A method, device and storage medium for analyzing the acoustic scattering characteristics of a three-dimensional sea surface containing bubbles

Abstract

A method, device and storage medium for analyzing the acoustic scattering characteristics of a three-dimensional sea surface containing bubbles, the method comprising the steps of: obtaining an incident wave vector of a sea surface containing bubbles; obtaining a scattered wave vector of the sea surface containing bubbles; decomposing the incident wave vector into a horizontal component of the incident wave and a vertical component of the incident wave; decomposing the scattered wave vector into a horizontal component of the scattered wave and a vertical component of the scattered wave; calculating a first-order small slope approximate scattering amplitude according to the horizontal component of the incident wave, the vertical component of the incident wave, the horizontal component of the scattered wave and the vertical component of the scattered wave; calculating a second-order small slope approximate scattering amplitude according to the horizontal component of the incident wave, the vertical component of the incident wave, the horizontal component of the scattered wave and the vertical component of the scattered wave. The present application summarizes the influence of bubbles on acoustic waves into three aspects: sound velocity attenuation, phase modulation and energy reduction, modifies a typical small slope approximation method, and proposes a method suitable for simulating the acoustic scattering characteristics of a three-dimensional sea surface containing bubbles.

Description

Technical Field

[0001] The present invention belongs to the technical field of sound scattering characteristic analysis, and in particular relates to a method, a device and a storage medium for analyzing the sound scattering characteristics of a three-dimensional sea surface containing bubbles. Background Art

[0002] In modern naval warfare, with the emergence of quiet submarines, anti-submarine detection technology has posed unprecedented challenges to the stealth of submarines. Acoustic scattering is the main method for detecting submarines, which effectively tracks, detects and strikes targets by utilizing the scattering characteristics of the target.

[0003] When active sonar is used to illuminate the sea surface containing bubbles, the sound waves must first be attenuated and absorbed by the bubble layer before reaching the sea surface, and then attenuated and absorbed by the bubbles after being scattered by the sea surface before reaching the receiver. At present, domestic and foreign scholars have conducted a lot of research on sea surface sound scattering, but there is little research on the sound scattering characteristics of sea surfaces containing bubbles. Summary of the invention

[0004] In view of the above problems, the present invention provides a method, device and storage medium for analyzing the acoustic scattering characteristics of a three-dimensional sea surface containing bubbles, which overcome the above problems or at least partially solve the above problems.

[0005] In order to solve the above technical problems, the present invention provides a method for analyzing the acoustic scattering characteristics of a three-dimensional sea surface containing bubbles, the method comprising the steps of:

[0006] Get the incident wave vector of the sea surface containing bubbles;

[0007] Obtaining a scattered wave vector of the bubble-containing sea surface;

[0008] Decomposing the incident wave vector into an incident wave horizontal component and an incident wave vertical component;

[0009] Decomposing the scattered wave vector into a scattered wave horizontal component and a scattered wave vertical component;

[0010] Calculate the first-order small slope approximate scattering amplitude according to the incident wave horizontal component, the incident wave vertical component, the scattered wave horizontal component and the scattered wave vertical component;

[0011] The second-order small-slope approximate scattering amplitude is calculated according to the incident wave horizontal component, the incident wave vertical component, the scattered wave horizontal component and the scattered wave vertical component.

[0012] Preferably, the expression of the horizontal component of the incident wave is:

[0013]

[0014] in, represents the projection vector of the incident wave vector in the bubble on the horizontal plane, k im represents the spatial wave number of the incident wave in the bubble, and Represents the unit vectors in the x and y directions, θ i and denote the incident angle and incident azimuth, respectively.

[0015] Preferably, the expression of the vertical component of the incident wave is:

[0016]

[0017] in, represents the projection of the scattered wave vector in the bubble on the horizontal plane, k sm represents the spatial wave number of the scattered wave in the bubble, θ s and represent the scattering angle and scattering azimuth, respectively.

[0018] Preferably, the expression of the horizontal component of the scattered wave is:

[0019]

[0020] Among them, q 0m represents the projection of the incident wave vector in the bubble in the z-axis direction, k 0m Represents vector The size of (can also be written as: the size of the projection vector of the incident wave vector on the horizontal plane), ω represents the angular frequency in the seawater when bubbles are not considered, and c represents the wave speed in the seawater when bubbles are not considered.

[0021] Preferably, the expression of the vertical component of the scattered wave is:

[0022]

[0023] Among them, q m represents the projection of the scattered wave vector in the bubble in the z-axis direction, k m Represents vector The size of (can also be written as: the size of the projection vector of the scattering wave vector on the horizontal plane).

[0024] Preferably, the expression of the first-order small slope approximate scattering amplitude is:

[0025]

[0026] in, represents the scattering amplitude, represents the first-order Bragg kernel function matrix, represents the integral in the x and y directions, Indicates location The cone wave intensity at Indicates location The height of sea surface fluctuation.

[0027] Preferably, the expression of the second-order small slope approximate scattering amplitude is:

[0028]

[0029] in, represents the second-order SSA coefficient matrix, The Fourier transform representing the height fluctuations of the rough sea surface, represents the wave number in spectral space.

[0030] The present invention also provides a three-dimensional bubble-containing sea surface acoustic scattering characteristic analysis device, the device comprising:

[0031] An incident wave vector acquisition module, used to acquire the incident wave vector of the sea surface containing bubbles;

[0032] A scattering wave vector acquisition module, used to acquire the scattering wave vector of the bubble-containing sea surface;

[0033] An incident wave vector decomposition module, used for decomposing the incident wave vector into an incident wave horizontal component and an incident wave vertical component;

[0034] A scattered wave vector decomposition module, used for decomposing the scattered wave vector into a scattered wave horizontal component and a scattered wave vertical component;

[0035] A first-order small slope approximate scattering amplitude calculation module, used to calculate the first-order small slope approximate scattering amplitude according to the incident wave horizontal component, the incident wave vertical component, the scattered wave horizontal component and the scattered wave vertical component;

[0036] The second-order small slope approximate scattering amplitude calculation module is used to calculate the second-order small slope approximate scattering amplitude according to the horizontal component of the incident wave, the vertical component of the incident wave, the horizontal component of the scattered wave and the vertical component of the scattered wave.

[0037] The present invention further provides an electronic device, comprising:

[0038] at least one processor; and,

[0039] a memory communicatively connected to the at least one processor; wherein,

[0040] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute any of the aforementioned three-dimensional bubble-containing sea surface sound scattering characteristics analysis methods.

[0041] The present invention also provides a non-transitory computer-readable storage medium, which stores computer instructions, and the computer instructions are used to enable the computer to execute any of the aforementioned three-dimensional bubble-containing sea surface acoustic scattering characteristics analysis methods.

[0042] One or more technical solutions in the embodiments of the present invention have at least the following technical effects or advantages: a three-dimensional sea surface sound scattering characteristics analysis method, device and storage medium provided in the present application summarize the influence of bubbles on sound waves into three aspects: sound velocity attenuation, phase modulation and energy reduction, correct the typical small slope approximation method, and propose a method suitable for simulating the sound scattering characteristics of a three-dimensional sea surface sound scattering characteristics containing bubbles. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0044] Figure 1(a) shows the wind speed when it is fixed at U 10 = 5m / s when the wind growth affects the wave power spectrum;

[0045] Figure 1(b) shows a schematic diagram of the effect of wind speed changes on the power spectrum of ocean waves when the wind domain is fixed at X = 30 km;

[0046] Figure 2(a) shows a schematic diagram of the comparison of the Elfouhaily slope spectra at different wind speeds;

[0047] Figure 2(b) shows a schematic diagram of the comparison of Elfouhaily slope spectra under different wind domains;

[0048] Figure 3(a) shows a schematic diagram of the comparison of the Elfouhaily curvature spectra at different wind speeds;

[0049] Figure 3(b) shows a schematic diagram of the comparison of Elfouhaily curvature spectra under different wind domains;

[0050] Figure 4 A schematic diagram of the Elfouhaily directional spectrum function is shown;

[0051] Figure 5(a)-5(f) A schematic diagram of the geometric model of the three-dimensional sea surface under different wind speeds and wind directions obtained based on the Elfouhaily sea spectrum simulation is shown;

[0052] Figure 6 A schematic diagram showing a plane acoustic wave incident on a three-dimensional sea surface is shown;

[0053] Figure 7 A schematic diagram showing the variation of the bubble group distribution function with water depth is shown;

[0054] Figure 8 A schematic diagram showing the variation of the bubble group distribution function with the bubble radius is shown;

[0055] Figure 9(a)-9(b) A schematic diagram of the simulation of the bubble group distribution function changing with wind speed is shown;

[0056] Fig.10 A schematic diagram showing the change of sound velocity profile in water caused by the bubble layer is shown;

[0057] Figure 11(a)-11(b) A schematic diagram of the attenuation coefficient of the bubble layer is shown;

[0058] Fig.12 A schematic diagram of the verification of the modified SSA algorithm is shown;

[0059] Figure 13(a)-13(d) A schematic diagram showing the comparison of the acoustic scattering intensity of two stations on the sea surface with bubbles and without bubbles under level 3 sea conditions is shown;

[0060] Figure 14(a)-14(d) A schematic diagram showing the comparison of the acoustic scattering intensity of the sea surface with bubbles and without bubbles at two stations under sea conditions of level 4 is shown;

[0061] Figure 15(a)-15(d) A schematic diagram showing the comparison of the acoustic scattering intensity of the sea surface with bubbles and without bubbles at two stations under sea conditions of level 5 is shown;

[0062] Fig.16 It is a structural schematic diagram of an electronic device provided by the present invention;

[0063] Fig.17 It is a structural schematic diagram of a non-transient computer-readable storage medium provided by the present invention. DETAILED DESCRIPTION

[0064] The present invention will be described in detail below in conjunction with specific implementations and examples, and the advantages and various effects of the present invention will be more clearly presented. It should be understood by those skilled in the art that these specific implementations and examples are used to illustrate the present invention, rather than to limit the present invention.

[0065] Throughout the specification, unless otherwise specifically stated, the terms used herein should be understood as meanings commonly used in the art. Therefore, unless otherwise defined, all technical and scientific terms used herein have the same meanings as those generally understood by those skilled in the art to which the present invention belongs. In the event of a conflict, the present specification takes precedence.

[0066] Unless otherwise specified, various raw materials, reagents, instruments and equipment used in the present invention can be purchased from the market or prepared by existing methods.

[0067] In the embodiment of the present application, the actual random sea wave can be approximately regarded as a stationary random process. For the sea surface that changes with time, the harmonic components of different frequencies can be multiplied by the time factor based on the dispersion relationship of the sea wave in the frequency domain, so that the sea wave height fluctuation at any time t that changes with time can be expressed as:

[0068]

[0069] in, is the power spectral density function of the two-dimensional ocean wave, δk x =2π / L x and δk y =2π / L y Represent the sampling intervals in the x and y directions respectively, is the spatial wave number vector, γ(k) is a complex Gaussian random sequence satisfying Gaussian distribution, and the superscript * represents the complex conjugate operation; represents the dispersion relation of a linear ocean wave in infinitely deep water, which relates the spatial frequency k = |k| to the temporal frequency, k m =363.2rad / m, g0 is the acceleration due to gravity.

[0070] In the embodiment of the present application, the deep sea surface spectrum model used in the present application is the Elfouhaily spectrum, and the one-dimensional spectrum form of the spectrum can be expressed as:

[0071] S(k)=k -3 (B L (k)+B H (k));

[0072] Among them, B L represents the low wave number curvature spectrum (long wave curvature spectrum), B H Represents the high-wavenumber curvature spectrum (short-wavelength curvature spectrum).

[0073] In the embodiment of the present application, the long-wave curvature spectrum can be expressed as:

[0074]

[0075] Among them, the parameters Inverse Wave Age Ω=U 10 / c(k p ), wave phase velocity k m=363.2rad / m, spectrum peak wave number and

[0076]

[0077] Among them, F p The relevant parameters involved are:

[0078]

[0079] in, is the dimensionless wind region introduced in the JONSWAP spectrum, which can be expressed as U 10 is the wind speed at a height of 10 m above the sea surface, and X is the wind domain, which represents the effective distance over which the wind transfers energy to the ocean.

[0080] In the embodiment of the present application, the short-wave curvature spectrum can be expressed as:

[0081]

[0082] Among them, α m is the generalized equilibrium parameter of small-scale waves, which can be expressed as:

[0083]

[0084] and u f is the sea surface friction wind speed (Friction velocity), sea surface friction wind speed u f The wind speed U(z) at the height z above the sea surface has the following relationship:

[0085]

[0086] In the embodiment of the present application, FIG. 1( a ) shows the wind speed when it is fixed at U 10 =5m / s, the influence of the growth of the wind domain on the power spectrum of the sea wave. Figure 1(b) shows the influence of the change of wind speed on the power spectrum of the sea wave when the wind domain is fixed at X=30km. It can be seen from the figure that with the increase of wind speed and the growth of the wind domain, the corresponding integral area of ​​the spectrum curve increases significantly. This means that with the increase of wind speed and the growth of the wind domain, the energy of the sea wave increases and the main energy distribution moves toward the long wave direction, that is, with the increase of wind speed and the growth of the wind domain, the energy of large-scale gravity waves will dominate.

[0087] In addition, as can be seen from Figure 1(a), the growth of the wind domain seems to only affect the large-scale gravity wave component, but has almost no effect on the small-scale capillary wave component. As can be seen from Figure 1(b), with the increase of wind speed, the energy of gravity waves and capillary waves increases, but the energy of gravity wave components is more sensitive to changes in wind speed.

[0088] In the embodiment of the present application, Figures 2(a) and (b) provide comparative schematic diagrams of Elfouhaily slope spectra under different wind speeds and wind domains. As can be seen from Figure 2(a), the slope of the sea wave increases with the growth of the wind domain. Moreover, the growth of the wind domain seems to have only an effect on the slope of large-scale gravity waves, but does not seem to have an effect on the slope of small-scale capillary waves. As can be seen from Figure 2(b), the slopes of the sea wave gravity wave component and the capillary wave component both increase with the increase of wind speed.

[0089] In the embodiment of the present application, Figures 3(a) and (b) provide schematic diagrams for comparing the Elfouhaily curvature spectrum under different wind speeds and wind domains. As can be seen from Figure 3(a), the growth of the wind domain seems to only affect the gravity wave component of the curvature spectrum, and has almost no effect on the capillary wave component of the curvature spectrum. As can be seen from Figure 3(b), the change in wind speed has a significant effect on both the gravity wave and capillary wave components of the curvature spectrum.

[0090] In the embodiment of the present application, the directional spectrum function of the Elfouhaily spectrum can be expressed as:

[0091]

[0092] in,

[0093] In the embodiments of the present application, Figure 4 The Elfouhaily directional spectrum function is given, where the wind speed is U 10 =5m / s, and the wind domain is fixed at X=30km. As can be seen from the figure, the Elfouhaily directional spectrum function cannot reflect the difference under headwind conditions. The Elfouhaily directional spectrum function obviously depends on the spatial wave number. Moreover, the smaller the spatial wave number, the more obvious the anisotropic characteristics of the directional spectrum function.

[0094] In the embodiments of the present application, Figure 5(a)-5(f) Based on the Elfouhaily sea spectrum, the Monte Carlo method is used to simulate the geometric model of the three-dimensional sea surface under different wind speeds and wind directions. 10 =3m / s, U in Figure 5(b) 10 =3m / s, U in Figure 5(c) 10 =3m / s, U in Figure 5(d) 10 =5m / s, U in Figure 5(e) 10 =5m / s, U in Figure 5(f) 10 =5m / s, Among them, U 10 represents the wind speed above the sea surface, Indicates the wind direction angle, the length and width of the sea surface are both 200m. Figure 5(a)-5(f) It can be seen that with the increase of wind speed, the sea surface fluctuates more violently and the waves are higher. At the same time, by comparing the sea surface with different wind directions, it can be seen that with the change of wind direction, the direction of sea wave changes significantly.

[0095] In the embodiments of the present application, Figure 6 As shown in Figure 2, when a plane sound wave is considered to be irradiated onto the sea surface from a space z < 0, the incident wave vector is Among them, k0 and q0 are its horizontal and vertical components respectively, q0=k i cosθ i , k i is the incident wave number; the scattered wave vector is Among them, k and q are its horizontal and vertical components respectively, q=k s cosθ s . Then the incident wave has the following form:

[0096]

[0097] In the present application example, p i represents the incident sound pressure, and the scattered wave has the following form:

[0098] p s =q -1 / 2 ∫exp(ik·r-iqz)S(k,k0)dk;

[0099] S(k,k0) is related to the propagation medium and is called represents the amplitude of the scattered wave with horizontal wave number k propagating in medium N from a plane incident wave with horizontal wave number k0 propagating in medium N. Then the field in the entire space can be described as:

[0100]

[0101] According to the invariance of the scattering amplitude in the small slope approximation, the scattering amplitude of the small slope approximation has the following form:

[0102]

[0103] Wherein, Q=q+q0, the exponential term exp[-i(k-k0)·r+iQh(r)] in the integrand is similar to the KA integral term, except that the SSA integral term is a weighted processing of the above exponential term.

[0104] It can be expressed by the Fourier transform of r:

[0105]

[0106] Where Φ is a function of the sea surface height fluctuation h(r). Then the scattering amplitude can be expressed as:

[0107]

[0108] Function By series expansion, we can get:

[0109]

[0110] Among them, functions Φ2, Φ3, ... are symmetric about variables ξ1, ξ2, ... and these functions have nothing to do with the height fluctuation of the sea surface, but are only functions of the horizontal spatial wave number. h(ξ) represents the Fourier transform of the height fluctuation of the rough sea surface, which is defined as:

[0111]

[0112] For the function Φ n The solution of can be expressed as follows:

[0113]

[0114] In the formula, B, B n represents the coefficient matrix obtained by series expansion, which is independent of the height fluctuation of the sea surface and can be solved according to the corresponding rough surface boundary conditions. δ(·) is the Dirac function. After a series of derivations, the scattering amplitude matrix can be expressed by the function Φ, and the following expression is obtained:

[0115] S(k,k0)=Φ0δ(k-k0)+i(q+q0)Φ0h(k-k0)+O(h 2 );

[0116] Comparing the above two formulas, we can find that:

[0117]

[0118] On this basis, the scattering amplitude of the first-order small slope approximation (SSA-I) can be obtained as follows:

[0119]

[0120] For the sea surface, its boundary is an absolute soft surface scattering, which belongs to the Dirichlet boundary value problem, and the total sound pressure on the boundary p| S =0, we can deduce that:

[0121] B(k,k0)=-1;

[0122] In order to obtain the scattering amplitude of the second-order small slope approximation, it is first necessary to modify the scattering amplitude expression and write it as a second-order function, that is:

[0123]

[0124] Solving the second-order term Φ2, we can obtain:

[0125]

[0126] According to the arbitrariness of h(ξ) and the symmetry of the integrand about ξ1 and ξ2, we can obtain:

[0127]

[0128] Therefore, the scattering amplitude of the second-order small slope approximation (SSA-II) can be expressed as:

[0129]

[0130] In the above formula,

[0131] M(k,k0;ξ)=B2(k,k0;k-ξ)+B2(k,k0;k0+ξ)+2QB(k,k0);

[0132] According to the Dirichlet boundary condition, it can also be deduced:

[0133] B2(k,k0;k′)=2q k′ ;

[0134] When considering cone wave illumination, the above equation becomes:

[0135]

[0136] The final scattered intensity can be expressed as:

[0137] σ=4πq0q|S(k,k0)| 2 .

[0138] In the embodiment of the present application, assuming that the bubble radius is between 10 μm and 1000 μm, that is, there are no bubbles larger than 1000 microns and smaller than 10 microns, the bubble group distribution function changes with the bubble radius as follows:

[0139]

[0140] Where a is the bubble radius in μm; z is the depth in m, u 10 is the wind speed 10 meters above the sea surface, in m / s, L(u 10 ) is a quantity related to wind speed, with the unit of m; G(a,z) is a quantity related to bubble radius and water depth;

[0141]

[0142] a ref (z) = 54.4 μm + 1.984 × 10 -6 z;

[0143]

[0144] So the number of bubble molecules per unit volume is:

[0145]

[0146] The total volume of bubbles per unit volume is:

[0147]

[0148] In the embodiment of the present application, the bubble group distribution function varies with water depth as follows: Figure 7 As shown in the figure, the bubble radius in the simulation is 10μm, 50μm, 100μm, 500μm, 1000μm, and the wind speed u 10 =15m / s; the bubble group distribution function changes with water depth as follows Figure 8 As shown in the simulation, the water depth is 0.7m, 1.8m, 4.0m, and the wind speed u 10 =15m / s. Figure 9 is a simulation diagram of the bubble group distribution function changing with wind speed, where the water depth in Figure 9(a) is 4m and the bubble radius in Figure 9(b) is 50 microns.

[0149] In the embodiment of the present application, Figure 7 -It can be seen from Figure 9 that: at the same depth, the smaller the bubble radius, the greater the proportion; as the depth increases, the proportion of bubbles decreases; as the wind speed increases, the proportion of bubbles increases.

[0150] In the embodiment of the present application, after taking bubbles into account, the speed of sound in water becomes:

[0151]

[0152] In the formula, c w =1490m / s is the speed of sound in water without bubbles, c m is the corrected speed of sound in water containing bubbles, P(z) = 10 5 (1.013+ρ w gz)pa is the absolute hydrostatic pressure in water, ρ w =1027kg / m 3 is the density of water, and κ0(z) ranges from 1.0 to 1.4.

[0153] In the embodiments of the present application, Fig.10 The following is a schematic diagram of the change in the sound velocity profile in water caused by the bubble layer when k is 1.0. Assume that there are only bubbles with a bubble radius of a in the water, and the number density of the bubbles per unit volume is N (in m -3 At the same time, assuming that the distance between the bubbles is far enough (the distance between the bubbles is greater than the square of the sound elimination coefficient, or another more stringent condition is that the distance is greater than the wavelength), the interaction between any two bubbles does not need to be considered.

[0154] Assume that the incident wave intensity is I inc , then the intensity of the incident wave becomes I after passing through a bubble inc σ. So we have:

[0155]

[0156] I(x)=I inc exp(-σNx);

[0157] After the sound wave passes through x, its energy becomes:

[0158]

[0159] Therefore, the sound elimination coefficient of a single bubble is:

[0160]

[0161] When there are bubbles of multiple sizes, the above formula becomes:

[0162]

[0163] In the embodiments of the present application, Figure 11(a)-11(b) The attenuation coefficient of the bubble layer is shown in Figure 11(a) with an incident frequency of 2kHz and Figure 11(b) with an incident frequency of 100kHz. It can be seen from the figure that with the increase of wind speed and incident frequency, the attenuation coefficient increases greatly, which is consistent with the actual situation.

[0164] The continuity equation proposed by the van Wijngaarden-Papani-colao model is:

[0165]

[0166] where ρ and c are the density and speed of sound of the bulk liquid, and β is the local fraction of volume occupied by the gas, given by:

[0167]

[0168] where R is the instantaneous radius of the bubble and n is their number per unit volume. When taking the time derivative of equation (1), n ​​must remain constant. This equation is valid for the case where all bubbles have the same equilibrium radius. But its extension to different bubble sizes is straightforward and will be considered later. Also, the bubbling medium will be described in an average sense, with P and u representing the average pressure and velocity.

[0169] Equation (1) can be proved as follows. Let Pm and u denote the average local mixture density and the center-of-mass velocity. Then the total mass conservation equation of the mixture can be written as:

[0170]

[0171] The average density can be expressed as:

[0172] ρ m =(1-β)ρ+βρ G ;

[0173] where ρ G is the gas density, when ρ G When <<ρ,

[0174] Substituting into formula (3) we can get:

[0175]

[0176] When β is small, the denominator on the right can be taken as 1, and the maximum is β 2 . Further specifying dβ / dt, we find a term proportional to dR / dt and a term proportional to dn / dt. To estimate this second term, we note that in the absence of fragmentation or coalescence, the bubble number density must satisfy a conservation equation of the form:

[0177]

[0178] where u B is the average velocity of the bubble field. Eliminate dn / dt in the formula using the formula, and we have:

[0179]

[0180] Because u B must be of the same order of magnitude as u, so the second term on the right is O(β) smaller than the corresponding term on the left and can be ignored. Furthermore, if ω and λ are typical frequencies and wavelengths of the waves, then the following approximation holds:

[0181]

[0182] Where Δβ is the oscillation amplitude of β, from which we can get:

[0183]

[0184] where c m is the speed of the pressure waves in the mixture. If, apart from the small effect of the compressibility of the liquid, the motion is caused solely by the change in volume of the bubbles, and if their number is not too large, then m is small compared to |u|, so the spatial part of dβ / dt can be neglected. Similarly, Then formula (5) can be expressed as:

[0185]

[0186] By using the acoustic relationship dρ = c -2 dP, this also applies to the average value, since the linear relationship between pressure and density is sufficient for a very wide range of common liquids. The formula is therefore consistent with the formula.

[0187] Similarly, in terms of average quantities, the momentum equation can be written as:

[0188]

[0189] Where M is the average mixture momentum flux. Substituting equation (3) into it, we can get:

[0190]

[0191] For the conditions described above, the quadratic term in u is small and βu is also small, so the relationship can be approximated as:

[0192]

[0193] The formula is the momentum equation of the van Wijngaarden-Papani-colao model. From this formula, it is easy to prove that the order of magnitude of u is βc m .

[0194] For a mixture containing bubbles of different sizes, we can define dν = f(a; x) da as the number of bubbles per unit volume, and the equilibrium radius is between a and a + da near point x. Then, given the volume fraction β, the formula is as follows:

[0195]

[0196] where R(a;x,t) represents the radius of a bubble at position x with equilibrium radius a at time t. It should be noted that no time dependence is indicated for the distribution function, since the same arguments given above for neglecting dn / dt indicate that f can be considered a constant during the propagation of the wave. For this expression for β, the continuity equation still holds and the momentum equation remains the same, however, for each x, a separate radial equation must be written for each a.

[0197] For the case of radial motion of bubbles, Keller gave an equation that approximates the compressibility of the liquid in the form of:

[0198]

[0199] where p B is the liquid pressure at the bubble interface, and satisfies the following relationship with the internal pressure p:

[0200]

[0201] σ and μ represent the surface tension and the viscosity of the liquid. For an isolated bubble, P in the formula is the pressure at the location of the bubble if the bubble does not exist. Foldy was the first to realize that in a dilute mixture, P coincides with the mean pressure defined in the previous section when B is of the lowest order. Under this condition, the bubbles do not interact with each other's fields, but with the mean field. If the liquid is interpreted in the sense of the mean volume, it can be said that at time t, the pressure is close to P(x,t) almost everywhere within the mean volume centered on x. Large deviations from this value occur only in the immediate vicinity of other bubbles, introducing the described bubble into the mean volume. Since the volume fraction is small, it is unlikely to break in the vicinity of another bubble. Moreover, since the mean volume must contain many bubbles, the effect of adding a new bubble on P can also be ignored.

[0202] The dots in the equations and represent total time derivatives, which for bubbles in a mixture must be interpreted as convection derivatives. However, the same arguments given earlier justify their interpretation as partial time derivatives. For ease of exposition, we will continue to use dots below.

[0203] Starting from the gas enthalpy equation and using the ideal gas state equation, we can get:

[0204]

[0205] where γ is the ratio of specific heats, K is the thermal conductivity, T is the temperature, and v is the velocity. If the bubble boundary moves much slower than the speed of sound in the gas, then the pressure can be considered uniform and the convective derivative of the gas velocity Dp / Dt is approximately equal to With these approximations, integrating the equation yields an explicit expression for the radial component of the gas velocity:

[0206]

[0207] Consider the motion boundary condition when r = R Then the pressure equation can be obtained:

[0208]

[0209] From these results, the temperature field can be obtained from the standard form of the energy equation:

[0210]

[0211] Among them, C p is the specific heat at constant pressure.

[0212] After eliminating u between and , by the usual acoustic approximation (i.e. keeping ρ and c unchanged), we can obtain:

[0213]

[0214] The time derivative of β is given by:

[0215]

[0216] Or, in the linear approximation

[0217]

[0218] Likewise,

[0219]

[0220] therefore,

[0221]

[0222] In the linearized form of the equations and

[0223] R = a(1+X), p = p0(1-ΦX);

[0224] From this we can get:

[0225]

[0226] where χ = D / ωa 2 , and D = (γ-1)K T T / γp0 is the thermal diffusivity of the gas. It should be noted that the function Φ is a complex number. p0=P in the equation ∞ +2σ / a is the undisturbed pressure in the bubble, where P ∞ is the hydrostatic pressure at infinity. Further definition:

[0227] Q=Pp ∞ ∝exp(iωt);

[0228] The linearized form of the Kähler equation is

[0229]

[0230] Multiply the formula by (1-iωa / c) and ignore c -2 Finally, we get:

[0231]

[0232] in is the bubble resonance frequency, b is the damping coefficient of the bubble, and they satisfy the following relationships:

[0233]

[0234]

[0235] Substituting into the wave equation, we can obtain:

[0236]

[0237] where the wavenumber in the mixture is given by the dispersion relation

[0238]

[0239] Where n(a) is the distribution function of the bubble.

[0240] According to the above two-dimensional small slope approximation method, combined with the equivalent medium method, due to the existence of bubble groups, the wave number changes during the propagation process. At this time, the wave number is taken as the calculated effective wave number, and the incident wave vector and the scattered wave vector are decomposed into horizontal components and vertical components, and it can be obtained:

[0241]

[0242] in,

[0243] Then the scattering amplitude of the first-order small slope approximation (SSA-I) is:

[0244]

[0245] The scattering amplitude of the second-order small slope approximation (SSA-I) is:

[0246]

[0247] To illustrate the correctness of the above modified small slope approximation algorithm, the project team used the modified small slope approximation method to obtain the single-station sound scattering intensity of the bubble sea surface and the classic paper "Low Frequency Sound Scattering from Rough Bubbly Ocean Surface: Small Perturbation Theory Based on the Reformed Helmholtz-Kirchhoff-Fresnel Method". Fig.12 The results are compared with Fig.12 The parameters used in the simulation are as follows: The wind speed at 10 meters above the sea surface is u 10 =2.57m / s, the incident frequency is f=100kHz, the incident azimuth and scattering azimuth are Numerical calculation shows that the root mean square error of the two algorithms is 2.66dB, which meets the requirement of the project assessment index that the root mean square error compared with the results of classic literature should not exceed 3dB.

[0248] Unless otherwise specified in the subsequent simulation, the parameters used are as follows: the sea surface size is 150m×150m, the cone wave factor g=L / 4, the segmentation interval is dx=dy=0.025m, the sea state is level 3-5 (corresponding to wind speeds of 5m / s, 7m / s, and 10m / s at 10 meters above the sea surface), and the wind direction angle is That is, along the negative direction of the x-axis. The incident wave frequency is f = 10kHz, and the incident azimuth and scattering azimuth are

[0249] In the embodiment of the present application, Figures 13 to 15 are respectively the comparison of the acoustic scattering intensity of the sea surface with bubbles and the sea surface without bubbles under sea conditions of level 3, level 4, and level 5. The incident angles in the simulation are θ i=30°(Figure 13(a)-Figure 15(a)), 45°(Figure 13(b)-Figure 15(b)), 60°(Figure 13(c)-Figure 15(c)), 75°(Figure 13(d)-Figure 15(d)). It can be seen from Figures 13-15 that: ① Regardless of whether the influence of bubbles is considered, there are peaks in the mirror direction of the scattering angle. This is because the sea surface has a mirror enhancement effect; ② When bubbles are considered, the maximum mirror value of the sea surface is smaller than the maximum value when bubbles are not considered. This is because after considering bubbles, the sound wave will first pass through the bubble layer before reaching the sea surface. After being scattered by the sea surface, it will pass through the bubble layer again before reaching the receiving sonar, and bubbles have a subtractive absorption effect on sound waves. Therefore, when bubbles are considered, the scattering maximum value decreases; ③ When bubbles are considered, the backward area (different incident angles correspond to different angle ranges, θ i =30° when the scattering angle range is θ s ≤-15°, θ i =45° when the scattering angle range is θ s ≤0°,θ i =60° when the scattering angle range is θ s ≤10°, θ i =75° when the scattering angle range is θ s The scattering intensity of the sound wave is obviously greater than that of the sea surface when the bubbles are not considered. This is because when the bubbles are considered, the backward energy of the sound wave is enhanced due to the scattering effect of the bubbles on the sound wave.

[0250] Reference below Fig.16 , which shows a schematic diagram of the structure of an electronic device 100 suitable for implementing the embodiment of the present disclosure. The electronic device in the embodiment of the present disclosure may include, but is not limited to, mobile terminals such as mobile phones, notebook computers, digital broadcast receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), vehicle terminals (such as vehicle navigation terminals), etc., and fixed terminals such as digital TVs, desktop computers, etc. Fig.16 The electronic device shown is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present disclosure.

[0251] like Fig.16 As shown, the electronic device 100 may include a processing device (e.g., a central processing unit, a graphics processing unit, etc.) 101, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 102 or a program loaded from a storage device 108 to a random access memory (RAM) 103. In the RAM 103, various programs and data required for the operation of the electronic device 100 are also stored. The processing device 101, the ROM 102, and the RAM 103 are connected to each other via a bus 104. An input / output (I / O) interface 105 is also connected to the bus 104.

[0252] Typically, the following devices may be connected to the I / O interface 105: an input device 106 including, for example, a touch screen, a touchpad, a keyboard, a mouse, an image sensor, a microphone, an accelerometer, a gyroscope, etc.; an output device 107 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; a storage device 108 including, for example, a magnetic tape, a hard disk, etc.; and a communication device 109. The communication device 109 may allow the electronic device 100 to communicate with other devices wirelessly or by wire to exchange data. Although the electronic device 100 having various devices is shown in the figure, it should be understood that it is not required to implement or have all the devices shown. More or fewer devices may be implemented or have alternatively.

[0253] In particular, according to an embodiment of the present disclosure, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present disclosure includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program contains program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from the network through the communication device 109, or installed from the storage device 108, or installed from the ROM 102. When the computer program is executed by the processing device 101, the above-mentioned functions defined in the method of the embodiment of the present disclosure are executed.

[0254] Reference below Fig.17 , which shows a structural schematic diagram of a computer-readable storage medium suitable for implementing an embodiment of the present disclosure, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it can implement a finite element mesh generation method for a multi-scale component model as described in any of the above.

[0255] It should be noted that the computer-readable medium disclosed above may be a computer-readable signal medium or a computer-readable storage medium or any combination of the above two. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present disclosure, a computer-readable storage medium may be any tangible medium containing or storing a program that may be used by or in combination with an instruction execution system, device or device. In the present disclosure, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, in which a computer-readable program code is carried. This propagated data signal may take a variety of forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination of the above. The computer readable signal medium may also be any computer readable medium other than a computer readable storage medium, which may send, propagate or transmit a program for use by or in conjunction with an instruction execution system, apparatus or device. The program code contained on the computer readable medium may be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (radio frequency), etc., or any suitable combination of the above.

[0256] The computer-readable medium may be included in the electronic device, or may exist independently without being installed in the electronic device.

[0257] The computer-readable medium carries one or more programs. When the one or more programs are executed by the electronic device, the electronic device: obtains at least two Internet Protocol addresses; sends a node evaluation request including the at least two Internet Protocol addresses to a node evaluation device, wherein the node evaluation device selects an Internet Protocol address from the at least two Internet Protocol addresses and returns it; receives the Internet Protocol address returned by the node evaluation device; wherein the obtained Internet Protocol address indicates an edge node in a content distribution network.

[0258] Alternatively, the computer-readable medium carries one or more programs, and when the one or more programs are executed by the electronic device, the electronic device: receives a node evaluation request including at least two Internet Protocol addresses; selects an Internet Protocol address from the at least two Internet Protocol addresses; and returns the selected Internet Protocol address; wherein the received Internet Protocol address indicates an edge node in a content distribution network.

[0259] Computer program code for performing the operations of the present disclosure may be written in one or more programming languages, or a combination thereof, including object-oriented programming languages, such as Java, Smalltalk, C++, and conventional procedural programming languages, such as "C" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a separate software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., through the Internet using an Internet service provider).

[0260] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to various embodiments of the present disclosure. In this regard, each square box in the flow chart or block diagram can represent a module, a program segment or a part of a code, and the module, the program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some implementations as replacements, the functions marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two square boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0261] The units involved in the embodiments described in the present disclosure may be implemented by software or hardware. The name of a unit does not limit the unit itself in some cases. For example, the first acquisition unit may also be described as a "unit for acquiring at least two Internet Protocol addresses".

[0262] The present application provides a method, device and storage medium for analyzing the acoustic scattering characteristics of a three-dimensional sea surface containing bubbles. The effects of bubbles on sound waves are summarized into three aspects: sound velocity attenuation, phase modulation and energy reduction. The typical small slope approximation method is corrected, and a method suitable for simulating the acoustic scattering characteristics of a three-dimensional sea surface containing bubbles is proposed.

[0263] It should be noted that, in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that the process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of more restrictions, the elements defined by the sentence "including one..." do not exclude the existence of other identical elements in the process, method, article or device including the elements. The above is only a specific implementation of the present application, so that those skilled in the art can understand or implement the present application. The various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features applied for herein.

[0264] In short, the above is only a preferred embodiment of the technical solution of the present invention, and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for analyzing the acoustic scattering characteristics of a three-dimensional sea surface containing bubbles, characterized in that: The method comprises the steps of: Get the incident wave vector of the sea surface containing bubbles; Obtaining a scattered wave vector of the bubble-containing sea surface; Decomposing the incident wave vector into an incident wave horizontal component and an incident wave vertical component; Decomposing the scattered wave vector into a scattered wave horizontal component and a scattered wave vertical component; Calculate the first-order small slope approximate scattering amplitude according to the incident wave horizontal component, the incident wave vertical component, the scattered wave horizontal component and the scattered wave vertical component; Calculate the second-order small slope approximate scattering amplitude according to the horizontal component of the incident wave, the vertical component of the incident wave, the horizontal component of the scattered wave and the vertical component of the scattered wave; Among them, the expression of the horizontal component of the incident wave is: ； in, represents the projection vector of the incident wave vector in the bubble on the horizontal plane, represents the spatial wave number of the incident wave in the bubble, and represents the unit vectors in the x and y directions, and denote the incident angle and the incident azimuth respectively; the expression of the vertical component of the incident wave is: ； in, represents the projection of the scattered wave vector in the bubble on the horizontal plane, represents the spatial wave number of the scattered wave in the bubble, and represents the unit vectors in the x and y directions, and denote the scattering angle and scattering azimuth respectively; the expression of the horizontal component of the scattered wave is: ； in, represents the projection of the incident wave vector in the bubble in the z-axis direction, Represents vector The size of represents the angular frequency in seawater when bubbles are not considered, represents the wave speed in seawater when bubbles are not considered. represents the projection vector of the incident wave vector in the bubble on the horizontal plane, represents the spatial wave number of the incident wave in the bubble, represents the incident angle; the expression of the vertical component of the scattered wave is: ； in, represents the projection of the scattered wave vector in the bubble in the z-axis direction, Represents vector The size of represents the projection vector of the scattered wave vector in the bubble on the horizontal plane, represents the spatial wave number of the scattered wave in the bubble, represents the scattering angle, represents the angular frequency in seawater when bubbles are not considered, represents the wave speed in seawater without considering bubbles; the expression of the first-order small slope approximate scattering amplitude is: ； in, represents the scattering amplitude, represents the first-order Bragg kernel function matrix, represents the integral in the x and y directions, Indicates location The cone wave intensity at Indicates location The height of sea surface fluctuation, represents the projection vector of the scattered wave vector in the bubble on the horizontal plane, represents the projection vector of the incident wave vector in the bubble on the horizontal plane, represents the projection of the incident wave vector in the bubble in the z-axis direction, represents the projection of the scattered wave vector in the bubble in the z-axis direction; the expression of the second-order small slope approximate scattering amplitude is: ； in, represents the second-order SSA coefficient matrix, The Fourier transform representing the height fluctuations of the rough sea surface, represents the wave number in the spectral space, represents the projection vector of the scattered wave vector in the bubble on the horizontal plane, represents the projection vector of the incident wave vector in the bubble on the horizontal plane, represents the projection of the incident wave vector in the bubble in the z-axis direction, represents the projection of the scattered wave vector in the bubble in the z-axis direction, represents the integral in the x and y directions, Indicates location The height of sea surface fluctuation, Indicates location The cone wave intensity at .

2. A three-dimensional sea surface sound scattering characteristic analysis device containing bubbles, used in the three-dimensional sea surface sound scattering characteristic analysis method containing bubbles according to claim 1, characterized in that: The device comprises: An incident wave vector acquisition module, used to acquire the incident wave vector of the sea surface containing bubbles; A scattering wave vector acquisition module, used to acquire the scattering wave vector of the bubble-containing sea surface; An incident wave vector decomposition module, used for decomposing the incident wave vector into an incident wave horizontal component and an incident wave vertical component; A scattered wave vector decomposition module, used for decomposing the scattered wave vector into a scattered wave horizontal component and a scattered wave vertical component; A first-order small slope approximate scattering amplitude calculation module, used to calculate the first-order small slope approximate scattering amplitude according to the incident wave horizontal component, the incident wave vertical component, the scattered wave horizontal component and the scattered wave vertical component; The second-order small slope approximate scattering amplitude calculation module is used to calculate the second-order small slope approximate scattering amplitude according to the horizontal component of the incident wave, the vertical component of the incident wave, the horizontal component of the scattered wave and the vertical component of the scattered wave.

3. An electronic device, characterized in that: The electronic device comprises: at least one processor; and, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the three-dimensional bubble-containing sea surface sound scattering characteristics analysis method as described in claim 1.

4. A non-transitory computer-readable storage medium storing computer instructions for causing the computer to execute the method for analyzing the acoustic scattering characteristics of a three-dimensional sea surface containing bubbles as claimed in claim 1.

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