Finite box rectangular horn shape optimization method and system based on hybrid model

Abstract

The invention discloses a finite box rectangular horn shape optimization method and system based on a hybrid model, and the method comprises the steps: carrying out the geometric discretization of a rectangular horn in the axial direction into rectangular pipeline sections which are connected end to end, and determining a to-be-optimized design variable; pre-calculating a radiation impedance matrix and a far-field directivity primary function vector under a finite box body by adopting an external radiation model; calculating an inlet impedance matrix and a speed transmission matrix of each rectangular pipeline section on the basis of a radiation impedance matrix and a current design variable by adopting a sound transmission model in the horn, obtaining a mouth output speed vector, and solving an acoustic performance index in combination with a far-field directivity primary function vector; and constructing a comprehensive objective function, and solving to obtain a finite box rectangular horn shape optimization scheme. According to the method, the edge diffraction and sound reflection effect in a limited box environment can be accurately simulated, and the radiation efficiency optimization and directivity control of the broadband of the rectangular horn are realized while the calculation cost is remarkably reduced.

Description

Technical Field

[0001] This invention belongs to the field of acoustic device design and optimization technology, specifically relating to a method and system for optimizing the shape of a finite box rectangular horn based on a hybrid model. Background Technology

[0002] Rectangular horns, as core electroacoustic components in modern professional sound reinforcement systems, are widely used due to their unique high radiation efficiency and controllable asymmetric directivity. Unlike axially oriented horns, rectangular horns can provide distinctly different directivity characteristics in both the horizontal and vertical planes, allowing for more precise control of sound wave coverage to match audience areas of different shapes, such as long and narrow or wide, thereby effectively reducing the reflection of ineffective sound energy and improving sound reinforcement clarity.

[0003] In early horn designs, the primary goal was to improve radiation efficiency through impedance matching. However, with the widespread adoption of high-power amplifier technology, the focus of contemporary electroacoustic engineering has shifted to the precise control of wideband directivity, i.e., the pursuit of "constant directivity" to ensure that the sound quality at off-axis listening positions remains consistent with the axial direction. To meet this stringent design requirement, empirical formulas or simple trial-and-error methods are no longer sufficient; high-precision numerical simulation tools are essential for prediction and design.

[0004] Currently, numerical simulations of horn sound fields mainly employ the finite element method (FEM) and the boundary element method (BEM). While these methods can provide high-precision sound field solutions for arbitrarily complex geometries, they face significant challenges when applied to shape optimization design. Shape optimization typically requires hundreds or even thousands of iterations, and the FEM or BEM methods necessitate re-meshing the updated geometric model and solving large-scale linear equations in each iteration. This enormous computational overhead makes them extremely inefficient in practical engineering optimization, even hindering the completion of design tasks within a reasonable timeframe.

[0005] To address computational efficiency issues, the pattern matching method, also known as the discrete multimodal method, has been introduced into horn shape optimization. This method discretizes the continuously changing horn profile into a series of rectangular pipe segments with uniform cross-sections. The sound field is described using the analytical solutions (i.e., characteristic mode expansion) of the Helmholtz equations within each pipe segment, and a velocity transmission matrix is ​​established through the continuity conditions at abrupt changes in the cross-section. Because the pattern matching method avoids cumbersome volume mesh generation and involves a matrix dimension much smaller than that of the finite element method (FE) and boundary element method (BEM), its computational speed is typically several orders of magnitude faster than the FE and BEM, making it considered an ideal tool for horn shape optimization.

[0006] However, existing horn optimization methods based on pattern matching have a key physical drawback: they typically assume the horn is mounted on an ideal, infinitely large baffle. This assumption stems from the fact that the radiation impedance of a rectangular piston under an infinitely large baffle has an analytical solution or a well-established semi-analytical calculation method, which can be directly used as the terminal boundary conditions required for pattern matching calculations. However, in practical acoustic engineering applications, horns are almost always mounted on enclosures with finite dimensions.

[0007] From an acoustic physics perspective, the presence of a finite enclosure introduces complex edge diffraction and surface reflection effects. These secondary sound waves interfere with the direct radiated sound waves at the horn mouth, significantly altering the acoustic radiation impedance at the mouth. This leads to a significant difference between the actual far-field directivity and the predictions under the infinite baffle model, especially in the mid-to-low frequency range where the wavelength is comparable to the enclosure size. Although some studies have attempted to introduce perfectly matched layers or combine them with the boundary element method to handle complex boundary conditions in mode-matching analysis, these works are mainly limited to the analysis of existing structures and have not yet truly integrated hybrid models capable of handling finite enclosure boundary conditions into an automated shape optimization process.

[0008] Therefore, existing technologies lack a rectangular horn shape optimization method that can maintain the high computational efficiency of the pattern matching method while accurately considering the influence of finite enclosure boundaries on sound radiation. Overcoming the design errors caused by the infinite baffle assumption and achieving precise control of the wideband directivity of rectangular horns under realistic physical boundary conditions is a pressing technical challenge in the field of electroacoustic design. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this invention provides a method and system for optimizing the shape of a finite-box rectangular horn based on a hybrid model. The method uses a hybrid model to model the sound field and optimize the shape of a finite-box rectangular horn. By combining the boundary element method with the pattern matching method, it overcomes the limitations of the traditional infinite baffle assumption, accurately simulating edge diffraction and sound reflection effects in a finite-box environment. This significantly reduces computational costs while achieving broadband radiation efficiency optimization and directivity control of the rectangular horn.

[0010] The present invention adopts the following technical solution.

[0011] The first aspect of this invention proposes a method for optimizing the shape of a finite-box rectangular horn based on a hybrid model, wherein the hybrid model includes an external radiation model and an internal sound transmission model of the horn, and the method includes: The rectangular horn is geometrically discretized along the axial direction into multiple rectangular pipe segments connected end to end, and the geometric parameters of the cross-section of each rectangular pipe segment are defined to determine the design variables to be optimized. An external radiation model is used to pre-calculate the radiation impedance matrix and far-field directivity basis function vector under a finite enclosure. An internal acoustic transmission model is used to calculate the inlet impedance matrix and velocity transmission matrix of each rectangular pipe section based on the radiation impedance matrix and the current design variables. The output velocity vector at the inlet is obtained by cascading the entire system. The acoustic performance index is then solved by combining the far-field directivity basis function vector. Based on the acoustic performance indicators, a comprehensive objective function containing multi-physics constraints is constructed. By solving the comprehensive objective function, an optimization scheme for the shape of a finite box-shaped rectangular horn is obtained.

[0012] Preferably, the step of geometrically discretizing the rectangular horn along the axial direction into multiple connected rectangular pipe segments and defining the geometric parameters of the cross-section of each rectangular pipe segment to determine the design variables to be optimized includes: Establish a three-dimensional rectangular coordinate system, and define the central axis of the sound wave propagation of the rectangular horn as... The axis will be perpendicular to The horizontal direction of the cross section of the shaft is defined as The axis will be perpendicular to The cross-section of the shaft is defined perpendicular to the direction of the cross-section. axis; The rectangular horn edge The axial direction is discretized in physical space as A rectangular pipe segment connected end to end, in which It is a positive integer greater than 2; For the A rectangular pipe segment, its cross-section defined in... The internal width in the axial direction is Define its cross-section in The internal height in the axial direction is , take the second to the third The rectangular pipe segment corresponding to , As design variables to be optimized, among which and With index The changes together constitute the geometric outline shape of the rectangular horn.

[0013] Preferably, the step of moving the rectangular horn along... The axial direction is discretized in physical space as A series of rectangular pipe segments connected end to end, including: Set the first rectangular pipe segment of the corresponding horn throat and the first rectangular pipe segment of the corresponding horn mouth. The axial length of each rectangular pipe segment is The second to the third in the middle The axial length of each rectangular pipe segment is , This is the total axial length of the rectangular horn.

[0014] Preferably, the step of pre-calculating the radiation impedance matrix and far-field directivity basis function vector under a finite enclosure using an external radiation model includes: For the physical boundary conditions of a rectangular horn mounted on a finite enclosure, the plane of the horn opening and the outer surface of the finite enclosure are meshed. Based on this, different orders of unit normalized modal velocity excitations are applied to the plane of the horn opening of the rectangular horn. The sound field under the corresponding excitation is solved using the boundary element method. The radiation impedance matrix characterizing the reaction of the finite enclosure to sound radiation and the far-field directivity basis function vector characterizing the independent radiation characteristics of each mode are calculated.

[0015] Preferably, the method of employing an internal sound transmission model for the horn, based on the radiation impedance matrix, calculates the inlet impedance matrix and velocity transmission matrix of each rectangular pipe segment based on the current design variables, and obtains the output velocity vector at the inlet through system cascading, including: The radiation impedance matrix is ​​used as the terminal boundary condition at the rectangular horn inlet; based on the abrupt change in cross-sectional dimensions at the interface of adjacent rectangular pipe segments corresponding to the current design variables, the inlet impedance matrix of each rectangular pipe segment is calculated, and then the corresponding velocity transmission matrix is ​​calculated. By cascading the velocity transmission matrices of all rectangular pipe segments, the output velocity vector at the inlet is obtained.

[0016] Preferably, the process of constructing the sound transmission model inside the horn includes: For any rectangular pipe segment, the sound pressure field and axial particle velocity field inside it are expanded into a superposition of characteristic modes. A normalized characteristic function, a propagation matrix inside the pipe, a characteristic impedance, and a mode coupling matrix are established. The mode coupling matrix includes a coupling matrix for describing sound pressure transmission and a coupling matrix for describing velocity transmission. Based on this, the mode matching method is used to derive the inlet impedance matrix and velocity transmission matrix of each rectangular pipe segment from the mouth to the throat segment by segment, corresponding to the abrupt changes in cross-sectional dimensions at the interface of adjacent rectangular pipe segments.

[0017] Preferably, the abrupt changes in cross-sectional dimensions at the interface of adjacent rectangular pipe segments include: at the interface of adjacent rectangular pipe segments, the cross-section expands in both horizontal and vertical directions, contracts in both horizontal and vertical directions, expands horizontally and contracts vertically, and contracts horizontally and expands vertically.

[0018] Preferably, the acoustic performance indicators include a plane wave reflection coefficient for quantifying the transmission loss of sound energy from the drive end to the horn mouth and a directivity diagram for describing the distribution of sound wave radiation intensity in three-dimensional space.

[0019] Preferably, the process of solving the plane wave reflection coefficient includes: The inlet impedance matrix of the first discrete pipe section at the throat of the horn is used as the throat impedance matrix. The reflection matrix is ​​derived using the throat impedance matrix and the characteristic admittance matrix of the throat input end. The plane wave reflection coefficient is obtained from the elements of the first row and first column of the reflection matrix.

[0020] Preferably, the process of solving the directional map includes: The far-field directivity of the rectangular horn is calculated based on the output velocity vector at the mouth and the far-field directivity basis function vector, and then the directivity map is obtained through normalization.

[0021] Preferably, the step of constructing a comprehensive objective function containing multiphysics constraints based on the acoustic performance indicators includes: Based on the acoustic performance indicators, the radiation efficiency target, shape smoothness target, constant directivity target, and coverage angle control target are obtained and then weighted and summed to obtain the comprehensive objective function.

[0022] Preferably, the radiation efficiency target is obtained based on the mean square value of the plane wave reflection coefficient within a wide bandwidth; The shape smoothness target term is obtained based on the second difference norm of the design variable vector; The constant directivity target term is obtained based on the variance of the full-band directivity map and the sound pressure level error at the preset coverage boundary angle; The coverage angle control target is obtained based on the mean square error between the actual sound pressure level attenuation value and the target attenuation value at the coverage boundary angle.

[0023] Preferably, the step of solving the comprehensive objective function to obtain the finite box-shaped rectangular horn shape optimization scheme includes: Calculate the analytical gradient of the comprehensive objective function with respect to the design variables, and construct the analytical Jacobian matrix; The analytical Jacobian matrix is ​​subjected to nonlinear least squares optimization to determine the update direction and step size of the design variables. The design variables are iteratively updated until the comprehensive objective function value satisfies the convergence condition. The optimal design variable vector is output to fit and generate the final rectangular horn three-dimensional geometric model.

[0024] A second aspect of this invention proposes a finite box rectangular horn shape optimization system based on a hybrid model, comprising: The parametric discretization modeling module is used to geometrically discretize the rectangular horn along the axial direction into multiple rectangular pipe segments connected end to end, define the geometric parameters of the cross-section of each rectangular pipe segment, and determine the design variables to be optimized. The hybrid acoustic calculation module is used to pre-calculate the radiation impedance matrix and far-field directivity basis function vector under a finite enclosure using an external radiation model; and to calculate the inlet impedance matrix and velocity transmission matrix of each rectangular pipe segment based on the radiation impedance matrix and the current design variables using an internal acoustic transmission model of the horn, and to obtain the output velocity vector of the inlet by cascading the entire system, so as to solve the acoustic performance index in combination with the far-field directivity basis function vector. The multiphysics optimization module is used to construct a comprehensive objective function containing multiphysics constraints based on the acoustic performance indicators, solve the comprehensive objective function, and obtain an optimization scheme for the shape of a finite box-shaped rectangular horn.

[0025] A third aspect of the present invention provides a terminal, including a processor and a storage medium; the storage medium is used to store instructions; the processor is used to perform operations according to the instructions to execute the steps of the method.

[0026] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.

[0027] Compared with the prior art, the beneficial effects of the present invention include at least the following: 1. This invention constructs a hybrid model and uses the boundary element method to accurately calculate the radiation impedance matrix in a finite enclosure environment. The modal coupling information contained in this matrix is ​​then incorporated into the velocity transmission matrix calculation using an internal mode-matching method. This overcomes the limitations of the infinite barrier assumption in traditional mode-matching methods, significantly improving prediction accuracy in real-world applications and eliminating the systematic errors introduced by the infinite barrier assumption. Experimental results show that the horn optimized using this invention exhibits a high degree of agreement between simulated and measured directivity patterns over a wide frequency band. This effectively solves the technical problem of performance degradation after packaging and the need for repeated prototyping and modification of products designed using traditional methods.

[0028] 2. This invention takes into account that during the shape optimization process, only the internal contour of the horn changes, while the external box size and mouth boundary remain unchanged. The boundary element method is used to calculate the external radiation impedance only once during the initialization stage. In hundreds or thousands of iterations, the internal velocity transmission matrix is ​​updated quickly using the analytical formula of the pattern matching method, which has a very small computational load. This step-by-step calculation strategy of one-time boundary element method pre-calculation and multiple pattern matching method iterations maintains the same computational accuracy as the full boundary element method while improving the computational efficiency by several orders of magnitude. This makes it possible to complete complex broadband, multi-objective shape optimization on ordinary computers, and cleverly solves the contradiction between computational accuracy and computational efficiency in the full numerical simulation method.

[0029] 3. This invention constructs a comprehensive objective function that includes sub-items of radiation efficiency, coverage angle control, constant directivity, and shape smoothness. This enables the design of horns that possess both high energy transmission efficiency and precise fit to specific audience coverage areas, resolving the technical contradiction in traditional designs where efficiency and directivity often come at opposite ends. More importantly, this invention derives and applies the analytical gradient of the objective function with respect to design variables. Utilizing an optimization algorithm driven by the analytical Jacobian matrix, it not only achieves higher numerical stability but also faster convergence, accurately capturing the impact of minute changes in design variables on sound field performance. This allows for the search for optimal geometric configurations that are difficult to discover using traditional methods, realizing multi-objective collaborative optimization based on analytical gradients and overcoming the limitations and algorithmic instability of traditional single-objective designs. Attached Figure Description

[0030] Figure 1 This is a traditional simulation diagram of the sound field of a rectangular horn.

[0031] Figure 2 This is a schematic diagram of a finite-box rectangular horn sound field modeling method based on a hybrid model.

[0032] Figure 3 This is a flowchart of a finite box rectangular horn sound field modeling method based on a hybrid model.

[0033] Figure 4 This is a flowchart of a finite box rectangular horn shape optimization method based on a hybrid model.

[0034] Figure 5 This is a structural block diagram of a finite box rectangular horn shape optimization system based on a hybrid model.

[0035] Figure 6 This is a flowchart of a finite-box rectangular horn sound field modeling method based on a hybrid model. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. The embodiments described in this application are merely some embodiments of this invention, and not all embodiments. Based on the spirit of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of this invention.

[0037] Embodiment 1 of this invention provides a method for optimizing the shape of a finite-box rectangular horn based on a hybrid model. Using finite-box rectangular horn sound field modeling as the core computational engine, a multi-physics objective function incorporating acoustic performance indicators and geometric constraints is established. A nonlinear optimization algorithm is then used to automatically adjust the internal geometric contour of the rectangular horn, thereby designing a horn structure that maintains broadband constant directivity and high radiation efficiency within a finite-size box (hereinafter referred to as a finite box). This solves the problem in existing technologies where neglecting edge diffraction and secondary reflection effects within a finite box leads to insufficient accuracy in horn sound field simulation. Figures 1-6 As shown, the hybrid model includes an external radiation model and a horn internal sound transmission model, and the method includes: Step 1: Discretize the rectangular horn along the axial direction into multiple rectangular pipe segments connected end to end, define the geometric parameters of the cross-section of each rectangular pipe segment, and determine the design variables to be optimized; More preferably, a discrete geometric model of the rectangular horn is established, and the rectangular horn to be optimized is discretized along the axial direction into multiple rectangular pipe segments with different widths and heights. The cross-sectional dimensions of each segment are defined as design variables to be optimized, including: 1) Establish a three-dimensional rectangular coordinate system, and define the central axis of the sound wave propagation of the rectangular horn as... The axis will be perpendicular to The horizontal direction of the cross section of the shaft is defined as The axis will be perpendicular to The cross-section of the shaft is defined perpendicular to the direction of the cross-section. axis; 2) Move the rectangular horn along... The axial direction is discretized in physical space as A rectangular pipe segment connected end to end, in which It is a positive integer greater than 2; 3) For the first A rectangular pipe segment, its cross-section defined in... The internal width in the axial direction is Define its cross-section in The internal height in the axial direction is , and With index The changes together constitute the geometric outline shape of the rectangular horn.

[0038] Specifically, this embodiment couples the mode matching method describing internal sound transmission with the boundary element method describing external sound radiation to construct a hybrid acoustic model that can accurately capture the details of internal high-order mode transmission while fully reflecting the influence of external physical boundaries. Modeling the sound field of a finite-box rectangular horn based on this hybrid model first requires constructing a discrete geometric model of the rectangular horn.

[0039] To facilitate numerical calculations by the computer, the continuously changing rectangular horn geometry must first be transformed into a discrete waveguide model of the pipe segment, as follows: (1) Establish coordinate system and discretize axis.

[0040] First, establish a three-dimensional Cartesian coordinate system. The central axis of the sound wave propagation of the rectangular horn is defined as... The axis will be perpendicular to The horizontal direction of the cross section of the shaft is defined as The axis will be perpendicular to The cross-section of the shaft is defined perpendicular to the direction of the cross-section. axis.

[0041] Next, move the rectangular horn along... The axial direction is discretized in physical space as A rectangular pipe segment connected end to end, in which It is a positive integer greater than 2. Specifically, the total axial length of the rectangular horn is set to... (Unit: meters).

[0042] To improve simulation accuracy, the first rectangular pipe segment (corresponding to the horn throat) and the second rectangular pipe segment were defined. The axial length of each rectangular pipe segment (corresponding to the horn opening) is... ; Set the second to the middle The axial length of each rectangular pipe segment is .

[0043] Wherein, the length of the intermediate pipe section The calculation formula is:

[0044] (2) Define the cross-sectional geometric parameters.

[0045] For the A rectangular pipe segment (of which) Values ​​range from 1 to (an integer), defining its cross-section in The internal width in the axial direction is Define its cross-section in The internal height in the axial direction is Accordingly, the first Cross-sectional area of ​​a rectangular pipe segment The calculation is as follows:

[0046] It should be noted that the width and height With index The changes in these parameters collectively constitute the geometric outline of the rectangular horn. In the optimization process of this embodiment, these parameters (especially those of the middle section) will be used as design variables to be optimized.

[0047] Before performing shape optimization, it is essential to clearly define the design space to be optimized and the geometric parameters to be optimized.

[0048] To achieve flexible control over the shape of the rectangular horn, this invention uses the cross-sectional dimensions of each discrete pipe segment inside the horn as mathematical optimization variables. Recalling the discrete model described above, the rectangular horn is divided into... There are several pipe sections. The size of the first pipe section (throat) is typically determined by the outlet size of the selected compression drive unit and must match the drive outlet to reduce reflections; therefore, it remains constant during optimization. The dimensions of each pipe section (orifice) are typically limited by the panel size of the speaker enclosure or industrial design requirements, and are also considered fixed boundary constraints during the optimization process.

[0049] Therefore, in this embodiment, the second to the third position located in the middle are selected. The cross-sectional dimensions of each rectangular pipe segment are used as variable parameters. Specifically, a width design variable vector is defined. for: in, Indicates the first The pipeline section is in Internal width along the axis. Define the height design variable vector. for: in, Indicates the first The pipeline section is in The internal height along the axial direction. Combining the two vectors above constitutes the system's total design variable vector. : The vector The dimension is Each Each combination of values ​​uniquely corresponds to a geometric shape of a rectangular horn.

[0050] Setting the initial geometry. To initiate the iterative search process, the total design variable vector needs to be defined. An initial value is set. In a preferred embodiment, a classic exponential cylindrical profile is used as the initial guessed shape. Specifically, the initial width and initial height are set according to the following formula:

[0051] in, For throat dimensions; This is the development constant calculated from the opening dimensions; For the first The axial coordinates of the segment. Setting a reasonable initial shape helps the optimization algorithm converge to the global optimum or a high-quality local optimum more quickly.

[0052] Step 2: Pre-calculate the radiation impedance matrix under the finite enclosure using an external radiation model. and far-field directional basis function vector Using the internal sound transmission model of the horn, in the radiation impedance matrix Based on this, the inlet impedance matrix of each rectangular pipe segment is calculated using the current design variables. and speed transmission matrix The output velocity vector at the mouth is obtained by cascading the entire system. In order to combine the far-field directional basis function vector Solve for the acoustic performance indicators; In existing shape optimization techniques, if high accuracy is desired, the finite element method or boundary element method is typically used for full-field simulation. However, this requires re-meshing the 3D volume mesh and solving a large-scale linear equation system with each shape iteration update, resulting in extremely high computational costs and optimization cycles lasting several days or even weeks. If high efficiency is desired, analytical methods are used, but this often comes at the cost of sacrificing geometric adaptability or boundary accuracy. This invention proposes a step-by-step computational strategy combining a single boundary element method pre-calculation with multiple pattern-matching iterations. Since only the internal contour of the horn changes during the shape optimization process, while the external box dimensions and mouth boundary remain unchanged, this invention utilizes the boundary element method to calculate the time-consuming external radiation impedance only once during the initialization phase. In hundreds or thousands of iterations, the internal velocity transmission matrix is ​​rapidly updated using the minimally computational pattern-matching analytical formula. This strategy maintains computational accuracy comparable to the full boundary element method while improving computational efficiency by several orders of magnitude, making it possible to perform complex broadband, multi-objective shape optimization on ordinary computers. Specifically: (1) The radiation impedance matrix and far-field directivity basis function vector under the finite enclosure are pre-calculated using an external radiation model, including: To address the physical boundary conditions of a rectangular horn mounted on a finite box, a mesh is created for the plane of the rectangular horn's opening and the outer surface of the finite box. Different orders of unit normalized modal velocity excitations are applied to the horn mouth plane of a rectangular horn. The surface acoustic pressure response distribution generated on the horn mouth plane under the corresponding excitation is solved using the boundary element method. The surface acoustic pressure response distribution is projected onto each order of characteristic modes to obtain the radiation impedance matrix characterizing the reaction of the finite enclosure to acoustic radiation. In addition, the far-field directivity basis function vector needs to be calculated for subsequent acoustic performance index solving.

[0053] In practice, an external radiation model under a finite enclosure environment is constructed based on the boundary element method. Considering the physical boundary conditions of a rectangular horn mounted on a finite enclosure, meshing is performed on the mouth of the rectangular horn and the outer surface of the finite enclosure. Different orders of unit normalized modal velocity excitation are applied to the mouth of the rectangular horn, and the external sound field is solved using the boundary element method to calculate the radiation impedance matrix characterizing the reaction of the finite enclosure to sound radiation. And the far-field directivity basis function vector characterizing the independent radiation characteristics of each mode. ; Preferably, the radiation impedance matrix The physical meaning and construction method of the matrix are as follows: It is a complex square matrix whose off-diagonal elements characterize the mutual coupling effect of sound energy between different orders of modes at the mouth of the horn due to sound diffraction at the edge of the finite box and sound reflection on the surface of the box. The specific construction method is as follows: Calculate when only the first [unclear] exists at the horn mouth. During the first unit velocity mode, the first generation generated at the mouth The reaction forces of the first sound pressure mode are used to determine the matrix elements. This allows for the precise quantification of the load effect of finite physical boundaries on sound wave radiation.

[0054] In this embodiment, the external radiation model in a finite enclosure environment is constructed as follows: The boundary element method is used to pre-calculate the external sound field characteristics, aiming to obtain a radiation impedance matrix that can accurately characterize the reaction of a finite enclosure to the acoustic radiation at the horn mouth, and a far-field directivity basis function vector that characterizes the independent radiation characteristics of each mode, as follows: 1) Physical boundary modeling and mesh generation: Construct a plane containing a rectangular horn nozzle (i.e., the first) in the computer. The three-dimensional geometric model of the outlet section of a rectangular pipe segment and the outer surface of the finite box on which the horn is installed.

[0055] Subsequently, the surface mesh of the three-dimensional geometric model is generated.

[0056] Specifically, the plane of the horn mouth is divided into multiple planar units, and the outer surface of the box is divided into multiple boundary element units.

[0057] The size of the grid cell should be less than one-sixth of the wavelength corresponding to the highest calculated frequency to ensure calculation accuracy.

[0058] 2) Calculate the radiation impedance matrix : The specific process of solving the acoustic radiation equation using the boundary element method is as follows: First, the boundary conditions of the plane at the horn mouth are set as velocity boundaries, and the outer surface of the box is set as a rigid wall boundary (i.e., the normal velocity is zero).

[0059] Secondly, apply the first... The unit normalized velocity modal excitation is denoted as... The sound pressure response distribution generated on the plane of the horn nozzle under this excitation was calculated using a boundary element solver.

[0060] Finally, the calculated sound pressure response distribution is projected onto the first... On the first characteristic mode, the radiation impedance matrix is ​​obtained. elements in .

[0061] The It is a dimension A complex square matrix whose elements The calculation formula is expressed as follows:

[0062] in, It is the first The sound pressure field (surface sound pressure response distribution) generated on the plane of the horn mouth by the unit velocity mode excitation. It is the first Normalized characteristic function of order; It is the area of ​​the horn mouth.

[0063] The matrix This includes the effects of all external physical environments on sound radiation, such as diffraction at the box edge and reflection from the panel, which constitutes the terminal load conditions for subsequent internal transmission calculations.

[0064] in, and These are the sound pressure mode amplitude vector and output velocity vector at the horn mouth, respectively.

[0065] 3) Calculate the far-field directivity basis function vector .

[0066] (2) Using the internal sound transmission model of the horn, based on the radiation impedance matrix, the inlet impedance (or admittance) matrix and velocity transmission matrix of each rectangular pipe section are calculated according to the current design variables. The output velocity vector at the inlet is obtained by cascading the entire system, including: The radiation impedance matrix As the terminal boundary condition at the rectangular horn mouth; Based on the abrupt change in cross-sectional dimensions at the interface of adjacent rectangular pipe sections, the pattern matching method is used to start from the horn nozzle along... z The inlet impedance matrix of each rectangular pipe segment is calculated by deriving the formula segment by segment in reverse direction from the negative axis toward the throat of the horn. (or entrance admittance matrix) ), speed transmission matrix ; Speed ​​transfer matrix of all rectangular pipe segments By cascading, the output velocity vector at the mouth is obtained. .

[0067] In practical implementation, a sound transmission model inside the horn is constructed based on the pattern matching method; the radiation impedance matrix is ​​then used. As the terminal boundary condition at the rectangular horn opening; based on the abrupt change in cross-sectional dimensions at the interface of adjacent rectangular pipe segments, the pattern matching method is used to start from the horn opening along... z The inlet impedance matrix of each rectangular pipe segment is calculated by deriving the formula segment by segment in reverse direction from the negative axis toward the throat of the horn. (or entrance admittance matrix) ), speed transmission matrix ; speed transfer matrix for all rectangular pipe segments By cascading the horn, the sound transmission relationship from one horn mouth to the other is established, and then the internal sound field distribution of the rectangular horn and the output velocity vector at the mouth are calculated. .

[0068] The construction process of the sound transmission model inside the horn includes: for any rectangular pipe segment, expanding the sound pressure field and axial particle velocity field inside it into a superposition of characteristic modes, and establishing a normalized characteristic function. Pipeline internal propagation matrix With characteristic impedance and a modal coupling matrix, the modal coupling matrix including a coupling matrix for describing sound pressure transmission. and the coupling matrix used to describe velocity transfer Based on this, the pattern matching method is used to derive, segment by segment, from the horn inlet along the negative z-axis towards the horn throat, constructing the inlet impedance matrix and velocity transmission matrix corresponding to the abrupt changes in cross-sectional dimensions at the interface of adjacent rectangular pipe segments. Details are as follows: The construction process of the internal acoustic transmission model specifically includes the modal expansion step: For any i i A rectangular pipe segment, containing the sound pressure field inside. and axial particle velocity field Expanded into a superposition of infinitely many feature modes:

[0069]

[0070] in, Indicates the first i Within the first rectangular pipe segment n The sound pressure coefficient of the first mode; Indicates the first i Within the first rectangular pipe segment n Volume velocity coefficients of the first mode; Indicates the first i Modal sound pressure vector within a rectangular pipe segment; Indicates the first i Modal volume velocity vector within a rectangular pipe segment; The normalized cross-sectional characteristic function is a combination of cosine functions that satisfy the boundary conditions of a rectangular rigid wall. and Normalized horizontal coordinates; This is the modal index, corresponding to the number of modes in the horizontal direction. and vertical mode number The combination of .

[0071] Preferably, the construction process of the internal acoustic transmission model further includes a coupling matrix calculation step: For the adjacent first i The rectangular pipe segment and the first i The modal coupling matrix is ​​calculated at the interface between +1 rectangular pipe segments, and the modal coupling matrix includes a coupling matrix describing the sound pressure transmission. and the coupling matrix used to describe velocity transfer ; The elements of the coupling matrix are obtained by calculating the overlap integral of the characteristic functions of the smaller cross-section pipe and the larger cross-section pipe at the interface. Taking cross-sectional expansion as an example, that is and At that time, matrix elements The calculation formula involves horizontal integral terms. Integral term in the vertical direction The product of these terms, the integral term analytically expresses the intermodal projection relationship of energy across cross sections of different scales.

[0072]

[0073] Preferably, the construction process of the internal sound transmission model further includes a velocity transmission matrix construction step: Construct the first i Speed ​​transmission matrix of a rectangular pipe segment This matrix defines the modal volume velocity vector at the inlet of this segment. Modal volume velocity vector at the next entry point Linear transformation relationship between .

[0074] Take a geometrical mutation case as an example ( , The speed transmission matrix The analytical calculation formula is expressed as follows:

[0075]

[0076] The definitions and meanings of the physical parameters in the formula are as follows: (Load impedance term): indicates the first... The impedance matrix at the inlet of the first rectangular pipe segment, which characterizes the impedance from the first... The acoustic load characteristics of the section pipe inlet looking towards the horn nozzle are calculated by using the radiation impedance matrix at the nozzle. As an initial condition, after the first... Section to the first It is obtained by recursively calculating the segment level by level in reverse; (Characteristic impedance term): Represents the current impedance term. The characteristic impedance matrix of a rectangular pipe segment is a diagonal matrix, with elements on the diagonal... It depends on the density of the air medium. Speed ​​of sound propagation Cross-sectional area of ​​the current pipeline section and the corresponding number Axial wavenumber of first mode This is used to quantify the inherent resistance characteristics of energy transmission in each mode within the pipe; (Propagation phase term): This represents the propagation matrix in cosine form, which is a diagonal matrix containing terms. (in The imaginary unit, (This refers to the length of the pipe section). This represents the propagation matrix in sinusoidal form, which is a diagonal matrix containing terms. ; The propagation matrix in tangent form is a diagonal matrix, with diagonal elements containing terms. The three matrices together describe the phase delay and amplitude modulation effects during sound wave propagation.

[0077] In this embodiment, the internal sound transmission model is constructed as follows: Using pattern matching, and based on acoustic waveguide theory, we accurately describe the propagation behavior of sound waves within each rectangular pipe segment and their coupling behavior at the interface of adjacent pipe segments, as follows: 1) Sound field modal expansion Assume the medium inside the pipe is air, and that the sound wave propagation process is linear and has no viscous loss.

[0078] For the A rectangular pipe segment, with any point inside it... sound pressure at the location and axial particle velocity Expanded into a superposition of infinitely many characteristic modes, the same as in formulas (6) and (7), where, Indicates the first n The sound pressure coefficient of the first mode; Indicates the first Volume velocity coefficients of first-order modes; index It actually represents a pair of non-negative integers. , respectively corresponding direction and The modal order of the direction.

[0079] 2) Define the normalized characteristic function The characteristic function The rigid wall boundary condition of the rectangular pipe must be satisfied, and its specific analytical expression is defined as follows:

[0080] in, , Normalization coefficient Defined as: when hour, ;when hour, This definition guarantees the orthogonality and normality of the characteristic functions, that is...

[0081] 3) Define the propagation matrix and characteristic impedance inside the pipe. To describe the sound wave at a length of... For propagation within a uniform pipe, the following diagonal matrix is ​​defined: Cosine propagation matrix Its diagonal element is ; Sine propagation matrix Its diagonal element is ; Tangent propagation matrix Its diagonal element is .

[0082] At the same time, define the first Characteristic impedance matrix of a pipe segment It is a diagonal matrix with diagonal elements of .

[0083] in, The imaginary unit; air density; Speed ​​of sound; is the free space wavenumber. For the first The axial wavenumber of the first mode is calculated using the following formula:

[0084] If the number inside the square root is negative, then take the complex root with a negative imaginary part, which represents the vanishing wave.

[0085] 4) Define the interface coupling matrix.

[0086] When the sound wave comes from the first The segment spread to the first During this period, due to the abrupt change in cross-sectional dimensions, scattering coupling will occur between modes.

[0087] In this embodiment, the coupling matrix is ​​defined by overlapping integrals.

[0088] First, define a one-dimensional integral function. (See formula (8)), used to describe the ratio of dimensional change in a single direction. Modal projection coefficients at time.

[0089] In particular, when the denominator is zero (i.e. degeneracy occurs), L'Hôpital's rule must be used to obtain the limit value.

[0090] Based on this, two key coupling matrices are defined: Extended Coupling Matrix This is applicable to cases where a small-section mode is projected onto a large-section mode. Its elements... This is the product of the horizontal and vertical integrals:

[0091] Shrinking coupling matrix : Applicable to the case where a large cross-section mode is projected onto a small cross-section mode.

[0092] For clarity, this algorithm explicitly defines the computational components involved. The parameter interchangeability.

[0093]

[0094] In this embodiment, the velocity transmission matrix is ​​calculated under all cross-sectional abrupt changes. and entrance impedance matrix as follows: This is the core calculation step in this embodiment. In order to handle horns of arbitrary shapes, it is necessary to exhaustively enumerate all possible geometric connections between adjacent pipe sections.

[0095] In this embodiment, the abrupt changes in cross-sectional dimensions at the interface of adjacent rectangular pipe segments are specifically divided into four scenarios: bidirectional expansion of the cross-section in both horizontal and vertical directions, bidirectional contraction of the cross-section in both horizontal and vertical directions, horizontal expansion and vertical contraction of the cross-section, and horizontal contraction and vertical expansion of the cross-section. These scenarios are then calculated in detail. Scenario 1: Two-way expansion ( and In this situation, sound waves enter from the narrower pipe into the wider pipe.

[0096] First, calculate the... Impedance matrix at the exit of the section Due to the continuity conditions of sound pressure and velocity at the interface, and considering modal orthogonality, The calculation method is shown in equation (9). Calculate the first... Impedance matrix at segment entrance :

[0097] Secondly, based on transmission line theory, the derivation of the first... Segment speed transmission matrix As shown in equation (10).

[0098] Scenario 2: Bidirectional contraction ( and In this situation, sound waves enter from the wider duct into the narrower duct. Calculations are typically simpler to perform in the admittance domain.

[0099] First, calculate the... Load admittance matrix at the segment exit :

[0100] in, It is the first The segment's entry admittance matrix; From the first Section to the The coupling matrix of segment 1. Calculate the coupling matrix of segment 2. Impedance matrix at segment entrance :

[0101] Secondly, derive the first Segment speed transmission matrix :

[0102] in, It is the characteristic admittance matrix.

[0103] Scenario 3: Horizontal expansion, vertical contraction ( and Such mixed situations cannot be directly applied using the single formula described above. This embodiment introduces a virtual intermediate interface, breaking down the process into "first horizontal expansion, then vertical contraction".

[0104] 1) Define intermediate variables (Admission of virtual interface):

[0105] in, It only includes the horizontal expansion ratio The coupling matrix.

[0106] 2) Calculate the first Equivalent load admittance at the section exit :

[0107] in, It only includes the vertical shrinkage ratio. The coupling matrix.

[0108] 3) Calculate the first The entrance impedance matrix of the segment , the same as formula (19).

[0109] 4) Calculate the velocity transfer matrix :

[0110] Scenario 4: Horizontal contraction, vertical expansion ( and This is the dual case of scenario three.

[0111] 1) Define intermediate variables Its form is the same as formula (21), where, It only includes the vertical expansion ratio The coupling matrix.

[0112] 2) Calculate the first Equivalent load admittance at the section exit Its form is the same as formula (22), where, It only includes the horizontal shrinkage ratio. The coupling matrix.

[0113] 3) Calculate the first The entrance impedance matrix of the segment , the same as formula (19).

[0114] 4) Calculate the velocity transfer matrix Its form is the same as formula (23).

[0115] Through the above steps, the velocity transmission matrix of each discrete pipe segment was obtained. and entrance impedance matrix These can be used for velocity transmission matrix cascading and horn plane wave reflection coefficient calculation, as detailed below: Throat impedance matrix The coupling relationship between sound pressure and volume velocity of each mode at the throat section is characterized, and the calculation formula is as follows:

[0116] in, The throat impedance matrix of the horn is represented and substituted into the following formula ( The plane wave reflection coefficient of the horn can then be obtained; This represents the impedance matrix calculated at the inlet of the first discrete pipe section at the throat of the horn.

[0117] Since the system is linear, from the throat of the horn (the first inlet) to the mouth of the horn (the second inlet)... The total velocity transmission relationship at the throat (exit section) can be obtained through matrix multiplication. The input velocity vector at the throat is defined as... The output velocity vector at the mouth is The transmission equation for the entire system is then:

[0118] Note the order of matrix multiplication, which usually corresponds to the spatial progression from the throat to the mouth.

[0119] (3) Solve for acoustic performance indicators: The complete process of calculating acoustic performance based on sound field modeling includes: Initialization and parameterization of design variables; based on the discrete geometric model, the throat and mouth dimensions of the rectangular horn are locked as fixed geometric boundary conditions; the cross-sectional width design variable vectors of the intermediate rectangular pipe segments, excluding the throat and mouth, are used. and highly designed variable vectors Defined as a vector of design variables to be optimized; initial values ​​of the design variables are set to form the initial outline of the horn; Perform forward acoustic calculations for the hybrid model; input the design variable vector of the current iteration step into the aforementioned sound field model; first, call the boundary element method calculation results or directly read the pre-calculated and stored finite box radiation impedance matrix. The matrix remains unchanged throughout the optimization process; secondly, the pattern matching method is invoked to recalculate the inlet impedance matrix of each internal pipe segment based on the current design variables. The velocity transfer matrix is ​​calculated and solved in cascade to obtain the output velocity vector at the mouth. Finally, combining the far-field directional basis function vectors The far-field directivity of the rectangular horn in the entire space or a specific region of interest was calculated. .

[0120]

[0121] After obtaining the internal sound field transmission characteristics and far-field sound pressure distribution of the horn through a hybrid model, it is necessary to further calculate two acoustic performance indicators that characterize the horn's radiation efficiency and directivity control capability: the throat reflection coefficient and the directivity map. The specific calculation process is as follows: The throat reflection coefficient quantifies the transmission loss of acoustic energy from the drive end to the horn mouthpiece. A smaller reflection coefficient amplitude indicates that the horn has higher acoustic radiation efficiency. First, calculate the reflection matrix. Using the throat impedance matrix Characteristic admittance matrix of the throat input end Derive the reflection matrix The reflection matrix describes the transformation relationship between the modes of the reflected wave and the modes of the incident wave, and the calculation formula is as follows:

[0122] in, This represents the reflection matrix.

[0123] Then the plane wave reflection coefficient can be determined. When the incident wave frequency is lower than the cutoff frequency of the first higher-order modes, only the plane wave component needs to be considered. Therefore, the reflection matrix is ​​extracted. The top-left element is used as the plane wave reflection coefficient. This coefficient is defined as the ratio of the plane wave component of the reflected wave at the throat to the plane wave component of the incident wave, that is:

[0124] in, Represents the plane wave reflection coefficient; Represents the reflection matrix The element in the first row and first column of the [database name]. The radiation efficiency of the horn can be determined by [reason]. The reaction, smaller A value indicates that more acoustic energy is transmitted into the horn and radiated outwards, while a value indicates that energy is reflected back to the drive end.

[0125] The directivity map is generated by normalizing the calculated far-field sound pressure distribution to produce a directivity map describing the radiation intensity distribution of sound waves in three-dimensional space. After obtaining the far-field sound pressure distribution, it is usually necessary to calculate the directivity pattern in order to quantify the horn's directivity performance. This directional pattern accurately characterizes the directional features of the horn. Its calculation formula is defined as follows:

[0126] Step 3: Construct a comprehensive objective function containing multi-physics constraints based on the acoustic performance indicators, solve the comprehensive objective function, and obtain the optimization scheme for the shape of the finite box rectangular horn.

[0127] Existing technologies often focus on a single metric (such as optimizing only throat impedance matching) or rely on the finite difference method to estimate the gradient when using gradient optimization algorithms. The finite difference method is not only computationally intensive but also susceptible to truncation errors, leading to local minima or non-convergence. This invention constructs a comprehensive objective function that includes radiation efficiency, shape smoothness, constant directivity, and coverage angle error. This enables the design of horns that possess both high energy transmission efficiency and precise fit to specific audience coverage areas, resolving the technical contradiction in traditional designs where "efficiency" and "directivity" often come at opposite ends. More importantly, this invention derives and applies the analytical gradient of the objective function with respect to design variables. The optimization algorithm driven by the analytical Jacobian matrix not only exhibits higher numerical stability but also faster convergence, accurately capturing the impact of minute changes in design variables on sound field performance, thereby searching for optimal geometric configurations that are difficult to discover using traditional methods. Specifically: (1) Construct a comprehensive objective function containing multiphysics constraints based on the acoustic performance indicators, including: The comprehensive objective function is obtained by weighting and summing the radiation efficiency, coverage angle control, constant directivity, and several shape smoothness constraint sub-items obtained from the acoustic performance indicators.

[0128] Based on the design requirements, a comprehensive objective function is constructed that includes radiation efficiency, geometric smoothness, and directivity control indicators. This function quantifies the total deviation between the current design and the ideal performance target; The comprehensive objective function The general form is the weighted sum of the sub-items:

[0129] in, For the radiation efficiency target term, For the shape smoothing target item, For a constant directional target term, For coverage angle control target items, , , These are positive real coefficients used to balance the weights of each item.

[0130] Preferably, the radiation efficiency target item The construction method is as follows: To ensure that acoustic energy can be efficiently transmitted from the drive head to free space, multiple discrete frequency points within the target operating frequency band are selected. Calculate the plane wave reflection coefficient at these frequency points. The sum of squares of the modulo;

[0131] The smaller this value, the better the acoustic impedance of the horn's throat matches the driving source, the less sound wave reflection, and the higher the radiation efficiency.

[0132] Preferably, the shape smoothing target item The construction method is as follows: To avoid drastic geometric abrupt changes, jagged edges, or discontinuities in the optimized horn profile, thereby ensuring manufacturability and preventing acoustic turbulence, the Tikhonov regularization method is introduced. The second-order central difference of the design variable vector with respect to the axial position is calculated to measure the rate of change of local curvature of the geometric profile and penalize it.

[0133] This forces optimization algorithms to tend to seek smooth, continuous, and gradually changing geometries.

[0134] Preferably, the constant directional target item The construction method is as follows: To ensure that the frequency response curve of the horn remains consistent at different off-axis angles, i.e. to achieve constant directivity, the variance of normalized directivity as a function of frequency is calculated in the direction of a specified off-axis angle.

[0135]

[0136] in, In direction and frequency The normalized directional level below, The average frequency in this direction satisfies

[0137] The smaller this value, the less the directivity pattern changes with frequency, and the more stable the sound field distribution.

[0138] Preferably, the coverage angle control target item The construction method is as follows: In order to precisely control the horn's beamwidth to match a specific audience area, the expected coverage boundary angle is defined; Calculate the mean square error between the actual sound pressure level attenuation value at the coverage boundary angle and the target attenuation value (usually set to attenuate 6 dB relative to the axial main lobe peak).

[0139]

[0140] This method stretches or compresses the main lobe width by forcing the sound pressure level at the boundary to converge toward the -6dB point, thus ensuring it precisely matches the design target.

[0141] (2) Solve the comprehensive objective function to obtain the finite box rectangular horn shape optimization scheme, including: Iterative solution based on analytical gradient: Calculate the analytical gradient of the comprehensive objective function with respect to the design variables, and construct the analytical Jacobian matrix; directly calculate the comprehensive objective function using mathematical analytical derivation. For each design variable and Use the partial derivatives to construct the Jacobian matrix; The analytical Jacobian matrix is ​​subjected to nonlinear least squares optimization to determine the update direction and step size of the design variables. The design variables are iteratively updated until the comprehensive objective function value satisfies the convergence condition, and the optimal design variable vector is output. The final rectangular horn 3D geometric model is then fitted and generated. The analytical Jacobian matrix is ​​input into a nonlinear least squares optimization algorithm (such as the Levenberg-Marquardt algorithm) to determine the update direction and step size of the design variables, and the width design variable vector is updated accordingly. and highly designed variable vectors Perform iterative updates, convergence determination, and output; After each iteration, check whether the preset convergence conditions are met. The convergence conditions include that the relative change in the comprehensive objective function value is less than a preset threshold, or that the number of iterations reaches a preset upper limit. If the convergence condition is met, the iteration is terminated and the optimal design variable vector is output. Spline interpolation is used to fit the discrete optimal width and height design variable vectors into a continuous curve, generating the final three-dimensional geometric model of the rectangular horn.

[0142] Compared to the traditional finite difference method, analytical gradient calculation avoids the repetitive sound field calculation required for perturbation of each variable, which greatly improves the calculation speed and numerical stability of optimization iteration.

[0143] In this embodiment, the iterative optimization process is performed as follows: After constructing a mathematical model describing the merits and demerits of the design, numerical optimization algorithms are used to automatically adjust the design variables. In order to find the overall objective function Minimize the optimal solution.

[0144] 1) Optimize Algorithm Configuration. Select an iterative optimization algorithm suitable for solving nonlinear least squares problems. In the preferred embodiment, the Levenberg-Marquardt algorithm is used. This algorithm combines the robustness of gradient descent with the fast convergence of the Gauss-Newton method, making it particularly suitable for acoustic optimization problems with numerous parameters and nonlinearity, as presented in this invention. Alternatively, the trust region reflection algorithm or other gradient-based optimization algorithms can also be used.

[0145] 2) Iterative Update Process. The optimization process is a cyclical iterative numerical computation process, specifically including the following sub-steps: Current State Evaluation: In the... In the next iteration, the current design variable vector The input is fed into the hybrid model to calculate the corresponding sound field distribution and the overall objective function value. Search direction determined: The optimization algorithm uses the gradient information of the objective function with respect to the design variables to calculate an update step size vector that can decrease the value of the objective function. Variable update and constraint check: Calculate new design variables. During this process, geometric constraint checks must be performed. Specifically, each updated width needs to be checked. and height Does it meet the physical constraints: non-negativity constraint? Box boundary constraints: The outer contour of the horn must not exceed the preset box volume range. If a constraint violation occurs, the variables will be forcibly pulled back into the feasible region using the projection method or penalty function method.

[0146] 3) Convergence Criteria and Result Output. After each iteration, check whether the preset convergence termination conditions are met. These termination conditions include, but are not limited to: objective function convergence: the relative change in the objective function between two consecutive iterations is less than a preset threshold. (For example Gradient convergence: The norm of the current gradient vector is less than a preset threshold. Step size convergence: The update step size of the design variables is extremely small, indicating that it has fallen into a local minimum; Maximum number of iterations: The number of iterations reaches a preset upper limit (e.g., 100 times). Once any of the above conditions are met, the optimization algorithm terminates and outputs the final width of the design variable vector. and highly designed variable vectors This optimal vector defines the optimized rectangular horn shape.

[0147] Through the above steps, this embodiment realizes a fully automated horn shape design process. This method utilizes a multiphysics objective function to optimize the horn's impedance matching characteristics and directional control capability in a finite enclosure environment, while ensuring a smooth and manufacturable geometric structure. This overcomes the shortcomings of traditional trial-and-error methods, such as long design cycles and unstable performance.

[0148] Embodiment 2 of this invention provides a finite-box rectangular horn shape optimization system based on a hybrid model. This system is built upon the aforementioned optimization method and can run as computer software, firmware, or dedicated hardware, enabling automated design of the rectangular horn's geometry. Figure 5 As shown, the system mainly includes the following in terms of logical functional architecture: The parametric discrete modeling module (discrete geometric modeling module) is used to geometrically discretize the rectangular horn along the axial direction into multiple rectangular pipe segments connected end to end and define the geometric parameters of the cross-section of each rectangular pipe segment to determine the design variables to be optimized. Specifically, the parametric discrete modeling module performs geometric discretization processing on the rectangular horn. This module is configured to use the throat dimensions, mouth dimensions, total axial length, and mounting box dimensions of the horn as basic constraints to establish a three-dimensional Cartesian coordinate system. It then divides the horn into multiple rectangular pipe segments along the axial direction and generates a cross-sectional width design variable vector to describe the internal contour of the horn. and highly designed variable vectors These two vectors are defined as independent and variable design variable vectors in the subsequent optimization process.

[0149] In this embodiment, the discrete geometry modeling module is used to convert the physical design requirements input by the user into a discrete mathematical model that can be recognized and processed by a computer, and to transmit the generated initial design variables to subsequent modules. The discrete geometry modeling module specifically includes: Parameter Input Unit: This unit is configured to receive physical constraint parameters input by the user. The physical constraint parameters include at least the total axial length of the rectangular horn. The number of discrete segments used for numerical computation The fixed dimensional constraints of the horn throat, i.e., the width of the first section. and height ; The fixed dimensional constraints of the horn mouth, i.e. the first Segment width and height The geometric dimensions (such as length, width, and depth) of the finite enclosure on which the horn is installed.

[0150] Axial Discretization Unit: This unit is connected to the parameter input unit and is configured to discretize based on the input total axial length. and discrete segment number Calculate along Axial slice thickness To adapt to the trapezoidal integral rule used in the subsequent hybrid acoustic calculation module and improve calculation accuracy, the axial discretization unit executes the following specific discretization logic: It combines the first discrete segment with the... The axial length of each discrete segment is set as The second to the third in the middle The axial length of each discrete segment is set as ,in .

[0151] Initial waveguide generation unit: This unit is configured as the starting point for generating optimization. Specifically, this unit automatically calculates the intermediate discrete segments (segment 2 to segment 3) based on a preset geometric function (in a preferred embodiment, an exponential or hyperbolic function) and the constraint dimensions of the throat and mouth. Initial width design variable vector of segment and initial height design variable vector The initial width design variable vector and the initial height design variable vector are encapsulated into an initial design variable vector. It is then sent to the multiphysics optimization module via the data bus.

[0152] The hybrid acoustic calculation module is used to pre-calculate the radiation impedance matrix and far-field directivity basis function vector under a finite enclosure using an external radiation model; and to calculate the inlet impedance matrix and velocity transmission matrix of each rectangular pipe segment based on the radiation impedance matrix and the current design variables using an internal acoustic transmission model of the horn, and to obtain the output velocity vector of the inlet by cascading the entire system, so as to solve the acoustic performance index in combination with the far-field directivity basis function vector. Specifically, the hybrid acoustic computing module is the core computing engine of the system, performing forward solving of the sound field based on the hybrid model. This module integrates solvers for two different acoustic algorithms, achieving high-precision calculations through deep coupling. The hybrid acoustic computing module specifically includes: The external impedance preset unit is configured to perform mesh generation and sound field calculation on the finite enclosure and horn mouth based on the boundary element method, obtain the radiation impedance matrix characterizing the reaction of the finite enclosure environment to sound radiation, and store it as a static boundary parameter; specifically, it involves an external radiation impedance calculation unit: this unit is constructed based on the boundary element method and is used to pre-calculate the acoustic characteristics of the external environment.

[0153] Mesh generation sub-unit: used to read the geometric dimensions of the finite box, construct a three-dimensional geometric model including the horn opening and the outer surface of the box, and perform surface meshing on it to generate boundary element mesh data.

[0154] Impedance solving sub-element: Used to solve the Helmholtz integral equation on the boundary element mesh. Specific operations include: applying unit velocity modal excitations of various orders to the horn nozzle, calculating the corresponding surface acoustic pressure response, and then integrating to obtain the radiation impedance matrix. .

[0155] Data caching subunit: Since the external housing dimensions remain unchanged during the horn internal shape optimization process, the impedance calculation subunit only needs to run once before the optimization process begins. The data caching subunit is used to store the calculated results. The matrix can be reused later, thus significantly saving computing resources.

[0156] The internal transmission iteration unit is configured based on the pattern matching method. During the optimization process, it calls the velocity transmission matrix algorithm based on the updated design variable vector, and calculates the current throat reflection coefficient and mouth modal velocity distribution data in conjunction with the radiation impedance matrix. Specifically, this involves an internal velocity transmission matrix calculation unit: this unit is constructed based on the pattern matching method and is used to calculate the internal sound field that varies with the design variables.

[0157] Feature mode library: stores normalized feature functions of rectangular waveguides. The analytical expression and its corresponding eigenvalue calculation logic.

[0158] Coupled matrix operation subunit: configured to receive the design variable vector of the current iteration step. Based on the size ratio of adjacent pipe sections, the built-in analytical formula for overlapping integrals is used to calculate the modal coupling matrix at each pair of adjacent interfaces. and .

[0159] Cascaded transmission subunits: configured to calculate the velocity transmission matrix for each segment of the pipeline using transmission line theory. And perform matrix multiplication. This allows for the establishment of the entire system velocity transmission equation from the throat to the mouthpiece, and the output of the throat reflection coefficient. Mouth velocity distribution vector .

[0160] The multiphysics optimization module is the core of the system's control. It constructs a comprehensive objective function with multiphysics constraints based on the acoustic performance indicators, solves the comprehensive objective function, and obtains an optimized shape scheme for the finite-box rectangular horn. It adjusts the design variables in reverse based on the sound field calculation results, involving the comprehensive objective construction module and the analytical gradient optimization module. Specifically, the integrated target construction module constructs an integrated evaluation function containing multi-physics constraints based on the sound field calculation results; This module contains a radiation efficiency calculation unit, a shape smoothness calculation unit, a constant directivity calculation unit, a coverage angle calculation unit, and a weighted summation unit. The radiation efficiency calculation unit calculates the radiation efficiency target item. It is used to calculate the mean square value of the plane wave reflection coefficient in a wide bandwidth to quantify the energy transfer efficiency; The shape smoothness calculation unit calculates the shape smoothness target item. It is used to calculate the second-order difference norm of the design variable vector to quantify the smoothness and continuity of the geometric profile; The constant directionality calculation unit calculates the constant directionality target item. It is used to calculate the variance of the full-band directivity pattern and the sound pressure level error at the preset coverage boundary angle, so as to quantify constant directivity performance and beamwidth control accuracy. The coverage angle calculation unit calculates the coverage angle control target item. It is used to calculate the mean square error between the actual sound pressure level attenuation value and the target attenuation value at the coverage boundary angle, and to precisely control the beamwidth of the horn to match a specific audience area; The weighted summation unit is used to synthesize the calculation results of the above units into a single comprehensive objective function value based on preset weight coefficients. .

[0161] Specifically, the analytical gradient optimization module performs reverse correction and update of the design variables; this module is equipped with an analytical Jacobian matrix builder, used to directly calculate the analytical partial derivatives of the integrated objective function with respect to each design variable, and uses a nonlinear least squares algorithm to determine the update step size of the design variables, driving the width design variable vector. and highly designed variable vectors The process continues iteratively until the combined objective function value satisfies the convergence condition.

[0162] In this embodiment, the analytical gradient optimization module specifically involves: Analytical Gradient Calculation Unit: This unit is a key component for achieving efficient optimization in this system. Unlike traditional systems using the finite difference method, this unit is configured to directly calculate the gradient using analytical mathematical formulas. This unit incorporates a velocity transfer matrix. Regarding design variables The analytical expression of the partial derivatives (i.e. and This unit is configured to perform chain rule matrix operations, applying the total objective function. For design variables The derivative is decomposed into the product of the derivative of the sound field variable with respect to the geometric dimensions, thus enabling fast and accurate output of the gradient vector. .

[0163] Iterative update control unit: This unit incorporates a nonlinear optimization algorithm (in a preferred embodiment, the Levenberg-Marquardt algorithm). This unit is configured to receive the current objective function value. and gradient vector Calculate the update step size of the design variables .

[0164] Constraint Sub-element: Before updating variables, this sub-element is configured to check whether the updated variables satisfy the "non-negativity" and "box size boundary" constraints. If not, the variables are forcibly truncated or projected to ensure that the generated design is physically manufacturable. This element will update the design variables... Feedback is sent to the hybrid acoustics calculation module, triggering the next iteration, until the preset convergence condition is met.

[0165] This embodiment also includes a human-computer interaction and result output module, used to provide users with an operation interface and output the final design results, involving: Data visualization unit: This unit is configured to display the optimized width design variable vector. and highly designed variable vectors The data is converted into a three-dimensional geometric model and rendered on the screen. At the same time, the calculated acoustic performance data is plotted into intuitive charts, including but not limited to: polar coordinate directivity plots, sound pressure level contour plots, and input impedance curves.

[0166] File export interface: This unit is configured to export the final optimized horn geometry model to a common computer-aided design (CAD) file format (such as STEP, IGES, or STL format) for direct import into CNC machine tools or 3D printing equipment for physical machining and manufacturing.

[0167] The modules mentioned above communicate with each other through an internal system data bus or shared memory mechanism to achieve real-time data transmission and interaction.

[0168] Embodiment 3 of the present invention provides a terminal, including a processor and a storage medium; the storage medium is used to store instructions; the processor is used to perform operations according to the instructions to execute the steps of the method. The terminal may be a desktop computer, a workstation, a server, or a cloud computing node. The processor may be a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), or a field-programmable gate array (FPGA).

[0169] Embodiment 4 of the present invention provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method. The computer-readable storage medium may include, but is not limited to, a hard disk, a solid-state drive (SSD), an optical disc (CD / DVD), a USB flash drive, a flash memory card, or network cloud storage space.

[0170] Compared with the prior art, the beneficial effects of the present invention include at least the following: 1. This invention constructs a hybrid model and uses the boundary element method to accurately calculate the radiation impedance matrix in a finite enclosure environment. The modal coupling information contained in this matrix is ​​then incorporated into the velocity transmission matrix calculation using an internal mode-matching method. This overcomes the limitations of the infinite barrier assumption in traditional mode-matching methods, significantly improving prediction accuracy in real-world applications and eliminating the systematic errors introduced by the infinite barrier assumption. Experimental results show that the horn optimized using this invention exhibits a high degree of agreement between simulated and measured directivity patterns over a wide frequency band. This effectively solves the technical problem of performance degradation after packaging and the need for repeated prototyping and modification of products designed using traditional methods.

[0171] 2. This invention takes into account that during the shape optimization process, only the internal contour of the horn changes, while the external box size and mouth boundary remain unchanged. The boundary element method is used to calculate the external radiation impedance only once during the initialization stage. In hundreds or thousands of iterations, the internal velocity transmission matrix is ​​updated quickly using the analytical formula of the pattern matching method, which has a very small computational load. This step-by-step calculation strategy of one-time boundary element method pre-calculation and multiple pattern matching method iterations maintains the same computational accuracy as the full boundary element method while improving the computational efficiency by several orders of magnitude. This makes it possible to complete complex broadband, multi-objective shape optimization on ordinary computers, and cleverly solves the contradiction between computational accuracy and computational efficiency in the full numerical simulation method.

[0172] 3. This invention constructs a comprehensive objective function that includes sub-items of radiation efficiency, coverage angle control, constant directivity, and shape smoothness. This enables the design of horns that possess both high energy transmission efficiency and precise fit to specific audience coverage areas, resolving the technical contradiction in traditional designs where efficiency and directivity often come at opposite ends. More importantly, this invention derives and applies the analytical gradient of the objective function with respect to design variables. Utilizing an optimization algorithm driven by the analytical Jacobian matrix, it not only achieves higher numerical stability but also faster convergence, accurately capturing the impact of minute changes in design variables on sound field performance. This allows for the search for optimal geometric configurations that are difficult to discover using traditional methods, realizing multi-objective collaborative optimization based on analytical gradients and overcoming the limitations and algorithmic instability of traditional single-objective designs.

[0173] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0174] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0175] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0176] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0177] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A method for optimizing the shape of a finite-box rectangular horn based on a hybrid model, wherein the hybrid model includes an external radiation model and an internal sound transmission model of the horn, characterized in that, The method includes: The rectangular horn is geometrically discretized along the axial direction into multiple rectangular pipe segments connected end to end, and the geometric parameters of the cross-section of each rectangular pipe segment are defined to determine the design variables to be optimized. An external radiation model is used to pre-calculate the radiation impedance matrix and far-field directivity basis function vector under a finite enclosure. An internal acoustic transmission model is used to calculate the inlet impedance matrix and velocity transmission matrix of each rectangular pipe section based on the radiation impedance matrix and the current design variables. The output velocity vector at the inlet is obtained by cascading the entire system. The acoustic performance index is then solved by combining the far-field directivity basis function vector. Based on the acoustic performance indicators, a comprehensive objective function containing multi-physics constraints is constructed. By solving the comprehensive objective function, an optimization scheme for the shape of a finite box-shaped rectangular horn is obtained.

2. The method for optimizing the shape of a finite box-shaped rectangular horn based on a hybrid model according to claim 1, characterized in that: The process involves geometrically discretizing the rectangular horn along its axial direction into multiple interconnected rectangular pipe segments and defining the geometric parameters of the cross-section of each segment to determine the design variables to be optimized, including: Establish a three-dimensional rectangular coordinate system, and define the central axis of the sound wave propagation of the rectangular horn as... The axis will be perpendicular to The horizontal direction of the cross section of the shaft is defined as The axis will be perpendicular to The cross-section of the shaft is defined perpendicular to the direction of the cross-section. axis; The rectangular horn edge The axial direction is discretized in physical space as A rectangular pipe segment connected end to end, in which It is a positive integer greater than 2; For the A rectangular pipe segment, its cross-section defined in... The internal width in the axial direction is Define its cross-section in The internal height in the axial direction is , take the second to the third The rectangular pipe segment corresponding to , As design variables to be optimized, among which and With index The changes together constitute the geometric outline shape of the rectangular horn.

3. The method for optimizing the shape of a finite box-shaped rectangular horn based on a hybrid model according to claim 2, characterized in that: The rectangular horn edge The axial direction is discretized in physical space as A series of rectangular pipe segments connected end to end, including: Set the first rectangular pipe segment of the corresponding horn throat and the first rectangular pipe segment of the corresponding horn mouth. The axial length of each rectangular pipe segment is The second to the third in the middle The axial length of each rectangular pipe segment is , This is the total axial length of the rectangular horn.

4. The method for optimizing the shape of a finite box-shaped rectangular horn based on a hybrid model according to claim 1, characterized in that: The method of pre-calculating the radiation impedance matrix and far-field directivity basis function vector under a finite enclosure using an external radiation model includes: For the physical boundary conditions of a rectangular horn mounted on a finite enclosure, the plane of the horn opening and the outer surface of the finite enclosure are meshed. Based on this, different orders of unit normalized modal velocity excitations are applied to the plane of the horn opening of the rectangular horn. The sound field under the corresponding excitation is solved using the boundary element method. The radiation impedance matrix characterizing the reaction of the finite enclosure to sound radiation and the far-field directivity basis function vector characterizing the independent radiation characteristics of each mode are calculated.

5. The method for optimizing the shape of a finite box-shaped rectangular horn based on a hybrid model according to claim 1, characterized in that: The method employs an internal sound transmission model for the horn. Based on the radiation impedance matrix, it calculates the inlet impedance matrix and velocity transmission matrix of each rectangular pipe segment according to the current design variables, and obtains the output velocity vector at the inlet through system cascading, including: The radiation impedance matrix is ​​used as the terminal boundary condition at the rectangular horn inlet; based on the abrupt change in cross-sectional dimensions at the interface of adjacent rectangular pipe segments corresponding to the current design variables, the inlet impedance matrix of each rectangular pipe segment is calculated, and then the corresponding velocity transmission matrix is ​​calculated. By cascading the velocity transmission matrices of all rectangular pipe segments, the output velocity vector at the inlet is obtained.

6. The method for optimizing the shape of a finite box-shaped rectangular horn based on a hybrid model according to claim 5, characterized in that: The process of constructing the sound transmission model inside the horn includes: For any rectangular pipe segment, the sound pressure field and axial particle velocity field inside it are expanded into a superposition of characteristic modes. A normalized characteristic function, a propagation matrix inside the pipe, a characteristic impedance, and a mode coupling matrix are established. The mode coupling matrix includes a coupling matrix for describing sound pressure transmission and a coupling matrix for describing velocity transmission. Based on this, the mode matching method is used to derive the inlet impedance matrix and velocity transmission matrix of each rectangular pipe segment from the mouth to the throat segment by segment, corresponding to the abrupt changes in cross-sectional dimensions at the interface of adjacent rectangular pipe segments.

7. A method for optimizing the shape of a finite box-shaped rectangular horn based on a hybrid model according to claim 5 or 6, characterized in that: The abrupt changes in cross-sectional dimensions at the interface of adjacent rectangular pipe segments include: at the interface of adjacent rectangular pipe segments, the cross-section expands in both horizontal and vertical directions, contracts in both horizontal and vertical directions, expands horizontally and contracts vertically, and contracts horizontally and expands vertically.

8. The method for optimizing the shape of a finite box-shaped rectangular horn based on a hybrid model according to claim 1, characterized in that: The acoustic performance indicators include the plane wave reflection coefficient, which quantifies the transmission loss of sound energy from the drive end to the horn mouth, and the directivity diagram, which describes the distribution of sound wave radiation intensity in three-dimensional space.

9. The method for optimizing the shape of a finite box-shaped rectangular horn based on a hybrid model according to claim 8, characterized in that: The process of solving the plane wave reflection coefficient includes: The inlet impedance matrix of the first discrete pipe section at the throat of the horn is used as the throat impedance matrix. The reflection matrix is ​​derived using the throat impedance matrix and the characteristic admittance matrix of the throat input end. The plane wave reflection coefficient is obtained from the elements of the first row and first column of the reflection matrix.

10. The method for optimizing the shape of a finite box-shaped rectangular horn based on a hybrid model according to claim 8, characterized in that: The process of solving the directional graph includes: The far-field directivity of the rectangular horn is calculated based on the output velocity vector at the mouth and the far-field directivity basis function vector, and then the directivity map is obtained through normalization.

11. The method for optimizing the shape of a finite box-shaped rectangular horn based on a hybrid model according to claim 1, characterized in that: The construction of a comprehensive objective function containing multiphysics constraints based on the acoustic performance indicators includes: Based on the acoustic performance indicators, the radiation efficiency target, shape smoothness target, constant directivity target, and coverage angle control target are obtained and then weighted and summed to obtain the comprehensive objective function.

12. The method for optimizing the shape of a finite box-shaped rectangular horn based on a hybrid model according to claim 11, characterized in that: The radiation efficiency target term is obtained based on the mean square value of the plane wave reflection coefficient within the broadband; The shape smoothness target term is obtained based on the second difference norm of the design variable vector; The constant directivity target term is obtained based on the variance of the full-band directivity map and the sound pressure level error at the preset coverage boundary angle; The coverage angle control target is obtained based on the mean square error between the actual sound pressure level attenuation value and the target attenuation value at the coverage boundary angle.

13. The method for optimizing the shape of a finite box-shaped rectangular horn based on a hybrid model according to claim 1, characterized in that: Solving the comprehensive objective function yields an optimized scheme for the shape of a finite box-shaped rectangular horn, including: Calculate the analytical gradient of the comprehensive objective function with respect to the design variables, and construct the analytical Jacobian matrix; The analytical Jacobian matrix is ​​subjected to nonlinear least squares optimization to determine the update direction and step size of the design variables. The design variables are iteratively updated until the comprehensive objective function value satisfies the convergence condition. The optimal design variable vector is output to fit and generate the final rectangular horn three-dimensional geometric model.

14. A finite box rectangular horn shape optimization system based on a hybrid model, comprising the method described in any one of claims 1-13, characterized in that, The system includes: The parametric discretization modeling module is used to geometrically discretize the rectangular horn along the axial direction into multiple rectangular pipe segments connected end to end, define the geometric parameters of the cross-section of each rectangular pipe segment, and determine the design variables to be optimized. The hybrid acoustic calculation module is used to pre-calculate the radiation impedance matrix and far-field directivity basis function vector under a finite enclosure using an external radiation model; and to calculate the inlet impedance matrix and velocity transmission matrix of each rectangular pipe segment based on the radiation impedance matrix and the current design variables using an internal acoustic transmission model of the horn, and to obtain the output velocity vector of the inlet by cascading the entire system, so as to solve the acoustic performance index in combination with the far-field directivity basis function vector. The multiphysics optimization module is used to construct a comprehensive objective function containing multiphysics constraints based on the acoustic performance indicators, solve the comprehensive objective function, and obtain an optimization scheme for the shape of a finite box-shaped rectangular horn.

15. A terminal, comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1-13.

16. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1-13.

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