Method for designing tough high-entropy nitride ceramic coating based on interpretable machine learning

Abstract

A method for designing a tough high-entropy nitride ceramic coating based on interpretable machine learning is characterized by comprising the following steps: step 1, acquiring hardness, elastic modulus and fracture toughness data of high-entropy nitride ceramic with known components; 2, removing maximum and minimum abnormal values in the data set, and carrying out normalization processing on features; 3, training the model by adopting a hyper-parameter grid search method; step 4, searching an optimal feature subset by using a recursive feature elimination (RFE) method; 5, calculating a single-factor SHAP value of each sample point of the ceramic hardness, the elastic modulus and the fracture toughness by adopting an SHAP interpretability method, evaluating the correlation of each feature and calculating a feature weight coefficient; and step 6, selecting binary nitrides with low cost as candidates, and further calculating and normalizing the weight coefficient of each nitride on the basis of the step 5. Through a machine learning method, the cost required by the experiment is greatly reduced, the experiment period is shortened, and the design and development of the high-entropy nitride ceramic coating are more efficiently promoted.

Description

Technical Field

[0001] The present invention relates to a high-entropy ceramic coating design technology, in particular to an intelligent design technology, specifically a method for designing tough high-entropy nitride ceramic coatings based on interpretable machine learning. Background Art

[0002] High-entropy nitride ceramics are ceramic solid solutions containing five or more cationic or anionic sublattices. The presence of multiple elements causes severe distortion of the lattice, hinders dislocation movement, and gives the material high hardness and high strength, making it widely used in high-end equipment manufacturing fields such as aerospace, cutting tools, and injection molds.

[0003] Currently, the huge unexplored compositional space makes trial and error experiments very costly. Although simulation methods such as density functional theory (DFT), molecular dynamics (MD) and thermodynamic models are widely used to study the calculation of the mechanical properties of high-entropy ceramic nitride coatings, these methods require a lot of computing resources, especially when faced with complex components, and there are large errors in the design. The hardness, modulus and fracture toughness of high-entropy ceramic nitrides are three key properties that determine the performance and service life of high-end equipment. How to simultaneously improve these mutually constrained properties has always been a key problem that needs to be overcome in the research and development of high-entropy ceramic nitride coatings. Summary of the Invention

[0004] The purpose of the present invention is to address the practical problems that the existing high-entropy nitride ceramic coating design requires a large amount of computing resources, especially when facing complex components, and there are large design errors. A high-entropy nitride ceramic performance prediction method using machine learning is invented, which can be widely used to design high-entropy nitride ceramic coatings with excellent comprehensive performance.

[0005] The technical solution of the present invention is:

[0006] A method for designing a tough high-entropy nitride ceramic coating based on interpretable machine learning, characterized by comprising the following steps:

[0007] Step 1: Obtain hardness, elastic modulus, and fracture toughness data of high-entropy nitride ceramics with known composition, and calculate relevant physical and chemical characteristics based on the corresponding composition.

[0008] Step 2: Remove the extremely large and extremely small outliers in the data set and normalize the features. The filtered data is used to construct a data set of high-entropy nitride ceramics and divide the ratio of the training set and the test set.

[0009] In step 3, the model is trained using the hyperparameter grid search method and evaluated using the K-fold cross-test method.

[0010] Step 4: Use the Recursive Feature Elimination (RFE) method to find the optimal feature subset, retrain and evaluate the model on the dataset; if the coefficient of determination R 2 is within the preset range, determine that the model is qualified; otherwise, repeat steps 2 to 4.

[0011] Step 5: Adopt the SHAP interpretability method to calculate the single-factor SHAP values of each sample point of ceramic hardness, elastic modulus, and fracture toughness, draw the partial dependence plot and perform linear fitting, evaluate the correlation of each feature, and calculate the feature weight coefficient.

[0012] Step 6: Select binary nitrides with lower costs as candidates, and further calculate and normalize the weight coefficients of each nitride based on step 5. Based on the actual situation and calculation results, design tough high-entropy ceramic nitrides.

[0013] The beneficial effects of the present invention are as follows:

[0014] By means of machine learning, the present invention greatly reduces the costs required for experiments, shortens the experimental period, and more efficiently promotes the design and development of high-entropy nitride ceramic coatings; constructs an XGBoost model and performs feature reduction processing to accurately seek the best feature subset to optimize the model, and the prediction results are more reliable; considers multiple key performance indicators such as hardness, modulus, and fracture toughness in the ceramic design process, rather than focusing on a single performance indicator, and designs a high-entropy nitride ceramic coating system with excellent comprehensive performance. Description of the Drawings

[0015] Figure 1 It is a flowchart for designing tough high-entropy ceramic nitride coatings based on interpretable machine learning of the present invention.

[0016] Figure 2 It is a hyperparameter grid search diagram of the XGBoost hardness prediction model in the embodiment of the present invention.

[0017] Figure 3 It is a recursive feature elimination training result diagram of the XGBoost hardness prediction model in the embodiment of the present invention.

[0018] Figure 4 It is a training comparison diagram of the XGBoost hardness prediction model in the embodiment of the present invention.

[0019] Figure 5 It is a fitting curve diagram of the average first ionization energy of key features in the hardness prediction model calculated based on the SHAP method in the embodiment of the present invention.

[0020] The attached drawings forming a part of the present specification are used to provide a further understanding of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. Detailed implementation manners

[0021] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0022] A method for designing a tough high-entropy nitride ceramic coating based on interpretable machine learning, as Figure 1 shown, includes the following steps:

[0023] Step 1: Obtain the hardness, modulus, and fracture toughness data of high-entropy ceramics with different components from published literature. If the data volume is insufficient, relevant properties can be calculated based on density functional theory; use formulas (1)-(2) to calculate the relevant characteristic quantities of ceramics. According to the obtained data and the calculated characteristic quantities, three types of data sets of the hardness, modulus, and fracture toughness of ceramics are constructed. In the present invention, the means obtained in Step 1 include consulting materials, density functional theory calculations, experiments, etc. The relevant characteristic quantities of the ceramics include the weighted average value and deviation value of the inherent properties of elements and binary nitrides. The inherent properties of elements include relative atomic mass, atomic radius, melting point, electron affinity, atomic density, mixing entropy, etc.; the inherent properties of binary nitrides include valence electron number, total energy, lattice constant, electronegativity, and unit atomic volume. The calculation of relevant characteristic quantities is shown in formulas (1)-(2). [[ID=!4]]

[0024]

[0025] Among them, M_P e is the weighted average value of a certain inherent property of the ceramic constituent element or binary nitride, D_P e is the standard deviation of a certain inherent property of the ceramic constituent element or binary nitride, c i is the molar ratio of the i-th element or binary nitride, P ei is the inherent property value of the i-th element or binary nitride, is the average value of a certain inherent property of all the ceramic constituent elements.

[0026] Step 2: Normalize the characteristic quantities of the three types of constructed data sets, and divide the three types of data sets with 90% as the training set and 10% as the test set. Normalization processing is used to eliminate the magnitude gap between features. Assuming the feature set is X = {x1, x2,..., x n}, the normalization processing of the features is shown in formula (3):

[0027]

[0028] Among them, X max and X min represent the maximum value and minimum value of a certain feature respectively, and X i represents a certain feature vector, Represents the normalized feature vector.

[0029] In step 2, the ratio of dividing the training set and the test set is 9:1.

[0030] Step 3: Use the training set divided in step 2 to build the hardness, modulus and prediction models.

[0031] Preferably, in step 3, select 5 hyperparameters of learning_rate, max_depth, n_estimators, subsample, and reg_lambda in the XGBoost model.

[0032] When applied industrially, the selection range of the hyperparameter learning_rate is 0.01 - 0.1, preferably [0.01, 0.02, 0.05, 0.1]; the selection range of max_depth is 0 - 10, preferably [3, 4, 5, 6]; the selection range of n_estimators is 0 - 300, preferably [50, 100, 200, 300]; the selection range of subsample is 0 - 1, preferably [0.6, 0.8, 1.0]; the selection range of min_child_weight is 0 - 5, preferably [1, 2, 3].

[0033] In the process of hyperparameter optimization, a 5-fold cross-validation method is used to evaluate the model performance. Specifically: each time, one of the subsets is used as the test set, and the remaining 4 subsets are combined as the training set. In this way, 5 times of training and testing are carried out in turn, each time using a different subset as the test set, and finally the average mean absolute error MAE of the 5 tests is used to evaluate the model performance.

[0034] In step 3, MAE is used as the evaluation index to evaluate the model performance, as shown in formula (4): [[ID=2D]]

[0035]

[0036] Where n represents the number of samples, X i Represents the experimental value of the target performance of the i-th sample, Represents the predicted value of the target performance of the i-th sample.

[0037] The specific steps are as follows:

[0038] Step 3.1: Select the hyperparameters with greater influence for optimization. The XGBoost hyperparameter selection and range are shown in Table 1.

[0039] Table 1 XGBoost hyperparameter selection and range

[0040]

[0041] Step 3.2: Evaluate the model using the 5-fold cross-validation method to ensure the generalization ability of the model, and compare the evaluation metric MAE of different hyperparameter grid searches. Taking the XGBoost hardness prediction model as an example, the specific hyperparameter grid search process is as Figure 2 shown. Due to the limitation of the grid space, only the effects of learning_rate and n_estimators on the MAE of the model when max_depth, subsample, and subsample are optimal are shown.

[0042] Step 3.3: Use the optimal hyperparameter combination for XGBoost training. The optimal hyperparameter combination is shown in Table 2.

[0043] Table 2 Optimal Hyperparameter Combination of XGBoost

[0044]

[0045] Step 4: Since the model feature space is huge, the RFE method is used to remove redundant features and find the optimal feature subset. In this embodiment, the minimum number of retained features is set to 2, and the step size is 5. The optimal number of features and feature subsets for each target are saved as shown in Table 3. Taking R 2 as the evaluation metric, compare the prediction results of the optimized XGBoost on the test set data with the actual results. The results are as Figure 3 shown. When the value of R 2 is greater than or equal to 0.9, the optimization can be stopped; otherwise, repeat steps 2 to 4.

[0046] In the said step 4, taking R 2 as the evaluation metric to evaluate the model performance, as shown in formula (5):

[0047]

[0048] Table 3 Optimal Feature Subsets of Three Performance Prediction Models

[0049]

[0050] Step 5: For the feature subset selected by the XGBoost model, use the SHAP interpretability method to calculate the single-factor SHAP values of each sample point of hardness, elastic modulus, and fracture toughness, draw the partial dependence plot, and perform linear fitting using the least squares method. The influence weight and correlation of each feature depend on the slope a. When a is positive, it means that the feature promotes the target performance; on the contrary, it plays an inhibitory role. Calculate the influence weight and correlation of each feature using equation (8). Among them, the fitting result of the average first ionization energy selected in the hardness prediction model is asFigure 5 as shown

[0051] Preferably, in step 5, for the predicted values of the hardness, modulus, and fracture toughness of the high-entropy nitride ceramics, the single-factor individual SHAP value f(x ij ) of the j-th feature of the i-th sample is calculated respectively;

[0052]

[0053] where F is the complete set of all influencing factors of the sample X i , S is a subset formed by any number of influencing factors in the sample X i , v(S) is the contribution generated by the combined action of the influencing factors included in the subset S, and v(S∪{j}) - v(S) is the contribution brought by the influencing factor j to this combined action.

[0054] In the said step 5, the linear fitting adopts the least squares method to ensure that the sum of the squares S of the errors of all SHAP sample points from the fitting line is the smallest, as shown in formula (7):

[0055]

[0056] where y i represents the predicted value of the i-th sample, a and b represent the slope and intercept of the fitting line, and ax i +b represents the fitting value of the i-th sample.

[0057] [[ID=CO32]]In the said step 5, the influence weight and correlation of each feature depend on the slope a. If a is positive, it means that this feature promotes the target performance; otherwise, it plays an inhibitory role. The absolute value of the slope a represents the degree of promotion or inhibition. The calculation of the weight coefficient of each feature is as shown in formula (8):

[0058]

[0059] where n represents the number of target characteristics, here n = 3; Z i represents the weight coefficient of the i-th feature; a i represents the slope of the i-th feature in the preferred feature subset under this target characteristic.

[0060] Step 6: Based on the actual situation and calculation results, select a variety of binary nitrides as candidates, and further calculate the weight coefficient and correlation of each nitride using formula (9) on the basis of step 5, and design a suitable tough high-entropy ceramic nitride. The calculation of the weight coefficient of the binary nitride is as shown in formula (9):

[0061]

[0062] Among them, Z* represents the weight coefficient of the binary nitride, and Z i represents the weight coefficient of the i-th feature, and t i represents the normalized eigenvalue of a certain binary nitride or its corresponding element.

[0063] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0064] The parts not involved in the present invention are the same as the prior art or can be implemented by the prior art.

Claims

1. A method for designing a tough high-entropy nitride ceramic coating based on interpretable machine learning, characterized in that, It includes the following steps: Step 1: Obtain hardness, elastic modulus, and fracture toughness data of high-entropy nitride ceramics with known composition, and calculate relevant physical and chemical characteristics based on the corresponding composition; Step 2: Remove the maximum and minimum outliers in the data set and normalize the features. The filtered data is used to construct a data set of high-entropy nitride ceramics and divide the ratio of training set and test set; Step 3: Use hyperparameter grid search method to train the model and use K-fold cross-test method to evaluate the model; Step 4, use the Recursive Feature Elimination (RFE) method to find the optimal feature subset, retrain and evaluate the model on the dataset; if the coefficient of determination R 2 is within the preset range, determine that the model is qualified; otherwise, repeat steps 2 to 4; Step 5: SHAP interpretability method was used to calculate the single factor SHAP value of each sample point of ceramic hardness, elastic modulus and fracture toughness, draw the local dependence diagram and perform linear fitting, evaluate the correlation of each feature and calculate the feature weight coefficient; Step 6: Select binary nitrides with lower costs as candidates, further calculate the weight coefficient of each nitride based on step 5 and normalize it; based on the actual situation and the calculation results, design a tough high-entropy ceramic nitride.

2. The method according to claim 1, characterized in that: The means of obtaining include consulting materials, density functional theory calculations, and experiments.

3. The method according to claim 1, wherein: In step 1, the relevant characteristic quantities of the ceramic include the weighted average and deviation values of the intrinsic properties of the elements and binary nitrides. The intrinsic properties of the elements include relative atomic mass, atomic radius, melting point, electron affinity, atomic density, and mixing entropy; the intrinsic properties of the binary nitride include the number of valence electrons, total energy, lattice constant, electronegativity, and unit atomic volume. The calculation of the relevant characteristic quantities is shown in formulas (1) and (2): Wherein, M_P e is the weighted average of an inherent property of a ceramic constituent element or a binary nitride, D_P e is the standard deviation of an inherent property of a ceramic constituent element or a binary nitride, c i is the molar ratio of the i-th element or binary nitride, P ei is the value of the inherent property of the i-th element or binary nitride, is the mean value of an inherent property of all the constituent elements of the ceramic.

4. The method according to claim 1, wherein: In step 2, normalization processing is adopted to eliminate the magnitude gap between features. Assuming the feature set is X = {x1, x2, ……, x n}, then the normalization processing of the features is shown in Equation (3): Among them, X max and X min represent the maximum and minimum values of a certain feature respectively, and X i represents a certain feature vector, represents the normalized feature vector.

5. The method according to claim 1, characterized in that: The ratio of the training set and the test set in step 2 is 9:

1.

6. The method according to claim 1, wherein: In step 3, select the five hyperparameters of the XGBoost model: learning_rate, max_depth, n_estimators, subsample, and reg_lambda. The range of the hyperparameter learning_rate is 0.01 to 0.1, preferably [0.01, 0.02, 0.05, 0.1]. The range of max_depth is 0 to 10, preferably [3, 4, 5, 6]. The range of n_estimators is 0 to 300, preferably [50, 100, 200, 300]. The range of subsample is 0 to 1, preferably [0.6, 0.8, 1.0]. The range of min_child_weight is 0 to 5, preferably [1, 2, 3]. During the hyperparameter optimization process, the 5-fold cross-validation method was used to evaluate the model performance. Each time, one of the subsets was used as the test set, and the remaining four subsets were combined as the training set. In this way, five training and testing cycles were performed in sequence, and a different subset was used as the test set each time. Finally, the average mean absolute error (MAE) of the five tests was used to evaluate the model performance.

7. The method according to claim 1, characterized in that: In step 3, MAE is used as the evaluation indicator to evaluate the model performance, as shown in formula (4): where n represents the number of samples, and X i represents the experimental value of the target performance of the i-th sample, and represents the predicted value of the target performance of the i-th sample.

8. The method according to claim 1, characterized in that: In step 4, the minimum number of features retained by the RFE method is 2, and the step size is 5; using R 2 as an evaluation metric to evaluate the model performance, as shown in formula (5):

9. The method according to claim 1, characterized in that: In step 5, for the predicted values of the hardness, modulus, and fracture toughness of the high-entropy nitride ceramics, the single-factor individual SHAP value f(x ij ) of the j-th feature of the i-th sample is calculated respectively; Among them, F is the sample X i the complete set of all influencing factors, and S is the sample X i a subset formed by any number of influencing factors in, v(S) is the contribution generated by the combined action of the influencing factors included in the subset S, and υ(S∪{j}) - ν(S) is the contribution brought by the influencing factor j to this combined action; linear fitting uses the least squares method to ensure that the sum of the squares S of the errors of all SHAP sample points from the fitting line is minimized, as shown in formula (7): Among them, y i represents the predicted value of the i-th sample, a and b represent the slope and intercept of the fitted line, ax i + b represents the fitted value of the i-th sample; The influence weight and correlation of each feature depend on the slope a. When a is positive, it means that the feature promotes the target performance; on the contrary, it plays an inhibitory role; the absolute value of the slope a represents the degree of promotion or inhibition; the calculation of each feature weight coefficient is shown in formula (8): where n represents the number of target characteristics, and here n = 3; Z i represents the weight coefficient of the i-th feature; a i represents the slope of the i-th feature in the preferred subset of features under this target characteristic.

10. The method according to claim 1, characterized in that: In step 6, the calculation of the weight coefficient of the binary nitride is shown in formula (9): Among them, Z* represents the weight coefficient of the binary nitride, and Z i represents the weight coefficient of the i-th feature, and t i represents the normalized feature value of a certain binary nitride or its corresponding element.

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