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

Abstract

The invention discloses a machining center lathe bed optimization method and device based on an integrated proxy model assisted evolutionary algorithm, and the method comprises the following steps: carrying out the three-dimensional modeling of an original pentahedral lathe bed, carrying out the static analysis and modal analysis of the original pentahedral lathe bed, and taking the quality of the lathe bed, the maximum static deformation and the first-order inherent frequency as optimization targets; selecting design variables, upper and lower limits of each design variable and a target function as constraints; obtaining corresponding test sample points between the design variables and the optimization targets through finite element analysis, and constructing a dynamic ensemble learning model by using the test sample points; and performing optimization solution to obtain a high-quality Pareto solution set by applying the previously established multi-objective optimization mathematical model of the pentahedron machining center lathe bed, selecting a high-quality solution, and performing simulation verification on an optimization result according to optimized structural parameters. According to the method, the number of expensive real fitness function evaluation times is effectively limited, the convergence of the algorithm and the diversity of the population are considered, and training data redundancy is prevented.

Description

Technical Field

[0001] The present invention belongs to the field of mechanical design, and relates to a design method for the key component structure of a pentahedron machining center, and specifically to a machining center bed optimization method and device based on an integrated agent model assisted evolutionary algorithm. Background Art

[0002] Machining centers, known as the "mother machine of industry", play a vital role in promoting the development of manufacturing. Therefore, improving the structural design and manufacturing level of machining centers is a core link in the development of advanced manufacturing technology.

[0003] With the continuous advancement of computer technology, computer-aided design (CAD) and optimization technology have been widely used in the engineering field. However, the design method based on simulation model requires a lot of time, manpower and material resources for each simulation, which greatly affects the R&D efficiency and causes waste of resources. In order to cope with this problem, the practice of introducing proxy model into the structural optimization design of machining center has been widely used in the field of structural optimization of key parts of machining center.

[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 when solving multi-objective optimization models, the quality of the solution set may be poor.

[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 difficult problem faced by the current 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 provide a method and device for optimizing the bed of a machining center based on an integrated agent model assisted evolutionary algorithm, so as to reduce the mass of the pentahedron machining center as much as possible while ensuring the machining accuracy and rigidity of the pentahedron machining center.

[0007] This paper proposes a new integrated agent model-assisted multi-objective optimization algorithm and applies it to the multi-objective design of the machining center bed. The algorithm aims to achieve lightweighting of the machining center more efficiently and accurately, while 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 the present invention is achieved through the following technical solutions:

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

[0010] (1) Conduct 3D modeling of the original pentahedral machining center bed, simplify the features of the parts, remove small features such as chamfers, fillets, threaded holes, etc. that have little effect on the analysis results, and obtain a simplified parametric model of the bed. Establish a finite element model of the bed, calculate the cutting force generated by the dual spindles of the machining center under extreme working conditions, and analyze the load boundary conditions borne by the bed. Apply load constraints to the finite element model, apply fixed constraints to the anchor bolt holes of the machining center, perform finite element simulation of its static and dynamic characteristics, and analyze its maximum static deformation, first-order natural frequency, and mass;

[0011] (2) The radius of the bed weight-reducing hole, the spacing and thickness of the ribs, and the inner and outer wall thicknesses are selected as design variables. The upper and lower limits of the design variables and the objective function are used as constraints. The bed mass, maximum static deformation, and first-order natural frequency are determined as the objective function, and a multi-objective optimization mathematical model for the bed is established.

[0012] (3) Use Latin hypercube design as the experimental design method to construct test sample points, substitute them into the finite element model to solve the corresponding objective function value, construct the initial sample set, and establish a high-precision heterogeneous integrated agent model; apply the previously established multi-objective optimization mathematical model of the bed, and use the dynamic integrated agent-assisted multi-objective evolutionary algorithm (AERVEA) to optimize and solve, and output the optimized structural parameters and the corresponding Pareto solution set;

[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 variable parameter values ​​of the bed design according to the optimization results, perform simulation verification, and analyze the errors.

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

[0016]

[0017] Among them: δ(X) is the maximum deformation of the bed, m(X) is the mass of the bed, and f(X) is the first-order natural frequency. init , f init , δ init is the initial bed mass, deformation and frequency; x i is the i-th design variable of the bed; n is the number of design variables, x min is the lower limit of the design variable, x max is the upper limit of the design variable.

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

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

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

[0021] The output of the global proxy model after dynamic weighting can be described as follows:

[0022]

[0023] Among them, y rbf is the predicted value of the RBF model, y krg is the predicted value of the Kriging model, FE represents the number of true fitness evaluations of the current optimization process, ω represents half of the maximum number of true evaluations, and y is the weighted prediction result of the heterogeneous integration agent model.

[0024] (33) Vector-based model management strategy: at a predefined number of iterations w max Within , the offspring population Off is generated by genetic operators, and the trained ensemble model Ensemble is used to evaluate the offspring, and RVEA is used as the optimizer to select the next generation of parents from P and the evaluated Off. This algorithm introduces an additional set of fixed reference vectors V0, and evaluates whether the model needs to increase diversity or convergence based on the fixed reference vectors and threshold δ. The variance provided by the Kriging model is used as an indicator to judge individual uncertainty, and APD is used as an indicator to judge convergence. The calculation formula of APD is:

[0025]

[0026] in is the distance from the target vector corresponding to the jth individual to the origin, θ j is the angle between the jth 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 is the maximum number of generations before updating the surrogate model, and α is a user-defined parameter that controls P(θ i ) rate of change, γ v is the minimum angle between the reference vector and any other reference vector in the current generation.

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

[0030] The second aspect of the present invention relates to a machining center bed optimization device based on an integrated agent model assisted evolutionary algorithm, comprising a memory and one or more processors, wherein 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 agent model assisted evolutionary algorithm of the present invention.

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

[0032] The present invention is designed from three aspects: the radius of the weight-reducing hole of the bed, the thickness of the rib plate, and the inner and outer wall thicknesses, and includes the following steps: three-dimensional modeling of the original bed, and analysis of its static and dynamic characteristics, with the mass of the bed, the maximum static deformation and the first-order natural frequency as optimization targets; the radius of the weight-reducing hole, the thickness of the rib plate, the inner and outer wall thicknesses are selected as design variables, and the upper and lower limit constraints of each design variable are determined; the experimental sample points corresponding to the design variables and the optimization targets are obtained by changing the structural optimization design variables and performing static, dynamic and thermodynamic finite element analysis, and an agent model is constructed using the experimental sample points; the previously established multi-objective optimization mathematical model for key components of the pentahedron machining center is applied, and a dynamic integrated agent-assisted multi-objective evolutionary algorithm (AERVEA) is used to optimize and solve, and output the optimized structural parameters and target response values, and finally the results are simulated and verified. The optimization design method proposed in the present invention uses integrated learning and adaptive technology to construct a high-precision heterogeneous integrated agent model with a small number of samples, effectively limiting the number of expensive true fitness function evaluations, and using the environmental selection operator to sort and screen the population to generate the optimal solution. Experimental results show that the algorithm achieves good optimization effects on the multi-objective optimization problem of the bed.

[0033] The present invention uses ensemble learning and dynamic weight allocation technology to construct a high-precision heterogeneous ensemble proxy model with a small number of samples, effectively limiting the number of expensive true fitness function evaluations, and uses vector-based model management technology to update the ensemble model, taking into account the convergence of the algorithm and the diversity of the population. Finally, the archive set is managed to prevent training data redundancy. Experimental results show that the algorithm achieves good optimization results in the multi-objective optimization problem of the pentahedron machining center bed.

[0034] The working principle of the present invention is: first, three-dimensional modeling of the bed and selection of design variables are performed, and then Latin hypercube sampling is performed on the design variables of the bed, and the bed mass, the maximum static deformation of the bed and the first-order natural frequency of the bed are used as the objective function to solve the contradiction between lightweighting and improving dynamic and static performance of the bed in the optimization design problem. Finite element analysis is performed on the samples to obtain the initial sample points. In the dynamic integrated agent-assisted multi-objective evolutionary algorithm (AERVEA), the initial sample points are used as the initial population, and 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 integrated learner Ensemble. The present invention manages the model based on vectors, and within a predefined number of iterations ω max Within, the offspring population Off is generated by genetic operators, and the offspring is evaluated using the trained ensemble model Ensemble. RVEA is used as the optimizer to select the next generation of parents from P and the evaluated Off. This algorithm evaluates whether the model needs to increase diversity or convergence based on the degree of change in the number of fixed reference vectors, and uses the 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 set is updated, and individuals with a fixed number of N are selected as samples for the next model training, which reduces the time for ensemble model training and improves the efficiency of the algorithm. Finally, the obtained Pareto solution set is screened and the optimal solution is obtained and verified by finite element simulation.

[0035] The advantages of the present invention are:

[0036] (1) The problem that the present invention intends to solve belongs to an expensive multi-objective optimization problem, with the optimization objectives of minimizing the maximum mass, minimizing the maximum deformation, and maximizing the first-order modal frequency. However, there is a contradiction between minimizing the maximum mass and minimizing the maximum deformation and the first-order modal frequency, because while reducing the weight of the machining center, its static and dynamic performance is often reduced, and it is often impossible to have the best of both worlds when optimizing the design. By performing multi-objective optimization on the machining center bed, the best balance between performance and cost can be achieved. This study will balance the trade-off relationship between these three indicators through an agent-assisted multi-objective evolutionary algorithm based on ensemble learning, solve and obtain a high-quality Pareto solution set, and select the optimal solution from it.

[0037] (2) The present invention proposes a dynamic integrated agent-assisted multi-objective evolutionary algorithm (AERVEA), which combines the global approximation performance of RBF and the local approximation performance of Kriging model, and dynamically assigns weights to the two models, establishes a high-precision heterogeneous integrated learner Ensemble, and reduces the actual evaluation cost. In addition, the algorithm uses vector-based management of the model, and new individuals will be used as new samples in the model training, so that the prediction accuracy of the model is continuously improved, and the convergence of the algorithm and the diversity of the population are taken into account during the optimization process to increase the efficiency of the algorithm and fully explore the target space to obtain PF (Pareto Front). Finally, the archive set is managed to prevent redundancy of training data. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0039] Figure 1 A flowchart of a machining center bed optimization method based on an integrated agent model assisted evolutionary algorithm provided by the present invention is shown;

[0040] Figure 2 A flow chart of a dynamic integrated agent-assisted multi-objective evolutionary algorithm (AERVEA) provided by the present invention is shown;

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

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

[0043] Figure 5The static deformation cloud diagram of the bed before optimization is shown;

[0044] Figure 6 The first-order modal cloud diagram of the bed before optimization is shown;

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

[0046] Figure 8 The static deformation cloud diagram of the bed after optimization is shown;

[0047] Fig. 9 The first-order modal cloud diagram of the bed after optimization 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 rib plate thickness, x6-transverse rib plate spacing, x7-longitudinal rib plate thickness, x8-longitudinal rib plate spacing, x9-side wall weight reduction hole diameter, x10-front and rear wall weight reduction hole diameter. DETAILED DESCRIPTION

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

[0050] Example 1

[0051] like Figure 1 The flowchart of the method of the present invention is shown in FIG. First, the original bed is three-dimensionally modeled, a bed finite element model is established, and static and dynamic characteristics finite element simulation is performed to analyze its maximum static deformation, first-order natural frequency, and mass; then the bed weight reduction hole radius, rib plate thickness and spacing, and wall thickness are selected as design variables, and the upper and lower limits of the design variables and the objective function are used as constraints. The bed mass, maximum static deformation, and first-order natural frequency are determined as the objective function, and a multi-objective optimization mathematical model for the bed is established;

[0052] Through experimental design, test sample points are constructed to establish a high-precision heterogeneous integrated agent model. The previously established multi-objective optimization mathematical model for the bed is applied to optimize and solve the problem through a dynamic integrated agent-assisted multi-objective evolutionary algorithm (AERVEA) and output the optimized structural parameters and the corresponding Pareto solution set.

[0053] Select the optimal solution from the output Pareto solution set as the final experimental result;

[0054] Conduct simulation to verify the results;

[0055] The following is a description with reference to specific embodiments.

[0056] like Figure 3The figure shows the three-dimensional model of a pentahedron machining center to be optimized. This type of vertical and horizontal composite pentahedron machining center is mainly composed of a column, a tool magazine, a ram, a bed, a workbench, a vertical spindle and a horizontal spindle. The main structure of the machine tool is a cross-saddle type with a compact structure; the machine tool guide rail adopts an imported rolling linear guide rail; the lead screw adopts a fixed tensile structure at both ends, and both adopts a high-rigidity ball screw pair with high transmission accuracy; the tool changing device adopts a disc-type manipulator tool magazine with short tool changing time and reliable performance.

[0057] like Figure 4 The figure shows the parametric 3D model of the bed of the pentahedron machining center in this example. The features of the parts are simplified, and small features such as chamfers, fillets, and threaded holes that have little effect on the analysis results are removed. At the same time, the dimensions of the parts are analyzed in association to achieve parametric modeling to improve the efficiency of simulation calculations.

[0058] Then, the static characteristics of the parts are studied, the parts are imported into Ansys, 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 parts for static analysis and modal analysis, and the maximum static deformation cloud map and the first-order natural frequency of the bed are obtained, such as Figure 5-6 shown.

[0059] Next, the design variables and design space of the bed are selected. In order to achieve the purpose of lightweighting, the selection of structural parameters mainly focuses on wall thickness, rib thickness and spacing, and weight-reducing hole radius, and avoids non-design domains to avoid affecting the overall structure of the pentahedron machining center. When designing constraints, attention should be paid to interference between dimensions to avoid failure in later model reconstruction.

[0060] like Figure 7 As shown in the figure, the radius of the weight-reducing hole, the thickness and spacing of the rib plate, and the wall thickness are taken 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 rib plate thickness, x6-transverse rib plate spacing, x7-longitudinal rib plate thickness, x8-longitudinal rib plate spacing, x9-side wall weight-reducing hole diameter, x10-front and rear wall weight-reducing 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 the selection of objective function, lightweight design criterion, static performance optimal criterion and dynamic performance optimal criterion are selected as the selection criteria of objective function.

[0064] In order to reduce the material consumption and manufacturing cost when manufacturing the parts of the pentahedron machining center, the following lightweight design criteria are formulated:

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

[0066] During the operation of the key parts of the pentahedron machining center, under the action of cutting force, tiny static deformation will occur. Static deformation will reduce the machining accuracy and cause the dimensional deviation of the parts to exceed the specified range, thus affecting the quality and performance of the product. In addition, static deformation will cause internal stress concentration of the parts, and may cause cracks and fractures, shortening the service life of the parts. Therefore, the following static performance optimization criteria are formulated:

[0067] F(x)=minσ(x) (6)

[0068] The dynamic performance of a pentahedron machining center is mainly reflected in its vibration resistance and stability during operation. As a key component of a pentahedron machining center, the quality of its dynamic performance will affect the quality of the workpiece. In theory, there are countless modes for parts, but low-order modes, especially the first-order natural frequency, are the frequency bands that a pentahedron machining center is most likely to reach during actual operation. When they are close to the actual operating frequency of the pentahedron machining center, they can easily excite the machining center to resonate and affect the machining quality. Therefore, the first-order natural frequency should be increased as much as possible to avoid the frequency band in which the pentahedron machining center operates. Therefore, the following optimal dynamic performance criteria are formulated:

[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 expressed as:

[0076]

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

[0078] Next, multi-objective optimization is performed on the bed.

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

[0080] Table 2

[0081]

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

[0083] like Figure 2 As shown in the figure, in this paper, a 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 a heterogeneous ensemble learner Ensemble. The output of the global proxy model after dynamic weighting can be described as follows:

[0084]

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

[0086] In comparison, RBF has no requirements for response characteristics, can fit any type of function well, and has more stable performance in high-dimensional multi-objective problems, so as a global model, it fits and predicts the target value of the population. Kriging has good continuity and differentiability, and can obtain better precision and prediction accuracy than RBF when there are a small number of targets. 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 on enhancing population diversity, so the weight of the diversity local proxy model is relatively large and slowly decreases as diversity increases. At the same time, a small amount of weight is added to the convergence local model to provide a certain convergence for the global model. The second half of the optimization process is just the opposite. Through the variant sigmoid function, the dominant relationship between the weight ratios of the two is quickly switched halfway through the optimization process.

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

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

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

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

[0092] This algorithm is based on the empty fixed reference vector The number of changes and threshold δ are used to evaluate whether the model needs to increase diversity or convergence. The variance provided by the Kriging model is used as an indicator to judge individual uncertainty, and APD is used as an indicator to judge convergence. When the number of changes is greater than the threshold δ, it means that the empty fixed reference vector If the number of increases exceeds a given threshold, diversity should be prioritized. In this case, the individuals that need to be re-evaluated should be selected based on the uncertainty information provided by the kriging model. On the contrary, if the empty fixed reference vector If the number change is less than the threshold δ, that is, the diversity of the population is not the main consideration, the convergence standard should be given priority, and the individual with the smallest APD should be selected according to the adaptive reference vector. The calculation formula of APD is:

[0093]

[0094] in is the distance from the target vector corresponding to the jth individual to the origin, θj is the angle between the jth 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 is the maximum number of generations before updating the surrogate model, and α is a user-defined parameter that controls P(θ i ) rate of change, γ v is the minimum angle between the reference vector and any other reference vector in the current generation.

[0097] Finally, the management of the archive set is to limit the computational time of retraining the Kriging model and prevent the training data in the archive set from being too large and affecting the efficiency of the algorithm. The amount of training data in this algorithm is fixed, so if the amount of available training data is greater than the size of the archive, some data needs to be discarded.

[0098] First, we add the most recently evaluated individuals to the archive, denoted by u, and remove duplicate data points. If the number of training data is still larger than the size of the archive, we remove some training samples other than the most recently evaluated individuals. To do this, we assign the most recently evaluated individuals to the adaptive reference vector V a and determine the inactive reference vector The remaining individuals are then assigned to the inactive reference vector The active adaptive reference vectors are clustered into Nu clusters, one data point is randomly selected from each cluster, and the rest are discarded. In this way, a fixed number of diverse training data sets are retained in the archive set, thereby maximizing the quality of the heterogeneous ensemble proxy model while limiting the computation time.

[0099] The initial population size of the experimental parameters is set to 100, the maximum number of true evaluations is set to 200, and 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, obtaining the optimized quality information, and performing static analysis and modal analysis, the optimized maximum deformation, maximum stress and the values ​​of the first six natural frequencies are obtained, such as Figure 8-9 As shown, and compared with that before optimization, as shown in the table, the feasibility of the optimization plan for the bed formulated in this paper is investigated.

[0103] The performance indicators 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 after the optimization of the bed size parameters are compared with those before and after the optimization, as shown in the table. This multi-objective optimization not only ensures the constraints, but also reduces the maximum stress by 14.37%, the maximum deformation of the bed by 4.73%, the first-order natural frequency by 2.59%, and the mass by 11.44% after the optimization of the size parameters. It can be seen that multiple objectives of the bed can be optimized at the same time through this optimization method, and the optimization of bed size of the same category can also refer to this optimization scheme.

[0107] The results show that the optimized design can effectively reduce the weight of the pentahedron machining center structure and optimize the dynamic and static performance, thereby achieving the goals of saving costs, energy conservation and environmental protection, and improving machining accuracy.

[0108] The optimization design method proposed in the present invention uses heterogeneous integrated agent model and dynamic weight allocation technology to construct a high-precision heterogeneous integrated agent model with a small number of samples, effectively limiting the number of expensive true fitness function evaluations, and uses vector-based model management technology to update the heterogeneous integrated agent model, and sorts and screens the population to generate the optimal solution. Experimental results show that the algorithm achieves good optimization effect on the multi-objective optimization problem of the bed of a pentahedron machining center.

[0109] Example 2

[0110] The present embodiment relates to a machining center bed optimization device based on an integrated agent model assisted evolutionary algorithm, including a memory and one or more processors, wherein 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 agent model assisted evolutionary algorithm of Example 1.

[0111] Example 3

[0112] This embodiment relates to a computer-readable storage medium on which a program is stored. When the program is executed by a processor, the machining center bed optimization method based on an integrated agent model assisted evolutionary algorithm of embodiment 1 is implemented.

[0113] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The protection scope of the present invention should not be regarded as limited to the specific forms described in the embodiments. The protection scope of the present 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 machining center bed optimization method based on an integrated agent model-assisted evolutionary algorithm, characterized in that: The steps include: (1) Conduct 3D modeling of the original pentahedral machining center bed, simplify the features of the parts, remove small features such as chamfers, fillets, threaded holes, etc. that have little effect on the analysis results, and obtain a simplified parametric model of the bed. Establish a finite element model of the bed, calculate the cutting force generated by the dual spindles of the machining center under extreme working conditions, and analyze the load boundary conditions borne by the bed. Apply load constraints to the finite element model, apply fixed constraints to the anchor bolt holes of the machining center, perform finite element simulation of its static and dynamic characteristics, and analyze its maximum static deformation, first-order natural frequency, and mass; (2) The radius of the bed weight-reducing hole, the spacing and thickness of the ribs, and the inner and outer wall thicknesses are selected as design variables. The upper and lower limits of the design variables and the objective function are used as constraints. The bed mass, maximum static deformation, and first-order natural frequency are determined as the objective function, and a multi-objective optimization mathematical model for the bed is established. (3) Use Latin hypercube design as the experimental design method to construct test sample points, substitute them into the finite element model to solve the corresponding objective function value, construct the initial sample set, and establish a high-precision heterogeneous integrated agent model; apply the previously established multi-objective optimization mathematical model of the bed, and use the dynamic integrated agent-assisted multi-objective evolutionary algorithm (AERVEA) to optimize and solve, and output the optimized structural parameters and the corresponding Pareto solution set; (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 variable parameter values ​​of the bed design according to the optimization results, perform simulation verification, and analyze the errors.

2. The machining center bed optimization method based on integrated agent model assisted evolutionary algorithm as claimed in claim 1 is characterized in that: The multi-objective optimization mathematical model of the bed described in step (2) includes: Among them: δ(X) is the maximum deformation of the bed, m(X) is the mass of the bed, and f(X) is the first-order natural frequency. init , f init , δ init is the initial bed mass, deformation and frequency; x i is the i-th design variable of the bed; n is the number of design variables, x min is the lower limit of the design variable, x max is the upper limit of the design variable.

3. The machining center bed optimization method based on integrated agent model assisted evolutionary algorithm as claimed in claim 1, characterized in that: The algorithm flow steps described in step (3) are: (31) Initialization: Use Latin hypercube sampling LHS to generate an initial population P of size N as the initial sample set, and use the finite element method to evaluate the true fitness value, setting the maximum number of true evaluations FE max ; The number of individuals u that need to be re-evaluated and used to update the ensemble model is the maximum number of generations before updating the surrogate model ω max ; (32) Constructing a heterogeneous ensemble agent learner: The evaluated individuals are used to establish a heterogeneous ensemble agent model with dynamic weight allocation. In this paper, an RBF model is used as a global model and a Kriging model is used as a local model. Dynamic weight allocation is performed on the two models to establish an ensemble learner Ensemble. The output of the global proxy model after dynamic weighting can be described as follows: Among them, y rbf is the predicted value of the RBF model, y krg is the predicted value of the Kriging model, FE represents the number of true fitness evaluations of 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 agent model; (33) Vector-based model management strategy: at a predefined number of iterations w max Within, the offspring population Off is generated by genetic operators, and the trained ensemble model Ensemble is used to evaluate the offspring, and RVEA is used as the optimizer to select the next generation of parents from P and the evaluated Off; an additional set of fixed reference vectors V0 is introduced, and the model needs to increase diversity or convergence according to the fixed reference vectors and threshold δ. The variance provided by the Kriging model is used as an indicator to judge individual uncertainty, and APD is used as an indicator to judge convergence; the calculation formula of APD is: in is the distance from the target vector corresponding to the jth individual to the origin, θ j is the angle between the jth individual and its assigned reference vector; in APD, P(θ j ) is the penalty function, defined as follows: where k is the number of targets, ω max is the maximum number of generations before updating the surrogate model, and α is a user-defined parameter that controls P(θ i ) rate of change, γ v is the minimum angle between the reference vector and other reference vectors in the current generation; (34) Archive set update: Select a fixed number of N individuals from archive set A1 as samples for the next model training.

4. A machining center bed optimization device based on an integrated agent model assisted evolutionary algorithm, characterized in that: It comprises a memory and one or more processors, wherein 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 integrated agent model assisted evolutionary algorithm as described in any one of claims 1-3.

5. A computer-readable storage medium, characterized in that: A program is stored thereon, and when the program is executed by a processor, the machining center bed optimization method based on an integrated agent model assisted evolutionary algorithm as described in any one of claims 1 to 3 is implemented.

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