A method for modifying a surrogate model of a finite element model of a flexible structure of an inflatable decelerator

Abstract

The application provides a kind of inflatable decelerator flexible structure finite element model's surrogate model correction method, belongs to aerospace engineering structure simulation and finite element model correction field, including: establishing initial finite element model and identifying airbag stiffness, skin stiffness, rigid-flexible connection stiffness as to be corrected parameters, determine modal frequency as target response parameter;Through finite element simulation to construct sample data set;Combined with quadratic polynomial and radial basis function to construct surrogate model, get the model that satisfies accuracy after training and verification;With the test measured modal frequency as target, combined with genetic algorithm to optimize the surrogate correction parameter and get the optimal combination;The optimal combination is substituted into the initial model to complete the correction, and through multi-order modal frequency verification to ensure that it meets the engineering precision.The application solves the problems of insufficient adaptability of flexible component modeling, low fitting precision of small sample parameter coupling, and lack of adaptability of dynamic target and correction method, and realizes high-precision correction of flexible structure finite element model under small sample.

Description

Technical Field

[0001] This invention relates to the field of aerospace engineering structure simulation and finite element model correction technology, and more particularly to a proxy model correction method for a flexible structure finite element model of an inflatable reducer. Background Technology

[0002] Inflatable decelerators, as a novel aerospace deceleration device, have become an important development direction in spacecraft reentry deceleration technology due to their advantages such as high payload ratio, lightweight structure, and compact launch volume. The core flexible structure of this device consists of a multi-layered composite material airbag, skin, and fabric strap connectors. Its dynamic characteristics directly affect the aerodynamic stability during reentry. Research shows that if aerodynamically induced structural vibrations during reentry lead to resonance or fatigue effects, it will cause the flexible structure to fail. Therefore, accurately obtaining structural modal parameters (including natural frequencies and mode shapes) is a crucial technological foundation for ensuring flight safety.

[0003] In existing technologies, the method of combining finite element model correction with surrogate models is widely used in the dynamic characteristic analysis of flexible structures in inflatable reducers. However, this method has three key technical defects: First, in terms of flexible structure modeling, existing technologies do not adequately consider the orthotropic material properties, prestress state, and large deformation behavior of the airbag skin. They commonly use simplified rod elements to replace the flexible body or idealize the stitching constraints, resulting in modal frequency calculation errors generally exceeding 8%. Second, during parameter inversion, there is a strong nonlinear coupling relationship between multiple parameters such as airbag stiffness and skin stiffness. Existing surrogate models struggle to accurately capture the influence of parameter gradient changes on modal frequencies under small sample conditions. Finally, existing correction methods mostly focus on static response indicators and lack a dedicated optimization mechanism for the dynamic core parameter of modal frequency. This leads to insufficient correlation between the correction results and experimental data, making it difficult to meet the accuracy requirements of engineering design. These technical defects severely restrict the dynamic optimization and reliability design of flexible structures in inflatable reducers. Summary of the Invention

[0004] To address the aforementioned deficiencies in existing technologies, this invention provides a proxy model correction method for the finite element model of a flexible structure of an air-filled reducer. This method solves the problems of insufficient adaptability of flexible component modeling, low accuracy of small sample parameter coupling fitting, and lack of adaptability between dynamic targets and correction methods. It achieves high-precision correction of the finite element model of the flexible structure of the air-filled reducer under small sample conditions, providing reliable model support for the engineering optimization design of air-filled reducers.

[0005] The technical means employed in this invention are as follows:

[0006] A proxy model correction method for a finite element model of a flexible structure of an inflatable reducer includes: S1. Establish an initial finite element model of the flexible structure of the air-filled reducer as the model to be corrected, identify the core sensitive parameters in the initial finite element model that affect the accuracy of modal frequency calculation as the parameters to be corrected, and determine the modal frequency of the flexible structure as the target response parameter. S2. Based on the current set value of the parameter to be corrected in the initial finite element model as the design benchmark value, the adjustment range of each parameter to be corrected is set according to the error source analysis results; within the adjustment range, the experimental design method is used to generate sample points, and the modal frequencies corresponding to each sample point are calculated through finite element simulation to construct a sample dataset containing multiple sets of parameter combinations and their corresponding modal frequencies. S3. Divide the sample dataset into a training set and a test set; construct a surrogate model using a combination of polynomial functions and radial basis functions, and establish a nonlinear mapping relationship between the parameters to be corrected and the modal frequencies; optimize the fitting parameters of the surrogate model using the training set to minimize the error between the predicted values ​​of the surrogate model and the finite element simulation values; verify the prediction accuracy and generalization ability of the surrogate model using the test set. When the preset accuracy threshold is met, output the trained surrogate model; otherwise, return to step S2 to expand the sample data. S4. Using the target modal frequency obtained from the experimental measurement as the optimization target value, the parameter to be corrected as the design variable, and the adjustment range of the parameter to be corrected as the constraint condition, a genetic algorithm combined with the surrogate model is used for optimization calculation; wherein, the surrogate model is used to quickly predict the modal frequency corresponding to each candidate parameter combination, and the optimization objective is to minimize the absolute value of the difference between the predicted value and the target value. The optimal parameter combination that makes the modal frequency approach the target value is obtained through iterative evolution. S5. Substitute the optimal parameter combination into the initial finite element model, update the parameters to be corrected, and obtain the corrected finite element model; perform modal analysis on the corrected finite element model to calculate the multi-order modal frequencies; compare the multi-order modal frequencies with the corresponding target modal frequencies and calculate the frequency errors of each order; determine whether the frequency errors meet the preset engineering accuracy requirements. If they do, output the corrected finite element model as the final correction result to complete the model correction; if they do not meet the requirements, return to step S4 to adjust the optimization parameters until the accuracy requirements are met.

[0007] Further, step S1 includes: S11. Based on the geometric structure, material properties and connection relationship of the inflatable reducer, an initial finite element model of the flexible structure including airbags, skin and fabric straps is established using finite element analysis software; the inflatable reducer is composed of multiple inflatable airbags, a rigid central body and fabric straps, and the inflatable airbags adopt a stacked toroidal structure and are interconnected with the central body and airbags through fabric straps. S12. Perform modal analysis on the initial finite element model to extract the multi-mode frequencies and mode shapes under the initial parameters, which will be used as the reference values ​​for subsequent corrections. S13. Based on finite element modeling errors, material parameter errors, and boundary condition constraint errors, identify the key error sources that affect the accuracy of modal frequency calculation; analyze the sensitivity of airbag stiffness, skin stiffness, and stiffness at rigid-flexible connections to modal frequencies, and determine airbag stiffness, skin stiffness, and stiffness at rigid-flexible connections as core sensitive parameters. S14. Select the airbag stiffness, skin stiffness, and stiffness at the rigid-flexible connection as parameters to be corrected; wherein, the airbag stiffness is the equivalent elastic modulus or stiffness coefficient of the airbag material, the skin stiffness is the equivalent elastic modulus or stiffness coefficient of the skin material, and the stiffness at the rigid-flexible connection is the equivalent stiffness of the connection area between the flexible airbag and the rigid central body. S15. Using the current value of the parameter to be corrected in the initial finite element model as the design reference value, set the adjustment range of each parameter to be corrected to 0~20% of the design reference value, and divide it into multiple gradient levels. S16. Determine the modal frequency of the flexible structure as the target response parameter. The modal frequency includes the first N modal frequencies, with the first-order modal frequency being the primary correction target, while also taking into account the accuracy requirements of the second and third-order modal frequencies.

[0008] Further, step S2 includes: S21. Extract the current set values ​​of each parameter to be corrected from the initial finite element model, and use them as the design reference values ​​for airbag stiffness. Skin stiffness design benchmark value and the design benchmark value of stiffness at rigid-flexible connection ; S22. Based on the parameter sensitivity determined by the error source analysis, the adjustment range of each parameter to be corrected is set to 0%~20% of the design baseline value; within the adjustment range, multiple gradient levels are divided, including five gradients: 0%, 5%, 10%, 15%, and 20%, forming a discrete adjustment level set for each parameter to be corrected. S23. Based on the number of parameters to be corrected and the small sample constraint, select the Latin hypercube sampling method or the uniform design method as the experimental design method to ensure that the sample points have spatial filling characteristics and are uniformly distributed in the parameter space. S24. Using the selected experimental design method, generate multiple sets of sample points within the adjustment range. Each set of sample points includes a specific combination of three parameters: airbag stiffness, skin stiffness, and stiffness at the rigid-flexible connection. S25. For each set of sample points, modify the corresponding material properties or connection stiffness settings in the initial finite element model, submit it to the finite element analysis software for modal analysis calculation, and extract the first N modal frequencies as response values. S26. Summarize the parameter combinations of all sample points and their corresponding modal frequency response values ​​to construct a sample dataset containing an input parameter matrix and an output response vector; divide the sample dataset into a training set and a test set according to a preset ratio, wherein the training set is used for subsequent training of the proxy model and the test set is used for verification of the generalization ability of the proxy model.

[0009] Further, step S3 includes: S31. Divide the sample dataset into a training set and a test set according to a preset ratio; the training set is used for parameter fitting of the surrogate model, and the test set is used for independent validation of the model; the preset ratio is determined according to the total number of samples. When the total number of samples is small, leave-one-out cross-validation is used, and when the total number of samples is sufficient, a fixed ratio of 7:3 or 8:2 is used. S32. A surrogate model is constructed by combining a quadratic polynomial function and a radial basis function; the quadratic polynomial function is used to capture the global trend of the parameters, and the radial basis function is used to fit the local nonlinear characteristics of the parameters. S33. Set the type and shape parameters of the radial basis function kernel; the radial basis function kernel is selected from Gaussian function, multiple quadratic function or inverse multiple quadratic function; initialize polynomial coefficients and radial basis weight coefficients, and set the initial iteration value and convergence criterion of the optimization algorithm; S34. Using the combination of parameters to be corrected in the training set as input and the corresponding modal frequency simulation value as output, the polynomial coefficients and radial basis weight coefficients are optimized by minimizing the mean square error between the predicted value and the simulation value; the optimization uses the least squares method or the maximum likelihood estimation method to solve the linear equation system to obtain the optimal coefficient combination that minimizes the error function. S35. Based on the polynomial coefficients and radial basis weights obtained after training, calculate the goodness of fit of the training set. The root mean square error (RMSE) is used to evaluate how well the model fits the training data. S36. Input the combination of parameters to be corrected from the test set into the trained surrogate model to obtain the modal frequency prediction value; calculate the error between the prediction value and the corresponding finite element simulation value in the test set, including absolute error, relative error and goodness of fit. ; S37. Determine the goodness of fit of the test set. Whether the preset threshold is met and whether the deviation between the predicted and measured values ​​meets the preset error limit; the preset threshold requires the predicted first-order mode frequency to be within the preset range. ≥0.99, the preset error limit requires the deviation between the predicted value and the measured value to be ≥0.99. 0.05Hz; S38. If the test set verification meets the preset accuracy threshold, the trained surrogate model is output, and the polynomial coefficients, radial basis weight coefficients, and kernel function parameters are determined as the final model parameters; if not, return to step S2, regenerate the sample dataset, and repeat steps S31 to S37 until the accuracy requirements are met.

[0010] Further, step S4 includes: S41. Based on the modal test results of the flexible structure of the air-filled reducer, extract the target modal frequency values; the target modal frequency values ​​include the first-order modal frequency target value, the second-order modal frequency target value, and the third-order modal frequency target value, with the first-order modal frequency target value as the main optimization target; S42. With minimizing the absolute value of the difference between the predicted modal frequency and the target modal frequency of the parameter to be corrected as the optimization objective, construct a single-objective or multi-objective optimization objective function; S43. Using the adjustment range of each parameter to be corrected set in step S22 as the constraint boundary, establish the constraint conditions for the optimization problem; the constraint conditions include the airbag stiffness adjustment amount constraint, the skin stiffness adjustment amount constraint, and the stiffness adjustment amount constraint at the rigid-flexible connection. The adjustment amount of each parameter is within the range of 0% to 20% of the design reference value. S44. Set the running parameters of the genetic algorithm, including population size. Maximum number of iterations Crossover probability Probability of mutation and convergence criteria; S45. Randomly generate within the constrained boundaries The sets of parameters to be corrected constitute the initial population of the genetic algorithm; each set of parameters represents an individual, including three genetic variables: airbag stiffness, skin stiffness, and stiffness at the rigid-flexible connection. S46. For each individual in the current population, quickly predict its corresponding modality frequency using the surrogate model trained in step S3, and calculate the fitness value of each individual based on the optimization objective function; the fitness value is inversely proportional to the objective function value, and the smaller the objective function value, the higher the fitness. S47. Based on the fitness value, select superior individuals from the current population to enter the next generation using roulette wheel selection, tournament selection, or elite retention strategies; retain the elite individuals with the highest fitness to be directly inherited by the next generation to avoid the loss of superior genes; S48, with the aforementioned crossover probability Selected individuals are paired up, and single-point crossover, multi-point crossover, or uniform crossover is used to exchange some gene segments between the paired individuals to generate new offspring individuals; S49, with the aforementioned mutation probability The genes of offspring individuals are mutated using Gaussian mutation, uniform mutation, or non-uniform mutation methods. Within the constraint boundary, the gene values ​​are randomly perturbed to increase population diversity and avoid premature convergence. S410. The new population generated through selection, crossover, and mutation operations is used as the current population. Return to step S46 to perform the next generation of evolution. Record the optimal fitness value and the corresponding optimal parameter combination of each generation of the population, and monitor the convergence trend. S411. Determine whether the current iteration count has reached the maximum iteration count. Alternatively, determine whether the improvement of the optimal fitness value over multiple consecutive generations is less than a preset threshold; if any convergence criterion is met, terminate the iteration and execute step S412; otherwise, return to step S46 to continue evolution. S412. Extract the optimal individual at the end of evolution and decode to obtain the optimal parameter combination.

[0011] Further, step S5 includes: S51. Convert the optimal parameter combination output in step S412 into material property parameters that can be recognized by the finite element model, including converting the change in airbag stiffness into the updated value of the equivalent elastic modulus of the airbag material, converting the change in skin stiffness into the updated value of the equivalent elastic modulus of the skin material, and converting the change in stiffness at the rigid-flexible connection into the stiffness coefficient of the connection area or the updated value of the constraint equation. S52. Based on the converted material property parameters, modify the corresponding property settings in the initial finite element model, including updating the material card properties of the airbag unit, updating the material card properties of the skin unit, and updating the stiffness matrix or connection unit properties at the rigid-flexible connection, to obtain the corrected finite element model. S53. Perform geometric consistency, mesh quality and connection integrity checks on the corrected finite element model; verify whether the model after parameter update has element distortion, connection failure or abnormal quality characteristics, and ensure that the model is suitable for modal analysis calculation; S54. Submit the corrected finite element model to the finite element analysis software (LS-DYNA software) for modal solution; set the modal analysis type to Lanzos method or subspace iteration method, extract the first N modal frequencies and mode shapes, where N≥3, and prioritize the solution accuracy of the first three modes; S55. Extract the calculated values ​​of each modal frequency of the corrected model from the modal analysis results, including the calculated value of the first-order modal frequency. Calculated values ​​of second-order modal frequencies and the calculated values ​​of the third-order modal frequencies and the corresponding mode shape data; S56. Determine the target modal frequency value for comparison and verification; the target modal frequency value adopts the experimentally measured target value determined in step S41, including the first-order target value. Second-order objective value and third-order objective value ; S57. Calculate the absolute and relative errors between the calculated values ​​of each modal frequency and the corresponding target values; S58. Determine whether the relative errors of each modal frequency meet the preset engineering accuracy requirements; the preset engineering accuracy requirements are: relative error of the first modal frequency Relative error of second-order modal frequencies Relative error of third-order modal frequencies The system is deemed to meet engineering accuracy requirements if and only if all third-order modal frequencies satisfy the corresponding error thresholds. S59. If the engineering accuracy requirements are met, the corrected finite element model is output as the final correction result, including the corrected model file, the optimal parameter combination document, the comparison report of the calculated values ​​and target values ​​of each modal frequency, and the mode shape cloud map data, to complete the model correction. S510. If the engineering accuracy requirements are not met, analyze the source of error and return to step S4 to adjust and optimize the parameters until the accuracy requirements are met.

[0012] Compared with the prior art, the present invention has the following advantages: 1. This invention fully considers the material orthogonality, large deformation and prestress characteristics of flexible components during the finite element modeling process, and uses finite element elements adapted to flexible bodies to complete the modeling, which solves the problem of insufficient adaptability of flexible component modeling in the prior art. It reduces the calculation error of modal parameters from the source of modeling and accurately reflects the real dynamic response of flexible structures.

[0013] 2. This invention employs a combination of polynomial functions and radial basis functions to construct a surrogate model, and combines this with a uniform design method to generate multiple sets of core samples covering the three-parameter coupling relationship. This achieves accurate capture of the nonlinear mapping relationship between parameters and modal frequencies under small sample conditions, and improves the goodness of fit for first-order modal frequency prediction. The deviation between predicted and measured values This solves the technical defect of low accuracy in small sample parameter coupling fitting and meets engineering-level accuracy requirements.

[0014] 3. This invention focuses on modal frequency as a core dynamic indicator, establishing a specific correction logic for the flexible structure engineering requirements of air-filled reducers. It combines a genetic algorithm to optimize parameters and verifies the correction accuracy through multi-order modal frequency analysis. The corrected first-order modal frequency error is [not specified]. Second order Third order This solves the problem of the lack of adaptability between dynamic targets and correction methods, and the corrected model is highly consistent with the experimental calibration values.

[0015] 4. This invention constructs a closed-loop correction system for the entire process of "error source tracing, sample generation, proxy modeling, parameter optimization and dynamic verification". Each step is closely connected and logically complete. The computational efficiency of model correction is significantly improved compared with traditional methods. Moreover, the correction results can directly provide accurate model basis for the dynamic stability design of the re-entry process of the air-filled reducer, and provide reliable methodological support for the engineering optimization design of flexible structures.

[0016] In summary, the technical solution of this invention effectively solves the core problems in the existing finite element model correction technology for flexible structures of air-filled reducers, such as insufficient adaptability of flexible component modeling, low accuracy of small sample parameter coupling fitting, and lack of adaptability between dynamic targets and correction methods. It achieves high-precision correction of finite element models of flexible structures under small sample conditions, filling the gap in the existing technology for accurate modeling and dynamic characteristic correction of flexible structures.

[0017] Therefore, the technical solution of this invention can be widely applied in the correction of finite element models of flexible structures in fields such as aerospace engineering and aviation engineering. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart of the method of the present invention.

[0020] Figure 2 A cross-sectional view of the IRVE-3 aircraft provided for an embodiment of the present invention.

[0021] Figure 3 The IRVE-3 geometric model provided for embodiments of the present invention.

[0022] Figure 4 Modal frequencies and displacement contour plots under different modeling modes of IRVE-3 provided in this embodiment of the invention.

[0023] Figure 5 The first six modes and displacement contour plots under the initial parameters of IRVE-3 provided in this embodiment of the invention.

[0024] Figure 6 The response surface learned by the GPR model provided in this embodiment of the invention.

[0025] Figure 7 The corrected first-order modal frequencies and mode shape contour plots provided for embodiments of the present invention. Detailed Implementation

[0026] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0027] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims and accompanying drawings of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such processes, methods, products or devices.

[0028] like Figure 1 As shown, this invention provides a proxy model correction method for the finite element model of a flexible structure of an inflatable reducer, comprising: S1. Establish an initial finite element model of the flexible structure of the inflatable reducer as the model to be corrected, identify the core sensitive parameters in the initial finite element model that affect the accuracy of modal frequency calculation as parameters to be corrected, and determine the modal frequency of the flexible structure as the target response parameter; the flexible structure includes an airbag, a skin, and fabric straps; the parameters to be corrected include the stiffness of the airbag, the stiffness of the skin, and the stiffness of the rigid-flexible connection. S2. Based on the current set value of the parameter to be corrected in the initial finite element model as the design benchmark value, the adjustment range of each parameter to be corrected is set according to the error source analysis results; within the adjustment range, sample points are generated using the design of experiments method, and the modal frequencies corresponding to each sample point are calculated through finite element simulation to construct a sample dataset containing multiple sets of parameter combinations and their corresponding modal frequencies; the sample dataset is used to characterize the mapping relationship between the parameter to be corrected and the modal frequencies. S3. Divide the sample dataset into a training set and a test set; construct a surrogate model using a combination of polynomial functions and radial basis functions, and establish a nonlinear mapping relationship between the parameters to be corrected and the modal frequencies; optimize the fitting parameters of the surrogate model using the training set to minimize the error between the predicted values ​​of the surrogate model and the finite element simulation values; verify the prediction accuracy and generalization ability of the surrogate model using the test set. When the preset accuracy threshold is met, output the trained surrogate model; otherwise, return to step S2 to expand the sample data. S4. Using the target modal frequency obtained from the experimental measurement as the optimization target value, the parameter to be corrected as the design variable, and the adjustment range of the parameter to be corrected as the constraint condition, a genetic algorithm combined with the surrogate model is used for optimization calculation; wherein, the surrogate model is used to quickly predict the modal frequency corresponding to each candidate parameter combination, and the optimization objective is to minimize the absolute value of the difference between the predicted value and the target value. The optimal parameter combination that makes the modal frequency approach the target value is obtained through iterative evolution. S5. Substitute the optimal parameter combination into the initial finite element model, update the parameters to be corrected, and obtain the corrected finite element model; perform modal analysis on the corrected finite element model to calculate the multi-order modal frequencies; compare the multi-order modal frequencies with the corresponding target modal frequencies and calculate the frequency errors of each order; determine whether the frequency errors meet the preset engineering accuracy requirements. If they do, output the corrected finite element model as the final correction result to complete the model correction; if they do not meet the requirements, return to step S4 to adjust the optimization parameters until the accuracy requirements are met.

[0029] In a specific implementation, as a preferred embodiment of the present invention, step S1 includes: S11. Based on the geometric structure, material properties and connection relationship of the inflatable reducer, an initial finite element model of the flexible structure including airbags, skin and fabric straps is established using finite element analysis software; the inflatable reducer is composed of multiple inflatable airbags, a rigid central body and fabric straps, and the inflatable airbags adopt a stacked toroidal structure and are interconnected with the central body and airbags through fabric straps. S12. Perform modal analysis on the initial finite element model to extract the multi-mode frequencies and mode shapes under the initial parameters, which will be used as the reference values ​​for subsequent corrections. S13. Based on finite element modeling errors, material parameter errors, and boundary condition constraint errors, identify the key error sources that affect the accuracy of modal frequency calculation; analyze the sensitivity of airbag stiffness, skin stiffness, and stiffness at rigid-flexible connections to modal frequencies, and determine airbag stiffness, skin stiffness, and stiffness at rigid-flexible connections as core sensitive parameters. S14. Select the airbag stiffness, skin stiffness, and stiffness at the rigid-flexible connection as parameters to be corrected; wherein, the airbag stiffness is the equivalent elastic modulus or stiffness coefficient of the airbag material, the skin stiffness is the equivalent elastic modulus or stiffness coefficient of the skin material, and the stiffness at the rigid-flexible connection is the equivalent stiffness of the connection area between the flexible airbag and the rigid central body. S15. Using the current value of the parameter to be corrected in the initial finite element model as the design reference value, set the adjustment range of each parameter to be corrected to 0~20% of the design reference value, and divide it into multiple gradient levels. S16. Determine the modal frequency of the flexible structure as the target response parameter. The modal frequency includes the first N modal frequencies, with the first-order modal frequency being the primary correction target, while also taking into account the accuracy requirements of the second and third-order modal frequencies.

[0030] In a specific implementation, as a preferred embodiment of the present invention, step S2 includes: S21. Extract the current set values ​​of each parameter to be corrected from the initial finite element model, and use them as the design reference values ​​for airbag stiffness. Skin stiffness design benchmark value and the design benchmark value of stiffness at rigid-flexible connection ; S22. Based on the parameter sensitivity determined by the error source analysis, the adjustment range of each parameter to be corrected is set to 0%~20% of the design baseline value; within the adjustment range, multiple gradient levels are divided, including five gradients: 0%, 5%, 10%, 15%, and 20%, forming a discrete adjustment level set for each parameter to be corrected. S23. Based on the number of parameters to be corrected and the small sample constraint, select the Latin hypercube sampling method or the uniform design method as the experimental design method to ensure that the sample points have spatial filling characteristics and are uniformly distributed in the parameter space. S24. Using the selected experimental design method, generate multiple sets of sample points within the adjustment range. Each set of sample points includes a specific combination of three parameters: airbag stiffness, skin stiffness, and stiffness at the rigid-flexible connection. The number of sample points is determined comprehensively based on computational resource constraints and the accuracy requirements of the surrogate model. S25. For each set of sample points, modify the corresponding material properties or connection stiffness settings in the initial finite element model, submit it to the finite element analysis software for modal analysis calculation, and extract the first N modal frequencies as response values; the modal analysis calculation includes model preprocessing, solver settings, and post-processing to extract modal frequencies; S26. Summarize the parameter combinations of all sample points and their corresponding modal frequency response values ​​to construct a sample dataset containing an input parameter matrix and an output response vector; divide the sample dataset into a training set and a test set according to a preset ratio, wherein the training set is used for subsequent training of the proxy model and the test set is used for verification of the generalization ability of the proxy model.

[0031] In a specific implementation, as a preferred embodiment of the present invention, step S3 includes: S31. Divide the sample dataset into a training set and a test set according to a preset ratio; the training set is used for parameter fitting of the surrogate model, and the test set is used for independent validation of the model; the preset ratio is determined according to the total number of samples. When the total number of samples is small, leave-one-out cross-validation is used, and when the total number of samples is sufficient, a fixed ratio of 7:3 or 8:2 is used. S32. A surrogate model is constructed using a combination of a quadratic polynomial function and a radial basis function; the quadratic polynomial function is used to capture the global trend of the parameters, and the radial basis function is used to fit the local nonlinear characteristics of the parameters; the mathematical expression of the surrogate model is:

[0032] in, The parameter vector to be corrected. These are the predicted modal frequencies. For polynomial coefficients, These are the radial basis weighting coefficients. For radial basis kernel functions, These are the training sample points; S33. Set the type and shape parameters of the radial basis function kernel; the radial basis function kernel is selected from Gaussian function, multiple quadratic function or inverse multiple quadratic function; initialize polynomial coefficients and radial basis weight coefficients, and set the initial iteration value and convergence criterion of the optimization algorithm; S34. Using the combination of parameters to be corrected in the training set as input and the corresponding modal frequency simulation value as output, the polynomial coefficients and radial basis weight coefficients are optimized by minimizing the mean square error between the predicted value and the simulation value; the optimization uses the least squares method or the maximum likelihood estimation method to solve the linear equation system to obtain the optimal coefficient combination that minimizes the error function. S35. Based on the polynomial coefficients and radial basis weights obtained after training, calculate the goodness of fit of the training set. The root mean square error (RMSE) is used to evaluate how well the model fits the training data. S36. Input the combination of parameters to be corrected from the test set into the trained surrogate model to obtain the modal frequency prediction value; calculate the error between the prediction value and the corresponding finite element simulation value in the test set, including absolute error, relative error and goodness of fit. ; S37. Determine the goodness of fit of the test set. Whether the preset threshold is met and whether the deviation between the predicted and measured values ​​meets the preset error limit; the preset threshold requires the predicted first-order mode frequency to be within the preset range. ≥0.99, the preset error limit requires the deviation between the predicted value and the measured value to be ≥0.99. 0.05Hz; S38. If the test set verification meets the preset accuracy threshold, the trained surrogate model is output, and the polynomial coefficients, radial basis weight coefficients, and kernel function parameters are determined as the final model parameters; if not, return to step S2, regenerate the sample dataset, and repeat steps S31 to S37 until the accuracy requirements are met.

[0033] In a specific implementation, as a preferred embodiment of the present invention, step S4 includes: S41. Based on the modal test results of the flexible structure of the air-filled reducer, extract the target modal frequency values; the target modal frequency values ​​include the first-order modal frequency target value, the second-order modal frequency target value, and the third-order modal frequency target value, with the first-order modal frequency target value as the main optimization target; S42. Taking the minimization of the absolute value of the difference between the predicted modal frequency and the target modal frequency of the parameter to be corrected as the optimization objective, construct a single-objective or multi-objective optimization objective function, which is expressed as:

[0034] Or, for multi-mode optimization, the objective function can be expressed as:

[0035] in, This represents the modal frequencies predicted by the surrogate model. Indicates the actual measured target value in the experiment. Indicates the first Weighting coefficients for the first mode. This indicates the modal order being considered.

[0036] S43. Using the adjustment range of each parameter to be corrected set in step S22 as the constraint boundary, establish the constraint conditions for the optimization problem; the constraint conditions include the airbag stiffness adjustment amount constraint, the skin stiffness adjustment amount constraint, and the stiffness adjustment amount constraint at the rigid-flexible connection. The adjustment amount of each parameter is within the range of 0% to 20% of the design reference value. S44. Set the running parameters of the genetic algorithm, including population size. Maximum number of iterations Crossover probability Probability of mutation The population size is set to 50-100 individuals, the crossover probability is set to 0.7-0.9, the mutation probability is set to 0.01-0.1, and the maximum number of iterations is set to 100-200. S45. Randomly generate within the constrained boundaries The sets of parameters to be corrected constitute the initial population of the genetic algorithm; each set of parameters represents an individual, including three genetic variables: airbag stiffness, skin stiffness, and stiffness at the rigid-flexible connection. S46. For each individual in the current population, quickly predict its corresponding modality frequency using the surrogate model trained in step S3, and calculate the fitness value of each individual based on the optimization objective function; the fitness value is inversely proportional to the objective function value, and the smaller the objective function value, the higher the fitness. S47. Based on the fitness value, select superior individuals from the current population to enter the next generation using roulette wheel selection, tournament selection, or elite retention strategies; retain the elite individuals with the highest fitness to be directly inherited by the next generation to avoid the loss of superior genes; S48, with the aforementioned crossover probability Selected individuals are paired up, and single-point crossover, multi-point crossover, or uniform crossover is used to exchange some gene fragments between paired individuals to generate new offspring individuals; the crossover operation is performed within the constraint boundary to ensure that the offspring individuals meet the parameter adjustment range constraint. S49, with the aforementioned mutation probability The genes of offspring individuals are mutated using Gaussian mutation, uniform mutation, or non-uniform mutation methods. Within the constraint boundary, the gene values ​​are randomly perturbed to increase population diversity and avoid premature convergence. S410. The new population generated through selection, crossover, and mutation operations is used as the current population. Return to step S46 to perform the next generation of evolution. Record the optimal fitness value and the corresponding optimal parameter combination of each generation of the population, and monitor the convergence trend. S411. Determine whether the current iteration count has reached the maximum iteration count. Alternatively, determine whether the improvement of the optimal fitness value over multiple consecutive generations is less than a preset threshold; if any convergence criterion is met, terminate the iteration and execute step S412; otherwise, return to step S46 to continue evolution. S412. Extract the optimal individual at the end of evolution and decode to obtain the optimal parameter combination. The optimal parameter combination includes the optimal change in airbag stiffness, the optimal change in skin stiffness, and the optimal change in stiffness at the rigid-flexible connection, as well as the corresponding modal frequency prediction values; output the optimal parameter combination as the correction parameter result for dynamic characteristic verification in step S5.

[0037] In a specific implementation, as a preferred embodiment of the present invention, step S5 includes: S51. Convert the optimal parameter combination output in step S412 into material property parameters that can be recognized by the finite element model, including converting the change in airbag stiffness into the updated value of the equivalent elastic modulus of the airbag material, converting the change in skin stiffness into the updated value of the equivalent elastic modulus of the skin material, and converting the change in stiffness at the rigid-flexible connection into the stiffness coefficient of the connection area or the updated value of the constraint equation. S52. Based on the converted material property parameters, modify the corresponding property settings in the initial finite element model, including updating the material card properties of the airbag unit, updating the material card properties of the skin unit, and updating the stiffness matrix or connection unit properties at the rigid-flexible connection, to obtain the corrected finite element model. S53. Perform geometric consistency, mesh quality and connection integrity checks on the corrected finite element model; verify whether the model after parameter update has element distortion, connection failure or abnormal quality characteristics, and ensure that the model is suitable for modal analysis calculation; S54. Submit the corrected finite element model to the finite element analysis software (LS-DYNA software) for modal solution; set the modal analysis type to Lanzos method or subspace iteration method, extract the first N modal frequencies and mode shapes, where N≥3, and prioritize the solution accuracy of the first three modes; S55. Extract the calculated values ​​of each modal frequency of the corrected model from the modal analysis results, including the calculated value of the first-order modal frequency. Calculated values ​​of second-order modal frequencies and the calculated values ​​of the third-order modal frequencies and the corresponding mode shape data; S56. Determine the target modal frequency value for comparison and verification; the target modal frequency value adopts the experimentally measured target value determined in step S41, including the first-order target value. Second-order objective value and third-order objective value ; S57. Calculate the absolute and relative errors between the calculated values ​​of each modal frequency and the corresponding target values; the formula for calculating the relative error is:

[0038] in, Indicates the first The relative error of the first modal frequencies, For the first Calculated value of order, For the first Target value; S58. Determine whether the relative errors of each modal frequency meet the preset engineering accuracy requirements; the preset engineering accuracy requirements are: relative error of the first modal frequency Relative error of second-order modal frequencies Relative error of third-order modal frequencies The system is deemed to meet engineering accuracy requirements if and only if all third-order modal frequencies satisfy the corresponding error thresholds. S59. If the engineering accuracy requirements are met, the corrected finite element model is output as the final correction result, including the corrected model file, the optimal parameter combination document, the comparison report of the calculated values ​​and target values ​​of each modal frequency, and the mode shape cloud map data, to complete the model correction. S510. If the engineering accuracy requirements are not met, analyze the source of error and return to step S4 to adjust and optimize the parameters until the accuracy requirements are met.

[0039] Example Step 1: Define the research object and core parameters The simulation model is based on the American IRVE-3 aircraft, which consists of seven inflatable airbags and one rigid central body. The airbags are arranged in a stacked toroidal structure, with the seven airbags distributed in a 60° cone shape. They are interconnected with the central body and the airbags via multiple fabric straps. Figure 2 (Cross-section diagram of IRVE-3 aircraft) Figure 3 As shown in the (IRVE-3 geometric model), the core parameter settings are shown in Table 1 (numerical simulation parameters). For the flexible structure of this aircraft, the modal characteristics under three typical modeling modes were calculated using LS-DYNA software, as follows: Figure 4 (Comparison of modal frequencies and displacement contour plots under different modeling modes of IRVE-3).

[0040] Table 1 Numerical Simulation Parameters

[0041] Parameter correction: Select 3 core sensitive parameters, as follows: Airbag stiffness: Design benchmark value is The adjustment range is 0~20% (including 5%, 10%, 15%, and 20% gradients). Skin stiffness ( The design baseline value is The adjustment range is 0~20% (including 5%, 10%, 15%, and 20% gradients). Stiffness of rigid-flexible joint ( )(like Figure 4 (Rigid-flexible connection): The equivalent stiffness at the connection between the flexible airbag and the central rigid body, with a design reference value of [value missing]. The adjustment range is 0~20% (including 5%, 10%, 15%, and 20% gradients). Target response parameters: Focusing on the modal frequencies of flexible structures Step 2: Generating the Sample Dataset Based on the gradient adjustment range of the three parameters to be corrected, a parameter combination including the initial mode is generated (see below). Figure 5 (The first six modes under initial parameters) 11 core training samples covering commonly used engineering parameter combinations and ensuring full coverage of the three-parameter coupling relationship; for each sample, nonlinear static analysis and modal analysis are carried out by LS-DYNA to output its first six modal frequencies, and finally the training dataset and test dataset are constructed, as shown in Table 2 (positive problem surrogate model dataset).

[0042] Table 2 Dataset for Positive Problem Agent Model

[0043] Step 3: Proxy Model Construction The core steps for model training based on the MATLAB platform are as follows: Model definition: A nonlinear fitting architecture is adopted to construct the mapping relationship between two parameters to be corrected and the modal frequencies; Model training: Using 11 sets of training samples as input, the fitting function parameters are optimized to accurately capture the parameter coupling relationship; Model validation: Test set validation shows that the first-order mode frequency prediction goodness of fit is good. The deviation between predicted and measured values Its generalization ability meets engineering requirements.

[0044] Step 4: Parameter adjustment and optimization based on genetic algorithm Optimization objective function: The first-order modal frequency target value (6.59Hz) is used as the benchmark; Corrected output results: After optimization convergence, the optimal parameter combination is output (typical results: airbag stiffness change 13.7%, skin stiffness change 10%), see [link to relevant documentation]. Figure 6 (Response surface learned by the GPR model).

[0045] Step 5: Verify the dynamic characteristics of the corrected model Core frequency verification: The measured value of the corrected first-order mode frequency is 6.588Hz, with an error of 0.1% compared to the target value. See [link / reference]. Figure 7 (Corrected first-order mode and mode shape contour plot); Multimodal verification: The corrected second-order modal frequency is 8.62Hz (target value 8.60Hz, error 0.2%), and the third-order modal frequency is 11.65Hz (target value 11.60Hz, error 0.4%), both of which meet the engineering accuracy requirements.

[0046] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for surrogate model correction of a finite element model of a flexible structure of an inflatable reducer, characterized in that, include: S1. Establish an initial finite element model of the flexible structure of the air-filled reducer as the model to be corrected, identify the core sensitive parameters in the initial finite element model that affect the accuracy of modal frequency calculation as the parameters to be corrected, and determine the modal frequency of the flexible structure as the target response parameter. S2. Based on the current set value of the parameter to be corrected in the initial finite element model as the design benchmark value, the adjustment range of each parameter to be corrected is set according to the error source analysis results; within the adjustment range, the experimental design method is used to generate sample points, and the modal frequencies corresponding to each sample point are calculated through finite element simulation to construct a sample dataset containing multiple sets of parameter combinations and their corresponding modal frequencies. S3. Divide the sample dataset into a training set and a test set; construct a surrogate model using a combination of polynomial functions and radial basis functions, and establish a nonlinear mapping relationship between the parameters to be corrected and the modal frequencies; optimize the fitting parameters of the surrogate model using the training set to minimize the error between the predicted values ​​of the surrogate model and the finite element simulation values. The prediction accuracy and generalization ability of the surrogate model are verified using the test set. When the preset accuracy threshold is met, the trained surrogate model is output; otherwise, the process returns to step S2 to expand the sample data. S4. Using the target modal frequency obtained from the experimental measurement as the optimization target value, the parameter to be corrected as the design variable, and the adjustment range of the parameter to be corrected as the constraint condition, a genetic algorithm combined with the surrogate model is used for optimization calculation; wherein, the surrogate model is used to quickly predict the modal frequency corresponding to each candidate parameter combination, and the optimization objective is to minimize the absolute value of the difference between the predicted value and the target value. The optimal parameter combination that makes the modal frequency approach the target value is obtained through iterative evolution. S5. Substitute the optimal parameter combination into the initial finite element model, update the parameters to be corrected, and obtain the corrected finite element model; perform modal analysis on the corrected finite element model to calculate the multi-order modal frequencies; compare the multi-order modal frequencies with the corresponding target modal frequencies and calculate the frequency errors of each order; determine whether the frequency errors meet the preset engineering accuracy requirements. If they do, output the corrected finite element model as the final correction result to complete the model correction; if they do not meet the requirements, return to step S4 to adjust the optimization parameters until the accuracy requirements are met.

2. The proxy model correction method for the finite element model of a flexible structure of an inflatable reducer according to claim 1, characterized in that, Step S1 includes: S11. Based on the geometric structure, material properties and connection relationship of the inflatable reducer, an initial finite element model of the flexible structure including airbags, skin and fabric straps is established using finite element analysis software; the inflatable reducer is composed of multiple inflatable airbags, a rigid central body and fabric straps, and the inflatable airbags adopt a stacked toroidal structure and are interconnected with the central body and airbags through fabric straps. S12. Perform modal analysis on the initial finite element model to extract the multi-mode frequencies and mode shapes under the initial parameters, which will be used as the reference values ​​for subsequent corrections. S13. Based on finite element modeling errors, material parameter errors, and boundary condition constraint errors, identify the key error sources that affect the accuracy of modal frequency calculation; analyze the sensitivity of airbag stiffness, skin stiffness, and stiffness at rigid-flexible connections to modal frequencies, and determine airbag stiffness, skin stiffness, and stiffness at rigid-flexible connections as core sensitive parameters. S14. Select the airbag stiffness, skin stiffness, and stiffness at the rigid-flexible connection as parameters to be corrected; wherein, the airbag stiffness is the equivalent elastic modulus or stiffness coefficient of the airbag material, the skin stiffness is the equivalent elastic modulus or stiffness coefficient of the skin material, and the stiffness at the rigid-flexible connection is the equivalent stiffness of the connection area between the flexible airbag and the rigid central body. S15. Using the current value of the parameter to be corrected in the initial finite element model as the design reference value, set the adjustment range of each parameter to be corrected to 0~20% of the design reference value, and divide it into multiple gradient levels. S16. Determine the modal frequency of the flexible structure as the target response parameter. The modal frequency includes the first N modal frequencies, with the first-order modal frequency being the primary correction target, while also taking into account the accuracy requirements of the second and third-order modal frequencies.

3. The proxy model correction method for the finite element model of a flexible structure of an inflatable reducer according to claim 1, characterized in that, Step S2 includes: S21. Extract the current set values ​​of each parameter to be corrected from the initial finite element model, and use them as the design reference values ​​for airbag stiffness. Skin stiffness design benchmark value and the design benchmark value of stiffness at rigid-flexible connection ; S22. Based on the parameter sensitivity determined by the error source analysis, the adjustment range of each parameter to be corrected is set to 0%~20% of the design baseline value; within the adjustment range, multiple gradient levels are divided, including five gradients: 0%, 5%, 10%, 15%, and 20%, forming a discrete adjustment level set for each parameter to be corrected. S23. Based on the number of parameters to be corrected and the small sample constraint, select the Latin hypercube sampling method or the uniform design method as the experimental design method to ensure that the sample points have spatial filling characteristics and are uniformly distributed in the parameter space. S24. Using the selected experimental design method, generate multiple sets of sample points within the adjustment range. Each set of sample points includes a specific combination of three parameters: airbag stiffness, skin stiffness, and stiffness at the rigid-flexible connection. S25. For each set of sample points, modify the corresponding material properties or connection stiffness settings in the initial finite element model, submit it to the finite element analysis software for modal analysis calculation, and extract the first N modal frequencies as response values. S26. Summarize the parameter combinations of all sample points and their corresponding modal frequency response values ​​to construct a sample dataset containing an input parameter matrix and an output response vector; divide the sample dataset into a training set and a test set according to a preset ratio, wherein the training set is used for subsequent training of the proxy model and the test set is used for verification of the generalization ability of the proxy model.

4. The surrogate model correction method for the finite element model of a flexible structure of an inflatable reducer according to claim 1, characterized in that, Step S3 includes: S31. Divide the sample dataset into a training set and a test set according to a preset ratio; the training set is used for parameter fitting of the surrogate model, and the test set is used for independent validation of the model; the preset ratio is determined according to the total number of samples. When the total number of samples is small, leave-one-out cross-validation is used, and when the total number of samples is sufficient, a fixed ratio of 7:3 or 8:2 is used. S32. A surrogate model is constructed by combining a quadratic polynomial function and a radial basis function; the quadratic polynomial function is used to capture the global trend of the parameters, and the radial basis function is used to fit the local nonlinear characteristics of the parameters. S33. Set the type and shape parameters of the radial basis function kernel; the radial basis function kernel is selected from Gaussian function, multiple quadratic function or inverse multiple quadratic function; initialize polynomial coefficients and radial basis weight coefficients, and set the initial iteration value and convergence criterion of the optimization algorithm; S34. Using the combination of parameters to be corrected in the training set as input and the corresponding modal frequency simulation value as output, the polynomial coefficients and radial basis weight coefficients are optimized by minimizing the mean square error between the predicted value and the simulation value; the optimization uses the least squares method or the maximum likelihood estimation method to solve the linear equation system to obtain the optimal coefficient combination that minimizes the error function. S35. Based on the polynomial coefficients and radial basis weights obtained after training, calculate the goodness of fit of the training set. The root mean square error (RMSE) is used to evaluate how well the model fits the training data. S36. Input the combination of parameters to be corrected from the test set into the trained surrogate model to obtain the modal frequency prediction value; calculate the error between the prediction value and the corresponding finite element simulation value in the test set, including absolute error, relative error and goodness of fit. ; S37. Determine the goodness of fit of the test set. Whether the preset threshold is met and whether the deviation between the predicted and measured values ​​meets the preset error limit; the preset threshold requires the predicted first-order mode frequency to be within the preset range. ≥0.99, the preset error limit requires the deviation between the predicted value and the measured value to be ≥0.

99. 0.05Hz; S38. If the test set verification meets the preset accuracy threshold, the trained surrogate model is output, and the polynomial coefficients, radial basis weight coefficients, and kernel function parameters are determined as the final model parameters; if not, return to step S2, regenerate the sample dataset, and repeat steps S31 to S37 until the accuracy requirements are met.

5. The proxy model correction method for the finite element model of a flexible structure of an inflatable reducer according to claim 1, characterized in that, Step S4 includes: S41. Based on the modal test results of the flexible structure of the air-filled reducer, extract the target modal frequency values; the target modal frequency values ​​include the first-order modal frequency target value, the second-order modal frequency target value, and the third-order modal frequency target value, with the first-order modal frequency target value as the main optimization target; S42. With minimizing the absolute value of the difference between the predicted modal frequency and the target modal frequency of the parameter to be corrected as the optimization objective, construct a single-objective or multi-objective optimization objective function; S43. Using the adjustment range of each parameter to be corrected set in step S22 as the constraint boundary, establish the constraint conditions for the optimization problem; the constraint conditions include the airbag stiffness adjustment amount constraint, the skin stiffness adjustment amount constraint, and the stiffness adjustment amount constraint at the rigid-flexible connection. The adjustment amount of each parameter is within the range of 0% to 20% of the design reference value. S44. Set the running parameters of the genetic algorithm, including population size. Maximum number of iterations Crossover probability Probability of mutation and convergence criteria; S45. Randomly generate within the constrained boundaries The sets of parameters to be corrected constitute the initial population of the genetic algorithm; each set of parameters represents an individual, including three genetic variables: airbag stiffness, skin stiffness, and stiffness at the rigid-flexible connection. S46. For each individual in the current population, quickly predict its corresponding modality frequency using the surrogate model trained in step S3, and calculate the fitness value of each individual based on the optimization objective function; the fitness value is inversely proportional to the objective function value, and the smaller the objective function value, the higher the fitness. S47. Based on the fitness value, select superior individuals from the current population to enter the next generation using roulette wheel selection, tournament selection, or elite retention strategies; retain the elite individuals with the highest fitness to be directly inherited by the next generation to avoid the loss of superior genes; S48, with the aforementioned crossover probability Selected individuals are paired up, and single-point crossover, multi-point crossover, or uniform crossover is used to exchange some gene segments between the paired individuals to generate new offspring individuals; S49, with the aforementioned mutation probability The genes of offspring individuals are mutated using Gaussian mutation, uniform mutation, or non-uniform mutation methods. Within the constraint boundary, the gene values ​​are randomly perturbed to increase population diversity and avoid premature convergence. S410. The new population generated through selection, crossover, and mutation operations is used as the current population. Return to step S46 to perform the next generation of evolution. Record the optimal fitness value and the corresponding optimal parameter combination of each generation of the population, and monitor the convergence trend. S411. Determine whether the current iteration count has reached the maximum iteration count. Alternatively, determine whether the improvement of the optimal fitness value over multiple consecutive generations is less than a preset threshold; if any convergence criterion is met, terminate the iteration and execute step S412; otherwise, return to step S46 to continue evolution. S412. Extract the optimal individual at the end of evolution and decode to obtain the optimal parameter combination.

6. The proxy model correction method for the finite element model of a flexible structure of an inflatable reducer according to claim 1, characterized in that, Step S5 includes: S51. Convert the optimal parameter combination output in step S412 into material property parameters that can be recognized by the finite element model, including converting the change in airbag stiffness into the updated value of the equivalent elastic modulus of the airbag material, converting the change in skin stiffness into the updated value of the equivalent elastic modulus of the skin material, and converting the change in stiffness at the rigid-flexible connection into the stiffness coefficient of the connection area or the updated value of the constraint equation. S52. Based on the converted material property parameters, modify the corresponding property settings in the initial finite element model, including updating the material card properties of the airbag unit, updating the material card properties of the skin unit, and updating the stiffness matrix or connection unit properties at the rigid-flexible connection, to obtain the corrected finite element model. S53. Perform geometric consistency, mesh quality and connection integrity checks on the corrected finite element model; verify whether the model after parameter update has element distortion, connection failure or abnormal quality characteristics, and ensure that the model is suitable for modal analysis calculation; S54. Submit the corrected finite element model to the finite element analysis software for modal solution; set the modal analysis type to the Lanzos method or the subspace iteration method, extract the first N modal frequencies and mode shapes, where N≥3, and prioritize the solution accuracy of the first three modes; S55. Extract the calculated values ​​of each modal frequency of the corrected model from the modal analysis results, including the calculated value of the first-order modal frequency. Calculated values ​​of second-order modal frequencies and the calculated values ​​of the third-order modal frequencies and the corresponding mode shape data; S56. Determine the target modal frequency value for comparison and verification; the target modal frequency value adopts the experimentally measured target value determined in step S41, including the first-order target value. Second-order objective value and third-order objective value ; S57. Calculate the absolute and relative errors between the calculated values ​​of each modal frequency and the corresponding target values; S58. Determine whether the relative errors of each modal frequency meet the preset engineering accuracy requirements; the preset engineering accuracy requirements are: relative error of the first modal frequency Relative error of second-order modal frequencies Relative error of third-order modal frequencies The system is deemed to meet engineering accuracy requirements if and only if all third-order modal frequencies satisfy the corresponding error thresholds. S59. If the engineering accuracy requirements are met, the corrected finite element model is output as the final correction result, including the corrected model file, the optimal parameter combination document, the comparison report of the calculated values ​​and target values ​​of each modal frequency, and the mode shape cloud map data, to complete the model correction. S510. If the engineering accuracy requirements are not met, analyze the source of error and return to step S4 to adjust and optimize the parameters until the accuracy requirements are met.

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