CN115081276B - Double-layer potential equivalent source far-field scattering sound field reconstruction method based on compressed sensing - Google Patents
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Abstract
The reconstruction method of the double-layer potential equivalent source far-field scattering sound field based on compressed sensing comprises the steps of firstly establishing a simulation environment according to a test target to obtain total sound pressure and scattering sound pressure response functions under different frequencies and various incidence angles; and then separating the scattered sound pressure and the incident sound pressure from the near-field total sound pressure according to the response function, establishing a compressed equivalent source model between the measuring point and the equivalent source surface, solving a source intensity Fourier coefficient by using a sparse algorithm, and finally calculating the far-field scattered sound pressure according to the obtained source intensity Fourier coefficient and the transfer function. According to the invention, compressed sensing and double-layer potential theory are introduced into the traditional equivalent source method, so that a sparse domain with strong equivalent source is searched, the relevance of a sensing matrix is reduced, and the reconstruction accuracy of a target far-field scattering sound field is improved under the condition of fewer measurement points.
Description
Technical Field
The invention relates to the field of target scattering and sound field reconstruction, in particular to a far-field scattering sound field reconstruction method.
Background
In an underwater environment, sound field distortion, including reflection, transmission, diffraction, or diffraction, occurs when sound waves encounter a target. The scattering acoustic field of the object is excited by the incident acoustic field, so the scattering acoustic field can be regarded as a wave that re-radiates after the object is excited. Far-field diffuse sound field is an important content of research on scattering characteristics of underwater targets. By knowing far-field scattering amplitude and phase of the underwater target, interference signals with the same amplitude and opposite phases can be transmitted by utilizing an interference principle, and scattering echoes at the far field of the target are weakened, so that the stealth effect of the underwater target is realized.
The equivalent source method is a numerical solution for solving the scattering problem of the target, and the basic principle is that the radiation or scattering sound field generated by the target with any shape can be represented by superposition of sound fields generated by source intensity on a virtual surface. The equivalent source method can avoid singular integral calculation of other methods in the problem of target scattering, and simultaneously overcomes the problem caused by complex target shape in engineering application. In the equivalent source sound field reconstruction process, complex sound pressure data (amplitude and phase) at all measurement points need to be acquired simultaneously. As the detection frequency increases, the number of acquisition instrument channels required increases, and the measurement cost is high. The number of actual measurement points is far smaller than the number of source intensities, so that the solving process of the equivalent source intensities has discomfort, and the problem of small measurement points can be solved by introducing a compressed sensing theory. The source intensity has sparsity in a certain domain, and the equivalent source method and compressed sensing can be combined, so that the accuracy of sound field reconstruction is improved by utilizing sparse reconstruction.
Disclosure of Invention
The invention provides a double-layer potential equivalent source far-field scattering sound field reconstruction method based on compressed sensing, which aims to overcome the defect of a large number of measurement points in a traditional equivalent source method.
The invention discloses a reconstruction method of a double-layer potential equivalent source far-field scattering sound field based on compressed sensing, which comprises the following steps:
s1, acquiring scattering sound pressure;
And establishing a simulation environment according to the underwater target structure and the material in the test. The relationship between the near-field total sound pressure P total (f, θ) and the scattered sound pressure P scat (f, θ) at each incident angle is obtained as follows:
Pscat(f,θ)＝Ptotal(f,θ)-Pin(f，θ) (1)
Where f is the detection frequency, θ is the different incident angles, and P in (f, θ) is the incident sound pressure. The response function H (f, theta) under the conditions of different detection frequencies and incidence angles is established as follows:
According to the response function, scattering sound pressure can be obtained from the near-field total sound pressure;
S2, constructing an equivalent source model of the measuring point and the equivalent source point;
and arranging M measuring points on a measuring surface near the target for synchronous measurement to obtain the sound pressure P scat at each measuring point on the measuring surface. N equivalent source points are configured on the equivalent source surface, and the equation between the sound pressure of the mth measuring point and N equivalent source intensities is as follows:
Wherein g d(rm,rn) is the derivative of the direction of the Green function between the sound pressure of the mth measuring point and the nth source intensity
Wherein k is wave number, r is distance between the measuring point and the source intensity,Is the directional derivative. According to the formula (3), the transmission relation between the measured sound pressure and the equivalent source intensity is written as a matrix form:
Pscat＝Gdqscat (5)
Wherein P scat is a sound pressure column vector obtained at M measuring points on a measuring surface, G d is a transmission matrix between each measuring point and equivalent source intensity, and q scat is a column vector formed by N equivalent source intensities on an equivalent source surface;
S3, solving a source strong sparse domain;
Because the equivalent source surface is axisymmetric, the equivalent source equation can be expanded into a Fourier series form along the azimuth and elevation directions of the virtual surface, and the Fourier coefficient with strong source has sparsity. And establishing a compressed equivalent source model between the measuring points and the source strong Fourier coefficients. The sound pressure of a measuring point in the sound field is P scat, and the discretized compression equivalent source equation is as follows:
Pscat＝FHC (6)
Wherein, C is the Fourier coefficient of the source intensity, and the transfer function F H between the Fourier coefficient of the source intensity and the measuring point is expressed as follows:
Wherein, Is a two-dimensional discrete fourier transform of the green's function directional derivative between the equivalent source point and the measurement point. M, N are the number of fast Fourier transform points, and k 1 and k 2 are the spatial frequencies corresponding to the source intensity azimuth angle and the pitch angle on the equivalent source surface.
In the formula (6), C is a sparse vector, F H can be regarded as a perception matrix, and the method directly utilizes a compressed perception technology to solve, namely, the minimum L1 norm problem:
Epsilon is the allowable upper error limit, epsilon in the formula (8) is taken as a small number, and a Fourier coefficient with strong source is obtained by solving;
s4, calculating a far-field scattering sound pressure reconstruction value;
Calculating a transfer function F re between the source strong Fourier coefficient and the far-field position, and calculating far-field scattering sound pressure by combining the source strong Fourier coefficient in the step S3 as follows:
Pre＝FreC (9)
Wherein P re is the far-field scattered sound pressure reconstruction value, and C is the source strong Fourier coefficient obtained in S3.
Compared with other target scattering sound field reconstruction methods, the method has the advantages that:
1) The equivalent source method has high calculation speed and high calculation precision, is suitable for reconstructing the scattered sound field of the target with any shape, and solves the problem of singular integration of some methods at the boundary.
2) The traditional equivalent source method has a large number of measurement points and is difficult to realize in actual engineering. Combining an equivalent source with a compressed sensing method, reducing the number of target near-field measuring points, expressing an equivalent source equation in a Fourier series form, and solving a source intensity Fourier coefficient based on the compressed sensing method so as to predict far-field scattering sound pressure. The problem of few measurement points in actual engineering is solved, and the reconstruction of the far-field scattering sound field by using a small number of measurement points is realized.
3) In the traditional equivalent source method, the sound field is the superposition of monopole sound sources on the virtual source surface, and the equivalent source equation is a single-layer potential expression. According to the invention, dipoles (double-layer potential) are used for replacing monopoles (single-layer potential) in the equivalent source strength equation, so that the condition number of a transmission matrix can be reduced, namely, the relevance of a sensing matrix in compressed sensing is reduced, and the accuracy of sparse reconstruction is improved. Based on a double-layer potential equivalent source and a compressed sensing method, the sparse reconstruction stability and accuracy are improved from the two aspects of reducing the correlation of a sensing matrix and increasing the sparsity of a source strong sparse domain, so that the accuracy of a reconstructed target far-field scattering sound field is further improved when the number of measuring points is small.
Drawings
FIG. 1 is an overall flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of a simulation environment.
Fig. 3 is a schematic diagram of a measurement plane and an equivalent source plane.
Fig. 4 is a graph of total sound pressure and direct wave sound pressure at various locations of near field measurement points.
Fig. 5 is a graph of the scattered sound pressure and theoretical sound pressure at various locations of the near field measurement point.
FIG. 6 is a graph of measurement point count versus far field 100m-120m scattered sound pressure amplitude versus error based on conventional equivalent source and compressed equivalent source methods.
FIG. 7 is a graph of condition number versus measurement point for single-layer potential and double-layer potential transfer matrices.
FIG. 8 is a graph of single-layer potential and double-layer potential sensing matrix correlation versus measurement point number.
FIG. 9 is a graph of measurement point count and far field 100m-120m scattered sound pressure amplitude versus error for compressing an equivalent source method based on single and double layer potentials.
Fig. 10 (a) is a graph of far field 100m-120m scattering sound pressure level reconstruction values based on a compressed equivalent source method when the number of measurement points is 100.
Fig. 10 (b) is a graph of the reconstructed value of scattering phase within one wavelength at the far field 100m based on the compressed equivalent source method when the number of measurement points is 100.
Detailed Description
The invention will now be described in detail with reference to the drawings and examples.
Referring to fig. 1, the specific implementation steps of the reconstruction method of the double-layered potential equivalent source far-field scattering sound field based on compressed sensing are as follows:
s1, acquiring scattering sound pressure;
The experimental simulation environment is shown in FIG. 2, and by utilizing the finite element frequency domain computing function of COMSOL simulation software, the method collects the sound pressure signals P total (f, theta) and P in (f, theta) collected by the sensors when plane waves incident at different angles have targets and have no targets at the measuring position, and then the scattered sound pressure P scat (f, theta) at the measuring position is
Pscat(f,θ)＝Ptotal(f,θ)-Pin(f，θ) (1)
Wherein f is the detection frequency, and θ is the different incident angles. The response function H (f, theta) of incidence of plane waves with different angles and different frequencies is established as follows:
The scattered sound pressure can be obtained from the near-field total sound pressure according to the response function H (f, θ).
S2, constructing an equivalent source model of the measuring point and the equivalent source point;
The conformal equivalent source surface is selected between the measuring surface and the target as shown in fig. 3, equivalent source points are configured on the selected equivalent source surface, and the number of the configured equivalent sources is N. Establishing a double-layer potential equivalent source model of a sound field between a measuring point and an equivalent source point, wherein an equation between sound pressure of an mth measuring point and N equivalent source intensities is as follows:
Wherein g d(rm,rn) is the derivative of the green's function direction between the sound pressure of the mth measuring point and the nth source intensity:
wherein k is wave number, r is distance between the measuring point and the source intensity, Is the directional derivative. The value of g d(rm,rn) has directionality compared to the green function, which is the main difference between the double-layer potential and single-potential layer equivalent source model. According to the formula (3), the transmission relation between the measured sound pressure and the equivalent source intensity is written as a matrix form:
Pscat＝Gdqscat (5)
Wherein P scat is a sound pressure column vector obtained at M measuring points on the measuring surface, G d is a transmission matrix between each measuring point and the equivalent source intensity, and q scat is a column vector formed by N equivalent source intensities on the equivalent source surface. Matrix G d is composed of G d(rm,rn), the condition number of matrix G d is smaller than that of the single-layer potential equivalent source transfer matrix when the measurement plane is conformal with the equivalent source plane.
S3, solving a source strong sparse domain;
Because the equivalent source surface is an axisymmetric cylindrical surface shape, the equivalent source equation in the formula (5) can be expanded into a Fourier series form along the azimuth and elevation directions of the virtual surface, and the Fourier coefficients with strong sources have sparsity. And establishing a compressed equivalent source model between the measuring points and the Fourier coefficients with strong sources. The sound pressure of a measuring point in the sound field is P scat, and the discretized compression equivalent source equation is as follows:
Pscat＝FHC (6)
Wherein, C is the Fourier coefficient of the source intensity, and the transfer function F H between the Fourier coefficient of the source intensity and the measuring point is expressed as follows:
Wherein, Is a two-dimensional discrete fourier transform of the green's function directional derivative between the equivalent source point and the measurement point. M, N are the points of the fast Fourier transform, and k 1 and k 2 are the spatial frequencies corresponding to the source strong azimuth angle and the pitch angle on the equivalent source surface. The two-dimensional discrete fourier transform is performed on the green function derivative transfer matrix G d, which is equivalent to two one-dimensional discrete fourier transforms, and the one-dimensional fourier transform does not change the rank of the matrix G d. Compared with single-layer potential, the equivalent source model of double-layer potential reduces the condition number of G d, thereby improvingTo reduce F H matrix dependencies.
In the formula (6), C is a sparse vector, F H can be regarded as a perception matrix, and the method is directly solved by using a compressed perception technology, namely, the method is converted into a minimum L1 norm problem:
Wherein epsilon is the allowable upper error limit, epsilon in the formula (8) is a small number, for example, 10 -6, and then a CVX convex optimization tool box is used for solving to obtain a Fourier coefficient C with strong source.
S4, calculating a far-field scattering sound pressure reconstruction value;
Calculating a transfer function F re between the source strong Fourier coefficient and the far-field position, and calculating far-field scattering sound pressure by combining the source strong Fourier coefficient C in the previous step, wherein the calculated far-field scattering sound pressure is:
Pre＝FreC (9)
Wherein P re is the far-field scattered sound pressure reconstruction value, and C is the source strong Fourier coefficient obtained in S3.
Description of examples: in order to verify the feasibility and illustrate the characteristics of the method, simulation analysis is performed. The simulation environment is shown in fig. 2, wherein the underwater target is approximately 10m long and 1.5m in radius. The near field measuring points are uniformly distributed on the cylindrical surface 5cm away from the target surface, and the far field measuring points are 100m away from the target. The calculation of the near-field total sound pressure and the direct wave sound pressure at the probe frequency of 1kHz by using COMSOL software is shown in fig. 4, and the separation of the near-field scattered sound pressure from the near-field total sound pressure by the response function H (f, θ) is shown in fig. 5. The equivalent source surface is set to be cylindrical conformal with the target, the equivalent source surface is placed between the target and the measuring surface, the radius is 1.52m, and the number of the equivalent sources N=1600 is uniformly distributed on the equivalent source surface. And constructing a measuring point and equivalent source point compression equivalent source model, and solving to obtain a Fourier coefficient C with strong source by using a CVX convex optimization tool box so as to calculate far-field scattering sound pressure. Fig. 6 is a graph of sound field reconstruction error based on a conventional equivalent source and a compressed equivalent source method, where the conventional equivalent source cannot accurately predict far-field scattering sound pressure, and the compressed equivalent source error is significantly smaller than the conventional equivalent source method. Fig. 7 is a graph of the condition number of the transmission matrix corresponding to the single-layer potential and the double-layer potential versus the number of measurement points, and fig. 8 is a graph of the vector correlation of the sensing matrix corresponding to the single-layer potential and the double-layer potential versus the number of measurement points, wherein the condition number and the correlation of the double-layer potential matrix are smaller when the number of measurement points is the same. Fig. 9 is a graph of error in sound field reconstruction based on the compression equivalent source method, and when the number of measurement points is 40-100, the average error of the single-layer potential and the double-layer potential compression equivalent source is about 4.56% and 3.92%, respectively, and the accuracy of sound field reconstruction can be improved by introducing double-layer potential. As shown in fig. 10, when the number of measurement points is 100, the relative error of the sound pressure amplitude reconstruction is about 4.12%, and the scattering phase reconstruction error is about 0.203rad. Compared with the traditional equivalent source method, the compressed equivalent source method solves the problem that the accuracy of sound field reconstruction is reduced when the number of measurement points is small. According to the invention, a double-layer potential theory is introduced in the compressed sensing reconstruction based on the equivalent source, so that the condition number of the transmission matrix is effectively reduced, the correlation of the sensing matrix F H is further reduced, and the far-field scattering sound pressure reconstruction when the number of measurement points is small is realized.
The embodiments described in the present specification are merely examples of implementation forms of the inventive concept, and the scope of protection of the present invention should not be construed as being limited to the specific forms set forth in the embodiments, and the scope of protection of the present invention and equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.
Claims (1)
1. A reconstruction method of a double-layer potential equivalent source far-field scattering sound field based on compressed sensing comprises the following steps:
s1, acquiring scattering sound pressure;
Establishing a simulation environment according to the underwater target structure and the material in the test; the relationship between the near-field total sound pressure P total (f, θ) and the scattered sound pressure P scat (f, θ) at each incident angle is obtained as follows:
Pscat(f,θ)＝Ptotal(f,θ)-Pin(f,θ) (1)
Wherein f is the detection frequency, θ is the different incident angles, and P in (f, θ) is the incident sound pressure; the response function H (f, theta) under the conditions of different detection frequencies and incidence angles is established as follows:
According to the response function, scattering sound pressure can be obtained from the near-field total sound pressure;
S2, constructing an equivalent source model of the measuring point and the equivalent source point;
M measuring points are distributed on a measuring surface near the target for synchronous measurement, and sound pressure P scat at each measuring point on the measuring surface is obtained; configuring N equivalent source points on an equivalent source surface; the equation between the sound pressure of the m-th measuring point and N equivalent source intensities is as follows:
wherein g d(rm,rn) is the derivative of the green's function direction between the sound pressure of the mth measuring point and the nth source intensity:
wherein k is wave number, r is distance between the measuring point and the source intensity, Is the directional derivative; according to the formula (3), the transmission relation between the measured sound pressure and the equivalent source intensity is written as a matrix form:
Pscat＝Gdqscat (5)
Wherein P scat is a sound pressure column vector obtained at M measuring points on a measuring surface, G d is a transmission matrix between each measuring point and equivalent source intensity, and q scat is a column vector formed by N equivalent source intensities on an equivalent source surface;
S3, solving a source strong sparse domain;
Because the equivalent source surface is in an axisymmetric shape, the equivalent source equation can be expanded into a Fourier series form along the azimuth and elevation directions of the virtual surface, and the Fourier coefficient with strong source has sparsity; establishing a compressed equivalent source model between the measuring points and the source strong Fourier coefficients; the sound pressure of a measuring point in the sound field is P scat, and the discretized compression equivalent source equation is as follows:
Pscat＝FHC (6)
Wherein, C is the Fourier coefficient of the source intensity, and the transfer function F H between the Fourier coefficient of the source intensity and the measuring point is expressed as follows:
Wherein, Two-dimensional discrete Fourier transform of the green function direction derivative between the equivalent source point and the measurement point; m, N is the number of fast Fourier transform points, and k 1 and k 2 are the spatial frequencies corresponding to the source intensity azimuth angle and the pitch angle on the equivalent source surface;
In the formula (6), C is a sparse vector, F H can be regarded as a perception matrix, and the method directly utilizes a compressed perception technology to solve, namely, the minimum L1 norm problem:
Constraint conditions
Epsilon is the allowable error upper limit, and a Fourier coefficient with strong source is obtained by solving;
s4, calculating a far-field scattering sound pressure reconstruction value;
Calculating a transfer function F re between the source strong Fourier coefficient and the far-field position, and calculating far-field scattering sound pressure by combining the source strong Fourier coefficient in the step S3 as follows:
Pre＝FreC (9)
Wherein P re is the far-field scattered sound pressure reconstruction value, and C is the source strong Fourier coefficient obtained in S3.
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