Methods for Localization and Feature Estimation of Random Sound Sources in Layered Media

Abstract

This invention relates to the field of random sound source localization and feature estimation technology, specifically to a method for random sound source localization and feature estimation in layered media, comprising the following steps: establishing a random sound source model in the layered media; at each observation point in the upper layer of the layered media, for multiple different frequencies corresponding to wavenumbers, using sensors to perform multiple independent sound wave field measurements to obtain sound wave field measurement data; dividing the region where the random sound source is located into a two-dimensional uniform grid, and determining the initial values ​​of the numerical solutions for the mean and variance of the random sound source based on the grid points; based on the sound wave field measurement data, and based on the kernel matrix singular value decomposition, solving the random sound source model in the layered media, iteratively updating the numerical solutions for the mean and variance of the random sound source to obtain the final numerical solutions for the mean and variance; this invention can achieve stable and high-precision reconstruction of the spatial distribution characteristics of random sound sources in layered media.

Description

Technical Field

[0001] This invention relates to the field of random sound source localization and feature estimation technology, specifically to a method for random sound source localization and feature estimation in a layered medium. Background Technology

[0002] In practical applications such as resource exploration, structural monitoring, and anomaly identification, underground sound sources (e.g., disturbances caused by crack propagation, fluid seepage, etc.) typically exhibit high uncertainty in terms of spatial distribution, excitation intensity, and mechanism of action. These sound sources can be considered as randomly occurring wave source terms in the underground medium, and their accurate identification is of great significance for tasks such as resource location, reservoir evaluation, disaster early warning, and anomaly analysis.

[0003] Current sound source reconstruction techniques are mostly based on deterministic models, typically assuming that the sound source has a known excitation mode or a stable spatial structure. However, in complex underground environments, these methods often struggle to capture the statistical characteristics of the sound source, such as the spatial fluctuations in its intensity distribution or the randomness of the excitation process. Furthermore, traditional methods are sensitive to observational noise, which can easily lead to unstable or even distorted estimation results, limiting their reliability and scalability in practical applications. This has become one of the key technical bottlenecks that urgently need to be overcome in the estimation of random sound sources in layered media.

[0004] To address the aforementioned problems, stochastic modeling methods, which have gradually emerged in recent years, have provided a new solution for sound source identification. By modeling underground sound sources as random fields with statistical structures (such as Gaussian white noise or generalized stochastic processes) and combining them with wave response observation data (such as ground or well vibration records), the statistical characteristics of sound sources, such as mean and covariance, can be reconstructed, thereby achieving a more comprehensive description of complex sound source distributions.

[0005] Although random sound source estimation models theoretically possess greater adaptability and stability, they still face multiple challenges in practical engineering contexts, including: (1) the complexity of modeling wave propagation under layered underground structures; (2) the fusion of multi-frequency observation data and the effective utilization of high-frequency responses; (3) stable estimation under data-constrained or sparse orbital conditions; and (4) the efficiency of parameter identification and numerical computation for random source term models. Therefore, it is urgent to develop a new random sound source reconstruction method that is stable and applicable in layered media, can effectively fuse multi-frequency observation information, and possesses robustness, in order to improve the analytical capability of complex underground sound sources and achieve accurate identification and effective analysis of the distribution of underground random sound sources. Summary of the Invention

[0006] In view of the above problems, the present invention provides a method for locating and estimating the features of random sound sources in layered media, which solves the technical problem in the prior art of how to achieve stable and high-precision reconstruction of the spatial distribution characteristics of sound sources with strong randomness and low regularity in layered underground media under the condition of observation noise.

[0007] This invention provides a method for locating and estimating the characteristics of random sound sources in a layered medium, comprising the following steps:

[0008] Step S1: Establish a layered medium random sound source model, wherein the layered medium random sound source model represents the relationship between the sound wave field and the mean and variance of the random sound source, and the layered medium includes an upper layer and a lower layer;

[0009] Step S2: Determine multiple observation points on the upper layer of the layered medium. For each observation point, use a sensor to perform multiple independent acoustic wave field measurements on each wave number corresponding to multiple different frequencies to obtain acoustic wave field measurement data.

[0010] Step S3: Divide the region where the random sound source is located into a two-dimensional uniform grid, and determine the initial values ​​of the numerical solutions for the mean and variance of the random sound source based on the grid points.

[0011] Step S4: Based on the sound wave field measurement data, and based on the kernel matrix singular value decomposition, solve the random sound source model of the layered medium, and iteratively update the numerical solutions of the mean and variance of the random sound source.

[0012] When the preset iteration termination condition is met, the final numerical solutions of mean and variance are obtained as the estimated statistical distribution characteristics of the random sound source.

[0013] Preferably, step S1 specifically includes:

[0014] Step S1-1: Determine the propagation process of time harmonic waves in the layered medium and the corresponding radiation conditions;

[0015] Step S1-2: Based on the propagation process and radiation conditions, obtain the location. and wavenumber in layered media Corresponding Green's function The time-harmonic sound wave propagation process is transformed into an equivalent stochastic integral form based on the Green's function, which serves as the stochastic sound source model for the layered medium.

[0016] Preferably, in step S1-2, the expression for the layered medium random sound source model is:

[0017]

[0018] in, Represents a given wavenumber Time position The sound wave field at that location, For random sound source regions, Indicates position and the corresponding wavenumber in layered media Green's function, Indicates position The mean of random sound sources at a given location. Indicates position The standard deviation of random sound sources at that location, Indicates position Brownian motion at the location The differential.

[0019] Preferably, step S2 specifically includes:

[0020] Selecting the upper region of the layered medium Given an observation point, Wavenumber corresponding to different frequencies At each observation point At each wave number The excited wave field proceeds Subsequent independent sample track measurements yielded acoustic wave field measurements. ;

[0021] in, Indicates the first One observation point, Indicates the first Number of waves, An index for the number of independent sample orbit measurements. , and , This represents the total number of independent sample orbit measurements. This represents the total number of wavenumbers. This represents the total number of observation points.

[0022] Preferably, step S3 specifically includes:

[0023] Determine the first and second coordinate directions for the region where the random sound source is located, and divide the region into equal parts along the first coordinate direction. The portions are divided equally along the second coordinate direction. Parts, forming 1 grid point;

[0024] The numerical expression for determining the mean of a random sound source is:

[0025]

[0026] The numerical solution expression for determining the variance of a random sound source is:

[0027]

[0028] in, Represents the mean of random sound sources At grid points Numerical solution at that location, Represents the variance of random sound sources At grid points Numerical solution at that location, express 3D real-valued vector space;

[0029] The initial values ​​for the numerical solutions of the mean and variance of a random sound source are respectively... , .

[0030] Preferably, step S4 specifically includes: step S4-1, obtaining a numerical solution for the mean of a random sound source. Step S4-2: Obtain the numerical solution of the variance of the random sound source. ;

[0031] Specifically, step S4-1 includes:

[0032] Step S4-1-1: The average measurement data of the acoustic wave field is obtained by averaging the number of independent sample track measurements based on the measured acoustic wave field values.

[0033] Step S4-1-2: Establish the sound wave field mean data vector and mean kernel matrix based on the mean measurement data of the sound wave field, and set the first discrimination parameter;

[0034] Step S4-1-3: Perform singular value decomposition on the mean kernel matrix to obtain the first singular value greater than the first discrimination parameter and the corresponding first left singular vector and first right singular vector; update the numerical solution of the random sound source mean based on the first singular value, the sound wave field mean data vector, the first left singular vector and the first right singular vector to obtain the final numerical solution of the random sound source mean.

[0035] Preferably, in step S4-1-1, the expression for the mean measurement data of the acoustic wave field is:

[0036]

[0037] in, Indicates the first The first observation point Sound wave field with a number of waves Mean measurement data, Indicates the first The first observation point The first wave number Second measurement of acoustic wave field The measured value;

[0038] In step S4-1-2, the expressions for the acoustic wave field mean data vector and mean kernel matrix are as follows:

[0039]

[0040]

[0041] in, This represents the wave field mean data vector. express 3D complex-valued vector space, Represents the mean kernel matrix, These represent the mesh subdivision step size in the first coordinate direction. Indicates position and wave number Green's function value, express 3D complex-valued matrix space;

[0042] In step S4-1-3, the step of updating the numerical solution of the random sound source mean based on the first singular value, the sound wave field mean data vector, the first left singular vector, and the first right singular vector specifically includes:

[0043] The numerical solution for calculating the mean of a random sound source is obtained using the following expression. :

[0044]

[0045] in, express Numerical solution of the source mean wavenumber. This represents the total number of first singular values. For singular value index, Indicates the first The first singular value Denotes the first left singular vector. Denotes the first right singular vector. Representing vectors conjugate transpose

[0046] ,Will Numerical solution of time source mean Candidate values ​​for numerical solutions of the sound source mean were determined;

[0047] right Make a judgment and complete the numerical solution of the mean of the random sound source. The updates specifically include:

[0048] judge Is it less than the first discrimination parameter? If not, then set Then repeat step S4-1-3; if so, set... ; to obtain the numerical solution of the final random sound source mean. .

[0049] Preferably, step S4-2 specifically includes:

[0050] Step S4-2-1: Take the variance of the real part and the variance of the imaginary part of the sound wave field measurement value with respect to the number of independent sample track measurements, and subtract them to obtain the variance measurement data of the sound wave field;

[0051] Step S4-2-2: Establish the acoustic wave field variance data vector and variance kernel matrix based on the variance measurement data of the acoustic wave field;

[0052] Step S4-2-3: Set the second discrimination parameter, perform singular value decomposition on the variance kernel matrix, obtain the second singular value greater than the second discrimination parameter and the corresponding second left singular vector and second right singular vector; update the numerical solution of the random sound source variance based on the second singular value, the sound wave field variance data vector, the second left singular vector and the second right singular vector, and obtain the final numerical solution of the random sound source variance.

[0053] Preferably, in step S4-2-1, the expression for the variance measurement data of the acoustic wave field is:

[0054]

[0055] in, Indicates the first The first observation point Sound wave field with a number of waves The variance measurement data, This indicates taking the real part of the complex value. This indicates taking the imaginary part of the complex value. and ;

[0056] In step S4-2-2, the expressions for the acoustic wave field variance data vector and variance kernel matrix are as follows:

[0057]

[0058]

[0059] in, Represents the wavefield variance data vector. Represents the variance kernel matrix. , , and ;

[0060] In step S4-2-3, the step of updating the numerical solution of the random sound source variance based on the second singular value, the sound wave field variance data vector, the second left singular vector, and the second right singular vector specifically includes:

[0061] The numerical solution for the variance of a random sound source is calculated using the following expression. :

[0062]

[0063] in, Indicates the first Numerical candidate values ​​for the source variance of wavenumbers. This represents the total number of second singular values. Indicates the first The second singular value, Denotes the second left singular vector. Denotes the second right singular vector. Representing vectors The conjugate transpose of;

[0064] Will Numerical solution of time source variance The numerical solution candidate values ​​for the source variance were determined.

[0065] right Make a judgment and complete the numerical solution of the variance of random sound sources. The updates specifically include:

[0066] judge Is it less than the second discrimination parameter? If not, then set Then repeat step S4-2-3; if so, set... The final numerical solution of the variance of the random sound sources is obtained. .

[0067] Compared with the prior art, the present invention has at least the following beneficial effects:

[0068] (1) Breaking through the limitations of deterministic modeling, realizing statistical reconstruction of random sound sources: This invention models the sound source as a random field with uncertainty and introduces two components, mean and variance, for joint reconstruction, which effectively solves the problem that existing methods cannot handle low regularity and random perturbation sound sources.

[0069] (2) Using Green's function in layered media to construct the mapping relationship between observations and source terms to maintain the physical accuracy of the model: This invention constructs an accurate Green's function expression for the reflection and transmission characteristics of waves in layered media, and establishes a numerical approximation relationship between wave field statistics (mean, variance) and source distribution by combining multi-frequency response data, thereby enhancing the adaptability of the model to the actual underground layered media background.

[0070] (3) A stable estimation algorithm based on singular value truncation is proposed to improve computational robustness and controllability: In the estimation process of mean and variance, singular value truncation and iterative convergence criteria are introduced respectively, which can effectively suppress the amplification effect of measurement noise on the estimation results and significantly improve the reconstruction accuracy and numerical stability under noise interference conditions. Attached Figure Description

[0071] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0072] Figure 1 The flowchart illustrates the method for locating and estimating the features of random sound sources in layered media provided by this invention.

[0073] Figure 2 A detailed flowchart of the method for locating and estimating the features of random sound sources in layered media provided by the present invention.

[0074] Figure 3 The diagrams show planar and three-dimensional representations of the exact solution for the mean value of a random sound source provided in a specific embodiment of the present invention.

[0075] Figure 4 The diagrams show planar and three-dimensional representations of the reconstructed numerical solution of the mean of a random sound source provided in a specific embodiment of the present invention.

[0076] Figure 5 The diagrams show planar and three-dimensional representations of the exact solution to the variance of a random sound source provided in a specific embodiment of the present invention.

[0077] Figure 6 The diagram shows planar and three-dimensional representations of the reconstructed numerical solution of the variance of a random sound source, provided for a specific embodiment of the present invention. Detailed Implementation

[0078] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0079] This invention proposes a method for locating and estimating the characteristics of random sound sources in layered media. By constructing a Green's function expression suitable for layered media and combining mean square processing and regularization algorithm design for multi-frequency response data, a stable estimation of the statistical distribution characteristics of random sound sources is achieved, thereby effectively improving the reconstruction accuracy and computational efficiency in non-uniform media and noise interference environments.

[0080] like Figure 1 , Figure 2 As shown, this invention discloses a method for locating and estimating the features of random sound sources in a layered medium. The specific implementation steps are as follows:

[0081] Step S1: Establish a layered medium random sound source model, wherein the layered medium random sound source model represents the relationship between the sound wave field and the mean and variance of the random sound source, and the layered medium includes an upper layer and a lower layer;

[0082] In this step, the present invention first establishes a propagation model of time-harmonic sound waves from a random sound source in a layered medium to describe the propagation process of time-harmonic sound waves in the layered medium. Then, a Green's function is constructed, and an equivalent stochastic integral equation is established as the stochastic sound source model in the layered medium. The form of the stochastic integral equation of the stochastic sound source model in the layered medium can be used for numerical solutions in subsequent steps. The specific process of this step is described in detail below.

[0083] The layered medium in this invention embodiment can be a two-layer medium having an upper medium and a lower medium. This invention uses the following partial differential equation to describe the propagation process of time-harmonic waves in the layered medium:

[0084]

[0085] Furthermore, the partial differential equations for the above propagation process satisfy the following radiation condition at infinity:

[0086]

[0087] in, Represents the Laplace operator. Represents the sound wave field. This represents the mean of a random sound source. This represents the standard deviation of a random sound source. Gaussian white noise represents the source of the interfering sound. Represents a position vector. express The length of the mold, Indicates about The partial derivatives, The imaginary unit, The wave number represents the number of sound waves propagating in a layered medium. This represents a 2-dimensional real-valued vector space.

[0088] yes Brownian motion in space formal derivative, and Together, they characterize the distribution characteristics of random sound sources. and Used to describe in Random sound source region in Its characteristics This represents the left and right boundary values ​​of the sub-region in the first and second coordinate directions. as well as All are real numbers.

[0089] The wave number, representing the propagation of sound waves in a layered medium, is expressed as:

[0090]

[0091] in, Indicates the frequency of sound waves, and These represent the wave number and velocity of the sound wave as it propagates in the upper medium, respectively. and These represent the wave number and velocity of the sound wave as it propagates in the lower medium, respectively. Pi and These represent the upper half-space containing the upper medium and the lower half-space containing the lower medium in a bilayer medium, respectively. express Values ​​in two coordinate directions.

[0092] Then, based on the symmetry, differential jump, and radiation condition satisfied at infinity of the Green's function, the time-harmonic sound wave propagation model is equivalently transformed into a stochastic integral representation by solving the Green's function corresponding to the propagation process in the layered medium that satisfies the above radiation condition.

[0093] Specifically, based on the propagation process and radiation conditions, the location is constructed. and wavenumber in layered media The corresponding Green's function It represents a given wavenumber in a layered medium context. Located in The unit point source is located at The response generated at that location.

[0094] The solution to the propagation process that satisfies the radiation condition is the sound wave field. It can be expressed as the following random integral:

[0095]

[0096] in, Represents a given wavenumber Time position The sound wave field at that location, For random sound source regions, Indicates position and the corresponding wavenumber in layered media Green's function, Indicates position The mean of random sound sources at a given location. Indicates position The standard deviation of random sound sources at that location, Indicates position Brownian motion at the location The differential.

[0097] The above random integral is used as the random sound source model of the layered medium.

[0098] Step S2: Determine multiple observation points on the upper layer of the layered medium. For each observation point, use a sensor to perform multiple independent acoustic wave field measurements on each wave number corresponding to multiple different frequencies to obtain acoustic wave field measurement data.

[0099] In this step, the present invention uses sensors in the upper medium to perform multiple observation points, multiple wavenumbers, and multiple independent acoustic wave field measurements, as described in detail below.

[0100] In the upper medium region Selected from There are 1 observation points, denoted as set. . Each observation point is used to receive wavefield observation data. Given... Wavenumber corresponding to different frequencies ,in, Indicates the first Wave number at each observation point At each wave number The excited wave field proceeds The acoustic wave field measurement values ​​obtained from the independent sample orbit measurement are denoted as follows: .in, Represents the set of observation points. Indicates the first One observation point, Indicates the first Number of waves, An index for the number of independent sample orbit measurements. , and , This represents the total number of independent sample orbit measurements. This represents the total number of wavenumbers. This represents the total number of observation points.

[0101] In some embodiments, multiple observation points can be uniformly distributed or, as needed, distributed in the upper region of the layered medium. Each observation point is equipped with an acoustic wave sensor to collect physical quantity information of the acoustic wave field at that location. The acoustic wave field may include one or more of the following: sound pressure at the particle location, particle velocity, and particle displacement. The corresponding physical quantity can be represented by a sensor of the appropriate type, such as a sound pressure sensor, velocity sensor, or displacement sensor. The acoustic wave field measurement data can be expressed in complex form, where the real part represents the wave field component corresponding to the cosine phase, and the imaginary part represents the wave field component corresponding to the sine phase. This representation is derived from the complex expression of the solution to the time-harmonic wave equation.

[0102] During the measurement process, the sound source is controlled to excite sound waves of predetermined frequencies for different operating frequencies, forming a specific wavenumber corresponding to each frequency. The sensor at each observation point performs multiple independent measurements at each wavenumber to obtain sound wavefield response data under different experimental conditions or random disturbances, thereby improving the statistical stability and noise immunity of the signal. Ultimately, measurement data of the sound wavefield physical quantities at each observation point, at each frequency (wavenumber), and under multiple measurements can be obtained, providing a reliable basis for subsequent data processing and estimation analysis.

[0103] Step S3: Divide the region where the random sound source is located into a two-dimensional uniform grid, and determine the initial values ​​of the numerical solutions for the mean and variance of the random sound source based on the grid points.

[0104] In this step, for the two-dimensional region of the layer where the random sound source is located... Perform the following two-dimensional uniform mesh partitioning:

[0105]

[0106]

[0107] in, Indicates the first coordinate direction The coordinates of each grid, , This represents the total number of grid cells in the first coordinate direction. This represents the left boundary value in the first coordinate direction. The grid partitioning step size is the first coordinate direction; Indicates the first in the second coordinate direction The coordinates of each grid, , This represents the total number of grid cells in the second coordinate direction. Indicates the left boundary value in the first coordinate direction. Let be the meshing step size in the second coordinate direction. The meshing step size satisfies:

[0108]

[0109]

[0110] Based on the above mesh partitioning, set Set the total number of grid points and define the grid points. , , And so on, until... .

[0111] Each grid point corresponds to a numerical solution for the mean and variance of a random sound source. In this invention, the total dimension of the numerical solution is determined by the number of grid points, which is equal to the total number of grid points. And determine the initial values ​​of the numerical solution. The expression for the mean numerical solution vector is:

[0112]

[0113] The expression for the variance numerical solution vector is:

[0114]

[0115] in, Represents the mean of random sound sources At grid points Numerical solution at that location, Represents the variance of random sound sources At grid points Numerical solution at that location, express A dimensional real-valued vector space.

[0116] In this step, the mean value of the random sound source is set. initial numerical solution Variance of random sound sources initial numerical solution .

[0117] Step S4: Based on the sound wave field measurement data, and based on the kernel matrix singular value decomposition, solve the random sound source model of the layered medium, and iteratively update the numerical solutions of the mean and variance of the random sound source.

[0118] When the preset iteration termination condition is met, the final numerical solutions of mean and variance are obtained as the estimated statistical distribution characteristics of the random sound source.

[0119] In this step, the mean value of the random sound source is first obtained. numerical solution This includes the following steps:

[0120] Step S4-1-1: Take the average of the measured acoustic wave field values ​​with respect to the number of independent sample track measurements to obtain the wave number. and observation points Lower acoustic wave field The mean measurement data is expressed as:

[0121]

[0122] in, Indicates the first The first observation point Sound wave field with a number of waves Mean measurement data, Indicates the first The first observation point The first wave number Secondary observation of acoustic wave field The measured value;

[0123] Step S4-1-2: Set the sound wave field mean value data vector:

[0124]

[0125] in, This represents the wave field mean data vector. express 3D complex-valued vector space.

[0126] Define the mean kernel matrix:

[0127]

[0128] in, Represents the mean kernel matrix, Indicates position and wave number Green's function value, express 3D complex-valued matrix space.

[0129] And define the mean value solution vector:

[0130]

[0131] Set the first discrimination parameter .

[0132] Step S4-1-3: Set the numerical solution for the mean of random sound sources Using Matlab's built-in functions to perform mean kernel matrix analysis Perform singular value decomposition to obtain greater than of The first singular value and the corresponding first left singular vector and the first right singular vector ,in, A positive integer represents a matrix. The singular value truncation number, and , Represents the real number field.

[0133] The following expression is used to iterate multiple times to calculate the numerical solution candidate value of the mean of a random sound source. :

[0134]

[0135] in, express Numerical solution of the source mean wavenumber. This represents the total number of first singular values. For singular value index, Indicates the first The first singular value Denotes the first left singular vector. Denotes the first right singular vector. Representing vectors conjugate transpose

[0136] ,Will Numerical solution of time source mean Candidate values ​​for numerical solutions of the sound source mean were determined;

[0137] Numerical solution candidate values ​​for the mean of random sound sources Make a judgment and complete the numerical solution of the mean of the random sound source. The updates specifically include:

[0138] judge Is it less than If not, then set Then repeat this step; if so, set... ; to obtain the numerical solution of the final random sound source mean. .

[0139] Subsequently, this invention obtains the variance of random sound sources. numerical solution This includes the following steps:

[0140] Step S4-2-1: Take the variance of the real part and the variance of the imaginary part of the acoustic wave field measurement value with respect to the number of independent sample track measurements, and subtract them to obtain the wave number. Observation points under the following circumstances wave field The variance combination measurement data is expressed as:

[0141]

[0142] in, Indicates the first The first observation point Sound wave field with a number of waves The variance measurement data, This indicates taking the real part of the complex value. This indicates taking the imaginary part of the complex value. and .

[0143] Step S4-2-2, let express At the grid splitting point The numerical solution at that point is defined by setting the wavefield variance data vector:

[0144]

[0145] in, This represents the wavefield variance data vector.

[0146] Define the variance kernel matrix:

[0147]

[0148] in, Represents the variance kernel matrix. , , and .

[0149] And define the variance numerical solution vector:

[0150]

[0151] Set the second discrimination parameter .

[0152] Step S4-2-3: Set the numerical solution for the variance of random sound sources. Using Matlab's built-in functions to calculate the variance kernel matrix Perform singular value decomposition to obtain greater than of The second singular value And the corresponding second left singular vector Second right singular vector ,in, A positive integer represents a matrix. Singular value truncation number.

[0153] The following expression is used to iterate multiple times to calculate the numerical solution candidate value of the mean of a random sound source. :

[0154]

[0155] in, Indicates the first Numerical candidate values ​​for the source variance of wavenumbers. This represents the total number of second singular values. Indicates the first The second singular value, Denotes the second left singular vector. Denotes the second right singular vector. Representing vectors The conjugate transpose of;

[0156] Will Numerical solution of time source variance The numerical solution candidate values ​​for the source variance were determined.

[0157] Candidate values ​​for numerical solutions to the variance of random sound sources Make a judgment and complete the numerical solution candidate values ​​for the variance of random sound sources. The updates specifically include:

[0158] judge Is it less than If not, then set Then repeat this step; if so, set... The final numerical solution of the variance of the random sound sources is obtained. .

[0159] Step S4-3: Output the numerical estimation results of the statistical characteristics of the sound source, and finally obtain the numerical solution of the sound source mean. Numerical solution of variance This completes the estimation of the statistical distribution characteristics of random sound sources.

[0160] To illustrate the effectiveness of the method proposed in this invention, the following detailed description of the above technical solution of this invention is provided through a specific embodiment.

[0161] Example 1

[0162] This embodiment discloses the specific values ​​of each parameter and the calculation process during the execution of the random sound source localization and feature estimation method in layered media, which are described in detail below.

[0163] Step 1: Consider the following time-harmonic acoustic wave equation with a random sound source in a layered medium:

[0164] (1)

[0165] Furthermore, the equation satisfies the following radiation condition at infinity:

[0166] (2)

[0167] wavenumber in the equation Defined as:

[0168] (3)

[0169] and , Pi, mean of random sound sources Take as:

[0170]

[0171] Variance of random sound sources Take as:

[0172]

[0173] And believe and Support sub-regions in Above, among which , and .

[0174] Step 2: Construct the Green's function and establish the equivalent stochastic integral equation. Solve for the Green's function in the layered medium corresponding to equations (1)–(2) in step S1, and transform the time-harmonic acoustic wave propagation model into an equivalent stochastic integral representation. Specifically, based on the radiation condition (2), construct the position-dependent Green's function. and the corresponding wavenumber in layered media Green's function It represents a given wavenumber in a layered medium context. Located at point The unit point source at point The response generated at the point. Then the solution to problem (1)-(2) in step 1, i.e., the wave field It can be expressed as the following random integral:

[0175]

[0176] Step 3: Collect random wavefield data from multiple frequency observation points in the upper medium using numerical simulation results. Select a region in the upper medium. There are 1 observation points, denoted as set. ,in, It is used to receive wavefield observation data. Given Different frequencies And obtain the corresponding wavenumber according to the wavenumber definition (3). At each observation point At each wave number The excited wave field proceeds Sub-independent sample orbit measurement, denoted as ,in, , and .

[0177] Step 4: Analyze the area where the random sound source is located. Perform mesh generation:

[0178]

[0179]

[0180] in, express and The step size of the mesh in the direction. , , and Based on the above mesh partitioning, set... Set the total number of grid points and define the grid points. , , And so on, until... .

[0181] Step 5: Calculate the mean of random sound sources The numerical solution specifically includes the following steps:

[0182] Step 5-1: Calculate the wavenumber by averaging the measurement data collected in Step 3 with respect to the number of sample orbits. Situation, observation point wave field Mean measurement data

[0183] ,

[0184] in, and .

[0185] Step 5-2: Set the wavefield mean data vector

[0186]

[0187] Set the mean kernel matrix

[0188]

[0189] And set the mean value solution vector

[0190]

[0191] in, and .

[0192] Step 5-3: Set the average value of random sound sources initial numerical solution and discrimination parameters .

[0193] Step 5-4: Settings Using Matlab's built-in functions, the mean kernel matrix in step 5-2 was processed. Perform singular value decomposition to obtain greater than of A singular value and the corresponding left singular vector and right singular vectors ,in, .calculate

[0194] (4)

[0195] in, . judge Is it less than If so, then set Proceed to step 6; otherwise, set... And repeat steps 5-4.

[0196] Step 6: Calculate the variance of random sound sources The numerical solution specifically includes the following steps:

[0197] Step 6-1: Take the variance of the real part and the variance of the imaginary part of the measurement data collected in Step 3, and subtract them to obtain the wavenumber. Situation, observation point wave field Variance combination measurement data

[0198] ,

[0199] in, and .

[0200] Step 6-2: Let express The meshing points described in step 4 The numerical solution at that point is defined by the wavefield variance data vector.

[0201]

[0202] Define the variance kernel matrix

[0203]

[0204] And set the variance numerical solution vector

[0205]

[0206] in, , , and .

[0207] Step 6-3: Set the variance of random sound sources initial numerical solution and discrimination parameters .

[0208] Step 6-4: Settings The variance kernel matrix in step 6-2 is processed using built-in Matlab functions. Perform singular value decomposition to obtain greater than of A singular value and the corresponding left singular vector and right singular vectors ,in, .calculate

[0209] (5)

[0210] in, Representing vectors The conjugate transpose of , and . judge Is it less than If so, then set Proceed to step 7; otherwise, set... And repeat steps 6-4.

[0211] Step 7: Output the numerical reconstruction results of the sound source statistical features. Output the numerical solution of the sound source mean obtained in Steps 5 and 6. Numerical solution of variance This completes the reconstruction of the statistical distribution characteristics of random sound sources.

[0212] like Figure 3 The diagram shows planar and three-dimensional schematics of the exact solution for the mean value of the random sound source obtained in this embodiment; as shown. Figure 4 The diagram shows planar and three-dimensional schematic representations of the reconstructed numerical solution of the random sound source mean obtained in this embodiment; as shown... Figure 5 The diagram shows planar and three-dimensional schematics of the exact solution to the variance of the random sound source obtained in this embodiment; as shown. Figure 6 The diagram shows the planar and three-dimensional schematic diagrams of the reconstructed numerical solution of the random sound source variance obtained in this embodiment.

[0213] While the specific embodiments of the present invention depict actions or steps in a particular order, this should be understood as requiring such actions or steps to be performed in the specific order shown or in sequential order, or requiring all illustrated actions or steps to be performed to achieve the desired result. In certain environments, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of this disclosure. Certain features described in the context of individual embodiments may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented individually or in any suitable sub-combination in multiple implementations.

[0214] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for locating and estimating the characteristics of random sound sources in a layered medium, characterized in that, Includes the following steps: Step S1: Establish a layered medium random sound source model, wherein the layered medium random sound source model represents the relationship between the sound wave field and the mean and variance of the random sound source, and the layered medium includes an upper layer and a lower layer; Step S2: Determine multiple observation points on the upper layer of the layered medium. For each observation point, use a sensor to perform multiple independent acoustic wave field measurements on each wave number corresponding to multiple different frequencies to obtain acoustic wave field measurement data. Step S3: Divide the region where the random sound source is located into a two-dimensional uniform grid, and determine the initial values ​​of the numerical solutions for the mean and variance of the random sound source based on the grid points. Step S4: Based on the sound wave field measurement data, and based on the kernel matrix singular value decomposition, solve the random sound source model of the layered medium, and iteratively update the numerical solutions of the mean and variance of the random sound source. When the preset iteration termination condition is met, the final numerical solutions of mean and variance are obtained as the estimated statistical distribution characteristics of the random sound source. Step S1 specifically includes: Step S1-1: Determine the propagation process of time harmonic waves in the layered medium and the corresponding radiation conditions; Step S1-2: Based on the propagation process and radiation conditions, obtain the location. and wavenumber in layered media The corresponding Green's function The time-harmonic sound wave propagation process is transformed into an equivalent stochastic integral form based on the Green's function, which serves as the stochastic sound source model for the layered medium. In step S1-2, the expression for the layered medium random sound source model is: in, Represents a given wavenumber Time position The sound wave field at that location, For random sound source regions, Indicates position and the corresponding wavenumber in layered media Green's function, Indicates position The mean of random sound sources at a given location. Indicates position The standard deviation of random sound sources at that location, Indicates position Brownian motion at the location The differential.

2. The method for locating and estimating the characteristics of random sound sources in layered media according to claim 1, characterized in that, Step S2 specifically includes: Selecting the upper region of the layered medium Given an observation point, Wavenumber corresponding to different frequencies At each observation point At each wave number The excited wave field proceeds Subsequent independent sample track measurements yielded acoustic wave field measurements. ; in, Indicates the first One observation point, Indicates the first Number of waves, An index for the number of independent sample orbit measurements. , and , This represents the total number of independent sample orbit measurements. This represents the total number of wavenumbers. This represents the total number of observation points.

3. The method for locating and estimating the characteristics of random sound sources in layered media according to claim 2, characterized in that, Step S3 specifically includes: Determine the first and second coordinate directions for the region where the random sound source is located, and divide the region into equal parts along the first coordinate direction. The portions are divided equally along the second coordinate direction. Parts, forming 1 grid point; The numerical expression for determining the mean of a random sound source is: The numerical solution expression for determining the variance of a random sound source is: in, Represents the mean of random sound sources At grid points Numerical solution at that location, Represents the variance of random sound sources At grid points Numerical solution at that location, express 3D real-valued vector space; The initial values ​​for the numerical solutions of the mean and variance of a random sound source are respectively... , .

4. The method for locating and estimating the characteristics of random sound sources in layered media according to claim 3, characterized in that, Step S4 specifically includes: Step S4-1, obtaining the numerical solution of the mean value of the random sound source. Step S4-2: Obtain the numerical solution of the variance of the random sound source. ; Specifically, step S4-1 includes: Step S4-1-1: The average measurement data of the acoustic wave field is obtained by averaging the number of independent sample track measurements based on the measured acoustic wave field values. Step S4-1-2: Establish the sound wave field mean data vector and mean kernel matrix based on the mean measurement data of the sound wave field, and set the first discrimination parameter; Step S4-1-3: Perform singular value decomposition on the mean kernel matrix to obtain the first singular value greater than the first discrimination parameter and the corresponding first left singular vector and first right singular vector; update the numerical solution of the random sound source mean based on the first singular value, the sound wave field mean data vector, the first left singular vector and the first right singular vector to obtain the final numerical solution of the random sound source mean.

5. The method for locating and estimating the characteristics of random sound sources in layered media according to claim 4, characterized in that, In step S4-1-1, the expression for the mean measurement data of the acoustic wave field is: in, Indicates the first The first observation point Sound wave field with a number of waves Mean measurement data, Indicates the first The first observation point The first wave number Second measurement of acoustic wave field The measured value; In step S4-1-2, the expressions for the acoustic wave field mean data vector and mean kernel matrix are as follows: in, This represents the wave field mean data vector. express 3D complex-valued vector space, Represents the mean kernel matrix, These represent the mesh subdivision step size in the first coordinate direction. Indicates position and wave number Green's function value, express 3D complex-valued matrix space; In step S4-1-3, the step of updating the numerical solution of the random sound source mean based on the first singular value, the sound wave field mean data vector, the first left singular vector, and the first right singular vector specifically includes: The numerical solution for calculating the mean of a random sound source is obtained using the following expression. : in, express Numerical solution of the source mean wavenumber. This represents the total number of first singular values. For singular value index, Indicates the first The first singular value Denotes the first left singular vector. Denotes the first right singular vector. Representing vectors The conjugate transpose of; ,Will Numerical solution of time source mean Candidate values ​​for numerical solutions of the sound source mean were determined; right Make a judgment and complete the numerical solution of the mean of the random sound source. The updates specifically include: judge Is it less than the first discrimination parameter? If not, then set Then repeat step S4-1-3; if so, set... ; to obtain the numerical solution of the final random sound source mean. .

6. The method for locating and estimating the characteristics of random sound sources in layered media according to claim 5, characterized in that, Step S4-2 specifically includes: Step S4-2-1: Take the variance of the real part and the variance of the imaginary part of the sound wave field measurement value with respect to the number of independent sample track measurements, and subtract them to obtain the variance measurement data of the sound wave field; Step S4-2-2: Establish the acoustic wave field variance data vector and variance kernel matrix based on the variance measurement data of the acoustic wave field; Step S4-2-3: Set the second discrimination parameter, perform singular value decomposition on the variance kernel matrix, obtain the second singular value greater than the second discrimination parameter and the corresponding second left singular vector and second right singular vector; update the numerical solution of the random sound source variance based on the second singular value, the sound wave field variance data vector, the second left singular vector and the second right singular vector, and obtain the final numerical solution of the random sound source variance.

7. The method for locating and estimating the characteristics of random sound sources in layered media according to claim 6, characterized in that, In step S4-2-1, the expression for the variance measurement data of the acoustic wave field is: in, Indicates the first The first observation point Sound wave field with a number of waves The variance measurement data, This indicates taking the real part of the complex value. This indicates taking the imaginary part of the complex value; In step S4-2-2, the expressions for the acoustic wave field variance data vector and variance kernel matrix are as follows: in, Represents the wavefield variance data vector. Represents the variance kernel matrix. , , and ; In step S4-2-3, the step of updating the numerical solution of the random sound source variance based on the second singular value, the sound wave field variance data vector, the second left singular vector, and the second right singular vector specifically includes: The numerical solution for the variance of a random sound source is calculated using the following expression. : in, Indicates the first Numerical candidate values ​​for the source variance of wavenumbers. This represents the total number of second singular values. Indicates the first The second singular value, Denotes the second left singular vector. Denotes the second right singular vector. Representing vectors The conjugate transpose of; Will Numerical solution of time source variance The numerical solution candidate values ​​for the source variance were determined. right Make a judgment and complete the numerical solution of the variance of random sound sources. The updates specifically include: judge Is it less than the second discrimination parameter? If not, then set Then repeat step S4-2-3; if so, set... The final numerical solution of the variance of the random sound sources is obtained. .

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