Milling head structure design method based on improved multi-target genetic algorithm

Abstract

The invention relates to the technical field of swing angle milling heads, and discloses a milling head structure design method based on an improved multi-target genetic algorithm. According to the method, parameters of a milling head structure serve as design parameters and comprise the front side depth L14, the radius R15, the rear side depth L16, the upper portion cutting depth FD1, the rib plate position Y-axis L1, the rib plate position X-axis L2, the rib plate depth FD2 and the like of the milling head, and the maximum static deformation S, the first-order inherent frequency H1 and the milling head shell mass M serve as optimization objects. A prediction model BWO-BP neural network model with higher fitting precision is obtained by using a white whale optimization algorithm to optimize hyper-parameters of a BP neural network model, a multi-target optimization model is solved based on the BWO-BP neural network model, and high-rigidity, light-weight and low-vibration performance optimization design of the milling head structure is carried out. Improvement and optimization starting from the structure of the milling head part are achieved, the comprehensive performance of the milling head is improved, and the milling head part has great significance in saving the manufacturing cost.

Description

Technical Field

[0001] The invention belongs to the technical field of swing angle milling heads and relates to a milling head structure design method, in particular to a milling head structure design method based on an improved multi-objective genetic algorithm. Background Art

[0002] Five-axis machine tools are widely used in a variety of machining fields and are indispensable equipment for the manufacture and processing of complex-shaped parts. The angular milling head, a key component of five-axis machine tools, plays a vital role in the manufacturing process. In the fields of intelligent manufacturing and precision machining, angular milling heads must simultaneously meet the requirements of high rigidity, lightweight, and low vibration. With the surge in demand for machining complex parts such as titanium alloy components in the aerospace field and integrated die-casting molds for new energy vehicles, improving the overall performance of angular milling heads has become the key to breaking through the technical bottlenecks of high-end equipment.

[0003] Prior art often employs an external structure around the milling head to increase its rigidity and reduce deformation and vibration during operation. For example, Chinese patent application publication number CN112247230A discloses a rigidity-enhancing structure for an offset-type swing-angle milling head. This structure, comprising an inner ring rotating assembly, an outer ring fixed housing, and a closed collar assembly, reduces the impact of vibration generated by the milling cutter during operation on the milling head structure. However, this external structure approach is uneconomical and increases material and installation costs.

[0004] During the design phase of the milling head structure, optimizing it to ensure it meets the requirements of high rigidity, lightweight, and low vibration is an economical and feasible way to improve milling head performance. Existing technologies for optimizing milling head structures include the paper "Analysis and Optimization of High Rigidity Structure of 45-degree B-Axis Milling Head with High Torque Mechanical Spindle." This paper identifies the weak links in milling head rigidity through finite element analysis, establishes a response surface model based on this, and conducts multi-objective optimization design for multiple key load-bearing components. However, the method described in this paper has the following drawbacks:

[0005] 1. Ignoring the parameters of the milling head structure itself, including the front depth, radius, back depth, upper resection depth, rib position Y axis, rib position X axis, rib depth, etc., which affect the comprehensive performance of the milling head;

[0006] 2. The multi-objective optimization design of multiple key load-bearing components has the problems of high assembly precision requirements and complex transmission chains.

[0007] In the current technological landscape, the structure of a swing milling head must simultaneously meet the requirements of high torque, high rigidity, and dynamic response. However, conventional designs face challenges such as complex transmission chains, high assembly precision requirements, and difficulty controlling thermal deformation. Consequently, improvements to existing technologies are needed. Summary of the Invention

[0008] In view of the problems existing in the above-mentioned prior art, the present invention discloses a milling head structure design method based on an improved multi-objective genetic algorithm, which can solve the deficiencies existing in the related art.

[0009] To achieve the above purpose, the present invention discloses the following technical solutions:

[0010] In a first aspect, the present invention provides a milling head structure design method based on an improved multi-objective genetic algorithm, the method comprising:

[0011] Acquiring parameters of a plurality of milling head structures, and constructing a design parameter data set of the milling head structure to be designed according to the parameters of the plurality of milling head structures;

[0012] Inputting the design parameter data set into a pre-trained BWO-BP neural network model, so that the BWO-BP neural network model predicts the maximum static deformation S, the first-order natural frequency H1, and the mass M of the milling head housing corresponding to the design parameters in the design parameter data set; wherein the BWO-BP neural network model is obtained by optimizing the hyperparameters of the BP neural network model using the Beluga optimization algorithm;

[0013] The design parameters in the BWO-BP neural network model are adjusted by a multi-objective genetic algorithm to obtain the optimal design parameter set of the milling head structure with the minimum maximum static deformation S, the maximum first-order natural frequency H1, and the minimum milling head shell mass M.

[0014] Preferably, the design parameters include the front depth L14, radius R15, rear depth L16, upper resection depth FD1, rib position Y-axis L1, rib position X-axis L2, and rib depth FD2 of the milling head.

[0015] Preferably, the hyperparameters of the BP neural network model include weights and threshold parameters between BP neural network nodes.

[0016] Further preferably, the Beluga whale optimization algorithm optimizes the hyperparameters of the BP neural network model including the following steps: using Beluga whale individuals to represent potential solutions, each Beluga whale individual calculates its own fitness value through a fitness calculation function, and takes the minimum fitness function value as the optimal fitness value; the Beluga whale optimization algorithm continuously changes the position of the Beluga whale individual through exploration, development and whale fall operations until the Beluga whale individual corresponding to the optimal fitness value is found; the node parameters contained in the optimal Beluga whale individual found are assigned to the BP neural network to achieve accurate prediction of the maximum static deformation S, first-order natural frequency H1, and milling head shell mass M of the milling head structure corresponding to the design parameters.

[0017] Preferably, the adjusting the parameters in the BWO-BP neural network model by a multi-objective genetic algorithm comprises:

[0018] A mathematical model for multi-objective optimization is established based on a multi-objective genetic algorithm and a BWO-BP neural network model, wherein the Pareto optimal solution set output by the mathematical model corresponds to the optimal design parameter set;

[0019] The mathematical model is:

[0020] min(S);

[0021] max(H1);

[0022] M(X)≤M0;

[0023] X=(x1,x2,...,x n ) T ;

[0024] x i1 ≤x i ≤x i2 ,i=1,2,...,n;

[0025] Where S is the maximum static deformation, H1 is the first-order natural frequency, M is the mass of the milling head shell, X is the decision vector, M0 is the initial mass, and x i is the value of each variable, x i1 is the lower limit of the value, x i2 The upper limit of the value.

[0026] Further preferably, the mathematical model for multi-objective optimization is established based on the multi-objective genetic algorithm and the BWO-BP neural network model, including:

[0027] Initialize the population and encode the weights and thresholds of the BP neural network with each individual in the population;

[0028] The prediction output of each individual is calculated by BP network, and the maximum static deformation S, the first-order natural frequency H1, and the mass M of the milling head shell of the individual are evaluated by multi-objective fitness function;

[0029] Then, the non-dominated sorting and crowding calculation are used to classify the population and select the Pareto frontier solution;

[0030] New populations are generated through multi-point crossover and mutation operations, and an elite retention strategy is introduced to maintain high-quality solutions. The selection pressure parameters are dynamically adjusted during the iteration process to balance global search and local development, and finally the Pareto optimal solution set is output to achieve multi-objective optimization.

[0031] In a second aspect, the present invention provides a milling head structure design device, the device comprising:

[0032] An acquisition unit is configured to acquire parameters of a plurality of milling head structures, and construct a design parameter data set of the milling head structure to be designed according to the parameters of the plurality of milling head structures;

[0033] Optimization unit: optimizes the hyperparameters of the BP neural network model using the Beluga optimization algorithm, and trains the optimized BP neural network model using the design parameter data set to obtain a BWO-BP neural network model;

[0034] Prediction unit: inputs the design parameter data set into the BWO-BP neural network model to output prediction results of the maximum static deformation S, the first-order natural frequency H1, and the mass M of the milling head shell corresponding to the design parameters;

[0035] Output unit: The design parameters in the BWO-BP neural network model are adjusted through a multi-objective genetic algorithm to obtain an optimal design parameter set of the milling head structure with the minimum maximum static deformation S, the maximum first-order natural frequency H1, and the minimum mass M of the milling head shell, and the optimal design parameter set is output as the design parameters of the milling head structure to be designed.

[0036] In a third aspect, the present invention provides an electronic device, comprising:

[0037] processor;

[0038] a memory for storing processor-executable instructions;

[0039] The processor implements the steps of the above-mentioned milling head structure design method based on the improved multi-objective genetic algorithm by running the executable instructions.

[0040] In a fourth aspect, the present invention provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the steps of the above-mentioned milling head structure design method based on the improved multi-objective genetic algorithm.

[0041] It can be seen from the above technical solutions that, compared with the prior art, the present invention has the following technical effects:

[0042] (1) The milling head structure design method based on the improved multi-objective genetic algorithm provided by the present invention takes the parameters of the milling head structure itself as design parameters, including the front side depth L14, radius R15, rear side depth L16, upper resection depth FD1, rib position Y axis L1, rib position X axis L2, rib depth FD2, etc. of the milling head, and takes the maximum static deformation S, the first-order natural frequency H1, and the mass M of the milling head shell as optimization objects. By optimizing the hyperparameters of the BP neural network model using the Beluga optimization algorithm, a prediction model BWO-BP neural network model with higher fitting accuracy is obtained, and a multi-objective optimization model is solved based on the BWO-BP neural network model to optimize the performance of the milling head structure with high rigidity, lightness, and low vibration, and realize the parameter design of the milling head structure including the front side depth, radius, etc., that is, the improvement and optimization starting from the structure of the milling head component itself is realized, and the comprehensive performance of the milling head is improved, which is of great significance for saving manufacturing costs.

[0043] (2) In the method provided by the present invention, multi-objective optimization of the maximum static deformation S, the first-order natural frequency H1, and the mass M of the milling head shell can enable the swing-angle milling head structure to simultaneously meet the requirements of large torque, high rigidity and dynamic response characteristics.

[0044] (3) In the method provided by the present invention, based on the performance prediction of the design parameters of the front depth L14, radius R15, rear depth L16, upper resection depth FD1, rib position Y-axis L1, rib position X-axis L2, and rib depth FD2 of the milling head, the Beluga optimization algorithm optimizes the hyperparameters of the BP neural network model to obtain a prediction model BWO-BP neural network model with higher fitting accuracy. Compared with the optimization of BP neural network by genetic algorithm, PSO algorithm, and WOA algorithm, it can more effectively improve the calculation accuracy and efficiency, thereby better meeting the needs of practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 The present invention is a flowchart of a milling head structure design method based on an improved multi-objective genetic algorithm provided by an exemplary embodiment.

[0046] Figure 2 It is a schematic diagram of design parameters of a milling head structure provided by an exemplary embodiment.

[0047] Figure 3 It is a schematic diagram of sensitivity analysis of parameters of a milling head structure provided by an exemplary embodiment.

[0048] Figure 4 This is a flowchart of applying the BWO optimization algorithm to improve the BP neural network provided by an exemplary embodiment.

[0049] Figure 5It is a verification of comparing the predicted value and actual value of the milling head shell mass M of the milling head structure using the BWO-BP neural network model provided by an exemplary embodiment.

[0050] Figure 6 It is a verification of comparing the predicted value and actual value of the first-order natural frequency H1 of the milling head structure using the BWO-BP neural network model provided by an exemplary embodiment.

[0051] Figure 7 It is a verification of comparing the predicted value and actual value of the maximum static deformation S of the milling head structure using the BWO-BP neural network model provided by an exemplary embodiment.

[0052] Figure 8 It is a flowchart of solving the milling head structure design parameters by using a BWO-BP neural network model combined with a multi-objective genetic algorithm provided by an exemplary embodiment.

[0053] Figure 9 It is a schematic structural diagram of a device provided by an exemplary embodiment.

[0054] Figure 10 It is a block diagram of a milling head structure design device provided by an exemplary embodiment. DETAILED DESCRIPTION

[0055] Exemplary embodiments will be described in detail herein, with examples illustrated in the accompanying drawings. In the following description, when referring to the drawings, like numbers in different figures represent like or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all possible implementations consistent with one or more embodiments of the present invention. Rather, they are merely examples of apparatuses and methods consistent with certain aspects of one or more embodiments of the present invention, as detailed in the appended claims.

[0056] It should be noted that in other embodiments, the steps of the corresponding method are not necessarily performed in the order shown and described in the present invention. In some other embodiments, the method may include more or fewer steps than those described in the present invention. In addition, a single step described in the present invention may be broken down into multiple steps for description in other embodiments, and multiple steps described in the present invention may be combined into a single step for description in other embodiments.

[0057] To further illustrate the present invention, the following examples are provided:

[0058] The existing related technologies for milling head structure optimization ignore the parameters of the milling head structure itself, including the front depth, radius, rear depth, upper resection depth, rib position Y-axis, rib position X-axis, rib depth, etc., which affect the comprehensive performance of the milling head. In addition, the existing milling head structure optimization design has the problems of high assembly precision requirements and complex transmission chain.

[0059] In order to solve the deficiencies existing in the related technologies, and in order to improve the rigidity of the milling head structure, reduce the shell mass of the milling head, and improve the vibration resistance of the milling head, the improvement of the vibration resistance can improve the operating accuracy of the milling head. The present invention proposes a milling head structure design method based on an improved multi-objective genetic algorithm.

[0060] Figure 1 This is a flowchart of a milling head structure design method based on an improved multi-objective genetic algorithm provided by an exemplary embodiment. Figure 1 As shown, the method may include the following steps:

[0061] Step S1: acquiring parameters of a plurality of milling head structures, and constructing a design parameter data set of the milling head structure to be designed according to the parameters of the plurality of milling head structures.

[0062] In order to evaluate the performance of the milling head structure corresponding to the design parameters of the milling head structure to be designed, and to obtain the design parameters of the milling head structure corresponding to the optimal performance, and ultimately as the design parameters of the milling head structure to be designed, it is necessary to obtain the parameters of several milling head structures in the early stage of design, and construct a design parameter data set of the milling head structure to be designed based on the parameters of the several milling head structures.

[0063] In one embodiment, based on the finite element analysis results of the milling head, design variables can be sampled from the finite element analysis of the milling head to establish a design parameter data set. For example, a DOE (Design of Experiments) module is used to design several milling head structures, and sensitivity and correlation analysis is performed on the parameters of the milling head structures to sample and establish a design parameter data set as shown in Table 1. The selected design parameter variables are the front side depth L14, radius R15, rear side depth L16, upper resection depth FD1, rib plate position Y axis L1, rib plate position X axis L2, and rib plate depth FD2. The design parameter variables of the milling head structure are shown in the following diagram: Figure 2 As shown. As a reference, the sensitivity analysis of the parameters of the milling head structure is as follows Figure 3 shown.

[0064] Table 1 Design parameter data set

[0065]

[0066] Step S2: input the design parameter data set into a pre-trained BWO-BP neural network model, so that the BWO-BP neural network model predicts the maximum static deformation S, the first-order natural frequency H1, and the mass M of the milling head shell corresponding to the design parameters in the design parameter data set; wherein the BWO-BP neural network model is obtained by optimizing the hyperparameters of the BP neural network model by the Beluga optimization algorithm.

[0067] When evaluating and predicting the performance of a milling head structure corresponding to the design parameters of a to-be-designed milling head structure, each variable parameter has varying degrees of influence on its performance. Changes in certain variable parameters can affect the degree of influence of other parameters. Directly evaluating the performance of the milling head structure corresponding to the parameters in the design parameter dataset results in low accuracy, a large workload, and low computational accuracy and efficiency. Therefore, the present invention optimizes the hyperparameters of a BP neural network model using the Beluga optimization algorithm, trains a BWO-BP neural network model using the design parameter dataset, and solves a multi-objective optimization model based on the BWO-BP neural network model, a predictive model with higher fitting accuracy.

[0068] In one embodiment, the BWO optimization algorithm (White Whale optimization algorithm) is applied to improve the BP neural network, and the improved flow chart is as follows: Figure 4 shown.

[0069] The dimensions of individual whales in the Beluga Whale optimization algorithm are determined by the structural parameters of the BP neural network. When optimizing the node parameters of the BP neural network, each individual whale calculates its own fitness value using a fitness calculation function. Lower fitness function values indicate more accurate training and better prediction accuracy for the model. The Beluga Whale algorithm continuously shifts the positions of individual whales through exploration, exploitation, and whale fall operations until the individual with the optimal fitness value is found. The node parameters contained in this optimal individual are then assigned to the BP neural network. After training, the optimized BP neural network accurately predicts the output function.

[0070] More specifically, in the Beluga optimization algorithm, in a population of Beluga whales, individual Beluga whales represent potential solutions, and their positions are determined by a set of parameters (such as weights and bias values). The Beluga whale population X is represented as:

[0071]

[0072] Where n is the size of the beluga whale population; d is the dimension of the design variable.

[0073] The White Whale optimization algorithm iteratively updates the position of the individual White Whale to find the optimal solution. f Transition from the exploration phase to the development phase. Balance factor B f Expressed as:

[0074] B f =B0 / (1-T / 2T max )

[0075] Where B0 is a random value in the range (0,1) that changes in each iteration. The exploration phase occurs when the balance factor B f >0.5, while the development phase occurs at B f ≤0.5. As the iteration T increases, B f The fluctuation range of decreases from (0,1) to (0,0.5), indicating that the probabilities of the development and exploration stages have changed significantly, while the probability of the development stage increases with the continuous increase of iteration T; T is the number of iterations; T max is the maximum number of iterations.

[0076] In the exploration phase, the Beluga optimization algorithm uses the swimming behavior of the Beluga whale to perform global search and update the Beluga whale's position to discover potential high-quality solution areas. The Beluga whale's position update model is:

[0077]

[0078] Where, is the new position of the i-th beluga whale in the j-th dimension; pj is randomly selected in the d-dimension; is the position of the i-th beluga whale in the j-th dimension; and are the current positions of the i-th and r-th beluga whales; r1 and r2 are random numbers in the range (0,1) used to enhance the random operator during the exploration phase. sin(2πr²) and cos(2πr²) are used to average the random numbers between the fins. Depending on the chosen odd and even dimensions, the updated positions reflect the synchronized or mirrored behavior of the beluga whales when swimming or diving.

[0079] During the development phase, the Beluga optimization algorithm simulates the predation behavior of beluga whales and performs local search to fine-tune the quality of the solution. To improve the algorithm's convergence, the Levy flight strategy was introduced. The model during the development phase is:

[0080]

[0081] Where, and is the current position of the i-th beluga whale and a random beluga whale; is the new position of the i-th beluga whale; is the best position in the white whale; r3 and r4 are random numbers in the range (0,1); C1=2r4(1-T / T max ) is the random jump intensity that measures the flight intensity of levy; L FA random number that conforms to the levy flight function.

[0082] At the same time, the introduction of the whale fall stage simulates the random loss of individuals in the beluga whale group, which helps to maintain the diversity of the population and avoid premature convergence. The specific model is:

[0083]

[0084] Where r5, r6, r7 are random numbers in the range of (0,1), and X step The step length for the white whale fall.

[0085] The initial weights and threshold parameters between nodes in each layer of the BP neural network have a significant impact on the prediction accuracy of the neural network. This embodiment uses the White Whale algorithm to optimize the weights and threshold parameters between nodes in the BP neural network, assigning the optimal solution to the BP neural network to achieve accurate prediction of the BP neural network.

[0086] To further compare and verify the BWO algorithm's optimization effect on the BP neural network's prediction accuracy, the BWO algorithm, genetic algorithm, PSO algorithm, and WOA algorithm were used to optimize the initial weights and thresholds of the BP neural network. Ten sets of simulation experiment sample points for milling head shell mass were selected. While ensuring the consistency of network training parameters, the prediction accuracy of the optimized neural network was tested. To objectively evaluate the optimization effect of each algorithm on the neural network's prediction accuracy, the mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), and mean absolute percentage error (MAPE) were used as evaluation indicators.

[0087] The root mean square error (RMSE) represents the sample standard deviation of the difference between the predicted value and the original value, which can illustrate the degree of sample dispersion. MAE is the mean absolute error, which represents the average value of the absolute error between the predicted value and the original value. MSE is the mean of the sum of squares of the errors of the corresponding points of the predicted data and the original data. MAPE represents the average value of the normalized results of the prediction error, which is also a commonly used evaluation indicator. The smaller these four evaluation indicators are, the higher the prediction accuracy is.

[0088] The relevant formula is as follows:

[0089]

[0090]

[0091] The data prediction effects of different neural networks are shown in Table 2 below.

[0092] Table 2 Comparison of data prediction effects

[0093]

[0094] By comparing various evaluation indicators, it can be seen that the fitting accuracy of the BP neural network improved by the Beluga optimization algorithm is much greater than that of the BP neural network and the BP neural network improved by the genetic algorithm. The fitting accuracy of the orthogonalized experimental design data of the milling head shell is higher, and a better parameter combination can be obtained when solving the Pareto solution (Pareto optimal solution) of the multi-objective optimization algorithm.

[0095] The fitting effect is verified as follows Figure 5 、 Figure 6 、 Figure 7 As shown, Figure 5 、 Figure 6 、 Figure 7 The results of the BWO-BP neural network model were compared with the actual values for the milling head housing mass M, first-order natural frequency H1, and maximum static deformation S. The analysis found that the BWO-BP neural network model can accurately predict the milling head housing mass, maximum static deformation, and first-order natural frequency with a low prediction error, meeting subsequent operational requirements. The BP neural network, optimized with the Beluga algorithm, can accurately predict relevant parameters. Combining this with a multi-objective genetic algorithm can optimize nonlinear functions and continuous variables within the design space.

[0096] Step S3, adjusting the design parameters in the BWO-BP neural network model through a multi-objective genetic algorithm to obtain an optimal design parameter set of the milling head structure with the minimum maximum static deformation, the maximum first-order natural frequency H1, and the minimum mass of the milling head shell.

[0097] The optimized BP neural network model BWO-BP neural network model combined with the multi-objective genetic algorithm has a good solution effect for the complex multi-objective and nonlinear optimization problem of the milling head structure design of the present invention. The BWO-BP neural network model combined with the multi-objective genetic algorithm solves the milling head structure design, mainly using the trained BWO-BP neural network model as the individual fitness calculation function in the multi-objective genetic algorithm. The specific algorithm flow is as follows Figure 8 shown.

[0098] In the process of solving the milling head structural design, first, the population is initialized, and each individual in the population is used to encode the weights and thresholds of the BP neural network. Subsequently, the predicted output of each individual is calculated through the BP network, and its performance is evaluated using a multi-objective fitness function, including the milling head shell mass M, the first-order natural frequency H1, and the maximum static deformation S performance. Next, the population is graded using non-dominated sorting and crowding calculation to screen out the Pareto frontier solution. New populations are generated through multi-point crossover and mutation operations, and an elite retention strategy is introduced to maintain high-quality solutions. The selection pressure parameters are dynamically adjusted during the iteration process to balance global search and local development. Finally, the Pareto optimal solution set is output to achieve multi-objective optimization of the milling head structural design.

[0099] In one embodiment, adjusting the parameters in the BWO-BP neural network model using a multi-objective genetic algorithm includes establishing a multi-objective optimization mathematical model based on the multi-objective genetic algorithm and the BWO-BP neural network model, wherein the Pareto optimal solution set output by the mathematical model corresponds to the optimal design parameter set. The corresponding multi-objective optimization design mathematical model for the milling head housing is established as follows:

[0100] min(S);

[0101] max(H1);

[0102] M(X)≤M0;

[0103] X=(x1,x2,...,x n ) T ;

[0104] x i1 ≤x i ≤x i2 ,i=1,2,...,n;

[0105] Where S is the maximum static deformation, H1 is the first-order natural frequency, M is the mass of the milling head shell, X is the decision vector, M0 is the initial mass, and x i is the value of each variable, x i1 is the lower limit of the value, x i2 The upper limit of the value.

[0106] The optimization objectives and constraints of the multi-objective optimization design are shown in Table 3.

[0107] Table 3 Optimization objectives and constraints

[0108]

[0109] For this model, any given two decision vectors X, Y∈R n , if and only if there is no Y∈R nWhen X is dominated, X is called the Pareto optimal solution, that is, the Pareto non-dominated solution set. There is no distinction between good and bad solutions in the non-dominated solution set. Users can choose the solution that better meets the design requirements according to their own needs.

[0110] In order to verify the effect of the method of the present invention, a simulation test was carried out to compare and verify the optimization effect of the optimal design parameter set of the milling head structure with the minimum maximum static deformation S, the maximum first-order natural frequency H1, and the minimum mass of the milling head shell.

[0111] The weight coefficient method is used to sort the Pareto frontier solutions. The mass coefficient is set to 0.5, the maximum deformation coefficient is set to 0.3, and the first-order natural frequency coefficient is set to 0.2. The final candidate points are obtained through analysis and comparison. The dimensional data (design parameters) of the optimized milling head structure are rounded and the model is updated for simulation analysis. The results are shown in Table 4 below.

[0112] Table 4 Final candidate points

[0113]

[0114] The optimization results were systematically analyzed through finite element simulation. The mass of the milling head housing was reduced from 1071.9 kg to 940.5 kg, a reduction of 12.26%. The overall maximum deformation was reduced by 4.8%, and the first-order natural frequency was increased by 13.48%, verifying the feasibility of the optimization results.

[0115] Figure 9 This is a schematic structural diagram of a device provided by an exemplary embodiment. Figure 9 At the hardware level, the device includes a processor 502, an internal bus 504, a network interface 506, a memory 508, and a non-volatile memory 510. Of course, it may also include hardware required for other functions. One or more embodiments of the present invention can be implemented based on software, such as the processor 502 reading the corresponding computer program from the non-volatile memory 510 into the memory 508 and then running it. Of course, in addition to software implementation, one or more embodiments of the present invention do not exclude other implementation methods, such as logic devices or a combination of software and hardware. In other words, the execution subject of the following processing flow is not limited to each logic unit, but can also be hardware or logic devices.

[0116] Please refer to Figure 10 , a milling head structure design device can be applied to Figure 9 In the device shown, to implement the technical solution of the present invention, the device may include:

[0117] An acquisition unit is configured to acquire parameters of a plurality of milling head structures, and construct a design parameter data set of the milling head structure to be designed according to the parameters of the plurality of milling head structures;

[0118] Optimization unit: optimizes the hyperparameters of the BP neural network model using the Beluga optimization algorithm, and trains the optimized BP neural network model using the design parameter data set to obtain a BWO-BP neural network model;

[0119] Prediction unit: inputs the design parameter data set into the BWO-BP neural network model to output prediction results of the maximum static deformation S, the first-order natural frequency H1, and the mass M of the milling head shell corresponding to the design parameters;

[0120] Output unit: The design parameters in the BWO-BP neural network model are adjusted through a multi-objective genetic algorithm to obtain an optimal design parameter set of the milling head structure with the minimum maximum static deformation S, the maximum first-order natural frequency H1, and the minimum mass M of the milling head shell, and the optimal design parameter set is output as the design parameters of the milling head structure to be designed.

[0121] The devices, modules, or units described in the above embodiments may be implemented by computer chips or entities, or by products having certain functions. A typical implementation device is a computer, which may be in the form of a personal computer, laptop computer, cellular phone, camera phone, smartphone, personal digital assistant, media player, navigation device, email transceiver, game console, tablet computer, wearable device, or any combination of these devices.

[0122] In a typical configuration, a computer includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0123] Memory may include non-permanent storage in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. Memory is an example of a computer-readable medium.

[0124] Computer-readable media include permanent and non-permanent, removable and non-removable media that can be used to store information using any method or technology. Information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, disk storage, quantum memory, graphene-based storage media or other magnetic storage devices, or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media does not include transitory media such as modulated data signals and carrier waves.

[0125] For the computer-readable medium (or computer-readable storage medium) as described above or in any other form, computer instructions may be stored thereon, which, when executed by a processor, implement one or more of the above-mentioned embodiments, thereby realizing the technical solution of the present invention.

[0126] The present invention further provides a computer program that, when executed by a processor, implements one or more of the above-described embodiments, thereby realizing the technical solution of the present invention. The computer program may be recorded on the above-described or any other form of computer-readable medium, and the present invention is not limited thereto.

[0127] It should also be noted that the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, commodity, or apparatus that includes a series of elements includes not only those elements but also other elements not explicitly listed, or includes elements inherent to such process, method, commodity, or apparatus. In the absence of further limitations, an element defined by the phrase "comprises a ..." does not exclude the presence of other identical elements in the process, method, commodity, or apparatus that includes the element.

[0128] The foregoing description describes specific embodiments of the present invention. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims can be performed in an order different from that described in the embodiments and still achieve the desired results. Furthermore, the processes depicted in the accompanying drawings do not necessarily require the specific order shown or the sequential order to achieve the desired results. In certain embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0129] The terms used in one or more embodiments of the present invention are for the purpose of describing specific embodiments only and are not intended to limit one or more embodiments of the present invention. The singular forms "a", "an", "the" and "the" used in one or more embodiments of the present invention and the appended claims are also intended to include plural forms, unless the context clearly indicates otherwise. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0130] The above description is merely a preferred embodiment of one or more embodiments of the present invention and is not intended to limit one or more embodiments of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of one or more embodiments of the present invention shall be included in the scope of protection of one or more embodiments of the present invention.

Claims

1. A milling head structure design method based on an improved multi-objective genetic algorithm, characterized by: The method comprises: Acquiring parameters of a plurality of milling head structures, and constructing a design parameter data set of the milling head structure to be designed according to the parameters of the plurality of milling head structures; Inputting the design parameter data set into a pre-trained BWO-BP neural network model, so that the BWO-BP neural network model predicts the maximum static deformation S, the first-order natural frequency H1, and the mass M of the milling head housing corresponding to the design parameters in the design parameter data set; wherein the BWO-BP neural network model is obtained by optimizing the hyperparameters of the BP neural network model using the Beluga optimization algorithm; The design parameters in the BWO-BP neural network model are adjusted by a multi-objective genetic algorithm to obtain the optimal design parameter set of the milling head structure with the minimum maximum static deformation S, the maximum first-order natural frequency H1, and the minimum milling head shell mass M.

2. The milling head structure design method according to claim 1, characterized in that: The design parameters include the front side depth L14, radius R15, rear side depth L16, upper resection depth FD1, rib position Y axis L1, rib position X axis L2, and rib depth FD2 of the milling head.

3. The milling head structure design method according to claim 1, characterized in that: The hyperparameters of the BP neural network model include weights and threshold parameters between BP neural network nodes.

4. The milling head structure design method according to claim 3, characterized in that: The white whale optimization algorithm optimizes the hyperparameters of the BP neural network model, including the following steps: using white whale individuals to represent potential solutions, each white whale individual calculates its own fitness value through a fitness calculation function, and takes the minimum fitness function value as the optimal fitness value; the white whale optimization algorithm continuously changes the position of the white whale individuals through exploration, development, and whale fall operations until the white whale individual corresponding to the optimal fitness value is found; the node parameters contained in the optimal white whale individual found are assigned to the BP neural network to achieve accurate prediction of the maximum static deformation S, first-order natural frequency H1, and milling head shell mass M of the milling head structure corresponding to the design parameters.

5. The milling head structure design method according to claim 1, characterized in that: The method of adjusting the parameters in the BWO-BP neural network model by using a multi-objective genetic algorithm includes: A mathematical model for multi-objective optimization is established based on a multi-objective genetic algorithm and a BWO-BP neural network model, wherein the Pareto optimal solution set output by the mathematical model corresponds to the optimal design parameter set; The mathematical model is: min(S); max(H1); M(X)≤M0; X=(x1,x2,...,x n ) T ; x i1 ≤x i ≤x i2 ,i=1,2,...,n; Where S is the maximum static deformation, H1 is the first-order natural frequency, M is the mass of the milling head shell, X is the decision vector, M0 is the initial mass, and x i is the value of each variable, x i1 is the lower limit of the value, x i2 The upper limit of the value.

6. The milling head structure design method according to claim 5, characterized in that: The mathematical model of multi-objective optimization is established based on the multi-objective genetic algorithm and the BWO-BP neural network model, including: Initialize the population and encode the weights and thresholds of the BP neural network with each individual in the population; The prediction output of each individual is calculated by BP network, and the maximum static deformation S, the first-order natural frequency H1, and the mass M of the milling head shell of the individual are evaluated by multi-objective fitness function; Then, the non-dominated sorting and crowding calculation are used to classify the population and select the Pareto frontier solution; New populations are generated through multi-point crossover and mutation operations, and an elite retention strategy is introduced to maintain high-quality solutions. The selection pressure parameters are dynamically adjusted during the iteration process to balance global search and local development, and finally the Pareto optimal solution set is output to achieve multi-objective optimization.

7. A milling head structure design device, characterized in that: The device comprises: An acquisition unit is configured to acquire parameters of a plurality of milling head structures, and construct a design parameter data set of the milling head structure to be designed according to the parameters of the plurality of milling head structures; Optimization unit: optimizes the hyperparameters of the BP neural network model using the Beluga optimization algorithm, and trains the optimized BP neural network model using the design parameter data set to obtain a BWO-BP neural network model; Prediction unit: inputs the design parameter data set into the BWO-BP neural network model to output prediction results of the maximum static deformation S, the first-order natural frequency H1, and the mass M of the milling head shell corresponding to the design parameters; Output unit: The design parameters in the BWO-BP neural network model are adjusted through a multi-objective genetic algorithm to obtain an optimal design parameter set of the milling head structure with the minimum maximum static deformation S, the maximum first-order natural frequency H1, and the minimum mass M of the milling head shell, and the optimal design parameter set is output as the design parameters of the milling head structure to be designed.

8. An electronic device, characterized in that: include: processor; a memory for storing processor-executable instructions; The processor implements the steps of the method according to any one of claims 1 to 6 by running the executable instructions.

9. A computer-readable storage medium having computer instructions stored thereon, characterized in that: When the instruction is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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