Alloy hardness prediction and component optimization method and system based on goose optimization algorithm

Abstract

The invention discloses an alloy hardness prediction and component optimization method based on a goose optimization algorithm, and the method comprises the following steps: S1, collecting chemical components of an alloy and corresponding hardness data, constructing a total data set, and carrying out the preprocessing; s2, based on a Pearson's correlation coefficient and mutual information, eliminating redundant component features and identifying key component features by adopting a two-step screening method; s3, by taking the key component features as input and the hardness as output, through grid search and cross validation, screening the primarily selected hardness prediction model and performing hyper-parameter optimization to obtain a final hardness prediction model; and S4, component optimization is carried out on the alloy, and the alloy component proportion with the optimal hardness performance is searched by adopting a goose optimization algorithm in combination with component constraint conditions. According to the alloy hardness prediction and component optimization method, high-precision prediction of the alloy hardness is achieved, the alloy component optimization efficiency and accuracy are remarkably improved, and scientific basis and technical support are provided for rapid design of high-performance alloy.

Description

Technical Field

[0001] The present invention relates to the technical field of metal alloy materials, and in particular to a method and system for alloy hardness prediction and composition optimization based on a GOOSE algorithm. Background Art

[0002] As one of the most widely used structural and functional materials in modern industry, alloy hardness directly impacts the wear resistance, deformation resistance, and service stability of components in practical engineering. In a variety of high-end applications, including aerospace, automotive manufacturing, rail transportation, mold processing, electronic packaging, and precision machinery, the hardness of alloys often determines the lifespan and reliability of key components. Therefore, designing metal alloys with high hardness to meet diverse performance requirements has become a key focus in materials design and development.

[0003] The hardness of an alloy is determined by multiple factors, including elemental composition, content ratio, microstructure, and processing technology, resulting in a complex mechanism for the formation of its properties. In high-dimensional compositional space, nonlinear coupling effects often exist between different elements. This makes the traditional "formulation-trial-verification" alloy design model, which relies on expert experience and trial and error, inefficient and costly, and difficult to achieve quantitative prediction and controllable optimization of hardness properties. Especially in the context of pursuing high performance, high precision, and customized design, existing methods have been unable to meet the technical requirements for rapid response to alloy design for complex applications.

[0004] In recent years, machine learning has demonstrated tremendous potential in materials science, providing a new path for predicting the properties and optimizing the composition of metallic materials. By building data-driven predictive models, machine learning can exploit the potential nonlinear relationships between alloy composition and performance from massive amounts of data. By constructing and optimizing predictive models, combined with efficient and accurate algorithms, it can effectively shorten R&D cycles, reduce experimental costs, and achieve global optimization of complex compositional spaces. In the design of high-hardness alloys, machine learning is expected to not only improve prediction accuracy but also reveal elemental synergies that are difficult to identify using traditional methods, thereby guiding the construction of new high-performance alloy systems.

[0005] In addition, with the development of intelligent optimization algorithms, swarm intelligence algorithms have gradually become an important means of optimizing alloy compositions due to their powerful global search capabilities and parallel computing advantages. In recent years, algorithms such as particle swarm optimization (PSO) and genetic algorithms (GA) have been applied to the performance optimization of alloy compositions. The GOOSE algorithm is a new type of swarm intelligence optimization algorithm proposed in recent years. It was published in the journal Evolving Systems in 2024. It simulates the collaborative behavior of wild geese in the process of foraging and vigilance, and has both efficient global search capabilities and fast convergence characteristics. However, there is currently no research on the application of the GOOSE algorithm to the field of alloy composition optimization, which provides new technical opportunities for the design of high-hardness alloys.

[0006] Currently, some publicly available technologies apply machine learning methods to the prediction and optimization of alloy properties, and related research and patent achievements continue to emerge. Patent application number CN202211545411.X discloses a machine learning-based method for predicting the tensile strength of Ti-6Al-4V (TC4) alloy, establishing an effective tensile strength model. Patent application number CN202411865984.X discloses a machine learning-based method and system for designing the composition of high-toughness amorphous alloys. This method decouples the complex "composition-performance" relationship and improves the efficiency of high-toughness amorphous alloy composition design. Patent application number CN202310108790.4 uses an extreme gradient boosting algorithm combined with a particle swarm optimization method to systematically optimize the composition of a new aviation aluminum alloy. However, existing technologies generally have the following limitations: On the one hand, most studies focus on specific metal systems, lack universal adaptability to multiple alloy systems, and have not yet formed a unified, portable design framework; on the other hand, current methods are mostly concentrated on the performance modeling link, and have failed to establish an integrated design process from feature screening, predictive modeling, model optimization to composition inversion. In particular, in design tasks with "high hardness" as the core performance indicator, there is a lack of systematic solutions with high-precision prediction capabilities and strong global optimization capabilities. More importantly, the algorithms currently commonly used in alloy composition optimization, such as genetic algorithms and particle swarm optimization, although they have certain global search capabilities, often face problems such as low search efficiency and easy to fall into local optimality when dealing with high-dimensional, strongly coupled, and multi-constrained alloy systems, making it difficult to meet the actual needs of rapid optimization design of modern high-performance alloys. Summary of the Invention

[0007] In light of the shortcomings of the aforementioned existing technologies, this paper provides an alloy hardness prediction and composition optimization method based on the goose optimization algorithm. This method aims to address the existing problems of a lack of systematic modeling of the alloy "composition-hardness" relationship, as well as the low efficiency, high cost, and poor design accuracy of traditional alloy development methods. This method constructs a high-precision, generalizable hardness prediction model, identifies key component characteristics that affect hardness, and uses an intelligent optimization algorithm to find high-hardness component combinations, thereby significantly improving the scientific nature and development efficiency of alloy design.

[0008] In order to achieve the above objects, the technical solution adopted by the present invention is:

[0009] A method for alloy hardness prediction and composition optimization based on a goose optimization algorithm, the method comprising the following steps:

[0010] S1: Based on public literature and existing experimental data, the chemical composition of the alloy and its corresponding hardness data are collected. The alloy composition is used as the input feature and the hardness is used as the target performance. The total data set is constructed and preprocessed.

[0011] S2: A two-step method based on correlation analysis and feature importance is used to screen key component features. First, the first step of screening is performed by calculating the Pearson correlation coefficient of the features in the total data set described in step S1 to screen out highly correlated features. Then, the remaining features are ranked according to the mutual information importance score, and the features are gradually added to the regression model according to the ranking. The second step of screening is performed using the regression model accuracy as the evaluation indicator to screen out key component features.

[0012] S3: Based on the final key component characteristics determined in step S2, with hardness as the output, a preliminary hardness prediction model is screened from multiple candidate machine learning regression models using regression model evaluation metrics, through grid search and cross-validation, and hyperparameter optimization is performed to obtain a final hardness prediction model; the regression model evaluation metrics include coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE);

[0013] S4: The final hardness prediction model obtained in step S3 is subjected to composition optimization. In combination with the composition constraints, a goose optimization algorithm is used to search for the alloy composition ratio with the best hardness performance.

[0014] The present invention is based on the alloy hardness prediction and composition optimization method of the goose optimization algorithm (GOOSE algorithm), which adopts an organic combination of machine learning strategy and GOOSE algorithm to achieve rapid and accurate design of high-hardness alloys. First, the redundant features are removed by a two-step screening method, which effectively solves the problems of noise feature interference and high computational cost faced by some alloys when constructing machine learning prediction models, significantly improves the generalization ability of the model and reduces the risk of overfitting. Secondly, with the help of machine learning algorithms, a high-precision target performance prediction model is established, which not only overcomes the long cycle and high cost problems caused by the large design space of traditional design methods to a certain extent, but also achieves accurate prediction of alloy hardness. Finally, combined with the powerful global optimization capability of the GOOSE algorithm, the alloy composition is further optimized, providing a scientific design idea and important reference basis for the development of new high-hardness alloys, which has significant practical value and broad application prospects.

[0015] As a preferred technical solution, the preprocessing includes normalization and missing value processing.

[0016] As a preferred technical solution, in step S2, the specific operation steps of the two-step method for screening key component characteristics include:

[0017] S21: drawing a correlation heat map for the data set, calculating the Pearson correlation coefficient between each component feature, and retaining the feature with higher fitting accuracy for feature pairs with an absolute value of the correlation coefficient greater than 0.90, and eliminating redundant features;

[0018] S22: Mutual information (MI) method is used to evaluate the nonlinear correlation between the features retained in step S21 and the hardness properties, and the features are sorted in descending order according to the MI value;

[0019] S23: According to the sorting result of step S22, a step-by-step addition strategy is used to input the features into the preset regression model one by one, and the RMSE of each step model is evaluated in combination with five-fold cross-validation; when the RMSE value is minimum and continuing to add features causes the RMSE to increase, the addition is terminated, and the currently included feature set is determined as the final key component feature.

[0020] Compared with the existing technology, the above technical solution can quickly and effectively screen out the key component characteristics corresponding to the hardness performance in the total data set, providing clear and reasonable component characteristic input for subsequent model establishment.

[0021] As a preferred technical solution, in step S3, the specific steps of screening the preliminary hardness prediction model and performing hyperparameter optimization include:

[0022] S31: using the final key component feature as input and the hardness performance as output, determining the best random seed through grid search, and dividing the set into a training set and a test set at an 8:2 ratio;

[0023] S32: Using the test set and the training set, a five-fold cross validation method is used to screen a preliminary hardness prediction model from multiple hardness prediction models using the coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE) as evaluation indicators; the mathematical expression is as follows:

[0024] (1)

[0025] (2)

[0026] (3)

[0027] Where n is the total number of data, is the test value, is the predicted value, is the average test value; R 2 The closer it is to 1, the better the fitting effect is, and the smaller the MAE and RMSE values ​​are, the higher the model precision and accuracy is;

[0028] S33: Using the grid search method and cross-validation strategy, the preliminary hardness prediction model determined in step S32 is globally optimized for hyperparameters, and its performance is evaluated by the coefficient of determination (R²) to obtain the final hardness prediction model for subsequent component optimization.

[0029] Compared with the existing technology, the above technical solution can realize the screening of a preliminary hardness prediction model from the multiple hardness prediction models as a subsequent component optimization model.

[0030] As a preferred technical solution, the specific operation steps of step S4 include:

[0031] S41: Based on the element distribution range of the dataset, alloy composition limitations, and target application requirements, establish constraints for composition optimization to narrow the alloy composition space and improve computational efficiency.

[0032] S42: The final hardness prediction model obtained in step S3 is used as the objective function, and the alloy composition space is searched under the constraints established in step S41 by adopting the goose optimization algorithm. The goose optimization algorithm updates the positions of candidate component combinations by simulating the behavior of the goose flock in the development stage and the exploration stage, and uses the objective function as the fitness of the optimization algorithm to evaluate the predicted hardness value of each candidate component combination; finally, the maximum predicted hardness value is obtained as the goal, and the optimal composition ratio of the alloy that meets the constraints is output.

[0033] As a preferred technical solution, the position update formula of the goose optimization algorithm in the development stage is:

[0034] (4)

[0035] (5)

[0036] Among them, F_F_S represents the falling speed of the object, which is the speed of the stone falling to the ground in this algorithm; D_G it represents the distance between the guarding goose and another goose that is resting or eating; T_A represents the average time it takes for the sound of a stone falling to the ground to propagate to each goose in the flock during the iteration process; Coe is a defined variable with a value between 0 and 1;

[0037] The position update formula in the exploration phase is:

[0038] (6)

[0039] Where dim represents the dimension of the problem; M_T represents the shortest propagation time recorded in the number of cycles; alpha is the linear decay convergence factor, ranging from 0 to 2; and Best_pos represents the best position found in the search space.

[0040] The algorithm iteratively updates the candidate component combination until the termination condition is met, and outputs the component ratio with the highest predicted hardness value and meeting the component constraints.

[0041] Compared with the existing technology, the above technical solution can achieve targeted alloy composition design, obtain the predicted optimal composition ratio under the established constrained optimization conditions, effectively narrow the alloy composition space and improve calculation efficiency.

[0042] As a preferred technical solution, the machine learning regression model includes at least two regression models among random forest, support vector regression, multilayer perceptron, ridge regression, Lasso regression, extreme gradient boosting, decision tree regression, K nearest neighbor regression and gradient boosting regression tree.

[0043] Another aspect of the present invention is to provide an alloy hardness prediction and composition optimization system based on the goose optimization algorithm, wherein the system uses the alloy hardness prediction and composition optimization method based on the goose optimization algorithm to perform alloy hardness prediction and composition optimization; the system comprises:

[0044] A data acquisition module is used to collect data on the chemical composition of the alloy and its corresponding hardness based on public literature and existing experimental data, and synthesize a total data set from the data;

[0045] A data processing module is used to pre-process the total data set according to the distribution characteristics of the content of each component and the median principle, including normalization and missing value processing;

[0046] A feature screening module is used to screen key component features using a two-step method. In the first step, highly correlated redundant features are eliminated based on the Pearson correlation coefficient analysis of the total data set. Then, features are sorted according to the mutual information importance score and evaluated by gradually adding features to achieve the second step of screening to determine the final key component features.

[0047] A model building module is used to, after determining the final key component characteristics, use the final key component characteristics as input and hardness as output, divide the training set into a test set, combine five-fold cross-validation, and screen a preliminary hardness prediction model from multiple candidate machine learning regression models based on regression model evaluation indicators; the regression model evaluation indicators include determination coefficient, mean absolute error, and root mean square error;

[0048] an optimization module for performing global hyperparameter optimization on the determined preliminary hardness prediction model using a grid search method and a cross-validation strategy, evaluating the regression model performance using a determination coefficient, and obtaining a final hardness prediction model as a subsequent hardness prediction component optimization model; and

[0049] The composition prediction module is used to search and output the alloy composition ratio scheme with the best predicted hardness value based on the optimized final hardness prediction model and the set alloy composition constraints using the goose optimization algorithm

[0050] As a preferred technical solution, the feature screening module includes:

[0051] The Pearson correlation analysis unit is used to calculate the Pearson correlation coefficient between each component feature in the data set, draw a correlation heat map, and build preliminary regression models for strongly correlated feature pairs with an absolute value of the correlation coefficient greater than 0.90, using alloy hardness as the target variable. The fitting accuracy is compared, and the features with better prediction effects are retained, while redundant features are eliminated to complete the first step of screening;

[0052] Mutual information analysis unit, used to evaluate the nonlinear correlation between the features retained after Pearson correlation analysis and the target hardness performance, sort the features based on the mutual information value (MI), and use a stepwise addition strategy to input the features into the regression model in sequence, combining cross-validation to evaluate the model performance at each step; and

[0053] The key component feature determination unit is used to calculate the root mean square error (RMSE) of each stage during the gradual feature addition process. When the RMSE value drops to the minimum and further feature addition leads to performance degradation, the addition is stopped and the feature set contained in this stage is confirmed as the final key component feature.

[0054] As a preferred technical solution, the model building module includes:

[0055] A data set partitioning unit is used to determine the optimal random seed through grid search, using the key component characteristics screened by the system as input and hardness performance as output target, and to partition the data set into training and test sets according to a preset ratio for model training and evaluation; and

[0056] The model selection unit is used to select the preliminary hardness prediction model with the best fitting performance from multiple candidate machine learning regression models based on the training set and the test set, using a five-fold cross-validation method and comprehensive regression model evaluation indicators.

[0057] Beneficial effects of the present invention:

[0058] The present invention proposes a method and system for alloy hardness prediction and composition optimization that integrates machine learning modeling and intelligent optimization algorithms. By innovatively combining the Pearson correlation coefficient and mutual information evaluation to construct a dual feature screening mechanism, not only are the alloy composition features that are highly correlated with hardness effectively identified, but the accuracy and efficiency of feature selection are also significantly improved. Grid search and cross-validation are used to screen out preliminary hardness prediction models from a variety of machine learning regression models, and combined with global hyperparameter tuning, the high accuracy and robustness of the prediction results are ensured. In addition, in response to the technical bottlenecks of existing optimization algorithms that are prone to falling into local optimality and low search efficiency when processing high-dimensional composition space, the present invention introduces a new swarm intelligence optimization algorithm, the GOOSE algorithm, for the first time. The deep integration of the GOOSE algorithm and the machine learning performance prediction model realizes efficient global optimization of complex alloy composition space, significantly improves the intelligence level and optimization accuracy of high-hardness alloy design, and provides a new technical path for building a universal, efficient, and scalable alloy hardness prediction and composition optimization system.

[0059] In general, the alloy hardness prediction and composition optimization method and system based on the goose optimization algorithm of the present invention not only have excellent prediction accuracy and optimization efficiency, but also can significantly reduce development costs and shorten the R&D cycle, and can meet the actual needs of rapid design of high-performance alloys. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 This is a flowchart of the operation steps of the alloy hardness prediction and composition optimization method based on the GOOSE algorithm in Example 1 of the present application;

[0061] Figure 2 This is a flowchart of the specific operating steps of step S2 in Example 1 of this application;

[0062] Figure 3This is a flowchart of the specific operating steps of step S3 in Example 1 of this application;

[0063] Figure 4 This is an evaluation diagram of the key component characteristics of the two-step screening method in Example 1 of this application;

[0064] Figure 5 This is an evaluation chart of the performance of each model algorithm and optimized prediction model in Example 1 of this application;

[0065] Figure 6 This is a schematic diagram of the structure of the alloy hardness prediction and composition optimization system based on the GOOSE algorithm in Example 1 of the present application. DETAILED DESCRIPTION

[0066] The following description is intended to disclose the present invention so that those skilled in the art can implement the present invention. The preferred embodiments described below are merely examples, and those skilled in the art may conceive of other obvious variations.

[0067] Example 1

[0068] This embodiment is based on the alloy hardness prediction and composition optimization method of the goose optimization algorithm, such as Figures 1 to 5 As shown, the method includes the following steps:

[0069] S1: Based on public literature and existing experimental data, the chemical composition of zinc alloy and its corresponding hardness data are collected. The alloy composition is used as the input feature and the hardness is used as the target performance. The total data set is constructed and preprocessed.

[0070] In this embodiment, a total of 174 hardness data of zinc-based alloys were collected through public literature and existing experimental data, covering 17 elements, including Zn, Al, Cu, Mg, Ca, Sr, Ti, Mn, Fe, Pb, Cd, Sn, Si, B, Re, La and Ce. The hardness value is mainly Vickers hardness (HV). According to the distribution characteristics of the content of each component and the median principle, the total data set was preprocessed, including normalization and missing value processing. Finally, all data in the total data set were manually proofread and repeatedly verified. The value range of each feature in the total data set used to train the regression model is shown in Table 1. The first column of Table 1 shows the characteristic elements of each component in the collected zinc alloy data, Zn, Al, Cu, Mg, Ca, Sr, Ti, Mn, Fe, Pb, Cd, Sn, Si, B, Re, La, Ce, and the alloy element composition unit is unified as mass percentage (wt%). The second column of Table 1 shows the value ranges for each characteristic element. For example, the Zn content "53.985-99.06" in the second row indicates that the Zn content in the collected zinc alloy data ranges from 53.985 to 99.06 (wt%). The third column of Table 1 shows the median value of each component content collected in the entire data set based on the distribution characteristics of the component content.

[0071] Table 1 Value range of input features

[0072] Parameters (wt%) Range Average Zn 53.985-99.06 89.593 Al 0-43 8.8945 Cu 0-5 1.0201 Mg 0-4.75 0.2682 Ca 0-1.18 0.0257 Sr 0-1.15 0.0233 Ti 0-1.1 0.0291 Mn 0-0.2 0.0147 Fe 0-0.3 0.0068 Pb 0-2 0.0120 Cd 0-0.05 0.0006 Sn 0-0.1 0.0007 Si 0-1.1 0.0806 B 0-0.12 0.0038 Re 0-0.25 0.0079 La 0-0.401 0.0084 Ce 0-0.301 0.0107

[0073] According to the numerical distribution characteristics of hardness and the median principle, the range of target performance (hardness) collected in the total data set is as follows:

[0074] Target Range Average Hardness (HV) 46.285-200 102.6958

[0075] It can be seen that the median value of the target performance (hardness) is 102.6958 HV.

[0076] S2: A two-step method based on correlation analysis and feature importance is used to screen key component features. First, the first step of screening is performed by calculating the Pearson correlation coefficient of the features in the total data set described in step S1 to screen out highly correlated features. Then, the remaining features are ranked according to the mutual information importance score, and the features are gradually added to the regression model according to the ranking. The second step of screening is performed using the regression model accuracy as the evaluation indicator to screen out key component features.

[0077] In one of the more preferred embodiments, see Figure 2 As shown, in step S2 of this embodiment, the specific operation steps of the two-step method for screening key component characteristics include:

[0078] S21: Draw a correlation heat map for the data set, calculate the Pearson correlation coefficient between each component feature, and for feature pairs with an absolute value of the correlation coefficient greater than 0.90, retain the feature with higher fitting accuracy and eliminate redundant features;

[0079] S22: Mutual information (MI) method is used to evaluate the nonlinear correlation between the features retained in step S21 and the hardness properties, and the features are sorted in descending order according to the MI value;

[0080] S23: According to the sorting results of step S22, a step-by-step addition strategy is used to input the features one by one into the preset regression model, and the root mean square error (RMSE) of the model at each step is evaluated in combination with five-fold cross-validation; when the RMSE value is minimum and continuing to add features causes the RMSE to increase, the addition is terminated, and the currently included feature set is determined as the final key component feature.

[0081] In this embodiment, a two-step screening method based on correlation analysis and feature importance is used to identify key component features and remove redundant features. Figure 4 As shown, in step S21, a correlation heat map is drawn for screening. The darker the color, the higher the correlation coefficient. By calculating the Pearson correlation coefficient between each component feature, for feature pairs with an absolute value of the correlation coefficient greater than 0.90, namely Cd and Fe, Sn and Pb, and Cd and Sn, preliminary prediction models are constructed using material hardness as the target variable. The fitting accuracy of the constructed models is compared, and the features with higher accuracy are retained. The redundant features Sn and Fe are successively removed, reducing the number of features from 17 to 15.

[0082] Continue to see Figure 4 Mutual Information (MI) was used to evaluate the nonlinear correlation between these 15 features and the target performance (hardness), and the features were ranked according to the MI value. By gradually adding features, the top-ranked features were input into the model in turn, and the model performance of each step was evaluated using five-fold cross-validation. The results showed that as the number of features increased from 1 to 5, the model RMSE decreased significantly; when the number of features reached 7, the RMSE dropped to the lowest (17.06), and adding features thereafter led to a decrease in performance. The 7 optimal input features finally selected were Zn, Cu, Al, Si, Mg, Ti, and Mn, which were determined as the final key component features.

[0083] S3: Based on the final key component features determined in step S2, with hardness as the output, a preliminary hardness prediction model is screened from multiple candidate machine learning regression models using regression model evaluation metrics such as coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE), through grid search and cross-validation, and hyperparameter optimization is performed.

[0084] In one of the more preferred embodiments, see Figure 3 As shown, in step S3 of this embodiment, the specific steps of screening the preliminary hardness prediction model and performing hyperparameter optimization include:

[0085] S31: Using the final key component characteristics as input and hardness performance as output to ensure reproducibility, the optimal random seed is determined through grid search and divided into training set and test set at an 8:2 ratio;

[0086] S32: Using the test set and the training set, the 5-fold cross-validation method is used to select a preliminary hardness prediction model from multiple hardness prediction models using the coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE) as evaluation indicators. The mathematical expression is as follows:

[0087] (1)

[0088] (2)

[0089] (3)

[0090] Where n is the total number of data, is the test value, is the predicted value, is the average test value; R 2 The closer it is to 1, the better the fitting effect is, and the smaller the MAE and RMSE values ​​are, the higher the model precision and accuracy are.

[0091] S33: Using the grid search method and cross-validation strategy, the global hyperparameter optimization of the preliminary hardness prediction model determined in step S32 is performed to determine the coefficient R 2 Its performance was evaluated to obtain the final hardness prediction model for subsequent composition optimization.

[0092] In one of the more preferred embodiments, see Figure 5As shown, specifically in the specific example of this embodiment, the final key component feature obtained by screening in step S23 is used as input, hardness is output, and the data set is randomly divided into training set and test set in a ratio of 8:2. Random forest (RF), support vector regression (SVR), multi-layer perceptron (MLP), ridge regression (Ridge Regression), Lasso regression (Lasso Regression), extreme gradient boosting (XGBoost), decision tree regression (DTR), K nearest neighbor regression (KNN) and gradient boosting regression tree (GBDT) are initially selected to construct a zinc alloy hardness prediction model. The five-fold cross validation method is used and the determination coefficient (R²), mean absolute error (MAE) and root mean square error (RMSE) are used as evaluation indicators to screen the preliminary hardness prediction model from multiple hardness prediction models. According to Figure 5 (a) It can be seen that the RF model performs best in the construction of hardness prediction models, and its performance is significantly better than other models. The fitting accuracy reaches 0.85, followed by GBDT and XGBoost, which reach 0.82 and 0.817 respectively.

[0093] The parameters of the optimal model RF are as follows:

[0094] Models Optimal hyperparameter RF n_estimators=200, criterion='friedman_mse', max_depth=None, max_features='sqrt', min_samples_leaf=1, min_samples_split=2

[0095] Continue to see Figure 5 As shown, in this embodiment, the grid search method and cross-validation strategy are used to perform global hyperparameter optimization on the preliminary hardness prediction model (RF) determined in step S32 to determine the coefficient R 2 The performance is evaluated to obtain the final hardness prediction model for subsequent component optimization. Figure 5 (c) and (d) show the model fitting performance before and after hyperparameter optimization, respectively. It can be seen that the fitting accuracy of the RF final test set reaches 0.85 through hyperparameter optimization. The results show that after the model and hyperparameters are determined, the prediction accuracy of the model is suitable for alloy design.

[0096] S4: The final hardness prediction model obtained in step S3 is subjected to composition optimization. In combination with the composition constraints, a goose optimization algorithm is used to search for the zinc alloy composition ratio with the best hardness performance.

[0097] In one of the more preferred embodiments, specifically in the specific example of this embodiment, according to the element distribution range of the data set, the zinc alloy composition restrictions and the target application requirements, the constraint conditions for composition optimization are set as Al: 5.0~11.0wt%, Cu: 1.0~6.0wt%, Mg: 0~0.1wt%, Ti: 0~0.4wt%, Mn: 0.1~0.6wt%, Si: 0~0.8wt%, and Zn participates in the prediction in the form of a remainder. The final hardness prediction model obtained is used as the objective function, and the GOOSE algorithm is used for optimization to search the zinc alloy composition space under the set constraints. The GOOSE algorithm updates the position of the candidate composition combination by simulating the behavior of the goose flock in the development stage and the exploration stage, and uses the objective function as the fitness of the optimization algorithm to evaluate the predicted hardness value of each candidate composition combination. Ultimately, the goal is to obtain the maximum predicted hardness value, and the optimal composition ratio of the zinc alloy that meets the constraints is output, which is listed as follows:

[0098] Composition Al Cu Mg Ti Si Zn HV Optimized result 11 4.5 0.017 0.4 0.8 Bal 142.5

[0099] This embodiment is based on the alloy hardness prediction and composition optimization method of the GOOSE algorithm. It combines a machine learning prediction model with an intelligent optimization algorithm. It effectively solves the problems of long cycle time and high cost caused by excessive trial and error in traditional zinc alloy design, and realizes the rapid and accurate design of high-hardness zinc alloy composition.

[0100] Furthermore, the present embodiment is based on the alloy hardness prediction and composition optimization system of the GOOSE algorithm. The system uses the alloy hardness prediction and composition optimization method based on the GOOSE algorithm to perform alloy hardness prediction and composition optimization. Figure 6 As shown in the figure, the system includes a data acquisition module, a data processing module, a feature screening module, a model building module, an optimization module, and a component prediction module. The functions of each module are as follows:

[0101] A data acquisition module is used to collect data on the chemical composition of zinc alloys and their corresponding hardness based on public literature and existing experimental data, and to synthesize a total data set from the data;

[0102] A data processing module is used to pre-process the total data set according to the distribution characteristics of the content of each component and the median principle, including normalization and missing value processing;

[0103] A feature screening module is used to screen key component features using a two-step method. The first step is to eliminate highly correlated redundant features based on the Pearson correlation coefficient analysis in the dataset, and then to sort the features according to the mutual information importance score and perform the second step of screening by gradually adding features for evaluation to determine the final key component features.

[0104] The model building module is used to divide the final key component characteristics into training and test sets after determining them, and then screen the preliminary hardness prediction model from multiple candidate machine learning regression models based on regression model evaluation indicators such as the coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE) by combining five-fold cross-validation.

[0105] The optimization module is used to optimize the global hyperparameters of the determined preliminary hardness prediction model using the grid search method and cross-validation strategy, evaluate the regression model performance based on the determination coefficient, and obtain the final hardness prediction model as the subsequent hardness prediction component optimization model.

[0106] The composition prediction module is used to search and output the alloy composition ratio scheme with the best predicted hardness value based on the optimized final hardness prediction model and the set alloy composition constraints using the goose optimization algorithm

[0107] Continue to see Figure 6 In this embodiment, the feature screening module includes a Pearson correlation analysis unit, a mutual information analysis unit, and a key component feature determination unit. The Pearson correlation analysis unit is configured to calculate the Pearson correlation coefficient between the component features in the data set, draw a correlation heat map, and for strongly correlated feature pairs with an absolute value greater than 0.90, respectively, construct preliminary regression models with the zinc alloy hardness as the target variable, compare their fitting accuracy, retain features with better prediction effects, and eliminate redundant features; the mutual information analysis unit is configured to evaluate the nonlinear correlation between the retained features after Pearson analysis and the target hardness performance, sort the features based on the mutual information value (MI), and use a stepwise addition strategy to input the features into the regression model in sequence, combining cross-validation to evaluate the model performance at each step; the key component feature determination unit is configured to calculate the root mean square error (RMSE) of each stage during the stepwise feature addition process. When the RMSE value drops to the minimum and further feature addition results in performance degradation, the addition is stopped, and the feature set contained in this stage is confirmed as the final key component feature.

[0108] Continue to see Figure 6In this embodiment, the model construction module includes a data set partitioning unit and a model selection unit. The data set partitioning unit is configured to determine the optimal random seed through a grid search method, with the key component characteristics screened out by the system as input and the hardness performance as the output target, and the data set is divided into a training set and a test set according to a preset ratio for model training and evaluation; the model selection unit is configured to use a five-fold cross-validation method based on the training set and the test set, and comprehensively consider performance indicators such as the coefficient of determination (R²), mean absolute error (MAE) and root mean square error (RMSE) to screen out the prediction model with the best fitting performance from multiple candidate machine learning regression models.

[0109] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions only describe the principles of the present invention. Various changes and improvements are possible without departing from the spirit and scope of the present invention, and such changes and improvements fall within the scope of the invention as claimed.

Claims

1. A method for alloy hardness prediction and composition optimization based on goose optimization algorithm, characterized in that: The method comprises the following steps: S1: Based on public literature and existing experimental data, the chemical composition of the alloy and its corresponding hardness data are collected. The alloy composition is used as the input feature and the hardness is used as the target performance. The total data set is constructed and preprocessed. S2: A two-step method based on correlation analysis and feature importance is used to screen key component features. First, the first step of screening is performed by calculating the Pearson correlation coefficient of the features in the total data set described in step S1 to screen out highly correlated features. Then, the remaining features are ranked according to the mutual information importance score, and the features are gradually added to the regression model according to the ranking. The second step of screening is performed using the regression model accuracy as the evaluation indicator to screen out key component features. S3: Based on the final key component characteristics determined in step S2, with hardness as the output, a preliminary hardness prediction model is screened from multiple candidate machine learning regression models based on regression model evaluation indicators, through grid search and cross-validation, and hyperparameter optimization is performed to obtain a final hardness prediction model; the regression model evaluation indicators include determination coefficient, mean absolute error, and root mean square error; S4: The final hardness prediction model obtained in step S3 is subjected to composition optimization. In combination with the composition constraints, a goose optimization algorithm is used to search for the alloy composition ratio with the best hardness performance.

2. The alloy hardness prediction and composition optimization method based on the goose optimization algorithm according to claim 1, characterized in that: The preprocessing includes normalization and missing value processing.

3. The alloy hardness prediction and composition optimization method based on the goose optimization algorithm according to claim 1, characterized in that: In step S2, the specific operation steps of the two-step method for screening key component characteristics include: S21: drawing a correlation heat map for the data set, calculating the Pearson correlation coefficient between each component feature, and retaining the feature with higher fitting accuracy for feature pairs with an absolute value of the correlation coefficient greater than 0.90, and eliminating redundant features; S22: using the mutual information method to evaluate the nonlinear correlation between the features retained in step S21 and the hardness performance, and sorting the features in descending order according to the mutual information value; S23: According to the sorting result of step S22, a step-by-step addition strategy is used to input the features into the preset regression model one by one, and the root mean square error of the model at each step is evaluated in combination with five-fold cross-validation; when the root mean square error value is minimized and continuing to add features causes the root mean square error to increase, the addition is terminated, and the currently included feature set is determined as the final key component feature.

4. The alloy hardness prediction and composition optimization method based on the goose optimization algorithm according to claim 1, characterized in that: In step S3, the specific steps of screening the preliminary hardness prediction model and performing hyperparameter optimization include: S31: using the final key component feature as input and the hardness performance as output, determining the best random seed through grid search, and dividing the set into a training set and a test set at an 8:2 ratio; S32: using the test set and the training set, adopting a five-fold cross validation method, and using the coefficient of determination, mean absolute error, and root mean square error as evaluation indicators to screen a preliminary hardness prediction model from multiple hardness prediction models; S33: Using the grid search method and cross-validation strategy, the preliminary hardness prediction model determined in step S32 is globally optimized for hyperparameters, and its performance is evaluated based on the determination coefficient to obtain the final hardness prediction model for subsequent component optimization.

5. The alloy hardness prediction and composition optimization method based on the goose optimization algorithm according to claim 1, characterized in that: The specific operation steps of step S4 include: S41: Based on the element distribution range of the dataset, alloy composition limitations, and target application requirements, establish constraints for composition optimization to narrow the alloy composition space and improve computational efficiency. S42: The final hardness prediction model obtained in step S3 is used as the objective function, and the alloy composition space is searched under the constraints established in step S41 by adopting the goose optimization algorithm. The goose optimization algorithm updates the positions of candidate component combinations by simulating the behavior of the goose flock in the development stage and the exploration stage, and uses the objective function as the fitness of the optimization algorithm to evaluate the predicted hardness value of each candidate component combination; finally, the maximum predicted hardness value is obtained as the goal, and the optimal composition ratio of the alloy that meets the constraints is output.

6. The alloy hardness prediction and composition optimization method based on the goose optimization algorithm as claimed in claim 5, characterized in that: The position update formula of the goose optimization algorithm in the development stage is: (4) (5) Among them, F_F_S represents the falling speed of the object, which is the speed of the stone falling to the ground in this algorithm; D_G it represents the distance between the guarding goose and another goose that is resting or eating; T_A represents the average time it takes for the sound of a stone falling to the ground to propagate to each goose in the flock during the iteration process; Coe is a defined variable with a value between 0 and 1; The position update formula in the exploration phase is: (6) Where dim represents the dimension of the problem; M_T represents the shortest propagation time recorded in the existing number of cycles; alpha is the linear decay convergence factor, ranging from 0 to 2; and Best_pos represents the best position found in the search space.

7. The alloy hardness prediction and composition optimization method based on the goose optimization algorithm as claimed in claim 1, characterized in that: The machine learning regression model includes at least two regression models of random forest, support vector regression, multilayer perceptron, ridge regression, lasso regression, extreme gradient boosting, decision tree regression, K nearest neighbor regression and gradient boosting regression tree.

8. An alloy hardness prediction and composition optimization system based on goose optimization algorithm, characterized in that: The system adopts the alloy hardness prediction and composition optimization method based on the goose optimization algorithm as described in any one of claims 1 to 7 to perform alloy hardness prediction and composition optimization; the system includes: A data acquisition module is used to collect data on the chemical composition of the alloy and its corresponding hardness based on public literature and existing experimental data, and synthesize a total data set from the data; A data processing module is used to pre-process the total data set according to the distribution characteristics of the content of each component and the median principle, including normalization and missing value processing; A feature screening module is used to screen key component features using a two-step method. In the first step, highly correlated redundant features are eliminated based on the Pearson correlation coefficient analysis of the total data set. Then, features are sorted according to the mutual information importance score and evaluated by gradually adding features to achieve the second step of screening to determine the final key component features. A model building module is used to, after determining the final key component characteristics, use the final key component characteristics as input and hardness as output, divide the training set into a test set, combine five-fold cross-validation, and screen a preliminary hardness prediction model from multiple candidate machine learning regression models based on regression model evaluation indicators; the regression model evaluation indicators include determination coefficient, mean absolute error, and root mean square error; an optimization module for performing global hyperparameter optimization on the determined preliminary hardness prediction model using a grid search method and a cross-validation strategy, evaluating the regression model performance using a determination coefficient, and obtaining a final hardness prediction model as a subsequent hardness prediction component optimization model; and The composition prediction module is used to apply the goose optimization algorithm to search and output the alloy composition ratio scheme with the optimal predicted hardness value based on the optimized final hardness prediction model and the set alloy composition constraints.

9. The alloy hardness prediction and composition optimization system based on the goose optimization algorithm as claimed in claim 8, characterized in that: The feature screening module includes: The Pearson correlation analysis unit is used to calculate the Pearson correlation coefficient between each component feature in the data set, draw a correlation heat map, and build preliminary regression models for strongly correlated feature pairs with an absolute value of the correlation coefficient greater than 0.90, using alloy hardness as the target variable. The fitting accuracy is compared, and the features with better prediction effects are retained, while redundant features are eliminated to complete the first step of screening; A mutual information analysis unit is used to evaluate the nonlinear correlation between the features retained after Pearson correlation analysis and the target hardness performance. The features are ranked based on the mutual information value and are sequentially input into the regression model using a stepwise addition strategy. The performance of the model is evaluated at each step in combination with cross-validation; and The key component feature determination unit is used to calculate the root mean square error of each stage during the gradual feature addition process. When the root mean square error value drops to the minimum and further adding features leads to performance degradation, the addition is stopped and the feature set contained in this stage is confirmed as the final key component feature.

10. The alloy hardness prediction and composition optimization system based on the goose optimization algorithm as claimed in claim 8, characterized in that: The model building module includes: A data set partitioning unit is used to determine the optimal random seed through grid search, using the key component characteristics screened by the system as input and hardness performance as output target, and to partition the data set into training and test sets according to a preset ratio for model training and evaluation; and The model selection unit is used to select the preliminary hardness prediction model with the best fitting performance from multiple candidate machine learning regression models based on the training set and the test set, using a five-fold cross-validation method and comprehensive regression model evaluation indicators.

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