High-resolution time-frequency domain shallow water mode separation method and system

Abstract

This invention relates to a high-resolution time-frequency domain shallow-sea mode separation method, comprising the following steps: acquiring the original time-domain signal; performing a time-domain warping transform on the original time-domain signal to obtain a warped signal; constructing a time-frequency sparse constraint optimization model, solving the constraint optimization problem to obtain a sparse time-frequency coefficient vector, rearranging the sparse time-frequency coefficient vector into a time-frequency coefficient matrix, and plotting a time-frequency spectrum; constructing a mask matrix for mode separation to obtain a sparse time-frequency coefficient matrix of a specified order mode, and reconstructing the warped signal corresponding to the specified order mode; and using an inverse warping transform to convert the warped signal back to the original time domain to obtain the original time-domain waveform signal of the specified order mode. This invention also relates to a system for implementing the high-resolution time-frequency domain shallow-sea mode separation method. This invention solves the problem of insufficient time-frequency domain resolution after the warping transform; reduces the difficulty of mask construction; improves the accuracy and robustness of single-sensor mode separation; and improves computational efficiency.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic signal processing technology, and specifically to a high-resolution time-frequency domain shallow sea mode separation method and system. Background Technology

[0002] The low-frequency sound field in shallow seas can be represented by a few propagation modes, which contain information about the sound source and the environment, forming a crucial physical basis for sound source localization and environmental parameter inversion in shallow seas. However, actual signals are the result of several modes superimposed and mixed with noise. Therefore, accurately separating each mode from the signal is a key problem that needs to be solved to realize modal applications. A common method is to use vertical or horizontal arrays for spatial sampling, thereby achieving mode separation directly in the wavenumber domain. However, array deployment faces problems such as high cost and operational difficulty, and may introduce additional errors due to mismatch in array element positions. In contrast, single-sensor-based modal separation methods significantly reduce system hardware overhead and operational complexity, making them more competitive in engineering. Warping transform is currently the main method for achieving mode separation of pulse or known-form signals acquired by a single hydrophone. Its implementation is simple and has robust processing performance, making it the preferred choice for engineering applications. Due to the lack of spatial sampling, single-sensor mode separation needs to be performed in the time-frequency domain. The role of the warping transform is to change the time-frequency structure of the signal, approximating the originally dispersed modal components into single-frequency components in the time-frequency domain, thus making it easier to separate them using mask filtering. Therefore, time-frequency domain resolution is crucial, directly determining the difficulty of mask construction and the accuracy of mode separation.

[0003] The shortcomings of existing technologies are as follows: Since existing methods only use conventional techniques such as short-time Fourier transform for time-frequency spectrum estimation, the inherent spectral leakage and background noise interference often make it difficult to meet the requirements for time-frequency resolution, which greatly limits mode separation. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a high-resolution time-frequency domain shallow sea mode separation method and system. Its purpose is to solve the problem of insufficient time-frequency domain resolution after Warping transform; reduce the difficulty of mask construction; improve the accuracy and robustness of single-sensor mode separation; and improve computational efficiency.

[0005] To solve the above problems, the technical solution provided by the present invention is as follows: A high-resolution time-frequency domain shallow sea mode separation method includes the following steps: S100. Acquire the original time-domain signal received by a single sensor in a low-frequency sound field in shallow sea, select the corresponding time origin, and perform a time-domain warping transformation on the original time-domain signal to obtain the warped signal. S200. The short-time Fourier time-frequency transform process of the Warped signal is constructed as a time-frequency sparse constraint optimization model. Then, the constraint optimization problem is solved iteratively using the fast iterative shrinking threshold algorithm to obtain a sparse time-frequency coefficient vector. The sparse time-frequency coefficient vector is rearranged into a time-frequency coefficient matrix to draw a time-frequency spectrum. S300. Construct a mask matrix for the modal energy distribution region in the time-frequency spectrum, use the mask matrix to filter out the time-frequency coefficient matrix of the specified order mode, and call the forward operator to reconstruct the Warped signal corresponding to the specified order mode; S400. The Warped signal of the specified order mode obtained by the reconstruction in step S300 is converted back to the original time domain using the inverse Warping transform, thereby separating the original time domain waveform signal of the specified order mode.

[0006] Preferably, the mathematical expression for the Warping transformation in step S100 is expressed as follows: Where t is used to characterize the original time-domain time variable; t r Used to characterize the earliest arrival time of a signal; The transformed Warped signal is expressed by the following formula: Wherein, s(t) is used to characterize the original time-domain signal received by a single sensor; Used for characterization Time derivative, factor This is used to ensure energy conservation between the signals before and after the Warping transformation.

[0007] Preferably, in step S200, the short-time Fourier time-frequency transform process is constructed as the following forward operator matrix: in, Used to characterize the forward operator, it is a 3D matrix; Used to characterize the rearranged 3D time-frequency coefficient column vector; The forward operator matrix is ​​expressed as follows: in, Used for characterization A sparse row block matrix of dimension 1, padded with zeros to 1 N Point window function vector To construct; Used for characterization A 3D block diagonal matrix is ​​expressed as follows: in, The matrix used to characterize the inverse Fourier transform is expressed by the following formula: .

[0008] Preferably, the objective function of the time-frequency sparse constraint optimization model is expressed by the following formula: in, This is a data fitting term used to constrain the reconstructed signal to approximate the original signal; This is a regularization term used to improve the sparsity of time-frequency coefficients; Used to characterize equilibrium parameters .

[0009] Preferably, the fast iterative shrinkage threshold algorithm in step S200 specifically includes the following sub-steps: S210. Parameter initialization: Set the maximum number of iterations, iteration step size, shrinkage threshold, and initial time-frequency coefficient vector; S220. Gradient Descent Iteration: Based on the set iteration step size The next time-frequency coefficient vector is calculated by updating along the negative gradient direction of the current time-frequency coefficient vector, expressed as follows: in: , These are used to characterize the current time-frequency coefficient vector and the next time-frequency coefficient vector, respectively. S230. Soft-threshold shrinkage filtering: Perform a soft-threshold shrinkage operation based on the shrinkage threshold on the amplitude of each time-frequency element in the time-frequency coefficient vector, and update the current time-frequency coefficient vector. The shrinkage threshold is expressed by the following formula: in, Used to characterize the contraction threshold; Used to characterize the time-frequency elements in the time-frequency coefficient vector; Used to characterize equilibrium parameters; Used for characterization The phase; S240. Bregman Accelerated Iteration: The time-domain signal vector used to accelerate convergence is synchronously iterated and updated using the Bregman acceleration algorithm until the maximum number of iterations is reached and the final sparse time-frequency coefficient solution is output. The Bregman acceleration algorithm is expressed by the following formula: Here, k represents the number of iterations.

[0010] Preferably, the time-frequency coefficient matrix in step S300 is expressed by the following formula: in, Used to characterize the rearranged time-frequency coefficient matrix; The mask matrix is ​​used to characterize the construction for the i-th mode; The time-frequency coefficient matrix used to characterize the i-th order mode; The dimension of the mask matrix is ​​the same as that of the time-frequency coefficient matrix, and only the elements of the modal energy distribution region in the mask matrix are set to 1, while the rest are set to 0; After rearranging the time-frequency coefficient matrix of the filtered specified mode into column vectors, the Warped signal corresponding to the specified mode is reconstructed using the following formula: in, The column vector is used to characterize the rearranged time-frequency coefficient matrix.

[0011] Preferably, the formula for the inverse warping transformation in step S400 is: Where t is used to characterize the original time-domain time variable; t r Used to characterize the earliest arrival time of the signal.

[0012] A system for implementing the aforementioned high-resolution time-frequency domain shallow sea mode separation method includes: Signal preprocessing module: used to perform preprocessing operations such as downsampling, removing DC components, and signal truncation on the raw time-domain signal acquired and received by the single hydrophone; Warping Transform Module: Used to perform nonlinear resampling on the preprocessed original time-domain signal and output the Warped signal; Constraint optimization problem solving module: used to construct the warped signal into the time-frequency sparse constraint optimization model, and to iteratively solve and calculate the time-frequency coefficient sparse solution of the warped signal by executing the fast iterative shrinking threshold algorithm; Mask filtering module: used to plot the sparse solution of the time-frequency coefficients as the time-frequency spectrum, and construct a mask matrix based on the modal energy distribution region in the time-frequency spectrum to achieve mode separation; Inverse Warping Transform Module: Used to transform the separated Warped signals of each mode from the Warped domain back to the original domain, thereby obtaining the original time-domain signals of each mode; The results visualization module is used to draw the separation results, which include the time-domain waveforms of each mode and the corresponding time-frequency spectrum; Computer equipment: including a memory and a processor, wherein the memory is used to store computer program instructions for the above-mentioned modules, and the processor is used to execute the programs of the various modules of the system.

[0013] Preferably, the mask filtering module is configured with an interactive mode separation interface; the interactive mode separation interface is used to: receive the vertex coordinates of several polygon regions of interest generated by the user clicking continuously on the time-spectrum graph, automatically establish closed polygon regions; then construct the mask matrix according to the selected regions to separate the time spectra of different modes, and finally call the forward operator to convert the time spectra back into time domain signals.

[0014] Compared with the prior art, the present invention has the following advantages: 1. Because this invention fully utilizes the physical characteristics of the signal and combines the Warping transform with the sparsity promotion method, it solves the problems of insufficient time-frequency resolution and difficult mask construction caused by the inherent spectral leakage and background noise interference in conventional time-frequency analysis methods. It achieves high-resolution time-frequency domain energy distribution estimation, clearly highlights the time-frequency characteristics of each mode, reduces the difficulty of mask construction, and improves the accuracy and robustness of single-sensor mode separation.

[0015] 2. Because the present invention uses a fast iterative shrinking threshold algorithm to solve the time-frequency sparse constraint optimization problem, it solves the problems of slow convergence speed, high computational complexity, and difficulty in meeting the efficiency requirements of actual received signal processing of traditional sparse promotion algorithms, thereby ensuring the computational efficiency and engineering feasibility of the system in actual shallow sea data processing. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the signal processing flow according to a specific embodiment of the present invention.

[0017] Figure 2 This is a schematic diagram of the time-domain waveform of the original signal in a specific embodiment of the present invention.

[0018] Figure 3 This is a schematic diagram of the time-domain waveform of the Warped signal in a specific embodiment of the present invention.

[0019] Figure 4a This is the original time spectrum (a) of a specific embodiment of the present invention.

[0020] Figure 4b This is a schematic diagram of the sparse time spectrum (b) of a specific embodiment of the present invention.

[0021] Figure 5 This is a schematic diagram of the construction of a polygonal mask according to a specific embodiment of the present invention.

[0022] Figure 6 This is a schematic diagram of the time spectrum corresponding to the first-order mode Warped signal in a specific embodiment of the present invention.

[0023] Figure 7 This is a schematic diagram of the Warped signal corresponding to the first-order mode in a specific embodiment of the present invention.

[0024] Figure 8 This is a schematic diagram of the original signal corresponding to the first-order mode in a specific embodiment of the present invention.

[0025] Figure 9 This is a schematic diagram of the time spectrum of the original signal of the first mode in a specific embodiment of the present invention. Detailed Implementation

[0026] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0027] This invention application claims a high-resolution time-frequency domain shallow sea mode separation method, characterized in that: as Figure 1 As shown, it includes the following steps: S100. Acquire the original time-domain signal received by a single sensor in a low-frequency sound field in shallow sea, select the corresponding time origin, and perform a time-domain warping transformation on the original time-domain signal to obtain the warped signal. S200. The short-time Fourier time-frequency transform process of the Warped signal is constructed as a time-frequency sparse constraint optimization model. Then, the fast iterative shrinking threshold algorithm is used to iteratively solve the constraint optimization problem to obtain a sparse time-frequency coefficient vector. The sparse time-frequency coefficient vector is rearranged into a time-frequency coefficient matrix to draw the time-frequency spectrum. S300. Construct a mask matrix for the modal energy distribution region in the time-frequency spectrum, use the mask matrix to filter out the time-frequency coefficient matrix of the specified order mode, and call the forward operator to reconstruct the Warped signal corresponding to the specified order mode. S400. The Warped signal of the specified order mode reconstructed in step S300 is converted back to the original time domain using the inverse Warping transform, thereby separating the original time domain waveform signal of the specified order mode.

[0028] It should be noted that due to the inherent sparsity of modes under low-frequency conditions in shallow seas, this characteristic is reflected in the time-frequency domain, meaning that the actual time-frequency energy distribution also exhibits sparsity. Based on this characteristic, the proposed method utilizes sparsity promotion theory to construct the time-spectrum estimation after the warping transform as a constrained optimization problem. This problem is solved using a fast iterative shrinking threshold algorithm to obtain a high-resolution time-spectrum, which is then separated into different modes using mask filtering.

[0029] It should be noted that, for the input signal, a suitable time origin is first selected, and the original signal is subjected to a time-domain warping transform to obtain the warped signal. Mathematically, the warping transform is a simple variable substitution, that is, replacing the time variable with a warping function.

[0030] It should be further explained that the mathematical expression for the Warping transformation in step S100 is expressed as follows: (1) (1) Where t is used to characterize the original time-domain time variable; t r Used to characterize the earliest arrival time of a signal; The transformed Warped signal is expressed by the following formula: (2) Where s(t) is used to characterize the raw time-domain signal received by a single sensor; Used for characterization Time derivative, factor This is used to ensure energy conservation between the signals before and after the Warping transformation.

[0031] It should be noted that the time-frequency transformation is constructed as a constrained optimization problem, and a sparse promotion method is used to perform sparse time-spectrum estimation of the warped signal. Assuming that an N-point warped signal is obtained after time-domain warping, a column vector is used... In step S200, the short-time Fourier time-frequency transform process is constructed as the forward operator matrix of equation (3) as follows: (3) in, Used to characterize the forward operator, it is a 3D matrix; Used to characterize the rearranged 3D time-frequency coefficient column vector; The forward operator matrix is ​​expressed as follows (4): (4) in, Used for characterization A sparse row block matrix of dimension 1, padded with zeros to 1 N Point window function vector The construction process involves cyclically shifting the window function vector to the right by i units, using the shifted vector as the diagonal element of the diagonal matrix, and finally arranging it row by row to obtain the following form (5): (5) Used for characterization A dimensional block diagonal matrix is ​​expressed by the following formula (6): (6) in, The matrix used to characterize the inverse Fourier transform is expressed by the following equation (7): (7).

[0032] It should be noted that, in order to obtain a time-frequency coefficient vector with the fewest non-zero elements, the short-time Fourier transform is transformed into the following constrained optimization problem; the objective function of the time-frequency sparse constraint optimization model is expressed by the following equation (8): (8) in, This is a data fitting term used to constrain the reconstructed signal to approximate the original signal; This is a regularization term used to improve the sparsity of time-frequency coefficients; Used to characterize equilibrium parameters This is used to achieve a balance between data fitting and sparsity. The constrained optimization problem given by Equation (8) is solved by a fast iterative shrinking threshold algorithm to obtain a sparse solution for the time-frequency coefficients.

[0033] It should be further explained that the fast iterative threshold shrinkage algorithm in step S200 specifically includes the following sub-steps: S210. Parameter initialization: Set the maximum number of iterations, iteration step size, shrinkage threshold, and initial time-frequency coefficient vector; S220. Gradient Descent Iteration: Based on the set iteration step size The next time-frequency coefficient vector is calculated by updating along the negative gradient direction of the current time-frequency coefficient vector, as expressed by equation (9): (9) in: , These are used to represent the current time-frequency coefficient vector and the next time-frequency coefficient vector, respectively. S230. Soft threshold shrinkage filtering: Perform a soft threshold shrinkage operation based on a shrinkage threshold on the amplitude of each time-frequency element in the time-frequency coefficient vector, and update the current time-frequency coefficient vector. The shrinkage threshold is expressed by the following formula (10): (10) in, Used to characterize the contraction threshold; Used to characterize the time-frequency elements in the time-frequency coefficient vector; Used to characterize equilibrium parameters; Used for characterization The phase; S240. Bregman Accelerated Iteration: The time-domain signal vector used to accelerate convergence is synchronously updated using the Bregman acceleration algorithm until the maximum number of iterations is reached and the final sparse time-frequency coefficient solution is output. The Bregman acceleration algorithm is expressed by the following equation (11): (11) Here, k represents the number of iterations. The sparse solution of the time-frequency coefficients can be obtained through the above iterative algorithm. The sparse time-frequency coefficient vector is then rearranged into a 3D matrix, and a time-frequency spectrum is plotted.

[0034] It should be noted that in step S300, a two-dimensional mask is constructed for the modal energy distribution region in the time-frequency spectrum to achieve separation of different modes. The time-frequency coefficient matrix is ​​expressed by the following equation (12): (12) in, Used to characterize the rearranged time-frequency coefficient matrix; Used to characterize the mask matrix constructed for the i-th mode; The time-frequency coefficient matrix used to characterize the i-th order mode; The mask matrix has the same dimension as the time-frequency coefficient matrix, and only the elements in the modal energy distribution region of the mask matrix are set to 1, while the rest are set to 0; After rearranging the time-frequency coefficient matrix of the filtered specified mode into column vectors, the Warped signal corresponding to the specified mode is reconstructed using the following equation (13): (13) in, Used to characterize the column vectors after the time-frequency coefficient matrix has been rearranged.

[0035] It should be noted that the formula for the inverse Warping transformation in step S400 is equation (14): (14) Where t is used to characterize the original time-domain time variable; t r Used to characterize the earliest arrival time of a signal.

[0036] This application also claims a system for implementing a high-resolution time-frequency domain shallow sea mode separation method, characterized in that it comprises: Signal preprocessing module: used for preprocessing operations such as downsampling, removing DC components, and signal truncation of the raw time-domain signal acquired and received by a single hydrophone; Warping Transform Module: Used to perform nonlinear resampling on the preprocessed original time-domain signal and output the warped signal; Constrained optimization problem solving module: It is used to construct the Warped signal into a time-frequency sparse constraint optimization model, and to iteratively solve and calculate the time-frequency coefficient sparse solution of the output Warped signal by executing a fast iterative shrinking threshold algorithm; Mask filtering module: used to plot the sparse solution of time-frequency coefficients as a time-frequency spectrum, and construct a mask matrix based on the modal energy distribution region in the time-frequency spectrum to achieve mode separation; Inverse Warping Transform Module: Used to transform the separated Warped signals of each mode from the Warped domain back to the original domain, thereby obtaining the original time-domain signals of each mode; Results visualization module: used to draw the separation results, which include the time-domain waveforms of each mode and the corresponding time-frequency spectrum; Computer equipment includes a memory and a processor. The memory stores the computer program instructions for the above modules, and the processor executes the programs for each module of the system.

[0037] It should be noted that the mask filter module is equipped with an interactive mode separation interface; the interactive mode separation interface is used for: The system receives the vertex coordinates of several polygon regions of interest generated by the user's continuous clicks on the time-spectrum graph, automatically establishes closed polygon regions, constructs a mask matrix according to the selected regions to separate the time spectra of different modes, and finally calls the forward operator to convert the time spectra back into time-domain signals.

[0038] Implementation Case 1: The invention is further illustrated below with reference to specific embodiments. A pulse signal emitted by a North Pacific right whale is used as the input signal. The distance between the sound source and the receiver is approximately 8.7 km, and the receiver is located at a sea depth of approximately 50 m. The signal sampling frequency is 409.6 Hz, and the original waveform of the signal is shown below. Figure 2 .

[0039] Step 1: Warping Transformation The original signal is subjected to a warping transform to obtain the warped signal, the time-domain waveform of which is shown in the figure. Figure 3 .

[0040] Step 2: Sparsity-Enhanced Temporal Spectrum Estimation If a short-time Fourier transform is directly applied to the Warped signal, the result shown in Figure 4(a) is obtained, with all time-frequency spectra displayed in decibels. Although the fourth-order mode can be roughly identified in the figure, severe energy aliasing poses a significant challenge to the user in constructing the mask matrix. This invention does not use conventional methods like the short-time Fourier transform, but instead uses the aforementioned sparsity promotion algorithm to iteratively calculate the sparse time-frequency coefficients.

[0041] In this example, the maximum number of iterations is set to 120, the step size is 0.002, and the sparsity parameter is determined by both the step size and the time-frequency coefficients, which is actually set to 0.148. The time-frequency spectrum of the sparse time-frequency coefficients obtained using the sparsity promotion algorithm is shown in Figure 4(b). Compared with Figure 4(a), the resolution is greatly improved, the background noise is suppressed, and the fourth-order modes are clearly separated.

[0042] Step 3: Modal Filtering The sparse time-frequency spectrum contains four approximately horizontal energy ridges, corresponding to the fourth mode. Here, we take the first mode as an example for mode filtering. First, we select a polygon in the sparse time-frequency spectrum that encloses the energy region of the first mode, such as... Figure 5 The white-bordered polygonal region is shown. Within this region, the mask matrix elements are set to 1, and all other elements are 0. By multiplying the mask matrix by a dot, the first-order mode can be filtered out, yielding the corresponding time-frequency spectrum, as shown below. Figure 6 As shown.

[0043] Performing an inverse time-frequency transform on the time spectrum yields the Warped signal corresponding to the first-order mode, as shown in the following figure. Figure 7 As shown.

[0044] Step 4: Inverse Warping Transformation Performing an inverse warping transform on the warped signal yields the original signal corresponding to the first-order mode, such as... Figure 8 As shown.

[0045] The results of time-frequency transformation of the first-order modal signal are shown in Figure 9 The figure shows a clear and smooth dispersion curve, which proves the reliability of the separation results.

[0046] In the above detailed description, various features are combined together in a single embodiment to simplify this disclosure. This approach to disclosure should not be construed as reflecting an intention that embodiments of the claimed subject matter require more features than are explicitly stated in each claim. Rather, as reflected in the appended claims, the invention is presented with fewer features than all of the features of the single disclosed embodiment. Therefore, the appended claims are hereby explicitly incorporated into the detailed description, wherein each claim stands alone as a preferred embodiment of the invention.

[0047] The disclosed embodiments have been described above to enable any person skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be applied to other embodiments without departing from the spirit and scope of this disclosure. Therefore, this disclosure is not limited to the embodiments given herein, but is consistent with the broadest scope of the principles and novel features disclosed in this application.

[0048] The foregoing description includes examples of one or more embodiments. It is certainly impossible to describe all possible combinations of components or methods in order to describe the above embodiments, but those skilled in the art will recognize that further combinations and arrangements of the various embodiments are possible. Therefore, the embodiments described herein are intended to cover all such changes, modifications, and variations that fall within the scope of the appended claims. Furthermore, the term "comprising" as used in the specification or claims is interpreted in a manner similar to the term "including," as interpreted when used as a conjunction in the claims. Additionally, the use of any term "or" in the specification of the claims is intended to mean "non-exclusive or."

[0049] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A high-resolution time-frequency domain shallow sea mode separation method, characterized in that: Includes the following steps: S100. Acquire the original time-domain signal received by a single sensor in a low-frequency sound field in shallow sea, select the corresponding time origin, and perform a time-domain warping transformation on the original time-domain signal to obtain the warped signal. S200. The short-time Fourier time-frequency transform process of the Warped signal is constructed as a time-frequency sparse constraint optimization model. Then, the constraint optimization problem is solved iteratively using the fast iterative shrinking threshold algorithm to obtain a sparse time-frequency coefficient vector. The sparse time-frequency coefficient vector is rearranged into a time-frequency coefficient matrix to draw a time-frequency spectrum. S300. Construct a mask matrix for the modal energy distribution region in the time-frequency spectrum, use the mask matrix to filter out the time-frequency coefficient matrix of the specified order mode, and call the forward operator to reconstruct the Warped signal corresponding to the specified order mode; S400. The Warped signal of the specified order mode obtained by the reconstruction in step S300 is converted back to the original time domain using the inverse Warping transform, thereby separating the original time domain waveform signal of the specified order mode.

2. The high-resolution time-frequency domain shallow sea mode separation method according to claim 1, characterized in that: The mathematical expression for the Warping transformation described in step S100 is expressed as follows: Where t is used to characterize the original time-domain time variable; t r Used to characterize the earliest arrival time of a signal; The transformed Warped signal is expressed by the following formula: Wherein, s(t) is used to characterize the original time-domain signal received by a single sensor; Used for characterization Time derivative, factor This is used to ensure energy conservation between the signals before and after the Warping transformation.

3. The high-resolution time-frequency domain shallow sea mode separation method according to claim 1, characterized in that: In step S200, the short-time Fourier time-frequency transform process is constructed as the following forward operator matrix: in, Used to characterize the forward operator, it is a 3D matrix; Used to characterize the rearranged 3D time-frequency coefficient column vector; The forward operator matrix is ​​expressed as follows: in, Used for characterization A sparse row block matrix of dimension 1, padded with zeros to 1 N Point window function vector To construct; Used for characterization A 3D block diagonal matrix is ​​expressed as follows: in, The matrix used to characterize the inverse Fourier transform is expressed by the following formula: 。 4. The high-resolution time-frequency domain shallow sea mode separation method according to claim 3, characterized in that: The objective function of the time-frequency sparse constraint optimization model is expressed by the following formula: in, This is a data fitting term used to constrain the reconstructed signal to approximate the original signal; This is a regularization term used to improve the sparsity of time-frequency coefficients; Used to characterize equilibrium parameters .

5. The high-resolution time-frequency domain shallow sea mode separation method according to claim 4, characterized in that: The fast iterative shrinkage threshold algorithm described in step S200 specifically includes the following sub-steps: S210. Parameter initialization: Set the maximum number of iterations, iteration step size, shrinkage threshold, and initial time-frequency coefficient vector; S220. Gradient Descent Iteration: Based on the set iteration step size The next time-frequency coefficient vector is calculated by updating along the negative gradient direction of the current time-frequency coefficient vector, expressed as follows: in: , These are used to characterize the current time-frequency coefficient vector and the next time-frequency coefficient vector, respectively. S230. Soft-threshold shrinkage filtering: Perform a soft-threshold shrinkage operation based on the shrinkage threshold on the amplitude of each time-frequency element in the time-frequency coefficient vector, and update the current time-frequency coefficient vector. The shrinkage threshold is expressed by the following formula: in, Used to characterize the contraction threshold; Used to characterize the time-frequency elements in the time-frequency coefficient vector; Used to characterize equilibrium parameters; Used for characterization The phase; S240. Bregman Accelerated Iteration: The time-domain signal vector used to accelerate convergence is synchronously iterated and updated using the Bregman acceleration algorithm until the maximum number of iterations is reached and the final sparse time-frequency coefficient solution is output. The Bregman acceleration algorithm is expressed by the following formula: Here, k represents the number of iterations.

6. The high-resolution time-frequency domain shallow sea mode separation method according to claim 3, characterized in that: The time-frequency coefficient matrix in step S300 is expressed by the following formula: in, Used to characterize the rearranged time-frequency coefficient matrix; The mask matrix is ​​used to characterize the construction for the i-th mode; The time-frequency coefficient matrix used to characterize the i-th order mode; The dimension of the mask matrix is ​​the same as that of the time-frequency coefficient matrix, and only the elements of the modal energy distribution region in the mask matrix are set to 1, while the rest are set to 0; After rearranging the time-frequency coefficient matrix of the filtered specified mode into column vectors, the Warped signal corresponding to the specified mode is reconstructed using the following formula: in, The column vector is used to characterize the rearranged time-frequency coefficient matrix.

7. The high-resolution time-frequency domain shallow sea mode separation method according to claim 2, characterized in that: The formula for the inverse Warping transform in step S400 is: Where t is used to characterize the original time-domain time variable; t r Used to characterize the earliest arrival time of the signal.

8. A system for implementing the high-resolution time-frequency domain shallow sea mode separation method according to any one of claims 1 to 7, characterized in that, include: Signal preprocessing module: used to perform preprocessing operations such as downsampling, removing DC components, and signal truncation on the raw time-domain signal acquired and received by the single hydrophone; Warping Transform Module: Used to perform nonlinear resampling on the preprocessed original time-domain signal and output the Warped signal; Constraint optimization problem solving module: used to construct the warped signal into the time-frequency sparse constraint optimization model, and to iteratively solve and calculate the time-frequency coefficient sparse solution of the warped signal by executing the fast iterative shrinking threshold algorithm; Mask filtering module: used to plot the sparse solution of the time-frequency coefficients as the time-frequency spectrum, and construct a mask matrix based on the modal energy distribution region in the time-frequency spectrum to achieve mode separation; Inverse Warping Transform Module: Used to transform the separated Warped signals of each mode from the Warped domain back to the original domain, thereby obtaining the original time-domain signals of each mode; The results visualization module is used to draw the separation results, which include the time-domain waveforms of each mode and the corresponding time-frequency spectrum; Computer equipment: including a memory and a processor, wherein the memory is used to store computer program instructions for the above-mentioned modules, and the processor is used to execute the programs of the various modules of the system.

9. The system according to claim 8, characterized in that: The mask filtering module is equipped with an interactive mode separation interface; the interactive mode separation interface is used for: The system receives the vertex coordinates of several polygon regions of interest generated by the user's continuous clicks on the time-spectrum graph and automatically establishes closed polygon regions. Then, the mask matrix is ​​constructed according to the selected region to separate the time spectrum of different modes. Finally, the forward operator is called to convert the time spectrum back into a time domain signal.

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