Design method for multi-objective collaborative optimization of mechanical properties of high-entropy alloy based on machine learning

Abstract

The invention discloses a design method for multi-objective collaborative optimization of mechanical properties of a high-entropy alloy based on machine learning, and belongs to the technical field of metal material design. Comprising the following steps: establishing a high-entropy alloy data set, and collecting component features to establish a feature set; determining a plurality of models for component design and optimizing the models; selecting two models with the most potential, screening an optimal feature set by using an exhaustion method, optimizing hyper-parameters by using a Bayesian optimization algorithm, and selecting an optimal model by integrating the R2 and the representation of the models on an extra data set; performing multi-objective optimization by combining a tensile strength and elongation model; the transition group high-entropy alloy with excellent performance is designed; the designed high-entropy alloy is prepared; and the performance is verified, and the target alloy material with multi-target performance collaborative optimization is obtained. According to the method, the alloy performance is predicted by using the machine learning model, the design process is optimized by using the genetic algorithm, the alloy components with excellent mechanical properties are quickly generated, and the high-entropy alloy with high strength and high plasticity is obtained at the same time.

Description

Technical Field

[0001] The present invention relates to a design method for optimizing the mechanical properties of high-entropy alloys, specifically to a design method for multi-objective collaborative optimization of the mechanical properties of high-entropy alloys based on machine learning, belonging to the technical field of metal material design. Background Art

[0002] As a representative of new alloys, high-entropy alloys exhibit excellent properties beyond those of traditional alloys in many aspects and have always been a research hotspot in the field of metal materials. The unique design concept and excellent properties endow high-entropy alloys with great development potential. Defined from the perspective of component content, high-entropy alloys refer to alloys mainly composed of five or more metal elements in equimolar ratio or approximate equimolar ratio, and the content of each element is usually controlled between 5% and 35%. Defined from the perspective of entropy, high-entropy alloys are multi-principal-element alloys with a mixing entropy greater than 1.61R (R is the gas constant). In recent years, 1.5R has often been used as the critical entropy value for the definition of HEAs. Generally speaking, the higher the entropy value of an alloy system, the lower the energy, and the more stable the system; in alloys, it is manifested that the higher the entropy value, the easier it is to form a simple solid solution phase.

[0003] Differences in the composition content of high-entropy alloys result in a wide variety of high-entropy alloys with a complex system. Since the research and development of high-entropy alloys to date, it mainly includes the following several typical high-entropy alloy systems, including: 3d transition high-entropy alloys (representative systems are: CoCrFeNiMn, AlCoCrCuFeNi, FeCoNiCr, etc.), refractory high-entropy alloys (representative system is: MoNbTaWV, etc.), lightweight HEAs (representative system is: AlLiMgZnSn, etc.) and noble metal high-entropy alloys (representative system is: RhIrPdPtNiCu, etc.), involving more than 30 kinds of element types in the periodic table of chemical elements. Among them, the 3d transition high-entropy alloy system has the largest research volume. A significant feature of this series of alloys is that the matrix alloy has relatively low strength but excellent plasticity at room temperature. Researchers have studied the possibility of applying this series of high-entropy alloys as engineering structural materials by exploring the effects of alloy preparation methods, processing techniques, the addition amount of each element or doping some other alloying elements on the evolution of alloy microstructure, property improvement and deformation behavior, etc. However, compared with the huge potential composition space of the 3d transition high-entropy alloy system, the existing research volume is still just the tip of the iceberg. There are many new alloy systems that have not been fully developed or even not developed at all, and the effects of adding certain alloying elements (such as: Al, Ti, V, Mo, etc.) on the alloy properties vary from alloy to alloy, and there is no particularly complete theory to accurately summarize them. Especially, Pradeep et al. proposed in 2015 that the design of high-entropy alloys should no longer be limited to the composition setting of equimolar ratio or approximate equimolar ratio. This includes some quaternary alloy systems (such as: WMoTaNb, etc.) into the scope of high-entropy alloys, which not only further increases the complexity of the potential composition space of high-entropy alloys, but also increases the difficulty of exploring the variation law of alloy properties and conducting composition design. Therefore, 3d transition high-entropy alloys have great development potential.

[0004] With the development of machine learning and its combination with various fields, the material gene engineering of machine learning plus materials has emerged and developed rapidly, playing an important role in guiding the synthesis and design of high-performance alloy materials. At present, many studies have reported the use of machine learning methods to guide the composition and performance design of high-entropy alloys. For example, the Chinese invention patent with the application publication number CN116092604A discloses a data-driven high-strength and high-toughness refractory high-entropy alloy and its preparation method. By establishing a machine learning model, setting the high-value threshold of the target performance, and screening the alloy composition based on the threshold, a high-strength and high-toughness refractory high-entropy alloy composition is obtained and verified by melting; the Chinese invention patent with the application publication number CN118748050A discloses a method for optimizing the composition of high-entropy alloys based on machine learning. By establishing a phase structure classification model and a hardness prediction regression model, high-hardness heptanary high-entropy alloys are searched in the constructed virtual space, and finally experimental verification is carried out. However, in the existing publicly disclosed machine learning design methods, there is no design that simultaneously optimizes the strength and toughness of transition metal high-entropy alloys as targets.

[0005] Therefore, there is still an improvement need in the prior art and machine learning methods for the development of high-performance 3d transition metal high-entropy alloys. Summary of the Invention

[0006] The object of the present invention is to solve the problems existing in the prior art and provide a design method for multi-objective collaborative optimization of the mechanical properties of high-entropy alloys based on machine learning. By using a machine learning model to predict the mechanical properties of high-entropy alloys and using operations such as selection, crossover, and mutation of the genetic algorithm to automate the optimization design process, alloy compositions with excellent mechanical properties are quickly generated, providing new ideas and methods for guiding the design of transition metal high-entropy alloys with high strength and plasticity.

[0007] To achieve the above object, the present invention adopts the following technical solutions: A design method for multi-objective collaborative optimization of the mechanical properties of high-entropy alloys based on machine learning, comprising the following steps:

[0008] S1. Collect data of transition metal high-entropy alloys:

[0009] Collect historical data on the composition content and mechanical properties of quaternary to heptanary transition metal high-entropy alloys through academic platforms, where the alloying elements include Fe, Co, Ni, Cr, Al, Ti, Cu, V, Mo, Mn, and Nb, and the mechanical property indexes include tensile strength and elongation;

[0010] S2. After cleaning the data, establish a high-entropy alloy data set and determine the composition features to establish a transition metal high-entropy alloy feature set:

[0011] Clean the collected data of transition metal high-entropy alloys, delete the duplicate input data, and establish a high-entropy alloy data set. Combine the atomic physical properties of the elements with their relevant empirical calculation formulas to comprehensively determine the empirical parameter features and element features, and standardize the determined features to establish a feature set of transition metal high-entropy alloys;

[0012] S3. Train machine models based on different algorithm mechanisms, and use feature importance to conduct preliminary screening of features:

[0013] Input the data sets of tensile strength and elongation established in step S2 above into the machine model respectively, and randomly divide the data sets into training sets and test sets. Use the training sets to train the machine model and the test sets to verify and test the model; then use the feature importance method to input the feature set into the machine model to screen the features, and use the determination coefficient R 2 as the evaluation criterion, and screen the features based on the importance evaluation of the input features by the current model, and delete the features with less contribution to the model;

[0014] S4. Select the two models with the best performance as alternative models with R 2 as the evaluation index. Use the exhaustive method to screen the feature sets of the alternative models and select the top ten groups with the best performance. Use the Bayesian optimization algorithm to optimize the hyperparameters, and screen out the best feature set and the corresponding hyperparameters:

[0015] Select the two models with the highest R 2 in the tensile strength model or the elongation model as alternative models. Use the exhaustive method to perform feature combination to further screen the global optimal solution of the feature problem in a larger range. Substitute the top ten groups of feature sets obtained by screening into the Bayesian optimization model to adjust and optimize the hyperparameters in the model corresponding to the feature set, and select the best feature set with the largest R 2 and the corresponding hyperparameters for each;

[0016] S5. Collect data again as a validation set to verify the two alternative models, and comprehensively select the best model as the model for final multi-objective optimization:

[0017] Collect the mechanical property data of high-entropy alloys that meet the requirements in step S1 above from the latest published platform data again, and put the collected data into the two alternative models of the tensile strength model or the elongation model for prediction and verification. Combine R 2 and the final prediction performances of the two alternative models to respectively select the best tensile strength model and the best elongation model as the models for final multi-objective optimization;

[0018] S6. Combine the best tensile strength model and the best elongation model for multi-objective optimization:

[0019] Input the best models of the tensile strength model and elongation model obtained in step S5 above into a multi-objective optimization program for optimization. The optimization method includes the following steps:

[0020] S61. Create multiple individuals as a population, input the filtered element characteristics. The content range of each element is set to 0-35%, and the content of each element is randomly generated within the given upper and lower limits. The content of each element is normalized so that the sum of all elements is 100%;

[0021] S62. Evaluate the performance of each alloy composition using a fitness function, normalize the ultimate tensile strength UTS and elongation EL, and use the Z value as the comprehensive performance evaluation index for all alloys in the population during each genetic iteration. Compare all the obtained compositions and output the alloy composition with the largest Z value;

[0022] The normalization formula is:

[0023] The calculation formula for the Z value is:

[0024] In the formula, min_UTS and max_UTS are respectively the minimum and maximum values of UTS in the initially generated population, and min_EL and max_EL are respectively the minimum and maximum values of EL in the initially generated population;

[0025] S63. Introduce a reward mechanism. If the UTS value of an individual exceeds 1.5 times the maximum UTS value in the current population, the fitness of this individual will be increased by a reward, and the fitness of this alloy will be multiplied by 2 to encourage the genetic algorithm to search for alloys with higher tensile strength;

[0026] S64. Alternately use the NSGA-II algorithm and the tournament selection method for selection, retain individuals with higher fitness, and select the best-performing individuals;

[0027] S65. The crossover operation generates two offspring by exchanging part of the genes of two parent individuals. The crossover method is single-point crossover, that is, randomly select a crossover point, and then exchange the genes of the parent individuals before and after this point, and normalize the two offspring after crossover so that their composition sum is 100%;

[0028] S66. Introduce a mutation operation during the genetic process. The composition of each element will be randomly adjusted according to the mutation probability, and the change range is 0.5 or 0.3. After mutation, normalize it so that the percentage sum of all elements is 100%;

[0029] S67. To maintain the diversity of the population and avoid early convergence of the algorithm, the NSGA-II algorithm also calculates the crowding distance for each individual. The specific method is as follows: 1) Sort each objective to find the minimum and maximum fitness values. 2) Handling of boundary individuals: After sorting, the minimum and maximum individuals, i.e., the individuals at the outermost edges in the objective space, will be assigned an infinite crowding distance. 3) Calculating the crowding of internal individuals: For the individuals in the middle of the objective space, calculate their crowding distances from adjacent individuals. 4) The total crowding distance of an individual is the weighted sum of its crowding distances on all objectives;

[0030] Assume that the objective values are sorted in the objective space. Then, the crowding distance of an individual is calculated from the differences in the objective values of its adjacent individuals. For each objective \(i\), the formula for calculating the crowding distance \(i(k)\) is expressed as: In the formula, \(f\) i (k) represents the value of individual \(k\) on objective \(i\), and are respectively the maximum and minimum values of this objective in the population;

[0031] The fitness function runs through the whole process, used to evaluate individual performance, guide selection and evolution. The crowding distance serves as a supplement in NSGA-II selection, used to solve the problem that the fitness function cannot distinguish individuals in the same non-dominated level, mainly focusing on the diversity of solutions. The combination of the two enables the algorithm to not only effectively optimize performance but also ensure the diversity and globality of solutions. By adjusting parameters such as the type or content of input elements, mutation rate, scale of tournament selection, or the number of the initial population, more alloy components with better performance can be designed;

[0032] S7. Adjust the parameters according to the design objectives to design a transition high-entropy alloy with excellent strength and plasticity properties:

[0033] Create an initial population by setting the number of the initial population, mutation rate, and number of iterations. Adjust the parameters by parameters such as the type or content of input elements, mutation rate, scale of tournament selection, or the number of the initial population. Calculate the fitness function after normalization processing, perform genetic mutation, and finally calculate the fitness function to obtain the final designed alloy composition;

[0034] S8. Prepare the designed transition high-entropy alloy according to the final designed alloy composition:

[0035] Prepare the transition high-entropy alloy screened and designed in the above step S7 by means of vacuum arc melting;

[0036] S9. Verify the performance to obtain the target alloy material with multi-objective performance co-optimization:

[0037] The as-prepared transition metal high-entropy alloy in step S8 is subjected to a room-temperature tensile property test to obtain the values of the tensile strength and elongation. Using the product of strength and plasticity as the comprehensive evaluation index for multi-objective optimization, it is compared and verified with the comprehensive properties of the existing as-cast transition metal high-entropy alloy under room-temperature uniaxial tension, so as to finally obtain an as-cast transition metal high-entropy alloy material with excellent properties.

[0038] In step S1, when collecting alloy composition data, a casting method of vacuum induction melting or vacuum arc melting is selected, and the tensile method is selected as room-temperature uniaxial tension.

[0039] In step S2, during the data cleaning process, duplicate input data is deleted. For alloys with the same composition, if the data differences are small, the average value is taken; if the data differences are large, all data is deleted.

[0040] The empirically determined parameter characteristics in step S2 include: valence electron concentration VEC, electronegativity Δχ, atomic size difference δ, mixing enthalpy ΔHmix, mixing entropy ΔSmix, boiling temperature T, free electron concentration e / a, electron work function w, melting temperature Tm, cohesive energy Ec, radius R, phase parameter O, density D, atomic number Z, van der Waals radius A, Pauling electronegativity B, modulus mismatch factor η, shear modulus difference ΔG, shear modulus G, first ionization energy E; the element characteristics comprehensively determined include: Al, Ti, Cr, Mn, Fe, Ni, Co, Mo, Nb, V, Cu.

[0041] In step S3, the machine learning models include deep learning DL, support vector machine SVM, random forest RF, extreme random tree ET, gradient boosting decision tree GBDT, and extreme gradient boosting XGBoost.

[0042] In step S3, the dataset is randomly divided into an 80% training set and a 20% test set.

[0043] In step S7, the finally designed alloy molecular formulas are: Cra1Alb1Tic1Fed1Nie1Vf1, Coa2Crb2Alc2Tid2Fee2Nif2, Coa3Crb3Alc3Fed3Nie3, and Coa4Crb4Alc4Fed4Nie4.

[0044] In the above molecular formulas, the value range of a1 is 17.7 - 18.3, the value range of b1 is 15.8 - 16.4, the value range of c1 is 0.5 - 1.1, the value range of d1 is 30.1 - 30.7, the value range of e1 is 32.4 - 33, and the value range of f1 is 1.6 - 2.2;

[0045] The value range of a2 is 4.3 to 4.9, the value range of b2 is 17.3 to 17.9, the value range of c2 is 17.0 to 17.6, the value range of d2 is 0.2 to 0.8, the value range of e2 is 30.3 to 30.9, and the value range of f2 is 29.2 to 29.8;

[0046] The value range of a3 is 7.6 to 8.2, the value range of b3 is 19.2 to 19.8, the value range of c3 is 17.0 to 17.6, the value range of d3 is 24.6 to 25.2, and the value range of e3 is 30.0 - 30.6;

[0047] The value range of a4 is 5.2 to 5.8, the value range of b3 is 18.9 to 19.5, the value range of c3 is 17.2 to 17.8, the value range of d3 is 27.0 to 27.6, and the value range of e3 is 30.2 to 30.8.

[0048] In the step S8, the preparation method of the transition metal high-entropy alloy includes the following steps:

[0049] S81. Calculate the mass fraction of each element in the designed composition, and select metal pellets with a purity higher than 99.9% packed in vacuum as alloy raw materials;

[0050] S82. Weigh the mass of each element component with an electronic balance, control the mass error within 0.001 g, and after weighing, pack it in vacuum for standby;

[0051] S83. Melt the alloy by means of vacuum arc furnace melting. Put each metal raw material into the melting tank in the furnace in the order of increasing melting point, then carry out gas washing and gas filling. After sealing, evacuate the sample chamber and introduce high-purity argon for protection;

[0052] S84. Turn on the power supply of the arc furnace welding machine, and after arc ignition, melt the pre-placed titanium sponge in the furnace for 1 - 2 minutes for in-furnace deoxidation;

[0053] S85. Remelt the alloy 5 times repeatedly. During each melting process, turn on the electromagnetic stirring, and turn over the alloy after each melting to obtain a transition metal high-entropy alloy ingot.

[0054] The beneficial effects of the present invention are:

[0055] 1) The present invention links the theory and methods of machine learning with the mechanical properties of transition metal high-entropy alloys, establishes a tensile strength model and an elongation model for transition metal high-entropy alloys, and through multi-objective optimization, links the two models together for the optimized design of the composition, so as to further improve the comprehensive performance of the alloy, can quickly generate alloy compositions with excellent mechanical properties, reduces the deviation risk caused by single models and single-objective optimization, expands the composition search space of high-entropy alloys, and realizes the efficient composition design of high-strength and high-toughness high-entropy alloys in the huge and complex composition space of high-entropy alloys.

[0056] 2) In the design method of the present invention, with the aid of a machine learning model, it provides new ideas and methods for discovering and guiding the design of transition metal high-entropy alloys with relatively high strength and plasticity, and through vacuum arc melting, a transition metal high-entropy alloy material with coordinated optimization of tensile strength and elongation is successfully obtained. Brief Description of the Drawings

[0057] Figure 1 is a flowchart of the design method of the present invention;

[0058] Figure 2 is the R 2 square comparison diagram of the tensile strength model in Example 1 of the present invention after the exhaustive method;

[0059] Figure 3 is the R 2 square comparison diagram of the elongation model in Example 1 of the present invention after the exhaustive method;

[0060] Figure 4 is the scatter diagram of the tensile strength XGBoost model for multi-objective optimization design in Example 1 of the present invention;

[0061] Figure 5 is the scatter diagram of the elongation ET model for multi-objective optimization design in Example 1 of the present invention;

[0062] Figure 6 is the scatter comparison diagram of the alloys in Examples 1-3 of the present invention and other transition metal high-entropy alloy materials with high strength and high plasticity;

[0063] Figure 7 is the room temperature tensile curve diagram of the transition metal high-entropy alloys with multi-objective optimization design in Examples 1-3 of the present invention. Detailed Embodiments

[0064] The present invention will be further explained below with reference to the drawings and specific embodiments.

[0065] Example 1: The present invention provides a design method for multi-objective collaborative optimization of the mechanical properties of high-entropy alloys based on machine learning, including the following steps:

[0066] S1. Collect data on transition metal high-entropy alloys:

[0067] Historical data on the composition and mechanical properties of quaternary to heptanary transition metal high-entropy alloys were obtained by querying literature through academic platforms such as CNKI and Web of Science and collecting laboratory data. The alloying elements include Fe, Co, Ni, Cr, Al, Ti, Cu, V, Mo, Mn, and Nb, and the mechanical property indexes include tensile strength and elongation. When collecting composition data, a casting method of vacuum induction melting or vacuum arc melting was selected, and the tensile method was selected as room temperature uniaxial tension. At the same time, the source of each data should be noted for subsequent viewing and sorting of data from the source.

[0068] S2. Establish a high-entropy alloy dataset after data cleaning and determine composition characteristics to establish a transition metal high-entropy alloy feature set:

[0069] The collected data on transition metal high-entropy alloys were cleaned, and duplicate-entered data were deleted to establish a high-entropy alloy dataset. For alloys with the same composition, if the data differed little, the average value was taken; if the data differed greatly, all were deleted. In this invention, 325 tensile strength data and 355 elongation data were collected in total. Based on the atomic physical properties of the elements and their relevant empirical calculation formulas, empirical parameter characteristics and element characteristics were comprehensively determined, and the determined characteristics were standardized to establish a transition metal high-entropy alloy feature set.

[0070] A total of 20 characteristics were comprehensively determined as empirical parameter characteristics, including: valence electron concentration VEC, electronegativity Δχ, atomic size difference δ, mixing enthalpy ΔHmix, mixing entropy ΔSmix, boiling temperature T, free electron concentration e / a, electron work function w, melting temperature Tm, cohesive energy Ec, radius R, phase parameter O, density D, atomic number Z, van der Waals radius A, Pauling electronegativity B, modulus mismatch factor η, shear modulus difference ΔG, shear modulus G, first ionization energy E; A total of 11 characteristics were comprehensively determined as element characteristics, including: Al, Ti, Cr, Mn, Fe, Ni, Co, Mo, Nb, V, Cu.

[0071] S3. Train machine models based on different algorithm mechanisms and conduct preliminary screening of features using feature importance:

[0072] The machine models include deep learning DL, support vector machine SVM, random forest RF, extreme random tree ET, gradient boosting decision tree GBDT, and extreme gradient boosting XGBoost. The datasets of tensile strength and elongation established in step S2 above were respectively input into the machine models, and the datasets were randomly divided into an 80% training set and a 20% test set. The training set was used to train the machine models, and the test set was used to verify and test the models.

[0073] Due to the empirical parameters, there may also be some repetitive or redundant information among the elemental compositions, which is not conducive to the prediction of the model. Therefore, the feature importance method is first used to input the feature set into the machine model to screen the features in order to determine the coefficient R 2 As the evaluation criterion, based on the importance evaluation of the input features by the current model, the features are screened, and the features with less contribution to the model are deleted; the four features Mo, Nb, V, and Cu with less contribution to the model are deleted, making the model more sensitive to the relationship between composition and performance, improving R2, and saving computing resources while improving the prediction accuracy.

[0074] S4. With R 2 As the evaluation index, the two models with the best performance are selected as the alternative models. The feature sets of the alternative models are screened by the exhaustive method and the top ten groups with the best performance are selected. The Bayesian optimization algorithm is used for hyperparameter optimization to screen out the best feature set and the corresponding hyperparameters:

[0075] Select the two models ET model and XGB model with the highest R in the tensile strength model as the alternative models, and use the exhaustive method for further feature combination screening. The screening range is 22 to 27 features. The best ten groups of feature sets obtained by screening are brought into the model optimized by Bayesian optimization. By optimizing the hyperparameters, finally select the group of features with the largest R 2 As the feature set of the final model. The feature group of the tensile strength XGB model finally selected after screening and hyperparameter optimization needs to further delete the features shear modulus difference ΔG, cohesive energy Ec, mixing enthalpy ΔHmix, boiling temperature T, Fe; the feature group of the ET model needs to further delete the features atomic number Z, electron work function w, density D, mixing enthalpy ΔHmix, melting temperature Tm. 2

[0076] Select the two models ET model and XGB model with the highest R in the elongation model as the alternative models, and use the exhaustive method for further feature combination screening. Considering that the accuracy of the elongation model is not as high as that of the tensile strength, the screening range is further expanded to 21 to 27 features. The best ten groups of feature sets obtained by screening are brought into the model optimized by Bayesian optimization. By optimizing the hyperparameters, finally select the group of features with the largest R 2 As the feature set of the final model. The feature group of the elongation XGB model finally selected after screening and hyperparameter optimization needs to further delete the features atomic size difference δ, boiling temperature T, phase parameter O, radius R, cohesive energy Ec, Al; the feature group of the ET model needs to further delete the features boiling temperature T, Pauling electronegativity B, mixing entropy ΔSmix, Fe, Mn, Ni. 2

[0077] Such as Figure 2 、 3 ​​They are respectively the comparison charts of the two models of tensile strength and the two models of elongation after exhaustive search.

[0078] S5. Collect data again as the validation set to validate the two alternative models, and comprehensively select the best model as the model for final multi-objective optimization:

[0079] Collect the mechanical property data of high-entropy alloys that meet the requirements in step S1 again from the latest published platform data, and put the collected data into the two alternative models of the tensile strength model or the elongation model for prediction and validation, combined with R 2 and the final prediction performances of the two alternative models, respectively select the best tensile strength model and the best elongation model as the models for final multi-objective optimization; Judging from the final results, it is more reasonable to select the XGB model for tensile strength and the ET model for the elongation model.

[0080] Such as Figure 4 、 5 They are respectively the scatter plots of the XGBoost of tensile strength and the ET model of elongation.

[0081] S6. Combine the best tensile strength model and the best elongation model for multi-objective optimization:

[0082] Input the best models of the tensile strength model and the elongation model obtained in step S5 above into the multi-objective optimization program for optimization; Through the crossover operation, the exchange of parental genes generates new individuals, maintaining the excellent characteristics of the parents; Through the mutation operation, introduce randomness and diversity to explore a new solution space; Through normalization, ensure that the generated offspring meet the constraint condition that the sum of elements is 100%.

[0083] S7. Adjust the parameters according to the design objectives to design a transition metal high-entropy alloy with excellent strength and plastic properties:

[0084] Input elements Co, Cr, Al, Ti, Mo, Fe, Mn, Ni, V, and set the content range of each element to 0-35%. Take the Z value as the comprehensive performance evaluation index of all alloys in the population during each genetic iteration. Through the formula Calculate and output the alloy composition with the largest Z value.

[0085] Through multiple parameter adjustments, set the initial population size to 500, the mutation rate to 0.1, and the number of iterations to 30 generations. Through creating an initial population, calculating the fitness function after normalization, performing genetic mutations, and finally calculating the fitness function, the composition Cr18Al16.1Ti0.8Fe30.4Ni32.7V1.9 is obtained.

[0086] S8. Prepare the designed transition metal high-entropy alloy according to the final designed alloy composition:

[0087] Prepare the transition metal high-entropy alloy screened and designed in the above step S7 by vacuum arc melting, including the following steps:

[0088] S81. Select Cr metal, Al metal, Ti metal, Fe metal, Ni metal, and V metal pellets with a purity higher than 99.9% as raw materials for alloy preparation;

[0089] S82. Prepare an ingot weighing 30 g according to the alloy composition, calculate the mass of each pure metal Cr, Al, Ti, Fe, Ni, and V required according to their molar content, take Cr: 5.481 g, Al: 2.544 g, Ti: 0.224 g, Fe: 9.443 g, Ni: 11.240 g, V: 0.567 g, and weigh and vacuum package the metal components in step S7 for standby;

[0090] S83. Use a vacuum arc furnace to melt the alloy. After cleaning the cavity, put the metal raw materials into the melting tank in the furnace in ascending order of melting point, then perform gas washing and gas filling. When the vacuum degree in the sample chamber reaches 5×10 -3 Close the valve below, slowly fill with nitrogen, and close the filling valve when the pressure gauge reading in the cavity is close to 0; the above is the gas washing process, repeat the gas washing once, and finally fill with gas to about -0.02 MPa.

[0091] S84. Adjust the distance between the upper electrode and the copper crucible to 3-5 mm, turn on the power switch, and press the automatic arc ignition button after normal operation. After arc ignition, first melt the pre-placed titanium sponge in the copper crucible for about 1 minute for in-furnace deoxidation, and then move the arc to the material to start melting, and the melting current is adjusted automatically.

[0092] S85: Repeatedly melt the alloy 5 times. Turn on the electromagnetic stirring during each melting process and turn over the alloy after each melting to improve the uniformity of the alloy composition, and obtain a Cr18Al16.1Ti0.8Fe30.4Ni32.7V1.9 transition metal high-entropy alloy ingot.

[0093] S9. Verify the performance to obtain a target alloy material with multi-objective performance synergistic optimization:

[0094] Perform a room temperature tensile property test on the transition metal high-entropy alloy prepared in the above step S8. Use a water jet to cut the ingot into tensile specimens with a gauge length of 5 mm and a thickness of 2.5 mm.

[0095] Figure 7 The room temperature uniaxial tensile curve of Cr18Al16.1Ti0.8Fe30.4Ni32.7V1.9 is shown, and its tensile strength is 1488 MPa and the elongation is 17%;

[0096] Figure 6 Show the comprehensive performance comparison of the as-cast transition metal high-entropy alloy designed in Example 1 and the reported as-cast transition metal high-entropy alloy under uniaxial tension at room temperature. It can be seen from this that the significant effects produced in this example are obtained under the same conditions, and an as-cast transition metal high-entropy alloy material with excellent performance is obtained.

[0097] Example 2: The difference from Example 1 is:

[0098] S7. Adjust the parameters according to the design goal to design a transition metal high-entropy alloy with excellent strength and plasticity:

[0099] Input elements Co, Cr, Al, Ti, Fe, Ni, and the content range of each element is set to 0-35%. Take the Z value as the comprehensive performance evaluation index of all alloys in the population during each genetic iteration. Through the formula Calculate and output the alloy composition with the largest Z value.

[0100] Through multiple parameter adjustments, set the initial population size to 500, the mutation rate to 0.1, and the number of iterations to 25 generations. By creating an initial population, calculating the fitness function after normalization, performing genetic mutations, and finally calculating the crowding distance, the composition Co4.6Cr17.6Al17.3Ti0.5Fe30.6Ni29.5 is obtained.

[0101] S8. Prepare the designed transition metal high-entropy alloy according to the final designed alloy composition:

[0102] Use vacuum arc melting to prepare the transition metal high-entropy alloy screened and designed in step S7 above; it includes the following steps:

[0103] S81. Select Co metal, Cr metal, Al metal, Ti metal, Fe metal, and Ni metal pellets with a purity higher than 99.9% as raw materials for alloy preparation;

[0104] S82. Prepare an ingot weighing 30 g according to the alloy composition. Calculate the mass of each pure metal Co, Cr, Al, Ti, Fe, and Ni required according to their molar contents in the components. Take Co: 1.589 g, Cr: 5.365 g, Al: 2.736 g, Ti: 0.140 g, Fe: 10.018 g, Ni: 11.240 g, V: 10.151 g, and weigh and vacuum package the metal components in step S7 for later use;

[0105] S83. Use a vacuum arc furnace to melt the alloy. After cleaning the cavity, put the metal raw materials into the melting tank in the furnace in ascending order of melting point, and then perform gas washing and gas filling. When the vacuum degree in the sample chamber reaches 5×10 -3Close the following valve and slowly fill it with nitrogen. When the reading of the chamber pressure gauge is close to 0, close the filling valve; The above is the gas washing process. Repeat the gas washing once, and finally fill it with gas to about -0.02 MPa.

[0106] S84. Adjust the distance between the upper electrode and the copper crucible to 3 - 5 mm. Turn on the power switch. After normal operation, press the automatic arc ignition button. After arc ignition, first melt the sponge titanium pre-placed in the copper crucible for about 1 minute for in-furnace deoxidation, and then move the arc to the material to start melting. The melting current is adjusted automatically.

[0107] S85: Repeatedly melt the alloy 5 times. During each melting process, turn on the electromagnetic stirring and turn over the alloy after each melting to improve the uniformity of the alloy composition, and obtain a Co4.6Cr17.6Al17.3Ti0.5Fe30.6Ni29.5 transition metal high-entropy alloy ingot.

[0108] S9. Verify the performance to obtain a target alloy material with multi-objective performance co-optimization:

[0109] Conduct a room temperature tensile property test on the transition metal high-entropy alloy prepared in step S8 above. Use a water jet to cut the ingot into tensile specimens with a gauge length of 5 mm and a thickness of 2.5 mm.

[0110] Figure 7 The room temperature uniaxial tensile curve of Co4.6Cr17.6Al17.3Ti0.5Fe30.6Ni29.5 is shown. Its tensile strength is 1470 MPa, and the elongation is 27.4%;

[0111] Figure 6 Show the comparison of the comprehensive room temperature uniaxial tensile properties between the as-cast transition metal high-entropy alloy designed in Example 2 and the reported as-cast transition metal high-entropy alloy. It can be seen from this that the significant effect produced in this example under the same conditions, and an as-cast transition metal high-entropy alloy material with excellent performance is obtained.

[0112] Example 3: The difference from Example 1 is:

[0113] S7. Adjust the parameters according to the design goal to design a transition metal high-entropy alloy with excellent strength and plasticity properties:

[0114] Input elements Co, Cr, Al, Fe, Ni, and the content range of each element is set to 0 - 35%. Take the Z value as the comprehensive performance evaluation index of all alloys in the population during each genetic iteration. Through the formula Calculate and obtain the alloy composition with the largest output Z value.

[0115] Through multiple parameter adjustments, the initial population size is set to 500, the mutation rate is 0.3, and the number of iterations is 14 generations. By creating an initial population, calculating the fitness function after normalization, performing genetic mutations, and finally calculating the crowding distance, the composition A: Co7.9Cr19.5Al17.3Fe24.9Ni30.3 is obtained.

[0116] The element content range is set to 0 - 40%. Through multiple parameter adjustments, the initial population size is set to 500, the mutation rate is 0.3, and the number of iterations is 15 generations. By creating an initial population, calculating the fitness function after normalization, performing genetic mutations, and finally calculating the crowding distance, the composition B: Co5.5Cr19.2Al17.5Fe27.3Ni30.5 is obtained.

[0117] S8. Prepare the designed transition - metal high - entropy alloy according to the final designed alloy composition:

[0118] Prepare the transition - metal high - entropy alloy screened and designed in the above step S7 by vacuum arc melting; the method includes the following steps:

[0119] S81. Select Co metal, Cr metal, Al metal, Fe metal, and Ni metal pellets with a purity higher than 99.9% as raw materials for alloy preparation.

[0120] S82. Prepare a 30 - g ingot according to the alloy composition. Calculate the mass of each pure metal Co, Cr, Al, Fe, Ni required according to the composition Co7.9Cr19.5Al17.3Fe24.9Ni30.3. Take Co: 2.730 g, Cr: 5.946 g, Al: 2.738 g, Fe: 8.156 g, Ni: 10.430 g;

[0121] Calculate the mass of each pure metal Co, Cr, Al, Fe, Ni required according to the composition Co5.5Cr19.2Al17.5Fe27.3Ni30.5. Take Co: 1.903 g, Cr: 5.862 g, Al: 2.772 g, Fe: 8.952 g, Ni: 10.511 g. Weigh the metal components in step S7 and vacuum - pack them for standby.

[0122] S83. Use a vacuum arc furnace to melt the alloy. After cleaning the cavity, put the metal raw materials into the melting tank in the furnace in ascending order of melting point, and then perform gas washing and gas filling. When the vacuum degree in the sample chamber reaches 5×10 -3 Then close the valve and slowly fill with nitrogen. When the reading of the cavity pressure gauge is close to 0, close the gas - filling valve; the above is the gas - washing process. Repeat the gas - washing once, and finally fill with gas to about - 0.02 MPa.

[0123] S84. Adjust the distance between the upper electrode and the copper crucible to 3 - 5 mm. Turn on the power switch. After normal operation, press the automatic arc ignition button. After arc ignition, first melt the pre - placed titanium sponge in the copper crucible for about 1 minute for in - furnace deoxidation, and then move the arc to the material to start melting. The melting current is adjusted automatically.

[0124] S85: Remelt the alloy 5 times. During each melting process, turn on the electromagnetic stirring and flip the alloy after each melting to improve the uniformity of the alloy composition, obtaining the transition - metal high - entropy alloy ingots of A: Co7.9Cr19.5Al17.3Fe24.9Ni30.3 and B: Co5.5Cr19.2Al17.5Fe27.3Ni30.5.

[0125] S9. Verify the performance to obtain the target alloy material with synergistic optimization of multi - objective performance:

[0126] Conduct room - temperature tensile property tests on the transition - metal high - entropy alloy prepared in step S8 above. Use a water jet to cut the ingot into tensile specimens with a gauge length of 5 mm and a thickness of 2.5 mm.

[0127] Figure 7 The room - temperature uniaxial tensile curves of Co7.9Cr19.5Al17.3Fe24.9Ni30.3 are shown. Its tensile strength is 1464 MPa and the elongation is 31.5%; the room - temperature uniaxial tensile curves of Co5.5Cr19.2Al17.5Fe27.3Ni30.5 are shown. Its tensile strength is 1540 MPa and the elongation is 23%.

[0128] Figure 6 Show the comparison of the comprehensive room - temperature uniaxial tensile properties between the as - cast transition - metal high - entropy alloy designed in Example 3 and the reported as - cast transition - metal high - entropy alloys. It can be seen from this the significant effect produced in this example under the same conditions, and an as - cast transition - metal high - entropy alloy material with excellent performance is obtained.

[0129] Table 1 shows the comparison results of the tensile strength, elongation, and strength - plasticity product between the alloys in Examples 1 - 3 and the alloys with a strength above 1200 MPa in the database of this article.

[0130]

[0131]

[0132] The results shown in Table 1 indicate that: the comprehensive performance of the high - entropy alloys designed in Examples 2 and 3 of the present invention can exceed the high - entropy alloy with the best comprehensive performance in the dataset, and the comprehensive performance of the high - entropy alloy designed in Example 1 ranks among the top in the database.

[0133] The present invention predicts the mechanical properties of high-entropy alloys by using a machine learning model, and automates the optimization design process through operations such as selection, crossover, and mutation of the genetic algorithm to quickly generate alloy compositions with excellent mechanical properties, providing new ideas and methods for guiding the design of transition metal high-entropy alloys with high strength and plasticity.

[0134] The above is only used to illustrate the technical solution of the present invention and not to limit it. Other modifications or equivalent replacements made by those of ordinary skill in the art to the technical solution of the present invention shall be covered within the scope of the claims of the present invention as long as they do not depart from the spirit and scope of the technical solution of the present invention.

Claims

1. A design method for multi-objective collaborative optimization of mechanical properties of high entropy alloys based on machine learning, characterized by: The following steps are involved: S1. Collect data on transition high entropy alloys: Collect historical data on the composition and mechanical properties of quaternary to heptad transition family high entropy alloys through academic platforms. The alloying elements include Fe, Co, Ni, Cr, Al, Ti, Cu, V, Mo, Mn and Nb. The mechanical properties include tensile strength and elongation. S2. After data cleaning, a high entropy alloy data set is established, and the composition characteristics are determined to establish a transition family high entropy alloy feature set: The collected transition high entropy alloy data are cleaned, and the high entropy alloy data set is established after deleting the duplicated data. The empirical parameter characteristics and element characteristics are comprehensively determined according to the atomic physical properties of the elements combined with their relevant empirical calculation formulas, and the determined characteristics are standardized to establish the transition high entropy alloy feature set; S3. Train machine models based on different algorithm mechanisms and use feature importance to perform preliminary feature screening: The tensile strength and elongation data sets established in step S2 are respectively input into the machine model, and the data sets are randomly divided into a training set and a test set. The training set is used to train the machine model, and the test set is used to verify the model. The feature set is then input into the machine model using the feature importance method to screen the features to determine the coefficient R 2 As an evaluation criterion, features are screened based on the importance assessment of the input features by the current model, and features that contribute less to the model are deleted; S4, R 2 As the evaluation index, the two best performing models are selected as candidate models. The feature sets of the candidate models are screened by exhaustive method and the top ten groups with the best performance are selected. The Bayesian optimization algorithm is used to optimize the hyperparameters and select the best feature set and corresponding hyperparameters: Select R in the tensile strength model or elongation model 2 The top two models are selected as candidate models. The exhaustive method is used to combine features to further screen the global optimal solution of the feature problem in a larger range. The top ten best feature sets obtained by screening are brought into the Bayesian optimization model to adjust and optimize the hyperparameters of the model corresponding to the feature set. The R models are selected according to their final performance. 2 Large optimal feature set and corresponding hyperparameters; S5. Collect data again as a validation set to validate the two candidate models, and comprehensively select the best model as the final model for multi-objective optimization: The mechanical properties data of high entropy alloys that meet the requirements of step S1 above are collected again from the latest published platform data, and the collected data are put into two alternative models of tensile strength model or elongation model for prediction and verification. 2 The best tensile strength model and the best elongation model were selected as the final models for multi-objective optimization based on the final prediction performance of the two alternative models; S6. Combine the optimal tensile strength model and the optimal elongation model for multi-objective optimization: The optimal models of the tensile strength model and the elongation model obtained in the above step S5 are simultaneously input into the multi-objective optimization program for optimization. The optimization method includes the following steps: S61, creating multiple individuals as a population, inputting the element characteristics after screening, setting the content range of each element to 0-35%, randomly generating the content of each element within the given upper and lower limits, and normalizing the content of each element so that the sum of all elements is 100%; S62, using the fitness function to evaluate the performance of each alloy component, normalizing the tensile strength UTS and the elongation EL, and using the Z value as the comprehensive performance evaluation index of all alloys in the population in each genetic iteration, comparing all the obtained components, and outputting the alloy component with the largest Z value; The normalization formula is: The formula for calculating the Z value is: Where min_UTS and max_UTS are the minimum and maximum values ​​of UTS in the initially generated population, min_EL and max_EL are the minimum and maximum values ​​of EL in the initially generated population; S63. Introduce a reward mechanism. If the UTS value of an individual exceeds 1.5 times the maximum UTS value in the current population, the fitness of the individual will be rewarded, and the fitness of the alloy will be multiplied by 2, encouraging the genetic algorithm to search for alloys with higher tensile strength; S64, use the NSGA-II algorithm and the tournament selection method to select alternately, retain individuals with higher fitness, and select the individuals with the best performance; S65, the crossover operation generates two offspring by exchanging some genes of two parent individuals. The crossover method is single-point crossover, that is, a crossover point is randomly selected, and then the genes of the parent individuals before and after the point are exchanged, and the two offspring after the crossover are normalized so that the sum of their components is 100%; S66. Introduce mutation operation in the genetic process. The composition of each element will be randomly adjusted according to the mutation probability, with a variation range of 0.5 or 0.

3. After mutation, normalization is performed so that the sum of the percentages of all elements is 100%; S67. In order to maintain the diversity of the population and avoid early convergence of the algorithm, the NSGA-II algorithm also calculates the crowding distance for each individual. The specific method is as follows: 1) Sort each target and find the minimum and maximum fitness values, 2) Processing of boundary individuals: After sorting, the minimum and maximum individuals, i.e. the individuals at the edge of the target space, will be assigned infinite crowding distances, 3) Calculate the crowding of internal individuals: For individuals in the middle of the target space, calculate their crowding distances with adjacent individuals, 4) The total crowding distance of an individual is the weighted sum of its crowding distances on all targets; Assuming that the target values ​​are sorted in the target space, the crowding distance of an individual is calculated by the difference in the target values ​​of its adjacent individuals. For each target iii, the calculation formula of the crowding distance i(k) is expressed as: In the formula, f i (k) represents the value of individual k on target i, and are the maximum and minimum values ​​of the target in the population respectively; S7. Adjust parameters according to design goals and design transition high entropy alloys with excellent strength and plasticity: Create an initial population by setting the initial population size, mutation rate and number of iterations, adjust parameters by inputting the type or content of elements, mutation rate, scale of tournament selection or number of initial population parameters, calculate the fitness function after normalization, perform genetic mutation, and finally calculate the fitness function to obtain the final designed alloy composition; S8. Prepare the designed transition high entropy alloy according to the final designed alloy composition: The transition high entropy alloy selected and designed in the above step S7 is prepared by vacuum arc melting; S9. Verify performance and obtain target alloy materials with multi-objective performance synergistic optimization: The room temperature tensile properties of the transition high entropy alloy prepared in the above step S8 are tested to obtain the values ​​of tensile strength and elongation. The strength-ductility product is used as a comprehensive evaluation index for multi-objective optimization to compare and verify the comprehensive properties of the existing cast transition high entropy alloy under room temperature uniaxial tension, so as to finally obtain a cast transition high entropy alloy material with excellent performance.

2. The design method of multi-objective collaborative optimization of high entropy alloy mechanical properties based on machine learning according to claim 1 is characterized by: In the step S1, when collecting alloy composition data, a casting method of vacuum induction melting or vacuum arc melting is selected, and a stretching method of room temperature uniaxial stretching is selected.

3. The design method of multi-objective collaborative optimization of high entropy alloy mechanical properties based on machine learning according to claim 1 is characterized by: In step S2, during the data cleaning process, the repeatedly entered data are deleted, and for alloys with the same composition, if the data are not much different, the average value is taken, and if the data are greatly different, all the data are deleted.

4. The design method of multi-objective collaborative optimization of high entropy alloy mechanical properties based on machine learning according to claim 1, characterized in that: In the step S2, the empirical parameter characteristics comprehensively determined include: valence electron concentration VEC, electronegativity Δχ, atomic size difference δ, mixing enthalpy ΔHmix, mixing entropy ΔSmix, boiling temperature T, free electron concentration e / a, electron work function w, melting temperature Tm, cohesive energy Ec, radius R, phase parameter O, density D, atomic number Z, van der Waals radius A, Pauling electronegativity B, modulus mismatch factor η, shear modulus difference ΔG, shear modulus G, first ionization energy E; the element characteristics comprehensively determined include: Al, Ti, Cr, Mn, Fe, Ni, Co, Mo, Nb, V, Cu.

5. The design method of multi-objective collaborative optimization of high entropy alloy mechanical properties based on machine learning according to claim 1, characterized in that: In step S3, the machine model includes deep learning DL, support vector machine SVM, random forest RF, extreme random tree ET, gradient boosting decision tree GBDT and extreme gradient boosting XGBoost.

6. The design method of multi-objective collaborative optimization of high entropy alloy mechanical properties based on machine learning according to claim 1, characterized in that: In step S3, the data set is randomly divided into 80% training set and 20% test set.

7. The design method of multi-objective collaborative optimization of high entropy alloy mechanical properties based on machine learning according to claim 1, characterized in that: In the step S7, the alloy molecular formulas finally designed are: Cra1Alb1Tic1Fed1Nie1Vf1, Coa2Crb2Alc2Tid2Fee2Nif2, Coa3Crb3Alc3Fed3Nie3 and Coa4Crb4Alc4Fed4Nie4.

8. The design method of multi-objective collaborative optimization of high entropy alloy mechanical properties based on machine learning according to claim 7, characterized in that: In the molecular formula, the value range of a1 is 17.7 to 18.3, the value range of b1 is 15.8 to 16.4, the value range of c1 is 0.5 to 1.1, the value range of d1 is 30.1 to 30.7, the value range of e1 is 32.4 to 33, and the value range of f1 is 1.6 to 2.2; The value range of a2 is 4.3~4.9, the value range of b2 is 17.3~17.9, the value range of c2 is 17.0~17.6, the value range of d2 is 0.2~0.8, the value range of e2 is 30.3~30.9, and the value range of f2 is 29.2~29.8; The value range of a3 is 7.6-8.2, the value range of b3 is 19.2-19.8, the value range of c3 is 17.0-17.6, the value range of d3 is 24.6-25.2, and the value range of e3 is 30.0-30.6; The value range of a4 is 5.2~5.8, the value range of b3 is 18.9~19.5, the value range of c3 is 17.2~17.8, the value range of d3 is 27.0~27.6, and the value range of e3 is 30.2~30.

8.

9. The design method of multi-objective collaborative optimization of high entropy alloy mechanical properties based on machine learning according to claim 1, characterized in that: The method for preparing the transition high entropy alloy in step S8 comprises the following steps: S81. Calculate the mass fraction of each element in the design composition. The alloy raw material shall be vacuum-packed metal pellets with a purity higher than 99.9%; S82, weigh the mass of each element component with an electronic balance, and control the mass error within 0.001g. After weighing, vacuum pack and set aside; S83, melting the alloy by a vacuum arc furnace, placing the metal raw materials in the melting tank in the furnace in order from low to high melting points, and then washing and inflating the sample chamber, vacuumizing the sample chamber after sealing, and introducing high-purity argon gas for protection; S84, turn on the power of the arc furnace welding machine, strike the arc, melt the titanium sponge pre-placed in the furnace, and deoxidize it in the furnace for 1 to 2 minutes; S85. The alloy is repeatedly melted for 5 times, electromagnetic stirring is turned on during each melting process, and the alloy is turned over after each melting to obtain a transition high entropy alloy ingot.

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