Satellite cabin panel assembly thermal layout optimization method considering thermal radiation

Abstract

This invention discloses a method for optimizing the thermal layout of satellite cabin components considering thermal radiation, belonging to the field of component layout optimization technology. The method includes: geometrically describing the components based on level set functions; constructing an interference model between components using Heaviside functions; estimating the global heat transfer matrix of satellite cabin radiation heat transfer in the space environment; dividing the satellite cabin layout area into finite element meshes; determining the global thermal load vector based on the component's heat source intensity distribution function using Heaviside functions and density projection methods; establishing the mapping relationship between component position parameters and the satellite cabin layout temperature field; constructing a satellite cabin thermal layout optimization model; and applying a gradient optimization algorithm to solve the satellite cabin thermal layout optimization model to obtain the optimal component layout scheme. The method of this invention avoids nonlinear iterative solutions, reduces the computational load, and obtains the optimal component layout scheme considering thermal radiation.

Description

Technical Field

[0001] This invention relates to the field of component layout optimization technology, and in particular to a method for optimizing the thermal layout of satellite cabin components considering thermal radiation. Background Technology

[0002] Satellite layout plays a crucial role in determining its on-orbit performance and functionality. The purpose of satellite layout design is to arrange electronic components or equipment in appropriate locations within the satellite to meet various system performance requirements, such as mass characteristics and thermal control. As a vital part of the overall satellite design, satellite layout design directly determines the satellite system's overall performance, development cost, design cycle, and design level. To accelerate the design process and shorten the manufacturing cycle, satellite layout optimization design methods have emerged, which reduce design complexity by combining optimization techniques.

[0003] However, existing satellite component layout optimization design technologies lack methods for optimizing component thermal layout in the face of the actual on-orbit thermal environment of satellites. Since the primary modes of heat transfer in space are conduction and radiation, the heat generated by internal instruments and equipment is first conducted to the outer surface of the cabin through the inner surface, and then dissipated into deep space via radiation. In numerical analysis, thermal radiation is a nonlinear boundary condition, requiring iteration during the solution process, which significantly increases the computational complexity of satellite temperature field numerical simulation, leading to reduced optimization efficiency and increased optimization costs.

[0004] Therefore, a thermal layout optimization method for satellite module components that considers thermal radiation is proposed. This method can achieve thermal layout optimization design of components under the influence of the actual on-orbit thermal environment of the satellite, and significantly reduce the computational complexity of the optimization process, improve optimization efficiency, and reduce optimization cost. Summary of the Invention

[0005] To address some or all of the technical problems existing in the prior art, the present invention provides a method for optimizing the thermal layout of satellite cabin components considering thermal radiation.

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

[0007] A method for optimizing the thermal layout of satellite module assemblies considering thermal radiation is provided, including:

[0008] The components are geometrically described based on the level set function, and the two-dimensional projection of the components is constructed using the Heaviside function to build an interference model between the components.

[0009] Based on the three-dimensional steady-state heat conduction control equation, the law of energy conservation and the law of radiation heat transfer, the global heat transfer matrix of the satellite's cabin radiative heat transfer under the space environment is estimated by utilizing the thermal power of the components.

[0010] Finite element meshing is performed on the satellite module layout area. Based on the heat source intensity distribution function of the component, the Heaviside function and density projection method are used to determine the heat load vector of the mesh element. The mesh element at the boundary of the satellite component is refined using the multi-resolution finite element method to determine the heat load vector of the refined mesh element. The global heat load vector is obtained by assembling the heat load vector of the mesh element.

[0011] Based on the global heat transfer matrix and global heat load vector, the mapping relationship between component position parameters and satellite panel layout temperature field is established using the heat transfer balance equation.

[0012] Based on the thermal layout requirements of the satellite cabin components, the optimization objective is determined. Based on the optimization objective, the interference model and the mapping relationship, a thermal layout optimization model for the satellite cabin panels is constructed. The gradient optimization algorithm is then applied to solve the thermal layout optimization model for the satellite cabin panels to obtain the optimal component layout scheme.

[0013] In some implementations, constructing a two-dimensional projection of the components using the Heaviside function to build an interference model between the components includes:

[0014] Based on the component's level set function, construct the overlapping area between components;

[0015] The Heaviside function is used to determine the area occupied by the two-dimensional projection of the overlapping area between components onto the layout area. The area occupied by the two-dimensional projection of the overlapping area between components onto the layout area represents the interference between components, and an interference model between components is constructed.

[0016] In some implementations, the interference model between the components is expressed as:

[0017] ;

[0018] in, Indicates the first The component and the first Interference between components Indicates the layout area. This refers to the Heaviside function. Represents the maximum value function. Indicates the first The level set function of each component Indicates the first The level set function of each component Represents an area element. Indicates the total number of components.

[0019] In some implementations, the estimation of the global heat transfer matrix of satellite cabin radiative heat transfer in the space environment, based on the three-dimensional steady-state heat conduction control equation, the law of energy conservation, and the law of radiative heat transfer, and utilizing the thermal power of the components, includes:

[0020] By combining the formulas and Solve for the approximate average temperature of the outer surface of the cabin plate. ;

[0021] Approximate average temperature of the outer surface of the cabin plate Substitute into the formula Solve for the approximate radiative heat transfer coefficient of the outer surface of the cabin plate. ;

[0022] Based on the approximate radiation heat transfer coefficient Estimate the global heat transfer matrix of the radiative heat transfer portion of the satellite module. ;

[0023] in, Indicates the first Thermal power of each component This indicates the total amount of heat dissipated by radiation. Indicates the total number of components. This represents the surface emissivity at the Robin boundary condition. This represents the Stefan-Boltzmann constant. This indicates the surface area of ​​the satellite's radiative heat dissipation panel. This indicates the temperature field of the satellite's panel layout. This represents the radiative heat transfer coefficient.

[0024] In some implementations, the step of performing finite element mesh generation on the satellite module layout area and determining the mesh element thermal load vector based on the component's heat source intensity distribution function using the Heaviside function and density projection method includes:

[0025] The satellite module layout area is uniformly discretized into a quadrilateral structure grid, and four-node rectangular elements are used for calculation. The temperature field is approximated by interpolation using piecewise bilinear polynomial functions, and the element equilibrium equation is derived.

[0026] Using the Heaviside function and density projection method, the heat source intensity of the corresponding element is obtained by interpolating the heat source intensity distribution function values ​​at the four nodes of the element.

[0027] Based on the planar four-node element finite element method and the element's heat source intensity, the element's thermal load vector is determined under the action of a constant heat source.

[0028] In some implementations, the unit thermal load vector is represented as:

[0029] ;

[0030] in, Represents the element thermal load vector. Indicates the heat source intensity of the unit. The superscript T indicates the area of ​​a unit cell;

[0031] The heat source intensity of a unit is expressed as:

[0032] ;

[0033] in, Indicates the first The heat source intensity of each component Indicates the first The level set function of the component in unit number The values ​​at each node Indicates the unit number The coordinates of each node This represents the Heaviside function.

[0034] In some implementations, the thermal load vector of the refined mesh element is represented as:

[0035] ;

[0036] in, Indicates the first thermal load vector of each boundary element Indicates the first The area covered by each boundary unit Indicates the first The heat source intensity of each boundary unit This represents the shape function matrix for temperature interpolation, with the superscript T indicating matrix transpose. Represents an area element. Indicates the first The number of material elements divided by each boundary element. Indicates the first The level set function of the component in the th... The first boundary unit The value at the center point of each material element Indicates the first The first boundary unit The coordinates of the center point of each material element Indicates the first The area of ​​each material unit.

[0037] In some implementations, the constructed satellite cabin thermal layout optimization model is represented as:

[0038] ;

[0039] in, Indicates design variables, Indicates the first The position coordinates of each component Indicates the first The rotation angle of each component Indicates the total number of components. This represents the objective function to be optimized. Represents the global heat transfer matrix. Represents the global thermal load vector. This indicates the temperature field of the satellite's panel layout. This indicates a geometric non-interference constraint on the components. Indicates the optimization range of the design variables. Indicates the first The component and the first Interference between components.

[0040] In some implementations, the optimization objective is to minimize the variance of the temperature distribution on the inner surface of the satellite module.

[0041] In some implementations, the gradient of the objective function with respect to the design variables is calculated using an automatic differentiation method. Based on the gradient of the objective function with respect to the design variables, a gradient optimization algorithm is applied to solve the satellite cabin thermal layout optimization model to obtain the optimal component layout scheme.

[0042] The main advantages of the technical solution of this invention are as follows:

[0043] The thermal layout optimization method for satellite cabin components considering thermal radiation of this invention can transform nonlinear heat transfer balance equations into linear equations by approximating the global heat transfer matrix of satellite cabin radiation heat transfer. This allows for the replacement of precise nonlinear finite element solutions with linear finite element approximation, achieving an approximate equivalent representation of the optimization objective while avoiding the iterative process of nonlinear solutions, thus significantly reducing the computational load. By employing level set functions to geometrically describe the components and using multi-resolution finite element methods to accurately obtain the thermal load vectors at the component boundaries, a mapping relationship between component position parameters and the satellite cabin layout temperature field is constructed, enabling accurate and efficient calculation of the gradient of the optimization objective with respect to design variables. Furthermore, by constructing a satellite cabin thermal layout optimization model based on the optimization objective, the interference model, and the mapping relationship, and applying a gradient optimization algorithm to solve the model, rapid optimization iteration of component layout schemes can be achieved to obtain the optimal component layout scheme considering thermal radiation. Attached Figure Description

[0044] 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, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0045] Figure 1 A flowchart illustrating the method for optimizing the thermal layout of satellite module assemblies considering thermal radiation, provided in an embodiment of the present invention.

[0046] Figure 2 A schematic diagram of an analysis unit provided in an embodiment of the present invention;

[0047] Figure 3 This is a schematic diagram of an adaptive encryption material unit provided in an embodiment of the present invention. Detailed Implementation

[0048] 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.

[0049] The technical solutions provided by the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0050] Because the satellite operates in a high-vacuum environment, the effects of air conduction and convective heat transfer on the satellite's temperature field can be ignored. The satellite can only exchange heat with deep space through radiation. Internally, heat exchange primarily relies on heat conduction through the modules, with some radiative heat exchange between devices. Although the variations in various external radiative heat flows in space are complex, they ultimately affect the satellite's temperature field through the application of specific heat flux boundary conditions, and these boundary conditions are linear. Therefore, to facilitate the optimized design of the satellite module thermal layout, the effects of various external radiative heat flows are ignored.

[0051] Furthermore, considering the typical thermal layout of satellite module components and the characteristics of the satellite's on-orbit operating environment, the following conditions are set:

[0052] All components are installed on the inner surface of the satellite module, while the outer surface of the satellite module is a radiative heat dissipation surface.

[0053] The effects of external space heat flow from the Sun and Earth on the satellite's modules are not considered.

[0054] Ignore heat transfer between different satellite panels, that is, set all sides of the satellite panels to be thermally insulating boundaries;

[0055] Heat exchange occurs between the components and the satellite cabin solely through thermal conduction, and the components are simplified as two-dimensional planar heat sources.

[0056] Ignore radiative heat transfer between components inside the satellite;

[0057] The outer space is a blackbody, which can completely absorb the radiated heat from the satellite's modules.

[0058] The satellite cabin panel assembly thermal layout optimization method considering thermal radiation provided in this embodiment of the invention performs thermal layout optimization design of the satellite cabin panel assembly based on the above-mentioned conditions.

[0059] refer to Figure 1 This invention provides a method for optimizing the thermal layout of satellite cabin assemblies considering thermal radiation. The method includes the following steps:

[0060] Step 1: Geometrically describe the components based on the level set function, construct the two-dimensional projection of the components using the Heaviside function, and build the interference model between the components;

[0061] Step 2: Based on the three-dimensional steady-state heat conduction control equation, the law of energy conservation and the law of radiation heat transfer, the global heat transfer matrix of the satellite's cabin radiation heat transfer in the space environment is estimated by utilizing the thermal power of the components.

[0062] Step 3: Perform finite element mesh generation on the satellite module layout area. Based on the heat source intensity distribution function of the component, use the Heaviside function and density projection method to determine the heat load vector of the mesh unit. Use the multi-resolution finite element method to refine the mesh unit at the boundary of the satellite component and determine the heat load vector of the refined mesh unit. Obtain the global heat load vector by assembling the heat load vector of the mesh unit.

[0063] Step 4: Based on the global heat transfer matrix and global heat load vector, establish the mapping relationship between component position parameters and satellite panel layout temperature field using the heat transfer balance equation;

[0064] Step 5: Determine the optimization objective based on the thermal layout requirements of the satellite cabin components. Based on the optimization objective, the interference model, and the mapping relationship, construct the thermal layout optimization model of the satellite cabin panels, and apply the gradient optimization algorithm to solve the thermal layout optimization model of the satellite cabin panels to obtain the optimal component layout scheme.

[0065] In this embodiment of the invention, the shape of the component, the thermal power of the component, and the heat source intensity distribution function of the component are predetermined according to actual conditions.

[0066] In this embodiment of the invention, the satellite module layout area is divided into finite element meshes. Based on the heat source intensity distribution function of the component, the heat load vector of the mesh element is determined using the Heaviside function and density projection method. Then, the mesh element at the boundary of the satellite component is refined using the multi-resolution finite element method. Based on the heat source intensity distribution function of the component, the heat load vector of the refined mesh element is re-determined using the Heaviside function and density projection method. By assembling the heat load vector of the mesh element, the global heat load vector of the satellite module layout area is obtained.

[0067] The satellite cabin panel thermal layout optimization method considering thermal radiation provided in this invention can transform the nonlinear heat transfer balance equation into a linear equation by approximating the global heat transfer matrix of the satellite cabin panel radiative heat transfer. This allows for the replacement of the exact nonlinear finite element solution with a linear finite element approximation, achieving an approximate equivalent representation of the optimization objective while avoiding the nonlinear iterative solution process and significantly reducing the computational load. By employing level set functions to geometrically describe the components and using multi-resolution finite element methods to accurately obtain the thermal load vectors at the component boundaries, a mapping relationship between component position parameters and the satellite cabin panel layout temperature field is constructed, enabling accurate and efficient calculation of the gradient of the optimization objective with respect to design variables. Furthermore, by constructing a satellite cabin panel thermal layout optimization model based on the optimization objective, the interference model, and the mapping relationship, and applying a gradient optimization algorithm to solve the model, rapid optimization iteration of the component layout scheme can be achieved to obtain the optimal component layout scheme considering thermal radiation.

[0068] In this embodiment of the invention, satellite module thermal layout optimization refers to optimizing the layout position of the modules to achieve the optimal performance indicators of a specific temperature field. In fact, the layout position of the modules determines the distribution of heat loads over the layout area, thus affecting the final temperature field. To achieve differentiable layout optimization design, it is necessary to construct an analytical mathematical model from the module position parameters to the heat load vector.

[0069] In this embodiment of the invention, a level set function is used to geometrically describe the component, as expressed by the following formula:

[0070] ;

[0071] in, Describes the level set function. The independent variable of the function is... Indicates the area covered by the component. Indicates the geometric boundaries of the component. Indicates the layout area. Indicates the layout area Medium component coverage area Areas outside of [the specified area].

[0072] According to the formula above, if point If a point is located inside the component's coverage area, then the level set function value of that point is greater than zero. If the point is located outside the component's coverage area, then the level set function value of that point is less than zero. satisfy If a point is found to be on the geometric boundary of the component, then that point must lie on the component's geometric boundary. Therefore, the geometry of a component can be implicitly represented by constructing a zero level line for a suitable level set function. Theoretically, level set functions can describe components with arbitrarily complex geometries.

[0073] Furthermore, when complex geometries cannot be described using simple closed forms, their level set functions can be derived using extremum functions, R functions, Kreisselmeier-Steinhauser (KS) functions, or... Mathematical tools such as norms are used to perform Boolean operations on simple level set functions. Given that the KS function is differentiable everywhere and easy to operate, in this embodiment of the invention, the KS function is used to approximate maximum or minimum value operations, thereby achieving an approximate construction of level set functions for complex shape components.

[0074] Specifically, if a complex-shaped component can be viewed as If the union of basic shape components is given, then the level set function of the complex shape component is... This can be obtained through the maximum value function. When using the KS function to approximate the maximum value function, it can be expressed as:

[0075] ;

[0076] in, This represents a preset positive number. The base of the natural logarithm. Indicates the first The level set function of the basic shape components.

[0077] Among them, parameters This determines the approximate accuracy of the KS function. The larger the value, the higher the approximate accuracy of the KS function. Generally, the parameter... The possible value is 40.

[0078] Furthermore, to avoid numerical overflow and reduce computational errors, the following equivalent form can be adopted:

[0079] ;

[0080] in, express The maximum value of the level set function of each basic shape component. , The value of changes as the level set function of the basic shape component changes during the iteration process.

[0081] Based on the level set function description form of the component defined above, a layout description function (LDF) is further defined to characterize the component layout scheme. The layout description function is expressed as:

[0082] ;

[0083] in, This represents the layout description function. , , These represent the level set functions of the first component, the second component, and the third component, respectively. The level set function of each component This represents the total number of components. Similarly, non-differentiable maximum operations are approximated using the KS function.

[0084] The geometric model described by the level set function can easily determine the relative positions of nodes and component boundaries, facilitating heat transfer analysis of the component layout system using the fixed-mesh finite element method. To avoid re-meshing the finite element mesh during layout optimization, in this embodiment of the invention, the Heaviside function is used to project the component geometric description function onto the density field of the fixed-mesh nodes. The Heaviside function is specifically expressed as:

[0085] ;

[0086] in, This refers to the Heaviside function. This represents the independent variable of the function.

[0087] In order to avoid Since the heaviside function is not differentiable at zero, a regularized heaviside function is further applied. The regularized heaviside function is expressed as:

[0088] ;

[0089] in, This represents the Heaviside regularization function. The independent variable of the function is... As a preset constant, This represents the half-width of the 0~1 transition interval of the Heaviside function, also known as the narrow half-width.

[0090] In topology optimization, it is usually referred to as To ensure the nonsingularity of the global stiffness matrix, a small positive number is set. In this embodiment of the invention, it is directly set to 0. This setting is because, in hot layout optimization, the parameters... It only determines that the thermal load vector of the mesh nodes in the uncomponent-covered area 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.

[0091] Furthermore, in this embodiment of the invention, the Heaviside function is used to construct the two-dimensional projection of the components and to build an interference model between the components, including:

[0092] Based on the component's level set function, construct the overlapping area between components;

[0093] The Heaviside function is used to determine the area occupied by the two-dimensional projection of the overlapping area between components onto the layout area. The area occupied by the two-dimensional projection of the overlapping area between components onto the layout area represents the interference between components, and an interference model between components is constructed.

[0094] In this embodiment of the invention, based on the level set function of the components, the overlapping region between components is represented as follows:

[0095] ;

[0096] in, Indicates the first The component and the first Overlapping areas between components Indicates the first Each component covers an area. Indicates the first Each component covers an area. Indicates the first The level set function of each component Indicates the first The level set function of each component.

[0097] According to the definition of the Heaviside function, the area occupied by the two-dimensional projection of a component onto the layout area can be expressed as:

[0098] ;

[0099] Therefore, the area occupied by the two-dimensional projection of the overlapping area between components onto the layout area is represented as:

[0100] ;

[0101] in, Indicates the first The area occupied by the two-dimensional projection of each component on the layout area. Indicates the layout area. Represents an area element. Indicates the first The component and the first The area occupied by the overlapping area between components in the layout area as a two-dimensional projection. This represents the Heaviside function.

[0102] Based on the above analysis, the interference between components is represented by the area occupied by the two-dimensional projection of the overlapping area between components onto the layout area. The interference model between components is then expressed as follows:

[0103] ;

[0104] in, Indicates the first The component and the first Interference between components Indicates the total number of components.

[0105] Furthermore, regarding the thermal layout of the satellite module assembly, the three-dimensional steady-state heat conduction control equation can be expressed as:

[0106] ;

[0107] in, This indicates the temperature field of the satellite's panel layout. Represents the heat source intensity distribution function. Indicates the thermal conductivity coefficient. , , These represent the thermal conductivity coefficients at... , , Components along the three coordinate axes, This represents the normal vector pointing outwards from the boundary. This represents the heat flux at the Neumann boundary condition. This represents the surface emissivity at the Robin boundary condition. This represents the Stefan-Boltzmann constant, also known as the blackbody radiation constant, whose value is... , Indicates ambient temperature. Represent the Neumann boundary conditions. This represents the Robin boundary condition.

[0108] It should be noted that the thermal layout optimization design for the satellite cabin assembly... The axial direction is along the length of the compartment plate. The axial direction is along the width of the compartment plate. The axis is along the thickness of the compartment plate and points from inside the compartment to outside the compartment, with the origin of the coordinate system located at the vertex of the inner surface of the compartment plate.

[0109] Furthermore, in this embodiment of the invention, since the components are freely arranged on the inner surface of the satellite module, the component layout is represented as follows:

[0110] ;

[0111] in, This represents the component layout, specifically the design variables for optimizing the thermal layout of the satellite module assembly. Indicates the first The position coordinates of each component Indicates the first The rotation angle of each component Indicates the total number of components.

[0112] Since the components are only installed on the inner surface of the satellite module, the heat source intensity distribution function can be denoted as: And it is directly related to the specific location of the component, then we have .

[0113] Nonlinear radiation boundary conditions can be approximated as convective heat transfer boundary conditions, specifically expressed as:

[0114] ;

[0115] in, This represents the radiative heat transfer coefficient.

[0116] Considering that when the satellite is in the space environment, the ambient temperature is approximately 0K, that is... Then there is . according to As can be seen, the radiative heat transfer coefficient depends on the temperature of the radiating surface, so it needs to be solved iteratively.

[0117] Temperature difference on the outer surface of the cabin The change in the equivalent radiative heat transfer coefficient of the outer surface of the cabin plate caused by this It can be represented as:

[0118] ;

[0119] in, This indicates the rate of temperature change on the outer surface of the cabin plate. .

[0120] According to the above formula, it can be seen that when hour, This means that when the temperature of the outer surface of the compartment changes by 1%, the equivalent radiative heat transfer coefficient changes by only 3%. This also implies that if the temperature difference on the outer surface of the compartment does not exceed 1% of its own temperature, the difference in the equivalent radiative heat transfer coefficient at different locations will not exceed 3%. Therefore, in this embodiment of the invention, it is assumed that the equivalent radiative heat transfer coefficient at different locations on the outer surface of the compartment is the same, i.e., it is assumed that the outer surface of the compartment is at a constant temperature, and a corresponding linear finite element approximate solution method is constructed.

[0121] In order to achieve a linear finite element approximation solution, it is necessary to determine a suitable approximate average temperature of the outer surface of the tank plate. Assumption: Without considering any external radiative heat flow, all heat generated by the satellite's internal components is dissipated through deep-space radiation. Therefore, when heat transfer reaches equilibrium, according to the law of conservation of energy:

[0122] ;

[0123] in, Indicates the first Thermal power of each component The total amount of heat dissipated by radiation can be expressed as follows, according to the law of radiation heat transfer:

[0124] ;

[0125] in, This indicates the surface area of ​​the satellite module for radiative heat dissipation.

[0126] Based on the above analysis, in this embodiment of the invention, based on the three-dimensional steady-state heat conduction control equation, the law of energy conservation, and the law of radiative heat transfer, the global heat transfer matrix of the satellite's cabin radiative heat transfer in the space environment is estimated using the thermal power of the components, further including:

[0127] By combining the formulas and Solve for the approximate average temperature of the outer surface of the cabin plate. ;

[0128] Approximate average temperature of the outer surface of the cabin plate Substitute into the formula Solve for the approximate radiative heat transfer coefficient of the outer surface of the cabin plate. ;

[0129] Based on the approximate radiation heat transfer coefficient Estimate the global heat transfer matrix of the radiative heat transfer portion of the satellite module. .

[0130] In this embodiment of the invention, the global heat transfer matrix of the satellite's radiative heat transfer portion in a space environment can be estimated and solved using the above method. Since the global heat transfer matrix can be considered fixed during the layout optimization process, the nonlinear heat transfer balance equation... It can be transformed into a linear equation, where, This represents the global thermal load vector.

[0131] In this embodiment of the invention, by approximating the global heat transfer matrix of the radiative heat transfer part of the satellite compartment, the nonlinear heat transfer balance equation can be transformed into a linear equation. The linear finite element approximation solution replaces the nonlinear finite element exact solution, realizing an approximate equivalent representation of the optimization objective. At the same time, the nonlinear solution iterative process is avoided, greatly reducing the optimization computation.

[0132] Furthermore, to achieve high-precision finite element analysis under a given layout scheme, it is necessary to explore geometric mapping techniques. Geometric mapping is defined as the modeling process from a geometric model described by a level set function to a mechanical analysis model. In the thermal layout optimization problem of satellite module assemblies, the translation and rotation of the assemblies directly determine the thermal load distribution in the finite element analysis model. Therefore, accurately describing the impact of changes in the component boundaries on the thermal load vector is crucial.

[0133] Considering both computational accuracy and cost, this embodiment of the invention employs density projection for feature mapping of the geometric model. Density projection is a simple and computationally inexpensive method, making it the most popular geometric mapping approach. Its main idea is to use a fixed finite element analysis mesh throughout the entire optimization iteration process, utilizing an intermediate density field to quantify the boundary effects of the material. Therefore, density projection is also known as the Euler method.

[0134] Based on the above analysis, the layout of the components determines the distribution of heat load within the layout area. Therefore, in this embodiment of the invention, the Heat Source Intensity Function (HSIF) is used to mathematically describe this.

[0135] Specifically, based on the Heaviside function, the heat source intensity distribution function on the layout region. It can be parsed as:

[0136] ;

[0137] in, Indicates the first The heat source intensity distribution function of each component Indicates the first The level set function of each component.

[0138] It should be noted that the above analytical formula for the heat source intensity distribution function is applicable to any form of component heat source intensity distribution model.

[0139] To facilitate optimization, it is assumed that the heat source intensity of each component is constant within its coverage area, i.e. , Indicates the first The heat source intensity of each component.

[0140] Furthermore, in this embodiment of the invention, the satellite module layout area is divided into finite element meshes. Based on the heat source intensity distribution function of the component, the heat load vector of the mesh element is determined using the Heaviside function and density projection method, including:

[0141] The satellite module layout area is uniformly discretized into a quadrilateral structure mesh, and four-node rectangular elements are used for calculation. The temperature field is approximated by interpolation using piecewise bilinear polynomial functions, and the element equilibrium equation is derived.

[0142] Using the Heaviside function and density projection method, the heat source intensity of the corresponding element is obtained by interpolating the heat source intensity distribution function values ​​at the four nodes of the element.

[0143] Based on the planar four-node element finite element method and the element's heat source intensity, the element's thermal load vector is determined under the action of a constant heat source.

[0144] Specifically, the layout region is uniformly discretized into a quadrilateral structure mesh, and four-node rectangular elements are used for calculation. The entire temperature field is approximated by interpolation using piecewise bilinear polynomial functions, and the corresponding element equilibrium equations are derived:

[0145] ;

[0146] in, Represents the heat transfer matrix of the unit cell. Represents the element temperature vector. Represents the element thermal load vector;

[0147] Furthermore, the element thermal load vector can be expressed as:

[0148] ;

[0149] in, Indicates the heat source intensity of the unit. The shape function matrix representing temperature interpolation, and This represents an area element, and the superscript T indicates the matrix transpose operation. This represents the heat flux at the Neumann boundary condition. This represents the Robin boundary condition.

[0150] Based on the eigenmap concept of density projection, the finite element analysis mesh remains unchanged, while the density of the mesh elements changes continuously as the boundary moves. Therefore, in this embodiment of the invention, a pseudo-heat source model (Ersatz HeatSource Model) is proposed. The heat source intensity of the corresponding element is obtained by interpolating the heat source intensity distribution function values ​​at the four nodes of the element, specifically expressed as:

[0151] ;

[0152] in, Indicates the first The heat source intensity of each component Indicates the first The level set function of the component in unit number The values ​​at each node Indicates the unit number The coordinates of each node. If a cell is completely covered by a component, then all four nodes of the corresponding cell are inside the component, and the corresponding Heaviside function value is 1. Therefore, the heat source intensity of that cell is... .

[0153] Furthermore, based on the planar four-node element finite element method and the element's heat source intensity, under constant heat source action, the element's thermal load vector can be derived as follows:

[0154] ;

[0155] in, The superscript T represents the area of ​​a unit cell, and the superscript T indicates the matrix transpose operation.

[0156] Furthermore, based on the mapping relationship of component geometry on the finite element mesh, the analysis elements can be divided into solid elements, cavity elements, and boundary elements. Solid elements represent elements whose nodes are all located inside the component's geometric region; cavity elements represent elements whose nodes are all located outside the component's geometric region; and boundary elements represent elements whose nodes are partially inside the component's geometric region, while the remaining nodes are outside. In the satellite module thermal layout optimization problem, the heat transfer stiffness matrix of different types of elements is the same, but the thermal load vectors are different. The thermal load vectors of both solid and cavity elements can be accurately calculated, with the thermal load vector of the cavity element being a zero vector. Therefore, in this embodiment of the invention, a multi-resolution finite element method is used to further refine the boundary mesh, thereby achieving accurate calculation of the thermal load vector of the boundary elements.

[0157] Traditional multi-resolution methods refine the mesh for the entire layout design domain. As the above analysis shows, mesh refinement does not arbitrarily affect the calculation of solid elements and cavity elements, but it introduces more computational load.

[0158] refer to Figure 2-3 In this embodiment of the invention, adaptive mesh refinement is performed only on boundary elements, accurately characterizing their thermal load vectors based on the actual material distribution within the elements. Specifically, each boundary element is adaptively divided into... Each material element is considered, and the center point of each material element is selected as the integration point. Therefore, the thermal load vector of the refined boundary element can be derived as follows:

[0159] ;

[0160] in, Indicates the first thermal load vector of each boundary element Indicates the first The area covered by each boundary unit Indicates the first The heat source intensity of each boundary unit This represents the shape function matrix for temperature interpolation, with the superscript T indicating matrix transpose. Indicates the first The number of material elements divided by each boundary element. Indicates the first The level set function of the component in the th... The first boundary unit The value at the center point of each material element Indicates the first The first boundary unit The coordinates of the center point of each material element Indicates the first The area of ​​each material unit.

[0161] Following the standard finite element analysis procedure, the global heat transfer matrix can be obtained by assembling the element stiffness matrices. and global thermal load vector Based on the above analysis, the global heat transfer matrix The global thermal load vector remains unchanged throughout the layout optimization iteration process. It changes as the component layout scheme changes, therefore, by solving a system of linear equations The obtained temperature field This will also change accordingly, thus enabling the modeling of the entire differentiable computational process from component position parameters to the corresponding layout temperature field.

[0162] Furthermore, in this embodiment of the invention, based on the above analysis results, the following satellite cabin thermal layout optimization model is constructed:

[0163] ;

[0164] in, This represents the objective function to be optimized. This indicates a geometric non-interference constraint on the components. This indicates the optimization range of the design variables.

[0165] Furthermore, in this embodiment of the invention, based on the isothermal thermal design requirements within the satellite cabin, the goal is to minimize the temperature gradient within the satellite cabin and improve the uniformity of temperature distribution. The thermal layout optimization objective is defined as minimizing the variance of the temperature distribution on the inner surface of the satellite cabin panels. Based on the above-defined thermal layout optimization objective, the optimization objective function can be expressed as:

[0166] ;

[0167] in, The variance represents the temperature distribution on the inner surface of the satellite module. This indicates the number of units divided on the inner surface of the satellite module. This represents the temperature vector of the inner surface of the satellite's fuselage. This indicates the average temperature of the inner surface of the satellite's fuselage. Represents an area element. A column vector whose elements are all 1s. Dimensions and temperature vector same.

[0168] Furthermore, in this embodiment of the invention, based on the satellite cabin thermal layout optimization model constructed above, the gradient of the optimization objective function with respect to the design variables is calculated using the automatic differentiation method. Based on the gradient of the optimization objective function with respect to the design variables, the gradient optimization algorithm is applied to solve the satellite cabin thermal layout optimization model to obtain the optimal component layout scheme.

[0169] Automatic Differentiation (AD) is a technique for automatically obtaining the derivatives of a computer program. It predefines the Jacobian matrices of various fundamental mathematical operators and defines the flow of gradient information according to the chain rule. The computation of any complex function can be decomposed into a combination of fundamental mathematical operations with analytical derivatives. Therefore, automatic differentiation utilizes the chain rule to sequentially accumulate the derivatives of a series of fundamental mathematical operators, ultimately achieving the calculation of the derivative of the complex function. Since the Jacobian matrix of each mathematical operator is analytically defined, the gradient accuracy obtained by automatic differentiation is equivalent to that of the analytical solution.

[0170] Automatic differentiation typically has two implementation modes: Forward Mode (FM) and Reverse Mode (RM). Forward Mode automatic differentiation calculates the corresponding derivatives simultaneously with the nodal function values, and in a single forward calculation, only the derivative of the objective function with respect to one design variable can be obtained. Therefore, in order to obtain... The Jacobian matrix of the design variables needs to be calculated. The forward computation process is repeated once. In contrast, backpropagation-based automatic differentiation first traces the forward computation process through a computational graph and then uses backpropagation to calculate the corresponding derivatives, obtaining the gradient of only one output variable in a single backpropagation process. Mathematically, backpropagation-based automatic differentiation is equivalent to the adjoint method. For the function... Because the function has Dimensional input variables and Dimensional output variables ,when At that time, the Jacobian matrix is ​​automatically calculated using forward mode differentiation. More efficient; when In this case, using the reverse mode for automatic differentiation calculation is more efficient.

[0171] The thermal layout optimization problem of satellite module assemblies typically involves 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... Therefore, in this embodiment of the invention, reverse mode automatic differentiation is used to ensure more efficient calculation.

[0172] Thanks to the significant advancements in machine learning, numerous tools for implementing inverse pattern automatic differentiation have been developed, such as PyTorch, TensorFlow, Autograd, and JAX. Currently, most mainstream deep learning frameworks support automatic differentiation. Therefore, in this embodiment of the invention, the satellite module hot layout optimization method can be implemented programmatically using the PyTorch framework, calling the built-in automatic differentiation tool for gradient calculation, and utilizing embedded functions in the PyTorch linear algebra module. Solve the system of linear equations to obtain the final temperature response.

[0173] Furthermore, in the problem of optimizing the thermal layout of satellite module assemblies, the module layout affects the global thermal load vector. However, it does not change the global heat transfer matrix. Then there is Further export Therefore, optimizing the objective function For component position parameters The analytical gradient can be expressed as:

[0174] .

[0175] in, express The inverse matrix.

[0176] 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.

[0177] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit 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 method for optimizing the thermal layout of satellite module assemblies considering thermal radiation, characterized in that, include: The components are geometrically described based on the level set function, and the two-dimensional projection of the components is constructed using the Heaviside function to build an interference model between the components. Based on the three-dimensional steady-state heat conduction control equation, the law of energy conservation and the law of radiation heat transfer, the global heat transfer matrix of the satellite's cabin radiative heat transfer under the space environment is estimated by utilizing the thermal power of the components. Finite element meshing is performed on the satellite module layout area. Based on the heat source intensity distribution function of the component, the Heaviside function and density projection method are used to determine the heat load vector of the mesh element. The mesh element at the boundary of the satellite component is refined using the multi-resolution finite element method to determine the heat load vector of the refined mesh element. The global heat load vector is obtained by assembling the heat load vector of the mesh element. Based on the global heat transfer matrix and global heat load vector, the mapping relationship between component position parameters and satellite panel layout temperature field is established using the heat transfer balance equation. Based on the thermal layout requirements of the satellite cabin components, the optimization objective is determined. Based on the optimization objective, the interference model and the mapping relationship, a thermal layout optimization model for the satellite cabin panels is constructed. The gradient optimization algorithm is then applied to solve the thermal layout optimization model for the satellite cabin panels to obtain the optimal component layout scheme. The method, based on the three-dimensional steady-state heat conduction control equation, the law of energy conservation, and the law of radiative heat transfer, estimates the global heat transfer matrix of the satellite's cabin radiative heat transfer in the space environment using the thermal power of the components, including: By combining the formulas and Solve for the approximate average temperature of the outer surface of the cabin plate. ; Approximate average temperature of the outer surface of the cabin plate Substitute into the formula Solve for the approximate radiative heat transfer coefficient of the outer surface of the cabin plate. ; Based on the approximate radiation heat transfer coefficient Estimate the global heat transfer matrix of the radiative heat transfer portion of the satellite module. ; in, Indicates the first Thermal power of each component This indicates the total amount of heat dissipated by radiation. Indicates the total number of components. This represents the surface emissivity at the Robin boundary condition. This represents the Stefan-Boltzmann constant. This indicates the surface area of ​​the satellite's radiative heat dissipation panel. This indicates the temperature field of the satellite's panel layout. This represents the radiative heat transfer coefficient.

2. The method for optimizing the thermal layout of satellite module assemblies considering thermal radiation according to claim 1, characterized in that, The method of constructing a two-dimensional projection of the components using the Heaviside function and building an interference model between the components includes: Based on the component's level set function, construct the overlapping area between components; The Heaviside function is used to determine the area occupied by the two-dimensional projection of the overlapping area between components onto the layout area. The area occupied by the two-dimensional projection of the overlapping area between components onto the layout area represents the interference between components, and an interference model between components is constructed.

3. The method for optimizing the thermal layout of satellite module assemblies considering thermal radiation according to claim 2, characterized in that, The interference model between the components is expressed as follows: ； in, Indicates the first The component and the first Interference between components Indicates the layout area. This refers to the Heaviside function. Represents the maximum value function. Indicates the first The level set function of each component Indicates the first The level set function of each component Represents an area element. Indicates the total number of components.

4. The method for optimizing the thermal layout of satellite module assemblies considering thermal radiation according to claim 1, characterized in that, The process of dividing the satellite cabin layout area into finite element meshes, and determining the thermal load vector of the mesh elements based on the heat source intensity distribution function of the components using the Heaviside function and density projection method, includes: The satellite module layout area is uniformly discretized into a quadrilateral structure mesh, and four-node rectangular elements are used for calculation. The temperature field is approximated by interpolation using piecewise bilinear polynomial functions, and the element equilibrium equation is derived. Using the Heaviside function and density projection method, the heat source intensity of the corresponding element is obtained by interpolating the heat source intensity distribution function values ​​at the four nodes of the element. Based on the planar four-node element finite element method and the element's heat source intensity, the element's thermal load vector is determined under the action of a constant heat source.

5. The method for optimizing the thermal layout of satellite module assemblies considering thermal radiation according to claim 4, characterized in that, The unit thermal load vector is represented as follows: ； in, Represents the element thermal load vector. Indicates the heat source intensity of the unit. The superscript T indicates the area of ​​a unit cell; The heat source intensity of a unit is expressed as: ； in, Indicates the first The heat source intensity of each component Indicates the first The level set function of the component in unit number The values ​​at each node Indicates the unit number The coordinates of each node This represents the Heaviside function.

6. The method for optimizing the thermal layout of satellite module assemblies considering thermal radiation according to claim 5, characterized in that, The thermal load vector of the refined mesh element is represented as: ； in, Indicates the first thermal load vector of each boundary element Indicates the first The area covered by each boundary unit Indicates the first The heat source intensity of each boundary unit This represents the shape function matrix for temperature interpolation, with the superscript T indicating matrix transpose. Represents an area element. Indicates the first The number of material elements divided by each boundary element. Indicates the first The level set function of the component in the th... The first boundary unit The value at the center point of each material element Indicates the first The first boundary unit The coordinates of the center point of each material element Indicates the first The area of ​​each material unit.

7. The method for optimizing the thermal layout of satellite module assemblies considering thermal radiation according to claim 1, characterized in that, The constructed satellite cabin thermal layout optimization model is represented as follows: ； in, Indicates design variables, Indicates the first The position coordinates of each component Indicates the first The rotation angle of each component Indicates the total number of components. This represents the objective function to be optimized. Represents the global heat transfer matrix. Represents the global thermal load vector. This indicates the temperature field of the satellite's panel layout. This indicates a geometric non-interference constraint on the components. Indicates the optimization range of the design variables. Indicates the first The component and the first Interference between components.

8. The method for optimizing the thermal layout of satellite module assemblies considering thermal radiation according to claim 1, characterized in that, The optimization objective is to minimize the variance of the temperature distribution on the inner surface of the satellite module.

9. The method for optimizing the thermal layout of satellite module assemblies considering thermal radiation according to claim 1, characterized in that, The gradient of the objective function with respect to the design variables is calculated using the automatic differentiation method. Based on the gradient of the objective function with respect to the design variables, the gradient optimization algorithm is applied to solve the thermal layout optimization model of the satellite cabin and obtain the optimal component layout scheme.

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