An equivalent source method for predicting underwater acoustic cross-medium propagation in channel space and an equivalent source intensity correction method

Abstract

The application belongs to the technical field of underwater acoustic detection, and discloses an equivalent source method for predicting underwater acoustic cross-medium propagation in a channel space. For an underwater structure in an actual project, a group of equivalent sources are arranged in the interior of the structure to describe the vibration-acoustic response of the structure. The vibration speed of the structure surface is obtained through simulation calculation or arrangement of an acceleration sensor measurement, so that the equivalent source intensity can be determined, and then an underwater structure acoustic radiation model is constructed. The equivalent source is analytically expressed by using a free field space Green function, which does not meet the boundary conditions and the sound velocity gradient characteristics of the ocean channel, and is not applicable to the calculation of channel underwater acoustic and cross-medium propagation. The equivalent source is constructed by using a displacement potential Green function to be unconditionally stable in the channel space, so as to meet the requirements of the channel boundary, the sound velocity gradient and the like, and to establish the underwater acoustic cross-medium propagation. The application arranges a group of equivalent sources in the interior of the structure, uses the vibration speed of the structure surface to solve the equivalent source intensity, describes the vibration-acoustic response of the structure, and establishes a transfer function equivalent source model of vibration-acoustic radiation.

Description

Technical Field

[0001] This invention belongs to, but is not limited to, the field of underwater acoustic detection technology, and particularly relates to an equivalent source method and an equivalent source intensity correction method for spatial underwater acoustic cross-medium propagation in a prediction channel. Background Technology

[0002] With the continuous improvement of underwater acoustic detection equipment, major naval powers worldwide have made low noise levels a key objective in the design and manufacture of next-generation warships. Currently, vibration reduction and noise reduction technologies still struggle to eliminate low-frequency (≤200 Hz) vibration noise from ships. This low-frequency noise radiated by ships not only propagates along the coastal waters but also extends to the semi-elastic seabed, propagating as ship seismic waves. Ship seismic waves, as a detectable physical field, are elastic waves generated by ship vibration noise and water disturbance on the semi-elastic seabed. The US and Russia have already used ship seismic waves as a novel means of underwater target identification and ship detection, and have developed a series of seismic wave-fused mines. Therefore, relying solely on underwater acoustics or seismic waves cannot accurately assess the acoustic stealth performance of underwater vehicles or effectively implement noise control.

[0003] In calculating the cross-medium propagation of radiated noise from underwater structures, the horizontal computational scale is typically on the order of kilometers or higher. Coupled with the requirements of ocean channel boundary conditions, the variation of sound velocity along the depth direction in seawater, and the semi-infinite space of the semi-elastic seabed, existing underwater acoustic modeling and grid-based methods have technical limitations, making it impossible to effectively establish a cross-medium propagation model for radiated noise from underwater structures. This is a fundamental challenge in underwater acoustic cross-medium computation. my country's research in underwater acoustic cross-medium computation started relatively late. Due to confidentiality, related technologies from abroad have not been reported, especially in the field of ship seismic waves. Domestic research mainly focuses on ship seismic wave identification, and there is a lack of theory and algorithms for underwater acoustic cross-medium propagation prediction. Therefore, to accurately assess the low-frequency acoustic stealth performance of underwater targets, it is necessary to overcome the limitations of existing numerical modeling. Constructing an effective underwater acoustic cross-medium prediction method is an urgent problem to be solved.

[0004] Currently, the main methods for underwater acoustic modeling include the ray method, parabolic equation method, normal wave method, wavenumber integral method, and domain discretization method. Early underwater acoustic modeling often used the ray method, which is computationally fast and has clear physical meaning, but due to its inherent high-frequency approximation characteristics, it is not suitable for low-frequency calculations. The parabolic equation method has become the most widely used method for solving underwater acoustic problems related to horizontal distance, but it has low computational efficiency for deep-sea problems, and the intuitive physical meaning of the solution is ambiguous. The normal wave method solves depth-related equations, and the cumulative contribution of each mode weighted according to the sound source depth is the total sound field. Current technology can solve problems involving fluid layers and viscoelastic layers of any number, but the coupling of normal waves in elastic seabeds becomes complex. The wavenumber integral method is a numerical implementation of the integral transformation of horizontally layered media. The sound field solution is the spectral integral of the solution of the depth-separated wave equation, which can handle underwater acoustic propagation in multi-layered fluids and elastic wave propagation in elastic media, but it is limited to point source and line source models. All four types of methods share the common problem of being unsuitable for underwater sound sources. For seismic wave calculations on semi-elastic seabeds, methods based on domain discretization and boundary element methods face the challenge of handling sound velocity gradients and large spatial scales.

[0005] The wave superposition method, also known as the equivalent source method, works on the principle that the sound field radiated by a structure is calculated by linearly superimposing the sound fields radiated by a set of equivalent sources located within it. The intensity of the equivalent sources is determined by the boundary normal velocity. This method eliminates the singularity problem of the Green's function and does not require truncation and discretization of the field space, and has been widely used in sound field calculations. However, because it uses the Green's function in free field space to express the equivalent sources, it does not satisfy the channel boundary conditions. Based on the wave superposition method, wave superposition models for solving underwater acoustic channels have been developed, but none of them are applicable to the calculation of elastic waves in a semi-elastic seabed. Based on the wave superposition method and the wavenumber integral method, a wavenumber integral superposition model for calculating ship seismic waves in a homogeneous shallow sea environment with a seawater-elastic seabed has been proposed by modifying the Green's function, but it does not consider the sound velocity gradient.

[0006] Numerical modeling of underwater acoustics is typically used for point and line source models, but it is not suitable for the cross-medium propagation of underwater acoustic source radiated noise. Mesh-based methods and wave superposition methods struggle to accurately describe channel characteristics, and currently, there is no effective method for predicting the cross-medium propagation of underwater acoustic source radiated noise. To address these issues and provide a practical and effective computational method, this invention proposes an equivalent source method for predicting the cross-medium propagation of underwater acoustics in the channel space. This method uses a set of equivalent sources located within the structure to characterize the structure's vibratory acoustic response, constructing an underwater structure acoustic radiation model. Based on this, a finite-layered depth-direction equivalent source model is used to construct an unconditionally stable equivalent source in the channel space to meet channel requirements and establish the underwater acoustic cross-medium propagation, with modifications made to the equivalent source intensity. Without requiring truncation or mesh discretization of the channel space, the cross-medium propagation of underwater structure radiated noise is calculated by the linear superposition of a set of equivalent sources located within the structure.

[0007] In practical marine engineering, ship equipment, underwater structures, and ocean observation systems, the underwater acoustic radiation generated by structural vibration excitation often does not propagate in an ideal free field. Instead, it is significantly constrained by multiple channel factors, such as sea surface pressure release boundaries, layered sound velocity profiles, and semi-elastic seabeds. Existing engineering analysis and prediction methods generally use free-field Green's functions or empirically modified models to extrapolate structural acoustic radiation. These methods have certain applicability in near-field conditions or simple water bodies, but in actual marine channels with significant sound velocity gradients, layered interface reflections, and solid-liquid coupling effects, problems such as sound field amplitude distortion, phase distortion, and unstable cross-medium response prediction occur, making it difficult to support the industrial application needs of engineering design, stealth assessment, and rapid acoustic environment prediction. Summary of the Invention

[0008] To address the problems existing in the prior art, this invention provides an equivalent source method for predicting the propagation of underwater acoustics across media in a spatial channel.

[0009] This invention is implemented as follows: an equivalent source method for predicting the propagation of underwater acoustics across media in a prediction channel, the method comprising:

[0010] S1: For underwater structures in actual engineering, a set of equivalent sources are arranged inside to describe the structural vibration and acoustic response. The vibration velocity on the surface of the structure is obtained by simulation calculation or by accelerometer measurement, and the intensity of the equivalent sources can be determined, thereby constructing an underwater structure acoustic radiation model.

[0011] S2: The equivalent source is expressed analytically by the Green function in free field space in equation (1), which does not satisfy the boundary conditions of the ocean channel and the characteristics of the sound speed gradient, and is not suitable for the calculation of underwater acoustics and its cross-medium propagation in the channel; the equivalent source that is unconditionally stable in the channel space is constructed by using the displacement potential Green function to satisfy the requirements of the channel boundary, the sound speed gradient and the semi-elastic infinite seabed and to establish the cross-medium propagation of underwater acoustics.

[0012] S3: Equivalent source intensity correction; Equation (3) gives the equivalent source intensity corresponding to the sound pressure, while the constructed channel space Green function corresponds to the displacement potential; therefore, the equivalent source intensity cannot be directly matched with the channel space Green function; the sound pressure p and the displacement potential ψ satisfy the same wave equation form, and thus the corresponding Helmholtz equation form is also the same.

[0013] S4: Field variable calculation; After determining the amplitude of each layer, the sound pressure in the seawater is calculated by equation (19) or equation (20) according to the principle of wave superposition and the relationship between sound pressure and displacement potential.

[0014] Furthermore, S1 specifically includes:

[0015] 1) The equivalent sources are distributed inside the structure, and the sound field radiated outward from the structure is calculated by the following formula.

[0016] (1)

[0017] In the formula, For the Green's function in free space, express An approximate estimate; for The volume velocity of the j-th equivalent source at location (e.g.) Figure 1 As shown in the figure, this is called the sound source intensity of the equivalent source;

[0018] 2) On the structural boundary surface S, the sound pressure and normal vibration velocity satisfy

[0019] (2)

[0020] In the formula, For position on the boundary surface The gradient operator; substituting equation (1) into equation (2) and applying it to the vibration velocity points on the N structural boundary surfaces, the equivalent source intensity vector s is determined by solving the equation.

[0021] (3)

[0022] In the formula, v represents the boundary normal velocity vector; D is the dipole matrix, whose elements are calculated by the following formula.

[0023] (4)

[0024] In the formula, Let represent the position vector of the i-th vibration velocity node on the boundary surface. , Indicates position The unit's external normal direction;

[0025] 3) Substitute the equivalent source intensity determined by equation (3) into equation (1) to determine the underwater structure acoustic radiation model.

[0026] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0027] To address the common problems in existing technologies for predicting cross-medium propagation of radiated noise from underwater structures under channel conditions, such as theoretical inconsistencies, poor model applicability, and insufficient numerical stability, this invention reconstructs the structural vibration-acoustic radiation process based on acoustic physics mechanisms and the characteristics of real ocean channels. By arranging a set of equivalent sources inside the structure and using the normal vibration velocity of the structural surface to invert the equivalent source intensity, the complex structural vibration problem is transformed into an excitation problem with a finite number of equivalent sources, thereby establishing an equivalent source model with a clearly defined physical meaning in the transfer function between structural vibration and acoustic radiation. This model avoids direct processing of complex structural geometry and material details, making the mapping relationship between vibration excitation and acoustic radiation response clearer and more stable, providing a repeatable and scalable modeling foundation for engineering applications.

[0028] This invention fully considers the objective facts of sound velocity variation with depth in actual marine environments and the semi-elastic properties of the seabed medium. It employs a finite layering method along the depth direction, dividing the seawater layer into several horizontal layers and introducing a semi-elastic infinite seabed layer to uniformly describe the sound velocity gradient characteristics and solid-liquid coupling effects. Based on this, by introducing force and acoustic continuity conditions and using the constructed direct global matrix method to solve for the unknown amplitudes in each layer, the obtained channel spatial equivalent source exhibits unconditional numerical stability. This stability effectively overcomes the numerical divergence problem that easily occurs in traditional recursive methods when the number of layers increases or the propagation distance increases, enabling the cross-medium propagation model to maintain reliable computational accuracy under low-frequency, far-field, and complex channel conditions.

[0029] This invention corrects the physical consistency of the equivalent source strength through theoretical derivation, enabling the equivalent source description to strictly match the physical field variable form used for channel spatial propagation. Therefore, the acoustic field and displacement field of underwater structure radiated noise propagating across the medium can be calculated by linear superposition of this set of equivalent sources, achieving a unified description of the vibration field, underwater acoustic field, and solid medium response within the same framework. This calculation method based on the linear superposition of equivalent sources not only maintains the inherent consistency between the field variables in a physical sense but also avoids truncation and grid discretization of the entire field space in numerical implementation, significantly reducing computational complexity and resource consumption.

[0030] From an engineering application perspective, the method of this invention relies solely on surface vibration velocity data during actual forecasting, eliminating the need for large-scale discrete modeling of the water body and seabed. This enables efficient and rapid forecasting of underwater structure radiated noise propagation across media. The method boasts high computational efficiency, strong stability, and low input data requirements, making it particularly suitable for parameter analysis, scheme comparison, and accurate evaluation of the low-frequency acoustic stealth performance of underwater targets during the engineering design phase. It provides a technically valuable tool for underwater equipment noise control, stealth design, and marine acoustic engineering applications. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the equivalent source discrete distribution provided in an embodiment of the present invention;

[0032] Figure 2 This is a schematic diagram of a distance-independent horizontally layered environmental cylindrical coordinate system provided in an embodiment of the present invention;

[0033] Figure 3 This is the equivalent source model of the cylindrical shell provided in the embodiments of the present invention;

[0034] Figure 4 The following are the calculation results of cross-medium propagation of radiated noise from a cylindrical shell at a depth of 150 m provided in this embodiment of the invention: (a) sound pressure cloud map; (b) vertical displacement level;

[0035] Figure 5 The following are the calculation results of cross-medium propagation of radiated noise from a cylindrical shell at a depth of 420 m provided in this embodiment of the invention: (a) sound pressure cloud map; (b) vertical displacement level;

[0036] Figure 6 The following are the calculation results of cross-medium propagation of radiated noise from a cylindrical shell at a depth of 700 m provided in this embodiment of the invention: (a) sound pressure cloud map; (b) vertical displacement level. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0038] This invention, from an engineering feasibility perspective, decomposes the complex structure-ocean environment coupling problem into two independent yet physically consistent subproblems: equivalent source description and channel propagation modeling. A displacement potential framework is used to seamlessly integrate these two subproblems. The core idea is not simply to replace the Green's function form, but to introduce a unified physical dimension and boundary adaptation mechanism at both the source description and channel propagation levels, fundamentally eliminating the mismatch between the free-field model and the actual ocean channel.

[0039] In the source description phase, a set of equivalent volume sources is strategically arranged within the structure to map the vibratory response of the complex structure into a finite-dimensional equivalent source intensity vector. This equivalent source is not an empirical assumption but is obtained through rigorous inversion of the boundary relationship between the normal vibration velocity and sound pressure on the structural surface. Regardless of whether the vibration velocity data comes from finite element simulations or acceleration or velocity sensors deployed in the engineering, a linear mapping relationship can be constructed using a dipole matrix, ensuring that the equivalent source intensity physically fully characterizes the sound power distribution radiated outwards from the structure. This process solves the problem in traditional methods where the geometric complexity of the structure is difficult to directly incorporate into the propagation model, decoupling subsequent propagation calculations from the specific structural form and significantly improving engineering applicability.

[0040] In the channel propagation modeling phase, considering the characteristics of horizontal stratification and depth-dependent parameter variations in typical marine environments, a cylindrical coordinate system and Hankel transformation are used to transform the three-dimensional problem into a one-dimensional depth propagation problem in the horizontal wavenumber domain. By introducing displacement potential as a unified field variable, Helmholtz equations satisfying their respective constitutive relations are constructed in the seawater layer and the semi-elastic seabed, respectively, allowing the propagation behavior of sound waves in liquid media and elastic solids to be handled within the same mathematical framework. Physical boundary conditions such as vertical displacement, continuous normal stress, and vanishing tangential stress are applied to each layer interface using the direct global matrix method, eliminating unknown amplitudes layer by layer, thereby obtaining the numerically unconditionally stable channel space displacement potential Green's function.

[0041] The construction process of this Green's function offers significant engineering advantages. Firstly, its coefficient matrix exhibits a diagonally dominant structure, with the upper and lower layers numerically decoupled, avoiding the numerical divergence problem that arises with increasing layer numbers in traditional recursive methods. Secondly, by performing complex plane offset processing on the integration path, singularities in the horizontal wavenumber integral are effectively avoided, ensuring computational stability even under long propagation distances and high-frequency conditions. This provides a reliable numerical foundation for rapid forecasting and parameter scanning in engineering applications.

[0042] In the equivalent source intensity correction mechanism, this invention further addresses the inconsistency of physical quantities often overlooked in existing technologies. The equivalent source intensity obtained from structural acoustic radiation inversion typically corresponds to a sound pressure-type point source, while the channel space Green's function is based on displacement potential. These two are not directly equivalent in terms of physical dimensions and boundary condition responses. By introducing a small ball vibration model, the correspondence between sound pressure and displacement potential is rigorously derived under the point source limiting condition, converting the equivalent source intensity in volume velocity form into a displacement potential equivalent source intensity in volume displacement form. This conversion is not an empirical proportional correction but is derived based on the asymptotic consistency of the Helmholtz equation solution, thus ensuring that the excitation mode of the equivalent source in the channel space perfectly matches the propagation model.

[0043] During the field variable reconstruction stage, the uplink and downlink wave amplitudes of each equivalent source in different layers are combined using the wave superposition principle and integral inversion is performed in the wavenumber domain to obtain the sound pressure distribution in seawater and the horizontal and vertical displacement responses in the elastic seabed. Since the equivalent source and channel Green's function have achieved physical consistency during the construction stage, the sound pressure field and solid displacement field can be obtained synchronously in the same calculation process, thus achieving true underwater acoustic-solid cross-medium propagation prediction. This characteristic has direct engineering value for seabed structure vibration assessment, underwater facility safety monitoring, and acoustic detection system design.

[0044] This invention systematically solves the problems of inaccurate acoustic radiation prediction, numerical instability, and difficulty in uniformly describing cross-medium responses under complex marine channel conditions by organically combining mechanisms such as equivalent source inversion, displacement potential channel modeling, source strength physical correction, and multi-field variable collaborative reconstruction. Its working principle has a clear physical basis and rigorous mathematical support, and can be directly embedded into existing engineering simulation and testing processes. It is suitable for industrial applications such as ship noise assessment, underwater structure design, and marine acoustic environment prediction, and has significant engineering practical value and promotional significance.

[0045] The present invention provides an equivalent source method for predicting the propagation of underwater acoustics across media in a spatial channel, comprising the following steps:

[0046] Step 1: For underwater structures in actual engineering projects, a set of equivalent sources are arranged inside to describe the structural vibration and acoustic response. The vibration velocity on the surface of the structure is obtained by simulation calculation or by accelerometer measurement, and the intensity of the equivalent sources can be determined. Then, an underwater structure acoustic radiation model is constructed. The specific steps are as follows:

[0047] 1) This group of equivalent sources is distributed inside the structure, such as... Figure 1 As shown. The sound field radiated outward from the structure is calculated by the following formula.

[0048] (1)

[0049] In the formula, For the Green's function in free space, express An approximate estimate; for The volume velocity of the j-th equivalent source at location (e.g.) Figure 1 As shown in the figure, the sound source intensity is called the equivalent source intensity.

[0050] 2) On the structural boundary surface S, the sound pressure and normal vibration velocity satisfy

[0051] (2)

[0052] In the formula, For position on the boundary surface The gradient operator. Substituting equation (1) into equation (2) and applying it to the vibration velocity points on the N structural boundary surfaces, the equivalent source intensity vector s is determined.

[0053] (3)

[0054] In the formula, v represents the boundary normal velocity vector; D is the dipole matrix, whose elements are calculated by the following formula.

[0055] (4)

[0056] In the formula, Let represent the position vector of the i-th vibration velocity node on the boundary surface. , Indicates position External direction of the unit.

[0057] 3) Substitute the equivalent source intensity determined by equation (3) into equation (1) to determine the underwater structure acoustic radiation model.

[0058] Step 2: The equivalent source expressed analytically using the free-field space Green's function in equation (1) does not satisfy the boundary conditions and sound velocity gradient characteristics of the ocean channel, and is not suitable for calculating underwater acoustic propagation in the channel. An equivalent source with unconditional stability in the channel characteristic space is constructed using the displacement potential Green's function to satisfy the channel characteristics and establish underwater acoustic propagation across media. The specific steps are as follows:

[0059] 1) For horizontally layered environments independent of distance, i.e., where the layers and the seawater-seabed interface are all horizontal, establish a cylindrical coordinate system (see...). Figure 2 As shown in the figure, to characterize the channel features, the seawater layer is divided into several horizontal layers based on the sound velocity gradient characteristics, taking into account the elastic seabed environment. The layers and their interfaces are numbered as follows: Figure 2 As shown in the figure. ρ m and c m Let ρ and c represent the density and velocity of sound of the m-th layer of seawater, respectively. p and c s Let represent the density of the elastic seabed medium, the compressive wave velocity, and the shear wave velocity, respectively, and λ and μ be the Lamé constants of the elastic seabed. Let m represent the displacement potential function in the m-th layer of seawater. and Let S represent the compressive and shear displacement potentials in a semi-elastic seabed, respectively. Assuming a time factor of exp(-iωt), and considering that the physical field is independent of θ, for an intensity S... ω The simple harmonic point source, the physical wave field of each layer satisfies the following Helmholtz equation in cylindrical coordinate form.

[0060] (5)

[0061] (6)

[0062] (7)

[0063] (8)

[0064] In the formula, δ represents the Dirac function. (m=1,2,...,N) represents the acoustic wave number in the m-th layer of seawater. and Let be the wave numbers of the semi-elastic seafloor compression wave and the shear wave, respectively. The Lamé constant satisfies... and .

[0065] 2) Apply the following Hankel transformation to equation (5)

[0066] (9)

[0067] (10)

[0068] In the formula, Indicates the horizontal wavenumber. For corresponding wavenumber kernel function, Let represent the zero-order Bessel function. The wave equation for depth separation in seawater corresponding to equation (5) is obtained as follows:

[0069] (11)

[0070] In the formula, This represents the vertical wavenumber.

[0071] A particular solution to equation (11) is a depth-dependent free-field Green's function. The corresponding homogeneous solution is Then the general solution is determined as

[0072] (12)

[0073] In the formula, and These represent the unknown amplitudes of the downflow and upflow waves in the j-th layer of seawater. The free-field Green's function and its relationship to depth are as follows:

[0074] (13)

[0075] In the formula, , .

[0076] Applying the Hankel transform to equation (6), the corresponding wave equation for depth separation is:

[0077] (14)

[0078] In the formula, Similarly, the wave equations for depth separation in the semi-elastic seabed corresponding to equations (7) and (8) are respectively...

[0079] (15)

[0080] (16)

[0081] In the formula, and are the vertical wave numbers corresponding to compression and shear waves, respectively. The solution to equation (14) is...

[0082] (17)

[0083] In the formula, and Let be the unknown amplitudes of the downflow and upflow waves in the m-th layer of seawater, respectively. In a semi-elastic seabed, only downflow waves exist, and the solutions to the corresponding depth-separated wave equations (15) and (16) are...

[0084] (18)

[0085] In the formula, and These represent the unknown amplitudes of the descending compression and shear waves in an elastic seabed.

[0086] From the wavenumber kernel function expression, it can be seen that the m-th layer of seawater contains and Two unknown amplitudes, elastic seabed contains and Two unknown amplitudes are given, and this series of unknown amplitudes can be determined by the interface continuity condition. After obtaining the unknown amplitudes, the Green's function of the channel spatial displacement potential is determined as follows:

[0087] (19)

[0088] (20)

[0089] In the formula, r and r s These represent the field point and the equivalent source location, respectively. .

[0090] 3) The unknown amplitude is solved using boundary conditions and the direct global matrix method to ensure that the constructed channel spatial displacement potential Green's function satisfies the marine environment requirements for propagation under channel characteristics. At the solid-liquid interface, vertical displacement and normal stress are continuous, while tangential stress is zero; at the liquid-liquid interface, vertical displacement and normal stress are continuous; at the sea surface, pressure release boundary conditions must be satisfied. In seawater, the sound pressure... and normal stress Each satisfies and Vertical displacement satisfy On an elastic seabed, horizontal and vertical displacements are calculated by the following formula.

[0091] (twenty one)

[0092] (twenty two)

[0093] According to Hooke's Law, normal stress and tangential stress for

[0094] (twenty three)

[0095] (twenty four)

[0096] The kernel function of the sound field parameters included in the boundary conditions is represented as the following vector.

[0097] (25)

[0098] make

[0099] (26)

[0100] (27)

[0101] For the homogeneous part of the solution in the m-th layer, the following matrix relationship can be obtained.

[0102] (28)

[0103] In the formula, the local coefficient matrix Calculation as follows

[0104] (29)

[0105] Active sound field kernel function The continuity of the kernel function superimposed on the homogeneous solution at the interface m separating the m-th and (m+1)-th layers can be expressed as:

[0106] (30)

[0107] In the formula, the superscript represents the interface number, and the interface depth z is omitted. m Furthermore, rewriting the above equation as follows:

[0108] (31)

[0109] Equation (31) is the continuity equation that must be satisfied at interface m. Applying equation (31) to interfaces 1 to N and assembling the components yields the following result.

[0110] (32)

[0111] In the formula, ,

[0112]

[0113] The boundary of sea surface pressure release has

[0114] (37)

[0115] Based on the fact that the tangential stress at the solid-liquid interface is zero, we obtain

[0116] (38)

[0117] make

[0118] (39)

[0119] (40)

[0120] By combining equations (32), (37), and (38), we obtain

[0121] (41)

[0122] For each The unknown amplitude of each layer is determined by solving equation (41). The local coefficient matrices at interface m-1 and interface m are shown in equation (42). Combined with equation (29), it can be seen that the coefficient matrix on the left side of equation (41) is a diagonally dominant matrix. This coefficient matrix can be divided into two numerically uncoupled systems. One is the system corresponding to the layer above the m-th layer, and the other is the system corresponding to the layer below the m-th layer. Both systems are well-state, eliminating the truncation error through the m-th layer, making this layer numerically equal to the half-space within the fading range. This coefficient matrix is ​​unconditionally stable.

[0123] (42)

[0124] Within the truncated wavenumber interval, the horizontal wavenumber is typically uniformly discretized as follows:

[0125] (43)

[0126] In the formula, M represents the total number of sampling points. Wave number forecast Commonly used as Due to the bilateral nature of the Discrete Fourier Transform, the horizontal calculation of the furthest distance is usually... To eliminate singularity issues in the computation process, the integration path is offset so that the integration contour is moved to the complex plane. The offset is typically taken as [value missing].

[0127] (44)

[0128] Step 3: Equivalent Source Intensity Correction. Equation (3) gives the equivalent source intensity corresponding to the sound pressure, while the constructed channel space Green's function corresponds to the displacement potential. Therefore, the equivalent source intensity cannot be directly matched with the channel space Green's function. The sound pressure p and the displacement potential ψ satisfy the same wave equation, and thus the corresponding Helmholtz equations are also the same. In the case of an omnidirectional point source, the sound field is only related to the distance of the point source, so its solution is applicable to the spherical coordinate system. Description. The sound pressure p and the displacement potential ψ satisfy the Helmholtz equation as follows:

[0129] (45)

[0130] The solution for its outward divergence mode is

[0131] (46)

[0132] Assume the sound field is generated by a small sphere of radius *a* in an infinitely large uniform fluid, and define the surface vibration velocity as... Surface displacement is The radial velocity and displacement are respectively

[0133] (47)

[0134] (48)

[0135] Substituting equation (46) into equation (47) and taking r=a, we get

[0136] (49)

[0137] When the small ball approaches the point source, its radius is much smaller than the wavelength of the sound wave. Solve equation (49) about get

[0138] (50)

[0139] Substituting equation (46) into equation (48) and taking r=a, we get

[0140] (51)

[0141] when Similarly, we can obtain

[0142] (52)

[0143] Substituting equation (50) into equation (46) and equation (52) into equation (46) respectively yields the following results:

[0144] (53)

[0145] (54)

[0146] Equation (53) is the expression for the sound pressure of a point source, where The volume velocity is the sound pressure intensity of the point source; Equation (54) is the expression for the displacement potential of the point source, where This refers to the volume displacement, i.e., the displacement potential intensity of the point sound source.

[0147] For the harmonic steady-state case with a time factor of the form exp(-iωt), let , Then the velocity and displacement satisfy ,thereby

[0148] (55)

[0149] make The equivalent source displacement potential intensity is represented by equation (3). for

[0150] (56)

[0151] Step 4: Field Variable Calculation. After determining the amplitude of each layer, the sound pressure in seawater is calculated using equation (19) or equation (20) based on the wave superposition principle and the relationship between sound pressure and displacement potential.

[0152] (57)

[0153] In the formula, The target field point position vector, , , and Let be the amplitudes of the ascending and descending waves of the l-th equivalent source in the m-th layer. Let .

[0154] (58)

[0155] Based on the integral path offset, the sound pressure value is in the form of:

[0156] (59)

[0157] According to equations (18), (21), and (22), the kernel functions of the horizontal and vertical displacements of the l-th equivalent source in the elastic seabed are:

[0158] (60)

[0159] (61)

[0160] In the formula, and Let be the downflow amplitudes of the compression and shear waves from the l-th equivalent source in the (N+1)-th layer (i.e., in the elastic seabed). Applying the inverse Hankel transform to equations (60) and (61), based on the wave superposition principle and integral path offset, the numerical forms of the horizontal and vertical displacements at the target point in the elastic seabed are:

[0161] (62)

[0162] (65)

[0163] Table 1 Ocean sound velocity profile data

[0164]

[0165] Using the sound velocity profile data shown in Table 1 (ocean depth 1000 m, density 1000 kg / m³, semi-elastic seabed density 2500 kg / m³, compression wave velocity 3098 m / s, shear wave velocity 1789 m / s), a cylindrical shell (length 2 m, radius 0.2 m, equivalent source model see...) was constructed. Figure 3 The results of cross-medium propagation of vibration radiated noise (60 Hz) at different depths are shown in the figure. Figures 4 to 6 The sound pressure level and vertical displacement level are defined as follows (where the coordinates of the projection point of the vertical displacement level trajectory at the seawater-seabed interface are x=50 m and y=0 m).

[0166]

[0167] To enable those skilled in the art to understand and implement the technical solution of this invention, several embodiments of the method of this invention are given below in conjunction with specific engineering application scenarios to fully illustrate the technical implementation process, working mechanism and operability of this invention, thereby demonstrating that the technical solution of this invention can be clearly and completely implemented and its technical effect can be stably achieved.

[0168] Example 1: Prediction of cross-medium propagation of radiated noise from underwater structures of ships.

[0169] Taking a typical steel ship hull structure as the research object, equivalent source points were arranged at several representative locations inside the hull. Normal vibration velocity data at multiple measuring points on the outer surface of the hull were obtained through finite element simulation or actual ship tests, constructing a structural boundary vibration velocity vector. Based on the linear mapping relationship between the velocity vector and the equivalent sources, the source intensity distribution of each equivalent source was solved, thus establishing an equivalent source description model between hull vibration and sound radiation. Subsequently, based on the actual sea area sound velocity profile, the seawater was divided into several horizontal layers along the depth direction, with a semi-elastic infinite seabed layer at the bottom. Combining the sea surface pressure release condition and the solid-liquid interface mechanical continuity condition, the direct global matrix method was used to solve for the uplink and downlink wave amplitudes in each layer, constructing a displacement potential propagation model that satisfies channel characteristics. Finally, by physically correcting the equivalent source intensity, the sound pressure distribution in the seawater and the displacement response in the seabed were calculated, realizing the prediction of cross-medium propagation of ship radiated noise. The calculation results are consistent with the measured data in terms of amplitude and phase variation trends, verifying the feasibility and reliability of the method.

[0170] Example 2: Analysis of seabed response caused by vibration of underwater pipeline structure.

[0171] For underwater pipeline structures laid on the seabed surface, a set of equivalent sources is arranged axially inside the pipeline. The normal vibration velocity of the pipeline's outer wall is measured by sensors, and the equivalent source intensity is obtained through inversion. This equivalent source model is used to describe the vibration and acoustic radiation behavior of the pipeline under fluid or mechanical excitation. In the channel modeling stage, considering the significant sound velocity gradient and soft seabed characteristics in shallow sea environments, a layered medium model and a semi-elastic seabed are used to describe the propagation of sound waves in the water and seabed. Through displacement potential Green's function calculation, not only the sound pressure field distribution in seawater is obtained, but also the horizontal and vertical displacements in the seabed medium are simultaneously obtained, which are used to assess the impact of pipeline vibration on the stability of the seabed soil. This embodiment demonstrates that the method of this invention is applicable to both acoustic prediction and solid medium response analysis, exhibiting good engineering scalability.

[0172] Example 3: Evaluation of the low-frequency acoustic stealth performance of underwater equipment.

[0173] Under low-frequency conditions, traditional numerical methods often require large-scale computational domains and dense grids, resulting in high computational costs and insufficient stability. In this embodiment, taking an underwater device as an example, the surface vibration velocity of its structure is obtained through experimental measurement, and the overall vibration and sound radiation characteristics are described using only a limited number of internally arranged equivalent sources. Without discretizing the seawater and seabed space as a whole, the far-field sound pressure distribution is directly calculated based on the equivalent source and channel propagation model to evaluate the low-frequency radiated noise level of the device under different operating conditions. The results show that this method significantly reduces computation time while maintaining computational accuracy, making it suitable for rapid engineering evaluation and scheme optimization.

[0174] Example 4: Prediction of cross-medium acoustic propagation under complex marine conditions.

[0175] For complex marine environments with multiple sound velocity abrupt changes and elastic seabeds, the accuracy of approximating the sound velocity gradient is improved by increasing the number of seawater layers, and the structural vibration source term is described using the same equivalent source. Even with a large number of layers, the direct global matrix method maintains numerical stability, and the calculation results do not show divergence, indicating that the method is feasible under complex channel conditions.

[0176] As can be seen from the above embodiments, the method of the present invention can be stably implemented under different types of underwater structures, different marine environmental conditions, and different engineering objectives, clearly revealing the implementation method and working process of the technical solution, and can effectively support and realize the overall technical concept described in the present invention.

[0177] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0178] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the equivalent source of underwater acoustic propagation across media in a forecasting channel, characterized in that, Includes the following steps: Multiple equivalent sources are arranged inside the underwater structure to characterize the acoustic radiation generated by structural vibration; Obtain the normal vibration velocity at multiple locations on the structural boundary surface; Construct an equivalent source intensity vector based on the normal vibration velocity; Channel space propagation is calculated using a displacement potential Green's function that satisfies the boundary conditions of the ocean channel and the layering characteristics of the medium. Based on the displacement potential Green's function, the field distribution in seawater and seabed media is calculated to achieve cross-medium acoustic prediction.

2. The method according to claim 1, characterized in that, By using the normal velocity vector formed by multiple vibration velocity measurement points on the structural boundary surface, and combining it with the Green's function gradient kernel function at the corresponding spatial location, a linear mapping relationship between the equivalent source intensity and the vibration velocity of the structural boundary is constructed, so as to obtain the source intensity distribution of each equivalent source through inversion.

3. The method according to claim 1, characterized in that, The equivalent source description process and the channel propagation calculation process are set to be independent of each other, so that changes in structural geometric parameters do not affect the construction of the channel propagation model.

4. A method for constructing the channel spatial displacement potential Green's function for underwater acoustic cross-medium propagation prediction, characterized in that: Using displacement potential as a unified field variable; Wave equations were established for both the stratified seawater medium and the seabed medium. Apply displacement continuity conditions and normal stress continuity conditions to each layered interface; The uplink and downlink amplitude values ​​in each layer are solved using the global matrix method, thereby obtaining the channel spatial displacement potential Green's function.

5. The method according to claim 4, characterized in that, By assembling the local coefficient matrices of each layered medium into a global matrix, the upper and lower layered systems are numerically independent, reducing the propagation error caused by layer truncation.

6. The method according to claim 4, characterized in that, During the horizontal wavenumber integration process, the integration path is subjected to complex plane offset processing to avoid singularities in the propagation calculation.

7. A method for equivalent source intensity correction and field reconstruction for underwater acoustic cross-medium propagation, characterized in that: The equivalent source intensity, characterized by volume velocity, obtained from structural acoustic radiation inversion, is converted into the displacement potential equivalent source intensity, characterized by volume displacement. The channel space displacement potential Green's function is excited using the equivalent source intensity of the displacement potential; Based on the principle of wave superposition, the sound pressure field in seawater and the displacement field in the seabed medium are reconstructed respectively.

8. The method according to claim 7, characterized in that, The equivalent source intensity conversion is achieved based on the physical consistency that the sound pressure and displacement potential satisfy the same form of wave equation.

9. The method according to claim 7, characterized in that, Under simple harmonic steady-state excitation conditions, the equivalent source strength of displacement potential is determined by the time differential relationship between structural vibration velocity and displacement.

10. The method according to claim 7, characterized in that, After obtaining the up and down wave amplitudes of each equivalent source in different layered media, the acoustic pressure field in seawater and the horizontal and vertical displacement fields in the seabed medium are reconstructed respectively, so as to realize the unified cross-medium prediction of underwater acoustic field and solid vibration field.

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