A method for predicting hardness of high entropy alloys based on machine learning

Abstract

A method for predicting the hardness of a high entropy alloy based on machine learning belongs to the technical field of prediction of the hardness of metal materials, and is used to solve the problem that the traditional method is time-consuming, labor-intensive and inaccurate in predicting the search performance of high entropy alloys with excellent performance. The method includes obtaining a training set of feature data used to predict the hardness of high entropy alloys; screening the feature data to obtain the optimal feature combination; selecting a machine learning model through a ten-fold cross-validation method; using the selected machine learning model and inputting the optimal feature combination for model training; predicting the hardness of unknown high entropy alloys according to the trained model, and selecting high entropy alloys with high predicted hardness and good prediction credibility. Compared with the existing exhaustive method that needs to arrange all feature combinations to find the optimal feature, the feature screening method in the present invention is not only more accurate in predicting the performance of high entropy alloys, but also saves computing resources and time when predicting the hardness of high entropy alloys based on machine learning algorithms.

Description

Technical Field

[0001] The present invention relates to the technical field of metal material hardness prediction, and in particular to a high entropy alloy hardness prediction method based on machine learning. Technical Background

[0002] Traditional metal alloys are generally composed of one or two main elements and some auxiliary elements. In traditional ternary alloys, the composition is often located near a vertex in the triangular phase diagram. In recent years, high entropy alloys that have attracted widespread attention are often composed of five or more elements, and the molar fraction of each element is between 5% and 35%. Therefore, high entropy alloys are sometimes also called multi-main element alloys. Because high entropy alloys contain high configuration entropy inside, they will produce high entropy effects inside high entropy alloys. According to the hypothesis of high entropy effect, when the configuration entropy of the alloy is high, the alloy will be more inclined to form a solid solution phase (SS) than an intermetallic compound phase (IM) or an amorphous phase (AM). Therefore, high entropy alloys often have better performance, such as higher strength and hardness, better wear resistance, excellent ductility, etc.

[0003] Traditional methods of searching for high-performance materials - high-entropy alloys, often characterize material properties through experiments, theories or calculations, but these methods are time-consuming and labor-intensive, and it is difficult to perform high-throughput material characterization. In addition, high-entropy alloys have a very large composition space and microstructure space, so it is very difficult to find high-entropy alloys with excellent performance by traditional methods. With the advent of the era of artificial intelligence and big data, the use of machine learning methods to find specific materials with excellent performance has gradually been applied to various high-performance material search problems.

[0004] Predicting material properties based on machine learning often requires the following steps: data collection, feature engineering, model selection and training, error analysis, and verification. The most important aspect of feature engineering is feature selection. The quality of feature selection will greatly affect the results of performance prediction, but there is no universally recognized method for selecting features suitable for predicting specific material properties. Therefore, how to find the most suitable feature screening method is particularly important in the process of applying machine learning to predict the hardness of high entropy alloys. Summary of the invention

[0005] In view of the above problems, the present invention proposes a high entropy alloy hardness prediction method based on machine learning to solve the problem that traditional methods are time-consuming, labor-intensive and inaccurate in predicting high entropy alloys with excellent search performance.

[0006] A high entropy alloy hardness prediction method based on machine learning comprises the following steps:

[0007] Step 1, obtaining a feature data training set for predicting the hardness of high entropy alloys;

[0008] Step 2: Screen the feature data to obtain the optimal feature combination;

[0009] Step 3: Select the machine learning model through the ten-fold cross-validation method;

[0010] Step 4: Use the selected machine learning model and input the optimal feature combination for model training;

[0011] Step 5: Predict the hardness of unknown high entropy alloys based on the trained model, and select high entropy alloys with high predicted hardness and good prediction credibility.

[0012] Furthermore, the high entropy alloy described in step one is an Al-Co-Cr-Cu-Fe-Ni system.

[0013] Furthermore, the characteristics described in step one include atomic radius difference, electronegativity difference, valence electron concentration, mixing enthalpy, configuration entropy, Ω parameter, Λ parameter, γ parameter, local electronegativity mismatch, number of mobile electrons, cohesive energy, modulus mismatch, local size mismatch, energy term, Navarro coefficient, work function, shear modulus, shear modulus difference, local modulus mismatch, and lattice distortion energy.

[0014] Furthermore, the screening of feature data in step 2 includes first determining the number of features in the feature combination, then using the Pearson correlation coefficient to screen features with high correlation, and finally using a genetic algorithm to obtain the optimal feature combination.

[0015] Furthermore, it is determined that the number of features in the feature combination is 3.

[0016] Furthermore, the principle of using the Pearson correlation coefficient to screen features with high correlation is to retain features with a Pearson correlation coefficient value greater than 0.95 as highly correlated features after screening.

[0017] Furthermore, the optimal characteristic combination is three characteristics of γ parameter, electron concentration and work function.

[0018] Furthermore, the machine learning model described in step 4 is a support vector regression algorithm model.

[0019] Furthermore, the support vector regression algorithm adopts a Gaussian kernel function, and uses Bayesian optimization to tune hyperparameters.

[0020] Beneficial technical effects of the present invention:

[0021] The present invention first determines the number of features in the feature combination, then uses the Pearson correlation coefficient to screen features with high correlation, and then uses a genetic algorithm to screen to obtain the optimal feature combination. Compared with the existing exhaustive method that needs to arrange all feature combinations to find the optimal feature, when applying a machine learning algorithm to predict the hardness of a high-entropy alloy, the feature screening method in the present invention is not only more accurate in predicting the performance of the high-entropy alloy, but also saves computing resources and time. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The present invention may be better understood by referring to the following description given in conjunction with the accompanying drawings, wherein the same or similar reference numerals are used throughout the drawings to represent the same or similar components. The accompanying drawings, together with the following detailed description, are incorporated in and form a part of this specification and are used to further illustrate the preferred embodiments of the present invention and to explain the principles and advantages of the present invention.

[0023] Figure 1 A schematic flow chart of a method for predicting hardness of a high entropy alloy based on machine learning according to an embodiment of the present invention is shown.

[0024] Figure 2 A precision verification diagram of the step of determining the number of features in a feature combination in a high entropy alloy hardness prediction method based on machine learning according to an embodiment of the present invention is shown.

[0025] Figure 3 A Pearson correlation coefficient diagram between different features of a high entropy alloy hardness prediction method based on machine learning according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0026] Hereinafter, exemplary embodiments of the present invention will be described in conjunction with the accompanying drawings. For the sake of clarity and conciseness, not all features of the actual implementation are described in the specification. However, it should be understood that many implementation-specific decisions must be made in the process of developing any such actual implementation in order to achieve the specific goals of the developer, for example, to meet those restrictions related to the system and business, and these restrictions may vary from implementation to implementation. In addition, it should be understood that although the development work may be very complex and time-consuming, it is only a routine task for those skilled in the art who benefit from the content of the present invention. Here, it should also be noted that in order to avoid obscuring the present invention due to unnecessary details, only the device structure and / or processing steps closely related to the scheme according to the present invention are shown in the accompanying drawings, and other details that are not very relevant to the present invention are omitted.

[0027] Figure 1FIG. 1 is a schematic flow chart of a method for predicting hardness of a high entropy alloy based on machine learning according to an embodiment of the present invention. Figure 1 As shown, a high entropy alloy hardness prediction method based on machine learning includes the following steps:

[0028] Step 1, obtaining a feature data training set for predicting the hardness of high entropy alloys;

[0029] According to an embodiment of the present invention, the high entropy alloy system in the present invention is an Al-Co-Cr-Cu-Fe-Ni system, and the data set used is 155 component data sets from the literature [1], including 1 ternary alloy, 22 quaternary alloys, 95 quinary alloys, 38 hexaary alloys and 20 formulas of physical characteristics, including atomic radius difference (δr), electronegativity difference (Δχ), valence electron concentration (VEC), mixing enthalpy (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), Navarro coefficient (F), work function (W), shear modulus (G), shear modulus difference (δG), local modulus mismatch (DG), lattice distortion energy (μ). By investigating more than ten published papers, we found the values ​​of the physical properties of each element used in the formulas of 20 physical characteristics, thereby obtaining 20 physical characteristic data sets with 155 groups as training data sets.

[0030] Step 2: Screen the feature data to obtain the optimal feature combination;

[0031] According to the embodiment of the present invention, the present invention first determines the number of features in the feature combination, and then uses the Pearson correlation coefficient to screen features with high correlation, and then uses a genetic algorithm to screen features.

[0032] The feature data set includes a variety of features related to the predicted performance, but not all features are helpful for the target performance prediction. Features can also be divided into useful features, useless features, and redundant features for the prediction of material physical properties. Therefore, it is necessary to further select features. The purpose of feature selection is to remove useless and redundant features, reduce the dimensionality of the original data set, and reduce the complexity of the model while improving accuracy.

[0033] Consider a verification method to verify that the support vector regression model containing several physical features can ensure sufficiently high prediction accuracy while keeping the number of features as small as possible, so as to ensure that the complexity of the trained model is low and the generalization ability is strong when facing the unknown high-entropy alloy composition space.

[0034] First, for all feature data sets, 200 feature combinations with different numbers of features are randomly selected, and then the corresponding feature data are selected for training and the accuracy is verified using the ten-fold cross-validation method. The accuracy results are as follows: Figure 2 As shown by Figure 2 It can be seen that the feature combination containing three features can not only guarantee a certain accuracy value, but also ensure that the number of features in the feature combination is small, and the accuracy value can be appropriately reduced, with the generalization ability of the model as the ultimate optimization goal to prevent overfitting.

[0035] Then use the Pearson correlation coefficient to remove features with high correlation; the Pearson correlation coefficient (PCC) is used to measure the correlation between two quantities, and its value ranges from -1 to +1. The closer the absolute value is to 1, the greater the correlation. Because there are highly correlated features in the feature data, one of them can be used to replace the other, and the replaced feature is called a redundant feature. In order to reduce the calculation time and improve the robustness of the model by removing irrelevant and redundant features, the Pearson correlation coefficient is used to obtain the pairwise correlation of features. For highly correlated features, only one of them is retained to reduce redundant information in subsequent modeling. Figure 3 Pearson correlation coefficients between different features are shown. Figure 3 As shown in the figure, the features with correlation greater than 0.95 are highly correlated. Furthermore, in order to select the features to be retained, the importance of each feature to the model is ranked by evaluating the test error of a certain feature on the model. The original data set is divided into a training set (80%) and a test set (20%) according to ten-fold cross validation, and an SVR Gaussian kernel is constructed for training based on a feature of the training set, and the test error is calculated using the root mean square error Rmse. Finally, five highly correlated and poorly effective features including energy term (A), lattice distortion energy (μ), shear modulus (G), shear modulus difference (δG), and electronegativity difference (Δχ) are removed, leaving 15 features.

[0036] In addition, the Pearson correlation coefficient between a single feature and hardness can be calculated to obtain the Pearson relationship between the feature and hardness, and the Pearson correlation coefficient values ​​can be arranged from large to small, and the features with low correlation with hardness can be removed, so that a set of features with high correlation with hardness can be obtained. However, the Pearson correlation coefficient describes the linear dependency between variables and has a good effect on the features of linear relationships. If there is a nonlinear relationship between the variables, the result of the Pearson correlation coefficient is very poor.

[0037] Finally, the genetic algorithm is used to screen the features; the characteristic of the genetic algorithm is that it can directly act on the structural object to operate without using the basic method of solving the optimization problem commonly used in complex mathematics such as derivation, and in the operation process, it is not required to manually set the optimization direction and solution range of each step in advance, and the genetic algorithm can be required to find its optimization direction and range in each iteration. The number of feature screening is limited in the present invention, and the effect of screening features is better. The determined population size is 100, and the number of iterations is 200. However, a stable result can be obtained by iterating to dozens of populations. When crossing, 10 individuals are selected from the population as one side of the parent generation, and then 10 individuals are selected as the other side, so that they are crossed one by one to generate new samples; the mutation probability is set to 0.01, and the genetic algorithm is executed multiple times to obtain different iteration results, but each screening result is in the top 6 of the feature ranking, and the first one is also found. Whether selecting from 20 features or fewer, the result of each selection is within the top six, and the optimal feature combination can be found in each case with less time, which shows that genetic algorithms can save feature screening time while ensuring accuracy.

[0038] Specifically, the main steps of the genetic algorithm include population initialization, selection, crossover, mutation, and fitness value calculation.

[0039] Population initialization: The number of feature selection in the present invention is three features, so each individual in the initial population, that is, each feature combination, also contains only three features. Each individual contains 20 data points, 3 of which are randomly set to 1, and the remaining 17 are set to 0. Such an individual can represent a feature combination containing three features. Repeat the above operation to generate several individuals to form the initial population of the genetic algorithm.

[0040] Selection: According to the fitness value, in accordance with certain rules and methods, select excellent individuals from the population in the form of probability and then put them into crossover mutation to generate the next generation of population. There are many kinds of selection operators. The commonly used selection operator is the proportional selection operator, which calculates the fitness and total fitness of each individual in the population, and takes the ratio of each individual's fitness to the total fitness as their respective relative fitness. The sum of the relative fitness of all individuals is 1. In a disk, the disk is divided into several parts according to the size of the relative fitness, and then a random number between 0 and 1 is generated. The individual to be selected is determined based on which part of the disk the random number is located. Repeat the operation to generate a new population.

[0041] Crossover: A common crossover operator is bitwise crossover, that is, randomly select individuals from two populations, randomly select a site, and exchange the values ​​of each bit between the site and the last site, or it can be said that the part between the first site and the site is exchanged, so that two offspring individuals are generated. Repeat the above operation several times to generate a new population of new offspring individuals. In order to ensure that a feature combination containing three features is still generated after the crossover operation, the present invention selects the parent individual for crossover. The positions and numbers corresponding to the situation where one is 1 and the other is 0 at each site in the two individuals are counted, and the positions and numbers corresponding to the situation where one is 1 and the other is 0 are counted, and vice versa. Half of the maximum value of the two numbers is the number of sites to be exchanged, and the corresponding number of sites are crossed, so as to ensure that the interior of the generated new individual still corresponds to the three features.

[0042] Mutation: You need to set a smaller value between [0,1] as the mutation probability first. When performing mutation operation on each individual, randomly take a value between [0,1]. If this value is smaller than the previously set value, flip the value of any site in this individual. To ensure that the individual corresponds to three characteristics, if a 1 site is flipped on an individual, a 0 site is relatively randomly found to flip as well. If a 1 site is flipped, a 0 site is relatively randomly found to flip.

[0043] Fitness value calculation: The general method is to obtain its ability to solve problems. The present invention uses the feature combination represented by the individual based on support vector regression to substitute into ten-fold cross validation and uses the root mean square error (RMSE) to evaluate the error value, thereby obtaining the fitness value corresponding to the individual itself from the error.

[0044] The optimal feature combination screened by the above method is the three features of γ parameter, electron concentration, and work function, which is used as the physical feature combination in subsequent machine learning.

[0045] Step 3: Select the machine learning model through the ten-fold cross-validation method;

[0046] According to an embodiment of the present invention, in order to statistically verify the generalization ability of the model, avoid overfitting, and improve the stability of the verification results, the present invention uses a ten-fold cross-validation segmentation data set, uses a variety of machine learning models to model the predicted hardness of high entropy alloys, and trains a variety of methods in the high entropy alloy training data set and compares the accuracy and stability. Finally, the support vector regression algorithm (SVR) is selected to accurately predict the hardness characteristics of high entropy alloys.

[0047] The data set was split using ten-fold cross validation, and the average of the accuracy of multiple ten-fold cross validations was obtained. The accuracy was calculated by the root mean square error, and the calculation formula is as follows:

[0048]

[0049] Among them, RMSE represents the root mean square error; m represents the total number of samples; x i represents the sample feature vector; y i represents the true value of the i-th sample; f(x i ) represents the predicted value of the model for the i-th sample.

[0050] Step 4: Use the selected machine learning model and input the optimal feature combination for model training;

[0051] The support vector regression algorithm is different from the general regression method. It fits a straight line in form: However, during training, it is not required to completely fit all the provided sample points, but it is allowed that the predicted value has a maximum deviation of ε from the true hardness value, that is, the loss is calculated only when the deviation between the predicted value and the true value is greater than ε. The loss function of support vector regression is minimized as:

[0052]

[0053] in, represents the slope of the straight line; C represents the regularization parameter; l ε represents the ε-insensitive loss function,

[0054]

[0055] For specific situations where the sample space cannot be well fitted with a linear equation, it can be The instance vector in the sample is transformed into Mapping to high dimensions, such as Figure 2 As shown, in high-dimensional cases, linear fitting of feature vectors can be used to fit all support vector machines. Replace all with Introduce slack variables and use the Lagrange multiplier method to solve the optimization problem:

[0056]

[0057] Where m represents the total number of training samples; α i Represents the Lagrange multiplier corresponding to each sample point in the Lagrange multiplier method. Since it is involved in the above optimization formula Only part of Since it is very difficult to map sample points to a suitable high-dimensional feature space that can linearly fit the sample points, and we do not know the appropriate mapping φ(·), we use the "kernel trick" to simplify the calculation in application, that is, setting the kernel function In this way, the corresponding support vector regression learning can be completed by setting a suitable kernel function in the high-dimensional space without finding a complex mapping equation. There are many types of commonly used kernel functions. The present invention selects the following Gaussian kernel function through comparison:

[0058]

[0059] After introducing the above kernel function, formula (1) is transformed into:

[0060]

[0061] The SMO optimization algorithm is used to solve the above optimization problem, solve the Lagrange multiplier, and obtain the support vector regression model.

[0062] Step 5: Predict the hardness of unknown high entropy alloys based on the trained model, and select high entropy alloys with high predicted hardness and good prediction credibility.

[0063] According to an embodiment of the present invention, in order to verify the necessity of the feature screening method and the effectiveness of the results, all situations of three feature combinations in the 20 features, totaling 1140 feature combinations, are substituted into the support vector regression algorithm for training and testing, and the relative test error is calculated by the ten-fold cross-validation method and the root mean square error calculation method, and the feature combinations are ranked for prediction accuracy from small to large according to the test error, as the criterion for judging the prediction accuracy of the feature screening method. Table 1 shows the top 20 feature combinations with the highest prediction accuracy searched by the exhaustive method.

[0064] Table 1

[0065]

[0066]

[0067] As can be seen from Table 1, compared with the exhaustive method to select the optimal feature combination, the method of the present invention first determines the number of features in the feature combination, then uses the Pearson correlation coefficient to screen features with high correlation, and then uses the genetic algorithm to screen features. The process is not only accurate, but also saves computing resources and time.

[0068] The high entropy alloy test set of the Al-Co-Cr-Cu-Fe-Ni system used in the present invention comes from the literature [1], which is a dataset of 614,143 Al-Co-Cr-Cu-Fe-Ni system high entropy alloy components with predicted hardness values ​​higher than 750 HV, which are searched from 1,895,147 specific components of the high entropy alloy of the Al-Co-Cr-Cu-Fe-Ni system. Predictive search in such a dataset is conducive to better finding excellent specific components of high entropy alloys. The specific components of high entropy alloys with higher hardness found in the predictive search process are shown in Table 2.

[0069] Table 2

[0070]

[0071]

[0072] The composition ratio of each element in the high entropy alloy shown in Table 2 is its corresponding molar ratio. The high entropy alloy with the highest predicted hardness is: Al 0.41 Co 0.2 Cr 0.18 Fe 0.16 Ni 0.05 , and its predicted hardness is 791.532194HV.

[0073] According to a comprehensive comparison of prediction accuracy and timeliness, the present invention draws the conclusion that selecting genetic algorithm for feature screening is the optimal feature screening method in the feature screening method in the process of high entropy alloy hardness prediction, and repeatedly performs feature screening by genetic algorithm to obtain the prediction feature combination with the best prediction performance - γ parameter, electron concentration, work function. Compared with the feature screening method of selecting the optimal feature combination by exhaustive method among 20 physical characteristics, the present invention first determines the number of features in the feature combination, then screens the features with large correlation by Pearson correlation coefficient, and then uses genetic algorithm to screen the features, which is more computationally resource-saving and time-saving. In addition, the process of first performing feature combination screening and then predicting the hardness of high entropy alloys and searching for high entropy alloys in virtual space by using machine learning models such as Gaussian kernel support vector regression is efficient and stable. The present invention constructs a complete and universal implementation framework for machine learning prediction of material properties, realizes a search method for exploring the specific composition of high-performance materials in a vast virtual space, successfully predicts and recommends several high-hardness high-entropy alloys, and predicts their corresponding hardness.

[0074] Although the present invention has been described according to a limited number of embodiments, it will be apparent to those skilled in the art, with the benefit of the above description, that other embodiments may be envisioned within the scope of the invention thus described. In addition, it should be noted that the language used in this specification is selected primarily for readability and teaching purposes, rather than for explaining or defining the subject matter of the present invention. Therefore, many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the appended claims. The disclosure of the present invention is illustrative, not restrictive, with respect to the scope of the present invention, which is defined by the appended claims.

Claims

1. A high entropy alloy hardness prediction method based on machine learning, characterized in that: The following steps are included: Step 1, obtaining a feature data training set for predicting the hardness of high entropy alloys; Step 2: Screen the feature data to obtain the optimal feature combination; Step 3: Select the machine learning model through the ten-fold cross-validation method; Step 4: Use the selected machine learning model and input the optimal feature combination for model training; Step 5: Predict the hardness of unknown high entropy alloys according to the trained model, and select high entropy alloys with high predicted hardness and good prediction credibility; The high entropy alloy in step 1 is an Al-Co-Cr-Cu-Fe-Ni system; The characteristics described in step 1 include atomic radius difference, electronegativity difference, valence electron concentration, mixing enthalpy, configuration entropy, Ω parameter, Λ parameter, γ parameter, local electronegativity mismatch, number of mobile electrons, cohesive energy, modulus mismatch, local size mismatch, energy term, Navarro coefficient, work function, shear modulus, shear modulus difference, local modulus mismatch, and lattice distortion energy; The screening of feature data in step 2 includes first determining the number of features in the feature combination, then using the Pearson correlation coefficient to screen features with high correlation, and finally using a genetic algorithm to obtain the optimal feature combination; Determine the number of features in the feature combination to be 3; The principle of using the Pearson correlation coefficient to screen features with high correlation is to retain features with a Pearson correlation coefficient value greater than 0.95 as highly correlated features after screening; The optimal characteristic combination is three characteristics: γ parameter, electron concentration, and work function; The machine learning model described in step 4 is a support vector regression algorithm model; The support vector regression algorithm adopts a Gaussian kernel function and uses Bayesian optimization to tune hyperparameters.

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