Digital equivalent source sound field reconstruction system based on underwater complex sound field environment

Abstract

The application discloses a digital equivalent source sound field reconstruction system based on an underwater complex sound field environment, and comprises the following modules: a sound pressure acquisition module that acquires radiated sound pressure data at a measurement point through a hydrophone array; an intelligent analysis module that, based on the radiated sound pressure data, derives a shallow sea sound pressure Green function by using a shallow sea Pekeris waveguide model, and constructs an underwater sound field equivalent source equation; a compressed sensing module that, based on the underwater sound field equivalent source equation, converts the underwater sound field equivalent source equation into a compressed sensing problem, and solves the compressed sensing problem by using an accelerated proximal gradient descent algorithm to obtain a compressed sensing equivalent source strength; and a sound field reconstruction module that constructs a free field Green function, and obtains underwater reconstructed sound pressure by combining the free field Green function with the compressed sensing equivalent source strength, so that the digital equivalent source sound field reconstruction of the underwater complex sound field environment is realized, the data processing efficiency is improved, and the demand for computing resources is reduced.

Description

Technical Field

[0001] This invention relates to the field of sound field reconstruction technology, and in particular to a digital equivalent source sound field reconstruction system based on complex underwater sound field environments. Background Technology

[0002] In the field of underwater acoustics research, the accurate simulation and reconstruction of underwater sound fields has always been a key research focus. From the early stages, researchers have continuously explored effective methods to analyze the complex characteristics of underwater sound fields. With the advancement of theoretical research, the equivalent source method has gradually emerged as a numerical solution for target scattering problems. Its core principle is that the radiation or scattering sound field generated by a target of any shape can be represented by the superposition of sound fields generated by source intensities on a virtual surface. This method effectively avoids the singular integral calculation problem faced by other methods when dealing with target scattering problems, and overcomes many challenges brought about by the complexity of target shapes in engineering applications. It has shown significant advantages in underwater sound field research. However, despite the progress made in underwater sound field research, current technology still faces many challenges.

[0003] Currently, in underwater digital equivalent source sound field reconstruction systems, traditional systems often require a large number of point sources to simulate the sound field. This not only increases the computational complexity but also places extremely high demands on measurement equipment and computing resources. Moreover, most equivalent source methods are based on monopole sound source theory. For complex underwater sound field environments, the limitations of monopole sound source theory are becoming increasingly apparent, making it difficult to accurately describe and simulate the actual sound field distribution.

[0004] Furthermore, in the field of near-field acoustic holography, most existing systems treat the target as an independently distributed point source. However, the sound radiation propagation model of continuously distributed structural sound sources such as underwater vehicles differs from this model. This leads to a large deviation between the sound source identification results and the actual situation, which greatly increases the difficulty and cost of implementation. Therefore, this paper proposes a digital equivalent source sound field reconstruction system based on the complex underwater sound field environment. Summary of the Invention

[0005] In order to overcome the above-mentioned defects of the prior art and to achieve the above objectives, the present invention proposes the following technical solution:

[0006] A digital equivalent source sound field reconstruction system based on complex underwater acoustic environments includes:

[0007] Sound pressure acquisition module: Acquires radiated sound pressure data at measurement points through a hydrophone array;

[0008] Intelligent Analysis Module: Based on radiated sound pressure data, the Green's function of shallow sea sound pressure is derived using the shallow sea Pekeris waveguide model, and the equivalent source equation of underwater sound field is constructed.

[0009] Compressed sensing module: Based on the underwater sound field equivalent source equation, the underwater sound field equivalent source equation is transformed into a compressed sensing problem, and the accelerated proximal gradient descent algorithm is used to solve the reduced L1 norm to obtain the compressed sensing equivalent source strength.

[0010] Sound field reconstruction module: Constructs a free-field Green's function, and obtains the underwater reconstructed sound pressure by combining the free-field Green's function with the equivalent source strength of compressed sensing, thereby realizing the digital equivalent source sound field reconstruction of complex underwater sound field environments.

[0011] The process of acquiring radiated sound pressure data is as follows:

[0012] The hydrophone array is arranged in a uniform grid distribution. According to the sampling theorem, the element spacing is set to... Where λ is the wavelength of the sound wave in water;

[0013] Initial sound pressure pressure data was acquired by synchronously sampling the hydrophone array. After outliers were removed from the acquired initial sound pressure pressure data using the 3σ criterion, the data was then transformed using FFT to obtain the frequency domain data, thus forming the radiated sound pressure pressure data. .

[0014] The shallow-sea Pekeris waveguide model is represented as follows:

[0015]

[0016] in, Indicates the horizontal distance of the field point. Indicates azimuth. Indicates the field depth. , , Together they form a cylindrical coordinate system, where k is the wave number, expressed as... , Represents angular frequency. This is radiated sound pressure data.

[0017] The process of deriving the Green's function for shallow sea acoustic pressure is as follows:

[0018] Define the shallow sea sound pressure Green's function as: z represents the field depth, and r represents the horizontal distance from the field point. The horizontal depth of the sound source. The horizontal distance from the sound source;

[0019] Based on the Pekeris waveguide model for shallow seas, the Green's function for sound pressure in shallow seas is derived using the image method. Considering the superposition effect of infinitely many reflections of sound waves in a shallow sea environment, the expression is:

[0020]

[0021] in, The Green's function for shallow sea sound pressure. Represents the imaginary unit. Indicates the direct wave path distance. Indicates the path distance after reflection from the water surface. This indicates the path distance after reflection from the bottom of the water. The water surface reflectance, Let be the reflection coefficient at the bottom of the water, k be the wave number, and n be the index.

[0022] The process of obtaining the equivalent source equation for the underwater sound field is as follows:

[0023] Three types of equivalent sources are defined, the first type being the equivalent source of a real sound source. The quantity is Second type of water surface reflection equivalent source The quantity is The third type of underwater reflection equivalent source The quantity is ;

[0024] The equivalent source strength vector is represented by the three types of equivalent sources as defined. , The total number of equivalent sources is determined by the Green's function of shallow sea acoustic pressure. The equivalent source equation for the underwater sound field is constructed as follows: ,in, For noise, For equivalent source strength, This is the theoretical sound pressure calculated using the underwater sound field equivalent source equation.

[0025] The process of transforming the equivalent source equation of the underwater sound field into a compressed sensing problem is as follows:

[0026] The problem of solving the equivalent source equation of the underwater sound field is transformed into an L1 norm minimization problem, assuming the noise threshold is... The problem can then be transformed as follows:

[0027] , For equivalent source strength, This is the noise threshold.

[0028] The process of obtaining the compressed sensing equivalent source strength by solving the L1 norm reduction using the accelerated proximal gradient descent algorithm is as follows:

[0029] The algorithm is initialized using an accelerated proximal gradient descent algorithm, and an objective function is defined. objective function The calculation formula is:

[0030] ,in, is the transpose of the Green's function for shallow sea sound pressure, and p is the radiated sound pressure data. This represents the current equivalent source distribution;

[0031] Then, the proximal operator is updated, and the iteration stopping condition is set when... Stop iteration when Represents the L2 norm;

[0032] Once the conditions are met, output the current optimal equivalent source strength estimate. And from the current best equivalent source strength estimate The corresponding compressed sensing equivalent source strength is separated from the data to form the compressed sensing equivalent source strength. .

[0033] The implementation process of the proximal operator update is as follows:

[0034] First, define the step size. Then, the equivalent source strength q is updated using the proximal operator for the vector. The update rules for element v in the data are as follows:

[0035] When v> The equivalent source after one iteration update The corresponding element is v− ;

[0036] When |v|≤ ,but The corresponding element in is 0;

[0037] When v<− ,but The corresponding element in is v+ .

[0038] The process of obtaining underwater reconstructed sound pressure is as follows:

[0039] The free-field Green's function is defined based on the shallow-sea Pekeris waveguide model and expressed as follows: , Let be the water surface reflection coefficient, and k be the wave number. For N measurement points, the true equivalent source has: In the case of , the i-th underwater reconstructed sound pressure The calculation formula is ,in, It is a strong source equivalent to compressed sensing. (i, j) represents the free-field Green's function value from the j-th true equivalent source to the i-th measurement point, where j is the index and .

[0040] The present invention has the following beneficial effects:

[0041] In this invention, firstly, by defining equivalent sources of real sound sources, equivalent sources of water surface reflection, and equivalent sources of underwater reflection, various reflection situations of sound waves during underwater propagation can be comprehensively considered, thereby simulating the underwater sound field more accurately. This method of classifying equivalent sources can describe the behavior of sound waves at different medium interfaces in more detail, making the simulation results closer to the actual sound field distribution. Combining various equivalent sources into equivalent source vectors allows for a more systematic handling of the generation and propagation process of sound waves in the mathematical model, which helps to improve the accuracy of sound field simulation.

[0042] Secondly, by utilizing compressed sensing theory, the number of measurement points is reduced. In traditional methods, a large number of measurement points are often required to accurately simulate the sound field. However, this technical solution, through compressed sensing, can reconstruct the far-field scattered sound field with fewer measurement points, thereby reducing the number of measurement points, simplifying the data processing process, improving data processing efficiency, and reducing the demand for computing resources. Attached Figure Description

[0043] Figure 1 This is a system block diagram of the digital equivalent source sound field reconstruction system based on complex underwater sound field environment proposed in this invention. Detailed Implementation

[0044] 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, and 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. Example 1

[0045] like Figure 1 As shown, the digital equivalent source sound field reconstruction system based on complex underwater sound field environment proposed in this invention includes:

[0046] Sound pressure acquisition module: Acquires radiated sound pressure data at measurement points through a hydrophone array;

[0047] The process of arranging the hydrophone array is as follows:

[0048] Pre-defined measurement points are used, and a hydrophone array is arranged in a uniform grid distribution. According to the sampling theorem, the element spacing is set to... Where λ is the wavelength of the sound wave in water, and λ is determined by the speed of sound c and the frequency f using the formula... Obtain;

[0049] Specifically, the element spacing obtained in this way can effectively avoid spatial aliasing and ensure that the collected data can truly reflect the sound field distribution;

[0050] For example: if the speed of sound c = 1500 m / s and the frequency of the sound source f = 500 Hz, then λ = 1500 / 500 = 3 m, and the spacing between array elements should be 3 / 2 = 1.5 m;

[0051] The logic for arranging the hydrophone array is that in shallow sea environments, strong reflections are easily formed between the water surface and the seabed. If the hydrophones are too close together, the reflected waves will interfere with the direct waves, resulting in the collected sound pressure data containing a lot of noise, which will affect the accuracy of subsequent analysis.

[0052] The hydrophone array was sampled synchronously, with the sampling frequency based on the highest frequency of the sound source. According to the Nyquist criterion, the sampling frequency satisfy To avoid aliasing in the time domain and ensure that the acquired signal can completely reproduce the true information of the sound source;

[0053] After removing outliers from the initial sound pressure data using the 3σ criterion, the data is then transformed using FFT to obtain the frequency domain data, thus forming the radiated sound pressure data. .

[0054] Intelligent Analysis Module: Based on radiated sound pressure data, the Green's function of shallow sea sound pressure is derived using the shallow sea Pekeris waveguide model, and the equivalent source equation of underwater sound field is constructed.

[0055] The Pekeris waveguide model for shallow seas is a theoretical model used to describe the propagation characteristics of sound waves in shallow sea environments with a uniform seawater layer and an elastic seabed. Unlike traditional non-trained learning models, sound waves propagate in shallow seas and are reflected at the water surface and seabed, which determines the propagation characteristics in shallow sea environments. In the Pekeris waveguide model, sound wave propagation in shallow seas satisfies the following wave equation:

[0056]

[0057] in, Indicates the horizontal distance of the field point. Indicates azimuth. Indicates the field depth. , , Together they form a cylindrical coordinate system, where k is the wave number, expressed as... , Represents angular frequency. This is radiated sound pressure data;

[0058] Specifically, in shallow sea environments, the sound field is formed by the superposition of direct waves and reflected waves from the water surface and bottom;

[0059] The process of deriving the Green's function for shallow sea acoustic pressure is as follows:

[0060] Define the shallow sea sound pressure Green's function as: Describe the point source in The sound field generated at (r,z), and the sound pressure response of the generated sound field at (r,z). The horizontal depth of the sound source. Let z be the horizontal distance from the sound source, z be the field depth, and r be the horizontal distance from the field point.

[0061] Based on the Pekeris waveguide model for shallow seas, the Green's function for sound pressure in shallow seas is derived using the image method. Considering the superposition effect of infinitely many reflections of sound waves in a shallow sea environment, the expression is:

[0062]

[0063] in, The Green's function for shallow sea sound pressure. Represents the imaginary unit. , , These represent the distances along different paths during the nth reflection. Indicates the direct wave path distance. Indicates the path distance after reflection from the water surface. This indicates the path distance after reflection from the bottom of the water. The water surface reflectance, Let be the reflection coefficient at the bottom of the water, and k be the wave number;

[0064] Specifically, the derivation of the Green's function is based on the Pekeris waveguide model in shallow seas, taking into account the superposition effect of multiple reflections of sound waves at the water surface and bottom in shallow sea environments. The Green's function derived by methods such as the mirror method can accurately describe the sound pressure response of the sound field generated by the point source at different locations at the measurement point. Compared with traditional methods, the Green's function derivation based on the Pekeris waveguide model in shallow seas is more physically meaningful and can better handle the complex sound field propagation problem in shallow sea environments.

[0065] Furthermore, The direct wave path distance is expressed as... ,

[0066] The path distance after reflection from the water surface is denoted as... , The path distance after reflection from the bottom of the water is expressed as... ;

[0067] Water surface reflectance In an approximate case, it is −1, meaning that when a sound wave is reflected from the water surface, its phase is reversed by 180°, and the water surface reflection coefficient is... The calculation formula is: The reflection coefficient reflects the proportion of energy reflected when a sound wave is reflected at the bottom of the water. , For the density of seawater and the speed of sound, , The density and speed of sound on the seabed;

[0068] underwater reflectivity The calculation formula is: ,in , For the density of seawater and the speed of sound, , The density and speed of sound on the seabed;

[0069] Define three types of equivalent sources:

[0070] The first category is equivalent sources of real sound sources. It is arranged inside the sound source, and its quantity is set to ;

[0071] The second type is the water surface reflection equivalent source. Arranged along the water surface, in quantities of This is used to simulate the effect of water surface reflection on the sound field;

[0072] The third type is underwater reflection equivalent sources. Arranged along the bottom of the water, the quantity is Used to simulate underwater reflection effects;

[0073] The equivalent source strength vector is represented by the three types of equivalent sources as defined. ,in, Total number of equivalent sources ;

[0074] Radiated sound pressure data obtained from measurements The sound pressure is superimposed from all equivalent sources, thus yielding the Green's function of sound pressure through shallow sea. The equivalent source equation for the underwater sound field is constructed as follows: ,in, For noise, For equivalent source strength, The theoretical sound pressure is calculated using the equivalent source equation of the underwater sound field.

[0075] Specifically, the construction of the entire equivalent source equation takes into account the characteristics of the shallow sea environment. Parameters such as seawater density, sound speed, water depth, and surface and bottom reflection coefficients are all incorporated into the model, enabling the equation to adapt well to the complex sound field propagation in the shallow sea environment. By combining different types of equivalent sources with Green's functions, the equivalent source equation is constructed. This equation can link the measured sound pressure with the equivalent source strength, thereby reconstructing the sound field by solving for the equivalent source strength. This innovatively transforms the complex sound field problem into a solvable mathematical problem.

[0076] Compressed sensing module: Based on the underwater sound field equivalent source equation, the underwater sound field equivalent source equation is transformed into a compressed sensing problem, and the accelerated proximal gradient descent algorithm is used to solve the reduced L1 norm to obtain the compressed sensing equivalent source strength.

[0077] The process of transforming the equivalent source equation of the underwater sound field into a compressed sensing problem is as follows:

[0078] The equivalent source exhibits sparsity, which is true in the case of a real sound source. In the equation, only the element corresponding to the actual location of the sound source is non-zero, and the equivalent source reflected on the water surface is... Equivalent source of underwater reflection In this array, only the elements corresponding to strong reflection paths are non-zero, and the overall sparsity is s≈0.2M. Assuming M=150, then there are approximately 0.2×150=30 non-zero elements.

[0079] Based on this sparsity property, the problem of solving the equivalent source equation of the underwater sound field is transformed into an L1 norm minimization problem, assuming the noise threshold is... The problem can then be transformed as follows:

[0080] , For equivalent source strength;

[0081] The process for determining the noise threshold ϵ is as follows:

[0082] Determined by the noise variance, the specific relationship is as follows: , where N is the amount of measurement data (number of array elements). The noise standard deviation is estimated by collecting ambient noise data when there is no noise source, σn≈0.1Pa;

[0083] Through this transformation, the originally difficult-to-solve overdetermined ill-conditioned problem is transformed into finding a solution with the minimum L1 norm under certain noise constraints, thereby effectively utilizing the sparsity of the equivalent source strength and improving the stability and accuracy of the solution.

[0084] The process of obtaining the compressed sensing equivalent source strength by solving the L1 norm reduction using the accelerated proximal gradient descent algorithm is as follows:

[0085] The algorithm is initialized using an accelerated proximal gradient descent (APG) algorithm, setting the initial equivalent source strength. Auxiliary variables The iteration number t=0 is set, and the Lipschitz constant is calculated. Where λmax represents the maximum eigenvalue of the source strength. This is the transpose of the Green's function for shallow sea acoustic pressure.

[0086] Define an objective function objective function Based on the current variables (current equivalent source distribution) The calculation is as follows:

[0087] , is the Green's function for shallow sea acoustic pressure, and p is the radiated acoustic pressure data;

[0088] Specifically, the physical meaning of this step is through the current equivalent source distribution. The gradient of the objective function is calculated using the measured radiated sound pressure data p. This gradient reflects the direction and rate of change of the objective function under the current equivalent source distribution.

[0089] Then, the proximal operator update is performed. First, the step size is defined. Then, the equivalent source strength q is updated using a soft thresholding function (proximal operator) for the vector. The update rules for element v in the data are as follows:

[0090] When v> The equivalent source after one iteration update The corresponding element is v− ;

[0091] When |v|≤ ,but The corresponding element in is 0;

[0092] When v<− ,but The corresponding element in is v+ ;

[0093] Specifically, the physical meaning of this soft thresholding operation is to adjust the estimated value of the equivalent source strength, setting the smaller source strength values ​​(within a certain range) to 0, thereby utilizing the sparsity of the equivalent source strength, which helps to find a more reasonable distribution of the equivalent source strength during the iteration process.

[0094] Set the iteration stopping condition, when Stop iteration when Represents the L2 norm;

[0095] Once the conditions are met, it indicates that the estimated value of the equivalent source strength has converged, the iteration process stops, and the current optimal estimated value of the equivalent source strength is output. And from the current best equivalent source strength estimate The corresponding compressed sensing equivalent source strength is separated from the data to form the compressed sensing equivalent source strength. .

[0096] Sound field reconstruction module: Constructs a free-field Green's function, and obtains the underwater reconstructed sound pressure by combining the free-field Green's function with the equivalent source strength of compressed sensing, so as to realize the digital equivalent source sound field reconstruction of complex underwater sound field environment;

[0097] In a free field (space without reflection), the Green's function contains only direct waves. Based on the theoretical foundation of the shallow-sea Pekeris waveguide model, the free-field Green's function is defined as follows: , Here, k is the water surface reflection coefficient, and k is the wave number. Represents the imaginary unit;

[0098] Specifically, in the shallow-sea Pekeris waveguide model, it is assumed that the seawater layer is homogeneous and the seabed is horizontal. When considering the free field (no reflection space), sound waves propagate only as direct waves. According to wave theory, the free-field Green's function describes the sound pressure field distribution generated by a point source in space. Based on the theoretical derivation of the shallow-sea Pekeris waveguide model, the free-field Green's function can be directly given by the model, and its expression is... It reflects the characteristics of sound waves propagating from the source to the observation point, and only considers the direct wave, without including other complex factors such as reflected waves;

[0099] The process of obtaining underwater reconstructed sound pressure by combining the free-field Green's function with the equivalent source strength of compressed sensing is as follows:

[0100] Known compressed sensing equivalent source strength Therefore, the reconstructed underwater sound pressure at a certain point is the sum of the sound pressures produced by all the real equivalent sources at that point. For N measurement points, the real equivalent sources have In the case of , the i-th underwater reconstructed sound pressure The formula for calculation is: ,in, To reconstruct sound pressure underwater, (i, j) represents the free-field Green's function value from the j-th true equivalent source to the i-th measurement point, where j is the index and ;

[0101] Specifically, this means that the sound pressure at each measurement point is the sum of the sound pressures contributed by each real equivalent source, thus simulating the distribution of the sound field generated by the real equivalent source in a free field.

[0102] Using the root mean square error of sound pressure (RMSE) as an indicator, the calculation formula is as follows:

[0103] ,in, Indicates theoretical sound pressure;

[0104] Specifically, the RMSE index reflects the relative deviation between the reconstructed underwater sound pressure and the theoretical sound pressure. The smaller the RMSE value, the closer the reconstructed sound pressure is to the theoretical sound pressure, that is, the better the reconstruction effect. A threshold of 5% for RMSE is set. When RMSE ≤ 5%, the reconstruction result is considered to meet the accuracy requirements and the reconstruction is qualified; otherwise, it is unqualified.

[0105] In the application, several formulas are calculated by removing dimensions and taking their numerical values. The formulas are established by collecting a large amount of data and simulating the most recent real situation. Some coefficients or weights in the formulas are set by those skilled in the art according to the actual situation, so they will not be elaborated here.

[0106] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0107] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A digital equivalent source sound field reconstruction system based on an underwater complex sound field environment, characterized in that, Comprise: A sound pressure acquisition module: acquiring the radiated sound pressure data at the measurement point through the hydrophone array; An intelligent analysis module: based on the radiated sound pressure data, using the shallow sea Pekeris waveguide model to deduce the shallow sea sound pressure Green function, and constructing the underwater sound field equivalent source equation; The shallow sea Pekeris waveguide model is expressed as: wherein, denotes the horizontal distance of the field point, denotes the azimuth angle, denotes the depth of the field point, , , together form the cylindrical coordinates, k is the wave number, and is denoted as , denotes the angular frequency, is the radiated sound pressure data; The process of deducing the shallow sea sound pressure Green function is: The shallow water pressure Green's function is defined as , z is the depth of the field point, r is the horizontal distance of the field point, is the horizontal depth of the sound source, is the horizontal distance of the sound source; Based on the shallow sea Pekeris waveguide model, the shallow sea sound pressure Green function is deduced by mirror method, considering the superposition effect of infinite reflection of sound wave in shallow sea environment, and the expression is: wherein, is the shallow water pressure Green function, denotes the imaginary unit, denotes the direct path distance, denotes the path distance after reflection on the water surface, denotes the path distance after reflection on the water bottom, is the water surface reflection coefficient, is the water bottom reflection coefficient, k is the wave number, and n is the index; the compressed sensing module: based on the underwater sound field equivalent source equation, the underwater sound field equivalent source equation is converted into a compressed sensing problem, and an accelerated proximal gradient descent algorithm is used to solve the L1 norm to obtain the compressed sensing equivalent source strength; A sound field reconstruction module: constructing the free field Green function, obtaining the underwater reconstructed sound pressure by combining the compressed sensing equivalent source strength with the free field Green function, and realizing the digital equivalent source sound field reconstruction of underwater complex sound field environment.

2. The digital equivalent source sound field reconstruction system based on underwater complex sound field environment according to claim 1, characterized in that, The process of acquiring the radiated sound pressure data is: The hydrophone array is arranged in a uniform grid distribution mode, and according to a sampling theorem, the array element spacing is set as wherein λ is the wavelength of the sound wave in water. The hydrophone array is synchronously sampled to collect initial sound pressure data. After removing abnormal values from the collected initial sound pressure data through a 3σ criterion, frequency domain data is obtained through FFT transformation to form the radiation sound pressure data .

3. The digital equivalent source sound field reconstruction system based on underwater complex sound field environment according to claim 1, characterized in that, The process of obtaining the underwater sound field equivalent source equation is: Three types of equivalent sources are defined, the first type of real sound source equivalent source , the number of , the second type of water surface reflection equivalent source , the number of , the third type of water bottom reflection equivalent source , the number of ; Three types of equivalent source representations are defined to represent the equivalent source strength vector , is the total number of equivalent sources, the underwater sound field equation of equivalent sources is constructed by shallow sea sound pressure Green function is expressed as: , where is the noise, is the equivalent source strength, is the theoretical sound pressure calculated by the underwater sound field equation of equivalent sources.

4. The digital equivalent source sound field reconstruction system based on underwater complex sound field environment according to claim 1, characterized in that, The process of converting the underwater sound field equivalent source equation into a compressed sensing problem is: The solving problem of the equivalent source equation of underwater sound field is converted into the L1 norm minimization problem, and the noise threshold is The conversion mode of the problem is represented as: ， is the equivalent source strength, is the noise threshold, where z is the field point depth, r is the field point horizontal distance, is the sound source horizontal depth, is the sound source horizontal distance, p is the radiated sound pressure data.

5. The digital equivalent source sound field reconstruction system based on underwater complex sound field environment according to claim 4, characterized in that, The process of solving the reduced L1 norm by using the accelerated proximal gradient descent algorithm to obtain the compressed sensing equivalent source strength is: By an accelerated proximal gradient descent algorithm, the algorithm is initialized and a target function is defined , the target function The calculation formula is: ， where, is the transpose of the shallow-water pressure Green's function, p is the radiated pressure data, is the current equivalent source distribution; proximal operator update is then performed and an iteration stopping condition is set, when the iteration is stopped, denotes the two-norm; After the condition is met, output the current optimal equivalent source strength estimation value And separate the corresponding compressed sensing equivalent source strength from the current optimal equivalent source strength estimation value Form a compressed sensing equivalent source strength .

6. The digital equivalent source sound field reconstruction system based on underwater complex sound field environment according to claim 5, characterized in that, The implementation process of proximal operator update is: First, define the step size Then, update the equivalent source strength q using the proximal operator, for the element v in the vector The update rule is as follows: When v , the corresponding element of the updated equivalent source strength after one iteration is v− ; When |v|≤ then the corresponding element in is 0; When v < − then the corresponding element in v+is v .​ 7. The digital equivalent source sound field reconstruction system based on underwater complex sound field environment according to claim 6, the process of obtaining the underwater reconstructed sound pressure is: Based on the shallow water Pekeris waveguide model, the free-field Green's function is defined as , is the water surface reflection coefficient, k is the wave number, for N measurement points, the real equivalent source has cases, the calculation formula of the i-th underwater reconstructed sound pressure is , is the compressed sensing equivalent source strength, (i,j) denotes the free-field Green function value from the jth real equivalent source to the ith measurement point, j is an index and .

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