Satellite component layout based on thermal metamaterials - integrated optimization design method for panel structure

Abstract

The application discloses a satellite component layout-cabin plate structure integrated optimization design method based on thermal metamaterials, and belongs to the technical field of satellite thermal management, which comprises the following steps: geometrically describing components, and calculating the interference between the components; selecting a planar four-node rectangular element to discretely design a design domain, and representing a component temperature field as an interpolation relationship of node temperatures; designing an optimization target and a constraint, converting the optimization target and the constraint into a standard optimization formula, and searching for an optimal component layout scheme; performing satellite cabin plate structure topology optimization design based on a thermal metamaterial design idea, determining a thermal metamaterial function type, and dividing a local cabin plate design domain; discretely designing each design unit, and performing topology optimization design on the discrete design units, searching for a microstructure with the highest matching degree of a macroscopic equivalent thermal conduction tensor and a design unit center position theoretical thermal conduction tensor; and assembling the microstructures to obtain a cabin plate structure. The application can realize global thermal management and local thermal management of a satellite cabin.

Description

Technical Field

[0001] This invention relates to the field of satellite thermal management technology, and in particular to an integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials. Background Technology

[0002] Thermal management (or thermal control) is a subsystem used to manage the heat exchange process inside and outside the satellite, ensuring that all parts of the satellite and onboard instruments and equipment remain within their normal operating temperature range throughout the mission, and achieving requirements such as ambient temperature, low temperature, constant temperature, and temperature uniformity control. Due to the alternating effects of solar radiation and Earth's shading, as well as the influence of solar radiation, Earth's albedo, and Earth's infrared radiation, there are significant differences in the thermal load effects inside and outside the satellite cabin. During its orbital flight, the satellite will experience high and low temperature environments. Therefore, the thermal management subsystem is like the satellite's "skin and clothing" for heat dissipation and insulation, playing a crucial role in ensuring the normal operation of the satellite.

[0003] Currently, satellite design trends are moving towards larger, smaller, and more energy-efficient designs. The increasing use of high-power payloads and the integration of onboard equipment are leading to continuously increasing payload power density and a sustained rise in overall system heat flux. This places increasingly higher demands on the heat transfer and dissipation capabilities, system integration, lightweight design, and reliability of satellite thermal management subsystems. Therefore, lightweight and efficient thermal management designs are essential to effectively meet these heat dissipation requirements.

[0004] Traditional satellite thermal management is divided into two categories: passive thermal management and active thermal management. Passive thermal management typically has advantages such as simplicity, reliability, long lifespan, and low cost. A typical existing technology achieves passive thermal management by optimizing the layout of heat-generating components within the satellite cabin. However, thermal management based on component layout optimization has poor flexibility and limited functionality, primarily managing the overall temperature field distribution at a global level. This cannot meet the more precise local thermal management needs of some specialized precision equipment within the satellite cabin. Examples include devices sensitive to temperature gradient magnitude, such as atomic clocks and onboard processors requiring uniform temperature distribution; and high-precision cameras and spectrometers sensitive to the direction of temperature gradients within components. Component layout optimization cannot precisely control the thermal field in localized areas of components, nor can it meet the local thermal management needs of such precision equipment and temperature-sensitive high-precision instruments. While active thermal management methods are powerful, diverse, and offer high flexibility and precision, the devices used in this approach are typically large in size and consume more energy, have lower reliability, and shorter lifespans. Summary of the Invention

[0005] To address some or all of the technical problems existing in the prior art, this invention provides an integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials. This optimization design method can improve the service life and on-orbit time of satellites, has good flexibility and comprehensive functions, and can simultaneously achieve global thermal management of the satellite cabin and more refined local thermal management for special precision instruments and equipment.

[0006] The technical solution of the present invention is as follows:

[0007] An integrated optimization design method for satellite component layout and panel structure based on thermal metamaterials is provided, including:

[0008] Geometric description of regular geometric shapes of two-dimensional components is performed based on parameterized level set functions. The Heaviside function is used to construct a two-dimensional projection of the three-dimensional shape of the satellite components, and interference calculation between satellite components is performed.

[0009] Based on the steady-state heat conduction equilibrium equation, a planar four-node rectangular element is selected to discretize the design domain, and the temperature field of the satellite component is expressed as the interpolation relationship of the nodal temperatures.

[0010] The multi-resolution finite element method is used to refine the mesh of the satellite component boundary, enabling the analysis and evaluation of the corresponding temperature field.

[0011] The design optimization objectives and constraints are based on the requirements for temperature field distribution and component layout of the satellite module.

[0012] The layout optimization objectives and constraints are transformed into standard optimization formulas. Automatic differentiation techniques are used to obtain the sensitivity of the objective function and constraints to design variables. Gradient optimization algorithms are applied to find the optimal component layout scheme.

[0013] Based on the design concept of thermal metamaterials, the topology optimization design of satellite compartment structure is carried out. According to the optimal component layout scheme and the requirements of key components on the satellite compartment for local thermal control function, the functional type of thermal metamaterials is determined and the local compartment design domain is divided.

[0014] The design domain is discretized to obtain multiple design units, and the theoretical heat conduction tensor value at the center of each design unit is expected to be calculated based on transformation thermal calculation.

[0015] Each design unit is discretized, and topology optimization is performed on the discretized design units. The inverse homogenization method is used to find the microstructure with the highest matching degree between the macroscopic equivalent heat conduction tensor and the theoretical heat conduction tensor at the center of the design unit.

[0016] The microstructures of each design unit are assembled to obtain a cabin structure with corresponding thermal metamaterial heat flow control function.

[0017] In some implementations, the geometric description of a two-dimensional component with a regular geometry based on a parameterized level set function is determined by the following formula:

[0018] ;

[0019] in, This represents a level set function that describes the shape of a component. and These represent half of the component's length and half its width, respectively. Indicates the coordinates of the geometric center of the satellite component. This indicates the rotation angle of the satellite component, with counterclockwise rotation from the horizontal direction being positive. and Together, they determine the placement of satellite components within the layout area. This represents the position coordinates of any point in the plane. Even number, ,parameter This determines the geometry of the component. This indicates that the origin is the center of the component and the major axis is... The relative position coordinates of the axis in the component's local coordinate system;

[0020] in, It is determined by the following formula:

[0021] .

[0022] In some implementations, the Heaviside function is a regularized Heaviside function, which is expressed as:

[0023] ;

[0024] in, This represents the Heaviside regularization function. The argument of the regularization Heaviside function is... It is a constant. This represents the half-width of the 0~1 transition interval of the Heaviside function.

[0025] In some implementations, interference calculations between satellite components are performed in the following manner:

[0026] The Heaviside function is used to construct a two-dimensional projection of the three-dimensional shape of the satellite component, where the first... Components The area occupied by the projection is expressed as:

[0027] ;

[0028] in, Indicates the first Components The two-dimensional projected area, Indicates the spatial region where the component is located. express The projection of the Heaviside function, Represents the description component The level set function of the shape, Representing an area element, when a component on a satellite module... With another component When overlap occurs, the overlapping spatial region is determined by the following formula:

[0029] ;

[0030] in, This indicates the size of the overlapping area between the two components. and Representing components respectively and components Size of the space occupied, and These respectively represent the description components. and components The level set function of the shape;

[0031] When two satellite assemblies overlap on the deck, the area of ​​the overlapping region is determined by the following formula:

[0032] ;

[0033] This indicates the area of ​​the overlapping region between two satellite components.

[0034] In some implementations, based on the steady-state heat conduction equilibrium equation, a planar four-node rectangular element discrete design domain is selected, and the satellite component temperature field is expressed as an interpolation relationship of nodal temperatures in the following manner:

[0035] ;

[0036] Indicates the heat source intensity of the unit. This indicates the constant heat source intensity per unit area of ​​a component.

[0037] In some implementations, the optimized formula is expressed as:

[0038] ;

[0039] in: Indicates the first The position vectors of each component. ; Represent design variables The design space must be satisfied, and the design variables for each component include the position coordinates of its reference point. and its rotation angle , , Indicated based on temperature field The objective function is represented by;

[0040] Based on the requirements, a temperature index is defined. The maximum temperature in the layout area is selected and approximated using the KS function as the objective function. The objective function is shown in the following formula:

[0041] ;

[0042] in, Represents the KS function, Indicates the adjustment parameter. Indicates the first Temperature of each node This indicates the number of nodes in the finite element mesh. This indicates the maximum temperature.

[0043] In some implementations, when determining the functional type of thermal metamaterials and dividing local panel design domains, the thermal sensitivity characteristics and heat transfer requirements of the components are evaluated and classified to distinguish the differences in the type and degree of heat flow control of the panel structure for different satellite components. Based on the classification, thermal metamaterial design schemes for panel structures that meet the heat flow control requirements are matched for the satellite components and local panel design domains are divided.

[0044] In some implementations, the design domain is discretized to obtain multiple design units, and the theoretical heat conduction tensor value at the center of each design unit is calculated based on transformational thermal calculations, including:

[0045] Based on the partitioning results of the design domain, a square grid is used to discretize the design domain at a specific size to obtain multiple design units;

[0046] Determine the boundary function of the thermal metamaterial design domain and the location of the center of each design unit in a local coordinate system constructed with the component center as the origin;

[0047] According to transformational thermodynamics, the form of the heat conduction equation remains unchanged before and after coordinate transformation, thus making the physical parameters of the material equivalent to the space.

[0048] By using coordinate transformation, the distortion of thermal flow lines is correlated with spatial deformation, thus establishing a one-to-one correspondence between material physical parameters and spatial variations.

[0049] The original space is transformed into a transformation space according to certain rules. Based on the correspondence, the heat conduction tensor distribution in the transformation space is determined, and the theoretical heat conduction tensor value at the center of each design unit is calculated and used as the target for subsequent structural optimization.

[0050] The heat conduction equation within the transformation space is expressed as:

[0051] ;

[0052] in, Represents the temperature distribution within the transformation space. Represents the heat conduction tensor within the transformation space. This represents gradient operation;

[0053] Determined by the following formula:

[0054] ;

[0055] The Jacobian matrix represents the coordinate partial derivative transformation between the original space and the transformed space. This represents the heat conduction tensor of the original space. Representing the Jacobian matrix The transpose operation. This represents a function used to calculate the determinant of a matrix.

[0056] In some implementations, the design unit is topology optimized in the following way:

[0057] Define the optimization objective, determine the topology optimization model based on the defined optimization objective, and set the micro-initial design parameters;

[0058] Accurate numerical simulation of heat conduction problems is performed to determine the finite element model and predefine the finite element analysis parameters;

[0059] Initialize design variables and begin iterative optimization;

[0060] Substitute the design variables and use the homogenization method to calculate the equivalent thermal conductivity tensor of the microstructure;

[0061] Based on the calculated equivalent heat conduction tensor, the values ​​of the objective function and constraint function are calculated.

[0062] The sensitivity is analyzed and filtered, and the design variables are updated based on the filtered sensitivity information;

[0063] After each update of the design variables, it is determined whether the design unit meets the convergence condition.

[0064] If the convergence condition is met, the optimization stops, and the optimal topology that satisfies the target heat conduction tensor requirement is obtained;

[0065] If the convergence condition is not met, the updated design variables are substituted into the homogenization calculation, sensitivity analysis, and design variable update steps to continue iterative optimization until the design unit meets the convergence condition.

[0066] In some implementations, each design unit is discretized in the following manner:

[0067] Each design unit is discretized into basic units with a specific resolution, and the pseudo-density of the basic units is... To optimize design variables in the design, ;

[0068] When the structure is composed of two materials, the SIMP interpolation model treats each basic element as an isotropic material with a specific thermal conductivity coefficient. The thermal conductivity coefficient of the basic element is expressed as:

[0069] ;

[0070] in, This represents the thermal conductivity coefficient of the basic unit. and These represent the thermal conductivity coefficients of the two materials, respectively. The time represents the thermal conductivity coefficient. Materials, The time represents the thermal conductivity coefficient. Materials.

[0071] The main advantages of the technical solution of this invention are as follows:

[0072] This invention presents an integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials. By rationally selecting the component topology description method and determining design variables, and designing optimization objectives and constraints according to the satellite cabin temperature field distribution requirements and component layout requirements, the layout optimization problem is refined into a standard optimization formula. Automatic differentiation technology is used to obtain the sensitivity of the objective function and constraints to the design variables, and gradient optimization algorithms are applied to find the optimal component layout scheme. Then, based on the obtained component layout results and the requirements of key components for local thermal control functional characteristics, the functional type of the thermal metamaterial is determined, and the local cabin design domain is divided. Based on the expected local heat conduction tensor distribution field calculated by transform thermal analysis, the design domain is discretized, and the topological configuration of each discrete unit is designed based on the inverse homogenization method. These are then assembled into an overall structure with thermal metamaterial functional characteristics. This method can improve satellite lifespan and on-orbit time, offers good flexibility and comprehensive functions, and can simultaneously achieve global thermal management of the satellite cabin and precise local thermal management for special precision instruments and equipment. Attached Figure Description

[0073] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and constitute a part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0074] Figure 1 A flowchart illustrating the integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials provided in this embodiment of the invention.

[0075] Figure 2 This is an overall schematic diagram of the integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials provided in this embodiment of the invention.

[0076] Figure 3 A schematic diagram of a component based on a parameterized level set function description is provided in an embodiment of the present invention;

[0077] Figure 4 This invention provides a schematic diagram of a finite element node affected by components and a multi-resolution finite element method.

[0078] Figure 5 A random layout scheme and corresponding temperature field distribution diagram provided in an embodiment of the present invention;

[0079] Figure 6 This invention provides a layout scheme optimized by temperature field performance and a corresponding temperature field distribution diagram.

[0080] Figure 7 A schematic diagram illustrating the function and design domain of a component area panel thermal metamaterial according to an embodiment of the present invention;

[0081] Figure 8 This is a schematic diagram of the boundary function of a cylindrical thermal stealth design domain in a local coordinate system with the component center as the origin, provided in an embodiment of the present invention.

[0082] Figure 9 This invention provides a schematic diagram of the boundary function of a cuboid thermal rotation design domain in a local coordinate system with the component center as the origin.

[0083] Figure 10 This is a schematic diagram illustrating a case where a local design domain is discretized into design units, as provided in an embodiment of the present invention.

[0084] Figure 11 This is a schematic diagram of an inverse homogenization topology optimization design process for a design unit, provided in an embodiment of the present invention.

[0085] Figure 12 This is a schematic diagram illustrating a topology optimization design process for each design unit, provided as an embodiment of the present invention.

[0086] Figure 13 This is a schematic diagram of the design topology optimization results for a local compartment with thermal stealth function at the location of a cylinder, provided in an embodiment of the present invention.

[0087] Figure 14 This is a schematic diagram of the design topology optimization results for a local compartment with a thermal rotation function at the location of a cuboid, provided in an embodiment of the present invention.

[0088] Figure 15 This is a schematic diagram of the temperature field distribution of control group 1 provided in an embodiment of the present invention;

[0089] Figure 16 This is a schematic diagram of the temperature field distribution of control group 2 provided in an embodiment of the present invention;

[0090] Figure 17 This is a schematic diagram of the temperature field distribution of experimental group 1 provided in an embodiment of the present invention. Detailed Implementation

[0091] 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 in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0092] The following is in conjunction with the appendix Figure 1 -Appendix Figure 17The technical solutions provided in the embodiments of the present invention will be described in detail.

[0093] First, it's important to note that the various components within a satellite cabin typically have different power levels and operating temperature ranges. The rationality of the component layout directly determines the overall temperature performance and heat dissipation level within the satellite cabin. Optimizing the thermal layout of satellite components can effectively reduce localized high temperatures and improve overall temperature distribution performance, making it a crucial means of achieving efficient passive heat dissipation during the overall satellite design phase. Furthermore, the quality of the satellite layout design directly determines the difficulty and cost of subsequent thermal control design. The satellite cabin structure is the primary carrier of heat conduction within the satellite cabin. Currently, the most common satellite cabin structure is a periodic honeycomb structure. This structure can be approximated as being composed of homogeneous materials, with the thermal conductivity of the cabin panels uniformly distributed in the plane, making it unable to adaptably match the unique heat transfer requirements of different components. Topology optimization design of the satellite cabin structure can effectively adjust and improve the propagation path of heat energy within the cabin structure, providing a highly reliable and low-cost passive thermal management method and serving as an important supplement to other satellite thermal management solutions. Thermal metamaterials are a new type of material with extraordinary thermophysical properties not found in traditional natural materials, including functions such as thermal stealth, heat concentration, and thermal rotation. Thermal metamaterials enable ingenious control of macroscopic heat flux and have broad application prospects in aerospace, energy, and electronics fields, such as heat harvesting and thermal protection of electronic devices. By using topology optimization techniques to design satellite module structures with thermal metamaterial functionality, the heat flux control capabilities of thermal metamaterials can be achieved using only conventional materials.

[0094] To clearly and completely illustrate the technical solution of this invention, this embodiment is described in detail in two stages. The first stage is satellite component layout optimization, which specifically includes: rationally selecting a component topology description method and determining design variables; designing optimization objectives and constraints based on the satellite cabin temperature field distribution requirements and component layout requirements; refining the layout optimization problem into a standard optimization formula; using automatic differentiation technology to obtain the sensitivity of the objective function and constraints to the design variables; and applying gradient optimization algorithms to find the optimal component layout scheme. The second stage is cabin structure topology optimization, which specifically includes: determining the thermal metamaterial functional type and dividing the local cabin design domain based on the component layout results obtained in the first stage and the requirements of key components for local thermal control functional characteristics; discretizing the design domain based on the expected local heat conduction tensor distribution field calculated by transformation thermal; designing the topological configuration of each discrete unit based on the inverse homogenization method; and assembling them into an overall structure with thermal metamaterial functional characteristics.

[0095] The above two-stage technical approach, targeting both layout and structure design objects, and employing both global and local perspectives, utilizes overall optimization and refined design to achieve agile management of the satellite cabin's temperature field distribution and heat flow path. The method provided in this invention can guide the design of the thermal management subsystem during the satellite conceptual design phase.

[0096] Existing methods for optimizing temperature field performance layout often employ heuristic or metaheuristic approaches, but these methods have limitations in practical applications. (Reference) Figure 2 In this embodiment of the invention, the first stage is the satellite component layout optimization design. By utilizing automatic differentiation technology for sensitivity analysis, the efficient gradient optimization design of the heat source component layout scheme can be effectively promoted. First, the arbitrary shape component is geometrically described based on the parametric level set function (LSF). The two-dimensional projection of the three-dimensional shape is constructed using the Heaviside function to realize the interference calculation between components. Then, based on the steady-state heat conduction balance equation, a planar four-node rectangular element is selected to discretize the design domain. The temperature field is expressed as the interpolation relationship of the nodal temperatures. The multi-resolution finite element method is used to further refine the mesh of the component boundary, realizing the analysis and evaluation of the corresponding temperature field, and constructing an end-to-end layout optimization model. Finally, for different design requirements, different temperature field performance indicators are calculated. A sensitivity analysis method based on automatic differentiation is proposed, which effectively avoids the complex and tedious gradient derivation process and improves the adaptability of the layout optimization method.

[0097] refer to Figure 2 In this embodiment of the invention, the second stage is the topology optimization design of the cabin structure. The geometry of the local cabin structure is designed by structural topology optimization technology, and the distribution of the equivalent heat conduction tensor in the local cabin is adjusted so that the local cabin structure has the heat flow control capability of thermal supermaterial.

[0098] Transformation thermodynamics, as a method for designing thermal metamaterials, leverages the property that governing equations remain form-invariant during coordinate transformations, achieving a distortion transformation of physical space by adjusting the spatial distribution of the thermal conductivity tensor of the medium. This method offers high flexibility and can be used to design thermal metamaterials with various functions and shapes, enabling ingenious control of macroscopic heat flux. However, the non-uniform and anisotropic distribution of the internal thermal conductivity tensor in transformation thermodynamically designed thermal metamaterials poses significant challenges to their realization and fabrication. Topology optimization, as a structural optimization design method with the highest degree of freedom and flexibility, has been widely applied in the design of various types of metamaterial structures.

[0099] Therefore, in this embodiment of the invention, a discrete design approach is adopted, discretizing the thermal metamaterial design domain into multiple square design units. Based on transformational thermal theory, the theoretical heat conduction tensor value at the center of each design unit can be calculated. Secondly, each design unit is discretized and topology optimization is performed. An inverse homogenization method is used to find the microstructure with the highest matching degree between the macroscopic equivalent heat conduction tensor and the theoretical heat conduction tensor at the center of the design unit. Finally, the microstructures of each design unit are assembled to obtain a thermal metamaterial topology structure that highly matches the calculation results of transformational thermal theory. This also means that the corresponding compartment structure possesses the heat flow control function of the corresponding thermal metamaterial.

[0100] The following is in conjunction with the appendix Figure 1-2 As shown, the integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials provided in this embodiment of the invention will be described in detail. The method includes the following steps S1-S9:

[0101] Step S1: Geometrically describe the regular geometric shape of the two-dimensional component based on the parameterized level set function, construct the two-dimensional projection of the three-dimensional shape of the satellite component using the Heaviside function, and perform interference calculation between the satellite components.

[0102] The calculation of the satellite's temperature field performance needs to be performed without interference or overlap between components. Therefore, the first consideration is how to describe the geometry of the components. Level set functions are mathematical tools for describing point sets in multidimensional space; they can effectively describe the geometry of components and the geometric relationships between them. In this embodiment of the invention, they are used... Indicates the first Components The space occupied. The shape is entirely determined by the level set function Therefore, when describing components with complex boundary shapes, it is sufficient to construct the corresponding level set function based on their shape.

[0103] For two-dimensional components with regular geometric shapes (such as rectangles, circles, or ellipses), an explicit hyperellipsoidal function can be used to construct an analytical level set function for a unified description.

[0104] Therefore, the geometric description of satellite components of arbitrary shape based on parameterized level set functions is determined by the following formula:

[0105] ;

[0106] in, This represents a level set function that describes the shape of a component. and These represent half of the component's length and half its width, respectively. Indicates the coordinates of the geometric center of the satellite component. This indicates the rotation angle of the satellite component, with counterclockwise rotation from the horizontal direction being positive. It means that by changing... , and The values ​​of the three parameters can control the movement (translation and rotation) of the component within the layout area. and Together, they determine the placement of satellite components within the layout area. This represents the position coordinates of any point in the plane. Even number, parameter This determines the geometry of the component. This indicates that the origin is the center of the component and the major axis is... The relative position coordinates of the axis in the component's local coordinate system. It is determined by the following formula:

[0107] .

[0108] As an example, when At that time, if Then the radius of the level set is A circle; if This indicates that the major semi-axis is The minor half-axis is An ellipse. For example, refer to... Figure 3 , Figure 3 This is a schematic diagram of a component described by a parametric level set function in the integrated optimization design method for satellite component layout and panel structure based on thermal metamaterials provided in this embodiment of the invention. Figure 3 A graph of the parameterized level set function describing the rectangular component is shown.

[0109] The geometric model based on the level set function can easily determine the relative positions of nodes and component boundaries, facilitating heat transfer analysis of the layout system using the fixed-mesh finite element method. To avoid re-meshing the finite element mesh during layout optimization, the component geometric description function needs to be projected onto the density field of the fixed-mesh nodes using the Heaviside function. Simultaneously, to avoid non-differentiability at zero points, a regularized Heaviside function is typically used, expressed as:

[0110] ;

[0111] in, This represents the Heaviside regularization function. The argument of the regularization Heaviside function is... It is a constant. This represents the half-width of the 0-1 transition interval of the Heaviside function, also known simply as the narrow half-width.

[0112] In topology optimization, it is usually referred to as To ensure the nonsingularity of the global stiffness matrix, a small number is set; in this embodiment, it is directly set to 0. This setting is because, in hot layout optimization, the parameters... It only determines that the heat source load vector of the grid nodes in the area covered by the heat source component is zero, which will not cause numerical singularity problems in solving the finite element equilibrium equations, and can also simplify the calculation process and improve the calculation efficiency.

[0113] In this embodiment of the invention, the Heaviside function is used to construct a two-dimensional projection of the three-dimensional shape of the satellite component, and interference calculations are performed between the satellite components.

[0114] For example, components The area occupied by the projection is expressed by the following formula:

[0115] ;

[0116] in, Representation Component The area occupied by the projection, Indicates the spatial region where the component is located. express The projection of the Heaviside function, This represents an area element. When one component on a satellite module overlaps with another component, the overlapping spatial region is determined by the following formula:

[0117] For example, components and If overlap occurs, the overlapping spatial region can be represented by the following formula:

[0118] ;

[0119] in, This indicates the size of the overlapping area between the two components. , Representing components respectively and components Size of the space occupied, , These respectively represent the description components. and components The horizontal set function of the shape.

[0120] The area of ​​the overlapping region is determined by the following formula:

[0121] ;

[0122] in, This indicates the area of ​​the overlapping region between two satellite components.

[0123] Step S2: Based on the steady-state heat conduction equilibrium equation, a planar four-node rectangular element is selected to discretize the design domain, and the temperature field of the satellite component is expressed as the interpolation relationship of the nodal temperatures;

[0124] Because the thermal distribution of satellite configurations is relatively complex, the assessment of temperature field distribution is typically performed using the finite element method. Therefore, taking a two-dimensional heat conduction problem as an example, the steady-state heat conduction equilibrium equation can be expressed as:

[0125] ;

[0126] in, Indicates the thermal conductivity coefficient; Let represent the heat source intensity distribution function; in the boundary conditions of the equation, This represents the temperature value at the Dirichlet boundary condition. This represents the heat flux at the Neumann boundary condition. This represents the normal vector pointing outwards from the boundary. This represents the Dirichlet boundary condition. This represents the Neumann boundary condition.

[0127] For example, in finite element analysis, a planar four-node rectangular element is selected to discretize the design domain, and the temperature field is expressed as an interpolation relationship of nodal temperatures, resulting in the element heat transfer equation:

[0128] ;

[0129] in, Represents the heat transfer matrix of the unit cell; Represents the temperature vector of the unit node; Represents the element node thermal load vector, where, It is obtained by calculation using the following formula:

[0130] ;

[0131] in, Indicates the heat source intensity of the unit; Represents a matrix of shape functions; This represents the transpose operation of a matrix of shape functions. This represents a small area element.

[0132] According to the planar four-node element finite element method, under a constant heat source (excluding...), (The nodes in the array), the element node thermal load vector can be derived as:

[0133] ;

[0134] Where A represents the unit area.

[0135] It should be noted that, in this embodiment of the invention, a node represents a mesh node obtained by discretizing a planar quadrilateral rectangular element.

[0136] Step S3: Use the multi-resolution finite element method to refine the mesh of the satellite component boundary to achieve analysis and evaluation of the corresponding temperature field;

[0137] In the layout problem, the components to be laid out are considered as uniform and constant heat sources, and the area occupied by the components represents the distribution of heat source loads. Therefore, changes in the heat source layout will lead to changes in the thermal load values ​​of the element nodes. The relative distance between nodes and components is determined based on the finite element mesh to assess the influence of the component's heat source intensity on the nodes. If the node is far from the component, it is not affected by the component's heat source intensity; if the node is very close to the component or inside the component, it indicates that the node is affected by the component's heat source intensity. Nodes near the component boundary are approximated using the Heaviside function.

[0138] Therefore, the calculation of the element heat source intensity can be expressed by Heaviside function interpolation for the four nodes as follows:

[0139] ;

[0140] in, This represents the constant heat source intensity per unit area of ​​a component. If a unit is completely covered by the component, then all four of its nodes are inside the component, and the corresponding Heaviside function value is 1. Therefore, the heat source intensity of this unit is... .

[0141] Based on the mapping relationship between component geometry and the finite element mesh, the analysis elements can be divided into solid elements, cavity elements, and boundary elements. In the thermal layout optimization problem, the heat transfer stiffness matrix of different types of elements is the same, but the nodal thermal load vectors are different. The equivalent nodal thermal load vectors of solid elements and cavity elements can be calculated accurately, with the nodal thermal load vector of cavity elements being zero. However, the calculation of the heat source intensity of boundary elements is inaccurate; therefore, the multi-resolution finite element method can be used to further refine the boundary mesh.

[0142] As an example, see reference Figure 4 , Figure 4This is a schematic diagram of the finite element nodes affected by the components and multi-resolution finite element method in the integrated optimization design method of satellite component layout-cabinet structure based on thermal metamaterials provided in the embodiments of the present invention. The mesh elements intersecting with the circular components are further divided into finite element elements. According to the above process, the nodal heat source intensity of the finer elements is further calculated to update the nodal heat source intensity of the original elements and obtain more accurate values.

[0143] According to standard finite element analysis procedures, the global heat transfer matrix can be obtained through element assembly. and global thermal load vector .

[0144] It should be noted that, It remains unchanged during the layout optimization process, while It varies with the layout of the heat source. Therefore, solving the heat transfer equations is necessary. The generated temperature field It is dynamic. This enables the entire finite element analysis process, from component position parameters to the generated temperature field.

[0145] Step S4: Design optimization objectives and constraints based on the satellite cabin temperature field distribution requirements and component layout requirements;

[0146] Step S5: Transform the optimization objective and constraints into standard optimization formulas, use automatic differentiation techniques to obtain the sensitivity of the objective function and constraints to design variables, and apply gradient optimization algorithms to find the optimal component layout scheme;

[0147] Based on the component geometric model and finite element analysis model, the optimization formula for the thermal layout optimization problem is established as follows:

[0148] ;

[0149] in: Indicates the first The position vectors of each component. ; Represent design variables The design space must be satisfied, and the design variables for each component include the position coordinates of its reference point. and its rotation angle ,Right now , Indicated based on temperature field The objective function is represented by;

[0150] Satellite temperature field distribution optimization can be defined by different temperature indices according to actual needs. Typically, the maximum temperature of the layout area is taken, and minimizing the maximum temperature reduces concentrated hotspots within the design domain, avoiding localized high temperatures. Since the maximum value function is usually not differentiable, the KS function is used to approximate the maximum value in this embodiment of the invention for ease of differentiation calculation, expressed as:

[0151] ;

[0152] in, Represents the KS function, Indicates the adjustment parameter. Represents the logarithmic function. Indicates the first Temperature of each node This indicates the number of nodes in the finite element mesh. Indicates the maximum temperature. Represents the base of the logarithmic function. These represent the temperature values ​​for each node. When the parameter... As the temperature gradually increases, the KS function approaches and eventually converges to its maximum value. Therefore, in this embodiment of the invention, the KS function achieves a smoothing effect by performing mathematical operations on the entire temperature field to optimize the maximum temperature.

[0153] In this embodiment of the invention, the temperature field target can be taken as thermal compliance, i.e. This represents the heat dissipation capacity of the satellite system. This calculation method is frequently used in the structural design of satellites, and its sensitivity is easy to derive. Therefore, it will not be described in detail in the embodiments of this invention.

[0154] Automatic Differentiation (AD) is an efficient and accurate computer program method for finding derivatives. It applies symbolic differentiation to basic operators, including substituting numerical values ​​for calculations, retaining intermediate results, and finally applying the derivative to the entire function through chain rule differentiation.

[0155] Temperature-driven layout optimization problems typically require setting an optimization objective and several design constraints. For ease of optimization, the objective function and constraint functions are usually integrated into a single loss function. This corresponds to situations with many input variables and few output variables; therefore, using inverse mode automatic differentiation is more efficient. Thanks to the significant advancements in machine learning, researchers have developed numerous inverse mode automatic differentiation tools, such as PyTorch, TensorFlow, Autograd, and JAX. Currently, most mainstream deep learning frameworks support automatic differentiation; therefore, in this embodiment of the invention, the hot layout optimization method is implemented programmatically using the PyTorch framework, calling the built-in automatic differentiation tool for sensitivity calculation.

[0156] In this embodiment of the invention, a simplified satellite temperature field performance layout optimization problem is considered. The size of the satellite module surface in the layout area is... The initial structure uses a uniform honeycomb panel (X-shaped sandwich) with a core volume fraction of 32%, and the equivalent thermal conductivity is [value missing]. The internal core material is composed of a highly thermally conductive metal with a thermal conductivity of [value missing]. Seven components to be laid out are placed within the layout area. The physical information of these components, such as size, mass, and heat source intensity, is shown in Table 1. Cuboid 2 is a high-precision camera component performing a specific observation task; therefore, its position and rotation angle should be fixed. Cuboids 3 and 4 are high-power devices with fixed positions and angles. Since only the layout of the first four components in Table 1 can be changed, this embodiment only lists the layout information of the first four components before and after optimization. All four boundaries of the compartment are set to Dirichlet boundary conditions, and the middle of the compartment... The area is also set as a heat sink, and the temperature is set to... .

[0157] Table 1 Physical information of the components to be laid out

[0158]

[0159] As an example, the aforementioned temperature field calculation process is observed through a set of random layout schemes. The layout schemes are as follows: The values ​​in parentheses represent the coordinates of each satellite component on the cabin panel, and the temperature field obtained through finite element analysis is shown in the figure. Figure 5 As shown, the initial random layout is quite crowded on the right side, resulting in an unreasonable overall temperature distribution within the module, with an average temperature of 49.02K. Therefore, optimization is carried out with minimizing the average temperature within the module as the objective, and the optimized layout scheme is as follows: The optimization results are as follows: Figure 6 As shown in the figure, after optimization, the components maintain a certain distance from each other and move closer to the heat sink. The temperature field distribution of the compartment is more uniform, and the average temperature in the area inside the component is optimized to 40.67K, which is 17.03% lower than that of the random layout.

[0160] Step S6: Based on the design concept of thermal metamaterials, perform topology optimization design of satellite module structure. Based on the obtained optimal component layout scheme and the requirements of key components on the satellite module for local thermal control function characteristics, determine the functional type of thermal metamaterials and divide the local module design domain.

[0161] For conventional materials in nature, their thermal conductivity tensor is uniformly distributed in space. According to the second law of thermodynamics, heat flows from the end with a higher temperature to the end with a lower temperature. If a non-uniform distribution of the thermal conductivity tensor in space can be achieved, the direction of heat flow can be artificially controlled at the macroscopic level. Such materials or structures that achieve extraordinary thermal properties through the artificial design of a non-uniform distribution of the thermal conductivity tensor are called thermal metamaterials. Typical thermal metamaterials include thermal stealth materials, thermal concentration materials, and thermal rotation materials.

[0162] For homogeneous materials, the temperature field exhibits a unidirectional gradient distribution in space, with isotherms arranged uniformly and parallelly, and heat flow is uniformly transferred from high-temperature regions to low-temperature regions. If a non-homogeneous target (target region) is placed within the homogeneous material, the background temperature field distribution will be disturbed, and the target can be detected by detecting changes in the background temperature field.

[0163] Thermal stealth involves placing a thermal cloak within a thermal metamaterial region between the target and background regions, allowing the object to remain hidden within the target area. Heat flow bypasses the thermal stealth region and returns to its original direction. By transforming coordinates, a singularity exists near the inner boundary of the thermal metamaterial region, causing the tangential component of the thermal conductivity to approach infinity, thus preventing external heat flow from reaching the target region. The thermal stealth material creates a region with an extremely small temperature gradient within the target area, while the temperature distribution and heat flow in the external background region remain undisturbed, consistent with the corresponding region of a homogeneous material. Therefore, the thermal stealth material achieves both stealth and thermal protection for objects within the target region.

[0164] In contrast to thermal stealth, heat concentration directs heat flow towards a central region, thus collecting thermal energy. Therefore, its radial thermal conductivity at its boundaries needs to approach infinity to concentrate heat towards the target area.

[0165] Thermal rotation can cause the heat flow conducted to the target area to rotate at a specific angle, and the temperature distribution in the target area will be reversed. The horizontal heat flow lines and orthogonal isotherms near the outer boundary of the thermally rotated material area will not be distorted, while the rotation angle of the heat flow lines and isotherms from the outer boundary to the inner boundary of the thermally rotated material area gradually increases.

[0166] Specifically, thermal metamaterial type matching and geometry design domain extraction include:

[0167] A heat transfer requirement analysis of satellite components is conducted. Due to differences in materials and functions, satellite components exhibit varying thermal sensitivity and heat transfer requirements during on-orbit operation. For example, onboard processors have strong heat dissipation requirements, propulsion fuel tanks need to maintain low temperatures, and optical components require low temperature gradients. The degree of heat transfer requirement also varies among components of different power levels and tiers. Therefore, it is necessary to first specify standards and solutions, and then evaluate and classify the components based on their thermal sensitivity and heat transfer requirements. This will differentiate the type and degree of heat flow control requirements of satellite components on the surrounding cabin structure. Finally, based on the classification results, a thermal metamaterial design scheme with corresponding functions will be matched to the component.

[0168] It should be noted that the standards and solutions described above vary depending on the requirements of different satellite components. Therefore, the standards and solutions in this invention depend on the different satellite components and their quantities.

[0169] For example, in this embodiment of the invention, the above method is used to perform fine thermal management design on the two components in Table 1: cylinder 2 (spaceborne processor chip) and cuboid 2 (high-precision camera). Based on the function and properties of the devices, it is known that the processor chip is highly sensitive to temperature gradients; excessive temperature gradients can lead to accelerated aging and failure of the chip in certain areas. With smaller temperature gradients, the chip performance is more stable. The high-precision camera is highly sensitive to temperature gradients in the direction orthogonal to the line of sight. When the main structure of the camera is in the line of sight (… When the temperature distribution is uneven in the orthogonal directions, uneven thermal expansion will occur, causing deviation in the camera's line-of-sight and reducing imaging accuracy. Therefore, topology optimization design is performed on the cabin structure in the region where cylinder 2 and cuboid 2 are located, such as... Figure 7 As shown, the area where the cylinder 2 is located is designed as a local compartment structure with thermal stealth function to eliminate the internal temperature gradient of the component, and the area where the cuboid 2 is located is designed as a local compartment structure with thermal rotation function to reverse the direction of heat flow so that the direction of the internal temperature gradient of the component meets the requirements.

[0170] It should be noted that the inner and outer boundaries of the thermal metamaterial design domain shown in the embodiments of the present invention are relatively regular or regular geometric configurations, but the method of the embodiments of the present invention can be applied to the design of thermal metamaterials of any shape.

[0171] Step S7: Discretize the design domain to obtain multiple design units, and calculate the expected theoretical heat conduction tensor value at the center of each design unit based on transformation thermal calculation;

[0172] In this embodiment of the invention, the design domain is discretized to obtain multiple design units, and the theoretical heat conduction tensor value at the center of each design unit is calculated based on transformational thermal calculations, further including:

[0173] Based on the partitioning results of the design domain, a square grid is used to discretize the design domain at a specific size to obtain multiple design units;

[0174] Determine the boundary function of the thermal metamaterial design domain and the location of the center of each design unit in a local coordinate system constructed with the component center as the origin;

[0175] According to transformational thermodynamics, the form of the heat conduction equation remains unchanged before and after coordinate transformation, thus making the physical parameters of the material equivalent to the space.

[0176] By using coordinate transformation, the distortion of thermal flow lines is correlated with spatial deformation, thus establishing a one-to-one correspondence between material physical parameters and spatial variations.

[0177] The original space is transformed into a transformation space according to certain rules. Based on this correspondence, the heat conduction tensor distribution in the transformation space is determined, and then the theoretical heat conduction tensor value at the center of each design unit is calculated, which is used as the target for subsequent structural optimization.

[0178] refer to Figure 8-9 Based on the above division results, the boundary functions of the local coordinate system design domain for the thermal supermaterials corresponding to cylinder 2 and cuboid 2, with the component center as the origin, can be obtained respectively, including:

[0179] ;

[0180] in, This represents the outer boundary function of the thermal metamaterial design domain corresponding to cylinder 2. This represents the angle variable in a local coordinate system with the component center as the origin. This represents the outer boundary function of the thermal metamaterial design domain corresponding to cuboid 2.

[0181] The foundation of transformational thermodynamics is that the form of the heat conduction equation remains unchanged before and after coordinate transformation. It equates the material's physical parameters with spatial equivalents, and through coordinate transformation, corresponds the distortion of heat flow lines to spatial deformation, establishing a one-to-one correspondence between material physical parameters and spatial changes. In the design process of thermal metamaterials, the original space is transformed into a transformed space according to certain rules. Based on this correspondence, the heat conduction tensor distribution within the transformed space is obtained. Filling the transformed space with a material possessing the corresponding heat conduction tensor allows for heat flow control. Therefore, the governing equation for the passive steady-state heat conduction problem in solids under isothermal conditions is:

[0182] ;

[0183] According to coordinate transformation theory, the form of the heat conduction equation remains unchanged in any space; therefore, the transformation space (real space) is valid. The heat conduction equation within can be expressed as:

[0184] ;

[0185] in, This represents the temperature distribution within the original space. Represents the temperature distribution within the transformation space. This represents the heat conduction tensor within the original space. Represents the heat conduction tensor within the transformation space. This represents the gradient operation, where the original space... and transformation space The internal thermal conductivity tensor relationship is:

[0186] ;

[0187] in, Represents the original space and transformation space Jacobian matrix of partial derivative transformation between coordinates. This represents the heat conduction tensor of the original space. Representing the Jacobian matrix The transpose operation. This represents the function used to calculate the determinant of a matrix. Therefore, based on the above coordinate transformation, a specific thermal conductivity tensor can be obtained, and material parameters can be adjusted to achieve the purpose of changing the temperature field and designing thermal metamaterials.

[0188] Specifically, for Figure 8 Thermal cloaking materials require the coordinates in the original space to be... Transformation of the region into space The region, enabling manipulation of the transformation space The purpose of area stealth is determined by the geometric transformation formula:

[0189] ;

[0190] in, , Let represent the polar radii of the original space and the transformed space in polar coordinates before and after the coordinate transformation, respectively. , Let represent the polar angles in the original space and the transformed space, respectively, in polar coordinates before and after the coordinate transformation. , Let represent the inner and outer boundary functions of the thermal metamaterial design domain corresponding to cylinder 2, respectively.

[0191] This leads to the design domain of thermal metamaterials. Jacobian matrix:

[0192] ;

[0193] Therefore, the formula for calculating the heat conduction tensor in the transformation region is:

[0194] ,in:

[0195] , , ;

[0196] In the above formula, This represents the heat conduction tensor of the transformed region after coordinate transformation. To reverse The coordinate transformation matrix, , , and These represent the components of the heat conduction tensor in the transformation region. , , and These represent the components of the heat conduction tensor in the polar coordinates describing the transformed region. This indicates the thermal conductivity of the base material.

[0197] Among them, parameters It is obtained by calculation using the following formula:

[0198] ;

[0199] Specifically, for Figure 9 Thermally rotating materials require the manipulation of the transformation space. The region is rotated at a certain angle, thereby achieving a macroscopic transformation of space. The geometric transformation formula for the reversal of heat flow in a region is:

[0200] ;

[0201] in, This represents the desired thermal flux torsion angle in the target region of the thermal metamorphic device under coordinate transformation. Represents a coordinate function. , This represents the boundary functions inside and outside the thermal metamaterial design domain corresponding to cuboid 2.

[0202] Therefore, the formula for calculating the heat conduction tensor in the transformation region is:

[0203] ,in, , , ;

[0204] In the above formula, This represents the heat conduction tensor of the transformed region after coordinate transformation. , , and These represent the components of the heat conduction tensor in the transformation region. , , and These represent the components of the heat conduction tensor in the polar coordinate description transformation region;

[0205] in, and The following formulas are used to calculate the results respectively:

[0206] ;

[0207] ;

[0208] Among them, based on the above formula and formula .

[0209] Based on the above methods, calculations can be performed separately. Figure 8 and Figure 9 The thermal conductivity tensor distribution field of two types of thermal metamaterials in the design domain.

[0210] Step S8: Discretize each design unit and perform topology optimization design on the discretized design units. Use the inverse homogenization method to find the microstructure with the highest matching degree between the macroscopic equivalent heat conduction tensor and the theoretical heat conduction tensor at the center of the design unit.

[0211] Specifically, in this embodiment of the invention, the theoretical heat conduction tensor value at the center of each design unit is calculated, each design unit is discretized and topology optimized, and an inverse homogenization method is used to find the microstructure with the highest matching degree between the macroscopic equivalent heat conduction tensor and the theoretical heat conduction tensor at the center of the design unit.

[0212] In this embodiment of the invention, each design unit is discretized into basic units with a specific resolution, and the pseudo-density of the basic units is... ( To optimize the design variables, a material inverse homogenization topology optimization formula based on the SIMP interpolation model is established. Topology optimization is performed on each design unit to obtain the optimized topology unit microstructure for each design unit.

[0213] As an example, this embodiment of the invention employs an inverse homogenization method based on homogenization theory for microstructure topology optimization design. Firstly, as... Figure 10 As shown, the design domain is discretized using a square grid. The design element uses the heat conduction tensor at the center point of the element, calculated using transformation thermal methods, as the target heat conduction tensor for that element. For each design element, it is further discretized into... A formula for material inverse homogenization topology optimization based on a SIMP interpolation model is established. The inverse homogenization design process can be found by referring to... Figure 11 .

[0214] When the structure is composed of two materials, the SIMP interpolation model treats each basic unit as an isotropic material with a specific thermal conductivity coefficient. The thermal conductivity of the unit is determined by the pseudo-density. Control, its value range is The thermal conductivity coefficient of a single element can be expressed as:

[0215] ;

[0216] in, This represents the thermal conductivity coefficient of the basic unit. and These represent the thermal conductivity coefficients of the two materials, respectively. The time represents the thermal conductivity coefficient. Materials, The time represents the thermal conductivity coefficient. Materials. Taking an intermediate density value has no practical physical meaning, therefore an appropriate penalty coefficient needs to be introduced. In one embodiment of the present invention, .

[0217] Therefore, in order to design a thermal conductivity tensor with a specific value Based on the microstructure, a topology optimization model is established:

[0218] ;

[0219] in, This represents the average pseudo-density within the design cell, representing the objective function. Indicates the design unit area. Indicates the number of basic units. This represents the macroscopic equivalent heat conduction tensor of the design unit. This represents the temperature at each finite element node in the microstructure. This represents the calculated local temperature field. Indicates the first Thermal conductivity of each unit This represents the target heat conduction tensor at the center of the design unit. Represents the overall thermal conductivity matrix of the structure. Indicates temperature. This indicates thermal load.

[0220] refer to Figure 12 In this embodiment of the invention, when performing topology optimization, the optimization objective is first defined, i.e., a target heat conduction tensor is given; based on this objective, the topology optimization model is determined, and initial microscopic design parameters are set; the heat conduction problem is accurately simulated numerically to determine the finite element model, and finite element analysis parameters are predefined; design variables are initialized, and iterative optimization begins; the design variables are substituted, and the equivalent heat conduction tensor of the microstructure is calculated using the homogenization method; based on the calculated equivalent heat conduction tensor, the values ​​of the objective function and constraint function are further calculated.

[0221] In order to determine how to adjust the design variables to optimize the objective function, an automatic differentiation method was used for sensitivity analysis.

[0222] Furthermore, the sensitivity is filtered, and the design variables are updated based on the filtered sensitivity information. After each update of the design variables, it is determined whether the design unit meets the convergence criteria. The convergence criteria are usually set based on indicators such as the rate of change of the objective function and the amount of change of the design variables. If the convergence criteria are met, the optimization stops, and the optimal topology that meets the target heat conduction tensor requirements is obtained. If the convergence criteria are not met, the updated design variables are substituted into the homogenization calculation, sensitivity analysis, and design variable update steps to continue iterative optimization until each design unit meets the convergence criteria.

[0223] Since the microstructure topology optimization process for each design unit is performed independently, parallel computing can be used to simultaneously conduct topology optimization designs for multiple design units in order to reduce design time. Then, the microstructures obtained from each design unit are assembled to obtain the topology structure for the local thermal metamaterial function. In this embodiment of the invention, the design results of the local compartments at the locations of cylinder 2 and cuboid 2 are as follows: Figure 13 and Figure 14 As shown.

[0224] Step S9: Assemble the microstructures of each design unit to obtain a cabin structure with corresponding thermal metamaterial heat flow control function.

[0225] To verify the effectiveness of the integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials provided in this embodiment of the invention, simulation experiments were conducted using control group 1, control group 2, and experimental group 1, based on the integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials provided in this embodiment of the invention. The results were then presented and compared. In control group 1, neither the component layout nor the cabin structure was optimized; in control group 2, the component layout was optimized, but the cabin structure was not; and in experimental group 1, both the component layout and the cabin structure were optimized.

[0226] Comparing the temperature field distribution results of control group 1 and control group 2, it can be seen that layout optimization significantly improved the global temperature field distribution, making the overall temperature inside the cabin more uniform. However, it could not achieve precise control over the local temperature gradient of each component. As shown in Table 2, although the average temperature of the component area in control group 2 was reduced by 8.4K compared to control group 1, the maximum temperature difference inside cylinder 2 and the temperature difference along the line of sight of cuboid 2 were still relatively large. The temperature field distribution results of experimental group 1 show that after the second stage of local structural topology optimization, the rationality of the temperature field distribution in the component areas of cylinder 2 and cuboid 2 was significantly improved, and the temperature field in other areas was almost unaffected. The average temperature of the component areas in experimental group 1 and control group 2 was almost the same. As shown in Table 2, compared to control group 2, the average temperature of the component area in experimental group 1 decreased by 1.33%. This is because the local structural topology optimization based on the thermal metamaterial design concept does not affect the global temperature field distribution. The maximum temperature difference in cylinder 2 decreased by 50.83%, and the maximum temperature difference along the line of sight of cuboid 2 decreased by 57.16%. Compared to control group 1, the average temperature of the component area in experimental group 1, after layout-structure two-stage optimization, decreased by 18.14%, the maximum temperature difference of cylinder 2 decreased by 53.01%, and the maximum temperature difference in the orthogonal direction of the line of sight of cuboid 2 decreased by 74.80%. Table 2 also shows the volume fraction of the sandwich material in the three cases. It can be seen that the volume fraction of the sandwich material in the experimental group increased by 0.8% compared to the control group, meaning that the mass of the cabin plate would be slightly improved. This is mainly because the results of topology optimization require post-processing, which will cause some quality deviation. This problem can be improved by using other post-processing techniques.

[0227] Table 2 Comparison of Results

[0228] Group Component area average temperature / K Maximum temperature difference of cylinder 2 / K Maximum temperature difference in the direction of perpendicularity of line of sight of cuboid 2 / K Sandwich material volume fraction Control group 1 49.02 13.30 11.39 32.7% Control group 2 40.67 12.71 6.70 32.7% Experimental group 1 40.13 6.25 2.87 33.5%

[0229] In summary, the integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials provided in this invention, by rationally selecting the component topology description method and determining the design variables, designs optimization objectives and constraints according to the satellite cabin temperature field distribution requirements and component layout requirements, refines the layout optimization problem into a standard optimization formula, and uses automatic differentiation technology to obtain the sensitivity of the objective function and constraints to the design variables. Gradient optimization algorithms are then applied to find the optimal component layout scheme. Based on the obtained component layout results and the requirements of key components for local thermal control functions, the functional type of the thermal metamaterial is determined and the local cabin design domain is divided. The design domain is discretized based on the expected local heat conduction tensor distribution field calculated by transform thermal calculation, and the topological configuration of each discrete unit is designed based on the inverse homogenization method. These units are then assembled into an overall structure with thermal metamaterial functional characteristics. This method can improve the satellite's service life and on-orbit time, offers good flexibility and comprehensive functions, and enables fine-tuning of the thermal field in local areas of the components, especially enabling more precise local thermal management of special precision instruments and equipment within the satellite cabin.

[0230] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Additionally, the terms "front," "back," "left," "right," "upper," and "lower" in this document refer to the placement shown in the accompanying drawings.

[0231] 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 them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A satellite component layout-cabinet structure integrated optimization design method based on thermal metamaterials, characterized in that, include: Geometric description of regular geometric shapes of two-dimensional components is performed based on parameterized level set functions. The Heaviside function is used to construct a two-dimensional projection of the three-dimensional shape of the satellite components, and interference calculation between satellite components is performed. Based on the steady-state heat conduction equilibrium equation, a planar four-node rectangular element is selected to discretize the design domain, and the temperature field of the satellite component is expressed as the interpolation relationship of the nodal temperatures. The multi-resolution finite element method is used to refine the mesh of the satellite component boundary, enabling the analysis and evaluation of the corresponding temperature field. The design optimization objectives and constraints are based on the requirements for temperature field distribution and component layout of the satellite module. The optimization objective and constraints are transformed into standard optimization formulas. Automatic differentiation technology is used to obtain the sensitivity of the objective function and constraints to design variables. Gradient optimization algorithm is applied to find the optimal component layout scheme. Based on the design concept of thermal metamaterials, the topology optimization design of satellite compartment structure is carried out. According to the optimal component layout scheme and the requirements of key components on the satellite compartment for local thermal control function, the functional type of thermal metamaterials is determined and the local compartment design domain is divided. The design domain is discretized to obtain multiple design units, and the theoretical heat conduction tensor value at the center of each design unit is expected to be calculated based on transformation thermal calculation. Each design unit is discretized, and topology optimization is performed on the discretized design units. The inverse homogenization method is used to find the microstructure with the highest matching degree between the macroscopic equivalent heat conduction tensor and the theoretical heat conduction tensor at the center of the design unit. The microstructures of each design unit are assembled to obtain a cabin structure with corresponding thermal metamaterial heat flow control function.

2. The integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials according to claim 1, characterized in that, The geometric description of a two-dimensional component with a regular geometric shape based on a parameterized level set function is determined by the following formula: ； in, This represents a level set function that describes the shape of a component. and These represent half of the component's length and half its width, respectively. Indicates the coordinates of the geometric center of the satellite component. This indicates the rotation angle of the satellite component, with counterclockwise rotation from the horizontal direction being positive. and Together, they determine the placement of satellite components within the layout area. This represents the position coordinates of any point in the plane. Even number, ,parameter This determines the geometry of the component. This indicates that the origin is the center of the component and the major axis is... The relative position coordinates of the axis in the component's local coordinate system; in, It is determined by the following formula: 。 3. The integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials according to claim 2, characterized in that, The Heaviside function uses a regularized Heaviside function, which is expressed as follows: ； in, This represents the Heaviside regularization function. The argument of the regularization Heaviside function is... It is a constant. This represents the half-width of the 0~1 transition interval of the Heaviside function.

4. The integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials according to claim 3, characterized in that, Interference calculations between satellite components are performed using the following method: The Heaviside function is used to construct a two-dimensional projection of the three-dimensional shape of the satellite component, where the first... Components The area occupied by the projection is expressed as: ； in, Indicates the first Components The two-dimensional projected area, Indicates the spatial region where the component is located. express The projection of the Heaviside function, Represents the description component The level set function of the shape, Representing an area element, when a component on a satellite module... With another component When overlap occurs, the overlapping spatial region is determined by the following formula: ； in, This indicates the size of the overlapping area between the two components. and Representing components respectively and components Size of the space occupied, and These respectively represent the description components. and components The level set function of the shape; When two satellite assemblies overlap on the deck, the area of ​​the overlapping region is determined by the following formula: ； This indicates the area of ​​the overlapping region between two satellite components.

5. The integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials according to claim 4, characterized in that, Based on the steady-state heat conduction equilibrium equation, a planar four-node rectangular element is selected as the discrete design domain. The temperature field of the satellite component is expressed as an interpolation relationship of the nodal temperatures in the following way: ； Indicates the heat source intensity of the unit. This represents the heat source intensity of a component with a constant cell area. When all four nodes of the cell are inside the component, the corresponding Heaviside function value is 1, and the heat source intensity of the cell is... .

6. The integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials according to claim 5, characterized in that, The optimized formula is expressed as: ； in: Indicates the first The position vectors of each component. ; Represent design variables The design space must be satisfied, and the design variables for each component include the position coordinates of its reference point. and its rotation angle , , Indicated based on temperature field The objective function is represented by; Based on the requirements, a temperature index is defined. The maximum temperature in the layout area is selected and approximated using the KS function as the objective function. The objective function is shown in the following formula: ； in, Represents the KS function, Indicates the adjustment parameter. Indicates the first Temperature of each node This indicates the number of nodes in the finite element mesh. This indicates the maximum temperature.

7. The integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials according to claim 1, characterized in that, When determining the functional type of thermal metamaterials and dividing the local panel design domain, the thermal sensitivity characteristics and heat transfer requirements of the components are evaluated and classified. The differences in the type and degree of heat flow control of the panel structure for different satellite components are distinguished. Based on the classification, thermal metamaterial design schemes for the panel structure that meet the heat flow control requirements are matched for the satellite components and the local panel design domain is divided.

8. The integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials according to claim 7, characterized in that, The design domain is discretized to obtain multiple design elements, and the theoretical heat conduction tensor value at the center of each design element is calculated based on transformational thermal calculations, including: Based on the partitioning results of the design domain, a square grid is used to discretize the design domain at a specific size to obtain multiple design units; Determine the boundary function of the thermal metamaterial design domain and the location of the center of each design unit in a local coordinate system constructed with the component center as the origin; According to transformational thermodynamics, the form of the heat conduction equation remains unchanged before and after coordinate transformation, thus making the physical parameters of the material equivalent to the space. By using coordinate transformation, the distortion of thermal flow lines is correlated with spatial deformation, thus establishing a one-to-one correspondence between material physical parameters and spatial variations. The original space is transformed into a transformation space according to certain rules. Based on the correspondence, the heat conduction tensor distribution in the transformation space is determined, and the theoretical heat conduction tensor value at the center of each design unit is calculated and used as the target for subsequent structural optimization. The heat conduction equation within the transformation space is expressed as: ； in, Represents the temperature distribution within the transformation space. Represents the heat conduction tensor within the transformation space. This represents gradient operation; Determined by the following formula: ； The Jacobian matrix represents the coordinate partial derivative transformation between the original space and the transformed space. This represents the heat conduction tensor of the original space. Representing the Jacobian matrix The transpose operation. This represents a function used to calculate the determinant of a matrix.

9. The integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials according to claim 7, characterized in that, The design unit is topology optimized using the following methods: Define the optimization objective, determine the topology optimization model based on the defined optimization objective, and set the micro-initial design parameters; Numerical simulation of heat conduction problem is performed to determine the finite element model and predefine finite element analysis parameters; Initialize design variables and begin iterative optimization; Substitute the design variables and use the homogenization method to calculate the equivalent thermal conductivity tensor of the microstructure; Based on the calculated equivalent heat conduction tensor, the values ​​of the objective function and constraint function are calculated. The sensitivity is analyzed and filtered, and the design variables are updated based on the filtered sensitivity information; After each update of the design variables, it is determined whether the design unit meets the convergence condition. If the convergence condition is met, the optimization stops, and the optimal topology that satisfies the target heat conduction tensor requirement is obtained; If the convergence condition is not met, the updated design variables are substituted into the homogenization calculation, sensitivity analysis, and design variable update steps to continue iterative optimization until the design unit meets the convergence condition.

10. The integrated optimization design method for satellite component layout and cabin structure based on thermal metamaterials according to claim 1, characterized in that, Each design unit is discretized in the following way: Each design unit is discretized into basic units with a specific resolution, and the pseudo-density of the basic units is... To optimize design variables in the design, ; When the structure is composed of two materials, the SIMP interpolation model treats each basic element as an isotropic material with a specific thermal conductivity coefficient. The thermal conductivity coefficient of the basic element is expressed as: ； in, This represents the thermal conductivity coefficient of the basic unit. and These represent the thermal conductivity coefficients of the two materials, respectively. The time represents the thermal conductivity coefficient. Materials, The time represents the thermal conductivity coefficient. Materials, This represents the penalty coefficient.

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