CN115389012B - Rapid forecasting method, system and medium for scattering sound field - Google Patents
Rapid forecasting method, system and medium for scattering sound field Download PDFInfo
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Abstract
The invention discloses a rapid forecasting method, a rapid forecasting system and a rapid forecasting medium for a scattering sound field, wherein the method comprises the following steps: performing two-dimensional Fourier transform processing on the target space image to obtain a first image spectrum representation; performing two-dimensional surface integration processing on the first image spectrum representation to obtain a second image spectrum representation; constructing a line integration and surface integration relationship based on priori knowledge to obtain an integration relationship representation; determining a third image spectral representation from the second image spectral representation and the integral relationship representation; performing line-segment-limited summation conversion processing on the third image spectrum representation to determine a fourth image spectrum representation; determining a two-dimensional spectral value solution based on the fourth image spectral representation; extracting based on the two-dimensional spectrum value to obtain a semicircular arc frequency domain sample value; determining scattered sound pressure representation, and obtaining a target directivity function based on the directivity characteristic; and according to the target directivity function, carrying out scattering sound field prediction by using the semicircular arc frequency domain sample value. The invention can improve the accuracy and efficiency of acoustic scattering field prediction.
Description
Technical Field
The invention relates to the technical field of underwater target identification, in particular to a rapid forecasting method, a rapid forecasting system and a rapid forecasting medium for a scattering sound field.
Background
For simple-shape targets, such as underwater targets meeting the conditions of cylindrical coordinates, elliptic cylindrical coordinates, spherical coordinates, conic coordinates and the like, a separation variable method can be used for obtaining an analytical solution of a Helmholtz equation, and an accurate expression of a scattering far field is obtained. In practical engineering applications, the shape of a real aquatic target is relatively complex and even arbitrary. Therefore, the scattered sound pressure cannot be obtained by the analysis method. Numerical methods such as Finite Element Method (FEM), finite difference time domain method (FDTD), and Boundary Element Method (BEM) can obtain a target dispersion solution of arbitrary shape. However, these methods have high computational costs and are not suitable for engineering applications. If the three-dimensional sphere target scattering characteristic is carried out by utilizing a finite element method, the three-dimensional sphere target scattering characteristic is split according to tetrahedral grids, and when the maximum grid unit adopts 1/6 wavelength, the target grid splitting result is obtained under different frequency conditions, as shown in fig. 1, the size of the grid unit is smaller and smaller along with the increase of the frequency, so that the grid quantity is increased sharply. Therefore, the finite element method for calculating the scattering sound field of the underwater target is not suitable for solving the scattering sound field of the wideband, high-frequency and large-scale target, although a more accurate solution can be obtained. The frequency-modulated broadband scattering sound field is obtained by adopting a frequency sweeping mode, and about one week is needed, so that the real-time calculation is obviously difficult to perform aiming at high frequency, broadband and fine frequency intervals, and the engineering application is not facilitated.
According to a sound field forecasting method applying the diffraction CT principle in the reverse direction, the forecasting efficiency and accuracy of the obtained sound field mainly depend on the efficiency and accuracy of spectrum calculation. From the efficiency point of view, the traditional 2D-DFT conversion has already been provided with a fast algorithm which is well-developed and widely known, and the efficiency of spectrum calculation of a sound field image model can be sufficiently ensured. And constructing an image model of the two-dimensional sound field by using the density, sound velocity and other acoustic parameters of the target and the water medium. The spatial sampling rate is δ=λ/10, where λ is the wavelength of the incident sound wave and the image size is 256×256, as fig. 2 (a) gives a two-dimensional image model of the target sound field with different cross-sectional shapes. Due to the method of imaging a spatial image on a finite grid, jagged boundaries are always present in the image, because the unit pixels of the image are sampled on a finite Cartesian grid, and boundary jagging is an inherent object imaging error. Increasing the sampling rate can only reduce errors to a certain extent but cannot be completely eliminated, in addition, increasing the spatial resolution of the sampling rate image can increase, the degree of saw tooth smoothness is reduced, but the cost for calculating the frequency spectrum is suddenly increased, and the real-time performance of sound field forecast is not facilitated. The sampled 2D-FFT algorithm directly spectrally solves the image and represents the spectral amplitude on a logarithmic scale, as shown in fig. 2 (b). It can be seen that the aliasing deviating from the true smooth boundary has a great influence on the spectral accuracy. Errors especially at high frequencies are very pronounced and even deviate from the correct spectral fluctuations trend, with erroneous results.
Taking an ellipsoidal target with a smooth boundary as an example, calculating the scattering far-field pointing distribution by adopting two methods of inverse diffraction CT and a time domain finite difference method (FDTD), and representing by using a normalized accumulation result of back projection in the range of (0-360). In fig. 3, the red dotted line is the result obtained by the FDTD algorithm, the blue solid line is obtained by the inverse diffraction CT method, and as a result, larger fluctuation occurs, and even the peak-to-valley inversion phenomenon occurs in the directions of 0 °,90 °,180 °,270 ° and the like.
Therefore, the method for constructing the sound field image model and carrying out sound field prediction in the prior art has the advantages that the calculation efficiency is improved, but the calculation accuracy still needs to be further improved.
Disclosure of Invention
In view of the above, the embodiments of the present invention provide a method, a system, and a medium for fast forecasting a scattering sound field, which can effectively improve accuracy and efficiency of acoustic scattering field forecasting.
In one aspect, an embodiment of the present invention provides a method for rapidly forecasting a diffuse sound field, including:
Performing two-dimensional Fourier transform processing on the target space image to obtain a first image spectrum representation;
Performing two-dimensional surface integration processing on the first image spectrum representation to obtain a second image spectrum representation;
constructing a line integration and surface integration relationship based on priori knowledge to obtain an integration relationship representation;
determining a third image spectral representation from the second image spectral representation and the integration relationship representation;
Performing line-limiting summation conversion processing on the third image spectrum representation to determine a fourth image spectrum representation;
determining a two-dimensional spectral value solution based on the fourth image spectral representation; extracting based on the two-dimensional spectrum value to obtain a semicircular arc frequency domain sample value;
Determining scattered sound pressure representation, and obtaining a target directivity function based on the directivity characteristic;
and according to the target directivity function, carrying out scattering sound field prediction through the semicircular arc frequency domain sample value.
Optionally, the method further comprises:
Constructing a two-dimensional sound field image model to obtain a target space image;
the expression of the two-dimensional sound field image model is as follows:
Wherein c 0 represents water density; ρ 0 represents the sound speed; c (x, y) represents the density of the target; ρ (x, y) represents the sound velocity of the target; when I (x, y) =0, it represents the water area, otherwise, it represents the target area.
Optionally, the expression of the first image spectrum representation is:
F(u,v)＝∫∫I(x,y)exp[-j(ux+vy)]dxdy
Wherein F (u, v) represents an image spectrum, I (x, y) represents a target space image, (x, y) represents an image pixel space coordinate, (u, v) represents a frequency domain coordinate, exp [ -j (ux+vy) ] is a basis function represented by a complex exponent.
Optionally, the expression of the second image spectral representation is:
Wherein F (u, v) represents an image spectrum, I (x, y) represents a target space image, and [ chi ] is a target surface area integral, Representing the rotation of the vector function,/>The unit vector of the ith line segment in the x direction is represented, exp [ -j (ux+vy) ] is a base function represented by a complex exponent.
Optionally, the constructing the line integration and the surface integration relationship based on the prior knowledge to obtain an integration relationship representation includes:
Determining a contour integral and surface integral relation through Stokes theorem to obtain integral relation expression;
Wherein the integral relationship represents the expression:
In the method, in the process of the invention, Representing a vector field with a continuous partial derivative in the target region, pi (·) dl representing a line integral of the closed target curve in a counter-clockwise direction, pi + (·) dS representing a two-dimensional surface integral, the target curve being the boundary of the target region surface.
Optionally, the expression of the third image spectral representation is:
Where F (u, v) denotes the image spectrum, I (x, y) denotes the image of the object space, and pi (. Cndot.) dl denotes the line integration of the closed object curve in the counter-clockwise direction, Exp [ -j (ux+vy) ] is a base function represented by a complex exponent,/>Representing the unit vector of the ith line segment in the x direction,/>Represents the unit vector of the ith line segment in the y direction, and j represents the imaginary part of the complex vector.
Optionally, the expression of the fourth image spectrum representation is:
Wherein θ n =2n/N represents the included angle between each line segment and the coordinate axis, a n and b n represent the slope and intercept of the nth line segment between nodes N and n+1, respectively, defined as (X n,yn) represents a discrete description of the coordinates (x, y) of the closed boundary, x n＝rncosθn and y n＝rn sinθn (n=1, 2, … N, N is the node number, N is the number of sum segments), exp [ -j (ux+vy) ] is a base function represented by a complex exponent, j representing the imaginary part of the complex vector.
Optionally, the determining the scattered sound pressure representation, based on the directional characteristic, obtains a target directivity function, including:
According to a Helmholtz equation for solving a scattering sound field, based on a diffraction CT principle of a BORN approximate condition, obtaining scattering sound pressure representation related to the density and sound velocity of a target and surrounding medium;
According to the scattered sound pressure representation, a target directivity function is obtained based on directivity characteristics of a scattered sound field;
wherein, the expression of the target directivity function is:
f(θ,k0)＝[γk+γρcosθ]IF[k0cosθ-k0,k0sinθ]
Where, gamma κ denotes the correlation coefficient of the density and sound velocity of the medium around the target, Θ is a scattering angle, I F ()' represents a frequency domain of a sound field image, [ k 0cosθ-k0,k0 sin θ ] represents a pair of semicircular arcs on a two-dimensional spectrum.
In another aspect, an embodiment of the present invention provides a diffuse sound field forecasting system, including:
the first module is used for carrying out two-dimensional Fourier transform processing on the target space image to obtain a first image spectrum representation;
The second module is used for carrying out two-dimensional area integration processing on the first image spectrum representation to obtain a second image spectrum representation;
the third module is used for constructing a contour integral and a surface integral relation based on priori knowledge to obtain integral relation representation;
A fourth module for determining a third image spectral representation from the second image spectral representation and the integration relationship representation;
a fifth module, configured to perform line-segment-limited summation conversion processing on the third image spectrum representation, and determine a fourth image spectrum representation;
A sixth module for determining a two-dimensional spectral value solution based on the fourth image spectral representation; extracting based on the two-dimensional spectrum value to obtain a semicircular arc frequency domain sample value;
a seventh module for determining a scattered sound pressure representation, obtaining a target directivity function based on the directivity characteristics;
and an eighth module, configured to predict a diffuse sound field according to the target directivity function by using the semicircular arc frequency domain sample value.
In another aspect, an embodiment of the present invention provides an electronic device, including a processor and a memory;
the memory is used for storing programs;
The processor executes the program to implement the method as described above.
In another aspect, embodiments of the present invention provide a computer-readable storage medium storing a program that is executed by a processor to implement a method as described above.
Embodiments of the present invention also disclose a computer program product or computer program comprising computer instructions stored in a computer readable storage medium. The computer instructions may be read from a computer-readable storage medium by a processor of a computer device, and executed by the processor, to cause the computer device to perform the foregoing method.
In the embodiment of the invention, firstly, two-dimensional Fourier transform processing is carried out on a target space image to obtain a first image spectrum representation; performing two-dimensional surface integration processing on the first image spectrum representation to obtain a second image spectrum representation; constructing a line integration and surface integration relationship based on priori knowledge to obtain an integration relationship representation; determining a third image spectral representation from the second image spectral representation and the integration relationship representation; performing line-limiting summation conversion processing on the third image spectrum representation to determine a fourth image spectrum representation; determining a two-dimensional spectral value solution based on the fourth image spectral representation; extracting based on the two-dimensional spectrum value to obtain a semicircular arc frequency domain sample value; determining scattered sound pressure representation, and obtaining a target directivity function based on the directivity characteristic; and according to the target directivity function, carrying out scattering sound field prediction through the semicircular arc frequency domain sample value. The invention derives the accurate expression of the two-dimensional spectrum by converting the two-dimensional integral of the two-dimensional Fourier transform into the line integral, and is used for forecasting the scattering far field of the target in the two-dimensional space. The invention not only overcomes the limitation of the shape of the object, but also improves the accuracy and efficiency of the acoustic scattering field prediction.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of meshing of a three-dimensional sphere at different frequencies;
FIG. 2 is a schematic view of a sound field image space model and a frequency spectrum;
FIG. 3 is a graph showing a comparison of projection normalized accumulated values of reverse diffraction CT and FDTD;
fig. 4 is a flow chart of a diffuse sound field forecasting method according to an embodiment of the present invention;
Fig. 5 is a schematic diagram of sample positions of forward and backward scattering of a sound field irradiated by an LFM signal according to an embodiment of the present invention;
FIG. 6 is a schematic diagram showing the comparison of calculation time of the prior art method and the embodiment of the present invention;
FIG. 7 is a schematic diagram of a technical route according to an embodiment of the present invention;
fig. 8 is a schematic diagram of a Stokes theorem-based high-precision spectrum calculation and scattering sound field prediction flow in an embodiment of the invention;
FIG. 9 is a schematic diagram of an image model of a two-dimensional sound field according to an embodiment of the present invention;
FIG. 10 is a schematic diagram showing the different number of segments constituting different target cross-sectional boundaries according to an embodiment of the present invention;
FIG. 11 is a high-precision frequency domain diagram of a model for solving different boundary targets based on Stokes theorem according to the embodiment of the invention;
FIG. 12 is a graph showing the contrast of the derived scattering sound pressure for the embodiment of the present invention and the prior art method;
Fig. 13 is a graph showing the scattering sound pressure directivity distribution of the embodiment of the present invention compared with the prior art method.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
In one aspect, referring to fig. 4, an embodiment of the present invention provides a method for rapidly forecasting a diffuse sound field, including:
Performing two-dimensional Fourier transform processing on the target space image to obtain a first image spectrum representation;
performing two-dimensional surface integration processing on the first image spectrum representation to obtain a second image spectrum representation;
constructing a line integration and surface integration relationship based on priori knowledge to obtain an integration relationship representation;
Determining a third image spectral representation from the second image spectral representation and the integral relationship representation;
performing line-segment-limited summation conversion processing on the third image spectrum representation to determine a fourth image spectrum representation;
Determining a two-dimensional spectral value solution based on the fourth image spectral representation; extracting based on the two-dimensional spectrum value to obtain a semicircular arc frequency domain sample value;
Determining scattered sound pressure representation, and obtaining a target directivity function based on the directivity characteristic;
And according to the target directivity function, carrying out scattering sound field prediction by using the semicircular arc frequency domain sample value.
Optionally, the method further comprises:
Constructing a two-dimensional sound field image model to obtain a target space image;
the expression of the two-dimensional sound field image model is as follows:
Wherein c 0 represents water density; ρ 0 represents the sound speed; c (x, y) represents the density of the target; ρ (x, y) represents the sound velocity of the target; when I (x, y) =0, it represents the water area, otherwise, it represents the target area.
Optionally, the expression of the first image spectral representation is:
F(u,v)＝∫∫I(x,y)exp[-j(ux+vy)]dxdy
Wherein F (u, v) represents an image spectrum, I (x, y) represents a target space image, (x, y) represents an image pixel space coordinate, (u, v) represents a frequency domain coordinate, exp [ -j (ux+vy) ] is a basis function represented by a complex exponent.
Optionally, the expression of the second image spectral representation is:
Wherein F (u, v) represents an image spectrum, I (x, y) represents a target space image, and [ chi ] dS represents a target surface area integral, Representing the rotation of the vector function,/>The unit vector of the ith line segment in the x direction is represented, exp [ -j (ux+vy) ] is a base function represented by a complex exponent.
Optionally, constructing the line integral and the surface integral relationship based on a priori knowledge to obtain an integral relationship representation, including:
Determining a contour integral and surface integral relation through Stokes theorem to obtain integral relation expression;
Wherein the integral relationship represents the expression:
In the method, in the process of the invention, Representing a vector field with a continuous partial derivative in the target region, pi (·) dl representing a line integral of the closed target curve in a counter-clockwise direction, pi + (·) dS representing a two-dimensional surface integral, the target curve being the boundary of the target region surface.
Optionally, the expression of the third image spectral representation is:
Where F (u, v) denotes the image spectrum, I (x, y) denotes the image of the object space, and pi (. Cndot.) dl denotes the line integration of the closed object curve in the counter-clockwise direction, Exp [ -j (ux+vy) ] is a base function represented by a complex exponent,/>Representing the unit vector of the ith line segment in the x direction,/>Represents the unit vector of the ith line segment in the y direction, and j represents the imaginary part of the complex vector.
Optionally, the expression of the fourth image spectral representation is:
Wherein θ n =2n/N represents the included angle between each line segment and the coordinate axis, a n and b n represent the slope and intercept of the nth line segment between nodes N and n+1, respectively, defined as (X n,yn) represents a discrete description of the coordinates (x, y) of the closed boundary, x n＝rncosθn and y n＝rn sinθn (n=1, 2, … N, N is the node number, N is the number of sum segments), exp [ -j (ux+vy) ] is a base function represented by a complex exponent, j representing the imaginary part of the complex vector.
Optionally, determining the scattered sound pressure representation, deriving the target directivity function based on the directivity characteristics, comprises:
According to a Helmholtz equation for solving a scattering sound field, based on a diffraction CT principle of a BORN approximate condition, obtaining scattering sound pressure representation related to the density and sound velocity of a target and surrounding medium;
according to the scattered sound pressure representation, obtaining a target directivity function based on directivity characteristics of the scattered sound field;
The expression of the target directivity function is as follows:
f(θ,k0)＝[γk+γρcosθ]IF[k0cosθ-k0,k0sinθ]
Where, gamma κ denotes the correlation coefficient of the density and sound velocity of the medium around the target, Θ is a scattering angle, I F ()' represents a frequency domain of a sound field image, [ k 0cosθ-k0,k0 sin θ ] represents a pair of semicircular arcs on a two-dimensional spectrum.
In another aspect, an embodiment of the present invention provides a diffuse sound field forecasting system, including:
the first module is used for carrying out two-dimensional Fourier transform processing on the target space image to obtain a first image spectrum representation;
The second module is used for carrying out two-dimensional surface integration processing on the first image spectrum representation to obtain a second image spectrum representation;
the third module is used for constructing a contour integral and a surface integral relation based on priori knowledge to obtain integral relation representation;
a fourth module for determining a third image spectral representation from the second image spectral representation and the integral relationship representation;
A fifth module, configured to perform line-segment-limited summation conversion processing on the third image spectrum representation, and determine a fourth image spectrum representation;
A sixth module for determining a two-dimensional spectral value solution based on the fourth image spectral representation; extracting based on the two-dimensional spectrum value to obtain a semicircular arc frequency domain sample value;
a seventh module for determining a scattered sound pressure representation, obtaining a target directivity function based on the directivity characteristics;
and an eighth module, configured to predict a diffuse sound field by using the semicircular arc frequency domain sample value according to the target directivity function.
The content of the method embodiment of the invention is suitable for the system embodiment, the specific function of the system embodiment is the same as that of the method embodiment, and the achieved beneficial effects are the same as those of the method.
Another aspect of the embodiment of the invention also provides an electronic device, which includes a processor and a memory;
the memory is used for storing programs;
The processor executes the program to implement the method as described above.
The content of the method embodiment of the invention is suitable for the electronic equipment embodiment, the functions of the electronic equipment embodiment are the same as those of the method embodiment, and the achieved beneficial effects are the same as those of the method.
Another aspect of the embodiments of the present invention also provides a computer-readable storage medium storing a program that is executed by a processor to implement a method as described above.
The content of the method embodiment of the invention is applicable to the computer readable storage medium embodiment, the functions of the computer readable storage medium embodiment are the same as those of the method embodiment, and the achieved beneficial effects are the same as those of the method.
Embodiments of the present invention also disclose a computer program product or computer program comprising computer instructions stored in a computer readable storage medium. The computer instructions may be read from a computer-readable storage medium by a processor of a computer device, and executed by the processor, to cause the computer device to perform the foregoing method.
The invention will be described in further detail with reference to a few specific examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
It should be noted that, when an object in water is immersed by planar acoustic wave irradiation, the Four ier diffraction theorem proves that the one-dimensional fourier transform of the scattering field is related to two sample values forming a semicircular arc in the two-dimensional fourier spectrum of the object. The radius of the semicircle is equal to the wave number k 0,k0 and is proportional to the frequency of the incident wave. This has been successfully used for medical image inversion where the scattered sound pressure and incident sound waves are known. The inverse use Four ier of the inverse diffraction theorem to predict the scattering sound field is a new idea for solving the acoustic problem. Assuming that the acoustic image model of the target in water is known, far-field scattered sound pressure can be predicted from samples extracted from the two-dimensional spectrum. If the submerged target sound field model is described as a binary or gray scale image, accurate frequency spectrum solution is necessary for forecasting the sound field. However, when the target material and the aqueous medium are uniform, an acoustic digital image model is constructed by the relevant acoustic parameters such as density and acoustic velocity of the different media, boundary jaggies and irregularities always exist at the otherwise smooth image boundary because the image pixel cells are sampled on rectangular grids under limited cartesian coordinates, and the boundary accuracy depends on the image space grid sampling rate. The jaggies existing at the boundary of the non-straight edge are inherent errors of target imaging, the sampling rate is increased, the errors can be reduced to a certain extent but cannot be completely eliminated, in addition, the spatial resolution of the image can be increased by increasing the sampling rate, and the time and storage cost of calculating the frequency spectrum are suddenly increased although the unevenness of the jaggies is reduced, so that the real-time performance of sound field forecasting is not facilitated. The method is characterized in that a 2D-FFT is directly applied to a digital image model to solve a frequency spectrum, fourier (FT) transformation originally based on continuous two-dimensional integration is converted into discrete domain calculation, and the influence of a sawtooth boundary deviating from a real boundary on the frequency spectrum precision is large. Particularly, the error at high frequency is very remarkable, even deviates from the correct spectrum fluctuation trend, and the peak-to-valley inversion phenomenon of the spectrum occurs in the local frequency band. According to the relation between the scattering far-field prediction and the position of the spectrum sample, if the frequency of the incident wave is higher, the radius of the circular arc used for sampling is larger, and especially, sampling in a high-frequency area causes that the backscattering sound field prediction is wrong.
The invention aims to improve the prediction precision of a scattering sound field of a target in water, and provides a calculation method for solving a high-precision two-dimensional Fourier transform numerical value, which is used for correcting a frequency spectrum error for sound field prediction. With known target geometry and acoustic parameters, a two-dimensional digital image model of the sound field is constructed. Based on Stokes theorem, the relation between the surface area and the line integral of the vector field is given, the two-dimensional integral of the continuous two-dimensional Fourier transform is converted into the line integral, the line integral is further described as the accumulated sum of finite length line segments with enough precision, an accurate expression of two-dimensional spectrum calculation is deduced, and the sample value on a specified circular arc on the corrected spectrum is extracted for scattering far field prediction. The method not only overcomes the limitation of the shape of the object, but also improves the accuracy and efficiency of acoustic scattering field prediction.
Specifically, the inverse Four ier diffraction theorem solves for a forward and backward scattering two-dimensional sound field:
Based on Four ier diffraction theorem, the proportional relation between the forward and backward scattering sound field of the target and a pair of semicircular tracks on the two-dimensional Four ier spectrum of the target is deduced by using the Born approximation, so that an approximation solution for solving a scattering integral equation is obtained. The water sound scattering problem is solved by reversely applying Four ier diffraction theorem, namely, by sampling the semicircular arcs on the spectrum of the target section image model, the circular arc track is shown in fig. 5, the scattering characteristic is rapidly predicted, and the method can effectively break through mesh division ideas such as FEM and FDTD.
According to the method, grid subdivision is not needed for sound field prediction, only the frequency domain of a sound field image model is needed to be solved, and then the interpolation method is adopted to extract sample values on circular arc tracks with different radiuses, so that the omnibearing and broadband scattering directional distribution under different sound wave irradiation conditions can be obtained, and the calculation efficiency is greatly improved. Taking a three-dimensional sphere with a radius of 0.5m as an example, comparing the calculation cost of the back scattering sound field obtained by an analytic method, a Finite Element Method (FEM) and a reverse diffraction CT method, fig. 6 (a) shows that the sound field calculation is performed by adopting the three-dimensional finite element method with the increase of k 0 R, and the calculation cost of the three methods all shows an ascending trend with the increase of frequency. When k 0 R is larger than 10, the FEM program is interrupted, the calculation can not be completed through the personal computer with limited memory, and the finite element method is not applicable to high-frequency calculation. When k 0 R >20, the inverse diffraction CT calculation time will exceed that of the analytical method, but be much lower than that of the FEM method, which differs by about 2 orders of magnitude. Although modeling can be performed by using a two-dimensional axisymmetric model in a finite element-based COMSOL multi-physical field, fig. 6 (b) shows that in the two-dimensional scattering sound field calculation, as k 0 R increases, the calculation time of the three methods increases, and the inverse diffraction CT method and FEM increase faster. But the computational time cost of the inverse diffraction CT method is much less than that of the analytical method and FEM.
Referring to fig. 7 and 8, the specific steps of an embodiment of the method of the present invention are as follows:
(1) Two-dimensional sound field image model construction
The object in the immersed water is irradiated by plane sound waves, and pixels in the two-dimensional sound field image model are represented by acoustic impedances related to the object and surrounding media and are represented by refraction factors. The luminance value of a pixel at (x, y) in the image space coordinates is defined as:
Where c 0 and ρ 0 are the water density and sound velocity in water. c (x, y) and ρ (x, y) are the density and speed of sound of the target. If I (x, y) =0, it is a water area, and is represented by black pixels in the image. The highlighted area represents the target area in water, described by I (·) =1- [ c 0ρ0/c (x, y) ρ (x, y) ]. An image model of a two-dimensional sound field is shown in fig. 9.
(2) Derivation and validation for numerical computation of two-dimensional fourier transforms
The two-dimensional fourier transform of the successive images I (x, y) is defined as:
F(u,v)＝∫∫I(x,y)exp[-j(ux+vy)]dxdy (2)
in the above formula, I (x, y) represents a spatial image, and (x, y) is the spatial coordinates of an image pixel. F (u, v) represents the image spectrum, and (u, v) represents the frequency domain coordinates. exp [ -j (ux+vy) ] is a base function represented by a complex exponent.
The formula (2) is a two-dimensional area, and can be rewritten as follows:
in the formula (3), ≡ ≡ds is the target surface area integral, Representing the rotation of the vector function,/>The unit vector is the ith line segment in the x direction. The Stokes theorem relates the surface area to the line integral of the vector field. If/>Is a vector field with continuous partial derivatives in the region S, then applying Stokes theorem can yield:
Wherein, phi (·) dl represents the line integration of the closed curve C in the counterclockwise direction, and +.cndot. (. Cndot.) dS represents a two-dimensional surface integral. Curve C corresponds to the boundary of the curved surface denoted by S. Thus, F (u, v) in equation (4) can be rewritten as:
In the formula (5) Integration in the mathematical midline is equivalent to summing a finite number of straight line segments with sufficiently small segment spacing. For a sufficiently small line segment, a two-dimensional fourier transform is obtained using the following summation formula:
Here, (x n,yn) is a discrete description of the coordinates (x, y) of the closed boundary. And x n＝rn cosθn and y n＝rn sinθn (n=1, 2, … N, N is the node number and N is the number of summing segments). θ n =2n/N, which is the angle between each line segment and the coordinate axis. The slope and intercept of the nth line segment between nodes n and n+1 are defined as a n and b n, expressed as:
To illustrate the effect of the number of segments on the resolution of spectral accuracy, R n is set to a constant value equal to R. Referring to fig. 8, the starting point segment node coordinates on the circular curve are (x 1,y1), and are divided into equally spaced line segments along the counterclockwise direction, and the segment node coordinates are (x 2,y2)…(xn+1,yn+1) in turn. To ensure that the curve is closed and meets Stokes' theorem, the last endpoint (x n+1,yn+1) coincides with the start point (x 1,y1). If n=4, 6, 8, the connecting line segment nodes will generate closed curves with square, hexagonal and octagonal boundaries. An object with a circular boundary may be represented by a limited but sufficient number of N segments. In fig. 10, symbol 'o' represents an end point of each segment, which is called a segment node.
When the target cross section is quadrangular, n=4. The result of the numerical computation spectrum at n=4 is solved. At this time, the coordinates of each segment of nodes are (xn,yn)＝[(R,0),(0,R),(-R,0),(0,-R),(R,0)],an＝[-1 1-1 1]],bn＝[R-R-R R],(n＝1,2,3,4)., and the a n,bn expression is substituted into (6), so that the two-dimensional Fourier transform numerical solution of the two-dimensional acoustic model image of which the cross section is square and infinitely long can be calculated:
It can be seen that the formula (8) is the same as the two-dimensional fourier transform analytic solution of the square image, and the accuracy of the high-precision frequency spectrum solving method is preliminarily verified.
(3) Diffuse sound field directional distribution forecast
According to He lmho ltz equation for solving the scattering sound field, based on the diffraction CT principle of the BORN approximate condition, the scattering sound pressure expression related to the density and sound velocity of the target and surrounding medium is obtained as follows:
In the above formula, p i (r ') is an incident sound pressure, r' = (x ', y') is a spatial coordinate of a target area in a sound field, and r is an arbitrary point in a far field. g (r|r ') is the far field green's function. Gamma κ is related to the density and speed of sound of the target and surrounding medium, and And θ represents the incident angle and the scattering angle, respectively, the scattering unit direction vector isConsidering only the directivity characteristics of the diffuse sound field, the corresponding directivity function expression is:
f(θ,k0)＝[γk+γρcosθ]IF[k0cosθ-k0,k0sinθ] (10)
The directivity function f (θ, k 0) given in the formula (10) is expressed in such a way that [ k 0cosθ-k0,k0 sin θ ] represents a pair of half arcs on the two-dimensional spectrum. The radius of the circular arc is k 0,k0, which is the wave number in water. The forward and backward scattering sound field pointing distribution arc track is shown in fig. 5.
The embodiments of the invention are further explained below in connection with specific applications:
(1) High precision spectral numerical computation
For comparison, spectra of several typical examples shown in fig. 11 were obtained. In fig. 11, a group of objects with arbitrary boundaries are shown immersed in water, and after image modeling according to formula (1), the image unit here is δ=0.1, and the image size is 256×256. It should be noted that the zigzags always appear at the boundaries of the image, see fig. 2 (a). The image is directly subjected to a 2D-FFT calculation to account for the spectral amplitude on a logarithmic scale, as shown in fig. 2 (b). It can be seen that small changes in image shape can result in significant changes in the spectral domain. The small saw tooth shape, which deviates from the true boundary, has a large influence on the spectrum, and especially for higher frequencies, the error becomes significant, which is a problem, see fig. 2 and 3. And (3) converting the continuous curve integration into a piecewise addition mode according to a high-precision frequency domain diagram obtained based on Stokes theorem to obtain continuous F (u, v). The spectral magnitudes are shown in fig. 11.
(2) Omnidirectional diffuse sound field calculation
The method solves the limitation on the shape of the target in the process of strictly resolving and solving the scattering sound field, and can calculate the scattering field of any object in the sound field. For verification, consider first a sphere target that can resolve the fringe field. The model in the two-dimensional sound field is a circular object with a radius of 0.55 m. LFM signal with emitted sound wave of 10 Hz-6.5 kHz and incident angleEqual to 0 deg.. Fig. 12 shows far-field scattered sound pressure distribution calculated using the present technique and separation variable based analytical method. The horizontal axis of the three figures is the azimuth angle (θ= -180 ° to 180 °) of the receiving transducer, and the vertical axis is the frequency of the incident sound wave. Brightness is a normalized value of the scattering sound pressure level. Fig. 12 (a) is a precise analytical solution of the omnidirectional fringe field. Fig. 12 (b) shows a prediction result of an omnidirectional scattering sound field obtained by a spectrum sampling method by calculating a high-precision spectrum based on Stokes theorem, and fig. 12 (c) shows a prediction result of extracting a frequency domain sample by using a 2D-FFT spectrum. The samples used in the calculations of the scattered fields of fig. 12 (b) and (c) are located on a series of paired semicircular arcs, the locations of the samples being shown in fig. 5.
Extracting the fringe field director distribution for incident sound frequencies f 0＝2kHz,f0 =6 kHz yields fig. 13. Comparison of the three methods at this frequency, where (a) f 0 =2 kHz, and (b) f 0 =6 kHz.
As can be seen from fig. 12, 13, the results obtained based on the present method are very close to the analytical solution. In fig. 12 (c) and 13, there is a significant error in the scattered sound pressure calculated using the 2D-FFT spectrum. Such errors also increase with increasing frequency. For receiver angles higher than 2kHz and 120 degrees, the frequency spectrum is directly solved by using 2D-FFT, and obvious errors occur in the extraction of predicted scattered sound pressure through frequency domain samples. There is a very significant error when the frequency is >6kHz, with a corresponding azimuth angle >50 degrees. As the azimuth angle increases, the error increases significantly, i.e., the predicted value of the back-scattered sound pressure even appears with the peak-to-valley inversion. After the frequency spectrum is corrected based on Stokes theorem, the phenomenon of error increase caused by frequency increase is eliminated, and the accuracy of sound field prediction is very close to that of an analysis method.
In summary, the present invention aims to reversely predict a scattering sound field by using Four ier diffraction theorem. The present invention predicts a diffuse sound field given the acoustic parameters of the object and surrounding medium, known as a positive acoustic problem. The method is simple and effective, and the direction distribution of the broadband LFM signal scattering sound field can be obtained only by carrying out one-time calculation on the two-dimensional frequency spectrum of the acoustic image and then extracting the sample at the designated position in the frequency domain. In order to ensure computational efficiency, accuracy of forecasting needs to be ensured. The key to using this approach is therefore to obtain a highly accurate spectrum. According to Stokes theorem, the two-dimensional integral of the continuous two-dimensional fourier transform is converted into a boundary integral and further represented using the sum of a limited number of line segments. Compared with the method that the 2D-FFT conversion is directly carried out on the image model, the obtained two-dimensional frequency spectrum overcomes the inherent high-frequency error caused by grid imaging, and effectively expands the predicted frequency bandwidth of scattered sound pressure. The object in practical application is three-dimensional, the 3D Fourier transform is also suitable for rapid calculation, the scheme is also suitable for a three-dimensional scattering sound field calculation method after expansion, and a new thought is provided for the omnidirectional scattering characteristic forecast of the underwater target, so that the method is suitable for engineering application.
In some alternative embodiments, the functions/acts noted in the block diagrams may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may in fact be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Furthermore, the embodiments presented and described in the flowcharts of the present invention are provided by way of example in order to provide a more thorough understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed, and in which sub-operations described as part of a larger operation are performed independently.
Furthermore, while the invention is described in the context of functional modules, it should be appreciated that, unless otherwise indicated, one or more of the described functions and/or features may be integrated in a single physical device and/or software module or one or more functions and/or features may be implemented in separate physical devices or software modules. It will also be appreciated that a detailed discussion of the actual implementation of each module is not necessary to an understanding of the present invention. Rather, the actual implementation of the various functional modules in the apparatus disclosed herein will be apparent to those skilled in the art from consideration of their attributes, functions and internal relationships. Accordingly, one of ordinary skill in the art can implement the invention as set forth in the claims without undue experimentation. It is also to be understood that the specific concepts disclosed are merely illustrative and are not intended to be limiting upon the scope of the invention, which is to be defined in the appended claims and their full scope of equivalents.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a usb disk, a removable hard disk, a Read-only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
Logic and/or steps represented in the flowcharts or otherwise described herein, e.g., a ordered listing of executable instructions for implementing logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution apparatus, device, or apparatus, such as a computer-based apparatus, processor-containing apparatus, or other apparatus that can fetch the instructions from the instruction execution apparatus, device, or apparatus and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution apparatus, device, or apparatus.
More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). In addition, the computer readable medium may even be paper or other suitable medium on which the program is printed, as the program may be electronically captured, via, for instance, optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner, if necessary, and then stored in a computer memory.
It is to be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution device. For example, if implemented in hardware, as in another embodiment, may be implemented using any one or combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.
While the preferred embodiment of the present invention has been described in detail, the present invention is not limited to the embodiments described above, and those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention, and these equivalent modifications or substitutions are included in the scope of the present invention as defined in the appended claims.
Claims (8)
1. A method for rapid forecasting of a diffuse sound field, comprising:
Performing two-dimensional Fourier transform processing on the target space image to obtain a first image spectrum representation;
Performing two-dimensional surface integration processing on the first image spectrum representation to obtain a second image spectrum representation;
constructing a line integration and surface integration relationship based on priori knowledge to obtain an integration relationship representation;
determining a third image spectral representation from the second image spectral representation and the integration relationship representation;
Performing line-limiting summation conversion processing on the third image spectrum representation to determine a fourth image spectrum representation;
The fourth image spectral representation has the expression:
Wherein θ n =2n/N represents the included angle between each line segment and the coordinate axis, a n and b n represent the slope and intercept of the nth line segment between nodes N and n+1, respectively, defined as (X n,yn) represents a discrete description of coordinates (x, y) of the closed boundary, x n＝rn cosθn and y n＝rn sinθn, n=1, 2, … N, N being the node number, N being the number of summed line segments, exp [ -j (ux+vy) ] being the basis function represented by a complex exponent, j representing the imaginary part of the complex vector;
determining a two-dimensional spectral value solution based on the fourth image spectral representation; extracting based on the two-dimensional spectrum value to obtain a semicircular arc frequency domain sample value;
Determining scattered sound pressure representation, and obtaining a target directivity function based on the directivity characteristic;
the determining the scattered sound pressure representation, based on the directional characteristic, obtains a target directivity function, comprising:
According to a Helmholtz equation for solving a scattering sound field, based on a diffraction CT principle of a BORN approximate condition, obtaining scattering sound pressure representation related to the density and sound velocity of a target and surrounding medium;
According to the scattered sound pressure representation, a target directivity function is obtained based on directivity characteristics of a scattered sound field;
wherein, the expression of the target directivity function is:
f(θ,k0)＝[γk+γρcosθ]IF[k0cosθ-k0,k0sinθ]
Where, gamma κ denotes the correlation coefficient of the density and sound velocity of the medium around the target, Θ is a scattering angle, ρ (x, y) represents the sound velocity of the target, ρ 0 represents the sound velocity in water, I F ()' represents the frequency domain of the sound field image, [ k 0cosθ-k0,k0 sin θ ] represents paired semicircular arcs on the two-dimensional spectrum;
and according to the target directivity function, carrying out scattering sound field prediction through the semicircular arc frequency domain sample value.
2. The rapid diffuse sound field forecasting method of claim 1, further comprising:
Constructing a two-dimensional sound field image model to obtain a target space image;
the expression of the two-dimensional sound field image model is as follows:
Wherein c 0 represents water density; ρ 0 represents the sound speed; c (x, y) represents the density of the target; ρ (x, y) represents the sound velocity of the target; when I (x, y) =0, it represents the water area, otherwise, it represents the target area.
3. The rapid sound field prediction method according to claim 1, wherein the expression of the first image spectrum representation is:
F(u,v)＝∫∫I(x,y)exp[-j(ux+vy)]dxdy
Wherein F (u, v) represents an image spectrum, I (x, y) represents a target space image, (x, y) represents an image pixel space coordinate, (u, v) represents a frequency domain coordinate, exp [ -j (ux+vy) ] is a basis function represented by a complex exponent.
4. The rapid sound field prediction method according to claim 1, wherein the expression of the second image spectrum representation is:
Wherein F (u, v) represents an image spectrum, I (x, y) represents a target space image, and [ chi ] is a target surface area integral, Representing the rotation of the vector function,/>The unit vector of the ith line segment in the x direction is represented, exp [ -j (ux+vy) ] is a base function represented by a complex exponent.
5. The method for rapidly forecasting the diffuse sound field according to claim 1, wherein the constructing the line integral and the surface integral relationship based on the prior knowledge to obtain the integral relationship representation comprises:
Determining a contour integral and surface integral relation through Stokes theorem to obtain integral relation expression;
Wherein the integral relationship represents the expression:
In the method, in the process of the invention, Representing a vector field with a continuous partial derivative in the target region, pi (·) dl representing a line integral of the closed target curve in a counter-clockwise direction, pi + (·) dS representing a two-dimensional surface integral, the target curve being the boundary of the target region surface.
6. The rapid sound field prediction method according to claim 1, wherein the expression of the third image spectrum representation is:
Where F (u, v) denotes the image spectrum, I (x, y) denotes the image of the object space, and pi (. Cndot.) dl denotes the line integration of the closed object curve in the counter-clockwise direction, Exp [ -j (ux+vy) ] is a base function represented by a complex exponent,/>Representing the unit vector of the ith line segment in the x direction,/>Represents the unit vector of the ith line segment in the y direction, and j represents the imaginary part of the complex vector.
7. A diffuse sound field forecasting system, comprising:
the first module is used for carrying out two-dimensional Fourier transform processing on the target space image to obtain a first image spectrum representation;
The second module is used for carrying out two-dimensional area integration processing on the first image spectrum representation to obtain a second image spectrum representation;
the third module is used for constructing a contour integral and a surface integral relation based on priori knowledge to obtain integral relation representation;
A fourth module for determining a third image spectral representation from the second image spectral representation and the integration relationship representation;
a fifth module, configured to perform line-segment-limited summation conversion processing on the third image spectrum representation, and determine a fourth image spectrum representation;
The fourth image spectral representation has the expression:
Wherein θ n =2n/N represents the included angle between each line segment and the coordinate axis, a n and b n represent the slope and intercept of the nth line segment between nodes N and n+1, respectively, defined as (X n,yn) represents a discrete description of coordinates (x, y) of the closed boundary, x n＝rn cosθn and y n＝rn sinθn, n=1, 2, … N, N being the node number, N being the number of summed line segments, exp [ -j (ux+vy) ] being the basis function represented by a complex exponent, j representing the imaginary part of the complex vector;
A sixth module for determining a two-dimensional spectral value solution based on the fourth image spectral representation; extracting based on the two-dimensional spectrum value to obtain a semicircular arc frequency domain sample value;
a seventh module for determining a scattered sound pressure representation, obtaining a target directivity function based on the directivity characteristics;
the determining the scattered sound pressure representation, based on the directional characteristic, obtains a target directivity function, comprising:
According to a Helmholtz equation for solving a scattering sound field, based on a diffraction CT principle of a BORN approximate condition, obtaining scattering sound pressure representation related to the density and sound velocity of a target and surrounding medium;
According to the scattered sound pressure representation, a target directivity function is obtained based on directivity characteristics of a scattered sound field;
wherein, the expression of the target directivity function is:
f(θ,k0)＝[γk+γρcosθ]IF[k0cosθ-k0,k0sinθ]
Where, gamma κ denotes the correlation coefficient of the density and sound velocity of the medium around the target, Θ is a scattering angle, ρ (x, y) represents the sound velocity of the target, ρ 0 represents the sound velocity in water, I F ()' represents the frequency domain of the sound field image, [ k 0cosθ-k0,k0 sin θ ] represents paired semicircular arcs on the two-dimensional spectrum;
and an eighth module, configured to predict a diffuse sound field according to the target directivity function by using the semicircular arc frequency domain sample value.
8. A computer-readable storage medium, characterized in that the storage medium stores a program that is executed by a processor to implement the method of any one of claims 1 to 6.
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