A strong earthquake magnitude sparse classification method for early warning

Abstract

The application provides a strong earthquake magnitude sparse classification method for early warning, specifically by constructing a training dictionary D, performing discrete Fourier transform on the P wave signal of the recorded shallow source strong earthquake to obtain a training sample, and constructing the training dictionary D; obtaining a to-be-classified vector y from the P wave signal of the to-be-classified shallow source strong earthquake; performing dimension reduction on the training dictionary D and the to-be-classified vector y, inputting the to-be-classified signal y, normalizing each column vector of the training dictionary D and the to-be-classified signal y, and solving a minimum L1 norm problem; the low-rank matrix recovery method can also be used to perform dimension reduction and dictionary optimization on the constructed training dictionary D, and through a block optimization calculation process, a sparse solution calculation residual minimum value is finally solved to determine the category of the to-be-classified vector y; the training dictionary can be optimized through the category i range and hierarchical sparse classification model according to the earthquake magnitude in the training dictionary D.

Description

Technical Field

[0001] This invention relates to the field of earthquake signal detection and early warning technology, and in particular to a sparse classification method for strong earthquake magnitudes for early warning. Background Technology

[0002] Earthquakes are among the most serious natural disasters threatening human life and property, often causing severe building damage and casualties, and triggering secondary disasters such as fires, floods, pipe leaks, the spread of bacteria and radioactive materials, landslides, tsunamis, collapses, and ground fissures. A major earthquake releases a large amount of energy in a very short time, causing devastating damage within tens of seconds or even a few seconds. With the development of global urbanization, cities have gradually become centers of political, economic, cultural, and social activities. Furthermore, the high population density and numerous buildings in cities make them particularly vulnerable to sudden earthquakes. The occurrence of earthquakes is beyond human control, a common characteristic of earthquakes and many other natural disasters. Due to the extreme complexity of the earthquake gestation and occurrence process, reliable short-term earthquake prediction is currently unavailable. Countries worldwide have focused their earthquake disaster mitigation measures on improving building earthquake resistance, earthquake early warning systems, and earthquake emergency rescue.

[0003] A strong earthquake refers to a powerful shaking of a site or engineering structure caused by an earthquake or blast. Earthquake early warning systems are typically based on strong earthquake record data. Real-time magnitude calculation and dissemination are crucial outputs of earthquake early warning systems and are key functions determining the success or failure of the warning. Magnitude is a quantity used to characterize the strength of an earthquake; generally, the larger the magnitude, the greater the energy released, meaning the magnitude essentially reflects the size of the earthquake itself. Currently, earthquake early warning systems have not adequately addressed the accuracy of magnitude estimation and the underestimation of magnitude in large-scale events. There is a widespread phenomenon of overestimation of magnitude for small earthquakes and underestimation of magnitude for large earthquakes, with significant deviations. This is partly because strong earthquake records include noise, especially when frequency band noise overlaps with the seismic signal frequency band, making it difficult to filter out and adversely affecting real-time magnitude estimation. Furthermore, the early warning magnitude is estimated based on extremely limited information from the initial rupture, making it difficult to directly obtain magnitude-related information from the P-wave. Summary of the Invention

[0004] In view of this, the present invention proposes a sparse classification method for strong earthquake magnitude that is oriented towards early warning, based on the idea of ​​sparse classification for rapid estimation of earthquake magnitude.

[0005] The technical solution of this invention is implemented as follows: This invention provides a sparse classification method for strong earthquake magnitudes for early warning, comprising the following steps:

[0006] S1: Construct a training dictionary D. The training sample set is the P-wave signal of the recorded shallow-source strong earthquake. The original time-domain P-wave signal or the transform domain signal of the original time-domain P-wave signal is taken as a series of features and arranged into a vector d. The dimension of vector d is m. Vector d is used as a training sample.

[0007] From d distinct shallow-source P-wave signals, vectors d obtained as described above are selected to form a training dictionary D = [d1, d2, d3, ..., d2]. C ]∈R m×n The training dictionary D has dimension m and contains a total of n training samples, where m is much smaller than n. Let the training dictionary D... i =[d i，1 d i，2 d i，3 , ...,d i，j ]∈R m×n Let i be the training set of class i, where i = 1, 2, 3, ..., c, ..., d i，j d i，j Let D represent j training samples of category i, where j ≤ n; the training dictionary D contains noise.

[0008] S2: Process the P-wave signal of the shallow-source strong earthquake to be classified according to the method in step S1 to obtain the m-dimensional vector to be classified, y, y∈R. m Let X be the sparse representation coefficients, and the sparse solution... The expression is:

[0009] Obtain linear expression ||·||1 represents L1 normal form, ||·||2 represents L2 normal form, and ε represents the tolerance error;

[0010] S3: Dimensionality reduction is performed on the training dictionary D and the vector to be classified y, and the vector y is classified: Input the signal to be classified y, and normalize the signal y with each column vector of the training dictionary D; use the low-rank matrix recovery method to optimize the constructed training dictionary D to obtain the low-rank structure A of the training dictionary D; perform principal component-based PCA feature extraction on the low-rank structure A to obtain the feature representation space M; project the training dictionary D and the vector to be classified y onto the feature representation space M to achieve dimensionality reduction of the training dictionary D and the vector to be classified y, where the dimensionality reduction of the vector to be classified y is y' = y*M, and the dimensionality reduction of the training dictionary D is D' = D*M; perform non-overlapping block partitioning on the training dictionary D and the vector to be classified y to obtain block D. p and y p The corresponding block D is calculated using the reciprocal of the mean squared error (MSE). p and y p Similarity S p S p =1 / MSE(yp D p ), thus obtaining the position weighting matrix W:

[0011] W1, W2, ..., W k It is the reciprocal of the similarity value calculated for each block in turn, W1, W2, ..., W k =1 / max(S) p );

[0012] pass Solving for sparse solutions λ is the regularization parameter; the category of the vector y to be classified is determined by calculating the minimum residual: identity(y) = arg min||yD i δ i (x)||2,δ i (x) are the sparse representation coefficients of the i-th class of training samples; after the classification vector y obtains the corresponding class, it is added to the training dictionary D as a new training sample;

[0013] S4: Divide the range of category i in the training dictionary D according to the earthquake magnitude, and further optimize the training dictionary.

[0014] Based on the above technical solutions, preferably, obtaining the low-rank structure A of the training dictionary D involves decomposing the training dictionary D into a combination of the low-rank structure A and the sparse matrix S, and solving an optimization problem: stA+S=D;||A|| * Let S be the sum of the singular values ​​of the matrix A with low rank structure A, and k be the weight of the sparse matrix S. The sparse matrix S is calculated using the augmented Lagrange multiplier algorithm, and the low rank structure A is obtained by inverse calculation.

[0015] Preferably, the step of performing principal component-based PCA feature extraction on the low-rank structure A to obtain the optimal feature representation space M is to let the low-rank structure A be a column vector, A = {x1, x2, x3, ... x}. q} p×q That is, the low-rank structure A consists of q p-dimensional vectors, where x is the vector. t x t+1 ∈x1, x2, x3, ..., x q Represent a vector of a low-rank column vector structure; perform data centralization: x t+1 =x t -μ; calculate the covariance matrix A0 is the data after centering the low-rank structure A; It is an A0-rank matrix; perform eigenvalue decomposition on the covariance matrix, and select the first q values ​​to form the feature representation space M.

[0016] More preferably, the non-overlapping segmentation of the training dictionary D and the vector to be classified y involves dividing the training dictionary D and the vector to be classified y into several non-overlapping regions, and traversing each region through the entire training dictionary D or the vector to be classified y in a right-to-left and bottom-to-top order.

[0017] More preferably, the step of classifying category i according to earthquake magnitude and further optimizing the training dictionary is based on training samples d. i，j The corresponding strong earthquake magnitudes of 4.0 to 9.0 are used as the value range for the category, with each increase of one magnitude creating a new category; based on the sparse solution... Each basis vector in category i of the training dictionary is represented as a sparse vector using a non-zero non-basic vector, where i = 1, 2, 3, ..., c, ..., d. i，j For each basis vector of each category, the following calculation is performed: Let DIS i (d i，j ) is the training sample d i，j The average distance from category i, DIS(d i,j ) is the training sample d i,j The average distance between J(d) and other categories; let J(d) i,j ) = DIS i (d i,j ) / DIS(d i,j For each training sample in that category, calculate J(d) as a basis vector. i,j ), get J(d) in the same category i,j The minimum value of J(d) i,j Replace the original basis vector with the sparse representation vector corresponding to the minimum value; update the corresponding class vector in the training dictionary; then repeat the above steps for other classes to optimize the basis vectors of each class in the training dictionary D.

[0018] Furthermore, in a more preferred embodiment, step S4, which further optimizes the training dictionary, includes an improvement and optimization step using a hierarchical sparse classification model: implementing an M-layer sparse classification representation for the vector to be classified, y = DM. x D MTo form a training dictionary containing K categories at M levels, the total number of layers is M, and x is the sparse representation coefficient. M is determined by the size of the training dictionary in the first layer. Before the sparse representation classification in the first layer, a sample closest to the vector to be classified y is selected from the training samples of each class to construct a training dictionary for sparse representation classification. From the obtained residuals, K1 classes that are closest to the vector to be classified y are selected. Then, all training samples of K1 classes are used to construct a training dictionary again to start the sparse representation classification in the first layer. After that, the training dictionary update operation is performed for each layer until the residuals meet the requirements or the size of the training dictionary is minimized.

[0019] Based on the above technical solutions, preferably, the value of the regularization parameter λ is 10. -4 .

[0020] The present invention provides a sparse classification method for strong earthquake magnitude for early warning, which has the following advantages compared with the prior art:

[0021] (1) This invention constructs a training dictionary containing noise and a vector to be classified by acquiring the signal of a shallow-source strong earthquake. The two are then subjected to dimensionality reduction and non-overlapping block processing to obtain the projection space of the training dictionary and the vector to be classified in a low-dimensional space. The sparse solution is obtained and the approximate category of the vector to be classified is obtained. Subsequently, the training dictionary is expanded and updated with samples, which can improve the accuracy of rapid estimation of strong earthquake magnitude and provide support for strong earthquake early warning. Machine learning is based on data. Traditional solution methods rely on a fixed period or amplitude, such as Nyquist sampling value, which limits their use. The method of this scheme is more flexible and comprehensive.

[0022] (2) After solving the low-rank structure of the training dictionary, the low-rank structure is closer to the original information of the training dictionary, contains less noise, and is easier to solve sparse solutions quickly.

[0023] (3) PCA-based feature extraction of low-rank structures can eliminate correlations in the original information and retain the main features in the original information;

[0024] (4) The non-overlapping block method is used to optimize the calculation process of sparse solutions, which can reduce the computational pressure and improve the computational speed.

[0025] (5) Further optimization of the training dictionary involves updating each sample of each type based on the distance within the same category and the distance between different categories, removing vectors with indistinct category features and low correlation, thereby further improving the reliability of the dictionary and category division.

[0026] (6) The hierarchical sparse classification model is used to improve and optimize the training dictionary by continuously reducing the number of categories in the dictionary, thereby limiting the range of test vectors. Attached Figure Description

[0027] 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 only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a flowchart of a sparse classification method for strong earthquake magnitudes for early warning, according to the present invention. Detailed Implementation

[0029] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0030] In recent years, sparse classification representation has become a popular area in machine learning. An N-dimensional discrete-time signal y can be represented by a set of orthogonal base linear combinations, y = Dx, where D is a dictionary composed of orthogonal bases, and the elements in the orthogonal dictionary are dictionary atoms; x is the representation coefficient of y in the dictionary. If most elements in x are zero, and only a small number of elements are non-zero, then the representation coefficients x can be considered sparse. In practical applications, for a signal y, a specific set of orthogonal bases alone cannot accommodate all signals. Therefore, a given dictionary D is insufficient for sparse representation of all signals. Thus, it is necessary to construct an overcomplete set of basis vectors, and this dictionary is called an overcomplete dictionary. Given a signal y and an overcomplete dictionary, sparse decomposition of the signal y is a problem of solving an underdetermined linear system. The goal of sparse decomposition is to find the representation coefficients x of the signal y under the overcomplete dictionary, and to minimize the number of non-zero elements in x, i.e., to minimize the norm of x. This optimization problem can be written as: P0: min||x||0s.ty = Dx. If X contains noise, the optimization problem can be rewritten as: min||x||0 st||y-Dx||2≤ε, where ε represents the maximum allowable error. Sparse representation of a signal under the 1-norm is a linear programming problem, which is easier to find the global optimum than the NP-hard problem under the 0-norm. Therefore, we use the 1-norm instead of solving for the 0-norm, and solve for the minimum 1-norm, thus obtaining the estimate of the sparse representation. Calculate the difference between the estimated value of y and y, and assign y to the category that minimizes the residual, which is then used as the category of the vector y to be classified.

[0031] Earthquake early warning systems often use data within three seconds of P-wave arrival for the initial report, with an additional report for each subsequent second of data. For example, with a sampling rate of 200Hz, there are 600 feature data points within the first three seconds of P-wave arrival, and 200 more feature data points for each subsequent second. Sparse classification algorithms require the dictionary to be an overcomplete redundant matrix, meaning the number of columns is much greater than the number of rows, inevitably resulting in a huge amount of data and computation. It is necessary to reduce the dimensionality of the original data through feature extraction, making the strong earthquake feature structure more compact in the updated feature space, and ensuring that the extracted feature vectors, as dictionary atoms, better reflect the essential information of the original earthquake. Early transform domain dimensionality reduction methods involved performing domain transformations on the original data using Fourier transforms or wavelet transforms, and then selecting feature vectors based on frequency or energy characteristics to form a redundant dictionary. However, transform domain feature extraction struggles to uncover latent features, and subsequent linear dimensionality reduction methods have been widely adopted due to their simplicity and effectiveness. Common linear dimensionality reduction methods include factor analysis (FA), principal component analysis (PCA), independent component analysis (ICA), linear discriminant analysis (LDA), and local projection method (LPP).

[0032] Principal Component Analysis (PCA) is a typical linear transformation method. Its basic idea is to recombine previously correlated indicators to form a new set of uncorrelated indicators. These new indicators are linear combinations or comprehensive indicators of the original indicators, and are used to replace the original indicators in subsequent analysis. PCA is based on the maximum variance criterion and optimizes the transformed covariance matrix through basis transformation. From a geometric perspective, PCA rotates the original coordinate axes to obtain mutually orthogonal coordinate axes, ensuring that the direction of these axes is the direction in which all data points are most dispersed. These new coordinate axes are arranged according to the magnitude of the obtained eigenvalues. From a probabilistic and statistical perspective, the variance of a random variable represents the information it contains; the larger the variance, the more information it contains. If the variance of a variable is zero or a constant, then the variable contains no information. This invention uses PCA dimensionality reduction combined with sparse representation classification methods for sparse classification prediction of magnitude in strong earthquake early warning.

[0033] like Figure 1 As shown, this invention provides a sparse classification method for strong earthquake magnitudes for early warning, comprising the following steps:

[0034] S1: Construct a training dictionary D. The training sample set is the P-wave signal of the recorded shallow-source strong earthquake. The original time-domain P-wave signal or the transform domain signal of the original time-domain P-wave signal is taken as a series of features and arranged into a vector d. The dimension of vector d is m. Vector d is used as a training sample. The signal transform domain used here can be one of discrete cosine transform, discrete Fourier transform, or wavelet transform.

[0035] Continue by selecting vectors d obtained as described above from c different categories of shallow-source P-wave signals to construct a training dictionary D = [d1, d2, d3, ..., d...]. C ]∈R m×n R m×n Let D be an m×n dimensional vector; the training dictionary D has a dimension of m, and contains a total of n training samples, where m is much smaller than n; let the training dictionary D... i =[d i，1 d i，2 d i，3 , ...,d i，j ]∈R m×n Let i be the training set of class i, where i = 1, 2, 3, ..., c, ..., d i，j Let D represent j training samples of category i, where j≤n; the training dictionary D contains noise; the training dictionary D is composed of basis vectors, and the signal is represented by the training dictionary D by the linear combination of the basis vectors.

[0036] S2: Process the P-wave signal of the shallow-source strong earthquake to be classified according to the method in step S1, and perform discrete Fourier transform to obtain the m-dimensional vector to be classified, y, y∈R. m Let x be an m-dimensional vector; let x be the sparse representation coefficients, where x is the vector type; sparse solution The expression is:

[0037] Obtain linear expression ||·||1 represents L1 normal form, ||·||2 represents L2 normal form, and ε represents the tolerance error; the tolerance error can be set manually.

[0038] S3: Dimensionality reduction is performed on the training dictionary D and the vector to be classified y, and the vector to be classified y is classified: Input the signal to be classified y, and normalize the signal to be classified y with each column vector of the training dictionary D; use the low-rank matrix recovery method to optimize the constructed training dictionary D to obtain the low-rank structure A of the training dictionary D;

[0039] Obtaining the low-rank structure A of the training dictionary D involves decomposing the training dictionary D into a combination of the low-rank structure A and the sparse matrix S, and then solving an optimization problem: stA+S=D;||A|| * Let S be the sum of the singular values ​​of the matrix A with low rank structure A, and k be the weight of the sparse matrix S. The sparse matrix S is calculated using the augmented Lagrange multiplier algorithm, and the low rank structure A is obtained by inverse calculation. The augmented Lagrange multiplier algorithm is a method for finding the extrema of the original function under constraints. By introducing Lagrange multipliers and a quadratic penalty term, the solution for each variable of the extrema of the original function is obtained. This method is a technique known to those skilled in the art.

[0040] Then, principal component analysis (PCA) is performed on the low-rank structure A to obtain the feature representation space M. Let the low-rank structure A be a column vector, A = {x1, x2, x3, ..., xn}. q} p×q That is, the low-rank structure A consists of q p-dimensional vectors, where x is the vector. t x t+1 ∈x1, x2, x3, ..., x q Represent a vector of a low-rank column vector structure; perform data centralization: X t+1 =X t -μ; calculate the covariance matrix A0 is the data after centering the low-rank structure A; A0 is the transformed rank matrix; eigenvalue decomposition is performed on the covariance matrix, and the first q values ​​are selected to form the feature representation space M. PCA feature extraction is a data processing method that, through dimensionality reduction, eliminates the correlation between original features, reduces data redundancy, and improves the efficiency of subsequent classification. By projecting onto the feature representation space, the dimensionality-reduced data retains as much of the original information as possible.

[0041] The training dictionary D and the vector to be classified y are projected onto the feature representation space M to achieve dimensionality reduction of both the training dictionary D and the vector to be classified y. The dimensionality reduction of the vector to be classified y is y' = y*M, and the dimensionality reduction of the training dictionary D is D' = D*M. Non-overlapping blocks are then performed on the training dictionary D and the vector to be classified y to obtain block D. p and y p The corresponding block D is calculated using the reciprocal of the mean squared error (MSE). p and y p Similarity S p S p =1 / MSE(y p D p ), thus obtaining the position weighting matrix W:

[0042] W1, W2, ..., W k It is the reciprocal of the similarity value calculated for each block in turn, W1, W2, ..., W k =1 / max(S) p );

[0043] In the above method, non-overlapping block partitioning of the training dictionary D and the vector to be classified y is to divide the training dictionary D and the vector to be classified y into several non-overlapping regions, and then traverse the entire training dictionary D or the vector to be classified y in the order from right to left and from bottom to top.

[0044] pass Solving for sparse solutions λ is the regularization parameter; the category of the vector y to be classified is determined by calculating the minimum residual: identity(y) = arg min||yD i δ i (x)||2,δ i (x) are the sparse representation coefficients of the i-th class of training samples; after the classification vector y obtains its corresponding class, it is added to the training dictionary D as a new training sample; the value of the regularization parameter λ is 10. -4 .

[0045] S4: Divide the range of category i in the training dictionary D according to earthquake magnitude, and further optimize the training dictionary: according to training samples d i，j The corresponding strong earthquake magnitudes of 4.0 to 9.0 are used as the value range for the category, with each increase of one magnitude creating a new category; based on the sparse solution... Each basis vector in category i of the training dictionary is represented as a sparse vector using a non-zero non-basic vector, where i = 1, 2, 3, ..., c, ..., d. i，j For each basis vector of each category, the following calculation is performed: Let DIS i (d i，j ) is the training sample d i，j The average distance from category i, DIS(d i，j ) is the training sample d i，j The average distance between J(d) and other categories; let J(d) i，j ) = DIS i (d i，j ) / DIS(d i，j For each training sample in that category, calculate J(d) as a basis vector. i，j ), get J(d) in the same category i，j The minimum value of J(d) i，j The process involves replacing the original basis vector with the sparse representation vector corresponding to the minimum value, updating the corresponding category vector in the training dictionary, and then repeating the above steps for other categories to optimize the basis vectors of each category in the training dictionary D. This optimization method continuously optimizes the vectors in each category of the dictionary, removing vectors with unclear category features and low correlation, thus improving classification.

[0046] As a further improvement to this scheme, due to the sudden and accidental nature of strong earthquake signals, the data volume of the strong earthquake sample database is limited and insufficient. The training samples in a single-layer sparse classification model are unlikely to yield excellent classification results. Therefore, a hierarchical sparse classification model can be used for improvement and optimization. The vector to be classified, y, is represented by an M-layer sparse classification model, where y = D. M x, D MTo create a training dictionary with K categories across M levels, where M is the total number of levels and x is the sparse representation coefficient, M is determined by the size of the first-level training dictionary. Before the first-level sparse representation classification, a training dictionary is constructed by selecting the nearest neighbor of the vector to be classified (y) from each class of training samples using KNN, kernel-induced distance, or Euclidean distance. From the resulting residuals, K1 categories closest to the vector to be classified (y) are selected, and then all training samples from these K1 categories are used to construct the training dictionary again to begin the first-level sparse representation classification. This process of updating the training dictionary is repeated for each layer until the residuals meet the requirements or the size of the training dictionary is minimized. In step S1, c is a constant, while K and K1 are variables in this method. The method for improving and optimizing the hierarchical sparse classification model is to continuously reduce the number of categories in the dictionary, thereby limiting the range of categories for the vector to be classified, which can further improve the efficiency and accuracy of classification.

[0047] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A sparse classification method for strong earthquake magnitudes for early warning, characterized in that: Includes the following steps: S1: Construct a training dictionary D. The training sample set is the P-wave signal of the recorded shallow-source strong earthquake. The original time-domain P-wave signal or the transform domain signal of the original time-domain P-wave signal is taken as a series of features and arranged into a vector d. The dimension of the vector d is m. The vector d is used as a training sample. From c distinct shallow-source P-wave signals, vectors d obtained as described above are selected to form a training dictionary D = [d1, d2, d3, ..., d2]. C ]∈R m×n ; The training dictionary D has dimension m and contains a total of n training samples, where m is much smaller than n; let the training dictionary D i =[d i，1 d i，2 d i，3 , ...,d i，j ]∈R m×n Let i be the training set of class i, where i = 1, 2, 3, ..., c, ..., d i，j d i，j Let D represent j training samples of category i, where j ≤ n; the training dictionary D contains noise. S2: the P wave signal of the shallow source strong earthquake to be classified is processed according to the method of step S1, and an m-dimensional vector to be classified y is obtained, y ∈ R m , let X be a sparse representation coefficient, and the sparse solution The expression is: Obtaining linear representation ||·||1 is L1 norm, ||·||2 is L2 norm, and ε is the allowable error. S3: Dimensionality reduction is performed on the training dictionary D and the vector to be classified y, and the vector y is classified: Input the signal to be classified y, and normalize the signal y with each column vector of the training dictionary D; use the low-rank matrix recovery method to optimize the constructed training dictionary D to obtain the low-rank structure A of the training dictionary D; perform principal component-based PCA feature extraction on the low-rank structure A to obtain the feature representation space M; project the training dictionary D and the vector to be classified y onto the feature representation space M to achieve dimensionality reduction of the training dictionary D and the vector to be classified y, where the dimensionality reduction of the vector to be classified y is y' = y*M, and the dimensionality reduction of the training dictionary D is D' = D*M; perform non-overlapping block partitioning on the training dictionary D and the vector to be classified y to obtain block D. p and y p The corresponding block D is calculated using the reciprocal of the mean squared error (MSE). p and y p Similarity S p S p =1 / MSE(y p D p ), thus obtaining the position weighting matrix W: W1, W2, ..., W k It is the reciprocal of the similarity value calculated for each block in turn, W1, W2, ..., W k =1 / max(S) p ); pass Solving for sparse solutions λ is the regularization parameter; the category of the vector y to be classified is determined by calculating the minimum residual: identity(y) = arg min||yD i δ i (x)||2,δ i (x) are the sparse representation coefficients of the i-th class of training samples; Once the classification vector y obtains its corresponding category, it is added to the training dictionary D as a new training sample. S4: Divide the range of category i in the training dictionary D according to the earthquake magnitude, and further optimize the training dictionary.

2. The method for sparse classification of strong earthquake magnitudes in an earthquake early warning system according to claim 1, wherein: The process of obtaining the low-rank structure A of the training dictionary D involves decomposing the training dictionary D into a combined structure of the low-rank structure A and the sparse matrix S, and then solving an optimization problem. stA+S=D;||A|| * Let S be the sum of the singular values ​​of the matrix A with low rank structure A, and k be the weight of the sparse matrix S. The sparse matrix S is calculated using the augmented Lagrange multiplier algorithm, and the low rank structure A is obtained by inverse calculation.

3. The sparse classification method for strong earthquake magnitudes for early warning as described in claim 2, characterized in that: The step of performing principal component-based PCA feature extraction on the low-rank structure A to obtain the optimal feature representation space M involves letting the low-rank structure A be a column vector, A = {x1, x2, x3, ..., xn}. q } p×q That is, the low-rank structure A consists of q p-dimensional vectors, where x is the vector. t x t+1 ∈x1, x2, x3, ..., x q Represent a vector of a low-rank column vector structure; perform data centralization: X t+1 =X t -μ; calculate the covariance matrix A0 is the data after centering the low-rank structure A; It is an A0-rank matrix; perform eigenvalue decomposition on the covariance matrix, and select the first q values ​​to form the feature representation space M.

4. The method of claim 3, wherein the method is a pre-alarm-oriented strong earthquake magnitude sparse classification method, characterized in that: The non-overlapping block segmentation of the training dictionary D and the vector to be classified y involves dividing the training dictionary D and the vector to be classified y into several non-overlapping regions, and then traversing each region through the entire training dictionary D or the vector to be classified y in a right-to-left and bottom-to-top order.

5. The method of claim 4, wherein the method is a pre-alarm-oriented strong earthquake magnitude sparse classification method, characterized in that: The process of classifying category i according to earthquake magnitude and further optimizing the training dictionary is based on training samples d. i，j The corresponding strong earthquake magnitudes of 4.0 to 9.0 are used as the value range for the category, with each increase of one magnitude creating a new category; based on the sparse solution... Each basis vector in category i of the training dictionary is represented as a sparse vector using a non-zero non-basic vector, where i = 1, 2, 3, ..., c, ..., d. i，j For each basis vector of each category, the following calculation is performed: Let DIS i (d i，j ) is the training sample d i，j The average distance from category i, DIS(d i，j ) is the training sample d i，j The average distance between J(d) and other categories; let J(d) i，j ) = DIS i (d i，j ) / DIS(d i，j For each training sample in that category, calculate J(d) as a basis vector. i,j ), get J(d) in the same category i,j The minimum value of minJ(d) i，j Replace the original basis vector with the sparse representation vector corresponding to the minimum value; update the corresponding class vector in the training dictionary; then repeat the above steps for other classes to optimize the basis vectors of each class in the training dictionary D.

6. The method of claim 5, wherein the method is a pre-alarm-oriented strong earthquake magnitude sparse classification method. Step S4 further optimizes the training dictionary, including the step of improving and optimizing it using a hierarchical sparse classification model: implementing an M-layer sparse classification representation for the vector to be classified, y = D. M x, D M Let M be the training dictionary containing K categories under M layers, with a total of M layers, where x is the sparse representation coefficient; M is determined by the size of the training dictionary in the first layer. Before the first layer of sparse representation classification, a sample that is closest to the vector to be classified y is selected from the training samples of each class to construct a training dictionary for sparse representation classification. From the obtained residuals, the K1 classes that are closest to the vector to be classified y are selected. Then, all the training samples of the K1 classes are used to construct a training dictionary again to start the first layer of sparse representation classification. After that, the training dictionary is updated for each layer until the residuals meet the requirements or the size of the training dictionary is minimized.

7. The method of claim 1, wherein the method is a sparse classification method for strong earthquake magnitude oriented to early warning. The value of the regularization parameter λ is 10. -4 .

Images