A method and system for predicting the hardness of high-entropy alloys

Abstract

This invention relates to a method and system for predicting the hardness of high-entropy alloys. The method includes: acquiring candidate features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system and establishing a dataset; training a Stacking ensemble model using the dataset; filtering candidate features using Pearson correlation coefficient, XGBoost evaluation model, random forest, genetic algorithm, XGBoost-based recursive feature elimination method, and exhaustive search method to determine the filtered features; establishing a classifier based on the filtered features using principal component analysis and logistic regression; constructing an alloy composition search space based on the trained Stacking ensemble model and the classifier; and predicting the hardness based on the alloy composition search space. This invention can improve the accuracy of hardness prediction for high-entropy alloys.

Description

Technical Field

[0001] This invention relates to the field of metal material design technology, and in particular to a method and system for predicting the hardness of high-entropy alloys. Background Technology

[0002] Traditional alloys are generally based on one or two alloys, with the addition of other different elements to improve material properties. High-entropy alloys, on the other hand, are designed using four or more main elements in equimolar or near-equimolar proportions. Due to their complex and variable structures, high-entropy alloys exhibit a variety of superior effects, including thermodynamic high-entropy effects, severe lattice distortion effects, slow diffusion effects, and the "cocktail" effect.

[0003] While high-entropy alloys may exhibit exceptional properties, their complex composition and structure make finding high-performance high-entropy alloys challenging. The primary screening methods rely on prior experience and trial-and-error, resulting in relatively low efficiency. In recent years, computational materials design technologies have rapidly advanced, significantly boosting the development of new materials. In particular, with the rapid rise and development of artificial intelligence over the past decade, machine learning has gradually been applied across various fields. Compared to traditional computational methods such as density functional theory (DFT) and molecular dynamics, machine learning only requires establishing a black-box model to predict material properties, greatly improving computational efficiency. Furthermore, with the development of interpretable machine learning, information previously unnoticed by humans can be gradually extracted from black-box models. Undoubtedly, machine learning is an excellent tool for exploring the complex principal components and structures of high-entropy alloys and predicting their properties. It can not only capture patterns beyond human prior experience but also significantly accelerate the design of high-performance materials and the discovery of new materials.

[0004] Bhandari et al. used a five-hidden-layer artificial neural network to predict the hardness of refractory high-entropy alloys and successfully predicted C. 0.1 Cr3Mo 11.9 Nb 20 Re 15 Ta 30 W 20The hardness is 695 HV. Wen et al. constructed a two-layer iterative machine learning system, combining support vector machine and utility function to search for candidate high-entropy alloys. Through seven rounds of iteration, they synthesized 42 high-entropy alloys, of which 17 alloys showed a hardness increase of more than 10%. Wang et al. synthesized 138 alloy samples through high-throughput experiments. Based on their hardness data, they constructed 120 combinations using three machine learning models and four descriptive factors. The optimal model selected from these combinations improved the overall alloy design efficiency by 200 times. Chang et al. used artificial neural networks to predict high-entropy alloys in the AlCoCrFeMnNi system and combined it with a simulated annealing algorithm to select candidate alloys from the search space, obtaining high-hardness high-entropy alloys. Although the above works have achieved good prediction results, in the synthesis verification stage, the low generalization performance of traditional machine learning algorithms leads to a larger deviation between the actual and predicted values, resulting in low prediction accuracy.

[0005] Therefore, in order to solve the above problems, it is urgent to provide a method or system that can improve the accuracy of hardness prediction of high-entropy alloys, so as to achieve the goal of designing high-hardness high-entropy alloys. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for predicting the hardness of high-entropy alloys, which can improve the accuracy of hardness prediction for high-entropy alloys.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] A method for predicting the hardness of high-entropy alloys, comprising:

[0009] Candidate features are obtained from the hardness data of AlCoCrCuFeNi system high-entropy alloys in the high-entropy alloy hardness database; and a dataset is constructed based on the candidate features and the corresponding hardness data of AlCoCrCuFeNi system high-entropy alloys. The hardness data of AlCoCrCuFeNi system high-entropy alloys includes: the molar ratio of each element in each system and the corresponding hardness; the candidate features include: valence electron concentration, mixing entropy, mixing enthalpy, atomic radius difference, electronegativity difference, average melting point of the alloy, local electronegativity mismatch, electron concentration, Gibbs free energy, shear modulus, Young's modulus, lattice distortion energy, shear modulus mismatch, energy in the enhancement model, condensation energy, Peierls-Nabarro factor, work function, local atomic radius mismatch, local modulus mismatch, shear modulus difference, average deviation of alloy atomic weight, average deviation of alloy family, average deviation of alloy specific volume, and synthesis parameters.

[0010] A Stacking ensemble model is trained using the dataset; the trained Stacking ensemble model includes a primary classifier and a secondary classifier; the trained Stacking ensemble model is used to determine the corresponding stiffness based on candidate features;

[0011] For candidate features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system, Pearson correlation coefficient, XGBoost evaluation model, random forest, genetic algorithm, XGBoost-based recursive feature elimination method and exhaustive method were used for screening to determine the screened features.

[0012] Based on the selected characteristics corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system, a classifier is established using principal component analysis and logistic regression; the classifier is used to classify the hardness of high-entropy alloys.

[0013] The alloy composition search space is constructed based on the trained Stacking ensemble model and the classifier.

[0014] The hardness of high-entropy alloys in the AlCoCrCuFeNi system is predicted based on the alloy composition search space.

[0015] Optionally, training the Stacking ensemble model using the dataset specifically includes:

[0016] The RandomForest, XGBoost, and CatBoost methods were used to determine the primary classifier.

[0017] Use a Bayesian regressor to determine the secondary classifier.

[0018] Optionally, the candidate features corresponding to the hardness data of the AlCoCrCuFeNi high-entropy alloy are screened using Pearson correlation coefficient, XGBoost evaluation model, random forest, genetic algorithm, XGBoost-based recursive feature elimination method, and exhaustive search method to determine the screened features, specifically including:

[0019] For candidate features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system, the Pearson correlation coefficient was used for correlation screening, and the candidate features were divided into 3 high correlation groups and 1 low correlation group with a threshold of 0.9. The candidate features in the high correlation group were added to the low correlation group, and the XGBoost evaluation model was used to determine the corresponding mean square error. The candidate features in each high correlation group with a mean square error less than the mean square error threshold were retained to obtain the features after the first screening.

[0020] The features after the first screening were subjected to random forest, genetic algorithm, and recursive feature elimination method based on XGBoost to obtain the features after the second screening.

[0021] An exhaustive method was used to obtain the filtered features after the second screening.

[0022] Optionally, the step of establishing a classifier based on the selected features corresponding to the hardness data of the high-entropy alloy in the AlCoCrCuFeNi system, using principal component analysis and logistic regression, specifically includes:

[0023] Data normalization was performed on the selected features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system.

[0024] Principal component analysis is used to reduce the dimensionality of the normalized features of the data;

[0025] Logistic regression is used to build a classifier based on the dimensionality-reduced features.

[0026] Optionally, the prediction of the hardness of the AlCoCrCuFeNi high-entropy alloy based on the alloy composition search space specifically includes:

[0027] Construct a dataset of element molar ratios for high-entropy alloys to be predicted, and use a classifier to determine whether the element molar ratio dataset exceeds a set hardness.

[0028] For data in the element molar ratio dataset that exceeds the set hardness, hardness prediction is performed using a trained Stacking ensemble model.

[0029] A hardness prediction system for high-entropy alloys, comprising:

[0030] The candidate feature acquisition module is used to acquire corresponding candidate features based on the hardness data of high-entropy alloys in the AlCoCrCuFeNi system from the high-entropy alloy hardness database; and to construct a dataset based on the candidate features and the corresponding hardness data of high-entropy alloys in the AlCoCrCuFeNi system; the hardness data of high-entropy alloys in the AlCoCrCuFeNi system includes: the molar ratio of each element in each system and the corresponding hardness; the candidate features include: valence electron concentration, mixing entropy, mixing enthalpy, atomic radius difference, electronegativity difference, average melting point of the alloy, local electronegativity mismatch, electron concentration, Gibbs free energy, shear modulus, Young's modulus, lattice distortion energy, shear modulus mismatch, energy in the enhancement model, condensation energy, Peierls-Nabarro factor, work function, local atomic radius mismatch, local modulus mismatch, shear modulus difference, average deviation of alloy atomic weight, average deviation of alloy family, average deviation of alloy specific volume, and synthesis parameters.

[0031] The trained Stacking ensemble model determination module is used to train the Stacking ensemble model using the dataset; the trained Stacking ensemble model includes a primary classifier and a secondary classifier; the trained Stacking ensemble model is used to determine the corresponding stiffness based on candidate features;

[0032] The filtered feature determination module is used to screen candidate features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system using Pearson correlation coefficient, XGBoost evaluation model, random forest, genetic algorithm, XGBoost-based recursive feature elimination method and exhaustive method to determine the filtered features.

[0033] The classifier building module is used to build a classifier based on the filtered features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system, using principal component analysis and logistic regression; the classifier is used to classify the hardness of high-entropy alloys.

[0034] The alloy composition search space construction module is used to construct the alloy composition search space based on the trained Stacking ensemble model and the classifier.

[0035] The hardness prediction module is used to predict the hardness of high-entropy alloys in the AlCoCrCuFeNi system based on the alloy composition search space.

[0036] Optionally, the trained Stacking ensemble model determination module specifically includes:

[0037] The primary classifier determination unit is used to determine the primary classifier using RandomForest, XGBoost, and CatBoost methods.

[0038] The secondary classifier determination unit is used to determine the secondary classifier using a Bayesian regressor.

[0039] Optionally, the filtered feature determination module specifically includes:

[0040] The first screening unit is used to screen candidate features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system. The Pearson correlation coefficient is used for correlation screening, and the candidate features are divided into 3 high correlation groups and 1 low correlation group with a threshold of 0.9. The candidate features in the high correlation group are added to the low correlation group, and the XGBoost evaluation model is used to determine the corresponding mean square error. The candidate features in each high correlation group with a mean square error less than the mean square error threshold are retained to obtain the features after the first screening.

[0041] The second screening unit is used to apply random forest, genetic algorithm, and XGBoost-based recursive feature elimination method to the features after the first screening to obtain the features after the second screening.

[0042] The feature determination unit after filtering is used to exhaustively search for the features after the second filtering to obtain the filtered features.

[0043] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0044] This invention provides a method and system for predicting the hardness of high-entropy alloys. It identifies candidate features based on existing data in a database, constructs and trains a Stacking ensemble model consisting of a primary classifier and a secondary classifier, filters the candidate features, and uses principal component analysis and logistic regression to build a classifier for the filtered features. An alloy composition search space is constructed based on the trained Stacking ensemble model and the classifiers. The classifiers are used for initial prediction, filtering out alloys with high hardness, and the trained Stacking ensemble model is used for secondary prediction. This effectively solves the problems of model overfitting and low prediction accuracy, improves model robustness, and ultimately enables the design of high-hardness, high-entropy alloys. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a schematic diagram of the hardness prediction method for high-entropy alloys provided by the present invention.

[0047] Figure 2 This is a schematic diagram illustrating the principle of a high-entropy alloy hardness prediction method provided by the present invention.

[0048] Figure 3 Build a flowchart for the classifier;

[0049] Figure 4 Flowchart for building the Stacking integration model;

[0050] Figure 5 Predicted fitting plot for hardness dataset. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] The purpose of this invention is to provide a method and system for predicting the hardness of high-entropy alloys, which can improve the accuracy of hardness prediction for high-entropy alloys.

[0053] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] Figure 1 This is a schematic diagram of the hardness prediction method for high-entropy alloys provided by the present invention. Figure 2 This is a schematic diagram illustrating the principle of a high-entropy alloy hardness prediction method provided by the present invention, as shown below. Figure 1 and Figure 2 As shown, the present invention provides a method for predicting the hardness of high-entropy alloys, comprising:

[0055] S101, obtain corresponding candidate features based on the AlCoCrCuFeNi system high-entropy alloy hardness data in the high-entropy alloy hardness database; and construct a dataset based on the candidate features and the corresponding AlCoCrCuFeNi system high-entropy alloy hardness data; the AlCoCrCuFeNi system high-entropy alloy hardness data includes: valence electron concentration (VEC), mixing entropy (Smix), mixing enthalpy (Hmix), atomic radius difference (δr), electronegativity difference (Δχ), average melting point of the alloy (Tm), local electronegativity mismatch (D.χ), electron concentration (e / a), Gibbs free energy (Gmix), shear modulus (G), Young's modulus (E), lattice distortion energy (μ), shear modulus mismatch (η), and energy in the enhancement model (A). The parameters include condensation energy (Ec), Peierls-Nabarro factor (F), work function (w), local atomic radius mismatch (Dr), local modulus mismatch (DG), shear modulus difference (δG), average deviation of alloy atomic weight (D.rw), average deviation of alloy family (Dv), average deviation of alloy specific volume (D.sv), and three synthetic parameters related to atomic radius and thermodynamics: Ω, Λ, and γ. Among these, VEC, Smix, Hmix, δr, Δχ, Tm, D.χ, e / a, Gmix, Ec, D.rw, Dv, D.sv, Ω, Λ, and γ are features constructed based on alloy phase formation rules, while η, Dr, A, F, w, G, δG, DG, μ, and E are features constructed based on the material's physical properties. As shown in Table 1, c in the formula...i This represents the molar ratio of each element. R in the Smix calculation formula is the gas constant (8.314 J·K). -1 ·mol -1 H i-j mix Represents the enthalpy of mixing between different alloying elements. min and r max Represents the minimum and maximum atomic radii of each element in a high-entropy alloy. VEC i r i , χ i (Tm) i (e / a) i G i E i Ec i w i v i sv i ,rw i Let be the valence electron concentration, atomic radius, electronegativity difference, melting point, electron concentration, shear modulus, Young's modulus, condensation energy, work function, group, specific volume, and atomic weight of element i in the high-entropy alloy, respectively. Let r, v, sv, and rw be the atomic radius, group, specific volume, and atomic weight of the high-entropy alloy, respectively. Let r, v, sv, and rw be k, and let r represent the atomic radius, group, specific volume, and atomic weight of each element in the high-entropy alloy. i v i sv i ,rw i Let it be k i Its general formula for calculation is:

[0056]

[0057] Table 1

[0058]

[0059]

[0060] A database of high-entropy alloy hardness was established based on the hardness data of high-entropy alloys in the AlCoCrCuFeNi system prepared by electric arc furnace melting.

[0061] S102, a Stacking ensemble model is trained using the dataset; the trained Stacking ensemble model includes a primary classifier and a secondary classifier; the trained Stacking ensemble model is used to determine the corresponding hardness based on candidate features.

[0062] S102 specifically includes:

[0063] like Figure 3As shown, the RandomForest, XGBoost, and CatBoost methods are used to determine the primary classifier.

[0064] Among them, based on the determination coefficients of the prediction results of ten machine learning algorithms through five-fold cross-validation, XGBoost, CatBoost, and RandomForest were finally selected as the modeling algorithms.

[0065] The specific method of five-fold cross-validation is as follows: the dataset is divided into 5 equal groups. In each training session, four groups are used as the training set and the remaining group is used as the test set. The 5 equally divided data will generate 5 different combinations of training and test sets. Each combination will result in a different model score. Finally, the average of the scores of the five groups is taken.

[0066] The ten machine learning algorithms selected are Gaussian kernel support vector machine (SVR-RBF), linear kernel support vector machine (SVR-Linear), K-nearest neighbors (KNN), Ridge regression, Lasso regression, decision tree (Cart), Random forest (RandomForest), XGBoost, CatBoost, and LightGBM.

[0067] By calculating the sum of the mean squared errors of various algorithms on datasets with different split ratios, the three machine learning algorithms with the smaller sum of mean squared errors were selected. Finally, ensemble algorithms such as XGBoost, CatBoost, and RandomForest were chosen as the modeling algorithms. This multi-faceted selection of machine learning algorithms not only considers the performance of each algorithm on the dataset but also the sensitivity of different machine learning algorithms to different training and test set split ratios, which helps to select algorithms with greater accuracy and stability.

[0068] Use a Bayesian regressor to determine the secondary classifier.

[0069] The specific steps for building the Stacking ensemble model include: First, dividing the dataset into training and test sets, and then dividing the training set into 5 equal parts. RandomForest, XGBoost, and CatBoost, acting as primary classifiers, are used sequentially to train on 4 parts of the training set. The remaining part of the training set and the test set are used to make predictions using the trained model. After 5 rounds of training, each primary classifier will obtain 5 sets of training set predictions and 5 sets of test set predictions. The 5 sets of training set predictions are concatenated and denoted as T1, and the 5 sets of test set predictions are averaged and denoted as P1. This training method is applied to all three primary classifiers to obtain T1, T2, T3, P1, P2, and P3. Finally, T1, T2, and T3 are used as feature inputs to train the secondary classifier, the Bayesian regressor. P1, P2, and P3 are used as test sets and fed into the trained Bayesian regressor to obtain the prediction results of the Stacking model.

[0070] S103. For candidate features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system, Pearson correlation coefficient, XGBoost evaluation model, random forest, genetic algorithm, recursive feature elimination method based on XGBoost and exhaustive method were used to screen and determine the screened features.

[0071] S103 specifically includes:

[0072] For candidate features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system, the Pearson correlation coefficient was used for correlation screening. The features were divided into three high correlation groups [D.sv, δr, Dχ, e / a, Dr, δG, D.rw, Dv, DG, Δχ, μ], [w, Ec, Tm, G, E], [F, A] and one low correlation group [VEC, Smix, Hmix, Ω, Λ, Gmix]. By adding features from each highly correlated group to a low-correlation group, and using the XGBoost evaluation model to determine the corresponding mean squared error, features with smaller mean squared errors from each highly correlated group are retained (since the highly correlated group [D.sv, δr, Dχ, e / a, Dr, δG, D.rw, Dv, DG, Δχ, μ] has 11 features, to prevent filtering out important features, 4 features are retained for this highly correlated group, while other highly correlated groups retain only one feature). This yields the features after the first selection: [VEC, Smix, Hmix, Ω, Λ, Gmix, D.sv, δr, e / a, δG, Ec, A]. Random forest, genetic algorithm, and recursive feature elimination method based on XGBoost are then used to apply these features after the first selection to obtain the features after the second selection: [VEC, Hmix, Λ, G, δr, δG, Ec].

[0073] The exhaustive method was used to obtain the filtered features [VEC, Hmix, Gmix, δG] after the second screening.

[0074] S104. Based on the selected features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system, a classifier is established using principal component analysis and logistic regression; the classifier is used to classify the hardness of high-entropy alloys.

[0075] S104 specifically includes:

[0076] like Figure 3 As shown, the selected features corresponding to the hardness data of the AlCoCrCuFeNi system high-entropy alloy are normalized.

[0077] Principal component analysis (PCA) is used to reduce the dimensionality of normalized features. The specific steps of PCA are as follows: First, the input data is normalized; then, the covariance matrix between each feature is calculated, and the eigenvalues ​​and eigenvectors of the covariance matrix are obtained. Since this invention reduces 4-dimensional eigenvectors to 3-dimensionality, the three largest eigenvalues ​​of the covariance matrix and their corresponding eigenvectors are selected. Finally, the original data is projected onto the selected eigenvector directions to complete the PCA dimensionality reduction.

[0078] Logistic regression was used to build a classifier based on the dimensionality-reduced features. The classifier was used to distinguish between high-entropy alloy samples with a hardness >600 and those with a hardness <600. This allows for priority screening of samples in the vast composition space before the Stacking model makes formal predictions, ensuring that the synthesized high-entropy alloy has high hardness.

[0079] S105, construct the alloy composition search space based on the trained Stacking ensemble model and the classifier. First, use the classifier to filter out alloys with a hardness > 600, then use the Stacking ensemble model to predict the true hardness. For example... Figure 5 As shown, the Stacking regression model, after five-fold cross-validation on the dataset, has an RMSE of 75 and an R-value of [missing value]. 2 The accuracy is 0.83, and it also demonstrates excellent performance on the ternary entropy alloy dataset. The accuracy of logistic regression classification is 0.94.

[0080] S106, predict the hardness of the high-entropy alloy of the AlCoCrCuFeNi system based on the alloy composition search space.

[0081] S106 specifically includes:

[0082] Construct a dataset of element molar ratios for high-entropy alloys to be predicted, and use a classifier to determine whether the element molar ratio dataset exceeds a set hardness.

[0083] For data in the element molar ratio dataset that exceeds the set hardness, hardness prediction is performed using a trained Stacking ensemble model.

[0084] To verify the accuracy of the Stacking model for high and low hardness data, high-hardness and low-hardness high-entropy alloys were selected for prediction and synthesis verification. The results are shown in Table 2.

[0085] Table 2

[0086]

[0087] This invention utilizes machine learning methods to extract the reasons for the high hardness of AlCoCrCuFeNi high-entropy alloys from big data. Pearson correlation coefficients were used to screen highly relevant features, and genetic algorithms, random forests, and recursive feature elimination were employed to select highly important features. Finally, an exhaustive search method was used to select the optimal feature combination. Through a series of feature selection methods, more representative descriptive factors for synthesizing high-hardness, high-entropy alloys were selected. These empirical parameters provide important guidance for future screening of high-hardness, high-entropy alloys.

[0088] In building the model, not only were classification algorithms used for initial screening of high-hardness data, but also the concept of ensemble learning was employed, with RandomForest, XGBoost, and CatBoost algorithms being stacked and fused. This not only identified potentially high-hardness high-entropy alloys but also improved the accuracy of predicting high-hardness high-entropy alloys, thus contributing to increased synthesis efficiency.

[0089] As another embodiment, the present invention also provides a hardness prediction system for high-entropy alloys, comprising:

[0090] The candidate feature acquisition module is used to acquire corresponding candidate features based on the hardness data of AlCoCrCuFeNi system high-entropy alloys in the high-entropy alloy hardness database; and to construct a dataset based on the candidate features and the corresponding hardness data of AlCoCrCuFeNi system high-entropy alloys; the hardness data of AlCoCrCuFeNi system high-entropy alloys includes: the molar ratio of each element in each system and the corresponding hardness; the candidate features include: valence electron concentration, mixing entropy, mixing enthalpy, atomic radius difference, electronegativity difference, average melting point of the alloy, local electronegativity mismatch, electron concentration, Gibbs free energy, shear modulus, Young's modulus, lattice distortion energy, shear modulus mismatch, energy in the enhancement model, condensation energy, Peierls-Nabarro factor, work function, local atomic radius mismatch, local modulus mismatch, shear modulus difference, average deviation of alloy atomic weight, average deviation of alloy family, average deviation of alloy specific volume, and synthesis parameters.

[0091] The trained Stacking ensemble model determination module is used to train the Stacking ensemble model using the dataset; the trained Stacking ensemble model includes a primary classifier and a secondary classifier; the trained Stacking ensemble model is used to determine the corresponding hardness based on candidate features.

[0092] The filtered feature determination module is used to screen candidate features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system using Pearson correlation coefficient, XGBoost evaluation model, random forest, genetic algorithm, XGBoost-based recursive feature elimination method, and exhaustive method to determine the filtered features.

[0093] The classifier building module is used to build a classifier based on the filtered features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system, using principal component analysis and logistic regression; the classifier is used to classify the hardness of high-entropy alloys.

[0094] The alloy composition search space construction module is used to construct the alloy composition search space based on the trained Stacking ensemble model and the classifier.

[0095] The hardness prediction module is used to predict the hardness of high-entropy alloys in the AlCoCrCuFeNi system based on the alloy composition search space.

[0096] The trained Stacking ensemble model determination module specifically includes:

[0097] The primary classifier determination unit is used to determine the primary classifier using RandomForest, XGBoost, and CatBoost methods.

[0098] The secondary classifier determination unit is used to determine the secondary classifier using a Bayesian regressor.

[0099] The filtered feature determination module specifically includes:

[0100] The first screening unit is used to screen candidate features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system. The Pearson correlation coefficient is used for correlation screening, and the candidate features are divided into 3 high correlation groups and 1 low correlation group with a threshold of 0.9. The candidate features in the high correlation group are added to the low correlation group, and the XGBoost evaluation model is used to determine the corresponding mean square error. The candidate features in each high correlation group with a mean square error less than the mean square error threshold are retained to obtain the features after the first screening.

[0101] The second screening unit is used to apply random forest, genetic algorithm, and XGBoost-based recursive feature elimination method to the features after the first screening to obtain the features after the second screening.

[0102] The feature determination unit after filtering is used to exhaustively search for the features after the second filtering to obtain the filtered features.

[0103] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0104] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for predicting the hardness of high-entropy alloys, characterized in that, include: Based on the hardness data of high-entropy alloys in the AlCoCrCuFeNi system from the high-entropy alloy hardness database, corresponding candidate features are obtained; and a dataset is constructed based on the candidate features and the corresponding hardness data of high-entropy alloys in the AlCoCrCuFeNi system. The hardness data of the AlCoCrCuFeNi system high-entropy alloys include: the molar ratio of each element in each system and the corresponding hardness; the candidate features include: valence electron concentration, mixing entropy, mixing enthalpy, atomic radius difference, electronegativity difference, average melting point of the alloy, local electronegativity mismatch, electron concentration, Gibbs free energy, shear modulus, Young's modulus, lattice distortion energy, shear modulus mismatch, energy in the reinforcement model, condensation energy, Peierls-Nabarro factor, work function, local atomic radius mismatch, local modulus mismatch, shear modulus difference, average deviation of alloy atomic weight, average deviation of alloy family, average deviation of alloy specific volume, and synthesis parameters. A Stacking ensemble model is trained using the dataset; the trained Stacking ensemble model includes a primary classifier and a secondary classifier; the trained Stacking ensemble model is used to determine the corresponding stiffness based on candidate features; For candidate features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system, Pearson correlation coefficient, XGBoost evaluation model, random forest, genetic algorithm, XGBoost-based recursive feature elimination method and exhaustive method were used for screening to determine the screened features. Based on the selected characteristics corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system, a classifier is established using principal component analysis and logistic regression; the classifier is used to classify the hardness of high-entropy alloys. The alloy composition search space is constructed based on the trained Stacking ensemble model and the classifier. The hardness of high-entropy alloys in the AlCoCrCuFeNi system is predicted based on the alloy composition search space. The candidate features corresponding to the hardness data of the AlCoCrCuFeNi high-entropy alloy system were screened using Pearson correlation coefficient, XGBoost evaluation model, random forest, genetic algorithm, XGBoost-based recursive feature elimination method, and exhaustive search method to determine the screened features, specifically including: For candidate features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system, the Pearson correlation coefficient was used for correlation screening, and the candidate features were divided into 3 high correlation groups and 1 low correlation group with a threshold of 0.

9. The candidate features in the high correlation group were added to the low correlation group, and the XGBoost evaluation model was used to determine the corresponding mean square error. The candidate features in each high correlation group with a mean square error less than the mean square error threshold were retained to obtain the features after the first screening. The features after the first screening were subjected to random forest, genetic algorithm, and recursive feature elimination method based on XGBoost to obtain the features after the second screening. An exhaustive method was used to obtain the filtered features after the second screening.

2. The method for predicting the hardness of a high-entropy alloy according to claim 1, characterized in that, The training of the Stacking ensemble model using the dataset specifically includes: The RandomForest, XGBoost, and CatBoost methods were used to determine the primary classifier. Use a Bayesian regressor to determine the secondary classifier.

3. The method for predicting the hardness of a high-entropy alloy according to claim 1, characterized in that, The process involves establishing a classifier based on the selected features corresponding to the hardness data of the high-entropy alloy in the AlCoCrCuFeNi system, using principal component analysis and logistic regression. Specifically, this includes: Data normalization was performed on the selected features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system. Principal component analysis is used to reduce the dimensionality of the normalized features of the data; Logistic regression is used to build a classifier based on the dimensionality-reduced features.

4. The method for predicting the hardness of a high-entropy alloy according to claim 1, characterized in that, The prediction of the hardness of high-entropy alloys in the AlCoCrCuFeNi system based on the alloy composition search space specifically includes: Construct a dataset of element molar ratios for high-entropy alloys to be predicted, and use a classifier to determine whether the element molar ratio dataset exceeds a set hardness. For data in the element molar ratio dataset that exceeds the set hardness, hardness prediction is performed using a trained Stacking ensemble model.

5. A hardness prediction system for high-entropy alloys, characterized in that, include: The candidate feature acquisition module is used to acquire corresponding candidate features based on the hardness data of high-entropy alloys in the AlCoCrCuFeNi system in the high-entropy alloy hardness database; and to construct a dataset based on the candidate features and the corresponding hardness data of high-entropy alloys in the AlCoCrCuFeNi system. The hardness data of the AlCoCrCuFeNi system high-entropy alloys include: the molar ratio of each element in each system and the corresponding hardness; the candidate features include: valence electron concentration, mixing entropy, mixing enthalpy, atomic radius difference, electronegativity difference, average melting point of the alloy, local electronegativity mismatch, electron concentration, Gibbs free energy, shear modulus, Young's modulus, lattice distortion energy, shear modulus mismatch, energy in the reinforcement model, condensation energy, Peierls-Nabarro factor, work function, local atomic radius mismatch, local modulus mismatch, shear modulus difference, average deviation of alloy atomic weight, average deviation of alloy family, average deviation of alloy specific volume, and synthesis parameters. The trained Stacking ensemble model determination module is used to train the Stacking ensemble model using the dataset; the trained Stacking ensemble model includes a primary classifier and a secondary classifier; the trained Stacking ensemble model is used to determine the corresponding stiffness based on candidate features; The filtered feature determination module is used to screen candidate features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system using Pearson correlation coefficient, XGBoost evaluation model, random forest, genetic algorithm, XGBoost-based recursive feature elimination method and exhaustive method to determine the filtered features. The classifier building module is used to build a classifier based on the filtered features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system, using principal component analysis and logistic regression; the classifier is used to classify the hardness of high-entropy alloys. The alloy composition search space construction module is used to construct the alloy composition search space based on the trained Stacking ensemble model and the classifier. The hardness prediction module is used to predict the hardness of high-entropy alloys in the AlCoCrCuFeNi system based on the alloy composition search space. The filtered feature determination module specifically includes: The first screening unit is used to screen candidate features corresponding to the hardness data of high-entropy alloys in the AlCoCrCuFeNi system. The Pearson correlation coefficient is used for correlation screening, and the candidate features are divided into 3 high correlation groups and 1 low correlation group with a threshold of 0.

9. The candidate features in the high correlation group are added to the low correlation group, and the XGBoost evaluation model is used to determine the corresponding mean square error. The candidate features in each high correlation group with a mean square error less than the mean square error threshold are retained to obtain the features after the first screening. The second screening unit is used to apply random forest, genetic algorithm, and XGBoost-based recursive feature elimination method to the features after the first screening to obtain the features after the second screening. The feature determination unit after filtering is used to exhaustively search for the features after the second filtering to obtain the filtered features.

6. The hardness prediction system for high-entropy alloys according to claim 5, characterized in that, The trained Stacking ensemble model determination module specifically includes: The primary classifier determination unit is used to determine the primary classifier using RandomForest, XGBoost, and CatBoost methods. The secondary classifier determination unit is used to determine the secondary classifier using a Bayesian regressor.

Images