Rapid Prediction Method and System for Satellite Structural Mechanical Properties

Abstract

This invention provides a method and system for rapid prediction of the mechanical properties of satellite structures, comprising: Step S1: Based on the vibration theory and buckling stability theory of thin-walled cylindrical shells, derive the approximate functional relationship between the geometric parameters, material parameters, mass parameters, and fundamental frequency and safety margin of the satellite's load-bearing cylinder; Step S2: Based on the approximate functional relationship, construct a logarithmic linear regression model for fundamental frequency prediction; Step S3: Based on the approximate functional relationship, construct a linear regression model with cross terms for safety margin prediction; Step S4: Based on multiple sets of parameter samples, train, statistically test, evaluate prediction accuracy, and verify physical consistency of the models in Steps S2 and S3; Step S5: Encapsulate the trained and validated model into a prediction tool, and based on the new input design parameters, output the predicted fundamental frequency and safety margin.

Description

Technical Field

[0001] This invention relates to the field of satellite structure design technology, specifically to a method and system for rapid prediction of the mechanical properties of satellite structures, applicable to the conceptual design, parameter optimization, and scheme selection stages of satellite structures. Background Technology

[0002] The satellite's first-order natural frequency (fundamental frequency) and structural safety margin are key indicators affecting the satellite's launch dynamics coupling and ultimate load-bearing capacity. The satellite's load-bearing cylinder, as the main load-bearing structure, is one of the most important determinants of the satellite's fundamental frequency and structural safety margin. Traditional satellite mechanical performance prediction mainly relies on the finite element analysis method. While this method offers high accuracy, it suffers from complex modeling, high computational costs, and long iteration cycles, making it difficult to meet the needs of rapid screening and optimization of massive amounts of solutions during the conceptual design phase. In recent years, purely data-driven "black box" models, such as neural networks, have been commonly used for data analysis and prediction. However, due to the lack of physical laws supporting them, they suffer from poor interpretability and weak extrapolation capabilities, and are rarely used for structural mechanical performance.

[0003] To clearly illustrate the innovativeness of this invention, the following comparative analysis of existing related technologies is conducted in conjunction with specific patents and literature:

[0004] Comparative literature (patent CN201910831918.3, A Satellite Structural Performance Prediction Method for Overall Design) discloses a satellite structural performance prediction method based on high-precision finite element simulation data and a polynomial response surface surrogate model. This method focuses on constructing a polynomial response surface through a large amount of training data to replace complex finite element analysis, thereby shortening the performance prediction time and improving the overall design efficiency. However, the "polynomial response surface surrogate model" constructed by this method is essentially still a data fitting method relying on pure mathematical statistics. Since its polynomial structure is not guided by specific physical laws (such as structural vibration or buckling mechanisms), when faced with input design parameters exceeding the range of the initial training samples, the model's extrapolation prediction ability is weak, and the prediction results often lack clear physical interpretability. In contrast, this invention does not blindly apply standard mathematical polynomials, but rather derives a specific regression equation structure based on the physical theory of vibration and buckling of thin-walled cylindrical shells. While ensuring computational efficiency, it significantly improves the interpretability and extrapolation confidence of the model.

[0005] In summary, existing technologies for predicting the structural mechanical performance of satellites suffer from problems such as low computational efficiency, insufficient physical interpretability, and weak model extrapolation capabilities. This invention effectively solves these problems through a novel approach combining physical mechanism knowledge with multiple regression modeling. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for rapid prediction of the structural mechanical properties of satellites.

[0007] According to a first aspect of the present invention, a method for rapidly predicting the structural mechanical properties of a satellite includes: Step S1: Based on the vibration theory and buckling stability theory of thin-walled cylindrical shells, derive the geometric parameters, material parameters, mass parameters, and fundamental frequency of the satellite's load-bearing cylinder. and safety margin Approximate functional relationship between them; Step S2: Based on the approximate functional relationship, construct a log-linear regression model for fundamental frequency prediction; Step S3: Based on the approximate functional relationship, construct a linear regression model with cross terms for safety margin prediction; Step S4: Based on multiple sets of parameter samples, train, statistically test, evaluate prediction accuracy, and verify physical consistency of the models from Steps S2 and S3. Step S5: Package the trained and validated model into a prediction tool, and output the predicted fundamental frequency based on the design parameters of the new input. and safety margin .

[0008] Preferably, in step S1: The geometric parameters include the height of the upper cylindrical segment. ,diameter Height of the lower conical section Bottom diameter Skin thickness The mass parameters include the total mass of the satellite. Center of mass height .

[0009] Preferably, step S2 specifically includes: Determining the fundamental frequency based on approximate functional relationships. f The relationship between the key parameters is exponential, and the following log-linear regression model is constructed:

[0010] in, For the intercept term, For regression coefficients, This is the random error term.

[0011] Preferably, step S3 specifically includes: Determining the safety margin based on approximate functional relationships It exhibits a linear relationship with multiple physically meaningful composite parameters, and the following linear regression model with interaction terms is constructed:

[0012] in, For the intercept term, For regression coefficients, This is the random error term.

[0013] Preferably, step S4 includes: Step S4.1: Obtain a dataset containing multiple sets of observations, the dataset being derived from historical designs, experiments, or parametric finite element analyses; the observations include the fundamental frequency. Safety margin Height of upper cylindrical section ,diameter Height of the lower conical section Bottom diameter Skin thickness Total mass of satellite Center of mass height

[0014] Step S4.2: Perform logarithmic transformation on the variables required for the fundamental frequency model, calculate composite variables for the safety margin model; divide the dataset into training and test sets; Step S4.3: Using the training set data, solve for the regression coefficients of the fundamental frequency model and the safety margin model using the least squares method respectively; Step S4.4: Perform F-test, t-test, and collinearity diagnosis on the model, and calculate the adjusted R², root mean square error, and mean absolute percentage error index. Step S4.5: Verify that the signs of the regression coefficients are in line with physical expectations to ensure that the model is physically reliable.

[0015] Preferably, step S4.5 specifically includes: For the fundamental frequency model, the expectation is... , The sign needs to be determined in conjunction with the influence of the centroid position; For the safety margin model, the expectation is... , , The sign reflects the influence of the slenderness ratio. The symbol reflects the influence of the conical segment on stability.

[0016] According to a second aspect of the present invention, a rapid prediction system for the structural mechanical properties of a satellite includes: Module M1: Based on the vibration theory and buckling stability theory of thin-walled cylindrical shells, derive the geometric parameters, material parameters, mass parameters, and fundamental frequency of the satellite's load-bearing cylinder. and safety margin Approximate functional relationship between them; Module M2: Constructs a log-linear regression model for fundamental frequency prediction based on an approximate functional relationship; Module M3: Constructs a linear regression model with cross terms for safety margin prediction based on approximate functional relationships; Module M4: Based on multiple sets of parameter samples, the models of Module M2 and Module M3 are trained, statistically tested, their prediction accuracy is evaluated, and their physical consistency is verified. Module M5: Encapsulates the trained and validated model into a prediction tool, outputting the predicted fundamental frequency based on the design parameters of the new input. and safety margin .

[0017] Preferably, in module M1: The geometric parameters include the height of the upper cylindrical segment. ,diameter Height of the lower conical section Bottom diameter Skin thickness The mass parameters include the total mass of the satellite. Center of mass height .

[0018] Preferably, module M2 specifically includes: Determining the fundamental frequency based on approximate functional relationships. f The relationship between the key parameters is exponential, and the following log-linear regression model is constructed:

[0019] in, For the intercept term, For regression coefficients, This is the random error term.

[0020] Preferably, the module M3 specifically includes: Determining the safety margin based on approximate functional relationships It exhibits a linear relationship with multiple physically meaningful composite parameters, and the following linear regression model with interaction terms is constructed:

[0021] in, For the intercept term, For regression coefficients, This is the random error term.

[0022] According to a third aspect of the present invention, a rapid prediction system for the structural mechanical properties of satellites based on physical mechanisms and multiple regression includes: The parameter input and preprocessing module is used to receive the design parameters of the load-bearing cylinder input by the user, and automatically complete the logarithmic transformation of the logarithmic values ​​and the calculation of composite characteristic quantities according to the requirements of the fundamental frequency prediction model and the safety margin prediction model. The physical mechanism constraint model library module is used to store prediction models and their regression coefficients that are trained according to the method in the first aspect and have a specific mathematical form (i.e., the log-linear form and the linear form with cross terms). The real-time prediction and calculation engine is used to call the models in the model library, substitute the preprocessed parameters into the model for instantaneous calculation, and obtain the predicted values ​​of the fundamental frequency and safety margin. The physical consistency verification and warning module is used to verify the rationality of the model during the model training phase according to preset physical rules (such as expected coefficient signs), and to issue a warning to the user when the combination of input parameters causes the prediction results to deviate significantly from physical common sense during the application phase. The results visualization and report output module is used to output the prediction results, confidence intervals, and comparisons with historical schemes in the form of graphs and reports.

[0023] Furthermore, the system is integrated into the satellite collaborative design and simulation platform in the form of a configurable plug-in. The plug-in can automatically call and adapt the corresponding prediction model according to the basic configuration of the load-bearing cylinder (cylinder or conical-cylinder combination) selected by the user.

[0024] Furthermore, the system is deployed as a cloud-based microservice, providing a performance prediction API interface that includes physical consistency verification functionality for remote design terminals to call.

[0025] According to a third aspect of the present invention, a satellite structure conceptual design optimization system is provided, which integrates the rapid prediction system described above, and can call the prediction system in real time during the design iteration cycle to evaluate and screen candidate design schemes.

[0026] According to a fourth aspect of the present invention, a non-volatile computer-readable storage medium is provided thereon storing a computer program that, when executed by a processor, specifically implements the rapid prediction method of the first aspect, which includes steps for physical mechanism derivation and physical consistency verification.

[0027] Compared with the prior art, the present invention has the following beneficial effects: In the initial mechanism derivation step, this method rigorously establishes physical relationships based on the underlying theory of thin-walled cylindrical shells. This step fundamentally endows the subsequent model with clear physical meaning, effectively overcoming the "black box" defect of traditional data-driven algorithms such as neural networks. This makes the prediction results not only highly interpretable, but also maintains extremely high extrapolation confidence when faced with new design parameters that exceed the range of historical samples.

[0028] In the process of constructing the predictive model, this method, based on the derived physical laws, tailors logarithmic linear form and linear regression form with cross terms for the fundamental frequency and safety margin, respectively. This explicit equation structure guided by physical mechanisms avoids the blind fitting and absurd results that standard multiple linear regression is prone to in complex structural problems. At the same time, it significantly reduces the dependence on massive training data, requiring only a small number of samples to construct a predictive model that closely fits the real mechanical laws.

[0029] In the model training and validation phases, this method innovatively introduces a dual-checking mechanism of statistics and physics. In addition to using various statistical test indicators to evaluate the fitting accuracy, it also enforces a physical consistency check step, rigorously verifying whether the signs of all regression coefficients conform to common-sense physical expectations. This screening mechanism completely eliminates the possibility of unreasonable results from the physical level, ensuring the absolute reliability and physical credibility of the final prediction results.

[0030] In the final prediction and packaging steps, the validated model with a specific mathematical form is transformed into an instantaneous computation engine that requires no numerical iteration. This lightweight, tool-based application completely breaks through the bottleneck of the complexity and time-consuming nature of traditional high-fidelity finite element simulation, significantly reducing the mechanical performance evaluation time of candidate structural schemes from several days to several seconds, thereby greatly improving the evaluation and optimization efficiency of satellite structures in the early stages of conceptual design and screening of massive schemes. Attached Figure Description

[0031] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 A schematic diagram of a satellite structure including a load-bearing cylinder (cone-cylinder combination) provided in an embodiment of the present invention; Figure 2 A flowchart of a fast prediction method provided in an embodiment of the present invention; Figure 3 This is a diagram of a fast prediction system architecture provided in an embodiment of the present invention. Detailed Implementation

[0032] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0033] Example 1: This embodiment provides a method for rapid prediction of the structural mechanical properties of satellites, including: Step S1: Based on the vibration theory and buckling stability theory of thin-walled cylindrical shells, derive the geometric parameters, material parameters, mass parameters, and fundamental frequency of the satellite's load-bearing cylinder. and safety margin Approximate functional relationship between them; Step S2: Based on the approximate functional relationship, construct a log-linear regression model for fundamental frequency prediction; Step S3: Based on the approximate functional relationship, construct a linear regression model with cross terms for safety margin prediction; Step S4: Based on multiple sets of parameter samples, train, statistically test, evaluate prediction accuracy, and verify physical consistency of the models from Steps S2 and S3. Step S5: Package the trained and validated model into a prediction tool, and output the predicted fundamental frequency based on the design parameters of the new input. and safety margin .

[0034] In this embodiment, in step S1: The geometric parameters include the height of the upper cylindrical segment. ,diameter Height of the lower conical section Bottom diameter Skin thickness The mass parameters include the total mass of the satellite. Center of mass height .

[0035] In this embodiment, step S2 specifically includes: Determining the fundamental frequency based on approximate functional relationships. f The relationship between the key parameters is exponential, and the following log-linear regression model is constructed:

[0036] in, For the intercept term, For regression coefficients, This is the random error term.

[0037] In this embodiment, step S3 specifically includes: Determining the safety margin based on approximate functional relationships It exhibits a linear relationship with multiple physically meaningful composite parameters, and the following linear regression model with interaction terms is constructed:

[0038] in, For the intercept term, For regression coefficients, This is the random error term.

[0039] In this embodiment, step S4 includes: Step S4.1: Obtain a dataset containing multiple sets of observations, the dataset being derived from historical designs, experiments, or parametric finite element analyses; the observations include the fundamental frequency. Safety margin Height of upper cylindrical section ,diameter Height of the lower conical section Bottom diameter Skin thickness Total mass of satellite Center of mass height

[0040] Step S4.2: Perform logarithmic transformation on the variables required for the fundamental frequency model, calculate composite variables for the safety margin model; divide the dataset into training and test sets; Step S4.3: Using the training set data, solve for the regression coefficients of the fundamental frequency model and the safety margin model using the least squares method respectively; Step S4.4: Perform F-test, t-test, and collinearity diagnosis on the model, and calculate the adjusted R², root mean square error, and mean absolute percentage error index. It should be noted that the "F-test" (overall significance test) mentioned in step S4.4 of this invention refers to a standard test method used to evaluate whether the constructed multiple regression model (including the fundamental frequency prediction model and the safety margin prediction model) has statistical significance as a whole. Specifically, it verifies, by calculating the F-statistic, whether the multiple input physical parameters (such as geometric parameters, mass parameters, and composite characteristics) as a whole can effectively establish a mapping relationship with the satellite's structural mechanical performance (fundamental frequency and safety margin). If this test is passed, it proves that the overall architecture of the constructed model is statistically valid, ruling out the possibility that the prediction results are random errors or coincidences.

[0041] It should be noted that the "t-test" (univariate significance test) mentioned in step S4.4 of this invention refers to a test method used to evaluate whether the regression coefficients of each specific physical characteristic variable in the model have statistically independent significance. Specifically, it means testing the degree of independent contribution of a single variable (e.g., examining skin thickness or centroid height alone) to the prediction results of satellite mechanical performance by calculating the t-statistic corresponding to each variable. Through this test, core physical parameters that have a substantial impact on mechanical performance can be effectively identified and retained, while invalid parameters are eliminated, thereby ensuring that the physical meaning of each coefficient in the model is accurate.

[0042] It should be noted that the "adjusted R²" (i.e., the adjusted coefficient of determination) mentioned in step S4.4 of this invention refers to a core statistical indicator used to measure the goodness of fit (i.e., explanatory power) of the regression equation to the sample dataset. Specifically, it introduces a penalty mechanism based on the number of independent variables in the model, building upon the traditional coefficient of determination R². Since the safety margin and other models in this invention introduce multiple composite physical interaction terms, using "adjusted R²" can effectively overcome the defect of blindly increasing variables leading to artificially high goodness of fit, objectively and truthfully reflecting the true explanatory proportion of the selected combination of physical characteristic parameters for changes in satellite mechanical performance, thereby quantitatively evaluating the actual predictive accuracy of the model.

[0043] Step S4.5: Verify that the signs of the regression coefficients are in line with physical expectations to ensure that the model is physically reliable.

[0044] In this embodiment, step S4.5 specifically includes: For the fundamental frequency model, the expectation is... , The sign needs to be determined in conjunction with the influence of the centroid position; For the safety margin model, the expectation is... , , The sign reflects the influence of the slenderness ratio. The symbol reflects the influence of the conical segment on stability.

[0045] Working principle: This method first establishes a basic theoretical framework based on the vibration theory and buckling stability theory of thin-walled cylindrical shells. Building upon this, it derives approximate mathematical functional relationships between the geometric parameters (such as height, diameter, and thickness) and mass parameters (such as total mass and center of mass height) of the satellite's load-bearing cylinder and its core mechanical performance indicators (fundamental frequency and safety margin). This step transforms purely data-driven approaches into a mechanistic study supported by physical theory, laying a solid physical foundation for the good interpretability of subsequent prediction models.

[0046] Based on the physical relationships derived above, this method constructs two specific regression model equations for different prediction targets. For the prediction of the fundamental frequency, since the derivation shows that it has a power-law relationship with the key parameters, a log-linear regression model is constructed. For the prediction of the safety margin, since it has a linear relationship with multiple physically meaningful composite parameters, a linear regression model including cross terms is constructed. This mathematical structure of the model, tailored to the physical mechanism, ensures that the form of the equations themselves conforms to the actual laws of mechanics.

[0047] Once the model equations are established, the model needs to be trained and its parameters solved using existing datasets obtained from historical designs, experiments, or finite element simulations. After obtaining the regression coefficients of each parameter using the least squares method, this approach not only requires the model to pass statistical tests (to ensure fitting accuracy and mathematical rigor) but also introduces a crucial physical consistency verification step. By rigorously checking whether the signs of the calculated regression coefficients conform to the expectations of common physical sense (e.g., an increase in mass leads to a decrease in the fundamental frequency), unreasonable fitting results are eliminated, ensuring the absolute credibility of the model in terms of physical logic.

[0048] The trained and dual-validated (statistical and physical) models are ultimately packaged into a fast computation engine or prediction tool. During the conceptual design and optimization phases of satellite structures, designers only need to input a new set of candidate structural parameters, and the system can directly substitute them into the equations for instantaneous calculations, outputting predicted values ​​for the fundamental frequency and safety margin within seconds. This fusion approach, while ensuring the physical reliability of the prediction results and possessing strong extrapolation capabilities, completely breaks through the efficiency bottleneck of traditional finite element analysis, which is time-consuming and labor-intensive.

[0049] Example 2: See Figure 1 In this embodiment, the satellite support cylinder consists of an upper cylindrical section (height...) ,diameter ) and the lower conical section (height) Top diameter Bottom diameter Composed of ) components, with a skin thickness of The total mass of the satellite is The height of the centroid from the root is .

[0050] See Figure 2 The rapid prediction method of the present invention is implemented according to the following steps: Data acquisition: Using parametric finite element software, changing... Seven design parameters were used to perform modal and static analyses, generating a dataset containing 5000 samples, each sample including the input parameters and the corresponding fundamental frequency. With safety margin .

[0051] Model construction: Based on formulas (1) and (2) in the invention, regression model structures for fundamental frequency and safety margin are established respectively.

[0052] Model training: 4000 samples were randomly selected as the training set. Least square regression was performed using Python's statsmodels library to obtain coefficient estimates.

[0053] Example results of fundamental frequency model:

[0054] All coefficient signs conform to physical expectations (of which...) A negative value indicates that the increase in the centroid has a slight negative impact on the fundamental frequency, which is reasonable.

[0055] Example results of the safety margin model:

[0056] coefficient A negative value indicates that an increase in the slenderness ratio reduces stability, which aligns with physical understanding.

[0057] Model validation: Evaluation was performed using the remaining 1000 test set samples. The mean absolute percentage error (MASE) for fundamental frequency prediction was 4.2%, and the MASE for safety margin prediction was 6.8%, indicating that the model has good generalization ability.

[0058] Tool-based application: The trained model coefficients are solidified and developed into a lightweight desktop application. After the user inputs seven design parameters, the program can instantly display the predicted fundamental frequency. With safety margin And provide a judgment on whether the design requirements are met.

[0059] Example 3: The single cylindrical configuration is applicable to load-bearing cylinders that are entirely cylindrical, which can be considered a special case of the model of this invention. In this case, the height of the conical section is set. Bottom diameter The model of this invention then automatically degenerates into: Fundamental frequency model:

[0060] Safety margin model: The simplified model described above was trained and validated using a dataset generated for cylindrical configurations, and high-precision, fast prediction capabilities were also achieved, demonstrating the universality of the method of this invention.

[0061] Example 4: See Figure 3 The rapid prediction system of the present invention includes: Web front-end interface: Allows users to input design parameters and guides the input in the form of forms and diagrams, and supports the selection of different load-bearing cylinder configurations.

[0062] Backend service: Deploys the trained regression model and physical validation rules, receives frontend requests, calls the model to perform calculations, and makes physical validity judgments.

[0063] Database: Stores historical design cases, model coefficients for different configurations, and prediction records.

[0064] Report generation module: Automatically generates analysis reports that include prediction results, confidence intervals, physical consistency indicators, and comparisons with historical solutions.

[0065] The system has been initially integrated into the collaborative design platform of a satellite design unit. In the early stages of design, it is used to quickly evaluate satellite structural schemes, reducing the performance evaluation time from several days in traditional finite element analysis to several seconds, and significantly improving the efficiency of design iteration.

[0066] The present invention also provides a rapid prediction system for the structural mechanical properties of satellites. The rapid prediction system for the structural mechanical properties of satellites can be implemented by executing the process steps of the rapid prediction method for the structural mechanical properties of satellites. That is, those skilled in the art can understand the rapid prediction method for the structural mechanical properties of satellites as a preferred embodiment of the rapid prediction system for the structural mechanical properties of satellites.

[0067] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0068] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for rapid prediction of the structural mechanical properties of satellites, characterized in that, include: Step S1: Based on the vibration theory and buckling stability theory of thin-walled cylindrical shells, derive the geometric parameters, material parameters, mass parameters, and fundamental frequency of the satellite's load-bearing cylinder. and safety margin Approximate functional relationship between them; Step S2: Based on the approximate functional relationship, construct a log-linear regression model for fundamental frequency prediction; Step S3: Based on the approximate functional relationship, construct a linear regression model with cross terms for safety margin prediction; Step S4: Based on multiple sets of parameter samples, train, statistically test, evaluate prediction accuracy, and verify physical consistency of the models from Steps S2 and S3. Step S5: Package the trained and validated model into a prediction tool, and output the predicted fundamental frequency based on the design parameters of the new input. and safety margin .

2. The method according to claim 1, characterized in that, In step S1: The geometric parameters include the height of the upper cylindrical segment. ,diameter Height of the lower conical section Bottom diameter Skin thickness The mass parameters include the total mass of the satellite. Center of mass height .

3. The method according to claim 2, characterized in that, Step S2 specifically includes: Determining the fundamental frequency based on approximate functional relationships. f The relationship between the key parameters is exponential, and the following log-linear regression model is constructed: in, For the intercept term, For regression coefficients, This is the random error term.

4. The method according to claim 2, characterized in that, Step S3 specifically includes: Determining the safety margin based on approximate functional relationships It exhibits a linear relationship with multiple physically meaningful composite parameters, and the following linear regression model with interaction terms is constructed: in, For the intercept term, For regression coefficients, This is the random error term.

5. The method according to claim 1, characterized in that, Step S4 includes: Step S4.1: Obtain a dataset containing multiple sets of observations, the dataset being derived from historical designs, experiments, or parametric finite element analyses; the observations include the fundamental frequency. Safety margin Height of upper cylindrical section ,diameter Height of the lower conical section Bottom diameter Skin thickness Total mass of satellite Center of mass height Step S4.2: Perform logarithmic transformation on the variables required for the fundamental frequency model, calculate composite variables for the safety margin model; divide the dataset into training and test sets; Step S4.3: Using the training set data, solve for the regression coefficients of the fundamental frequency model and the safety margin model using the least squares method respectively; Step S4.4: Perform F-test, t-test, and collinearity diagnosis on the model, and calculate the adjusted R², root mean square error, and mean absolute percentage error index. Step S4.5: Verify that the signs of the regression coefficients are in line with physical expectations to ensure that the model is physically reliable.

6. The method according to claim 1, characterized in that, Step S4.5 specifically includes: For the fundamental frequency model, the expectation is... , The sign needs to be determined in conjunction with the influence of the centroid position; For the safety margin model, the expectation is... , , The sign reflects the influence of the slenderness ratio. The symbol reflects the influence of the conical segment on stability.

7. A rapid prediction system for the structural mechanical properties of satellites, characterized in that, include: Module M1: Based on the vibration theory and buckling stability theory of thin-walled cylindrical shells, derive the geometric parameters, material parameters, mass parameters, and fundamental frequency of the satellite's load-bearing cylinder. and safety margin Approximate functional relationship between them; Module M2: Constructs a log-linear regression model for fundamental frequency prediction based on an approximate functional relationship; Module M3: Constructs a linear regression model with cross terms for safety margin prediction based on approximate functional relationships; Module M4: Based on multiple sets of parameter samples, the models of Module M2 and Module M3 are trained, statistically tested, their prediction accuracy is evaluated, and their physical consistency is verified. Module M5: Encapsulates the trained and validated model into a prediction tool, outputting the predicted fundamental frequency based on the design parameters of the new input. and safety margin .

8. The system according to claim 7, characterized in that, In module M1: The geometric parameters include the height of the upper cylindrical segment. ,diameter Height of the lower conical section Bottom diameter Skin thickness The mass parameters include the total mass of the satellite. Center of mass height .

9. The system according to claim 8, characterized in that, Module M2 specifically includes: Determining the fundamental frequency based on approximate functional relationships. f The relationship between the key parameters is exponential, and the following log-linear regression model is constructed: in, For the intercept term, For regression coefficients, This is the random error term.

10. The system according to claim 8, characterized in that, The module M3 specifically includes: Determining the safety margin based on approximate functional relationships It exhibits a linear relationship with multiple physically meaningful composite parameters, and the following linear regression model with interaction terms is constructed: in, For the intercept term, For regression coefficients, This is the random error term.

Images