High-entropy alloy structure performance collaborative prediction method adopting active learning strategy

Abstract

The invention provides a high-entropy alloy structure performance collaborative prediction method adopting an active learning strategy, and belongs to the technical field of machine learning application. The method solves the problems that the prior art depends on a fixed data set, cooperative and accurate prediction of the structure performance of the high-entropy alloy cannot be achieved under the conditions of sample scarcity and uneven distribution, and the generalization ability is weak. The technical scheme comprises the following steps: constructing and preprocessing a data set; constructing a feature set based on the properties of materials, and determining a key feature subset through multi-stage screening; training an initial collaborative prediction model; an active learning strategy is adopted, and high-value samples are screened through uncertainty calculation and clustering analysis for experiments; and an experimental result is fed back to the model for iterative optimization. According to the method, the prediction precision and generalization ability of a complex component space are remarkably improved, the model interpretability is enhanced, continuous autonomous optimization under the small sample condition is achieved, the method is suitable for various high-entropy alloy systems, and the research and development efficiency of materials can be greatly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of machine learning application, and particularly relates to a high-entropy alloy microstructure and performance collaborative prediction method adopting an active learning strategy. BACKGROUND

[0002] High-entropy alloy is a new alloy system based on the design concept of multi-principal elements, which is composed of five or more main elements in equal atomic ratio or near equal atomic ratio. Its high configuration entropy effect can stabilize the solid solution phase and endow the material with excellent comprehensive performance, such as high strength, high hardness, good wear resistance and thermal stability, etc., which shows broad application prospects in aerospace, energy equipment, national defense and military industry, etc.

[0003] However, the composition space of high-entropy alloy is extremely broad, and the element combination and ratio vary greatly, resulting in complex microstructure and strong performance sensitivity. Traditional material research and development methods mainly rely on experimental trial and error, experience rule summary or thermodynamic calculation (such as CALPHAD method). These methods have obvious shortcomings when dealing with multi-component and high-dimensional composition design: experimental screening is time-consuming, labor-intensive and costly; the extrapolation of empirical rules is limited; thermodynamic calculation relies on accurate phase diagram database and has weak prediction ability for new systems, making it difficult to realize efficient and accurate composition-microstructure-performance integrated design.

[0004] In recent years, data-driven machine learning methods have provided a new way for material performance prediction. Existing researches use support vector machines, random forests, neural networks and other models to make certain progress in microstructure classification prediction, hardness, strength and other performance regression prediction of high-entropy alloy. However, most of the existing methods are based on passive training of fixed data sets, which have the following limitations:

[0005] 1. Data scarcity and uneven distribution: the experimental samples of high-entropy alloy are limited, and the composition distribution is uneven, resulting in low prediction reliability of the model in the sparse sample area.

[0006] 2. Difficulty in collaborative prediction: there is a complex coupling relationship between microstructure and mechanical properties. When both are included in a unified prediction framework, problems such as unbalanced sample labels and insufficient feature representation are encountered.

[0007] 3. Insufficient generalization ability: traditional machine learning models have limited generalization ability in unseen systems or composition areas, making it difficult to meet the material design needs under multiple system and process conditions.

[0008] 4. Low model iteration efficiency: lacking a mechanism for actively guiding experiments, the model cannot independently identify new samples that are most critical for model improvement, resulting in low efficiency of experimental resource utilization.

[0009] Therefore, there is an urgent need for a collaborative prediction method that can integrate material feature engineering, machine learning, and active learning strategies to achieve precise, efficient, and iterative optimization of high-entropy alloy composition-microstructure-performance integrated prediction, thereby accelerating the design and development process of new materials. SUMMARY

[0010] The present application aims to overcome the problems in the background art and provide a high-entropy alloy microstructure performance collaborative prediction method using an active learning strategy. The present application integrates feature engineering, machine learning, and active learning strategies to build a collaborative prediction model of high-entropy alloy microstructure performance. By analyzing the composition space uncertainty through active learning, key samples are automatically selected for experimental supplementation, and the model is iteratively optimized, thereby significantly improving the prediction accuracy and cross-system generalization ability under limited data conditions, achieving efficient and precise material composition design and performance prediction.

[0011] To achieve the above-mentioned application purpose, the technical scheme adopted by the present application is as follows: a high-entropy alloy microstructure performance collaborative prediction method using an active learning strategy, comprising the following steps:

[0012] Step 1: Data construction and preprocessing: collect and organize literature reports and experimentally measured high-entropy alloy sample data, construct a dataset containing composition, preparation process, microstructure, and performance information, wherein the microstructure is represented by the phase structure of high-entropy alloy, and the performance is represented by hardness; clean and merge the data; classify and encode samples with the same phase structure according to hardness to obtain labels containing sample phase structure and hardness level information; divide the dataset into training set and test set according to a predetermined proportion;

[0013] Step 2: Feature construction and selection: based on the properties of materials, construct a feature set containing element atomic properties, thermodynamic parameters, and electronic structure information, and convert the preparation process into features through one-hot encoding; use a multi-stage feature selection method to select the feature set, and determine the optimal feature subset based on cross-validation of the training set;

[0014] Step 3: Model training: based on the optimal feature subset, construct a high-entropy alloy microstructure performance collaborative prediction model, optimize the hyperparameters of the model, and then train the model to obtain an initial prediction model;

[0015] Step 4: Active learning selects uncertainty samples: construct a potential composition space under multi-element constraints, use the trained initial prediction model to calculate the uncertainty of samples in the composition space, and obtain their information entropy values; select the composition samples with the highest prediction uncertainty in different regions as experimental objects through clustering methods;

[0016] Step 5: Experimental preparation and characterization: Prepare high-entropy alloys according to the samples selected by active learning, test their actual phase structure and hardness data, and add the experimental results to the original training set after coding;

[0017] Step 6: Model improvement: Add new samples obtained in step 5 to the original training set, retrain the model, and realize iterative optimization of the model;

[0018] Step 7: Evaluate the model's prediction performance: Determine whether the model's prediction accuracy or generalization ability meets the requirements. If it does, the entire process is complete. If not, return to step 4 and reiterate the training.

[0019] Further, in step 1, samples with the same phase structure are classified into low, medium, and high levels using hardness three-partitioning, and are coded in increasing order; the preset ratio is 8:2. This technical feature solves the technical problem of poor model training stability caused by the lack of unified basis for data set division and the ambiguity of performance level division standards in the prior art. Performance three-partitioning classification and incremental coding make the label information more standardized and interpretable, and the classic division ratio of 8:2 can ensure that the training set has sufficient sample support for model learning rules, while the test set can objectively verify the model's generalization ability, laying a data foundation for the accuracy of subsequent model training.

[0020] Further, the multi-stage feature selection method in step 2 includes variance threshold screening, Pearson correlation analysis, sequential forward selection method, and genetic algorithm feature selection method; before using the sequential forward selection method and genetic algorithm feature selection method, the highest F1_score machine learning model is selected as the base model through cross-validation of the training set. This technical feature solves the technical problem of low feature selection accuracy caused by the omission of key features or the retention of redundant features by a single feature selection method, and the blindness of base model selection. Multi-stage screening can gradually eliminate invalid features and compress feature dimensions, and in combination with the optimal base model, it can accurately locate the feature subset strongly related to the target attribute, effectively improving the subsequent model training efficiency and prediction accuracy.

[0021] Further, in step 2, the material science descriptors constructed include the weighted average value P calculated based on the atomic properties of elements, the overall average mismatch degree δP of the alloy, the extreme mismatch degree ΔP, and the extended atomic size difference Xe, the chemical bond mismatch Xc, the mixing enthalpy ΔHm and the mixing entropy ΔSm; the calculation formulas of the weighted average value P, the average mismatch degree δP and the extreme mismatch degree ΔP are as follows:

[0022]

[0023]

[0024]

[0025] wherein, Ci represents the atomic fraction of the i-th element, and Pi represents the atomic descriptor value of the i-th element, and n is the number of elements in the alloy. The technical problems of the traditional material descriptor being difficult to comprehensively characterize the composition and microstructure performance correlation of high-entropy alloys, and the single characteristic dimension leading to insufficient model prediction reliability are solved. The atomic, thermodynamic and electronic structure multi-dimensional coverage of the essential characteristics of high-entropy alloys, combined with the precise calculation formula, can quantize the influence of composition difference on microstructure performance, significantly improve the correlation between features and target attributes, and provide high-quality input for efficient model learning.

[0026] Further, in the Pearson correlation analysis, the Pearson correlation coefficient r between two features is xy The calculation formula is:

[0027]

[0028] wherein, λ represents the number of samples, x i and y i respectively represent the value of feature x and feature y in the i-th sample, respectively represent the sample mean of feature x and feature y, and r xy represents the Pearson correlation coefficient between the features, wherein:

[0029]

[0030]

[0031] If the absolute value of the Pearson correlation coefficient between two features is greater than 0.9, the feature with a larger absolute value of the Pearson correlation coefficient with the target attribute is retained, and the target attribute is the phase structure and hardness grade. The technical problems of high correlation redundant features existing in the feature set, increasing the model calculation amount and easily introducing noise are solved, and the technical effects are: accurately identifying and removing redundant features, reducing the feature space dimension on the premise of retaining key information, reducing the model training burden, and at the same time improving the stability and precision of model prediction.

[0032] Further, in the step 2, the feature selection method and the evaluation index of model performance are calculated by the following formula:

[0033]

[0034]

[0035]

[0036] Wherein, TP represents the case of correctly predicting positive samples as positive, FP refers to the case of incorrectly predicting negative samples as positive, FN represents the case of incorrectly predicting positive samples as negative, F1_score is used as the main evaluation index, and Precision and Recall are used as auxiliary indexes. The technical problem of single or unclear evaluation index in the prior art, which cannot comprehensively measure the feature selection effect and model performance, is solved. Through the combination of main and auxiliary indexes, the feature selection quality and model prediction ability are comprehensively and objectively evaluated, the decision-making error caused by single index deviation is avoided, and it is ensured that the selected feature subset and trained model meet the actual prediction requirements.

[0037] Further, in step 4, when constructing the potential composition space, the alloy elements are limited to 4-6 according to the definition of high-entropy alloy, and the proportion of each element is limited to 0 or 5-35%, and Latin hypercube sampling is used to generate uniformly distributed samples. The technical problems of invalid samples (such as not meeting the definition of high-entropy alloy) caused by unconstrained construction of potential composition space and uneven sample distribution caused by unreasonable sampling method are solved, and the technical effects are: ensuring that the generated samples meet the basic characteristics of high-entropy alloy, Latin hypercube sampling can realize uniform coverage of the composition space, and avoiding sample concentration in local area, providing comprehensive and effective candidate set for active learning to select high-value samples.

[0038] Further, in step 4, the specific method of uncertainty calculation is: performing N times Bootstrap resampling on the original training set, reconstructing N different training sets, retraining N different models using the optimal model and optimal feature subset, and obtaining the probability distribution of N prediction results for each sample in the composition space; the uncertainty is determined by calculating the information entropy, and the information entropy calculation formula is:

[0039]

[0040] Wherein, C refers to the total number of categories, p i refers to the probability of the i-th category. Thus, the technical problem of inaccurate sample uncertainty evaluation by single model and difficulty in accurately positioning high-information-value samples is solved, and the technical effect is: the ensemble model constructed by Bootstrap self-sampling can effectively quantify the uncertainty of sample prediction, and the information entropy calculation can intuitively reflect the information value of the sample, so as to accurately select the high-value samples that can improve the model performance for active learning.

[0041] Further, in step 4, the samples with calculated entropy values are clustered using the K-Means mean clustering algorithm, the within-cluster sum of squares under different clustering numbers is calculated by the "elbow method" to determine the clustering number, and the sample with the highest information entropy is selected from each cluster as the experimental candidate to ensure that the selected sample covers different key areas of the composition space. This technical feature solves the technical problem that the high-uncertainty samples screened are prone to concentrate in local areas, resulting in insufficient coverage of the composition space. By dividing the composition space area through clustering and accurately determining the clustering number through the "elbow method", it is ensured that the selected experimental candidate samples uniformly cover the entire composition space, avoiding experimental redundancy and maximizing the efficiency of model iteration optimization.

[0042] Further, in step 5, the selected high-entropy alloy samples are prepared by arc melting and laser cladding process; X-ray diffraction is used to determine the phase composition and crystallographic information of the coating; the hardness of the high-entropy alloy sample is measured by a Vickers hardness tester with a load of 0.3 kg and a holding time of 15 s, and the average of five measurements is taken as the hardness test result. This technical feature solves the technical problem in the prior art that the preparation and characterization process of high-entropy alloys is not standardized, the experimental data has large errors, and reliable samples cannot be provided for model iteration. The standardized preparation and characterization process ensures the accuracy and repeatability of the experimental data, and high-quality new samples can effectively compensate for the deficiencies of the original training set, significantly improving the prediction accuracy and generalization ability of the model after iteration optimization.

[0043] Compared with the prior art, the present application has the following advantages:

[0044] 1. High prediction accuracy, suitable for complex composition space. The present application constructs a collaborative prediction framework for the microstructure and performance of high-entropy alloys by fusing feature engineering, machine learning and active learning. This method can achieve accurate and stable prediction in a system with multiple main elements, high dimensionality and scarce samples. Active learning is used to analyze the uncertainty of the composition space, automatically identify weak areas of model cognition, and guide experimental verification. Through iterative feedback, the model is continuously optimized, significantly improving the prediction accuracy and reliability in a large composition space, overcoming the low efficiency and insufficient generalization caused by traditional methods relying on trial and error and thermodynamic calculations.

[0045] 2. Strong feature expression ability and better model interpretability. The present application uses a multi-stage feature selection strategy to extract a key feature subset strongly related to microstructure and performance from atomic, thermodynamic, electronic structure and process parameter descriptors. Through variance filtering, correlation analysis, sequential forward selection and genetic algorithm, the dimensionality is gradually reduced, redundancy is removed, and the robustness of the model is enhanced. The selected features have clear physical meaning, such as weighted average property, atomic mismatch degree, mixing enthalpy, etc., which not only improves the prediction efficiency, but also enhances the physical interpretability of the results, helping to understand the internal relationship between composition and performance.

[0046] 3. The model has active learning ability and can be iteratively optimized autonomously. The present application introduces an active learning mechanism, which enables the model to actively guide experiments. The Bootstrap ensemble quantifies the prediction uncertainty, and the clustering algorithm selects high-value samples covering different regions of the composition space for experimental verification. A small number of key experiments can effectively compensate for data defects, realize the closed-loop iteration of "intelligent screening-experimental feedback-model optimization", and significantly improve the prediction performance and cross-system generalization ability of the model under small sample conditions.

[0047] 4. The method has strong applicability and excellent engineering application value. The method flow of the present application is standardized and does not depend on specific alloy systems or processes, so it has high universality. It has been verified to be effective in CoCrFeNiAlTi, CoCrFeNiAlMn and other high-entropy alloy systems, and has good migration and adaptability. Therefore, the method can be used as a general intelligent prediction tool and applied to the composition design and performance optimization of high-entropy alloy coatings, refractory alloys and other new material systems, providing efficient and accurate solutions for material research and development in the fields of aerospace, energy equipment, national defense and military industry, and has a wide application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0048] The accompanying drawings are included to provide a further understanding of the present application, and constitute a part of the specification, which together with the embodiments of the present application, serve to explain the present application, and do not constitute a limitation of the present application.

[0049] Figure 1 The prediction flowchart of the present application.

[0050] Figure 2 The data set classification diagram of the present application.

[0051] Figure 3 The cross-validation results of different models in the present application.

[0052] Figure 4 The sequential forward feature selection results.

[0053] Figure 5 The genetic algorithm feature selection results.

[0054] Figure 6 The intra-group sum of squares under different cluster numbers.

[0055] Figure 7 The prediction results of CoCrFeNiAlTi alloy system, wherein figure (a) is the prediction result of the original model trained based on the original data; figure (b) is the prediction result of the improved model after active learning iteration.

[0056] Figure 8 Prediction results for CoCrFeNiAlMn alloy system, where figure (a) is the prediction result of the original model trained based on the original data; figure (b) is the prediction result of the improved model after active learning iteration.

[0057] Figure 9 Prediction results for MoNbTiVZr alloy system, where figure (a) is the prediction result of the original model trained based on the original data; figure (b) is the prediction result of the improved model after active learning iteration. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below in combination with the drawings and examples. Of course, the specific examples described herein are only used to explain the present application, and are not used to limit the present application.

[0059] As shown in Figure 1 The embodiment provides a high-entropy alloy microstructure and performance synergistic prediction method using an active learning strategy. After collecting and arranging the data set, features are constructed and feature selection is performed. The optimal model is selected for hyperparameter optimization to train the model. The active learning strategy is used to calculate the uncertainty through the model. The sample is selected by the clustering algorithm for experimental characterization and then iteratively fed back. The model is retrained, and finally the generalization ability of the model is verified. The specific process is as follows:

[0060] Step 1: Construct a data set of high-entropy alloy about phase structure and hardness. Preprocess the data. For the same composition alloy with the same process, if the hardness difference is large or the phase structure is different, the composition alloy is excluded. If the phase structure is the same and the hardness difference is small, the average value is taken as the substitute. There are 140 FCC phase, 254 BCC phase, 174 FCC+BCC phase and 434 SS+IM phase samples, a total of 1002 samples. The hardness is divided into three equal parts, divided into low, medium and high three levels, and then the high-entropy alloy samples are classified in ascending order. Specifically, the FCC phase corresponds to "0, 1, 2", the BCC phase corresponds to "3, 4, 5", the FCC+BCC phase corresponds to "6, 7, 8", and the SS+IM phase corresponds to "9, 10, 11", as shown in Figure 2 The data set is divided into training set and test set in the ratio of 8:2.

[0061] Step 2: After calculating the material descriptors, a feature set was obtained, and different process parameters were added to the feature set in the form of one-hot encoding, a total of 98 features. The feature set was screened by variance threshold screening, Pearson correlation analysis, sequential forward selection feature selection method and genetic algorithm feature selection method in turn. Variance threshold screening eliminates constant features by setting the feature threshold to 0, and calculates the variance of each feature value in the training set. Pearson correlation analysis removes some features between highly linearly dependent feature groups by calculating the correlation coefficient between two features. If the absolute value of PCC between two features is greater than 0.9, only the feature with a larger absolute value of PCC with the target attribute is retained. After these two steps, the number of features is reduced from 98 to 44. Before using the sequential forward selection feature selection method, the feature set constructed using all features is used to evaluate the classification effect of five models, including random forest classifier (RF), support vector machine classifier (SVM), extreme gradient boosting classifier (XGBoost), light gradient boosting classifier (LightGBM) and neural network (NN) on the training set using ten-fold cross-validation. The F1_score index is used as the standard, and the results are shown in Figure 3 Fig. 2. Finally, the LightGBM model is selected as the sequential forward selection feature selection method, and the results are shown in Figure 4 Fig. 3. The top 25 features are selected for genetic algorithm feature selection, and the results are shown in Figure 5 Fig. 4. The final number of features is determined to be 16.

[0062] Step 3: When training the LightGBM model, the Bayesian optimization method is first used to optimize the model hyperparameters, combined with ten-fold cross-validation training of the training set for 100 times, to obtain the hyperparameters, as shown in Table 1. After training on the training set and testing on the test set, a model with an F1_score of 0.88 on the training set and an F1_score of 0.81 on the test set is obtained.

[0063] Table 1 LightGBM hyperparameter optimization results

[0064]

[0065] Step 4: Using the active learning strategy, Bootstrap resampling is used to resample the training set 1000 times to generate 1000 bootstrap datasets. Based on the 1000 bootstrap datasets, 1000 Lightgbm models are constructed. The element Co, Cr, Fe, Ni, Al, Ti, Nb, Mo generates a composition space, and when constructing the composition space, according to the definition of high-entropy alloy, the alloy elements are limited to 4-6 kinds, and the proportion of each element is limited to 0 or 5-35%, and Latin hypercube sampling is used to generate uniformly distributed samples, a total of 51866 samples are generated, and the probability of each sample belonging to a specific class is calculated by 1000 models, and the information entropy value of each sample is obtained. The elbow method is used to determine the number of clusters as 8, as shown in Figure 6 , and then clustering analysis is performed, and the K-means method is used to obtain the sample with the highest information entropy (i.e., the largest uncertainty) from each cluster, a total of 8 samples.

[0066] Step 5: Eight high-entropy alloy samples selected by active learning are prepared by laser cladding and tested. Microstructure analysis uses X-ray diffraction to measure the phase composition and crystallographic information of the coating. The surface hardness of the coating is measured by a Vickers hardness tester, with a load of 0.3 kg and a holding time of 15 s. To ensure the accuracy of the test results, five measurements are taken and the average value is taken as the test result of the surface hardness. The classification results are shown in Table 2.

[0067] Table 2: Results of samples selected by active learning strategy

[0068]

[0069] Step 6: The 8 samples representing the training set are added to the training set to retrain the model, and an improved model is obtained through active learning iteration, and the test set accuracy is improved from 0.81 to 0.85.

[0070] Step 7: The accuracy of the improved model is judged to meet the requirements, and the iteration training is ended. To verify the model generalization, the original model trained using the original training set and the improved model trained using the training set supplemented by the active learning strategy are used to predict the CoCrFeNiAlTi, CoCrFeNiAlMn, and NbTiZrVMo alloy systems, as shown in Figure 7 , Figure 8 and Figure 9 , the prediction of the two models is inconsistent with the real experimental data, and the improved model has higher prediction accuracy, indicating that the model generalization ability is improved, proving the effectiveness of the active learning strategy.

[0071] The above merely describes preferred embodiments of the present application and is not used to limit the present application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A high-entropy alloy microstructure and performance synergy prediction method using an active learning strategy, characterized in that, The method comprises the following steps: Step 1: data construction and preprocessing: collecting and sorting literature reports and experimentally measured high-entropy alloy sample data, constructing a data set containing composition, preparation process, microstructure and performance information, wherein the microstructure is represented by the phase structure of the high-entropy alloy, and the performance is represented by hardness; the data is cleaned and merged; samples with the same phase structure are classified and coded according to hardness, and a label containing sample phase structure and hardness level information is obtained; the data set is divided into a training set and a test set according to a predetermined proportion; Step 2: feature construction and selection: based on the material properties, a feature set containing element atomic properties, thermodynamic parameters and electronic structure information is constructed, and the preparation process is converted into features by one-hot encoding; a multi-stage feature selection method is used to select the feature set, and the optimal feature subset is determined by cross-validation of the training set; Step 3: model training: based on the optimal feature subset, a high-entropy alloy phase structure and hardness collaborative prediction model is constructed, the model is optimized for hyperparameters and then trained to obtain an initial prediction model; Step 4: active learning selects uncertainty samples: under the condition of multiple element constraints, a potential composition space is constructed, the initial prediction model is used to calculate the uncertainty of the samples in the composition space, and the information entropy value is obtained; the highest prediction uncertainty of the component samples in different regions is selected as the experimental object by clustering method; Step 5: experimental preparation and characterization: high-entropy alloys are prepared according to the samples selected by active learning, and the actual phase structure and hardness data are tested, and the experimental results are coded and added to the original training set; Step 6: model improvement: the new samples obtained in step 5 are added to the original training set, and the model is retrained to realize the iterative optimization of the model; Step 7: evaluate the prediction performance of the model: determine whether the prediction accuracy or generalization ability of the model meets the requirements, if it meets the requirements, the whole process is completed, if it does not meet the requirements, return to step 4 and reiterate the training.

2. The method of claim 1, wherein the method is characterized by, In step 1, the samples with the same phase structure are classified by hardness three equal division method, divided into low, medium and high three levels, and then coded in increasing order; the predetermined proportion is 8:

2.

3. The method of claim 1, wherein the method is characterized by, The multi-stage feature selection method in step 2 includes variance threshold screening, Pearson correlation analysis, sequential forward selection method and genetic algorithm feature selection method; Before using the sequential forward selection method and genetic algorithm feature selection method, the machine learning model with the highest F1_score is selected as the base model through cross-validation of the training set.

4. The method of claim 1 or 3, wherein the method is characterized by, In step 2, the material descriptors constructed include the weighted average value P calculated based on the element atomic properties, the overall average mismatch degree δP of the alloy, the extreme mismatch degree ΔP, and the extended atomic size difference Xe, the chemical bond mismatch Xc, the mixing enthalpy ΔHm and the mixing entropy ΔSm; the calculation formulas of the weighted average value P, the average mismatch degree δP and the extreme mismatch degree ΔP are as follows: ， ， ， where C i represents the atomic fraction of the i-th element, and P i represents the atomic descriptor value of the i-th element, and n is the number of elements.

5. The method of claim 3, wherein the method is characterized by, In the Pearson correlation analysis, the Pearson correlation coefficient r between two features xy The calculation formula is: ， where λ denotes the number of samples, x i and y i denote the value of feature x and feature y in the i-th sample, respectively, denote the sample mean of feature x and feature y, respectively, r xy denotes the Pearson correlation coefficient between the features, where: ， ， If the absolute value of the Pearson correlation coefficient between two features is greater than 0.9, the feature with the larger absolute value of the Pearson correlation coefficient with the target attribute is retained, and the target attribute is the phase structure and hardness level.

6. The method of claim 1, wherein the method is characterized by, In step 2, the feature selection method and the evaluation index of model performance are calculated by the following formula: ， ， ， Where TP represents the correct prediction of positive samples as positive, FP refers to the wrong prediction of negative samples as positive, FN represents the wrong prediction of positive samples as negative, F1_score is the main evaluation index, and Precision and Recall are auxiliary indexes.

7. The method of claim 1, wherein the method is characterized by, In step 4, when constructing the potential composition space, the alloy elements are limited to 4-6 according to the definition of high-entropy alloys, and the proportion of each element is limited to 0 or 5-35%. Latin hypercube sampling is used to generate uniformly distributed samples.

8. The method of claim 1, wherein the method is characterized by, In step 4, the specific method of uncertainty calculation is: N times Bootstrap resampling is performed on the original training set, N different training sets are reconstructed, the optimal model and optimal feature subset are used to retrain to obtain N different models, and the probability distribution of N prediction results is obtained for each sample in the composition space. The uncertainty is determined by calculating the information entropy, and the information entropy calculation formula is: ， Where C refers to the total number of categories, and pi refers to the probability of the i-th category.

9. The method of claim 1 or 8, wherein the method is characterized by, In step 4, the samples with calculated entropy values are clustered using the K-Means mean clustering algorithm. The intra-cluster sum of squares under different clustering numbers is calculated by the "elbow method" to determine the clustering number. The sample with the highest information entropy is selected from each cluster as the experimental candidate to ensure that the selected samples cover different key areas of the composition space.

10. The method of claim 1, wherein the method is characterized by, In step 5, the selected high-entropy alloy samples are prepared by arc melting and laser cladding process. X-ray diffraction is used to determine the phase composition and crystallographic information of the coating. Vickers hardness tester is used to measure the hardness of the high-entropy alloy samples, with a load of 0.3 kg and a holding time of 15 s. The average value of five measurements is taken as the hardness test result.

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