Underground shallow vibration field multispectral energy fusion method based on low-rank tensor

Abstract

An underground shallow vibration field multispectral energy fusion method based on a low-rank tensor comprises the following steps: selecting a point on the earth surface as an origin of coordinates, selecting an east-west direction as an x axis, selecting a south-north direction as a z axis, and simultaneously selecting a direction perpendicular to the x axis and the z axis as a y axis to obtain an explosion vibration signal; a variational mode decomposition (VMD) method is adopted to extract a frequency component of a signal collected by the sensor. Decomposing the complex signal into a plurality of intrinsic mode functions with different frequency bands, and extracting each frequency component from the intrinsic mode functions; a sparse single-frequency energy field is calculated by using a WTVGSR algorithm; and fusing a multispectral energy field based on a low-rank tensor approximation method.

Description

Technical Field

[0001] The present invention relates to a fusion method, in particular to a multi-spectral energy fusion method of an underground shallow vibration field based on a low-rank tensor. Background Art

[0002] In shallow underground detection and imaging, multispectral fusion of energy fields is a core technical approach for accurately characterizing the energy field distribution characteristics of underground explosions. This technique effectively reflects the extent of damage caused by underground explosions to underground targets and serves as a key indicator for analyzing the energy conduction patterns of such ammunition explosions and assessing the destructive effectiveness of underground weapons. However, in actual measurements, due to the high power and wide area of ​​impact of the explosions and the limited number of test sensors, the measured data is extremely sparse, affecting the accuracy of energy field reconstruction and posing significant challenges to accurately identifying the energy field distribution characteristics.

[0003] Compared with large-area, large-volume, deep-level, and long-period positioning scenarios such as earthquake monitoring, deep coal mining, and oil and gas resource exploration, the shallow underground space has the following differences: (1) The depth of the explosion source is usually limited to a shallow space of hundreds of meters, which belongs to the problem of shallow space energy field reconstruction and imaging; (2) The shallow surface geological structure is complex, including various media such as sand, gravel, rock, and mud, and it is impossible to refer to the existing deep stratum model structure, which belongs to the problem of near-surface complex space energy field reconstruction and imaging; (3) The constitutive properties of the soil in the near-field of the explosion are elastic-plastic, and the elastic waves are greatly affected by ground reflection and refraction. The P-wave and S-wave wave groups are complexly mixed, and are affected by the surface reflection and refraction effects to form multi-modal energy field interference fringes, which is a multi-modal energy field coupling interference problem; (4) The sudden change of the shallow underground medium structure and the limitation of sensor layout lead to spatial omissions and modal imbalance in the energy field data, which belongs to the energy field reconstruction problem under unstructured data.

[0004] To address these challenges, single-spectrum energy field reconstruction methods for shallow underground spaces have made some progress. Interpolation methods are used to estimate the intensity distribution of shock waves across the entire explosion field. A spline fitting method, combined with node optimization, achieves optimal sensor placement, thereby improving the accuracy of reconstructing the airborne shock wave pressure field under incomplete data conditions. Furthermore, using underground explosion dynamics theory to forward-model parameters such as vibration and stress in the explosion field, the effects of the blast load on specific underground structures are determined, allowing for the reconstruction of the energy field. Although some progress has been made in reconstructing underground explosion vibration energy, existing deep-seated stratum models are not directly applicable, as the blast source is typically confined to shallow depths of less than 100 meters and the shallow surface structure is complex and contains multiple media. Furthermore, the sudden changes in the underground medium structure and the limitations of sensor placement lead to spatial gaps and modal imbalance in the data. This makes single-spectrum methods inaccurate when processing unstructured data and makes it difficult to effectively address complex interference and data gaps.

[0005] While progress has been made in multispectral fusion of shallow subsurface energy fields, several key issues and challenges remain. Traditional principal component analysis (PCA) methods can effectively extract key feature information from multiple image fusions. However, due to the complexity of subsurface structures and the anisotropy of seismic waves, PCA's applicability to subsurface energy field reconstruction is limited. It fails to fully account for the heterogeneity and anisotropy of the subsurface medium, resulting in low reconstruction accuracy. Laplace pyramid transforms effectively fuse image details through multiscale analysis, but their effectiveness is limited when dealing with the complexity of subsurface media and data sparsity. Furthermore, they consume significant amounts of large-scale data processing and computational time, making it difficult to achieve the required accuracy. Coupled non-negative matrix factorization (CNMF) can effectively decompose and reconstruct image information for fusion, but its application in subsurface energy field reconstruction is hampered by incomplete data and noise. While it can extract shared feature information, its reconstruction accuracy often falls short of practical requirements in complex shallow subsurface geological structures.

[0006] Therefore, given the complexity of shallow underground media, existing methods still have significant deficiencies in data sparsity, medium anisotropy, and computational efficiency. This results in low reconstruction accuracy for energy field fusion, and is particularly difficult in achieving anisotropic reconstruction. To address this, this paper proposes a multi-spectral energy fusion method for shallow underground vibration fields based on low-rank tensors. Summary of the Invention

[0007] In order to solve the defects in the prior art, the present invention discloses a multi-spectral energy fusion method of shallow underground vibration field based on low-rank tensor, and its technical solution is as follows:

[0008] S1. Select a point on the ground as the coordinate origin, with the east-west direction as the x-axis, the north-south direction as the z-axis, and the direction perpendicular to the x- and z-axes as the y-axis. Deploy the sensor array and acquire the explosion vibration signal.

[0009] S2. Decompose the sensor signal using the variational mode decomposition (VMD) method to extract the frequency components of multiple intrinsic mode functions (IMFs);

[0010] S3. Use the WTV-GSR algorithm to construct an attenuation tomography model and reconstruct a sparse single-frequency energy field;

[0011] S4. Fusion of multi-spectral energy fields based on low-rank tensor approximation method, including:

[0012] S4.1 Model the single spectrum energy field data into a tensor form;

[0013] S4.2 Constructing an energy field multispectral imaging model;

[0014] S4.3 uses the ADMM algorithm to solve the fusion model and output the fusion energy field.

[0015] The present invention also discloses a multi-spectral energy fusion system for underground shallow vibration fields based on low-rank tensors. The system executes the above-mentioned method and is characterized in that it includes: a signal acquisition module: used to deploy a sensor array and obtain explosion vibration signals; a signal decomposition module: using the VMD method to decompose the signal and extract frequency components; a single spectrum reconstruction module: executing the WTV-GSR algorithm to reconstruct a sparse single-frequency energy field; a multi-spectral fusion module: fusing multi-spectral energy fields based on a low-rank tensor approximation model and outputting the fusion results.

[0016] The present invention also discloses an application of the above method in evaluating the damage effectiveness of underground weapons, which is characterized in that the damage degree of the explosion to the underground structure is analyzed by fusing the energy field.

[0017] Beneficial effects

[0018] 1. In the reconstruction stage of the single spectrum sparse energy field, the present invention adopts the WTVGSR combined optimization strategy to reconstruct the energy field of the shock wave signal, which can effectively overcome the problem of low energy field reconstruction accuracy caused by data sparsity.

[0019] 2. This method can stably reconstruct a continuous and physically consistent single-spectrum energy field distribution when the observation data is incomplete, providing a reliable input basis for subsequent multi-spectrum fusion.

[0020] 3. The adopted low-rank tensor fusion framework has wide applicability and can effectively adapt to energy fusion tasks under different frequency combinations, excitation source locations and geological structure environments.

[0021] 4. By introducing the ADMM optimization framework and combining it with linearization and adaptive penalty mechanisms, the convergence speed and stability of the optimization process under multi-constraint coupling conditions are significantly improved.

[0022] 5. In the process of fusing data from different modal energy fields, this method shows strong robustness and controllability, avoiding the risk of falling into local optimality. It also has strong interpretability and adjustability, and can be flexibly adjusted according to different needs, ensuring high real-time and practicality in complex environments.

[0023] 6. Compared with traditional fusion methods, the present invention can provide more accurate and stable underground energy field reconstruction results under challenges such as data sparsity, noise interference and anisotropy. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is the energy field multi-spectrum fusion step;

[0025] Figure 2This is a schematic diagram of the layout of detectors and explosion points. DETAILED DESCRIPTION

[0026] This paper proposes a multi-spectral energy fusion method for shallow underground vibration fields based on low-rank tensors. This method aims to leverage the advantages of low-rank tensor approximation to efficiently fuse multi-spectral energy field data from shallow underground layers and reconstruct accurate energy field images. The key technologies of this method include the following aspects:

[0027] S1. Obtain explosion vibration signal;

[0028] Select a point on the surface as the coordinate origin, select the east-west direction as the x-axis, the north-south direction as the z-axis, and the direction perpendicular to the x-axis and z-axis as the y-axis. Use measuring tools such as a laser rangefinder and a tape measure to calibrate and measure the size of the area to be measured, set the area to m×n meters, and the grid size to 1*1 meter. Then, lay out sensors at equal intervals in the area, with a spacing of d meters between sensors to ensure that the ray coverage rate reaches 60%. Check all sensors to ensure that they are working properly. After the layout is completed, select the source location and lay out the sensor array. After all equipment is connected, excite the source and observe the quality of the received signal to ensure that the sensor signal is received normally.

[0029] For example, see Figure 2 As shown in the figure, use the tool to mark and measure the area to be tested, which is 20 meters long and 20 meters wide. Test the sensors to ensure that they are working properly. Then, lay out the sensor array, as shown in the figure. Figure 2 As shown in the figure, the earthquake source coordinates were set at (10, 10, 26). Seismic signals were measured at (9, 9, 19) to verify the accuracy of the reconstruction results. All equipment was connected and an explosion test was performed. The received signals were observed to ensure proper sensor reception. Thirty-six sensors were evenly spaced across a 20m x 20m area on the surface, with 4m between sensors.

[0030] S2, signal decomposition;

[0031] The present invention adopts the variational mode decomposition (VMD) method to extract the frequency components of the signal collected by the sensor. The complex signal is decomposed into multiple intrinsic mode functions (IMFs) with different frequency bands, and each frequency component is extracted from them. To ensure the decomposition accuracy, the VMD threshold in the present invention is 0.8 of the peak value and the number of layers is 6 to decompose the signal. After the decomposition is completed, the Fourier transform is performed on each IMF component and its spectral energy is calculated. We select the dominant component with energy accounting for more than 80% of the total energy for analysis, and its corresponding center frequency is defined as the main frequency of the signal. This frequency component can effectively reflect the main characteristics of the original signal, which is helpful for subsequent energy attenuation analysis and target recognition tasks.

[0032] S3, calculate the sparse single-frequency energy field using the WTVGSR algorithm;

[0033] S3.1. Constructing a tomographic model

[0034] In complex shallow underground media, P-wave propagation does not follow a straight path, which poses a challenge to the construction of the tomographic kernel function. At the same time, due to the large explosion power and wide impact area, the limited number of test sensors makes the measured data extremely sparse. Accurately constructing the tomographic kernel function can ensure that the dispersion information in the energy ratio eigenvector is more consistent with the dispersion characteristics during the actual propagation process, thereby improving the accuracy of the reconstruction. According to the Futterman absorption attenuation model, viscoelastic media have an absorption and attenuation effect on the propagation of shock waves, and an attenuation tomographic model is constructed:

[0035] Lq=K′ (1)

[0036] Where, L=(l ij ) (M-1)×N It is called the attenuation tomography kernel function matrix, q=(q j ) N×1 is the decay eigenvector, K'=(k i ) (M-1)×1 is the energy ratio eigenvector, M is the total number of detectors, N is the number of grids, i is the serial number of the propagation ray, j is the serial number of the grid, l ij is the distance of the i-th propagation ray passing through the j-th grid, i is the detector number, k i is the slope of the fitted straight line of the log spectrum ratio of the ith detector to the reference signal within the effective frequency range, q j is the quality factor q value of the j-th grid.

[0037] S3.2. Solving the tomographic model using a weighted variational algorithm based on group sparsity regularization First, the viscoelastic wave equation is used to obtain the initial value q′ of the attenuation tomographic matrix iteration; then the iterative initial value q′ is substituted into the weighted variational algorithm (WTV) to iteratively solve Lq = K', obtaining a noisy estimate. The tomographic kernel function matrix Lq=K' is a large underdetermined system of equations. It is difficult for the equations to converge to an exact solution in the high-dimensional vector space. A feasible solution is obtained by adding constraints to the equations.

[0038] The WTV regularization term is used to enhance the ability to preserve the edges of the structure in the reconstructed image while suppressing noise in the smooth area. The weight coefficient of the WTV regularization term is no longer a fixed hyperparameter, but a learnable parameter related to the data space structure. The corresponding objective function model is:

[0039]

[0040] Among them, G WTV(q) is the weighted total variation regularization term formula as follows:

[0041]

[0042] Where ▽ represents the differential operator; i is the serial number of the propagation ray; ω i The weight coefficient varies with space, with the weight decreasing at the edge of the image and increasing in the flat area, thereby achieving coordinated regulation of edge protection and denoising in smooth areas. The formula is as follows:

[0043]

[0044] ε is a regularization parameter used to prevent the denominator from being 0. In this invention, it is set to 10. -6 .

[0045] In order to efficiently solve the above non-smooth objective function, this paper adopts the alternating direction multiplier method (ADM M). This method introduces auxiliary variables by variable splitting. Convert the original problem into an equivalent constrained optimization form:

[0046]

[0047] λ is the regularization coefficient, and its value range is [0,1]. After constructing the corresponding Lagrange multiplier function, the ADMM algorithm updates the variables alternately through the following three sub-problems:

[0048]

[0049] Among them, ρ is the penalty parameter, which is generally set in the range of [0.1, 10]. In the experiment, ρ = 1 works better. Through the above iterative method, we can gradually converge to the sparse solution under total variation regularization and obtain the attenuation feature vector with high fidelity and low artifacts. Provides accurate initial estimates for subsequent group sparse modeling.

[0050] Will As the initial value, use the group sparse method to reduce The artifact is obtained by removing the result q. The sparse representation model constructed to solve q is:

[0051]

[0052] Where λ is the regularization parameter, and its value range is [0, 1]. G is the group sparsity coefficient, D G To achieve an adaptive dictionary, the present invention uses the KSVD algorithm to train the seismic wave dictionary. Since Equation (6) is a combinatorial optimization problem and cannot be solved directly, an iterative soft threshold algorithm is used to iteratively optimize Equation (6) to obtain the attenuation feature vector q. The iterative process is as follows:

[0053]

[0054] Wherein, c is a constant, which is 1 in the present invention; t is the number of iterations, and the iterative process is terminated after the convergence condition is met or the maximum number of iterations is reached.

[0055] S3.3. Rebuilding the Energy Field

[0056] In the process of underground vibration wave propagation, in addition to considering the attenuation caused by the incomplete elasticity of the dielectric material, the geometric attenuation caused by the increase of the wavefront during the propagation process should also be considered to establish an energy field reconstruction calculation model. Among them A j represents the signal amplitude spectrum of the jth grid, j = 1, 2, ..., N, t j and Q j Represent the travel time and Q value in the jth grid, and introduce the geometric damping x -n , n = -1. The single spectrum energy field is reconstructed by combining absorption attenuation and geometric attenuation.

[0057] S4, fusion of multi-spectral energy fields based on low-rank tensor approximation method;

[0058] S4.1. Single spectrum energy field data tensor expansion of shallow underground energy field;

[0059] The single spectrum data of the shallow underground energy field to be fused is modeled in the form of a tensor. As an extension of high-dimensional data, tensors can simultaneously represent multi-dimensional data features, which is convenient for describing information of different frequency bands and different spatial positions. In the present invention, the low-frequency energy field and the high-frequency energy field are respectively constructed as third-order tensor representations, and the low-frequency energy field D and the high-frequency energy field G are respectively represented as D∈R m′×n′×d and G∈R m×n×d′ , where m′ and n′ are the spatial dimensions of the low-frequency energy field, d is the frequency dimension of the low-frequency energy field, m and n are the spatial dimensions of the high-frequency energy field, and d′ is the frequency dimension of the high-frequency energy field.

[0060] S4.2. Constructing an energy field multispectral imaging model;

[0061] The present invention further constructs a fusion observation model between low-frequency and high-frequency energy fields. Assuming that the fusion target is the high-resolution energy field tensor X, it is subjected to spatial downsampling and spectral downsampling to obtain two degraded observation tensors, the low-frequency observation tensor y D and the high-frequency observation tensor y G Assume two single spectrum energy field diagrams, and express the single spectrum energy field with lower frequency as D∈R m ′×n′×d , the single spectrum energy field with higher frequency is represented by G∈R m×n×d′, the fused image is represented as X∈R m×n×d , the three dimensions involved are the width, height and depth of the image.

[0062] The low-frequency energy field D can be regarded as generated by spatial degradation of the fusion result graph X. In order to simulate this degradation process, the present invention adopts a point spread function combined with downsampling method.

[0063] First, a point spread kernel is used to blur the fused image to simulate the spatial blurring effect caused by the imaging system. The point spread kernel B performs a convolution operation on each depth channel to simulate the spatial blurring process of the imaging system:

[0064] D blur (:,:,e)=D(:,:,e)*B for e=1,2,...d (9)

[0065] Among them, * represents a two-dimensional convolution operation, D blur is the blurred image.

[0066] Next, the blurred image is passed through the downsampling operator P s Perform spatial downsampling to obtain a low-resolution image D∈R m′×n′×d :

[0067] D=P s (D blur ) (10)

[0068] Among them, P s Represents the spatial downsampling operator using bilinear interpolation, s represents the spatial downsampling factor, which is 2 in this invention. The weighted average of the 2×2 neighborhood pixels corresponding to each target low-resolution position in the original image is performed. At the same time, in order to unify the dimension to achieve image fusion, this paper uses bilinear interpolation to upsample the low-resolution image to a high-resolution size, aligning it with the original image in the spatial dimension, thereby effectively fusing multi-source image information at the same spatial scale.

[0069] The high-frequency energy field is generated by spectrally degrading the fused image, which is downsampled by the spectral response function (SRF) to obtain an observation image with fewer frequency channels.

[0070] The fusion problem is modeled as the following mathematical problem. The tensor nuclear norm is introduced as a regularization term to control the rank value of each dimension and construct the optimization objective:

[0071]

[0072] Among them, ||χ (k) || * is the nuclear norm of the tensor expansion matrix in the kth mode, λ is the regularization weight, αk Control the low-rank strength of each dimension, P λ is the spectral degradation operator, S∈R D′×D is the spectral degradation matrix, which is spanned by the spectral response function. The value range of k is 1, 2, and 3 (three dimensions). Images with different structural characteristics have different parameter configurations.

[0073] S4.3, solution of multi-spectral energy field fusion model;

[0074] Due to the coupling relationship between the rank constraints of tensors on different modules, the above optimization problem is difficult to solve directly. The present invention uses the ADMM algorithm to solve the fusion model. k∈{1,2,3}, for χ (k) Introduce auxiliary variable M k =χ (k) , the fusion model is rewritten as:

[0075]

[0076] (1) Establishing the augmented Lagrangian function

[0077] Introducing the Lagrange multiplier Λ k and penalty factor μ k , construct the augmented Lagrangian function, where i is the index of the modular expansion direction:

[0078]

[0079] (2) Linearized adaptive penalty alternating direction method iterative solution

[0080] The above formula is a differentiable convex function. By taking the partial derivatives of each variable in the above formula, we can find the values ​​of each variable that makes the function take the minimum value. The linearized adaptive penalty alternating direction method is introduced to solve this problem. The iterative process is as follows:

[0081] 1) Update M k , fix other variables, extract the k The closed-form solution of the nuclear norm minimization is performed using the singular value threshold decomposition (SVT):

[0082]

[0083] 2) Update X (k) This problem is a weighted least squares problem with multiple tensor regularizations, and a closed-form solution cannot be directly obtained. The present invention adopts a tensor-based gradient descent method for numerical solution, constructing the objective function gradient and repeatedly iteratively updating X until convergence.

[0084] 3) Update the Lagrange multiplier Λ k

[0085] Λk =Λ k +μ k (χ (k) -M k )

[0086] Repeat the above updating process until (χ k -χ k+1 ) / χ k <1×10 -5 The iteration stops when the convergence is achieved, and the converged one is output as the fusion energy field, which is then reconstructed into a three-dimensional energy distribution map through inverse tensorization operation.

[0087] The present invention first extracts the dominant frequency signal features based on variational mode decomposition (VMD), then constructs a spectral attenuation tomography model. Based on this, the weighted variational method (WTV) is used to obtain an initial estimate. Group sparsity regularization (GSR) is then used to eliminate artifacts and suppress noise interference, achieving a precise inversion of the attenuation eigenvector. By accounting for multiple physical factors such as propagation path, spectral attenuation, and geometric damping, this method can stably reconstruct a continuous and physically consistent single-spectrum energy field distribution even when observation data is incomplete, providing a reliable input foundation for subsequent multi-spectral fusion.

[0088] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions merely illustrate the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A multi-spectral energy fusion method for shallow underground vibration fields based on low-rank tensors, characterized by: S1. Select a point on the ground as the coordinate origin, with the east-west direction as the x-axis, the north-south direction as the z-axis, and the direction perpendicular to the x- and z-axes as the y-axis. Deploy the sensor array and acquire the explosion vibration signal. S2. Decompose the sensor signal using the variational mode decomposition (VMD) method to extract the frequency components of multiple intrinsic mode functions (IMFs). S3. Use the WTV-GSR algorithm to construct an attenuation tomography model and reconstruct a sparse single-frequency energy field; S4. Fusion of multi-spectral energy fields based on low-rank tensor approximation method, including: S4.1 Model the single spectrum energy field data into a tensor form; S4.2 Constructing an energy field multispectral imaging model; S4.3 uses the ADMM algorithm to solve the fusion model and output the fusion energy field.

2. The multi-spectral energy fusion method for shallow underground vibration fields based on low-rank tensors according to claim 1 is characterized by: The step S1 includes the following contents: measuring the size of the area to be measured and arranging sensors at equal intervals to ensure that the ray coverage rate is ≥60%; setting the source position and exciting the source to receive the explosion vibration signal.

3. The multi-spectral energy fusion method for shallow underground vibration fields based on low-rank tensors according to claim 1 is characterized by: The step S3 includes the following contents: S3.

1. According to the Futterman absorption-reduction model, viscoelastic media absorb and attenuate vibration waves. An attenuation tomography model is constructed: Lq=K' (1) Where, L=(l ij ) (M-1)×N It is called the attenuation tomography kernel function matrix, q=(q j ) N×1 is the decay eigenvector, K'=(k i ) (M-1)×1 is the energy ratio eigenvector; M is the total number of detectors, N is the number of grids, i is the serial number of the propagation ray, j is the serial number of the grid, l ij is the distance of the i-th propagation ray passing through the j-th grid, i is the detector number, k i is the slope of the fitted straight line of the log spectrum ratio of the ith detector to the reference signal within the effective frequency range, q j is the quality factor q value of the j-th grid. S3.

2. Use the viscoelastic wave equation to determine the initial value of the attenuation tomography matrix. Use the weighted variational algorithm (WTV) to iteratively solve the noisy estimation result. Then, combine it with group sparsity regularization to eliminate artifacts and obtain the attenuation eigenvector q. S3.

3. Establishment of energy field reconstruction calculation model: Among them: A j represents the signal amplitude spectrum of the jth grid, j = 1, 2, ..., N, t j and Q j Represent the travel time and Q value in the jth grid, and introduce the geometric damping x -n ,n=-1.

4. The method for multi-spectral energy fusion of shallow underground vibration fields based on low-rank tensors according to claim 3 is characterized by: The step S3.2 includes the following contents: First, the viscoelastic wave equation is used to obtain the initial value q′ of the attenuation tomography matrix iteration; then the iterative initial value q′ is substituted into the weighted variational algorithm WTV to iteratively solve Lq = K', and a noisy estimation result is obtained. Finally, As the initial value, use the group sparse method to reduce The artifact is obtained, and the result q is obtained; the sparse representation model constructed to solve q is: Among them, λ is the regularization parameter, α G is the group sparsity coefficient, D G is an adaptive dictionary, G is a sparse overlapping group. Since Equation (2) is a combinatorial optimization problem and cannot be solved directly, the IST algorithm is used to iteratively optimize Equation (2) to obtain the attenuated feature vector q.

5. A multi-spectral energy fusion system for shallow underground vibration fields based on low-rank tensors, which executes the method of claim 1, characterized in that: include: Signal acquisition module: used to deploy sensor arrays and acquire explosion vibration signals; Signal decomposition module: uses VMD method to decompose the signal and extract frequency components; Single spectrum reconstruction module: executes the WTV-GSR algorithm to reconstruct the sparse single-frequency energy field; multi-spectrum fusion module: fuses the multi-spectrum energy field based on the low-rank tensor approximation model and outputs the fusion result.

6. A non-volatile storage medium, characterized in that: The non-volatile storage medium includes a stored program, wherein when the program is executed, the device where the non-volatile storage medium is located is controlled to execute the method according to any one of claims 1 to 4.

7. A terminal device, characterized in that: The terminal device includes: a processor, a memory, a communication interface and a bus; the processor, the memory and the communication interface are connected through the bus and communicate with each other; the memory stores executable program code; the processor runs a program corresponding to the executable program code by reading the executable program code stored in the memory, so as to execute the method as described in any one of claims 1 to 4 above.

8. Application of the method according to any one of claims 1 to 4 in evaluating the damage effectiveness of underground weapons, characterized in that: The extent of damage caused by the explosion to underground structures is analyzed by fusion energy fields.

Images