CN-117763910-B - Antenna substrate vibration fundamental frequency optimization method based on machine learning

CN117763910BCN 117763910 BCN117763910 BCN 117763910BCN-117763910-B

Abstract

An antenna substrate vibration fundamental frequency optimization method based on machine learning belongs to the technical field of large-area thin-wall plate vibration optimization. The method comprises the steps of identifying an active subspace, adaptively constructing a proxy model in the active subspace, calling a Kriging proxy model to estimate a sensitivity index, and optimizing and reconstructing an antenna substrate in a design space. The invention combines the sensitivity analysis method based on the active subspace and the self-adaptive dotting strategy with the Bayesian optimization method, establishes a global optimization framework of the vibration fundamental frequency of the antenna substrate based on machine learning, and can efficiently complete the global optimization design of the fundamental frequency of the large-scale antenna substrate. The optimization verification of the large-scale antenna substrate with complex constraint shows that the method can overcome the problem of premature convergence of the traditional method, can obtain a design with better fundamental frequency under smaller calculation consumption, and greatly improves the efficiency of optimizing the fundamental frequency of the antenna substrate.

Inventors

WANG CHANGGUO
GUO JIAMING
LIU HONGWEI
TAN HUIFENG

Assignees

哈尔滨工业大学

Dates

Publication Date: 20260508
Application Date: 20231225

Claims (2)

1. The method for optimizing the vibration fundamental frequency of the antenna substrate based on machine learning is characterized by comprising the following steps of: Step one, identifying active subspaces Sampling in the antenna substrate initial design space to generate N 0 samples as a set, marking as initial sample set S 0 , selecting N 1 samples from S 0 , marking as S 1 , estimating gradient vector of sample antenna substrate vibration fundamental frequency in S 1 set by finite element simulation and finite difference method By gradient vectors to these S 1 sample points The method comprises the steps of averaging to estimate elements of a covariance matrix C, carrying out feature decomposition on the covariance matrix C to obtain feature values and feature vectors, identifying an active subspace by analyzing the relative sizes among the feature values, and after the active subspace is found, approximating the mapping between an original input variable x 0 and variables in the active subspace to: x 0 ＝W 1 u+W 2 z≈W 1 u (13) In the formula (13), W 1 and W 2 are active subspace vectors and inactive subspace vectors respectively, and u and z are active variables and inactive variables respectively; Step two, self-adaptively constructing a proxy model in the active subspace Kriging proxy model for adaptively constructing vibration fundamental frequency of antenna substrate in active subspace The new added sample point u new is determined as the point corresponding to the maximum MSE using the unaware point MSE estimated by the Kriging proxy model: In equation (14), S 0,u is the mapping of the initial sample set S 0 in the subspace; step three, calling a Kriging proxy model to estimate sensitivity index The quasi-Monte Carlo method is introduced to use the constructed Kriging proxy model Performing sensitivity analysis, reconstructing an initial design space according to a sensitivity analysis result, and selecting sensitive variables to form a new design space, wherein insensitive variables are fixed at the mean value all the time; optimizing and reconstructing the antenna substrate in the design space Using a bayesian optimization method to optimize an antenna substrate in a reconstruction space, it is desirable to improve a global search of a sampling function of the EI using a criterion to detect an unexplored but promising region while improving prediction accuracy, the sampling function of the sampling criterion of the EI being represented in a closed form: in the formula (1), EI (x) is an EI function value corresponding to an observation point x, phi (·) and phi (·) are cumulative distribution and probability density functions of standard normal distribution respectively, y min is the minimum value in an evaluation sample, For the Kriging proxy model predictive value, Predicting square root of variance for Kriging proxy model; for the constraint optimization problem, the constraint comprises the weight of the structure and the thermally induced displacement of the structure, and a proxy model G j (x),j＝1,…,n g of a constraint function is established, wherein n g represents the number of the constraint functions, and the obeying mean value of a random variable G j (x) corresponding to the jth constraint function is assumed to be The normal too distribution with standard deviation s g,j (x) satisfies the expected probability P [ G j (x) > 0] by the following formula (2): the constraint EI sampling function CEI (x) is expressed as:
2. The method for optimizing the vibration fundamental frequency of the antenna substrate based on machine learning according to claim 1, wherein in the second step, the process of adaptively constructing the Kriging proxy model in the active subspace is as follows: Step two, mapping all samples in S 0 to an active subspace u by using the relation in a formula (13), recording a new sample set as S 0,u , extracting N 2 points from S 0,u as initial samples, mapping the kth initial sample u k back to an initial variable space by the formula (13) to obtain x k , and obtaining the vibration fundamental frequency y k of the antenna substrate by finite element calculation so as to form an initial training data set T= { u k ,y k }; training the Kriging proxy model by using the initial training data set T to obtain a proxy model Step two and three, using proxy model Estimating the MSE of all samples in S 0,u , the new point being identified by equation (14); Step two, defining convergence criteria as: Wherein maxMSE represents the maximum MSE of all samples in S 0,u , and the superscript represents the iteration number, cr is the convergence threshold, which is equal to 5×10 -6 ; When the convergence criterion is not met, u new is mapped to an initial input space, the vibration fundamental frequency y new of the antenna substrate is calculated through calling a finite element, then a new training point { u new ,y new } is added to T for updating, and the Kriging proxy model is retrained in the second step, and if the convergence criterion is met, the Kriging proxy model is considered to meet the accuracy requirement.

Description

Antenna substrate vibration fundamental frequency optimization method based on machine learning Technical Field The invention belongs to the technical field of vibration optimization of large-area thin-wall plates, and particularly relates to an antenna substrate vibration fundamental frequency optimization method based on machine learning. Background At present, as satellite transmission is normalized and scaled up, the substrate on which the antenna is mounted is also being scaled up and reduced in weight. Because the traditional aerospace device is constrained by a carrier rocket, the efficiency maximization under the condition of large system such as carrying and launching weight is achieved by strict folding and accommodating design and constraint of the thickness of the substrate. Therefore, it is generally employed to hinge the unit substrates to each other and to spread the unit substrates into a preset configuration when reaching a predetermined track. However, the large sheet structure has great flexibility due to the hinge connection, and the vibration generated during the on-orbit task execution is very easy to cause the attitude movement of the rigid body of the satellite center, thereby influencing the satellite load function failure and further causing the task failure. Therefore, research on the vibration control and optimization method of the large-size antenna substrate structure with the hinge connection is of great significance. However, frequency optimization for large-sized antenna substrate structures presents a great challenge, the main problem being that the size of the optimization problem or the dimension of the design space is too large, since an increase in the structure size corresponds to a greater number of hinges and panels. Furthermore, various linear and nonlinear constraints must be considered throughout the optimization process. For example, the structural mass must be kept below a prescribed threshold in view of the limits of the emission costs, and the maximum displacement of the antenna substrate structure under thermal load should be taken into account in view of structural safety and stability of deployment. At the same time, calculating the frequency and complex constraints of the antenna substrate structure requires a large number of high-precision samples. Comprehensively analyzing the above problems, the present invention addresses such problems using an efficient optimization and active subspace (AC) method based on a proxy model. And (3) performing dimension reduction reconstruction on the design space by adopting an active subspace method and combining with self-adaptive kriging (step four) and Global Sensitivity Analysis (GSA), and then optimizing an antenna substrate in the reconstructed design space by utilizing a high-efficiency optimization algorithm to finally obtain the optimal fundamental frequency. And compared with the optimization of the original space, the optimization effect of reconstructing the dimension-reducing space is quicker and more efficient. Disclosure of Invention The invention aims to solve the problems in the prior art and provides an antenna substrate vibration fundamental frequency optimization method based on machine learning. The method of the invention is a high-efficiency dimension reduction optimization method based on a proxy model and an active subspace (AC). In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: an antenna substrate vibration fundamental frequency optimization method based on machine learning, the method comprising the following steps: Step one, identifying active subspaces Sampling in the antenna substrate initial design space to generate N 0 samples as a set, marking as initial sample set S 0, selecting N 1 samples from S 0, marking as S 1, estimating gradient vector of sample antenna substrate vibration fundamental frequency in S 1 set by finite element simulation and finite difference method By gradient vectors to these S 1 sample pointsThe method comprises the steps of averaging to estimate elements of a covariance matrix C, carrying out feature decomposition on the covariance matrix C to obtain feature values and feature vectors, identifying an active subspace by analyzing the relative sizes among the feature values, and after the active subspace is found, approximating the mapping between an original input variable x 0 and variables in the active subspace to: x0＝W1u+W2z≈W1u (13) In the formula (13), W 1 and W 2 are active subspace vectors and inactive subspace vectors respectively, and u and z are active variables and inactive variables respectively; Step two, self-adaptively constructing a proxy model in the active subspace Kriging proxy model for adaptively constructing vibration fundamental frequency of antenna substrate in active subspaceThe new added sample point u new is determined as the point corresponding to the maximum MSE using the unaware point