A high-hardness high-entropy alloy composition design method based on ensemble learning

Abstract

The present application relates to high-entropy alloy hardness prediction technical field, more specifically, it is a kind of high-hardness high-entropy alloy composition design method based on ensemble learning, and the design method steps are as follows: based on high-entropy alloy system, obtain the data set for predicting the hardness of high-entropy alloy, then the composition data in initial data set is self-encoded, the hardness distribution hidden space of high-entropy alloy is obtained, and the hidden space is sampled using Gaussian mixture distribution model, obtain the sample points participating in prediction, then different feature combinations are selected for modeling for multiple machine learning, construct multiple models, and the model is trained and evaluated, and then the qualified model is screened out to form ensemble model, by using ensemble learning method, multiple machine learning models are combined to form ensemble model, and the sample points participating in prediction are predicted, then alloy preparation and test are carried out, and finally the design of high-hardness high-entropy alloy composition is realized.

Description

Technical Field

[0001] This invention relates to the field of high-entropy alloy hardness prediction technology, and more specifically to a high-hardness high-entropy alloy composition design method based on ensemble learning. Background Technology

[0002] High-entropy alloys are a class of alloys composed of five or more main elements in similar atomic percentages. These alloys have attracted widespread attention due to their unique microstructure and excellent physical, chemical, and mechanical properties. Compared to traditional alloys, high-entropy alloys exhibit characteristics such as high hardness, excellent corrosion resistance, and good high-temperature performance, making them potentially valuable for applications in aerospace, military, automotive manufacturing, and energy sectors.

[0003] Despite the many advantages of high-entropy alloys, several challenges remain in their design. Traditional alloy design methods are often based on trial and error, which are not only time-consuming and costly, but also make it difficult to systematically explore and optimize complex compositional spaces.

[0004] Data-driven methods, such as machine learning, are playing an increasingly prominent role in alloy research and development. By establishing the complex relationship between input features and material targets, machine learning methods can achieve rapid prediction of material properties, thus playing an important role in guiding the design of materials, including high-entropy alloys.

[0005] Chinese Patent Publication No. CN116092604B proposes a data-driven method for preparing high-strength, high-toughness, refractory, and high-entropy alloys. This method can extract information from high-entropy alloy datasets and predict composition points that may possess target properties, significantly accelerating the design and optimization of high-entropy alloy compositions. However, current machine learning methods in materials science mainly use single models to model and predict material properties or chemical structures. While these methods have achieved some predictive effectiveness, the results are not precise enough, and they can only make simple predictions, making it difficult to design specific compositions for high-entropy alloys. Although machine learning algorithms have excellent learning, modeling, and predictive capabilities, these models can only guarantee prediction accuracy within the composition distribution range when the training dataset contains fewer than 300 data points, and cannot explore unknown spaces. Ensemble learning methods can integrate multiple machine learning models to obtain better prediction results than a single machine learning machine.

[0006] In summary, this invention develops a high-hardness, high-entropy alloy composition design method based on ensemble learning, which has significant theoretical and practical value. It plays a crucial role in promoting the development of materials science and realizing the rapid iteration of novel high-hardness, high-entropy alloys. Summary of the Invention

[0007] This invention provides a method for designing high-hardness, high-entropy alloy compositions based on ensemble learning. It obtains the latent space of the hardness distribution of high-entropy alloys using a differential autoencoder algorithm, and then samples the latent space using a Gaussian mixture model combined with a Markov chain Monte Carlo method to select candidate points. Subsequently, an ensemble learning method is used to combine multiple machine learning models and predict the participating sample points. Finally, a performance function is used to select high-hardness, high-entropy alloy composition points. This addresses the problems of low prediction accuracy of single machine learning models, difficulty in finding high-hardness, high-entropy alloy composition points, and difficulty in exploring the composition space of unknown high-entropy alloys.

[0008] The specific technical solution of this invention is as follows:

[0009] A design method for high-hardness, high-entropy alloy composition based on ensemble learning, the steps of which are as follows:

[0010] S1: A dataset for predicting the hardness of high-entropy alloys is obtained based on the high-entropy alloy system. The high-entropy alloy system is the Al-Co-Cr-Cu-Fe-Ni system. Multiple composition and corresponding hardness data are collected based on this system. Combined with the physical characteristics of high-entropy alloys, a dataset for further analysis is formed. The number of data in the dataset is 100-300.

[0011] Twenty physical characteristics of high-entropy alloys were used to describe the fundamental properties of the alloys and the factors influencing their performance. These characteristics are: atomic radius difference (δr), electronegativity difference (Δχ), valence electron concentration (VEC), enthalpy of mixing (ΔH), configurational entropy (ΔS), Ω parameter (Ω), Λ parameter (Λ), γ parameter (γ), local electronegativity mismatch (D.χ), number of mobile electrons (e / a), cohesive energy (Ec), modulus mismatch (η), local size mismatch (Dr), energy term (A), Nabarro coefficient (F), work function (W), shear modulus (G), shear modulus difference (δG), local modulus mismatch (DG), and lattice distortion energy (μ). The calculation of these characteristics relied on the elemental physical property values ​​provided in existing literature (Hardness prediction of AlCoCrCuFeNi system high-entropy alloys based on machine learning, author: Rui Zou), and were calculated according to their formulas. These were then integrated with compositional data to form an initial dataset for further analysis.

[0012] S2: Then, the composition data in the dataset is self-encoded to obtain the hardness distribution latent space of the high-entropy alloy;

[0013] S3: Use a Gaussian mixture distribution model to sample the latent space, with a sample size of 1000-3000, to obtain sample points for prediction.

[0014] S4: Use different feature combinations to model multiple machine learning methods, build multiple models, train and evaluate the models, select qualified models, and then form an ensemble model.

[0015] S5: Based on the ensemble model, predict the participating sample points and obtain the hardness prediction results;

[0016] S6: Select experimental points for sample preparation using performance function sorting, and then test the hardness of the sample points. The hardness value must reach 800HV or higher. If the tested hardness value is lower than the 800HV standard, repeat steps S2 to S5, and use the updated dataset to retrain, validate, and screen the model to optimize the alloy composition design and ultimately achieve the design of a high-hardness, high-entropy alloy composition. Conversely, if the hardness value is higher than the 800HV standard, further performance evaluation and application exploration will be conducted.

[0017] As a technical solution of this invention, in S1, based on the Al-Co-Cr-Cu-Fe-Ni system, 278 composition and corresponding hardness data are collected. Combining this with the physical characteristics of high-entropy alloys, there are approximately several data points for each of the 20 physical features, resulting in 278 data points. Each data point includes three parts: the first part contains 6 compositions, the second part contains 20 features, and the third part is hardness, which is the target feature. Therefore, the initial dataset is configured with 278 rows x 27 columns. The initial dataset is then divided into a training set and a test set, randomly allocated in a 4:1 ratio. The training set contains 222 data points, and the test set contains 56 data points.

[0018] As a technical solution of the present invention, in S2, the latent representation of the Al-Co-Cr-Cu-Fe-Ni high-entropy alloy dataset is learned by differential autoencoder. Both the encoder and decoder parts of the differential autoencoder are represented by neural networks. The encoder's role is to accept the input data and convert it into a low-dimensional latent space. The decoder reconstructs these latent representations back to the original high-dimensional data. The input data passes through the encoder of the differential autoencoder, which maps the composition data to a two-dimensional latent space. Then, the decoder maps the two-dimensional latent space data back to the original composition data. The training parameters of the differential autoencoder are adjusted by comparison loss.

[0019] As a technical solution of the present invention, in S2, the latent space is divided into a high-hardness region greater than 600HV and other regions. A neural network classifier is trained by a neural network method, and the region greater than 600HV is set as the high-hardness region, and the region less than 600HV is set as the low-hardness region.

[0020] As one technical solution of the present invention, the grid training parameters of the neural network classifier are set as follows: the initial learning rate is set to 0.0001, the training batch size is set to 32, and the number of training rounds is set to 400.

[0021] As a technical solution of the present invention, in S3, an initial sample is randomly selected from the Gaussian mixture model and 10,000 iterations are performed. In each iteration, a suggested next sample is generated based on the current sample using the multivariate normal distribution method. The current sample and the suggested sample are then merged and passed to the classifier trained in S2. The classifier outputs the classification probabilities of the two samples. If the acceptance probability of the suggested sample is higher than that of the current sample, the suggested sample is retained as the sample for the next iteration; otherwise, it is discarded. Through this method, 1,352 sample points are obtained to participate in the subsequent screening.

[0022] As a technical solution of the present invention, in S4, the models involved in the integration include, but are not limited to, SVR, CatBoost, LightGBM, Back Propagation Neural Networks, Random Forest, XGBoost, and AdaBoost models.

[0023] As a technical solution of the present invention, in S4, an iterative feature addition method is used to train the model under different training set distributions. The iterative feature addition starts from an initial subset, which only contains elements of the component, and then new features are added gradually, one feature at a time. In each iteration, the final feature set of the model is selected by the change in the model's RMSE value. The RMSE calculation process is as follows:

[0024]

[0025] Where y i Represents true hardness. The model predicts the stiffness, and n represents the number of samples.

[0026] As a technical solution of the present invention, in S5, multiple machine learning models trained in S4 are used to predict the hardness values ​​of the high-entropy alloy composition points participating in the screening, and the average of the predicted hardness values ​​provided by the integrated model and the standard deviation of the predicted hardness values ​​are calculated.

[0027] As a technical solution of the present invention, in S6, the performance function is the upper confidence limit (UCB) function, and the calculation formula is:

[0028] UCB(x)= μ(x)+ κσ(x) (3)

[0029] In the formula, μ(x) is the predicted mean of the component point, and σ(x) is the predicted standard deviation of the component point; in order to balance the utilization of the model and the development of unknown points, k is set to 0.2.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] 1. This invention obtains the latent space of hardness distribution of high-entropy alloys by using a differential autoencoder algorithm, and uses a Gaussian mixture model combined with a Markov chain Monte Carlo method to sample and select sample points for candidate screening. Then, an ensemble learning method is used to combine multiple machine learning models to form an ensemble model, and predict the sample points. Finally, alloy preparation and testing are carried out to achieve the design of high-hardness, high-entropy alloy composition. Attached Figure Description

[0032] Figure 1 This is a flowchart of the high-entropy alloy composition design of this invention;

[0033] Figure 2 This is a two-dimensional latent space graph of the high-entropy alloy composition dataset of this invention;

[0034] Figure 3 This is a Spearman rank correlation coefficient diagram between different features of the present invention;

[0035] Figure 4 This is a graph showing the RMSE results of multiple machine learning models of this invention under different training set proportions. Detailed Implementation

[0036] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and should not be construed as limiting the scope of the invention.

[0037] Example 1:

[0038] Step 1: As Figure 1-4 As shown, the high-entropy alloy system in this invention is the Al-Co-Cr-Cu-Fe-Ni system, and 278 composition and corresponding hardness data were collected based on this system.

[0039] Simultaneously, 20 physical characteristics were identified to describe the fundamental properties of the alloy and the factors influencing its performance. These are: atomic radius difference (δr), electronegativity difference (Δχ), valence electron concentration (VEC), enthalpy of mixing (ΔH), configuration entropy (ΔS), Ω parameter (Ω), Λ parameter (Λ), γ parameter (γ), local electronegativity mismatch (D.χ), number of mobile electrons (e / a), cohesive energy (Ec), modulus mismatch (η), local size mismatch (Dr), energy term (A), Nabarro coefficient (F), work function (W), shear modulus (G), shear modulus difference (δG), local modulus mismatch (DG), and lattice distortion energy (μ). The calculation of these characteristics relied on the elemental physical property values ​​provided in the literature (Hardness prediction of AlCoCrCuFeNi system high-entropy alloys based on machine learning, author: Rui Zou), and were calculated according to their formulas; these were then integrated with the composition data to form an initial dataset for further analysis.

[0040] Step 2: Perform self-encoding on the composition data in the dataset to obtain the hardness distribution latent space of the high-entropy alloy. The latent space is divided into a high-hardness region greater than 600 HV and other regions.

[0041] It should be noted that the component dataset proposed in this paper refers to the component portion of 278 data points, and the corresponding latent space refers to the two-dimensional space mapped from the high-dimensional space by the encoder through the differential autoencoder.

[0042] This invention uses a differential autoencoder to learn the latent representation of an Al-Co-Cr-Cu-Fe-Ni high-entropy alloy dataset. The encoder's role is to accept input data and transform it into a lower-dimensional latent space. During this process, the encoder attempts to preserve important features of the data, which are necessary for reconstructing the input data. These features are encoded in the latent space by a neural network decoder, which attempts to reconstruct the input data. The decoder aims to generate an output that is as close as possible to the original input, thereby learning an effective representation of the data. These latent representations are then reconstructed back into the original high-dimensional data. Both the encoder and decoder parts of the differential autoencoder use neural networks. Optimal encoder and decoder network parameters are obtained by optimizing the loss function, and then variational parameters are used to sample and reconstruct the signal. In a specific embodiment, the network training parameters are set as follows: initial learning rate is set to 0.001, weight decay value is set to 0.0001, training batch size is set to 64, and training epochs are set to 600.

[0043] Loss = Loss {重构损失} +Loss {DL散度} (1)

[0044] The input data is processed by the encoder of the differential autoencoder, which maps the component data to a two-dimensional latent space. Then, the decoder maps the two-dimensional latent space data back to the original component data. The training parameters of the differential autoencoder are adjusted by comparing the final loss.

[0045] Finally, the two-dimensional latent space diagram of the component data distribution in this specific embodiment is as follows: Figure 2 As shown, the component points of different systems produce significantly different boundaries in the two-dimensional latent space.

[0046] Subsequently, this invention trained a neural network classifier using a neural network method, classifying regions with a hardness greater than 600 HV as high-hardness regions and those with a hardness less than 600 HV as low-hardness regions. The training and test sets were randomly allocated in a 4:1 ratio, with 222 data entries in the training set and 56 in the test set. The grid training parameters for this classifier were set as follows: initial learning rate of 0.0001, training batch size of 32, and number of training epochs of 400, using five-fold cross-validation. The neural network classifier achieved an accuracy of 0.89 on the training set and 0.85 on the test set. In existing materials science, a value above 0.6 is generally considered to provide good accuracy.

[0047] Step 3: Use a Gaussian mixture distribution model to sample the latent space, selecting 1000-3000 samples to obtain sample points for prediction.

[0048] This invention uses the component dataset of this system to train a Gaussian mixture model. To determine the optimal number of Gaussian components in the Gaussian mixture model, this embodiment employs the elbow algorithm. This algorithm evaluates the impact of different component numbers on the model's goodness of fit, searching for an inflection point where adding more Gaussian components no longer significantly improves the model's goodness of fit. Based on the results of the elbow algorithm, the optimal number of Gaussian components was determined to be 6, with a mean negative log-likelihood of -1.16.

[0049] After determining the optimal number of Gaussian components, the present invention further uses the Markov chain Monte Carlo method to sample the Gaussian mixture model (the Gaussian mixture model with 6 Gaussian components).

[0050] This embodiment first randomly selects an initial sample from the Gaussian mixture model and performs 10,000 iterations. In each iteration, a proposed next sample is generated based on the current sample using a multivariate normal distribution method. The current sample and the proposed sample are then merged and passed to the classifier trained in step two. The classifier outputs the classification probabilities of the two samples. If the proposed sample has a higher acceptance probability than the current sample, it is retained as the sample for the next iteration; otherwise, it is discarded. Using this method, we obtained 1352 sample points for subsequent screening. These sample points are considered to be high-entropy alloy composition points that may have high hardness values.

[0051] It should be noted that the 10,000 iterations refer to an initial sample, each iteration generating a suggested sample. If the suggested sample is retained, it becomes the initial sample for the next iteration, and so on, for a total of 10,000 iterations. If any samples are retained after 10,000 iterations, they are used as sample points. Calculations show that a total of 1,352 sample points were retained.

[0052] Step 4: Use different feature combinations to model multiple machine learning methods, build multiple models, train and evaluate the models, select qualified models, and then form an ensemble model.

[0053] This invention utilizes machine learning methods such as SVR, CatBoost, LightGBM, Back Propagation Neural Networks, Random Forest, XGBoost, and AdaBoost.

[0054] First, Spearman's rank correlation coefficient is used to filter features with a correlation greater than 0.95. Spearman's rank correlation coefficient assesses the correlation between two variables, that is, the degree of their correlation and the direction in which their values ​​change in the same way. Its value ranges from -1 to +1; the closer the absolute value is to 1, the stronger the correlation. Since highly correlated features exist in the feature data, one can be used to replace the other. The Spearman rank correlation coefficient graph between different features is shown below. Figure 3 As shown.

[0055] It should be noted that the "two variables" mentioned above refer to two variables in the concept, which actually involve the comparison of characteristics and hardness other than composition.

[0056] We then used an iterative feature addition method to train the model under different training set distributions. The iterative feature addition started with an initial subset containing only elements, and then new features were added one at a time. In each iteration, the final feature set of the model was selected based on the change in the model's RMSE value. For each machine learning method, we trained 100 machine learning models and selected the 20 models with the lowest RMSE values ​​as the ensemble model. For each machine learning algorithm, we built and trained 100 different model instances. These models included SVR, CatBoost, LightGBM, Back Propagation Neural Networks, RandomForest, and XGBoost, each applied in different combinations of feature sets and training distributions. After training, we used the root mean square error (RMSE) as a performance metric to evaluate these models. RMSE is a commonly used metric that measures the difference between the model's predictions and the actual observations. A lower RMSE value generally indicates better prediction accuracy. The final RMSE results for each model at different scales are shown in the figure below. Figure 4 As shown.

[0057]

[0058] Where y i Represents true hardness. The model predicts the stiffness, and n represents the number of samples.

[0059] After training and evaluating all models, we selected the top 20 models with the lowest RMSE values ​​from the 100 models built using each machine learning method. These models were considered the best performing models and were chosen to build the final ensemble model. The ensemble model improves the accuracy and robustness of predictions by combining the predictions of multiple models. In this way, we hope that the ensemble model can integrate the advantages of different individual models, reduce potential overfitting, and ultimately provide more reliable predictions when faced with unknown data.

[0060] Step 5: Select different feature combinations for multiple machine learning models, build multiple models, train and evaluate the models, select qualified models, and then form an ensemble model.

[0061] According to an embodiment of the present invention, multiple machine learning models trained in step four are used to predict the hardness values ​​of the high-entropy alloy composition points participating in the screening. To predict the hardness value of each specific high-entropy alloy composition point, an ensemble learning method is employed.

[0062] The core advantage of ensemble learning technology lies in its multi-model fusion strategy. This invention organically integrates multiple different machine learning models, each learning independently during training and capturing different features and inherent patterns in the data. In the prediction phase, by comprehensively considering the outputs of each model, not only are the strengths of individual models extracted, but the limitations of any single model are also avoided, thus optimizing the overall prediction performance.

[0063] Specifically, for each composition point, we not only calculated the mean of the predicted hardness values ​​provided by the ensemble model, but also the standard deviation of these predictions. The prediction mean gives the model's collective prediction of the hardness at that composition point, while the standard deviation provides a quantitative indicator of the prediction uncertainty. For each machine learning method, there are 20 machine learning models; therefore, in this embodiment, a total of 180 machine learning models are involved in predicting the hardness of the composition point.

[0064] Step 6: Select experimental points for preparation based on the performance function ranking, and test the hardness of the sample points;

[0065] If the hardness obtained in step six does not meet the predetermined requirements, the alloy composition characteristic data is added to the dataset, and steps four and five are repeated until the hardness obtained in step six meets the preset requirements.

[0066] According to an embodiment of the present invention, the performance function is the upper confidence limit (UCB) function.

[0067] UCB(x)= μ(x)+ κσ(x) (3)

[0068] μ(x) is the predicted mean of the component point, and σ(x) is the predicted standard deviation of the component point. To balance the utilization of the model and the development of unknown points, k is set to 0.2. UCB simply represents a ranking that combines the predicted mean and standard deviation.

[0069] Finally, we selected Al45Co23Cr18Cu1Fe7Ni5, Al44Co15Cr22Cu5Fe8Ni6, and Al44Co16Cr15Fe13Ni12 as the final composition points.

[0070] To ensure the high quality of the alloy, we strictly select metallic materials with a purity exceeding 99.9% as raw materials. The preparation process begins with grinding the surface of the raw materials to carefully remove the surface oxide layer that could affect the alloy's performance. Subsequently, ultrasonic cleaning technology is used for thorough cleaning to remove any residual impurities and contaminants. The cleaned materials are then placed in an oven for complete drying to eliminate potential problems caused by moisture.

[0071] After preparing the raw materials, we precisely calculated the required mass of each metal raw material based on the molar ratio of each alloy component. Then, the various metal raw materials, after ultrasonic cleaning and precise weighing, were prepared for the next step of the alloy melting process. We used induction melting to prepare the alloy, a method that provides a uniform and controllable heating environment to promote thorough metal fusion. To ensure uniform alloy composition, we performed at least six repeated melting processes on each alloy sample, allowing the alloy to cool and then turning it after each melting to ensure uniform distribution of the components within the alloy.

[0072] After the alloy preparation was completed, we conducted hardness tests on the resulting high-entropy alloy samples. The purpose of the test was to ensure that the alloy's hardness value met our stringent requirements for high-performance materials, namely, a hardness value of 800 HV or higher. If the measured hardness value reached this standard, we could consider the alloy preparation successful and proceed with further performance evaluation and application exploration.

[0073] If the hardness value does not reach 800 HV, the actual measured hardness values ​​at these three composition points are recorded and fed back into our machine learning dataset. This data feedback mechanism helps us continuously improve and adjust the algorithm model, further enhancing the accuracy of alloy design through iterative learning.

[0074] Next, we will repeat steps 2 through 5, using the updated dataset to retrain, validate, and filter the model to optimize the alloy composition design. Through this dynamic iterative approach, we gradually approach the ideal alloy ratio, ultimately achieving the design of a high-hardness, high-entropy alloy composition.

[0075] The embodiments of the present invention are given for the purposes of illustration and description, and are not intended to be exhaustive or to limit the invention to the forms disclosed. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features.

Claims

1. A method for designing the composition of high-hardness, high-entropy alloys based on ensemble learning, characterized in that, Includes the following steps: S1. Dataset Construction: Based on the Al-Co-Cr-Cu-Fe-Ni high-entropy alloy system, collect 100-300 alloy composition data and their corresponding measured hardness data, and combine them with the physical characteristics of high-entropy alloys to form an initial dataset for analysis. S2. Latent Space Construction: A differential autoencoder is used to autoencode the component data in the dataset. The training loss is composed of reconstruction loss and KL divergence. The high-dimensional component data is mapped to a low-dimensional space to obtain the hardness distribution latent space of the high-entropy alloy. A neural network classifier is trained to divide the latent space into high-hardness region and low-hardness region. S3. Latent space sampling: The latent space of the hardness distribution is fitted using a Gaussian mixture distribution model, and the MCMC sampling algorithm is used for sampling. During the sampling process, the high hardness probability of the sample is output by the hardness classifier trained in step S2. The sample acceptance rate is determined according to the probability, guiding the sampling to be biased towards the high hardness region, and 1000-3000 virtual component sample points are selected to participate in the prediction. S4. Ensemble Model Construction: For multiple machine learning algorithms, different feature combinations are selected using the iterative feature addition method to model them separately, resulting in multiple base models; the root mean square error (RMSE) is used as the evaluation index to select the base models with qualified prediction performance to form an ensemble prediction model. S5. Hardness prediction and experimental site selection: The integrated prediction model is used to predict the hardness of the virtual composition sample points obtained in step S3. The mean and standard deviation of the hardness prediction for each sample point are obtained. The upper confidence bound UCB efficiency function is used to sort all sample points, balance exploration and utilization, and select the sample points with higher ranking as experimental points for alloy preparation and hardness testing. The target hardness value should reach above 800 HV. S6. Closed-loop iterative optimization: If the measured hardness value of the experimental point is lower than 800 HV, the composition and corresponding measured hardness data of the experimental point are added to the initial dataset of step S1. Steps S2 to S5 are repeated. The differential autoencoder, hardness classifier, Gaussian mixture distribution model and ensemble prediction model are retrained synchronously using the updated dataset to dynamically optimize the alloy composition design. If the measured hardness value is higher than the 800 HV standard, the alloy composition is further evaluated for performance and its applications are explored.

2. The high-hardness, high-entropy alloy composition design method based on ensemble learning according to claim 1, characterized in that, In step S1, 278 composition and corresponding hardness data are collected and combined with 20 high-entropy alloy physical characteristics to form an initial dataset; the initial dataset is then randomly divided into a training set and a test set in a 4:1 ratio, with 222 data points in the training set and 56 data points in the test set.

3. The high-hardness, high-entropy alloy composition design method based on ensemble learning according to claim 1, characterized in that, In step S2, the differential autoencoder includes two parts: an encoder and a decoder, both of which are constructed using neural networks. The encoder maps the input component data to a two-dimensional latent space, and the decoder reconstructs the two-dimensional latent space data back to the original component dimension. During training, network parameters are adjusted by comparing the total loss.

4. The high-hardness, high-entropy alloy composition design method based on ensemble learning according to claim 3, characterized in that, In step S2, the latent space is divided into a high-hardness region greater than 600HV and other regions using 600HV as a threshold; the hardness classifier is obtained by training a neural network method.

5. The high-hardness, high-entropy alloy composition design method based on ensemble learning according to claim 4, characterized in that, The training parameters for the hardness classifier are set as follows: initial learning rate is set to 0.0001, training batch size is set to 32, and number of training rounds is set to 400.

6. The high-hardness, high-entropy alloy composition design method based on ensemble learning according to claim 5, characterized in that, In step S3, the specific steps of MCMC sampling include: randomly selecting an initial sample from the Gaussian mixture model and performing 10,000 iterations; in each iteration, generating a proposed sample based on the current sample using a multivariate normal distribution; inputting the current sample and the proposed sample into the hardness classifier to obtain their respective high hardness classification probabilities; if the classification probability of the proposed sample is higher than that of the current sample, the proposed sample is retained as the current sample for the next iteration, otherwise it is discarded; after the iteration is completed, the retained samples are the sample points participating in the subsequent screening.

7. The high-hardness, high-entropy alloy composition design method based on ensemble learning according to claim 6, characterized in that, In step S4, the machine learning algorithms involved in modeling include, but are not limited to, SVR, CatBoost, LightGBM, BackPropagation Neural Networks, Random Forest, XGBoost, and AdaBoost models.

8. The high-hardness, high-entropy alloy composition design method based on ensemble learning according to claim 7, characterized in that, In step S4, the iterative feature addition method starts from an initial subset containing only element components and gradually adds new physical features, adding only one feature at a time; In each iteration, the final feature set is selected based on the changes in the model's RMSE value; the formula for calculating RMSE is: in Represents true hardness. The predicted stiffness of the model, Represents the number of samples.

9. The high-hardness, high-entropy alloy composition design method based on ensemble learning according to claim 8, characterized in that, In step S5, for each virtual component sample point, the integrated model outputs the prediction results of multiple base models, and calculates the average predicted hardness and the standard deviation of the prediction for that sample point.

10. The high-hardness, high-entropy alloy composition design method based on ensemble learning according to claim 9, characterized in that, In step S5, the formula for calculating the upper confidence bound UCB performance function is as follows: In the formula, This is the predicted mean value for that component point. This represents the prediction standard deviation for that component point; to balance the utilization of the model with the development of unknown points, Set it to 0.2.

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