Prediction method of sea surface waves excited by underwater axisymmetric target sound source

Abstract

The present invention relates to a method for predicting seawater surface waves excited by an underwater axisymmetric target sound source. The method comprises the following steps: establishing a calculation model for the acoustic radiation of an axisymmetric shell; determining the equivalent point source intensity within the shell; establishing a model for seawater surface waves excited by an underwater point sound source in a semi-infinite water area; and calculating the displacement of the seawater surface waves excited by the axisymmetric shell. This method overcomes the fundamental flaw of the prior art, which treats underwater target sound sources, which are actually volumetric sound sources, as point sound sources. This method corrects the theoretical basis for the inevitable inaccuracies inherent in the prior art, significantly improving prediction accuracy and filling a gap in the prior art.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater target detection, and in particular to a method for predicting sea surface waves excited by an underwater axisymmetric target sound source. Background Art

[0002] When an acoustic signal radiated from water strikes the air-seawater interface, it also induces a weakly oscillating disturbance at this interface. During particle motion, the surface tension of seawater acts as the primary restoring force. This means that the radiated acoustic wave in water forms a surface wave at the seawater-air interface, commonly referred to as a seawater surface wave. Clearly, this surface wave, like the Scholte wave propagating at the seawater-seafloor interface, is caused by the radiated noise from an underwater target striking two different interfaces and carries information about the underwater target's source.

[0003] The radiation noise generated by the navigation of underwater targets consists of a continuous spectrum and a line spectrum. Compared with the continuous spectrum, the line spectrum is mainly concentrated in the low-frequency band, which is conducive to the excitation and detection of sea surface waves excited by the radiation noise of complex underwater sound sources. By adopting optical detection means, sea surface waves with smaller amplitudes can be detected, and the underwater target sound source information can be demodulated from them, which then develops into a new underwater target detection method. Therefore, obtaining information about underwater targets from sea surface waves excited by underwater sound sources is expected to provide a new technical path for underwater target detection, submarine communication, etc., namely, "acoustic-laser" joint detection. In the existing technology, for the modeling research of sea surface waves excited by the radiation noise of underwater targets, the conventional practice is to regard the complex underwater target as a point sound source, and then conduct simulation calculations, characteristic research, application prediction, etc. on this basis. The defects of the existing technology are:

[0004] 1. Because the energy of seawater surface waves excited by noise radiated by underwater targets is relatively weak, their range is relatively short compared to the wavelength of low-frequency sound sources. Furthermore, since underwater targets themselves are not point sound sources, the existing technology's crude simplification of underwater sound sources as point sound sources clearly has a fundamental theoretical flaw. Underwater targets must be considered volumetric sound sources. Therefore, the existing technology's treatment of volumetric sound sources as point sound sources is clearly irrational, and its theoretical basis is inherently flawed, inevitably leading to inaccurate results.

[0005] 2. Since the outer layers of many underwater target structures are shells, most of them can be simplified into simple three-dimensional axisymmetric structures, and three-dimensional axisymmetric structures can be analyzed using two-dimensional symmetric models, but there is no such research in the existing technology, let alone related technical solutions, so there is actually a vacuum in this field. Summary of the Invention

[0006] In response to the above-mentioned problems, the present invention provides a method for predicting sea surface waves excited by an underwater axisymmetric target sound source. Its purpose is to reverse the fundamental defect of the existing technology that a point sound source replaces the actual underwater target (volume) sound source, correct the theoretical basis for the inaccurate results that are inevitably generated by the existing technology, greatly improve the prediction accuracy, and fill the existing technical gaps.

[0007] In order to solve the above problems, the technical solution provided by the present invention is:

[0008] A method for predicting sea surface waves excited by an underwater axisymmetric target sound source comprises the following steps:

[0009] S100. Establish an axisymmetric shell acoustic radiation calculation model;

[0010] S200. Determine the equivalent point source intensity inside the shell;

[0011] S300. Establishing a sea surface wave model excited by an underwater point sound source in a semi-infinite water area;

[0012] S400. Calculate the displacement of the sea surface wave excited by the axisymmetric shell; the displacement of the sea surface wave excited by the axisymmetric shell is the final result of the present invention.

[0013] Preferably, the coordinate parameters of the shell structure of the axisymmetric shell sound radiation calculation model in S100 are established in an axisymmetric coordinate system, wherein the axisymmetric structure target is symmetrical about the z-axis, and the exciting force is also symmetrical about the z-axis.

[0014] Preferably, the axisymmetric shell sound radiation calculation model in S100 is expressed as follows:

[0015] -ω 2 a s u-iνb s u+c s u=f e +f p

[0016] Where: ω is the angular frequency; i is the unit imaginary number; ν is the damping coefficient; u is the surface normal displacement of the shell, expressed as follows:

[0017]

[0018] Where: q r is the vibration mode D corresponding to the rth vibration mode r The amplitude of q is the column vector composed of qr; D is the vibration mode D r The matrix formed;

[0019] a s is the corresponding modal mass matrix, which is expressed as follows:

[0020] a s =D T M s D

[0021] Where: D T is the transposed matrix of D, where the superscript T indicates the matrix transposed; M s is the mass matrix of the structure;

[0022] b s is the corresponding modal damping matrix, which is expressed as follows:

[0023] b s =D T C s D

[0024] Where: C s is the damping matrix of the structure;

[0025] c s is the corresponding modal stiffness matrix, which is expressed as follows:

[0026] c s =D T K s D

[0027] Among them: K s is the stiffness matrix of the structure;

[0028] f e is the modal external force matrix, which is expressed as follows:

[0029] f e =D T F e

[0030] Where: Fe is the external exciting force applied to the surface of the structure;

[0031] f p is the modal acoustic pressure matrix, which is expressed as follows:

[0032] f p =D T F p

[0033] Among them: F p is the acoustic pressure exerted by the fluid on the surface of the structure.

[0034] Preferably, S200 specifically includes the following steps:

[0035] S210. Establish an equivalent point source location model;

[0036] S220. Calculate the equivalent point source intensity.

[0037] Preferably, the equivalent point source position model in S210 is expressed as follows:

[0038]

[0039] Where: p(r Si ) is the sound pressure on the surface of the structure; M is the number of equivalent point sources, in units; r Si is the position vector corresponding to the i-th structural surface contour point; r Ol is the position vector of the lth equivalent point source; α(r Ol ) is the intensity corresponding to the lth equivalent point source; G(r Si ,r Ol ) is the corresponding Green's function, which is expressed as follows:

[0040]

[0041] Where: k f is the wave number in water, expressed as follows:

[0042] k f =ω / c f

[0043] cf is the speed of sound in seawater; γ is the sea surface reflection coefficient; r ' is the horizontal distance from the structure surface node to the equivalent point source; d Oi is the distance from the equivalent point source to the sea surface; z Ol is the coordinate of the equivalent point source surface node in the z direction; Si is the coordinate of the node on the surface of the structure in the z direction.

[0044] Preferably, the equivalent point source intensity in S220 is expressed as follows:

[0045] (-ω 2 a s -iνb s +c s -D T G)Hα=f e

[0046] Where: Hα is expressed as follows:

[0047] u=Hα.

[0048] Preferably, the seawater surface wave model excited by the underwater point sound source in the semi-infinite water area in S300 is expressed as follows:

[0049]

[0050] Where: η is the wave height, expressed as follows:

[0051] z=η(r)

[0052] θ is the incident angle of the sound wave; υ is the attenuation coefficient, which is expressed as follows:

[0053]

[0054] Where: μ is the viscosity of seawater; k is the wave number of the seawater surface wave; g is the acceleration of gravity; T is the surface tension of seawater;

[0055] p i is the incident sound wave, expressed as follows:

[0056] p i +p r =0

[0057] Where: pr is the reflected sound wave.

[0058] Preferably, the displacement of the seawater surface wave excited by the axisymmetric shell is calculated in S400 and expressed as follows:

[0059] η 总 =ηα

[0060] Where: η 总 After calculating the intensity corresponding to each equivalent point source using the axisymmetric shell sound radiation calculation model, substitute it into the seawater surface wave model excited by the underwater point sound source in the semi-infinite water area to obtain each corresponding surface wave amplitude, and perform linear superposition and sum it; η is the column vector corresponding to the surface wave amplitude η corresponding to each equivalent point source position.

[0061] Preferably, in S300, under the action of seawater surface tension, the surface dynamic boundary condition is expressed as follows:

[0062]

[0063] in: is the velocity potential function, which is expressed as follows:

[0064]

[0065] Where: M(z) is a function related to z.

[0066] Preferably, the incident sound wave and the reflected sound wave in S300 meet the conditions expressed as follows:

[0067]

[0068] Wherein: vi is the vibration velocity of the incident sound wave; vr is the vibration velocity of the reflected sound wave.

[0069] Compared with the prior art, the present invention has the following advantages:

[0070] 1. The theoretical basis of this invention is to treat underwater targets as volumetric sound sources. The corresponding technical solutions developed on this basis fundamentally overcome the fundamental flaw of existing technologies that use point sound sources instead of actual volumetric sound sources. This corrects the theoretical basis for the inevitable inaccurate results of existing technologies and greatly improves the accuracy of predictions.

[0071] 2. Since the present invention provides a new technical path for predicting sea surface waves excited by underwater complex target sound sources, that is, it provides a method for predicting sea surface waves excited by underwater axisymmetric target (taking the shell as an example) sound sources, it fills the technical gap in the existing technology, that is, it achieves technical effects that are higher than the existing technology through a different technical path. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 A schematic flow chart of a forecasting method according to a specific embodiment of the present invention;

[0073] Figure 2 This is a schematic diagram of an axisymmetric housing structure according to a specific embodiment of the present invention;

[0074] Figure 3 A schematic diagram of seawater surface waves according to a specific embodiment of the present invention;

[0075] Figure 4 Schematic diagram of the axisymmetric shell structure established for verifying the seawater surface wave model excited by the axisymmetric shell of the present invention;

[0076] Figure 5a This is a schematic diagram comparing the results obtained by the prediction method of the present invention and the results obtained by the finite element method when verifying the sea surface wave model excited by the axisymmetric shell of the present invention at a sound source frequency of 100 Hz;

[0077] Figure 5b Schematic diagram comparing the results obtained by the prediction method of the present invention and the results obtained by the finite element method when verifying the sea surface wave model excited by the axisymmetric shell of the present invention at a sound source frequency of 500 Hz;

[0078] Figure 5c This is a schematic diagram comparing the results obtained by the prediction method of the present invention and the results obtained by the finite element method when verifying the sea surface wave model excited by the axisymmetric shell of the present invention when the sound source frequency is 1000 Hz. DETAILED DESCRIPTION

[0079] The present invention is further illustrated below with reference to specific examples. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0080] like Figure 1 As shown, a method for predicting sea surface waves excited by an underwater axisymmetric target sound source comprises the following steps:

[0081] S100. Establish an axisymmetric shell sound radiation calculation model.

[0082] like Figure 2 As shown, in this specific embodiment, the coordinate parameters of the shell structure of the axisymmetric shell sound radiation calculation model in S100 are established in an axisymmetric coordinate system, wherein the axisymmetric structure target is symmetrical about the z-axis, and the exciting force is also symmetrical about the z-axis.

[0083] It should be noted that since the axisymmetric structure target is symmetrical about the z-axis, the exciting force is also symmetrical about the z-axis. Therefore, the structure can be simplified into an axisymmetric shell. It is assumed that it is far away from the seabed or located in the deep sea. That is, the influence of the seabed on the sea surface waves excited by it can be ignored. In other words, it is assumed that the shell sound source is located in semi-infinite seawater.

[0084] In this specific embodiment, the axisymmetric shell sound radiation calculation model in S100 is expressed as follows:

[0085] -ω 2 a s u-iνb s u+c s u=f e +f p (1)

[0086] Where: ω is the angular frequency; i is the unit imaginary number; ν is the damping coefficient; u is the surface normal displacement of the shell, expressed as follows:

[0087]

[0088] Where: q r is the vibration mode D corresponding to the rth vibration mode r The amplitude of q is given by q r The column vector is composed of vibration mode D r The matrix formed.

[0089] It should be noted that the principle of formula (2) is that for an undamped system, considering the first m vibration modes of the shell, according to the modal superposition principle, the normal displacement of any point on the shell surface can be expressed as the sum of the contributions of each mode, so formula (2) can be listed.

[0090] a s is the corresponding modal mass matrix, expressed as follows:

[0091] a s =D T M s D (3)

[0092] Where: D T is the transposed matrix of D, where the superscript T indicates the matrix transposed; M s is the mass matrix of the structure.

[0093] b s is the corresponding modal damping matrix, expressed as follows:

[0094] b s =D T C s D (4)

[0095] Where: C s is the damping matrix of the structure.

[0096] c s is the corresponding modal stiffness matrix, expressed as formula (5):

[0097] c s =D T K s D (5)

[0098] Among them: K s is the stiffness matrix of the structure.

[0099] f e is the modal external force matrix, expressed as follows:

[0100] f e =D T F e (6)

[0101] Among them: F e is the external exciting force applied to the surface of the structure.

[0102] f p is the modal acoustic pressure matrix, expressed as follows:

[0103] f p =D T F p (7)

[0104] Among them: F p The pressure generated by the sound waves exerted by the fluid on the surface of the structure.

[0105] It should be noted that the principle of formula (1) is that for an underwater axisymmetric shell, its motion equation is expressed as formula (8):

[0106] -ω 2 M s u-iνC s u+K s u=F e +F p (8)

[0107] Substitute equation (2) into equation (8) and multiply it by D on the left. T Formula (8) can be further transformed into formula (1).

[0108] It needs to be further explained that in Figure 2 In the above equation, based on the wave superposition principle, the sound field radiated by the axisymmetric shell is regarded as the superposition of the sound fields radiated by several source points on its z-axis. The intensity of each source point is determined by the condition satisfying formula (1).

[0109] S200. Determine the equivalent point source intensity inside the shell.

[0110] In this specific embodiment, S200 specifically includes the following steps:

[0111] S210. Establish an equivalent point source location model.

[0112] Considering the axisymmetric nature of the shell and the external forces, the velocity of the shell on any intersection line parallel to the z-axis with the shell surface must be equal. To this end, equivalent point sources can be evenly distributed along the symmetry axis of the shell, with the number of equivalent point sources set to M. At the same time, the same number of structural surface nodes can be evenly spaced on half of the symmetric surface of the plane where the shell intersects the z-axis.

[0113] In this specific embodiment, in S210, according to the wave superposition principle, the sound pressure at the corresponding node of the shell, that is, the equivalent point source position model is expressed as follows:

[0114]

[0115] Where: p(r Si ) is the sound pressure on the surface of the structure; M is the number of equivalent point sources, in units; r Si is the position vector corresponding to the i-th structural surface contour point; r Ol is the position vector of the lth equivalent point source; α(r Ol ) is the intensity corresponding to the lth equivalent point source.

[0116] In this specific embodiment, formula (9) is also expressed in matrix form, as expressed by formula (10):

[0117] p=Gα (10)

[0118] G(r Si ,r Ol ) is the corresponding Green’s function. Since it is a semi-infinite ocean space, the Green’s function is expressed as follows:

[0119]

[0120] Where: k f is the wave number in water, expressed as follows:

[0121] k f =ω / c f (12)

[0122] cf is the speed of sound in seawater; γ is the sea surface reflection coefficient; r ' is the horizontal distance from the structure surface node to the equivalent point source; d Oi is the distance from the equivalent point source to the sea surface; z Ol is the coordinate of the equivalent point source surface node in the z direction; Si is the spatial coordinate of the node on the surface of the structure in the z direction.

[0123] It should be noted that, considering the impedance mismatch between seawater and air, the seawater-air interface is a pressure release boundary, so γ can be taken as -1.

[0124] S220. Calculate the equivalent point source intensity; specifically:

[0125] S221. According to the linearized Euler equation, we can list equation (13):

[0126]

[0127] Where: n is the outer normal direction of the shell.

[0128] S222. Substitute equation (13) into equation (9) to obtain equation (14):

[0129]

[0130] Where: ▽ is the Laplace operator.

[0131] S223. Express equation (14) in matrix form and express it according to equation (15):

[0132] u=Hα (15)

[0133] S224. Considering the sound pressure p generated by the equivalent point source on the surface of the structure and F p If they are equal, then substitute equations (10) and (15) into equation (1) to obtain equation (16):

[0134] (-ω 2 a s -iνb s +c s )Hα=f e +D T Gα (16)

[0135] S225. Finally, after the processing of moving items and merging, the equivalent point source intensity in S220 can be expressed as formula (17):

[0136] (-ω 2 a s -iνb s +c s -D T G)Hα=f e (17)

[0137] The equivalent point source intensity can be calculated by formula (17).

[0138] S300. Establish a seawater surface wave model excited by an underwater point sound source in a semi-infinite water area.

[0139] In this specific embodiment, the seawater surface wave model excited by the underwater point sound source in the semi-infinite water area in S300 is expressed as follows:

[0140]

[0141] Where: η is the wave height, expressed according to formula (19):

[0142] z=η(r) (19)

[0143] It should be noted that if Figure 3 As shown, for the sea surface wave excited by an underwater point sound source, its wavefront equation is equation (19), and the z-axis of the coordinate system is an ideal flat water surface.

[0144] θ is the incident angle of the sound wave; υ is the attenuation coefficient, which is expressed as follows:

[0145]

[0146] Where: μ is the viscosity of seawater; g is the acceleration due to gravity; T is the surface tension of seawater.

[0147] It should be noted that since there are only longitudinal waves in seawater, when a point sound source propagates in seawater, there is no vertical disturbance at the depth of the point sound source, that is, the vertical vibration velocity is 0. Then, the undisturbed condition in the z direction (i.e., the z-axis direction) at the depth of the sound source can be obtained, which can be expressed as follows:

[0148]

[0149] Where: h0 is the depth of the sound source.

[0150] In this specific embodiment, in S300, under the action of seawater surface tension, the surface dynamic boundary condition is expressed as follows:

[0151]

[0152] in: is the velocity potential function, expressed as follows:

[0153]

[0154] Where: M(z) is a function related to z; k is the wave number of the sea surface wave.

[0155] It should be noted that the governing equations and boundary conditions for the seawater surface waves described are linear and homogeneous, and the separation of variables method is used to solve the general solution of the governing equations. Based on the initial velocity conditions of the seawater surface waves excited by the acoustic wave, it can be seen that the velocity potential governing equation has a traveling wave solution, thus obtaining the velocity potential function expressed in Equation (23).

[0156] Then, substitute formula (23) into formula (21) to obtain formula (24):

[0157]

[0158] The general solution of this differential equation is equation (25):

[0159] M(z)=a1e kz +a2e -kz (25)

[0160] Among them: a1, a2 are unknown coefficients.

[0161] Substituting formula (25) into formula (23) and using formula (21), we can obtain formula (26):

[0162]

[0163] The condition for formula (26) to be valid is formula (27):

[0164]

[0165] make Where A′ is the unknown coefficient, the velocity potential function can be expressed as formula (28):

[0166]

[0167] Substituting the velocity potential function into the boundary condition of the sea surface (22), we can obtain (29):

[0168]

[0169] Assume that the wavefront equation is expressed as formula (30):

[0170] η=Ae -ikr (30)

[0171] Substituting formula (30) into formula (29), we can simplify formula (31):

[0172]

[0173] Then the velocity potential function can be written as formula (32):

[0174]

[0175] Substitute the velocity potential function (32) into the linearized free surface kinematic conditions In the equation (33), we can get:

[0176]

[0177] Since the impedance difference between water and air is large, air can generally be regarded as an absolutely soft medium relative to water, that is, the transmission of the incident sound wave can be ignored. Then, the sound pressure continuity condition can be used to obtain Equation (34):

[0178] p i +p r =0 (34)

[0179] Where: p i is the incident sound wave; p r To reflect sound waves.

[0180] In this specific embodiment, based on the relationship between particle velocity, sound pressure, and acoustic impedance, the amplitude of the vibration velocity can be obtained and expressed as follows:

[0181]

[0182] Where: v i is the vibration velocity of the incident sound wave; v r is the vibration velocity of the reflected sound wave.

[0183] According to the linearized Euler equation, the total normal velocity amplitude of the particle can be obtained from equation (35) and expressed as equation (36):

[0184]

[0185] According to the relationship between V and amplitude A, V = Aω, the amplitude of the particle at the seawater-air interface monitoring point is expressed as follows:

[0186]

[0187] Substituting equation (37) into equation (30), we can obtain the sea surface wave expression when the sea surface is flat and the seawater is a semi-infinite space, which can be expressed as equation (38):

[0188]

[0189] It should be noted that in formula (38), the effect of seawater viscosity on the attenuation of seawater surface waves is not considered.

[0190] Considering that the amplitude of sea surface waves exhibits an exponential decay law as the propagation distance increases, the model of sea surface waves excited by a point sound source under a flat sea surface can be expressed as follows:

[0191]

[0192] Finally, the model is extended to a three-dimensional spatial model, and the seawater surface wave model excited by an underwater point sound source in a semi-infinite water area is expressed according to formula (18), which will not be repeated here.

[0193] S400. Calculate the displacement of the seawater surface wave excited by the axisymmetric shell; the displacement of the seawater surface wave excited by the axisymmetric shell is the final result of the present invention.

[0194] In this specific embodiment, the displacement of the seawater surface wave excited by the axisymmetric shell is calculated in S400 and expressed as follows:

[0195] η 总 =ηα (40)

[0196] Where: η 总 After calculating the intensity corresponding to each equivalent point source using the axisymmetric shell sound radiation calculation model, the intensity is substituted into the seawater surface wave model excited by the underwater point sound source in the semi-infinite water area to obtain each corresponding surface wave amplitude, and the sum of the linear superposition is performed; η is the column vector corresponding to the surface wave amplitude η corresponding to each equivalent point source position.

[0197] It should be noted that the principle of Equation (40) is that, according to the wave superposition principle, the seawater surface wave excited by an axisymmetric shell can be regarded as the linear superposition of surface waves excited by several equivalent point sources with certain intensities. After calculating the intensity corresponding to each equivalent point source using Equation (17), it is substituted into Equation (18) to obtain the amplitude of each corresponding surface wave, and then linear superposition is performed to finally obtain Equation (40).

[0198] In order to further verify the practicality of the present invention, this specific embodiment also provides a seawater surface wave model verification of an axisymmetric shell excitation containing specific data, as follows:

[0199] like Figure 4 As shown in the figure, a finite element model of a combined shell of two hemispheres and cylinders is constructed. The radius of the hemisphere is 1m, the length of the cylinder is 5m, and the thickness of the shell is 0.01m. The material is set to steel, with a Young's modulus and Poisson's ratio of 200GPa and 0.3 respectively. The sound source depth is set to 35m. A circumferential single-frequency excitation force is applied to the center point of the symmetry axis of the combined shell, F e The amplitude is 10N.

[0200] For the convenience of comparative analysis, referring to the definition of sound pressure level in underwater sound, the seawater surface wave displacement level is defined as follows:

[0201]

[0202] Where: L η is the displacement level of sea surface wave, where the reference displacement η ref =10 -9 m.

[0203] like Figure 5a to Figure 5c As shown, the simulation results obtained by the prediction method of the present invention are compared with the simulation results obtained by the finite element method; wherein, Figure 5a The results of the present invention and the finite element method are compared when the sound source frequency is 100 Hz. Figure 5b The results of the present invention and the finite element method are compared when the sound source frequency is 500 Hz. Figure 5c The results of the present invention are compared with those of the finite element method when the sound source frequency is 1000 Hz.

[0204] In order to accurately measure the error between the two, the relative error in statistics is used to evaluate the calculation accuracy of the method in the report, and the physical quantity is defined as expressed in formula (42):

[0205]

[0206] Where: J is the number of samples; Φ is the value of the sea surface wave.

[0207] Substituting the simulated experimental results obtained by the finite element method and the prediction method of the present invention at three different sound source frequencies into formula (42), the relative errors can be obtained as shown in Table 1:

[0208] Table 1. Comparison table of relative errors between the finite element method and the prediction method of the present invention

[0209] Sound source frequency (Hz) Relative error 100 3.2％ 500 5.7％ 1000 6.1％

[0210] As can be clearly seen in Table 1, at different frequencies, the relative errors between the finite element simulation results and the results of the present invention are small, and the two are highly consistent. In other words, the present invention achieves technical results superior to those of existing technologies by employing a different technical approach beyond the commonly used finite element method.

[0211] In the foregoing detailed description, various features are grouped together in a single embodiment to simplify the disclosure. This method of disclosure should not be interpreted as reflecting an intention that embodiments of the claimed subject matter require more features than are expressly recited in each claim. On the contrary, as reflected in the appended claims, the invention comprises less than all the features of any individual disclosed embodiment. The appended claims are hereby expressly incorporated into the detailed description, with each claim standing on its own as a separate preferred embodiment of the invention.

[0212] The above description of the disclosed embodiments is intended to enable any person skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments without departing from the spirit and scope of the present disclosure. Therefore, the present disclosure is not limited to the embodiments presented herein but is intended to be consistent with the broadest scope of the principles and novel features disclosed herein.

[0213] The foregoing description includes examples of one or more embodiments. Of course, it is not possible to describe all possible combinations of components or methods for the purposes of describing the above embodiments, but one of ordinary skill in the art will recognize that the various embodiments may be further combined and arranged. Therefore, the embodiments described in this invention are intended to cover all such changes, modifications and variations that fall within the scope of protection of the appended claims. Furthermore, to the extent that the term "comprising" is used in the specification or claims, the term is intended to be encompassed in a manner similar to the term "including," as explained in terms of "including," used as a transitional word in the claims. Furthermore, any use of the term "or" in the specification of the claims is intended to mean a "non-exclusive or."

[0214] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting sea surface waves excited by an underwater axisymmetric target sound source, characterized by: The following steps are involved: S100. Establish an axisymmetric shell acoustic radiation calculation model; S200. Determine the equivalent point source intensity inside the shell; S300. Establishing a sea surface wave model excited by an underwater point sound source in a semi-infinite water area; The seawater surface wave model excited by an underwater point sound source in a semi-infinite water area described in S300 is expressed as follows: Where: η is the wave height, expressed as follows: z=η(r) θ is the incident angle of the sound wave; V is the attenuation coefficient, which is expressed as follows: Where: μ is the viscosity of seawater; g is the acceleration of gravity; T is the surface tension of seawater; k is the wave number of the seawater surface wave; p i is the incident sound wave, expressed as follows: p i +p r =0 Where: p r To reflect sound waves; S400. Calculate the displacement of the seawater surface wave excited by the axisymmetric shell; the displacement of the seawater surface wave excited by the axisymmetric shell is the final result.

2. The method for predicting sea surface waves excited by an underwater axisymmetric target sound source according to claim 1, characterized in that: The coordinate parameters of the shell structure of the axisymmetric shell sound radiation calculation model in S100 are established in an axisymmetric coordinate system, wherein the axisymmetric structure target is symmetrical about the z-axis, and the exciting force is also symmetrical about the z-axis.

3. The method for predicting sea surface waves excited by an underwater axisymmetric target sound source according to claim 2, characterized in that: The calculation model for the sound radiation of the axisymmetric shell described in S100 is expressed as follows: -ω 2 a s u-ivb s u+c s u=f e +f p Where: ω is the angular frequency; i is the unit imaginary number; ν is the damping coefficient; u is the surface normal displacement of the shell, expressed as follows: Where: q r is the vibration mode D corresponding to the rth vibration mode r The amplitude of q is given by q r The column vector is composed of the vibration mode D r The matrix formed; a s is the corresponding modal mass matrix, which is expressed as follows: a s =D T M s D Where: D T is the transposed matrix of D, where the superscript T indicates the matrix transposed; M s is the mass matrix of the structure; b s is the corresponding modal damping matrix, which is expressed as follows: b s =D T C s D Where: C s is the damping matrix of the structure; c s is the corresponding modal stiffness matrix, which is expressed as follows: c s =D T K s D Among them: K s is the stiffness matrix of the structure; f e is the modal external force matrix, which is expressed as follows: f e =D T F e Among them: F e is the external exciting force applied to the surface of the structure; f p is the modal acoustic pressure matrix, which is expressed as follows: f p =D T F p Among them: F p The pressure generated by the sound waves exerted by the fluid on the surface of the structure.

4. The method for predicting sea surface waves excited by an underwater axisymmetric target sound source according to claim 3, characterized in that: S200 specifically includes the following steps: S210. Establish an equivalent point source location model; S220. Calculate the equivalent point source intensity.

5. The method for predicting sea surface waves excited by an underwater axisymmetric target sound source according to claim 4, characterized in that: The equivalent point source position model described in S210 is expressed as follows: Where: p(r Si ) is the sound pressure on the surface of the structure; M is the number of equivalent point sources, in units; r Si is the position vector corresponding to the i-th structural surface contour point; r Ol is the position vector of the lth equivalent point source; α(r Ol ) is the intensity corresponding to the lth equivalent point source; G(r Si ,r Ol ) is the corresponding Green's function, which is expressed as follows: Where: k f is the wave number in water, expressed as follows: k f =ω / c f c f is the speed of sound in seawater; γ is the sea surface reflection coefficient; r' is the horizontal distance from the structure surface node to the equivalent point source; d Oi is the distance from the equivalent point source to the sea surface; z Ol is the coordinate of the equivalent point source surface node in the z direction; Si is the spatial coordinate of the node on the surface of the structure in the z direction.

6. The method for predicting sea surface waves excited by an underwater axisymmetric target sound source according to claim 5, characterized in that: The equivalent point source intensity in S220 is expressed as follows: (-ω 2 a s -iνb s +c s -D T G)Hα(f e Where: Hα is expressed as follows: u=Hα.

7. The method for predicting sea surface waves excited by an underwater axisymmetric target sound source according to claim 6, characterized in that: In S400, the displacement of the sea surface wave excited by the axisymmetric shell is calculated and expressed as follows: or 总 =ηα Where: η 总 After calculating the intensity corresponding to each equivalent point source using the axisymmetric shell sound radiation calculation model, substitute it into the seawater surface wave model excited by the underwater point sound source in the semi-infinite water area to obtain each corresponding surface wave amplitude, and perform linear superposition and sum it; η is the column vector corresponding to the surface wave amplitude η corresponding to each equivalent point source position.

8. The method for predicting sea surface waves excited by an underwater axisymmetric target sound source according to claim 7, characterized in that: In S300, under the action of seawater surface tension, the surface dynamic boundary condition is expressed as follows: in: is the velocity potential function, which is expressed as follows: Where: M(z) is a function related to z; k is the wave number of the sea surface wave.

9. The method for predicting sea surface waves excited by an underwater axisymmetric target sound source according to claim 8, characterized in that: The incident sound wave and the reflected sound wave in S300 meet the conditions, which are expressed as follows: Where: v i is the vibration velocity of the incident sound wave; v r is the vibration velocity of the reflected sound wave.

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