ML-based linear guide rail constraint optimization method, device, medium and program product

Abstract

The application discloses an ML-based linear guide rail constraint optimization method, equipment, medium and program product, and the method comprises the steps of: (1) taking friction resistance as a constraint, constructing a simulation model and a multi-target constraint optimization model capable of simultaneously optimizing static stiffness, total mass and maximum contact stress; (2) generating a current task sample set based on constraint perception Bayesian sampling of historical data migration learning, and establishing a sample database and a migration Gaussian process proxy model; (3) generating an external weight vector and a neighborhood dense internal weight vector under a multi-target decomposition framework, and generating a candidate point set; (4) clustering a joint weight set, and screening an optimal candidate point corresponding to a representative weight; (5) performing finite element simulation verification on the optimal candidate point, updating the sample database and the proxy model, returning to step (3), and outputting an optimal solution until a termination condition is met. The application can significantly reduce the finite element simulation cost while ensuring the optimization accuracy.

Description

Technical Field

[0001] This invention relates to the fields of intelligent optimization design, surrogate model optimization and multi-objective evolutionary optimization, and in particular to a linear guide constraint optimization method, device, medium and program product based on ML (Machine Learning). Background Technology

[0002] Linear guides are key moving components in precision mechanical equipment, widely used in CNC machine tools, industrial robots, automated production lines, and precision testing equipment. They primarily enable high-precision linear motion guidance and load transfer. Their structural performance directly determines the positioning accuracy, dynamic response speed, and operational stability of the equipment system. Linear guide design typically requires comprehensive consideration of multiple performance indicators, including static stiffness, total mass, and maximum contact stress, to achieve the design goals of high stiffness, lightweight construction, and high reliability.

[0003] Traditional linear guide structure design often relies on engineering experience or finite element simulation trial-and-error methods, typically using a single performance index as the optimization objective. Improvements are achieved through repeated adjustments of structural parameters and simulation verification. Linear guide structures involve multiple design variables, and these performance indices are interdependent. For example, increasing static stiffness often accompanies an increase in total mass, and reducing maximum contact stress may require altering raceway geometry parameters. Traditional single-objective optimization or experience-based design struggles to obtain the overall optimal solution across multiple performance indices, and extensive finite element simulations result in low design efficiency and long design cycles.

[0004] In recent years, multi-objective optimization methods have been applied to engineering structural design, enabling the acquisition of Pareto optimal solution sets among multiple conflicting optimization objectives and providing various trade-off solutions for design. To reduce the high computational costs associated with finite element simulation, surrogate models are typically used to approximate the mapping relationship between design variables and performance indicators. Among these, the transfer Gaussian process surrogate model possesses strong nonlinear fitting capabilities and uncertainty representation abilities, making it suitable for complex engineering optimization problems. By establishing a transfer Gaussian process surrogate model, structural performance can be accurately predicted based on a small number of simulation samples, reducing the number of finite element calculations and improving optimization efficiency.

[0005] However, the following problems still exist in the multi-objective optimization process based on the surrogate model: First, traditional initial sampling makes little use of historical data, resulting in low sample utilization; second, fixed external weights are difficult to adapt to complex Pareto front shapes, which can easily lead to weight vacancies or insufficient optimization search; third, there is a lack of a unified coupling mechanism between gradient information, design improvement information and constraint information, resulting in unclear candidate point generation directions; and fourth, if a large number of candidate points are directly screened, redundant comparisons can be easily introduced and computational complexity can be increased.

[0006] Therefore, a linear guide constraint optimization method is needed that simultaneously considers historical data migration, dense weight generation, comprehensive gradient guidance, and representative weight selection. Summary of the Invention

[0007] In view of the above limitations of the existing technology, and considering the design requirements of linear guide rails for three optimization objectives of static stiffness, total mass, and maximum contact stress, as well as friction resistance constraints, this invention proposes a linear guide rail constraint optimization method, device, medium, and program product based on ML.

[0008] To achieve the above objectives, the first aspect of the present invention provides a linear guide rail optimization design method, the method comprising the steps of: S1. Using the dimensions of the guide rail, slider, raceway and ball as design parameters, with the objectives of maximizing static stiffness, minimizing total mass and minimizing maximum contact stress, and with frictional resistance as constraint, a simulation model and a multi-objective constraint optimization model are established. S2. Construct the design space according to the range of design parameters. After generating the current task sample set by constraint-aware Bayesian sampling based on historical data transfer learning, obtain the real simulation results through finite element evaluation of the simulation model, establish a sample database and construct a transfer Gaussian process proxy model. S3 generates an external weight vector and a dense neighborhood internal weight vector within the multi-objective decomposition framework. It constructs a comprehensive gradient direction based on local gradients and multi-objective expectation improvement indicators, and generates a candidate point set by combining internal and external weight sampling. S4. Combine the internal and external weights to form a joint weight set, use agglomerative hierarchical clustering to filter the joint weight set, use a surrogate model to predict candidate points, and combine the ideal point and constraint violation degree to filter the optimal candidate point. S5: Perform finite element simulation evaluation on the optimal candidate point to obtain the true target value, update the sample database and surrogate model, and return to step S3 until the termination condition is met, and output the optimal solution.

[0009] Optionally, step S1 specifically includes the following steps: S1.1, taking into account the structural characteristics of linear guide rails, the slider length, slider width, slider height, slider oil groove depth, raceway curvature radius, raceway center distance, raceway groove depth, raceway transition fillet radius, ball diameter, guide rail length, guide rail width, and guide rail height are used as design parameters. S1.2, Based on the load conditions of the linear guide structure and the material selected for the linear guide, a three-dimensional model is constructed using three-dimensional modeling software and parameterized to obtain a parameterized model. S1.3, import the parametric model, the load conditions of the linear guide structure and the key boundary conditions into the finite element analysis pre- and post-processing software for finite element analysis to obtain the finite element analysis model; S1.4. Using the solver of the structural optimization and multiphysics simulation software, static load analysis is performed on the finite element analysis model to obtain the static stiffness, total mass, maximum contact stress, and frictional resistance simulation model of the linear guide rail. S1.5 Based on the simulation model of the static stiffness, total mass, maximum contact stress, and frictional resistance of the linear guide, a multi-objective constrained optimization model of the linear guide is constructed. The objective of maximizing static stiffness is transformed into the form of minimizing its inverse, thus unifying the three optimization objectives into a minimization problem. The specific expression is as follows: , , , , In the above formula, This indicates the search for the optimal solution to the design parameters. This indicates the design parameters of the linear guide. Indicates the length of the slider. Indicates the slider width. Indicates the height of the slider. Indicates the radius of curvature of the raceway. Indicates the center distance of the raceways. Indicates the depth of the raceway groove. Indicates the length of the guide rail. Indicates the guide rail height. Indicates the width of the guide rail. Indicates the diameter of the ball bearing. Indicates the radius of the raceway transition fillet. Indicates the depth of the slider oil groove. This represents minimizing the negative static stiffness, maximum contact stress, and total mass of the linear guide. This indicates the design parameters of the linear guide. The corresponding negative static stiffness value is This indicates the design parameters of the linear guide. The corresponding static stiffness function at time, This indicates the design parameters of the linear guide. The maximum contact stress corresponding to this time, This indicates the design parameters of the linear guide. The corresponding maximum contact stress function, This indicates the design parameters of the linear guide. The corresponding total mass at that time Indicates design parameters The linear guide is divided into The total mass function obtained by summing the parts is This indicates the density of the linear guide. Indicates design parameters The volume of the linear guide corresponding to that time. This indicates taking the maximum value within the parentheses, used to define the degree of constraint violation when the frictional resistance exceeds the maximum permissible frictional resistance. Indicate design parameters The frictional resistance of the linear guide rail, This indicates the maximum allowable frictional resistance of the linear guide. Indicate design parameters The degree of constraint violation of the frictional resistance of the linear guide rail. This indicates a feasible solution. Indicates an infeasible solution. This represents the constraints that need to be satisfied. Indicate design parameters The frictional resistance of the linear guide must not exceed the maximum permissible frictional resistance.

[0010] Optionally, step S2 specifically includes the following steps: S2.1, Determine the value range of each design parameter according to the design requirements and material properties of the linear guide, and construct the design space based on the value range; S2.2, Constraint-aware Bayes sampling based on historical data transfer learning is adopted to read the simulation samples of objective function and constraint function obtained in historical optimization tasks, construct a historical sample library, and combine it with the initial samples in the current design space to form the current task sample set; The constraint-aware Bayesian sampling method based on historical simulation data transfer learning includes the following steps: S2.2.1, Construct a historical sample database With the current task sample set : , , In the above formula, Indicates historical mission, Indicates the current task. The total number of samples in the historical sample database. This represents the total number of samples in the current task sample set. , The first and second missions are respectively the historical missions and the current missions. A vector of design variables, for 3D real space, To design variable dimensions, , The first and second missions are respectively the historical missions and the current missions. A multi-objective function vector, Indicates the first One objective function, These are the constraint function values ​​for the historical task and the current task, respectively. Represents the constraint function; S2.2.2, for each objective function and constraint functions We construct transfer Gaussian process surrogate models with task labels to achieve coupled learning of historical and current data: , , In the above formula, For task tags, For the first The output of the Gaussian process surrogate model for each objective function. The output of the Gaussian process surrogate model for the constraint function is... For Gaussian processes, , These are the mean functions of the objective function and the constraint function, respectively. , These are the kernel functions for the objective function and the constraint function, respectively. S2.2.3, for any candidate point to be sampled By using posterior inference from a Gaussian process surrogate model, the predicted mean of the objective function is obtained. The prediction variance of the objective function The predicted mean of the constraint function Prediction variance of constraint functions And define the constraint feasibility probability. : , In the above formula, The cumulative distribution function of the standard normal distribution. It is a very small positive number; S2.2.4, Constructing Sampling Criteria : , In the above formula, For the expected improvement value of multiple objectives, To predict variance based on each target The normalized total probability, The minimum Euclidean distance between the candidate point and the current task sample set. For historical sample support, , , , These are the first non-negative weight coefficient, the second non-negative weight coefficient, the third non-negative weight coefficient, and the fourth non-negative weight coefficient, respectively. S2.2.5, in the design space Internal solution for optimal sampling points : , In the above formula, The input variable that makes the function reach its maximum value. This represents the maximum value that the function can achieve. Will Submit the data to the simulation platform for finite element evaluation to obtain the corresponding objective function values. and constraint function values and will Add to the current task sample set Complete one sampling; S2.2.6 Repeat steps S2.2.1 to S2.2.5 until the preset maximum number of samples is reached or the optimized convergence condition is met, and generate the current task sample set. ; S2.3, for the current task sample set The current task sample points are evaluated by finite element method through simulation model to obtain real simulation results of static stiffness, total mass, maximum contact stress and frictional resistance. The real simulation results are combined with the historical sample library to form a sample database. S2.4, Based on the sample database, establish migration Gaussian process proxy models for static stiffness function, total mass function, maximum contact stress function and friction resistance constraint function respectively; wherein, the task correlation coefficient is used to characterize the correlation between historical optimization tasks and current tasks, so as to realize historical knowledge transfer and suppress negative transfer.

[0011] Optionally, step S3 specifically includes the following steps: S3.1, within the multi-objective decomposition framework, the simplex method is used to generate a uniformly distributed set of external weight vectors in the objective space, as expressed below: , In the above formula, Let k represent the set of external weight vectors, and k represent the number of external weight vectors. This represents the first external weight vector. This represents the second external weight vector. This represents the k-th external weight vector; S3.2, for each external weight vector Identify the dense internal weight vector that is orthogonally farthest from the external weight vector within its neighborhood. Multiple dense internal weight vectors are generated through linear combination, and their expression is as follows: , In the above formula, The final selected dense internal weight vector, The independent variable that makes the function reach its maximum value, This represents the maximum value that the function can achieve. for The set of neighborhood weights, The orthogonal distance between the two weight vectors; S3.3, In order to guide the parameters to search for a better region, obtain the changing trends of each objective function and constraint function when moving along different design variables near the current candidate point, for the current candidate point to be updated. Based on the established Gaussian transfer process surrogate model, the local gradients of each objective function and constraint function at the candidate point are calculated, and the local gradient matrix is ​​constructed. : , In the above formula, Indicates the first surrogate model for each objective function The target gradient vector obtained by differentiation Represents a surrogate model for constraint functions The gradient vector of the constraint function obtained by differentiation, for 3D real space, To design variable dimensions; S3.4, Since the objective functions and constraint functions have different dimensions, their gradient vectors have significantly different magnitudes. Directly using these vectors would lead to the search process being dominated by gradient vectors with larger magnitudes. Therefore, the gradient vectors are normalized to obtain unit vectors that only represent the gradient direction. , , In the above formula, For the first The normalized objective gradient of each objective function. To normalize the constraint gradient, It is a very small positive number. The L2 norm of a vector; S3.5, if the search is performed only along the gradient direction of a single objective, it is easy to get trapped in a local optimum or ignore the optimization effect of other objectives. Therefore, it is necessary to evaluate the improvement potential of moving along different gradient directions in terms of the Pareto front of the overall multi-objective optimization problem; define the current non-dominated front approximation point set. ,in For the first Objective function values ​​at each frontier point For the number of frontier points, For the first The static stiffness at each leading edge point is taken as the negative true value. For the first The true value of the total mass of each frontier point. For the first The true value of the maximum contact stress at each leading edge point; for candidate points The predicted mean of the objective function is output using a Gaussian transfer process surrogate model. With the predicted standard deviation Single-objective expected improvement index: relative to the frontier points in the non-dominated frontier approximation point set. , No. The first goal in Expected improvement value of a single objective under each weight direction for: In the above formula, Candidate points On the q-th objective relative to the 1st objective A cutting-edge point The expected improvement The cumulative function of the standard normal distribution. Let be the standard normal probability density function. Based on this, three types of comprehensive improvement indices are constructed, collectively referred to as multi-objective expected improvement information, which are used to comprehensively evaluate the improvement potential of candidate points to the Pareto front. These indices will subsequently be used for weighted fusion of gradient directions. Euclidean Comprehensive Improvement Index : This metric is used to characterize the degree of improvement in the Euclidean distance from the candidate point to the Pareto front, and prioritizes guiding the search to advance towards the Pareto front along the shortest path. In the above formula, To obtain the expected improvement values ​​of the three objectives using the Euclidean norm, we obtain the candidate points towards the th... Overall improvement distance in each weight direction To select the value with the shortest improvement distance among all weight directions; Max min type comprehensive improvement index : This metric is used to characterize the optimal value of the worst improvement effect among all objectives, ensuring that all objectives are improved in a balanced manner during the search process, and avoiding the situation where a single objective is optimal while other objectives degenerate; In the above formula, In the first Under each weighted direction, the objective with the largest expected improvement value among the three objectives is selected. This maximum value represents the expected improvement value under this direction, that is, the optimal improvement level that can be achieved in this direction. The value represents the expected improvement. Super-volume comprehensive improvement index : This indicator directly quantifies the hypervolume improvement of the Pareto front and guides the search to expand the coverage of the Pareto front. In the above formula, As a preset reference point, and satisfying , To define the supervolume from the reference point to the new frontier after adding candidate points, The hypervolume from the reference point to the original frontier before adding candidate points. This is an improvement in volume; Based on the current set of approximate points of the non-dominated front, a local Pareto front approximate surface in the target space is constructed using polynomial fitting or support vector machine methods, providing geometric information of the target space for the subsequent construction of the Pareto front induced direction. S3.6, The normalized target gradient is weighted and fused based on the three types of comprehensive improvement indicators, as shown in the following expression: Euclidean fusion direction: , Max-min type fusion direction: , Ultra-volumetric fusion direction: , In the above formula, For the first 1 candidate point Euclidean weights This is the index of the optimal frontier point for the Euclidean index. Weights are of type max and min. The direction index that minimizes the max-min type improvement index. For super-volume weights, The direction index that minimizes the improvement index of the hypervolume type, and satisfies ; S3.7, introduces constraints on feasible probability. To ensure that the search direction prioritizes the constrained feasible region, the final comprehensive gradient vector is defined as follows: In the above formula, , , , The first non-negative weight coefficient, the second non-negative weight coefficient, the third non-negative weight coefficient, and the fourth non-negative weight coefficient are respectively, satisfying the following: , This indicates the L2 normalization operation, which ensures the consistency and stability of the gradient direction; S3.8 generates offspring individuals within the design space based on the combined gradient direction, weight-induced search direction, and Pareto front-induced direction. The formula is as follows: In the above formula, For feasible region projection operators, To determine the step size parameter for the overall gradient direction, The step size parameter is used to guide the search direction based on weights. Let be the step size parameter for the Pareto front induction direction. Uniformly distributed random numbers are used to adjust the direction of the integrated gradient. The step size perturbation, Uniformly distributed random numbers are used to adjust weights and guide the search direction. The step size perturbation, Uniformly distributed random numbers are used to adjust the direction of Pareto front induction. The step size perturbation, The formula is to guide the search direction based on weights. ,in External preference weights For the i-th candidate point, The direction of Pareto front induction; S3.9, the Pareto front induced direction is calculated through gradient mapping between the target space and the design space. The specific steps are as follows: using polynomial fitting or support vector machine methods, an approximate surface of the local Pareto front in the target space is constructed. Calculate the optimal front edge point of the surface. Normal vector at point Through the local target gradient matrix Mapping back to the design space yields ; S3.10, based on the comprehensive gradient direction, weight-induced search direction, and Pareto front-induced direction, generates a set of candidate points within the design space; for each external weight... and each dense internal weight generated therefrom Calculate the corresponding candidate points respectively: , in, For the first 1 candidate point For the reason With the Candidate points generated by dense internal weights For feasible region projection operators, This represents the direction of the overall gradient.

[0012] Optionally, step S4 specifically includes the following steps: S4.1, the set of external weight vectors generated in step S3 With the set of internal weight vectors Merge to form a joint weight vector set Calculate the joint weight set Construct a weight distance matrix by calculating the Euclidean distance between any two weight vectors. The expression for the elements of the weighted distance matrix is ​​as follows:

[0013] In the above formula, For the first The index of each weight vector. For the first The index of each weight vector. , The first A weight vector, For the first The preference weights of each weight vector in the first objective. For the first The preference weights in the second objective are the preference weights. For the first The preference weights of the weight vectors in the third objective. For the first The preference weights of each weight vector in the first objective. No. The preference weights of the weight vectors in the second objective. For the first The preference weights of the weight vectors in the third objective. For the first The weight vector at the th weight vector in the th... The preference weights of each objective For the first The weight vector at the th weight vector in the th... The preference weights of each objective; S4.2, Agglomerative hierarchical clustering method is used to cluster the joint weight vector set. Clustering screening was performed to obtain Each weighted cluster The number of clusters is preset with weights; S4.3 uses a Gaussian transfer process surrogate model to predict the objective function value and constraint violation degree of each candidate point, which are then used for subsequent screening based on representative weight vectors. The expression is as follows: , In the above formula, For the first Target static stiffness values ​​for candidate points For the first The total quality target value of the candidate points For the first The maximum target value of contact stress at each candidate point For the first Preset violation degree of frictional resistance at each candidate point, constraint violation degree This indicates that the constraint is satisfied. This indicates a violation of the constraints; S4.4, for each weight cluster The mean vector of all weight vectors within a cluster is calculated and used as the cluster center. The weight vector that has the closest Euclidean distance to the cluster center is selected as the representative weight vector of the cluster. Based on representative weight vector The ICDP fitness function is used to filter all candidate points corresponding to the cluster, and the parameter with the smallest fitness value is selected as the optimal candidate point of the cluster. The ICDP fitness function is defined as follows: , In the above formula, For the first The representative weight vector at the th ... The weight of each goal For the first The objective function at the candidate point The actual function value below, To preset the ideal point, This is the ideal value under the first objective. This is the ideal value under the second objective. This is the ideal value under the third objective. This is a dynamic penalty coefficient. The degree of violation of the frictional resistance constraint at the candidate point; S4.5, Integration The optimal candidate points of each weighted cluster constitute the optimal candidate point set. Based on the requirements of maximizing static stiffness, minimizing total mass, minimizing maximum contact stress, and constraining frictional resistance, from The candidate point with the best overall performance is selected as the final optimal candidate point.

[0014] Optionally, the specific calculation steps of the agglomerative hierarchical clustering method are as follows: S4.2.1, joint weight set Each weight vector in the algorithm is considered as an independent cluster, resulting in an initial cluster set. ,in, For the 1st cluster, the 2nd cluster, ..., the Nth cluster, For the first Each cluster contains only one weight vector. Based on the average link criterion, the weight vectors of any two clusters in the current cluster set are calculated. Inter-cluster distance The expression for calculating inter-cluster distance is as follows: , In the above formula, Clusters The number of weight vectors included. For the first A weight vector, For the first A weight vector, These are elements of the weighted distance matrix; S4.2.2, Find the two clusters with the smallest inter-cluster distance. Merge them into a new cluster Then remove the original cluster from the initial cluster set. Join a new cluster The number of clusters has been updated to When the number of clusters in the initial cluster set is equal to the preset weight cluster number When the time comes, stop the clustering operation and obtain the final result. Each weighted cluster.

[0015] Optionally, step S5 specifically includes the following steps: S5.1, the optimal candidate points obtained in step S4 are evaluated by finite element simulation to obtain the true objective function values ​​corresponding to each optimal candidate point, including the static stiffness, total mass and maximum contact stress of the linear guide rail, and the friction resistance constraint function value is calculated. S5.2, add the optimal candidate point and its corresponding true objective function value and constraint function value to the sample database, and retrain the transfer Gaussian process surrogate model in combination with the historical sample database; S5.3 Determine whether the termination condition is met. The termination condition includes reaching the maximum number of iterations or the objective function convergence condition. If the termination condition is met, output the optimal solution; otherwise, return to step S3 to continue iterative optimization.

[0016] Secondly, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor, when executing the computer program, implements the steps of the aforementioned linear guide constraint optimization method based on ML.

[0017] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the steps of the aforementioned ML-based linear guide constraint optimization method.

[0018] Fourthly, the present invention provides a computer program product, including a computer program, which, when executed by a processor, implements the steps of the aforementioned ML-based linear guide constraint optimization method.

[0019] In summary, compared with the prior art, the technical solutions conceived in this invention have the following main advantages: 1. To address the problem that traditional single-objective optimization is difficult to balance multiple performance indicators and has high simulation costs, this invention establishes a three-objective optimization model for static stiffness, total mass, and maximum contact stress, and introduces constraint-aware Bayesian sampling based on historical data transfer learning. By making full use of historical data in the initial sampling stage, the number of calls to expensive finite element simulations is significantly reduced, effectively balancing multiple performance indicators while greatly shortening the design cycle.

[0020] 2. To address the problem that fixed external weights are difficult to adapt to complex Pareto front shapes, which can easily lead to weight vacancies or insufficient optimization search, this invention generates external weight vectors within a multi-objective decomposition framework and generates dense internal weight vectors in their neighborhood through linear combination, forming a hierarchical search preference from the outside to the inside. This can adaptively cover irregular Pareto fronts, avoid weight vacancies, and enhance the algorithm's ability to explore feasible regions with complex constraints.

[0021] 3. To address the problem that the lack of a unified coupling mechanism between gradient information, design improvement information, and constraint information leads to unclear candidate point generation directions, this invention constructs a comprehensive gradient direction based on local gradients and multi-objective expected improvement indices (Euclidean, max-min, and hypervolume comprehensive improvement indices). This organically integrates the target improvement potential with the constraint feasibility probability, guiding candidate points to be generated along the Pareto optimal direction, thereby improving the targeting and efficiency of the search.

[0022] 4. To address the problem that direct screening of a large number of candidate points easily introduces redundant comparisons and increases computational complexity, this invention constructs a joint weight set from the internal and external weight vectors, uses agglomerative hierarchical clustering to obtain representative weight vectors, and then uses the ICDP (Improved Constrained Dominance Principle) fitness function to screen the candidate points corresponding to the representative weight vectors, effectively reducing the redundancy of candidate point comparisons and improving the representativeness of the solution set and screening efficiency.

[0023] In summary, this invention provides a multi-objective constraint optimization design method for linear guideways that combines a migration Gaussian process proxy model, integrated gradient guidance, and joint weighted clustering screening mechanism. While ensuring optimization accuracy, it significantly reduces the cost of finite element simulation and achieves synergistic optimization of the static stiffness, total mass, maximum contact stress, and frictional resistance constraints of the linear guideway. Attached Figure Description

[0024] Figure 1 A simplified flowchart of a linear guide constraint optimization method based on machine learning provided by this invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0026] Please see Figure 1 This invention provides a linear guide optimization design method, applicable to multi-objective optimization design of linear guides. Specifically, the method includes steps S1 to S5.

[0027] S1 uses the dimensions of the guide rail, slider, raceway and ball as design parameters, aims to maximize static stiffness, minimize total mass and minimize maximum contact stress, and uses frictional resistance as a constraint to establish a simulation model and a multi-objective constraint optimization model.

[0028] The specific steps of step S1 are as follows: S1.1, taking into account the structural characteristics of linear guide rails, the slider length, slider width, slider height, slider oil groove depth, raceway curvature radius, raceway center distance, raceway groove depth, raceway transition fillet radius, ball diameter, guide rail length, guide rail width, and guide rail height are used as design parameters. S1.2, Based on the load conditions of the linear guide structure and the material selected for the linear guide, a three-dimensional model is constructed using three-dimensional modeling software and parameterized to obtain a parameterized model. S1.3, import the parametric model, the load conditions of the linear guide structure and the key boundary conditions into the finite element analysis pre- and post-processing software for finite element analysis to obtain the finite element analysis model; S1.4. Using the solver of the structural optimization and multiphysics simulation software, static load analysis is performed on the finite element analysis model to obtain the static stiffness, total mass, maximum contact stress, and frictional resistance simulation model of the linear guide rail. S1.5 Based on the simulation model of the static stiffness, total mass, maximum contact stress, and frictional resistance of the linear guide, a multi-objective constrained optimization model of the linear guide is constructed. The objective of maximizing static stiffness is transformed into the form of minimizing its inverse, thus unifying the three optimization objectives into a minimization problem. The specific expression is as follows: , , , , In the above formula, This indicates the search for the optimal solution to the design parameters. This indicates the design parameters of the linear guide. Indicates the length of the slider. Indicates the slider width. Indicates the height of the slider. Indicates the radius of curvature of the raceway. Indicates the center distance of the raceways. Indicates the depth of the raceway groove. Indicates the length of the guide rail. Indicates the guide rail height. Indicates the width of the guide rail. Indicates the diameter of the ball bearing. Indicates the radius of the raceway transition fillet. Indicates the depth of the slider oil groove. This represents minimizing the negative static stiffness, maximum contact stress, and total mass of the linear guide. This indicates the design parameters of the linear guide. The corresponding negative static stiffness value is This indicates the design parameters of the linear guide. The corresponding static stiffness function at time, This indicates the design parameters of the linear guide. The maximum contact stress corresponding to this time, This indicates the design parameters of the linear guide. The corresponding maximum contact stress function, This indicates the design parameters of the linear guide. The corresponding total mass at that time Indicates design parameters The linear guide is divided into The total mass function obtained by summing the parts is This indicates the density of the linear guide. Indicates design parameters The volume of the linear guide corresponding to that time. This indicates taking the maximum value within the parentheses, used to define the degree of constraint violation when the frictional resistance exceeds the maximum permissible frictional resistance. Indicate design parameters The frictional resistance of the linear guide rail, This indicates the maximum allowable frictional resistance of the linear guide. Indicate design parameters The degree of constraint violation of the frictional resistance of the linear guide rail. This indicates a feasible solution. Indicates an infeasible solution. This represents the constraints that need to be satisfied. Indicate design parameters The frictional resistance of the linear guide must not exceed the maximum permissible frictional resistance.

[0029] S2. Based on the range of design parameters, a design space is constructed. After generating the current task sample set by constraint-aware Bayesian sampling based on historical data transfer learning, the real simulation results are obtained through finite element evaluation of the simulation model. A sample database is established and a transfer Gaussian process proxy model is constructed.

[0030] The specific steps of step S2 are as follows: S2.1 Determine the value range of each design parameter based on the design requirements and material properties of the linear guide, and construct the design space based on the value range; S2.2, Constraint-aware Bayes sampling based on historical data transfer learning is adopted to read the simulation samples of objective function and constraint function obtained in historical optimization tasks, construct a historical sample library, and combine it with the initial samples in the current design space to form the current task sample set; Constraint-aware Bayesian sampling based on historical data transfer learning includes the following steps: S2.2.1, Construct a historical sample database With the current task sample set : , , In the above formula, Indicates historical mission, Indicates the current task. The total number of samples in the historical sample database. This represents the total number of samples in the current task sample set. , The first and second missions are respectively the historical missions and the current missions. A vector of design variables, for 3D real space, To design variable dimensions, , The first and second missions are respectively the historical missions and the current missions. A multi-objective function vector, Indicates the first One objective function, These are the constraint function values ​​for the historical task and the current task, respectively. Represents the constraint function; S2.2.2, for each objective function and constraint functions We construct transfer Gaussian process surrogate models with task labels to achieve coupled learning of historical and current data: , , In the above formula, For task tags, For the first The output of the Gaussian process surrogate model for each objective function. The output of the Gaussian process surrogate model for the constraint function is... For Gaussian processes, , These are the mean functions of the objective function and the constraint function, respectively. , These are the kernel functions for the objective function and the constraint function, respectively. S2.2.3, for any candidate point to be sampled By using posterior inference from a Gaussian process surrogate model, the predicted mean of the objective function is obtained. The prediction variance of the objective function The predicted mean of the constraint function Prediction variance of constraint functions And define the constraint feasibility probability. : , In the above formula, The cumulative distribution function of the standard normal distribution. It is a very small positive number; S2.2.4, Constructing Sampling Criteria : , In the above formula, For the expected improvement value of multiple objectives, To predict variance based on each target The normalized total probability, The minimum Euclidean distance between the candidate point and the current task sample set. For historical sample support, , , , These are the first non-negative weight coefficient, the second non-negative weight coefficient, the third non-negative weight coefficient, and the fourth non-negative weight coefficient, respectively. S2.2.5, in the design space Internal solution for optimal sampling points : , In the above formula, The input variable that makes the function reach its maximum value. This represents the maximum value that the function can achieve. Will Submit the data to the simulation platform for finite element evaluation to obtain the corresponding objective function values. and constraint function values and will Add to the current task sample set Complete one sampling; S2.2.6 Repeat steps S2.2.1 to S2.2.5 until the preset maximum number of samples is reached or the optimized convergence condition is met, and generate the current task sample set. ; S2.3, for the current task sample set The current task sample points are evaluated by finite element method through simulation model to obtain real simulation results of static stiffness, total mass, maximum contact stress and frictional resistance. The real simulation results are combined with the historical sample library to form a sample database. S2.4, Based on the sample database, establish migration Gaussian surrogate models for static stiffness function, total mass function, maximum contact stress function and friction resistance constraint function respectively; among them, the task correlation coefficient is used to characterize the correlation between historical optimization tasks and current tasks, so as to realize historical knowledge transfer and suppress negative transfer.

[0031] S3 generates an external weight vector and a dense neighborhood internal weight vector within a multi-objective decomposition framework. It constructs a comprehensive gradient direction based on local gradients and multi-objective expectation improvement indicators, and generates a candidate point set by combining internal and external weight sampling.

[0032] The specific steps of step S3 are as follows: S3.1, within the multi-objective decomposition framework, the simplex method is used to generate a uniformly distributed set of external weight vectors in the objective space, as expressed below: , In the above formula, Let k represent the set of external weight vectors, and k represent the number of external weight vectors. This represents the first external weight vector. This represents the second external weight vector. This represents the k-th external weight vector; S3.2, for each external weight vector Identify the dense internal weight vector that is orthogonally farthest from the external weight vector within its neighborhood. Multiple dense internal weight vectors are generated through linear combination, and their expression is as follows: , In the above formula, The final selected dense internal weight vector, The independent variable that makes the function reach its maximum value, This represents the maximum value that the function can achieve. for The set of neighborhood weights, The orthogonal distance between the two weight vectors; S3.3, In order to guide the parameters to search for a better region, obtain the changing trends of each objective function and constraint function when moving along different design variables near the current candidate point, for the current candidate point to be updated. Based on the established Gaussian transfer process surrogate model, the local gradients of each objective function and constraint function at the candidate point are calculated, and the local gradient matrix is ​​constructed. : , In the above formula, Indicates the first surrogate model for each objective function The target gradient vector obtained by differentiation Represents a surrogate model for constraint functions The gradient vector of the constraint function obtained by differentiation, for 3D real space, To design variable dimensions; S3.4, due to the different dimensions of the objective functions and constraint functions, the magnitudes of their gradient vectors vary considerably. Directly using these vectors would lead to the search process being dominated by gradient vectors with larger magnitudes. Therefore, the gradient vectors are normalized to obtain unit vectors that only represent the gradient direction. , , In the above formula, For the first The normalized objective gradient of each objective function. To normalize the constraint gradient, It is a very small positive number. The L2 norm of a vector; S3.5, if the search is performed only along the gradient direction of a single objective, it is easy to get trapped in a local optimum or ignore the optimization effect of other objectives. Therefore, it is necessary to evaluate the improvement potential of moving along different gradient directions in terms of the Pareto front of the overall multi-objective optimization problem; define the current non-dominated front approximation point set. ,in For the first Objective function values ​​at each frontier point For the number of frontier points, For the first The static stiffness at each leading edge point is taken as the negative true value. For the first The true value of the total mass of each frontier point. For the first The true value of the maximum contact stress at each leading edge point; for candidate points The predicted mean of the objective function is output using a Gaussian transfer process surrogate model. With the predicted standard deviation Single-objective expected improvement index: relative to the frontier points in the non-dominated frontier approximation point set. , No. The first goal in Expected improvement value of a single objective under each weight direction for: In the above formula, Candidate points On the q-th objective relative to the 1st objective A cutting-edge point The expected improvement The cumulative function of the standard normal distribution. Let be the standard normal probability density function. Based on this, three types of comprehensive improvement indices are constructed, collectively referred to as multi-objective expected improvement information, which are used to comprehensively evaluate the improvement potential of candidate points to the Pareto front. These indices will subsequently be used for weighted fusion of gradient directions. Euclidean Comprehensive Improvement Index : This metric is used to characterize the degree of improvement in the Euclidean distance from the candidate point to the Pareto front, and prioritizes guiding the search to advance towards the Pareto front along the shortest path. In the above formula, To obtain the expected improvement values ​​of the three objectives using the Euclidean norm, we obtain the candidate points towards the th... Overall improvement distance in each weight direction To select the value with the shortest improvement distance among all weight directions; Max min type comprehensive improvement index : This metric is used to characterize the optimal value of the worst improvement effect among all objectives, ensuring that all objectives are improved in a balanced manner during the search process, and avoiding the situation where a single objective is optimal while other objectives degenerate; In the above formula, In the first Under each weighted direction, the objective with the largest expected improvement value among the three objectives is selected. This maximum value represents the expected improvement value under this direction, that is, the optimal improvement level that can be achieved in this direction. The value represents the expected improvement. Super-volume comprehensive improvement index : This indicator directly quantifies the hypervolume improvement of the Pareto front and guides the search to expand the coverage of the Pareto front. In the above formula, As a preset reference point, and satisfying , To define the supervolume from the reference point to the new frontier after adding candidate points, The hypervolume from the reference point to the original frontier before adding candidate points. This is an improvement in volume; Based on the current set of approximate points of the non-dominated front, a local Pareto front approximate surface in the target space is constructed using polynomial fitting or support vector machine methods, providing geometric information of the target space for the subsequent construction of the Pareto front induced direction. S3.6, the normalized target gradient is weighted and fused based on the three types of comprehensive improvement indicators, as shown in the following expression: Euclidean fusion direction: , Max-min type fusion direction: , Ultra-volumetric fusion direction: , In the above formula, For the first 1 candidate point Euclidean weights This is the index of the optimal frontier point for the Euclidean index. Weights are of type max and min. The direction index that minimizes the max-min type improvement index. For super-volume weights, The direction index that minimizes the improvement index of the hypervolume type, and satisfies ; S3.7, introduces constraints on feasible probability. To ensure that the search direction prioritizes the constrained feasible region, the final comprehensive gradient vector is defined as follows: In the above formula, , , , The first non-negative weight coefficient, the second non-negative weight coefficient, the third non-negative weight coefficient, and the fourth non-negative weight coefficient are respectively, satisfying the following: , This indicates the L2 normalization operation, which ensures the consistency and stability of the gradient direction; S3.8 generates offspring individuals within the design space based on the combined gradient direction, weight-induced search direction, and Pareto front-induced direction. The formula is as follows: In the above formula, For feasible region projection operators, To determine the step size parameter for the overall gradient direction, The step size parameter is used to guide the search direction based on weights. Let be the step size parameter for the Pareto front induction direction. Uniformly distributed random numbers are used to adjust the direction of the integrated gradient. The step size perturbation, Uniformly distributed random numbers are used to adjust weights and guide the search direction. The step size perturbation, Uniformly distributed random numbers are used to adjust the direction of Pareto front induction. The step size perturbation, The formula is to guide the search direction based on weights. ,in External preference weights For the i-th candidate point, The direction of Pareto front induction; S3.9, the Pareto front induced direction is calculated through gradient mapping between the target space and the design space. The specific steps are as follows: using polynomial fitting or support vector machine methods, an approximate surface of the local Pareto front in the target space is constructed. Calculate the optimal front edge point of the surface. Normal vector at point Through the local target gradient matrix Mapping back to the design space yields ; S3.10, based on the comprehensive gradient direction, weight-induced search direction, and Pareto front-induced direction, generates a set of candidate points within the design space; for each external weight... and each dense internal weight generated therefrom Calculate the corresponding candidate points respectively: , in, For the first 1 candidate point For the reason With the Candidate points generated by dense internal weights For feasible region projection operators, This represents the direction of the overall gradient.

[0033] S4. The internal and external weights are combined to form a joint weight set. Agglomerated hierarchical clustering is used to filter the joint weight set. The surrogate model is used to predict candidate points. The optimal candidate point is selected by combining the ideal point and the constraint violation degree.

[0034] The specific steps of step S4 are as follows: S4.1, the set of external weight vectors generated in step S3 With the set of internal weight vectors Merge to form a joint weight vector set Calculate the joint weight set Construct a weight distance matrix by calculating the Euclidean distance between any two weight vectors. The expression for the elements of the weighted distance matrix is ​​as follows:

[0035] In the above formula, For the first The index of each weight vector. For the first The index of each weight vector. , The first A weight vector, For the first The preference weights of each weight vector in the first objective. For the first The preference weights in the second objective are the preference weights. For the first The preference weights of the weight vectors in the third objective. For the first The preference weights of each weight vector in the first objective. No. The preference weights of the weight vectors in the second objective. For the first The preference weights of the weight vectors in the third objective. For the first The weight vector at the th weight vector in the th... The preference weights of each objective For the first The weight vector at the th weight vector in the th... The preference weights of each objective; S4.2, Agglomerative hierarchical clustering method is used to cluster the joint weight vector set. Clustering screening was performed to obtain Each weighted cluster The number of clusters is preset with weights; The specific calculation steps of the agglomerative hierarchical clustering method are as follows: S4.2.1, joint weight set Each weight vector in the algorithm is considered as an independent cluster, resulting in an initial cluster set. ,in, For the 1st cluster, the 2nd cluster, ..., the Nth cluster, For the first Each cluster contains only one weight vector. Based on the average link criterion, the weight vectors of any two clusters in the current cluster set are calculated. Inter-cluster distance The expression for calculating inter-cluster distance is as follows: , In the above formula, Clusters The number of weight vectors included. For the first A weight vector, For the first A weight vector, These are elements of the weighted distance matrix; S4.2.2, Find the two clusters with the smallest inter-cluster distance. Merge them into a new cluster Then remove the original cluster from the initial cluster set. Join a new cluster The number of clusters has been updated to When the number of clusters in the initial cluster set is equal to the preset weight cluster number When the time comes, stop the clustering operation and obtain the final result. Each weighted cluster.

[0036] S4.3 uses a Gaussian transfer process surrogate model to predict the objective function value and constraint violation degree of each candidate point, which are then used for subsequent screening based on representative weight vectors. The expression is as follows: , In the above formula, For the first Target static stiffness values ​​for candidate points For the first The total quality target value of the candidate points For the first The maximum target value of contact stress at each candidate point For the first Preset violation degree of frictional resistance at each candidate point, constraint violation degree This indicates that the constraint is satisfied. This indicates a violation of the constraints; S4.4, for each weight cluster The mean vector of all weight vectors within a cluster is calculated and used as the cluster center. The weight vector that has the closest Euclidean distance to the cluster center is selected as the representative weight vector of the cluster. Based on representative weight vector The ICDP fitness function is used to filter all candidate points corresponding to the cluster, and the parameter with the smallest fitness value is selected as the optimal candidate point of the cluster. The ICDP fitness function is defined as follows: , In the above formula, For the first The representative weight vector at the th ... The weight of each goal For the first The objective function at the candidate point The actual function value below, To preset the ideal point, This is the ideal value under the first objective. This is the ideal value under the second objective. This is the ideal value under the third objective. This is a dynamic penalty coefficient. The degree of violation of the frictional resistance constraint at the candidate point; S4.5, Integration The optimal candidate points of each weighted cluster constitute the optimal candidate point set. Based on the requirements of maximizing static stiffness, minimizing total mass, minimizing maximum contact stress, and constraining frictional resistance, from The candidate point with the best overall performance is selected as the final optimal candidate point.

[0037] S5: Perform finite element simulation evaluation on the optimal candidate point to obtain the true target value, update the sample database and surrogate model, and return to step S3 until the termination condition is met, and output the optimal solution.

[0038] The specific steps of step S5 are as follows: S5.1, the optimal candidate points obtained in step S4 are evaluated by finite element simulation to obtain the true objective function values ​​corresponding to each optimal candidate point, including the static stiffness, total mass and maximum contact stress of the linear guide rail, and the friction resistance constraint function value is calculated. S5.2, add the optimal candidate points and their corresponding true objective function values ​​and constraint function values ​​to the sample database, and retrain the transfer Gaussian process surrogate model in combination with the historical sample database; S5.3, determine whether the termination condition is met. The termination condition includes reaching the maximum number of iterations or the objective function convergence condition. If the termination condition is met, output the optimal solution; otherwise, return to step S3 to continue iterative optimization.

[0039] Example 1 illustrates the optimization performance of the proposed ML-based linear guide constraint optimization method using the benchmark test function MW14. MW14 is a constraint-type objective test function with three-objective single-constraint characteristics, and its expression is as follows: , ,

[0040] , In the above formula, This indicates minimizing three objective functions. For decision vector variables, , These are the first decision variable and the second decision variable, respectively. , , These are three objective functions to be minimized: the first objective function, the second objective function, and the third objective function. For variable link coefficients, This represents the constraints that need to be satisfied. For constraint functions, , These are the first auxiliary function and the second auxiliary function, respectively. It represents the negative value of static stiffness. For total mass, This represents the maximum contact stress.

[0041] The above benchmark test functions are processed through steps S1 to S5 of the linear guide constraint optimization method based on ML provided by the present invention to obtain experimental results.

[0042] To further illustrate this embodiment, a linear guide constraint optimization method based on ML is compared with another classic SMES-RBF algorithm. The maximum number of simulation evaluations in this embodiment is set to 1000, and the experimental results are shown in Table 1. Under the same number of simulation samples, the method of this embodiment obtains the smallest IGD value, which is significantly smaller than that of SMES-RBF. It can be considered that the method of this embodiment has good performance in the linear guide constraint optimization design problem.

[0043] Table 1. Comparison of optimization results of different methods

[0044] This invention provides a linear guide constraint optimization method based on machine learning. By constructing a migration Gaussian process proxy model that integrates historical data to reduce simulation costs, and designing a multi-objective optimization mechanism based on comprehensive gradient direction guidance and dense weight clustering screening, it can efficiently solve complex multi-objective problems involving constraints on static stiffness, total mass, maximum contact stress, and frictional resistance. While ensuring optimization accuracy, it significantly improves the representativeness and diversity of Pareto solution sets, providing a systematic solution for constraint multi-objective optimization design of linear guide structures.

[0045] Secondly, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor, when executing the computer program, implements the steps of the linear guide constraint optimization method based on ML described in the foregoing embodiments.

[0046] The memory can be volatile or non-volatile, or a combination of both. Non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory can be random access memory (RAM), used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memory of this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0047] The processor can be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in this invention. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in this invention can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.

[0048] The method steps of this invention can be implemented in hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in this application, or combinations thereof.

[0049] Software implementation can be achieved by executing functional modules (such as procedures, functions, etc.). Software code can be stored in memory and executed by the processor. Memory can be implemented in the processor or outside the processor.

[0050] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the steps of the aforementioned ML-based linear guide constraint optimization method.

[0051] Computer storage media can include various media that can store program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0052] Fourthly, the present invention provides a computer program product, including a computer program, which, when executed by a processor, implements the steps of the aforementioned ML-based linear guide constraint optimization method.

[0053] Specifically, computer program products include: data signals, data signals embodied in a carrier wave, or computer-readable storage media.

[0054] It should be noted that the various technical features described in this invention can be combined with each other without conflict.

[0055] Those skilled in the art should understand that the above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A linear guide constraint optimization method based on machine learning, characterized in that, include: S1. Using the dimensions of the guide rail, slider, raceway and ball as design parameters, with the objectives of maximizing static stiffness, minimizing total mass and minimizing maximum contact stress, and with frictional resistance as constraint, a simulation model and a multi-objective constraint optimization model are established. S2. Construct the design space according to the range of design parameters. After generating the current task sample set by constraint-aware Bayesian sampling based on historical data transfer learning, obtain the real simulation results through finite element evaluation of the simulation model, establish a sample database and construct a transfer Gaussian process proxy model. S3 generates an external weight vector and a dense neighborhood internal weight vector within the multi-objective decomposition framework. It constructs a comprehensive gradient direction based on local gradients and multi-objective expectation improvement indicators, and generates a candidate point set by combining internal and external weight sampling. S4. Combine the internal and external weights to form a joint weight set, use agglomerative hierarchical clustering to filter the joint weight set, use a surrogate model to predict candidate points, and combine the ideal point and constraint violation degree to filter the optimal candidate point. S5: Perform finite element simulation evaluation on the optimal candidate point to obtain the true target value, update the sample database and surrogate model, and return to step S3 until the termination condition is met, and output the optimal solution.

2. The method as described in claim 1, characterized in that, Step S1 specifically includes: S1.1, taking into account the structural characteristics of linear guide rails, the slider length, slider width, slider height, slider oil groove depth, raceway curvature radius, raceway center distance, raceway groove depth, raceway transition fillet radius, ball diameter, guide rail length, guide rail width, and guide rail height are used as design parameters. S1.2, Based on the load conditions of the linear guide structure and the material selected for the linear guide, a three-dimensional model is constructed using three-dimensional modeling software and parameterized to obtain a parameterized model. S1.3, import the parametric model, the load conditions of the linear guide structure and the key boundary conditions into the finite element analysis pre- and post-processing software for finite element analysis to obtain the finite element analysis model; S1.

4. Using the solver of the structural optimization and multiphysics simulation software, static load analysis is performed on the finite element analysis model to obtain the static stiffness, total mass, maximum contact stress, and frictional resistance simulation model of the linear guide rail. S1.5 Based on the simulation model of the static stiffness, total mass, maximum contact stress, and frictional resistance of the linear guide, a multi-objective constrained optimization model of the linear guide is constructed. The objective of maximizing static stiffness is transformed into the form of minimizing its inverse, thus unifying the three optimization objectives into a minimization problem. The specific expression is as follows: ， ， ， ， In the above formula, This indicates the search for the optimal solution to the design parameters. This indicates the design parameters of the linear guide. Indicates the length of the slider. Indicates the slider width. Indicates the height of the slider. Indicates the radius of curvature of the raceway. Indicates the center distance of the raceways. Indicates the depth of the raceway groove. Indicates the length of the guide rail. Indicates the guide rail height. Indicates the width of the guide rail. Indicates the diameter of the ball bearing. Indicates the radius of the raceway transition fillet. Indicates the depth of the slider oil groove. This represents minimizing the negative static stiffness, maximum contact stress, and total mass of the linear guide. This indicates the design parameters of the linear guide. The corresponding negative static stiffness value is This indicates the design parameters of the linear guide. The corresponding static stiffness function at time, This indicates the design parameters of the linear guide. The maximum contact stress corresponding to this time, This indicates the design parameters of the linear guide. The corresponding maximum contact stress function, This indicates the design parameters of the linear guide. The corresponding total mass at that time Indicates design parameters The linear guide is divided into The total mass function obtained by summing the parts is This indicates the density of the linear guide. Indicates design parameters The volume of the linear guide rail corresponding to that time. This indicates taking the maximum value within the parentheses, used to define the degree of constraint violation when the frictional resistance exceeds the maximum permissible frictional resistance. Indicate design parameters The frictional resistance of the linear guide rail, This indicates the maximum allowable frictional resistance of the linear guide. Indicate design parameters The degree of constraint violation of the frictional resistance of the linear guide rail. This indicates a feasible solution. Indicates an infeasible solution. This represents the constraints that need to be satisfied. Indicate design parameters The frictional resistance of the linear guide must not exceed the maximum permissible frictional resistance.

3. The method as described in claim 1, characterized in that, Step S2 specifically includes: S2.1, Determine the value range of each design parameter according to the design requirements and material properties of the linear guide, and construct the design space based on the value range; S2.2, Constraint-aware Bayes sampling based on historical data transfer learning is adopted to read the simulation samples of objective function and constraint function obtained in historical optimization tasks, construct a historical sample library, and combine it with the initial samples in the current design space to form the current task sample set; The constraint-aware Bayesian sampling based on historical data transfer learning includes the following steps: S2.2.1, Construct a historical sample database With the current task sample set : ， ， In the above formula, Indicates historical mission, Indicates the current task. The total number of samples in the historical sample database. This represents the total number of samples in the current task sample set. , The first and second missions are respectively the historical missions and the current missions. A vector of design variables, for 3D real space, To design variable dimensions, , The first and second missions are respectively the historical missions and the current missions. A multi-objective function vector, Indicates the first One objective function, , These are the constraint function values ​​for the historical task and the current task, respectively. Represents the constraint function; S2.2.2, for each objective function and constraint functions We construct transfer Gaussian process surrogate models with task labels to achieve coupled learning of historical and current data: ， ， In the above formula, For task tags, For the first The output of the Gaussian process surrogate model for each objective function. The output of the Gaussian process surrogate model for the constraint function is... For Gaussian processes, , These are the mean functions of the objective function and the constraint function, respectively. , These are the kernel functions for the objective function and the constraint function, respectively. S2.2.3, for any candidate point to be sampled By using posterior inference from a Gaussian process surrogate model, the predicted mean of the objective function is obtained. The prediction variance of the objective function The predicted mean of the constraint function Prediction variance of constraint functions And define the constraint feasibility probability. : ， In the above formula, The cumulative distribution function of the standard normal distribution. It is a very small positive number; S2.2.4, Constructing Sampling Criteria : ， In the above formula, For the expected improvement value of multiple objectives, To predict variance based on each target The normalized total probability, The minimum Euclidean distance between the candidate point and the current task sample set. For historical sample support, , , , These are the first non-negative weight coefficient, the second non-negative weight coefficient, the third non-negative weight coefficient, and the fourth non-negative weight coefficient, respectively. S2.2.5, in the design space Internal solution for optimal sampling points : ， In the above formula, The input variable that makes the function reach its maximum value. This represents the maximum value that the function can achieve. Will Submit the data to the simulation platform for finite element evaluation to obtain the corresponding objective function values. and constraint function values and will Add to the current task sample set Complete one sampling; S2.2.6 Repeat steps S2.2.1 to S2.2.5 until the preset maximum number of samples is reached or the optimized convergence condition is met, and generate the current task sample set. ; S2.3, for the current task sample set The current task sample points are evaluated by finite element method through simulation model to obtain real simulation results of static stiffness, total mass, maximum contact stress and frictional resistance. The real simulation results are combined with the historical sample library to form a sample database. S2.4, Based on the sample database, establish migration Gaussian process proxy models for static stiffness function, total mass function, maximum contact stress function and friction resistance constraint function respectively; wherein, the task correlation coefficient is used to characterize the correlation between historical optimization tasks and current tasks, so as to realize historical knowledge transfer and suppress negative transfer.

4. The method as described in claim 1, characterized in that, Step S3 specifically includes: S3.1, within the multi-objective decomposition framework, the simplex method is used to generate a uniformly distributed set of external weight vectors in the objective space, as expressed below: ， In the above formula, Let k represent the set of external weight vectors, and k represent the number of external weight vectors. This represents the first external weight vector. This represents the second external weight vector. This represents the k-th external weight vector; S3.2, for each external weight vector Identify the dense internal weight vector that is orthogonally farthest from the external weight vector within its neighborhood. Multiple dense internal weight vectors are generated through linear combination, and their expression is as follows: ， In the above formula, The final selected dense internal weight vector, The independent variable that makes the function reach its maximum value, This represents the maximum value that the function can achieve. for The set of neighborhood weights, The orthogonal distance between the two weight vectors; S3.3, In order to guide the parameters to search for a better region, obtain the changing trends of each objective function and constraint function when moving along different design variables near the current candidate point, for the current candidate point to be updated. Based on the established Gaussian transfer process surrogate model, the local gradients of each objective function and constraint function at the candidate point are calculated, and the local gradient matrix is ​​constructed. : ， In the above formula, Indicates the first surrogate model for each objective function The target gradient vector obtained by differentiation Represents a surrogate model for constraint functions The gradient vector of the constraint function obtained by differentiation, for 3D real space, To design variable dimensions; S3.4, Since the objective functions and constraint functions have different dimensions, their gradient vectors have significantly different magnitudes. Directly using these vectors would lead to the search process being dominated by gradient vectors with larger magnitudes. Therefore, the gradient vectors are normalized to obtain unit vectors that only represent the gradient direction. ， ， In the above formula, For the first The normalized objective gradient of each objective function. To normalize the constraint gradient, It is a very small positive number. The L2 norm of a vector; S3.5, if the search is performed only along the gradient direction of a single objective, it is easy to get trapped in a local optimum or ignore the optimization effect of other objectives. Therefore, it is necessary to evaluate the improvement potential of moving along different gradient directions in terms of the Pareto front of the overall multi-objective optimization problem; define the current non-dominated front approximation point set. ,in For the first Objective function values ​​at each frontier point For the number of frontier points, For the first The static stiffness at each leading edge point is taken as the negative true value. For the first The true value of the total mass at each frontier point. For the first The true value of the maximum contact stress at each leading edge point; for candidate points The predicted mean of the objective function is output using a Gaussian transfer process surrogate model. With the predicted standard deviation Single-objective expected improvement index: relative to the frontier points in the non-dominated frontier approximation point set. , No. The first goal in The expected improvement value of a single objective under each weight direction for: In the above formula, Candidate points On the q-th objective relative to the 1st objective A cutting-edge point The expected improvement The cumulative function of the standard normal distribution. Let be the standard normal probability density function. Based on this, three types of comprehensive improvement indices are constructed, collectively referred to as multi-objective expected improvement information, which are used to comprehensively evaluate the improvement potential of candidate points to the Pareto front. These indices will subsequently be used for weighted fusion of gradient directions. Euclidean Comprehensive Improvement Index : This metric is used to characterize the degree of improvement in the Euclidean distance from the candidate point to the Pareto front, and prioritizes guiding the search to advance towards the Pareto front along the shortest path. In the above formula, To obtain the expected improvement values ​​of the three objectives using the Euclidean norm, we obtain the candidate points towards the th... Overall improvement distance in each weight direction To select the value with the shortest improvement distance among all weight directions; Max min type comprehensive improvement index : This metric is used to characterize the optimal value of the worst improvement effect among all objectives, ensuring that all objectives are improved in a balanced manner during the search process, and avoiding the situation where a single objective is optimal while other objectives degenerate; In the above formula, In the first Under each weighted direction, the objective with the largest expected improvement value among the three objectives is selected. This maximum value represents the expected improvement value under this direction, that is, the optimal improvement level that can be achieved in this direction. The value represents the expected improvement. Super-volume comprehensive improvement index : This indicator directly quantifies the hypervolume improvement of the Pareto front and guides the search to expand the coverage of the Pareto front. In the above formula, As a preset reference point, and satisfying , To define the supervolume from the reference point to the new frontier after adding candidate points, The hypervolume from the reference point to the original frontier before adding candidate points. This is an improvement in volume; Based on the current set of approximate points of the non-dominated front, a local Pareto front approximate surface in the target space is constructed using polynomial fitting or support vector machine methods, providing geometric information of the target space for the subsequent construction of the Pareto front induced direction. S3.6, The normalized target gradient is weighted and fused based on the three types of comprehensive improvement indicators, as shown in the following expression: Euclidean fusion direction: , Max-min type fusion direction: , Ultra-volumetric fusion direction: , In the above formula, For the first 1 candidate point Euclidean weights This is the index of the optimal frontier point for the Euclidean index. Weights are of type max and min. The direction index that minimizes the max-min type improvement index. For super-volume weights, The direction index that minimizes the improvement index of the hypervolume type, and satisfies ; S3.7, introduces constraints on feasible probability. To ensure that the search direction prioritizes the constrained feasible region, the final comprehensive gradient vector is defined as follows: In the above formula, , , , The first non-negative weight coefficient, the second non-negative weight coefficient, the third non-negative weight coefficient, and the fourth non-negative weight coefficient are respectively, satisfying the following: , This indicates the L2 normalization operation, which ensures the consistency and stability of the gradient direction; S3.8 generates offspring individuals within the design space based on the combined gradient direction, weight-induced search direction, and Pareto front-induced direction. The formula is as follows: In the above formula, For feasible region projection operators, To determine the step size parameter for the overall gradient direction, The step size parameter is used to guide the search direction based on weights. Let be the step size parameter for the Pareto front induction direction. Uniformly distributed random numbers are used to adjust the direction of the integrated gradient. The step size perturbation, Uniformly distributed random numbers are used to adjust weights and guide the search direction. The step size perturbation, Uniformly distributed random numbers are used to adjust the direction of Pareto front induction. The step size perturbation, The formula is to guide the search direction based on weights. ,in External preference weights For the i-th candidate point, The direction of Pareto front induction; S3.9, the Pareto front induced direction is calculated through gradient mapping between the target space and the design space. The specific steps are as follows: using polynomial fitting or support vector machine methods, an approximate surface of the local Pareto front in the target space is constructed. Calculate the optimal front edge point of the surface. Normal vector at point Through the local target gradient matrix Mapping back to the design space yields ; S3.10, based on the comprehensive gradient direction, weight-induced search direction, and Pareto front-induced direction, generates a set of candidate points within the design space; for each external weight... and each dense internal weight generated therefrom Calculate the corresponding candidate points respectively: ， in, For the first 1 candidate point For the reason With the Candidate points generated by dense internal weights For feasible region projection operators, This represents the direction of the overall gradient.

5. The method as described in claim 1, characterized in that, Step S4 specifically includes: S4.1, the set of external weight vectors generated in step S3 With the set of internal weight vectors Merge to form a joint weight vector set Calculate the joint weight set Construct a weight distance matrix by calculating the Euclidean distance between any two weight vectors. The expression for the elements of the weighted distance matrix is ​​as follows: In the above formula, For the first The index of each weight vector. For the first The index of each weight vector. , The first A weight vector, For the first The preference weights of each weight vector in the first objective. For the first The preference weights in the second objective are the preference weights. For the first The preference weights of the weight vectors in the third objective. For the first The preference weights of each weight vector in the first objective. No. The preference weights of the weight vectors in the second objective. For the first The preference weights of the weight vectors in the third objective. For the first The weight vector at the th weight vector in the th... The preference weights of each objective For the first The weight vector at the th weight vector in the th... The preference weights of each objective; S4.2, Agglomerative hierarchical clustering method is used to cluster the joint weight vector set. Clustering screening was performed to obtain Each weighted cluster The number of clusters is preset with weights; S4.3 uses a Gaussian transfer process surrogate model to predict the objective function value and constraint violation degree of each candidate point, which are then used for subsequent screening based on representative weight vectors. The expression is as follows: ， In the above formula, For the first Target static stiffness values ​​for candidate points For the first The total quality target value of the candidate points For the first The maximum target value of contact stress at each candidate point For the first Preset violation degree of frictional resistance at each candidate point, constraint violation degree This indicates that the constraint is satisfied. This indicates a violation of the constraints; S4.4, for each weight cluster The mean vector of all weight vectors within a cluster is calculated and used as the cluster center. The weight vector that has the closest Euclidean distance to the cluster center is selected as the representative weight vector of the cluster. Based on representative weight vector The ICDP fitness function is used to filter all candidate points corresponding to the cluster, and the parameter with the smallest fitness value is selected as the optimal candidate point of the cluster. The ICDP fitness function is defined as follows: ， In the above formula, For the first The representative weight vector at the th ... The weight of each goal For the first The objective function at the candidate point The actual function value below, To preset the ideal point, This is the ideal value under the first objective. This is the ideal value under the second objective. This is the ideal value under the third objective. This is a dynamic penalty coefficient. The degree of violation of the frictional resistance constraint at the candidate point; S4.5, Integration The optimal candidate points of each weighted cluster constitute the optimal candidate point set. Based on the requirements of maximizing static stiffness, minimizing total mass, minimizing maximum contact stress, and constraining frictional resistance, from The candidate point with the best overall performance is selected as the final optimal candidate point.

6. The method as described in claim 5, characterized in that, The specific calculation steps of the agglomerative hierarchical clustering method are as follows: S4.2.1, joint weight set Each weight vector in the algorithm is considered as an independent cluster, resulting in an initial cluster set. ,in, For the 1st cluster, the 2nd cluster, ..., the Nth cluster, For the first Each cluster contains only one weight vector. Based on the average link criterion, the weight vectors of any two clusters in the current cluster set are calculated. Inter-cluster distance The expression for calculating inter-cluster distance is as follows: ， In the above formula, Clusters The number of weight vectors included. For the first A weight vector, For the first A weight vector, These are elements of the weighted distance matrix; S4.2.2, Find the two clusters with the smallest inter-cluster distance. Merge them into a new cluster Then delete the original cluster from the initial cluster set. Join a new cluster The number of clusters has been updated to When the number of clusters in the initial cluster set is equal to the preset weight cluster number Stop the clustering operation when the time is right, and obtain the final result. Each weighted cluster.

7. The method as described in claim 1, characterized in that, Step S5 specifically includes: S5.1, the optimal candidate points obtained in step S4 are evaluated by finite element simulation to obtain the true objective function values ​​corresponding to each optimal candidate point, including the static stiffness, total mass and maximum contact stress of the linear guide rail, and the friction resistance constraint function value is calculated. S5.2, add the optimal candidate point and its corresponding true objective function value and constraint function value to the sample database, and retrain the transfer Gaussian process surrogate model in combination with the historical sample database; S5.3 Determine whether the termination condition is met. The termination condition includes reaching the maximum number of iterations or the objective function convergence condition. If the termination condition is met, output the optimal solution; otherwise, return to step S3 to continue iterative optimization.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-7.

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