Method and system for calculating acoustic radiation of elastic structure under turbulence pulsating pressure excitation

Abstract

The invention discloses a method and a system for calculating sound radiation of an elastic structure under turbulence pulsating pressure excitation, a statistical finite element method and a wave superposition method are coupled, and a statistical finite element coupling wave superposition algorithm is provided to realize accurate prediction of a long-distance radiation sound field. And predicting the radiation sound field of the elastic structure under turbulence excitation by adopting a statistical finite element coupling wave superposition algorithm. The statistical finite element coupling wave superposition method can avoid generation of singular integrals of boundary elements needing to be processed by a statistical finite element coupling boundary element method, the calculation amount is reduced, the calculation efficiency of the radiation sound field is improved, and meanwhile, the statistical finite element coupling wave superposition method does not need to be just like the statistical finite element method. And the grid of the whole radiation sound field is modeled, so that the far-field radiation sound field can be predicted, and the method has the advantage of high calculation speed.

Description

Technical Field

[0001] The present invention relates to a method for calculating flow-induced structure noise, and particularly to a method and system for calculating the acoustic radiation of an elastic structure under the excitation of turbulent pulsating pressure. Background Art

[0002] When vehicles such as automobiles, airplanes, and submarines move at high speeds, the fluid will generate turbulent pulsating pressure on the surface of the structure, thereby causing flow-induced structure noise. For an underwater vehicle, the flow-induced noise of the structure is an important factor affecting the acoustic stealth performance of the vehicle. How to accurately predict the radiation sound field of the flow-induced noise is an important issue that needs to be considered when designing the structure of an underwater vehicle to improve its acoustic stealth performance.

[0003] Acoustic experiments are a powerful support for flow-induced noise prediction. However, experimental research has problems such as high cost, long cycle, and difficulty in achieving ideal experimental conditions. Usually, numerical algorithms are required to predict the experiment before the experiment, so as to calculate the best model parameters, thereby reducing the time cycle and funding requirements of experimental research. In recent years, with the increasing popularity of computer technology, numerical algorithms have been widely used in flow-induced noise prediction. Currently, the commonly used numerical algorithms for flow-induced noise prediction include the statistical finite element method and the statistical finite element coupled boundary element method. The statistical finite element method needs to perform a complete modeling of the radiation sound field, which leads to an increase in the amount of calculation and difficulty in calculating far-field problems. The statistical finite element method coupled with the boundary element method reduces the dimension of the grid of the radiation sound field, enabling it to calculate far-field problems. However, the boundary element method has problems such as a full-rank coefficient matrix, singular element integration, and non-unique solutions, resulting in a slow calculation speed of the boundary element method. Therefore, how to accurately and efficiently predict far-field flow-induced noise is an urgent problem for those skilled in the art. Summary of the Invention

[0004] Object of the Invention: Aiming at the above problems, the present invention proposes a method and system for calculating the acoustic radiation of an elastic structure under the excitation of turbulent pulsating pressure, which can accurately predict the far-distance radiation sound field and has the advantage of fast calculation speed.

[0005] Technical Solution: The technical solution adopted by the present invention is a method for calculating the acoustic radiation of an elastic structure under the excitation of turbulent pulsating pressure, including the following steps:

[0006] Step 1, perform numerical modeling according to the structure of the object to be measured, divide the modeled geometric model into discrete grids, construct the motion equations of each node on the geometric grid based on the FEM principle, and obtain the elastic structure vibration coefficient matrix of the object to be measured through the motion equations of each node;

[0007] Step 2: Based on the elastic structure vibration coefficient matrix, establish an elastic structure acoustic radiation grid model. According to the spatial positions of the elastic structure vibration coefficient matrix and the elastic structure geometric grid, establish an elastic structure acoustic radiation grid model with the number of nodes greater than or equal to the number of nodes of the elastic structure geometric grid;

[0008] The vibration expression on the surface of the elastic structure acoustic radiation grid model is:

[0009] {v n} = [T][st] -1 {F}

[0010] where the [T] matrix is the transfer matrix between the elastic structure acoustic radiation grid and the elastic structure grid, [st] is the dynamic stiffness matrix, {F} is the load vector applied to the structure, and {v n} is the vibration vector on the surface of the elastic structure acoustic radiation grid model.

[0011] The transfer matrix [T] between the elastic structure acoustic radiation grid and the elastic structure grid is:

[0012]

[0013] where the normal vector n k = [n kx n ky n kz , and n kx , n ky and n kz are the normal cosine components in the x, y, and z directions of node k respectively.

[0014] Step 3: Set several virtual points inside the elastic structure acoustic radiation grid model to construct a virtual source model with the same shape as the acoustic model; the virtual source model is:

[0015] {Q} = [D G -1 {v n}

[0016] where Q is the source strength of the virtual point source, {v n} is the vibration vector on the surface of the elastic structure acoustic radiation grid model, and D G is the transfer matrix between the source strength of the virtual point source and the normal velocity on the structure surface.

[0017] The transfer matrix D G between the source strength of the virtual point source and the normal velocity on the structure surface is:

[0018]

[0019] ​where x is an arbitrary node on the structure surface, ξ is an arbitrary virtual point source, r x is the coordinate of node x on the structure surface, r ξ is the coordinate of the virtual point source, k is the wave number,

[0020] Step 4: Set several field points as required in the radiation sound field of the virtual source model. Subsequently, according to the spatial position relationship between the virtual source model and the field points, establish a virtual source radiation sound field model through the Green's function of the radiation sound field;

[0021] Step 5: Calculate the coupling matrix by multiplying the inverse matrix of the transfer matrix between the virtual point source strength and the normal velocity of the structure surface and the transfer matrix between the elastic structure acoustic radiation grid and the elastic structure grid. Couple the virtual source radiation sound field model with the elastic structure acoustic radiation model through the coupling matrix to obtain the elastic structure radiation sound field model; The expression of the elastic structure radiation sound field model is:

[0022] [H swr = {T G} T [T c [st] -1

[0023] In the formula, [H swr is the transfer matrix between the excitation and the radiation sound field, D G is the transfer matrix between the virtual point source strength and the normal velocity of the structure surface, T c is the coupling matrix, and [st] is the dynamic stiffness matrix.

[0024] Step 6: Establish a numerical model of turbulent pulsating pressure according to the elastic structure radiation sound field model;

[0025] The establishment of the numerical model of turbulent pulsating pressure includes: obtaining the matrix dimension of the turbulent pulsating pressure according to the elastic structure radiation sound field model. The loading direction of the turbulent pulsating pressure is the normal direction of the node, and the amplitude of the turbulent pulsating pressure can be calculated through a semi-empirical formula. According to the empirical formula of the turbulent pulsating pressure and the elastic structure radiation sound field model, fill the amplitude data after meshing the elastic structure radiation sound field model into the matrix of the numerical model of the turbulent pulsating pressure to obtain the numerical model of the turbulent pulsating pressure.

[0026] Step 7: Calculate the flow-induced noise of the radiation sound field according to the numerical model of the turbulent pulsating pressure. The calculation of the flow-induced noise of the radiation sound field is calculated by the formula:

[0027]

[0028] In the formula, [S PP is the power spectral density matrix at the radiation sound field, [H swrThe transfer matrix between the excitation and the radiation sound field is the turbulent pulsating pressure excitation matrix, and its expression is:

[0029]

[0030] where I is the number of excitation points for applying turbulent excitation, i = 1, 2, …, I, and the diagonal elements are the auto-spectra of the excitation spectra, which can be obtained through semi-empirical formulas or experimental measurements. The non-diagonal elements are the cross-spectra of the excitation spectra, representing the correlation degree between the excitation at point i and the excitation at point I.

[0031] The present invention provides a prediction system for the sound radiation of an elastic structure under turbulent pulsating pressure excitation, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the above-mentioned calculation method for the sound radiation of an elastic structure under turbulent pulsating pressure is realized.

[0032] Beneficial effects: Compared with the prior art, the present invention has the following advantages: The method of the present invention couples the statistical finite element method and the wave superposition method, and proposes a statistical finite element coupled wave superposition algorithm to achieve accurate prediction of the far-field radiation sound field. The statistical finite element coupled wave superposition algorithm is used to predict the radiation sound field of an elastic structure under turbulent excitation. The statistical finite element coupled wave superposition method can avoid the singular integral of the boundary elements that need to be processed in the statistical finite element coupled boundary element method, reduce the calculation amount, improve the calculation efficiency of the radiation sound field. At the same time, the statistical finite element method coupled with the wave superposition method does not need to model the entire grid of the radiation sound field like the statistical finite element method, so that the far-field radiation sound field can be predicted and has the advantage of fast calculation speed. The present invention couples the statistical finite element method and the wave superposition method to achieve accurate prediction of the far-field radiation sound field. The method of the present invention has the advantages of high accuracy of calculation results and fast calculation speed, and provides a new research approach for predicting the structure radiation sound field under turbulent pulsating pressure in the future. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is the flow chart of the calculation method for the sound radiation of an elastic structure under turbulent pulsating pressure according to the present invention;

[0034] Figure 2 is a comparison diagram of the curve of the radiation sound pressure level of a flat plate under turbulent pulsating pressure excitation calculated by the method of the present invention and the calculation results of the finite element method with respect to frequency. DETAILED DESCRIPTION OF THE INVENTION

[0035] The technical solutions of the present invention will be further described below with reference to the drawings and embodiments.

[0036] The calculation method of the structural radiated sound field under the excitation of turbulent pulsating pressure according to the present invention is as follows, refer to Figure 1 , including the following steps:

[0037] Step 1: Establish the vibration coefficient matrix of the elastic structure. Model according to the structure of the target to be measured, and perform mesh division on the modeled geometric model. Based on the FEM principle, construct the motion equation of the elastic structure, and the motion equation can be expressed as:

[0038]

[0039] where [M], [C], and [K] are the mass, damping, and stiffness matrices of the structure respectively. {F} is the load vector applied to the structure, and {u} is the displacement vector of each node of the structure.

[0040] (Equation (1)) is the motion equation of the entire structure. Assuming that the motion of the entire structure is a simple harmonic motion (the time factor is e jωt , ω is the angular frequency), (Equation (1)) can be simplified to the following form:

[0041] [st]{u} = {F} (2)

[0042] where the dynamic stiffness matrix [st] of the structure = -ω 2 [M] + jω[C] + [X]. For an elastic structure, usually the load vector applied to the structure is a known quantity, and the displacements and velocities of each node of the structure are unknown quantities. Therefore, it is necessary to perform LU decomposition on the dynamic stiffness matrix [st] to obtain the vibration coefficient matrix of the elastic structure (the vibration coefficient matrix of the elastic structure is the inverse matrix [st] -1 ) of the dynamic stiffness matrix [st].

[0043] Step 2: According to the vibration coefficient matrix of the elastic structure in the previous step, establish the acoustic radiation mesh model of the elastic structure. The acoustic radiation mesh model is a closed mesh model, while the mesh model of the elastic structure can be a non-closed mesh model. Therefore, for a non-closed elastic structure mesh model, it is necessary to use the surface filling method to add several rigid walls to construct the non-closed elastic structure mesh model into a closed elastic structure acoustic radiation mesh model.

[0044] The acoustic radiation mesh model of the elastic structure needs to include the elastic structure mesh, that is, the elastic structure mesh is a part of the acoustic radiation mesh of the elastic structure, and the number of nodes of the acoustic radiation mesh model of the elastic structure is greater than or equal to that of the elastic structure mesh. The acoustic radiation mesh of the elastic structure and the elastic structure mesh are connected through the transfer matrix [T], and the [T] matrix is expressed as:

[0045]

[0046] The normal vector n of the node at node k k = [nkx n ky n kz , n kx , n ky and n kz are the normal cosine components in the x, y, and z directions of node k, respectively.

[0047] The vibration on the surface of the elastic structural acoustic radiation grid model can be expressed as:

[0048] {v n} = [T]{u} = [T][st] -1 {F} (4)

[0049] Step 3: Based on the elastic structural acoustic radiation grid model from the previous step, establish a virtual source model. Based on the wave superposition method principle, several virtual point sources are set inside the acoustic radiation grid model to construct a virtual source surface similar in shape to the elastic structural acoustic radiation grid model. The sound pressure at a field point in the radiation sound field can be expressed as the superposition of the radiation sound fields of all virtual source points. Establish the transfer matrix between the structural surface vibration velocity and the source strength of the virtual source points. Assume v n is the normal vibration velocity of the structural surface, and Q is the source strength of the virtual point source. The transfer matrix can be expressed as:

[0050] {v n} = [D G {Q} (5)

[0051] Performing singular value decomposition on the transfer matrix can obtain the inverse matrix of this matrix:

[0052] {Q} = [D G -1 {v n} (6)

[0053] where D G is the transfer matrix between the source strength of the virtual point source and the normal velocity of the structural surface:

[0054]

[0055] where x is an arbitrary node on the structural surface, ξ is an arbitrary virtual point source, r x is the coordinate of node x on the structural surface, r ξ is the coordinate of the virtual point source, and k is the wave number.

[0056] Step 4: Based on the virtual source model {Q} derived in the previous step, establish a virtual source radiation sound field model. First, several field points are set in the radiation sound field of the virtual source model. Subsequently, according to the spatial position relationship between the virtual source model and the field points, considering the transfer relationship of displacement and vibration velocity in equation (4), establish a virtual source radiation sound field model through the Green's function: ​

[0057] P = {T G}{Q} (8)

[0058] where {T G} describes the propagation characteristics of the virtual source point in the free field, and its expression is: TG = iρωG(|r - r0|), where ρ is the density of the free field medium and G is the free field Green's function.

[0059] Step 5. Based on the virtual source radiation sound field model in the previous step, establish an elastic structure radiation sound field model. First, establish a coupling matrix T according to the number of virtual sources in the virtual source radiation sound field model and the number of grid nodes in the elastic structure sound radiation model:

[0060] [T c = [D G -1 [T] (9)

[0061] Couple the virtual source radiation sound field model with the elastic structure sound radiation model through the coupling matrix to obtain the elastic structure radiation sound field model:

[0062] [H swr = {T G} T [T c [st] -1 = {T G} T [D G -1 [T][st] -1 (10)

[0063] Step 6. Based on the elastic structure radiation sound field model in the previous step, establish a numerical model of turbulent pulsating pressure.

[0064] First, obtain the matrix dimension of the turbulent pulsating pressure according to the elastic structure radiation sound field model. The loading direction of the turbulent pulsating pressure is the normal direction of the node. Therefore, the matrix dimension is the number of nodes on the surface of the elastic structure radiation sound field model where no constraint conditions are applied. The amplitude of the turbulent pulsating pressure can be calculated through a semi-empirical formula. For complex structures with curvature, the boundary layer parameters need to be calculated by CFD to correct the semi-empirical formula.

[0065] The numerical model includes two parts: auto-spectrum and cross-spectrum, and can be constructed into a matrix in the following form:

[0066]

[0067] where I is the number of excitation points applying turbulent excitation, and i = 1, 2,..., I. The diagonal element is the auto-spectrum of the excitation spectrum and can be obtained through a semi-empirical formula or experimental measurement. The non-diagonal element ​​The cross-spectrum of the hook excitation spectrum represents the correlation degree between the excitation at point i and the excitation at point I.

[0068] Step 7: Based on the turbulent pulsating pressure numerical model obtained in the previous step, predict the flow-induced noise of the radiated sound field. According to the correlation function theory in statistics, the response of an elastic structure can be represented by the autocorrelation function R of the structural velocity v(x, t). vv Assuming that the turbulent pulsating pressure is stationary and fully developed, then R vv can be written as:

[0069]

[0070] The auto-spectral density of the pressure at point z in the radiated sound field is defined as the time Fourier transform of R vv :

[0071]

[0072] The power spectral density at point z in the radiated sound field can be expressed as:

[0073]

[0074] Combining equation (14) with the turbulent pulsating pressure numerical model of the previous step and writing it in matrix form can be expressed as:

[0075]

[0076] Equation (15) is the expression after combining the turbulent pulsating pressure numerical model and the radiated sound field of the elastic structure. Through this expression, the decibel value of the flow-induced noise of the radiated sound field can be predicted.

[0077] Figure 2 For the comparison of the calculation results of the statistical finite element algorithm and the algorithm of the present invention for the vibration and sound radiation of a flat plate structure under the excitation of turbulent pulsating pressure. The flat plate model is a thin plate model with a length of 0.46 m, a width of 0.33 m, and a thickness of 0.0048 m, and the material is aluminum. The turbulent pulsating pressure in equation (12) is obtained by calculating through the semi-empirical formula of the Corcos model. The spatial-frequency spectrum expression of the Corcos model is:

[0078]

[0079] where γ1 and γ2 are the attenuation rates in the flow direction and spanwise direction of the fluid respectively, ξ1 and ξ2 are the distances between points on the structure surface along the flow direction and spanwise direction of the fluid respectively, U c = 0.65U0 is the turbulent convection velocity, U0 is the flow velocity of the turbulent free stream, and I is the number of nodes on the structure surface.

[0080] The comparison results show that in the calculation of structural acoustic radiation under turbulent pulsating pressure excitation, the statistical finite element coupled wave superposition algorithm of the present invention is in good agreement with the calculation results of the statistical finite element method.

[0081] Table 1 shows the comparison of the calculation speed of the method of the present invention with that of the statistical finite element coupled boundary element method. It can be seen from the figure that the calculation speed of the method of the present invention is faster than that of the finite element coupled boundary element method.

[0082] In one embodiment, a prediction system for elastic structural acoustic radiation under turbulent pulsating pressure excitation is provided, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the above-mentioned calculation method for elastic structural acoustic radiation under turbulent pulsating pressure excitation is implemented.

[0083] Table 1 Comparison of the calculation speed of the method of the present invention with that of the statistical finite element coupled boundary element method

[0084]

[0085] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0086] The present application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for realizing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0087] These computer program instructions can also be stored in a computer-readable memory capable of guiding a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured product including an instruction device, and the instruction device realizes the functions in the process Figure 1One or more processes and / or boxes Figure 1 The functions specified in one box or more boxes.

[0088] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one Figure 1 One or more processes and / or boxes Figure 1 box or more boxes.

Claims

1. A calculation method for acoustic radiation of an elastic structure under turbulent pulsating pressure excitation, characterized in that, It includes the following steps: Step 1: Perform numerical modeling according to the structure of the target to be measured, divide the modeled geometric model into discrete grids, construct the motion equations of each node on the geometric grid based on the FEM principle, and obtain the elastic structure vibration coefficient matrix of the target to be measured through the motion equations of each node; Step 2: Establish an elastic structure acoustic radiation grid model according to the elastic structure vibration coefficient matrix, and establish an elastic structure acoustic radiation grid model with the number of nodes greater than or equal to the number of nodes of the elastic structure geometric grid according to the spatial position of the elastic structure vibration coefficient matrix and the elastic structure geometric grid; Step 3: Set several virtual points inside the elastic structure acoustic radiation grid model to construct a virtual source model with the same shape as the acoustic model; Step 4: Set several field points according to requirements in the radiation sound field of the virtual source model, and then establish a virtual source radiation sound field model through the Green's function of the radiation sound field according to the spatial position relationship between the virtual source model and the field points; Step 5: Calculate the coupling matrix by multiplying the inverse matrix of the transfer matrix between the virtual point source strength and the normal velocity of the structure surface and the transfer matrix between the elastic structure acoustic radiation grid and the elastic structure grid, and couple the virtual source radiation sound field model and the elastic structure acoustic radiation model through the coupling matrix to obtain the elastic structure radiation sound field model; Step 6: Establish a numerical model of turbulent pulsating pressure according to the elastic structure radiation sound field model; Step 7: Calculate the flow-induced noise of the radiation sound field according to the numerical model of the turbulent pulsating pressure.

2. The calculation method of the acoustic radiation of an elastic structure under the excitation of turbulent pulsating pressure according to claim 1, characterized in that The vibration expression on the surface of the elastic structure acoustic radiation grid model is: {v n} = [T][st] -1 {F} In the formula, the [T] matrix is the transfer matrix between the elastic structural acoustic radiation grid and the elastic structural grid, [st] is the dynamic stiffness matrix, {F} is the load vector applied to the structure, and {v n} is the vibration vector on the surface of the elastic structural acoustic radiation grid model.

3. The calculation method of the sound radiation of an elastic structure under the excitation of turbulent pulsating pressure according to claim 2, wherein The transfer matrix [T] between the elastic structure acoustic radiation grid and the elastic structure grid is: In the formula, the node normal vector n at node k k = [n kx n ky n kz , where n kx , n ky and n kz are the normal cosine components of node k in the x, y, and z directions, respectively.

4. The calculation method for the sound radiation of an elastic structure under turbulent pulsating pressure excitation according to claim 1, characterized in that, The virtual source model is: {Q} = [D G -1 {v n}​ where Q is the source strength of the virtual point source, {v n} is the vibration vector on the surface of the elastic structural acoustic radiation mesh model, and D G is the transfer matrix between the source strength of the virtual point source and the normal velocity of the structure surface.

5. The calculation method of the acoustic radiation of an elastic structure under the excitation of turbulent pulsating pressure according to claim 4, characterized in that, The transfer matrix D between the virtual point source strength and the normal velocity of the structure surface G is as follows: where \(x\) is an arbitrary node on the structure surface, \(\xi\) is an arbitrary virtual point source, \(r\) x is the coordinate of the node \(x\) on the structure surface, \(r\) ξ is the coordinate of the virtual point source, \(k\) is the wave number, 6. The calculation method of the acoustic radiation of an elastic structure under the excitation of turbulent pulsating pressure according to claim 1, characterized in that The expression of the elastic structure radiation sound field model is: [H swr = {T G} T [T c [st] -1 where, [H swr is the transfer matrix between the excitation and the radiated sound field, D G is the transfer matrix between the virtual point source strength and the normal velocity of the structural surface, T c is the coupling matrix, and [st] is the dynamic stiffness matrix.

7. The calculation method of the acoustic radiation of an elastic structure under the excitation of turbulent pulsating pressure according to claim 1, characterized in that, The establishment of the numerical model of turbulent pulsating pressure includes: obtaining the matrix dimension of the turbulent pulsating pressure according to the elastic structure radiation sound field model, the loading direction of the turbulent pulsating pressure is the normal direction of the node, the amplitude of the turbulent pulsating pressure can be calculated through a semi-empirical formula, and according to the empirical formula of the turbulent pulsating pressure and the elastic structure radiation sound field model, filling the amplitude data after meshing the elastic structure radiation sound field model into the matrix of the numerical model of the turbulent pulsating pressure to obtain the numerical model of the turbulent pulsating pressure.

8. The calculation method for acoustic radiation of an elastic structure under turbulent pulsating pressure excitation according to claim 1, characterized in that, The calculation of the flow-induced noise of the radiation sound field, the calculation formula is: where, [S PP is the power spectral density matrix at the radiation sound field, [H swr is the transfer matrix between the excitation and the radiation sound field, is the turbulent pulsating pressure excitation matrix.

9. The calculation method of acoustic radiation of an elastic structure under turbulent pulsating pressure excitation according to claim 8, characterized in that: The expression of the turbulent pulsating pressure excitation matrix is: Where I is the number of excitation points for applying turbulent excitation, i = 1, 2, …, I, and the diagonal elements are the auto-spectra of the excitation spectra, which can be obtained through semi-empirical formulas or experimental measurements. The non-diagonal elements are the cross-spectra of the excitation spectra, representing the correlation degree between the excitation at point i and the excitation at point I.

10. A prediction system for the acoustic radiation of an elastic structure under turbulent pulsating pressure excitation, characterized in that: It includes a memory, a processor, and a computer program stored on the memory and executable on the processor, and is characterized in that when the processor executes the computer program, it implements the calculation method of elastic structure acoustic radiation under the excitation of turbulent pulsating pressure according to any one of claims 1 to 9.

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