A multi-objective bi-layer optimization method and component layout optimization system for suppressing electromagnetic force and self-gravity noise.

Abstract

A multi-objective, two-layer optimization method suitable for gravitational wave detection spacecraft aims to simultaneously suppress electromagnetic and self-gravitational noise. This method employs a two-layer optimization structure to ensure bidirectional interaction and feedback between the upper and lower layers, meeting the spacecraft's requirements for extremely high sensitivity. By optimizing the layout of internal equipment, the cleanliness and stability of the surrounding environment for testing are improved. This invention defines layout optimization as a two-layer optimization problem, clearly defining decision variables, constraints, and objective functions, and solving it as a mixed-integer optimization problem. It utilizes an efficient multi-objective, two-layer hybrid optimization method combining NSGA-III and the DE algorithm, and employs collision detection and penalty function strategies to handle geometric constraints. This invention effectively resolves optimization conflicts under multi-physics coupling effects, achieving efficient resource allocation and performance improvement. It has significant advantages in efficiency, scalability, and adaptability in handling geometric constraints, greatly improving the solution efficiency and stability of optimization problems.

Description

Technical Field

[0001] This invention relates to the field of space gravitational wave detection technology, specifically to a multi-objective, two-layer optimization method and component layout optimization system for suppressing electromagnetic force and self-gravity noise in spacecraft. Background Technology

[0002] Spacecraft capable of detecting gravitational waves use laser interferometry to capture minute distance changes between freely suspended test masses on adjacent spacecraft as gravitational waves pass by, in order to invert the characteristics of the gravitational wave signal. To achieve picometer-level ranging accuracy at distances of millions of kilometers, interference from other noise sources must be minimized to ensure an extremely clean electromagnetic and thermal environment within the test mass region. The operation of internal spacecraft equipment is a major source of noise; therefore, in addition to the design of individual components, the layout design of spacecraft components is a critical operation for ensuring the cleanliness of the environment surrounding the test mass.

[0003] Existing research primarily focuses on optimizing spacecraft mass characteristics, such as center of mass and moment of inertia, and single physics parameters, such as magnetic and temperature fields, through component layout design. However, research on the coupling and interaction of multiphysics and their comprehensive optimization is relatively insufficient. Regarding constraint handling, non-interference constraints between components are a fundamental condition for the rationality of layout optimization schemes. Currently, geometric methods (such as the finite circle method and geometric projection method) are mainly used for this purpose. However, these methods have poor scalability and are difficult to adapt to complex environments and dynamic changes. Furthermore, existing research generally adopts a phased optimization strategy, dividing it into two steps: component allocation and location selection. Although this method has achieved some success in practice, because the optimization of each stage is relatively independent, the decision in the first stage cannot fully consider the influence of the second stage, lacking an effective interaction and feedback mechanism, and making it difficult to meet stringent parameter design requirements.

[0004] Therefore, there is an urgent need for an efficient optimization method with multiphysics indexes as the optimization target to improve the constraint handling and solution solving capabilities in spacecraft component layout design, thereby effectively suppressing electromagnetic force and self-gravity noise.

[0005] Content of the invention

[0006] To meet the extremely high sensitivity requirements of gravitational wave detection spacecraft, it is crucial to ensure that the surrounding environment for testing meets the stringent requirements of scientific missions. This necessitates effectively suppressing the coupling noise from the electromagnetic field and the self-gravitational field generated by the spacecraft platform. Electromagnetic field noise is typically reduced by using magnetic shielding materials, optimizing cable routing, and equipment layout, while self-gravitational field noise primarily depends on the mass distribution design of the spacecraft platform. Traditional methods often target individual physical fields, independently addressing these two types of noise, which struggles to effectively manage their coupling effects. This invention provides a multi-objective, two-layer optimization method suitable for suppressing electromagnetic and self-gravitational noise in gravitational wave detection spacecraft. By optimizing the layout design with electromagnetic and self-gravitational field indicators as targets, it can effectively suppress the coupling effects of these two types of noise.

[0007] The technical solution adopted by this invention to solve its technical problem is as follows:

[0008] A multi-objective, bi-layer optimization method for suppressing electromagnetic and self-gravitational noise in gravitational wave detection spacecraft is proposed. Its key feature is the simultaneous suppression of both types of noise through multi-objective optimization, and the use of a bi-layer optimization structure to ensure bidirectional interaction and feedback between the upper and lower layers. First, addressing the noise suppression requirements of electromagnetic and self-gravitational fields, the spacecraft component layout design is defined as a multi-objective, bi-layer optimization problem to determine the orientation and position of each component. For constraint handling, a collision detection method is used to determine whether components overlap, while a penalty function method is employed to handle the constraints. In terms of the solution method, the upper-layer problem discretizes the continuous position search space through region partitioning to reduce the search space and improve algorithm efficiency, and then applies the NSGA-III (Nondominated Sorting Genetic Algorithm III) algorithm for solving. After obtaining the initial optimization results, the lower-layer problem focuses on a refined local search of the region selected by the upper layer. Through close collaboration and iteration in these two stages, the quality of the solution and the stability of the algorithm are effectively improved.

[0009] Specifically, the steps include the following:

[0010] S1. The spacecraft component layout is defined as a multi-objective bi-layer optimization problem to simultaneously suppress noise from electromagnetic fields and self-gravitational fields. The multi-objective bi-layer optimization problem includes an upper-layer problem and a lower-layer problem. The upper-layer problem is responsible for the orientation and region selection of the components, and the lower-layer problem further refines the specific location selection of the components based on the results of the upper-layer problem.

[0011] S2. In the above-level problem, the Non-Dominated Sorting Genetic Algorithm (NSGA-III) is used to solve it, including the discretization of the continuous position search space by dividing it into regions, and the application of the NSGA-III algorithm for global optimization to generate a preliminary Pareto solution set.

[0012] S3. In the lower-level problem, the differential evolution algorithm (DE) is used to adjust the position selection in the initial Pareto solution set generated by the upper-level problem in order to optimize the specific layout of the components;

[0013] S4. Introduce a two-way interaction and feedback mechanism to ensure coordination and consistency between upper-level and lower-level issues, and achieve optimized layout design through layered iterative optimization;

[0014] S5. In terms of constraint handling, collision detection method is used to determine whether there is overlap between components, and penalty function strategy is combined to handle constraint conditions to ensure the rationality and operability of the layout design scheme;

[0015] S6. Define optimization objectives including magnetic induction intensity value, magnetic induction intensity gradient, self-gravitational bias and self-gravitational stiffness, and design a comprehensive evaluation model as the objective function of the layout optimization design problem. Optimize the layout scheme and seek the optimal solution by simultaneously minimizing the objective function.

[0016] Furthermore, the region partitioning discretization process adopts a bearing surface region partitioning method based on regular hexagonal grids to ensure the rationality of component location region selection.

[0017] Furthermore, in the upper-level and lower-level problems, a hybrid encoding strategy is adopted to encode the design variables, including binary encoding, permutation encoding, and real number encoding, to adapt to design variables with different characteristics.

[0018] Furthermore, the design variables for the upper-level problem include the component's mounting surface, rotation angle, and mounting area, while the design variables for the lower-level problem include the component's specific position coordinates within the selected area.

[0019] Furthermore, the collision detection method employs a hierarchical bounding volume (BVH) algorithm, which constructs a multi-level bounding volume structure to achieve rapid localization and detection of geometric interference between components.

[0020] Furthermore, the method is applicable to gravitational wave detection spacecraft with a frustum structure, wherein the upper and lower base surfaces are both hexagonal, and the upper and lower base surfaces are connected by six oblique trapezoidal sidewalls to form the load-bearing surface of the component layout.

[0021] Second, the present invention also provides a component layout optimization system suitable for gravitational wave detection spacecraft, characterized in that it includes:

[0022] The upper-level optimization module is used to perform global optimization of component layout using the NSGA-III algorithm to generate a preliminary Pareto solution set;

[0023] The lower-level optimization module is used to perform local optimization on the upper-level solution set using the differential evolution algorithm (DE) to generate the final optimal solution set;

[0024] The collision detection module is used to determine geometric interference between components;

[0025] The load-bearing surface region division module is used to divide the load-bearing surface into regular hexagonal grids, supporting discretized design space;

[0026] The hybrid encoding module is used to encode discrete and continuous variables in a hybrid manner, supporting variable processing during the optimization process.

[0027] Furthermore, the upper-level optimization module and the lower-level optimization module ensure the coordination and consistency of global and local objectives through a two-way interaction and feedback mechanism.

[0028] Furthermore, the collision detection module employs a hierarchical bounding volume (BVH)-based algorithm, using axis-aligned bounding boxes (AABB) to determine interference between components.

[0029] Furthermore, the bearing surface area division module uses a regular hexagonal grid for discretization to ensure the rationality of component location selection.

[0030] Furthermore, the hybrid encoding module uses binary encoding and permutation encoding for discrete variables and real number encoding for continuous variables.

[0031] Third, the present invention also provides a gravitational wave detection spacecraft, characterized in that it adopts the multi-objective dual-layer optimization method described above for component layout design in order to suppress electromagnetic force and self-gravity noise.

[0032] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0033] This method achieves optimized layout design through hierarchical iterative optimization, meeting the requirements of electromagnetic and gravitational fields, thereby achieving the system's top-level sensitivity target. Compared with traditional component layout optimization methods, it is no longer limited to the optimization of a single physics field, but rather involves the comprehensive optimization of multi-objective problems, effectively addressing optimization conflicts under the coupling effect of multiple physics fields, and achieving more efficient resource allocation and performance improvement. In addition, it uses collision detection technology to replace traditional geometric methods for interference judgment, effectively improving the efficiency, scalability, and adaptability of geometric constraint handling. The bi-directional interaction and feedback mechanism introduced by the two-layer optimization method ensures the coordination and consistency of global and local objectives, avoiding the limitations caused by the independent optimization of each stage in traditional methods, thereby improving the efficiency and stability of solving the optimization problem. Attached Figure Description

[0034] Figure 1 This is a configuration diagram of a gravitational wave detection spacecraft.

[0035] Figure 2 Define a coordinate system diagram, which includes the spacecraft body coordinate system, the bearing surface coordinate system, and the component coordinate system.

[0036] Figure 3 The diagrams show the partitioning of the bearing surfaces, illustrating the partitioning effects of the bottom bearing surface and the side bearing surface of the spacecraft under different specified hexagonal side lengths.

[0037] Figure 4 The flowchart shows the multi-objective, two-layer hybrid optimization method.

[0038] Figure 5 Flowchart for optimizing component layout. Detailed Implementation

[0039] The technical solution of the present invention will be explained in detail below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the scope of protection of the present invention.

[0040] Space gravitational wave detection captures gravitational wave signals by detecting extremely small distance changes between two test masses (TMs) within adjacent spacecraft. This requires the test masses to be located in locations with extremely high electromagnetic cleanliness and mechanical and thermal stability, thus imposing stringent design specifications for electromagnetic and self-gravitational fields. Optimizing the layout design of spacecraft equipment is an effective way to ensure that spacecraft meet these requirements. However, traditional layout design optimization methods cannot effectively solve for solutions that meet these stringent requirements. Therefore, we propose a multi-objective, two-layer optimization method suitable for electromagnetic force and self-gravitational noise suppression in gravitational wave detection spacecraft. The specific implementation of this method is described below.

[0041] In this invention, in response to the need for noise suppression of electromagnetic fields and self-gravitational fields, the spacecraft component layout design is defined as a multi-objective, two-layer optimization problem. The aim is to minimize electromagnetic interference and self-gravitational effects by accurately deciding the orientation and position of each component, thereby improving the accuracy of gravitational wave detection.

[0042] The gravitational wave detection spacecraft platform is a frustum structure with hexagonal upper and lower bases, connected by six oblique trapezoidal sidewalls. These surfaces collectively form the load-bearing surface for the component layout. In the center of the gravitational wave detection spacecraft is the core module, which houses the core payload. The core module is connected to the outer modules via vertical bulkheads, forming an internal structure that is both compartmentalized and mutually supportive. This design ensures the safety and stability of the core payload while providing the necessary support and connections for the layout of the outer components.

[0043] Spacecraft components are divided into two categories: one category consists of payload components directly related to the scientific mission, such as telescopes and optical platforms. Their layout is determined by the scientific team based on scientific objectives and mission requirements, and therefore is considered a known condition or constraint during the optimization process. The other category comprises operable components to be laid out, including payload electronics and subsystem components, such as temperature controllers and power controllers. Through optimized design, these components are placed rationally on the spacecraft's effective load-bearing surface.

[0044] To ensure model feasibility and improve computational efficiency during modeling and analysis, this invention introduces several assumptions and simplifications: Although the upper and lower surfaces of the spacecraft platform are not strictly regular hexagons, they are approximated as regular hexagons for simplified geometric modeling. Furthermore, the model only considers the influence of the static magnetic field. For interference generated at the inspection mass by the payload core components and satellite platform structure, it is assumed to be a known fixed value that does not change with component layout. In the analysis of the environment surrounding the inspection mass, only the indicators at the center point of the inspection mass are evaluated. The shape of each component to be laid out is represented by a cuboid with the largest outer envelope, and it is assumed that the centroid of the component coincides with its geometric center. The layout design restricts the orthogonal placement of each component. In numerical analysis, components are simplified as point masses located at their centroids, or further divided into multiple independent sub-components as needed, each treated as a point mass unit, to optimize computational efficiency while retaining necessary analytical accuracy.

[0045] The properties of the component to be laid out include its size, mass, magnetic moment, position, and orientation; that is, the properties of the component to be laid out are represented as follows: Where, N c d represents the total number of components to be laid out. i This represents the component's size vector, including length, width, and height attributes. i Indicates the quality of the component, m i It is the magnetic moment vector of the component, set according to measured data, reflecting the magnetic properties of the component in its own coordinate system. i The vector representing the position of the component's centroid, o i This indicates its spatial orientation, which can be described using Euler angles, quaternions, or rotation matrices. During the optimization process, d... i ,w i The attributes remain unchanged, m i ,r i ,o i Update according to changes in design variables.

[0046] Definition of decision variables

[0047] The design of component layout focuses on decisions regarding component position and orientation. Analysis reveals that the design variables for each component are determined by (f...). i ,θi ,s i ,p i ,x i ,y i ) indicates. f i ,θ i ,s i Three variables together determine the spatial orientation of the component, s i ,p i ,x i ,y i The spatial location of the components is determined jointly, and the specific definitions of each decision variable are shown in Table 1. When a variable is discrete, its value is selected from a predefined set. For example, S = {0, 1, 2, 3, 4, 5} represents the satellite's bearing surfaces 0 to 5 available for component installation, and the variable s... i The set of values ​​S′ is a subset of S, determined by the constraints. When the variable is of continuous type, the variable value is selected from a predefined range. For example, the component in s i Specific location on the surface (x) i ,y i In p i The value of r is taken within the range where the center point of the region is the center and r is the radius.

[0048] As can be seen from the above, the design variables for all components of this invention are: It can be known that there are a total of 6N. c This problem involves several decision variables, including both discrete and continuous variables, constituting a mixed integer programming problem. This invention employs a two-level optimization method to solve the problem. The design variables of the upper-level problem are defined as follows: The optimization variables for the lower-level problem are defined as follows:

[0049] Table 1 Definition of Decision Variables

[0050]

[0051]

[0052] Constraint Definition

[0053] To ensure the rationality and operability of the layout design scheme, this invention relates to three types of constraints, as shown below.

[0054] (1) Geometric constraints

[0055] Geometric constraints are crucial for ensuring the successful installation and operation of all components, and mainly include the following aspects:

[0056] A. The geometric constraints between the components to be laid out are represented as follows:

[0057]

[0058] In the formula, ΔV ij I(ΔV) represents the overlap volume between component i and component j. ij >0) is an indicator function that takes the value 1 when the overlap volume between two components is greater than zero, and 0 otherwise. This constraint requires that all pairs of components to be laid out must not overlap, that is, the components must be independent of each other, ensuring that there is no interference between any two components.

[0059] B. Geometric constraints between the component to be laid out and the IOMA of the core component of the load section:

[0060]

[0061] Where, n I This indicates the number of components in the IOMA constraint. This constraint ensures that the component to be laid out does not interfere with the IOMA components.

[0062] C. Geometric constraints between the components to be laid out and the satellite platform:

[0063]

[0064] In the formula, ΔV is V represents the overlap volume between component i and the satellite platform. i This represents the volume of component i. The indicator function is I(ΔV). is <V i The value is 1 when the overlap volume between component i and the satellite platform is less than the component's own volume, indicating that the component to be laid out is not completely inside the satellite platform. Conversely, the value is 0. This constraint ensures that all components to be laid out are completely inside the satellite platform.

[0065] (2) Static stability constraints

[0066] Static stability constraints refer to the position of the spacecraft's center of mass, representing constraints on the deviation of the center of mass from its position. The position of the center of mass is crucial to the spacecraft's stability. This constraint requires that the deviation of the center of mass along the x and y axes be within tolerable limits. This is achieved by calculating the deviation between the actual and desired center of mass positions and comparing it to the maximum allowable deviation.

[0067]

[0068] Where, N ie c represents the number of child components that component i is divided into, c = (c x ,c y δc represents the components of the spacecraft's desired center of mass position along the x and y axes. x ,δc y This indicates the tolerable deviation of the centroid from the x-axis and y-axis.

[0069] (3) Constraints of each component and each variable

[0070] Considering the performance requirements and impact characteristics of each component, constraints are imposed on variables such as component mounting surface, mounting direction, and the load-bearing surface selected for the component. These variable constraints can be expressed as follows, including discrete and continuous variables. Discrete variables range from a set; for example, the mounting surface or load-bearing surface of a component may only be selectable from several predefined options. Continuous variables take values ​​within an interval; for example, the mounting direction or location of a component may vary within a specific range.

[0071]

[0072]

[0073] Optimize target definition

[0074] When the simulated values ​​of a certain layout scheme at the measurement point TM are lower than the target criteria, it indicates that the layout scheme meets the design requirements.

[0075] First, based on the requirements of the scientific mission, four key performance indicators at the TM (Magnetic Induction Intensity), magnetic induction gradient, self-gravitational bias, and self-gravitational stiffness are defined, and target values ​​are set for each indicator, as shown in Table 2. Next, each performance indicator is calculated. Finally, an optimization objective function is constructed to evaluate and guide the optimized design of the layout scheme.

[0076] Table 2. Indicator Definition Table

[0077]

[0078] Index Calculation: The calculation method for each index value at the measurement point, which involves the center point positions of the two TMs of the spacecraft.

[0079] A. Magnetic flux density value

[0080] All components or sub-components within a spacecraft can be equivalent to magnetic dipoles, each with a magnetic dipole moment of m. i The position is determined by the vector r from the centroid of the component to the measurement point r0. i The magnetic field strength B at position r0 inside the spacecraft is the cumulative result of the effects of all magnetic dipoles, calculated by the following formula:

[0081]

[0082] Where X represents the current layout scheme, which determines all position vectors r ijThe value of μ0 is a known constant, with a value of 4π × 10⁻⁶. -7 Tm / A. B o This represents the magnetic field interference generated at position r0 by the IOMA core components and satellite platform structure. The magnitude of the magnetic induction intensity |B| at position r0 is obtained by calculating the modulus of the overall magnetic field intensity vector B. Other index values ​​are also obtained by taking the modulus of the vector or tensor.

[0083] B. Magnetic induction gradient

[0084] The magnetic flux density gradient describes the rate of change of the magnetic field at a given location r0 along various directions. It is a second-order tensor, which is approximated in this invention using the finite difference method. Specifically, each component of the gradient tensor... It can be defined as the magnetic induction intensity component B i The partial derivative with respect to the coordinate direction j is given by the following formula:

[0085]

[0086] Where i and j can take the x, y, or z directions respectively. Δr j This represents a small displacement along the coordinate direction j. Finally, the magnetic field gradient tensor... Defined in the following matrix form:

[0087]

[0088] C. Self-gravitational bias

[0089] The self-gravity experienced by TM originates from the gravitational interaction between itself and the spacecraft, and obeys the law of universal gravitation. The self-gravity bias generated by the spacecraft system at r0 is as follows:

[0090]

[0091] Where G is the gravitational constant, with a value of 6.67 × 10⁻⁶. -11 m 3 / kg / s 2 At the measuring point r0 in TM, the calculation of the self-gravitational bias is divided into two parts: the self-gravitational effects of the IOMA core components and satellite platform structure are predefined as a known constant F. o The self-gravitational effect of the component to be laid out is calculated by the summation term in the formula, which depends on the mass distribution of the component.

[0092] D. Gravitational Stiffness

[0093] At the point r0 to be measured, the change in the self-gravitational field can be characterized by the self-gravitational stiffness K. The self-gravitational stiffness describes the response of the gravitational field to small positional shifts in different directions. To quantify these changes, the spatial rate of change of the gravitational components is approximated using the finite difference method. This is related to the magnetic flux density gradient. The calculation method is similar, with each element of the stiffness matrix (K(X,r0)) ij Represents the gravitational component F i With a small displacement Δr in the coordinate direction j j The rate of change of is given by the following formula:

[0094]

[0095] The specific expression of the self-gravitational gradient tensor K(r0) is as follows, which clearly shows the local changes of the gravitational field in various directions.

[0096]

[0097] To effectively evaluate the performance of different layout schemes of a spacecraft at the test point r0 during the optimization process, this invention designs a comprehensive evaluation model, which serves as the objective function of the layout optimization design problem. The layout optimization design problem involves two test points, namely the center points of two TMs, denoted as r0. TM1 and r TM2 The corresponding objective function is defined as O(X, r). TM1 ) and P(X,r TM2 This invention optimizes the layout scheme and seeks the optimal solution by simultaneously minimizing these two objective functions. The specific objective function expressions are as follows:

[0098]

[0099] Where M represents the number of indicators, w i T represents the weight of the i-th indicator in the overall evaluation. i (X, r0) represents the calculated value of the i-th index at position r0 for layout scheme X, ref i This represents the target value of the i-th indicator. c This represents the penalty weight for each constraint G(X).

[0100] Analysis shows that the objective function consists of two parts: one part measures the difference between the calculated index value and the target index value, and the other part evaluates the degree to which the layout scheme violates the design constraints. When T... i (X,r0)≤ref iWhen the target value is 0, it indicates that the indicator has been met. At this point, the value of the max function is 0, and the outer In function is also 0. The purpose of using the logarithmic function is to accelerate the descent rate as the deviation decreases, thereby enabling the optimization problem to converge more effectively when approaching the target value. Simultaneously, if the layout scheme does not violate design constraints, the constraint terms are also 0. Therefore, the ultimate goal of this invention is to find a layout scheme where the objective function values ​​at both measurement points are 0, thus fully satisfying all performance indicators and design constraints.

[0101] Based on the above description of design variables, objective function, and constraints, the mathematical model for the layout optimization design problem of this invention is defined as follows:

[0102]

[0103] Building upon this foundation, this invention further defines the layout optimization design problem as a multi-objective, bi-level optimization problem, comprising two levels of optimization tasks, with one task nested within the other. The external optimization problem is referred to as the upper-level optimization problem, and the internal optimization problem as the lower-level optimization problem. Decision-makers in the upper-level task typically possess complete knowledge of the lower-level problem, while lower-level decision-makers optimize their own strategies solely based on the upper-level decisions, ensuring that constraints are satisfied and guaranteeing the feasibility of the solution.

[0104] The decision vector for the lower-level problem is X. l It can be viewed as a decision vector X for the higher-level problem. u The optimal response is achieved by selecting the component region p in the upper-level task and then selecting the specific location based on region p in the lower-level task.

[0105] Therefore, the lower-level problem involves constraints:

[0106] g1(X l )=||X l -C p ||2-r p ≤0

[0107] Among them, C p r represents the geometric center corresponding to region p. p Let p be the radius of region p. The mathematical model for the bi-level optimization problem is as follows:

[0108]

[0109] The layout optimization design problem is a complex mixed-integer optimization problem involving both discrete and continuous decision variables. The high dimensionality and nonlinearity of continuous decision variables within a vast search space can lead to inefficiency and multiple entrapments in local optima. This invention proposes an efficient multi-objective bilevel hybrid optimization approach (MOBLHO). In the upper-level problem, to reduce the search space and improve algorithm efficiency, the continuous position search space is discretized through region partitioning and solved using the Non-dominated Sorting Genetic Algorithm III (NSGA-III). As an advanced multi-objective genetic algorithm, NSGA-III can effectively handle multi-objective optimization problems and converge quickly to the Pareto optimal front while maintaining population diversity. After obtaining preliminary optimization results, the lower-level problem focuses on further refined local searches of the regions selected in the upper-level problem. This stage employs the Differential Evolution (DE) algorithm, which is particularly effective in applications with continuous parameter spaces and suitable for precise local searches. By utilizing the local search of the DE algorithm, key continuous decision variables can be further explored and optimized based on the solutions to higher-level problems, leading to more accurate and optimized solutions. The hybrid optimization method proposed in this study significantly improves the problem-solving efficiency by combining the efficiency of discretization with the powerful search capabilities of the differential evolution algorithm. Furthermore, through close collaboration and iteration in two stages, it effectively enhances the quality of the solution and the stability of the algorithm.

[0110] A. Division of bearing surface area

[0111] To meet the requirements of discretized design space in higher-level optimization problems, this invention proposes a method for partitioning the bearing surface region based on a regular hexagonal mesh. The regular hexagon possesses good space-filling and symmetry properties, effectively supporting the discretization of complex spaces.

[0112] Assume the side length of each hexagon is 'a' and the coordinates of its center point are 'C'. hij =(x ij ,y ij ), where i and j are the grid numbers along the x-axis and y-axis, respectively. Due to the geometric properties of a hexagonal grid, adjacent columns of grids will be misaligned along the y-axis. Therefore, the regular hexagon h ij Center point coordinates C hij for:

[0113]

[0114] To ensure the rationality of component location area selection, this invention only considers regular hexagonal grids whose center point is located inside the bearing surface and whose distance from the boundary is greater than a given threshold ε as optional areas.

[0115] B. Encoding

[0116] When using evolutionary algorithms to solve optimization problems, encoding is the process of converting design variables into genotypes that the algorithm can directly manipulate. Genotypes, or the genetic information encoding of an individual, are typically composed of binary strings, lists of real numbers, or permutation sequences, corresponding to binary encoding, real number encoding, and permutation encoding, respectively. This encoding mechanism is the core of evolutionary algorithms, defining the search space of the problem domain and directly affecting the efficiency and performance of the algorithm. This study employs a hybrid encoding strategy to address the different characteristics of the design variables, enabling more effective representation and processing of these variables during the optimization process. Specifically, for the component's direction variable f... i Rotation angle θ i and installation bearing surface s i Binary encoding is used, which can concisely represent different discrete states; for the installation area p i The selection of the installation location employed a permutation coding method. This coding ensures that each installation area can only be exclusively occupied by one component, avoiding conflicts in area allocation. For variables involving continuous space, the precise coordinates x of the installation location are used. i and y i Real-number encoding was used to support detailed searching and adjustments during the optimization process. This hybrid encoding method allows the study to flexibly address the diversity and complexity of design variables, improving solution efficiency.

[0117] C. Interference Judgment Methods—Collision Detection

[0118] This invention employs an efficient algorithm based on Bounding Volume Hierarchy (BVH) to determine geometric interference between components. The method first constructs a multi-level bounding volume structure for the geometric model of each component, typically using an axis-aligned bounding box (AABB) as the basic form. Through a progressively refined bounding volume hierarchy, this method can recursively achieve rapid localization and detection of interference regions.

[0119] The core of this interference discrimination process lies in utilizing the hierarchical structure provided by BVH to filter collision regions between components in stages. First, the algorithm uses a fast bounding volume intersection test to screen geometric objects that may interfere. Then, for bounding volume regions detected as potentially interfering, the algorithm recursively enters finer levels, narrowing the detection range until precise geometric intersection calculations are performed at the final refined level. Through this layer-by-layer filtering and recursive refinement mechanism, this method can maintain high efficiency while ensuring the accuracy of collision detection.

[0120] The significant advantage of this method lies in its use of the hierarchical structure of BVH to decompose complex geometric interference problems into multiple low-complexity subproblems, thereby significantly reducing computational time complexity. This hierarchical detection mechanism can quickly screen out potential collision regions, effectively avoiding the high computational cost of global fine-grained detection. Furthermore, since each component in this invention is simplified to a cuboid and its geometry is approximated using an axis-aligned bounding box, the collision detection process is more efficient. Especially in multiphysics optimization scenarios involving dynamically updated component layouts and recalculated interference relationships, this method exhibits extremely high flexibility and scalability.

[0121] D. Multi-objective bi-level hybrid optimization method

[0122] This invention proposes a multi-objective, two-layer hybrid optimization method to solve complex optimization problems in spacecraft component arrangement. First, in the preprocessing stage, components are grouped according to their size, with large components and small components respectively assigned to set C. l and C s At the same time, the bearing surface is divided into several optional regions, forming a set P of optional regions corresponding to large components and small components. l and P s In the upper-level optimization, the NSGA-III algorithm is used to globally optimize the component layout. Specifically, the algorithm performs orientation selection for each component. i ,θ i Region selection i ,p i and initial location selection x i ,y i This process ultimately generates a preliminary Pareto solution set (CPF). The goal of this stage is to obtain diverse and high-quality preliminary layout schemes through extensive solution space exploration.

[0123] Lower-level optimization builds upon upper-level optimization, further refining the component layout. Specifically, the DE algorithm is used to optimize the position selection x in the upper-level solution set. i ,yi The DE algorithm precisely adjusts the position of each component. By refining the search for component positions, it optimizes local solutions and ultimately generates the final set (FS). This step ensures that the optimal component layout is obtained while considering local constraints and fine-tuning.

[0124] Specifically, in the component layout operation module, the large component collection C is first... l The corresponding region undergoes preliminary optimization to generate a preliminary Pareto Front (LPF) solution set. These solutions are then used to update the component set C. s The corresponding set of optional regions P s This approach provides more favorable layout conditions for the optimization of small components. The optimization of small components also employs the NSGA-III algorithm, optimizing within the updated selectable regions to generate multiple new Pareto Front (SPF) solutions. Next, through a Pareto Front synthesis strategy, the solutions of each SPF are merged to form a complete Pareto Front (CPF). This synthesis step ensures the global optimality and diversity of the final layout scheme, thus providing rich and efficient multi-objective optimization solutions for the arrangement of spacecraft components. Through collaborative optimization between upper and lower layers, combined with in-depth mining and integration of solution sets, this method achieves an effective balance between global and local objectives in the design of complex systems.

[0125] Compared with traditional component layout design optimization methods, the method proposed in this invention innovates in several aspects, including design objective definition, geometric constraint handling, objective function design, bearing surface region partitioning, hybrid coding strategy formulation, multi-objective bilayer hybrid optimization method design, and integrated innovation in solving the layout design optimization problem of gravitational wave detection spacecraft. These innovations effectively reduce the solution space of the optimization problem, improve the solution efficiency, and provide new possibilities for obtaining layout design schemes that satisfy electromagnetic field and self-gravitational field indices.

Claims

1. A multi-objective, two-layer optimization method for suppressing electromagnetic force and self-gravitational noise in gravitational wave detection spacecraft, characterized in that, include: S1. The spacecraft component layout is defined as a multi-objective bi-layer optimization problem to simultaneously suppress noise from electromagnetic fields and self-gravitational fields. The multi-objective bi-layer optimization problem includes an upper-layer problem and a lower-layer problem. The upper-layer problem is responsible for the orientation selection and region selection of the components, and the lower-layer problem further refines the specific location selection of the components based on the results of the upper-layer problem. S2. In the above-level problem, the non-dominated sorting genetic algorithm NSGA-III is used to solve it, including the discretization of the continuous position search space by dividing it into regions, and the application of the NSGA-III algorithm for global optimization to generate a preliminary Pareto solution set. S3. In the lower-level problem, the differential evolution algorithm (DE) is used to adjust the position selection in the initial Pareto solution set generated by the upper-level problem in order to optimize the specific layout of the components; S4. Introduce a two-way interaction and feedback mechanism to ensure coordination and consistency between upper-level and lower-level issues, and achieve optimized layout design through layered iterative optimization; S5. In terms of constraint handling, collision detection method is used to determine whether there is overlap between components, and penalty function strategy is combined to handle constraint conditions to ensure the rationality and operability of the layout design scheme; S6. Define optimization objectives including magnetic induction intensity value, magnetic induction intensity gradient, self-gravitational bias and self-gravitational stiffness, and design a comprehensive evaluation model as the objective function of the layout optimization design problem. Optimize the layout scheme and seek the optimal solution by simultaneously minimizing the objective function.

2. The method according to claim 1, characterized in that, The discretization process for the region division adopts a bearing surface region division method based on regular hexagonal grids to ensure the rationality of component location region selection.

3. The method according to claim 1, characterized in that, In the upper-level and lower-level problems, a hybrid coding strategy is used to encode the design variables, wherein discrete variables are encoded using binary coding and permutation coding, and continuous variables are encoded using real number coding.

4. The method according to claim 3, characterized in that, The design variables for the upper-level problem include the component's mounting surface, rotation angle, and mounting area, while the design variables for the lower-level problem include the component's specific position coordinates within the selected area.

5. The method according to claim 1, characterized in that, The collision detection method adopts the hierarchical bounding volume (BVH) algorithm, which realizes rapid localization and detection of geometric interference between components by constructing a multi-level bounding volume structure.

6. The method according to claim 1, characterized in that, The method is applicable to gravitational wave detection spacecraft with a frustum structure, wherein the upper and lower base surfaces are both hexagonal, and the upper and lower base surfaces are connected by six oblique trapezoidal sidewalls to form the load-bearing surface of the component layout.

7. The method according to claim 1, characterized in that, The objective function of the comprehensive evaluation model is: Where M represents the number of indicators, w i T represents the weight of the i-th indicator in the overall evaluation. i (X, r0) represents the calculated value of the i-th index at position r0 for layout scheme X, ref i w represents the target value of the i-th indicator. c This represents the penalty weight for each constraint G(X).

8. The method according to claim 7, characterized in that, The constraints include geometric constraints, static stability constraints, and constraints on the variables of each component. The geometric constraints ensure that there is no overlap between components, the static stability constraints ensure that the center of mass of the spacecraft is within the allowable range, and the constraints on the variables of each component ensure that the mounting surface, mounting direction, and bearing surface of the components meet the design requirements.

9. A component layout optimization system suitable for gravitational wave detection spacecraft, characterized in that, include: The upper-level optimization module is used to perform global optimization of component layout using the NSGA-III algorithm to generate a preliminary Pareto solution set; The lower-level optimization module is used to perform local optimization on the upper-level solution set using the differential evolution algorithm (DE) to generate the final optimal solution set. The collision detection module is used to determine geometric interference between components; The load-bearing surface region division module is used to divide the load-bearing surface into regular hexagonal grids, supporting discretized design space; The hybrid encoding module is used to encode discrete and continuous variables in a hybrid manner, supporting variable processing during the optimization process.

10. The component layout optimization system according to claim 9, characterized in that, The upper-level optimization module and the lower-level optimization module ensure the coordination and consistency of global and local objectives through a two-way interaction and feedback mechanism.

11. The component layout optimization system according to claim 9, characterized in that, The collision detection module uses an algorithm based on hierarchical bounding volume (BVH) to determine interference between components using axis-aligned bounding boxes (AABB).

12. The component layout optimization system according to claim 9, characterized in that, The bearing surface area division module uses a regular hexagonal grid for discretization to ensure the rationality of component location selection.

13. The component layout optimization system according to claim 9, characterized in that, The hybrid encoding module uses binary encoding and permutation encoding for discrete variables and real number encoding for continuous variables.

14. A gravitational wave detection spacecraft, characterized in that, The component layout design is carried out using the multi-objective bilayer optimization method as described in any one of claims 1 to 6, in order to suppress electromagnetic force and self-gravity noise.

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