Multi-target double-layer optimization method for electromagnetic force and self-gravity noise suppression and component layout optimization system

Abstract

A multi-target double-layer optimization method suitable for a gravitational wave detection spacecraft aims at suppressing electromagnetic force and self-gravitational noise at the same time, adopts a double-layer optimization structure, ensures bidirectional interaction and feedback between an upper layer and a lower layer, meets the requirement of the spacecraft for extremely high sensitivity, and improves the sensitivity of the spacecraft by optimizing the layout of internal equipment of the spacecraft. The cleanliness and the stability of the inspection quality and the surrounding environment are improved; layout optimization is defined as a double-layer optimization problem, decision variables, constraint conditions and a target function are defined, and the problem is solved as a mixed integer optimization problem; an efficient multi-target double-layer hybrid optimization method combining NSGA-III and DE algorithms is adopted, and geometric constraints are processed by using collision detection and penalty function strategies. According to the method, optimization conflicts under the multi-physics field coupling effect can be effectively solved, efficient resource allocation and performance improvement are achieved, the method has remarkable advantages in the aspects of efficiency, expansibility and adaptability of geometric constraint processing, and the solving efficiency and stability of optimization problems are greatly improved.

Description

Technical Field

[0001] The present invention relates to the technical field of space gravitational wave detection, and particularly relates to a multi-objective two-layer optimization method and a component layout optimization system for suppressing electromagnetic force and self-gravitational noise of a spacecraft. Background Art

[0002] Space gravitational wave detection spacecrafts capture the tiny distance changes between the freely suspended test masses on adjacent spacecrafts when gravitational waves pass through by means of laser interferometry ranging technology, so as to invert the characteristics of gravitational wave signals. In order to achieve a picometer-level ranging accuracy at a distance of millions of kilometers, it is necessary to maximize the elimination of the interference of other noise sources and ensure that the test mass area has an extremely clean electromagnetic and force-thermal environment. The operation of the internal equipment of the spacecraft is the main source of noise. Therefore, in addition to the single-unit level design, the layout design of the spacecraft components is a key operation to ensure the cleanliness of the environment around the test mass.

[0003] Existing research mainly focuses on optimizing the mass characteristics of the spacecraft, such as the center of mass and moment of inertia, and single physical field indicators, such as magnetic field and temperature field, through component layout design. However, the research on the coupled interaction of multiple physical fields and their comprehensive optimization is relatively insufficient. In terms of constraint handling, the non-interference constraint between components, as the basic condition for the rationality of the layout optimization scheme, mainly adopts geometric methods (such as the finite circle method and geometric projection method) for processing at present, but the scalability of these methods is poor and it is difficult to meet the requirements of complex environments and dynamic changes. In addition, existing research generally adopts a phased optimization strategy, which is divided into two steps: component allocation and position selection. Although this method has achieved certain results in practice, due to the relatively independent optimization of each stage, the decision-making in the first stage cannot fully consider the influence of the second stage, lacking an effective interaction and feedback mechanism, and it is difficult to meet the strict index design requirements.

[0004] Therefore, there is an urgent need for an efficient optimization method with multi-physical field indicators as the optimization goal to improve the constraint handling and solution ability of the spacecraft component layout design, and thus effectively suppress electromagnetic force and self-gravitational noise.

[0005] Content of the Invention

[0006] Facing the extremely high sensitivity requirements of gravitational wave detection spacecraft, it is necessary to ensure that the environment around the test mass meets the strict requirements of the scientific mission, which requires effectively suppressing the coupling noise of the electromagnetic field and self-gravitational field generated by the spacecraft platform. Electromagnetic field noise is usually reduced by using magnetic shielding materials, optimizing cable routing and equipment layout, while self-gravitational field noise mainly depends on the mass distribution design of the spacecraft platform. Traditional methods often target a single physical field and independently handle these two types of noise, making it difficult to effectively deal with their coupling effects. The present invention provides a multi-objective two-layer optimization method for suppressing electromagnetic force and self-gravitational noise in gravitational wave detection spacecraft, which optimizes the layout design with the electromagnetic field and self-gravitational field indicators as the objectives, and can effectively suppress the coupling influence of these two types of noise.

[0007] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0008] A multi-objective two-layer optimization method for suppressing electromagnetic force and self-gravitational noise in gravitational wave detection spacecraft, characterized in that it simultaneously suppresses the two types of noise through multi-objective optimization and adopts a two-layer optimization structure to ensure the two-way interaction and feedback mechanism between the upper and lower layers. First, aiming at the noise suppression requirements of the electromagnetic field and self-gravitational field, the layout design of spacecraft components is defined as a multi-objective two-layer optimization problem to determine the direction and position selection of each component. In terms of constraint handling, a collision detection method is used to judge whether there is an overlap between components, and at the same time, a penalty function method is used to handle the constraint conditions. In terms of the solution method, the upper-layer problem discretizes the continuous position search space through region division to reduce the search space and improve the algorithm operation efficiency, and then applies the NSGA-III (Nondominated Sorting Genetic Algorithm III) algorithm for solution. After obtaining the preliminary optimization result, the lower-layer problem will focus on the fine local search of the region selected by the upper layer. Through the close cooperation and iteration of the two stages, the quality of the solution and the stability of the algorithm are effectively improved.

[0009] Specifically, it includes the following steps:

[0010] S1. Define the layout of spacecraft components as a multi-objective two-layer optimization problem to simultaneously suppress the noise of the electromagnetic field and self-gravitational field. Among them, the multi-objective two-layer optimization problem includes an upper-layer problem and a lower-layer problem. The upper-layer problem is responsible for the direction selection and region selection of components, and the lower-layer problem further refines the specific position selection of components based on the results of the upper-layer problem;

[0011] S2. In the upper-layer problem, use the non-dominated sorting genetic algorithm (NSGA-III) for solution, including discretizing the continuous position search space through region division and applying 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 preliminary Pareto solution set generated by the upper - level problem, so as to optimize the specific layout of components.

[0013] S4. A two - way interaction and feedback mechanism is introduced to ensure the coordination between the upper - level problem and the lower - level problem, and the optimal design of the layout scheme is realized through hierarchical iterative optimization.

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

[0015] S6. Optimization objectives including magnetic - induction intensity value, magnetic - induction intensity gradient, self - gravitational bias, and self - gravitational stiffness are defined, and a comprehensive evaluation model is designed as the objective function of the layout - optimization design problem. The layout scheme is optimized and the optimal solution is sought by minimizing the objective function simultaneously.

[0016] Furthermore, the discrete processing of the area division adopts a method for dividing the load - bearing surface area based on a regular - hexagon grid to ensure the rationality of the component - position area selection.

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

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

[0019] Furthermore, the collision - detection method adopts the bounding - volume hierarchy (BVH) algorithm, and the rapid positioning and detection of geometric interference between components are realized by constructing a multi - level bounding - volume structure.

[0020] Furthermore, the method is applicable to a gravitational - wave detection spacecraft with a frustum - like structure, where the upper and lower bases are both hexagons, and the upper and lower bases are connected by six inclined trapezoidal side walls to form the load - bearing surface for the component layout.

[0021] Second, the present invention also provides a component - layout optimization system applicable to a gravitational - wave detection spacecraft, which is characterized by including:

[0022] An upper - level optimization module, which is used to globally optimize the component layout through the NSGA - III algorithm and generate a preliminary Pareto solution set.

[0023] The lower - layer optimization module is used to locally optimize the upper - layer solution set through the differential evolution algorithm (DE) to generate the final optimal solution set;

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

[0025] The bearing - surface area division module is used to divide the bearing surface into regular - hexagon meshes to support the discretized design space;

[0026] The hybrid coding module is used to perform hybrid coding on discrete and continuous variables to support variable processing during the optimization process.

[0027] Furthermore, the upper - layer optimization module and the lower - layer 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 adopts an algorithm based on the bounding volume hierarchy (BVH) to judge the interference between components through the axis - aligned bounding box (AABB).

[0029] Furthermore, the bearing - surface area division module uses regular - hexagon meshes for discretization processing to ensure the rationality of component position selection.

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

[0031] Thirdly, the present invention also provides a gravitational - wave detection spacecraft, which is characterized in that the above - mentioned multi - objective two - layer optimization method is used for component layout design to suppress electromagnetic force and self - gravitational noise.

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

[0033] Through hierarchical iterative optimization, this method realizes the optimal design of the layout scheme, meets the index requirements of the electromagnetic field and the self - gravitational field, and thus achieves the top - level sensitivity target of the system. Compared with the traditional component layout optimization method, it is no longer limited to the optimization of a single physical field, but is a comprehensive optimization of multi - objective problems, effectively coping with the optimization conflicts under the multi - physical - field coupling effect, and realizing more efficient resource allocation and performance improvement; in addition, the collision detection technology is used to replace the traditional geometric method for interference judgment, effectively improving the efficiency, scalability and adaptability of geometric constraint processing; the two - way interaction and feedback mechanism between the upper and lower layers introduced by the two - layer optimization method ensures the coordination and consistency of global and local objectives, avoiding the limitations brought by the independent optimization in each stage of the traditional method, and thus improving the efficiency and stability of solving the optimization problem. Description of the Drawings

[0034] Figure 1 It is a configuration diagram of the gravitational - wave detection spacecraft.

[0035] Figure 2 It is a diagram defining a coordinate system, including the spacecraft body coordinate system, the bearing surface coordinate system, and the component coordinate system.

[0036] Figure 3 It is an effect diagram of the bearing surface division, respectively showing the division effects of the bottom bearing surface and the side wall bearing surface of the spacecraft under different specified hexagon side lengths.

[0037] Figure 4 It is a flow chart of the multi-objective two-layer hybrid optimization method.

[0038] Figure 5 It is a flow chart of the component layout optimization. Specific implementation manner

[0039] The technical solution of the present invention will be explained in detail below in conjunction with the accompanying drawings and embodiments, but the protection scope of the present invention should not be limited thereby.

[0040] Space gravitational wave detection captures gravitational wave signals by detecting extremely small distance changes between two test masses (TM) in adjacent spacecrafts. This requires that the positions of the test masses have extremely high electromagnetic environment cleanliness and force and heat environment stability, thus posing strict design indicators for the electromagnetic field and self-gravitational field. The layout design optimization of spacecraft equipment is an effective way to ensure that the spacecraft meets these indicator requirements. However, traditional layout design optimization methods cannot effectively solve the scheme that meets these stringent indicator requirements. Therefore, we propose a multi-objective two-layer optimization method applicable to the suppression of electromagnetic force and self-gravitational noise of gravitational wave detection spacecrafts. The following is the specific implementation manner of this method.

[0041] In the present invention, aiming at the requirements of suppressing electromagnetic field and self-gravitational field noise, the layout design of spacecraft components is defined as a multi-objective two-layer optimization problem, aiming to minimize electromagnetic interference and self-gravitational effects by accurately determining the direction and position of each component, thereby improving the accuracy of gravitational wave detection.

[0042] The platform of the gravitational wave detection spacecraft is a frustum structure, the upper and lower bases of which are both hexagons, and the upper and lower bases are connected by six inclined trapezoidal side walls. These surfaces together form the bearing surface for component layout. In the middle of the gravitational wave detection spacecraft, a core module is set up to place the core payload. The core module is connected to the outer cabin through vertical partitions, forming an internal structure that is both separated and mutually supported. This design not only ensures the safety and stability of the core payload, but also provides the necessary support and connection for the layout of the outer components.

[0043] Spacecraft components are divided into two categories: one is the payload components directly related to the execution of scientific missions, such as telescopes, optical platforms, etc. Their layout is determined by the scientific team according to scientific goals and mission requirements, so they are regarded as known conditions or constraints during the optimization process. The other is the operable components to be laid out, including payload electronics components and subsystem components, such as temperature controllers, power controllers, etc. Through optimization design, the components to be laid out are reasonably placed on the effective bearing surface of the spacecraft.

[0044] During the modeling and analysis process, to ensure the feasibility of the model and improve the calculation efficiency, the present invention introduces several assumptions and simplifications: Although the upper and lower bottom surfaces of the spacecraft platform are not strictly regular hexagons, for the sake of simplifying geometric modeling, it is approximated as a regular hexagon for processing. In addition, the model only considers the influence of the static magnetic field part. For the interference generated by the payload core components and the satellite platform structure at the test mass, it is assumed to be a known fixed value and does not change with the component layout. In the analysis of the environment around the test mass, only the indicators at the center point of the test mass are focused on for evaluation. The shape of each component to be laid out is represented by the largest enclosing cuboid. At the same time, it is assumed that the center of mass of the component coincides with the geometric center, and the orthogonal placement of each component is restricted in the layout design. In numerical analysis, the component is simplified as a particle located at the center of mass, or further divided into multiple independent sub-components as needed, and each is regarded as a particle unit to optimize the calculation efficiency while retaining the necessary analysis accuracy.

[0045] The attributes of the components to be laid out cover their size, mass, magnetic moment, position and orientation, that is, the attributes of the components to be laid out are expressed as Among them, N c is the total number of components to be laid out, d i represents the size vector of the component, including the attributes of length, width and height. w i represents the mass of the component, m i is the magnetic moment vector of the component, which is set according to the measured data and reflects the magnetic characteristics of the component in its own coordinate system. r i represents the position vector of the center of mass of the component, o i then represents its spatial orientation, and the specific orientation of the component can be described in the form of Euler angles, quaternions or rotation matrices, etc. During the optimization process, d i , w i attributes remain unchanged, m i , r i , o i are updated according to the change of the design variables.

[0046] Definition of decision variables

[0047] The design of the component layout focuses on the decision of the component position and orientation. It is analyzed that the design variables of each component are (f i , θi , s i , p i , x i , y i ) is represented by f i , θ i , s i The three variables together determine the spatial orientation of the component, s i , p i , x i , y i together determine the spatial position of the component. The specific definitions of each decision variable are shown in Table 1. Among them, when the variable is of discrete type, the variable value is selected from a predefined set. For example, S = {0, 1, 2, 3, 4, 5} means that the 0th to 5th bearing surfaces of the satellite are available for component installation, and the value set S' of the variable s i is a subset of S, depending on the constraint conditions. When the variable is of continuous type, the variable value is selected within a predefined range. For example, the specific position (x i , y i ) of the component on the s i plane is within the range with the center point of the p i area as the center and r as the radius.

[0048] As can be seen from the above, the design variables of all components of the present invention are It can be seen that there are a total of 6N c decision variables, and both discrete and continuous variables are involved at the same time, which is a mixed integer programming problem. The present invention uses a two-layer optimization method to optimize and solve. The design variables of the upper-layer problem are defined as The optimization variables of the lower-layer problem are defined as

[0049] Table 1 Definition Table of Decision Variables

[0050]

[0051]

[0052] Constraint Definition

[0053] To ensure the rationality and operability of the layout design scheme, the present invention involves three types of constraints, as follows.

[0054] (1) Geometric Constraints

[0055] Geometric constraints are the key to ensuring the successful installation and operation of all components, mainly including the following aspects:

[0056] A. Geometric constraints between components to be laid out, represented as:

[0057]

[0058] Wherein, ΔV ij represents the overlapping volume between component i and component j. I(ΔV ij >0) is an indicator function, which takes the value of 1 when the overlapping volume between the two components is greater than zero, and 0 otherwise. This constraint requires that there should be no overlap between all pairs of components to be laid out, that is, the components must be independent of each other to ensure that there is no interference between any two components.

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

[0060]

[0061] Wherein, n I represents the number of components in IOMA. This constraint ensures no interference between the components to be laid out and the IOMA components.

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

[0063]

[0064] Wherein, ΔV is represents the overlapping volume between component i and the satellite platform, and V i represents the volume of component i. The indicator function I(ΔV is <V i ) indicates that it takes the value of 1 when the overlapping volume between component i and the satellite platform is less than its own volume, at this time the component to be laid out is not completely inside the satellite platform, otherwise, it takes the value of 0. This constraint ensures that all components to be laid out are completely inside the satellite platform.

[0065] (2) Static stability constraint

[0066] The static stability constraint notes the position of the center of mass of the spacecraft, representing the center of mass deviation constraint of the spacecraft. The position of the center of mass is crucial for the stability of the spacecraft. This constraint requires that the deviations of the center of mass on the x-axis and y-axis are within the tolerable range, which is achieved by calculating the deviation between the actual center of mass position and the expected center of mass position and comparing it with the maximum allowable deviation.

[0067]

[0068] Wherein, N ie represents the number of sub-components into which component i is divided, and c=(c x , c y ) represents the components of the expected center of mass position of the spacecraft on the x-axis and y-axis. δc x , δc y represent the tolerable deviations of the center of mass on the x-axis and y-axis.

[0069] (3) Constraints on Variables of Each Component

[0070] Considering the performance requirements and influencing characteristics of each component, constraints are imposed on variables such as the component mounting surface, mounting direction, and the load-bearing surface for component selection. The variable constraints can be expressed as follows, including discrete variables and continuous variables. The range of discrete variables is 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 position of a component may vary within a specific range.

[0071]

[0072]

[0073] Definition of Optimization Objectives

[0074] When the calculated index value (simulated values) of a certain layout scheme at the measurement point TM is lower than the target index value (target criteria), it indicates that the layout scheme meets the design requirements.

[0075] First, according to the scientific mission requirements, four key performance indicators at TM are defined: the magnetic induction intensity, magnetic induction intensity gradient, self-gravitational bias, and self-gravitational stiffness at TM, and target index values are set for each indicator, as shown in Table 2. Then, the values of each performance indicator are calculated. Finally, an optimization objective function is constructed to evaluate and guide the optimized design of the layout scheme.

[0076] Table 2 Index Definition Table

[0077]

[0078] Index Calculation: The calculation method for the value of each indicator at the measurement point, and the measurement points involved include the central point positions of two TMs of the spacecraft.

[0079] A. Magnetic Induction Intensity Value

[0080] All components or sub-components within the spacecraft can be equivalent to magnetic dipoles, and the magnetic dipole moment of each magnetic dipole is m i , and the position is represented by the vector r from the center of mass of the component to the measurement point r 0 The magnetic field intensity B at the position r within the spacecraft is the cumulative result of the influence of all magnetic dipoles and is calculated by the following formula: i where X represents the current layout scheme, which determines all position vectors r 0

[0081]

[0082] ​​ij Value of. Vacuum permeability μ 0 Is a known constant, with a value of 4π×10 -7 T·m / A. B o Represents the magnetic field interference generated by the IOMA core components and the satellite platform structure at r 0 The magnitude of the magnetic induction intensity |B| at position r 0 Is obtained by calculating the modulus of the overall magnetic field intensity vector B, and other index values are also obtained by taking the modulus of vectors or tensors.

[0083] B. Magnetic induction intensity gradient

[0084] The magnetic induction intensity gradient describes the rate of change of the magnetic field in all directions at a certain position r 0 Is a second-order tensor, and the present invention approximately calculates it by the finite difference method. Specifically, each component of the gradient tensor Can be defined as the partial derivative of the magnetic induction intensity component B i With respect to the coordinate direction j, and the formula is as follows:

[0085]

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

[0087]

[0088] C. Self-gravitational bias

[0089] The self-gravitational force received by the TM results from the gravitational interaction between itself and the spacecraft, following the law of universal gravitation. The self-gravitational bias generated by the spacecraft system at r 0 Is as follows:

[0090]

[0091] Where, G is the gravitational constant, with a value of 6.67×10 -11 m 3 / kg / s 2 . At the measurement point r 0 In the TM, the calculation of the self-gravitational bias is divided into two parts: the self-gravitational effects of parts such as the IOMA core components and the satellite platform structure are predefined as known constants F o ; the self-gravitational effects of the components to be laid out are calculated through the summation term in the formula and depend on the mass distribution of the components.

[0092] D. Self-gravitational stiffness

[0093] At the point to be measured r 0 , the change of the self-gravitational field can be characterized by the self-gravitational stiffness K. The self-gravitational stiffness describes the change response of the gravitational field to small displacements of position in different directions. To quantify these changes, the finite difference method is used to approximately calculate the spatial change rate of the gravitational components. Similar to the calculation method of the magnetic induction intensity gradient , each element of the stiffness matrix (K(X, r 0 )) ij represents the change rate of the gravitational component F i with respect to the small displacement Δr j in the coordinate direction j. The formula is as follows:

[0094]

[0095] The specific expression of the self-gravitational gradient tensor K(r 0 ) is as follows, clearly showing the local changes of the gravitational field in all directions.

[0096]

[0097] To effectively evaluate the performance of different layout schemes of the spacecraft at the position of the point to be measured r 0 during the optimization process, the present invention designs a comprehensive evaluation model and uses it as the objective function of the layout optimization design problem. There are two points to be measured involved in the layout optimization design problem, which are the center point positions of two TMs, denoted as r TM1 and r TM2 . Define the corresponding objective functions as O(X, r TM1 ) and P(X, r TM2 ). The present invention optimizes the layout scheme and seeks the optimal solution by simultaneously minimizing these two objective functions. The specific expressions of the objective functions are as follows:

[0098]

[0099] where M represents the number of indicators, w i represents the weight of the i-th indicator in the comprehensive evaluation, T i (X, r 0 ) represents the calculated value of the i-th indicator of the layout scheme X at the position r 0 , ref i represents the target value of the i-th indicator. w c represents the penalty weight of each constraint G(X).

[0100] Analysis shows that the objective function consists of two parts: one part is used to measure the difference between the calculated indicator value and the target indicator value, and the other part is used to evaluate the degree of violation of the layout scheme against the design constraints. When Ti (X, r 0 ) ≤ ref i When this is the case, it indicates that the index meets the standard. At this time, the value of the max function is 0, and the value of the outer In function is also 0. The purpose of selecting the logarithmic function is to accelerate the descent speed when the deviation decreases, so that the optimization problem converges more effectively when approaching the target value. At the same time, if the layout scheme does not violate the design constraints, the constraint term is also 0. Therefore, the ultimate goal of the optimization of the present invention is to find a layout scheme such that the objective function values of the two measurement points are both 0, thus fully meeting all performance indicators and design constraints.

[0101] Based on the above descriptions of the design variables, objective function, and constraint conditions, the mathematical model of the layout optimization design problem of the present invention is defined as follows:

[0102]

[0103] On this basis, the layout optimization design problem of the present invention is further defined as a multi-objective bi-level optimization problem, which includes two levels of optimization tasks, where one optimization task is nested in the other. The external optimization problem is called the upper-level optimization problem, and the internal optimization problem is called the lower-level optimization problem. The decision maker of the upper-level task usually has complete knowledge of the lower-level problem, while the lower-level decision maker only relies on the upper-level decision, optimizes its own strategy, and at the same time ensures that the constraints are met to guarantee the feasibility of the solution.

[0104] The decision vector of the lower-level problem is denoted as X l and can be regarded as the optimal response to the decision vector X u of the upper-level problem. The present invention completes the selection of the component area p in the upper-level task, and the lower-level task realizes the selection of the specific position based on the area p.

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

[0106] g 1 (X l ) = ||X l - C p || 2 - r p ≤ 0

[0107] where C p represents the geometric center corresponding to the area p, and r p is the radius of the area p. The mathematical model of the bi-level optimization problem is as follows:

[0108]

[0109] The layout optimization design problem is a complex mixed-integer optimization problem that simultaneously includes discrete and continuous decision variables. The high-dimensional and non-linear characteristics exhibited by continuous decision variables in a vast search space may lead to low efficiency and multiple local optimal solutions during the optimization process. The present invention proposes an efficient multi-objective bilevel hybrid optimization method (multi-objective bilevel NSGA-III and DE hybrid optimization approach, MOBLHO). In the upper-level problem, to reduce the search space and improve the algorithm's running efficiency, the continuous position search space is discretized through regional partitioning, and the Non-dominated Sorting Genetic Algorithm III (NSGA-III) is used for solution. As an advanced multi-objective genetic algorithm, NSGA-III can effectively handle multi-objective optimization problems and can quickly converge to the Pareto optimal front while maintaining population diversity. After obtaining the preliminary optimization results, the lower-level problem focuses on further fine local search for the regions selected by the upper-level problem. In this stage, the Differential Evolution (DE) algorithm is adopted, which is particularly effective in the application of continuous parameter space and is suitable for precise local search. Through the local search of the DE algorithm, based on the solution of the upper-level problem, the key continuous decision variables can be further explored and optimized to achieve a more precise and optimized solution. The hybrid optimization method proposed in this study significantly improves the problem-solving efficiency by combining the efficiency of discretization processing with the powerful search ability of the differential evolution algorithm. At the same time, through the close cooperation and iteration of the two stages, the quality of the solution and the stability of the algorithm are effectively improved.

[0110] A. Division of the bearing surface area

[0111] To meet the requirements of the discretized design space in the upper-level optimization problem, the present invention proposes a method for dividing the bearing surface area based on a regular hexagonal grid. Regular hexagons have good space filling and symmetry, which can effectively support the discretization of complex spaces.

[0112] Assume that the side length of each hexagon is a, and the center point coordinates are C hij =(x ij , y ij ), where i and j are the numbers of the grid along the x-axis and y-axis directions respectively. Due to the geometric characteristics of the hexagonal grid, the grids in adjacent columns are arranged in a staggered manner in the y-axis direction. Therefore, the center point coordinates C ij of the regular hexagon h hij are:

[0113]

[0114] To ensure the rationality of the selection of the component position area, the present invention only considers a regular hexagonal grid with its center point located inside the bearing surface and the distance from the boundary greater than a given threshold ε as the optional area.

[0115] B. Encoding

[0116] When using an evolutionary algorithm to solve optimization problems, encoding is the process of converting design variables into genotypes that can be directly manipulated by the algorithm. Genotypes, which are the genetic information encodings of individuals, usually consist of binary strings, real number lists, or permutation sequences, corresponding to binary encoding, real number encoding, and permutation encoding respectively. This encoding mechanism is the core of the evolutionary algorithm, defining both the search space of the problem domain and directly affecting the efficiency and performance of the algorithm. In this study, a hybrid encoding strategy was adopted for the different characteristics of the design variables to more effectively represent and process these variables during the optimization process. Specifically, for the orientation variable f i , rotation angle θ i and installation bearing surface s i binary encoding was used, which can concisely express different discrete states; for the selection of the installation area p i , permutation encoding was adopted, which ensures that each installation area can only be occupied by one component exclusively, avoiding conflicts in area allocation; for variables involving continuous space, the exact coordinates x i and y i of the installation position, real number encoding was used to support fine-grained search and adjustment during the optimization process. Through this hybrid encoding method, the study can flexibly handle the diversity and complexity of design variables and improve the solution efficiency.

[0117] C. Interference Judgment Method - Collision Detection

[0118] The present invention adopts an efficient algorithm based on the Bounding Volume Hierarchy (BVH) to discriminate geometric interference between components. This method first constructs a multi-level bounding volume structure for the geometric model of each component, usually selecting the Axis-Aligned Bounding Box (AABB) as the basic form of the bounding volume. Through the gradually refined bounding volume hierarchy structure, this method can quickly locate and detect the interference area in a recursive manner.

[0119] The core of this interference discrimination process lies in using the hierarchical structure provided by BVH to filter the collision regions between components in stages. First, the algorithm screens the geometric objects that may interfere through a fast bounding volume intersection test. Subsequently, for the detected bounding volume regions that may have interference, the algorithm further recursively enters a finer level to narrow the detection range until precise geometric intersection calculations are performed at the final refined level. Through this mechanism of layer-by-layer filtering and recursive refinement, this method can ensure the accuracy of collision detection while maintaining high efficiency.

[0120] The significant advantage of this method is that it uses the hierarchical structure of BVH to decompose complex geometric interference problems into multiple sub-problems with low complexity, thereby significantly reducing the computational time complexity. This hierarchical detection mechanism can quickly screen out potential collision regions and effectively avoid the high computational cost brought by global fine-grained detection. In addition, since each component of the present invention is simplified to a cuboid and the axis-aligned bounding box is used to approximate its geometric shape, the process of collision detection is more efficient. Especially in the scenario of multi-physics field optimization, where the component layout is dynamically updated and the interference relationship is recalculated, this method shows extremely high flexibility and scalability.

[0121] D. Multi-objective two-layer hybrid optimization method

[0122] The present invention proposes a multi-objective two-layer hybrid optimization method to solve the complex optimization problems in spacecraft component layout. First, in the preprocessing stage, the components are grouped according to their volume sizes, and the large components and small components are respectively classified into sets C l and C s , and at the same time, the bearing surface is divided into several optional regions to form the optional region sets P l and P s corresponding to the large components and small components. In the upper-layer optimization, the NSGA-III algorithm is used to globally optimize the component layout. Specifically, the algorithm makes direction selection f i , θ i , region selection s i , p i and preliminary position selection x i , y i for each component, and finally generates a preliminary Pareto solution set CPF (Candidate Pareto Front). The goal of this stage is to obtain diverse and high-quality preliminary layout plans through extensive exploration of the solution space.

[0123] Based on the upper-layer optimization, the lower-layer optimization further refines the component layout. Specifically, the DE algorithm is used to optimize the position selection x i , yi , precisely adjust the position of each component. The DE algorithm optimizes the local solution by performing a refined search for the component positions and finally generates the optimal solution set FS (Final Set). This step ensures obtaining the best layout plan for the components while considering local constraints and fine-tuning.

[0124] Specifically, in the component layout operation module, first, initially optimize the area corresponding to the large component set C l to generate the initial Pareto front solution set LPF (Large Pareto Front). Then, these solution sets are used to update the set of optional areas P s corresponding to the small component set C s , providing more favorable layout conditions for the optimization of small components. The optimization of small components also uses the NSGA-III algorithm to optimize within the updated optional areas and generate multiple new Pareto front solution sets SPFs (Small Pareto Front). Next, through the Pareto front integration strategy, merge each SPFs solution set to form the complete Pareto solution set CPF. This integration step ensures the global optimality and diversity of the final layout plan, thus providing rich and efficient multi-objective optimization solutions for the arrangement of spacecraft components. Through the collaborative optimization of the upper and lower layers and the combination of 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 methods for optimizing component layout design, the method proposed in the present invention has innovations in multiple aspects, including the definition of design objectives, the handling of geometric constraints, the design of objective functions, the division of the bearing surface area, the formulation of a hybrid coding strategy, the design of a multi-objective two-layer hybrid optimization method, and the 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 and improve the solution efficiency, providing new possibilities for obtaining a layout design plan that meets the electromagnetic field and self-gravitational field indicators.

Claims

1. A multi-objective two-level optimization method for electromagnetic force and self-gravitation noise suppression of gravitational wave detection spacecraft, characterized in that: include: S1. Define the layout of spacecraft components as a multi-objective two-level optimization problem to simultaneously suppress the noise of electromagnetic field and self-gravitational field, wherein the multi-objective two-level optimization problem includes an upper-level problem and a lower-level problem, wherein the upper-level problem is responsible for the direction selection and area selection of the components, and the lower-level problem further refines the specific location selection of the components based on the results of the upper-level problem; S2. In the above-mentioned upper-level problem, a non-dominated sorting genetic algorithm (NSGA-III) is used to solve the problem, including discretizing the continuous position search space by region partitioning, and applying the NSGA-III algorithm for global optimization to generate a preliminary Pareto solution set; S3. In the lower-level problem, a differential evolution algorithm (DE) is used to adjust the position selection in the preliminary Pareto solution set generated by the upper-level problem to optimize the specific layout of the components; S4. Introduce a two-way interaction and feedback mechanism to ensure the coordination between the upper and lower level issues, and achieve the optimal design of the layout plan through hierarchical iterative optimization; S5. In terms of constraint processing, a collision detection method is used to determine whether there is overlap between components, and a penalty function strategy is used to process the constraints 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-gravity bias and self-gravity 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 area division discretization process adopts a bearing surface area division method based on a regular hexagonal grid to ensure the rationality of the component location area selection.

3. The method according to claim 1, characterized in that In the upper-level problem and the lower-level problem, 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 numbers.

4. The method according to claim 3, characterized in that: The design variables of the upper-level problem include the installation surface, rotation angle, and installation area of ​​the component, and the design variables of the lower-level problem include the specific position coordinates of the component in the selected area.

5. The method according to claim 1, characterized in that The collision detection method adopts a bounding volume hierarchy (BVH) algorithm to achieve rapid positioning 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 a gravitational wave detection spacecraft with a prism structure, wherein the upper bottom surface and the lower bottom surface are both hexagonal, and the upper and lower bottom surfaces are connected by six oblique trapezoidal side walls to form a bearing surface for component layout.

7. The method according to claim 1, characterized in that The objective function of the comprehensive evaluation model is: Among them, M represents the number of indicators, w i represents the weight of the ith indicator in the comprehensive evaluation, T i (X, r0) represents the calculated value of the ith index of the layout solution X at position r0, ref i represents the target value of the ith indicator, w c Represents the penalty weight of 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 component variables. The geometric constraints ensure that there is no overlap between components, the static stability constraints ensure that the center of mass position of the spacecraft is within an allowable range, and the constraints on component variables ensure that the installation surface, installation direction and bearing surface selection of the component meet the design requirements.

9. A component layout optimization system for a gravitational wave detection spacecraft, characterized in that: include: The upper optimization module is used to perform global optimization of component layout through the NSGA-III algorithm and generate a preliminary Pareto solution set; The lower layer optimization module is used to locally optimize the upper layer solution set through the differential evolution algorithm (DE) to generate the final optimal solution set; Collision detection module, used to determine the geometric interference between components; The bearing surface area division module is used to divide the bearing surface into regular hexagonal grids and support the discretization of the design space; The hybrid coding module is used to perform hybrid coding of discrete and continuous variables to support variable processing during the optimization process.

10. The component layout optimization system according to claim 9, characterized in that: The upper optimization module and the lower optimization module ensure the coordination and consistency of global and local goals 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 adopts an algorithm based on a bounding volume hierarchy (BVH) and performs interference judgment between components through an axis-aligned bounding box (AABB).

12. The component layout optimization system according to claim 9, characterized in that: The bearing surface area division module adopts regular hexagonal grids for discretization processing to ensure the rationality of component position selection.

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

14. A gravitational wave detection spacecraft, characterized in that: The multi-objective double-layer optimization method as described in any one of claims 1 to 6 is used to perform component layout design to suppress electromagnetic force and self-gravitation noise.

Images