A pinn-based six-dimensional force sensor elastomer structure parameter optimization method

Abstract

To address the limitations of traditional orthogonal experimental methods, which rely on experience and have limited parameter search capabilities, and response surface methodology, which is heavily reliant on the number of finite element simulation samples and has high computational costs, in optimizing the structural parameters of a six-dimensional force sensor elastomer, this invention proposes a method for optimizing the structural parameters of a six-dimensional force sensor elastomer based on a physical information neural network. The technical approach involves: taking the six-dimensional force sensor elastomer structure as the research object, selecting the length of the floating beam, the length of the strain beam, the width of the floating beam, the width of the strain beam, and the beam thickness as design variables; constructing multiple combinations of structural dimensions through orthogonal experiments, and obtaining the strain response data corresponding to each dimension combination using finite element analysis; establishing an elastomer mechanical model, and introducing the constitutive relations, governing equations, and boundary conditions of the mechanical model as physical constraints into the neural network training process; simultaneously using finite element strain data to supervise and correct the network, thereby constructing a high-precision mapping model between structural parameters and strain response; and further combining this mapping model with a multi-objective genetic algorithm (NSGA-III) to optimize the search for the elastomer structural parameters. This invention reduces the requirement for finite element simulation samples while achieving high-precision prediction of the mechanical response of the elastomer structure, significantly improving the efficiency of structural parameter optimization.

Description

Technical Field

[0001] This invention relates to the field of six-dimensional torque sensor structure design and modeling optimization technology, specifically to a method for optimizing the structural parameters of an elastic body for a six-dimensional force sensor. Background Technology

[0002] Currently, six-dimensional force sensors typically employ elastic body structures such as three-beam or cross-beam structures to convert external loads into measurable strain signals. The geometric parameters of the elastic body have a decisive influence on the sensor's sensitivity, stiffness, overload capacity, and coupling characteristics of its components; therefore, the structural parameters of the elastic body need to be optimized. Existing structural parameter optimization designs often adopt a "finite element simulation + experimental design" approach. For example, multiple sets of size combinations are generated through orthogonal experimental design, and the strain response at key locations of the strain beam is modeled, calculated, and extracted in finite element software. Then, methods such as range analysis are used to select the optimal parameter combination. This type of method is mature and easy to implement, but when there are many design variables and multiple load conditions need to be considered, the number of finite element simulations increases significantly with the number of combinations, resulting in high modeling and calculation costs. At the same time, orthogonal experiments are based on discrete level combinations for comparison and selection, making it difficult to guarantee obtaining globally optimal or near-globally optimal parameter solutions. Another type of method is proxy modeling methods such as response surface methodology, which establishes an approximate functional relationship between structural parameters and response to reduce the number of finite element calls during the optimization iteration process. However, to ensure the fitting accuracy and generalization ability of the surrogate model, a large-scale simulation sample is usually required. In the optimization problem of six-dimensional force sensor elastomers, the workload of sample generation and strain data acquisition and processing is large, which makes it difficult to meet the needs of rapid iterative design. Summary of the Invention

[0003] To overcome the problems of existing six-dimensional force sensor elastomer structural parameter design methods, such as reliance on experience for parameter selection, insufficient continuous design space optimization capability, and high cost of repeated finite element method calls during optimization, this invention proposes a six-dimensional force sensor elastomer structural parameter optimization method based on a physical information neural network. The method takes a cross-beam type six-dimensional force sensor elastomer as the research object. First, the elastomer structure is parameterized, and geometric parameters that significantly affect sensor sensitivity and stiffness are selected as design variables. Then, a supervisory sample is constructed based on orthogonal experimental design and finite element simulation to establish the relationship between structural dimension combinations and strain response. On this basis, the strain beam and floating beam in the elastomer are modeled as equivalent beams, and a mechanical constraint model describing the relationship between beam deflection, section rotation angle, bending moment, and shear force is established based on Timoshenko beam theory. This mechanical constraint and finite element supervisory data are jointly introduced into the training process of the physical information neural network to obtain a high-precision mapping model between structural parameters and strain response. Finally, a multi-objective optimization problem is constructed based on the mapping model to search for the elastomer structural parameters, and the optimization results are verified through finite element verification. Through the above technical solution, the present invention improves the efficiency of optimizing the structural parameters of a six-dimensional force sensor elastomer while reducing finite element sample dependence and lowering optimization calculation costs.

[0004] To achieve the above objectives, the specific technical solution of the present invention is as follows:

[0005] This invention proposes a method for optimizing the structural parameters of a six-dimensional force sensor elastic body based on a physical information neural network. The method is mainly implemented through four stages: parametric modeling of the elastic body structure and finite element sample construction; equivalent mechanical modeling based on Timoshenko beam theory; construction and training of the physical information neural network mapping model; and multi-objective optimization and finite element verification based on a surrogate model. The overall method includes the following steps:

[0006] Step 1: Determine the initial structure of the six-dimensional force sensor elastomer to be optimized, and select key geometric parameters that have a significant impact on the mechanical properties of the elastomer as design variables;

[0007] Step 2-1: Within the preset value range of the design variables, several sets of structural dimension combinations are generated using the orthogonal experimental design method. For each dimension combination, an elastic body finite element model is established in the finite element analysis software, preset boundary conditions and load conditions are applied, and strain response data at predetermined measurement points of the strain beam are calculated and extracted to form a finite element supervision dataset.

[0008] Step 2-2: Perform range analysis on the orthogonal experimental finite element results to determine the degree of influence of different design variables on the strain response, and obtain one or more sets of reference size combinations that can characterize the mechanical response of the elastic body, so as to provide a basis for subsequent equivalent mechanical modeling, physical constraint proxy modeling and structural parameter optimization.

[0009] Step 3-1: Based on the elastic body structure, establish an equivalent mechanical model, approximate the strain beam and floating beam in the elastic body as short beams, and establish the governing equations, constitutive relations and boundary conditions describing the relationship between deflection, cross section rotation, shear deformation, bending moment and shear force according to Timoshenko beam theory;

[0010] Step 3-2: Based on the force balance relationship and flexibility distribution relationship of the overall cross beam elastic body, establish the mapping relationship between the external load and the equivalent load at the end of the target strain beam, and introduce the equivalent load as part of the boundary condition of the target strain beam into the subsequent surrogate model training process;

[0011] Step 4-1: Construct a physical information neural network (PINN) mapping model, taking the structural geometric parameters and the position parameters within the effective analysis domain of the target strain beam as network inputs, and the dimensionless field variables characterizing the mechanical state of the target strain beam as network outputs, thereby establishing a parameterized mapping model between structural parameters and strain response field;

[0012] Step 4-2: In the PINN mapping model, the first and second derivatives of the network output with respect to the position parameters are calculated, and the derivatives with respect to the actual physical coordinates are obtained by combining the variable transformation relationship. Then, physical quantities such as shear angle, bending moment, shear force and equilibrium equation residuals are constructed.

[0013] Step 4-3: Construct a physical loss function, and introduce the control equation residuals, boundary condition residuals, and finite element strain supervision errors in the equivalent mechanical model into the training process of the physical information neural network. Optimize and solve the network parameters to obtain a high-precision mapping model between structural parameters and strain response.

[0014] Step 4-4: The PINN mapping model is trained using a phased optimization strategy, including a pre-training phase based on physical constraints, a fusion training phase that incorporates finite element supervision data, and a refinement phase based on a second-order optimization method, in order to improve the training stability and convergence accuracy of the mapping model.

[0015] Step 5: Based on the trained PINN mapping model, construct a multi-objective optimization problem. Define the objective function according to the mechanical response results predicted by the mapping model or the performance indicators derived from it, and use a multi-objective optimization algorithm to search for the design variables to obtain one or more sets of optimal structural parameter combinations.

[0016] Step 6: Re-import the optimal combination of structural parameters into the finite element analysis software to establish a verification model, and perform simulation solutions under the same boundary conditions and load conditions as the initial sample analysis. Compare and analyze the mechanical response and key performance indicators of the elastic body before and after optimization to verify the effectiveness of the structural parameter optimization method.

[0017] Furthermore, in step 1, taking the cross-beam type six-dimensional force sensor elastomer structure as the research object, the main deformation region and strain-sensitive region of the elastomer under external load are analyzed, and it is determined that the main flexible deformation of the elastomer is concentrated in the strain beam and floating beam regions. Since the structural response of the elastomer is mainly determined by the geometric characteristics of the above-mentioned regions, the subsequent structural parameter optimization focuses on the key dimensions of the strain beam and floating beam.

[0018] Based on the sensitivity of elastic body sensitivity, structural stiffness, overload capacity, and force-moment separation performance to geometric parameters, the floating beam length, strain beam length, floating beam width, strain beam width, and beam thickness are selected as five design variables in the structural parameter optimization, denoted as follows: , , , and .

[0019] After determining the above five design variables, a predetermined range of values ​​is set for each design variable based on the initial structural dimensions and design requirements, for use in subsequent orthogonal experimental design, finite element sample construction, and structural parameter optimization search.

[0020] Further, in step 2-1, within the range of values ​​for the five design variables determined in step 1, an orthogonal array is constructed using a multi-factor, multi-level orthogonal experimental design method to generate several sets of structural dimension combinations. Preferably, each design variable is set with multiple discrete levels to form a five-factor, multi-level experimental design, and based on this, no fewer than 16 sets of structural dimension combinations are constructed.

[0021] For each of the aforementioned size combinations, a corresponding three-dimensional solid model of the elastic body is established in the finite element analysis software. Based on the size combinations, parametric modeling is performed on structural regions within the elastic body, such as strain beams, floating beams, and loading blocks. Through this method, finite element sample models corresponding one-to-one with each structural size combination can be generated.

[0022] Regarding the finite element boundary condition settings, fixed constraints are applied to the connection area between the elastomer and the base to simulate the fixed connection relationship under actual installation conditions; preferably, fixed constraints are applied to the bolt hole area and pin hole area of ​​the outer beam of the elastomer. Regarding the load condition settings, the loads include force loads along the X, Y, and Z directions and moment loads about the X, Y, and Z directions. These loads can be applied directly through the loading block's force-bearing surface or through remote point coupling to apply pure force / moment loads.

[0023] After completing the finite element method (FEM) solution, strain response data at predetermined measurement points on the elastic strain beam are extracted to form a finite element monitoring dataset. These predetermined measurement points are preferably located on the surface of the strain beam.

[0024] Furthermore, in step 2-2, a range analysis is performed on the finite element strain response results obtained in step 2 to statistically analyze the influence of each design variable on the strain response at different levels, thereby obtaining a sensitivity ranking of different size factors and an optimal combination of levels. Through this analysis, the primary and secondary influence relationships of each design variable on the strain capacity can be quantitatively compared, thus providing a basis for subsequent structural parameter optimization.

[0025] Specifically, the strain response results of each design variable at each level are statistically analyzed, and the corresponding mean and range of the response are calculated. The larger the range, the more significant the influence of the design variable on the strain response, and therefore it should be given greater attention in subsequent optimization processes.

[0026] For different load conditions, range analysis can be performed separately to obtain the optimal dimensional combination for each condition. Since the stress form and strain distribution characteristics of the elastic body differ under different load conditions, the optimal combination for each condition may be the same or different.

[0027] After obtaining the analysis results for each working condition, the range analysis results under multiple working conditions are further compared and integrated to determine a set of reference size combinations in a comprehensive sense. These reference size combinations can serve as the initial reference structure for subsequent physical constraint proxy modeling, multi-objective optimization search, and finite element verification.

[0028] Furthermore, in step 3-1, based on the elastic body geometric samples and strain response characteristics obtained in steps 2 and 3, an equivalent mechanical model of the cross-beam elastic body is established. This equivalent mechanical model is used to describe the deformation and internal force evolution of the key stressed beam segment of the elastic body under external loads, and provides a theoretical basis for the physical constraint terms in the subsequent physical information neural network.

[0029] In this step, the strain beam and floating beam in the cross-shaped elastic body are approximated as short beams, and the Timoshenko beam theory is used to describe the bending and shear deformations of the beams. Let the target strain beam be along the axial coordinate... Distribution, beam deflection is The cross-sectional rotation angle is The shear angle is The geometric relationship is then expressed as: ;

[0030] Bending moment With section rotation angle satisfy: shear force With shear angle satisfy: ;

[0031] The governing equations of the model are: , ,in, It is a distributed load along the axial direction; under conditions without distributed load... Thus further obtain ;

[0032] Furthermore, the surface fiber strain at any location on the beam satisfies the following relationship with the section rotation gradient: ,in, The distance from the measuring point to the neutral layer.

[0033] Furthermore, in step 3-2, based on the establishment of the equivalent mechanical model of a single target strain beam, in order to map the stress state of the overall cross beam elastic body to the boundary conditions of the free end of the target strain beam, the present invention further establishes the mapping relationship between the external load and the equivalent shear force at the end of the target strain beam.

[0034] For different load conditions, the equivalent load at the free end of the target strain beam can be expressed as a function of external force or moment with respect to structural geometric parameters, material parameters, and section parameters. The equivalent load expressions under different load conditions can be established based on the same overall stress analysis and compliance compatibility method, and used respectively in the physical constraint proxy modeling process under the corresponding load conditions.

[0035] Along Horizontal force load in the direction Taking the working condition as an example, for the rectangular cross-sections of the floating beam and the target strain beam, their areas and moments of inertia are defined as follows: , , , ;

[0036] Further define the intermediate variables related to the flexibility of the two beam segments: , ;

[0037] Based on the overall flexibility distribution of the cross beam, the equivalent end shear force borne by the free end of the target strain beam is expressed as: ;in, The load is applied externally to the elastic loading block. The equivalent end shear force... Used to construct the shear boundary conditions at the free end of the target strain beam; for other force loads or moment loads, the corresponding equivalent load relationship at the free end can be established according to the same overall force analysis and flexibility coordination approach for the cross beam.

[0038] Furthermore, in step 4-1, based on the equivalent mechanical model and equivalent end shear force relationship established in steps 4 and 5, a physical information neural network (PINN) mapping model is constructed. This mapping model is used to establish a parameterized correspondence between the geometric parameters of the elastic body structure and the strain response field of the target strain beam, thereby providing a fast surrogate model for subsequent structural parameter optimization.

[0039] The input features of the PINN mapping model include at least structural geometric parameters and positional parameters: ,in, This represents the positional parameters defined along the effective domain of the target strain beam;

[0040] To reduce the impact of local three-dimensional boundary effects at the fixed end of the beam root and the connection area at the beam end on the one-dimensional equivalent model of the strained beam, an effective analysis domain is defined along the axial direction of the target strained beam, and dimensionless coordinates are constructed within the effective analysis domain. The satisfy: , ,in, and These are the preset effective domain boundary lengths for the root and the end, respectively;

[0041] The PINN network outputs dimensionless mechanical fields, including dimensionless deflection. With dimensionless rotation ,Right now: ,in, These are the parameters for the neural network. By using the deflection field and cross-sectional rotation field as network outputs, subsequent bending moment, shear force, and strain responses can all be derived from unified field variables, thereby enhancing the physical consistency and interpretability of the model.

[0042] Furthermore, in step 4-2, when constructing the physical constraint terms, the PINN network outputs the dimensionless position parameters. The first and second derivatives are calculated, and their relationship with respect to the actual sampling position is obtained based on the variable transformation relationship. The derivative is preferably calculated using automatic differentiation to avoid truncation errors and numerical instability problems associated with traditional numerical differencing.

[0043] Specifically, let the dimensionless deflection and dimensionless rotation angle output by the network be respectively... and Then you can obtain its information about The derivative: , , and And using the chain rule, it is converted into information about actual physical coordinates. The derivative of satisfies: , ;

[0044] Furthermore, to ensure consistency of physical dimensions under different geometric combinations and to improve numerical stability during training, the dimensionless output is restored to the actual physical quantity, satisfying: , ,in, and Is with , , and The scaling factor related to parameters is preferably: , .

[0045] Further, in step 4-3, the training objective of the physical information neural network is composed of physical constraint terms and supervision correction terms. The physical constraint terms ensure that the network output satisfies the control equations and boundary conditions in the equivalent mechanical model, while the supervision correction terms ensure that the network prediction results are consistent with the finite element strain samples. Based on this, the present invention constructs a joint loss function composed of a weighted average of the control equation residual loss, boundary condition loss, and supervision correction loss, in the form: ,in , , Preset weights.

[0046] In the loss function:

[0047] (I) Residual loss of governing equations The PINN mapping model is used to constrain the equilibrium relationship and governing equations of the target strain beam. Preferably, the residual loss of the governing equations corresponds to the moment equilibrium equation and the shear force equilibrium equation, i.e.: and Under conditions of no distributed load, further consideration can be made. Define dimensionless residual: and Further construction: ;

[0048] (II) Boundary condition loss To constrain the target strain beam to meet preset boundary conditions at the root and free ends, preferably, a fixed-support boundary condition is used at the root, i.e.: The free end is constrained by zero bending moment and equivalent end load, that is: , Therefore, the boundary condition loss can be constructed as: ;

[0049] (III) Monitoring and correcting losses To ensure consistency between the network-predicted strain and the finite element strain data, the predicted strain is obtained from the rotation gradient: To improve the numerical stability of training across load and size combinations, the supervision error needs to be normalized, defined as follows: ,structure: .

[0050] Furthermore, in step 4-4, the training of the PINN mapping model employs a phased optimization strategy to coordinate the relationship between physical constraint satisfaction, finite element supervision correction, and high-precision convergence, including:

[0051] (I) Physically Constrained Pre-training Phase: A first-order optimizer is used in the following phase: and Training is performed with the primary objective of initializing the physics solution space, preferably using the Adam optimizer to perform the pre-training phase;

[0052] (II) Supervision and Correction Integration Stage: While maintaining the residuals of the governing equations and the boundary condition constraints, gradually improve... The value is used to introduce finite element strain data for monitoring and correction. The number of training steps can be gradually increased, thus allowing the network to smoothly transition from a "pure physics solution" to a "physical constraint + supervised correction" solution.

[0053] (III) Second-stage refinement stage: The network parameters that have achieved initial convergence are further solved with high precision using a second-order optimization method. The second-order optimization method is preferably a quasi-Newton optimization algorithm, and more preferably the L-BFGS-B algorithm, to improve the convergence accuracy and loss function descent efficiency in the later stages of network training.

[0054] Furthermore, in step 5, after the PINN mapping model is trained, an optimization problem for the elastic body structural parameters can be constructed based on the mechanical response results predicted by the network. This optimization problem uses the design variables determined in step 1 as decision variables and the mapping model as a rapid evaluation model for the structural response.

[0055] The objective function is preferably derived from multiple physical quantities predicted by the mapping model or performance metrics derived therefrom. The performance metrics include at least: relative... Evaluation indicators include norm index, maximum relative error, peak strain error, PDE residual norm, and energy error;

[0056] Furthermore, given any combination of design variables, inputting these variables into a trained PINN mapping model allows for the rapid acquisition of the strain response field and related physical quantities of the target strain beam under the corresponding structural parameters. This approach avoids repeatedly building finite element models and performing costly numerical solutions for each candidate size combination during the optimization search process, thereby significantly improving the efficiency of structural parameter search.

[0057] The multi-objective optimization algorithm is based on non-dominated sorting, preferably the NSGA-III algorithm. This algorithm is used to optimize the design variables. By performing a search, one or more sets of Pareto optimal design variable combinations can be obtained for subsequent finite element verification and engineering design selection.

[0058] Furthermore, in step 6, for one or more optimal combinations of design variables obtained in step 10, a corresponding elastic body verification model is re-established in the finite element analysis software, and simulation analysis is performed under the same or corresponding boundary conditions and load conditions as in step 2. Through the verification model, the mechanical response of the optimization results under high-fidelity numerical analysis conditions can be re-evaluated, thereby verifying the reliability of the optimization results of the proxy model.

[0059] In the finite element verification process, it is preferable to compare and analyze the simulation results of the initial structure before optimization and the optimized structure under the same working conditions. By comparing the differences between the two in strain response distribution, structural deformation characteristics, and internal force or stress-related results, the improvement effect of the optimal combination of design variables on the mechanical properties of the elastic structure can be evaluated.

[0060] The key performance indicators include static response under single-dimensional load, resistance to eccentric loading, and force-moment separation capability. Furthermore, based on engineering design requirements, a comprehensive evaluation can be conducted on the structure before and after optimization in terms of sensitivity, strain distribution uniformity, structural safety margin, and multi-condition integrated performance.

[0061] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0062] This invention provides a method for optimizing the structural parameters of a six-dimensional force sensor elastomer based on a physical information neural network. The method includes: determining the initial structure and design variables of a cross-beam type six-dimensional force sensor elastomer; constructing a structural dimension combination and strain monitoring dataset through orthogonal experiments and finite element simulation; establishing an equivalent mechanical model of a strain beam and a floating beam based on Timoshenko beam theory, and further establishing the compliance distribution relationship between external loads and the equivalent shear force at the end of the target strain beam; constructing a physical information neural network mapping model with structural geometric parameters and dimensionless position coordinates of the effective domain as inputs, and dimensionless deflection field and dimensionless rotation field as outputs; obtaining a high-precision mapping model between structural parameters and strain response by jointly training the network using control equation residuals, boundary condition residuals, and finite element monitoring correction errors; and finally, using a multi-objective optimization algorithm based on the mapping model to search for the elastomer structural parameters, and verifying the optimization results through finite element simulation. This invention fully utilizes the prior mechanical information of the cross-beam elastomer, and can still achieve high-precision response prediction under finite element sample conditions. At the same time, it significantly reduces the dependence on repeated finite element analysis in the structural optimization process, and improves the efficiency and engineering feasibility of the structural parameter optimization design of the six-dimensional force sensor elastomer. Attached Figure Description

[0063] To fully illustrate the technical concepts of the embodiments of the present invention or the prior art, the accompanying drawings will be briefly described below. It should be understood that the following drawings correspond only to some embodiments of the present invention, and those skilled in the art can still derive other technical illustrations based on these drawings without any inventive contribution.

[0064] Figure 1 This is an overall flowchart of the method for optimizing the structural parameters of a six-dimensional force sensor elastomer provided in an embodiment of the present invention;

[0065] Figure 2 This is a schematic diagram of the three-dimensional structure of the cross-beam type six-dimensional force sensor elastomer provided in an embodiment of the present invention;

[0066] Figure 3 Provided for embodiments of the present invention Under working conditions and A simplified equivalent mechanical model of the target strain beam under operating conditions;

[0067] Figure 4 This is a schematic diagram of the PINN physical constraint mapping model structure provided in an embodiment of the present invention;

[0068] Figure 5 The optimized structure and orthogonal experimental reference structure provided for embodiments of the present invention are in... Comparison of strain response under operating conditions.

[0069] Figure 6 The optimized structure and orthogonal experimental reference structure provided for embodiments of the present invention are in... Comparison chart of resistance to eccentric load under working conditions. Detailed Implementation

[0070] The technical solutions disclosed in this invention will be explained in detail with reference to the accompanying drawings. It should be understood that the embodiments listed below are for illustrative purposes only and do not represent all implementations of this invention. Within the scope of knowledge of those skilled in the art, any other solutions that can be derived by referring to these specific examples without substantial research and development innovation should be included within the scope of patent protection of this invention.

[0071] To further clarify the technical implementation process of this invention in optimizing the structural parameters of a six-dimensional force sensor elastomer, this section will provide a detailed description of the specific embodiments of this invention in conjunction with the accompanying drawings. Figure 1 The overall process of the six-dimensional force sensor elastomer structure parameter optimization method based on physical information neural network proposed in this invention is shown.

[0072] like Figure 1 As shown, this embodiment constructs a method for optimizing the structural parameters of a six-dimensional force sensor elastomer based on a physical information neural network, mainly including:

[0073] Step 100: Define the initial structure and design variables of the six-dimensional force sensor elastomer, namely the initial cross-beam elastomer and the length of the floating beam. Length of strain beam Floating beam width , strain beam width and beam thickness ;

[0074] Step 200: Construct multiple sets of structural size combinations based on orthogonal experiments, perform mechanical response simulation in ANSYS, collect strain response data corresponding to each size combination, and form a small sample supervision dataset;

[0075] Step 300: Establish an equivalent mechanical model of the elastic body, wherein the physical constraints in the model include the constitutive relation of the strain beam, the governing equations, and the boundary conditions;

[0076] Step 400: Construct a physical information neural network mapping model for the elastic strain beam, and combine it with finite metadata for supervised correction to establish the mapping relationship between structural parameters and strain response;

[0077] Step 500: Invoke the mapping model using a multi-objective optimization algorithm to search for the optimal combination of structural parameters within the effective domain of the design variables.

[0078] Step 600: Combine the optimal design variables in the finite element software to establish a verification model, evaluate and verify the mechanical response and key performance indicators of the elastomer before and after optimization under the load conditions.

[0079] It should be noted that, Figure 1 The flowchart shown summarizes the overall technical approach of this invention, while the invention can be further refined into several technical steps during its specific implementation. To facilitate the explanation of the specific implementation of this invention, the following will describe the implementation process of this invention in terms of parametric modeling, finite element sample construction, equivalent mechanical model establishment, physical information neural network training, and structural parameter optimization, in conjunction with each step in the invention's description.

[0080] The specific implementation process of this method includes the following parts:

[0081] Step 1: Select the cross-beam type six-dimensional force sensor elastomer as the research object and establish its initial three-dimensional structural model, see... Figure 2 The initial structural model includes structural components such as external beams, floating beams, strain beams, and loading blocks.

[0082] Design variables for structural parameter optimization are determined on the initial structural model. These design variables include the floating beam length, strain beam length, floating beam width, strain beam width, and beam thickness, denoted as […]. , , , and .

[0083] After determining the above design variables, a predetermined value range is set for each design variable based on the initial structural dimensions and design requirements. The predetermined value ranges are shown in the table below and are used for generating dimension combinations in subsequent orthogonal experimental design.

[0084]

[0085] After completing step 1, the initial structural model of the elastomer and the set of design variables are obtained. The predetermined value ranges of each design variable are also determined and used as input for step 2-1.

[0086] Step 2-1: First, based on the design variables obtained in Step 1... Based on the predetermined value range, an orthogonal array was constructed using a multi-factor, multi-level orthogonal experimental design method. Then, several combinations of structural dimensions were generated according to the orthogonal array, as shown in the table below:

[0087]

[0088] For each combination of structural dimensions, a corresponding three-dimensional finite element model of the elastic body is established in the finite element analysis software. After establishing the finite element model, boundary conditions and load cases are applied to the model. The boundary conditions include applying fixed constraints to the connection area between the outer beam and the base of the elastic body; the load cases include along... , , Force load in direction and around , , Moment load in the direction of force.

[0089] Furthermore, the load can be applied directly to the corresponding force-bearing surface of the loading block, or it can be applied as a pure force or pure moment load through remote point coupling. After setting the boundary conditions and loads, the finite element model corresponding to each set of structural dimensions is solved.

[0090] After completing the finite element method (FEM) solution, strain response data at predetermined measurement points of the elastic strain beam are extracted. The geometric parameters corresponding to each set of structural dimensions and their corresponding strain response data are saved to form a finite element supervision dataset. This finite element supervision dataset serves as the supervisory sample input for range analysis in step 2-2 and subsequent training of the physical information neural network.

[0091] Step 2-2, for each load condition, according to the design variables , , , and Range analysis was performed on the strain response results at different levels. By calculating the mean and range of the strain response of each design variable at different levels, the ranking of the degree of influence of each design variable on the strain response was obtained.

[0092] After completing the range analysis for each load condition, the optimal level combination for each condition was determined. Then, the optimal combinations obtained under different conditions were comprehensively compared to obtain a set of reference dimension combinations in a comprehensive sense, as shown in the table below:

[0093]

[0094] Furthermore, the reference size combination is saved as the initial reference structure for subsequent agent modeling and structural optimization. The reference size combination also serves as the reference basis for the establishment of the equivalent mechanical model in step 3-1 and the multi-objective optimization search in step 5.

[0095] Step 3-1: First, based on the elastic body structural parameters determined in Step 1 and the corresponding geometric relationships of the finite element model in Step 2, select the target strain beam and the floating beam as equivalent analysis objects. Then, approximate the target strain beam and the floating beam as short beams respectively, and establish the corresponding beam element equivalent models, see... Figure 3 .

[0096] Along Horizontal force load in the direction Taking the working condition as an example (the derivation of the mechanical model under other working conditions is similar), the Timoshenko beam theory is used to mechanically describe the target strain beam, and the beam deflection is defined. Sectional rotation angle and shear angle Wherein, the shear angle satisfies: .

[0097] The relationship between bending moment and shear force is established based on the beam's section parameters and material parameters. The bending moment... and shear force They are represented as follows: , ;in, For elastic modulus, Shear modulus This is the shear correction factor. Let be the cross-sectional area of ​​the beam. Let be the moment of inertia of the cross section.

[0098] After establishing the constitutive relation, the equilibrium equations for the target strain beam are further established. These equilibrium equations are expressed as: , ;in, For the distributed load along the beam axis, under the condition of no distributed load, take... .

[0099] After establishing the equilibrium equations, the boundary conditions for the target strain beam are further set. Among these boundary conditions, the root boundary is preferably a fixed-support boundary, i.e.: The free end boundary preferably satisfies the zero bending moment condition and the end shear force condition, that is: , .in, The target strain beam analysis length, The equivalent end load at the free end of the target strain beam is... Further determination is made in step 3-2.

[0100] Furthermore, based on the location of the measuring points on the surface of the target strain beam, a relationship between surface strain and the section rotation gradient is established. The surface strain is expressed as: ,in, This represents the distance from the measuring point to the neutral layer.

[0101] The reference values ​​for some parameters in the calculation formula are shown in the table below:

[0102]

[0103] After completing the above definitions, the equivalent mechanical model of the target strain beam is obtained, including geometric relations, constitutive relations, equilibrium equations, boundary conditions, and strain expressions. This equivalent mechanical model serves as the input basis for establishing the equivalent end load relations in step 3-2 and constructing the physical loss function in step 4-3.

[0104] Step 3-2: First, based on the equivalent mechanical model of the target strain beam established in Step 3-1, clarify the equivalent end load in the boundary conditions at the free end of the target strain beam. It is not a directly given quantity, but is determined by the force distribution relationship of the overall cross-beam elastic body under external load.

[0105] In a specific implementation, along Horizontal force load in the direction Taking the working condition as an example, the cross-sectional area and moment of inertia of the floating beam and the target strain beam are defined respectively. For the floating beam: , For the target strain beam: , .

[0106] Based on the length, material, and cross-sectional parameters of the floating beam and the target strain beam, corresponding equivalent compliance terms are constructed. These equivalent compliance terms are expressed as follows: , ;in, This represents the equivalent flexibility term related to the deformation capacity of the floating beam. This represents the equivalent compliance term related to the deformation capacity of the target strain beam. Based on the compliance distribution of the overall cross beam, the equivalent end shear force borne by the free end of the target strain beam is calculated. The equivalent end shear force is expressed as: ;in, This refers to the horizontal force load applied to the elastic loading block. Through the above calculations, the integral cross-beam structure can be... The stress problem under the working condition is transformed into an equivalent end load input at the free end of the target strain beam.

[0107] Furthermore, the result obtained in step 3-2 Substitute the free end boundary conditions from step 3-1: This allows for the specific determination of the free-end boundary conditions in the equivalent boundary value problem of the target strain beam. It serves as an important input for constructing the boundary condition loss term in subsequent step 4-3, and also as the basis for boundary constraints for physical quantity recovery and residual calculation in steps 4-1 and 4-2.

[0108] For except For other force or moment load conditions besides those mentioned above, the corresponding equivalent load relationships at the free ends can be established in this embodiment according to the same overall force analysis and flexibility coordination approach. The equivalent end loads under different load conditions can be used as the boundary inputs for the load conditions in subsequent physical information neural network modeling.

[0109] Step 4-1: First, based on the structural design variables determined in Step 1 and the equivalent mechanical model established in Step 3, construct a physical information neural network mapping model for the target strain beam. This mapping model is used to establish the functional relationship between the structural geometric parameters and the strain response of the target strain beam.

[0110] Determine the input variables of the PINN mapping model. The input variables include structural geometric parameters and positional parameters, expressed as follows: ;in, , , , and These correspond to the five design variables determined in step 1. This represents the dimensionless position coordinates defined along the effective analysis domain of the target strain beam.

[0111] In order to construct the position parameters First, the effective analysis domain is determined along the axial direction of the target strain beam. Specifically, boundary regions are reserved at the root and ends of the target strain beam, and the intermediate region is used as the effective analysis interval for the subsequent PINN mapping model; then, the effective length is defined based on the effective analysis interval. ,satisfy: ;in, and These are the preset effective domain boundary lengths for the root and the end, respectively;

[0112] After determining the effective length, the axial physical coordinates of the target strain beam are... Dimensionless processing is performed to obtain the position parameters. ,satisfy: ;in, Through the above processing, target strain beams with different geometric combinations can be uniformly mapped to the same dimensionless analysis interval for use in subsequent PINN mapping models.

[0113] After determining the input variables, the PINN backbone network structure is further established. The PINN backbone network preferably adopts a feedforward fully connected neural network structure, whose input end receives... The output terminal outputs the dimensionless mechanical field quantity of the target strain beam.

[0114] In this embodiment, the PINN network output includes dimensionless deflection. and dimensionless cross section rotation angle , is represented as: .in, Represents the neural network mapping function. This represents network parameters.

[0115] After completing the above operations, a PINN mapping model is obtained, which takes structural geometric parameters and dimensionless position coordinates as inputs and dimensionless deflection field and dimensionless rotation field as outputs. This mapping model serves as the basic model for derivative calculation and physical quantity recovery in step 4-2, and for the construction of the joint loss function in step 4-3.

[0116] Step 4-2: First, use the PINN mapping model constructed in Step 4-1 as the base model, and then use any set of structural geometric parameters... and its corresponding dimensionless position parameters Input the model. Then, obtain the dimensionless deflection output by the network. and dimensionless cross section rotation angle .

[0117] The network outputs position parameters. Calculate the first and second derivatives separately. Preferably, an automatic differentiation method is used to obtain them: , , and This is to avoid the discrete errors that may be introduced when using numerical difference methods.

[0118] After obtaining the dimensionless derivative, the network output is restored to the corresponding physical quantity. Specifically, the dimensionless deflection is... With dimensionless cross section rotation angle Multiply by the preset scaling factor to obtain the deflection in physical dimensions. and cross section rotation angle ,satisfy: , ;in, and The scaling factor is related to the external load, material parameters, cross-sectional parameters, and effective length, i.e.: , .

[0119] Based on dimensionless coordinates With physical coordinates The relationship between the dimensionless derivatives is used to transform the dimensionless derivatives into terms about physical coordinates. The derivative of . The transformation relationship satisfies the chain rule: , From this, we can obtain the deflection and cross-sectional rotation angle with respect to the physical coordinates. The first and second derivatives.

[0120] In obtaining , After calculating its derivative, the physical quantities required to construct the physical loss function in step 4-3 are further calculated.

[0121] Step 4-3: Construct each loss term in the physical loss function:

[0122] Loss term of the governing equation: ,in, , ;

[0123] Loss term for boundary conditions: ;

[0124] Loss items for supervised data: ,in, , .

[0125] The total loss function is obtained by weighting and combining the three types of loss terms: .in, , and These are preset weights used to adjust the strength of each loss term during the training process.

[0126] After completing the above operations, the total loss function used for training the PINN mapping model is obtained. The total loss function serves as the optimization objective of the phased training strategy in step 4-4, and is used to iteratively update the network parameters.

[0127] Step 4-4: First, the total loss function obtained in step 4-3 is... The PINN mapping model parameters are then updated in stages according to a pre-defined training process, using the finite element supervised dataset established in step 2 and the input samples defined in step 4-1 as the optimization target for network training.

[0128] The PINN mapping model is pre-trained with physical constraints. This stage primarily optimizes the residual loss of the governing equations and the boundary condition loss, updating the network parameters to ensure the network output initially satisfies the fundamental mechanical laws and boundary constraints of the target strain beam. Through this training stage, a set of initial network parameters is obtained, and the deflection and rotation fields output by the network possess reasonable physical characteristics.

[0129] After completing the physical constraint pre-training, finite element strain supervision data is introduced into the network training process. In this stage, while maintaining the continuous participation of the control equation residuals and boundary condition residuals in the training, a supervised correction loss is added, and the weight of the supervision terms in the total loss function is gradually increased. Through this training method, the network output gradually approximates the finite element strain samples while satisfying the physical constraints, thereby establishing a high-precision mapping relationship between structural parameters and strain response.

[0130] After supervised and corrected fusion training is completed, the network parameters that have initially converged are further optimized. This stage employs a high-precision optimization method to refine all network parameters, thereby improving the convergence performance and final prediction accuracy in the later stages of network training. Preferably, the high-precision optimization method uses a second-order quasi-Newton optimization algorithm, and more preferably, the L-BFGS-B algorithm.

[0131] Furthermore, the structural block diagram of the PINN physical constraint mapping model is as follows: Figure 4 As shown, the training sample parameters of the model are listed in the table below:

[0132]

[0133] The training strategy and optimization parameters of the model are shown in the table below:

[0134]

[0135] After completing the above training process, the trained PINN mapping model is obtained. Given any set of structural and positional parameters, this mapping model can output the dimensionless deflection field and dimensionless rotation field corresponding to the target strain beam. Furthermore, it obtains the strain response and related mechanical quantities through the physical quantity recovery and loss construction methods in steps 4-2 and 4-3. This trained mapping model serves as the foundational model for constructing the multi-objective optimization problem and searching for structural parameters in step 5.

[0136] Step 5: First, use the PINN mapping model trained in Steps 4-4 as a fast structural response prediction model. Then, use the design variables determined in Step 1... As optimization variables, the predetermined value range of each design variable is used as the optimization search domain.

[0137] A multi-objective optimization problem is established based on the optimization requirements. The objective functions of each objective function in this multi-objective optimization problem are determined by the calculation results of the trained PINN mapping model and are used to evaluate the mechanical response performance of the elastomer under different combinations of structural parameters.

[0138] During the optimization calculation process, any set of design variables to be evaluated is input into the PINN mapping model, and combined with the position parameters within the effective analysis domain of the target strain beam, the strain response and related physical quantities under the corresponding structural parameters are calculated. Furthermore, the corresponding objective function value is obtained based on the calculation results.

[0139] Furthermore, the objective function may include relative Indicators include norm, maximum relative error, peak strain error, governing equation residual norm, and energy error. These indicators can be used individually or combined to form a multi-objective optimization problem according to optimization requirements.

[0140] After constructing the multi-objective optimization problem, a multi-objective optimization algorithm is invoked to search for the design variables. Preferably, the multi-objective optimization algorithm is a multi-objective genetic optimization algorithm based on non-dominated sorting, and more preferably, the NSGA-III algorithm.

[0141] In the optimization search process, an initial population is first generated, and the trained PINN mapping model is used to quickly evaluate each combination of design variables in the population. Then, based on the calculation results of each objective function, non-dominated sorting, reference point allocation, and population iterative updates are performed to gradually obtain better combinations of structural parameters.

[0142] After completing the predetermined number of algebras or meeting the stopping condition, one or more sets of Pareto optimal design variable combinations are output. These Pareto optimal design variable combinations are used for finite element verification in step 6 and serve as candidate optimization results for subsequent engineering design selection.

[0143] Step 6: Select the Pareto optimal design variable combination obtained in Step 5 as the optimization result. Re-import the optimization result into the finite element analysis software to establish the corresponding three-dimensional verification model of the elastic body.

[0144] Furthermore, the reference size combination obtained in step 2-2 is selected as the comparison object. The reference size combination is preferably a reference structural parameter combination obtained through orthogonal experiments and range analysis, used to compare its performance with the structural parameter combination optimized in this invention under the same conditions.

[0145] After establishing the finite element verification model, the same boundary conditions, load conditions, material parameters, and mesh generation principles were applied to both the reference structure and the optimized structure. By maintaining consistent finite element analysis conditions, the simulation results of the two types of structures were made comparable.

[0146] In a specific implementation, the strain responses of the target strain beams of the reference structure and the optimized structure under typical load conditions are first compared and analyzed. The comparison includes the strain distribution on the surface of the strain beam, the strain values ​​at characteristic measuring points, and the peak strain response, which are used to evaluate the improvement effect of the optimized structure in terms of sensitivity and strain output characteristics.

[0147] Furthermore, finite element analysis cases for the reference structure and the optimized structure can be established under eccentric or off-center loading conditions, and the degree of strain distribution deviation, local stress changes, and output stability of the two can be compared. Through this comparison, the off-center loading resistance of the optimized structure can be evaluated.

[0148] For implementations requiring evaluation of decoupling performance, the response results of the reference structure and the optimized structure can be extracted under corresponding load and moment conditions, and the changes in their additional response in non-target directions can be compared. This comparison allows for the evaluation of the improved force-moment separation capability of the optimized structure.

[0149] After completing the above comparative analysis, based on the results of the reference structure and the optimized structure in terms of strain response, force-moment separation capability, and resistance to eccentric loading, it is determined whether the optimal combination of design variables obtained in step 5 has achieved the expected optimization goal. If the optimized structure is superior to the reference structure in the main performance indicators, then the structural parameter optimization method based on physical information neural network proposed in this invention is considered effective. Experimental comparison

[0150] The optimized structure obtained by the method of this invention is compared and analyzed with the reference structure obtained by the traditional orthogonal experimental method.

[0151] In the experimental setup, a cross-beam type six-dimensional force sensor elastomer was used as the research object. A reference structural model obtained by orthogonal experimental design and an optimized structural model obtained by the method of this invention were established. Both types of structures were solved using the same material parameters, boundary conditions, load conditions, and finite element analysis settings. Comparative analyses were conducted on strain response, force-moment separation capability, and resistance to eccentric loading.

[0152] Figure 5The results show a comparison of the mechanical properties of the orthogonal experimental reference structure and the optimized structure of this invention under the same working conditions. First, regarding the strain response of the target strain beam, the optimized structure of this invention achieves a better strain response distribution in the target strain beam region. The strain values ​​and peak strain responses at its characteristic measurement points are superior to those of the reference structure, indicating that the method of this invention can further improve the strain output characteristics of the elastic body.

[0153] Furthermore, regarding resistance to eccentric loads, Figure 6 Comparison of the response results of the reference structure and the optimized structure under eccentric loading conditions reveals that the strain disturbance amplitude of the optimized structure under eccentric loading conditions is slightly increased compared to the reference structure. This indicates that the optimized structure obtained by this invention, while improving the strain response characteristics of the elastomer, also has a certain impact on the resistance to eccentric loading. Analysis of the simulation results shows that this impact is generally small and does not change the basic working capacity of the structure under the stated load conditions. Therefore, the method of this invention, while improving the strain output capability of the elastomer, still meets the engineering design requirements.

[0154] Furthermore, regarding the force-torque separation capability, a comparison of the response results of the reference structure and the optimized structure under corresponding force and torque load conditions shows that the additional response of the optimized structure in the non-target direction is suppressed to a certain extent, indicating that its force-torque separation capability is improved.

[0155] In summary, this invention addresses the limitations of traditional orthogonal experimental methods in optimizing the structural parameters of six-dimensional force sensor elastomers, which suffer from limited search capabilities and high costs associated with repetitive finite element method calculations. It proposes a structural parameter optimization method based on a physical information neural network. This method establishes a high-precision mapping model between structural parameters and strain response, and combines it with a multi-objective optimization algorithm to achieve structural parameter search within a continuous design space. This yields optimization results superior to those of traditional orthogonal experimental reference structures, validating the effectiveness of the proposed method.

[0156] The beneficial effects of this invention are as follows:

[0157] (1) This invention combines an equivalent mechanical model with a physical information neural network to establish a mapping relationship between structural parameters and strain response under finite sample conditions, thereby reducing the dependence on large-scale finite element samples;

[0158] (2) The present invention introduces the trained PINN mapping model into the structural parameter optimization process, avoiding repeated high-cost finite element solutions for each candidate size combination during the optimization iteration process, thereby improving the efficiency of the structural parameter optimization design of the six-dimensional force sensor elastomer.

[0159] (3) The combination of structural parameters optimized by the present invention exhibits better strain response characteristics than the orthogonal test reference structure under the same conditions, which can effectively improve the utilization efficiency of the elastic body for strain output. At the same time, simulation results show that the optimization process will affect the performance against off-center load to a certain extent, but the overall impact is small, and the obtained structure has practical engineering application prospects.

Claims

1. A method for optimizing the structural parameters of an elastomer in a six-dimensional force sensor, characterized in that, Includes the following steps: (1) Determine the initial structure of the six-dimensional force sensor elastomer to be optimized, and determine several design variables, including the length of the floating beam, the length of the strain beam, the width of the floating beam, the width of the strain beam, and the thickness of the beam; (2) Based on orthogonal experimental design, generate several sets of structural size combinations, and establish a finite element model for each size combination in finite element analysis software, apply specified boundary conditions and load conditions, calculate and extract strain response data at predetermined measuring points on the elastic body for each size combination, and form a finite element supervision dataset. (3) An equivalent mechanical model is established based on the elastic body structure. The equivalent mechanical model is a beam model based on Timoshenko beam theory, which includes the relationship between bending moment, shear force, constitutive and geometric parameters. (4) Construct a Physical Information Neural Network (PINN) mapping model. During the network training process, the control equations and boundary conditions of the equivalent mechanical model are introduced as physical constraints into the loss function of the network training. At the same time, the network is trained using finite element strain data as a supervision correction term to obtain a high-precision mapping model from structural parameters to strain response. (5) Based on the mapping model, define multiple objective functions and combine them with a multi-objective optimization algorithm to search for the design variables and obtain one or more sets of optimal design variable combinations; (6) Combine the optimal design variables in the finite element software to establish a verification model, evaluate and verify the mechanical response and key performance indicators of the elastic body under the load condition before and after optimization.

2. The method according to step (1) of claim 1, characterized in that, The initial structure of the elastic body is a cross-beam elastic body structure, and the floating beam and strain beam are approximated as short beams in the equivalent model.

3. The method according to step (2) of claim 1, characterized in that, Within the preset value range of the design variables, an orthogonal table is constructed using a multi-factor, multi-level orthogonal experimental design to generate no fewer than 16 combinations of structural dimensions; A finite element analysis model is established for each of the structural dimension combinations. The boundary conditions include constraints on the connection area between the outer beam and the base of the elastic body. The load conditions include force loads along the X / Y / Z directions and moment loads around the X / Y / Z directions. The loads are applied in a manner consistent with the engineering calibration (e.g., loading block loads, remote point coupling).

4. The method according to step (3) of claim 1, characterized in that, The equivalent mechanical model of the Timoshenko beam theory includes at least the following relationships and equations: (1) Deflection Sectional rotation angle and shear angle Geometric relationship between them: ; (2) Constitutive relation: bending moment shear force ,in For elastic modulus, Shear modulus This is the shear correction factor. Let be the cross-sectional area of ​​the beam. The moment of inertia of the cross section; (3) Equilibrium equations: , ,in It is a distributed load along the axial direction; (4) The root boundary conditions are preferably as follows: , The preferred boundary conditions at the free end are: and ,in This is the equivalent end shear force.

5. The equivalent end shear force according to claim 4 Its characteristics are, Obtained from the external load through the structural flexibility distribution relationship, along Horizontal force load in the direction For example, the compliance allocation relationship is as follows: ,in and For beam segment length and material parameters , and cross-sectional parameters , A defined equivalent compliance term.

6. The method according to step (4) of claim 1, characterized in that, The input features of the PINN mapping model include at least structural geometric parameters and positional parameters. ;in For dimensionless coordinates in the effective domain, satisfying , , , These are the preset effective domain boundary lengths for the root and the end, respectively; The output of the PINN network is a dimensionless mechanical field, including dimensionless deflection. With dimensionless rotation The physical quantities are obtained through scaling relationships related to material and geometric parameters: , The scaling factor is related to , , , The parameters are related to ensure dimensional consistency and numerical stability among different geometric combinations.

7. The method according to step (4) of claim 1, characterized in that, When constructing physical constraint terms, by adjusting the network output regarding... The first and second derivatives are used to calculate the information about the actual sampling position. The derivative of , and satisfies the chain relation: , And construct the bending moment accordingly. Shear force And the balancing residuals are used for the calculation of the physical residual term (preferably achieved through automatic differentiation).

8. The method according to claim 7, characterized in that, The physical loss function is composed of the following weighted combinations: (1) Residual loss of governing equations Used for constraints: , ; (2) Boundary condition loss Used to constrain root support conditions and end supports , ; (3) Monitor and correct losses This is used to constrain the consistency between network-predicted strain and finite element strain data; The total loss satisfies: ,in , , Preset weights; The monitoring and correction loss Constructed using strain prediction error, the predicted strain is obtained from the rotation angle gradient: ,in The distance from the patch location to the neutral layer is used; and the supervision error is normalized to improve the numerical stability of training across load and size combinations.

9. The method according to step (4) of claim 1, characterized in that, The training of the PINN mapping model employs a phased optimization strategy, including: (1) Physical constraint pre-training stage: A first-order optimizer is used in the physical constraint pre-training stage. and Training is conducted with the primary objective of initializing the physics solution space. (2) Supervision, correction and integration stage: gradually improve Supervision and correction are carried out by introducing finite element strain data; (3) Second-stage refinement stage: The second-order quasi-Newton method (L-BFGS-B) is used to refine all network parameters in order to improve convergence accuracy (preferably set optimization parameters such as maximum function call to ensure stable convergence).

10. The method according to step (5) of claim 1, characterized in that, The objective function of the constructed multi-objective optimization problem is derived from multiple physical quantities predicted by the mapping model or indices derived therefrom. The indices include at least: relative L2 norm index, maximum relative error, peak strain error, PDE residual norm, and energy error. The multi-objective optimization algorithm is a multi-objective optimization algorithm based on non-dominated sorting (preferably NSGA-III algorithm).

11. The method according to step (6) of claim 1, characterized in that, The key performance indicators include at least: static response under single-dimensional load, resistance to eccentric load, and force-moment separation capability; and under the same boundary conditions and load conditions, the finite element results of the initial structure before optimization and the optimized structure are compared to verify the improvement effect of the optimal combination of design variables.

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