Sound barrier shape optimization method based on isogeometric particle swarm singular boundary method

Abstract

The invention belongs to the technical field of road traffic noise reduction, and particularly relates to a sound barrier shape optimization method based on an isogeometric particle swarm singular boundary method. Comprising the steps of building a sound barrier geometric model, building a sound barrier shape optimization model, building a Burton Miller type singular boundary method program, calculating sound pressure, carrying out particle swarm iterative solution, outputting an optimization result and the like. According to the method, the model is optimized based on the isogeometric singular boundary method of the basic solution of the acoustic control equation for the first time, the model is applied to the optimization design of the sound barrier, the sound barrier is optimized by combining the particle swarm optimization method, only the size of the target function is needed, complex sensitivity derivation is not needed, and when the sound barrier with the complex shape is calculated, the method is simple and convenient to operate. The method has great flexibility and high efficiency, seamless integration between CAD and CAE is realized by introducing isogeometric analysis, namely representing geometric boundaries by using an NURBS function, and a tedious grid division step in an optimization process is avoided, so that the precision and efficiency of sound barrier optimization are remarkably improved.

Description

Technical field:

[0001] The present invention belongs to the technical field of road traffic noise reduction, and specifically relates to a sound barrier shape optimization method based on the isogeometric particle swarm singular boundary method, which is used to more simply optimize the sound barrier to improve the noise reduction effect. Background technology:

[0002] With the rapid expansion of modern transportation networks, traffic noise pollution has become a significant environmental issue affecting the quality of life of urban residents. Optimizing the shape of sound barriers is crucial for noise reduction and project cost control. In this context, sound barriers, as the primary means of blocking noise transmission, are widely used to reduce noise levels. They offer significant sound absorption, a flexible and controllable protection range, and ease of maintenance. However, the design of traditional sound barriers is often based on experience or simple rules, lacking optimization and customization. This results in poor noise reduction effectiveness, high costs, or overly complex modeling. Therefore, it is particularly important to develop a simple and more efficient method for optimizing the shape of sound barriers.

[0003] In traditional noise reduction effect analysis methods of sound barriers, it is usually necessary to install entities on both sides of the road to test the sound barriers in order to obtain relevant data for analysis and evaluation. This method is not only time-consuming but also consumes a lot of manpower. In recent years, in order to simplify the process related to sound barrier modeling, numerical simulation has become an alternative sound barrier simulation solution, among which finite element and boundary element methods are the main means. However, the meshing cost of the finite element method is high, and the boundary discretization error of complex geometric models is also large; in contrast, the boundary element method can reduce the problem to one dimension for solution without dividing the regional grid, but this method involves complex singular numerical integration problems. When optimizing the shape of the sound barrier, the shape will change every time it is optimized, so repeated modeling is required, which is time-consuming and labor-intensive. The existing technology can avoid the problem of repeated modeling by introducing isogeometric analysis (see document 2T.JR Hughes, JA Cottrell, Y.Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering, 194 (2005) 4135-4195), making CAD and CAE seamlessly connected, thereby improving optimization efficiency. Some scholars have combined isogeometric with boundary elements to optimize the shape of sound barriers (see document 3C.Liu, L.Chen, W.Zhao, H.Chen, Shape optimization of sound barrier using an isogeometric fast multipole boundary element method in two dimensions, Engineering Analysis with Boundary Elements, 85 (2017) 142-157.), but because boundary elements involve complex and tedious singular numerical integration problems, they may not be the best choice for non-professionals or those who need to solve problems quickly.

[0004] The Burton–Miller singular boundary method (Fu ZJ, Chen W, and Gu Y (2014) Burton–Miller-type singular boundary method for acoustic radiation and scattering. J. Sound Vib. 333:3776-93.), as a meshless semi-analytical method, has the advantages of being truly meshless, integral-free, mathematically simple, and easy to program, showing important application prospects in simulation. Particle swarm optimization (PSO) is an optimization algorithm based on swarm intelligence, inspired by the social behavior of bird flocks or fish schools (Shaaban AM, Anitescu C, Atroshchenko E, and Rabczuk T (2020) Shape optimization by conventional and extended isogeometric boundary element method with PSO for two-dimensional Helmholtz acoustic problems. Eng. Anal. Boundary Elem. 113:156-69.). PSO searches for the optimal solution by simulating the collaboration and competition of individuals in a group. It has the advantages of fast convergence, few parameters, and easy implementation, and is widely used in various optimization problems. Acoustic optimization involves multiple fields, such as noise control, acoustic material design, and acoustic structure optimization. Its goal is usually to minimize noise, maximize acoustic performance, or meet specific acoustic design requirements. Since acoustic problems usually have characteristics such as nonlinearity, multimodality, and high dimensionality, traditional optimization methods are often difficult to solve efficiently. The particle swarm optimization algorithm shows great potential in acoustic optimization and can effectively solve problems such as noise control, acoustic material design, and acoustic structure optimization. Its advantages such as strong global search capability, strong adaptability, and easy implementation make it an important tool in the field of acoustic optimization. In the future, with the advancement of computing technology and the improvement of algorithms, the application of PSO in acoustic optimization will be more extensive and in-depth.

[0005] In the prior art, Chinese patent CN109800491A discloses a numerical simulation method for the noise reduction performance of sound barriers, comprising the following steps: Step 1: Based on the noise reduction mechanism of sound barriers and the Helmholtz integral solution of the acoustic wave equation, a three-dimensional numerical model of the sound barrier structure is established; Step 2: Structural meshing of the three-dimensional numerical model of the sound barrier structure is performed, and the surface structural mesh of the three-dimensional numerical model of the sound barrier structure is selected and set as the acoustic envelope mesh; Step 3: Parameterization of the structural mesh and acoustic envelope mesh of the three-dimensional numerical model of the sound barrier structure is performed; Step 4: Calculation of the sound pressure level contour map behind the sound barrier using the three-dimensional boundary element method; Step 5: The noise reduction performance of the sound barrier is demonstrated by the changes in the sound pressure level contour map behind the sound barrier. This invention uses the three-dimensional boundary element method to analyze the actual noise reduction effect of sound barriers. The numerical model constructed can provide the most intuitive theoretical basis for predicting the noise reduction performance of different sound barrier materials and different sound barrier structures.

[0006] Chinese patent CN113652983B discloses a machine learning-based sound barrier design method, comprising the following steps: S1: Selecting a basic optimization model for the sound barrier using an acoustic metamaterial; Constructing a fitness function that adapts to the desired acoustic wave frequencies; Constructing several initial configurations based on the parameters to be optimized in the basic optimization model; S2: Evaluating the fitness function of each genetic algorithm configuration using finite element simulation software; Selecting the configuration with the largest fitness function and retaining it as the parent of the next generation; S3: Repeating step S2 until the fitness function between two adjacent generations reaches the required threshold, thereby obtaining the optimal sound barrier design. Using machine learning, the sound insulation and noise reduction requirements are abstracted into a fitness function representation, enabling intelligent search for the optimal sound barrier, making it simple and easy to operate.

[0007] The above-mentioned existing technologies suffer from the problems of cumbersome, difficult, and inefficient sound barrier optimization processes. The inventors' research and analysis have revealed no prior art method that combines the isogeometric and Burton-Miller singular boundary methods with the particle swarm optimization algorithm to achieve simple and efficient sound barrier shape optimization. Therefore, the invention of a sound barrier shape optimization method based on the isogeometric particle swarm singular boundary method can address the shortcomings of the existing technologies, simplify the optimization process and cost, improve noise reduction effectiveness, and provide a new development direction for the field of sound barrier optimization. Summary of the invention:

[0008] The purpose of the present invention is to overcome the shortcomings of the existing technology. Based on the improvement of the existing technology, a method is designed to combine the isogeometric, Burton-Miller type singular boundary method and the particle swarm optimization algorithm to perform simple and efficient shape optimization of the sound barrier, especially a sound barrier shape optimization method based on the isogeometric particle swarm singular boundary method, which solves the problems of complicated process, difficult operation and low efficiency in the existing technology.

[0009] To achieve the above object, the present invention provides a sound barrier shape optimization method based on the isogeometric particle swarm singular boundary method, comprising the following steps:

[0010] Step S1: Creating a sound barrier geometric model: Building a sound barrier geometric model based on the geometric parameters of the sound barrier to be optimized, wherein the geometric parameters include the width, height, and position of the sound barrier in space; importing the information of the built model into a calculation program, and obtaining interpolation points of its boundary through the program;

[0011] Step S2: Establishing a sound barrier shape optimization model: Based on the known air density, the speed of sound propagation in air, the frequency of the sound source, the selected shape design variables and the corresponding boundary conditions, a sound barrier shape optimization model based on the isogeometric singular boundary method is established in combination with the particle swarm optimization method;

[0012] Step S3: Establish a program and calculate sound pressure: Using the sound barrier shape optimization model established in step S2, the boundary interpolation points obtained by the program in step S1 are used as configuration nodes of the singular boundary method, and a Burton-Miller type singular boundary method program is compiled to accurately calculate the sound pressure at the observation point; the average sound pressure level is calculated based on the sound pressure of several observation points in the observation area, and the average sound pressure level value is the objective function;

[0013] Step S4: Particle swarm iterative solution: Using the sound barrier shape optimization model established in step S2, the objective function, termination conditions, initial conditions, and upper and lower limits of the shape design variables of the Burton-Miller type singular boundary method are set, and the particle swarm optimization method is used for iterative solution to find the optimal solution in turn to obtain the optimal shape;

[0014] Step S5: Output optimization results: Utilize the optimization program established in step S4 to output the final optimized shape of the sound barrier after precise calculation, and perform performance evaluation of the optimization results by measuring the sound pressure level in the observation area.

[0015] The geometric model of the sound barrier in step S1 of the present invention is described by NURBS, and the control point coordinates, weights, node vectors, and order of the curve in the geometric model are extracted, and this information is substituted into the boundary curve expression:

[0016]

[0017] Where p is the t-th control point, m is the number of control points, is the NURBS spline basis function, is the B-spline basis function of degree p, ω t is the weight of the t-th control point, is the parameter space coordinate; the NURBS interpolation point is used as the boundary configuration node of the sound barrier, and n nodes are configured on the boundary of the sound barrier

[0018] The acoustic control equation used in step S2 of the present invention is:

[0019]

[0020] in is the Laplace operator, is the wave number, ω = 2πf is the angular frequency, c is the speed of sound, f is the frequency, Ω represents the sound field area, x is the spatial coordinate, and p(x) is the sound pressure amplitude at x;

[0021] For the above acoustic control equations, Dirichlet conditions and Newman boundary conditions are usually considered:

[0022]

[0023] in is the boundary Γ p The known sound pressure on is the boundary Γ v The known normal velocity on ρ is the density of air.

[0024] The step of establishing a sound barrier shape optimization model based on the isogeometric singular boundary method in step S2 of the present invention includes:

[0025] S2-1: Define the objective function and constraints, select the shape design variables, give their upper and lower limits, set the maximum number of iterations and convergence parameters, where the objective function is set to the total sound pressure in the observation area;

[0026] S2-2: The numerical solution of each boundary point is expressed as a linear accumulation of basic solutions. The basic solution corresponding to the two-dimensional Helmholtz equation is:

[0027]

[0028] in is the zero-order Hankel function of the first kind, The Euclidean distance between the field point x and the source point s; Combining all equations, we get the linear equation system of the singular boundary method:

[0029]

[0030] Right now:

[0031] Βα=b

[0032] in:

[0033]

[0034]

[0035] S2-3: Since the source point and field point of the singular boundary method coincide, singularities will appear on the diagonal of the equation system, so the source point intensity factor is introduced:

[0036]

[0037] Where γ is Euler's constant, is the fundamental solution of Laplace's equation, L j Indicates the source point s j The influence range, that is, the source point s on the physical boundary j-1 and source point s j+1 The previous half arc length.

[0038] The Burton Miller type singular boundary method program described in step S3 of the present invention is written in MATLAB.

[0039] In step S3 of the present invention, the linear equations established in step S2 are solved to obtain all source point densities α, and then the function value of any point in the domain is calculated according to the following equation:

[0040]

[0041] The average sound pressure level of several observation points in the observation area is used as the objective function.

[0042] In step S4 of the present invention, the objective function established in step S3 is substituted into the particle swarm optimization algorithm for iteration to find the optimal solution. The speed and position update formula in the iteration is:

[0043]

[0044] In the particle swarm optimization algorithm, ω represents the inertia weight, which determines the extent to which the current velocity of the particle is affected by its previous velocity; v max Indicates the maximum speed limit of the particle; represents the individual optimal solution reached by particle numbered t during the mth iteration; is the global optimal solution of the entire group at the mth iteration; c1 and c2 are learning factors respectively; and It is a random number between 0 and 1.

[0045] The measurement indicator for evaluating the performance of the optimization result of the sound barrier described in step S5 of the present invention is the sound pressure or sound pressure level change of the observation point in the observation area. A line graph is drawn of the sound pressure level change of the observation point in the observation area in step S3, and its change is observed. If the sound pressure level generally decreases, it is determined that the optimization effect is significant; if no obvious change is seen, it is determined that the optimization effect is poor.

[0046] Compared with the prior art, the present invention has the following beneficial effects: (1) This application is the first to use the isogeometric singular boundary method optimization model based on the basic solution of the acoustic control equation, and apply it to the optimization design of the sound barrier, and proposes to optimize the sound barrier in combination with the particle swarm optimization method. This method only requires the size of the objective function and does not require complex sensitivity derivation. When calculating the sound barrier with a relatively complex shape, it has great flexibility and efficiency; (2) Compared with the traditional CAE software core algorithm, such as the finite element method and the boundary element method, the method involved in this application has significant advantages such as no need for meshing, faster calculation speed, and easier programming. By introducing isogeometric analysis, that is, using NURBS functions to represent geometric boundaries, seamless integration between CAD and CAE is achieved, avoiding the tedious meshing steps in the optimization process, thereby significantly improving the accuracy and efficiency of the sound barrier optimization; the method of this application is scientifically and rationally designed, simple and fast, with high accuracy and flexibility, and provides a new research direction for the field related to sound barrier shape optimization. Description of the drawings:

[0047] Figure 1 This is a schematic flow chart of the sound barrier shape optimization method based on the isogeometric particle swarm singular boundary method involved in the present invention.

[0048] Figure 2 This is a schematic diagram of a two-dimensional model of a semi-Y-shaped sound barrier involved in an embodiment of the present invention.

[0049] Figure 3 This is a schematic diagram of the final optimization model of the sound barrier at initial, 100 Hz, and 300 Hz frequencies involved in an embodiment of the present invention.

[0050] Figure 4 This is a schematic diagram of the final optimized model of the sound barrier at frequencies of 700 Hz and 1000 Hz involved in an embodiment of the present invention.

[0051] Figure 5 This is the iterative change of the objective function during the optimization process at frequencies of 100 Hz, 300 Hz, 700 Hz, and 1000 Hz involved in the embodiment of the present invention.

[0052] Figure 6 These are the changes in sound pressure levels at observation points at frequencies of 100 Hz, 300 Hz, 700 Hz, and 1000 Hz involved in the embodiments of the present invention.

[0053] Description of the accompanying drawings: Boundary A to be optimized, observation area B. Specific implementation method:

[0054] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0055] Example 1:

[0056] This embodiment relates to a sound barrier shape optimization method based on the isogeometric particle swarm singular boundary method, such as Figure 1 As shown, the following steps are included:

[0057] Step S1: Creating a sound barrier geometric model: Building a sound barrier geometric model based on the geometric parameters of the sound barrier to be optimized, wherein the geometric parameters include the width, height, and position of the sound barrier in space; importing the information of the built model into a calculation program, and obtaining interpolation points of its boundary through the program;

[0058] Step S2: Establishing a sound barrier shape optimization model: Based on the known air density, the speed of sound propagation in air, the frequency of the sound source, the selected shape design variables and the corresponding boundary conditions, a sound barrier shape optimization model based on the isogeometric singular boundary method is established in combination with the particle swarm optimization method;

[0059] Step S3: Establish a program and calculate sound pressure: Using the sound barrier shape optimization model established in step S2, the boundary interpolation points obtained by the program in step S1 are used as configuration nodes of the singular boundary method, and a Burton-Miller type singular boundary method program is compiled to accurately calculate the sound pressure at the observation point; the average sound pressure level is calculated based on the sound pressure of several observation points in the observation area, and the average sound pressure level value is the objective function;

[0060] Step S4: Particle swarm iterative solution: Using the sound barrier shape optimization model established in step S2, the objective function, termination conditions, initial conditions, and upper and lower limits of the shape design variables of the Burton-Miller type singular boundary method are set, and the particle swarm optimization method is used for iterative solution to find the optimal solution in turn to obtain the optimal shape;

[0061] Step S5: Output optimization results: Utilize the optimization program established in step S4 to output the final optimized shape of the sound barrier after precise calculation, and perform performance evaluation of the optimization results by measuring the sound pressure level in the observation area.

[0062] The sound barrier geometric model described in step S1 of this embodiment is described by NURBS. The control point coordinates, weights, node vectors, and curve order in the geometric model are extracted and substituted into the boundary curve expression:

[0063]

[0064] Where p is the t-th control point, m is the number of control points, is the NURBS spline basis function, is the B-spline basis function of degree p, ω t is the weight of the t-th control point, is the parameter space coordinate; the NURBS interpolation point is used as the boundary configuration node of the sound barrier, and n nodes are configured on the boundary of the sound barrier

[0065] The acoustic control equation used in step S2 of this embodiment is:

[0066]

[0067] in is the Laplace operator, is the wave number, ω = 2πf is the angular frequency, c is the speed of sound, f is the frequency, Ω represents the sound field area, x is the spatial coordinate, and p(x) is the sound pressure amplitude at x;

[0068] For the above acoustic control equations, Dirichlet conditions and Newman boundary conditions are usually considered:

[0069]

[0070] in is the boundary Γ p The known sound pressure on is the boundary Γ v The known normal velocity on ρ is the density of air.

[0071] The step of establishing the sound barrier shape optimization model based on the isogeometric singular boundary method in step S2 of this embodiment includes:

[0072] S2-1: Define the objective function and constraints, select the shape design variables, give their upper and lower limits, set the maximum number of iterations and convergence parameters, where the objective function is set to the total sound pressure in the observation area, and the observation area is designed according to the actual situation;

[0073] S2-2: The numerical solution of each boundary point is expressed as a linear accumulation of basic solutions. The basic solution corresponding to the two-dimensional Helmholtz equation is:

[0074]

[0075] in is the zero-order Hankel function of the first kind, The Euclidean distance between the field point x and the source point s; Combining all equations, we get the linear equation system of the singular boundary method:

[0076]

[0077] Right now:

[0078] Βα=b

[0079] in:

[0080]

[0081]

[0082] S2-3: Since the source point and field point of the singular boundary method coincide, singularities will appear on the diagonal of the equation system, so the source point intensity factor is introduced:

[0083]

[0084] Where γ is Euler's constant, is the fundamental solution of Laplace's equation, L j Indicates the source point s j The influence range, that is, the source point s on the physical boundary j-1 and source point s j+1 The previous half arc length.

[0085] The Burton-Miller type singular boundary method program described in step S3 of this embodiment is written in MATLAB.

[0086] In step S3 of this embodiment, the linear equations established in step S2 are solved to obtain the density α of all source points, and then the function value of any point in the domain is calculated according to the following equation:

[0087]

[0088] The average sound pressure level of several observation points in the observation area is used as the objective function.

[0089] In step S4 of this embodiment, the objective function established in step S3 is substituted into the particle swarm optimization algorithm for iteration to find the optimal solution. The speed and position update formula during the iteration is:

[0090]

[0091] In the particle swarm optimization algorithm, ω represents the inertia weight, which determines the extent to which the current velocity of the particle is affected by its previous velocity; v max Indicates the maximum speed limit of the particle; represents the individual optimal solution reached by particle numbered t during the mth iteration; is the global optimal solution of the entire group at the mth iteration; c1 and c2 are learning factors, which control the acceleration weights of particles towards their own optimal solution and the global optimal solution when updating the speed; and It is a random number between 0 and 1, which introduces the necessary randomness into the algorithm to avoid falling into local optimality.

[0092] The measurement indicator for evaluating the performance of the optimization result of the sound barrier described in step S5 of this embodiment is the sound pressure or sound pressure level change of the observation point in the observation area. A line graph is drawn of the sound pressure level change of the observation point in the observation area in step S3 to observe its change. If the sound pressure level generally decreases, the optimization effect is significant; if no obvious change is seen, the optimization effect is poor.

[0093] NURBS (Non-Uniform Rational B-Splines), a mathematical model widely used in computer-aided design (CAD) and computer graphics, is used to accurately define and render complex curves and surfaces. NURBS combines the advantages of B-Spline and Bezier curves, providing precise control over curve shape and flexible manipulation of curve geometry and topological properties.

[0094] Example 2:

[0095] This embodiment involves the application of the sound barrier shape optimization method based on the isogeometric particle swarm singular boundary method described in Example 1 to the shape optimization of a semi-Y-shaped sound barrier.

[0096] like Figure 2 As shown, a two-dimensional model of a semi-Y-shaped sound barrier has a boundary A that needs to be optimized and an observation area B. The width of the sound barrier is L x =0.3m, height is L y =6m, of which the upper half is inclined at 30 degrees. The NURBS information of the two-dimensional model of the sound barrier is shown in Table 1. The point sound source is placed at a height of 1m from the ground. Assuming that the ground and the sound barrier boundary are both Newman boundary conditions, the objective function is defined as the average sound pressure level of 100 observation points in the observation area. The left boundary of the sound barrier is selected as the optimization area. Six control points are inserted in the inclined part between control points P7 and P8 through refinement. The position of the control point is along the vertical direction of the inclined boundary as the design variable of the shape. The upper and lower distances of the variables are 0.1 as the limit. At P9 and P8, the control points are inserted into the inclined part through refinement. 10 Twelve control points were inserted into the vertical section between the two sides. The horizontal coordinates of these 12 control points were used as shape design variables, with an upper limit of 6.1 and a lower limit of 5.9. The maximum number of iterations of the particle swarm optimization program was set to 50, and an equal geometry singular boundary method optimization model was established to optimize the sound barrier.

[0097]

[0098] like Figure 3 As shown in Figure 2, they are the final optimized models of the sound barrier at 400Hz and 700Hz frequencies respectively. Figure 4 As shown in Figure 2, they are the iterative change curves of the objective function and area respectively. Figure 5 The curve of the sound pressure level change at the observation point is shown in Figure 2. It can be seen that the sound pressure level at the observation point has been significantly reduced after optimization.

[0099] In summary, the sound barrier shape optimization method of this embodiment is based on the isogeometric singular boundary method, directly utilizing the semi-analytical fundamental solution of the acoustic problem as a function, replacing the finite element mesh with NURBS interpolation nodes, and combining the particle swarm optimization method to optimize the sound barrier shape. This method is characterized by simple mathematical theory and ease of implementation. It requires only discrete nodes, eliminating the need for meshing and numerical integration. The introduction of isogeometry allows for seamless integration between CAD and CAE, avoiding the meshing stage during the optimization process and improving the accuracy and efficiency of sound barrier optimization. It is simple, fast, stable, and precise, capable of accurately and efficiently optimizing the shape of sound barriers, providing a new, simple, and efficient technical approach for sound barrier shape optimization.

Claims

1. A sound barrier shape optimization method based on isogeometric particle swarm singular boundary method, characterized in that: The steps include: Step S1: Creating a sound barrier geometric model: Building a sound barrier geometric model based on the geometric parameters of the sound barrier to be optimized, wherein the geometric parameters include the width, height, and position of the sound barrier in space; importing the information of the built model into a calculation program, and obtaining interpolation points of its boundary through the program; Step S2: Establishing a sound barrier shape optimization model: Based on the known air density, the speed of sound propagation in air, the frequency of the sound source, the selected shape design variables and the corresponding boundary conditions, a sound barrier shape optimization model based on the isogeometric singular boundary method is established in combination with the particle swarm optimization method; Step S3: Establish a program and calculate sound pressure: Using the sound barrier shape optimization model established in step S2, the boundary interpolation points obtained by the program in step S1 are used as configuration nodes of the singular boundary method, and a Burton-Miller type singular boundary method program is compiled to accurately calculate the sound pressure at the observation point; the average sound pressure level is calculated based on the sound pressure of several observation points in the observation area, and the average sound pressure level value is the objective function; Step S4: Particle swarm iterative solution: Using the sound barrier shape optimization model established in step S2, the objective function, termination conditions, initial conditions, and upper and lower limits of the shape design variables of the Burton-Miller type singular boundary method are set, and the particle swarm optimization method is used for iterative solution to find the optimal solution in turn to obtain the optimal shape; Step S5: Output optimization results: Utilize the optimization program established in step S4 to output the final optimized shape of the sound barrier after precise calculation, and perform performance evaluation of the optimization results by measuring the sound pressure level in the observation area.

2. The sound barrier shape optimization method based on the isogeometric particle swarm singular boundary method according to claim 1 is characterized by: The sound barrier geometry model described in step S1 is described by NURBS. The control point coordinates, weights, node vectors, and curve order in the geometry model are extracted and substituted into the boundary curve expression: Where p is the t-th control point, m is the number of control points, is the NURBS spline basis function, is the B-spline basis function of degree p, ω t is the weight of the t-th control point, is the parameter space coordinate; the NURBS interpolation point is used as the boundary configuration node of the sound barrier, and n nodes are configured on the boundary of the sound barrier 3. The sound barrier shape optimization method based on the isogeometric particle swarm singular boundary method according to claim 1 is characterized by: The acoustic control equation used in step S2 is: in is the Laplace operator, is the wave number, ω = 2πf is the angular frequency, c is the speed of sound, f is the frequency, Ω represents the sound field area, x is the spatial coordinate, and p(x) is the sound pressure amplitude at x; For the above acoustic control equations, Dirichlet conditions and Newman boundary conditions are usually considered: in is the boundary Γ p The known sound pressure on is the boundary Γ v The known normal velocity on ρ is the density of air.

4. The sound barrier shape optimization method based on the isogeometric particle swarm singular boundary method according to claim 1 is characterized by: The steps of establishing the sound barrier shape optimization model based on the isogeometric singular boundary method in step S2 include: S2-1: Define the objective function and constraints, select the shape design variables, give their upper and lower limits, set the maximum number of iterations and convergence parameters, where the objective function is set to the total sound pressure in the observation area; S2-2: The numerical solution of each boundary point is expressed as a linear accumulation of basic solutions. The basic solution corresponding to the two-dimensional Helmholtz equation is: in is the zero-order Hankel function of the first kind, The Euclidean distance between the field point x and the source point s; Combining all equations, we get the linear equation system of the singular boundary method: Right now: Βα=b in: S2-3: Since the source point and field point of the singular boundary method coincide, singularities will appear on the diagonal of the equation system, so the source point intensity factor is introduced: Where γ is Euler's constant, is the fundamental solution of Laplace's equation, L j Indicates the source point s j The influence range, that is, the source point s on the physical boundary j-1 and source point s j+1 The previous half arc length.

5. The sound barrier shape optimization method based on the isogeometric particle swarm singular boundary method according to claim 1 is characterized by: The Burton-Miller type singular boundary method program described in step S3 is written in MATLAB.

6. The sound barrier shape optimization method based on the isogeometric particle swarm singular boundary method according to claim 1, characterized in that: In step S3, the linear equations established in step S2 are solved to obtain the density α of all source points, and then the function value of any point in the domain is calculated according to the following equation: The average sound pressure level of several observation points in the observation area is used as the objective function.

7. The sound barrier shape optimization method based on the isogeometric particle swarm singular boundary method according to claim 1 is characterized by: In step S4, the objective function established in step S3 is substituted into the particle swarm optimization algorithm for iteration to find the optimal solution. The speed and position update formula in the iteration is: In the particle swarm optimization algorithm, ω represents the inertia weight, which determines the extent to which the current velocity of the particle is affected by its previous velocity; v max Indicates the maximum speed limit of the particle; represents the individual optimal solution reached by particle numbered t during the mth iteration; is the global optimal solution of the entire group at the mth iteration; c1 and c2 are learning factors respectively; and It is a random number between 0 and 1.

8. The method for optimizing the shape of a sound barrier based on the isogeometric particle swarm singular boundary method according to claim 1, characterized in that: The measurement indicator for evaluating the performance of the optimization result of the sound barrier described in step S5 is the sound pressure or sound pressure level change of the observation point in the observation area. A line graph is drawn of the sound pressure level change of the observation point in the observation area in step S3 to observe its change. If the sound pressure level generally decreases, it is judged that the optimization effect is significant; if no obvious change is seen, it is judged that the optimization effect is poor.

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