WO2024082778A1

WO2024082778A1 - Parameter-topology hybrid optimization method for electromagnetic device design

Info

Publication number: WO2024082778A1
Application number: PCT/CN2023/111240
Authority: WO
Inventors: 杨雪松; 王兰兰
Original assignee: 电子科技大学长三角研究院(湖州)
Priority date: 2022-10-21
Filing date: 2023-08-04
Publication date: 2024-04-25
Also published as: CN115795936A

Abstract

The present invention relates to the field of microwave circuit and antenna optimization. Disclosed is a parameter-topology hybrid optimization method for electromagnetic device design. In the method, an adjoint sensitivity analysis method is used to simultaneously solve gradient information of structural parameter variables and material density variables, thereby achieving gradient optimization of the device structure and topological shape, and the method has the characteristics of high convergence rate and high optimization efficiency; the topological shape in an optimization area is characterized by the pixel material density, the correlation between the material density variable and the finite element mesh is reduced, and thus, finite element meshes having different precision can be used at different stages of the optimization process, to balance the optimization efficiency and the calculation accuracy. Compared with a conventional material distribution method, pixel density values are used as topological optimization variables, the optimized structure has smooth boundaries, thereby reducing errors during processing.

Description

A parameter-topology hybrid optimization method for electromagnetic device design

Technical Field

The invention relates to the technical field of microwave circuit or antenna design optimization, and in particular to a parameter-topology hybrid optimization method for electromagnetic device design.

Background technique

Topology optimization algorithm belongs to a higher-level optimization technology. It can optimize the size, shape, and topological connectivity of the entire optimization area, which is conducive to the automatic design of devices. Some literatures give the application of topology optimization algorithm in the design of microwave devices such as metal antennas and filters, and obtain good optimization results. The scalar isotropic material with penalization method (SIMP) is a commonly used topology optimization algorithm with strong topology optimization ability and fast convergence speed. In 2014, E. Hassan et al. used SIMP to optimize monopole antennas in the article "Topology optimization of metallic antennas" (IEEE Transactions on Antennas and Propagation, 2014, 62(5): 2488-2500). In 2017, J. Wang et al. used SIMP to optimize patch antennas in the article "Antenna radiation characteristics optimization by a hybrid topological method" (IEEE Transactions on Antennas and Propagation, 2017, 65(6): 2843-2854).

SIMP is based on fixed grid optimization, which has obvious disadvantages. The optimized model has a stepped boundary, and structural parameters such as the device port position cannot be adjusted during the optimization process. In 2014, E. Hassan et al. (IEEE Transactions on Antennas and Propagation, 2014, 62(5): 2488-2500) used a very dense grid to divide the optimization area, which made electromagnetic simulation calculations difficult. In 2017, J. Wang et al. (IEEE Transactions on Antennas and Propagation, 2017, 65(6): 2843-2854) combined SIMP and the level-set method (LSM) to obtain a model with smooth boundaries, but the optimization process was relatively complicated.

As for the adjustment of structural parameters in the topology optimization process, L. Chen et al. proposed a two-layer algorithm optimization scheme in the article "A novel topological optimization method for multi-substance-sensor microfluidics devices," (IEEE Sensors Journal, 2022: 1-1). The outer layer uses a genetic algorithm (GA) to optimize the structural parameters, and the inner layer uses the method of moving asymptotes (MMA) to optimize the topological shape. Under this optimization framework, the structural parameters obtained by the outer layer algorithm require a complete topology optimization design. For complex microwave device design problems, the two-layer optimization algorithm solution has too much computational complexity and converges very slowly.

Technical Solutions

In order to solve the problems that the existing topology optimization algorithm cannot adjust the structural parameters and the model is jagged, the present invention proposes a parameter-topology hybrid optimization method for electromagnetic device design, and takes the structural parameters and material density values of microwave devices as optimization variables. MMA is used to perform gradient optimization on the optimization variables, where the gradient information of the optimization variables is obtained by the adjoint sensitivity analysis method.

The specific implementation steps of the parameter-topology hybrid optimization method for electromagnetic device design are as follows:

Step 1: Create an initial model of the microwave circuit or antenna and determine the structure that needs to be optimized for structural parameters and the area that needs to be optimized for topology. The structural parameter variables that need to be optimized are defined as The shape of the topology optimization area is based on the material density of the pixel point. To characterize, the number of variables that the algorithm needs to process is After the optimization variables are defined, the initial values of the optimization variables are generated by random methods. .

Step 2: When performing topological optimization on the design area, in order to ensure the continuity of the topological structure and prevent the appearance of a checkerboard structure in the topological optimization area, the pixel material density variable Perform spatial median filtering, that is

in, Represents pixel The surrounding radius is less than A collection of pixels, is the weight factor, defined as:

At the end of the optimization process, the material density variable will become a binary distribution. In order to remove the gray value of the pixel, Perform regularized Heaviside filtering, that is

in, is the coefficient that controls the transition width of the Heaviside mapping filter, The expression is:

Step 3: According to the current optimization variable value and the required calculation accuracy, the model is divided into tetrahedral meshes. The tetrahedral mesh is used for electromagnetic full-wave simulation. The topology optimization area is divided into When the feed port position or meshing accuracy changes, The value of will also change. The material density in each grid is the average value of the material density of the pixels in the grid, that is

in, Represents a triangular mesh The number of pixels in the image.

Step 4: According to the finite element theory, the electromagnetic wave equation can be discretized into a linear equation, namely

in, represents the system matrix, represents the basis function coefficients, represents the excitation vector.

According to the optimization objective function , solve the adjoint equation:

in, and They are The real and imaginary parts of .

Step 5: According to the theory of adjoint sensitivity analysis, find the structural variables and triangle material density variables The gradient value of:

System Matrix About Geometry Variables The derivative of is calculated from the derivatives of the finite element mesh vertices with respect to the Cartesian coordinates:

in, Representation and structural parameters Related Vertices of Axis coordinates.

The topology optimization area is a two-dimensional metal surface, and the triangular material density variable is mapped to the conductivity of the material in the optimization area. :

in, and represent the minimum and maximum values of conductivity, respectively.

System Matrix About Material Density Variables in Triangular Meshes The derivative of is:

Step 6: Map the gradient of the material density variable in the triangular mesh to the material density gradient of the pixel point, that is,

in, Represents a triangular mesh The material density, , and Represents the triangular mesh The original material density of the pixel within, the material density after spatial median filtering, and the material density after regularized Heaviside filtering.

Step 7: Update optimization variables using MMA , is the number of algorithm iterations.

Step 8: Repeat steps 2-7 until the algorithm converges, that is .

Beneficial Effects

The beneficial effects of the present invention are: 1) the optimization method proposed in the present invention can optimize structural parameters and topological shapes at the same time, and the optimization freedom is higher; 2) the definition of the material density value of the pixel point does not depend on the grid of the topological optimization area, and the grid division can be adjusted at any time during the optimization process to balance the full-wave simulation speed and calculation accuracy; 3) the material density value of the pixel point is used to describe the topological structure of the optimization area. Compared with the traditional SIMP, the optimized model has a smooth boundary and can be directly processed without subsequent processing.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a flowchart of the algorithm implementation;

FIG2 is a schematic diagram of the initial structure of the antenna;

Figure 3 is the objective function variation curve;

FIG4 is a feeding point position variation curve;

Figure 5 is a diagram showing the shape change of the topology optimization area;

Figure 6 shows the S parameters and radiation pattern of the optimized antenna.

Embodiments of the present invention

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

The present invention provides a parameter-topology hybrid optimization method for electromagnetic device design, which can be used to optimize microwave devices or antennas. Taking a microstrip patch antenna as an example, the present invention provides a specific optimization process of the optimization method, as shown in FIG1. FIG2 shows a structural diagram of the initial optimized antenna model. The antenna dielectric substrate is FR4 ( =4.4,tan =0.002), and the radiating patch is fed through the back-feed coaxial connector. The position of the feeding point and the shape of the radiating patch play a decisive role in the impedance matching and radiation characteristics of the antenna. The parameter-topology hybrid optimization method can be used to optimize the antenna structure with better performance.

The feeding point of the antenna moves only in the plane where the patch is located. Axis and The axis coordinates are determined, so the structural parameter variables that need to be optimized for the antenna are When the feed point position changes, the grid of the radiating patch needs to be re-divided, and the fixed grid optimization of traditional SIMP is not applicable.

The radiation patch is the topology optimization area of the algorithm, with a side length of Lg = 60mm. （ =600) pixel point material density matrix characterizes the shape of the optimization area and generates material density variables .

In order to obtain a linearly polarized antenna operating at 2.6 GHz, the objective function is defined as:

in, is the main polarization target value of the antenna, Optimized angle for primary polarization.

The main polarization direction is defined as Axis direction, through experience, we know that the antenna adopts a left-right symmetrical structure to ensure good polarization purity, and the feeding point position is only Axis movement, the movement range is By setting the structural symmetry, the number of optimization variables is halved to .

The antenna is optimized by the parameter-topology hybrid optimization method. The objective function changes during the optimization process as shown in Figure 3. The objective function shows a downward trend overall. The feed point position changes during the optimization process as shown in Figure 4. In the early stage of optimization, the feed point position is constantly adjusted within the optimization area; in the later stage of optimization, the topology optimization area develops towards a binary distribution, and the feed point position basically does not change. In the later stage of optimization, the coefficients of the Heaviside filter function are If the feed point position changes, the objective function curve will have a corresponding mutation.

The change of material distribution in the topology optimization area during the optimization process is shown in Figure 5. The optimized topology shape has smooth boundaries, which can reduce processing and testing errors.

The antenna optimized by HFSS software is simulated, and the simulated S parameters and radiation pattern are shown in Figure 6.

The invention proposes a parameter-topology hybrid optimization method for electromagnetic device design, which is used for microwave circuit or antenna design. The invention can optimize the structural parameters and topological shape of electromagnetic devices at the same time, and ensure that the final optimized structure has a smooth boundary without increasing the number of grids. The parameter-topology hybrid optimization method does not directly optimize the material density of the finite element grid. The accuracy of the grid division can be adjusted during the optimization process. The finite element grid with lower accuracy is used in the early stage to reduce the optimization time; the finite element grid with higher accuracy is used in the later stage to ensure the accuracy of the optimization.

The above descriptions are only preferred embodiments of the present invention, and all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

Claims

A parameter-topology hybrid optimization method for electromagnetic device design, characterized in that it includes the following steps:

Step 1: Create an initial model of the microwave circuit or antenna, determine the structure that needs to be optimized and the area that needs to be optimized. The structural parameter variables that need to be optimized are defined as The shape of the topology optimization area is based on the material density of the pixel point. To characterize, the number of variables that the algorithm needs to process is After the definition of the optimization variables is completed, the initial values of the optimization variables are generated by random methods. ;

Step 2: When performing topological optimization on the design area, in order to ensure the continuity of the topological structure and prevent the appearance of a checkerboard structure in the topological optimization area, the pixel material density variable Perform spatial median filtering, that is

in, Represents pixel The surrounding radius is less than A collection of pixels, is the weight factor, defined as:

At the end of the optimization process, the material density variable will become a binary distribution. In order to remove the gray value of the pixel, Perform regularized Heaviside filtering, that is

in, is the coefficient that controls the transition width of the Heaviside mapping filter, The expression is:

Step 3: Tetrahedral meshing is performed on the model according to the current optimization variable values and the required calculation accuracy. The tetrahedral mesh is used for electromagnetic full-wave simulation. The topology optimization area is divided into When the feed port position or meshing accuracy changes, The value of will also change, and the material density in each grid is the average value of the material density of the pixels in the grid, that is

in, Represents a triangular mesh The number of pixels in the

Step 4: According to the finite element theory, the electromagnetic wave equation can be discretized into a linear equation, namely

in, represents the system matrix, represents the basis function coefficients, represents the excitation vector;

According to the optimization objective function , solve the adjoint equation:

in, and They are The real and imaginary parts of

Step 5: According to the theory of adjoint sensitivity analysis, find the structural variables and triangle material density variables The gradient value of:

System Matrix About Geometry Variables The derivative of is calculated from the derivatives of the finite element mesh vertices with respect to the Cartesian coordinates:

in, Representation and structural parameters Related Vertices of Axis coordinates;

The topology optimization area is a two-dimensional metal surface, and the triangular material density variable is mapped to the conductivity of the material in the optimization area. :

in, and Respectively represent the minimum and maximum values of electrical conductivity;

System Matrix About Material Density Variables in Triangular Meshes The derivative of is:

Step 6: Map the gradient of the material density variable in the triangular mesh to the material density gradient of the pixel point, that is,

in, Represents a triangular mesh The material density, , and Represents the triangular mesh The original material density of the pixel points within, the material density after spatial median filtering and the material density after regularized Heaviside filtering;

Step 7: Update optimization variables using MMA , is the number of algorithm iterations;

Step 8: Repeat steps 2-7 until the algorithm converges, that is .
A parameter-topology hybrid optimization method for electromagnetic device design as described in claim 1, characterized in that in step 1, the material density value of the pixel point in the topology optimization area is used as a topology optimization variable to represent the shape of the topology optimization area.
The parameter-topology hybrid optimization method for electromagnetic device design according to claim 1 is characterized in that in step 1, adjoint sensitivity analysis is used to solve the gradients of structural parameter variables and material density variables.
A parameter-topology hybrid optimization method for electromagnetic device design as described in claim 1, characterized in that a spatial median filter function and a regularized Heaviside filter function are used in step 1 to ensure the continuity of the topological shape and reduce the grayscale value of the topological shape.
A parameter-topology hybrid optimization method for electromagnetic device design as described in claim 1, characterized in that the material density of the pixel point defined in step 1 is independent of the mesh division of the topology optimization area, and the optimization speed and calculation accuracy can be balanced by changing the mesh division during the optimization process.