Spacecraft component layout optimization method considering rotational inertia and vibration frequency

Abstract

The invention discloses a spacecraft component layout optimization method considering rotational inertia and vibration frequency, which comprises the following steps of: presetting boundary dimensions of a spacecraft cabin and a plurality of components to be arranged and respectively carrying out approximate description to obtain a three-dimensional approximate model, setting a phi function according to the three-dimensional approximate model and calculating a non-interference constraint, setting a centroid error constraint and a safety distance constraint, calculating the rotational inertia of the spacecraft, carrying out finite element analysis on the structure of the spacecraft, setting a characteristic equation and solving the characteristic equation to obtain the vibration frequency of the spacecraft, and taking the rotational inertia and the vibration frequency of the spacecraft as optimization targets. And constructing a spacecraft component layout double-target optimization model by taking the non-interference constraint, the centroid error constraint and the safe distance constraint as constraint terms, and performing optimization solution on the spacecraft component layout double-target optimization model to obtain a spacecraft component layout optimization scheme meeting constraint conditions. According to the method, the spacecraft component layout optimization problem considering the quality characteristic and the vibration frequency characteristic at the same time can be efficiently and accurately processed.

Description

Technical Field

[0001] The invention relates to the technical field of spacecraft design, and in particular to a spacecraft component layout optimization method taking into account rotational inertia and vibration frequency. Background Art

[0002] The key task of spacecraft design is to enable the spacecraft to carry high-precision instruments and equipment under the constraints of limited mass, volume, etc., and to operate reliably in orbit for a long time. Spacecraft component layout design refers to placing several components to be laid out in a given limited spacecraft space under the premise of meeting some necessary constraints to achieve the best performance indicators. The intervals between components performing different tasks need to be reasonably controlled to ensure the independence and efficiency of the work, and different components performing the same task need to be properly arranged and placed to ensure the consistency and accuracy of the work.

[0003] At present, the layout design of spacecraft components mainly relies on the experience of engineers to provide several optimal layout solutions that meet the requirements of spacecraft flight missions. However, with the increase in the number of spacecraft components, considering the complex working conditions of spacecraft in orbit, it is much more difficult to improve the layout effect by relying solely on experience. Therefore, the intelligent optimization design of spacecraft component layout can shorten the spacecraft design cycle, save development costs, and improve the overall performance of the spacecraft.

[0004] The layout problem is theoretically an NP-Hard problem. The spacecraft layout optimization problem belongs to a type of layout problem with performance constraints. The solution space of the optimization design problem considering the spacecraft performance objectives has the characteristics of strong constraints, high dimensions, multiple extreme values, non-convexity, and nonlinearity. It requires the comprehensive application of knowledge from various disciplines such as aerospace, statics, dynamics, geometry, and thermodynamics. Some scholars first applied numerical optimization methods to the study of spacecraft component layout optimization design problems. They used a combination of sequential linear programming and feasible direction optimization methods to find the location of spacecraft payloads so that their inertial cross product is minimized, thereby reducing the need for spacecraft propulsion attitude control. At the same time, the geometric and electromagnetic interference between payloads is imposed as constraints. This combination strategy not only improves the efficiency and accuracy of the layout plan, but also reduces the design cost and time. Some scholars considered the target performance of the overall mass distribution characteristics of the spacecraft when studying the spacecraft layout problem, that is, the overall moment of inertia, the center of mass design position, etc. In addition to considering the target of the mass characteristic distribution of the spacecraft, some scholars also considered the thermal field distribution characteristics of the spacecraft, transformed the traditional single-objective spacecraft layout optimization problem into a multi-objective optimization problem, constructed two objective functions, namely the heat dissipation function and the spacecraft center of mass function, and applied the research method to the layout design of the Brazilian multi-mission space platform. Some scholars further optimized the spacecraft layout design in theory based on the engineering practice that has been successfully launched. The optimization process mainly considered the optimization targets such as mass characteristics, thermal uniformity, and residual magnetic strength.

[0005] Although the research on spacecraft component layout has been going on for a long time, the current research mainly focuses on the design of optimization algorithms under a single constraint. When multiple complex constraints are coupled, the computational efficiency is low and the computational cost increases exponentially. In addition, the use of a certain optimization algorithm to solve such general problems has great limitations. In addition, the multi-physics constraints considered are relatively simple and cannot fully describe the various complex physical states of spacecraft in orbit. The spacecraft layout optimization problem in multi-physics fields belongs to a multi-objective and multi-constrained combinatorial optimization problem. When solving such problems, it is easy to encounter optimization difficulties, low computational efficiency, and easy to fall into local optimal solutions. Due to this limitation, the research on spacecraft layout optimization based on high-fidelity multi-physics models has not been effectively carried out. Summary of the invention

[0006] In order to solve the above problems, this application studies the model construction of the spacecraft component layout optimization design problem, mainly considering the two indicators of mass characteristics and dynamic characteristics, and proposes an effective spacecraft component layout optimization method.

[0007] A method for optimizing the layout of spacecraft components considering moment of inertia and vibration frequency, characterized in that the method comprises:

[0008] S1. Preset the dimensions of the spacecraft cabin and multiple components to be arranged, make approximate descriptions based on the dimensions of the spacecraft cabin and the multiple components to be arranged, obtain three-dimensional approximate models of the spacecraft cabin and the multiple components to be arranged, construct a reference coordinate system with the geometric center of the three-dimensional approximate model of the spacecraft cabin as the coordinate origin, and preset the position parameters of the three-dimensional approximate model corresponding to each component to be arranged in the reference coordinate system;

[0009] S2, setting the Φ function between the three-dimensional approximate models corresponding to the components to be arranged and the Φ function between the three-dimensional approximate model of each component to be arranged and the three-dimensional approximate model of the spacecraft cabin according to the position parameters and calculating the non-interference constraints;

[0010] S3, preset a centroid error threshold, take the geometric center of the spacecraft as the expected centroid, take the centroid of the spacecraft obtained after layout as the actual centroid, and construct a centroid error constraint based on the centroid error threshold, the expected centroid and the actual centroid;

[0011] S4, preset a maximum safety distance threshold and a minimum safety distance threshold, calculate the centroid distance between the components to be laid out, and construct a safety distance constraint between the components to be laid out according to the maximum safety distance threshold, the minimum safety distance threshold constraint and the centroid distance between the components to be laid out;

[0012] S5. Construct a stellar coordinate system with the center of mass of the spacecraft as the coordinate origin, calculate the moment of inertia of the spacecraft about the stellar coordinate system, perform finite element analysis on the structure of the spacecraft, obtain a global stiffness matrix and a global mass matrix, set and solve characteristic equations according to the global stiffness matrix and the global mass matrix, and obtain the vibration frequency of the spacecraft;

[0013] S6. Taking the spacecraft's moment of inertia and vibration frequency as optimization targets, and taking non-interference constraints, center of mass error constraints, and safety distance constraints as constraints, a dual-objective optimization model for spacecraft component layout is constructed. The dual-objective optimization model for spacecraft component layout is optimized and solved to obtain an optimization plan for spacecraft component layout that meets the constraints.

[0014] Preferably, the non-interference constraint in S2 is specifically expressed by the formula:

[0015]

[0016] Where c1(X) represents the total interference on the load-bearing plate, Δ ab (a=0,1,2,...,N;b=1,2,...,N,a≠b) represents the interference between component a and component b, component 0 represents the spacecraft cabin, Δ 0b represents the interference between component b and the spacecraft cabin, and X represents the layout plan of the component to be laid out in the spacecraft cabin.

[0017] Preferably, the centroid error constraint in S3 is specifically expressed by the formula:

[0018] c2(X)=|x c -x e |-δx e ≤0

[0019] c3(X)=|y c -y e |-δy e ≤0

[0020] Where c2(X) represents the center of mass error of the spacecraft in the x direction, c3(X) represents the center of mass error of the spacecraft in the y direction, (x c ,y c ) represents the actual center of mass of the spacecraft, (x e ,y e ) represents the desired center of mass of the spacecraft, δx e and δy e Respectively represent the centroid error thresholds in the x and y directions, both are non-negative numbers.

[0021] Preferably, the safety distance constraint in S4 is specifically expressed by the formula:

[0022]

[0023] In the formula, c4(X) represents the minimum distance between components to be laid out, c5(X) represents the maximum distance between components to be laid out, and d ab Represents the centroid distance between components a and b to be laid out, and They respectively represent the minimum safety distance threshold and the maximum safety distance threshold between components to be laid out.

[0024] Preferably, in S5, a finite element analysis is performed on the structure of the spacecraft to obtain a global stiffness matrix and a global mass matrix, and a characteristic equation is set and solved according to the global stiffness matrix and the global mass matrix to obtain the vibration frequency of the spacecraft. The specific process is as follows:

[0025] S51, determining a plane four-node rectangular unit model corresponding to the bearing plate on the spacecraft cabin and performing finite element division to obtain a plurality of rectangular units;

[0026] S52, randomly selecting a component to be laid out from the components to be laid out, calculating the distance between four nodes of each rectangular unit in a plurality of rectangular units and the selected component to be laid out, and using the Heaviside function to calculate the Heaviside function values ​​corresponding to the four nodes of each rectangular unit;

[0027] S53, calculating the stiffness matrix and mass matrix of each rectangular unit under the influence of the selected component to be laid out according to the Heaviside function values ​​corresponding to the four nodes of each rectangular unit and the unit area constant stiffness matrix and mass matrix of the selected component to be laid out;

[0028] S54, selecting another component to be laid out from the components to be laid out again, until all the components to be laid out are selected, and repeating steps S52 and S53 to obtain the stiffness matrix and mass matrix of each rectangular unit under the influence of each component to be laid out;

[0029] S55. A global stiffness matrix and a global mass matrix are obtained by assembling a number of rectangular units. Characteristic equations are set and solved according to the global stiffness matrix and the global mass matrix to obtain the vibration frequency of the spacecraft.

[0030] Preferably, the stiffness matrix and mass matrix of each rectangular unit under the influence of the selected component to be laid out in S53 are specifically expressed by the formula:

[0031]

[0032] in,

[0033] Where, d j H represents the distance from the jth node of each rectangular unit to the selected component to be laid out. ε (d j ) is the Heaviside function value corresponding to the jth node of each rectangular unit, j = 1, 2, 3, 4, K c and M c represents the unit area constant stiffness matrix and mass matrix of the selected component to be laid out, K e and M e represents the stiffness matrix and mass matrix of each rectangular unit under the influence of the selected components to be laid out, ε represents the half bandwidth, and α represents a positive constant tending to zero.

[0034] Preferably, the dual-objective optimization model for spacecraft component layout in S6 is specifically expressed by the formula:

[0035]

[0036] Where X represents the layout scheme of the components to be arranged in the spacecraft cabin, f1(X) represents the moment of inertia of the spacecraft after the components to be arranged are arranged according to the layout scheme X, and f2(X) represents the vibration frequency of the spacecraft after the components to be arranged are arranged according to the layout scheme X.

[0037] Preferably, in S6, the dual-objective optimization model of the spacecraft component layout is optimized and solved to obtain an optimization plan for the spacecraft component layout that satisfies the constraint conditions. The specific process is as follows:

[0038] S61. Calculate the moment of inertia of the spacecraft and derive the gradient of the moment of inertia based on the moment of inertia;

[0039] S62, deriving the gradient of the eigenvalue based on the eigenvalue equation of the spacecraft, and converting the gradient of the calculated vibration frequency into the gradient of the calculated eigenvalue;

[0040] S63. Considering the diversity metric, the to-be-placed layout schemes are expanded into a set of diversified layout schemes, the diversity between any two layout schemes in a set of diversified layout schemes is evaluated using similarity, the dual-objective optimization model of the spacecraft component layout is transformed, and the spacecraft component layout optimization model considering diversity is obtained and optimized and solved, thereby obtaining several sets of diversified geometric non-interference layout schemes;

[0041] S64, taking a plurality of groups of diversified geometric non-interference layout solutions as initial solutions and performing single-objective optimization on each of them, and selecting the single-objective optimal layout solution from the solutions with better single-objective performance;

[0042] S65. Based on the single-objective optimal layout plan, the SNC algorithm is introduced to convert the dual-objective optimization model of spacecraft component layout into a single-objective optimization model with orthogonal constraints added. The gradient of the moment of inertia and the gradient of the eigenvalue are used to solve the single-objective optimization model with orthogonal constraints using the gradient algorithm to obtain the intelligent Pareto approximate optimal solution set. The layout plans in the intelligent Pareto approximate optimal solution set are all spacecraft component layout optimization plans that meet the constraints.

[0043] Preferably, the spacecraft component layout optimization model considering diversity in S63 is specifically expressed by the formula:

[0044]

[0045] In the formula, X * represents a variety of layout solutions, f(X * ) represents the objective function of the similarity of the diverse layout solutions. (m,n) represents the similarity between the mth layout scheme and the nth layout scheme in the diversified layout schemes, Represents the position parameter of the i-th component to be laid out in the p-th layout scheme among the diversified layout schemes. represents the center coordinates and deflection angle of the i-th component to be laid out in the p-th layout scheme, and M represents the total number of layout schemes after considering diversity.

[0046] Preferably, the single-objective optimization model with orthogonal constraints added in S65 is specifically expressed by the formula:

[0047]

[0048] In the formula, f * (X) represents the new Pareto approximate point to be solved, U l+1 and U l-1 They represent the two adjacent approximate points before and after the Pareto approximate point with the largest intelligent distance from the current known Pareto point, N 12 (*) indicates the vector corresponding to the constructed approximate line.

[0049] The above-mentioned spacecraft component layout optimization method considering the moment of inertia and vibration frequency, presets the outer dimensions of the spacecraft cabin and multiple components to be laid out and respectively describes them approximately, obtains the three-dimensional approximate model of the spacecraft cabin and multiple components to be laid out, constructs a reference coordinate system with the geometric center of the three-dimensional approximate model of the spacecraft cabin as the coordinate origin, presets the position parameters of the three-dimensional approximate model corresponding to each component to be laid out in the reference coordinate system, sets the Φ function and calculates the non-interference constraint, sets the center of mass error constraint and the safety distance constraint, constructs the stellar coordinate system with the center of mass of the spacecraft as the coordinate origin, calculates the moment of inertia of the spacecraft about the stellar coordinate system, performs finite element analysis on the structure of the spacecraft, sets the characteristic equation and solves it, obtains the vibration frequency of the spacecraft, takes the moment of inertia and vibration frequency of the spacecraft as the optimization target, constructs a dual-objective optimization model of the spacecraft component layout with the non-interference constraint, the center of mass error constraint and the safety distance constraint as the constraint items, optimizes and solves the dual-objective optimization model of the spacecraft component layout, and obtains the spacecraft component layout optimization scheme that meets the constraint conditions. The method can more efficiently and accurately handle the spacecraft component layout optimization problem that considers both mass characteristics and vibration frequency characteristics at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a flow chart of a method for optimizing the layout of spacecraft components taking into account the moment of inertia and vibration frequency in one embodiment of the present invention;

[0051] Figure 2 is a simplified schematic diagram of the overall structure of a spacecraft in one embodiment of the present invention;

[0052] Figure 3 is a schematic diagram of the layout of a single component to be arranged on a load-bearing plate in a spacecraft cabin in one embodiment of the present invention;

[0053] Figure 4 The influence of the component layout on the stiffness matrix and mass matrix of the rectangular unit in one embodiment of the present invention;

[0054] Figure 5A schematic diagram of an intelligent orthogonal constraint in an embodiment of the present invention;

[0055] Figure 6 is a region formed by a smart distance represented by a Lamé curve in one embodiment of the present invention;

[0056] Figure 7 It is a schematic diagram of the layout of six components to be arranged on the bearing plate of a spacecraft in one embodiment of the present invention;

[0057] Figure 8 It is a layout scheme for minimizing the single objective of moment of inertia in one embodiment of the present invention;

[0058] Fig. 9 This is a layout scheme for maximizing a single target of vibration frequency in one embodiment of the present invention;

[0059] Fig.10 A schematic diagram of an intelligent Pareto approximate optimal solution for dual-objective optimization of moment of inertia and vibration frequency in one embodiment of the present invention;

[0060] Fig.11 This is an example of a layout solution corresponding to a partial intelligent Pareto approximate optimal solution in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings.

[0062] See also Figure 1 , a method for optimizing the layout of spacecraft components considering the moment of inertia and vibration frequency, the method comprising the following steps:

[0063] S1. Preset the outer dimensions of the spacecraft cabin and multiple components to be arranged, make approximate descriptions based on the outer dimensions of the spacecraft cabin and multiple components to be arranged, obtain three-dimensional approximate models of the spacecraft cabin and multiple components to be arranged, construct a reference coordinate system with the geometric center of the three-dimensional approximate model of the spacecraft cabin as the coordinate origin, and preset the position parameters of the three-dimensional approximate model corresponding to each component to be arranged in the reference coordinate system.

[0064] Specifically, referring to the structure of the classic multi-layer box-type spacecraft cabin, the mathematical model of the spacecraft engineering example is simplified. The simplified overall structure of the spacecraft is as follows: Figure 2 As shown. The spacecraft cabin is a rectangular parallelepiped, including side walls and load-bearing plates. For the convenience of calculation, the load-bearing plates are designed as quadrilateral structures. The quadrilateral structure matches the cross-section of the spacecraft cabin in the xoy direction. The components to be laid out are approximately described as cylinders or rectangular parallelepipeds. The mass distribution of all components to be laid out is uniform, and the geometric centers coincide with the center of mass, as shown in Figure 3Consider the layout design of components on this load-bearing plate.

[0065] To describe the position of aerospace component layout, three coordinate systems need to be introduced: reference coordinate system, celestial coordinate system and component coordinate system. Among them: the reference coordinate system O-xyz, the origin is the geometric center of the docking surface or installation measurement reference surface of the spacecraft, which is used to determine the layout and installation position of each component to be laid out and calculate the center of mass coordinates of the spacecraft; the celestial coordinate system O'-x'y'z', the origin is located at the center of mass of the spacecraft, which is used to give the moment of inertia and product of inertia values ​​in the mass characteristics of the spacecraft; the component coordinate system O"-x"y"z", the origin is located at the center of mass of each component to be laid out, which is used to calculate the moment of inertia of each component about its own coordinate axis.

[0066] In the reference coordinate system O-xyz, the position of each component to be laid out is represented by a set of position parameters (x i ,y i ,z i ,θ i ) means, where (x i ,y i ,z i ) represents the center coordinates of the components to be laid out, θ i Indicates the rotation angle of the component to be arranged around its center of mass. For the components to be arranged installed on the same bearing plate, since the installation base of these components to be arranged is the same, the coordinate z of all components to be arranged on the same bearing plate in the height direction is i It is known that the height of the component to be laid out determines the coordinate z of the component to be laid out in the height direction. i is half of the height. In this way, the coordinates of the center of mass of the spacecraft as a whole in the height direction can be obtained by weighted calculation according to the mass of the components, and it remains unchanged during the optimization process, so the three-dimensional layout design problem is based on the two-dimensional layout design. Therefore, once the plane center coordinates and rotation angles of the components to be laid out are determined, the layout plan is determined. The layout plan of the components to be laid out of the spacecraft can be written as:

[0067] X={X i =(x i ,y i ,θ i )|i=1,2,...,N} (1)

[0068] Where, X i represents the position parameter of the i-th component to be laid out, N represents the number of components to be laid out, x i and i Indicates the coordinate values ​​of the i-th component to be laid out along the x and y directions in the reference coordinate system, (x i ,y i) is determined by the geometric dimensions of the load-bearing plate corresponding to the i-th component to be arranged. For components to be arranged without placement angle requirements, θ i The value range of is [0,π). For components to be laid out with orthogonal placement requirements, θ i The value of is {0,π / 2}. In particular, for components with a circular bottom surface, such as a cylinder, θ i Can be fixed to 0.

[0069] S2. According to the position parameters, the Φ function between the three-dimensional approximate models corresponding to the components to be arranged and the Φ function between the three-dimensional approximate model of each component to be arranged and the three-dimensional approximate model of the spacecraft cabin are set, and the non-interference constraints are calculated.

[0070] Specifically, for the problem of optimizing the layout of spacecraft components, the first consideration is that there should be no interference between components and between components and the spacecraft cabin during the installation process. Taking a load-bearing plate in the spacecraft cabin as an example, the non-interference constraint on the load-bearing plate is expressed as:

[0071]

[0072] Where c1(X) represents the total interference on the load-bearing plate, Δ ab (a=0,1,2,...,N;b=1,2,...,N,a≠b) represents the interference between component a and component b. When a=0, component a represents the spacecraft cabin, Δ 0b Represents the interference between component b and the spacecraft cabin. The total interference is 0, indicating that there is no interference between components and between components and the spacecraft cabin.

[0073] In the process of spacecraft component layout design, three-dimensional approximate models are constructed and position parameters are determined according to the dimensions of the spacecraft cabin and multiple components to be laid out. The Φ function is calculated and the interference between components is determined by the position parameters of the three-dimensional approximate model corresponding to the components. The Φ function between the position parameters of the components should satisfy the following properties:

[0074]

[0075] In the formula, a and b represent any two components to be laid out. represents the distance between the 3D approximate models corresponding to any two components a and b to be laid out. , it means that the 3D approximate models corresponding to the two components to be laid out do not interfere with each other. In this case, we can appropriately reduce Bring the two components to be laid out closer to each other;

[0076] when , it means that the boundaries of the 3D approximate models corresponding to the two components to be laid out just touch each other;

[0077] when , it means that the 3D approximate models corresponding to the two components to be laid out have interfered with each other. In this case, we can increase the Separate the two components to be laid out from each other.

[0078] Therefore, by constructing the Φ function expression, the calculation of the interference amount between spacecraft components can be expressed by a completely equivalent Φ function value. The distance between the three-dimensional approximate models corresponding to the components a and b to be laid out can be calculated by the Φ function. like The interference amount Δ ab Set to 0, if This indicates that interference has occurred between the two components. At this time, the specific amount of interference can be obtained.

[0079] S3, preset a centroid error threshold, take the geometric center of the spacecraft as the expected centroid, take the centroid of the spacecraft obtained after layout as the actual centroid, and construct a centroid error constraint based on the centroid error threshold, the expected centroid and the actual centroid;

[0080] Specifically, the static stability of the spacecraft is also a factor that needs to be considered. If the static stability is too large, it will inevitably affect the maneuverability of the spacecraft. Therefore, when designing a spacecraft, it is required that the center of mass error between the actual center of mass of the spacecraft and the expected center of mass is as small as possible and kept within an allowable error range. Generally, the geometric center of the spacecraft is taken as the expected center of mass. The center of mass error constraint can be described as:

[0081] c2(X)=|x c -x e |-δx e ≤0 (4)

[0082] c3(X)=|y c -y e |-δy e ≤0 (5)

[0083] Where c2(X) represents the center of mass error of the spacecraft in the x direction, c3(X) represents the center of mass error of the spacecraft in the y direction, (x c ,y c ) represents the actual center of mass of the spacecraft, (x e ,y e ) represents the desired center of mass of the spacecraft, δx e and δy e Respectively represent the centroid error thresholds in the x and y directions, both are non-negative numbers.

[0084] S4. Preset a maximum safety distance threshold and a minimum safety distance threshold, calculate the centroid distance between the components to be laid out, and construct a safety distance constraint between the components to be laid out according to the maximum safety distance threshold, the minimum safety distance threshold constraint, and the centroid distance between the components to be laid out.

[0085] Specifically, in the engineering practice of spacecraft design, it is found that some functional equipment may interact with each other during the on-orbit operation of the spacecraft, thus affecting the working accuracy of the equipment. Considering the processing needs such as the installation of equipment components and the layout of wires in the spacecraft equipment compartment, a certain safety distance should be maintained when placing components. In addition, some or a group of collaborative equipment need to be kept within a feasible distance when working together. Once the threshold distance is exceeded, a subsystem of the spacecraft may not work properly. Therefore, this distance constraint is defined as a safety and feasibility constraint, which can be expressed as a minimum distance constraint or a maximum distance constraint:

[0086]

[0087] In the formula, c4(X) represents the minimum distance between components to be laid out, c5(X) represents the maximum distance between components to be laid out, and d ab Represents the centroid distance between components a and b to be laid out, which can be directly calculated. and They represent the minimum safety distance threshold and the maximum safety distance threshold between the components to be laid out, which are preset according to the spacecraft mission performance. When considering the safety distance constraint, the case of a = 0 does not need to be considered.

[0088] S5. Construct a stellar coordinate system with the center of mass of the spacecraft as the coordinate origin, calculate the moment of inertia of the spacecraft about the stellar coordinate system, perform finite element analysis on the structure of the spacecraft, obtain the global stiffness matrix and the global mass matrix, set the characteristic equation according to the global stiffness matrix and the global mass matrix and solve it to obtain the vibration frequency of the spacecraft.

[0089] Specifically, the moment of inertia of a spacecraft reflects the inertia of the spacecraft in a rotating state. In order to achieve attitude control more efficiently, the moment of inertia of the spacecraft is generally reduced as much as possible during spacecraft design. In the stellar coordinate system O'-x'y'z' used to calculate the moment of inertia, the axes of the stellar coordinate system are the central inertia axes of the spacecraft, so the inertia product of the spacecraft system is zero. The moment of inertia calculation formula of the spacecraft is:

[0090]

[0091] Where, I represents the moment of inertia of the spacecraft, I x′x′ ,I y′y′ and I z′z′They are the moments of inertia of the spacecraft about the stellar coordinate system in the x', y' and z' axes, which can be directly calculated.

[0092] In addition, the vibration problem of the structure is also one of the key concerns when designing a spacecraft. During the active phase of the spacecraft launch, it will experience resonance, which will cause structural damage or local instability, affecting the normal operation of the equipment and may even lead to immeasurable consequences. The vibration problem of the structure is a relatively vivid virtual problem, especially in the theoretical analysis of the frequency, damping and vibration mode of the structure. The analysis of the vibration problem is usually based on the establishment of a materialized mathematical model, and the use of software programming to realize the graphical data to simplify the analysis and calculation process.

[0093] Furthermore, in S5, a finite element analysis is performed on the structure of the spacecraft to obtain a global stiffness matrix and a global mass matrix. The characteristic equation is set and solved according to the global stiffness matrix and the global mass matrix to obtain the vibration frequency of the spacecraft. The specific process is as follows:

[0094] S51. Determine the plane four-node rectangular unit model corresponding to the load-bearing plate on the spacecraft cabin and perform finite element division to obtain a plurality of rectangular units.

[0095] For the vibration analysis of the layout of spacecraft components, in this embodiment, the area occupied by the load-bearing plate on the spacecraft cabin is represented by a plane four-node rectangular unit model and finite element division is performed to obtain a number of rectangular units. Figure 4 In the divided grid, the components to be laid out are regarded as uniform mass blocks, and the rectangular units occupied by the components to be laid out (corresponding to Figure 4 The non-blank grids in the figure represent the distribution of the stiffness and mass of the components to be laid out. Therefore, the change of the position of the components to be laid out will bring about the change of the structural stiffness matrix and mass matrix of the rectangular unit, which will further affect the global stiffness matrix and global mass matrix of the spacecraft structure.

[0096] S52, randomly selecting a component to be laid out from the components to be laid out, calculating the distance between four nodes of each rectangular unit in a plurality of rectangular units and the selected component to be laid out, and using the Heaviside function to calculate the Heaviside function values ​​corresponding to the four nodes of each rectangular unit.

[0097] First, the distances between the four nodes of each rectangular unit in a number of rectangular units and the selected components to be laid out are calculated, and the degree of influence of the selected layout components on the stiffness matrix and mass matrix of each rectangular unit is determined based on the distances: if the node is far away from the component to be laid out, it means that the stiffness matrix and mass matrix of the rectangular unit corresponding to the node are not affected by the component to be laid out, such as Figure 4Most of the black nodes in the grid; if the node is very close to the component to be laid out or the node is inside the component to be laid out, it means that the stiffness matrix and mass matrix of the rectangular unit corresponding to the node are affected by the component to be laid out, such as Figure 4 The bold black nodes in the figure. Figure 4 The degree to which the nodes near the black solid line in the figure are affected by the components to be laid out is approximately described using the Heaviside function:

[0098]

[0099] In the formula, H ε (d j ) represents the Heaviside function value corresponding to the jth node of each rectangular unit, that is, the degree to which the jth node is affected by the selected component to be laid out, d j It represents the distance from the jth node of each rectangular unit to the selected component to be laid out, which can be directly calculated, j = 1, 2, 3, 4. If the calculated distance is a negative value, it means that the jth node of the rectangular unit is inside the selected component to be laid out. If the calculated distance is a positive value, it means that the jth node of the rectangular unit is outside the selected component to be laid out. ε represents the half bandwidth, which is generally 1-2 unit cells in size. α represents a small amount to avoid the occurrence of matrix singularity.

[0100] S53, calculating the stiffness matrix and mass matrix of each rectangular unit under the influence of the selected component to be laid out according to the Heaviside function values ​​corresponding to the four nodes of each rectangular unit and the stiffness matrix and mass matrix of the selected component to be laid out.

[0101] The stiffness matrix and mass matrix of each rectangular element in the plane four-node rectangular element model under the influence of the selected components to be laid out can be expressed by the Heaviside function values ​​corresponding to the four nodes:

[0102]

[0103] In the formula, K e and M e represents the stiffness matrix and mass matrix of each rectangular unit under the influence of the selected components to be laid out, d j Represents the distance from the jth node of each rectangular unit to the selected component to be laid out, j = 1, 2, 3, 4, H ε (d j ) is d j The corresponding Heaviside function value, K c and M cRepresents the unit area constant stiffness matrix and mass matrix of the selected component to be laid out. If a rectangular unit is completely covered by a component to be laid out, then the four nodes of the rectangular unit are all inside the component to be laid out, and the corresponding Heaviside function values ​​are all 1. Then the stiffness matrix and mass matrix of the rectangular unit are the unit area constant stiffness matrix and mass matrix of the component, that is: K e =K c , M e =M c .

[0104] Furthermore, when the stiffness matrix and mass matrix of each rectangular unit are calculated by the above calculation method, the calculation of the mass matrix and stiffness matrix corresponding to the rectangular units intersecting with the boundary of the selected component to be laid out is obviously inaccurate. The multi-resolution finite element method can be used to further subdivide the rectangular units intersecting with the boundary of the selected component to be laid out, such as Figure 4 As shown in the partial enlarged view of , the rectangular unit that intersects with the boundary of the selected rectangular component to be laid out is further divided inside it, and the above calculation process is repeated, so that the mass matrix and stiffness matrix of the rectangular unit can be determined more accurately.

[0105] The load-bearing plate of the spacecraft cabin itself also needs to consider the stiffness matrix and mass matrix. Therefore, the stiffness matrix and mass matrix obtained by the influence of the above-mentioned components to be laid out on the rectangular unit should be further superimposed on the basis of the load-bearing plate itself.

[0106] S54, selecting another component to be laid out from the components to be laid out again, until all the components to be laid out are selected, and repeating steps S52 and S53 to obtain the stiffness matrix and mass matrix of each rectangular unit under the influence of each component to be laid out;

[0107] S55. A global stiffness matrix and a global mass matrix are obtained by assembling a number of rectangular units. Characteristic equations are set and solved according to the global stiffness matrix and the global mass matrix to obtain the vibration frequency of the spacecraft.

[0108] Specifically, according to the standard finite element analysis program, the global stiffness matrix K and the global mass matrix M can be obtained by assembling rectangular units. K and M change with the change of component layout. The global stiffness matrix and the global mass matrix are further obtained according to the mass matrix and stiffness matrix of each rectangular unit. This is the basic theory of the finite element method and is a mature system. It will not be explained here.

[0109] The analysis of the inherent characteristics of a spacecraft structure during vibration can be reduced to solving the following discrete form of the eigenvalue equation:

[0110] Kφ=λMφ (12)

[0111] Where λ = ω 2 ,φ T Mφ=1

[0112] Where K and M are the global stiffness matrix and global mass matrix of the spacecraft structure, ω is the vibration frequency, λ is the eigenvalue, and φ is the eigenmode.

[0113] Therefore, rewriting the above discrete form of the eigenvalue equation gives the characteristic equation |K-ω 2 M|=0 and solve, the vibration frequency ω obtained is also variable.

[0114] S6. Taking the spacecraft's moment of inertia and vibration frequency as optimization targets, and taking non-interference constraints, center of mass error constraints, and safety distance constraints as constraints, a dual-objective optimization model for spacecraft component layout is constructed. The dual-objective optimization model for spacecraft component layout is optimized and solved to obtain an optimization plan for spacecraft component layout that meets the constraints.

[0115] Furthermore, the dual-objective optimization model for spacecraft component layout is as follows:

[0116]

[0117] Where ω represents the vibration frequency of the spacecraft.

[0118] When considering the dynamic objectives, maximizing the vibration frequency of the spacecraft is selected as the design objective to suppress resonance. Since the optimization problem is generally handled by minimizing the objective function, the opposite of the vibration frequency is used as the optimization objective here. When considering the non-interference constraints between components, since the equality constraints will strictly limit the values ​​of the design variables and reduce the degree of freedom of the design, the equality constraints are rewritten as inequality constraints, thus constituting a dual-objective optimization problem.

[0119] Theoretically, when all components are close together, the moment of inertia of the spacecraft is minimal. However, at this time, the components are very close to each other and far away from the fixed support boundary, which leads to local stiffness and mass concentration inside the spacecraft and a low vibration frequency. In order to meet the design goal of maximizing the vibration frequency, the components need to be placed close to the boundary fixed support, which will increase the moment of inertia. There is a conflict between these two goals, so the optimal solution to the layout design problem that considers both the moment of inertia and the vibration frequency optimization should be a set of Pareto approximate optimal solutions.

[0120] In order to optimize and solve the dual-objective optimization model of spacecraft component layout (corresponding to formula (13)), the present invention proposes a gradient-based and diverse multi-objective optimization algorithm, and solves the problem by deriving the analytical / semi-analytical sensitivity (that is, the gradient) of the objectives (including the moment of inertia and vibration frequency) during gradient calculation.

[0121] Furthermore, in S6, the dual-objective optimization model of spacecraft component layout is optimized and solved to obtain the spacecraft component layout optimization solution that meets the constraint conditions. The specific process is as follows:

[0122] S61. Calculate the moment of inertia of the spacecraft and derive the gradient of the moment of inertia based on the moment of inertia.

[0123] S62. The gradient of the eigenvalue is derived based on the eigenvalue equation of the spacecraft, and the gradient of the calculated vibration frequency is converted into the gradient of the calculated eigenvalue.

[0124] Specifically, the calculation of the moment of inertia can be obtained by an analytical formula (Formula (8)) according to the definition, and its corresponding gradient calculation is also easy to obtain. The calculation process of the vibration frequency is relatively complicated: if its gradient is directly derived, it involves the changes of the stiffness matrix and the mass matrix, and the calculation process is relatively cumbersome; if the difference method is directly used to approximate the gradient calculation, it will bring certain numerical errors, so the semi-analytical sensitivity method is used to solve the gradient of the vibration frequency. The process is as follows:

[0125] If the eigenvalue λ is a single eigenvalue (i.e., its corresponding eigenmode φ is unique), then λ is differentiable, and the eigenvalue equation (corresponding to formula (12)) is i Derivation gives:

[0126]

[0127] Multiply both ends of the above formula by φ T , using the symmetry of the stiffness matrix and the mass matrix and the eigenvalue equation to simplify, the calculation formula for the gradient of the single eigenvalue to the design variable is obtained, which is specifically expressed as follows:

[0128]

[0129] Among them, λ and φ are solved in advance by the eigenvalue equation.

[0130] The above formula (15) can be used to solve problems involving characteristic frequency optimization or constraints. and The method of calculating sensitivity using the differential method is called semi-analytical sensitivity.

[0131] According to λ=ω 2It is easy to know that the changing trends of the eigenfrequency ω and the eigenvalue λ are the same. Therefore, in the design example, the gradient of the eigenvalue λ can be directly calculated instead of the gradient of the eigenfrequency ω.

[0132] S63. Consider the diversity measurement index, expand the layout scheme to be arranged into a group of diversified layout schemes, use cosine similarity to evaluate the diversity between any two layout schemes in a group of diversified layout schemes, transform the dual-objective optimization model of spacecraft component layout, obtain the spacecraft component layout optimization model considering diversity and optimize the solution, and obtain several groups of diversified geometric non-interference layout schemes.

[0133] Specifically, since gradient optimization has serious initial value dependence, it is very easy to fall into the local optimum after iteration, so it is difficult to obtain the layout solution with the best global performance. In order to obtain more and better layout solutions, it is not possible to simply optimize by randomly generating many initial layout solutions. This method is not only time-consuming and labor-intensive, but also unscientific. Therefore, the idea of ​​diversity metrics can be added to the optimization process to guide the optimization to generate layout solutions with diversity. The spacecraft component layout optimization problem considers a variety of performance indicators and calculates the degree of diversity of a set of layout solutions. Therefore, in addition to the design objectives being different from those of traditional optimization problems, the design variables are also different from those of traditional optimization problems. The layout solutions of the components to be laid out are expanded into a set of diversified layout solutions, expressed as:

[0134]

[0135] In the formula, X * Indicates diversified layout solutions, represents the position parameter of the i-th component to be laid out in the p-th layout scheme among the diversified layout schemes. M represents the total number of layout schemes after considering diversity in each optimization process. Represents the center coordinates and deflection angle of the i-th component to be laid out in the p-th layout scheme among the diversified layout schemes.

[0136] In the spacecraft component layout optimization problem, each layout scheme in a set of layout schemes uniquely corresponds to a set of vectors describing the geometric position coordinates, so the selected diversity metric is calculated based on vectors. The cosine similarity can be used to evaluate the diversity between two layout schemes:

[0137]

[0138] Where, X m represents the vector corresponding to the mth layout scheme in the diversified layout scheme, X n Represents the vector corresponding to the nth layout scheme in the diversified layout scheme, similarity (m,n)Represents the similarity between the mth layout scheme and the nth layout scheme, 1≤m,n≤M.

[0139] Or use Gaussian similarity to calculate the distance between the vectors corresponding to two layout solutions to evaluate the diversity between the two solutions:

[0140]

[0141] Wherein, σ represents a bandwidth function determined by vectors corresponding to the mth layout scheme and the nth layout scheme in the diversified layout schemes.

[0142] Therefore, the spacecraft component layout optimization model considering diversity is specifically expressed as:

[0143]

[0144] In the formula, f(X * ) represents the objective function of the similarity of diverse layout solutions, X * Indicates diverse layout solutions, similarity (m,n) Represents the similarity between the mth layout scheme and the nth layout scheme in the diversified layout scheme. The similarity value represents the similarity between two diversified layout schemes, so obtaining the layout scheme with the maximum diversity is equivalent to obtaining the layout scheme with the minimum similarity. In addition, in this optimization problem, the objective function is to limit the similarity between the overall schemes by controlling the maximum value of the similarity between the diversified layout schemes. After traversing all the layout schemes, the similarity between any two layout schemes should be obtained, and there will be multiple similarity values. Here, only the maximum value of the similarity is limited, and the lower the maximum value of the similarity is, the better. The lower the maximum value of the similarity is, the higher the diversity of the layout scheme will be.

[0145] The above-mentioned spacecraft component layout optimization model considering diversity (corresponding to formula (18)) is optimized and solved to obtain several groups of diverse geometric non-interference layout schemes.

[0146] S64. Take several groups of diverse geometric non-interference layout solutions as initial solutions and perform single-objective optimization on them respectively, and select the single-objective optimal layout solution from the solutions with better single-objective performance.

[0147] S65. Based on the single-objective optimal layout plan, the SNC algorithm is introduced to convert the dual-objective optimization model of spacecraft component layout into a single-objective optimization model with orthogonal constraints added. The gradient of the moment of inertia and the gradient of the eigenvalue are used to solve the single-objective optimization model with orthogonal constraints using the gradient algorithm to obtain the intelligent Pareto approximate optimal solution set. The layout plans in the intelligent Pareto approximate optimal solution set are all spacecraft component layout optimization plans that meet the constraints.

[0148] Specifically, in order to solve the spacecraft component layout optimization problem considering multi-physics field performance (such as the moment of inertia I and vibration frequency ω in this application), the Pareto frontier generation mechanism SNC (Smart Normal Constraint) is first introduced into the layout optimization algorithm. The main idea of ​​SNC is to transform the multi-objective optimization problem into several single-objective optimization problems by continuously adding and updating linear constraints during the optimization process, limiting the scope of the solution space, and then solving it in a specific design space, such as Figure 5 shown.

[0149] Furthermore, the specific process of S65 is as follows:

[0150] S651. Use two single-objective optimal layout solutions as reference positioning points, and connect the two reference positioning points to construct an approximate line.

[0151] Figure 5 In, f 1* The layout plan corresponding to the target value f1 of the moment of inertia and the maximum vibration frequency target value f2 is the smallest, f 2* The layout plan corresponding to the minimum moment of inertia target value f1 and the maximum vibration frequency target value f2 is to connect these two points f 1* and f 2* Construct an approximate line.

[0152] S652, preset a smart distance threshold, generate a number of evenly distributed approximate points on the approximate line, calculate the smart distance between two adjacent approximate points, compare the smart distance with the smart distance threshold, and screen out multiple approximate points that meet the requirements of the smart distance threshold.

[0153] The calculation formula for the i-th approximate point is:

[0154]

[0155] in,

[0156] In the formula, and It is a parameter variable. The fixed increment δ can be increased from 0 to 1 to produce uniformly distributed points on the Pareto frontier. δ is given according to actual needs. A smaller δ value will produce a larger number of approximate points. Generally, represents the minimum Euclidean distance from a point to its surrounding PIT (Practically Insignificant Trade-off) region that defines a smart distance. d represents the distance vector between the center points of two PIT regions. P 1 and P 2They are the constructed approximate Pareto frontier vertices, corresponding to the reference positioning points corresponding to the two single-objective optimal layout solutions in S651.

[0157] In the SNC algorithm, the generation of the Pareto solution set is determined by the smart distance between the approximate points in the design space. The definition of smart distance is that no approximate point in the Pareto solution set falls within the region formed by the smart distance corresponding to any other approximate point. The region formed by the smart distance can be represented by a Lamé curve, see Figure 6 , Figure 6 The area enclosed by the four arc segments is the area formed by the smart distance corresponding to a certain approximate point. The calculation formula of the smart distance s is as follows:

[0158] s=||Ad|| p ,0≤p≤2 (20)

[0159] in,

[0160] Where s represents the smart distance, A is a user-defined vector, d is the distance measure between the center points of two PIT regions (i.e., approximate points), and ||Ad|| p is the p-norm of the vector Ad, a i (i=1,2) and p are user-defined parameters used to determine the distribution of intelligent Pareto points for a specific problem. i (i=1,2) corresponds to the change in the i-th design goal that can cause a significant difference between two approximate points when other design goals remain unchanged. The threshold of the preset smart distance s is 1. The smart distance s between any two adjacent approximate points>1 meets the requirements. Through screening, multiple approximate points that meet the requirements are obtained.

[0161] S653. Take multiple approximate points as known Parato points, add orthogonal constraints to the dual-objective optimization model of spacecraft component layout, and use the gradient algorithm to solve the single-objective optimization model with orthogonal constraints through the gradient of the moment of inertia and the gradient of the eigenvalue. Generate new Parato points and determine whether to retain them. The retained new Parato points constitute the intelligent Pareto approximate optimal solution set.

[0162] Furthermore, the single-objective optimization model with orthogonal constraints added is described as:

[0163]

[0164] In the formula, f * (X) represents the new Pareto point to be solved, U l is the Pareto approximate point with the largest intelligent distance from the currently known Pareto point, Ul+1 and U l-1 They represent the Pareto approximate point U with the largest intelligent distance from the current known Pareto point. l The two adjacent approximate points before and after, N 12 (*) indicates the connection point f 1* and f 2* Construct the vector corresponding to the approximate line, where f 1* The layout plan corresponding to the target value f1 of the moment of inertia and the maximum vibration frequency target value f2 is the smallest, f 2* Layout plan when the corresponding moment of inertia target value f1 is minimum and the vibration frequency target value f2 is maximum.

[0165] like Figure 5 As shown, the additional linear constraints here correspond to Figure 5 The shaded area in the figure is perpendicular to the approximate line, so it is called an orthogonal constraint. According to the gradient of the moment of inertia and the gradient of the vibration frequency, a new Pareto point can be generated by solving the problem using a gradient algorithm. However, the new Pareto points generated by single-objective optimization do not necessarily fall into the intelligent Pareto optimal solution set. Therefore, it is necessary to determine whether to retain the new Pareto point based on the dominant solution and the intelligent distance. The retained new Pareto points constitute the intelligent Pareto approximate optimal solution set.

[0166] The characteristic of this smart distance method is that only one scalar value, the smart distance, is required to define the region formed by the smart distance corresponding to the approximate point. This allows the algorithm to identify whether a new Pareto point is a smart Pareto approximate optimal solution, and to determine to what extent this point is smart. Therefore, the SNC method can search the design space more efficiently and determine which known Pareto point is most likely to produce a new Pareto point.

[0167] Furthermore, a spacecraft component layout optimization method considering rotational inertia and vibration frequency in the present invention is verified through numerical simulation.

[0168] like Figure 7 As shown, Figure 7 As shown in the figure, it is assumed that in the two-dimensional plane rectangular design area D on the surface of the load-bearing plate with a size of 10×10, three cube components with a size of 4×4×4 and three cylindrical components with a bottom radius of 2 and a height of 4 need to be placed, and the mass of each component is 10. The error between the system center of mass of the desired structure and the geometric center of the spacecraft does not exceed 0.001, and the minimum safety distance threshold between the components is 0.2. And the installation boundary condition of the designed load-bearing plate is four-sided fixed support.

[0169] Firstly, a diversified initial value single-objective gradient optimization algorithm is used to solve the layout solutions for minimizing the moment of inertia and maximizing the vibration frequency respectively.

[0170] Then, the optimal layout scheme with a single objective is selected from several groups of diverse layout schemes obtained by solving.

[0171] See also Figure 8 and Fig. 9 , Figure 8 The following is the layout scheme with the smallest moment of inertia. At this time, the target moment of inertia is 2203.74, and the vibration frequency characteristic value corresponding to this layout scheme is 24305.25; Fig. 9 The figure shows the layout scheme when the vibration frequency eigenvalue is the largest. At this time, the vibration frequency eigenvalue is 39019.95, and the moment of inertia corresponding to this layout scheme is 8952.72. It is not difficult to find that driven by the moment of inertia optimization goal, the components to be laid out move together to the center. Driven by the maximum vibration frequency goal, the components to be laid out disperse near the boundary to achieve the local optimum of the target performance. It can be seen from the two layout results that the two single-objective optimal layout schemes have well controlled the interference between components. And using the gradient optimization method based on semi-analytical sensitivity technology, it is possible to find a layout optimization scheme with better performance in a certain physical field of the spacecraft system.

[0172] Then, the intelligent orthogonal constraint method is introduced, and the single-objective optimal layout solution obtained above is used as the reference positioning point for multi-objective optimization for further optimization, and the intelligent Pareto approximate optimal solution set is obtained.

[0173] like Fig.10 As shown, Fig.10 The intelligent Pareto approximate optimal solution set of dual-objective optimization with rotational inertia and vibration frequency as the targets is shown in the figure. In addition to the two layout schemes used as reference positioning points when the single-objective optimization is mentioned above, another 15 layout schemes are obtained. These 15 layout schemes are all designs after balancing the rotational inertia optimization target and the vibration frequency optimization target. The target values ​​corresponding to each layout scheme are shown in Table 1.

[0174]

[0175]

[0176] Fig.11 The following diagram shows the layout scheme corresponding to some intelligent Pareto approximate optimal solution sets, where Fig.11 (a) Schematic diagram of the layout corresponding to Scheme 5 in Table 1; Fig.11 (b) Schematic diagram of the layout corresponding to Scheme 6 in Table 1; Fig.11 (c) Schematic diagram of the layout corresponding to Scheme 12 in Table 1.

[0177] It can be seen from the above numerical simulation verification that the diversified initial value single-objective gradient optimization algorithm combined with the intelligent orthogonal constraint method can better solve the dual-objective optimization problem of spacecraft component layout.

[0178] The above-mentioned spacecraft component layout optimization method considering the moment of inertia and vibration frequency presets the outer dimensions of the spacecraft cabin and multiple components to be laid out and makes approximate descriptions respectively, obtains the three-dimensional approximate model of the spacecraft cabin and multiple components to be laid out, constructs a reference coordinate system with the geometric center of the three-dimensional approximate model of the spacecraft cabin as the coordinate origin, presets the position parameters of the three-dimensional approximate model corresponding to each component to be laid out in the reference coordinate system, sets the Φ function and calculates the non-interference constraint, sets the center of mass error constraint and the safety distance constraint, constructs the stellar coordinate system with the center of mass of the spacecraft as the coordinate origin, calculates the moment of inertia of the spacecraft with respect to the stellar coordinate system, performs finite element analysis on the structure of the spacecraft, sets the characteristic equation and solves it, obtains the vibration frequency of the spacecraft, takes the moment of inertia and vibration frequency of the spacecraft as the optimization target, and constructs a dual-objective optimization model for the layout of the spacecraft components with the non-interference constraint, the center of mass error constraint and the safety distance constraint as the constraint items, optimizes and solves the dual-objective optimization model for the layout of the spacecraft components, and obtains the optimization plan for the layout of the spacecraft components that meets the constraint conditions. This method uses the φ function to characterize the geometric and positional relationships between components, and more efficiently handles the non-interference constraints between components. When calculating the vibration frequency of the spacecraft instrument panel, the finite element method is used to construct the stiffness and mass of the structure, which improves the accuracy of the calculation. In addition, for the spacecraft component layout optimization problem that simultaneously considers the mass characteristics and vibration frequency characteristics, a gradient-based diversified multi-objective optimization algorithm is designed, and the derivation of semi-analytical sensitivity is given, which greatly saves the tedious gradient calculation work.

[0179] The above is a detailed introduction to a spacecraft component layout optimization method that takes into account the moment of inertia and vibration frequency provided by the present invention. This article uses specific examples to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the core idea of ​​the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of the present invention, the present invention can also be improved and modified, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A method for optimizing the layout of spacecraft components considering moment of inertia and vibration frequency, characterized in that: The method comprises: S1. Preset the dimensions of the spacecraft cabin and multiple components to be arranged, make approximate descriptions based on the dimensions of the spacecraft cabin and the multiple components to be arranged, obtain three-dimensional approximate models of the spacecraft cabin and the multiple components to be arranged, construct a reference coordinate system with the geometric center of the three-dimensional approximate model of the spacecraft cabin as the coordinate origin, and preset the position parameters of the three-dimensional approximate model corresponding to each component to be arranged in the reference coordinate system; S2, setting the Φ function between the three-dimensional approximate models corresponding to the components to be arranged and the Φ function between the three-dimensional approximate model of each component to be arranged and the three-dimensional approximate model of the spacecraft cabin according to the position parameters and calculating the non-interference constraints; S3, preset a centroid error threshold, take the geometric center of the spacecraft as the expected centroid, take the centroid of the spacecraft obtained after layout as the actual centroid, and construct a centroid error constraint based on the centroid error threshold, the expected centroid and the actual centroid; S4, preset a maximum safety distance threshold and a minimum safety distance threshold, calculate the centroid distance between the components to be laid out, and construct a safety distance constraint between the components to be laid out according to the maximum safety distance threshold, the minimum safety distance threshold constraint and the centroid distance between the components to be laid out; S5. Construct a stellar coordinate system with the center of mass of the spacecraft as the coordinate origin, calculate the moment of inertia of the spacecraft about the stellar coordinate system, perform finite element analysis on the structure of the spacecraft, obtain a global stiffness matrix and a global mass matrix, set and solve characteristic equations according to the global stiffness matrix and the global mass matrix, and obtain the vibration frequency of the spacecraft; S6. Taking the spacecraft's moment of inertia and vibration frequency as optimization targets, and taking non-interference constraints, center of mass error constraints, and safety distance constraints as constraints, a dual-objective optimization model for spacecraft component layout is constructed. The dual-objective optimization model for spacecraft component layout is optimized and solved to obtain an optimization plan for spacecraft component layout that meets the constraints.

2. The method for optimizing the layout of spacecraft components considering the moment of inertia and vibration frequency as claimed in claim 1, characterized in that: The non-interference constraint in S2 is specifically expressed by the formula: Where c1(X) represents the total interference on the load-bearing plate, Δ ab (a=0,1,2,...,N;b=1,2,...,N,a≠b) represents the interference between component a and component b, component 0 represents the spacecraft cabin, Δ 0b represents the interference between component b and the spacecraft cabin, and X represents the layout plan of the component to be laid out in the spacecraft cabin.

3. The method for optimizing the layout of spacecraft components considering the moment of inertia and vibration frequency as claimed in claim 2, characterized in that: The centroid error constraint in S3 is specifically expressed as: c2(X)=|x c -x e |-δx e ≤0 c3(X)=|y c -y e |-δy e ≤0 Where c2(X) represents the center of mass error of the spacecraft in the x direction, c3(X) represents the center of mass error of the spacecraft in the y direction, (x c ,y c ) represents the actual center of mass of the spacecraft, (x e ,y e ) represents the desired center of mass of the spacecraft, δx e and δy e Respectively represent the centroid error thresholds in the x and y directions, both are non-negative numbers.

4. The method for optimizing the layout of spacecraft components considering the moment of inertia and vibration frequency as claimed in claim 3, characterized in that: The safety distance constraint in S4 is specifically expressed by the formula: In the formula, c4(X) represents the minimum distance between components to be laid out, c5(X) represents the maximum distance between components to be laid out, and d ab Represents the centroid distance between components a and b to be laid out, and They respectively represent the minimum safety distance threshold and the maximum safety distance threshold between components to be laid out.

5. The method for optimizing the layout of spacecraft components considering the moment of inertia and vibration frequency as claimed in claim 4, characterized in that: In S5, the finite element analysis of the structure of the spacecraft is performed to obtain the global stiffness matrix and the global mass matrix. The characteristic equation is set and solved according to the global stiffness matrix and the global mass matrix to obtain the vibration frequency of the spacecraft. The specific process is as follows: S51, determining a plane four-node rectangular unit model corresponding to the bearing plate on the spacecraft cabin and performing finite element division to obtain a plurality of rectangular units; S52, randomly selecting a component to be laid out from the components to be laid out, calculating the distance between four nodes of each rectangular unit in a plurality of rectangular units and the selected component to be laid out, and using the Heaviside function to calculate the Heaviside function values ​​corresponding to the four nodes of each rectangular unit; S53, calculating the stiffness matrix and mass matrix of each rectangular unit under the influence of the selected component to be laid out according to the Heaviside function values ​​corresponding to the four nodes of each rectangular unit and the unit area constant stiffness matrix and mass matrix of the selected component to be laid out; S54, selecting another component to be laid out from the components to be laid out again, until all the components to be laid out are selected, and repeating steps S52 and S53 to obtain the stiffness matrix and mass matrix of each rectangular unit under the influence of each component to be laid out; S55. A global stiffness matrix and a global mass matrix are obtained by assembling a number of rectangular units. Characteristic equations are set and solved according to the global stiffness matrix and the global mass matrix to obtain the vibration frequency of the spacecraft.

6. The method for optimizing the layout of spacecraft components considering the moment of inertia and vibration frequency as claimed in claim 5, characterized in that: The stiffness matrix and mass matrix of each rectangular unit in S53 under the influence of the selected components to be laid out are specifically expressed by the formula: in, Where, d j H represents the distance from the jth node of each rectangular unit to the selected component to be laid out. ε (d j ) is the Heaviside function value corresponding to the jth node of each rectangular unit, j = 1, 2, 3, 4, K c and M c represents the unit area constant stiffness matrix and mass matrix of the selected component to be laid out, K e and M e represents the stiffness matrix and mass matrix of each rectangular unit under the influence of the selected components to be laid out, ε represents the half bandwidth, and α represents a positive constant tending to zero.

7. The method for optimizing the layout of spacecraft components considering the moment of inertia and vibration frequency as claimed in claim 6, characterized in that: The dual-objective optimization model for spacecraft component layout in S6 is specifically expressed as follows: Where X represents the layout scheme of the components to be arranged in the spacecraft cabin, f1(X) represents the moment of inertia of the spacecraft after the components to be arranged are arranged according to the layout scheme X, and f2(X) represents the vibration frequency of the spacecraft after the components to be arranged are arranged according to the layout scheme X.

8. The method for optimizing the layout of spacecraft components considering the moment of inertia and vibration frequency as claimed in claim 7, characterized in that: In S6, the dual-objective optimization model of spacecraft component layout is optimized and solved to obtain the spacecraft component layout optimization solution that meets the constraints. The specific process is as follows: S61. Calculate the moment of inertia of the spacecraft and derive the gradient of the moment of inertia based on the moment of inertia; S62, deriving the gradient of the eigenvalue based on the eigenvalue equation of the spacecraft, and converting the gradient of the calculated vibration frequency into the gradient of the calculated eigenvalue; S63. Considering the diversity metric, the to-be-placed layout schemes are expanded into a set of diversified layout schemes, the diversity between any two layout schemes in a set of diversified layout schemes is evaluated using similarity, the dual-objective optimization model of the spacecraft component layout is transformed, and the spacecraft component layout optimization model considering diversity is obtained and optimized and solved, thereby obtaining several sets of diversified geometric non-interference layout schemes; S64, taking a plurality of groups of diversified geometric non-interference layout solutions as initial solutions and performing single-objective optimization on each of them, and selecting the single-objective optimal layout solution from the solutions with better single-objective performance; S65. Based on the single-objective optimal layout plan, the SNC algorithm is introduced to convert the dual-objective optimization model of spacecraft component layout into a single-objective optimization model with orthogonal constraints added. The gradient of the moment of inertia and the gradient of the eigenvalue are used to solve the single-objective optimization model with orthogonal constraints using the gradient algorithm to obtain the intelligent Pareto approximate optimal solution set. The layout plans in the intelligent Pareto approximate optimal solution set are all spacecraft component layout optimization plans that meet the constraints.

9. The method for optimizing the layout of spacecraft components considering the moment of inertia and vibration frequency as claimed in claim 8, characterized in that: The spacecraft component layout optimization model considering diversity in S63 is specifically expressed by the formula: Where, X * represents a variety of layout solutions, f(X * ) represents the objective function of the similarity of the diverse layout solutions. (m,n) represents the similarity between the mth layout scheme and the nth layout scheme in the diversified layout schemes, Represents the position parameter of the i-th component to be laid out in the p-th layout scheme among the diversified layout schemes. represents the center coordinates and deflection angle of the i-th component to be laid out in the p-th layout scheme, and M represents the total number of layout schemes after considering diversity.

10. The method for optimizing the layout of spacecraft components considering the moment of inertia and vibration frequency as claimed in claim 9, characterized in that: The single-objective optimization model with orthogonal constraints added in S65 is specifically expressed as follows: In the formula, f * (X) represents the new Pareto approximate point to be solved, U l+1 and U l-1 They represent the two adjacent approximate points before and after the Pareto approximate point with the largest intelligent distance from the current known Pareto point, N 12 (*) indicates the vector corresponding to the constructed approximate line.

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