Contact mechanical structure parameter optimization method using incomplete finite element response

Abstract

A contact mechanical structure parameter optimization method using incomplete finite element response comprises the following steps: establishing a contact mechanical structure parameterization model, determining design variables, target responses and engineering constraints; generating an initial sample set and performing finite element analysis; training a classification proxy model with all state sample sets, and training a regression proxy model with complete response sample sets; constructing a joint collection function, and generating a batch of candidate design points in a point-by-point batch mode; performing finite element analysis on the candidate design points, and retraining the classification proxy model and the regression proxy model; cyclically generating and evaluating the candidate design points, updating the Pareto non-dominated solution set based on the true response, and selecting representative solutions from the final true response Pareto non-dominated solution set; performing parameter rounding and finite element recalculation, and determining the final engineering manufacturing parameters. The method can utilize incomplete response states, consider double performance constraints, avoid evaluation resource waste, and improve the authenticity of optimization results.

Description

Technical Field

[0001] This invention relates to the field of electronic information technology, and more specifically to a method for optimizing the parameters of contact mechanical structures using incomplete finite element responses. Background Technology

[0002] Contact-type mechanical structures are widely used in flexible clamping, assembly positioning, sealing and clamping, and friction transmission. Their dimensions and configurations simultaneously affect contact pressure, normal reaction force, structural strength, and operational stability. For mechanical structures involving flexible materials, large deformations, and frictional contact, the above responses and design parameters typically exhibit significant nonlinear coupling. Individual design points require computationally expensive finite element analysis (FEM) to obtain; therefore, it is necessary to employ surrogate models and sequential optimization methods to reduce the number of FEM evaluations.

[0003] Existing surrogate model-based structural optimization methods typically rely on finite element samples that can return all responses. When certain parameter combinations fail to yield all the preset responses during geometric updates, mesh generation, nonlinear solutions, or result extraction, common approaches include directly deleting the design point or using zero values, boundary values, penalty values, and surrogate predictions to fill in the missing responses. However, direct deletion results in the loss of complete finite element response tendency information in the parameter region, while artificial supplementation introduces non-realistic mechanical responses into the regression model, affecting target prediction and uncertainty estimation.

[0004] Furthermore, contact-type mechanical structures typically require that the maximum contact pressure not exceed the risk control limit, the normal reaction force not fall below the stable operating limit, and the material strength requirements be met. If the above-mentioned contact pressure and normal reaction force constraints are not considered simultaneously during the candidate selection stage, or if insufficiently accurate strength proxies and target prediction values ​​are directly used for the final engineering judgment, it is easy to waste evaluation resources and distort the optimization results. Summary of the Invention

[0005] In view of this, the present invention provides a method for optimizing the parameters of contact mechanical structures by utilizing incomplete finite element responses. This method takes advantage of the incomplete response state and considers dual performance constraints simultaneously, thereby avoiding waste of evaluation resources and improving the authenticity of the optimization results.

[0006] A method for optimizing the parameters of contact mechanical structures using incomplete finite element response includes: S1. Establish a parametric model of the contact mechanical structure and determine the design variables, target response and engineering constraints. S2, generate an initial sample set and perform finite element analysis. Mark each design point as a complete response state or an incomplete response state according to whether all preset responses are obtained. For complete response design points, record their design variables, state labels and all target responses and include them in the state sample set and the complete response sample set. For incomplete response design points, only record their design variables and state labels and include them only in the state sample set. S3, train the classification surrogate model with the full set of state samples and the regression surrogate model with the full set of response samples; S4, based on the trained classification surrogate model and regression surrogate model, constructs a joint acquisition function, and generates a batch of candidate design points using a point-by-point batching method; S5, perform finite element analysis on the candidate design points, update the classification dataset and regression dataset based on the response results, and retrain the classification surrogate model and regression surrogate model; S6. Based on the updated training classification surrogate model and regression surrogate model in step S5, candidate design points are generated and evaluated in a loop. After each batch of finite element analysis is completed, the design points with all preset responses are merged with the existing design points. The Pareto non-dominated solution set is updated based on the real response until the cumulative number of new finite element evaluations reaches the preset total number. S7. Select a representative solution from the final Pareto nondominated solution set of the true response, perform parameter rounding and finite element recalculation, and determine the rounded parameters that satisfy all engineering constraints as the final engineering manufacturing parameters.

[0007] The method for optimizing the parameters of contact mechanical structures using incomplete finite element response provided by the present invention has the following advantages: 1. This invention uses both complete and incomplete response design points as state learning samples, and only uses design points that have obtained all preset responses for target regression, without using artificial numerical values ​​to fill in missing responses. This solves the problem that directly deleting these points would lose the completeness of the finite element response's tendency information in the parameter region, utilizing the information contained in incomplete responses through a classification proxy model. Furthermore, it avoids the problem of introducing non-realistic mechanical responses into the regression model through artificial value addition, ensuring that the regression model is trained solely on real mechanical responses. This preserves the completeness of the finite element response's tendency information while preventing non-realistic responses from interfering with the regression model and prediction uncertainty.

[0008] 2. This invention incorporates contact pressure constraints, normal reaction force constraints, and complete response probability into the candidate design point scoring, and adopts a point-by-point batching method that considers the set of candidates to be evaluated to reduce the overlap of improvement effects of candidate points in the same batch. This solves the problem of wasted evaluation resources caused by not simultaneously considering contact pressure and normal reaction force constraints. By using a joint acquisition function, evaluation resources are preferentially allocated to regions that meet performance constraints and have a high complete response probability. Furthermore, point-by-point batching avoids the overlap of improvement effects of candidate points within the same batch, thus balancing multi-objective improvement potential, engineering feasibility, and finite element evaluation resource utilization efficiency.

[0009] 3. This invention updates the Pareto undominated solution set using the true maximum contact pressure and the true normal reaction force, verifies material strength using the true maximum equivalent stress, and performs parameter rounding and finite element recalculation with the same settings on the representative solution. Addressing the shortcomings of directly using insufficiently accurate strength proxies and target predictions for final engineering decisions, this invention establishes the determination of final engineering parameters based on true finite element responses and recalculation verification, ensuring the authenticity, verifiability, and manufacturing feasibility of the optimization results. Attached Figure Description

[0010] Figure 1 A flowchart illustrating a method for optimizing the parameters of a contact mechanical structure using incomplete finite element responses; Figure 2 This is a schematic diagram of the rigid-flexible coupling structure of the flexible gripper in the verification case of this invention; Figure 3 This is a distribution diagram of the complete response state of the initial sample in the verification case of this invention; Figure 4 This is a Pareto front evolution diagram of the real finite element response in the verification case of this invention; Figure 5 This is a comparison chart of the finite element recalculation results before and after parameter rounding in the verification case of this invention. Detailed Implementation

[0011] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain embodiments of the present invention, and should not be construed as limiting the present invention.

[0012] Please see Figure 1 The present invention provides a method for optimizing the parameters of a contact mechanical structure using an incomplete finite element response, the method comprising steps S1 to S7: S1. Establish a parametric model of the contact mechanical structure and determine the design variables, target response, and engineering constraints.

[0013] Specifically, step S1 includes: Select dimensional or angular parameters that affect the local compliance of the contact surface, the structural support stiffness, and the load transfer path to form a design variable vector. , , , They are the 1st, 2nd, and 3rd respectively. One design variable, The total number of design variables, This indicates transpose, and a finite element model is established that includes parametric geometry, material properties, mesh generation, contact relationships, boundary conditions, and load conditions. With maximum contact pressure Minimum and normal reaction forces To maximize the optimization objective, construct the objective function. ,in, It's about design variable vectors. Vector-valued functions; The engineering constraints include design variable boundaries, structural geometric constraints, contact pressure risk constraints, normal reaction force constraints, and material strength constraints. Among these, the contact pressure risk constraint is the maximum contact pressure. Not exceeding the preset contact pressure risk control upper limit Normal reaction force constraint represents normal reaction force Not lower than the preset anti-slip force lower limit Material strength constraints represent the maximum equivalent stress. Not exceeding the allowable strength of the material .

[0014] S2 generates an initial sample set and performs finite element analysis. Each design point is marked as either a complete response state or an incomplete response state based on whether all preset responses are obtained. For complete response design points, their design variables, state labels, and all target responses are recorded and included in the state sample set and the complete response sample set. For incomplete response design points, only their design variables and state labels are recorded and included only in the state sample set.

[0015] Specifically, step S2 includes: Within the design variable boundary, an initial sample set is generated using Latin hypercube sampling. Finite element analysis is then performed on each design point in the initial sample set using the same parametric geometric model, material properties, mesh generation rules, contact relationships, boundary conditions, and load conditions. Pre-defined preset responses to be extracted for each design point are specified, including target responses and verification responses. and As the target response, As a verification response; When all preset responses are obtained at the same design point, the design point is marked as a complete response state, and the finite element analysis response state label of the design point is also added. Recorded as When a design point does not receive all the preset responses, the design point is marked as having an incomplete response state, denoted as . The complete response state and incomplete response state are determined solely based on whether the design point obtains all preset responses, not on whether the obtained target responses satisfy engineering constraints. For a complete response design point, its design variables, state labels, and all target responses are recorded and simultaneously included in both the state sample set and the complete response sample set. For an incomplete response design point, only its design variables and state labels are recorded and only included in the state sample set. The incomplete response state only indicates that the design point did not obtain all preset responses under the preset finite element analysis process, and does not indicate that the corresponding mechanical structure is physically unmanufacturable or inoperable.

[0016] S3 trains a classification surrogate model with the full set of state samples and a regression surrogate model with the full set of response samples.

[0017] Specifically, step S3 includes: Independent data admission branches are established based on the initial sample set. These branches combine design variables and state labels from both complete and incomplete response design points to form a classification dataset. , For the first Design variable vectors for each design point For the first The response status labels of each design point will yield the results for all design points in the target response. and Composition of regression dataset , For the first The actual value of the maximum contact pressure at each design point. For the first The true value of the normal reaction force at each design point, and This response is retained separately for material strength verification. Using classification datasets The kernel function of the radial basis function kernel Gaussian process classification model is used to train the model. for:

[0018] in, The signal variance of the classification kernel function, To design variable vectors The One portion, To design variable vectors The One portion, For the classification kernel function, the first The characteristic length scale of each design variable; Candidate design points are output from the Gaussian process classification model. Probability of obtaining all preset responses , Indicates that, given design variables Under the condition of, response status label The conditional probability of taking the value 1; Using regression datasets Training maximum contact pressure separately and normal reaction force The Matérn 3 / 2 kernel Gaussian process regression model, its kernel function for:

[0019] in, The signal variance of the regression kernel function. The distance between design points is normalized according to the characteristic lengths of each design variable; The kernel function magnitude, feature length, and noise parameters of the classification surrogate model and the regression surrogate model are determined through marginal likelihood optimization. The regression surrogate model then outputs the following parameters: and The predicted mean and prediction uncertainty; for the maximum equivalent stress The regression surrogate model does not output The predicted value is used as the actual material strength check response after finite element analysis, and only the candidate design point is used as the candidate design point.

[0020] S4, based on the trained classification surrogate model and regression surrogate model, constructs a joint acquisition function and generates a batch of candidate design points using a point-by-point batching method.

[0021] Specifically, step S4 includes: Within the design variable boundary, a set of candidate design points is generated using Sobol low-difference sequences. Before calling the regression surrogate model and the classification surrogate model, the candidate design points are pre-screened based on geometric constraints according to the dimensional or configurational relationships between the components of the contact mechanical structure. For candidate design points pre-screened through geometric constraints, according to The corresponding regression surrogate model and The predicted mean and prediction uncertainty of the corresponding regression surrogate model are used to calculate the expected overvolume improvement of the batch, taking into account the contact pressure constraint and normal reaction force constraint. Among them, the contact pressure constraint is the candidate design point. Not exceeding the preset contact pressure risk control upper limit Normal reaction force constraint is the candidate design point Not lower than the preset anti-slip force lower limit , This represents the set of candidate design points that have been selected but have not yet undergone finite element evaluation within the same batch; Calculate the complete response probability of candidate design points based on the classification surrogate model. ,according to Construct a joint acquisition function, To jointly acquire function values, the multi-objective improvement potential of the target response, the possibility of satisfying performance constraints, and the possibility of obtaining all preset responses are unified into a candidate design point score; The selection of candidate design points is determined using a point-by-point batching method: when starting to select the current batch, Let the set be empty; first, select the candidate design point with the highest score from the joint acquisition function from the candidate design point set, and let it be denoted as . and add it ,at this time When selecting the next candidate design point for the current batch, Instead of directly selecting the candidate design point with the second highest score in the joint acquisition function, let's assume that the design point with the second highest score is... If candidate points and Very close. Possible improvements and High overlap, then... Included back, The added value of improvements will decrease. Therefore, The potential improvements to the target caused by existing candidate design points are taken into account. The joint acquisition function (JAC) values ​​of the remaining candidate design points are recalculated. The recalculated JAC values ​​represent the expected multi-objective improvements that each candidate design point can achieve compared to the existing candidate design points in this batch. The candidate design point with the largest recalculated JAC value is then selected from the remaining candidate design points and added to the list. At this point, a candidate point located in a different parameter region that can improve another part of the Pareto solution set may receive a higher score and thus be selected as the second candidate point; this process continues point by point in the same manner until... When the number of candidate design points reaches the preset batch size, the batch size will be... The batch of candidate design points to be simulated has been identified.

[0022] The above point-by-point batching method differs from directly selecting the first few candidate design points according to the initial joint acquisition function value. It can reduce the overlap of the expected improvement effects of each candidate design point in the same batch, and make the improvement of the current target space by the same batch of candidate design points complementary.

[0023] S5 performs finite element analysis on the candidate design points, updates the classification and regression datasets based on the response results, and retrains the classification and regression surrogate models.

[0024] Specifically, step S5 includes: The batch of candidate design points to be evaluated generated in step S4 is received. Finite element analysis is performed on the candidate design points using the same finite element model and analysis settings as the initial samples. The complete response state of each candidate design point is determined according to the state determination method in step S2. For candidate design points that obtain all target responses, their design variables, Status tags, real and reality Add to the classification dataset respectively and regression dataset And record the truth As a subsequent material strength verification response; for candidate design points where not all target responses were obtained, only their design variables and... Adding status labels to the classification dataset After completing the data writing for the current batch of candidate design points, use the updated classification dataset. Retrain the classification agent model to obtain the updated full response probability. Using the updated regression dataset Retraining The corresponding regression surrogate model and The corresponding regression surrogate model yields the updated target response prediction mean and prediction uncertainty; the updated classification surrogate model and regression surrogate model are used to generate the next batch of candidate design points.

[0025] S6. Based on the updated training classification surrogate model and regression surrogate model in step S5, candidate design points are generated and evaluated in a loop. After each batch of finite element analysis is completed, the design points with all preset responses are merged with the existing design points. The Pareto non-dominated solution set is updated based on the real response until the cumulative number of newly added finite element evaluations reaches the preset total number of times.

[0026] Specifically, step S6 includes: Before the optimization of candidate design points begins, the total number of finite element evaluations for newly added candidate design points is pre-set. Using the updated training classification surrogate model and regression surrogate model obtained in step S5, the complete response probability, target response prediction distribution, and joint acquisition function value of the candidate design points are recalculated. The next batch of candidate design points is generated according to the point-by-point batching method in step S4, and finite element analysis is performed on the generated candidate design points. For each batch of candidate design points whose finite element analysis is completed, the number of design points for which finite element analysis was actually performed is counted in the cumulative number of newly added finite element evaluations. Regardless of whether the design point obtains all the preset responses, it is counted as one finite element evaluation. The training classification surrogate model and regression surrogate model are updated using the finite element response results of the current batch for use in the generation and scoring of the next batch of candidate design points. Obtained in the current batch , and All design points of the preset response are combined with the design points of the initial sample set and all design points of the preset response obtained in previous batches to form a cumulative complete response design point set. The engineering constraints of the cumulative complete response design point set are checked, for the first... A complete response design point , For the first The maximum equivalent stress at each complete response design point is used to construct the engineering constraint vector. The design variables are located within the preset boundaries, satisfy the structural geometric constraints, and satisfy the requirements. The design points constitute the set of real-response feasible designs, where the symbols This indicates that all components in the engineering constraint vector are not greater than zero. For each design point in the set of feasible designs with real responses, construct a target vector that is uniformly minimized, expressed as follows: , No. The target vector of a complete response design point, for any two design points and If satisfied , For the first The target vector of a complete response design point, and It is no worse than the design point in all components of the target vector. Then determine the design point. Dominant design point The design points in the set of feasible designs for the true response that are not dominated by other design points are retained, and the Pareto non-dominated solution set of the current true response is composed of all retained design points. When the cumulative number of new finite element evaluations has not reached the preset total number, the next batch of candidate design points will continue to be generated and evaluated; when the preset total number has been reached, the generation of candidate design points and finite element evaluation will be stopped, and the final Pareto non-dominated solution set of the true response will be selected as the candidate representative solution.

[0027] S7. Select a representative solution from the final Pareto nondominated solution set of the true response, perform parameter rounding and finite element recalculation, and determine the rounded parameters that satisfy all engineering constraints as the final engineering manufacturing parameters.

[0028] Specifically, step S7 includes: Receive the final Pareto non-dominated solution set of the true response output from step S6, and apply it to each design point in the Pareto non-dominated solution set of the true response. Cost and The loss is normalized and calculated according to the following formula: Weighted distance between each nondominated solution and the ideal point:

[0029] in, and These are the normalized th A non-dominated solution Cost and loss, and For target weight and ; Select weighted distance The smallest design point is used as the representative solution. The design parameters are rounded according to manufacturing precision, while maintaining the parametric model, material properties, mesh generation, contact relationships, boundary conditions, and load conditions unchanged. Finite element recalculation is performed on the structure before and after rounding, and the results are based on the actual structure after rounding. , and All engineering constraints were re-verified. If the constraints were met, the rounded design parameters were determined as the final engineering manufacturing parameters.

[0030] To verify the invention, a verification case of optimizing the flexible gripper structure parameters was conducted.

[0031] This verification case specifically uses a flexible gripper for holding citrus fruits as the application object, such as... Figure 2 As shown, the gripper includes a flexible substrate 10 and a locally rigid support insert 20. The front beam wall thickness is selected. Rear side beam wall thickness and beam inclination angle As design variables, their ranges are 2. 3mm, 2 4mm and -25° 25°, set Structural geometric constraints; with maximum contact pressure Minimum and single finger normal reaction force The maximum is the optimization target, and it is set. , and Engineering constraints.

[0032] Within the design variable range, 100 initial design points were generated using Latin hypercube sampling, and finite element analysis was performed using a unified parametric model, material properties, mesh rules, contact relationships, boundary conditions, and load conditions. For example... Figure 3 As shown, 36 design points were obtained. , and All preset responses were obtained, but 64 design points did not receive all preset responses; all 100 state samples were used to train the classification agent model, and 36 complete response samples were used for training. and The corresponding regression surrogate model.

[0033] In the candidate set of Sobol pre-screened by geometric constraints, the simultaneous inclusion and Two probability constraints Calculate the multi-objective improvement and compare it with the complete response probability. Multiplication was used to form a joint acquisition function; three candidate design points were selected in each batch using a point-by-point batching method. A total of six new finite element evaluations were completed across two batches, with four candidate points obtaining all preset responses and two candidate points not obtaining all preset responses. The classification dataset increased from 100 sets to 106 sets, and the regression dataset increased from 36 sets to 40 sets. Four new complete response points were identified. All are below 0.017 MPa. and It also meets the requirements for the lower limit of anti-slip force and the allowable strength of materials, respectively.

[0034] After each evaluation, the Pareto non-dominated solution set is updated with the true finite element response. For example... Figure 4 As shown, at a fixed reference point, the two-dimensional hypervolume increased from the initial 0.00830618 to 0.00894413 after two rounds of evaluation, a relative increase of 7.68%. This indicates that the addition of complete response points expands the true target space coverage in the directions of low contact pressure and high normal reaction force. The final cumulative Pareto non-dominated solution set contains 6 true response design points that satisfy engineering constraints.

[0035] Representative solutions are selected from the final Pareto non-dominated solution set using the equal-weighted ideal point distance, with the following parameters: , and Round it according to manufacturing precision. , and And perform finite element recalculation of the structure before and after rounding with the same settings. For example... Figure 5 As shown, the rounded structure , and The values ​​are 0.0026428 MPa, 2.8724 N, and 0.27205 MPa, respectively, which meet the constraints of contact pressure, normal reaction force, material strength, and structural geometry. Therefore, the rounded parameters are determined as the prototype manufacturing parameters, verifying the feasibility of the present invention.

[0036] In summary, the contact mechanical structure parameter optimization method utilizing incomplete finite element response according to the above embodiments has the following beneficial effects: 1. This invention uses both complete and incomplete response design points as state learning samples, and only uses design points that have obtained all preset responses for target regression, without using artificial numerical values ​​to fill in missing responses. This solves the problem that directly deleting these points would lose the completeness of the finite element response's tendency information in the parameter region, utilizing the information contained in incomplete responses through a classification proxy model. Furthermore, it avoids the problem of introducing non-realistic mechanical responses into the regression model through artificial value addition, ensuring that the regression model is trained solely on real mechanical responses. This preserves the completeness of the finite element response's tendency information while preventing non-realistic responses from interfering with the regression model and prediction uncertainty.

[0037] 2. This invention incorporates contact pressure constraints, normal reaction force constraints, and complete response probability into the candidate design point scoring, and adopts a point-by-point batching method that considers the set of candidates to be evaluated to reduce the overlap of improvement effects of candidate points in the same batch. This solves the problem of wasted evaluation resources caused by not simultaneously considering contact pressure and normal reaction force constraints. By using a joint acquisition function, evaluation resources are preferentially allocated to regions that meet performance constraints and have a high complete response probability. Furthermore, point-by-point batching avoids the overlap of improvement effects of candidate points within the same batch, thus balancing multi-objective improvement potential, engineering feasibility, and finite element evaluation resource utilization efficiency.

[0038] 3. This invention updates the Pareto undominated solution set using the true maximum contact pressure and the true normal reaction force, verifies material strength using the true maximum equivalent stress, and performs parameter rounding and finite element recalculation with the same settings on the representative solution. Addressing the shortcomings of directly using insufficiently accurate strength proxies and target predictions for final engineering decisions, this invention establishes the determination of final engineering parameters based on true finite element responses and recalculation verification, ensuring the authenticity, verifiability, and manufacturing feasibility of the optimization results.

[0039] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for optimizing the parameters of a contact mechanical structure using incomplete finite element response, characterized in that, include: S1. Establish a parametric model of the contact mechanical structure and determine the design variables, target response and engineering constraints. S2, generate an initial sample set and perform finite element analysis. Mark each design point as a complete response state or an incomplete response state according to whether all preset responses are obtained. For complete response design points, record their design variables, state labels and all target responses and include them in the state sample set and the complete response sample set. For incomplete response design points, only record their design variables and state labels and include them only in the state sample set. S3, train the classification surrogate model with the full set of state samples and the regression surrogate model with the full set of response samples; S4, based on the trained classification surrogate model and regression surrogate model, constructs a joint acquisition function, and generates a batch of candidate design points using a point-by-point batching method; S5, perform finite element analysis on the candidate design points, update the classification dataset and regression dataset based on the response results, and retrain the classification surrogate model and regression surrogate model; S6. Based on the updated training classification surrogate model and regression surrogate model in step S5, candidate design points are generated and evaluated in a loop. After each batch of finite element analysis is completed, the design points with all preset responses are merged with the existing design points. The Pareto non-dominated solution set is updated based on the real response until the cumulative number of new finite element evaluations reaches the preset total number. S7. Select a representative solution from the final Pareto nondominated solution set of the true response, perform parameter rounding and finite element recalculation, and determine the rounded parameters that satisfy all engineering constraints as the final engineering manufacturing parameters.

2. The method for optimizing the parameters of contact mechanical structures using incomplete finite element response as described in claim 1, characterized in that, Step S1 specifically includes: Select dimensional or angular parameters that affect the local compliance of the contact surface, the structural support stiffness, and the load transfer path to form a design variable vector. , , , They are the 1st, 2nd, and 3rd respectively. One design variable, The total number of design variables, This indicates transpose, and a finite element model is established that includes parametric geometry, material properties, mesh generation, contact relationships, boundary conditions, and load conditions. With maximum contact pressure Minimum and normal reaction forces To maximize the optimization objective, construct the objective function. ; The engineering constraints include design variable boundaries, structural geometric constraints, contact pressure risk constraints, normal reaction force constraints, and material strength constraints. Among these, the contact pressure risk constraint is the maximum contact pressure. Not exceeding the preset contact pressure risk control upper limit Normal reaction force constraint represents normal reaction force Not lower than the preset anti-slip force lower limit Material strength constraints represent the maximum equivalent stress. Not exceeding the allowable strength of the material .

3. The method for optimizing the parameters of contact mechanical structures using incomplete finite element response as described in claim 2, characterized in that, Step S2 specifically includes: Within the design variable boundary, an initial sample set is generated using Latin hypercube sampling. Finite element analysis is then performed on each design point in the initial sample set using the same parametric geometric model, material properties, mesh generation rules, contact relationships, boundary conditions, and load conditions. Pre-defined preset responses to be extracted for each design point are specified, including target responses and verification responses. and As the target response, As a verification response; When all preset responses are obtained at the same design point, the design point is marked as a complete response state, and the finite element analysis response state label of the design point is also added. Recorded as When a design point does not receive all the preset responses, the design point is marked as having an incomplete response state, denoted as . The complete response state and incomplete response state are determined solely based on whether the design point obtains all preset responses, not on whether the obtained target responses satisfy engineering constraints. For a complete response design point, its design variables, state labels, and all target responses are recorded and simultaneously included in both the state sample set and the complete response sample set. For an incomplete response design point, only its design variables and state labels are recorded and only included in the state sample set. The incomplete response state only indicates that the design point did not obtain all preset responses under the preset finite element analysis process, and does not indicate that the corresponding mechanical structure is physically unmanufacturable or inoperable.

4. The method for optimizing the parameters of contact mechanical structures using incomplete finite element response according to claim 3, characterized in that, Step S3 specifically includes: Independent data admission branches are established based on the initial sample set. These branches combine design variables and state labels from both complete and incomplete response design points to form a classification dataset. , For the first Design variable vectors for each design point For the first The response status labels of each design point will yield the results for all design points in the target response. and Composition of regression dataset , For the first The actual value of the maximum contact pressure at each design point For the first The true value of the normal reaction force at each design point, and This response is retained separately for material strength verification. Using classification datasets The kernel function of the radial basis function kernel Gaussian process classification model is used to train the model. for: in, The signal variance of the classification kernel function, To design variable vectors The One portion, To design variable vectors The One portion, For the classification kernel function, the first The characteristic length scale of each design variable; Candidate design points are output from the Gaussian process classification model. Probability of obtaining all preset responses , Indicates that, given design variables Under the condition of, response status label The conditional probability of taking the value 1; Using regression datasets Training maximum contact pressure separately and normal reaction force The Matérn 3 / 2 kernel Gaussian process regression model, its kernel function for: in, The signal variance of the regression kernel function. The distance between design points is normalized according to the characteristic lengths of each design variable; The kernel function magnitude, feature length, and noise parameters of the classification surrogate model and the regression surrogate model are determined through marginal likelihood optimization. The regression surrogate model then outputs the following parameters: and The predicted mean and prediction uncertainty; for the maximum equivalent stress The regression surrogate model does not output The predicted value is used as the actual material strength check response after finite element analysis, and only the candidate design point is used as the candidate design point.

5. The method for optimizing the parameters of contact mechanical structures using incomplete finite element responses according to claim 4, characterized in that, Step S4 specifically includes: Within the design variable boundary, a set of candidate design points is generated using Sobol low-difference sequences. Before calling the regression surrogate model and the classification surrogate model, the candidate design points are pre-screened based on geometric constraints according to the dimensional or configurational relationships between the components of the contact mechanical structure. For candidate design points pre-screened through geometric constraints, according to The corresponding regression surrogate model and The predicted mean and prediction uncertainty of the corresponding regression surrogate model are used to calculate the expected bulk overvolume improvement taking into account contact pressure constraints and normal reaction force constraints. Among them, the contact pressure constraint is the candidate design point. Not exceeding the preset contact pressure risk control upper limit Normal reaction force constraint is a candidate design point Not lower than the preset anti-slip force lower limit , This represents the set of candidate design points that have been selected but have not yet undergone finite element evaluation within the same batch; Calculate the complete response probability of candidate design points based on the classification surrogate model. ,according to Construct a joint acquisition function, To jointly acquire function values, the multi-objective improvement potential of the target response, the possibility of satisfying performance constraints, and the possibility of obtaining all preset responses are unified into a candidate design point score; The selection of candidate design points is determined using a point-by-point batching method: when starting to select the current batch, Let the set be empty; first, select the candidate design point with the highest score from the joint acquisition function from the candidate design point set, and let it be denoted as . and add it ,at this time When selecting the next candidate design point for the current batch, The potential improvements to the target objectives that may be achieved by existing candidate design points are taken into account. The joint acquisition function value of the remaining candidate design points is recalculated, and the candidate design point with the largest recalculated joint acquisition function value is selected and added to the list. Continue selecting points one by one in the above manner until... When the number of candidate design points reaches the preset batch size, the batch size will be... The batch of candidate design points to be simulated has been identified.

6. The method for optimizing the parameters of contact mechanical structures using incomplete finite element response according to claim 5, characterized in that, Step S5 specifically includes: The batch of candidate design points to be evaluated generated in step S4 is received. Finite element analysis is performed on the candidate design points using the same finite element model and analysis settings as the initial samples. The complete response state of each candidate design point is determined according to the state determination method in step S2. For candidate design points that obtain all target responses, their design variables, Status tags, real and reality Add to the classification dataset respectively and regression dataset And record the truth As a subsequent material strength verification response; for candidate design points where not all target responses were obtained, only their design variables and... Adding status labels to the classification dataset After completing the data writing for the current batch of candidate design points, use the updated classification dataset. Retrain the classification agent model to obtain the updated full response probability. Using the updated regression dataset Retraining The corresponding regression surrogate model and The corresponding regression surrogate model yields the updated target response prediction mean and prediction uncertainty; the updated classification surrogate model and regression surrogate model are used to generate the next batch of candidate design points.

7. The method for optimizing the parameters of contact mechanical structures using incomplete finite element response according to claim 6, characterized in that, Step S6 specifically includes: Before the optimization of candidate design points begins, the total number of finite element evaluations for newly added candidate design points is pre-set. Using the updated training classification surrogate model and regression surrogate model obtained in step S5, the complete response probability, target response prediction distribution, and joint acquisition function value of the candidate design points are recalculated. The next batch of candidate design points is generated according to the point-by-point batching method in step S4, and finite element analysis is performed on the generated candidate design points. For each batch of candidate design points whose finite element analysis is completed, the number of design points for which finite element analysis was actually performed is counted in the cumulative number of newly added finite element evaluations. Regardless of whether the design point obtains all the preset responses, it is counted as one finite element evaluation. The training classification surrogate model and regression surrogate model are updated using the finite element response results of the current batch for use in the generation and scoring of the next batch of candidate design points. Obtained in the current batch , and All design points of the preset response are combined with the design points of the initial sample set and all design points of the preset response obtained in previous batches to form a cumulative complete response design point set. The engineering constraints of the cumulative complete response design point set are checked, for the first... A complete response design point , For the first The maximum equivalent stress at each complete response design point is used to construct the engineering constraint vector. The design variables are located within the preset boundaries, satisfy the structural geometric constraints, and satisfy the requirements. The design points constitute the set of real-response feasible designs; For each design point in the set of feasible designs with true response, construct a target vector that is uniformly minimized, expressed as follows: , No. The target vector of a complete response design point, for any two design points and If satisfied , For the first The target vector of a complete response design point, and It is no worse than the design point in all components of the target vector. Then determine the design point. Dominant Design Point The design points in the set of feasible designs for the true response that are not dominated by other design points are retained, and the Pareto non-dominated solution set of the current true response is composed of all retained design points. When the cumulative number of newly added finite element evaluations has not reached the preset total number, the next batch of candidate design points will continue to be generated and evaluated; when the preset total number is reached, the generation of candidate design points and finite element evaluation will be stopped.

8. The method for optimizing the parameters of contact mechanical structures using incomplete finite element response according to claim 7, characterized in that, Step S7 specifically includes: Receive the final Pareto non-dominated solution set of the true response output from step S6, and apply it to each design point in the Pareto non-dominated solution set of the true response. Cost and The loss is normalized and calculated according to the following formula: Weighted distance between each nondominated solution and the ideal point: in, and These are the normalized th A non-dominated solution Cost and loss, and For target weight and ; Select weighted distance The smallest design point is used as the representative solution. The design parameters are rounded according to manufacturing precision, while maintaining the parametric model, material properties, mesh generation, contact relationships, boundary conditions, and load conditions unchanged. Finite element recalculation is performed on the structure before and after rounding, and the results are based on the actual structure after rounding. , and All engineering constraints were re-verified. If the constraints were met, the rounded design parameters were determined as the final engineering manufacturing parameters.

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