Hardness prediction method for seven-element refractory high-entropy alloy based on symbolic algorithm assisted machine learning

Abstract

The application discloses a seven-element refractory high-entropy alloy hardness prediction method based on a symbolic algorithm assisted machine learning, which comprises the following steps: 1, collecting the composition and hardness data of five to seven-element refractory high-entropy alloys, and calculating initial characteristic input parameters according to the alloy element composition percentage and combined field knowledge; 2, using the initial characteristic parameters to screen the optimal machine learning model; 3, obtaining the best feature combination through the cross-recursive feature elimination method and the exhaustive method, and training the screened machine learning model, and obtaining the hardness prediction model of the seven-element refractory high-entropy alloy through the Bayesian optimization hyperparameter; 4, using the symbolic algorithm to obtain a new multi-element refractory high-entropy alloy hardness prediction characteristic parameter. The application can realize the purpose of quickly developing multi-element new high-hardness refractory high-entropy alloys by reducing the to-be-predicted composition system space through the converted characteristic parameters, and can design and predict two seven-element refractory high-entropy alloys with high hardness, and has a wide application prospect.

Description

Technical Field

[0001] This invention belongs to the field of metallic materials technology, and in particular relates to a method for predicting seven-element refractory high-entropy alloys based on machine learning and symbolic regression. Background Technology

[0002] Refractory high-entropy alloys are a new type of alloy material with advantages such as high strength, high hardness, high wear resistance, and high corrosion resistance. However, due to their complex composition and preparation process, predicting and optimizing their performance is extremely difficult.

[0003] Traditional methods for predicting alloy properties mainly rely on experiments and empirical formulas. This approach is not only time-consuming and labor-intensive, but also has limited prediction accuracy.

[0004] With the development of machine learning technology, more and more researchers are beginning to try using machine learning methods to predict alloy properties. Machine learning is a method of making predictions and decisions by learning and understanding data. It can learn useful information from large amounts of data and then use this information to predict new data. In alloy property prediction, machine learning can learn from a large amount of experimental data to identify key factors affecting alloy properties and then predict alloy properties based on these factors. Machine learning-based methods for predicting the hardness of refractory high-entropy alloys can significantly improve the efficiency and accuracy of predictions compared to traditional methods, providing a powerful tool for the design and optimization of refractory high-entropy alloys. However, research has revealed that existing machine learning models still have certain shortcomings in predicting the accuracy of multi-component refractory high-entropy alloys. Summary of the Invention

[0005] The present invention aims to address the shortcomings of the existing technology by proposing a method for predicting the hardness of seven-element refractory high-entropy alloys based on symbolic algorithm-assisted machine learning, in order to efficiently predict seven-element refractory high-entropy alloys and reduce prediction errors.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0007] The present invention provides a method for predicting the hardness of seven-element refractory high-entropy alloys based on symbolic algorithm-assisted machine learning, characterized by the following features:

[0008] Step 1: After obtaining the composition and hardness data of five- to seven-element refractory high-entropy alloys through literature and laboratory data, calculate the original characteristic parameters of the composition and hardness data through inherent properties and empirical formulas. Then, use domain knowledge to initially select hardness-related characteristic parameters from the original characteristic parameters and form the original hardness characteristic dataset. Divide the original hardness characteristic dataset into a hardness characteristic training set and a hardness characteristic test set.

[0009] Step 2: Input the hardness feature training set into several different machine learning models for training, and obtain several trained machine learning models accordingly.

[0010] The determination coefficient values ​​of several trained machine learning models under different test set proportions are calculated and compared, so as to select the trained machine learning model with the largest determination coefficient value as the hardness prediction model of multi-component refractory high-entropy alloy.

[0011] Step 3: Process the original hardness feature dataset using the ten-fold cross-recursive feature elimination method to obtain the average accuracy and optimal accuracy under different numbers of hardness features. Based on the average accuracy and optimal accuracy, select a preliminary set of hardness features from the original hardness feature dataset.

[0012] The initial set of hardness features is processed using an exhaustive method to obtain the accuracy of all hardness feature combinations under the hardness prediction model of multi-component refractory high-entropy alloys. The hardness feature combination with the highest accuracy is then selected as the optimal hardness feature subset.

[0013] Step 4: Input the optimal hardness feature subset into the hardness prediction model of the multi-component refractory high-entropy alloy, and use the Bayesian optimization algorithm to fine-tune the parameters of the multi-component refractory high-entropy alloy hardness prediction model, so as to obtain the seven-component refractory high-entropy alloy hardness prediction model.

[0014] Step 5: Use a symbolic algorithm to transform the optimal hardness feature subset and construct a new hardness feature parameter to narrow down the range of alloy composition systems to be explored.

[0015] Step 6: Based on the converted new hardness characteristic parameters, select refractory high-entropy alloy components that meet the mechanical performance requirements from the range of alloy composition systems to be explored, and input them into the seven-element refractory high-entropy alloy hardness prediction model for prediction, and obtain the predicted seven-element high-hardness refractory high-entropy alloy.

[0016] Step 7: Prepare and experimentally verify the predicted seven-element high-hardness refractory high-entropy alloy.

[0017] The characteristic of the seven-element refractory high-entropy alloy hardness prediction method based on symbolic algorithm-assisted machine learning described in this invention is that the characteristics of the preliminary hardness feature set in step 3 include: valence electron concentration, specific heat capacity difference, lattice constant difference, molar volume difference, grain size, activation energy mismatch, Gibbs free energy, sixth work function, and parameter δBo.

[0018] The features of the optimal hardness feature subset in step 3 include: specific heat capacity difference, molar volume difference, grain size, activation energy mismatch, Gibbs free energy, sixth work function, and parameter δBo.

[0019] The predicted composition of the seven-element high-hardness refractory high-entropy alloy in step 6 is WNbV2Zr2CrMo2Ti and WNbV2Zr2Cr2MoTa, where the subscripts represent the atomic proportions of each element.

[0020] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the hardness prediction method for the seven-element refractory high-entropy alloy, and the processor is configured to execute the program stored in the memory.

[0021] The present invention discloses a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program is executed by a processor to perform the steps of the seven-element refractory high-entropy alloy hardness prediction method.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0023] 1. Compared to traditional shallow machine learning models based on statistical strategies, this invention is more accurate. Cross-validation can reduce the bias caused by sample partitioning in refractory high-entropy alloy datasets, providing a more stable estimate of model performance. Bayesian optimization can more intelligently select sample points, reducing the number of evaluations required, thus making it more efficient in finding the optimal hyperparameters.

[0024] 2. The method for predicting the hardness of seven-element refractory high-entropy alloys provided by this invention is designed for the huge unexplored space of multi-principal-element refractory high-entropy alloys. It uses a machine learning prediction model assisted by symbolic algorithms to screen the unexplored composition system space according to the required mechanical properties, which effectively improves the prediction efficiency. It is simple to operate and is suitable for exploring multi-principal-element alloys in unknown composition space, with broad application prospects.

[0025] 3. This invention explores two different seven-element refractory high-entropy alloys, WNbV2Zr2CrMo2Ti and WNbV2Zr2Cr2MoTa, using a machine learning prediction model. Both new refractory high-entropy alloys exhibit high hardness characteristics. Attached Figure Description

[0026] Figure 1 R for different models of this invention 2 Precision map;

[0027] Figure 2 This is the recursive feature elimination diagram in this invention;

[0028] Figure 3 This is the feature elimination diagram using the exhaustive method in this invention;

[0029] Figure 4 This is a diagram illustrating the accuracy of the hardness prediction model of this invention.

[0030] Figure 5 These are the new feature parameters obtained by symbolic feature transformation in this invention;

[0031] Figure 6 Vickers hardness diagrams of the alloys WNbV2Zr2CrMo2Ti and WNbV2Zr2Cr2MoTa obtained in this invention. Detailed Implementation

[0032] In this embodiment, a method for predicting the hardness of a seven-element refractory high-entropy alloy based on symbolic algorithm-assisted machine learning includes:

[0033] Step 1: After obtaining the composition and hardness data of five- to seven-element refractory high-entropy alloys through publicly available literature and laboratory data, calculate the original characteristic parameters of the composition percentage and hardness data through the inherent properties of the alloy and empirical formulas. Then, use domain knowledge to initially select hardness-related characteristic parameters from the original characteristic parameters and form the original hardness characteristic dataset. Divide the original hardness characteristic dataset into a hardness characteristic training set and a hardness characteristic test set.

[0034] Step 2: Input the hardness feature training set into four different machine learning models for training. After training, four trained machine learning models are obtained. In this embodiment, the four machine learning models are: K-Nearest Neighbors (KNN) model, Light GBM (LGB) model, XGBoost (XGB) model, and Random Forest (RF) model.

[0035] Calculate and compare the coefficients of determination (R²) of four trained machine learning models under different test set proportions. 2 ) value, such as Figure 1 As shown, the comparison reveals that the KNN model's accuracy is significantly lower than the other three machine learning models. Furthermore, since this invention requires the use of a machine learning model to derive unexplored multi-component refractory high-entropy alloy systems, the model needs to possess good generalization ability, combined with R... 2 The corresponding trained random forest model was selected as the hardness prediction model for multi-element refractory high-entropy alloys.

[0036] Step 3: Process the original hardness feature dataset using the ten-fold cross-recursive feature elimination method to obtain the average accuracy and optimal accuracy for different numbers of hardness features, such as... Figure 2 As shown, based on the average accuracy and optimal accuracy, a preliminary set of hardness features is selected from the original hardness feature dataset. In this embodiment, the specific preliminary set of hardness features obtained is as follows: average valence electron concentration (Vec), specific heat capacity difference (δcp), lattice constant difference (δa), molar volume difference (δVm), average grain size (DS), activation energy fit (D.QI), Gibbs free energy (Gmix), and sixth-order work function (W).^ 6) and parameter δBo;

[0037] Subsequently, an exhaustive method was used to process the initial set of hardness features, obtaining the accuracy of all hardness feature combinations under the hardness prediction model for multi-component refractory high-entropy alloys. The hardness feature combination with the highest accuracy was then selected as the optimal subset of hardness features. Figure 3 As shown, the characteristics of the obtained optimal hardness feature subset are: specific heat capacity difference (δcp), molar volume difference (δVm), grain size (DS), activation energy mismatch (D.QI), Gibbs free energy (Gmix), and sixth-order work function (W). ^ 6) and parameter δBo.

[0038] Step 4: Input the obtained optimal hardness feature subset into the hardness prediction model for multi-element refractory high-entropy alloys, and use Bayesian optimization to adjust and optimize the model's hyperparameters. The hyperparameter optimization includes num_leaves, max_depth, learning_rate, and n_estimators, with hyperparameter ranges of 5–100, 3–9, 0.01–0.2, and 10–1000, respectively. By combining the optimal feature combination with a Bayesian-optimized random forest model, an efficient prediction model for the hardness of multi-element refractory high-entropy alloys can be established, resulting in a seven-element refractory high-entropy alloy hardness prediction model. The accuracy of the hardness prediction model is as follows: Figure 4 As shown;

[0039] Step 5: Use a symbolic algorithm to transform the optimal hardness feature subset and construct a new hardness feature parameter. In specific implementation, the symbolic algorithm is used to transform the optimal feature combination to construct a new hardness feature parameter, denoted as H. k The specific formula is as follows:

[0040]

[0041] The symbolic algorithm used is derived from the optimization of hyperparameters including num_leaves, max_depth, learning_rate, and n_estimators, with hyperparameter ranges of 5–100, 3–9, 0.01–0.2, and 10–1000, respectively; the results show that when H k When the value is greater than 0.2, the Vickers hardness is not less than 450 HV. Furthermore, as H... k With the increase of H, Vickers hardness shows an increasing trend. When designing multi-element high-hardness refractory high-entropy alloys, H should be excluded first. k Components with a value <0.2 can significantly reduce the prediction space. The results are as follows... Figure 5 As shown, this narrows down the range of alloy composition systems to be explored;

[0042] Step 6: Based on the obtained new hardness characteristic parameters, select refractory high-entropy alloy components that meet the mechanical performance requirements from the range of alloy composition systems to be explored, and input them into the seven-element refractory high-entropy alloy hardness prediction model for prediction, to obtain the predicted seven-element high-hardness refractory high-entropy alloy.

[0043] Step 7: Prepare and experimentally verify the predicted seven-element high-hardness refractory high-entropy alloy.

[0044] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0045] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

[0046] In this embodiment, the predicted seven-element refractory high-entropy alloys were all prepared according to the following steps:

[0047] Step 1: Take the various metal raw materials according to the predicted alloy composition. Use a file to coarsely grind the metal surface to remove the thicker oxide layer, and then use sandpaper to finely grind it to obtain a smoother surface. Place the ground metal raw materials into a container filled with ethanol. Clean using an ultrasonic cleaner. The ultrasonic waves generate tiny bubbles in the ethanol. When these bubbles burst rapidly, they generate strong shock waves that can remove tiny impurities and residues from the metal surface. After ultrasonic cleaning, the metal raw materials need to be removed and dried. According to the experimental ratio, accurately weigh the required amount of various raw materials using a precision balance, with a weighing accuracy of ±0.001g.

[0048] Step 2: Open the furnace of the vacuum non-consumable arc melting equipment and place the prepared raw materials into the crucible in order of increasing melting point. Close the furnace, start the vacuum pump, and extract the air from the melting chamber to achieve a high vacuum. Evacuate the equipment to 8×10⁻⁶. -4 When the pressure is below 0.05 MPa, argon gas is introduced into the melting chamber as a protective gas, and the flow rate of argon gas is adjusted so that the pressure in the melting chamber reaches 0.05 MPa.

[0049] Step 3: First, adjust the current to 20A and initiate the arc using a tungsten needle (as an electrode), generating an arc discharge between the tungsten needle and the metal raw material to start the melting process. Then, adjust the current to 180A to melt the titanium ingot for 2 minutes. At high temperatures, this absorbs residual oxygen in the furnace. After the titanium ingot is melted, proceed to melt the other prepared metal raw materials. The alloy is melted multiple times, each time for 5 minutes. After each melting, once the alloy has cooled, use a turning spoon to flip it, ensuring uniform heating and mixing to prevent component segregation. During each melting cycle, ensure the alloy remains in a liquid state for 5 minutes. This helps to further ensure sufficient mixing and reaction between alloying elements, achieving a homogeneous alloy structure. Repeat the melting process 12 times. After melting, a seven-element refractory high-entropy alloy is obtained.

[0050] Implementation Case 1:

[0051] The predicted seven-element refractory high-entropy alloy in this embodiment includes refractory elements Nb, V, Ta, Mo, Zr, and a high-melting-point (Tm>3000℃) refractory element W. The predicted composition of the seven-element refractory high-entropy alloy is WNbV2Zr2CrMo2Ti, where the subscripts represent the atomic percentages of the seven elements in the alloy, i.e., the atomic percentages of W, Nb, V, Zr, Cr, Mo, Ti, and Ta are 10.00 at.%, 10.00 at.%, 20.00 at.%, 20.00 at.%, 10.00 at.%, 20.00 at.%, and 10.00 at.%, respectively.

[0052] As shown in Table 1, according to the method of the present invention, the predicted hardness of WNbV2Zr2CrMo2Ti alloy is 684.31 (HV), and the hardness of the alloy tested by Vickers hardness tester is 680.86±25.67 (HV). The relative error between the predicted value and the hardness value is 0.5%.

[0053] The alloy's hardness was tested to be 680.86±25.67 (HV).

[0054] Implementation Case 2:

[0055] The seven-element refractory high-entropy alloy predicted in this embodiment includes refractory elements Nb, V, Ta, Mo, Zr, and a high-melting-point (T) alloy. m The predicted composition of the seven-element refractory high-entropy alloy (>3000℃) is WNbV2Zr2Cr2MoTa, where the subscripts represent the atomic percentages of the seven elements in the alloy, namely, W, Nb, V, Zr, Cr, Mo, and Ta, which are 10.00 at.%, 10.00 at.%, 20.00 at.%, 20.00 at.%, 20.00 at.%, 10.00 at.%, and 10.00 at.%, respectively.

[0056] As shown in Table 1, according to the method of the present invention, the predicted hardness of WNbV2Zr2Cr2MoTa alloy is 742.65 (HV), and the hardness of the alloy tested by Vickers hardness tester is 748.54±20.67 (HV). The relative error between the test and the hardness value is 0.79%.

[0057] As can be seen from the above embodiments, the alloy hardness value predicted by the prediction method of the present invention is not much different from its experimental value, and the relative error is within 1%.

[0058] Table 1

[0059]

[0060] The above are merely exemplary embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the hardness of seven-element refractory high-entropy alloys based on symbolic algorithm-assisted machine learning, characterized in that, include: Step 1: After obtaining the composition and hardness data of five- to seven-element refractory high-entropy alloys through literature and laboratory data, calculate the original characteristic parameters of the composition and hardness data through inherent properties and empirical formulas. Then, use domain knowledge to initially select hardness-related characteristic parameters from the original characteristic parameters and form the original hardness characteristic dataset. Divide the original hardness characteristic dataset into a hardness characteristic training set and a hardness characteristic test set. Step 2: Input the hardness feature training set into several different machine learning models for training, and obtain several trained machine learning models accordingly. The determination coefficient values ​​of several trained machine learning models under different test set proportions are calculated and compared, so as to select the trained machine learning model with the largest determination coefficient value as the hardness prediction model of multi-component refractory high-entropy alloy. Step 3: Process the original hardness feature dataset using the ten-fold cross-recursive feature elimination method to obtain the average accuracy and optimal accuracy under different numbers of hardness features. Based on the average accuracy and optimal accuracy, select a preliminary set of hardness features from the original hardness feature dataset. The initial set of hardness features is processed using an exhaustive method to obtain the accuracy of all hardness feature combinations under the hardness prediction model of multi-component refractory high-entropy alloys. The hardness feature combination with the highest accuracy is then selected as the optimal hardness feature subset. Step 4: Input the optimal hardness feature subset into the hardness prediction model of the multi-component refractory high-entropy alloy, and use the Bayesian optimization algorithm to fine-tune the parameters of the multi-component refractory high-entropy alloy hardness prediction model, so as to obtain the seven-component refractory high-entropy alloy hardness prediction model. Step 5: Use a symbolic algorithm to transform the optimal hardness feature subset and construct a new hardness feature parameter to narrow down the range of alloy composition systems to be explored. Step 6: Based on the converted new hardness characteristic parameters, select refractory high-entropy alloy components that meet the mechanical performance requirements from the range of alloy composition systems to be explored, and input them into the seven-element refractory high-entropy alloy hardness prediction model for prediction, and obtain the predicted seven-element high-hardness refractory high-entropy alloy. Step 7: Prepare and experimentally verify the predicted seven-element high-hardness refractory high-entropy alloy.

2. The method for predicting the hardness of seven-element refractory high-entropy alloys based on symbolic algorithm-assisted machine learning according to claim 1, characterized in that, The characteristics of the preliminary hardness feature set in step 3 include: valence electron concentration, specific heat capacity difference, lattice constant difference, molar volume difference, grain size, activation energy mismatch, Gibbs free energy, sixth work function, and parameter δBo.

3. The method for predicting the hardness of seven-element refractory high-entropy alloys based on symbolic algorithm-assisted machine learning according to claim 2, characterized in that: The features of the optimal hardness feature subset in step 3 include: specific heat capacity difference, molar volume difference, grain size, activation energy mismatch, Gibbs free energy, sixth work function, and parameter δBo.

4. The method for predicting the hardness of seven-element refractory high-entropy alloys based on symbolic algorithm-assisted machine learning according to claim 3, characterized in that, The predicted composition of the seven-element high-hardness refractory high-entropy alloy in step 6 is WNbV2Zr2CrMo2Ti and WNbV2Zr2Cr2MoTa, where the subscripts represent the atomic proportions of each element.

5. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the hardness prediction method for any of the seven-element refractory high-entropy alloys according to claims 1-4, and the processor is configured to execute the program stored in the memory.

6. A computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is run by the processor, it executes the steps of the hardness prediction method for any of the seven-element refractory high-entropy alloys as described in claims 1-4.

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