Aluminum alloy milling parameter optimization method based on improved Bayesian neural network

Abstract

The invention relates to the technical field of numerical control machining process optimization, in particular to an aluminum alloy milling parameter optimization method based on an improved Bayesian neural network, and the method comprises the following steps: S1, building an aluminum alloy thin-wall part milling finite element model based on a Johnson-Cook constitutive model; s2, carrying out a single-factor milling experiment, and verifying the reliability of the finite element model; s3, constructing a Bayesian neural network model fused with a multi-head attention mechanism, and establishing a mapping relation between process parameters and surface quality indexes; s4, establishing a multi-objective optimization model based on the MHA-BNN prediction model, and solving by adopting an NSGA-II algorithm; and S5, performing experimental verification and analysis on an optimization result. According to the method, a multi-head attention mechanism is introduced into a Bayesian neural network, and a milled surface roughness and residual stress probability prediction model is constructed; and a multi-objective optimization framework fusing physical constraint and data driving is established, collaborative optimization of the surface roughness, the residual stress and the processing efficiency is realized, and meanwhile, the problem that a traditional deep learning method is insufficient in prediction precision under a small sample condition is solved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of numerical control machining process optimization, and particularly relates to an aluminum alloy thin-walled part milling parameter multi-objective optimization method based on a multi-head attention Bayesian neural network (MHA-BNN). BACKGROUND

[0002] Aluminum alloy is widely used in the fields of aerospace and automobile manufacturing due to its excellent specific strength, corrosion resistance and lightweight characteristics. However, its low stiffness and high thermal expansion coefficient lead to elastic deformation and thermal-mechanical coupling effects in the milling process, causing problems such as difficulty in controlling surface roughness, residual stress concentration and low machining efficiency. Traditional optimization methods such as Taguchi method and TOPSIS method rely on linear assumptions and empirical models, and are difficult to represent the complex nonlinear relationship between milling parameters and multiple objectives. While deep learning-based optimization methods have made breakthroughs in prediction accuracy, they are limited by the lack of experimental data in industrial scenarios and the lack of quantification of model uncertainty.

[0003] How to determine better process parameter combinations to achieve a balance between objectives is of great practical application in improving part quality, reducing production costs, enhancing part performance and functionality, and increasing product added value. Pankaj et al. optimized the milling parameters of EN19 steel by combining the Taguchi method with the TOPSIS method, and determined the optimal parameter combination through variance analysis. Gopal et al. used grey relational analysis (GRA) and the technique for order preference by similarity to an ideal solution (TOPSIS) to optimize the milling process of magnesium-based composite materials with hard alloy tools. Shun established a multi-objective optimization model for numerical control milling by considering various complex constraints through theoretical analysis and analytical method, with machining efficiency, machining energy consumption and machining quality as optimization objectives, achieving multi-objective parameter optimization of the milling process. Although the above methods have made certain progress, traditional optimization methods based on analytical models and empirical regression still have the problem of insufficient modeling accuracy. With the rapid development of data-driven manufacturing concepts and technologies, advanced technologies such as deep learning are used to achieve a lean and stable manufacturing process, providing a new approach to process optimization. Ghosh et al. used a Bayesian neural network combined with a beetle antenna search algorithm to significantly improve the optimization accuracy of aluminum alloy milling parameters. Yang Y et al. proposed a HSS-MFM hybrid modeling method combined with an improved OBL-NSGA-II algorithm, successfully achieving global optimization of complex surface milling parameters. Lin et al. based on a radial basis function neural network-multi-objective particle swarm optimization algorithm (RBFNN-MOPSO) optimized the cutting parameters of titanium alloy by comprehensively considering energy saving and tool wear.

[0004] Although significant progress has been made in constructing neural network prediction models, data-driven deep learning models require large amounts of data, while milling experiments themselves are costly and time-consuming. Therefore, how to construct deep learning prediction models suitable for small sample data has become a key problem that urgently needs to be solved in the field of milling parameter optimization. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a multi-objective optimization method for milling parameters of thin-walled aluminum alloy parts based on an improved Bayesian neural network. First, a milling simulation model of the thin-walled structure is constructed using finite element theory. Based on the effective milling simulation data obtained from the finite element model, a Bayesian neural network with a multi-head attention mechanism (MHA-BNN) is used to model the nonlinear mapping relationship between milling input parameters and multi-objective performance responses. Variational inference and Monte Carlo sampling mechanisms are introduced to express the uncertainty of the model output, and an attention mechanism is used to enhance the weighted interaction between input features. The parameters of the attention mechanism are introduced into probability distribution modeling. Furthermore, a multi-objective optimization framework integrating a data-driven model and a physical experience model is constructed based on the MHA-BNN prediction model. An NSGA-II optimization strategy with an uncertainty-enhanced multi-objective fitness function as its core is proposed to obtain a stable and uniformly distributed Pareto optimal solution set, providing data support and theoretical basis for the subsequent high-performance intelligent machining process design of thin-walled aluminum alloy parts.

[0006] To achieve the above-mentioned technical objectives and effects, the present invention is implemented through the following technical solution:

[0007] The method for optimizing aluminum alloy milling parameters based on an improved Bayesian neural network includes the following steps:

[0008] S1: Based on the Johnson-Cook (JC) constitutive model, a finite element model for milling thin-walled aluminum alloy 6061-T6 parts was constructed using ABAQUS;

[0009] S2: Design and conduct single-factor milling experiments to verify the effectiveness of the finite element model under typical working conditions;

[0010] S3: Construct a Bayesian neural network prediction model that integrates a multi-head attention mechanism to obtain the nonlinear mapping relationship between milling process parameters and surface roughness and residual stress;

[0011] S4: Based on the trained MHA-BNN prediction model, establish a multi-objective optimization model that integrates data-driven methods and processing physical constraints, and solve it using the NSGA-II optimization algorithm;

[0012] S5: Analyze and verify the results of the multi-objective optimization of milling parameters obtained in S4.

[0013] Furthermore, step S1 specifically includes: importing the three-dimensional models of the workpiece and tool created by Soilidworks into ABAQUS, using a thermo-coupled element (C3D8T) with a unit size of 0.15mm to locally refine the mesh in the material cutting area, and using C3D4T tetrahedral elements with a mesh size of 0.5mm to divide the tool.

[0014] Based on the JC constitutive parameters of aluminum alloy 6061-T6, the material properties of the workpiece and tool, such as density, failure parameters, and elastic modulus, are set through the property module of ABAQUS.

[0015] In the explicit dynamic analysis, in order to suppress the non-physical oscillation phenomenon caused by low-order element distortion, the mean strain formulation method is adopted to enhance the hourglass mode control effect, and combined with the enhanced hourglass control algorithm to improve the overall simulation stability; the element distortion is controlled by setting a distortion tolerance ratio of 0.1, and the element deletion function is enabled to remove elements that have suffered severe damage.

[0016] Furthermore, step S2 specifically includes:

[0017] Based on the processing experience parameter range and the actual performance of the machine tool, a single-factor variable milling experiment was designed to verify the reliability of the established finite element simulation model for milling thin-walled aluminum alloy parts.

[0018] The experiment was conducted on a VMC850 three-axis vertical machining center. The workpiece material was 6161-T6 aluminum alloy, consistent with the simulation model. The cutting tool was a TiSiN-coated solid carbide end mill. Surface roughness was measured using a Mitutoyo SJ-410 roughness measuring instrument, and residual stress was measured using a Stress Technologies XL-640 X-ray stress analyzer. Residual stress on the machined surface was non-destructively detected based on the principle of X-ray diffraction. All other machining and boundary condition settings were consistent with the simulation model to ensure comparability between the experiment and the numerical simulation.

[0019] Furthermore, step S3 specifically includes:

[0020] In traditional BNNs, the network weight parameters θ are modeled as random variables, and their posterior distribution p(θ|Δ) is learned through Bayesian inference, where Δ is the training dataset. Based on variational inference, a variational distribution q is introduced. φ(θ) approximates the true posterior and is optimized by maximizing the lower bound of evidence (ELBO):

[0021]

[0022] Where p(θ) is the prior distribution (such as Gaussian distribution), and KL is the KL divergence.

[0023] The core idea of ​​combining Multi-Head Attention (MHA) with Bayesian Neural Networks (BNNs) is to introduce probability distribution modeling into the parameters of the attention mechanism. The parameter formula of the attention mechanism is ( W i V and fusion matrix W O Each is assigned a probability distribution. Taking the query projection matrix of the i-th attention head as an example:

[0024]

[0025] Similarly, other projection matrices W i K W i V and W O All follow a Gaussian distribution, and their mean and variance are learnable variational parameters.

[0026] Input feature X is used to generate query, key, and value vectors through probabilistic projection:

[0027] Q i =XW i Q ,K i =XW i K V i =XW i V (W i Q W i K W i V ~q φ (3)

[0028] The attention output of each head is:

[0029]

[0030] The final output is obtained through the probabilistic fusion matrix W. O get:

[0031] MultiHead(Q,K,V)=Concat(head1,...,head h W OW O ~N(μ) O , σ O (5) The overall prediction output y of MHA-BNN can be expressed as:

[0032] p(y|X,D)=∫p(y|X,θ)q φ (θ)dθ(6)

[0033] Where θ contains all attention head parameters and BNN weights. In actual calculations, it is approximated using Monte Carlo sampling:

[0034]

[0035] S represents the number of samples. This represents the forward propagation result of the s-th sample.

[0036] The training objective of MHA-BNN is to maximize the following ELBO:

[0037]

[0038] Furthermore, step S4 specifically includes:

[0039] Based on the trained MHA-BNN prediction model, a multi-objective optimization framework integrating a data-driven model and a physical experience model is proposed. The main considerations are the CNC milling machine spindle speed *n* and the cutting width *a*. e Feed rate v f and cutting depth a p As design variables, and with process parameters constrained within allowable ranges, the objective functions for surface roughness and residual stress are further defined using the output mean and confidence interval of the MHA-BNN prediction model. The objective function for optimizing material removal rate adopts an empirical model. Considering tool life, cutting force constraints, and chatter stability constraints, a multi-objective optimization framework is constructed as follows:

[0040] Minimize:F(U)=(minf1(x),minf2(x),minf3(x))

[0041] U=(n,v c ,a e ,a p ) T

[0042]

[0043] The above optimization model is solved using the NSGA-II evolutionary algorithm. The trained MHA-BNN prediction model is then used as the fitness function of the NSGA-II algorithm to obtain the Pareto front solution set.

[0044] Furthermore, step S5 specifically includes:

[0045] The Pareto front solution set obtained using the NSGA-II algorithm was analyzed. Considering the typical working conditions of thin-walled aluminum alloy parts and the importance of different optimization objectives, several representative non-dominated solutions were selected from the solution set. The selected parameter combinations were then applied to actual milling experiments to verify the applicability of the multi-objective optimization method constructed based on the MHA-BNN prediction model and the NSGA-II optimization algorithm in actual machining. The balance characteristics of different parameter combinations among surface quality, residual stress, and machining efficiency were analyzed, ultimately achieving experimental verification of the optimization results.

[0046] The beneficial effects of this invention are:

[0047] This invention addresses the problems of insufficient model accuracy, high experimental costs, and poor prediction performance under small sample conditions in traditional milling parameter optimization methods. It proposes a multi-objective optimization method that integrates a Bayesian neural network with a multi-head attention mechanism and a non-dominated sorting genetic algorithm, offering the following advantages:

[0048] First, this invention enhances the ability of Bayesian neural networks to recognize high-dimensional nonlinear features by introducing a multi-head attention mechanism. This enables more effective capture of the complex coupling relationships between process parameters such as spindle speed, feed rate, depth of cut, and width of cut, overcoming the problem of overfitting in traditional deep learning models under small sample conditions. The uncertainty of the prediction results is explicitly output through probabilistic modeling, and the prediction interval is quantified by combining variational inference and Monte Carlo sampling. This ensures high accuracy in the prediction results while quantifying the uncertainty.

[0049] Secondly, based on the predictive model, this invention constructs a multi-objective optimization framework that combines a data-driven model with machining physical constraints. It considers three key optimization objectives: surface roughness, residual stress, and machining efficiency. Furthermore, it introduces cutting force constraints, chatter stability constraints, and tool life constraints to make the optimization results more in line with the safety and feasibility requirements of the actual machining environment.

[0050] Finally, based on the constructed MHA-BNN prediction model, the NSGA-II optimization algorithm was used to solve the Pareto front solution set in the constrained design space. Parameter combinations with practical engineering significance were then selected, and the method was validated through actual milling experiments, achieving closed-loop verification of the multi-objective optimization method for milling parameters. This method not only provides a high-precision, interpretable parameter optimization scheme for machining thin-walled aluminum alloy parts but also possesses good versatility, extending to multi-objective process optimization tasks for other difficult-to-machine metal materials. It has significant engineering application value and potential for widespread application.

[0051] Of course, any system or product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0052] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 A finite element model for milling simulation of thin-walled aluminum alloy parts, built based on ABAQUS;

[0054] Figure 2 A schematic diagram of the overall configuration for the milling experiment;

[0055] Figure 3 The following is a comparison of experimental and simulation results for single-factor milling: (a) Influence of spindle speed on surface roughness and residual stress; (b) Influence of feed rate on surface roughness and residual stress; (c) Influence of milling width on surface roughness and residual stress; (d) Influence of milling depth on surface roughness and residual stress.

[0056] Figure 4 A schematic diagram of the multi-head attention mechanism;

[0057] Figure 5 Flowchart for constructing the MHA-BNN integrated prediction model;

[0058] Figure 6 The training and validation loss curves for MHA-BNN and BNN are shown.

[0059] Figure 7 A comparison chart of various neural network prediction metrics;

[0060] Figure 8 Plots showing the predicted mean and 95% confidence intervals for MHA-BNN and BNN;

[0061] Figure 9 MHA-BNN-NSGA-II hybrid optimization framework diagram;

[0062] Figure 10 The optimal Pareto solution set graph; Detailed Implementation

[0063] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] Example 1

[0065] This embodiment describes a method for optimizing aluminum alloy milling parameters based on an improved Bayesian neural network, including:

[0066] like Figure 1 As shown, a 3D model of an aluminum alloy thin-walled structural component and cutting tool, created using SolidWorks, is imported into the ABAQUS simulation platform. The workpiece material is defined as an elasto-plastic model, and thermo-coupled elements (C3D8T) are used to describe the thermo-elasto-plastic behavior of the material during milling. To balance computational efficiency and accuracy, the cutting area is locally meshed with an element size of 0.15 mm, while the non-cutting area uses a coarse mesh. The cutting tool is a carbide quad-helical end mill, meshed using C3D4T tetrahedral elements with a mesh size of 0.5 mm. The cutting tool is considered a rigid body, and the effect of tool wear is not considered. The tool-workpiece contact interface adopts the Coulomb friction model with a friction coefficient μ = 0.2.

[0067] The Johnson-Cook model was used for the constitutive model of 6061-T6 aluminum alloy. Material properties, including density, elastic modulus, Poisson's ratio, strain rate sensitivity coefficient, and failure parameters, were set using the ABAQUS property module. The average strain method was used to enhance the hourglass mode control effect, and an enhanced hourglass control algorithm was combined to improve overall simulation stability. Element distortion was controlled by setting a distortion tolerance ratio of 0.1, and the element deletion function was enabled to remove severely damaged elements. A fixed constraint was applied to the bottom of the workpiece (U1 = U2 = U3 = 0) to simulate actual clamping conditions.

[0068] To verify the reliability of the finite element model, a single-factor variable milling experiment was designed based on the processing experience parameter range and the actual performance of the machine tool, as shown in Table 1, to verify the reliability of the established finite element simulation model for milling thin-walled aluminum alloy parts.

[0069] Table 1. Parameter values ​​of single-factor experiments

[0070]

[0071] like Figure 2As shown, the experiment was conducted on a VMC850 three-axis vertical machining center. The workpiece material was 6161-T6 aluminum alloy, consistent with the simulation model. The cutting tool was a TiSiN-coated solid carbide end mill. Surface roughness was measured using a Mitutoyo SJ-410 roughness measuring instrument, and residual stress was measured using a Stress Technologies XL-640 X-ray stress analyzer. Residual stress on the machined surface was non-destructively detected based on the principle of X-ray diffraction. All other machining and boundary condition settings were consistent with the simulation model to ensure the comparability between the experiment and the numerical simulation.

[0072] Figure 3 This study compares simulated and experimental values ​​for two key performance indicators, surface roughness and residual stress, using single-factor experiments. Overall, the experimental data and simulation results show good consistency, but some deviations remain. The residual stress error on the machined surface ranges from 5.25% to 8.58%, while the maximum error for surface roughness is 5.99%. Within the given parameter range, a clear linear correlation exists between spindle speed and surface quality indicators, while parameters such as feed rate and depth of cut exhibit significant nonlinear coupling characteristics with surface properties. In general, the simulation results and experimental data show consistent trends, and the errors are within acceptable limits (≤10%), indicating that the finite element model has high accuracy and reliability in predicting surface roughness and residual stress during the milling of thin-walled aluminum alloy parts. This provides a highly reliable data source for subsequent data-driven modeling and optimization.

[0073] Example 2

[0074] Traditional BNNs struggle to fully capture the complex nonlinear relationships between high-dimensional, strongly coupled process parameters. For example... Figure 4 As shown, leveraging the dynamic feature selection and high-dimensional interactive modeling advantages of MHA, each attention head independently learns the importance of different process parameters, strengthening the identification of key parameters such as spindle speed and feed rate. This further reduces the overfitting risk of the BNN network model under small sample data, achieving high-precision milling prediction modeling under small sample conditions. The hybrid model of the multi-head attention mechanism Bayesian neural network (MHA-BNN) is shown below. Figure 5 As shown, it consists of three parts: a Bayesian probabilistic coding layer, a multi-head attention feature interaction module, and an uncertainty quantization module.

[0075] Based on the original 17 sets of single-factor simulation data, Latin hypercube sampling (LHS) was used to generate 143 parameter combinations, covering the entire design space. At the same time, batch normalization was performed on the input data to ensure that all input data were roughly within the same value range before being used for training and validation of the MHA-BNN model.

[0076] 160 sets of milling simulation data were divided into training, validation, and test sets in a 6:1:1 ratio. In the Bayesian probabilistic coding layer, each input dimension was probabilistically mapped through a Gaussian-parameterized linear layer. After layer normalization and nonlinear transformation using the GELU activation function, a Dropout mechanism with a probability of 0.1 was introduced to suppress overfitting. Subsequently, four independent attention heads were set in the Bayesian multi-head attention layer to capture the coupling relationship of multidimensional machining parameters. The uncertainty quantification module consisted of a two-level Bayesian fully connected network. The first layer expanded the features to 128 dimensions, and the second layer projected them back to 64 dimensions to maintain dimensionality consistency. Finally, probabilistic inference was achieved through a Monte Carlo Dropout strategy.

[0077] The training and validation loss curves after running are as follows: Figure 6 As shown, the two models exhibit different convergence characteristics and generalization abilities. The training and validation losses of the MHA-BNN model are both relatively high in the early stages of training, but decrease rapidly and stabilize with increasing training iterations, converging to around 0.4 after 132 iterations. This indicates good generalization ability without significant overfitting or underfitting. In contrast, while the training loss of the BNN shows a decreasing trend, it stagnates after converging to around 1.4 after 80 iterations. The validation loss exhibits fluctuating rebounds in the later stages of training, reflecting insufficient efficiency in learning complex features and a certain risk of overfitting. In conclusion, the MHA-BNN model outperforms the BNN in training stability and generalization performance, demonstrating that introducing a multi-head attention mechanism has certain advantages in improving the generalization ability of Bayesian neural networks.

[0078] To further validate the performance of the proposed model in real-world prediction tasks, a comparative analysis was conducted on several typical network models, including Radial Basis Function Neural Networks (RBFNN), Standard Backpropagation Neural Networks (BPNN), and Bayesian Neural Networks (BNN). To ensure fairness in the comparison, the same dataset partitioning strategy and training parameter configuration were used uniformly. Figure 7 As shown, the performance differences of different models in the surface roughness and residual stress prediction tasks are quite significant. The comprehensive comparison results show that MHA-BNN is superior to RBFNN, BPNN and traditional BNN in terms of prediction accuracy, result stability and uncertainty quantification ability, and is more suitable for multi-objective process parameter prediction under small sample conditions.

[0079] The prediction results of MHA-BNN and BNN are as follows: Figure 8As shown, the shaded area represents the 95% confidence interval (±1.96 standard deviations), used to characterize the distribution characteristics of the model's predictions. In the Ra prediction task, both models' predictions fit the experimental data well. However, in the more complex Rs prediction task, the BNN's predictions exhibited greater fluctuations, with significantly lower prediction accuracy and stability compared to the MHA-BNN. Table 2 shows the differences between MHA-BNN and BNN in terms of prediction accuracy and fitting ability. Overall, the relatively narrow confidence interval of the MHA-BNN reflects the model's higher reliability in its predictions, exhibiting better prediction accuracy and lower prediction uncertainty.

[0080] Table 2 Comparison of prediction performance between MHA-BNN and BNN models

[0081]

[0082] Example 3

[0083] To further achieve a balance between surface quality, residual stress, and machining efficiency in the milling parameters of thin-walled aluminum alloy parts, a multi-objective optimization framework integrating a data-driven model and a physical experience model was constructed based on the MHA-BNN prediction model trained in Example 2 for multi-objective optimization.

[0084] Using the spindle speed n and cutting width a of the CNC milling machine e Feed rate v f and cutting depth a p As design variables, the mean surface roughness and confidence interval width, the mean residual stress and confidence interval width, and the empirical model of material removal rate output by the trained MHA-BNN model are used as optimization objectives. A multi-objective optimization model is constructed, taking into account relevant process parameter constraints. For example... Figure 9 The diagram shows the NSGA-II hybrid optimization framework. The specific parameters are configured as follows: the initial population size is 100, the maximum number of iterations is set to 300 generations; the crossover operation uses the simulated binary crossover (SBX) algorithm, with a crossover probability of 0.9 and a distribution index of 15; multinomial mutation is adopted, with the mutation probability set according to the dimension of the decision variable and the distribution index set to 20.

[0085] The optimal Pareto solution set obtained is as follows Figure 10 As shown, the Pareto front exhibits a significant hierarchical topological structure from the perspective of the three-dimensional solution set distribution, indicating that the optimization algorithm achieves an effective balance between different objectives. When pursuing a higher material removal rate, roughness and residual stress increase simultaneously, which is consistent with the basic laws of milling. Therefore, processing efficiency cannot be significantly improved while ensuring a good surface quality. However, in practical industrial applications, it is usually necessary to maximize production efficiency while meeting surface quality requirements.

[0086] Based on the typical working conditions of thin-walled parts and the importance of each optimization objective, and according to the uniformity of Pareto solutions in the target space, four typical solutions with practical engineering significance were selected from 97 non-dominated solutions. Milling experiments were conducted to verify the selected parameter combinations, and the experimental results are shown in Table 7. Solutions A and B are applicable to precision machining, with the former focusing on surface quality optimization and the latter on residual stress control. Solution C is suitable for high-efficiency manufacturing scenarios, while solution D represents a balance between quality and efficiency. Solution E is the milling parameter combination determined based on machining experience, i.e., the milling parameter combination to be optimized.

[0087] Table 3 Optimization and Experimental Verification Results

[0088]

[0089] Analysis of the validation experimental data in Table 3 shows that the optimized machining parameters significantly improved various indicators. Parameter group A performed best in surface roughness, reducing it by 68.75% compared to parameter group E. Parameter group B, by further reducing the spindle speed and appropriately increasing the cutting width, achieved optimal residual stress, reducing it by 17.3% compared to group E. Due to the conservative feed rate, the material removal rate of both parameter groups was relatively low. Parameter group C significantly improved machining efficiency by 36.9% compared to parameter group E, and also outperformed parameter group E to varying degrees in terms of surface roughness and residual stress control. Solution D achieved a good balance between quality and efficiency, reducing surface roughness by 17.6%, residual stress by 23.1%, and improving machining efficiency by 19.5%.

[0090] In summary, this invention proposes a multi-objective optimization method for milling parameters of thin-walled aluminum alloy parts based on MHA-BNN and NSGA-II, achieving an effective balance between surface roughness, residual stress, and machining efficiency under small sample conditions. High-precision finite element simulation replaces some experimental measurements, providing reliable data for subsequent modeling. The introduction of a multi-head attention mechanism significantly improves the prediction accuracy and stability of the Bayesian neural network. By integrating the MHA-BNN prediction model and the NSGA-II non-dominated sorting algorithm, a multi-objective optimization model is constructed, and a multi-objective Pareto solution search is conducted. This method, through the combination of model prediction and experimental verification, ensures the reliability of the parameter optimization scheme in engineering applications, avoiding the high cost and low efficiency problems of traditional experimental or empirical optimization methods. It provides a scientific decision-making basis for the machining of typical thin-walled parts in the aerospace field and has the potential to be extended to the manufacturing processes of other metallic materials and complex structural parts, demonstrating significant engineering applicability and promotional value.

[0091] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A multi-objective optimization method for milling parameters of thin-walled aluminum alloy parts based on an improved Bayesian neural network, characterized in that, Includes the following steps: S1: Based on the Johnson-Cook (JC) constitutive model, a finite element model for milling thin-walled aluminum alloy 6061-T6 parts was constructed using ABAQUS; S2: Design and conduct single-factor milling experiments to verify the effectiveness of the finite element model under typical working conditions; S3: Construct a Bayesian neural network prediction model that integrates a multi-head attention mechanism to obtain the nonlinear mapping relationship between milling process parameters and surface roughness and residual stress; S4: Based on the MHA-BNN prediction model trained in S3, a multi-objective optimization model integrating data-driven methods and processing physical constraints is established and solved using the NSGA-II optimization algorithm; S5: Experimentally verify and analyze the multi-objective optimization results of the milling parameters obtained in S4.

2. The multi-objective optimization method for milling parameters of thin-walled aluminum alloy parts based on an improved Bayesian neural network as described in claim 1, characterized in that, The milling simulation model in S1 is as follows: the three-dimensional models of the workpiece and the tool created using Solidworks are imported into ABAQUS, and the thermo-coupled element (C3D8T) is used to locally refine the mesh in the material cutting area, with an element size of 0.15mm. Based on JC constitutive parameters, the material properties of the workpiece and tool, including density, elastic modulus, Poisson's ratio and failure parameters, are set through the property module of ABAQUS. In explicit dynamic analysis, the average strain method is used to enhance the control effect of the hourglass mode, and the simulation stability is improved by combining the enhanced hourglass control algorithm. Cell distortion is controlled by setting a distortion tolerance ratio of 0.1, and cell deletion is enabled to remove severely damaged cells.

3. The multi-objective optimization method for milling parameters of thin-walled aluminum alloy parts based on an improved Bayesian neural network as described in claim 1, characterized in that, The experimental scheme in S2: Based on the processing experience parameter range and the actual performance of the machine tool, a single-factor variable milling experiment was designed to verify the reliability of the finite element model. The experiment was carried out on a VMC850 three-axis vertical machining center. The workpiece material was 6161-T6 aluminum alloy, and the cutting tool was a TiSiN coated solid carbide end mill. Surface roughness was measured using a Mitutoyo SJ-410 roughness measuring instrument, and residual stress was measured using a non-destructive X-ray stress analyzer.

4. The multi-objective optimization method for milling parameters of thin-walled aluminum alloy parts based on an improved Bayesian neural network as described in claim 1, characterized in that: The Bayesian neural network prediction model that incorporates a multi-head attention mechanism constructed in step S3: The core idea of ​​combining Multi-Head Attention (MHA) with Bayesian Neural Networks (BNNs) is to introduce probability distribution modeling into the parameters of the attention mechanism. The parameter formula of the attention mechanism is ( and fusion matrix W O Each is assigned a probability distribution. Taking the query projection matrix of the i-th attention head as an example: The final output is obtained through the probabilistic fusion matrix W. O get: MultiHead(Q,K,V)=Concat(head1,...,head h )W O ,W O ~N(μ O ,σ O ) (2) The overall prediction output y of MHA-BNN can be expressed as: p(y|X,D)=∫p(y|X,θ)q φ (θ)dθ (3) The training objective of MHA-BNN is to maximize the following ELBO:

5. The multi-objective optimization method for milling parameters of thin-walled aluminum alloy parts based on an improved Bayesian neural network as described in claim 1, characterized in that: The multi-objective optimization framework constructed in step S4, which combines the hybrid data-driven model and the physical experience model, is as follows: Minimize:F(U)=(minf1(x),minf2(x),minf3(x)) U=(n,v c ,a e ,a p ) T Based on the trained MHA-BNN prediction model, a multi-objective optimization framework integrating a data-driven model and a physical experience model is proposed. The main considerations are the CNC milling machine spindle speed *n* and the cutting width *a*. e Feed rate v f and cutting depth a p As design variables, and with process parameters limited to allowable ranges, the objective functions for surface roughness and residual stress are further defined by the output mean and confidence interval of the MHA-BNN prediction model. The objective function for optimizing material removal rate adopts an empirical model, while considering tool life, cutting force constraints, and chatter stability constraints.

6. The multi-objective optimization method for milling parameters of thin-walled aluminum alloy parts based on an improved Bayesian neural network as described in claim 1, characterized in that: The optimization result analysis specifically includes: The Pareto front solution set obtained using the NSGA-II algorithm was analyzed. Considering the typical working conditions of thin-walled aluminum alloy parts and the importance of different optimization objectives, several representative non-dominated solutions were selected from the solution set. The selected parameter combinations were then applied to actual milling experiments to verify the applicability of the multi-objective optimization method constructed based on the MHA-BNN prediction model and the NSGA-II optimization algorithm in actual machining. The balance characteristics of different parameter combinations among surface quality, residual stress, and machining efficiency were analyzed, ultimately achieving experimental verification of the optimization results.

7. The application of the method as described in any one of claims 1-6 in the process of optimizing milling parameters for thin-walled aluminum alloy parts.

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