Multi-objective optimization method for pod-shaped composite material space thin-wall deployable structure

Abstract

The invention relates to the technical field of aerospace, in particular to a multi-objective optimization method for a pod-shaped composite space thin-wall deployable structure. The method comprises the following steps: selecting an optimal sample point for uniformizing the space deployable structure in an interval range of structure parameters; constructing a finite element analysis model of the pod-shaped composite material space thin-wall deployable structure; the method comprises the following steps: by taking a damage failure criterion as a failure mode judgment basis of fibers and a matrix of a pod-shaped composite material, describing an evolution path of material rigidity in a damage development process by utilizing a bilinear rigidity degradation model after failure occurs, and constructing a random forest model based on adaptive particle swarm optimization as an agent model; and a Pareto leading edge optimal solution is obtained by calling the proxy model and is used as an optimal pod rod structure. In this way, the axial bearing capacity and folding performance of the unfolded structure are comprehensively improved, and the optimized structure can show more excellent mechanical performance and adaptability to different scenes in a complex space environment.

Description

Technical Field

[0001] The present invention generally relates to the field of aerospace technology, and more particularly to a multi-objective optimization method for a pod-shaped composite material space thin-wall deployable structure. Background Art

[0002] Composite materials, due to their high specific strength and high specific stiffness, have become ideal materials for thin-walled deployable structures in space and are widely used in the aerospace field. Among them, pod-shaped structures are more widely used, but the multi-layer structure of pod-shaped composite materials and the anisotropic properties of the materials increase the difficulty of optimal design. For example, during the unfolding and folding process, the layers of material in the structure will exhibit a complex stress state, which may cause problems such as interlayer delamination and failure of the material. However, traditional failure criteria do not take into account multi-stress coupling, ignore the effect of shear on body damage, and the material fails in an instant "brittle collapse" without a real gradual damage process, making the calculation of delamination and interlayer damage inaccurate.

[0003] Currently, the finite element analysis method is mostly used to analyze the mechanical properties of pod-shaped composite thin-walled deployable structures. However, traditional finite element models are often complex and time-consuming to calculate. Especially in multi-objective optimization problems, a large number of finite element analysis calculations need to be performed multiple times to meet data requirements, which significantly increases the computational cost.

[0004] Due to the aforementioned material and structural characteristics, pod-like deployable structures exhibit complex nonlinear mechanical behavior, particularly when compressed and folded. Therefore, balancing these various mechanical properties becomes a key issue in structural design. Existing design methods typically optimize for a single objective, such as maximizing structural stiffness or minimizing weight. This approach proves insufficient for the design of deployable structures in space. Summary of the Invention

[0005] According to the present invention, a multi-objective optimization scheme for a pod-shaped composite material spatial thin-walled deployable structure is provided. This scheme can solve the technical problem of how to balance different mechanical properties for multi-objective optimization design.

[0006] In a first aspect of the present invention, a multi-objective optimization method for a pod-shaped composite material spatial thin-walled deployable structure is provided. The method comprises:

[0007] Set the optimization variables, optimization objectives and constraints for the pod-shaped composite material spatial thin-walled deployable structure;

[0008] The Latin hypercube sampling method is used to select the optimal sample points for spatially expandable structural homogenization within the range of structural parameters and construct the optimal sample library.

[0009] Based on the optimization variables in the optimal sample library, a finite element analysis model of a pod-shaped composite spatial thin-walled deployable structure is constructed;

[0010] An improved Hashin-Puck damage failure criterion is used as a basis for determining the failure mode of the fiber and matrix of a pod-shaped composite material. After failure occurs, a bilinear stiffness degradation model is used to describe the evolution path of the material stiffness during the damage development process. Analysis results are obtained based on the finite element analysis model, and the analysis results include the optimization target of the multi-objective optimization. The optimization variables of the finite element analysis model and the optimization target of the multi-objective optimization are used as the target data set.

[0011] Construct a random forest model based on adaptive particle swarm optimization as a proxy model, and use the target dataset to train the proxy model to obtain the trained proxy model;

[0012] The range of optimization variables is set, and the multi-objective optimization algorithm of NSGA-Ⅲ is used to calculate the Pareto frontier optimal solution by calling the proxy model. Based on the structural parameters in the Pareto frontier optimal solution, the optimal pod-shaped composite material spatial thin-walled deployable structure is obtained.

[0013] In a second aspect of the present invention, an electronic device is provided. The electronic device comprises at least one processor; and a memory communicatively connected to the at least one processor; the memory storing instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method of the first aspect of the present invention.

[0014] Compared with the prior art, the present invention has the following beneficial technical effects:

[0015] This application combines the improved Hashin–Puck damage criterion with the bilinear degradation model to introduce the shear and normal stress coupling effect, which is particularly suitable for the interlaminar effect analysis of multi-layer composite materials. It can more realistically reflect the material behavior under complex stress conditions. It can more accurately describe various failure modes such as fiber breakage, matrix cracking and interlaminar delamination, avoid the sudden return of stiffness to zero, and improve the accuracy of failure prediction. This application proposes a random forest model based on adaptive particle swarm optimization as a proxy model. The prediction results can be directly output through training with a data set obtained by a small amount of finite element calculations, which significantly reduces the computational complexity and greatly improves the computational efficiency. The axial bearing capacity and folding performance of the structure after unfolding are comprehensively improved through multi-objective optimization methods, balancing multiple performance requirements. The optimized structure can exhibit better mechanical properties and adaptability to different scenarios in complex spatial environments.

[0016] It should be understood that the contents described in the summary of the invention are not intended to limit the key or important features of the embodiments of the present invention, nor are they intended to limit the scope of the present invention. Other features of the present invention will become readily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The above and other features, advantages and aspects of the embodiments of the present invention will become more apparent with reference to the following detailed description in conjunction with the accompanying drawings. In the accompanying drawings, the same or similar reference numerals represent the same or similar elements, wherein:

[0018] Figure 1 A flowchart of a multi-objective optimization method for a pod-shaped composite material spatial thin-wall deployable structure according to an embodiment of the present invention is shown;

[0019] Figure 2 A schematic diagram of a pod-shaped cross-section thin-walled structure according to an embodiment of the present invention is shown;

[0020] Figure 3 A schematic diagram of a pod-shaped cross-section thin-wall structure according to an embodiment of the present invention is shown;

[0021] Figure 4 A simplified schematic diagram of a finite element winding simulation geometric model of a pod-shaped cross-section rod according to an embodiment of the present invention is shown;

[0022] Figure 5 A schematic diagram of the construction process of a simplified finite element winding simulation geometric model of a pod-shaped cross-section rod according to an embodiment of the present invention is shown;

[0023] Figure 6 shows a block diagram of an exemplary electronic device capable of implementing embodiments of the present invention;

[0024] Among them, 600 is an electronic device, 601 is a computing unit, 602 is a ROM, 603 is a RAM, 604 is a bus, 605 is an I / O interface, 606 is an input unit, 607 is an output unit, 608 is a storage unit, and 609 is a communication unit. DETAILED DESCRIPTION

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0026] In this document, the term "and / or" simply describes a relationship between related objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. Furthermore, the character " / " in this document generally indicates that the related objects are in an "or" relationship.

[0027] Figure 1 A flow chart of a multi-objective optimization method for a pod-shaped composite material spatial thin-wall deployable structure according to an embodiment of the present invention is shown.

[0028] The method includes:

[0029] S101. Set the optimization variables, optimization objectives and constraints of the pod-shaped composite material spatial thin-walled deployable structure.

[0030] In this embodiment, the pod-shaped composite material is, for example, a pod stem composite material.

[0031] In this embodiment, if Figure 2 and Figure 3 As shown in the figure, the optimization objectives are determined according to the process requirements. The optimization objectives include: maximum axial compressive buckling load, minimum folding moment, and minimum failure index of the pod rod when rolled up based on the improved Hashin-Puck damage failure criterion. The optimization variables (i.e., structural parameters) of the pod-shaped composite material spatial thin-walled deployable structure include: ply thickness (t), ply angle (ψ), curvature radius (including side arc radius (r1) and center arc radius (r2)), flash length (ω), and center angle (θ). The constraint condition is the unit length density of the spatial deployable structure. L represents the length of the pod rod composite material.

[0032] The parameter range of the pod-shaped composite material space thin-walled deployable structure is shown in Table 2:

[0033]

[0034] Table 2

[0035] S102. Selecting optimal sample points for spatially expandable structural homogenization within the interval of structural parameters by using the Latin hypercube sampling method to construct an optimal sample library.

[0036] In this embodiment, the Latin hypercube sampling method is used to select the optimal sample points for spatially expandable structural homogenization within the interval range of the structural parameters to construct the optimal sample library, specifically including:

[0037] The dimension of the structural parameter space of the optimal Latin hypercube sampling method is determined based on the number of optimization variables N, and H sample points are selected. The steps for selecting sample points are as follows: divide each dimension of the parameter space into H non-overlapping intervals, so that each interval has the same probability; randomly select H points from each interval in each dimension of the parameter space; randomly select the points selected in the previous step from each dimension of the parameter space, and form the selected points into a sample vector (1, 2...N) T , H sample points form an N×H sample point matrix; the number of sampling is set to n, and n N×H sample point matrices are established; the discretized energy criterion is used to perform a uniform evaluation on the established sample point matrix, and the optimal matrix is ​​evaluated and selected under this criterion as the optimal sample matrix to obtain the optimal sample library. The sample points in the optimal sample matrix are used as the optimal sample points.

[0038] As an implementation of this embodiment, the total number of optimization variables is set to 6, namely: ply thickness (t), ply angle (ψ), curvature radius (including side arc radius (r1) and center arc radius (r2)), flash length (ω), and center angle (θ). The variable space dimension of the optimal Latin hypercube sampling method is determined, and 80 sample points are selected. The specific sampling process is as follows: First, each dimension is divided into 80 non-overlapping intervals, and the probability of each interval is equal. Then, 80 sample points are randomly selected from each interval of each dimension. The selected sample points are randomly selected from each dimension and combined into a sample vector (1,2,3,4,5,6)^T, ultimately forming a 6×80 sample point matrix containing 80 sample points. The number of sampling is set to 40, generating 40 groups of 6×80 dimensional sample point matrices. Then, the discretized energy criterion is used to evaluate the uniformity of all sample point matrices, and the sample matrix with the best uniformity under this criterion is finally selected as the final sample set.

[0039] The discretization energy criterion is an indicator used to evaluate or optimize the uniformity of the spatial distribution of sampling points. It quantifies the degree of spatial dispersion by calculating the "energy" between sample points. The goal is to make the sample points cover the parameter space as evenly as possible, avoiding clustering or holes. The discretization energy criterion focuses more on the differences between sample points, ensuring that the sample points are not only evenly distributed but also consistent. Riesz s-Energy is selected to measure the repulsive energy of all pairs of points in the point set, where the energy E s The lower (P) is, the better the uniformity of the sample matrix is. The formula is as follows:

[0040]

[0041] Among them, E s(P) represents repulsion energy; s represents repulsion index, which is a positive real number used to control the speed of "energy decay". The smaller s is, the greater the contribution of distant points to energy (global uniformity), and the larger s is, the more significant the impact of close points on energy (local uniformity). Setting s = 2 makes the harmonic energy calculation stable and balances global and local characteristics; || p i -p j || represents point p i and p j The Euclidean distance between two points reflects the degree of separation between them in space. The smaller the distance, the closer the two points are, and the greater the contribution to energy (the stronger the repulsion). The formula is as follows:

[0042]

[0043] Among them, p i 、p j Respectively represent the i-th and i-th sample points in the point set P; is the coordinate value of the i-th sample point in the k-th dimension; is the coordinate value of the jth sample point in the kth dimension; d is the number of dimensions of the space where the sample point is located; k is the number of dimensions, that is, the subscript index variable for dimension-by-dimensional summation.

[0044] In some embodiments, the samples can also be normalized, and then the optimal Latin hypercube sampling method can be used to select the uniform optimal sample points of the spatially expandable structure. That is, the structural parameters are first standardized using the Min-Max normalization method. Specifically, for each variable (i.e., each column of the sample point matrix), its maximum and minimum values ​​are first determined, and the value of the variable is mapped to the interval [0, 1] using the following formula.

[0045] S103. Based on the optimized variables in the optimal sample library, a finite element analysis model of a pod-shaped composite material spatial thin-walled deployable structure is constructed.

[0046] In the simplified model, since the pod-shaped cross-section rod is a symmetrical component, finite element analysis can be performed on half of the pod-shaped cross-section rod to simplify the model and speed up the analysis.

[0047] As an implementation method of this embodiment, Figure 4 A simplified finite element winding simulation geometric model is shown taking a pod-shaped cross-section rod as an example. For example, the cross-sectional parameters of the pod rod in the finite element simulation are: side arc radius r1 = 40 mm, center angle θ = 45°, center arc radius r2 = 45 mm, rod length L = 2000 mm, burr length w = 5 mm, the 0° direction of the composite material layup is the axial direction of the pod rod, the layup angles of the side arc and center arc segments of the pod rod are [45, -45, -45, 45], and the single layer thickness of the composite material layup is t = 0.02 mm.

[0048] like Figure 5 As shown, the simplified finite element winding simulation geometric model is constructed as follows:

[0049] (1) Simplified model:

[0050] In the entire model, create the following parts: upper rolling shaft, lower rolling shaft, reel assembly, and pod-shaped cross-section rod part simplified into half.

[0051] (2) Determine the analysis steps:

[0052] (2.1) Flattening: Apply loads to the top and bottom of the simplified pod-shaped cross-section rod to completely flatten it;

[0053] (2.2) End clamping: fix the roller and the front end of the simplified pod-shaped cross-section rod to each other;

[0054] (2.3) Tension applied at the tail end: Apply a load in the opposite direction to the tail end of the simplified pod-shaped cross-section rod;

[0055] (2.4) Winding: The roller drives the simplified pod-shaped cross-section rod to rotate at a constant speed, and the pod-shaped cross-section rod is completely flattened by the upper and lower rolling shafts and is gradually wound by the roller.

[0056] (3) Set the connection relationship between each component:

[0057] (3.1) In the flattening analysis step, the flash edge of the simplified pod-shaped section is bound so that the two surfaces are glued together and no longer separated. The degrees of freedom of the flash edge node are not considered during the analysis process, which shortens the calculation time.

[0058] (3.2) The roller and the upper and lower rolling axes are all constrained by rigid bodies, and the reference point is defined as the center of mass of the rigid body;

[0059] (3.3) In the winding analysis step, the upper and lower outer surfaces of the simplified pod-shaped cross-section rod are in contact with the outer surfaces of the upper and lower rolling shafts respectively, and the kinematic contact method is used for analysis.

[0060] (4) Load application: Based on the actual situation, determine the load application method for the simplified pod-shaped cross-section rod winding process.

[0061] (4.1) In the flattening analysis step, the front end of the simplified pod-shaped cross-section rod is flattened by applying displacement to the upper and lower rolling axes;

[0062] (4.2) In the end compression analysis step, a pressure (100 MPa) along the negative y-axis is applied to the simplified pod-shaped cross-section rod (30 mm from the end of the pod-shaped cross-section) and continues to act during the winding process;

[0063] (4.3) In the analysis step of applying tension at the tail end, a force of 10 N is applied to the tail end of the simplified pod-shaped cross-section rod along the negative direction of the x-axis, and the force is applied throughout the winding process to ensure that the pod-shaped cross-section rod remains horizontal during the winding process.

[0064] (5) Grid division: For the simplified pod-shaped cross-section rod, a refined grid is used in the first 30 mm of the end, with a grid setting of 1 mm, and the grid of the remaining part is set to a larger grid, which can greatly shorten the calculation time.

[0065] (6) Simplify the model and perform finite element analysis.

[0066] S104. Using the improved Hashin-Puck damage failure criterion as a basis for determining the failure mode of the fiber and matrix of the pod-shaped composite material, after failure occurs, using a bilinear stiffness degradation model to describe the evolution path of the material stiffness during the damage development process, and obtaining analysis results based on the finite element analysis model, the analysis results including the optimization target of the multi-objective optimization; and using the optimization variables of the finite element analysis model and the optimization target of the multi-objective optimization as target data sets.

[0067] In this embodiment, the improved Hashin-Puck damage failure criterion is used as a basis for judging the failure mode of the fiber and matrix of the pod-shaped composite material, and the failure mode is determined by stress analysis.

[0068] The improved Hashin-Puck damage failure criterion includes:

[0069] When the normal stress in the main direction of the material is not less than 0, if the fracture energy density of the fiber stretching is not less than 1, the fiber tensile failure occurs; specifically, it is expressed as:

[0070] When σ 11 When ≥0, the fiber tensile failure is:

[0071]

[0072] When the normal stress in the main direction of the material is less than 0, if the fracture energy density of the fiber compression is not less than 1, the fiber compression failure occurs; specifically, it is expressed as:

[0073] When σ 11 When <0, the fiber compression failure is:

[0074]

[0075] When the normal stress component of the fracture surface is greater than 0, if the fracture energy density of the matrix tension is not less than 1, the matrix tension failure occurs; specifically, it is expressed as:

[0076] When σ nWhen (θ)>0, the matrix tensile failure criterion is:

[0077]

[0078] When the normal stress component of the fracture surface is less than 0, if the fracture energy density of the matrix compression is not less than 1, the matrix compression failure occurs; specifically, it is expressed as:

[0079] When σ n When (θ)<0, the matrix failure criterion is:

[0080]

[0081] Among them, F mc is the fracture energy density of matrix compression; F mt is the fracture energy density of matrix tension; F fc F is the fracture energy density of fiber compression; ft is the fracture energy density of fiber tension; the parameters ft are the fiber tension direction, fc are the fiber compression direction, mt are the matrix tension direction, and mc are the matrix compression direction; σ 11 The first normal stress in the main direction of the material; S is the shear strength, where S 12 、S 23 and S 13 Respectively represent the shear strength in their respective directions; X T Indicates the tensile strength along the fiber reinforcement direction; X C Indicates the compressive strength along the fiber reinforcement direction; Y T Indicates the strength perpendicular to the tensile direction of the fiber; σ n (θ) is the normal direction of the fracture surface; σ nt (θ) is the tangential stress component of the fracture surface; σ nl (θ) is the stress component in the fiber direction.

[0082] σ n =σ 22 cos 2 θ+σ 33 sin 2 θ+2σ 23 cosθsinθ

[0083] σ nl =σ 12 cosθ+σ 13 sinθ

[0084] σ nt =-σ 22 cosθsinθ+σ 33 cosθsinθ+2σ 23 (2cos 2 θ-1)

[0085]

[0086] Among them, σ 22 is the second normal stress in the main direction of the material; σ 33 is the third normal stress in the main direction of the material; σ 12 , σ 13 and σ 23 Represents the shear stress in the corresponding direction; Y C Indicates the strength perpendicular to the fiber compression direction, μ nl Characterizes the influence factor of normal tensile stress corresponding to longitudinal shear stress on failure, μ nt Characterizes the "amplification" or "inhibition" effect of normal tensile stress on failure corresponding to tangential shear stress.

[0087] Furthermore, after failure occurs, a bilinear stiffness degradation model is used to describe the evolution path of material stiffness during damage development, and analysis results are obtained based on the finite element analysis model. Specifically, the bilinear stiffness degradation criterion is used to determine the onset of damage to the matrix, and the formula is as follows:

[0088]

[0089] Among them, d i represents the damage progression index of the i-th failure mode, which is used to control the linear degradation of the corresponding stiffness component; represents the damage initiation equivalent displacement, represents the final failure equivalent displacement.

[0090]

[0091] in, is the equivalent stress at the onset of damage; σ i,wq is the equivalent stress; δ i,eq is the equivalent displacement; G i is the fracture energy of the i-th failure mode; F i is the failure criterion function value under the i-th failure mode, F i There are three situations: i =1 means that the failure mode happens to occur, F i <1 means no failure, F i >1 indicates that the failure condition has been exceeded.

[0092] The bilinear degradation curve is used to model the staged decrease of material stiffness and strength, which can truly reflect the nonlinear softening behavior from microcrack initiation to macro fracture during the damage development process.

[0093] In this embodiment, analysis results are obtained based on the finite element analysis model, and the analysis results include optimization targets of multi-objective optimization; specifically, they include: axial compressive buckling load, folding moment, and failure index of the pod rod when rolled up based on the Hashin-Puck criterion of the pod-shaped composite material spatial thin-walled deployable structure.

[0094] As an implementation method of this embodiment, the improved Hashin-Puck damage failure criterion and bilinear degradation criterion are introduced in the Abaqus solution stage by calling the Vumat subroutine, a corresponding finite element analysis model is established and submitted for calculation, and the required calculation results are derived after the calculation is completed, specifically including the axial compressive buckling load, folding moment, and failure index of the pod-shaped composite material spatial thin-walled deployable structure when the pod rod is rolled up based on the improved Hashin-Puck damage failure criterion; by introducing the bilinear stiffness degradation criterion, Abaqus can smoothly and stably transition to failure after simulating crack initiation, accurately consume fracture energy, and truly reflect the process of the material or interface gradually losing its bearing capacity after damage.

[0095] By coupling the improved Hashin-Puck damage failure criterion with a bilinear stiffness degradation model, it is possible to distinguish between four failure mechanisms: fiber tension / compression and matrix tension / compression. The coupled criterion is more sensitive at the damage initiation point, accurately capturing the complex damage initiation between composite layers. This improves the continuity and accuracy of damage evolution, enhances numerical stability, and avoids instability caused by sudden stiffness changes. The degradation rate can be calibrated based on experimental data, improving the accuracy and robustness of the predictions, enhancing the physical realism of composite failure predictions while ensuring the computational efficiency and reliability of the simulation. This more accurately simulates material failure and load transfer, providing more reliable engineering predictions and enabling continuous damage evolution.

[0096] In this embodiment, the optimization variables of the finite element analysis model (the optimization variables in S103 ) and the optimization objectives of the multi-objective optimization are used as target data sets.

[0097] As an embodiment of the present invention, after obtaining the optimization target of the multi-objective optimization, the optimization variables of the finite element analysis model and the optimization target of the multi-objective optimization can be normalized to obtain a target data set. Specifically, the data set can be normalized using the Min-Max normalization method, including:

[0098] First, for each optimization variable and optimization target, find the maximum and minimum values, and use the following formulas 1 and 2 to scale the values ​​of each optimization variable and optimization target on the variable to the interval [0,1]. Formula 1:

[0099] The formula for normalizing the optimization variables is:

[0100]

[0101] in, represents the original value of the i-th sample of the optimization variable on the j-th optimization target variable, min(x (j) ) represents the minimum value of the j optimization target variables of the optimization target, max(x (j) ) represents the maximum value of the jth optimization target variable of the optimization target, It represents the normalized value of the optimization target, which ranges from [0,1].

[0102] Formula 2: The formula for normalizing the optimization target is:

[0103]

[0104] in, Indicates the original value of the i-th sample of the optimization target on the j-th optimization target variable, min(y (j) ) represents the minimum value of the jth optimization target variable, max(y (j) ) represents the maximum value of the jth optimization target variable of the optimization variable, It represents the normalized value of the optimization variable, which ranges from [0,1].

[0105] Normalization is to eliminate dimensional differences, accelerate model convergence, and prevent features with large values ​​from dominating the training process.

[0106] S105. Construct a random forest model based on adaptive particle swarm optimization as a proxy model, train the proxy model using the target data set, and obtain a trained proxy model.

[0107] In this embodiment, the first 90% normalized data set in the target data set is used as the training group. The input data are: ply thickness, ply angle, curvature radius (side arc and center arc), and center angle. The output targets are: axial compressive buckling load, folding moment, and failure index based on the Hashin-Puck criterion.

[0108] In this embodiment, a random forest model based on adaptive particle swarm optimization is constructed as a proxy model, specifically including:

[0109] S601. Use the APSO optimization algorithm to optimize the hyperparameters of the random forest (RF) model to obtain optimized model parameters.

[0110] S6011. Initialize the particle swarm. The position of each particle corresponds to a set of RF parameters, namely the initialization parameters. The initialization parameters include: particle swarm speed, position, inertia, learning factor, and maximum number of iterations. The hyperparameters that need to be optimized for RF include: the number of trees, maximum depth, minimum number of split samples, minimum number of leaf node samples, and maximum number of features.

[0111] Set the value range of the hyperparameters that RF needs to optimize, and perform constraint processing at the same time. Round the integer parameters (number of trees, maximum depth, minimum number of split samples, minimum number of leaf node samples) to the nearest integer, and keep the floating point precision for the proportional parameters (maximum number of features).

[0112] S6012. Calculate the fitness of each particle: The fitness function is a constraint condition for APSO algorithm optimization. By calculating the fitness of each particle and comparing them, the position of the updated particle can be determined. When the global fitness reaches the maximum, each particle is in its optimal position. In this embodiment, the errors of multiple optimization objectives are integrated into a single fitness value. The fitness function and mean square error formula are as follows:

[0113] Fitness(x i )=w1·MSE(F 屈曲 )+w2·MSE(M 折叠 )+w3·MSE(D Hashin-Puck )

[0114]

[0115] Among them, MSE(F 屈曲 ) is the mean square error of the buckling load prediction value, MSE(M 折叠 ) is the mean square error of the folding moment prediction value, MSE(D Hashin-Puck ) is the mean square error of the failure index prediction value, w1 is the weight of the axial compressive buckling load, w2 is the weight of the folding moment, and w3 is the weight of the failure index. In order to balance multiple objectives, equal weights are used to make w1 = w2 = w3 = 1 / 3); y true_i Represents the true value of the i-th sample, represents the predicted value of the i-th sample, and n is the total number of samples.

[0116] In the fitness function, MSE is calculated by 5-fold cross validation, and the formula is:

[0117]

[0118] Among them, MSE s (O i ) is the sth compromise output O iThe mean square error of ; e represents the number of folds of data division in cross-validation, that is, the data set is divided into e subsets.

[0119] S6013, update individual optimum and global optimum: find the individual optimum of each particle and set the optimal position of the particle in the current iteration as the global optimum; where p best is the optimal position of the current particle, g best is the global optimal position.

[0120] For each particle i, if the position x of the current iteration i (t) is better than the previous individual optimal position p best,i (t-1), then update:

[0121]

[0122] where f(x i (t)) is the objective function, x i (t) is the position of particle i at the tth iteration.

[0123] Global optimal position g best The update formula is:

[0124]

[0125] That is, the best one is selected from the individual optimal values ​​of all particles as the global optimal one, that is, the p values ​​of all individual particles are compared. best The fitness value, the best fitness value p best Position as the global optimal position g best .

[0126] S6014. Adjust the inertia weight and acceleration coefficient according to the adaptive strategy: The inertia weight w and acceleration coefficients c1 and c2 will be adaptively adjusted with the algebraic t to balance exploration and development. The adaptive inertia weight formula is as follows:

[0127]

[0128] Among them, ω(t) is the inertia weight at the tth iteration; ω max is the maximum inertia weight, set to 0.9; ω min The minimum inertia weight is set to 0.4; T max is the maximum number of iterations, set to 100.

[0129] The acceleration factor formula is as follows:

[0130]

[0131] Among them, c 1max is the maximum value of c1; c1min is the minimum value of c1; c 2max is the maximum value of c2; c 2min is the minimum value of c2; t is the number of generations; T is the number of iterations; for example, set c 1max =2.5,c 1min =0.5,c 2min =0.5,c 2max =2.5.

[0132] S6015. Update the velocity and position of the particle.

[0133] The formula for updating particle velocity is as follows:

[0134]

[0135] in, The velocity of particle i in the tth generation, w is the inertia weight, which is initially 0.9 and linearly decreases to 0.4; c1 and c2 are acceleration coefficients, where c1 represents the individual learning factor, usually 2.0; c2 represents the social learning factor, usually 2.0; d1 and d2 are random numbers uniformly distributed on (0, 1); p best is the optimal position of the current particle, g best is the global optimal position;

[0136] The formula for updating the particle position is as follows:

[0137]

[0138] in, represents the position of particle i in generation t; represents the position of particle i in the t+1 generation; represents the velocity of particle i in the t+1th generation.

[0139] S6016. Iterate the above S6011-S6015 until the set maximum number of iterations is reached, and output the model hyperparameters corresponding to the global optimal fitness.

[0140] S602: Construct an initial random forest proxy model. The specific process is as follows:

[0141] S6021. The sample characteristics of the dataset used in this embodiment, i.e., the optimization variables, are m=5. N samples are extracted from the training set of the normalized dataset using the Bootstrap sampling method with replacement. trees A training subset S i In this embodiment, N is selected trees =5.

[0142] S6022. For each subset S i, at each split, randomly select from m = 5 features candidate features, m represents the total number of features in the data set (i.e., optimization variables: ply thickness, ply radius, etc.); m try Indicates the number of randomly selected split features for each node of a single decision tree when splitting; using the mean square error (MSE) as the splitting criterion, select the features and split points that minimize the MSE. The specific formula is as follows:

[0143]

[0144] in, is the mean of the sample responses within the node, y i is the sample response value. Splitting stops when the number of sample nodes is less than 5, the number of leaf node samples is less than 1, or the tree depth is greater than 10. During this process, each tree is allowed to grow freely without pruning.

[0145] S6023. Repeat the above S6021-S6022 to form a series of decision trees, and finally form a forest.

[0146] S6024. Aggregate the results of all decision trees and take the arithmetic mean as the final output. The formula is as follows:

[0147]

[0148] in, is the final prediction value, Q is the total number of decision trees, h t (x) The prediction of the t-th tree for sample x.

[0149] S603: Input the optimized model parameters into the initial random forest proxy model.

[0150] The hyperparameters optimized by APSO, including the number of trees p1, maximum depth p2, minimum number of split samples p3, minimum number of leaf node samples p4, and maximum number of features p5, were input into the constructed initial RF proxy model. The normalized last 10% of the data set was used as the test group. The axial compressive buckling load, folding moment, and failure index based on the Hashin-Puck criterion of the test group were calculated using the RF proxy model optimized by the APSO algorithm. The quality of the proxy model was then verified using the root mean square error and determination coefficient formula.

[0151] The root mean square error RMSE is:

[0152]

[0153] The formula for the coefficient of determination R-squared statistic is:

[0154]

[0155] Among them, N' is the number of all samples in the data set, y true_i The true value of the i-th sample, The predicted value of the i-th sample, Represents the square of the prediction error of the i-th sample.

[0156] When the average RMSE of all target variables is less than 5% and the R-squared statistic of all target variables is R 2 >0.95, which proves that the proxy model has high accuracy and the predicted mechanical properties are consistent with the simulation results, proving that the PSO-CNN proxy model can achieve efficient and high-precision prediction of the mechanical properties of composite materials;

[0157] By optimizing the number of filters, convolution kernel size, number of fully connected neurons, and learning rate of the CNN using PSO, combined with multi-layer nonlinear transformations using the ReLU activation function, the proxy model is able to efficiently extract the complex features of composite pod rods and accurately predict mechanical properties. The introduction of activation functions in both convolutional and fully connected layers ensures the model's ability to model nonlinear relationships, while PSO's global search eliminates the limitations of manual parameter adjustment and significantly improves predictive performance. The convolutional neural network is then optimized using a particle swarm algorithm, addressing the difficulty of manually selecting optimal hyperparameters for the convolutional neural network.

[0158] S106. Set the range of optimization variables, use the NSGA-III multi-objective optimization algorithm to call the agent model to obtain the Pareto frontier optimal solution as the optimal pod rod structure.

[0159] The multi-objective optimization algorithm using NSGA-III obtains the Pareto frontier optimal solution by calling the surrogate model, including:

[0160] S1061. First, the structural parameters are converted into a continuous coding form according to their respective upper / lower limits. A group of structural parameters in the continuous coding form are used as individuals. An initial parent population is randomly generated. The fitness of each individual is calculated, and a reference direction is generated.

[0161] In this embodiment, each individual X i is a vector consisting of a set of structural parameters:

[0162] X i =[x1,x2,x3,…,x n ]

[0163] Where n is the number of structural parameters, X i Represents a vector composed of structural parameters, that is, a set of structural parameter combinations, such as: X i =[layer thickness, layer angle, curvature radius...]; xj It means X i The jth parameter represents a degree of freedom in the optimization problem. For example, if j = 1, it represents the thickness of the general layer. Each structural parameter x j There is a corresponding upper and lower limit, denoted as x j min and x j min ; Structural parameters are optimization variables.

[0164] For each individual x i Its structural parameters are randomly generated in the following way:

[0165]

[0166] Randomly generate the initial parent population:

[0167]

[0168] Where N" is the population size, and each component is drawn uniformly within its allowable range.

[0169] In this embodiment, generating a reference direction includes:

[0170] Generate H reference directions uniformly in the 3D target space (maximum buckling load, minimum folding moment, minimum failure index) The Das-Dennis method (uniform weight vector generation method) is used to ensure that the direction covers the entire interval and at the same time for all r j Standardize||r j ||=1;

[0171] S1062: For each individual in the parent population, call the proxy model and determine the constraint conditions to predict the target value.

[0172] In this example, it is necessary to determine the optimization constraints for the pod-shaped composite material space thin-wall deployable structure:

[0173] ld=4ρt(τ+θd1+θd2)

[0174] Where ld is the linear mass density, ρ is the material density, t is the ply thickness, and τ is a length parameter of the structure (a pod-shaped composite material spatial thin-walled deployable structure). d1 is the first random number, d2 is the second random number, and d1 and d2 are uniformly distributed on (0, 1).

[0175] For each individual x in the parent generation i The target value is quickly calculated using the APSO-RF proxy model. The formula is as follows:

[0176]

[0177] The maximization objective (compressive buckling load) is then negated and converted into a unified "minimization" form to obtain the fitness vector for non-dominated sorting.

[0178] S1063. Perform selection, crossover, and mutation operations on the parent population to generate a child population, and merge the parent population with the child population to obtain a mixed population.

[0179] In this embodiment, we first select an operator: a binary tournament is used to randomly select two individuals from the incidental data for comparison, and N independent tournaments are performed, each time from P t The winning individual is copied to the parent pool as the "parent" for subsequent crossover and mutation; secondly, the crossover operator: the individual pairs (X p , X q ) with probability p c Execute the crossover operator and produce two offspring (Y p , Y q ); then perform mutation operator: each offspring Y obtained after crossover is transformed into a new offspring with the probability p related to the dimension m =1 / d applies polynomial mutation to each component independently, and the mutation formula is:

[0180]

[0181] Among them, η m Take 40 as the polynomial variation distribution index;

[0182] After completing crossover and mutation, we get N b Each of them brings its own individuals, forming a descendant population:

[0183] Q t ={y i |i=1,…,N b}

[0184] Finally, the parent P t With offspring Q t Merge to obtain a mixed population so that they can compete together in the subsequent S1064:

[0185] R t =P t ∪Q t ,|R t |=2N b

[0186] S1064. Perform non-dominated sorting on the mixed population in sequence to obtain each frontier layer, assign individuals in the mixed population to the reference direction with the closest distance, and fill each frontier layer with individuals in sequence;

[0187] In this embodiment, firstly, the mixed population R t The non-dominated sorting is performed in sequence to obtain the first frontier layer F1, the second frontier layer F2, etc.; the target value is then translated and scaled within each frontier layer, and a simple pre-normalization is performed based on the ideal point to ensure the comparability of different targets; then, for each individual X and each reference direction r j Calculate the projection distance, assign individuals to the nearest reference direction, count the number of individuals in each direction (i.e., crowding), and calculate the projection distance formula as follows:

[0188]

[0189] Among them, z * For the ideal point.

[0190] Finally, the new generation of P is filled starting from the frontier layer F1. t+1 , until the cumulative number of individuals is close to N. For the layer FL that cannot be filled in the last layer, the individuals assigned to the reference direction with the lowest congestion are preferentially selected.

[0191] The calculation formula for crowding distance is as follows:

[0192]

[0193] in, is the crowding distance contribution of individual i on the mth objective function, and are the objective function values ​​of the adjacent individuals of individual i on the target, and are the maximum and minimum values ​​on the target m, respectively.

[0194] S1065. Iterate the above S1062-S1064 until convergence to obtain a Pareto solution set; wherein the convergence condition may be that the maximum number of iterations is reached or the population fitness tends to converge.

[0195] If the maximum number of iterations is reached or there is no significant improvement in the Pareto frontier over multiple generations, the iteration is terminated; otherwise, the number of iterations is increased by 1 and the process returns to S1062.

[0196] S1066. Select the Pareto frontier optimal solution from the Pareto solution set using the TOPSIS method.

[0197] For each Pareto solution x in the Pareto solution set i The three target values ​​f j (x i ) (maximum buckling load, minimum folding moment, minimum failure index) are normalized to eliminate dimensional differences and make the various objectives directly comparable. The formula is:

[0198]

[0199] Where x i represents the i-th Pareto solution, f j (x i ) represents the solution x i The original value at the jth target corresponds to the “maximum buckling load” (positive value) when j=1, the “folding moment” (minimization target) when j=2, and the “failure index” (minimization target) when j=3. represents the Pareto solution x i The normalized value of the j-th target.

[0200] The maximum axial compressive buckling load, minimum folding moment, and minimum failure index of the pod rod when rolled up based on the Hashin-Puck criterion in the Pareto solution set are taken as the ideal solution, and the minimum axial compressive buckling load, maximum folding moment, and maximum failure index of the pod rod when rolled up based on the Hashin-Puck criterion are taken as the negative ideal solution. The distance from each Pareto solution to the ideal solution and the negative ideal solution is calculated:

[0201]

[0202] Where C i No relative progress, represents the distance from the ith solution to the ideal solution, Represents the distance from the i-th solution to the negative ideal solution.

[0203] The solution with the largest relative progress is taken as the optimal solution, that is, press C i Sort the vectors from largest to smallest and take the design vector X* corresponding to the largest one as the optimal structural parameters of the pod-shaped composite material spatial thin-wall deployable structure (i.e., optimization variables: ply thickness (t), ply angle (ψ), curvature radius (including side arc radius (r1) and center arc radius (r2)), flash length (ω), and center angle (θ)). The optimal pod-shaped composite material spatial thin-wall deployable structure is constructed with the optimal structural parameters, i.e., the optimized pod-shaped composite material spatial thin-wall deployable structure.

[0204] In some embodiments, after obtaining the optimization results, the optimized pod-shaped composite spatial thin-wall deployable structure is experimentally verified. The experiments include testing the axial compressive buckling load, the folding moment, and the failure exponential moment based on the Hashin-Puck criterion to verify whether the optimization results meet the design objectives.

[0205] This paper proposes a multi-objective optimization method for pod-shaped composite thin-walled deployable spatial structures. The optimization objectives are maximum axial compressive buckling load, minimum folding moment, and a failure index based on the Hashin–Puck criterion, with unit length density as a constraint. To significantly improve the convergence rate and solution diversity of the optimization process, the paper innovatively incorporates the adaptive particle swarm optimization (APSO) algorithm into the hyperparameter tuning of a random forest (RF) surrogate model, constructing a high-precision and high-performance APSO-RF surrogate model. This introduced APSO-RF surrogate model significantly reduces simulation overhead while ensuring evaluation accuracy.

[0206] The simplified finite element rollup model proposed in this paper achieves rapid prediction of the axial compressive buckling load, folding moment, and Hashin–Puck failure index of pod-shaped structures by rationally reducing the complexity of simulation modeling and parameter setting. Compared with traditional high-fidelity simulation and experimental methods, this model significantly reduces the degrees of freedom and solution time while preserving key mechanical properties, significantly improving computational efficiency. It is also easy to deploy and can output multiple performance indicators in real time during the design iteration phase, demonstrating its high engineering practical value.

[0207] The present invention introduces an improved Hashin–Puck damage criterion combined with a bilinear degradation model. Compared with the traditional Hashin criterion, firstly, the introduction of the Hashin–Puck multi-mode failure description can distinguish between the four failure mechanisms of fiber tension / compression and matrix tension / compression, and accurately capture the complex damage initiation between composite layers; secondly, a bilinear degradation curve is used to model the material stiffness and strength in a staged manner, which can truly reflect the nonlinear softening behavior from microcrack initiation to macroscopic fracture during the damage development process; thirdly, the coupled criterion is more sensitive at the initial point of damage, and the degradation rate can be calibrated according to experimental data, which improves the accuracy and robustness of the prediction. The introduction of this improved criterion not only enhances the physical reality of composite material failure prediction, but also ensures the computational efficiency and reliability of the simulation.

[0208] The present invention proposes a multi-objective optimization method for pod-shaped composite spatial thin-walled deployable structures. Compared with traditional methods, this method is no longer limited to a single performance indicator, but simultaneously incorporates axial compressive buckling load, folding moment and failure risk based on the Hashin–Puck criterion into the optimization objectives. By constructing an APSO-RF efficient proxy model and coordinating with the NSGA-III algorithm to simultaneously search for multiple objectives in a high-dimensional design space, a complete Pareto frontier solution set is generated, providing multiple optimal compromise solutions for engineering design. NSGA-III maintains group diversity with the help of reference direction and crowding distance, preventing the algorithm from falling into local optimality, thereby ensuring uniform distribution and coverage of solution sets under different working conditions. Ultimately, this method maximizes the structural buckling bearing capacity, optimizes the folding performance and minimizes the failure risk, and improves the overall mechanical properties under multiple constraints, providing a systematic and efficient technical path for the lightweight and safety design of composite spatial thin-walled deployable structural members.

[0209] According to an embodiment of the present invention, the present invention further provides an electronic device.

[0210] Figure 6 A schematic block diagram of an electronic device 600 that can be used to implement an embodiment of the present invention is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital assistants, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present invention described and / or claimed herein.

[0211] The electronic device 600 includes a computing unit 601 that can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 602 or a computer program loaded from a storage unit 608 into a random access memory (RAM) 603. Various programs and data required for the operation of the electronic device 600 can also be stored in the RAM 603. The computing unit 601, the ROM 602, and the RAM 603 are connected to each other via a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.

[0212] Multiple components in the electronic device 600 are connected to the I / O interface 605, including an input unit 606, such as a keyboard, a mouse, etc.; an output unit 607, such as various types of displays, speakers, etc.; a storage unit 608, such as a magnetic disk, an optical disk, etc.; and a communication unit 609, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 609 allows the electronic device 600 to exchange information / data with other devices via a computer network such as the Internet and / or various telecommunication networks.

[0213] The computing unit 601 can be a variety of general-purpose and / or specialized processing components with processing and computing capabilities. Some examples of the computing unit 601 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units that run machine learning model algorithms, a digital signal processor (DSP), and any appropriate processor, controller, microcontroller, etc. The computing unit 601 performs the various methods and processes described above, such as methods S101 to S106. For example, in some embodiments, methods S101 to S106 can be implemented as a computer software program that is tangibly contained in a machine-readable medium, such as a storage unit 608. In some embodiments, part or all of the computer program can be loaded and / or installed on the electronic device 600 via the ROM 602 and / or the communication unit 609. When the computer program is loaded into the RAM 603 and executed by the computing unit 601, one or more steps of the methods S101 to S106 described above can be performed. Alternatively, in other embodiments, the computing unit 601 may be configured to execute methods S101 to S106 in any other appropriate manner (eg, by means of firmware).

[0214] Various embodiments of the systems and techniques described herein can be implemented in digital electronic circuit systems, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on a chip (SOCs), programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments can include being implemented in one or more computer programs that are executable and / or interpreted on a programmable system comprising at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0215] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in the present invention can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solution of the present invention can be achieved. This is not limited herein.

[0216] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

Claims

1. A multi-objective optimization method for a pod-shaped composite material space thin-wall deployable structure, characterized in that: include: Set the optimization variables, optimization objectives and constraints for the pod-shaped composite material spatial thin-walled deployable structure; The Latin hypercube sampling method is used to select the optimal sample points for spatially expandable structural homogenization within the range of structural parameters and construct the optimal sample library. Based on the optimization variables in the optimal sample library, a finite element analysis model of a pod-shaped composite spatial thin-walled deployable structure is constructed; The improved Hashin-Puck damage failure criterion is used as the basis for judging the failure mode of the fiber and matrix of the pod-shaped composite material. After failure occurs, a bilinear stiffness degradation model is used to describe the evolution path of the material stiffness during the damage development process. The analysis results are obtained based on the finite element analysis model, and the analysis results include the optimization objectives of the multi-objective optimization. The optimization variables of the finite element analysis model and the optimization objectives of the multi-objective optimization are used as target data sets; Construct a random forest model based on adaptive particle swarm optimization as a proxy model, train the proxy model using the target dataset, and obtain the trained proxy model; The range of optimization variables is set, and the multi-objective optimization algorithm of NSGA-Ⅲ is used to calculate the Pareto frontier optimal solution by calling the proxy model. Based on the structural parameters in the Pareto frontier optimal solution, the optimal pod-shaped composite material spatial thin-walled deployable structure is obtained.

2. The method according to claim 1, characterized in that The method of selecting the optimal sample points for spatially expandable structural homogenization within the interval of the structural parameters by the Latin hypercube sampling method includes: Divide each dimensional space into several non-overlapping intervals so that each interval has the same probability; randomly select several sample points from each interval in each dimensional space, and form the sample vectors from the selected sample points. After several samplings, the sample point matrix is ​​obtained; Using a discretized energy criterion to perform a uniform evaluation on the sample point matrix to obtain an optimal sample matrix; The sample points in the optimal sample matrix are taken as the optimal sample points.

3. The method according to claim 2, characterized in that The discretized energy criterion includes: Among them, E s (P) is the repulsive energy; ||p i -p j || represents point p i and p j The Euclidean distance between them; s is the repulsion index; P is the sample point matrix; p i 、p j Respectively represent the i-th and j-th sample points in the point set P; is the coordinate value of the i-th sample point in the k-th dimension; is the coordinate value of the jth sample point in the kth dimension; d is the dimension of the space where the sample point is located; k is the number of dimensions.

4. The method according to claim 1, wherein The improved Hashin-Puck damage failure criterion includes: When the normal stress in the main direction of the material is not less than 0, if the fracture energy density of the fiber stretching is not less than 1, the fiber tensile failure occurs; When the normal stress in the main direction of the material is less than 0, if the fracture energy density of fiber compression is not less than 1, the fiber compression fails; When the normal stress component of the fracture surface is greater than 0, if the fracture energy density of the matrix tension is not less than 1, the matrix tension fails; When the normal stress component of the fracture surface is less than 0, if the fracture energy density of the matrix compression is not less than 1, the matrix compression fails.

5. The method according to claim 1, characterized in that The bilinear stiffness degradation model is: Among them, d i is the damage progression index of the i-th failure mode; is the equivalent displacement of failure; δ i,eq is the equivalent displacement; is the equivalent displacement at the onset of damage; G i is the fracture energy of the i-th failure mode; is the equivalent stress at the onset of damage; σ i,eq is the equivalent stress; F i is the failure criterion function value under the i-th failure mode.

6. The method according to claim 1, characterized in that After obtaining the optimization target of the multi-objective optimization, the optimization variables of the finite element analysis model and the optimization target of the multi-objective optimization are normalized respectively to obtain the target data set.

7. The method according to claim 6, characterized in that The random forest model based on adaptive particle swarm optimization is constructed; comprising: The APSO optimization algorithm is used to optimize the hyperparameters of the random forest model to obtain the optimized model parameters; Construct an initial random forest proxy model and input the optimized model parameters into the initial random forest proxy model.

8. The method according to claim 1, characterized in that The multi-objective optimization algorithm using NSGA-III calculates the Pareto frontier optimal solution by calling the surrogate model, including: A set of structural parameters in the form of continuous encoding is used as individuals, the initial parent population is randomly generated, the fitness of each individual is calculated, and a reference direction is generated; For each individual in the parent population, the agent model is called and constraints are determined to predict the target value; Perform selection, crossover, and mutation operations on the parent population to generate a child population, and merge the parent population with the child population to obtain a mixed population; Perform non-dominated sorting on the mixed population in turn to obtain each frontier layer, assign individuals in the mixed population to the reference direction with the closest distance, and fill each frontier layer with individuals in turn; Iterate the above process until convergence to obtain the Pareto solution set; The TOPSIS method is used to select the Pareto frontier optimal solution from the Pareto solution set.

9. The method according to claim 8, characterized in that For each individual in the parent population, calling the agent model and determining the constraint conditions to predict the target value includes: Determine the constraint conditions of the pod-shaped composite material space thin-walled deployable structure, and calculate the target value for each individual of the parent generation through the agent model; The constraints are: ld=4ρt(τ+θd1+θd2) Where ld is the linear mass density, ρ is the material density, t is the ply thickness, τ is the length parameter of the pod-shaped composite material spatial thin-walled deployable structure; d1 is the first random number, and d2 is the second random number.

10. An electronic device comprising at least one processor; and a memory communicatively connected to the at least one processor; characterized in that: The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the method according to any one of claims 1 to 9.

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