Flexible hinge finite element design method assisted by machine learning

Abstract

The invention discloses a machine learning assisted flexible hinge finite element design method, and relates to the technical field of flexible hinge design. Constructing a structure parameter library of the flexible hinge; converting the structure parameter library into a three-dimensional model library through three-dimensional modeling; performing simulation analysis on the three-dimensional model in different working environments, and constructing a corresponding grid library; a three-dimensional simulation database of the flexible hinge is generated by using simulation software; establishing a structure parameter and performance characteristic parameter library by utilizing a machine learning method; optimizing the design scheme through a machine learning method; and predicting design parameters based on machine learning, and performing flexible hinge performance characteristic prediction and scheme optimization. A machine learning method is adopted to predict an optimal design scheme of the flexible hinge, finite element analysis software is combined to simulate mechanical properties of a three-dimensional model of the flexible hinge, and a performance evaluation index is verified through a finite element experiment, so that the experiment cost is reduced, the design efficiency is improved, and expensive experiments and heavy calculation requirements are avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of flexible hinge design, and in particular to a flexible hinge finite element design method assisted by machine learning. Background Art

[0002] Flexible hinges have attracted widespread attention in various high-end mechanical systems due to their gapless transmission, high flexibility, high precision and strong load-bearing capacity. Their performance directly affects the transmission and guiding functions of the flexible structure, and is of great significance to improving the motion performance of mechanical systems in ultra-precision motion and guiding mechanisms.

[0003] However, the complex working environment and changeable mechanical conditions of the flexible hinge make its design face severe challenges. Different combinations of design parameters, such as semi-circular arc radius, hinge thickness, hinge width, hinge length and load, will significantly affect the performance of the flexible hinge, such as load-bearing capacity, stiffness and rotation performance. Therefore, it is very important to conduct in-depth research on the design scheme of the flexible hinge and its corresponding mechanical properties under specific working conditions. In addition, due to the long processing cycle of the flexible hinge and the difficulty in controlling the experimental conditions, the experimental optimization cost is high and the simulation calculation is large, which also makes the design and application of the flexible hinge difficult. Summary of the invention

[0004] In order to address the shortcomings of the background technology, the present invention provides a machine learning-assisted finite element design method for flexible hinges, which adopts a machine learning method to predict the optimal design scheme of the flexible hinge, combines finite element analysis software to simulate the mechanical properties of the three-dimensional model of the flexible hinge, and verifies the performance evaluation indicators of maximum bearing capacity, rotational stiffness and maximum rotation angle through finite element experiments, thereby reducing experimental costs and improving design efficiency, avoiding expensive experiments and heavy computing requirements.

[0005] To achieve the above object, the present invention adopts the following technical solution: a machine learning-assisted finite element design method for a flexible hinge, comprising the following steps:

[0006] Step 1: Create a structural parameter library for the flexible hinge

[0007] Different structural parameters are selected as input variables to construct the structural parameter library of the flexible hinge. The structural parameters include the semicircular arc radius R, hinge width W, hinge thickness t and hinge length L.

[0008] Step 2: Create a 3D model library for the flexible hinge

[0009] According to the data of the structural parameter library of the flexible hinge, a three-dimensional model of the flexible hinge is established by using a three-dimensional modeling software to obtain different design schemes, and the structural parameter library is converted into a three-dimensional model library of the flexible hinge for numerical simulation;

[0010] Step 3: Create a mesh library corresponding to the flexible hinge 3D model

[0011] The three-dimensional models of the flexible hinges in different design schemes are simulated and analyzed under different working environments using three-dimensional mesh drawing software and finite element analysis software. The mechanical properties of the flexible hinges are analyzed through mesh division of the three-dimensional model and finite element mesh analysis. The corresponding flexible hinge mesh models are generated according to different structural parameters, and the mesh library corresponding to the three-dimensional model is constructed using the generated mesh data.

[0012] Step 4: Establish a 3D simulation database for the flexible hinge

[0013] Based on the physical model and material properties, boundary conditions are defined and simulation software is used to generate a three-dimensional simulation database of the flexible hinge;

[0014] Step 5: Use machine learning methods to establish a library of structural parameters and performance characteristic parameters

[0015] Using machine learning methods, the corresponding relationship between structural parameters and their performance characteristics under specific load conditions is associated with the parameters generated by finite element simulation results, which serves as a parameter library for machine learning;

[0016] Step 6: Optimize the design scheme through machine learning methods

[0017] 6.1. Select a machine learning algorithm suitable for flexible hinge optimization and choose the optimal algorithm combination based on the complexity of the problem and the size of the data;

[0018] 6.2. Divide the machine learning parameter library into training set and validation set, perform data preprocessing to ensure the quality of input data, perform model selection and hyperparameter tuning, and use cross-validation to evaluate the performance of the model on different data subsets to avoid overfitting;

[0019] 6.3. Use the evaluation indicators in the machine learning regression algorithm to measure the fitting effect of the model;

[0020] 6.4. Comprehensively compare the fitting effects of various output parameters under different input parameters, and select the best machine learning algorithm corresponding to each output parameter based on the evaluation index. Finally, select the machine learning model that best suits each output parameter;

[0021] Step 7: Predict the performance characteristics of the flexible hinge and optimize the solution

[0022] 7.1. Predicting design parameters based on machine learning

[0023] Based on the optimal machine learning algorithm, the design parameters of the flexible hinge with the best maximum bearing capacity F_max, rotational stiffness k_θ and maximum rotation angle θ_max are predicted under the conditions of input semicircular arc radius R, hinge width W, hinge thickness t and hinge length L respectively;

[0024] 7.2. Establishing a 3D model of the flexible hinge

[0025] Use 3D modeling software to build a 3D model of the flexible hinge;

[0026] 7.3 Simulation and performance evaluation

[0027] The 3D model of the flexible hinge is simulated using finite element analysis software, and verified experimentally through CFD. The maximum load-bearing capacity F_max, rotational stiffness k_θ and maximum rotation angle θ_max are calculated to obtain the key performance evaluation indicators of the flexible hinge.

[0028] 7.4 Iterative Optimization Design Scheme

[0029] Iteratively optimize the design parameters, optimize the design scheme of the flexible hinge based on comprehensive consideration of the performance requirements of key performance evaluation indicators, and update the parameter library of machine learning until the optimal solution for the flexible hinge that meets the performance requirements is obtained.

[0030] Furthermore, the step three specifically includes:

[0031] 3.1 Model division and mesh refinement

[0032] The three-dimensional model of the flexible hinge is divided into two parts: the structural area on both sides of the hinge and the weak area in the middle of the hinge. The structural area on both sides of the hinge is divided using a coarse grid, and the weak area in the middle of the hinge is meshed.

[0033] 3.2 Node numbering and unit division

[0034] Number each node, and select the unit type to divide different parts into units according to the structural characteristics of the model;

[0035] 3.3 Calculation and solution of stiffness matrix

[0036] Based on the finite element mesh, the stiffness matrix of each unit is calculated and integrated into the overall stiffness matrix. The system equations are solved using the direct method or iterative method to calculate the displacement, stress and strain distribution of each node.

[0037] 3.4 Grid independence analysis

[0038] By gradually refining the grid, the influence of different grid densities on the calculation results is evaluated, and the grid independence analysis is performed. On the basis of the convergence of the results, the optimal grid density that balances the calculation efficiency and accuracy is selected;

[0039] 3.5. Automatically generate grid database

[0040] Write script code for automatic mesh generation, generate corresponding flexible hinge mesh models according to different structural parameters, and use the generated mesh data to build a mesh library corresponding to the three-dimensional model.

[0041] Furthermore, the step 4 specifically includes:

[0042] 4.1. Define the physical model

[0043] A three-dimensional solid mechanics model is used to perform finite element simulation in combination with material nonlinearity and elastic modulus, and the deformation and stress distribution of the flexible hinge are simulated under different loading conditions;

[0044] 4.2. Establishing Boundary Conditions

[0045] Define the load F to simulate the actual working load, and set boundary conditions in the structural area on both sides of the hinge to constrain it to ensure that the deformation of the flexible hinge meets the actual working conditions;

[0046] 4.3 Numerical Solution

[0047] The least squares iteration method is used to solve the linear and nonlinear terms to ensure that the stress and strain of the flexible hinge under the applied load can be accurately captured, and the displacement, stress and strain distribution of each node are calculated. The nonlinear deformation behavior of the material is comprehensively considered to obtain the characteristics of stress distribution, rotation angle and stiffness;

[0048] 4.4 Post-processing analysis

[0049] The performance characteristics of the flexible hinge are obtained by post-processing, including the maximum load-bearing capacity F_max, rotational stiffness k_θ and maximum rotation angle θ_max;

[0050] 4.5 Parameter optimization and result analysis

[0051] By changing the structural parameters of the flexible hinge and the applied load F, the influence on the performance characteristics of the flexible hinge is studied, sensitivity analysis is performed, and the structural parameters are optimized to meet the performance requirements of the design scheme.

[0052] Furthermore, the selection of machine learning algorithms in step six includes extreme gradient boosting, random forest, support vector machine, adaptive enhancement and deep learning model.

[0053] Furthermore, the cross validation in step 6 selects K-fold cross validation, with K=5 or K=10.

[0054] Furthermore, the evaluation index in step 6 includes the determination coefficient R 2and mean squared error MSE.

[0055] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention uses various machine learning methods to model, simulate and analyze the relationship between different design schemes of flexible hinges and their performance characteristics, and the effectiveness of the optimization of the flexible hinge design scheme is ensured through finite element simulation verification. The machine learning method can self-iterate and optimize, reduce the need for physical experiments, reduce material waste and production costs, effectively save experimental costs and improve calculation efficiency. In addition, the requirements of key performance evaluation indicators such as maximum bearing capacity F_max, rotational stiffness k_θ and maximum rotation angle θ_max are comprehensively considered to improve the design accuracy and reliability of the flexible hinge, which helps to significantly shorten the design and development cycle, can quickly generate and evaluate a variety of design schemes, and accelerate the time to market. At the same time, the machine learning model has multi-objective optimization capabilities, can accurately adjust between multiple design parameters, ensure that the overall performance is optimal, and provide a more accurate and efficient flexible hinge design scheme while significantly reducing experimental costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a flow chart of the method of the present invention;

[0057] Figure 2 is a structural diagram of a flexible hinge;

[0058] Figure 3 is a schematic diagram of the semicircular arc radius R = a and R = b of the flexible hinge;

[0059] Figure 4 is a schematic diagram of the hinge width W=a and W=b of the flexible hinge;

[0060] Figure 5 is a schematic diagram of the hinge thickness t=a and t=b of the flexible hinge;

[0061] Figure 6 is a schematic diagram of the hinge lengths L = a and L = b of the flexible hinge;

[0062] Figure 7 This is a schematic diagram of mesh division of the three-dimensional model of the flexible hinge;

[0063] Figure 8 It is a schematic diagram of the finite element simulation results. DETAILED DESCRIPTION

[0064] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0065] like Figures 1 to 8 As shown in the figure, a machine learning-assisted finite element design method for flexible hinges is proposed. Figure 1 As shown, the following steps are included:

[0066] Step 1: Create a structural parameter library for the flexible hinge

[0067] Structural combination of flexible hinges Figure 2 As shown in the figure, different structural parameters are selected as input variables to construct the structural parameter library of the flexible hinge. The structural parameters include the semicircular arc radius R, hinge width W, hinge thickness t and hinge length L. In order to facilitate the understanding of the specific position of the structural parameters, Figure 3 A schematic diagram showing the semicircular arc radii R = a and R = b of the flexible hinge, Figure 4 A schematic diagram showing the hinge widths W = a and W = b of a flexible hinge, Figure 5 Schematic diagram showing the hinge thickness t=a and t=b of a flexible hinge, Figure 6 A schematic diagram of the hinge lengths L=a and L=b of the flexible hinge is shown for subsequent 3D modeling, mesh drawing, and finite element performance analysis.

[0068] Step 2: Create a 3D model library for the flexible hinge

[0069] According to the data of the structural parameter library of the flexible hinge, a three-dimensional model of the flexible hinge is established through three-dimensional modeling software such as SolidWorks / ProE to obtain different design schemes, and the structural parameter library is converted into a three-dimensional model library of the flexible hinge that can be used for numerical simulation.

[0070] Step 3: Create a mesh library corresponding to the flexible hinge 3D model

[0071] The three-dimensional mesh drawing software ICEM and the finite element analysis software ANSYS Workbench are used to simulate and analyze the three-dimensional models of the flexible hinges in different design schemes under different working environments. The mechanical properties of the flexible hinges are analyzed through the mesh division of the three-dimensional model and the finite element mesh. The corresponding flexible hinge mesh model is generated according to different structural parameters, and the mesh library corresponding to the three-dimensional model is constructed using the generated mesh data, including:

[0072] 3.1 Model division and mesh refinement

[0073] First, the three-dimensional model of the flexible hinge is divided into two parts: the structural area on both sides of the hinge and the weak area in the middle of the hinge, so that appropriate mesh division can be performed on different areas respectively. Then, coarse mesh division is used for the structural area on both sides of the hinge, and a larger unit size is used to reduce the amount of calculation. The mesh is encrypted for the weak area in the middle of the hinge, and a smaller unit size is used to ensure that the accurate stress and strain distribution is captured, so as to ensure the calculation accuracy of the weak area in the middle of the hinge. Figure 7 As shown, a schematic diagram of mesh division of the three-dimensional model of the flexible hinge is shown;

[0074] 3.2 Node numbering and unit division

[0075] Number each node according to the custom rules to ensure the accuracy and continuity of the node numbering in the weak area in the middle of the hinge. According to the structural characteristics of the model, select appropriate unit types (such as SOLID187, SOLID95, etc.) to divide different parts into units to ensure the rationality of the grid distribution and the consistency of the calculation;

[0076] 3.3 Calculation and solution of stiffness matrix

[0077] Based on the finite element mesh, the stiffness matrix of each unit is calculated and integrated into the overall stiffness matrix. The system equations are solved using the direct method or iterative method to calculate the displacement, stress and strain distribution of each node, and analyze the mechanical properties of the flexible hinge;

[0078] 3.4 Grid independence analysis

[0079] By gradually refining the grid, the influence of different grid densities on the calculation results is evaluated, and grid independence analysis is performed to ensure the convergence and stability of the results. On the basis of the convergence of the results, the optimal grid density that balances the calculation efficiency and accuracy is selected to ensure the accuracy of the simulation results;

[0080] 3.5. Automatically generate grid database

[0081] Write script code for automatic mesh generation, generate corresponding flexible hinge mesh models according to different structural parameters, and use the generated mesh data to build a mesh library corresponding to the three-dimensional model to improve the model's automated processing capabilities and facilitate subsequent simulation analysis.

[0082] Step 4: Establish a 3D simulation database for the flexible hinge

[0083] Based on the physical model and material properties, boundary conditions are defined and simulation software is used to generate a three-dimensional simulation database of the flexible hinge, including:

[0084] 4.1. Define the physical model

[0085] Finite element simulation is performed using a three-dimensional solid mechanics model combined with material nonlinearity and elastic modulus. Flexible hinges are usually made of 7075 aluminum alloy or beryllium bronze, both of which have high strength and toughness. Titanium alloys can also be used to meet the requirements of specific environments. The material's elastic modulus, Poisson's ratio and other parameters are used to define the stress-strain relationship, and the deformation and stress distribution of the flexible hinge are simulated under different loading conditions.

[0086] 4.2. Establishing Boundary Conditions

[0087] Define load F, which is the load along the length direction of the flexible hinge during the simulation process to simulate the actual working load. It is used as a supplementary input variable in subsequent machine learning. Boundary conditions are set in the structural area on both sides of the hinge to constrain it, so as to ensure that the deformation of the flexible hinge meets the actual working conditions. According to the path of load F and the set boundary conditions, ensure that the model can accurately reflect the force and deformation characteristics of the flexible hinge.

[0088] 4.3 Numerical Solution

[0089] The least squares iteration method is used to solve the linear and nonlinear terms to ensure that the stress and strain of the flexible hinge under the applied load can be accurately captured, and the displacement, stress and strain distribution of each node are calculated, with particular attention paid to the stress concentration in the weak area in the middle of the hinge. The nonlinear deformation behavior of the material is comprehensively considered to obtain the characteristics of stress distribution, rotation angle and stiffness;

[0090] 4.4 Post-processing analysis

[0091] The performance characteristics of the flexible hinge are obtained by post-processing, including the maximum load-bearing capacity F_max, rotational stiffness k_θ and maximum rotation angle θ_max. Figure 8 As shown, a schematic diagram of the finite element simulation results is shown. The maximum bearing capacity F_max is obtained by integrating the stress distribution of each node, the rotational stiffness k_θ is obtained by calculating the differential of the stress distribution in the direction of the rotation angle θ, and the maximum rotation angle θ_max is obtained by calculating the relationship between displacement and force;

[0092] 4.5 Parameter optimization and result analysis

[0093] By changing the structural parameters of the flexible hinge and the applied load F, the influence on the performance characteristics of the flexible hinge is studied, the sensitivity analysis of each input variable is carried out, and the structural parameters are optimized to meet the performance requirements of the design scheme.

[0094] Step 5: Use machine learning methods to establish a library of structural parameters and performance characteristic parameters

[0095] Using the machine learning method, the parameters generated according to the finite element simulation results of ANSYS Workbench are used to associate the correspondence between the structural parameters and their performance characteristics under specific load conditions. The input parameters include the semicircular arc radius R, hinge width W, hinge thickness t and hinge length L, and the output parameters include the maximum bearing capacity F_max, rotational stiffness k_θ and maximum rotation angle θ_max.

[0096] Step 6: Optimize the design scheme through machine learning methods

[0097] 6.1. Select machine learning algorithms suitable for flexible hinge optimization, including but not limited to extreme gradient boosting (XGBoost), random forest, support vector machine (Gaussian support vector machine SVM-Gaussian and linear support vector machine SVM-Linear), adaptive boosting (AdaBoost) and deep learning models (such as 2-layer, 3-layer, 4-layer artificial neural networks ANN20-20, ANN30-30, ANN40-40, etc.), and select the optimal algorithm combination according to the complexity of the problem and the size of the data to ensure the accuracy of the model;

[0098] 6.2. To prevent overfitting during the training of machine learning algorithms, the machine learning parameter library should be divided into training set and validation set in an appropriate ratio. The recommended ratio is 8:2 or other reasonable ratios. At the same time, necessary data preprocessing should be performed, including feature scaling (such as standardization or normalization), missing value processing, data cleaning, etc., to ensure the quality of input data, and model selection and hyperparameter tuning should be performed. Methods such as Grid Search or Bayesian Optimization should be used to optimize the hyperparameter configuration of the model to ensure the generalization ability and stability of the model. In addition, cross-validation (such as K-fold cross-validation, usually K=5 or K=10) should be used to evaluate the performance of the model on different data subsets to further verify the robustness of the model and avoid overfitting.

[0099] 6.3. Use the commonly used evaluation indicators in machine learning regression algorithms, including the coefficient of determination (R 2 ) and mean square error (MSE) are used to measure the fitting effect of the model. The specific formula of the evaluation index is as follows:

[0100]

[0101] The coefficient of determination is used to measure the degree of fit between the model's predicted value and the actual value. Its value is between 0 and 1. The closer the value is to 1, the better the model's fit is. The mean square error represents the square average of the difference between the predicted value and the actual value. It is used to measure the overall level of the prediction error. The smaller the MSE, the smaller the prediction error of the model and the better the fit is.

[0102] 6.4. Comprehensively compare the fitting effects of various output parameters under different input parameters to determine the coefficient (R 2 ) and mean square error (MSE) are used as evaluation indicators to select the best machine learning algorithm corresponding to each output parameter. For example, in the fitting process of the maximum bearing capacity F_max, the support vector machine (SVM) performs best; in the fitting process of the maximum rotation angle θ_max, the artificial neural network (ANN) performs best; in the fitting process of the rotational stiffness k_θ, the random forest (RandomForest) performs best. Finally, based on the criteria of maximizing the coefficient of determination and minimizing the mean square error, the most suitable machine learning model for each output parameter is selected to ensure the accuracy and robustness of the model prediction, and to improve the design efficiency and optimization effect through performance prediction.

[0103] Step 7: Predict the performance characteristics of the flexible hinge and optimize the solution

[0104] 7.1. Predicting design parameters based on machine learning

[0105] Based on the optimal machine learning algorithm, the design parameters of the flexible hinge with the best maximum bearing capacity F_max, rotational stiffness k_θ and maximum rotation angle θ_max are predicted under the conditions of input semicircular arc radius R, hinge width W, hinge thickness t and hinge length L respectively;

[0106] 7.2. Establishing a 3D model of the flexible hinge

[0107] Use SolidWorks / ProE and other 3D modeling software to build a 3D model of the flexible hinge;

[0108] 7.3 Simulation and performance evaluation

[0109] The finite element analysis software ANSYS Workbench was used to simulate the three-dimensional model of the flexible hinge, and the CFD experiment was used to verify the maximum load-bearing capacity F_max, rotational stiffness k_θ and maximum rotation angle θ_max to obtain the key performance evaluation indicators of the flexible hinge;

[0110] 7.4 Iterative Optimization Design Scheme

[0111] Iteratively optimize the design parameters, optimize the design scheme of the flexible hinge based on comprehensive consideration of the maximum bearing capacity F_max, rotational stiffness k_θ and maximum rotation angle θ_max performance requirements, and update the machine learning parameter library until the optimal solution for the flexible hinge that meets the performance requirements is obtained.

[0112] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms of assembly without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0113] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A machine learning-assisted finite element design method for flexible hinges, characterized in that: The following steps are involved: Step 1: Create a structural parameter library for the flexible hinge Different structural parameters are selected as input variables to construct the structural parameter library of the flexible hinge. The structural parameters include the semicircular arc radius R, hinge width W, hinge thickness t and hinge length L. Step 2: Create a 3D model library for the flexible hinge According to the data of the structural parameter library of the flexible hinge, a three-dimensional model of the flexible hinge is established by using a three-dimensional modeling software to obtain different design schemes, and the structural parameter library is converted into a three-dimensional model library of the flexible hinge for numerical simulation; Step 3: Create a mesh library corresponding to the flexible hinge 3D model The three-dimensional models of the flexible hinges in different design schemes are simulated and analyzed under different working environments using three-dimensional mesh drawing software and finite element analysis software. The mechanical properties of the flexible hinges are analyzed through mesh division of the three-dimensional model and finite element mesh analysis. The corresponding flexible hinge mesh models are generated according to different structural parameters, and the mesh library corresponding to the three-dimensional model is constructed using the generated mesh data. Step 4: Establish a 3D simulation database for the flexible hinge Based on the physical model and material properties, boundary conditions are defined and simulation software is used to generate a three-dimensional simulation database of the flexible hinge; Step 5: Use machine learning methods to establish a library of structural parameters and performance characteristic parameters Using machine learning methods, the corresponding relationship between structural parameters and their performance characteristics under specific load conditions is associated with the parameters generated by finite element simulation results, which serves as a parameter library for machine learning; Step 6: Optimize the design scheme through machine learning methods (6.1) Select a machine learning algorithm suitable for flexible hinge optimization and choose the optimal algorithm combination based on the complexity of the problem and the size of the data; (6.2) Divide the machine learning parameter library into training set and validation set, perform data preprocessing to ensure the quality of input data, perform model selection and hyperparameter tuning, and use cross-validation to evaluate the performance of the model on different data subsets to avoid overfitting; (6.3) Use the evaluation indicators in the machine learning regression algorithm to measure the fitting effect of the model; (6.4) Comprehensively compare the fitting effects of various output parameters under different input parameters, and use the evaluation index to select the best machine learning algorithm corresponding to each output parameter. Finally, select the machine learning model that best suits each output parameter; Step 7: Predict the performance characteristics of the flexible hinge and optimize the solution (7.1) Predicting design parameters based on machine learning Based on the optimal machine learning algorithm, the design parameters of the flexible hinge with the best maximum bearing capacity F_max, rotational stiffness k_θ and maximum rotation angle θ_max are predicted under the conditions of input semicircular arc radius R, hinge width W, hinge thickness t and hinge length L respectively; (7.2) Establish a three-dimensional model of the flexible hinge Use 3D modeling software to build a 3D model of the flexible hinge; (7.3) Simulation and performance evaluation The 3D model of the flexible hinge is simulated using finite element analysis software, and verified experimentally through CFD. The maximum load-bearing capacity F_max, rotational stiffness k_θ and maximum rotation angle θ_max are calculated to obtain the key performance evaluation indicators of the flexible hinge. (7.4) Iterative optimization design solution Iteratively optimize the design parameters, optimize the design scheme of the flexible hinge based on comprehensive consideration of the performance requirements of key performance evaluation indicators, and update the parameter library of machine learning until the optimal solution for the flexible hinge that meets the performance requirements is obtained.

2. The method for flexure hinge design assisted by machine learning according to claim 1, characterized in that: The step three specifically includes: (3.1) Model division and mesh refinement The three-dimensional model of the flexible hinge is divided into two parts: the structural area on both sides of the hinge and the weak area in the middle of the hinge. The structural area on both sides of the hinge is divided using a coarse grid, and the weak area in the middle of the hinge is meshed. (3.2) Node numbering and unit division Number each node, and select the unit type to divide different parts into units according to the structural characteristics of the model; (3.3) Calculation and solution of stiffness matrix Based on the finite element mesh, the stiffness matrix of each unit is calculated and integrated into the overall stiffness matrix. The system equations are solved using the direct method or iterative method to calculate the displacement, stress and strain distribution of each node. (3.4) Grid independence analysis By gradually refining the grid, the influence of different grid densities on the calculation results is evaluated, and the grid independence analysis is performed. On the basis of the convergence of the results, the optimal grid density that balances the calculation efficiency and accuracy is selected; (3.5) Automatically generate grid database Write script code for automatic mesh generation, generate corresponding flexible hinge mesh models according to different structural parameters, and use the generated mesh data to build a mesh library corresponding to the three-dimensional model.

3. The method for flexure hinge design assisted by machine learning according to claim 1, characterized in that: The step 4 specifically includes: (4.1) Define the physical model A three-dimensional solid mechanics model is used to perform finite element simulation in combination with material nonlinearity and elastic modulus, and the deformation and stress distribution of the flexible hinge are simulated under different loading conditions; (4.2) Establish boundary conditions Define the load F to simulate the actual working load, and set boundary conditions in the structural area on both sides of the hinge to constrain it, so as to ensure that the deformation of the flexible hinge meets the actual working conditions; (4.3), numerical solution The least squares iteration method is used to solve the linear and nonlinear terms to ensure that the stress and strain of the flexible hinge under the applied load can be accurately captured, and the displacement, stress and strain distribution of each node are calculated. The nonlinear deformation behavior of the material is comprehensively considered to obtain the characteristics of stress distribution, rotation angle and stiffness; (4.4) Post-processing analysis The performance characteristics of the flexible hinge are obtained by post-processing, including the maximum load-bearing capacity F_max, rotational stiffness k_θ and maximum rotation angle θ_max; (4.5) Parameter optimization and result analysis By changing the structural parameters of the flexible hinge and the applied load F, the influence on the performance characteristics of the flexible hinge is studied, sensitivity analysis is performed, and the structural parameters are optimized to meet the performance requirements of the design scheme.

4. The method for flexure hinge design assisted by machine learning according to claim 1, characterized in that: The selection of machine learning algorithms in step six includes extreme gradient boosting, random forest, support vector machine, adaptive boosting and deep learning model.

5. The method for flexure hinge design assisted by machine learning according to claim 1, characterized in that: The cross validation in step 6 selects K-fold cross validation, with K=5 or K=10.

6. The method for flexure hinge design assisted by machine learning according to claim 1, characterized in that: The evaluation index in step six includes the determination coefficient R 2 and mean squared error MSE.

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