Aluminum-based material rolling process optimization method based on response surface method and machine learning

Abstract

The invention discloses an aluminum-based material rolling process optimization method based on a response surface method and machine learning, which comprises the following steps: collecting related data of an aluminum-based material rolling process, and establishing a rolling process database; determining key rolling process parameters influencing the performance of the aluminum-based material based on the database; a mathematical model used for describing the key rolling process parameters and the relation between the interaction of the key rolling process parameters and the aluminum-based material performance indexes is established, and prediction results of the aluminum-based material performance indexes under different key rolling process parameter combinations are calculated according to the mathematical model. Aluminum-based materials with performance indexes meeting preset requirements and key rolling process parameter combinations corresponding to the aluminum-based materials are predicted to serve as a preliminary optimization result data set; and constructing a back propagation artificial neural network model optimized by a genetic algorithm to predict aluminum-based material performance indexes corresponding to different key rolling process parameter combinations, and screening out an optimal key rolling process parameter combination and an aluminum-based material performance index corresponding to the optimal key rolling process parameter combination from the aluminum-based material performance indexes. According to the method, the quality of the aluminum-based material is remarkably improved through the proposed collaborative optimization strategy.

Description

Technical Field

[0001] This invention relates to the field of rolling process technology, and in particular to an optimization method for rolling processes of aluminum-based materials based on response surface methodology and machine learning. Background Technology

[0002] Aluminum-based materials are a class of metallic materials made primarily of aluminum through alloying or composite with other materials. They mainly include wrought aluminum alloys, cast aluminum alloys, and aluminum-based composite materials. With their low density, high specific strength, excellent corrosion resistance, electrical and thermal conductivity, and good recyclability, aluminum-based materials have become indispensable basic materials in aerospace, new energy vehicles, rail transportation, electronics and information technology, and construction.

[0003] In industrial production, processes such as rolling, heat treatment, and surface treatment have a crucial impact on the microstructure and properties of aluminum-based materials. Rolling, in particular, involves hundreds of parameters, including uncoiling tension, rolling pressure, annealing temperature, and coiling tension. These parameters exhibit complex linear and nonlinear relationships, directly or indirectly determining the material's mechanical properties, surface quality, and microscopic defects. However, due to the interactions between process parameters, traditional aluminum-based materials still face certain performance bottlenecks under extreme service conditions. For example, balancing high strength and high ductility is difficult; achieving lightweight often involves trade-offs between corrosion resistance and conductivity; and in precision applications such as battery aluminum foil, pinhole defects, thickness uniformity, and surface quality remain significant limiting factors.

[0004] Therefore, identifying and balancing key parameters within a complex process parameter space has become one of the core methods for improving the overall performance of aluminum-based materials. The rolling process involves hundreds of process parameters, and a comprehensive study of all parameters would consume a significant amount of manpower, material resources, and financial resources. Therefore, how to identify the key factors that significantly affect the target performance and analyze their influence patterns based on sample data is a pressing technical problem that needs to be solved in the production of aluminum-based materials. Summary of the Invention

[0005] To address the shortcomings of existing technologies, at least one embodiment of the present invention provides a method for optimizing the rolling process of aluminum-based materials based on response surface methodology and machine learning, and in particular, a collaborative optimization strategy for the rolling process of aluminum-based materials based on response surface methodology and machine learning.

[0006] At least one embodiment of the present invention provides a method for optimizing the rolling process of aluminum-based materials based on response surface methodology and machine learning, characterized in that the method includes the following steps:

[0007] Collect relevant data on aluminum-based material rolling processes and establish a rolling process database;

[0008] Based on the database, key rolling process parameters affecting the properties of aluminum-based materials were determined.

[0009] A mathematical model is established to describe the relationship between key rolling process parameters and their interactions and the performance indicators of aluminum-based materials. Based on the mathematical model, the predicted performance indicators of aluminum-based materials under different combinations of key rolling process parameters are calculated. From this, aluminum-based materials with performance indicators that meet the preset requirements and the corresponding combinations of key rolling process parameters are predicted, which serve as the preliminary optimization result dataset.

[0010] Based on the preliminary optimization result dataset, a backpropagation artificial neural network model optimized by a genetic algorithm is constructed to predict the performance indicators of aluminum-based materials corresponding to different combinations of key rolling process parameters, and the optimal combination of key rolling process parameters and the corresponding performance indicators of aluminum-based materials are selected from it.

[0011] In embodiments of the present invention, key rolling process parameters affecting the properties of aluminum-based materials are determined based on the database, including:

[0012] Dimensionless processing is performed on different rolling process parameters;

[0013] Based on the dimensionless processing results, Plackett-Burman design in response surface methodology was used to separate the main effects and quantify their statistical significance with the minimum number of experiments through a partially orthogonal experimental structure. Pareto chart analysis was then used to screen out the key rolling process parameters that affect the performance of aluminum-based materials.

[0014] The steepest ramp test was used to approximate the optimal range of the key rolling process parameters, and the influence of the key rolling process parameters and their interactions on the performance indicators of aluminum-based materials was analyzed in combination with Box-Behnken design.

[0015] In embodiments of the present invention, key rolling process parameters affecting the properties of aluminum-based materials are screened out through Pareto chart analysis, including:

[0016] The Pareto chart provides an intuitive analysis of the individual and interactive effects of various factors on the properties of aluminum-based materials, ranking them accordingly.

[0017] Calculate the t-value, effect value, standard error, and sensitivity coefficient in the Pareto chart to determine the critical rolling process parameters.

[0018] In embodiments of the present invention, a mathematical model is established to describe the relationship between key rolling process parameters and their interactions and the properties of aluminum-based materials. Based on the mathematical model, prediction results of aluminum-based material performance indicators under different combinations of key rolling process parameters are calculated. From this, aluminum-based materials with performance indicators meeting preset requirements and their corresponding key rolling process parameter combinations are predicted, forming a preliminary optimization result dataset, including:

[0019] The Box-Behnken design based on response surface methodology was used to generate an experimental matrix, which was then used to investigate the interaction effects of key rolling process parameters on the properties of aluminum-based materials.

[0020] A mathematical model was established using regression analysis to describe the influence of key rolling process parameters and their interactions on the properties of aluminum-based materials. The key rolling process parameters of the mathematical model were evaluated using analysis of variance.

[0021] The mathematical model is used to calculate the predicted performance indicators of aluminum-based materials under different combinations of key rolling process parameters.

[0022] The influence of different combinations of key rolling process parameters on the performance indicators of aluminum-based materials was analyzed by using 3D surface plots and contour plots. The aluminum-based materials that meet the preset requirements and their corresponding combinations of key rolling process parameters were identified as preliminary optimization results.

[0023] In embodiments of the present invention, a mathematical model is established using regression analysis to describe the influence of key rolling process parameters and their interactions on the properties of aluminum-based materials, including:

[0024] A multivariate quadratic regression equation model was established to describe the influence of key rolling process parameters and their interactions on the properties of aluminum-based materials.

[0025] The regression coefficients of the multivariate quadratic polynomial regression equation model were determined using the least squares fitting method.

[0026] The established model was evaluated as a whole through analysis of variance, and the influence weights and patterns of the individual and interactive effects of each key rolling process parameter on the performance indicators of aluminum-based materials were further analyzed.

[0027] In embodiments of the present invention, the established model is evaluated holistically through analysis of variance, and the influence weights and patterns of the individual and interactive effects of each key rolling process parameter on the performance indicators of aluminum-based materials are further analyzed, including:

[0028] The performance metrics of the mathematical model are obtained through analysis of variance.

[0029] The F-value of the model is calculated to evaluate the overall performance of the model;

[0030] The p-value of the calculation model is used to evaluate the impact of single-factor and multi-factor effects on the properties of aluminum-based materials;

[0031] Calculate the coefficient of determination R of the model. 2 Adjusted coefficient of determination R 2 adj and the predictive determination coefficient R 2 pre To evaluate the predictive power of the model and to analyze and optimize the conditions for the performance of aluminum-based materials.

[0032] In an embodiment of the present invention, the backpropagation neural network optimized by the genetic algorithm is an optimized hybrid model GA-BP-ANN.

[0033] In embodiments of the present invention, constructing a backpropagation artificial neural network model optimized by a genetic algorithm includes:

[0034] The initial weights and thresholds are optimized using a genetic algorithm. After obtaining the optimal weights and thresholds, they are introduced into the BP-ANN model to construct the GA-BP-ANN optimization algorithm model.

[0035] Calculate the ideal number of neurons in the model;

[0036] Through MSE, RMSE, MAE and R 2 Analyze the performance of the model;

[0037] The model can be intuitively analyzed through the fitting effect graph;

[0038] The performance of the model can be intuitively analyzed by comparing the trend charts of training loss and validation loss with those of other models, as well as the error distribution chart.

[0039] The GA-BP-ANN model was trained using the BBD result key parameter dataset, and the RSM model and GA-BP-ANN model were validated using industrial-grade experiments.

[0040] At least one embodiment of the present invention also provides an electronic device, characterized in that it comprises:

[0041] At least one processor; and,

[0042] A memory communicatively connected to the at least one processor; wherein,

[0043] The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method as described above.

[0044] At least one embodiment of the present invention also provides a computer-readable storage medium storing a computer program, characterized in that the computer program, when executed by a processor, implements the method described above.

[0045] Compared with the prior art, the embodiment of the present invention provides an optimization method for aluminum-based material rolling process based on machine learning and response surface methodology, which has the following beneficial effects:

[0046] 1) This invention proposes an optimization method for aluminum-based material rolling processes (especially an optimization method combining response surface methodology (RSM) and machine learning), aiming to improve the production efficiency and product performance of aluminum-based materials (such as battery aluminum foil). By using Plackett-Burman design (PBD) combined with steepest ramp tests, the influence of multiple process parameters (such as rolling speed, rolling pressure, and rolling temperature) on the performance indicators of aluminum-based materials is analyzed, and a response surface model is constructed to help optimize the parameter combination. Furthermore, a genetic algorithm (GA) is used to optimize the backpropagation artificial neural network (BP-ANN) prediction model, improving the mechanical properties of aluminum-based materials and reducing quality defects such as pinhole rate and strip breakage rate.

[0047] 2) This method combines machine learning algorithms with traditional process optimization, which not only improves the mechanical properties of aluminum-based materials but also effectively reduces the defect rate in production. Through precise modeling and analysis of the interactions of multiple process parameters, key parameters in the production process can be optimized, ensuring the quality and stability of aluminum-based materials. Simultaneously, through experimental verification and model optimization, and after several rounds of prediction-experiment-feedback-prediction-experiment-feedback…, the consistency between theoretical optimization and actual production is ensured, further improving production efficiency. Attached Figure Description

[0048] One or more embodiments are illustrated by way of example with reference to the accompanying drawings, and these illustrative descriptions do not constitute a limitation on the embodiments.

[0049] Figure 1 This is a flowchart of the aluminum-based material rolling process optimization method based on machine learning and response surface methodology used in an embodiment of the present invention.

[0050] Figure 2 This is a schematic diagram of the core topology of the GA-BP-ANN model used in the embodiments of the present invention;

[0051] Figure 3 This is a Pareto chart of the rolling process parameters used in the embodiments of the present invention, where orange represents positive effects and blue represents negative effects;

[0052] Figure 4This is a schematic diagram of the RSM model prediction results analysis used in the embodiments of the present invention, wherein (a) is a comparison between the model prediction value and the experimental value, and (b) is a normal probability distribution diagram of the residuals;

[0053] Figure 5 The following are the RSM multi-parameter 3D response surfaces and contour plots used in the embodiments of the present invention, wherein (a), (b) and (c) are three-dimensional surface plots of uncoiling tension-rolling hydraulic pressure, uncoiling tension-winding tension, and winding tension-rolling hydraulic pressure, respectively; (d), (e) and (f) are their corresponding contour plots.

[0054] Figure 6 This is a schematic diagram of the optimal combination of rolling process parameters and the corresponding pinhole DPU in an embodiment of the present invention;

[0055] Figure 7 This is a schematic diagram of the iterative evolution process of the genetic algorithm used in the embodiments of the present invention;

[0056] Figure 8 This is a schematic diagram of neuron topology optimization in the GA-BP-ANN model used in an embodiment of the present invention;

[0057] Figure 9 This is a schematic diagram showing the comparison of fitting effects between the GA-BP-ANN and BP-ANN models used in embodiments of the present invention.

[0058] Figure 10 This is a schematic diagram illustrating the changing trends of training loss and validation loss of the GA-BP-ANN and BP-ANN models with the number of iterations in an embodiment of the present invention.

[0059] Figure 11 This is a schematic diagram comparing the prediction results and experimental results of the RSM and GA-BP-ANN models in an embodiment of the present invention.

[0060] Figure 12 This is a schematic diagram of the pinhole distribution obtained by detection in an embodiment of the present invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details are presented in the embodiments of the present invention to facilitate a better understanding of the invention. However, the technical solutions claimed in the present invention can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the following embodiments is for ease of description and should not constitute any limitation on the specific implementation of the present invention. The various embodiments can be combined with and referenced by each other without contradiction.

[0062] Machine learning algorithms such as neural networks can be used to effectively model the nonlinear coupling relationships between rolling parameters, thereby improving target performance. In view of this, this invention proposes a collaborative optimization strategy (GA-BP-ANN) based on response surface methodology (RSM) and genetic algorithm (GA) to optimize a backpropagation neural network. This is an integrated strategy combining parameter selection, collaborative optimization, and intelligent modeling to improve the final performance of aluminum-based materials.

[0063] To address the technical problems mentioned in the background section, this invention employs a combination of response surface methodology (RSM) and machine learning with experimental verification to study the influence of rolling process parameters on the properties of aluminum-based materials. To this end, Plackett-Burman design (PBD) is used, and Pareto charts are employed to determine the significance of each process parameter and its weight. Furthermore, steepest ramp tests are combined to approximate the optimal range of key rolling process parameters. Then, Box-Behnken design (BBD) experimental modeling is used to study the influence trend of the interaction of key process parameters on the properties of aluminum-based materials. Finally, a backpropagation artificial neural network (BP-ANN) model optimized based on a genetic algorithm (GA) is used to predict the properties of aluminum-based materials corresponding to different combinations of operating parameters. The effectiveness of the RSM prediction and the BP-ANN prediction results optimized based on the genetic algorithm are verified through industrial-scale experiments. Comparative analysis is conducted, and the optimal model and corresponding parameter combination are selected.

[0064] The implementation details of the above method are described in detail below through examples. The following content is only for the convenience of understanding the implementation details and is not necessary for implementing this solution.

[0065] Example 1

[0066] This embodiment provides a method for optimizing the rolling process of aluminum-based materials, particularly a method for optimizing the rolling process of battery aluminum foil based on response surface methodology (RSM) and machine learning. This method uses RSM and GA-BP-ANN for comparative analysis to find the optimal combination of rolling process parameters. It achieves bidirectional verification based on industrial-grade experimental research and model prediction, aiming to improve the pinhole rate and comprehensive mechanical properties of aluminum-based materials. It should be noted that although this embodiment uses the pinhole rate of battery aluminum foil as an example, the technical solution of this invention is not limited to this. The technical solution of this invention is applicable to any aluminum-based material, including aluminum plates, aluminum strips, aluminum foils, aluminum-based composite materials, and aluminum alloys. The predictive analysis of the mechanical properties of aluminum-based materials includes tensile strength, yield strength, elongation, hardness, impact toughness, elastic modulus, fatigue strength, and creep properties. The rolling process parameters include total rolling force, coiling tension, uncoiling tension, rolling speed, rolling oil temperature, rolling oil flow rate, rolling oil pressure, and rolling pressure, etc., which are not limited.

[0067] To achieve the above objectives, the specific execution process of the technical solution adopted in this embodiment is as follows.

[0068] like Figure 1 As shown, this embodiment employs a battery aluminum foil rolling process optimization method based on response surface methodology, machine learning, and industrial-grade experimental verification and comparison. The main steps include:

[0069] Step 1: Collect rolling process parameter data from multiple sources, including industrial production, published literature, and experimental records, and establish a rolling process database;

[0070] Step 2: Using Plackett-Burman design (PBD) based on response surface methodology combined with steepest ramp tests, we explored the key parameters affecting the performance of the battery aluminum foil.

[0071] Step 3: A mathematical model was established using Box-Behnken design (BBD) based on response surface methodology to analyze the influence of the combined interaction of rolling process parameters on the pinhole defect rate of battery aluminum foil.

[0072] Step 4: Analyze the dataset of BBD optimization results. Based on the dataset, construct a backpropagation artificial neural network model (GA-BP-ANN) optimized by genetic algorithm to predict the pinhole defect rate of battery aluminum foil corresponding to the combination of key process parameters.

[0073] Step 5: Verify the prediction results of RSM and GA-BP-ANN models through industrial-scale experiments, and further optimize process parameters.

[0074] The following provides a detailed explanation of each step.

[0075] Step 1: Collect data from multiple sources, including historical production data, published literature, and experimental records, to establish a rolling process database.

[0076] In step 1, industrial production data typically includes records of various process parameters during production (such as the rotational speed, temperature, and tension of each rolling pass), as well as the corresponding performance data of the battery aluminum foil (such as the number of pinholes and mechanical properties). This data is mainly obtained through the production workshop's data management system and quality inspection reports. Published literature on battery aluminum foil production explores the impact of different process parameters on the performance of battery aluminum foil, particularly the effects of rolling temperature, rolling speed, and rolling force. This data is mainly obtained through academic papers, technical reports, patents, and industry research. Experimental records come from experimental studies on battery aluminum foil, including experimental data under different process conditions (such as the rolling speed, temperature, and tension in the experiment). This data is mainly obtained through laboratories or collaborative research teams, especially those with detailed records and data analysis. Small datasets are obtained by appropriately expanding the small dataset samples using Generative Adversarial Networks (GANs) or Synthetic Minority Oversampling Techniques (SMOTE). Finally, all data are collected, organized, and refined to establish a rolling process database.

[0077] The process of organizing the collected data mainly includes the following three aspects.

[0078] 1) Data cleaning mainly includes handling missing values, outliers, and duplicate values. For missing values, imputation methods can be selected, such as using the mean, median, or mode to fill in the missing values, or deleting rows or columns containing missing values. For outliers, statistical methods (such as box plots, Z-scores, etc.) are used to detect and handle them to ensure data quality and accuracy. For duplicate values, duplicate records are checked and deleted to prevent them from affecting model training.

[0079] 2) Data transformation, including standardization and normalization. Standardization transforms data into a distribution with a mean of 0 and a standard deviation of 1, ensuring that each feature has the same dimension, which is convenient for training machine learning models. Normalization maps data to the interval [0,1], which is usually used in distance metric sensitive algorithms (such as KNN, SVM, etc.) so that all features are compared on the same scale.

[0080] 3) Data splitting: The data is divided into training and test sets. The training set is used for model training and parameter optimization, while the test set is used to evaluate the model's performance on unseen data. Typically, the data is split according to a certain ratio (e.g., 70% training set, 30% test set, or 80% training set, 20% test set). Cross-validation (e.g., K-fold cross-validation) is used to further verify the model's generalization ability and improve its stability.

[0081] Step 2: Using Plackett-Burman design (PBD) combined with steepest climb tests, we explored the key parameters affecting the performance of battery aluminum foil.

[0082] In step 2, based on the establishment of the rolling process database, since different process parameters (such as the seven main rolling process parameters: total rolling force, coiling tension, uncoiling tension, rolling speed, rolling oil temperature, rolling oil flow rate, and rolling oil pressure) have different dimensions, preprocessing is used to make these different process parameters dimensionless. Plackett-Burman design (PBD) is then used to screen out key process parameters that can significantly affect the performance of battery aluminum foil (such as pinhole rate and mechanical properties) through Pareto charts. Further steepest ramp test design is used to confirm the optimal range of the key parameters.

[0083] Furthermore, in step 2, the Plackett-Burman Design (PBD) implementation process is as follows:

[0084] Based on the establishment of the database, the data is standardized before PBD design analysis to allow different parameters to be compared under the same standard. The formula is as follows:

[0085]

[0086] Where Xstd is the standardized value, X is the original value, and μ and σ are the mean and standard deviation of the corresponding data, respectively;

[0087] Multiple initial rolling process parameters are used. By constructing an orthogonal matrix, the main effect of each factor can be estimated independently, and the number of experiments is designed. An orthogonal matrix is ​​constructed by encoding different factors at two levels, and subsequent rows are generated through a cyclic right shift, ultimately forming an orthogonal matrix where each column corresponds to a factor X. i ;

[0088] For each factor X i The average response difference at high / low levels is calculated using the following formula:

[0089] Effect_(X_i)=(∑(Y∣x_i=+1)-∑(Y∣X_i=-1)) / (N / 2)

[0090] Where N is the number of trials and Y is the response value.

[0091] Then, by calculating the covariance matrix, the relationships between the parameters are analyzed. The formula is as follows:

[0092]

[0093] Where, x ki It is the i-th variable value of the k-th process parameter. It is the mean of the i-th variable, x kj It is the j-th variable value of the k-th process parameter. It is the mean of the j-th scalar; using ANOVA to calculate the p-value through F-test, the three most critical rolling process parameters are selected.

[0094] Furthermore, in step 2, the process of using the Pareto chart to screen key parameters is as follows:

[0095] By combining PBD variance analysis, and comparing the parameters in the Pareto chart with the ordinary t-critical threshold and the multiple correction threshold, we can further analyze the t-values, effect sizes, standard errors, and sensitivity coefficients of each parameter to determine the key parameters.

[0096] Furthermore, in step 2, the implementation process of optimizing the rolling process through the steepest ramp test is as follows:

[0097] The mathematical formula for establishing a first-order linear model is as follows:

[0098] y = β0 + β1x1 + β2x2 + ... + β k x k +∈

[0099] Among them, the coefficient β was determined based on the regression analysis of PBD. k ∈ represents the existing error;

[0100] The direction of the climb is determined by the regression coefficients, and the gradient vector is (β0, β1, ... β). k The step size is adjusted according to the proportion of the contribution of the factor change to the response, as shown in the following formula:

[0101]

[0102] Where, β i ,β j It is the regression coefficient, Δx i This represents the range of variation for the i-th parameter (factor).

[0103] By iteratively adjusting key parameters, the extreme regions of the response surface (such as optimal mechanical properties, minimum pinhole count, and minimum breakage rate) are rapidly approximated, and the optimal range of values ​​for the key parameters is determined. Finally, using Plackett-Burman design (PBD) combined with the steepest ramp test, the most critical parameter factors affecting the performance of battery aluminum foil are investigated (ultimately, this embodiment determines three key process parameters to study the impact of pinhole defects in battery aluminum foil).

[0104] Step 3: A mathematical model was established using Box-Behnken design (BBD) based on response surface methodology to analyze the influence of the combined interaction of rolling process parameters on the pinhole defect rate of battery aluminum foil.

[0105] Specifically, step 3 can be further divided into the following steps:

[0106] Step 3.1: A Box-Behnken design (BBD) based on response surface methodology is used to generate an experimental matrix. This matrix handles combinations located at the midpoint of the experimental space edge, avoiding factor combinations under extreme conditions. It is symmetrical, rotatable, and efficient. This approach is used to investigate the interactive effects of key rolling process parameters on the performance of battery aluminum foil.

[0107] In step 3.1, a Box-Behnken design (BBD) generates a randomized experimental sequence, and the pinhole defect rate is used as the response variable for analysis. Three key parameters need to be determined, with three levels (+1, 0, -1). A partial factorial design is used to identify the main effects and interactions between the factors. Axial point experiments are designed, with two extreme values ​​for each factor, to detect nonlinear effects. Intermediate value experiments are conducted among the factors to evaluate experimental error and ensure the reliability of the model.

[0108] Step 3.2: After data preprocessing, a multiple quadratic regression mathematical model is established, the least squares method (OLS) is used to fit the model, and ANOVA analysis and coefficients are used to test the significance of the model.

[0109] Further, in step 3.2, the relationship between rolling process parameters and battery aluminum foil performance is described using response surface methodology. A mathematical model is established by using analysis of variance to build a multinomial regression equation (in this embodiment, a multiple quadratic regression equation). The fitting coefficients are calculated using the least squares (OLS) method from Python's statsmodels library. The general form of the response surface methodology model is as follows:

[0110]

[0111] Where Y represents the response variable (pinhole defect), β represents the model coefficients (β0 is the baseline term, β...). i For linear terms, β ii For the squared term, β ij (for interactive items), X i X j This indicates experimental factors (such as uncoiling tension, rolling hydraulic pressure, and winding tension). X represents the squared term of the factor. i X j The interaction between factors is represented by k, where k is the number of factors, and ∈ represents the overall experimental error term. Analysis of variance is used to evaluate model performance, and the relationship between factors and response values ​​is reflected through response surfaces and contour plots. Ultimately, this achieves optimization and effective prediction of the rolling process.

[0112] In step 3.3, analysis of variance (ANOVA) is performed to determine the significance of each parameter and the performance of the model;

[0113] Furthermore, in step 3.3, the coefficients of each parameter and interaction term are obtained through regression analysis, and the predicted results of the battery aluminum foil performance under different parameter combinations are calculated.

[0114] The model was tested for significance using ANOVA, and several metrics were used to evaluate the model's goodness of fit:

[0115] R 2 As the coefficient of determination, the closer to 1 the better, if R 2 A value >0.9 indicates that the model can explain more than 90% of the parameter variation;

[0116] The p-value is used to test whether the regression coefficient is significant. If p < 0.05, it indicates that the parameter has a significant impact on the result. For example, p = 0.001 for unwinding tension indicates that it has a great impact on strength.

[0117] Furthermore, in step 3.3, it is checked whether the residuals conform to a normal distribution. The distribution of normal residual probabilities is used to explain the difference between the model's predicted values ​​and the actual values, making the model's significance more reliable.

[0118] 1) Use a variance distribution line plot;

[0119] 2) Use the model to fit the effect diagram.

[0120] Step 3.4: Visually analyze the impact of key parameter combinations on the performance of battery aluminum foil using 3D surface plots and contour plots to find the optimal parameter combination.

[0121] Furthermore, in step 3.4, after analyzing the significance of the fitted regression model, multiple response surface plots (3D surface plots or contour plots in this embodiment) are plotted to visually demonstrate the influence of different combinations of battery aluminum foil process parameters on the response variable, battery aluminum foil performance parameters (which can be multiple performance parameters, i.e., multiple objectives). For example, the effects of the interaction between uncoiling tension and rolling hydraulic pressure, the interaction between uncoiling tension and winding tension, and the interaction between rolling hydraulic pressure and winding tension on battery aluminum foil performance are used. The response surface plots are then used to find the process parameter combination that optimizes the battery aluminum foil performance indicators.

[0122] Step 4: Analyze the dataset of BBD optimization results. Based on the dataset, construct a backpropagation artificial neural network model (GA-BP-ANN) optimized by genetic algorithm to predict the pinhole defect rate of battery aluminum foil corresponding to the combination of key process parameters.

[0123] Develop programs, write algorithm libraries, and import data to run tests using the Python language in PyCharm Community Edition software.

[0124] 1) Use a genetic algorithm to iteratively obtain the optimal weights and thresholds;

[0125] 2) Introduce weights and thresholds into BP-ANN, and determine the optimal hidden layer neurons through testing using RSM sample data.

[0126] 3) Establish a GA-BP-ANN optimization model and analyze its performance.

[0127] 4) Expand the sample data appropriately, train the model, and make predictions.

[0128] Furthermore, the specific process of constructing a backpropagation artificial neural network model based on genetic algorithm optimization is as follows:

[0129] To address the problem of minima in the prediction model of BP artificial neural network, a genetic algorithm is used to iteratively optimize the BP artificial neural network, adjust the model structure, and continuously reset the initial weights and thresholds by adjusting the population size, crossover probability, mutation probability, and maximum number of iterations of the genetic algorithm.

[0130] Based on the establishment and improvement of the database, in the process of optimizing the production of battery aluminum foil rolling process, the optimal weights and thresholds are imported into BP-ANN to establish a BP artificial neural network model. The data of different process parameter combinations (such as uncoiling tension, rolling oil pressure and winding tension) and the corresponding battery aluminum foil performance indicators (pinhole count and mechanical properties) are input into GA-BP-ANN and used as training data for BP artificial neural network.

[0131] Through MSE, RMSE, MAE and R 2 To further evaluate the model's performance;

[0132] The optimal combination of rolling process parameters is used to predict the performance index values ​​of battery aluminum foil and optimize the production process of battery aluminum foil.

[0133] Furthermore, in step 4, a GA-BP artificial neural network prediction model is established:

[0134] A backpropagation (BP) artificial neural network model is established, where ① the number of nodes in the input layer equals the number of process parameters; ② the hidden layer typically has 1-2 layers, and the neurons in each layer can be determined through optimization using a genetic algorithm; ③ the number of nodes in the output layer represents the performance indicators of the battery aluminum foil to be predicted (e.g., one output node represents the pinhole rate, and two output nodes represent multiple mechanical performance indicators).

[0135] The GA-BP-ANN model was trained multiple times using the ReLU (Rectified Linear Unit) activation function, and hyperband combined with an early stopping mechanism was used for parameter tuning. The MSE, RMSE, MAE, and R-values ​​of the model were then measured after multiple training iterations. 2 To determine the indicators.

[0136] Further, in step 4.1, the specific process of using a genetic algorithm to iteratively obtain the optimal weights and thresholds is as follows:

[0137] After data preprocessing, an initial population with initial weights and thresholds for a BP artificial neural network is generated. This initial population is then transferred to the BP artificial neural network for training and validation. The fitness of the algorithm model gradually decreases until it stabilizes through iterations using a genetic algorithm (GA), as shown in the following formula:

[0138]

[0139] Where F represents the fitness of GA, Yi is the prediction result, and Oi is the experimental result.

[0140] The established GA-BP-ANN core topology is as follows: Figure 2 As shown.

[0141] Furthermore, in step 4.2, the specific process of introducing weights and thresholds into the BP-ANN and determining the optimal hidden layer neurons through testing with RSM sample data is as follows:

[0142] The optimized weights and thresholds were imported into the BA-ANN algorithm to establish the GA-BP-ANN optimized algorithm model. The GA-BP-ANN model was trained 480 times using the ReLU (Rectified Linear Unit) activation function, and hyperband combined with an early stopping mechanism was used for parameter tuning. The training settings included a convergence threshold of 0.001, a maximum of 500 iterations, and a fixed learning rate of 0.001. A single hidden layer was used, with a number of neurons in the hidden layer... Where n1 is the number of neurons in the input layer (n1 = 3), n0 is the number of neurons in the output layer (n0 = 1), and C is a constant, C ∈ [0, 10]. The network structure is optimized by adjusting the number of neurons in the hidden layer (from 2 to 12).

[0143] Furthermore, in step 4.3, the GA-BP-ANN optimization model is established, and the specific process of model performance analysis is as follows:

[0144] Based on the above single-layer hidden layer design, RMSE, MAE, and R are used. 2 A stable GA-BP-ANN algorithm model was established through multiple training-validation-testing of the neural network program. Input data was used to validate the model's performance. To enhance the persuasiveness of the research and highlight the optimization effect of introducing the genetic algorithm (GA), this paper compares and analyzes the performance of the BP-ANN model without GA optimization with that of the GA-BP-ANN model. The established GA-BP-ANN framework diagram is as follows:

[0145] Step 5: Validate the RSM and GA-BP-ANN models through industrial-grade experiments.

[0146] Furthermore, the specific process of step 5 is as follows:

[0147] 1) Comparison of GA-BP-ANN and RSM results

[0148] 2) Analysis of Industrial-Grade Experimental Results

[0149] For model prediction validation, it is necessary to train the model based on these optimized parameter combinations and then validate the model using experimental data, thereby more accurately optimizing the battery aluminum foil production process.

[0150] It should be noted that if there is a discrepancy between the experimental test results and the predicted results, the test results will be used as the basis for correcting the entire design system. Through several rounds of prediction-experiment-feedback-prediction-experiment-feedback..., it is ensured that the selected optimal combination of process parameters can achieve the expected results in real production, and further improve the quality and production efficiency of battery aluminum foil.

[0151] In summary, a novel method for optimizing the rolling process of battery aluminum foil was developed by combining a BP artificial neural network based on genetic algorithm optimization with response surface methodology. This method establishes a high-precision model of the process parameters and performance of battery aluminum foil, thereby improving the performance of battery aluminum foil products.

[0152] Example 2

[0153] The following detailed explanation uses specific examples, along with data tables and charts, but these are not the only examples:

[0154] In this embodiment, a method for optimizing the rolling process of battery aluminum foil based on response surface methodology, machine learning, and experimental verification analysis is presented. Seven main rolling process parameters (total rolling force, coiling tension, uncoiling tension, rolling speed, rolling oil temperature, rolling oil flow rate, and rolling oil pressure) are selected, and three key parameters are chosen for optimization to study their impact on the pinhole DPU (diminished porosity) of the battery aluminum foil. The method includes the following steps:

[0155] Step 1: Collect rolling process parameter data from multiple sources, including industrial production, published literature, and experimental records, and establish a rolling process database.

[0156] In optimizing the aluminum foil rolling process for batteries, data collection and analysis are crucial. First, industrial production data provides the most direct foundation, including records of various process parameters used in production, such as rolling speed, temperature, and tension. It also records performance indicators of the aluminum foil under these parameters, such as pinhole count and mechanical properties. Second, published literature offers valuable references. Many studies have explored the impact of different process parameters (e.g., rolling temperature, rolling speed, rolling force) on the quality of battery aluminum foil. These studies provide theoretical support on how to adjust these parameters and identify which factors are most important for optimizing battery aluminum foil performance. Finally, experimental records are an indispensable data source in the optimization process. Experimental records include data from battery aluminum foil production experiments conducted under different process conditions, recording the rolling speed, temperature, tension, and other parameters used in each experiment, as well as the performance of the battery aluminum foil under these conditions. These real-world data provide genuine production feedback, verify the accuracy of the predictive model, and provide a strong basis for adjusting process parameters, helping to successfully establish a rolling process database. In this embodiment, based on extensive practical experience and after preliminary screening, seven main rolling process parameters (A: total rolling force, B: coiling tension, C: uncoiling tension, D: rolling speed, E: rolling oil temperature, F: rolling oil flow rate, and G: rolling oil pressure) were selected to study the impact of rolling process parameters on pinhole DPU, collect data, and establish a database.

[0157] Step 2: Based on the establishment of the database, Plackett-Burman design (PBD) using response surface methodology combined with the steepest ramp test was used to explore the key parameter factors affecting the performance of battery aluminum foil.

[0158] Based on the establishment of the database, the data is standardized before PBD design analysis to allow different parameters to be compared under the same standard. The formula is as follows:

[0159]

[0160] Where Xstd is the standardized value, X is the original value, and μ and σ are the mean and standard deviation of the corresponding data, respectively;

[0161] By encoding different factors at two levels, with the lowest value encoded as -1 and the highest value as +1, these codes are used to construct an orthogonal matrix. Subsequent rows are then generated by cyclically shifting the matrix to the right, ultimately forming a 23-column orthogonal matrix, with each column corresponding to a factor X. i ;

[0162] For each factor X i The average response difference at high / low levels is calculated using the following formula:

[0163] Effect_(X_i)=(∑(Y∣X_i=+1)-∑(Y∣X_i=-1)) / (N / 2)

[0164] Where N is the number of trials and Y is the response value.

[0165] Then, by calculating the covariance matrix, the relationships between the parameters are analyzed. The formula is as follows:

[0166]

[0167] Where, x ki It is the i-th variable value of the k-th process parameter. It is the mean of the i-th variable, x kj It is the j-th variable value of the k-th process parameter. It is the mean of the j-th scalar.

[0168] In this embodiment, as shown in Table 1, seven main rolling process parameters (A. total rolling force, B. coiling tension, C. uncoiling tension, D. rolling speed, E. rolling oil temperature, F. rolling oil flow rate, and G. rolling oil pressure) and 16 dummy variables were selected to estimate the experimental error. A 23-column matrix was generated using a standard PBD table (the first 7 columns are real factors, and the last N=16 columns are dummy variables). The dummy variables are not involved in process adjustment but are only used for error estimation in data analysis. Finally, 24 experimental treatments were performed, and then the significance of the real factors was tested.

[0169] Table 1. Levels and response values ​​of each factor in the Plackett-Burman design

[0170]

[0171]

[0172] Furthermore, in step 2, the steepest ramp test is used to optimize the rolling process:

[0173] The mathematical formula for establishing a first-order linear model is as follows:

[0174] y = β0 + β1x1 + β2x2 + ... + β k x k +∈

[0175] Among them, the coefficient β was determined based on the regression analysis of PBD. k ∈ represents the existing error;

[0176] The direction of the climb is determined by the regression coefficients, and the gradient vector is (β0, β1, ... β). k The step size is adjusted according to the proportion of the contribution of the factor change to the response, as shown in the following formula:

[0177]

[0178] Where, β i ,β j It is the regression coefficient, Δx i This represents the range of variation for the i-th parameter (factor).

[0179] By iteratively adjusting key parameters, the extreme regions of the response surface (such as the lowest pinhole DPU and optimal mechanical properties) are rapidly approximated, and the optimal range of values ​​for the key parameters is determined. Finally, using Plackett-Burman design (PBD) combined with the steepest ramp test, the most critical parameter factors affecting the performance of the battery aluminum foil are explored (ultimately, three key process parameters were determined in this embodiment).

[0180] In this embodiment, N=24 experiments and Y=1 response value (pinhole DPU (numbers / 10,000 m²)) were used to investigate the influence of pinhole DPU on the finished aluminum-based material. Preliminary analysis, using Pareto, identified the three most influential parameters as: uncoiling tension, winding tension, and rolling hydraulic pressure. Figure 3 As shown, intuitive analysis reveals three key rolling process parameters that affect pinhole defects in batteries (C: uncoiling tension, G: rolling hydraulic pressure, and B: coiling tension).

[0181] Step 3: A mathematical model was established using Box-Behnken design (BBD) based on response surface methodology to analyze the influence of the combined interaction of rolling process parameters on the pinhole defect rate of battery aluminum foil.

[0182] Based on the three key rolling process parameters selected through PBD and steepest ramp test design, response surface modeling was performed to establish a multiple second-order regression equation for the three process parameters: uncoiling tension, rolling hydraulic pressure, and coiling tension. This equation was then used to predict the performance indicators of battery aluminum foil (such as pinhole count DPU). The second-order regression equation can capture the linear relationship between process parameters and their possible quadratic effects, thus providing a reliable mathematical model for predicting the pinhole DPU of battery aluminum foil.

[0183] To ensure the effectiveness of the model, analysis of variance (ANOVA) was used to check its adequacy, assess its fit to the data, and evaluate the significance of each process parameter. ANOVA was used to determine which process parameters significantly impact the quality of battery aluminum foil, which interaction effects require close attention, and the model's explanatory and predictive capabilities.

[0184] Based on response surface methodology and analysis of variance, the rolling process parameters were optimized to find the optimal combination of process parameters. In the experiment, actual production was carried out according to the optimized parameter combination, and the performance indicators of battery aluminum foil (such as pinhole DPU and mechanical properties) were compared to verify the accuracy of the model prediction and the optimization effect.

[0185] Furthermore, in step 3.1, the Box-Behnken design (BBD) for generating the experimental matrix is ​​specifically implemented as follows:

[0186] In this embodiment, the effects of the interaction of three parameters—uncoiling tension, rolling hydraulic pressure, and winding tension—on pinhole DPU were studied through experimental design. The uncoiling tension was set at 25 N / mm. 2 Up to 50 N / mm 2 The rolling hydraulic pressure ranged from 4 MPa to 5.2 MPa, and the coiling tension ranged from 45 N / mm to 60 N / mm. Table 2 shows the design and results of 17 randomized trials involving three factors, including 15 test points with different factor combinations and 3 center points used to evaluate experimental error. This unequal random distribution effectively represents the factor space by eliminating unnecessary test points, thus ensuring the rationality of the design. The strategy of varying the number of trials in the design maintained statistical accuracy, captured the curvature of the response, and reduced experimental costs.

[0187] Table 2. Factors and levels in the Box-Behnken experiment

[0188]

[0189]

[0190] Furthermore, in step 3.2, the specific implementation of establishing the multiple quadratic regression equation is as follows:

[0191] See Formula (1). The Box-Behnken Design (BBD) establishes a mathematical model, which quickly and effectively identifies the optimal combination of process parameters corresponding to the expected results through the interaction of different variables. Based on the analysis results of the Box-Behnken Design (BBD) and the steepest ramp test, the three main factors are identified, and the three levels of each factor are coded (-1, 0, +1) with the pinhole DPU as the response value. Three parallel trials are set up for each test point. A total of 17 trials with three centers and three levels are designed to improve the predictive accuracy of the model.

[0192]

[0193] Where Y represents pinhole DPU, C represents uncoiling tension, G represents rolling hydraulic pressure, and B represents coiling tension. CG, CB, and GB represent the interaction of rolling process parameters, C 2 G2 and B 2 These represent the secondary effects of each factor. The plus and minus signs indicate the synergistic and antagonistic effects of the parameters on the response, respectively.

[0194] Furthermore, based on steps 3.1 and 3.2, step 3.3 yields the specific process of the analysis of variance:

[0195] The analysis of variance for BBD is shown in Table 3. The F-value is used to assess the significance of each factor and the model as a whole on the response variable, while the P-value reflects the significance level; typically, a P-value less than 0.05 indicates statistical significance. As can be seen from the table, the F-value of this model is 39.18, and the P-value is much less than 0.0001, indicating that the model fits the experimental data well in the equation and has strong overall significance. The coefficient of determination (R²) of the model... 2 The adjusted coefficient of determination (R²) is 0.9805, indicating that 98.05% of the experimental data fluctuations can be explained by the written model given by the equation, demonstrating high fitting accuracy. 2 adj The prediction determination coefficient (R²) is 0.9555, indicating that the model maintains high stability in explaining the variation of pinhole DPU. 2 pre The value is 0.9380, and R... 2 adj and R 2 pre The difference between the values ​​is less than 2%, further indicating that the model has good predictive ability and can be used to analyze and optimize the processing conditions of pinhole DPUs.

[0196] Table 3. Analysis of Variance of Box-Behnken Design Results

[0197]

[0198]

[0199] Furthermore, in step 3.3, such as Figure 4 As shown, a visual analysis of the fitting plot illustrates the reliability of the established model. (See...) Figure 4 Analysis of variance and fit plot).

[0200] Furthermore, in step 3.4, 3D surface plots and contour plots are used to visually analyze the impact of different parameter combinations on the performance (multi-objective) of the battery aluminum foil:

[0201] By fitting a regression model and analyzing its significance, multiple response surface plots (3D surface plots or contour plots in this example) are generated to visually demonstrate the impact of different combinations of battery aluminum foil process parameters on the response variable, battery aluminum foil performance parameters (which can be multiple performance parameters, i.e., multiple objectives). For example, the effects of uncoiling tension and rolling pressure, uncoiling tension and winding tension, and rolling pressure and winding tension on pinhole defects in battery aluminum foil are used. The response surface plots are then used to find the optimal combination of process parameters that optimizes the performance indicators of the battery aluminum foil.

[0202] like Figure 5 As shown, the RSM multi-parameter 3D response surface and contour plots are as follows: (a), (b) and (c) are the three-dimensional surface plots of uncoiling tension-rolling hydraulic pressure, uncoiling tension-winding tension, and winding tension-rolling hydraulic pressure, respectively; (d), (e) and (f) are their corresponding contour plots.

[0203] like Figure 6 As shown, the optimal rolling process parameters predicted by RSM analysis are: uncoiling tension 37.5 N / mm. 2 The rolling hydraulic pressure is 4.6 MPa, and the winding tension is 52.5 N / mm. After verification through some industrial-grade experiments, the corresponding pinhole DPU value is 337.216 pinholes / 10,000 square meters.

[0204] Step 4: Based on the dataset of BBD optimization results, construct a backpropagation artificial neural network model (GA-BP-ANN) optimized by genetic algorithm to predict the pinhole defect rate of battery aluminum foil corresponding to the combination of key process parameters.

[0205] Based on the BBD dataset and with appropriate data expansion, a neural network is used to optimize the rolling process of battery aluminum foil. In this process, different combinations of process parameters (such as uncoiling tension, rolling hydraulic pressure, and winding tension) and corresponding battery aluminum foil performance indicators (such as pinhole DPU and mechanical properties) are used as input and output data. By establishing a BP artificial neural network model, this data is used to train the model, helping it learn the complex nonlinear relationship between process parameters and battery aluminum foil performance, thereby enabling performance prediction for different future combinations of process parameters.

[0206] However, BP-ANN may encounter the problem of local minima during training, meaning that in some cases, the network error may get stuck at a non-ideal local minimum, leading to poor prediction performance. To overcome this problem, a genetic algorithm is introduced to optimize the BP-ANN. The genetic algorithm is an optimization algorithm that simulates the natural selection process. It iteratively optimizes the initial weights and thresholds of the BP artificial neural network through random selection, crossover, and mutation. The optimized BP artificial neural network model can accurately predict the impact of different combinations of rolling process parameters on the performance of battery aluminum foil, providing strong decision support for optimizing the production process of battery aluminum foil.

[0207] Furthermore, the specific process of establishing the GA-BP artificial neural network prediction model in step 4 is as follows:

[0208] Furthermore, in step 4.1, the specific process of using a genetic algorithm to iteratively obtain the optimal weights and thresholds is as follows:

[0209] The genetic algorithm iteratively determines the optimal weights and thresholds, performs downsampling and smoothing on the rolling process parameters and pinhole DPU data, and then generates the initial weight and threshold population for the BP-ANN, which is used for subsequent training and validation. The genetic algorithm (GA) parameters are set as follows: population size 30, crossover probability 0.7, mutation probability 0.1, and maximum number of iterations 100. Figure 7 As shown, the fitness value tends to stabilize after about 95 GA iterations.

[0210] Furthermore, in step 4.2, the specific process of introducing weights and thresholds into the BP-ANN and determining the optimal hidden layer neurons through testing with RSM sample data is as follows:

[0211] The optimized weights and thresholds were imported into the BA-ANN algorithm to establish the GA-BP-ANN optimized algorithm model. The GA-BP-ANN model was trained 480 times using the ReLU (Rectified Linear Unit) activation function, and hyperband combined with an early stopping mechanism was used for parameter tuning. The training settings included a convergence threshold of 0.001, a maximum of 500 iterations, and a fixed learning rate of 0.001. A single hidden layer was used, with a number of neurons in the hidden layer... Where n1 is the number of neurons in the input layer (n1 = 3), n0 is the number of neurons in the output layer (n0 = 1), and C is a constant, C ∈ [0, 10]. The network structure is optimized by adjusting the number of neurons in the hidden layer (from 2 to 12). Model performance is compared by means of mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE), and coefficient of determination (R²). 2 To conduct an evaluation. For example... Figure 8 As shown, the model with 11 hidden neurons exhibits the best performance, with the lowest MSE, RMSE, and MAE values, and the highest R0. 2 The value indicates that the model under this configuration has excellent prediction accuracy and lower error. Therefore, 11 hidden neurons (3-11-1) were determined as the optimal structural parameter for the GA-BP-ANN algorithm model.

[0212] Furthermore, in step 4.3, the GA-BP-ANN optimization model is established, and the specific process of model performance analysis is as follows:

[0213] Based on the above single-layer hidden layer design, RMSE, MAE, and R² are used. A stable GA-BP-ANN algorithm model is established through multiple training-validation-testing neural network programs. Input data is used to validate the model performance. The lowest RMSE and MAE values ​​obtained are 4.84 × 10⁻⁶. -2 and 4.42×10 -2 As can be seen, RMSE≈MAE, indicating a uniform error distribution with no extreme values, further demonstrating the excellent overall performance of the established algorithm model. To enhance the persuasiveness of the research and highlight the optimization effect of introducing a genetic algorithm (GA), this paper compares and analyzes the performance of the BP-ANN model without GA optimization and the GA-BP-ANN model. Figure 8 As shown, the determination coefficient (R²) of the BP-ANN model 2 The R-value is 0.9810, while the R-value of the GA-BP-ANN model is... 2 The result is as high as 0.9947. The results show that the prediction points of GA-BP-ANN are almost completely distributed on the diagonal, indicating that it has a better fit to the actual process rules and verifying the effectiveness of genetic algorithms in improving the prediction accuracy of models.

[0214] The trends of training loss and validation loss of BP-ANN and GA-BP-ANN models with the number of iterations, such as... Figure 9As shown in the diagram, comparative analysis reveals that after the 200th generation, the convergence speed of BP-ANN slows down, and the training loss stabilizes after the 360th generation, but the validation loss remains significantly higher than the training loss. In contrast, GA-BP-ANN begins to converge after the 80th generation, the training loss stabilizes after the 230th generation, and the validation loss is highly similar to the training loss. This result indicates that GA-BP-ANN effectively accelerates the model's convergence speed and significantly reduces the final loss value by optimizing the initial weights through a genetic algorithm, avoiding the premature convergence problem of BP-ANN, which is prone to getting trapped in local optima. The stagnant validation loss of BP-ANN after the 200th generation indicates a decline in the model's generalization ability; while the simultaneous decrease in training and validation losses in GA-BP-ANN further validates its advantage in suppressing overfitting. In summary, the introduction of a hybrid optimization strategy significantly improves the model's training efficiency and generalization performance.

[0215] By appropriately expanding the training dataset, the prediction accuracy and overall processing efficiency of the GA-BP-ANN model can be effectively improved. Based on this, the GA-BP-ANN model is used to optimize the rolling process parameters (uncoiling tension 37.5 N / mm) on the response surface. 2 The pinhole DPU was predicted under rolling oil pressure of 4.6 MPa and coiling tension of 52.5 N / mm, and the result was 336.562 (pinholes / 10,000 m²). This is only 6.54 × 10⁻¹ pinholes / 10,000 m² different from the RSM result, with a relative error of no more than 0.26%. In summary, the GA-BP-ANN model constructed in this study can effectively predict pinhole DPU under different rolling process conditions within a given range.

[0216] Furthermore, in step 5, the prediction results of the RSM and GA-BP-ANN models are verified through industrial-scale experiments, and the specific process for further optimizing the process parameters is as follows:

[0217] By combining a genetic algorithm (GA) and a backpropagation artificial neural network (BP-ANN), further optimization, prediction, and selection are performed. In this process, the BP artificial neural network model is first optimized using a genetic algorithm, then trained based on the optimized parameter combinations, and finally validated using experimental data. The BP artificial neural network can accurately predict the quality and performance of battery aluminum foil under different combinations of process parameters, thereby more precisely optimizing the battery aluminum foil production process.

[0218] If the experimental test results deviate from the predicted results, the entire design system will be corrected based on the test results. This process of prediction-experiment-feedback-prediction-experiment-feedback continues until the optimal combination of process parameters is selected to achieve the expected results in actual production, further improving the quality and production efficiency of battery aluminum foil.

[0219] Furthermore, in step 5.1, the specific process of comparing the results of GA-BP-ANN and RSM is as follows:

[0220] Both RSM and GA-BP-ANN have shown strong application potential in modeling process variables for process optimization. However, the statistical error of the model can affect its generalization ability, and thus its prediction accuracy. This study evaluates the performance of the two models, mainly using MSE, RMSE, MAE, and RSM. 2 As shown in Table 4, these are the indicators. Figure 10 and Figure 11 The results show that the GA-BP-ANN model has lower error values ​​and higher fitting accuracy compared to RSM. The comparison between actual and predicted values ​​is shown in the figure below. The figure clearly shows that both models exhibit good fitting effects, but GA-BP-ANN has higher accuracy. GA-BP-ANN can effectively handle complex nonlinear relationships between process parameters, indicating that compared to the quadratic multiple regression equation of RSM, the neural network model has stronger expressive power, wider applicability, and higher fitting accuracy. However, the optimization ability of GA-BP-ANN depends on sufficient data samples, which is one of the limitations of neural network models. Therefore, combining RSM with auxiliary analysis can be used to initially screen key parameters and quickly verify the impact of parameter combinations on pinhole DPUs. Combining this with GA-BP-ANN for accurate prediction helps to significantly improve the efficiency of process parameter optimization.

[0221] Table 4. Comparison of prediction performance between RSM and GA-BP-ANN models

[0222]

[0223] Furthermore, in step 5.2, the specific process of analyzing the industrial-grade experimental results is as follows:

[0224] To verify the prediction accuracy of the two constructed models, this study adjusted the rolling process parameters and designed and implemented an industrial-scale verification experiment. The specific method is as follows: 10 tons of 1060 aluminum alloy raw material were put into production, and four rolls of aluminum foil were randomly selected from this batch of finished products as test samples (roll numbers labeled (a)–(d)). The length of a single roll ranged from 26,000 to 42,000 meters, with a total weight of 5187 kg. Subsequently, these four rolls of samples underwent rigorous pinhole detection, and the obtained pinhole distribution diagram is shown below. Figure 12 As shown, the corresponding pinhole DPU values ​​are summarized in Table 5.

[0225] Figure 12In the graphs ((a)-(d)), the horizontal axis represents the width of the aluminum coil (called the transverse dimension), and the vertical axis represents the length of the aluminum coil (called the longitudinal dimension). The pinhole detection equipment detects the maximum transverse and longitudinal dimensions of the pinhole and uses the larger one as the basis for pinhole rating. The pinhole rating details are shown in Table 9. Finally, the letter X or Y indicates whether the selected dimension is the maximum transverse or longitudinal dimension. For example, if the detection equipment detects that the maximum transverse dimension of a pinhole is greater than its maximum longitudinal dimension, and its maximum transverse dimension is greater than 200 μm and less than or equal to 300 μm, then the pinhole is marked as "Pinhole 3X". In the pinhole rating details table, pinhole 1 can be further subdivided into grades 1, 1.6, 1.7, 1.8, and 1.9, where pinholes greater than 30 μm and less than or equal to 60 μm are pinhole 1, 60–70 μm are pinhole 1.6, 70–80 μm are pinhole 1.7, and so on. The test results showed that the pinhole DPU of all sample rolls was between 310 and 360 pinholes / 10,000 m², with an average pinhole DPU of 336.021 pinholes / 10,000 m² for the four rolls, which is basically consistent with the predicted value (336.562 pinholes / 10,000 m²) of the established GA-BP-ANN model. In particular, the measured DPU of samples (b) and (c) was almost identical to the predicted value, which fully verified the reliability of the constructed GA-BP-ANN optimization model.

[0226] Table 5. Sample parameters and pinhole DPU

[0227]

[0228] Furthermore, based on steps 3.4 and 5.1, the predicted values ​​of the two models, RSM and GA-BP-ANN, and the actual industrial production results (336.021 units / 10,000 square meters) are compared, as shown in Table 6.

[0229] Table 6. Comparison of Model Predictions and Experiments

[0230] Model Forecast value (units / 10,000 square meters) Difference from experimental value (number per 10,000 square meters) <![CDATA[Prediction accuracy (10 -2 )]]> RSM 337.216 1.195 98.05 GA-BP-ANN 336.562 0.541 99.47

[0231] Example 3

[0232] Another embodiment of the present invention relates to an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the methods described in the above embodiments.

[0233] The memory and processor are connected via a bus, which can include any number of interconnecting buses and bridges, connecting various circuits of one or more processors and memories. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0234] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0235] Specifically, all programs involved in this invention were developed using the Python language in PyCharm Community Edition software:

[0236] 1) From core program development to subsequent optimization and upgrades, especially in the data reading method, the original sequential reading was changed to the sliding window averaging method instead of the original grouping method, which significantly improved the data reading speed; at the same time, the model and data were migrated to the GPU processor for parallel computing, which greatly improved the program's running efficiency.

[0237] 2) The genetic algorithm has been improved by adding an optimal individual retention mechanism, adopting a fast training strategy for fitness evaluation, and introducing a visualization function for the evolutionary process;

[0238] 3) Optimize neural network training, implement an early stopping mechanism to prevent overfitting, use the Adam optimizer instead of SGD, and add validation set monitoring.

[0239] Before optimization, the program took about 6 seconds to read the same data, but after optimization, it was shortened to 2-3 seconds. When processing 4,000 data entries, the program's running time was reduced from 60 seconds to 25 seconds, resulting in a significant improvement in overall running efficiency.

[0240] Example 4

[0241] Another embodiment of the present invention relates to a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the methods of the above embodiments.

[0242] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0243] Example 5

[0244] Another embodiment of the present invention relates to a computer program product, including a computer program that, when executed by a processor, implements the methods of the above embodiments.

[0245] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing the present invention, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of the present invention.

Claims

1. A method for optimization of rolling process of aluminum based materials based on response surface methodology and machine learning, characterized in that, The method comprises the following steps: Collecting rolling process related data of aluminum-based materials to establish a rolling process database; Determining key rolling process parameters affecting the performance of aluminum-based materials based on the database; Establishing a mathematical model for describing the relationship between the key rolling process parameters and their interactions and the performance indicators of aluminum-based materials, and calculating the predicted results of the performance indicators of aluminum-based materials under different combinations of key rolling process parameters based on the mathematical model, from which the aluminum-based materials with performance indicators meeting the preset requirements and the corresponding combinations of key rolling process parameters are predicted as a preliminary optimization result dataset; Based on the preliminary optimization result dataset, a back propagation artificial neural network model optimized by a genetic algorithm is constructed to predict the performance indicators of aluminum-based materials corresponding to different combinations of key rolling process parameters, and the optimal combination of key rolling process parameters and the corresponding performance indicators of aluminum-based materials are screened out.

2. The response surface method and machine learning based aluminum based material rolling process optimization method of claim 1, wherein, Determining key rolling process parameters affecting the performance of aluminum-based materials based on the database comprises: Non-dimensionalizing different rolling process parameters; According to the non-dimensionalization results, using the Plackett-Burman design in the response surface method, the main effects are separated and their statistical significance is quantified through a partial orthogonal test structure with the minimum number of tests, and the key rolling process parameters affecting the performance of aluminum-based materials are screened out through Pareto chart analysis; The optimal interval of the key rolling process parameters is approached using the steepest ascent test, and the influence law of the key rolling process parameters and their interactions on the performance indicators of aluminum-based materials is analyzed combining with the Box-Behnken design.

3. The response surface method and machine learning based aluminum based material rolling process optimization method of claim 2, wherein, Screening out the key rolling process parameters affecting the performance of aluminum-based materials through Pareto chart analysis comprises: According to the Pareto chart, the influence of the factors alone and their interactions on the performance of aluminum-based materials is intuitively analyzed and sorted; The t value, effect value, standard error and sensitivity coefficient in the Pareto chart are calculated to determine the key rolling process parameters.

4. The response surface method and machine learning based aluminum based material rolling process optimization method of claim 1, wherein, Establishing a mathematical model for describing the relationship between the key rolling process parameters and their interactions and the performance of aluminum-based materials, and calculating the predicted results of the performance indicators of aluminum-based materials under different combinations of key rolling process parameters based on the mathematical model, from which the aluminum-based materials with performance indicators meeting the preset requirements and the corresponding combinations of key rolling process parameters are predicted as a preliminary optimization result dataset, comprises: Using the Box-Behnken design of the response surface method to generate a test matrix, and using the test matrix to explore the interactive influence of the key rolling process parameters on the performance of aluminum-based materials; Using a regression analysis method to establish a mathematical model to describe the influence law of the key rolling process parameters and their interactions on the performance of aluminum-based materials, and using variance analysis to evaluate the key rolling process parameters of the mathematical model; According to the mathematical model, the predicted results of the performance indicators of aluminum-based materials under different combinations of key rolling process parameters are calculated; Through three-dimensional surface graph and contour graph analysis of the influence of different key rolling process parameter combinations on the performance index of aluminum-based materials, the aluminum-based material and its corresponding key rolling process parameter combination that meet the preset requirements are found as the preliminary optimization result.

5. The response surface method and machine learning based aluminum based material rolling process optimization method of claim 4, wherein, A regression analysis method is used to establish a mathematical model to describe the influence of key rolling process parameters and their interactions on the performance of aluminum-based materials, including: A multiple quadratic regression equation model is established to describe the influence of key rolling process parameters and their interactions on the performance of aluminum-based materials; The regression coefficients of the multiple quadratic polynomial regression equation model are determined using the least squares fitting method; Through variance analysis, the overall evaluation of the established model is carried out, and the influence weight and law of each key rolling process parameter and its interaction on the performance index of aluminum-based materials are further analyzed.

6. The response surface method and machine learning based aluminum-based material rolling process optimization method of claim 5, wherein, Through variance analysis, the overall evaluation of the established model is carried out, and the influence weight and law of each key rolling process parameter and its interaction on the performance index of aluminum-based materials are further analyzed, including: Through variance analysis, the performance index of the mathematical model is obtained; The F value of the model is calculated to evaluate the overall performance of the model; The P value of the model is calculated to evaluate the influence of single factor and multiple factors on the performance of aluminum-based materials; The determination coefficient R of the model of the calculation model 2 , the adjusted determination coefficient R 2 adj and the predicted determination coefficient R 2 pre to evaluate the predictive power of the model for the analysis and optimization of the conditions of the performance of aluminum-based materials.

7. The response surface method and machine learning based aluminum based material rolling process optimization method of claim 1, wherein, The genetic algorithm optimized back propagation neural network is an optimized hybrid model GA-BP-ANN.

8. The response surface method and machine learning based aluminum-based material rolling process optimization method of claim 7, wherein, The genetic algorithm optimized back propagation artificial neural network model is constructed, including: Using the initial weight and threshold value optimized by the genetic algorithm, the optimal weight and threshold value are obtained and introduced into the BP-ANN model to construct the GA-BP-ANN optimization algorithm model; The ideal number of neurons of the model is calculated; The performance of the model is analyzed by MSE, RMSE, MAE and R 2 analyzing the performance of the model; The model is analyzed intuitively through the fitting effect diagram; The performance of the model is analyzed intuitively by comparing the training loss and validation loss trend chart and error distribution chart of other models; The GA-BP-ANN model is trained using the BBD result key parameter data set, and the RSM model and GA-BP-ANN model are verified in combination with industrial grade experiments.

9. An electronic device, comprising: Including: At least one processor; And The memory is in communication connection with the at least one processor; wherein The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the aluminum-based material rolling process optimization method based on response surface method and machine learning according to any one of the preceding claims 1 to 8.

10. A computer readable storage medium storing a computer program, characterized in that, The computer program is executed by the processor to implement the aluminum-based material rolling process optimization method based on response surface method and machine learning according to any one of the preceding claims 1 to 8.

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