such as zero-point time and measurement environment during GPR data acquisition, the hyperbolic wave in the B-scan exhibits irregular shifts, resulting in different hyperbolic wave structures for the same target object. Therefore, registration of the trace data in the B-scan is necessary to reduce the cumulative error caused by reconstruction. The original B-scan data can be represented as:

[0071] B-scan = X(i,j)

[0072] Where i = 1, 2, 3, ... n; j = 1, 2, 3, ... m.

[0073] Dividing it into blocks according to the displacement direction, the resulting one-dimensional A-scan data is as follows:

[0074] W j =X j [1,2,...,n]={W j (1),W j (2),W j (3),...W j (n)}

[0075] Because GPR data exhibits complex correlations in both the spatial and temporal domains, this embodiment registers A-scan channel data from two aspects. In the spatial domain, since data acquisition typically requires designing multiple parallel survey lines, it is difficult to determine the starting position of each survey line. Therefore, it is necessary to stitch continuous B-scan data in the horizontal spatial position. Since the relative positions of the array antennas do not change, the starting positions of the B-scan data profiles are always equal. Registration can be based on calculating the gradient direction and gradient magnitude of one-dimensional channel data within adjacent B-scan data, aligning corresponding channel data within continuous B-scan data sequentially. W... j The gradient direction and gradient magnitude of (i) are defined as follows:

[0076]

[0077]

[0078] G x =([W j+1 (i-1)+2W j+1 (i)+W j+1 (i+1)]

[0079] -[W j-1 (i-1)+2W j-1 (i)+W j-1 (i+1)])

[0080] G y =([W j-1 (i-1)+2W j (i-1)+W j+1 (i-1)]

[0081] -[W j-1 (i+1)+2W j (i+1)+W j+1 (i+1)])

[0082] Among them, G x Indicates in X j The horizontal derivative of (i), G y This represents its vertical derivative. The classic SIFT algorithm uses the correlation between features to determine the optimal registration relationship, but when SIFT is used directly for channel data registration, the number of correct correspondences is insufficient to confirm the matching accuracy due to the significant differences in echo signal intensity mapping.

[0083] Therefore, this embodiment combines the improved PSO-SIFT algorithm's region partitioning idea, fully utilizes the continuous correlation and spatial structure characteristics between data within the B-scan array, and designs a back-character feature descriptor such as... Figure 3As shown, the improved feature descriptor contains more neighborhood information.

[0084] Because the target region in B-scan data exhibits a hyperbolic wave structure with high structural symmetry, the region partitioning approach offers better advantages over the original SIFT algorithm in addressing irregular offsets in trace data. The added neighborhood information further stabilizes the descriptors. A 9×9 square neighborhood is used as the data gradient statistics range. By calculating the gradient direction and accumulated gradient magnitude at each point, a feature vector with dimensions of 9×8 = 72 is obtained. Finally, registration is completed through multiple feature matching steps, and the registration result is as follows: Figure 4 As shown, the correspondence between the channel data in the B-scan array is clearly demonstrated.

[0085] In the time domain, since the transmit and receive distances of the array antennas are equal and do not change, ideally, the starting points of consecutive A-scan data should be completely consistent. The correlation coefficient C between the reference channel and the registration channel in the B-scan array is calculated sequentially, assuming the reference channel data is W. r The registration data is W. c C can be represented as:

[0086]

[0087] The two A-scan data points corresponding to the maximum coefficients are considered as the most approximate traces and are used as inputs to the subsequent data generation model for sampling. Pseudo-trace data is then generated through interpolation. Two registration trace sets W = (W1, W2, ... W2) are extracted from the continuous B-scan array. N ) and W′=(W1′,W2′,...W N Let (x,y),σ,θ and (x′,y′),σ′,θ′ represent the position, magnitude, and principal direction of the registration traces W and W′ in the corresponding B-scan data, respectively. The matching results are as follows: Figure 5 As shown.

[0088] In subsequent steps, the three types of information (x, y), σ, and θ between the extracted feature point pairs are retained as additional feature information F in the data reconstruction model. During the iterative process, this information is used as a shallow feature constraint and concatenated with the deep feature information extracted from the controllable VAE to form the latent vector Z. The concatenated latent vector not only possesses more advanced abstract latent space features but also shallow characteristics such as spatial location, amplitude, and principal direction. When the decoder reconstructs the data, it can effectively eliminate irregular offsets between data points and improve the accuracy of the reconstructed array field.

[0089] S2. Input the additional feature information and trace data into a preset controllable variational autoencoder for processing to obtain the reconstructed dense time-varying array. This includes the following steps:

[0090] (1) Convolve and resample the input channel data to compress the data into a low-dimensional vector; normalize the additional feature information of the input as a constraint vector;

[0091] (2) Input the low-dimensional vector and the constraint vector into the encoder, perform joint distribution sampling on the low-dimensional vector and the constraint vector, generate a latent vector containing shallow information and deep features, and project it onto the latent variable space of the constraint approximation.

[0092] (3) Interpolate and sample between the latent vectors in the two latent spaces to form a time-varying sequence composite vector;

[0093] (4) Input the time-varying sequence synthesis vector into the decoder to generate reconstructed channel data; perform latent space interpolation reconstruction on all the remaining latent vectors to obtain the complete dense time-varying array.

[0094] Next, the processing procedure of the controllable variational autoencoder will be explained in detail.

[0095] (1) Controllable variational autoencoder

[0096] To address the issue of VAEs failing to balance reconstruction loss and KL divergence, this embodiment introduces a controllable variational autoencoder (ControlVAE), which stabilizes the KL divergence value by dynamically adjusting the weights of the KL divergence. Inspired by control systems, ControlVAE uses feedback control to sample the KL divergence at each training step and adjusts the hyperparameter β(t) accordingly through an iterative algorithm to stabilize the KL divergence at the desired value.

[0097] The Controllable Variational Autoencoder (ControlVAE) is trained twice. The first training iteration aims to train the decoder to approximate the posterior distribution of the real data, generating high-quality reconstructed data. The second training iteration maps the latent vectors sampled by latent space interpolation back to the trace data, increasing the spatial data density. The latent vectors embed constraint information, mitigating irregular offset phenomena.

[0098] During model training, the KL divergence output at training step t is sampled and represented by V. K ′ L (t) represents the sampled KL divergence and the set expected V. KL The difference e(t) is given by the following formula:

[0099] e(t) = V KL -V K ′ L (t)

[0100] Using e(t) as feedback to calculate the hyperparameter β(t), the variational lower bound function of ControlVAE is then:

[0101] LconVAE =E Q(z|x) [logP θ (x∣z)]-β(t)KL(Q Φ (z∣x)‖P θ (z))

[0102] The hyperparameter β(t) is defined as follows:

[0103]

[0104] K p and K i This is a constant set by prior knowledge. When the KL divergence drops below the expected value, the controller slows down the decline by decreasing the hyperparameter β(t), i.e., decreasing the penalty for KL divergence in the variational lower bound function. Simultaneously, the decreased hyperparameter β(t) increases the variational lower bound function, thus increasing the KL divergence until it exceeds the expected value. Similarly, when the KL divergence exceeds the expected value, the controller decreases it by increasing the hyperparameter β(t), i.e., increasing the penalty for KL divergence in the variational lower bound function.

[0105] The first term of the hyperparameter β(t) dynamically influences its value based on the difference e(t), causing the KL divergence to dynamically increase or decrease in a favorable direction. The second term of the hyperparameter β(t) sums the cumulative differences generated by the training samples, producing a gradually increasing correction until the sign of the difference changes. This ensures that β(t) gradually changes in a direction that favors the KL divergence approaching its desired value. The calculation process of the hyperparameter β(t) is as follows: Figure 6 As shown.

[0106] (2) Construction of Constrained Embedded Latent Vectors

[0107] For GPR pseudochannel data generation, if the latent vectors input to the decoder contain sufficient feature information, it can not only effectively preserve the structural information in the original data but also minimize irregular offsets between data. Therefore, this embodiment designs a constraint-embedded ControlVAE to extract features and reconstruct constraints on A-scan channel data, constructing latent vectors containing multiple feature information.

[0108] In feature extraction, ControlVAE's convolutional and pooling layers convolve and subsample the input trace data, compressing it into a low-dimensional vector S. The positions (x, y), amplitude σ, and principal direction θ of the registered trace set extracted in Section 2 are normalized, and F = ((x, y), σ, θ) is used as the synchronous input constraint vector. The compressed low-dimensional vector S and the constraint vector are input to the encoder, which performs multivariate Gaussian distribution processing, decomposing the input vector into a mean vector μ and a standard deviation vector λ that conform to a multivariate Gaussian distribution. Using a reparameterization technique, the standard deviation is multiplied by a random noise e that conforms to a standard normal distribution. i The mean is then added to obtain the normal distribution h of the reconstructed parameters. Finally, samples are taken from the reconstructed parameters and concatenated with the conditional vector to obtain the latent vector Z, which contains both shallow information and deep features, as shown below. Figure 7 As shown. The latent vectors follow a normal distribution and are generated by sampling from the joint distribution of the input data and the conditional vectors.

[0109] (3) Continuous implicit space interpolation

[0110] During training, the encoder receives two consecutive A-scan inputs each time, generating two corresponding latent vectors and projecting them into a latent variable space that approximates the constraints. The decoder receives one latent vector each time and generates one reconstructed channel data. After training, the decoder can map the features in the latent feature space back to the reconstructed A-scan channel data as accurately as possible. Then, we use the ControlVAE mentioned above for sampling, which is equivalent to breaking down the basic units of the two channels. The encoder establishes a mapping between these elements and points in a prior distribution region in the latent space and the input. This mapping is achieved through the decoder's reconstruction loss and under the latent variable reparameter constraints. A new time-varying sequence synthesis vector Znew is formed by interpolating and sampling between the vectors in the latent space corresponding to the two input data, and then the decoder reconstructs and generates pseudo-channel data Snew within the spatial region. The interpolation process is as follows: Figure 8 As shown, simultaneously inputting Sq and Se into the encoder generates two latent vectors Zq and Ze. Since the latent feature space is continuous, interpolation within it is reasonable. The channel data Snew reconstructed by the decoder and its corresponding latent feature vector Znew are derived by the following equation:

[0111] Znew = Zq + rand(0,1)(Ze - Zq)

[0112] Snew = decoder(Znew)

[0113] By performing spatial interpolation reconstruction once on the registered trace set selected for registration, one latent space pseudo-trace data is obtained. After performing latent space interpolation reconstruction on all other registered traces, a complete dense time-varying array is obtained.

[0114] Next, experiments will be conducted to verify the advancement of the dense time-varying array construction method based on controllable variational autoencoders described in this embodiment.

[0115] (1) Experimental Dataset

[0116] This embodiment uses three sets of GPR simulated data and seven sets of real data obtained from detecting underground buried pipelines to verify and analyze the proposed method. The scanning interval for the seven sets of real data is 1 meter; the three sets of simulated data were obtained from GPRMAX simulation, with a data interval of 0.5 meters. These B-scan slices form a 10-sample dataset, used to train a time-varying data generation network based on ControlVAE. To reduce redundant features and shorten computation time during network training, the original data was uniformly cropped to 512 pixels × 512 pixels.

[0117] (2) Training details and evaluation indicators

[0118] The experimental hardware platform consisted of an Intel(R) Core(TM) i7-10700 CPU @ 2.90GHz, 32GB of RAM, and an NVIDIA GTX2070 GPU. The software environment was Windows 10 operating system. During training, K... p and K i The values ​​were set to 0.01 and 0.001 respectively. A pair of sequence B-scan data were input sequentially for training. The network structure and parameters were adjusted by verifying the changes in the loss function and manually observing the effect of the generated images. The lower the value of the loss function, the smaller the gap between the generated data and the real data, until high-quality time-varying data was generated.

[0119] The experiment used mutual information (MI), structural similarity (SSIM), and root mean square error (RMSE) to evaluate the quality of B-scan data composed of generated time-varying data. RMSE measures the error between the generated image and the original data; MI indicates the amount of original data information contained in the generated data; and SSIM reflects structural information similarity, defining B-scan as data with independent structural information composed of three factors: brightness, contrast, and structure. The mean was used as an estimate of brightness, the standard deviation as an estimate of contrast, and the covariance as a measure of structural similarity. The definitions of each evaluation index are as follows:

[0120]

[0121] Among them, (x i ",y i ") represents (x i ′,y iThe transformed coordinates of the element values ​​are '', where n represents the total number of elements in the input data.

[0122]

[0123] MI(X1,X2)=H(X1)+H(X2)-H(X1,X2)

[0124] Where H(S1,S2) represents the joint information entropy of the input sequence B-scan.

[0125]

[0126] in, It is the average value of X1. It is the average of X2. It is the variance of X1. It is the variance of X². It is the covariance of X1 and X2. c1 = (k1L) 2 c2 = (k2L) 2 SSIM is a constant used for stabilization, where L is the dynamic range of element values, and k1 = 0.01, k2 = 0.03. The structural similarity range is 0 to 1; when two data points are identical, the SSIM value equals 1.

[0127] (3) Generation and Quantitative Analysis of GPR Time-Varying Data

[0128] To verify the effectiveness of the model in this embodiment, bicubic spline interpolation, HANTS interpolation, GAN network interpolation, and VAE interpolation were used to interpolate the real GPR pipeline time-varying dataset. The generated results were normalized to a pixel space of 0–255, and local arrays of the same regions a and b generated by each method were extracted and enlarged for comparison. The results are as follows: Figure 9 As shown, the original data region a contains a hyperbolic wave structure that partially overlaps with high-frequency clutter. (From...) Figure 9 (a) It can be seen that in bicubic interpolation, high-frequency clutter is still densely packed, obscuring the structural information of the top part of the hyperbolic wave. In HANTS interpolation, the bottom clutter is not completely removed, obscuring part of the hyperbolic wave. In VAE interpolation, the hyperbolic wave structure is significantly weakened, and the structural information is not well preserved. In GAN interpolation and the method of this embodiment, the hyperbolic wave structure is clearly characterized, and the feature information is well preserved. However, the method of this embodiment has a better suppression effect on high-frequency clutter, and most of the high-frequency clutter is removed.

[0129] The original data region b exhibits a distinct hyperbolic wave structure with irregular offsets. Figure 9(b) It can be seen that in bicubic interpolation, the irregular offset problem in the hyperbolic wave structure is more severe, and the hyperbolic wave can no longer be clearly distinguished. In HANTS interpolation and VAE interpolation, the problem of irregular offset between data is alleviated, but the hyperbolic wave structure is significantly weakened. GAN interpolation and the method in this embodiment preserve the hyperbolic wave structure characteristics better, the layered boundaries at different depths are obvious, and the irregular offset phenomenon is reduced. However, as... Figure 10 As shown, GAN interpolation introduces significant irregular offsets, indicating that the model is not stable.

[0130] The experimental results above demonstrate that the method described in this embodiment can obtain the latent space data of a time-varying sequence array, clearly characterize hyperbolic wave features, suppress irregular offsets between data points, and improve spatial data density. This verifies the effectiveness and robustness of this embodiment.

[0131] Dense time-varying arrays were generated using different interpolation methods for two types of datasets. Real slices at the same positions as the original sparse array were extracted and quantitatively analyzed. The average values ​​of MI, RMSE, and SSIM in the normalized pixel space were calculated, and the results are shown in Table 1. A higher MI value indicates stronger continuity of information in the generated array; a lower RMSE value indicates smaller error between the generated and original arrays; and a higher SSIM value indicates more similar structural relationships between the generated and original arrays. Table 1 shows that the time-varying array generated using the method in this embodiment outperforms the other four methods in terms of mutual information, mean square error, and structural similarity. Numerically, compared to bicubic interpolation, the method in this embodiment reduces RMSE by 60% and improves SSIM by 48%. Compared to HANTS interpolation, the method in this embodiment reduces RMSE by 54% and improves SSIM by 28%. This demonstrates that the constrained embedding data generation model can effectively reduce irregular offsets. Compared to GAN interpolation, the method in this embodiment improves SSIM by 4% and reduces RMSE by 29%. Compared to VAE interpolation, the method in this embodiment improves SSIM by 14% and reduces RMSE by 38%. This demonstrates the importance of the controller dynamically adjusting the loss weights for both generation quality and learning ability. These three metrics indicate that the reconstructed data generated by the method in this embodiment is of high quality, outperforming other methods in terms of information relevance and structural continuity.

[0132] Table 1 Comparison of objective evaluation metrics for different algorithms on reconstructing different datasets

[0133]

[0134] (4) Three-dimensional reconstruction experiment

[0135] (4-1) The ControlVAE-based data generation method in this embodiment is used to construct a dense time-varying array of the real dataset, and data interpolation is performed in the sparse array space. By interpolating the feature vectors between two points in the latent space, the generated data is controlled to be tilted between different sampling sources. Figure 11 As shown, in order to more intuitively demonstrate the effectiveness of the method in improving data density, the reconstruction process expands the 1024 channels of B-scan data in every two sequences of sparse dataset to 5120 channels. That is, eight B-scan profiles composed of pseudo-channel data are interpolated in every two B-scan data to obtain a three-dimensional dense time-varying array similar to C-scan.

[0136] The spatial data density of the reconstructed time-varying array is improved. Segments are selected from the original sparse array and the reconstructed dense time-varying array, and 3D visualization analysis is performed using optical flow imaging algorithms. The 3D reconstruction results and cross-sectional views are shown below. Figure 12 , Figure 13 As shown. By Figure 12 (b) and Figure 13 (b) The comparison shows that the three-dimensional model constructed by the original sparse time-varying array has poor feature continuity, and the hyperbolic wave structure features are lost as the survey line moves. However, the dense time-varying array field reconstructed by the method in this embodiment has a clear background in the three-dimensional structure model obtained by three-dimensional visualization, retains the hyperbolic wave structure features and obvious stratigraphic structure information, and improves the structural continuity of hyperbolic waves in the three-dimensional model.

[0137] (4-2) Experiment on the effectiveness of constraint embedding

[0138] To verify whether the constraints embedded in the ControlVAE model help eliminate irregular offsets between data, a dense array generated directly using ControlVAE without constraint embedding and a dense time-varying array generated using the method in this embodiment are compared in 3D visualization. The comparison results are as follows: Figure 14 The hyperbolic peaks are calibrated and used as alignment points for intuitive visualization. The results are as follows: Figure 15 As shown. By Figure 14 (a) It can be seen that the hyperbolic wave portion without embedded constraints has a large amount of structural overlap. During the reconstruction process, the error gradually accumulates, causing the 3D model to fail to accurately reflect the true distribution and structural orientation of the underground target object. Figure 14 (b) shows that the dense time-varying array 3D model reconstructed by constrained embedding has a clear layer background and high continuity of hyperbolic wave structure.

[0139] Depend on Figure 15(b) It can be seen that before constraint embedding, irregular offsets between data lead to inaccurate peak positions and even missing values. However, the constraint embedding algorithm used in this embodiment can accurately detect and register hyperbolic feature regions. The embedding of constraint information effectively eliminates irregular offsets between data, reduces the cumulative error generated by reconstruction, and makes the reconstructed 3D model have better structural continuity, better representing the distribution and orientation of the target object.

[0140] The experimental results above show that in the construction of dense time-varying arrays, the constraint embedding obtained through data registration can effectively reduce the impact of irregular offsets between data on data reconstruction. The time-varying data generation network based on ControlVAE can improve the spatial data density. The constructed dense time-varying array has small error and high accuracy, effectively characterizing the true distribution of underground structures.

[0141] Example 2

[0142] This embodiment discloses a dense time-varying array construction system based on a controllable variational autoencoder, including:

[0143] The first acquisition module is used to acquire two-dimensional profile data, which is collected by ground penetrating radar.

[0144] The second acquisition module is used to perform time-varying data registration on trace data in two-dimensional profile data based on regional joint feature constraints, and to acquire additional feature information.

[0145] The dense time-varying array acquisition module is used to input additional feature information and trace data into a preset controllable variational autoencoder for processing to obtain the reconstructed dense time-varying array.

[0146] Among them, the controllable variational autoencoder extracts the deep feature information of the channel data and uses the additional feature information as a shallow feature constraint for iterative iteration to obtain a dense time-varying array.

[0147] It should be noted that the first acquisition module, the second acquisition module, and the dense time-varying array acquisition module mentioned above correspond to the steps in Embodiment 1. The examples and application scenarios implemented by these modules and their corresponding steps are the same, but they are not limited to the content disclosed in Embodiment 1. It should be noted that these modules, as part of the system, can be executed in a computer system such as a set of computer-executable instructions.

[0148] Example 3

[0149] Embodiment 3 of the present invention provides an electronic device, including a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When the computer instructions are executed by the processor, they complete the steps of the above-described method for constructing a dense time-varying array based on a controllable variational autoencoder.

[0150] Example 4

[0151] Embodiment 4 of the present invention provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps of the above-described method for constructing a dense time-varying array based on a controllable variational autoencoder.

[0152] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0153] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0154] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0155] The descriptions of each embodiment in the above embodiments have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0156] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for constructing a dense time-varying array based on a controllable variational autoencoder, characterized in that, include: Two-dimensional profile data is acquired, which is collected by ground-penetrating radar; Based on regional joint feature constraints, time-varying data registration is performed on trace data in two-dimensional profile data to obtain additional feature information. The additional feature information and trace data are input into a preset controllable variational autoencoder for processing to obtain the reconstructed dense time-varying array. Among them, the controllable variational autoencoder extracts the deep feature information of the channel data and uses the additional feature information as a shallow feature constraint for iterative iteration to obtain a dense time-varying array. The method of performing time-varying data registration on trace data in two-dimensional profile data based on regional joint feature constraints to obtain additional feature information includes: The two-dimensional profile data is divided into blocks according to the displacement direction to obtain one-dimensional trace data; Calculate the gradient direction and gradient magnitude of adjacent one-dimensional trace data, and align the corresponding trace data in consecutive one-dimensional trace data according to the gradient direction and gradient magnitude. use The square neighborhood is used as the range for data gradient statistics. By calculating the gradient direction and gradient magnitude of each point, the feature vector is obtained for feature matching to obtain a two-dimensional profile data array. The correlation coefficients of the reference trace and the registration trace in the two-dimensional profile data array are calculated sequentially. The two one-dimensional trace data corresponding to the maximum value of the coefficient are regarded as the most approximate traces. The position, amplitude and main direction of the most approximate traces are used as additional feature information. The step of inputting the additional feature information and trace data into a preset controllable variational autoencoder for processing includes: The input channel data is convolved and second-sampled to compress the data into a low-dimensional vector; the additional feature information of the input is normalized and used as a constraint vector. The low-dimensional vector and the constraint vector are input into the encoder. The low-dimensional vector and the constraint vector are jointly sampled to generate a latent vector containing shallow information and deep features, which is then projected onto the latent variable space of the constraint approximation. Interpolation sampling between latent vectors in two latent spaces forms a time-varying sequence composite vector; The time-varying sequence is synthesized into a vector and input into the decoder to generate reconstructed channel data; latent space interpolation is performed on all the remaining latent vectors to reconstruct the complete dense time-varying array.

2. The method for constructing a dense time-varying array based on a controllable variational autoencoder as described in claim 1, characterized in that, The joint distribution sampling of the low-dimensional vector and the constraint vector specifically involves: inputting the low-dimensional vector and the constraint vector into the encoder, processing them with a multivariate Gaussian distribution, decomposing the input vector into a mean vector and a standard deviation vector that conform to a multivariate Gaussian distribution, using the reparameterization technique, multiplying the standard deviation by a random noise that conforms to a standard normal distribution and adding the mean to obtain the normal distribution of the reconstructed parameters; sampling from the reconstructed parameters and concatenating them with the condition vector to obtain a latent vector that simultaneously contains shallow information and deep features.

3. The method for constructing a dense time-varying array based on a controllable variational autoencoder as described in claim 1, characterized in that, The process of interpolating and sampling between latent vectors in two latent spaces to form a new time-varying sequence synthesis vector specifically involves: establishing a mapping between a point in a prior distribution region in the latent space and the input, which is achieved through decoder reconstruction loss and latent variable reparameter constraints; and then interpolating and sampling between latent vectors in the two latent spaces to form a time-varying sequence synthesis vector.

4. The method for constructing a dense time-varying array based on a controllable variational autoencoder as described in claim 1, characterized in that, In the training process of a controllable variational autoencoder, feedback control is used for each training step. Divergence is sampled, and hyperparameters are adjusted accordingly using an iterative algorithm. to make The divergence stabilizes at the expected value.

5. The method for constructing a dense time-varying array based on a controllable variational autoencoder as described in claim 1, characterized in that, The controllable variational autoencoder includes a convolutional layer, a pooling layer, an encoder, and a decoder connected in sequence.

6. A dense time-varying array construction system based on a controllable variational autoencoder, characterized in that, include: The first acquisition module is used to acquire two-dimensional profile data, which is collected by ground penetrating radar. The second acquisition module is used to perform time-varying data registration on trace data in two-dimensional profile data based on regional joint feature constraints, and to acquire additional feature information; including: The two-dimensional profile data is divided into blocks according to the displacement direction to obtain one-dimensional trace data; Calculate the gradient direction and gradient magnitude of adjacent one-dimensional trace data, and align the corresponding trace data in consecutive one-dimensional trace data according to the gradient direction and gradient magnitude. use The square neighborhood is used as the range for data gradient statistics. By calculating the gradient direction and gradient magnitude of each point, the feature vector is obtained for feature matching to obtain a two-dimensional profile data array. The correlation coefficients of the reference trace and the registration trace in the two-dimensional profile data array are calculated sequentially. The two one-dimensional trace data corresponding to the maximum value of the coefficient are regarded as the most approximate traces. The position, amplitude and main direction of the most approximate traces are used as additional feature information. A dense time-varying array acquisition module is used to input additional feature information and trace data into a preset controllable variational autoencoder for processing, and to obtain the reconstructed dense time-varying array; including: The input channel data is convolved and second-sampled to compress the data into a low-dimensional vector; the additional feature information of the input is normalized and used as a constraint vector. The low-dimensional vector and the constraint vector are input into the encoder. The low-dimensional vector and the constraint vector are jointly sampled to generate a latent vector containing shallow information and deep features, which is then projected onto the latent variable space of the constraint approximation. Interpolation sampling between latent vectors in two latent spaces forms a time-varying sequence composite vector; The time-varying sequence is synthesized into a vector and input into the decoder to generate reconstructed channel data; the remaining latent vectors are reconstructed by latent space interpolation to obtain the complete dense time-varying array. Among them, the controllable variational autoencoder extracts the deep feature information of the channel data and uses the additional feature information as a shallow feature constraint for iterative iteration to obtain a dense time-varying array.

7. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, complete the steps of the dense time-varying array construction method based on a controllable variational autoencoder as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, complete the steps of the dense time-varying array construction method based on a controllable variational autoencoder as described in any one of claims 1-5.

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