Weak magnetic signal processing method and system for buried target based on symplectic geometry modal decomposition

Abstract

This invention relates to the field of magnetic anomaly detection technology. It discloses a method and system for processing weak magnetic signals of buried targets based on symplectic geometric mode decomposition. The method includes: a trajectory matrix acquisition step: constructing a trajectory matrix of the original buried target weak magnetic signal based on the original buried target weak magnetic signal; a symplectic geometric matrix acquisition step: obtaining the eigenvalues ​​of the trajectory matrix based on symplectic geometric similarity transformation, and reconstructing eigenvectors based on the trajectory matrix features to obtain the symplectic geometric matrix; an initial symplectic geometric component acquisition step: obtaining the initial symplectic geometric components based on the symplectic geometric matrix using a diagonal averaging algorithm; and a complete buried target weak magnetic signal acquisition step: recombining the initial symplectic geometric components using cosine similarity and information entropy to obtain the complete buried target weak magnetic signal. This invention obtains a complete weak magnetic anomaly signal by calculating the cosine similarity of the signal component with other components, recombining the component signals, calculating the information entropy of the recombined signal components, and comparing it with the components recombined in the previous round as a termination condition. The recombination process does not require subjectively defined parameters, thus improving the accuracy of detection.

Description

Technical Field

[0001] This invention relates to the field of magnetic anomaly detection technology, and more specifically, to a method and system for processing weak magnetic signals of buried targets based on symplectic geometric mode decomposition. Background Technology

[0002] Magnetic anomaly detection identifies ferromagnetic targets by revealing anomalies in the environmental magnetic field. It is a passive target detection method widely used in fields such as aircraft submarine detection, marine monitoring, underground and underwater ferromagnetic object detection, and geological exploration, and can obtain rich magnetic information about the target. However, with increasing distance and interference from environmental noise, the energy of the magnetic anomaly signal decreases sharply, leading to a significant decline in the detection capability of the magnetic detection system and a corresponding increase in its false alarm rate and missed detection rate. Therefore, weak magnetic anomaly signal processing has become an important research area in weak magnetic detection. Currently, the main limitations of magnetic anomaly signal processing methods include:

[0003] 1. Filtering methods: The design of filters may cause signal distortion or fail to effectively filter out noise. Low-pass filtering can cause signal phase changes and signal delays, affecting the accuracy of judging magnetic anomaly signals.

[0004] 2. Wavelet transform, similar to the window-adjustable Fourier transform method, suffers from mode aliasing. When decomposing a signal, it selects the wavelet basis and the number of decomposition levels based on prior information, resulting in poor adaptability.

[0005] 3. Empirical mode decomposition methods, while extracting modal components, also introduce cumulative errors, resulting in poor noise robustness and mode aliasing issues;

[0006] 4. The ensemble empirical mode decomposition method has empirically set variables, poor adaptability, cannot completely neutralize added white noise for single components, and has a large computational load.

[0007] Therefore, in view of the shortcomings of the above-mentioned classical signal processing methods in magnetic anomaly detection, it is urgent to develop a buried target weak magnetic signal processing method and system based on symplectic geometric mode decomposition to overcome the above-mentioned shortcomings. Summary of the Invention

[0008] To address the above problems, this invention provides a method for processing weak magnetic signals of buried targets based on symplectic geometric mode decomposition, comprising:

[0009] Trajectory matrix acquisition steps: Construct the trajectory matrix of the original buried target weak magnetic signal based on the original buried target weak magnetic signal;

[0010] Steps for obtaining the symplectic geometric matrix: Obtain the trajectory matrix eigenvalues ​​based on the symplectic geometric similarity transformation, and reconstruct the eigenvectors based on the trajectory matrix eigenvalues ​​to obtain the symplectic geometric matrix;

[0011] The initial symplectic geometric components are obtained by using a diagonal averaging algorithm based on the symplectic geometric matrix.

[0012] Steps for obtaining the complete buried target weak magnetic signal: The initial symplectic geometric components are recombined using cosine similarity and information entropy to obtain the complete buried target weak magnetic signal.

[0013] The above-mentioned method for processing weak magnetic signals of buried targets, wherein the trajectory matrix acquisition step includes:

[0014] Obtain the one-dimensional time series x = x1, x2, ..., x of the original buried target weak magnetic signal. n Where n is the signal length of the original buried target weak magnetic signal;

[0015] Using Takens' embedding theorem, the trajectory matrix X is obtained by reconstructing the phase space of the one-dimensional time series x:

[0016] d represents the embedding dimension, τ represents the delay time, and m = n - (d - 1);

[0017] Calculate the power spectral density of the one-dimensional time series x, and determine the embedding dimension d of the trajectory matrix X based on the power spectral density.

[0018] The above-mentioned method for processing weak magnetic signals of buried targets, wherein the step of determining the embedding dimension of the trajectory matrix X based on the power spectral density includes:

[0019] The frequency at which the one-dimensional time series x reaches its maximum peak value is obtained based on the power spectral density.

[0020] The frequency ratio is obtained by comparing the frequency at which the maximum peak value is obtained with the sampling frequency.

[0021] When the frequency ratio is less than a threshold, the embedding dimension is set to d = n / 3; when the frequency ratio is greater than or equal to the threshold, the embedding dimension is set to d = 1.2 × frequency ratio, and τ is 1.

[0022] The above-mentioned method for processing weak magnetic signals of buried targets, wherein the step of obtaining the symplectic geometric matrix includes:

[0023] Construct the covariance matrix Where A = X T X, where X is the trajectory matrix;

[0024] The Hamiltonian matrix W is obtained from the covariance matrix, where W = M. 2 ;

[0025] Based on the Hamiltonian matrix W, an orthogonal symplectic geometric matrix G is constructed through a symplectic geometric similarity transformation;

[0026] The eigenvector matrix Q is obtained by decomposing the orthogonal symplectic geometric matrix G using QR decomposition.

[0027] Construct a coefficient matrix S using the eigenvector matrix Q and the trajectory matrix X;

[0028] The initial single-component reconstruction matrix Z is obtained through the coefficient matrix S and the eigenvector matrix Q. i ;

[0029] The initial single-component reconstruction matrix Z is obtained through... i Obtain the symplectic geometric matrix Z.

[0030] The above-mentioned method for processing weak magnetic signals of buried targets, wherein the initial symplectic geometric component acquisition step includes:

[0031] The initial single component of the symplectic geometric matrix Z is reconstructed using a diagonal averaging algorithm. i Perform the transformation to obtain d sets of one-dimensional time series Y i ;

[0032] The one-dimensional time series Y described in group d i Obtain the initial symplectic geometric components of group d;

[0033] The initial symplectic geometric component matrix is ​​obtained based on the initial symplectic geometric components described in group d.

[0034] The above-mentioned method for processing the weak magnetic field signal of a buried target, wherein the step of acquiring the complete weak magnetic field signal of the buried target includes:

[0035] Cosine similarity recombination step: After constructing a class set based on the initial symplectic geometric component matrix, cosine similarity recombination is performed on each class based on the cosine similarity between each class in the class set;

[0036] Information entropy comparison terminates the recombination step: Calculate the information entropy of each class before and after recombination. When the information entropy of the recombined class is greater than the information entropy of the class before recombination, terminate the cosine similarity recombination step and take the class before recombination as the complete buried target weak magnetic signal.

[0037] The aforementioned method for processing weak magnetic signals from buried targets, wherein the cosine similarity reconstruction step includes:

[0038] The initial symplectic geometric component matrix is ​​constructed into a class set T, T = t1, t2, ..., t d , where t is the class;

[0039] Cosine similarity is calculated for class t1 and the remaining (d-1) classes respectively to obtain the cosine similarity.

[0040] Select the two classes with the highest cosine similarity to form a new class. and the new class Add it to the class set T and replace class t1.

[0041] The aforementioned method for processing weak magnetic signals from buried targets, wherein the information entropy comparison and termination of recombination step includes:

[0042] Compute class t1 and the new class Information entropy;

[0043] When new class If the information entropy of class t1 is less than the information entropy of class t1, then return to execute the cosine similarity recombination step;

[0044] When new class When the information entropy of class t1 is greater than or equal to the information entropy of class t1, the cosine similarity recombination step is terminated, and class t1 is output as the complete buried target weak magnetic signal.

[0045] The present invention also provides a buried target magnetic field weakening signal processing system based on symplectic geometric mode decomposition, wherein the buried target magnetic field weakening signal processing method described in any one of the above-mentioned methods is applied, and the buried target magnetic field weakening signal processing system includes:

[0046] The trajectory matrix acquisition unit constructs the trajectory matrix of the original buried target weak magnetic signal based on the original buried target weak magnetic signal;

[0047] The symplectic geometric matrix acquisition unit obtains the trajectory matrix eigenvalues ​​of the trajectory matrix based on the symplectic geometric similarity transformation, and reconstructs the eigenvectors based on the trajectory matrix eigenvalues ​​to obtain the symplectic geometric matrix.

[0048] The initial symplectic geometric component acquisition unit obtains the initial symplectic geometric components based on the symplectic geometric matrix through a diagonal averaging algorithm.

[0049] The complete buried target weak magnetic signal acquisition unit recombines the initial symplectic geometric components using cosine similarity and information entropy to obtain the complete buried target weak magnetic signal.

[0050] The aforementioned buried target weak magnetic signal processing system, wherein the initial symplectic geometric component acquisition unit includes:

[0051] The cosine similarity recombination module constructs a class set based on the initial symplectic geometric component matrix, and then performs cosine similarity recombination on each class based on the cosine similarity between each class in the class set.

[0052] The information entropy comparison termination module calculates the information entropy of each class before and after recombination. When the information entropy of the recombined class is greater than the information entropy of the class before recombination, the cosine similarity recombination step is terminated, and the class before recombination is taken as the complete buried target weak magnetic signal.

[0053] The advantages of this invention compared to existing technologies are as follows: This invention reconstructs weak magnetic anomaly signals based on an improved symplectic geometric mode decomposition (SMD) method using cosine similarity and information entropy. Traditional SMD methods obtain initial SMD components that are a forced decomposition of the original signal. These initial SMD components contain noise and target signal components. Reconstruction of the target signal components is a crucial aspect of traditional SMD. Introducing too much noise during reconstruction results in reconstructed components carrying a large amount of noise information, reducing the quality of the target signal. This invention, however, calculates the cosine similarity between the signal components and other components, analyzes the correlation between signal components, and reconstructs the component signals. It then calculates the information entropy of the reconstructed signal components and compares it with the previous round of reconstructed components as a termination condition, obtaining a complete weak magnetic anomaly signal. The reconstruction process does not require subjectively defined parameters, thus improving detection accuracy.

[0054] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures pointed out in the description and the drawings. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a flowchart of the buried target weak magnetic signal processing method of the present invention;

[0057] Figure 2 for Figure 1 The step-by-step flowchart of step S1;

[0058] Figure 3 for Figure 1 Flowchart of step S2;

[0059] Figure 4 for Figure 1 The step-by-step flowchart of step S3;

[0060] Figure 5 for Figure 1 Flowchart of step S4 in the middle section;

[0061] Figure 6 This is the application flowchart for step S4;

[0062] Figure 7 This is a schematic diagram of the buried target weak magnetic signal processing system of the present invention;

[0063] Figure 8 A comparative diagram of technical approaches for processing weak magnetic anomaly signals of buried targets. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] The illustrative embodiments and descriptions of the present invention are used to explain the invention, but are not intended to limit the invention. Furthermore, elements / components using the same or similar reference numerals in the drawings and embodiments are used to represent the same or similar parts.

[0066] The terms "first," "second," "S1," "S2," etc., used in this document do not specifically refer to any order or sequence, nor are they intended to limit the invention. They are merely used to distinguish elements or operations described using the same technical terms.

[0067] The directional terms used in this article, such as up, down, left, right, front, or back, are for reference only when referring to the accompanying drawings. Therefore, the use of directional terms is for illustrative purposes and not to limit this work.

[0068] The terms “include,” “including,” “have,” “contain,” etc., used in this article are all open-ended terms, meaning that they include but are not limited to.

[0069] The term "and / or" as used herein includes any or all of the things mentioned.

[0070] The term "multiple" in this article includes "two" and "more than two"; the term "multiple groups" in this article includes "two groups" and "more than two groups".

[0071] Certain terms used to describe this application will be discussed below or elsewhere in this specification to provide additional guidance to those skilled in the art in describing the application.

[0072] Please see Figure 1 , Figure 1 This is a flowchart of the buried target weak magnetic signal processing method of the present invention. Figure 1 As shown, a method for processing weak magnetic field signals of buried targets according to the present invention includes:

[0073] Trajectory matrix acquisition step S1: Construct the trajectory matrix of the original buried target weak magnetic signal based on the original buried target weak magnetic signal;

[0074] Step S2 for obtaining the symplectic geometric matrix: Obtain the trajectory matrix eigenvalues ​​of the trajectory matrix based on the symplectic geometric similarity transformation, and reconstruct the eigenvectors based on the trajectory matrix eigenvalues ​​to obtain the symplectic geometric matrix;

[0075] Step S3 for obtaining initial symplectic geometric components: Obtain initial symplectic geometric components based on the symplectic geometric matrix using a diagonal averaging algorithm;

[0076] Step S4: Obtain the complete buried target weak magnetic signal by recombining the initial symplectic geometric components through cosine similarity and information entropy.

[0077] Based on this, the present invention employs a symplectic geometric spectral analysis algorithm to effectively suppress environmental noise and extract target weak magnetic signals under low signal-to-noise ratio conditions. Specifically, firstly, a trajectory matrix is ​​constructed using the weak magnetic signal; then, the eigenvalues ​​of the trajectory matrix are obtained based on the symplectic geometric similarity transformation; and finally, the initial symplectic geometric matrix is ​​obtained by reconstructing the eigenvectors. Next, the corresponding initial symplectic geometric components are obtained through diagonal averaging. Finally, by combining cosine similarity and information entropy, the components are recombined to obtain the symplectic geometric components, thereby achieving the decomposition and reconstruction of the weak magnetic signal, suppressing background noise, and extracting the weak magnetic anomaly signal.

[0078] Please refer to Figure 2 , Figure 2 for Figure 1 The flowchart of step S1 is shown below. Figure 2 As shown, the trajectory matrix acquisition step S1 includes:

[0079] S11: Obtain the one-dimensional time series x = x1, x2, ..., x of the original buried target weak magnetic signal. n Where n is the signal length of the original buried target weak magnetic signal;

[0080] S12: Using Takens' embedding theorem, the one-dimensional time series x is reconstructed in phase space to obtain the trajectory matrix X:

[0081] d represents the embedding dimension, τ represents the delay time, and m = n - (d - 1);

[0082] S13: Calculate the power spectral density of the one-dimensional time series x, and determine the embedding dimension d of the trajectory matrix X based on the power spectral density.

[0083] The step of determining the embedding dimension of the trajectory matrix X based on the power spectral density includes:

[0084] The frequency at which the one-dimensional time series x reaches its maximum peak value is obtained based on the power spectral density.

[0085] The frequency ratio is obtained by comparing the frequency at which the maximum peak value is obtained with the sampling frequency.

[0086] When the frequency ratio is less than a threshold, the embedding dimension is set to d = n / 3; when the frequency ratio is greater than or equal to the threshold, the embedding dimension is set to d = 1.2 × frequency ratio, and τ is 1.

[0087] Specifically, the original weak magnetic signal of the buried target is a one-dimensional time series x = x1, x2, ..., x n Let n be the signal length. Using Takens' embedding theorem, it is found that a multidimensional time series matrix, i.e., a trajectory matrix, can be constructed from a one-dimensional time series using topological equivalence methods. Therefore, phase space reconstruction of the time series yields the trajectory matrix X:

[0088]

[0089] In equation (1), d represents the embedding dimension, τ represents the delay time, and m = n - (d - 1). In the trajectory matrix X, the dimension d is obtained based on the signal's PSD. The PSD of the original signal x is calculated, and the frequency f at the maximum peak value is found. maz Let frequency f max With sampling frequency F s Calculate the ratio; when the ratio is less than the set value of 10... -3 If so, then the embedding dimension d = n / 3; otherwise, d = 1.2 × (F s / f max ), τ is 1.

[0090] Please refer to Figure 3 , Figure 3 for Figure 1 The step-by-step flowchart for step S2. (See attached flowchart.) Figure 3 As shown, the steps for obtaining the symplectic geometric matrix include:

[0091] S21: Construct the covariance matrix Where A = X T X, where X is the trajectory matrix;

[0092] S22: Obtain the Hamiltonian matrix W, W = M, based on the covariance matrix. 2 ;

[0093] S23: Construct an orthogonal symplectic geometric matrix G based on the Hamilton matrix W through a symplectic geometric similarity transformation;

[0094] S24: Obtain the eigenvector matrix Q by decomposing the orthogonal symplectic geometric matrix G through QR decomposition;

[0095] S25: Construct the coefficient matrix S using the eigenvector matrix Q and the trajectory matrix X;

[0096] S26: Obtain the initial single-component reconstruction matrix Z using the coefficient matrix S and the eigenvector matrix Q. i ;

[0097] S27: Reconstruct matrix Z using the initial single component i Obtain the symplectic geometric matrix Z.

[0098] The reconstructed matrix can be used to construct the covariance matrix. Where A = X T X. According to the definition of symplectic geometry, the covariance matrix M is insufficient to obtain the symplectic geometric matrix. Therefore, another Hamiltonian matrix W = M is obtained. 2 Construct the orthogonal symplectic geometric matrix G:

[0099]

[0100] In equation (2), matrices G and B are a symplectic orthogonal matrix and an upper triangular matrix, respectively. However, equation (2) contains two unknown matrices (G and B). In this case, matrix G needs to be obtained through a symplectic geometric similarity transformation. Set a Householder matrix Q and construct matrix H = [Q 0; 0Q]. It can be proven that Q is also a Householder matrix, so matrix G can be replaced by matrix H.

[0101] At the same time, according to W=M 2 According to the theorem, assuming σ i =√λ i If (i = 1, 2, ..., d) are the eigenvalues ​​of matrix A, then λ1, λ2, ..., λ3 are the eigenvalues ​​of matrix B, and Q i (i = 1, 2, ..., d) is matrix A 2 The eigenvectors corresponding to the eigenvalues ​​are the symplectic geometric similarity transformations. Since the eigenvalues ​​of matrices A and B are correlated, the problem of finding an unknown matrix B can be transformed into a problem of finding an unknown matrix A.

[0102] Through symplectic geometric similarity transformation, matrix Q preserves the essential characteristics of the original signal, and QR decomposition is used to transform matrix A. 2 By decomposing the matrix, we can obtain the eigenvector matrix Q.

[0103] The coefficient matrix S is constructed using the eigenvector matrix Q and the original trajectory matrix X:

[0104]

[0105] The reconstructed matrix Z is obtained using the eigenvector matrix Q and the coefficient matrix S:

[0106] Z i =Q i S i #(4)

[0107] Among them, Z i (i = 1, 2, ..., d) is also called the initial single-component reconstruction matrix. In this case, the reconstruction matrix Z is composed of d sets of initial single-component reconstruction matrices Z. i Composition: Z = Z1 + Z2 + ... + Z d .

[0108] Please refer to Figure 4 , Figure 4 for Figure 1 The step-by-step flowchart for step S3. (See attached flowchart.) Figure 4 As shown, the initial symplectic geometric component acquisition step includes:

[0109] S31: Reconstruct matrix Z from each of the initial single components in the symplectic geometric matrix Z using a diagonal averaging algorithm. i Perform the transformation to obtain d sets of one-dimensional time series Y i ;

[0110] S32: Through the one-dimensional time series Y described in group d i Obtain the initial symplectic geometric components of group d;

[0111] S33: Obtain the initial symplectic geometric component matrix based on the initial symplectic geometric components described in group d.

[0112] Specifically, Z obtained through the symplectic geometric similarity transformation is an m×d reconstruction matrix, which needs to be further converted into a one-dimensional time series. Diagonal averaging, as a commonly used transformation algorithm, has accurate information conversion capabilities. Therefore, diagonal averaging is used to reconstruct the single-component matrix Z. i The transformation is performed using (1≤k≤d) to obtain a one-dimensional initial single-component signal of length n. Ultimately, d one-dimensional initial single-component signals can be obtained, and the sum of all initial single-component signals is the original signal. Assume Z... i The element in is defined as z ij (1≤i≤m, 1≤j≤d). Let d* = min(m, d), m * = max(m, d) and 1 ≤ i ≤ m, 1 ≤ j ≤ d, if m < d, then there is Otherwise Its conversion expression is:

[0113]

[0114] The initial single - component reconstruction matrix Z can be made through formula (5) i Converted into a one - dimensional time series Y i , and the obtained y1, y2,..., y n Are the points of the one - dimensional time series Y i For each initial single - component reconstruction matrix, diagonal averaging can obtain a one - dimensional time series, and then d groups of initial single - component signals Y1, Y2,..., Y d That is, the initial symplectic geometric component matrix. The initial symplectic geometric component matrix Y is obtained, but the single components are not independent of each other and need to be component - recombined.

[0115] Please refer to Figure 5 , Figure 5 Is Figure 1 The sub - step flowchart of step S4 in Figure 5 As shown, the complete buried target weak magnetic signal acquisition step S4 includes:

[0116] Cosine similarity recombination step S41: After constructing a class set based on the initial symplectic geometric component matrix, perform cosine similarity recombination on each class through the cosine similarity between each class in the class set;

[0117] Information entropy comparison termination recombination step S42: Calculate the information entropy of each class before and after recombination. When the information entropy of the class after recombination is greater than the information entropy of the class before recombination, terminate the cosine similarity recombination step and use the class before recombination as the complete buried target weak magnetic signal.

[0118] Among them, the cosine similarity recombination step S42 includes:

[0119] Construct the initial symplectic geometric component matrix into a class set T, T = t1, t2,..., t d , where t is a class; ​​​​​​​​Add it to the class set T and replace class t1.

[0122] The information entropy comparison termination recombination step S43 includes:

[0123] Compute class t1 and the new class Information entropy;

[0124] When new class If the information entropy of class t1 is less than the information entropy of class t1, then return to execute the cosine similarity recombination step;

[0125] When new class When the information entropy of class t1 is greater than or equal to the information entropy of class t1, the cosine similarity recombination step is terminated, and class t1 is output as the complete buried target weak magnetic signal.

[0126] Please refer to Figure 6 , Figure 6 This is the application flowchart for step S4. Specifically, the symplectic geometric similarity transformation process is a forced decomposition of the original signal, resulting in the initial single-component signal Y. i Since they are not independent, it is necessary to reconstruct mutually independent single components by utilizing the essential characteristics of each initial symplectic geometric component, i.e., cosine similarity and information entropy reconstruction algorithms.

[0127] a: Initial symplectic geometric component cosine similarity recombination

[0128] The initial single components are considered to be of different categories (t) i =Y i These constitute the set T (T = t1, t2, ..., t) of the original single component categories. d ). Utilizing the cosine similarity (t) between categories i Reconstruct a single component, and define the cosine similarity of the vectors as:

[0129]

[0130] x and y represent the input vectors, and θ represents the angle between the vectors. The signal to be decomposed contains a large amount of disordered noise. To optimize the reconstruction of the initial single-component signal, the information entropy of the signal is introduced as the termination condition for reconstruction.

[0131] b: Information entropy comparison terminates reorganization

[0132] In information theory, information entropy quantifies the average information content. Its value measures the average uncertainty and complexity of a signal. The Shannon entropy is defined as follows:

[0133]

[0134]

[0135] Where p represents probability, and H(X) represents the magnitude of information entropy. The value of information entropy represents a measure of the uncertainty of a signal, and it can be used to estimate the complexity of the signal; the more uncertain and complex the signal, the greater its entropy value.

[0136] QR decomposition yields several eigenvalues ​​and corresponding symplectic geometric matrices. The main feature information is concentrated in the first few eigenvalues ​​and the symplectic geometric matrix. Therefore, for a class set T, an initial class t1 is selected, and cosine similarity is calculated with the remaining (d-1) classes. Then, the two classes (t1, t2) with the highest cosine similarity are selected. i Combine them into a new class. Replace t1 in the original class set T with Then remove t1 from the original set. This results in a new set. Similarly, after h-th cosine similarity recombination, if If the information entropy increases, then the recombined [structure] is considered to be [recombined]. The introduction of excessive background noise has made it more complex. (Recombined) Compare Noise has higher energy. The class obtained through recombination was... Let SGC be the symplectic geometric component of the magnetic anomaly signal, i.e., the weak magnetic signal of a completely buried target. A reconstruction termination condition was established:

[0137]

[0138] When the recombined components obtained in the i-th recombination Information entropy When the value increases, it indicates that more noise components have been introduced into the reconstructed signal. At this point, reconstruction terminates; otherwise, it continues. The signal x(n) at the termination point is represented as:

[0139]

[0140] Among them, t i (n) is a subset of class T, and The cosine similarity is relatively small, and the SGC after (h-1) recombinations is

[0141] This invention reconstructs magnetic anomaly signals and suppresses noise by utilizing cosine similarity and information entropy, thereby achieving the reconstruction of the initial symplectic geometric components and obtaining a complete magnetic anomaly signal. Please refer to [the relevant documentation / information]. Figure 8 , Figure 8 A comparative diagram of technical approaches for processing weak magnetic anomaly signals of buried targets.

[0142] Please refer to Figure 7 , Figure 7This is a schematic diagram of the buried target weak magnetic signal processing system of the present invention. Figure 7 As shown, the buried target magnetic field weakening signal processing system based on symplectic geometric mode decomposition of the present invention is characterized in that it applies the buried target magnetic field weakening signal processing method described in any one of the above-mentioned methods, and the buried target magnetic field weakening signal processing system includes:

[0143] The trajectory matrix acquisition unit 11 constructs the trajectory matrix of the original buried target weak magnetic signal based on the original buried target weak magnetic signal;

[0144] The symplectic geometric matrix acquisition unit 12 obtains the trajectory matrix eigenvalues ​​of the trajectory matrix based on the symplectic geometric similarity transformation, and reconstructs the eigenvectors based on the trajectory matrix eigenvalues ​​to obtain the symplectic geometric matrix.

[0145] The initial symplectic geometric component acquisition unit 13 obtains the initial symplectic geometric components based on the symplectic geometric matrix through a diagonal averaging algorithm.

[0146] The complete buried target weak magnetic signal acquisition unit 14 recombines the initial symplectic geometric components through cosine similarity and information entropy to obtain the complete buried target weak magnetic signal.

[0147] The initial symplectic geometric component acquisition unit 14 includes:

[0148] The cosine similarity recombination module 141, after constructing a class set based on the initial symplectic geometric component matrix, performs cosine similarity recombination on each class based on the cosine similarity between each class in the class set;

[0149] The information entropy comparison termination recombination module 142 calculates the information entropy of each class before and after recombination. When the information entropy of the recombined class is greater than the information entropy of the class before recombination, the cosine similarity recombination step is terminated, and the class before recombination is taken as the complete buried target weak magnetic signal.

[0150] In summary, this invention analyzes the correlation between signal components by calculating the cosine similarity between the signal component and other components, and reconstructs the component signals. The information entropy of the reconstructed signal component is calculated and compared with the component reconstructed in the previous round as a termination condition, thereby obtaining a complete weak magnetic anomaly signal. The reconstruction process does not require subjectively defined parameters, thus improving the accuracy of detection.

[0151] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A buried target weak magnetic signal processing method based on symplectic geometry modal decomposition, characterized in that, include: Trajectory matrix acquisition steps: Construct the trajectory matrix of the original buried target weak magnetic signal based on the original buried target weak magnetic signal; Steps for obtaining the symplectic geometric matrix: Obtain the trajectory matrix eigenvalues ​​based on the symplectic geometric similarity transformation, and reconstruct the eigenvectors based on the trajectory matrix eigenvalues ​​to obtain the symplectic geometric matrix; The initial symplectic geometric components are obtained by using a diagonal averaging algorithm based on the symplectic geometric matrix. Steps for obtaining the weak magnetic signal of a completely buried target: The initial symplectic geometric components are recombined using cosine similarity and information entropy to obtain the weak magnetic signal of the completely buried target; The step of acquiring the weak magnetic signal of the completely buried target includes: Cosine similarity recombination steps: After constructing a class set based on the initial symplectic geometric component matrix, each class is recombined using the cosine similarity between each class in the class set; Information entropy comparison terminates the recombination step: Calculate the information entropy of each class before and after recombination. When the information entropy of the recombined class is greater than the information entropy of the class before recombination, terminate the cosine similarity recombination step and take the class before recombination as the complete buried target weak magnetic signal. The cosine similarity recombination step includes: The initial symplectic geometric component matrix is ​​constructed into a class set T. , ,…, , where t is the class; Choose class t1 and the remaining Cosine similarity is calculated for each class to obtain the cosine similarity score. Select the two classes with the highest cosine similarity to form a new class. and the new class Add it to the class set T and replace class t1; The information entropy comparison to terminate recombination step includes: Compute class t1 and the new class Information entropy; When new class If the information entropy of class t1 is less than the information entropy of class t1, then return to execute the cosine similarity recombination step; When new class When the information entropy of class t1 is greater than or equal to the information entropy of class t1, the cosine similarity recombination step is terminated, and class t1 is output as the complete buried target weak magnetic signal.

2. The method for processing weak magnetic signals of buried targets as described in claim 1, characterized in that, The trajectory matrix acquisition steps include: Obtain the one-dimensional time series of the original buried target weak magnetic signal. Where n is the signal length of the original buried target weak magnetic signal; Using Takens' embedding theorem, the trajectory matrix X is obtained by reconstructing the phase space of the one-dimensional time series x: d represents the embedding dimension. Represents the delay time, and ; Calculate the power spectral density of the one-dimensional time series x, and determine the embedding dimension d of the trajectory matrix X based on the power spectral density.

3. The method for processing weak magnetic signals of buried targets as described in claim 2, characterized in that, The step of determining the embedding dimension of the trajectory matrix X based on the power spectral density includes: The frequency at which the one-dimensional time series x reaches its maximum peak value is obtained based on the power spectral density. The frequency ratio is obtained by comparing the frequency at which the maximum peak value is obtained with the sampling frequency. When the frequency ratio is less than a threshold, the embedding dimension is set to... When the frequency ratio is greater than or equal to the threshold, the embedding dimension is set to... And τ takes the value 1.

4. The method for processing weak magnetic signals of buried targets as described in claim 3, characterized in that, The steps for obtaining the symplectic geometric matrix include: Constructing the covariance matrix ,in X is the trajectory matrix; The Hamiltonian matrix W is obtained from the covariance matrix. ; Based on the Hamilton matrix W, an orthogonal symplectic geometric matrix G is constructed through a symplectic geometric similarity transformation. The eigenvector matrix Q is obtained by decomposing the orthogonal symplectic geometric matrix G using QR decomposition. Construct a coefficient matrix S using the eigenvector matrix Q and the trajectory matrix X; The initial single-component reconstruction matrix is ​​obtained through the coefficient matrix S and the eigenvector matrix Q. ; The initial single-component reconstruction matrix Obtain the symplectic geometric matrix .

5. The method for processing weak magnetic signals of buried targets as described in claim 4, characterized in that, The initial symplectic geometric component acquisition step includes: The symplectic geometric matrix is ​​processed using a diagonal averaging algorithm. Each of the initial single-component reconstruction matrices in Perform the transformation to obtain d sets of one-dimensional time series. ; The one-dimensional time series described in group d Obtain the initial symplectic geometric components of group d; The initial symplectic geometric component matrix is ​​obtained based on the initial symplectic geometric components described in group d.

6. A buried target weak magnetic field signal processing system based on symplectic geometric mode decomposition, characterized in that, The buried target magnetic field weakening signal processing method according to any one of claims 1-5, wherein the buried target magnetic field weakening signal processing system comprises: The trajectory matrix acquisition unit constructs the trajectory matrix of the original buried target weak magnetic signal based on the original buried target weak magnetic signal; The symplectic geometric matrix acquisition unit obtains the trajectory matrix eigenvalues ​​of the trajectory matrix based on the symplectic geometric similarity transformation, and reconstructs the eigenvectors based on the trajectory matrix eigenvalues ​​to obtain the symplectic geometric matrix. The initial symplectic geometric component acquisition unit obtains the initial symplectic geometric components based on the symplectic geometric matrix through a diagonal averaging algorithm. A complete buried target weak magnetic signal acquisition unit recombines the initial symplectic geometric components using cosine similarity and information entropy to obtain the complete buried target weak magnetic signal. The complete buried target weak magnetic signal acquisition unit includes: The cosine similarity recombination module constructs a class set based on the initial symplectic geometric component matrix, and then performs cosine similarity recombination on each class based on the cosine similarity between each class in the class set. The information entropy comparison termination module calculates the information entropy of each class before and after recombination. When the information entropy of the recombined class is greater than the information entropy of the class before recombination, the cosine similarity recombination step is terminated, and the class before recombination is taken as the complete buried target weak magnetic signal. The cosine similarity recombination module includes: constructing the initial symplectic geometric component matrix into a class set T. , ,…, Where t is a class; select class t1 and the remaining Cosine similarity is calculated for each class to obtain the cosine similarity score; the two classes with the highest cosine similarity are then combined into a new class. and the new class Add it to the class set T and replace class t1; The information entropy comparison termination and recombination module includes: calculating class t1 and the new class t1. Information entropy; when a new class If the information entropy of class t1 is less than the information entropy of class t1, then return to execute the cosine similarity recombination step; when the new class t1 is less than the information entropy of class t1, then return to execute the cosine similarity recombination step. When the information entropy of class t1 is greater than or equal to the information entropy of class t1, the cosine similarity recombination module is terminated, and class t1 is output as the complete buried target weak magnetic signal.

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