Two-stage serial heat pipe constrained layout optimization method based on mixed integer programming

Abstract

The application discloses a two-stage serial heat pipe constraint layout optimization method based on mixed integer programming, relates to the technical field of component layout optimization, and comprises the following steps: determining the number of components in a component layout area, the structural size of the components, the power of the components, the number of heat pipes, the structural size of the heat pipes, the performance parameters of the heat pipes and the arrangement form of the heat pipes; determining the number of heat pipes required by each component; constructing and solving an optimization model of the distribution relationship between the components and the heat pipes to obtain the distribution relationship between the components and the heat pipes; using continuous coordinates to describe the central positions of the components, linearly modeling constraint conditions and a preset optimization target, and constructing a component layout optimization model based on mixed integer programming; and solving the component layout optimization model to obtain the position of each component in the component layout area. The application can realize the optimization solution of the component layout under the consideration of quality characteristic requirements and heat pipe constraints, has low optimization solution difficulty, is high in efficiency, and has small influence of the component scale on the solution efficiency.

Description

Technical Field

[0001] This invention relates to the field of component layout optimization technology, and in particular to a two-stage serial heat pipe constrained layout optimization method based on mixed integer programming. 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 on the satellite to meet various system performance requirements, such as mass characteristics and thermal control. As an important part of the overall satellite design, satellite layout design directly determines the overall performance, development cost, design cycle, and design level of the satellite system.

[0003] Existing satellite systems typically deploy a certain number of heat pipes within a layout area to dissipate heat from components within that area, thus transferring the heat generated by the components outside the layout area. To obtain a component layout scheme that meets both quality characteristics and heat pipe heat dissipation constraints, Chinese patent document CN115859571A, entitled "Component Layout Optimization Design Method Based on Integer Programming under Heat Pipe Constraints," discloses a method for optimizing component layout under heat pipe constraints based on integer programming. This method decomposes the component layout optimization problem under heat pipe heat dissipation constraints into a component-heat pipe allocation optimization problem and a detailed component layout optimization problem. By solving these two optimization problems, a component layout scheme that meets both quality characteristics and heat pipe heat dissipation constraints is obtained. However, when solving the detailed component layout optimization problem, the above method employs a heuristic layout search method based on sequential layout sampling. In practical applications, this heuristic layout search method based on sequential layout sampling has low search efficiency, high search difficulty, and low optimization efficiency. Furthermore, as the size of the components increases, the search difficulty increases significantly, and the optimization efficiency decreases drastically.

[0004] Furthermore, existing heat pipe-constrained layout optimization methods typically assume no direct heat exchange between components, with heat dissipation occurring solely through heat pipes. However, in real-world satellite systems, the close proximity or contact between components leads to significant thermal coupling effects, resulting in localized heat accumulation, increased temperature gradients, and impacts system thermal stability and component lifespan. Summary of the Invention

[0005] To address some or all of the technical problems existing in the prior art, this invention provides a two-stage serial heat pipe constrained layout optimization method based on mixed integer programming.

[0006] The technical solution of the present invention is as follows: A two-stage serial heat pipe constrained layout optimization method based on mixed integer programming is provided, including: Determine the number of components, structural dimensions of components, power of components, number of heat pipes, structural dimensions of heat pipes, performance parameters of heat pipes, and arrangement of heat pipes within the component layout area; Based on the structural dimensions of each component and the arrangement of the heat pipes, determine the number of heat pipes required for each component; With the goal of minimizing the maximum actual heat conduction power of the heat pipe, and with the heat conduction capacity constraint and longitudinal dimension capacity constraint of the heat pipe as constraints, an optimization model for the distribution relationship between the components and the heat pipe is constructed and solved to obtain the distribution relationship between the components and the heat pipe. The center position of the component is described by continuous coordinates. The constraints are non-interference between components and component layout areas, non-interference between components, distribution relationship between components and heat pipes, centroid constraint of component system, and thermal coupling constraint between components. The constraints and preset optimization objectives are linearized and modeled to construct a component layout optimization model based on mixed integer programming. The thermal coupling constraint between components means that the interval between components is not less than a preset distance threshold, and the temperature difference between components with an interval less than the preset distance threshold does not exceed a preset temperature difference threshold. Solve the component layout optimization model to obtain the position of each component in the component layout area.

[0007] In some optional implementations, the optimized model for the allocation relationship between the components and the heat pipes is expressed as follows: ; in, This indicates a preset parameter. Used for equivalent substitution to optimize the objective function , This represents the actual thermal conductivity of the k-th heat pipe. This represents an auxiliary binary variable used to describe the reference heat pipe of the i-th component. This indicates that the j-th heat pipe is the reference heat pipe for the i-th component. The reference heat pipe for a component is defined as the heat pipe with the smallest index among all the heat pipes used by the component. This represents a binary variable used to describe the distribution relationship between components and heat pipes. This indicates that the i-th component is placed on the k-th heat pipe. This indicates that the i-th component is not placed on the k-th heat pipe. This represents the transformation matrix corresponding to the i-th component. The element in the j-th row and k-th column, the transformation matrix For one A matrix, and the j-th element in the j-th row of the matrix is... One element is 1, and the rest of the elements of the matrix are 0. This represents the height of the i-th component. Indicates the maximum permissible height. This represents the power of the i-th component. This represents the number of heat pipes required for the i-th component. This represents the maximum thermal conductivity of a given heat pipe. Indicates the number of components. Indicates the number of heat pipes; Based on the arrangement of the heat pipes, all heat pipes are sequentially numbered starting from number 1 along the arrangement direction.

[0008] In some optional implementations, the lower left corner of the component layout area is selected as the origin of the coordinate system, and the horizontal direction of the component layout area is used as the coordinate system. The vertical direction of the component layout area is along the axis. In the axial direction, a two-dimensional Cartesian coordinate system is constructed. Based on the constructed two-dimensional Cartesian coordinate system, the constraints and preset optimization objectives are linearized and modeled to construct a component layout optimization model based on mixed integer programming.

[0009] In some optional implementations, the non-interference constraint between the components and the component layout regions is modeled as follows: ; in, Indicates the first The center coordinates of each component Indicates the first The width of each component, Indicates the first The height of each component Indicates the width of the component layout area. Indicates the height of the component layout area. Indicates the number of components; Wherein, the width of a component represents its length in the horizontal direction of the component layout area, the height of a component represents its length in the vertical direction of the component layout area, the width of the component layout area represents the length of the component layout area in its horizontal direction, and the height of the component layout area represents the length of the component layout area in its vertical direction.

[0010] In some alternative implementations, the non-interference constraints between components are modeled as follows: ; in, Indicates an indicator variable. Indicates the first The center coordinates of each component Indicates the first The width of each component, Indicates the first The height of each component It is a positive number.

[0011] In some alternative implementations, the width of the heat pipe is set to... , No. The heat pipes used in each component are numbered as follows: The constraint modeling of the allocation relationship between the components and the heat pipe is as follows: ; in, Indicates the first The x-coordinate of the center position of each heat pipe Indicates the first The x-coordinate of the center position of each heat pipe Indicates the first The x-coordinate of the center position of each heat pipe Indicates the number of heat pipes.

[0012] In some alternative implementations, the centroid constraint model of the component system is as follows: ; in, Indicates the first The quality of each component The ordinate represents the position of the expected centroid. The vertical coordinate representing the position of the centroid of the component system. This indicates the pre-set centroid deviation in the coordinate system. The component along the axial direction.

[0013] In some alternative implementations, the thermal coupling constraints between the components are modeled as follows: ; in, Indicates the first The component and the first Each component in Distance along the axis Indicates the first The component and the first Each component in Distance along the axis For positive integers, This indicates a preset distance threshold. , , , , It is a binary indicator variable. , Indicates the first Operating temperature of each component Indicates the first Operating temperature of each component This indicates the preset temperature difference threshold. For positive integers, Indicates the base temperature of the heat pipe. Indicates the first The power of each component Indicates the first The equivalent thermal resistance of each component to its associated heat pipe. This represents the equivalent thermal resistance of the coupling between components. Used to represent all related to the first The components whose interval is less than a preset distance threshold are the components of the first component. Additional temperature rise caused by individual components.

[0014] In some optional implementations, the component layout optimization model based on mixed-integer programming is expressed as: ; in, Indicates the component layout scheme. .

[0015] In some alternative implementations, a mathematical programming solver or an integer programming algorithm is used to solve the component layout optimization model based on mixed integer programming.

[0016] The main advantages of the technical solution of this invention are as follows: The two-stage serial heat pipe constraint layout optimization method based on hybrid integer programming of the present invention decomposes the component layout optimization problem under heat pipe constraints into a component-heat pipe allocation optimization problem and a component layout optimization problem under a given component-heat pipe allocation relationship. It uses integer programming to solve the component layout optimization problem under the given component-heat pipe allocation relationship. It can achieve the optimization solution of component layout under considering quality characteristic requirements and heat pipe constraints. The optimization solution is easy and efficient. Moreover, the optimization solution efficiency is less affected by the component size. It can still achieve fast optimization solution when the component size is large. Attached Figure Description

[0017] 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: Figure 1 This is a schematic diagram of a component layout under heat pipe constraints provided in an embodiment of the present invention; Figure 2 The flowchart illustrates a two-stage serial heat pipe constrained layout optimization method based on mixed integer programming, as provided in this embodiment of the invention. Detailed Implementation

[0018] 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.

[0019] The technical solutions provided by the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0020] refer to Figure 1 In satellite systems, heat pipes in the component layout area are typically arranged in a horizontally uniform manner to achieve better heat transfer. The component layout optimization problem under heat pipe constraints mainly studies how to achieve better heat dissipation performance and quality characteristics of the system through component layout design, given the location of the heat pipes. The component layout optimization problem under heat pipe constraints includes the following performance design requirements: The centroid of the component system along the vertical direction of the component layout area should be located within the given centroid range and as close as possible to the desired centroid. The components must be placed on heat pipes to ensure that the heat generated by the components themselves can be dissipated through the heat pipes; The total heat dissipation of each heat pipe must not exceed its maximum allowable heat dissipation capacity; The total heat dissipation of different heat pipes should be as close as possible to ensure that the temperature distribution within the component layout area is as uniform as possible and to avoid heat concentration.

[0021] To solve the aforementioned component layout optimization problem under heat pipe constraints, improve optimization efficiency, and enhance the feasibility and quality of the obtained component layout scheme, this invention provides a two-stage serial heat pipe constraint layout optimization method based on mixed integer programming.

[0022] refer to Figure 2 The two-stage serial heat pipe constrained layout optimization method based on mixed integer programming provided in this embodiment of the invention includes the following steps S1-S5: Step S1: Determine the number of components, structural dimensions of components, power of components, number of heat pipes, structural dimensions of heat pipes, performance parameters of heat pipes, and arrangement of heat pipes within the component layout area. In this embodiment of the invention, based on the actual component layout, the number of components to be arranged in the component layout area, the structural dimensions of each component, the power of each component, the number of heat pipes used for heat dissipation in the component layout area, the structural dimensions of the heat pipes, the performance parameters of the heat pipes, and the arrangement of the heat pipes in the component layout area are determined.

[0023] In this embodiment of the invention, the performance parameters of the heat pipe include: the maximum thermal conductivity of the heat pipe; the arrangement of the heat pipe includes: the arrangement position of each heat pipe within the component layout area.

[0024] Step S2: Determine the number of heat pipes required for each component based on the structural dimensions of each component and the arrangement of the heat pipes. In this embodiment of the invention, the number of heat pipes required for each component is determined based on the structural dimensions of each component within the component layout area and the arrangement of the heat pipes.

[0025] In this embodiment of the invention, the number of heat pipes required for each component represents the number of heat pipes that need to be contacted when the current component is placed within the component layout area. Given the structural dimensions of the component and the arrangement of the heat pipes, this number of heat pipes can be calculated based on the width of the component, the width of the heat pipes, and the spacing between adjacent heat pipes. Here, the width of the component represents the horizontal length of the component within the component layout area, and the width of the heat pipe represents the horizontal length of the heat pipe within the component layout area.

[0026] Step S3: With minimizing the maximum actual heat conduction power of the heat pipe as the optimization objective, and with the heat conduction capacity constraint and longitudinal dimension capacity constraint of the heat pipe as the constraint conditions, construct and solve the optimization model of the distribution relationship between the component and the heat pipe to obtain the distribution relationship between the component and the heat pipe. In this embodiment of the invention, the heat pipe thermal conductivity capacity constraint means that the total thermal conductivity of the heat pipe does not exceed the maximum thermal conductivity allowed by the heat pipe itself. Specifically, it can also be expressed as the total power of all components placed on the heat pipe that is heated by the current heat pipe does not exceed the maximum thermal conductivity allowed by the heat pipe itself.

[0027] In this embodiment of the invention, the longitudinal dimension capacity constraint means that the total height of all components placed on each heat pipe does not exceed the maximum allowable height. The height of a component represents its length in the vertical direction of the component layout area.

[0028] In this embodiment of the invention, the maximum allowable height is predetermined according to the actual situation, and is usually the length of the component layout area in the vertical direction.

[0029] Step S4: The center position of the component is described by continuous coordinates. The constraints are non-interference between components and component layout areas, non-interference between components, distribution relationship between components and heat pipes, centroid constraint of component system, and thermal coupling constraint between components. The constraints and the preset optimization objectives are linearized and modeled to construct a component layout optimization model based on mixed integer programming. In this embodiment of the invention, based on the actual situation and performance design requirements of the component layout optimization problem under heat pipe constraints, the constraints of the optimization problem are determined, specifically including: non-interference constraints between components and component layout areas, non-interference constraints between components, constraints on the distribution relationship between components and heat pipes, constraints on the centroid of the component system, and constraints on thermal coupling between components.

[0030] Among them, the non-interference constraint between components and component layout areas means that there is no interference between the boundaries of the component and component layout areas; the non-interference constraint between components means that there is no interference between any two components; the allocation relationship constraint between components and heat pipes means that the components intersect with the heat pipes they are assigned to, but do not intersect with the other heat pipes; the centroid constraint of the component system includes the calculation method constraint of the centroid position of the component system and the deviation constraint between the centroid position of the component system and the desired centroid position; the thermal coupling constraint between components means that the interval between components is not less than a preset distance threshold, and the temperature difference between components with an interval less than the preset distance threshold does not exceed a preset temperature difference threshold.

[0031] In this embodiment of the invention, the optimization objective is specifically determined based on actual needs.

[0032] Specifically, based on the actual situation and performance design requirements of the component layout optimization problem under heat pipe constraints, the optimization objective is to minimize the deviation between the longitudinal centroid of the component system and the desired centroid. Here, longitudinal refers to the vertical direction of the component layout area.

[0033] Step S5: Solve the component layout optimization model to obtain the position of each component in the component layout area.

[0034] In this embodiment of the invention, the component layout optimization model based on mixed integer programming is directly solved using existing mathematical programming solvers or integer programming algorithms to obtain the corresponding component layout scheme, and then the position of each component in the component layout area is obtained.

[0035] The two-stage serial heat pipe constraint layout optimization method based on hybrid integer programming provided in this invention decomposes the component layout optimization problem under heat pipe constraints into a component-heat pipe allocation optimization problem and a component layout optimization problem under a given component-heat pipe allocation relationship. It uses integer programming to solve the component layout optimization problem under the given component-heat pipe allocation relationship. It can achieve the optimization solution of component layout under considering quality characteristic requirements and heat pipe constraints. The optimization solution is easy and efficient. Moreover, the optimization solution efficiency is less affected by the component size. It can still achieve fast optimization solution when the component size is large.

[0036] Furthermore, in this embodiment of the invention, for ease of description and model building, all heat pipes are sequentially numbered starting from number 1 along the arrangement direction of the heat pipes according to their arrangement.

[0037] Furthermore, in this embodiment of the invention, based on the sequentially numbered heat pipes, with the optimization objective of minimizing the maximum actual thermal conductivity of the heat pipes, and with the constraints of heat pipe thermal conductivity capacity and longitudinal dimension capacity as constraints, the constructed optimization model for the allocation relationship between components and heat pipes is expressed as follows: ; in, This indicates a preset parameter. Used for equivalent substitution to optimize the objective function , This represents the actual thermal conductivity of the k-th heat pipe. This represents an auxiliary binary variable used to describe the reference heat pipe of the i-th component. This indicates that the j-th heat pipe is the reference heat pipe for the i-th component. The reference heat pipe for a component is defined as the heat pipe with the smallest index among all the heat pipes used by the component. This represents a binary variable used to describe the distribution relationship between components and heat pipes. This indicates that the i-th component is placed on the k-th heat pipe. This indicates that the i-th component is not placed on the k-th heat pipe. This represents the transformation matrix corresponding to the i-th component. The element in the j-th row and k-th column, the transformation matrix For one A matrix, and the j-th element in the j-th row of the matrix is... One element is 1, and the rest of the elements of the matrix are 0. This represents the height of the i-th component. Indicates the maximum permissible height. This represents the power of the i-th component. This represents the number of heat pipes required for the i-th component. This represents the maximum thermal conductivity of a given heat pipe. Indicates the number of components. Indicates the number of heat pipes.

[0038] In this embodiment of the invention, in the above-described optimization model for the allocation relationship between components and heat pipes, This is used to define the longitudinal dimension capacity constraint. If this condition is met, the longitudinal dimension capacity constraint is satisfied. This is used to define the heat pipe thermal conductivity constraint. If this condition is met, the heat pipe thermal conductivity constraint is satisfied.

[0039] In this embodiment of the invention, preset parameters are used. Used for equivalent substitution to optimize the objective function Furthermore, using preset parameters Equivalent substitution optimization objective function At the same time, add constraints. When constraints When satisfied, it means ,when If the minimum value is reached, then the condition must be met. By using preset parameters to equivalently replace the objective function and setting corresponding constraints, the use of maximum value calculations in integer programming optimization can be avoided, thus improving the efficiency of optimization.

[0040] In this embodiment of the invention, by optimizing the above-mentioned component and heat pipe allocation relationship optimization model, a binary variable is obtained. This determines which heat pipes the components are placed on, i.e., the component-heat pipe distribution relationship. Specifically, when the i-th component is placed on... When using a heat pipe, a binary variable satisfy and .

[0041] Furthermore, in this embodiment of the invention, in order to facilitate description and model building, improve optimization and solution efficiency, and ensure the feasibility of the obtained component layout scheme, it is set that: all components are square structures, all components are rigid bodies with uniform mass distribution, the centroid of the component coincides with the geometric center of the component, and the components are arranged in the component layout area in a horizontal direction parallel to the component layout area.

[0042] Furthermore, in this embodiment of the invention, in order to facilitate description and model construction, a point in the component layout area is selected as the origin of the coordinate system, and a Cartesian coordinate system is constructed. The center position of the component is described based on the constructed Cartesian coordinate system.

[0043] Specifically, to further facilitate description and model building, the lower left corner of the component layout area is selected as the origin of the coordinate system, and the horizontal direction of the component layout area is taken as the coordinate system. The vertical direction of the component layout area is along the axis. Construct a two-dimensional Cartesian coordinate system along the axis.

[0044] Furthermore, in this embodiment of the invention, the two-dimensional Cartesian coordinate system constructed in the above manner is further defined as follows: The center coordinates of each component are , No. The width of each component is , No. The height of each component is The width of the component layout area is The height of the component layout area is .

[0045] It should be noted that, in the embodiments of the present invention, the width of the component represents the length of the component in the horizontal direction of the component layout area, the height of the component represents the length of the component in the vertical direction of the component layout area, the width of the component layout area represents the length of the component layout area in its horizontal direction, and the height of the component layout area represents the length of the component layout area in its vertical direction.

[0046] Furthermore, based on the above settings, the following non-interference constraints are established between components and component layout areas: .

[0047] Furthermore, in this embodiment of the invention, the Phi function is used to determine the formula for calculating the interference between any two components, an indicator variable is introduced and the method of large numbers is combined to linearize the formula for calculating the interference, thereby modeling the non-interference constraint between components.

[0048] In this embodiment of the invention, the following is defined: The component and the first The interference between the components is To ensure that there is no interference between components, the amount of interference... The following conditions must be met: .

[0049] In this embodiment of the invention, the Phi function method is used to calculate the interference between any two components.

[0050] Specifically, the two components are respectively the first The component and the first Taking one component as an example, the formula for calculating the interference between two components is as follows: ; in, Indicates the first The center coordinates of each component Indicates the first The width of each component, Indicates the first The height of each component.

[0051] Expanding the absolute value operation in the above formula for calculating the interferometric amount, the formula for calculating the interferometric amount can be equivalently transformed into: .

[0052] Furthermore, indicator variables are introduced. By linearizing the above interference calculation formula using the method of large numbers, we obtain the following equivalent constraint, which is the non-interference constraint between components: ; in, It should be a relatively large positive number, set according to the specific situation, for example... This requires that all inequalities in the above-mentioned non-interference constraints between components be satisfied simultaneously.

[0053] In the above-mentioned non-interference constraints between components, when At that time, Can be converted If the inequality If true, it means that the non-interference constraint between components is satisfied; when At that time, Can be converted ,because Since it is a large positive constant, this inequality applies regardless of whether interference occurs between components. This holds true consistently. In this embodiment of the invention, through constraints... It can be required that at least one of the four indicator variables is equal to 1, which can guarantee that the component layout scheme obtained by solving satisfies the non-interference constraint between components.

[0054] Furthermore, in this embodiment of the invention, it is set that: each heat pipe has the same structural dimensions, and the width of the heat pipe is... , No. The heat pipes used in each component are numbered as follows: .

[0055] It should be noted that the width of the heat pipe refers to its length in the horizontal direction within the component layout area.

[0056] In this embodiment of the invention, the allocation relationship between components and heat pipes requires that there be an intersecting relationship between the components and the heat pipes they use, and that there be no intersecting relationship between the components and the other heat pipes.

[0057] Based on the above settings, the intersection relationship between the component and the heat pipe it uses can be modeled as follows: ; in, Indicates the first The x-axis coordinates the center position of each heat pipe.

[0058] Expanding the absolute value operation in the above intersection relation can be equivalently transformed into: .

[0059] Furthermore, based on the above settings, when the first The heat pipes used in each component are numbered as follows: , No. The component and the first The heat pipe and the first None of the heat pipes intersect; therefore, the non-intersecting relationship between the component and the other heat pipes can be modeled as follows: ; in, Indicates the first The x-coordinate of the center position of each heat pipe Indicates the first The x-axis coordinates the center position of each heat pipe.

[0060] Based on the above settings and analysis, the following constraints on the allocation relationship between components and heat pipes are established in this embodiment of the invention: .

[0061] Furthermore, define: the first The mass of each component is The expected coordinates of the centroid are .

[0062] In this embodiment of the invention, since the component layout optimization problem under heat pipe constraints only considers the vertical centroid constraint, the following component system centroid constraint is established: ; in, The vertical coordinate representing the position of the centroid of the component system. This indicates the pre-set centroid deviation in the coordinate system. The component along the axial direction.

[0063] Furthermore, considering that in actual satellite operation, components in the component layout area will experience direct heat transfer due to their geometric proximity, i.e., a thermal coupling effect. This thermal coupling effect can lead to local heat accumulation, altering the temperature distribution of the components themselves and potentially affecting the heat dissipation efficiency of the heat pipes. To ensure the thermal stability of the component layout scheme, this embodiment of the invention introduces inter-component thermal coupling constraints. These constraints are used to ensure that the interval between components is not less than a preset distance threshold, and that the temperature difference between components with intervals less than the preset distance threshold does not exceed a preset temperature difference threshold.

[0064] In this embodiment of the invention, in order to integrate the thermal coupling constraints between components into the mixed integer programming framework, a discretization method based on the component projection interval is used to determine the interval between components. Simultaneously, to simplify calculations and maintain linearity, a conservative criterion is adopted: if two components are in... Axial direction and If the distances along the axis are all less than the preset distance threshold, then the interval between the two components is determined to be less than the preset distance threshold.

[0065] Specifically, with the first The component and the first Taking one component as an example, two components in Axial direction and The distances along the axes are expressed as follows: ; ; in, Indicates the first The component and the first Each component in Distance along the axis Indicates the first The component and the first Each component in Distance along the axial direction.

[0066] In this embodiment of the invention, in order to construct thermal coupling constraints between components, three sets of binary indicator variables are introduced, specifically including: a first set of binary indicator variables. and , The first group of binary indicator variables is used to eliminate absolute value operations in the distance calculation formula; the second group of binary indicator variables... and , The second set of binary indicator variables is used to represent the two components in Axial direction and Whether the distance along the axis is less than a preset distance threshold; the third group of binary indicator variables. , The third set of binary indicator variables is used to indicate whether thermal coupling exists between two components.

[0067] Based on the first set of binary indicator variables, and by linearizing the above distance calculation formula using the method of large numbers, the following equivalent form is obtained: ; ; in, This should be a relatively large positive number. The specific value should be set according to the actual situation, for example, set to the diagonal length of the layout area.

[0068] Based on the second set of binary indicator variables, the following distance determination constraints are established: ; in, This indicates a preset distance threshold, which can be set according to the actual situation.

[0069] The distance determination constraint described above is used to ensure that if and only if hour, ; and used to ensure that if and only if hour, .

[0070] Based on the established second and third sets of binary indicator variables, the following thermal coupling decision constraints are established: ; The above thermal coupling determination constraint is used to ensure that if and only if hour, That is, if and only if the two components are Axial direction and When the distances in both axial directions are less than a preset distance threshold, it is determined that there is thermal coupling between the two components.

[0071] Based on the established third set of binary indicator variables, the following conditional temperature difference constraint is established: ; in, Indicates the first Operating temperature of each component Indicates the first Operating temperature of each component This indicates a preset temperature difference threshold, which can be set according to actual conditions. This should be a relatively large normal number. The specific value should be set according to the actual situation, such as the maximum operating temperature of the component.

[0072] The aforementioned conditional temperature difference constraint is used to ensure that if and only if hour, That is, if and only if the two components are Axial direction and When the distances in both axial directions are less than a preset distance threshold, the temperature difference between the two components must not exceed a preset temperature difference threshold.

[0073] Furthermore, each component is abstracted as a thermal node. The temperature of a component is determined by its own power and the heat exchange between the component and the outside environment. Let: The equivalent thermal resistance of each component to its corresponding heat pipe is The equivalent thermal resistance of the coupling between components is The equivalent thermal resistance from the component to its heat pipe is determined by the component's packaging form, internal structure, and the characteristics of the mounting interface (such as a thermal pad), and is used as a known constant input. The coupling equivalent thermal resistance between components is used to characterize the intensity of direct thermal interaction caused by the proximity of components, and the specific value is pre-calibrated as a constant based on thermal simulation or design experience of typical engineering scenarios.

[0074] Based on the above settings, the operating temperature of the component can be estimated using the following formula: ; in, Indicates the base temperature of the heat pipe. Indicates the first The power of each component Indicates the first The power of each component Used to represent all related to the first The components whose interval is less than a preset distance threshold are the components of the first component. Additional temperature rise caused by individual components.

[0075] In this embodiment of the invention, based on the above analysis, the established inter-component thermal coupling constraint is expressed as follows: .

[0076] In this embodiment of the invention, by introducing inter-component thermal coupling constraints, the thermal reliability of the component layout scheme can be significantly enhanced. Potential local overheating problems can be avoided in the initial stage of satellite overall design, thereby improving the overall performance and design quality of the entire satellite component system. Simultaneously, when constructing inter-component thermal coupling constraints, a flexible constraint of "proximity determination → temperature difference limitation" is adopted, rather than a simple geometric distance embargo. This provides the optimization algorithm with a mathematical space for intelligent trade-offs between "layout compactness" and "thermal stability," better meeting the actual needs of engineering design. Through reasonable parameter definition and thorough linearization modeling, complex thermophysical phenomena can be characterized and solved within an efficient mixed-integer programming framework.

[0077] Furthermore, in this embodiment of the invention, when the optimization objective is to minimize the deviation between the longitudinal centroid of the component system and the desired centroid, the corresponding optimization objective function can be expressed as: .

[0078] Furthermore, in this embodiment of the invention, based on the above settings and analysis, the component layout optimization model based on mixed integer programming is expressed as follows: ; in, Indicates the component layout scheme. .

[0079] Furthermore, in this embodiment of the invention, the mathematical programming solver used to solve the component layout optimization model based on mixed integer programming is the SCIP optimization solver or the CPLEX optimization solver; the integer programming algorithm used to solve the component layout optimization model based on mixed integer programming is the branch and bound method.

[0080] The two-stage serial heat pipe constraint layout optimization method based on hybrid integer programming provided in this invention decomposes the component layout optimization problem under heat pipe constraints into a component-heat pipe allocation optimization problem and a component layout optimization problem under a given component-heat pipe allocation relationship. It uses integer programming to solve the component layout optimization problem under the given component-heat pipe allocation relationship. It can achieve the optimization solution of component layout under considering quality characteristic requirements and heat pipe constraints. The optimization solution is easy and efficient. Moreover, the optimization solution efficiency is less affected by the component size. It can still achieve fast optimization solution when the component size is large.

[0081] 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.

[0082] 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 two-stage serial heat pipe constrained layout optimization method based on mixed integer programming, characterized in that, include: Determine the number of components, structural dimensions of components, power of components, number of heat pipes, structural dimensions of heat pipes, performance parameters of heat pipes, and arrangement of heat pipes within the component layout area; Based on the structural dimensions of each component and the arrangement of the heat pipes, determine the number of heat pipes required for each component; With minimizing the maximum actual thermal conductivity of the heat pipe as the optimization objective, and with the thermal conductivity capacity constraint and longitudinal dimension capacity constraint of the heat pipe as the constraint conditions, an optimization model for the distribution relationship between the component and the heat pipe is constructed and solved to obtain the distribution relationship between the component and the heat pipe. The center position of the component is described by continuous coordinates. The constraints are non-interference between components and component layout areas, non-interference between components, distribution relationship between components and heat pipes, centroid constraint of component system, and thermal coupling constraint between components. The constraints and preset optimization objectives are linearized and modeled to construct a component layout optimization model based on mixed integer programming. The thermal coupling constraint between components means that the interval between components is not less than a preset distance threshold, and the temperature difference between components with an interval less than the preset distance threshold does not exceed a preset temperature difference threshold. Solve the component layout optimization model to obtain the position of each component in the component layout area.

2. The two-stage serial heat pipe constrained layout optimization method based on mixed integer programming according to claim 1, characterized in that, The optimized model for the allocation relationship between the components and the heat pipe is expressed as follows: ； in, This indicates a preset parameter. Used for equivalent substitution to optimize the objective function , This represents the actual thermal conductivity of the k-th heat pipe. This represents an auxiliary binary variable used to describe the reference heat pipe of the i-th component. This indicates that the j-th heat pipe is the reference heat pipe for the i-th component. The reference heat pipe for a component is defined as the heat pipe with the smallest index among all the heat pipes used by the component. This represents a binary variable used to describe the distribution relationship between components and heat pipes. This indicates that the i-th component is placed on the k-th heat pipe. This indicates that the i-th component is not placed on the k-th heat pipe. This represents the transformation matrix corresponding to the i-th component. The element in the j-th row and k-th column, the transformation matrix For one A matrix, and the j-th element in the j-th row of the matrix is... One element is 1, and the rest of the elements of the matrix are 0. This represents the height of the i-th component. Indicates the maximum permissible height. This represents the power of the i-th component. This represents the number of heat pipes required for the i-th component. This represents the maximum thermal conductivity of a given heat pipe. Indicates the number of components. Indicates the number of heat pipes; Based on the arrangement of the heat pipes, all heat pipes are sequentially numbered starting from number 1 along the arrangement direction.

3. The two-stage serial heat pipe constrained layout optimization method based on mixed integer programming according to claim 1 or 2, characterized in that, The bottom left corner of the component layout area is selected as the origin of the coordinate system, and the horizontal direction of the component layout area is used as the coordinate system. The vertical direction of the component layout area is along the axis. In the axial direction, a two-dimensional Cartesian coordinate system is constructed. Based on the constructed two-dimensional Cartesian coordinate system, the constraints and preset optimization objectives are linearized and modeled to construct a component layout optimization model based on mixed integer programming.

4. The two-stage serial heat pipe constrained layout optimization method based on mixed integer programming according to claim 3, characterized in that, The non-interference constraint between the components and the component layout regions is modeled as follows: ； in, Indicates the first The center coordinates of each component Indicates the first The width of each component, Indicates the first The height of each component Indicates the width of the component layout area. Indicates the height of the component layout area. Indicates the number of components; Wherein, the width of a component represents its length in the horizontal direction of the component layout area, the height of a component represents its length in the vertical direction of the component layout area, the width of the component layout area represents the length of the component layout area in its horizontal direction, and the height of the component layout area represents the length of the component layout area in its vertical direction.

5. The two-stage serial heat pipe constrained layout optimization method based on mixed integer programming according to claim 4, characterized in that, The non-interference constraint between components is modeled as follows: ； in, Indicates an indicator variable. Indicates the first The center coordinates of each component Indicates the first The width of each component, Indicates the first The height of each component It is a positive number.

6. The two-stage serial heat pipe constrained layout optimization method based on mixed integer programming according to claim 5, characterized in that, Setting: The width of the heat pipe is , No. The heat pipes used in each component are numbered as follows: The constraint modeling of the allocation relationship between the components and the heat pipe is as follows: ； in, Indicates the first The x-coordinate of the center position of each heat pipe Indicates the first The x-coordinate of the center position of each heat pipe Indicates the first The x-coordinate of the center position of each heat pipe Indicates the number of heat pipes.

7. The two-stage serial heat pipe constrained layout optimization method based on mixed integer programming according to claim 6, characterized in that, The centroid constraint model of the component system is as follows: ； in, Indicates the first The quality of each component The ordinate represents the position of the expected centroid. The vertical coordinate representing the position of the centroid of the component system. This indicates the pre-set centroid deviation in the coordinate system. The component along the axial direction.

8. The two-stage serial heat pipe constrained layout optimization method based on mixed integer programming according to claim 7, characterized in that, The thermal coupling constraint between components is modeled as follows: ； in, Indicates the first The first component and the first Each component in Distance along the axis Indicates the first The first component and the first Each component in Distance along the axis For positive integers, This indicates a preset distance threshold. , , , , It is a binary indicator variable. , Indicates the first Operating temperature of each component Indicates the first Operating temperature of each component This indicates the preset temperature difference threshold. For positive integers, Indicates the base temperature of the heat pipe. Indicates the first The power of each component, Indicates the first The equivalent thermal resistance of each component to its associated heat pipe. This represents the equivalent thermal resistance of the coupling between components. Used to represent all related to the first The components whose interval is less than a preset distance threshold are the components of the first component. Additional temperature rise caused by individual components.

9. The two-stage serial heat pipe constrained layout optimization method based on mixed integer programming according to claim 8, characterized in that, The component layout optimization model based on mixed integer programming is expressed as follows: ； in, Indicates the component layout scheme. .

10. The two-stage serial heat pipe constrained layout optimization method based on mixed integer programming according to claim 1, characterized in that, Solve the component layout optimization model based on mixed integer programming using a mathematical programming solver or an integer programming algorithm.

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