Sound field model construction method based on mixture of parabolic equation theory and finite element method

Abstract

The invention discloses a sound field model construction method based on a mixture of a parabolic equation theory and a finite element method, and belongs to the technical field of sound field propagation. According to the method, a sound field is divided into a far-field region and a near-field region, a parabolic equation is established in the far-field region, a PINN model is constructed, an initial sound field result calculated by the parabolic equation is corrected and optimized by using the PINN model in each step of calculation by the parabolic equation, and a final sound field result is obtained. The method comprises the following steps: performing grid division in a near-field region, establishing a wave equation in each grid unit, constructing a unit stiffness matrix and a unit mass matrix, finally assembling a global stiffness matrix and a global mass matrix, and further solving detailed information of a three-dimensional sound field; and sound field information at the junction is processed through a multi-physics field coupling boundary condition at the junction. According to the method, a proper calculation method can be selected according to the physical characteristics of different areas, and the propagation rules of sound waves in different scales and environments can be better reflected.

Description

Technical Field

[0001] This invention belongs to the field of sound field propagation technology, specifically a sound field model construction method based on a hybrid of parabolic equation theory and finite element method. Background Technology

[0002] The laws governing ocean sound propagation are fundamental topics in acoustics research, and numerical calculations and predictions of the ocean sound field are the basis for studies on ocean sound propagation, reverberation, and inversion. When sound waves encounter soliton propagation during their propagation within the ocean, the presence of soliton internal waves causes temporal and spatial variations in the ocean sound velocity profile, thus affecting the sound signal. Therefore, it is necessary to study theoretical modeling methods for sound field propagation in the presence of soliton internal waves.

[0003] Traditional underwater acoustic propagation theory has been highly effective in explaining numerous marine acoustic propagation phenomena. This theory aims to meet the constraints of the marine environment on the underwater sound field and the needs of underwater sound propagation calculation. By extracting key elements from the actual sound propagation process, and according to the different characteristics of the marine environment, appropriate assumptions and approximations are used, discarding certain generalities to achieve the effectiveness of the method, thereby shaping a variety of underwater acoustic propagation theoretical models.

[0004] With the continuous deepening of the exploration of ocean acoustic propagation theory, more stringent expectations have been placed on the computational accuracy and speed of underwater acoustic propagation models. Since the 1960s, methods such as the finite difference method and the finite element method have been gradually applied by researchers to the field of underwater acoustic calculation.

[0005] The finite difference method (FDM) directly processes differential operators to discretize and solve the wave equation. It can simulate wave field characteristics in various complex media and in geometrically irregular elastic seabed environments, and also has applications in scattering problems. In recent years, a series of methods have emerged and developed, including staggered grid finite difference methods, finite difference methods with arbitrary even-order accuracy, irregular grid finite difference methods, and implicit difference methods. These emerging methods have significantly improved the accuracy of numerical simulations and powerfully promoted the wider application of the finite difference method.

[0006] The Finite Element Method (FEM) is commonly used as a general numerical solution method for solving partial differential equations with complex boundaries. Its core idea is to divide the physical domain into a finite number of interconnected elements. Then, leveraging the interrelationships between these elements, a system of finite element equations is constructed. Solving this system yields exact or approximate solutions within each element, thus transforming the complex boundary value problem into solving a large system of equations. Because of this, the FEM can produce extremely accurate numerical results when dealing with complex marine environments.

[0007] The parabolic equation (PE) is an approximate wave equation used to describe the propagation of sound waves in media such as oceans. In the three-dimensional case, it simplifies the complex three-dimensional wave problem into a series of two-dimensional problems that are solved step-by-step along the propagation direction by making specific approximations to the wave equation. This method is highly efficient in handling long-distance, low-frequency sound wave propagation and can effectively calculate important sound field parameters such as sound wave propagation loss and sound pressure distribution. Its basic principle is based on the forward scattering assumption of sound propagation, neglecting the effect of backscattering, thus making the equation more mathematically feasible to solve.

[0008] Currently, common underwater acoustic propagation theories include ray theory, normal mode theory, parabolic equation theory, and fast field transformation methods. Ray theory commonly uses programs like Bellhop and Ray. This theory primarily uses sound rays to study underwater sound propagation laws and is widely used due to its high computational efficiency and clear physical meaning. However, a drawback of ray theory is that its inherent high-frequency approximation leads to reduced accuracy in sound field calculations. Common normal mode theory models include Kraken and Couple. Normal mode models are built on the assumption of distance independence, offering advantages such as relatively low computational cost and fast processing speed. However, since this model neglects the energy conversion between different normal modes, it can only be applied to problems related to sound propagation where the sound channel changes slowly in the horizontal dimension. Fast Field Program (FFP) models commonly use programs like FFP, Scooter, Spark, and OASES. Fast field models separate the wave equations by assuming horizontal layering of the medium. Simultaneously, they derive accurate integral expressions for the sound field within each layer based on boundary conditions. It features high computational accuracy, but it is slow to compute and has difficulty handling sound propagation problems in complex underwater acoustic environments.

[0009] Therefore, it is necessary to propose a sound field model construction method (PPFEM) based on a hybrid of parabolic equation theory and finite element method to solve the above-mentioned technical problems in the existing technology. Summary of the Invention

[0010] The purpose of this invention is to provide a sound field model construction method based on a hybrid of parabolic equation theory and finite element method. In the far field region, the PINN model is introduced to correct the sound field, and in the near field region, a multi-scale adaptive mesh generation method and a boundary condition adjustment method based on physical information are introduced to better reflect the propagation law of sound waves at different scales and under different environments.

[0011] To achieve the above objectives, the present invention provides the following technical solution:

[0012] A method for constructing a sound field model based on a hybrid approach combining parabolic equation theory and the finite element method, comprising the following steps:

[0013] Step 1: Divide the sound field into a far-field region and a near-field region based on distance criteria and geometric conditions;

[0014] Step 2: In the far-field region, establish a parabolic equation and perform approximation, then construct the PINN model, embed the parabolic equation into the PINN model loss function, and use existing sound field data as input to train the PINN model; the sound field data includes spatial location (x,z), sound source parameters, and marine environment parameters; the output of the PINN model is the key parameters of the sound field, including sound pressure p(x,z) and propagation loss TL;

[0015] In each step of the parabolic equation calculation, the initial sound field result calculated by the parabolic equation is corrected using the trained PINN model. Finally, the corrected sound field result is fused with the initial sound field result to obtain the final sound field result.

[0016] Step 3: In the near-field region, firstly, mesh generation is performed. Then, wave equations are established and discretized within each mesh element to construct the element stiffness matrix K for each mesh element. e and the unit mass matrix M e And based on the real-time calculation results of the sound field, the boundary conditions are dynamically adjusted;

[0017] Finally, the element stiffness matrix K of each mesh element is... e and the unit mass matrix M e The global stiffness matrix K and global mass matrix M are assembled, and the detailed information of the three-dimensional sound field is solved by combining the boundary conditions and excitation source.

[0018] Step 4: Process the sound field information at the boundary between the far-field and near-field regions through multi-physics coupling boundary conditions, including sound pressure continuity, normal particle velocity continuity, smooth transition of sound velocity profile, and dynamic adjustment of environmental parameters.

[0019] Compared with the prior art, the present invention has the following advantages:

[0020] 1. In the far-field region, this invention introduces a sound field correction method based on Physical Information Neural Network (PINN), which enables high-precision correction and optimization of the sound field results in real time at each step of the parabolic equation (PE) calculation, ensuring the efficiency and accuracy of the calculation process, while enhancing the model's adaptability to complex marine environments.

[0021] 2. In the near-field region, this invention uses a multi-scale adaptive mesh generation method to flexibly adjust the mesh density and optimize the use of computing resources. At the same time, it uses a boundary condition adjustment method based on physical information to dynamically adjust the boundary conditions, reducing the impact of boundary reflections and further improving computational efficiency.

[0022] 3. This invention uses multi-physics field coupled boundary conditions to process the sound field information at the interface, which not only ensures the continuity of sound pressure and particle velocity, but also considers the dynamic changes of sound velocity profile and environmental parameters, thereby processing the sound field information at the interface more accurately and improving the calculation accuracy and adaptability of the entire model.

[0023] 4. This invention can adapt to various scales and environments. It can effectively perform sound field calculations in both deep and shallow sea areas, and can better reflect the propagation law of sound waves in different scales and environments based on the actual physical characteristics of different regions. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below.

[0025] Figure 1 This is a flowchart of a method for constructing a sound field model based on a hybrid approach combining parabolic equation theory and the finite element method. Detailed Implementation

[0026] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0027] Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] Example

[0029] like Figure 1 As shown in the figure, this embodiment describes a method for constructing a sound field model based on a combination of parabolic equation theory and finite element method.

[0030] This method divides the entire three-dimensional computational domain into different sub-regions based on the characteristics of the sound field and computational requirements. In large-scale homogeneous regions far from the sound source and complex boundaries, the parabolic equation method is used for calculation because sound wave propagation is relatively regular in these regions, and the parabolic equation can quickly provide relatively accurate results with relatively low computational resource consumption. However, in regions close to the sound source, with complex marine topography (such as submarine mountains and trenches) or artificial structures (such as oil drilling platforms and submarine cables), the sound wave scattering and reflection phenomena are complex, and the geometry is irregular. In these areas, the finite element method can more accurately describe the changes in the sound field.

[0031] The sound field model construction method based on the hybrid theory of parabolic equations and the finite element method in this embodiment includes the following steps:

[0032] Step 1: Divide the sound field into far-field and near-field regions based on distance criteria and geometric conditions (environmental conditions).

[0033] In a three-dimensional ocean acoustic field model, the division of the far-field and near-field regions is crucial for accurately calculating acoustic field characteristics. This embodiment proposes a method for dividing the far-field and near-field regions based on sound field propagation characteristics, as follows: Step 1.1, Near-field region division.

[0034] The near-field region refers to the area surrounding a sound source, where the characteristics of the sound field are directly affected by the sound source, resulting in drastic changes and complex geometric boundary conditions. In the near-field region, the phase and amplitude of sound waves vary significantly, and the propagation path and intensity of the sound field are significantly influenced by the sound source and the surrounding environment.

[0035] The criteria for defining the near-field region are as follows:

[0036] Distance criterion: The near-field region typically encompasses a wavelength range around the sound source, i.e., r ≤ λ, where r is the distance from the sound source and λ is the wavelength of the sound wave. This ensures high-resolution capture of near-field fluctuation phenomena (such as the near-field phase-sensitive region of the sound source).

[0037] Geometric conditions: In areas near the sound source, with complex marine topography (such as submarine mountains, trenches, etc.) or large artificial structures (such as offshore drilling platforms, subsea oil pipelines, etc.), sound wave scattering and reflection phenomena are complex and the geometry is irregular. Therefore, these areas are also classified as near-field regions. Forced coverage of complex scattering or reflection areas (such as far-field wakes of submarine mountains).

[0038] For the near-field region, both the distance criterion and the geometric condition must be met simultaneously, and the two are independent and complementary. The distance criterion is a division based on purely physical scale (e.g., when λ=150m, the near-field range is r≤150m), while the "close to the sound source" in the geometric condition emphasizes the direct impact of geometric complexity on the sound field (e.g., if the sound source is adjacent to the drilling platform outriggers, additional marking is required even if r<λ).

[0039] Step 1.2, Far-field region division

[0040] The far-field region refers to the area far from the sound source, where the characteristics of the sound field tend to be stable, the propagation path and intensity of the sound waves are mainly affected by the marine environment, and the changes in the sound field are relatively gentle.

[0041] The criteria for dividing the far-field region are as follows:

[0042] Distance standard: The far field region usually includes the region that is more than one wavelength away from the sound source, i.e., r > λ, where r is the distance from the sound source and λ is the wavelength of the sound wave.

[0043] Geometric conditions: In large-scale uniform regions far from the sound source and complex boundaries, sound wave propagation is relatively regular and the sound field changes gently. These regions are classified as far-field regions.

[0044] For the far-field region, both distance criteria and geometric conditions must be met simultaneously, and the two are independent and complementary.

[0045] Step 2: The far-field region is determined as the computational region dominated by PE (parabolic equation).

[0046] For regions with relatively homogeneous media and simple boundaries in the far field, the computational domain dominated by the parabolic equation (PE) is defined. For example, in the deep ocean, in large areas far from the sound source, with relatively flat seabed topography and no complex obstacles, PE, based on its efficient computational characteristics for large-scale, low-frequency sound wave propagation, quickly calculates macroscopic sound field parameters such as the approximate propagation path and propagation loss. Its calculation process mainly relies on the approximation of the wave equation by the parabolic equation, simplifying the three-dimensional sound field problem into a series of two-dimensional calculations along the propagation direction, solving for sound field information at different distances through a step-by-step approach.

[0047] In this embodiment, a parabolic equation is established and approximated in the far-field region. Then, a PINN model is constructed, and the parabolic equation is embedded in the PINN model loss function. Existing sound field data is used as the input to the PINN model to train it. The sound field data includes spatial location (x,z), sound source parameters, and marine environmental parameters. At each step of the parabolic equation calculation, the initial sound field result calculated by the trained PINN model is corrected. Finally, the corrected sound field result is fused with the initial sound field result to obtain the final sound field result.

[0048] Step 2.1: Establish the parabolic equation and perform approximation.

[0049] In three dimensions, for sound pressure p(x,y,z), the standard parabolic equation (PE) is:

[0050]

[0051] Where k = ω / c0 is the wave number (ω is the angular frequency, and c0 is the reference sound speed); n(x,y,z) = c0 / c(x,y,z) is the refractive index, and c(x,y,z) is the sound speed distribution.

[0052] In the far-field region, where the medium is relatively homogeneous and the boundaries are simple, the sound velocity distribution is c(x,y,z)≈c(x), therefore the refractive index is n(x,y,z)≈n(x). Simultaneously, due to the propagation of large-scale, low-frequency sound waves, the second derivative terms in the y and z directions... The impact is relatively small, so an approximation method can be used.

[0053] A common approximation is to ignore the second derivative term, resulting in a simplified parabolic equation: The approximate equations can be more conveniently used to calculate macroscopic parameters such as the propagation path and propagation loss of sound waves on a large scale.

[0054] Assuming a spatial step size of Δx, the first derivative with respect to the x-direction is obtained using a forward difference scheme. Discretization yields:

[0055]

[0056] After simplification, the formula used for step-by-step calculation is obtained:

[0057] p(x+Δx,y,z)=p(x,y,z)(1+ikn 2 (x)Δx)

[0058] Using this formula, starting from the sound source location (assuming x = 0), and given the initial sound pressure p(0, y, z), the sound pressure p(x, y, z) at different distances x can be calculated step by step, thus obtaining the sound pressure distribution information during the sound wave propagation process.

[0059] The propagation loss TL (in decibels) can be calculated using the following formula:

[0060]

[0061] Where p(0,y,z) is the sound pressure at the sound source, and p(x,y,z) is the sound pressure at a distance x from the sound source.

[0062] Under this PE approximation, the sound wave propagation path can be approximately described using ray theory. According to Snell's law, n(x)sinθ(x)=constant, where θ(x) is the angle between the sound wave ray and the x-axis.

[0063] Under the far-field approximation, the curvature of the sound ray is relatively small. Assuming the initial angle is approximately θ0 and the sound speed changes slowly, the sound ray angle θ(x) at a distance x can be approximated as:

[0064]

[0065] Here we assume that the speed of sound changes slightly mainly in the y-direction. For more complex cases, this can be extended to changes in the two-dimensional yz plane.

[0066] By continuously updating the angle θ(x), the propagation path of the sound wave in the far-field propagation region can be roughly determined.

[0067] Boundary condition handling (taking the ocean surface as an example): On the ocean surface z = 0, it is usually assumed that the pressure is released as the boundary condition, i.e., p(x,y,0) = 0.

[0068] Step 2.2: Correcting the sound field based on Physical Information Neural Network (PINN)

[0069] Step 2.2.1, PINN Model Construction

[0070] A PINN model is constructed, incorporating the physical laws of the sound field (such as the parabolic equation) as constraints into the loss function of the neural network. The network input includes spatial coordinates (horizontal distance x, depth z), sound source parameters, and marine environmental parameters, and the output consists of key parameters of the sound field (sound pressure p(x,z) and propagation loss TL).

[0071] The specific steps are as follows:

[0072] (1) Acquiring sound field data: Using marine acoustic equipment (sonar), information such as sound pressure and propagation loss is collected in the actual marine environment. Then, Bellhop is used to perform numerical simulations under specific marine environmental conditions to generate sound field data. The collected and simulated data are processed to obtain spatial coordinates (i.e., spatial position (x,z)), sound source parameters, and environmental parameters, which are then used as inputs to the network.

[0073] Among them, marine environmental parameters include sound velocity profile c(r,z), seabed topography and elevation and sediment parameters, seawater temperature-salinity profile and three-dimensional current field data;

[0074] Sound source parameters include sound source geometric location parameters (r_s, z_s), spectral characteristic parameters (center frequency f0 and -3dB bandwidth Δf), radiating source level SL, time-domain waveform parameters (pulse width τ and modulation type), and spatial directivity parameters (azimuth angle α, elevation angle β, and beam opening angle). ).

[0075] (2) Define the network structure: Choose a suitable neural network structure, such as a multilayer perceptron (MLP) or a convolutional neural network (CNN), to adapt to the characteristics of the sound field data.

[0076] (3) Constructing the loss function: Embed the physical constraints (parabolic equation) into the loss function. The loss function is expressed as L = L data +L physics ; among which, L data It is a data loss function used to fit existing sound field data; L physics It is the physical loss, used to ensure that the network output satisfies the physical laws of the parabolic equation.

[0077] (4) Training the PINN model: Using existing sound field data (historical measurement data, sound field data collected in step (1)) as input, train the PINN model. During the training process, optimize the loss function and adjust the network parameters so that the sound field results output by the network conform to the data patterns and meet the physical constraints.

[0078] Step 2.2.2, Sound Field Correction and Optimization

[0079] At each step of the PE calculation, the sound field results are corrected using the PINN model. The specific steps are as follows:

[0080] (1) PE calculation: The initial sound field result p in the far field region is calculated using the PE method. PE(X,Z) Starting from the sound source location, given the initial sound pressure p(0,y,z), the sound pressure distribution at different distances is calculated using the method described in step 2.1, thus obtaining the initial sound field result p during the sound wave propagation process. PE(X,Z) .

[0081] (2) PINN correction: p PE(X,Z) As input to the PINN model, the sound field is corrected using the PINN model to obtain the corrected sound field result p. PINN(X,Z) .

[0082] A well-trained PINN model can predict the corresponding sound pressure correction coefficient α(x,z) based on the input current spatial location (x,z), the corresponding sound source parameters, and the corresponding marine environment parameters. α(x,z) is determined based on the input p... PE(X,Z) Correction is performed to obtain the corrected sound field result p. PINN(X,Z) The calculation formula is p PINN(X,Z) =α(x,z)·p PE(X,Z) .

[0083] (3) Result fusion: The corrected sound field result p PINN(X,Z) The initial sound field result p calculated by PE PE(X,Z) The sound field is then fused to obtain the final sound field result p. final(X,Z) .

[0084] This embodiment uses a weighted average method: p final(X,Z) =β·p PINN(X,Z) +(1-β)·p PE(X,Z) Wherein, β is the weighting coefficient, and in this embodiment, β is taken as 0.7.

[0085] By introducing the PINN model to correct the sound field results, the sound field calculation in the PE-dominant region has the following advantages:

[0086] Improved computational accuracy: The PINN model can use physical laws to perform high-precision correction on the initial sound field results of PE calculation, which significantly improves the accuracy of sound field calculation in the far field region.

[0087] Enhanced adaptability: The PINN model can adapt to complex marine environments, such as random sound speed disturbances and slight seabed topographic undulations, thus improving the robustness of sound field calculation.

[0088] Real-time optimization: The PINN model can optimize the sound field results in real time at every step of the PE calculation, ensuring the efficiency and accuracy of the calculation process.

[0089] Step 3: The near-field region is determined as the computational domain dominated by FEM (Finite Element Method).

[0090] The near-field region and areas with complex boundary conditions are designated as the computational region dominated by FEM. For example, near a sound source, the sound field around the source changes extremely drastically, and the approximate calculation of PE may cause significant deviations. Therefore, the high-precision computing power of FEM is needed to accurately delineate the subtle details of the sound field. Furthermore, in shallow sea areas, if there are complex seabed topography such as coral reefs or submarine mountains, or large artificial structures such as offshore drilling platforms or subsea oil pipelines, FEM can accurately handle these complex geometric shapes and boundary conditions.

[0091] FEM discretizes a continuous physical region into a finite number of cells, constructs and solves a system of equations based on the inherent connections between the cells, and then obtains detailed sound field information such as sound pressure and particle velocity within these regions.

[0092] In this embodiment, a multi-scale adaptive mesh generation method is used to generate the mesh in the near-field region. Then, a wave equation is established and discretized within each mesh cell to construct the element stiffness matrix K for each mesh cell. e and the unit mass matrix M e Furthermore, a boundary condition adjustment method based on physical information is used to dynamically adjust the boundary conditions according to the real-time calculation results of the sound field; finally, the element stiffness matrix K of each mesh element is... e and the unit mass matrix M e The global stiffness matrix K and global mass matrix M are assembled, and the detailed information of the three-dimensional sound field is solved by combining boundary conditions and excitation sources.

[0093] Step 3.1: Establish the wave equation and its variational form.

[0094] In the frequency domain, the wave equation satisfied by sound waves is:

[0095]

[0096] Where p is the sound pressure, ω is the angular frequency, ρ is the density of the medium, and c is the speed of sound.

[0097] Its corresponding variational form (weak form) is:

[0098]

[0099] Where Ω is the computational domain (the entire three-dimensional region of sound field propagation), w is the test function, and n is the boundary outward normal vector, used to describe the physical behavior of sound pressure on the boundary (reflection / radiation conditions).

[0100] Step 3.2, Discretization Process

[0101] Step 3.2.1: Shape function and nodal sound pressure representation of sound pressure.

[0102] In the finite element analysis of a three-dimensional sound field, for a tetrahedral element (a common type of three-dimensional element), let the sound pressure p(x,y,z) within the element be expressed by the shape function N. i (i = 1, 2, 3, 4, representing the four node numbers of the tetrahedral element) and nodal sound pressure p i Represented as:

[0103]

[0104] For tetrahedral elements, their shape function has a specific expression. Taking node 1 as an example, let the coordinates of the four vertices of the tetrahedral element be (x1, y1, z1), (x2, y2, z2), (x3, y3, z3), and (x4, y4, z4), and the shape function N1(x, y, z) be:

[0105]

[0106] Where V is the volume of the tetrahedral element, calculated using the following formula:

[0107]

[0108] and, Similarly, expressions for N2, N3, and N4 can be written.

[0109] Step 3.2.2: Construct the element stiffness matrix

[0110] Construct the element stiffness matrix K based on the variational form of the wave equation. e :

[0111] The elements of the element stiffness matrix are defined as follows:

[0112] In a three-dimensional Cartesian coordinate system Expanded to:

[0113]

[0114] For each tetrahedral element e, the above expression needs to be integrated over its volume.

[0115] Due to the complexity of the shape function, numerical integration methods are typically used; this embodiment employs the Gaussian integration method. (The calculation is then performed.) For example, first calculate separately Then substitute them In the expression, Gaussian integral formula is then used to perform integration within the tetrahedral element volume to obtain... The value of can be calculated using the same method. e All elements.

[0116] Step 3.2.3: Construct the element mass matrix

[0117] Unit mass matrix M e yuan Defined as:

[0118] Similarly, the above expression needs to be integrated over the volume of the tetrahedral element. The element mass matrix M is calculated using the Gaussian integral method. e All elements.

[0119] This embodiment selects tetrahedral elements for discretization in the three-dimensional sound field and describes the representation of sound pressure in tetrahedral elements, using shape functions and nodal sound pressure. The calculation formula and derivation process of the shape function are given in detail. Then, the construction of the element stiffness matrix is ​​introduced, defining the element expressions and explaining that numerical integration methods are typically used for calculation. Next, the construction of the element mass matrix is ​​explained, also with its definition and calculation method. Finally, it is mentioned that these matrices will serve as the foundation for constructing the equations of the entire three-dimensional sound field finite element system, providing support for subsequent solutions.

[0120] Step 3.3: Multi-scale adaptive mesh generation

[0121] To improve computational efficiency and accuracy, a multi-scale adaptive mesh generation method is introduced. In the near-field region, the characteristics of the sound field vary with the distance from the sound source. Near the sound source, the sound field changes more strongly, with complex geometric boundary conditions and sound wave scattering and reflection phenomena, requiring a finer mesh to accurately capture the detailed changes in the sound field. In the near-field region, far from the sound source, the sound field changes relatively gently, but is still more complex than in the far-field region.

[0122] Therefore, in the near-field region, especially near the sound source and complex boundaries, a finer mesh is used to capture detailed changes in the sound field; in the near-field region, further away from the sound source and with simpler boundaries, a coarser mesh is used to reduce computational load. The specific steps are as follows:

[0123] (1) Initial Mesh Generation: An initial mesh is generated based on the geometry and boundary conditions of the computational domain. First, the geometry of the computational domain is analyzed to identify different features, including the location of the sound source and the undulations of the seabed topography. Second, the boundary conditions of the computational domain are defined, including the ocean surface, seabed, and far-field boundaries. Different boundary conditions will have different effects on the sound field distribution. Gmsh is used for initial mesh generation; Gmsh can automatically generate a mesh based on the geometry.

[0124] (2) Error estimation: Calculate the error estimate of the sound pressure on each grid cell, and determine whether the grid needs to be refined based on the magnitude of the error estimate.

[0125] A wave equation is established within each grid cell and discretized based on tetrahedral elements. For each tetrahedral element, its residual is calculated, and the error estimate for each tetrahedral element is calculated based on the residual. The calculation formula is as follows:

[0126] μ e =h e ·||r e ||

[0127] Among them, h e It is the characteristic dimension of the tetrahedral element, r e It is the residual vector of the tetrahedral element; the element that needs to be refined is identified based on the calculated error estimate.

[0128] (3) Mesh refinement: Based on the error estimate, an error threshold is set, and tetrahedral elements with error estimates greater than the error threshold are marked as elements that need to be refined. The elements that need to be refined are then mesh refined to generate new sub-elements.

[0129] (4) Iterative update: Repeat step (2) error estimation and step (3) mesh refinement process until the error estimate of all mesh cells meets the accuracy requirements of the preset error threshold.

[0130] Step 3.4: Dynamic Boundary Condition Handling

[0131] In FEM calculations, dynamic boundary condition processing is an important means to improve calculation accuracy. This embodiment introduces a boundary condition adjustment method based on physical information, which dynamically adjusts the boundary conditions according to the real-time calculation results of the sound field.

[0132] (1) Sound pressure boundary condition: Set a Dirichlet boundary condition with zero sound pressure on the outer boundary of the near field region (i.e. the boundary where it intersects with the far field region).

[0133] (2) Absorbing boundary conditions: Set absorbing boundary conditions on the outer boundary of the near field region to simulate an infinite space and avoid interference from reflected sound waves.

[0134] (3) Dynamic Adjustment: During the FEM calculation, the current sound pressure distribution is obtained at each time step or iteration step. Based on the real-time calculated sound pressure distribution, a feedback mechanism is introduced to automatically adjust the parameters of the boundary conditions according to the difference between the real-time calculated sound pressure distribution and the expected sound field characteristics. If the calculation results show that the sound pressure reflection near the boundary is strong, the absorption coefficient can be automatically increased to reduce reflection.

[0135] The feedback mechanism includes the following:

[0136] Data type: The sound pressure phase correction returned for the FEM region (near field region) is used for the phase compensation term in the PE equation; the returned scattered energy density distribution is used to correct the equivalent attenuation coefficient of PE.

[0137] Conversion method: The FEM region boundary data is mapped to the virtual sound source items of the PE region using the Equivalent Source Method (ESM).

[0138] The formula for iterative calculation of the PE region based on feedback data is as follows:

[0139] Q new =Q old +α·ΔQ feedback

[0140] Among them, Q new Q is the corrected equivalent sound source intensity. old The equivalent sound source intensity before correction, α is the relaxation factor, and ΔQ feedback This is the sound source correction amount in the feedback data.

[0141] Iteration termination condition: When the relative error of sound pressure in two consecutive iterations satisfies Termination at time; where p n and p n-1 These represent the acoustic pressure solutions of adjacent iteration steps, where n is the iteration number, and its specific value depends on the number of iterations. The termination condition ensures the convergence of data transfer between regions.

[0142] By introducing a multi-scale adaptive mesh generation method and a dynamic boundary condition handling method, not only is the efficiency and accuracy of FEM calculation improved, but the model's adaptability to complex marine environments is also enhanced.

[0143] Through the above steps, the element discretization process based on tetrahedral elements in the three-dimensional sound field was completed, and the element stiffness matrix K was constructed. e and the unit mass matrix M e These matrices will serve as the foundation for constructing the equations of the entire three-dimensional sound field finite element system, used to solve for physical quantities such as sound pressure and particle velocity in the sound field. In the subsequent construction of the overall system, the element stiffness matrix K of each element needs to be calculated. e and the unit mass matrix M e The global stiffness matrix K and global mass matrix M are assembled according to certain rules, and combined with boundary conditions and excitation sources, the detailed information of the three-dimensional sound field is finally solved.

[0144] Step 4, Equations at the boundary (interface)

[0145] At the boundary between the far-field and near-field regions, it is necessary to ensure the continuity of the sound field. To this end, this embodiment proposes an innovative multi-physics coupling boundary condition to more accurately process the sound field information at the boundary. The specific content of the multi-physics coupling boundary condition is described in detail below.

[0146] Step 4.1, Sound pressure continuity

[0147] At the boundary between the far-field region (PE region) and the near-field region (FEM region), the sound pressure should remain consistent. Let the sound pressure in the PE region be p. PE The sound pressure in the FEM region is p FEM Then at the boundary, the following must be satisfied: p PE =p FEM ;

[0148] If the calculation result for the PE region is p at the boundary PE(X,Z) The sound pressure vector at the node at the boundary of the FEM region is p. FEM Then, for the FEM node corresponding to the boundary with the PE region, we have: p PE(X,Z) =p FEM .

[0149] Step 4.2, Continuity of Normal Particle Velocity

[0150] The normal component of the particle velocity should remain continuous at the boundary. Let the normal particle velocity at the boundary of the far-field region (PE region) be v. PE The normal particle velocity at the boundary of the near-field region (FEM region) is v. FEM After calculating the vibration velocity based on the sound pressure gradient, the following condition is satisfied at the interface: v PE =v FEM .

[0151] In numerical calculations, this condition is specifically achieved using the sound pressure gradient calculated by the finite element method. In the near-field region, the sound pressure gradient is calculated by differentiating the shape function; in the far-field region, the sound pressure gradient is calculated by difference, and then the two are made equal at the boundary to convey the information.

[0152] Step 4.3: Smooth transition of sound velocity profile

[0153] At the boundary, the sound velocity profile c(r,z) typically differs depending on the calculation methods used in the PE and FEM regions. Therefore, this example introduces a transitional sound velocity profile c. trans(r,z) The transitional sound velocity profile c trans(r,z) A smooth transition between the PE and FEM regions is specifically defined as: c trans(r,z) =α·c PE(r,z) +(1-α)·c FEM(r,z) ;

[0154] Where α is a smoothing function, ranging from 0 to 1, used to control the degree of smoothness in the transition; c PE(r,z) It is the sound speed profile in the far field region, c FEM(r,z) It is the sound velocity profile in the near-field region;

[0155] Step 4.4: Dynamic Adjustment of Environmental Parameters

[0156] At the boundary, changes in marine environmental parameters also affect the propagation of the sound field. Therefore, this embodiment introduces a dynamic adjustment mechanism for environmental parameters, dynamically adjusting the environmental parameters at the boundary based on the calculation results of the PE and FEM regions.

[0157] Step 4.4.1, Water Depth Adjustment

[0158] At the boundary, the water depth h is dynamically adjusted using a weighted average: h trans =β·h PE +(1-β)·h FEM Where β is a weighting coefficient, which is adjusted according to actual needs, and h PE It is the water depth in the far field region, h FEM It refers to the water depth in the near-field area, h trans It is the transition water depth parameter.

[0159] Step 4.4.2, Temperature Adjustment

[0160] At the boundary, the temperature T is dynamically adjusted using an interpolation method: T trans =T PE +γ·(T FEM -T PE ); where γ is the interpolation coefficient, dynamically adjusted according to the position of the boundary, and T PE It is the temperature in the far-field region, T FEM It refers to the near-field temperature, T. trans It is the transition temperature parameter.

[0161] Step 4.4.3, Flow rate adjustment

[0162] At the boundary, the flow velocity V is dynamically adjusted using a weighted average: V trans =δ·V PE +(1-δ)·V FEM Where δ is the weighting coefficient, which is adjusted according to actual needs, and V PE It is the flow velocity in the far field region, V FEM It is the near-field velocity, V trans It is the transition speed parameter.

[0163] This embodiment introduces multi-physics field coupling boundary conditions, which not only ensures the continuity of sound pressure and particle velocity, but also considers the dynamic changes of sound velocity profile and environmental parameters, thereby processing the sound field information at the boundary more accurately and improving the calculation accuracy and adaptability of the entire model.

[0164] Through the above steps, this embodiment constructs a complete and effective sound field model based on a hybrid PE and FEM. According to the characteristics of the sound field and computational requirements, the entire three-dimensional computational region is divided into different sub-regions. In large-scale uniform regions far from the sound source and complex boundaries, the parabolic equation method is used for calculation because sound wave propagation is relatively regular in these regions, allowing the parabolic equation to quickly provide relatively accurate results with relatively low computational resource consumption. However, in regions close to the sound source, with complex marine topography (such as submarine mountains and trenches) or artificial structures (such as oil drilling platforms and submarine cables), the sound wave scattering and reflection phenomena are complex, and the geometry is irregular. Therefore, the finite element method can more accurately describe the changes in the sound field. The sound field model construction method in this embodiment meets the accuracy and efficiency requirements for calculating complex marine sound fields.

[0165] The embodiments of the present invention are only used to illustrate the technical solutions of the present invention and are not intended to limit it. For those skilled in the art, it will be understood that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for constructing a sound field model based on a hybrid approach of parabolic equation theory and finite element method, characterized in that: This method Includes the following steps; Step 1: Divide the sound field into a far-field region and a near-field region based on distance criteria and geometric conditions; Step 2: In the far-field region, establish a parabolic equation and perform approximation, then construct the PINN model, embed the parabolic equation into the PINN model loss function, and use existing sound field data as input to train the PINN model; the sound field data includes spatial location (x,z), sound source parameters, and marine environment parameters; the output of the PINN model is the key parameters of the sound field, including sound pressure p(x,z) and propagation loss TL; In each step of the parabolic equation calculation, the initial sound field result calculated by the parabolic equation is corrected using the trained PINN model. Finally, the corrected sound field result is fused with the initial sound field result to obtain the final sound field result. Step 3: In the near-field region, firstly, mesh generation is performed. Then, wave equations are established and discretized within each mesh element to construct the element stiffness matrix K for each mesh element. e and the unit mass matrix M e And based on the real-time calculation results of the sound field, the boundary conditions are dynamically adjusted; Finally, the element stiffness matrix K of each mesh element is... e and the unit mass matrix M e The global stiffness matrix K and global mass matrix M are assembled, and the detailed information of the three-dimensional sound field is solved by combining the boundary conditions and excitation source. Step 4: Process the sound field information at the boundary between the far-field and near-field regions through multi-physics coupling boundary conditions, including sound pressure continuity, normal particle velocity continuity, smooth transition of sound velocity profile, and dynamic adjustment of environmental parameters.

2. The method for constructing a sound field model based on a hybrid of parabolic equation theory and finite element method according to claim 1, characterized in that, In step 1, the near-field region division criteria are as follows: Based on the distance standard, the area within one wavelength range around the sound source is divided into the near field region, i.e., r≤λ; where r is the distance from the sound source and λ is the wavelength of the sound wave. Based on geometric conditions, areas near the sound source, areas with complex marine topography, or areas with large artificial structures are classified as near-field areas. For the near-field region, both distance criteria and geometric conditions must be met simultaneously, and the two are independent and complementary.

3. The method for constructing a sound field model based on a hybrid of parabolic equation theory and finite element method according to claim 1, characterized in that, In step 1, the criteria for dividing the far-field region are as follows: Based on the distance standard, the region that is more than one wavelength away from the sound source is divided into the far field region, i.e., r > λ; Based on geometric conditions, large-scale uniform regions far from the sound source or complex boundaries are divided into far-field regions; For the far-field region, both distance criteria and geometric conditions must be met simultaneously, and the two are independent and complementary.

4. The method for constructing a sound field model based on a hybrid of parabolic equation theory and finite element method according to claim 1, characterized in that, The steps for constructing and training the PINN model in step 2 are as follows: (1) Collect sound field data in the actual marine environment, including spatial location (x,z), sound source parameters and marine environment parameters; (2) Select a neural network and embed the parabolic equation as a constraint into the loss function of the neural network. The loss function is expressed as: L = L data +L physics , where L data It is a data loss function used to fit existing sound field data; L physics It is the physical loss, used to ensure that the network output satisfies the physical laws of the parabolic equation; (3) The collected sound field data and historical measurement data are used as inputs to the neural network. By optimizing the loss function and adjusting the network parameters, the sound field output of the neural network can conform to the data pattern and meet the physical constraints.

5. The method for constructing a sound field model based on a hybrid of parabolic equation theory and finite element method according to claim 4, characterized in that, The process of collecting acoustic field data in a real marine environment is as follows: Sound pressure and propagation loss are collected in a real marine environment using marine acoustic equipment. Then, Bellhop is used to perform numerical simulations under marine environmental conditions. The collected and simulated data are then processed to obtain the spatial location (x, z), sound source parameters, and marine environmental parameters.

6. The method for constructing a sound field model based on a hybrid of parabolic equation theory and finite element method according to claim 1, characterized in that, In step 2, the steps for correcting and fusing the initial sound field results using the PINN model are as follows: (1) The initial sound field result p in the far field region was calculated using the parabolic equation method. PE(X,Z) ; (2) p PE(X,Z) When input into a pre-trained PINN model, a fully trained PINN model can predict the corresponding sound pressure correction coefficient α(x,z) based on the current spatial location (x,z), the corresponding sound source parameters, and the corresponding marine environment parameters. Based on α(x,z), the model then modulates the p... PE(X,Z) The correction is performed to obtain the corrected sound field result p. PINN(X,Z) The calculation formula is p PINN(X,Z) =α(x,z)·p PE(X,Z) ; (3) p PINN(X,Z) With p PE(X,Z) The sound field is then fused to obtain the final sound field result p. final(X,Z) The calculation formula is p final(X,Z) =β·p PINN(X,Z) +(1-β)·p PE(X,Z) Where β is the weighting coefficient.

7. The method for constructing a sound field model based on a hybrid of parabolic equation theory and finite element method according to claim 1, characterized in that, In step 2, Marine environmental parameters include sound velocity profile c(r,z), seabed topography and elevation and sediment parameters, seawater temperature-salinity profile and three-dimensional current field data; The sound source parameters include the sound source geometric location parameters (r_s, z_s), spectral characteristic parameters, radiating sound source level SL, time-domain waveform parameters, and spatial directivity parameters. Among them, the spectral characteristic parameters include the center frequency f0 and the -3dB bandwidth Δf; the time-domain waveform parameters include the pulse width τ and the modulation type; and the spatial directivity parameters include the azimuth angle α, the elevation angle β, and the beam opening angle.

8. The method for constructing a sound field model based on a hybrid of parabolic equation theory and finite element method according to claim 1, characterized in that, In step 3, mesh generation is performed using a multi-scale adaptive mesh generation method, and the specific steps are as follows: (1) First, the geometry of the computational region is analyzed to identify different features, including the location of the sound source and the undulation of the seabed topography; second, the boundary conditions of the computational region are defined, including the ocean surface, seabed, and far-field boundary, and the initial mesh is generated using Gmsh. (2) Establish the wave equation within each grid cell and discretize it based on tetrahedral elements. For each tetrahedral element, calculate its residual, and then calculate the error estimate for each tetrahedral element based on the residual. The calculation formula is as follows: m e =h e ·||r e || Among them, h e It is the characteristic dimension of the tetrahedral element, r e It is the residual vector of the tetrahedral element; (3) Set an error threshold based on the error estimate, mark the tetrahedral elements whose error estimate is greater than the error threshold as elements that need to be refined, and refine their mesh to generate new sub-elements; (4) Repeat steps (2) and (3) until the error estimates of all grid cells meet the accuracy requirements of the preset error threshold.

9. The method for constructing a sound field model based on a hybrid of parabolic equation theory and finite element method according to claim 1, characterized in that, In step 3, the boundary conditions are dynamically adjusted using a boundary condition adjustment method based on physical information. The specific steps are as follows: (1) Set a Dirichlet boundary condition with zero sound pressure on the outer boundary of the near-field region; (2) Set absorbing boundary conditions on the outer boundary of the near field region to simulate an infinite space and avoid interference from reflected sound waves; (3) Introduce a feedback mechanism to automatically adjust the parameters of the boundary conditions based on the difference between the real-time calculated sound pressure distribution and the expected sound field characteristics. If the calculation results show that the sound pressure reflection near the boundary is strong, the absorption coefficient will be automatically increased to reduce the reflection.

10. The method for constructing a sound field model based on a hybrid of parabolic equation theory and finite element method according to claim 1, characterized in that, In step 4, the steps for processing the sound field information at the boundary between the far-field and near-field regions are as follows: (1) At the boundary between the far-field and near-field regions, the sound pressure needs to remain consistent. Let the sound pressure in the far-field region be p. PE The sound pressure level in the near-field region is p FEM Then at the boundary, p satisfies: PE =p FEM ; (2) At the boundary between the far-field and near-field regions, the normal component of the particle velocity needs to remain continuous. Let the normal particle velocity at the boundary of the far-field region be v. PE The normal particle velocity at the boundary of the near-field region is v. FEM Then at the boundary, the following condition is satisfied: v PE =v FEM ; The sound pressure gradient is calculated by differentiating the shape function in the near field region and by calculating the difference in the far field region. The two are then made equal at the boundary to transmit information. (3) At the boundary between the far-field and near-field regions, the sound speed profile c(r,z) will differ depending on the calculation method used in the far-field and near-field regions. Therefore, a transitional sound speed profile c is introduced. trans(r,z) c trans(r,z) A smooth transition between the far-field and near-field regions is defined as: c trans(r,z) =α·c PE(r,z) +(1-α)·c FEM(r,z) ; Where α is a smoothing function, ranging from 0 to 1, used to control the degree of smoothness in the transition; c PE(r,z) It is the sound speed profile in the far field region, c FEM(r,z) It is the sound velocity profile in the near-field region; (4) At the boundary between the far field region and the near field region, a dynamic adjustment mechanism for environmental parameters is introduced to dynamically adjust the water depth, temperature and flow velocity at the boundary based on the calculation results of the far field region and the near field region. At the boundary, the water depth h is dynamically adjusted using a weighted average: h trans =β·h PE +(1-β)·h FEM Where β is the weighting coefficient, h PE It is the water depth in the far field region, h FEM It refers to the water depth in the near-field area, h trans It is the transition water depth parameter; At the boundary, the temperature T is dynamically adjusted using an interpolation method: T trans =T PE +γ·(T FEM -T PE ); where γ is the interpolation coefficient, T PE It is the temperature in the far-field region, T FEM It refers to the near-field temperature, T. trans It is a transition temperature parameter; At the boundary, the flow velocity V is dynamically adjusted using a weighted average: V trans =δ·V PE +(1-δ)·V FEM Where δ is the weighting coefficient, V PE It is the flow velocity in the far field region, V FEM It is the near-field velocity, V trans It is the transition speed parameter.

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