Machining center bed optimization method and device based on integrated agent model assisted evolutionary algorithm

Abstract

A method and apparatus for optimizing machining center beds based on an ensemble surrogate model-assisted evolutionary algorithm includes the following steps: 3D modeling of the original pentahedral machining center bed, followed by static and modal analysis, with the bed's mass, maximum static deformation, and first-order natural frequency as optimization objectives; selection of design variables, with upper and lower limits for each design variable and the objective function as constraints; obtaining corresponding experimental sample points between the design variables and optimization objectives through finite element analysis, and constructing a dynamic ensemble learning model using these experimental sample points; applying the previously established multi-objective optimization mathematical model for the pentahedral machining center bed to obtain a high-quality Pareto solution set, selecting superior solutions, and verifying the optimization results through simulation based on the optimized structural parameters. This invention effectively limits the number of evaluations of the expensive real fitness function, balances algorithm convergence and population diversity, and prevents redundant training data.

Description

Technical Field

[0001] This invention belongs to the field of mechanical design and relates to a design method for the structure of key components of a five-sided machining center. Specifically, it relates to a method and device for optimizing the bed of a machining center based on an integrated surrogate model-assisted evolutionary algorithm. Background Technology

[0002] Machining centers, often referred to as "mother machines of industry," play a crucial role in driving the development of the manufacturing industry. Therefore, improving the structural design and manufacturing capabilities of machining centers is a core aspect of developing advanced manufacturing technologies.

[0003] With the continuous advancement of computer technology, computer-aided design (CAD) and optimization techniques have been widely applied in the engineering field. However, simulation-based design methods require significant time, manpower, and resources for each simulation, greatly impacting R&D efficiency and wasting resources. To address this issue, the practice of introducing surrogate models into the structural optimization design of machining centers has been widely adopted in the field of structural optimization of key components in machining centers.

[0004] Although introducing surrogate models into the structural optimization design of machining centers can effectively improve design efficiency, reduce experimental costs and shorten the design cycle, this method also faces some challenges. For example, when the number of design variables increases or the number of samples is small, the accuracy of the surrogate model will decrease, and the quality of the solution set may be poor when solving multi-objective optimization models.

[0005] In addition, under the premise of ensuring the dynamic and static characteristics of the machining center bed, "weight reduction" design of the machining center is also a challenge currently faced in the field of machining center structural design. Summary of the Invention

[0006] The present invention aims to overcome the above-mentioned shortcomings of the prior art and provides a method and apparatus for optimizing the bed of a machining center based on an integrated surrogate model-assisted evolutionary algorithm, so as to reduce the mass of the five-sided machining center as much as possible while ensuring the machining accuracy and rigidity of the five-sided machining center.

[0007] This invention proposes a novel integrated surrogate model-assisted multi-objective optimization algorithm and applies it to the multi-objective design of machining center beds. This algorithm aims to achieve lightweighting of machining centers more efficiently and accurately, while simultaneously improving the overall stability and dynamic stiffness of the machining center, thereby performing multi-objective optimization of the machining center bed.

[0008] The objective of this invention is achieved through the following technical solution:

[0009] The first aspect of this invention relates to a multi-objective optimization design method for machining center beds based on a surrogate model, comprising the following steps:

[0010] (1) A three-dimensional model of the original five-sided machining center bed was created. The features of the parts were simplified, and small features such as chamfers, fillets, and threaded holes that had little impact on the analysis results were removed to obtain a simplified parametric model of the bed. A finite element model of the bed was established, the cutting force generated by the dual spindles of the machining center under extreme working conditions was calculated, and the load boundary conditions borne by the bed were analyzed. Load constraints were applied to the finite element model, and fixed constraints were applied to the anchor bolt holes of the machining center. Static and dynamic characteristics were simulated by finite element model to analyze its maximum static deformation, first natural frequency, and mass.

[0011] (2) Select the radius of the weight reduction hole, the spacing and thickness of the stiffener plate, and the thickness of the inner and outer walls as design variables. With the upper and lower limits of the design variables and the objective function as constraints, determine the bed mass, maximum static deformation, and first natural frequency as objective functions, and establish a multi-objective optimization mathematical model for the bed.

[0012] (3) Using Latin hypercube design as the experimental design method, test sample points are constructed, and they are substituted into the finite element model to obtain the corresponding objective function values. An initial sample set is constructed, and a high-precision heterogeneous integrated surrogate model is established. The previously established multi-objective optimization mathematical model of the bed is applied, and the optimization solution is obtained through the dynamic integrated surrogate-assisted multi-objective evolutionary algorithm (AERVEA), and the optimized structural parameters and the corresponding Pareto solution set are output.

[0013] (4) Based on the finite element analysis results of the initial bed structure, the optimal solution is selected from the output Pareto solution set as the final experimental result and compared with the performance of the initial bed.

[0014] (5) Modify the design variable parameter values ​​of the bed according to the optimization results, and perform simulation verification to analyze the error.

[0015] Preferably, the multi-objective optimization mathematical model for the bed described in step (2) includes:

[0016]

[0017] Where: δ(X) is the maximum deformation of the bed, m(X) is the mass of the bed, and f(X) is the first natural frequency. init f init δ init For the initial bed mass, deformation, and frequency; x i Let x be the i-th design variable of the bed; n is the number of design variables, x min As the lower bound of the design variable, x max To set an upper limit for the design variables.

[0018] Preferably, the algorithm flow steps in step (3) are as follows:

[0019] (31) Initialization: An initial population P of size N is generated using Latin Hypercube Sampling (LHS) as the initial sample set, and the true fitness value is evaluated using the finite element method. The maximum number of true evaluations FE is set. max The number of individuals that need to be re-evaluated and used to update the ensemble model (u) and the maximum number of generations (ω) before updating the surrogate model. max .

[0020] (32) Constructing a heterogeneous ensemble learner: The evaluated individuals are used to build a heterogeneous ensemble learner model with dynamic weight allocation. In this paper, an RBF (Radial Basis Function Neural Network) is used as the global model and a Kriging model is used as the local model. Dynamic weight allocation is performed on the two models to build an ensemble learner.

[0021] After dynamic weighting, the output of the global proxy model can be described in the following form:

[0022]

[0023] Among them, y rbf This is the predicted value from the RBF model, y krg is the predicted value of the Kriging model, FE represents the number of times the true fitness evaluation is performed in the current optimization process, ω represents half of the maximum number of true evaluations, and y is the weighted prediction result of the heterogeneous ensemble surrogate model.

[0024] (33) Vector-based model management strategy: within a predefined number of iterations w max Within this algorithm, a progeny population Off is generated using genetic operators, and the offspring are evaluated using a pre-trained ensemble model (Ensemble). RVEA is used as the optimizer to select the next generation parent from P and the evaluated Off. This algorithm introduces an additional fixed reference vector V0. Based on the fixed reference vector and a threshold δ, it evaluates whether the model needs increased diversity or convergence. The variance provided by the Kriging model is used as an indicator of individual uncertainty, and APD is used as an indicator of convergence. The formula for calculating APD is:

[0025]

[0026] in θ is the distance from the target vector corresponding to the j-th individual to the origin. j It is the angle between the j-th individual and its assigned reference vector. In APD, P(θ) j ) is the penalty function, defined as follows:

[0027]

[0028] Where k is the number of targets, ω max It represents the maximum number of algebras before updating the proxy model, where α is a user-defined parameter that controls P(θ). i The rate of change of γ v It is the minimum angle between the reference vector and other reference vectors in the current generation.

[0029] (34) Archive set update: Select a fixed number of individuals (N) from the archive set A1 as samples for the next model training.

[0030] A second aspect of the present invention relates to a machining center bed optimization device based on an integrated surrogate model-assisted evolutionary algorithm, comprising a memory and one or more processors, wherein the memory stores executable code, and the one or more processors execute the executable code to implement the machining center bed optimization method based on an integrated surrogate model-assisted evolutionary algorithm of the present invention.

[0031] A third aspect of the invention relates to a computer-readable storage medium having a program stored thereon that, when executed by a processor, implements the machining center bed optimization method based on an integrated surrogate model-assisted evolutionary algorithm of the present invention.

[0032] This invention designs the bed from three aspects: the radius of the weight reduction hole, the thickness of the stiffener plate, and the thickness of the inner and outer walls. The steps include: 3D modeling of the original bed and analyzing its static and dynamic characteristics, using the bed's mass, maximum static deformation, and first-order natural frequency as optimization objectives; selecting the radius of the weight reduction hole, the thickness of the stiffener plate, and the thickness of the inner and outer walls as design variables, and determining the upper and lower limits of each design variable; obtaining corresponding experimental sample points between the design variables and optimization objectives by changing the structural optimization design variables and performing static, dynamic, and thermodynamic finite element analysis, and constructing a surrogate model using these experimental sample points; applying the previously established multi-objective optimization mathematical model for key components of a five-sided machining center, using the Dynamic Integrated Surrogate-Assisted Multi-Objective Evolutionary Algorithm (AERVEA) to optimize and solve the problem, outputting the optimized structural parameters and target response values; and finally, verifying the results through simulation. The optimization design method proposed in this invention uses ensemble learning and adaptive techniques to construct a high-precision heterogeneous ensemble surrogate model with a smaller number of samples, effectively limiting the number of evaluations of the expensive real fitness function. It uses an environment selection operator to sort and screen the population to generate the optimal solution. Experimental results show that the algorithm achieves good optimization results in the multi-objective optimization problem of bed.

[0033] This invention utilizes ensemble learning and dynamic weight allocation techniques to construct a high-precision heterogeneous ensemble surrogate model with a smaller sample size, effectively limiting the number of evaluations required by the expensive true fitness function. Vector-based model management techniques are employed to update the ensemble model, balancing algorithm convergence with population diversity. Finally, the archive set is managed to prevent training data redundancy. Experimental results demonstrate that this algorithm achieves excellent optimization performance on the multi-objective optimization problem of a five-sided machining center bed.

[0034] The working principle of this invention is as follows: First, a 3D model of the bed is performed and design variables are selected. Then, Latin hypercube sampling is performed on the design variables of the bed, with the bed mass, maximum static deformation, and first-order natural frequency as objective functions to solve the contradiction between lightweighting and improving dynamic and static performance in the optimization design of the bed. Finite element analysis is performed on the samples to obtain initial sample points. In the Dynamic Integrated Agent-Assisted Multi-Objective Evolutionary Algorithm (AERVEA), the initial sample points are used as the initial population. An RBF (Radial Basis Function Neural Network) is used as the global model, and a Kriging model is used as the local model. Dynamic weights are assigned to the two models to establish an ensemble learner. This invention manages the model based on vectors, within a predefined number of iterations ω. max Within this algorithm, a progeny population Off is generated using genetic operators, and the offspring are evaluated using a pre-trained ensemble model. RVEA is used as the optimizer to select the next generation parent from P and the evaluated Off. This algorithm assesses whether the model needs increased diversity or convergence based on the degree of change in the number of fixed reference vectors, using variance provided by the Kriging model as an indicator of individual uncertainty and APD as an indicator of convergence to guide the selection of new samples. Finally, the archive is updated, selecting a fixed number of individuals N as samples for the next model training, reducing the ensemble model training time and improving the algorithm's efficiency. Finally, the obtained Pareto solution set is filtered to obtain the optimal solution, which is then verified through finite element simulation.

[0035] The advantages of this invention are:

[0036] (1) The problem to be solved by this invention belongs to the category of expensive multi-objective optimization problems, with the optimization objectives being to minimize the maximum mass, the maximum deformation, and the first-order modal frequency. However, there is a contradiction between minimizing the maximum mass, minimizing the maximum deformation, and maximizing the first-order modal frequency, because reducing the weight of a machining center often reduces its static and dynamic performance, making it difficult to achieve both in optimization design. By performing multi-objective optimization on the machining center bed, the optimal balance between performance and cost can be achieved. This study will use an surrogate-assisted multi-objective evolutionary algorithm based on ensemble learning to balance the trade-offs among these three indicators, obtain a high-quality Pareto solution set, and select the optimal solution from it.

[0037] (2) This invention proposes a dynamic ensemble-assisted multi-objective evolutionary algorithm (AERVEA), which combines the global approximation performance of the RBF model and the local approximation performance of the Kriging model. It dynamically assigns weights to the two models, establishing a high-precision heterogeneous ensemble learner, Ensemble, thus reducing the actual evaluation cost. Furthermore, the algorithm employs vector-based model management, using new individuals as new samples for training, continuously improving the model's prediction accuracy. During optimization, it balances algorithm convergence with population diversity to increase efficiency and fully explore the target space to obtain the Pareto Front (PF). Finally, it manages the archive set to prevent redundancy of training data. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 The flowchart illustrates a machining center bed optimization method based on an integrated surrogate model-assisted evolutionary algorithm provided by the present invention.

[0040] Figure 2 The flowchart of the Dynamic Integrated Agent-Assisted Multi-Objective Evolutionary Algorithm (AERVEA) provided by the present invention is shown;

[0041] Figure 3 A three-dimensional model of a five-sided machining center according to an embodiment of the present invention is shown;

[0042] Figure 4 A parametric three-dimensional model of the bed of a five-sided machining center according to an embodiment of the present invention is shown;

[0043] Figure 5The optimized fore-bed static deformation contour plot is shown;

[0044] Figure 6 The first-order modal contour plot of the optimized forebed is shown;

[0045] Figure 7 A schematic diagram of optimized parameters for the bed of a five-sided machining center according to an embodiment of the present invention is shown;

[0046] Figure 8 The optimized static deformation cloud diagram of the bed is shown.

[0047] Figure 9 The first-order modal contour plot of the optimized bed is shown;

[0048] In the figure, x1 - side wall thickness, x2 - front and rear wall thickness, x3 - upper side wall thickness, x4 - lower side wall thickness, x5 - transverse stiffener thickness, x6 - transverse stiffener spacing, x7 - longitudinal stiffener thickness, x8 - longitudinal stiffener spacing, x9 - side wall weight reduction hole diameter, x10 - front and rear wall weight reduction hole diameter. Detailed Implementation

[0049] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0050] Example 1

[0051] like Figure 1 The flowchart shown is a process for the method of this invention. First, a three-dimensional model of the original bed is created, a finite element model of the bed is established, and static and dynamic finite element simulations are performed to analyze its maximum static deformation, first natural frequency, and mass. Then, the radius of the weight reduction holes, the thickness and spacing of the stiffeners, and the wall thickness are selected as design variables. The upper and lower limits of the design variables and the objective function are used as constraints to determine the bed mass, maximum static deformation, and first natural frequency as objective functions, and a multi-objective optimization mathematical model of the bed is established.

[0052] Experimental sample points were constructed through experimental design, and a high-precision heterogeneous integrated surrogate model was established. The previously established multi-objective optimization mathematical model of the bed was applied, and the optimization solution was obtained through the dynamic integrated surrogate-assisted multi-objective evolutionary algorithm (AERVEA), and the optimized structural parameters and the corresponding Pareto solution set were output.

[0053] The optimal solution is selected from the output Pareto solution set as the final experimental result;

[0054] The results were verified through simulation.

[0055] The following description is based on specific embodiments.

[0056] like Figure 3The image shown is a 3D model of a certain type of five-sided machining center to be optimized in this example. This type of vertical and horizontal composite five-sided machining center mainly consists of a column, tool magazine, ram, bed, worktable, vertical spindle, and horizontal spindle. The main structure of the machine tool is a cross-saddle type, with a compact structure. The machine tool guideways use imported rolling linear guideways. The lead screw adopts a two-end fixed tension structure, and all use high-rigidity ball screw pairs, resulting in high transmission accuracy. The tool changer adopts a disc-type robotic tool magazine with short tool change time and reliable performance.

[0057] like Figure 4 The image shown is a parametric 3D model of the bed of the five-sided machining center in this example. The features of the parts are simplified by removing minor features such as chamfers, fillets, and threaded holes that have little impact on the analysis results. Simultaneously, correlation analysis is performed on the dimensions of the parts to achieve parametric modeling and improve simulation efficiency.

[0058] Then, the static characteristics of the components are studied. The components are imported into Ansys, the magnitude of the cutting force generated by cutting is calculated, and the forces and constraints, including the cutting force, are applied to the finite element model of the components for static and modal analysis. The maximum static deformation contour plot and the first natural frequency of the bed are obtained, such as... Figure 5-6 As shown.

[0059] Next, the design variables and design space for the machine bed are selected. To achieve lightweighting, the selection of structural parameters mainly focuses on wall thickness, stiffener thickness and spacing, and the radius of weight-reducing holes, while avoiding non-design domains to prevent impacting the overall structure of the five-sided machining center. When designing constraints, attention must be paid to interference between dimensions to avoid failure in later model reconstruction.

[0060] like Figure 7 As shown, the radius of the weight reduction hole, the thickness and spacing of the stiffeners, and the wall thickness are used as design variables, specifically: x1 - side wall thickness, x2 - front and rear wall thickness, x3 - upper side wall thickness, x4 - lower side wall thickness, x5 - transverse stiffener thickness, x6 - transverse stiffener spacing, x7 - longitudinal stiffener thickness, x8 - longitudinal stiffener spacing, x9 - side wall weight reduction hole diameter, x10 - front and rear wall weight reduction hole diameter, and upper and lower limit constraints are set. The design variable table is shown in Table 1 below.

[0061] Table 1 Bed Design Parameters

[0062]

[0063] In selecting the objective function, the lightweight design criterion, the static performance optimization criterion, and the dynamic performance optimization criterion were chosen as the selection criteria.

[0064] To reduce material consumption and manufacturing costs during the production of parts for five-sided machining centers, the following lightweight design principles are established:

[0065] F(x)=minM(x) (5)

[0066] During operation, key components of a five-sided machining center undergo minute static deformation under cutting forces. This static deformation reduces machining accuracy, causing dimensional deviations to exceed specified limits, thus affecting product quality and performance. Furthermore, static deformation can lead to internal stress concentration, potentially causing cracks and fractures, and shortening component lifespan. Therefore, the following optimal static performance criteria are established:

[0067] F(x)=minσ(x) (6)

[0068] The dynamic performance of a pentahedral machining center is mainly reflected in its vibration resistance and stability during operation. As a key component of the pentahedral machining center, the quality of its dynamic performance directly affects the quality of the machined workpiece. Theoretically, components possess countless modes, but the lower-order modes, especially the first-order natural frequency, are the frequency range most likely to be reached by the pentahedral machining center during actual operation. When these frequencies are close to the actual operating frequency of the pentahedral machining center, resonance can easily be induced, affecting machining quality. Therefore, the first-order natural frequency should be increased as much as possible to avoid the operating frequency range of the pentahedral machining center. Therefore, the following optimal dynamic performance criteria are established:

[0069] F(x)=min-f(x) (7)

[0070] Then set the constraints:

[0071] x min ≤x≤x max , i = 1, 2, ..., n;

[0072]

[0073] f(x)>f init ;

[0074] δ(x)<δ init ;

[0075] The mathematical model can be represented as:

[0076]

[0077] Where: δ(X) is the maximum deformation of the bed, m(X) is the mass of the bed, and f(X) is the first natural frequency. init f init δ initFor the initial bed mass, deformation, and frequency; x i Let x be the i-th design variable of the bed; n is the number of design variables. min and x max See the table above.

[0078] Next, multi-objective optimization of the bed frame will be performed.

[0079] The selected DOE method is Latin hypercube design, and the sampling type is CCD sampling. Therefore, after determining the range of values ​​for each parameter and the number of test points, the system will randomly generate 150 test point combinations within this range. The local combination data is shown in the table below.

[0080] Table 2

[0081]

[0082] The evaluated individuals are used to build a heterogeneous integrated agent model with dynamic weight allocation.

[0083] like Figure 2 As shown, this paper employs an RBF (Radial Basis Function Neural Network) as the global model and a Kriging model as the local model, respectively. Dynamic weights are assigned to both models to establish a heterogeneous ensemble learner. The output of the global proxy model after dynamic weighting can be described as follows:

[0084]

[0085] Among them, y rbf This is the predicted value from the RBF model, y krg is the predicted value of the Kriging model, FE represents the number of times the true fitness evaluation is performed in the current optimization process, ω represents half of the maximum number of true evaluations, and y is the weighted prediction result of the heterogeneous ensemble model.

[0086] In comparison, RBF has no requirements on response characteristics, can fit any type of function well, and has more stable performance in high-dimensional multi-objective problems. Therefore, it is used as a global model to fit and predict the target values ​​of the population. Kriging, on the other hand, has good continuity and differentiability, and can achieve better accuracy and prediction accuracy than RBF when the number of targets is small. Therefore, as a local model, it can achieve better performance by modeling and predicting the target values ​​separately.

[0087] In the first half of the optimization process, the focus is primarily on enhancing population diversity. Therefore, the weight of the diversity-based local proxy model is relatively large and decreases slowly as diversity increases. At the same time, a small amount of weight is added to the convergent local model to provide some convergence to the global model. The second half of the optimization process is exactly the opposite. A variant of the sigmoid function is used to quickly switch the dominant relationship between the weights of the two models halfway through the optimization process.

[0088] In terms of model management, this algorithm adopts a vector-based model management strategy:

[0089] First, at the predefined number of iterations w max Within this process, a progeny population Off is generated through genetic operators, and the progeny is evaluated using a trained ensemble model Ensemble. RVEA is used as an optimizer to select the next generation parent from P and the evaluated Off.

[0090] This algorithm introduces a set of fixed reference vectors V0 and a set of adaptive vectors V of the same number. a The fixed reference vector V0 is uniformly distributed in the target space, while the adaptive vector V a Then, the solution is scaled according to the range of Pareto optimal solutions to obtain uniformly distributed solutions.

[0091] The reference vector V used in this algorithm is generated as follows: first, a set of uniformly distributed reference points are generated on the unit hyperplane using the canonical simplex design method; then, the corresponding reference vector is obtained by projecting the reference points from the hyperplane onto the hypersphere.

[0092] This algorithm is based on an empty fixed reference vector. The changes in quantity and the threshold δ are used to assess whether the model needs more diversity or convergence. Variance provided by the Kriging model is used as an indicator of individual uncertainty, and APD is used as an indicator of convergence. A fixed reference vector is used in the empty space. If the change in the number of vectors exceeds the threshold δ, this means that the empty fixed reference vector... When the number of individuals exceeds a given threshold, diversity should be prioritized. In this case, individuals requiring re-evaluation should be selected based on the uncertainty information provided by the Kriging model. Conversely, if an empty fixed reference vector exists... If the change in population size is less than the threshold δ, meaning population diversity is not a primary consideration, then the convergence criterion should be prioritized, and the individual with the smallest APD should be selected based on the adaptive reference vector. The formula for calculating APD is:

[0093]

[0094] in θ is the distance from the target vector corresponding to the j-th individual to the origin.j It is the angle between the j-th individual and its assigned reference vector. In APD, P(θ) j ) is the penalty function, defined as follows:

[0095]

[0096] Where k is the number of targets, ω max It represents the maximum number of algebras before updating the proxy model, where α is a user-defined parameter that controls P(θ). i The rate of change of γ v It is the minimum angle between the reference vector and other reference vectors in the current generation.

[0097] Finally, there's the management of the archive set. Managing the training data in the archive set is to limit the computation time of retraining the Kriging model and prevent the training data in the archive set from becoming too large and affecting the efficiency of the algorithm. In this algorithm, the amount of training data is fixed. Therefore, if the amount of available training data exceeds the size of the archive set, some data needs to be discarded.

[0098] First, the most recently evaluated individuals are added to the archive, denoted as u, and duplicate data points are removed. If the amount of training data still exceeds the size of the archive, some training samples other than the most recently evaluated individuals are removed. To do this, the most recently evaluated individuals are assigned to an adaptive reference vector V. a And determine the inactive reference vectors within it. That is, an empty vector. Then the remaining individuals are assigned to the inactive reference vector. The active adaptive reference vectors are clustered into Nu clusters, and a data point is randomly selected from each cluster, with the remaining data discarded. This preserves a fixed number of diverse training datasets in the archive set, thereby maximizing the quality of the heterogeneous ensemble surrogate model while limiting computation time.

[0099] The initial population size for this experiment was set to 100, and the maximum number of true evaluations was set to 200. The optimized parameters are shown in Table 3 below.

[0100] Table 3 Comparison of Design Variables Before and After Optimization

[0101]

[0102] By assigning material properties to the optimized bed, the optimized mass information is obtained, and static and modal analyses are performed to obtain the values ​​of the optimized maximum deformation, maximum stress, and the first six natural frequencies, such as... Figure 8-9 As shown in the table, the feasibility of the optimization scheme for the bed developed in this paper is examined by comparing it with the original scheme.

[0103] The performance metrics before and after optimization are compared, as shown in Table 3.

[0104] Table 4 Comparison of Machining Center Before and After Optimization

[0105]

[0106] The results of optimizing the bed dimensions are compared with those before optimization and the original bed, as shown in the table. This multi-objective optimization not only ensured the constraints, but also reduced the maximum stress by 14.37%, the maximum bed deformation by 4.73%, the first natural frequency by 2.59%, and the mass by 11.44% after optimization compared to before. It is evident that this optimization method can simultaneously optimize multiple objectives of the bed, and this optimization scheme can also be referenced for optimizing the dimensions of similar bed types.

[0107] The results show that optimized design can effectively reduce the weight of the five-sided machining center structure and optimize its dynamic and static performance, thereby achieving the goals of cost saving, energy conservation and environmental protection, and improved machining accuracy.

[0108] The proposed optimization design method utilizes a heterogeneous integrated surrogate model and dynamic weight allocation technology to construct a high-precision heterogeneous integrated surrogate model with a smaller sample size, effectively limiting the number of evaluations of the expensive true fitness function. It employs vector-based model management technology to update the heterogeneous integrated surrogate model and sorts and filters the population to generate the optimal solution. Experimental results demonstrate that the algorithm achieves good optimization results in the multi-objective optimization problem of a pentahedral machining center bed.

[0109] Example 2

[0110] This embodiment relates to a machining center bed optimization device based on an integrated surrogate model-assisted evolutionary algorithm, including a memory and one or more processors. The memory stores executable code, and when the one or more processors execute the executable code, they are used to implement the machining center bed optimization method based on an integrated surrogate model-assisted evolutionary algorithm of Embodiment 1.

[0111] Example 3

[0112] This embodiment relates to a computer-readable storage medium storing a program that, when executed by a processor, implements the machining center bed optimization method based on an integrated surrogate model-assisted evolutionary algorithm as described in Embodiment 1.

[0113] The embodiments described in this specification are merely examples of implementations of the inventive concept. The scope of protection of this invention should not be considered as limited to the specific forms stated in the embodiments. The scope of protection of this invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A method for optimizing the bed of a machining center based on an ensemble surrogate model-assisted evolutionary algorithm, characterized in that, Includes the following steps: (1) A three-dimensional model of the original five-sided machining center bed was created, and the features of the parts were simplified. Small features such as chamfers, fillets, and threaded holes that had little impact on the analysis results were removed to obtain a simplified parametric model of the bed. A finite element model of the bed was established, and the cutting force generated by the dual spindles of the machining center under extreme working conditions was calculated. The load boundary conditions borne by the bed were analyzed, load constraints were applied to the finite element model, and fixed constraints were applied to the anchor bolt holes of the machining center. Static and dynamic characteristics were simulated by finite element model to analyze its maximum static deformation, first natural frequency, and mass. (2) Select the radius of the weight reduction hole, the spacing and thickness of the stiffeners, and the thickness of the inner and outer walls as design variables. Determine the bed mass, maximum static deformation, and first natural frequency as objective functions, and use the upper and lower limits of the design variables and the objective function as constraints to establish a multi-objective optimization mathematical model for the bed. (3) Using Latin hypercube design as the experimental design method, experimental sample points are constructed, and these are substituted into the finite element model to obtain the corresponding objective function values. An initial sample set is constructed, and a high-precision heterogeneous integrated surrogate model is established. The previously established multi-objective optimization mathematical model of the bed is applied, and the optimization solution is obtained through the dynamic integrated surrogate-assisted multi-objective evolutionary algorithm AERVEA, and the optimized structural parameters and the corresponding Pareto solution set are output. Within a predefined number of iterations... Within this process, a progeny population Off is generated using genetic operators, and a pre-trained ensemble surrogate model is used to evaluate the progeny. AERVEA is used as the optimizer to select the next generation parent from the initial population P and the evaluated Off. An additional set of fixed reference vectors is introduced. Based on a fixed reference vector and a threshold To assess whether the model needs more diversity or convergence, we use the variance provided by the Kriging model as an indicator of individual uncertainty and APD as an indicator of convergence; the formula for calculating APD is: （3） in It is the distance from the origin to the target vector corresponding to the j-th individual. It is the angle between the j-th individual and its assigned reference vector; in APD, It is a penalty function, defined as follows: （4） in It is the number of targets. It is the maximum number of generations before updating the proxy model. These are user-defined parameters that control... rate of change, It is the minimum angle value between the reference vector and other reference vectors in the current generation; This represents half of the maximum number of actual assessments set during the initial assessment. (4) Based on the finite element analysis results of the initial bed structure, the optimal solution is selected from the output Pareto solution set as the final experimental result and compared with the performance of the initial bed. (5) Modify the design variable parameter values ​​of the bed according to the optimization results, and perform simulation verification to analyze the error.

2. The machining center bed optimization method based on ensemble surrogate model-assisted evolutionary algorithm as described in claim 1, characterized in that, The multi-objective optimization mathematical model for the bed mentioned in step (2) includes: （1） in: For the maximum deformation of the bed, Bed quality This is the first-order natural frequency; , , Initial bed mass, frequency, and deformation; Let be the i-th design variable of the bed; n is the number of design variables. To design the lower bound of the variable, To set an upper limit for the design variables.

3. The machining center bed optimization method based on ensemble surrogate model-assisted evolutionary algorithm as described in claim 1, characterized in that, The algorithm flow for step (3) is as follows: (31) Initialization: An initial population P of size N is generated using Latin hypercube sampling (LHS) as the initial sample set, and the true fitness value is evaluated using the finite element method. The maximum number of true evaluations is set. Reassess and update the number of individuals in the ensemble model. Maximum number of generations before updating the proxy model ; (32) Constructing a heterogeneous ensemble agent learner: The evaluated individuals are used to build a heterogeneous ensemble agent model with dynamic weight allocation; an RBF is used as the global model and a Kriging model is used as the local model. Dynamic weight allocation is performed on the two models to build an ensemble learner. After dynamic weighting, the output of the global proxy model is described in the following form: （2） in, These are the predicted values ​​from the RBF model. These are the predictions from the Kriging model, where FE represents the number of times the true fitness evaluation has been performed in the current optimization process. This represents half of the maximum number of actual assessments. This is the prediction result of the weighted heterogeneous integrated proxy model; (33) Archive set update: In the archive set Select a fixed number of individuals, N, as samples for the next model training iteration.

4. A machining center bed optimization device based on an integrated surrogate model-assisted evolutionary algorithm, characterized in that, The system includes a memory and one or more processors, wherein the memory stores executable code, and the one or more processors execute the executable code to implement the machining center bed optimization method based on the integrated surrogate model-assisted evolutionary algorithm as described in any one of claims 1-3.

5. A computer-readable storage medium, characterized in that, It stores a program that, when executed by a processor, implements the machining center bed optimization method based on the integrated surrogate model-assisted evolutionary algorithm as described in any one of claims 1-3.

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