Underwater target sound scattering rapid forecasting method based on NURBS hybrid grid and Kirchhoff approximation

Abstract

The invention discloses an underwater target sound scattering rapid forecasting method based on an NURBS hybrid grid and Kirchhoff approximation. The underwater target sound scattering rapid forecasting method comprises the following steps: establishing a geometric model by adopting NURBS parameters; generating a parameterized grid for the geometric model through a node insertion algorithm, identifying and combining overlapped vertexes in units caused by overlapping of control points, correcting the units containing the overlapped vertexes into triangular units, and generating a hybrid grid containing the triangular units and quadrilateral units; according to the incident wave direction and the normal vector of the calculation unit, judging whether the unit is located in a sound wave illumination area or not, and recording the illuminated unit to form an effective integral area; based on Kirchhoff high-frequency approximation, constructing an area component expression of a scattering sound field potential function of the rigid target under a far-field condition; a plate element method is adopted, the area component expression is converted into algebraic operation of vertex coordinates on each unit in the effective integral region, and the scattering contribution value of each unit is calculated; and traversing all the effective integral region units, and calculating the target intensity.

Description

Technical Field

[0001] This invention relates to a rapid prediction method for underwater target acoustic scattering, and more particularly to a rapid prediction method for underwater target acoustic scattering based on NURBS hybrid grid and Kirchhoff approximation. Background Technology

[0002] Accurate and efficient prediction of the acoustic scattering characteristics of underwater targets is crucial for sonar detection, target identification, and acoustic stealth design. Existing methods mainly include numerical methods (such as the finite element method and boundary element method) and high-frequency approximation methods (such as geometric acoustics and the Kirchhoff approximation). The computational cost of traditional numerical methods increases sharply with increasing frequency, making them unsuitable for large-scale, high-frequency problems. High-frequency physical acoustic methods, represented by the Kirchhoff approximation, are highly efficient, but their application relies on planar mesh discretization and numerical integration of the illuminated area of ​​the target; they can only accurately simulate complex surfaces when the mesh size is very small.

[0003] Traditional workflows typically employ separate 3D modeling software for geometric design, followed by surface mesh generation using specialized tools. This process is cumbersome and reliant on manual operation. Mesh quality directly impacts the accuracy and stability of Kirchhoff integral calculations. Furthermore, traditional numerical integration methods (such as Gaussian integration) still incur computational costs when calculating the contribution of each element.

[0004] Therefore, it is of great significance to provide a fast prediction method for underwater target acoustic scattering based on NURBS hybrid grid and Kirchhoff approximation. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a rapid prediction method for underwater target acoustic scattering based on NURBS hybrid grids and Kirchhoff approximation, which realizes rapid and automatic processing of the entire process from target geometric description to acoustic prediction results.

[0006] Technical solution: The present invention provides a rapid prediction method for underwater target acoustic scattering based on NURBS hybrid grids and Kirchhoff approximation, comprising:

[0007] A geometric model of the underwater target was established using NURBS parameters;

[0008] A parameterized mesh is generated for the geometric model using a node insertion algorithm. Overlapping vertices in the cells caused by overlapping control points are identified and merged. Cells containing overlapping vertices are corrected to triangular cells, generating a hybrid mesh containing triangular and quadrilateral cells.

[0009] Based on the direction of the incident wave, calculate the normal vector of each element on the target surface, determine whether the element is located in the area illuminated by the sound wave, and record the illuminated triangular and quadrilateral elements to form the effective integration region.

[0010] Based on the Kirchhoff high-frequency approximation, a surface integral expression for the scattered acoustic potential function of a rigid target under far-field conditions with both transmitter and receiver in place is constructed.

[0011] Using the plate element method, the area integral expression is transformed into algebraic operations of vertex coordinates for each triangular and quadrilateral unit within the effective integration region, and the scattering contribution value of each unit is calculated.

[0012] By traversing all effective integration region cells and superimposing the scattering contribution values ​​of each cell, the total scattering field of the target is obtained, and the target intensity is calculated.

[0013] Furthermore, the node insertion algorithm refines the parameter space by uniformly inserting new nodes into the original node vector of the NURBS model. The new control points are obtained by linear interpolation of the original control points. The number of triangular and quadrilateral elements in the mesh is controlled by the number of newly inserted nodes.

[0014] Furthermore, determining whether the unit is located in the acoustic illumination area involves: calculating the outward normal vector of the unit, and the unit direction vectors of the lines connecting the transmitting transducer and the receiving hydrophone to the center of the unit; if the angle between the outward normal vector and the two unit direction vectors is acute, then the unit is determined to be illuminated.

[0015] Furthermore, the area integral under far-field conditions is expressed as follows: the scattered acoustic potential function is proportional to the area integral of the product of the cosine of the angle between the incident wave direction and the surface element normal vector on the illuminated surface S0 and a complex exponential phase factor related to the vector from the surface element to the reference point.

[0016] Furthermore, the surface integral expression of the scattered acoustic field potential function is:

[0017]

[0018] In the formula, k is the wave number, the integral surface S0 is the geometric bright region surface of the scatterer, r is the distance from the surface element dS to the transducer M, r is the incident sound ray, and θ is the angle between r and the unit normal vector n of the surface element.

[0019] Furthermore, in the hybrid mesh, quadrilateral elements are used to discretize the regular curved surface regions of the target surface, and triangular elements are used to handle the singular points or overlapping control points on the curved surface.

[0020] Furthermore, the method for calculating the area integral contribution value of the triangular element is as follows: the triangular element is transformed into a two-dimensional coordinate system, and its area integral contribution value is expressed as a weighted sum of the coordinates of the three vertices, wherein the weighting factor includes a complex exponential term related to the wave number and the incident direction.

[0021] Furthermore, the method for calculating the area integral contribution value of the quadrilateral element is as follows: the quadrilateral element is transformed into a two-dimensional coordinate system, and its area integral contribution value is expressed as a weighted sum of the coordinates of the four vertices, wherein the weighting factor includes a complex exponential term related to the wave number and the incident direction.

[0022] The computer device of the present invention includes one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs, when executed by the processors, implement the steps of the fast underwater target acoustic scattering prediction method based on NURBS hybrid grid and Kirchhoff approximation.

[0023] The present invention discloses a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the steps of a rapid underwater target acoustic scattering prediction method based on NURBS hybrid grid and Kirchhoff approximation.

[0024] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0025] (1) Starting from the NURBS model based on CAD standards, this invention automatically generates a mixed mesh of triangles and quadrilaterals by inserting parametric nodes. The mesh generation process is completed by the self-developed algorithm proposed in this invention, realizing the integration of the target geometric model and the mesh model, avoiding the cumbersome process of relying on commercial software for independent mesh generation in the traditional way.

[0026] (2) The hybrid mesh of the present invention can not only ensure the accuracy of most areas of the surface, but also properly handle singular points, and can handle engineering targets with complex surfaces.

[0027] (3) By adjusting the number of nodes inserted, the number of grids can be quickly changed, which facilitates the study of grid convergence. This method has controllable computational accuracy and good convergence.

[0028] (4) The present invention uses the plate element method to transform the integral calculation of the scattered sound field on the target surface into algebraic operations on triangular and quadrilateral elements, which significantly improves the calculation efficiency compared with the traditional Gaussian integral method. Attached Figure Description

[0029] Figure 1 This is a flowchart of the method described in this invention.

[0030] Figure 2 This is a schematic diagram of the hybrid mesh on a 1 / 8 spherical surface according to the present invention.

[0031] Figure 3 This is a schematic diagram of the rigid sphere NURBS model of the present invention.

[0032] Figure 4 This is a comparison chart of the predicted and analyzed rigid sphere target strength of the present invention. Detailed Implementation

[0033] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0034] like Figure 1 As shown, this embodiment provides a fast prediction method for underwater target acoustic scattering based on NURBS hybrid grids and Kirchhoff approximation, including:

[0035] (1) Establish the geometric model of the underwater target using NURBS parameters;

[0036] This embodiment considers the scattering sound field characteristics of a rigid sphere with a radius of a = 1m. Since the rigid sphere has a regular shape, the integral I can be directly solved to obtain the Kirchhoff approximation analytical solution, as follows:

[0037]

[0038] Where k is the wave number.

[0039] To verify the reliability of the calculation results, the root mean square error (L) is taken. 2 Norm)

[0040]

[0041] Where, N f The number of frequency points.

[0042] The sphere is accurately constructed using NURBS spline functions. The specific expressions for the spline functions and the target geometry are as follows:

[0043]

[0044]

[0045] Where, N i,p (ξ) represents the p-order univariate NURBS basis function in the ξ direction, M j,q (η) represents the q-order univariate NURBS basis function in the η direction. B is a bivariate NURBS basis function. i,jHere, S represents the NURBS control point, and S represents the target geometric surface. Control point B i,j The corresponding weights, m and n, represent the number of control points in the ξ and η directions, respectively.

[0046] (2) Through the node insertion algorithm, a parameterized mesh is generated for the geometric model, the overlapping vertices in the cells caused by the overlap of control points are identified and merged, the cells containing overlapping vertices are corrected to triangular cells, and a hybrid mesh containing triangular cells and quadrilateral cells is generated.

[0047] Specifically, the node insertion algorithm achieves refinement by inserting new nodes into the original node vector. During this process, both the number of node intervals and the number of control points increase. Taking a one-dimensional curve as an example, the new nodes... Insert into a given node vector The generation of a new node vector can be written as The new spline basis functions can be obtained from the new node vectors and new control points. It can be from the original control point Linear interpolation yields:

[0048]

[0049]

[0050] Node insertion on a surface can be achieved by applying this algorithm to each row or column of control points. Taking a 1 / 8 sphere as an example, the initial surface is defined by only one NURBS element and nine control points. This is accomplished by uniformly inserting several new nodes within each node interval of the original node vector. The refined mesh is obtained, where positive integers s and t are the row and column indices, respectively, and their values ​​range from... , s n and t n This represents the number of new nodes. For example, inserting 5 nodes will generate 6 × 6 = 36 parameterized units, such as... Figure 2 The images show a 1 / 8 spherical model and a 1 / 8 spherical mesh model, respectively. At the corner point (0, 0, 0), elements with overlapping control points are treated as triangular elements, while the rest are quadrilateral elements. The number of meshes in the hybrid mesh is determined by the number of nodes s in the inserted node interval. n and t n Precise control.

[0051] For a complete sphere, the original NURBS model constructed using node vectors E=[0, 0, 0, 0.25, 0.25, 0.5, 0.5, 0.75, 0.75, 1, 1, 1] and H=[0, 0, 0, 0.5, 0.5, 1, 1, 1] and 45 control points is as follows: Figure 3 As shown, Figure 3 These are the initial geometric model of a rigid sphere and the spherical mesh model, respectively. The four node intervals determined by vector E are (0, 0.25), (0.25, 0.5), (0.5, 0.75), and (0.75, 1); the two node intervals determined by vector H are (0, 0.5) and (0.5, 1). Therefore, the initial model contains 4 × 2 NURBS elements. After inserting 9 new nodes in each node interval, 40 × 20 = 800 parametric elements are obtained, including 2 × 40 = 80 triangular elements and 40 × (20 - 2) = 720 quadrilateral elements, as shown below. Figure 3 As shown, the triangular elements are mainly concentrated around the points (-1, 0, 0) and (1, 0, 0). When the number of new nodes inserted in each node interval is equal, 2n × n parameterized elements are generated, and the resulting mesh will contain 4n triangular elements and 2n × (n - 2) quadrilateral elements.

[0052] (3) Calculate the normal vector of each element on the target surface according to the direction of the incident wave, determine whether the element is located in the area illuminated by the sound wave, and record the illuminated triangular and quadrilateral elements to form an effective integration area.

[0053] Specifically, given the direction of the incident wave, the surface elements of the underwater target are traversed; it is determined whether an element is illuminated, and the illuminated triangular and quadrilateral elements are recorded, forming the effective integration region for calculating the scattered sound field. The specific steps are: first, calculate the outward normal vector n of the discrete element, and then find the unit vector of the line connecting the transmitting transducer, the receiving hydrophone, and the element center, denoted as R. T With R R Then calculate the normal vector n and the unit vector R. T R R If the included angles are both acute, it means that the unit is illuminated.

[0054] (4) Based on the Kirchhoff high-frequency approximation, construct the surface integral expression of the scattering acoustic potential function of a rigid target under far-field conditions when the transmitter and receiver are combined;

[0055] From the Kirchhoff high-frequency approximation, the Helmholtz integral formula satisfied by the scattered acoustic potential function of a rigid target when the transmitter and receiver are combined can be obtained as follows:

[0056]

[0057] In the formula, k is the wave number, A is an arbitrary amplitude, the integral surface S0 is the geometric bright region surface of the scatterer, r is the distance from the surface element dS to the transducer M, r is the incident sound ray, and θ is the angle between r and the unit normal vector n of the surface element.

[0058] Under far-field conditions, the influence of the acoustic path difference between the center of the surface element and the transmitting transducer and receiving hydrophone on the phase is mainly considered. In the above formula, the exponent of the integrand is taken as... r0 is the distance from transducer M to the reference point, ∆r is the sound path difference, and the denominator of the formula is taken as... , can be obtained

[0059]

[0060] If we consider the sound ray r and r0 in the far field to be parallel, the sound path difference is approximately: , where r s Let dS be the vector from the surface element dS to the reference point. The integral in this equation can be expressed as:

[0061] .

[0062] (5) Using the plate element method, the area integral expression is transformed into algebraic operations of vertex coordinates for each triangular and quadrilateral unit in the effective integration area, and the scattering contribution value of each unit is calculated.

[0063] Specifically, the plate element method is used to quickly calculate the surface integral, transforming the integral operation of the scattered sound field into an algebraic operation. For each triangular or quadrilateral planar element within the illuminated region, it is transformed to a two-dimensional coordinate system, and the numerical integral is solved in the new coordinate system. This step transforms the numerical integration problem into a simple complex exponential summation, reducing the computational load.

[0064] The surface integral on the triangle I i for

[0065]

[0066] The area integral of the quadrilateral I j for

[0067]

[0068]

[0069] Among them, (x) n y n Let be the coordinates of the vertices of the triangle or quadrilateral, and the coordinate transformation relationship is: ,

[0070] , .

[0071] (6) Traverse all effective integration region cells, superimpose the scattering contribution values ​​of each cell to obtain the total scattering field of the target, and calculate the target intensity.

[0072] Specifically, iterate through all illuminated area cells and calculate the contribution I of each cell. j Or I j By superimposing and traversing all illuminated area cells, the total scattered field φ is obtained. s The incident wave potential function at the target location. Given the definition of target intensity, the target intensity can be obtained as follows:

[0073]

[0074] The calculation frequency band is f = 2kHz~10kHz, with a step size of 50Hz. Table 1 shows the L intensity of the spherical target under different grids. 2 Norm.

[0075] Table 1:

[0076] Grid number Number of triangular units Number of quadrilateral units <![CDATA[Maximum grid size h max (m)]]> <![CDATA[L 2 Norm 1 240 6960 0.0741 0.4115 2 320 12480 0.0556 0.2396 3 400 19600 0.0445 0.1527 4 480 28320 0.0371 0.1077 5 560 38640 0.0318 0.0795 6 640 50560 0.0278 0.0606 7 720 64080 0.0247 0.0494 8 800 79200 0.0225 0.0410

[0077] It can be seen that as the number of grids increases, L 2 The norm gradually decreases, such as Figure 4 The figure shows a comparison between the calculation results of grid 6 and the Kirchhoff approximate analytical solution. It can be seen that the calculation results of the method of the present invention are in good agreement with the Kirchhoff approximate analytical solution.

Claims

1. A rapid prediction method for underwater target acoustic scattering based on NURBS hybrid grid and Kirchhoff approximation, characterized in that, include: A geometric model of the underwater target was established using NURBS parameters; A parameterized mesh is generated for the geometric model using a node insertion algorithm. Overlapping vertices in the cells caused by overlapping control points are identified and merged. Cells containing overlapping vertices are corrected to triangular cells, generating a hybrid mesh containing triangular and quadrilateral cells. Based on the direction of the incident wave, calculate the normal vector of each element on the target surface, determine whether the element is located in the area illuminated by the sound wave, and record the illuminated triangular and quadrilateral elements to form the effective integration region. Based on the Kirchhoff high-frequency approximation, a surface integral expression for the scattered acoustic potential function of a rigid target under far-field conditions with both transmitter and receiver in place is constructed. Using the plate element method, the area integral expression is transformed into algebraic operations of vertex coordinates for each triangular and quadrilateral unit within the effective integration region, and the scattering contribution value of each unit is calculated. By traversing all effective integration region cells and superimposing the scattering contribution values ​​of each cell, the total scattering field of the target is obtained, and the target intensity is calculated.

2. The rapid prediction method for underwater target acoustic scattering according to claim 1, characterized in that, The node insertion algorithm refines the parameter space by uniformly inserting new nodes into the original node vector of the NURBS model. The new control points are obtained by linear interpolation of the original control points. The number of triangular and quadrilateral elements in the mesh is controlled by the number of newly inserted nodes.

3. The rapid prediction method for underwater target acoustic scattering according to claim 1, characterized in that, The determination of whether the unit is located in the acoustic illumination area is specifically made by: calculating the outer normal vector of the unit, and the unit direction vectors of the lines connecting the transmitting transducer and the receiving hydrophone to the center of the unit; if the angle between the outer normal vector and the two unit direction vectors is an acute angle, then the unit is determined to be illuminated.

4. The rapid prediction method for underwater target acoustic scattering according to claim 1, characterized in that, The area integral under far-field conditions is expressed as follows: the scattered acoustic potential function is proportional to the area integral of the product of the cosine of the angle between the incident wave direction and the surface element normal vector on the illuminated surface S0 and a complex exponential phase factor related to the vector from the surface element to the reference point.

5. The rapid prediction method for underwater target acoustic scattering according to claim 1, characterized in that, The surface integral expression of the scattered acoustic potential function is: In the formula, k Wave number, integral surface S 0 represents the geometric bright region surface of the scatterer. r For surface element d S To transceiver M distance, r For incident sound rays, θ for r With the unit normal vector of the surface element n The included angle.

6. The rapid prediction method for underwater target acoustic scattering according to claim 1, characterized in that, In the hybrid mesh, quadrilateral elements are used to discretize regular curved surface regions of the target surface, while triangular elements are used to handle singular points or overlapping control points on the surface.

7. The rapid prediction method for underwater target acoustic scattering according to claim 1, characterized in that, The method for calculating the surface integral contribution value of the triangular element is as follows: the triangular element is transformed into a two-dimensional coordinate system, and its surface integral contribution value is expressed as a weighted sum of the coordinates of the three vertices, wherein the weighting factor includes a complex exponential term related to the wave number and the incident direction.

8. The rapid prediction method for underwater target acoustic scattering according to claim 1, characterized in that, The method for calculating the area integral contribution value of the quadrilateral element is as follows: the quadrilateral element is transformed into a two-dimensional coordinate system, and its area integral contribution value is expressed as a weighted sum of the coordinates of the four vertices, wherein the weighting factor includes a complex exponential term related to the wave number and the incident direction.

9. A computer device, characterized in that, It includes one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs, when executed by the processors, implement the steps of a fast underwater target acoustic scattering prediction method based on NURBS hybrid grid and Kirchhoff approximation as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of a fast underwater target acoustic scattering prediction method based on NURBS hybrid grid and Kirchhoff approximation as described in any one of claims 1-8.

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