Method for screening high-hardness high-entropy alloy assisted by particle swarm optimization algorithm and machine learning

Abstract

The application particle swarm optimization algorithm assisted machine learning screening high-hardness high-entropy alloy method belongs to the technical field of metal materials, and the method comprises the following steps: obtaining AlCoCrCuFeNi system high-entropy alloy hardness data and candidate features, establishing composition-hardness data set and feature data set; randomly oversampling the composition-hardness data set and training the SVM-rbf model, and using PSO to optimize the SVM-rbf model, so that the high-entropy alloy composition ratio with high hardness value can be obtained; the candidate features of the feature data set are preliminarily screened by using GA; the characteristics of the screened features are analyzed, the feature set is expanded, and GA feature selection is used to obtain the optimized feature group, so that the model prediction accuracy is improved; the RF hardness prediction model is established by using the optimized feature group, the optimized modeling features are used as the input features of the hardness prediction model according to the optimization result of the established composition optimization model, and the model is run, so that the high-entropy alloy composition ratio with high hardness value and the corresponding hardness value can be effectively predicted.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of metal materials, and particularly relates to a method for screening high-hardness high-entropy alloys by using a particle swarm optimization algorithm assisted machine learning. BACKGROUND

[0002] High-entropy alloys have multiple principal components and complex structure formation mechanisms, resulting in a very large composition design space of high-entropy alloys. Using the traditional trial-and-error method, it is difficult to predict the specific performance of high-entropy alloys by using the first principle and molecular dynamics methods.

[0003] The progress of machine learning technology provides a good way to change this situation. Some related researches on alloy composition-performance prediction have been carried out at home and abroad. Wang Jiong et al. synthesized 138 alloy samples through high-throughput experiments, constructed 120 combinations according to the hardness data of the alloy samples and using three machine learning models and four description factors, and screened out the optimal model, which improved the alloy design efficiency by 200 times. Chang et al. used composition weighting and density characteristics to establish a three-layer artificial neural network to predict the hardness of AlCoC random forest MnNi high-entropy alloy system. Bakr et al. used artificial neural network to predict the hardness of high-entropy alloy, and the determination coefficient of the final model reached 0.88. Although these methods have achieved certain prediction effect, the prediction result is not accurate enough, and the above methods can only simply predict, and it is still difficult to design the specific composition of high-entropy alloys.

[0004] In addition, the patent "CN107609647 A" discloses a neural network (BPNN) model for predicting the influence of different alloy compositions and heat treatment process parameters on mechanical properties; "CN111063401A" discloses a method for predicting the structure and mechanical properties of Mg-Zn-Zr series alloy in the heat treated state; "CN110010210A" discloses a multi-element alloy prediction method based on a BP neural network model; "CN114783540A" discloses a multi-element alloy performance prediction method based on a particle swarm optimization BP neural network; "CN112216356A" discloses a high-entropy alloy hardness prediction method based on machine learning; "CN110010210B" discloses a multi-element alloy composition design method based on machine learning and oriented to performance requirements; "CN115061435A" discloses a machine learning method for quickly predicting the hardness of high-entropy alloys and its preparation process. The main goal of these prediction methods is to predict the performance of the material, which to some extent accelerates the screening of the material. The above-mentioned inventions only simply predict the target high-entropy alloy, but the present invention combines optimization algorithms with machine learning algorithms to establish two modules, including a high-hardness high-entropy alloy composition optimization module and a high-entropy alloy hardness prediction module, which not only can predict the hardness of high-entropy alloys using machine learning, but also can optimize the composition ratio of high-hardness alloy samples through optimization algorithms. SUMMARY

[0005] The present application provides a particle swarm optimization algorithm assisted machine learning method for screening high-hardness high-entropy alloys. The present application contains two modules, namely a high-hardness high-entropy alloy composition optimization module and a high-entropy alloy hardness prediction module. The high-hardness high-entropy alloy composition optimization module uses a particle swarm algorithm to search for the composition ratio of high-hardness high-entropy alloys, and the high-entropy alloy hardness prediction module is used to predict the hardness of high-entropy alloys searched by the high-hardness high-entropy alloy composition optimization module. The two modules work together to design high-hardness high-entropy alloys.

[0006] To solve the above technical problems, the technical scheme adopted by the present application is as follows: a particle swarm optimization algorithm assisted machine learning method for screening high-hardness high-entropy alloys, comprising: a high-hardness high-entropy alloy composition optimization module and a high-entropy alloy hardness prediction module, the high-hardness high-entropy alloy composition optimization module uses a particle swarm algorithm to search for the composition ratio of high-hardness high-entropy alloys, and the high-entropy alloy hardness prediction module is used to predict the hardness of high-entropy alloys searched by the high-hardness high-entropy alloy composition optimization module. The specific steps are as follows:

[0007] S101, obtain the corresponding candidate features from the AlCoCrCuFeNi system high-entropy alloy composition-hardness data set; and construct a feature data set according to the candidate features and the corresponding AlCoCrCuFeNi system high-entropy alloy composition-hardness data set;

[0008] The construction method of the high-hardness high-entropy alloy composition optimization module is:

[0009] S102, from the linear models with stronger extrapolation ability: ridge regression Ridge, Lasso, support vector machine based on Gaussian kernel SVM-rbf and artificial neural network ANN, select the support vector based on Gaussian kernel SVM-rbf for constructing the machine learning algorithm of the high-hardness high-entropy alloy composition optimization module;

[0010] S103, random oversampling operation is performed on the composition-hardness data set:

[0011] The high-entropy alloy composition-hardness data set is divided into hardness values with a step size of 100, the high-entropy alloy samples between different hardness intervals are classified, and random oversampling operation is performed on the classification results to ensure that different composition optimization models can be obtained, and different high-entropy alloy composition distribution ratios are designed;

[0012] S104, training the composition optimization data set after random oversampling using the SVM-rbf algorithm to obtain the composition optimization model:

[0013] According to the composition optimization data set of the AlCoCrCuFeNi system high-entropy alloy after random oversampling, the SVM-rbf is used to establish the composition optimization model and perform hyperparameter optimization; the hyperparameter optimization method uses the Bayesian optimization method, and the ten-fold cross-validation method is used to assist in optimizing the hyperparameters during the hyperparameter optimization process;

[0014] S105, the composition optimization model of the AlCoCrCuFeNi system high-entropy alloy is constructed and optimized, and the particle swarm optimization algorithm is used to optimize the optimization problem to obtain the optimized composition mole ratio of the high-entropy alloy, and the specific operation is as follows:

[0015] According to the composition optimization model of the AlCoCrCuFeNi system high-entropy alloy, the optimization problem is constructed; the objective function of the optimization problem is the maximum hardness value of the decision plane fitted by the SVM-rbf; the constraint condition of the optimization problem is the mole ratio interval of different metal elements;

[0016] The construction method of the high-entropy alloy hardness prediction module is:

[0017] S106, select the random forest RandForest from the algorithms with good non-linear mapping capability: XGBoost, random forest RandForest (RF), SVM-rbf, ANN, and machine learning algorithms with good extrapolation capability: Ridge, Lasso, to construct a machine learning algorithm for high-entropy alloy hardness prediction module for hardness prediction of synthesized high-entropy alloys;

[0018] S107, the candidate features corresponding to the AlCoCrCuFeNi system high-entropy alloy feature data are respectively screened by random forest RandForest, SFS, SBS, and GA to determine the optimal feature selection method and obtain the screened features;

[0019] S108, according to the characteristics of the screened features corresponding to the AlCoCrCuFeNi system high-entropy alloy feature data, a new feature set is established, and feature selection is performed again to obtain optimized modeling features;

[0020] The feature set [gamma, delta chi, VEC, F, omega, e / a, E, delta G] selected by GA is analyzed, and it is found that most of the features are related to modulus, atomic radius, and misfit of electronegativity difference and related parameters;

[0021] The E, G, chi and bulk modulus K screened in GA are taken as original data, and 5 misfit-related features are calculated. For the gamma parameter, it is related to the misfit of metal atomic size, so the atomic radius r is also calculated for misfit-related features. The recalculated features and the features selected by GA are integrated together to form a feature set containing 35 feature parameters. Through GA, the optimized modeling features [VEC, G, M. E] are obtained by reselecting the features;

[0022] S109, according to the screened features corresponding to the AlCoCrCuFeNi system high-entropy alloy feature data, the screened features are [VEC, G, M. E]; a hardness prediction model is established by using random forest RandForest and the hyperparameters are optimized; the hyperparameter optimization method uses Bayesian optimization method, and the ten-fold cross-validation method is used to assist in optimizing the hyperparameters during the hyperparameter optimization process;

[0023] S110, use the alloy composition ratio interval found by the high-hardness high-entropy alloy composition optimization module in step S105 to construct an input feature set. Input the feature set into the high-entropy alloy hardness prediction module to obtain the high-hardness high-entropy alloy hardness prediction value, i.e. the hardness value of the high-entropy alloy composition with high hardness and the corresponding hardness value.

[0024] Further, the candidate features of the feature dataset include: 7 molar ratio weighted features, 3 thermodynamic parameters, 3 misfit parameters, 6 synthesis parameters, totaling 19 candidate features.

[0025] The molar ratio weighted features include: average temperature Tm, condensation energy Ec, valence electron concentration VEC, electron concentration e / a, Young's modulus E, shear modulus G, and sixth power of work function w 6 ;

[0026] The thermodynamic parameters include: mixing entropy ΔSmix, mixing enthalpy ΔHmix, and Gibbs free energy ΔGmix.

[0027] The misfit parameters include: atomic radius mismatch δr, shear modulus mismatch δG, and Pauling electronegativity difference Δχ.

[0028] The synthesis parameters include: F, A, Ω, μ, and γ.

[0029] Further, the specific selection process of the step S102 is as follows:

[0030] Step 1) The grid search method is used for hyperparameter optimization, and the ten-fold cross-validation method is used to assist in optimizing the hyperparameters during the hyperparameter optimization process.

[0031] Step 2) According to the determination coefficient R2 and the root mean square error RMSE of the prediction results of the data of the four machine learning algorithms tested by the ten-fold cross-validation, the SVM-rbf is finally selected as the modeling algorithm.

[0032] Further, the specific selection process of the step S106 is as follows:

[0033] Step 1) The grid search method is used for hyperparameter optimization, and the ten-fold cross-validation method is used to assist in optimizing the hyperparameters.

[0034] Step 2) According to the determination coefficient R2 and the root mean square error RMSE of the prediction results of the data of the six machine learning algorithms tested by the ten-fold cross-validation, the RandForest is finally selected as the modeling algorithm.

[0035] Further, the step S107 uses the random forest RandForest, SFS, SBS, and GA to perform feature selection, determines the optimal feature selection method, and obtains the filtered features, which specifically include:

[0036] The SBS, the SFS and the random forest RandForest are evaluated by using ten-fold cross validation method to reserve the RMSE of different feature numbers, so as to determine the optimal feature group selected by each feature selection algorithm, and when using these feature selection methods, the number of features in the target feature set is gradually reduced from 19 to 1, and the RMSE in different cases is evaluated by using ten-fold cross validation method;

[0037] For the GA, firstly, the GA is used for global search on the feature set, and the optimal solution feature combination [gamma, delta chi, VEC, F, omega, e / a, E, delta G] is obtained, the feature group contains eight features; in order to prevent missing the feature group with less contained features and higher accuracy, the maximum number of features reserved in the feature set is set to 7, 6, 5 and 4 respectively, and the genetic algorithm is used for iteration, at this time, it is found that the error of the selected feature group is greater than the error in the global search, but the RMSE of the GA selected feature group is converged below 65 through iteration, which shows that the GA is better than other feature selection methods in most conditions, and finally, the RMSE of the optimal feature group selected by each feature selection method is that the GA obtains the minimum error, so the GA is used as the feature selection method

[0038] The method has the advantages and positive effects that the method provided by the application is used for screening high-hardness high-entropy alloys by using a particle swarm optimization algorithm assisted machine learning, candidate features are determined according to existing data in a database, an AlCoCrCuFeNi system high-entropy alloy composition-hardness data set and an AlCoCrCuFeNi system high-entropy alloy feature data set are respectively constructed, a random forest RandForest is used to fit the AlCoCrCuFeNi system high-entropy alloy composition-hardness data set to obtain a high-entropy alloy hardness prediction model, random oversampling is performed on the AlCoCrCuFeNi system high-entropy alloy composition-hardness data set, and a SVM-rbf is used to fit the high-entropy alloy composition-hardness data set after random oversampling to obtain a high-entropy alloy composition optimization model.

[0039] For constructing the high-entropy alloy hardness prediction model, a two-stage feature selection process was implemented. The feature set was expanded using the characteristics of the feature groups initially selected by a genetic algorithm, and more targeted feature selection was performed. A high-hardness high-entropy alloy design framework was constructed based on the high-entropy alloy hardness prediction model and the high-entropy alloy composition optimization model. Specifically, the particle swarm optimization algorithm was used to optimize the high-entropy alloy composition optimization model, obtaining the optimized molar ratio of the high-entropy alloy composition. This molar ratio was used to construct a feature set, which was then used as the input features of the high-entropy alloy hardness prediction model to obtain the predicted value of the high-hardness high-entropy alloy, thereby selecting target high-entropy alloys. During model construction, the optimization algorithm was used in the feature selection and parameter tuning steps of machine learning modeling, significantly improving the model's prediction accuracy. In designing high-entropy alloys, the particle swarm optimization algorithm was used to search for the composition ratio of high-hardness high-entropy alloys, avoiding blindness in the high-entropy alloy design process and enabling the efficient design of high-entropy alloys with high hardness target values. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of a method for screening high-hardness, high-entropy alloys using particle swarm optimization algorithm-assisted machine learning, as provided by the present invention.

[0041] Figure 2 This is a schematic diagram of the reverse high-entropy alloy composition optimization design process provided by the present invention.

[0042] Figure 3 (a) is a line graph of the selected hardness prediction model algorithm, and (b) is a line graph of the selected composition optimization model algorithm.

[0043] Figure 4 Line graphs were selected for the hardness prediction model features. In the figure: (a) are the RMSE values ​​of the models RandForest, SFS, and SBS when retaining different numbers of features; (b) are the RMSE iteration curves of the model when GA performs global search and retains 7, 6, 5, and 4 features; and (c) are the iteration curves of further optimizing features using GA after expanding the feature set.

[0044] Figure 5 The graph shows the optimization effects of different optimization algorithms on the component optimization model.

[0045] Figure 6 This is a feature calculation method for further expanding the feature set based on the feature selection results.

[0046] Figure 7The fitting graphs for the hardness dataset are shown in the figures: (a) is the fitting graph of the feature set before optimization under ten-fold cross-validation, (b) is the fitting graph of the feature set before optimization under leave-one-out cross-validation, (c) is the fitting graph of the feature set after optimization under ten-fold cross-validation, and (d) is the fitting graph of the feature set after optimization under leave-one-out cross-validation. DETAILED DESCRIPTION

[0047] In order to make the purposes, features and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application are described in detail below.

[0048] As shown in Figure 1 , Figure 2 A method for screening high-hardness high-entropy alloys with the aid of a particle swarm optimization algorithm and machine learning, comprising: a high-hardness high-entropy alloy composition optimization module and a high-entropy alloy hardness prediction module, the high-hardness high-entropy alloy composition optimization module uses a particle swarm optimization algorithm to search for the composition ratio of high-hardness high-entropy alloys, and the high-entropy alloy hardness prediction module is used to predict the hardness of the high-entropy alloys searched by the high-hardness high-entropy alloy composition optimization module. The specific steps are as follows:

[0049] S101, obtaining corresponding candidate features from the AlCoCrCuFeNi system high-entropy alloy hardness data; and constructing a feature dataset according to the candidate features and the corresponding AlCoCrCuFeNi system high-entropy alloy composition-hardness dataset; the AlCoCrCuFeNi system high-entropy alloy composition-hardness dataset includes the molar ratio of each element contained in the system and the corresponding hardness; the candidate features of the feature dataset include:

[0050] Molar ratio weighted features: average temperature (Tm), cohesive energy (Ec), valence electron concentration (VEC), electron concentration (e / a), Young's modulus (E), shear modulus (G), and work function (w). The calculation method is as shown in formula (1):

[0051]

[0052] Wherein, α represents the above-mentioned parameters, c i represents the molar ratio of each element of the high-entropy alloy, and α i represents the parameter α value of each element of the high-entropy alloy. Since the yield strength of the HEA is related to w 6 , w 6 is added to the feature set.

[0053] Thermodynamic parameters: mixing entropy (ΔSmix), mixing enthalpy (ΔHmix), and Gibbs free energy (ΔGmix). The calculation method is as shown in formulas (2), (3) and (4):

[0054]

[0055] AGmix = AHmix - Tm * ASmix (3)

[0056]

[0057] where R is the gas constant and its specific value is 8.314, represent the mixing enthalpy between different metal elements in high-entropy alloys.

[0058] The synthetic parameters constructed by predecessors: F, A, Omega, mu, gamma. The calculation method is shown in formula (5) (6) (7) (8) (9) (10):

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] Mistaken parameters atomic radius mismatch (delta r), shear modulus mismatch (delta G), Pauling electronegativity difference (Delta chi):

[0066]

[0067]

[0068]

[0069] Wherein r and chi can be obtained from formula (1).

[0070] The AlCoCrCuFeNi system high-entropy alloy is prepared by arc furnace smelting method, and the hardness data constitutes the composition-hardness database of high-entropy alloy.

[0071] Figure 1 Mainly divided into two modules, S102-S105 is high-hardness high-entropy alloy composition optimization module, S106-S109 is high-entropy alloy hardness prediction module.

[0072] Said S102-S105 is high-hardness high-entropy alloy composition optimization module, specifically comprising:

[0073] S102, select a machine learning algorithm for constructing a high-entropy alloy composition reverse design from a linear model with strong extrapolation ability (Ridge, Lasso), a support vector machine based on a Gaussian kernel (SVM-rbf), and an artificial neural network (ANN) based on the composition-hardness dataset; the machine learning algorithm for constructing a high-entropy alloy composition reverse design is used to design a high-hardness value high-entropy alloy composition. Specifically, it includes:

[0074] As shown in Figure 3 (b), the ten-fold cross-validation method is used to evaluate the fitting accuracy of the four machine learning algorithms on the feature dataset to determine the candidate model of the composition optimization model.

[0075] The four machine learning algorithms are all optimized using the grid search method, and the ten-fold cross-validation method is used to assist in optimizing the hyperparameters during the hyperparameter optimization process.

[0076] Among them, according to the determination coefficient (R2) and the root mean square error (RMSE) of the prediction results of the four machine learning algorithms on the data through ten-fold cross-validation test, finally select SVM-rbf as the modeling algorithm. The formula for calculating the determination coefficient is: The formula for calculating the root mean square error is:

[0077] The ten-fold cross-validation method is as follows: the dataset is divided into 10 groups, and 9 groups are taken as the training set and the remaining group is taken as the test set. The 10 groups of data will produce 10 different training set and test set combinations, and each combination will get a different model score. Finally, take the average of the ten scores.

[0078] S103, use random oversampling operation on the composition-hardness dataset to expand the dataset; specifically, it includes:

[0079] The high-entropy alloy composition-hardness dataset is divided into hardness values with a step size of 100, and the high-entropy alloy samples in different hardness intervals are classified, and the classification results are randomly oversampled to ensure that different composition optimization models can be obtained, and then different high-entropy alloy composition ratios are designed.

[0080] S104, use the composition-data set after random oversampling to train the SVM-rbf algorithm selected in step S102 to obtain a composition optimization model; the specific steps are as follows:

[0081] According to the expanded composition-data set, a composition optimization model is established using SVM-rbf and hyperparameter optimization; the hyperparameter optimization method uses the Bayesian optimization method, and the ten-fold cross-validation method is used to assist in optimizing the hyperparameters during the hyperparameter optimization process.

[0082] S105, construct an optimization problem for the obtained component optimization model, and use a particle swarm optimization algorithm to optimize the optimization problem to obtain a high-entropy alloy component molar ratio; the specific steps are as follows:

[0083] The selection basis of the particle swarm optimization algorithm is that the particle swarm optimization algorithm is a classic swarm intelligence optimization algorithm, and domestic and foreign scholars have made a lot of improvements on the particle velocity and position updating and the optimization of PSO parameters on the basis of this algorithm, such as Comprehensive learning PSO (CL_PSO), Hierarchical PSO Time-Varying Acceleration (HPSO_PVAC), Phasor PSO (P_PSO) and other improved algorithms based on PSO. In the intelligent optimization algorithm, the particle swarm has the characteristics of few parameters and fast updating speed, so it is widely used in optimization problems. As shown in the following table, we compared the above particle swarm and the improvement of the particle swarm algorithm, and finally found that the original particle swarm algorithm has the characteristics of fast convergence speed and good global convergence when optimizing the component optimization model constructed in step S104. Therefore, we use the traditional particle swarm optimization algorithm as the optimization algorithm. Figure 5

[0084] The principle of the particle swarm optimization algorithm is that the particle swarm optimization algorithm is a swarm intelligence optimization algorithm inspired by bird foraging. Due to the information sharing between each particle, the particle swarm optimization algorithm can gather from disordered particles to ordered particles, and find the global optimal solution through group cooperation. In the optimization process, the particle swarm optimization algorithm constantly updates the speed v id and position x id of each particle to find the optimal solution, and the update formula of v id and x id is:

[0085]

[0086]

[0087] where w is the inertia weight used to improve the convergence ability. c1 and c2 are learning factors used to adjust the search degree of the local optimal value and the global optimal value respectively, and balance the relationship between the convergence speed and the possibility of falling into a local optimal solution. rand1 and rand2 are random numbers between 0 and 1. is the optimal solution of the d-dimensional i-th particle in the k-th iteration, is the global optimal solution of the d-dimensional i-th particle after the k-th iteration.

[0088] ​An optimization problem is constructed according to the obtained component optimization model; a target function of the optimization problem is a maximum hardness value of a decision plane of SVM-rbf fitting; and a constraint condition of the optimization problem is a molar ratio interval of different metal elements;

[0089] The constraint condition of the optimization problem constructed according to the obtained component optimization model is mainly based on that the molar ratio of each element of the high-entropy alloy is between 5% and 35%, and the molar ratio intervals of Co, Cr, Cu, Fe and Ni are set according to the range; as shown in Table 2, the Pearson correlation coefficient (PCC) of Al and alloy hardness is the largest, so the content of the Al element which has a strong positive correlation with the alloy hardness is used as a setting basis, and the content of the Al element is adjusted accordingly.

[0090] The calculation method of the PCC is as follows: wherein the numerator is the covariance between the characteristics u i and the characteristics v i , and the denominator is the product of the standard deviations of the characteristics u i and the characteristics v i .

[0091] Table 2

[0092]

[0093] The particle swarm optimization algorithm is used to find the maximum value of the optimization problem, and the optimized high-entropy alloy component molar ratio with a high hardness target value is obtained.

[0094] The S106-S109 is a high-entropy alloy hardness prediction module, specifically comprising:

[0095] S106, using the feature data set, selecting a machine learning algorithm for constructing a high-entropy alloy hardness prediction from algorithms with good nonlinear mapping ability (XGBoost, random forest RandForest, SVM-rbf, ANN) and machine learning algorithms with good extrapolation ability (ridge regression Ridge, Lasso); the machine learning algorithm for constructing a high-entropy alloy hardness prediction is used for hardness prediction of the synthesized high-entropy alloy. Specifically comprising:

[0096] As shown in Figure 3 (a), ten-fold cross-validation method is used to evaluate the fitting accuracy of the six machine learning algorithms on the feature data set, and the candidate model of the hardness prediction model is determined.

[0097] The six machine learning algorithms are all optimized by using the grid search method, and the ten-fold cross-validation method is used to assist in optimizing the hyperparameters in the hyperparameter optimization process.

[0098] The selected six machine learning algorithms are XGBoost, SVM-rbf, ANN, Ridge, Lasso, RandForest.

[0099] Among them, according to the determination coefficient and the root mean square error of the prediction results of XGBoost, SVM-rbf, ANN, Ridge, Lasso, and RandForest on the data through ten-fold cross-validation test, RandForest is finally selected as the modeling algorithm.

[0100] In S107, the candidate features corresponding to the characteristic data of the AlCoCrCuFeNi high-entropy alloy system are respectively screened by using RandForest, SFS, SBS, and GA to determine the optimal feature selection method and obtain the screened features. Feature selection is mainly to reduce data redundancy, improve prediction accuracy, reduce model complexity, and improve model interpretability. Specifically, it includes:

[0101] As shown in Figure 4 (a), the RMSE of SBS, SFS, and RandForest under the condition of retaining different numbers of features is evaluated by using ten-fold cross-validation method to determine the optimal feature group selected by each feature selection algorithm. When using these feature selection methods, the number of features in the target feature set is gradually reduced from 19 to 1, and the RMSE under different conditions is evaluated by using ten-fold cross-validation method. As shown in Figure 4 (b), first, the GA is used to perform global search on the feature set to obtain the optimal solution feature combination [γ, Δχ, VEC, F, Ω, e / a, E, δG], which contains eight features. In order to prevent missing features with fewer features and higher accuracy, the maximum number of features retained in the feature set is set to 7, 6, 5, and 4, respectively, and the genetic algorithm is used for iteration. At this time, it is found that the error of the selected feature group is greater than that of the global search, but the RMSE of the GA selected feature group converges to below 65 through iteration, which indicates that the GA performs better than other feature selection methods under most conditions. As shown in Table 3, among the RMSE of the optimal feature group selected by each feature selection method, the GA achieves the smallest error, so the GA is selected as the feature selection method.

[0102] Table 3

[0103] Algorithm Optimal feature set RMSE GA γ, Δχ, VEC, F, Ω, e / a, E, δG 64.09 SFS δr, Ec, VEC, ΔHmix, Ω, E, G 67.32 SBS Δχ, Ec, VEC, Λ, w, F, δG 67.00 RF δr, VEC, F, Λ, w, δG, μ, G, A, Ec, Ω, ΔSmix, ΔHmix 68.99

[0104] S108, according to the screened features corresponding to the characteristic data of the AlCoCrCuFeNi system high-entropy alloy, analyze the influence of the feature group [γ, Δχ, VEC, F, Ω, e / a, E, δG] on hardness, and find that most of the features show the promoting effect of modulus misfit information or modulus information on solid solution strengthening. These information has a very important guiding role for improving the model. Establish a new feature set and perform feature selection again to obtain the final modeling features;

[0105] The Young's modulus E, shear modulus G, Pauling electronegativity χ and bulk modulus (K) selected by GA are used as the original data, and the Figure 6 characteristics related to the misfit of the five moduli are calculated. For the γ parameter, it is related to the misfit of the atomic size, so the atomic radius (r) is also expanded to include the misfit characteristics using the calculation method in the table. The recalculated features are integrated with the features selected by GA to form a feature set containing 35 feature parameters, and feature selection is performed again by GA. As shown in Figure 4 (c), GA selects the feature group [VEC, G, M. E] with less redundancy as the modeling feature group.

[0106] As shown in Figure 7 (a), Figure 7 (b), Figure 7 (c), Figure 7 (d), the determination coefficient and root mean square error of the feature group [γ, Δχ, VEC, F, Ω, e / a, E, δG] before optimization and the feature group [VEC, G, M. E] after optimization under ten-fold cross-validation and leave-one-out cross-validation are evaluated respectively; the determination coefficient and root mean square error of the feature group [VEC, G, M. E] after optimization under ten-fold cross-validation and leave-one-out cross-validation are improved to a certain extent compared with the feature group [γ, Δχ, VEC, F, Ω, e / a, E, δG] before optimization, and the redundancy of the features is reduced.

[0107] The specific method of the leave-one-out cross-validation method is as follows: the data set with a sample size of N is evenly divided into N groups, N-1 of which are taken as the training set and the remaining 1 sample is taken as the test set each time. N groups of evenly divided data will produce N different combinations of training set and test set. Each combination will get a different model score, and finally the average of N scores is taken.

[0108] S109, according to the screened features corresponding to the characteristic data of the AlCoCrCuFeNi system high-entropy alloy, adopt RF to establish a hardness prediction model and perform hyperparameter optimization;

[0109] The hyperparameter optimization method adopts the Bayesian optimization method, and the ten-fold cross-validation method is used to assist in optimizing the hyperparameters during the hyperparameter optimization process;

[0110] According to the optimization result of the component optimization model constructed according to S105, [VEC, G, M.E] is constructed as an input feature of the hardness prediction model constructed according to S109, and the hardness value of the candidate high-entropy alloy is obtained, that is, the component proportioning of the high-entropy alloy with the target high hardness value and the corresponding hardness value are obtained.

[0111] Table Four

[0112]

[0113] The present application combines machine learning and optimization methods, which not only can predict the hardness of high-entropy alloy by machine learning, but also can obtain the component proportioning of high-entropy alloy with high hardness in AlCoCrCuFeNi system by optimization algorithm.

[0114] To achieve the above-mentioned objectives, a high-hardness high-entropy alloy component optimization module and a high-entropy alloy hardness prediction module are constructed. The RF is selected as the algorithm for establishing the hardness value prediction model of the high-entropy alloy in the high-entropy alloy hardness prediction module. The GA is selected from the RF, SFS, SBS and GA as the feature selection method, and the best feature combination is preliminarily selected from the feature set by using the GA. According to the characteristics of the selected feature set, the data set features are expanded and the GA is used for reselecting the features, and finally the optimal feature set is obtained. This method not only improves the model accuracy, but also reduces the feature redundancy. For the high-hardness high-entropy alloy component optimization module, the SVM-rbf is selected as the algorithm for establishing the model. The data set is oversampled to change the data set distribution, and the SVM-rbf model is established by using the data set, so as to establish the optimization problem. The optimal solution of the optimization problem is obtained by using the particle swarm optimization algorithm, that is, the component proportioning scheme of the high-entropy alloy with high hardness value is obtained. According to the optimization result of the constructed component optimization model, the feature set is constructed as the input feature of the hardness prediction model, and the hardness value of the candidate high-entropy alloy is obtained, that is, the component proportioning of the high-entropy alloy with the target high hardness value and the corresponding hardness value are obtained. To ensure the accuracy of the constructed model, the cross-validation is used in the whole process of model evaluation and feature selection.

[0115] Through a series of modeling and optimization, the high-hardness high-entropy alloy component optimization module and the high-entropy alloy hardness prediction module are constructed. In this way, not only the component proportioning of the high-entropy alloy with high hardness value is obtained, but also the accuracy of predicting the component of the high-entropy alloy with high hardness value is improved, thereby helping to further improve the synthesis efficiency of the high-hardness high-entropy alloy.

[0116] The above-described embodiments are only part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those skilled in the art based on the embodiments in the present application without creative labor fall within the protection scope of the present application.

Claims

1. A method for screening high-hardness high-entropy alloys with the aid of a particle swarm optimization algorithm assisted machine learning, characterized in that, The application relates to a high-hardness high-entropy alloy composition optimization module and a high-entropy alloy hardness prediction module. S101, obtaining corresponding candidate features from an AlCoCrCuFeNi system high-entropy alloy composition-hardness data set; and constructing a feature data set according to the candidate features and the corresponding AlCoCrCuFeNi system high-entropy alloy composition-hardness data set; The construction method of the high-hardness high-entropy alloy composition optimization module is as follows: S102, selecting a support vector based on a Gaussian kernel SVM-rbf from linear models with strong extrapolation capabilities, such as ridge regression Ridge, Lasso, a support vector machine SVM-rbf based on a Gaussian kernel and an artificial neural network ANN, to be used as a machine learning algorithm for constructing the high-hardness high-entropy alloy composition optimization module; S103, performing a random oversampling operation on the composition-hardness data set: The high-entropy alloy composition-hardness data set is divided into hardness values at a step length of 100, high-entropy alloy samples between different hardness intervals are classified, and a random oversampling operation is performed on the classification results to ensure that different composition optimization models can be obtained, and different high-entropy alloy composition ratios are designed; S104, training the composition optimization data set after the random oversampling by using the SVM-rbf algorithm to obtain a composition optimization model: According to the composition optimization data set after the random oversampling of the AlCoCrCuFeNi system high-entropy alloy, a composition optimization model is established by using the SVM-rbf, and hyperparameter optimization is performed; the hyperparameter optimization method adopts a Bayesian optimization method, and a ten-fold cross-validation method is used to assist in optimizing the hyperparameters during the hyperparameter optimization process; S105, constructing an optimization problem for the composition optimization model of the AlCoCrCuFeNi system high-entropy alloy, and using a particle swarm optimization algorithm to optimize the optimization problem to obtain the optimized composition mole ratio of the high-entropy alloy, and the specific operation is as follows: According to the composition optimization model of the AlCoCrCuFeNi system high-entropy alloy, an optimization problem is constructed; a target function of the optimization problem is a maximum hardness value of a decision plane fitted by the SVM-rbf; and a constraint condition of the optimization problem is a mole ratio interval of different metal elements; The construction method of the high-entropy alloy hardness prediction module is as follows: S106, selecting a random forest RandForest from algorithms with good nonlinear mapping capabilities, such as XGBoost, RandForest, SVM-rbf, ANN and machine learning algorithms with good extrapolation capabilities, such as ridge regression Ridge and Lasso, to be used as a machine learning algorithm for constructing the high-entropy alloy hardness prediction module, and the machine learning algorithm for constructing the high-entropy alloy hardness prediction module is used for hardness prediction of synthesized high-entropy alloys. ​ S107, the candidate features corresponding to the characteristic data of the AlCoCrCuFeNi system high-entropy alloy are respectively screened by using a random forest (RandForest), a sequential forward feature selection method (SFS), a sequential backward feature selection method (SBS), and a genetic algorithm (GA), so as to determine an optimal feature selection method and obtain screened features; S108, a new feature set is established according to the characteristics of the screened features corresponding to the characteristic data of the AlCoCrCuFeNi system high-entropy alloy, feature selection is re-performed, and optimized modeling features are obtained; The feature group [γ, Δχ, VEC, F, Ω, e / a, E, δG] selected by the GA is analyzed, and it is found that most of the features are related to the modulus, atomic radius, and misfit of the electronegativity difference and related parameters; E, G, χ, and the bulk modulus K screened in the GA are taken as original data, 5 misfit-related features are calculated, and for the γ parameter, it is related to the misfit of the metal atomic size, so the atomic radius r is also calculated to obtain misfit-related features. The recalculated features and the features screened by the GA are integrated together to form a feature set containing 35 feature parameters, and the optimized modeling features [VEC, G, M, E] are obtained by re-performing feature selection by the GA; S109, according to the screened features corresponding to the characteristic data of the AlCoCrCuFeNi system high-entropy alloy, the screened features are [VEC, G, M, E]; a hardness prediction model is established by using a random forest RandForest, and hyperparameter optimization is performed; the hyperparameter optimization method adopts a Bayesian optimization method, and a ten-fold cross-validation method is used to assist in optimizing the hyperparameters during the hyperparameter optimization process; S110, the input feature set is constructed by using the alloy composition distribution interval found by the high-hardness high-entropy alloy composition optimization module in step S105, and the feature set is input into the high-entropy alloy hardness prediction module to obtain the high-hardness high-entropy alloy hardness prediction value, that is, the high-entropy alloy composition with high hardness and the corresponding hardness value.

2. The method of claim 1, wherein the particle swarm optimization algorithm assisted machine learning is used to screen high hardness high entropy alloys. The candidate features of the feature data set include 7 molar ratio weighted features, 3 thermodynamic parameters, 3 misfit parameters, and 6 synthesis parameters, totaling 19 candidate features; wherein the molar ratio weighted features include: average temperature Tm, cohesive energy Ec, valence electron concentration VEC, electron concentration e / a, Young's modulus E, shear modulus G, sixth power of work function w 6 ; The thermodynamic parameters include mixing entropy ΔSmix, mixing enthalpy ΔHmix, and Gibbs free energy ΔGmix; The misfit parameters include atomic radius misfit δr, shear modulus misfit δG, and Pauling electronegativity difference Δχ; The synthesis parameters include F, A, Ω, μ, and γ.

3. The method of claim 1, wherein the particle swarm optimization algorithm assisted machine learning is used to screen high hardness high entropy alloys. The specific selection process of step S102 is as follows: Step 1) hyperparameter optimization is performed by using a grid search method, and a ten-fold cross-validation method is used to assist in optimizing the hyperparameters during the hyperparameter optimization process; Step 2) according to the determination coefficient R2 and the root mean square error RMSE of the data prediction results of the four machine learning algorithms in the ten-fold cross-validation test, the SVM-rbf is finally selected as the modeling algorithm.

4. The method of claim 1, wherein the particle swarm optimization algorithm assisted machine learning is used to screen high hardness high entropy alloys. The specific selection process of step S106 is as follows: Step 1) hyperparameter optimization is performed by using a grid search method, and a ten-fold cross-validation method is used to assist in optimizing the hyperparameters during the hyperparameter optimization process; Step 2) According to the ten-fold cross-validation test, the coefficient of determination R2 and the root mean square error RMSE of the prediction results of six machine learning algorithms on the data are determined, and finally the random forest RandForest is selected as the modeling algorithm.

5. The method of claim 1, wherein the particle swarm optimization algorithm assisted machine learning is used to screen high hardness high entropy alloys. The step S107 adopts the random forest RandForest, SFS, SBS and GA for feature selection, determines the optimal feature selection method, and obtains the screened features, and specifically comprises: The ten-fold cross-validation method is used to evaluate the RMSE of SBS, SFS and random forest RandForest under the condition of retaining different numbers of features, so as to determine the optimal feature group selected by each feature selection algorithm. When using these feature selection methods, the number of features contained in the target feature set is gradually reduced from 19 to 1, and the RMSE under different conditions is evaluated by using the ten-fold cross-validation method; For GA, firstly, the GA is used for global search on the feature set to obtain the optimal solution feature combination [γ, Δχ, VEC, F, Ω, e / a, E, δG], which contains eight features. In order to prevent missing features with less contained features and higher accuracy, the maximum number of features retained in the feature set is set to 7, 6, 5 and 4 respectively, and the genetic algorithm is iterated. At this time, it is found that the error of the selected feature group is greater than that in the global search, but the RMSE of the feature group selected by GA converges to below 65 through iteration, which shows that GA is better than other feature selection methods in most conditions. Finally, among the RMSE of the optimal feature group selected by each feature selection method, GA obtains the smallest error, so GA is selected as the feature selection method.

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