Method, device, equipment and medium for determining phase formation of multi-principal element high-temperature alloy

Abstract

The application is suitable for the technical field of high-temperature alloy design, and provides a method for determining phase formation of a multi-principal-element high-temperature alloy, which comprises the following steps: generating a candidate alloy according to a first rule in a design strategy for phase formation of the multi-principal-element high-temperature alloy, screening the candidate alloy according to a second rule in the design strategy, and determining whether the phase of the multi-principal-element high-temperature alloy is formed according to a screening result, so that the dependence on a machine learning model is eliminated when the phase formation of the multi-principal-element high-temperature alloy is determined, and the determination speed and accuracy are improved, and the implementation cost is reduced.

Description

Technical Field

[0001] This invention belongs to the field of high-temperature alloy design technology, and particularly relates to a method, apparatus, equipment and medium for determining the formation of multi-principal-element high-temperature alloy phases. Background Technology

[0002] For decades, the development of nickel-based superalloys has greatly benefited the power generation industry and aerospace engineering. However, the development of nickel-based superalloys has approached their operating temperature limits, and they are inherently expensive and dense. To further improve the efficiency of aero engines and gas turbine engines while protecting the environment, there is a need to develop new high-temperature structural materials that are low-cost, lightweight, and resistant to high temperatures.

[0003] The discovery of multi-principal element alloys (MPEAs) has provided a new paradigm for designing novel high-performance structural materials. Unlike most traditional alloys developed based on a single principal element, MPEAs are typically composed of three or more different elements, with no single element dominating. This multi-component element alloying approach offers extensive opportunities for compositional design to achieve desired performance combinations. Among them, L12 precipitation-strengthened MPEAs exhibit an excellent combination of strength and ductility. Furthermore, due to the high entropy and slow diffusion effects, L12 precipitation-strengthened MPEAs demonstrate significant thermal stability under long-term aging treatment at high temperatures. In addition to high stability, high concentrations of aluminum, iron, chromium, and titanium can reduce the density and cost of MPEAs; most reported MPEAs have densities below 8.0 g / cm³. 3 The microstructure of L12 precipitation-strengthened MPEAs is similar to that of nickel-based superalloys, and an anomalous increase in yield stress with increasing temperature has also been observed. Therefore, these MPEAs are also known as high-entropy superalloys or multi-principal-element superalloys (MPESAs). Based on these advantages, MPESAs show great potential in high-temperature engineering applications.

[0004] In developing such materials, a goal-oriented key design strategy is a prerequisite, including low-cost raw materials, low density, high L12 dissolution temperature, high melting temperature, good microstructural stability, strong oxidation resistance, excellent creep resistance, and high strength and acceptable ductility. Among these, the alloy's microstructure has a significant impact on various properties. For example, the ideal microstructure for nickel-based superalloys is a face-centered cubic (FCC) + L12 two-phase structure. Therefore, exploring suitable chemical compositions that can generate ideal microstructures without forming harmful intermetallic phases is crucial for developing the desired materials. However, the chemical composition space for MPESAs is almost infinite, making it challenging to find suitable compositions with superior properties.

[0005] Predicting the phase formation of MPEAs requires significant time and material costs to determine the alloy microstructure solely through experimental characterization. While existing phase diagram calculation methods can effectively calculate MPEA phase formation, commercially available phase diagram calculation software is prohibitively expensive. Machine learning (ML) is a simple yet effective technique for predicting phase formation and has been applied in materials science. It can establish potential mapping relationships between material composition, processing, empirical parameters, and material properties, and then, through effective adjustments and optimizations, help to quickly search a broad compositional space, thereby accelerating the development of materials with superior properties. ML has been applied to predict the phase formation of MPEAs and high-temperature alloys. Previous research has laid an important foundation and demonstrated that ML can accelerate alloy design, saving considerable manpower and time. However, these studies primarily focus on building ML models and then using them to predict alloy phase formation, rather than providing specific, general design strategies. Furthermore, ML models are often "black boxes" with many parameters, and many studies in materials science do not publicly disclose raw data, algorithm parameters, or model code. Therefore, it is difficult for other researchers to replicate these results (models), meaning the models are not shareable. The inability to share models is a key problem that needs to be addressed when applying machine learning to materials science. Summary of the Invention

[0006] The purpose of this invention is to provide a method, apparatus, equipment, and medium for determining the formation of multi-principal-element high-temperature alloy phases, aiming to solve the problems of slow determination speed, low accuracy, and high implementation cost of multi-principal-element high-temperature alloy phase formation caused by existing technologies.

[0007] On one hand, the present invention provides a method for determining the formation of multi-principal-element high-temperature alloy phases, the method comprising the following steps:

[0008] Candidate alloys are generated according to the first rule in the design strategy for phase formation of multi-principal-element high-temperature alloys.

[0009] According to the second rule in the design strategy, the candidate alloys are screened, and based on the screening results, it is determined whether the phase of the multi-principal element high-temperature alloy is formed.

[0010] Preferably, prior to the step of generating candidate alloys according to the first rule in the design strategy for multi-principal element high-temperature alloy phase formation, the method further includes:

[0011] Based on the first training dataset and the second training dataset, a first classification algorithm for predicting the first classification target and a second classification algorithm for predicting the second classification target are determined respectively.

[0012] Based on the first classification algorithm, a feature reduction strategy is used to reduce the initial feature set of the first training dataset to obtain the first optimal feature set;

[0013] Based on the second classification algorithm, the feature reduction strategy is used to reduce the initial feature set of the second training dataset to obtain the second optimal feature set;

[0014] The Shapley additive interpretation analysis method was used to calculate the SHAP value of each best feature in the first best feature set and the SHAP value of each best feature in the second best feature set.

[0015] Based on the SHAP values ​​of all best features in the first best feature set and the SHAP values ​​of all best features in the second best feature set, the first rule and the second rule that promote the formation of the microstructure of multi-principal element high-temperature alloys are obtained.

[0016] Preferably, the step of reducing the initial feature set of the first training dataset to obtain a first optimal feature set based on the first classification algorithm includes:

[0017] The initial feature set of the first training dataset is reduced by using a recursive feature addition method to obtain the first optimal feature subset;

[0018] When a feature is deleted from the initial feature set, the first optimal feature subset is reduced using a semi-exhaustive iterative feature elimination method to obtain a second optimal feature subset. The second optimal feature subset is then used as the initial feature set for the next iteration. The process then jumps to the step of reducing the initial feature set of the first training dataset using a recursive feature addition method until no feature is deleted from the initial feature set, thus obtaining the first optimal feature set.

[0019] Preferably, the step of reducing the initial feature set of the first training dataset using a recursive feature addition method to obtain a first optimal feature subset includes:

[0020] The importance score of each initial feature in the initial feature set of the first training dataset is obtained using the first classification algorithm.

[0021] Based on the importance scores, a series of initial feature subsets are constructed;

[0022] Machine learning models are constructed based on each of the initial feature subsets, wherein all of the machine learning models employ the first classification algorithm to predict the first classification target;

[0023] Based on the prediction accuracy of all the machine learning models, the initial feature subset corresponding to the machine learning model with the highest prediction accuracy is determined as the first optimal feature subset.

[0024] Preferably, the step of using a semi-exhaustive iterative feature elimination method to reduce the first optimal feature subset to obtain a second optimal feature subset includes:

[0025] The importance score of each best feature in the first best feature subset is obtained using the first classification algorithm.

[0026] A machine learning model is constructed based on the first optimal feature subset to obtain the first model;

[0027] Based on the importance scores, the currently traversed feature to be deleted is selected from the first optimal feature subset, and a machine learning model is constructed based on the other features in the first optimal feature subset excluding the currently deleted feature, to obtain the second model;

[0028] Determine whether the prediction accuracy of the second model is higher than that of the first model;

[0029] If so, the current feature to be deleted is removed from the first optimal feature subset, and execution continues to the step of building a machine learning model based on the first optimal feature subset; otherwise, execution continues to the step of selecting the currently traversed current feature to be deleted from the first optimal feature subset according to the order of importance scores.

[0030] Preferably, the second rule includes an optimal range of preset empirical parameters, including average valence electron concentration, enthalpy of mixing, and average melting point. The step of screening the candidate alloys according to the second rule in the design strategy and determining whether a phase of the multi-principal element high-temperature alloy has formed based on the screening results includes:

[0031] Calculate the average valence electron concentration, enthalpy of mixing, and average melting point of the candidate alloys respectively;

[0032] Determine whether the average valence electron concentration, mixing enthalpy, and average melting point of the candidate alloy respectively meet the optimal ranges for the average valence electron concentration, mixing enthalpy, and average melting point in the design strategy;

[0033] If so, it is determined that the phase of the multi-principal element high-temperature alloy has formed; otherwise, it is determined that the phase of the multi-principal element high-temperature alloy has not formed.

[0034] On the other hand, the present invention provides an apparatus for determining the formation of multi-principal-element high-temperature alloy phases, the apparatus comprising:

[0035] The alloy generation unit is used to generate candidate alloys according to the first rule in the design strategy for multi-principal-element high-temperature alloy phase formation.

[0036] The phase formation determination unit is used to screen the candidate alloys according to the second rule in the design strategy, and determine whether the phase of the multi-principal element high-temperature alloy is formed based on the screening results.

[0037] Preferably, the device further includes:

[0038] The classification algorithm determination unit is used to determine, based on the first training dataset and the second training dataset, a first classification algorithm for predicting a first classification target and a second classification algorithm for predicting a second classification target, respectively.

[0039] The first feature reduction unit is used to reduce the initial feature set of the first training dataset based on the first classification algorithm and using a feature reduction strategy to obtain the first optimal feature set.

[0040] The second feature reduction unit is used to reduce the initial feature set of the second training dataset based on the second classification algorithm and the feature reduction strategy to obtain the second optimal feature set.

[0041] The SHAP value calculation unit is used to calculate the SHAP value of each best feature in the first best feature set and the SHAP value of each best feature in the second best feature set using the Shapley additive interpretation analysis method.

[0042] The design strategy determination unit is used to obtain the first rule and the second rule that promote the formation of microstructure of multi-principal element superalloys based on the SHAP values ​​of all best features in the first best feature set and the SHAP values ​​of all best features in the second best feature set.

[0043] On the other hand, the present invention also provides a computing device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to perform the steps described in the method for determining the formation of multi-principal-element high-temperature alloy phases.

[0044] On the other hand, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps described in the method for determining the formation of multi-principal-element high-temperature alloy phases.

[0045] This invention generates candidate alloys based on the first rule in the design strategy for phase formation of multi-principal high-temperature alloys, and then screens the candidate alloys according to the second rule in the design strategy. Based on the screening results, it determines whether the phase of the multi-principal high-temperature alloy has formed. This allows the determination of phase formation of multi-principal high-temperature alloys to be free from the dependence on machine learning models, improves the speed and accuracy of the determination, and reduces the implementation cost. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating the implementation of the method for determining the formation of multi-principal-element high-temperature alloy phases provided in Embodiment 1 of the present invention.

[0047] Figure 2 This is a flowchart illustrating the implementation of the method for determining the formation of multi-principal-element high-temperature alloy phases provided in Embodiment 2 of the present invention.

[0048] Figure 3 This is a schematic diagram illustrating the working principle of the recursive feature addition method and the semi-exhaustive iterative feature elimination method in the method for determining the formation of multi-principal element high-temperature alloy phases provided in Embodiment 2 of the present invention;

[0049] Figure 4 This is a schematic diagram of the feature deletion screening process in the method for determining the formation of multi-principal-element high-temperature alloy phases provided in Embodiment 2 of the present invention;

[0050] Figure 5 This is a schematic diagram of the results of verifying the target classification model in the method for determining the formation of multi-principal-element high-temperature alloy phases provided in Embodiment 2 of the present invention;

[0051] Figure 6 This is a schematic diagram illustrating the reasonable range of element content that promotes the "FCC+L12" dual-phase microstructure in the method for determining the formation of multi-principal-element high-temperature alloy phases provided in Embodiment 2 of the present invention.

[0052] Figure 7 This is a schematic diagram illustrating the optimal range of preset empirical parameters that promote the formation of the "FCC+L12" dual-phase microstructure in the method for determining the formation of multi-principal-element high-temperature alloy phases provided in Embodiment 2 of the present invention.

[0053] Figure 8 This is a flowchart illustrating the implementation of the method for determining the formation of multi-principal-element high-temperature alloy phases provided in Embodiment 3 of the present invention.

[0054] Figure 9 This is a schematic diagram of the structure of the device for determining the formation of multi-principal-element high-temperature alloy phases provided in Embodiment 4 of the present invention;

[0055] Figure 10 This is a schematic diagram of the structure of the computing device provided in Embodiment 5 of the present invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0057] The specific implementation of the present invention will be described in detail below with reference to specific embodiments:

[0058] Example 1:

[0059] Figure 1 The implementation flow of the method for determining the formation of multi-principal element high-temperature alloy phases provided in Embodiment 1 of the present invention is shown. For ease of explanation, only the parts related to the embodiments of the present invention are shown, and are described in detail below:

[0060] In step S101, a candidate alloy is generated according to the first rule in the design strategy for the formation of multi-principal-element high-temperature alloy phases.

[0061] In this embodiment of the invention, the design strategy for the formation of multi-principal high-temperature alloy phases is a pre-obtained rule for rapidly designing MPESAs with an “FCC+L12” dual-phase microstructure. To obtain the “FCC+L12” dual-phase microstructure, the content of each element in the alloy needs to be within a reasonable range. Based on this, the first rule in the design strategy for the formation of multi-principal high-temperature alloy phases specifies the reasonable range of element content. In the process of designing multi-principal high-temperature alloys, several candidate alloys are generated according to the reasonable range of element content specified in the first rule. These candidate alloys are the MPESAs to be confirmed.

[0062] In one feasible embodiment, the specific implementation method for obtaining the design strategy for the formation of multi-principal-element high-temperature alloy phases is described in the following embodiment two, and will not be repeated here.

[0063] In step S102, candidate alloys are screened according to the second rule in the design strategy, and the formation of phases in multi-principal element high-temperature alloys is determined based on the screening results.

[0064] In this embodiment of the invention, the range of empirical parameters for the alloy is a standard for determining whether a candidate alloy has an "FCC+L12" dual-phase microstructure. Based on this, the second rule in the design strategy specifies the optimal range of preset empirical parameters. According to these optimal ranges of preset empirical parameters, it is possible to quickly and accurately determine whether the candidate alloy has an "FCC+L12" dual-phase microstructure. If it has an "FCC+L12" dual-phase microstructure, the formation of MPESAs is determined, and the candidate alloy is thus determined to be an MPESAs. Here, according to the optimal range of preset empirical parameters specified in the second rule, the candidate alloy is screened. Based on the screening results, it is determined whether the phase of the multi-principal element high-temperature alloy has formed. Among these, the preset empirical parameters are those commonly used in alloy design, including the average valence electron concentration. ), enthalpy of mixing (ΔH) mix and average melting point ).

[0065] In one feasible embodiment, the phase formation of a multi-principal element superalloy is determined through the following steps:

[0066] ① Calculate the average valence electron concentration, mixing enthalpy, and average melting point of the candidate alloys respectively;

[0067] ② Determine whether the average valence electron concentration, mixing enthalpy, and average melting point of the candidate alloy respectively meet the optimal ranges for the average valence electron concentration, mixing enthalpy, and average melting point in the design strategy;

[0068] ③ If yes, it is determined that the phase of the multi-principal element high-temperature alloy has formed; otherwise, it is determined that the phase of the multi-principal element high-temperature alloy has not formed.

[0069] In this embodiment of the invention, the candidate alloy is calculated. ΔH mix as well as Determine whether these values ​​fall within a specified range, i.e., determine Does it meet the optimal range of average valence electron concentration and ΔH specified in the design strategy? mix Does it meet the optimal range of mixing enthalpy specified in the design strategy, and If the average melting point falls within the optimal range specified in the design strategy, the candidate alloy is determined to have an "FCC+L12" dual-phase microstructure, indicating MPESAs phase formation. Otherwise, the candidate alloy is determined not to have an "FCC+L12" dual-phase microstructure, indicating MPESAs phase formation has not occurred. The optimal range for average valence electron concentration is specified in the design strategy. The optimal range for the enthalpy of mixing is -15.35 < ΔH. mix <-9.73kJ·mol -1 The optimal range of average melting point is

[0070] By using the above steps ①-③, the phase formation of multi-principal element high-temperature alloys can be determined, thereby improving the speed and accuracy of judging the phase formation of multi-principal element high-temperature alloys.

[0071] In this embodiment of the invention, candidate alloys are generated according to the first rule in the design strategy for phase formation of multi-principal high-temperature alloys, and the candidate alloys are screened according to the second rule in the design strategy. Based on the screening results, it is determined whether the phase of the multi-principal high-temperature alloy has formed. This enables the determination of phase formation of multi-principal high-temperature alloys to be free from the dependence on machine learning models, improves the judgment speed and accuracy, and reduces the implementation cost.

[0072] Example 2:

[0073] Figure 2 The implementation flow of the method for determining the formation of multi-principal element high-temperature alloy phases provided in Embodiment 2 of the present invention is shown. For ease of explanation, only the parts related to the embodiments of the present invention are shown, and are described in detail below:

[0074] In step S201, based on the first training dataset and the second training dataset, a first classification algorithm for predicting the first classification target and a second classification algorithm for predicting the second classification target are determined respectively.

[0075] In this embodiment of the invention, several pre-provided classification algorithms are used to construct corresponding initial models. With all classification algorithms using default parameters, 10-fold cross-validation is used to assess the accuracy of each initial model in predicting the first classification target on the first training dataset. The classification algorithm used by the initial model with the highest accuracy in predicting the first classification target is determined as the first classification algorithm. Similarly, 10-fold cross-validation is used to assess the accuracy of each initial model in predicting the second classification target on the second training dataset. The classification algorithm used by the initial model with the highest accuracy in predicting the second classification target is determined as the second classification algorithm. Here, the first classification target is whether the L12 phase exists in the alloy, denoted as Target-A, and the second classification target is whether there are other phases besides the L12 phase in the alloy, denoted as Target-B.

[0076] Specifically, Table 1 shows the nine classification algorithms provided and the average accuracy of each classification algorithm with 10-fold cross-validation. As can be seen from Table 1, the GBC algorithm has the highest accuracy in predicting Target-A, while XGBC is more favorable for predicting Target-B. Therefore, the GBC algorithm is determined as the first classification algorithm for predicting Target-A, and the XGBC algorithm is determined as the second classification algorithm for predicting Target-B.

[0077] Table 1

[0078]

[0079] In a feasible embodiment, before determining the first classification algorithm for predicting the first classification target and the second classification algorithm for predicting the second classification target based on the first training dataset and the second training dataset, respectively, the first training dataset and the second training dataset are constructed. Both training datasets are used to build machine learning models. Specifically, the construction of these two training datasets is achieved through the following steps:

[0080] ① Collect the first training dataset, in which the data contained in the first training dataset consisted only of the chemical formula and phase composition of each sample (i.e., alloy). The phase composition of these samples in the first training dataset had multiple phase types, including "FCC", "FCC + other phases", "FCC + L12" and "FCC + L12 + other phases". The phases in "other phases" include BCC, HCP, B2, σ, Laves, etc. In addition, the samples marked "other phases" do not necessarily contain all other phases, but contain one or more of them.

[0081] ② Based on phase composition, the samples in the first training dataset are divided into two categories. One category of samples is labeled as None-L12-phase, meaning that these alloys do not have L12 phase precipitation, and the other category of samples is labeled as Have-L12-phase, meaning that these alloys have L12 phase precipitation. Specifically, the samples in the first training dataset with phase composition of "FCC" and "FCC + other phases" are denoted as None-L12-phase, and the samples in the first training dataset with phase composition of "FCC + L12" and "FCC + L12 + other phases" are denoted as Have-L12-phase.

[0082] ③ Take all the samples in the first training dataset that are labeled as Have-L12-phase as the second training dataset, and then label the samples in the second training dataset that have a phase composition of "FCC+L12" as None-other-phases, that is, no other phases are precipitated except for the L12 phase, and label the samples in the second training dataset that have a phase composition of "FCC+L12+other phases" as Have-other-phases, that is, other phases are precipitated except for the L12 phase;

[0083] ④ Collect and construct some initial features for mapping the target (i.e., the phase composition of the sample) for each sample in the first training dataset and the second training dataset, and supplement these initial features into the first training dataset and the second training dataset respectively to obtain a more complete first training dataset and the second training dataset. At this time, the construction of the first training dataset and the second training dataset is completed. The first training dataset is used to build a classification model to predict Target-A, and the second training dataset is used to build a classification model to predict Target-B. The initial features of the samples include the heat treatment process parameters of the alloy, the content of various elements in the alloy (i.e., chemical composition), and empirical parameters commonly used to judge the formation of alloy phases. Specifically, Table 2 shows the representation and meaning of each initial feature used to build the machine learning model.

[0084] Table 2

[0085]

[0086]

[0087] As an example, the first training dataset (hereinafter referred to as dataset A) contains 983 samples, of which 440 are in the None-L12-phase class and 543 are in the Have-L12-phase class. The second training dataset (hereinafter referred to as dataset B) contains 347 samples in the None-other-phase class and 196 samples in the Have-other-phase class. Dataset B consists of all the samples in the Have-L12-phase class from dataset A.

[0088] In another feasible embodiment, after the first training dataset and the second training dataset are constructed, the data in the first training dataset and the second training dataset are preprocessed. Specifically, the text data is digitized. For example, in the Cooling Method category, "water quenching" is numbered 1, "air cooling" is numbered 2, "furnace cooling" is numbered 3, "oil quenching" is numbered 4, and other cooling methods or unspecified cooling methods are recorded as 0.

[0089] In step S202, based on the first classification algorithm, a feature reduction strategy is used to reduce the initial feature set of the first training dataset to obtain the first optimal feature set.

[0090] In this embodiment of the invention, based on the first classification algorithm, a feature reduction strategy is used to reduce the initial feature set of the first training dataset, so as to select representative features from the initial feature set of the first training dataset to construct the final classification model. All the selected representative features constitute the first optimal feature set.

[0091] In a feasible embodiment, the initial feature set of the first training dataset is reduced through the following steps:

[0092] (1) The initial feature set of the first training dataset is reduced by using the recursive feature addition method to obtain the first optimal feature subset;

[0093] In this embodiment of the invention, the initial feature set of the first training dataset is reduced using a recursive feature addition method through the following steps:

[0094] i. Use the first classification algorithm to obtain the importance score of each initial feature in the initial feature set of the first training dataset;

[0095] ii. Construct a series of initial feature subsets based on importance scores;

[0096] iii. Construct machine learning models based on each initial feature subset. All machine learning models use the first classification algorithm to predict the first classification target.

[0097] iv. Based on the prediction accuracy of all machine learning models, the initial feature subset corresponding to the machine learning model with the highest prediction accuracy is determined as the first optimal feature subset.

[0098] In embodiments of the present invention, such as Figure 3 The diagram illustrates the principle of the recursive feature addition method. First, the importance score of each initial feature in the initial feature set of the first training dataset is obtained using the first classification algorithm. All initial features are then sorted in descending order of importance score. Next, starting with the initial feature with the highest importance score, features are added sequentially to construct a series of initial feature subsets (e.g., {F1}, {F1,F2}, {F1,F2,F3}, ..., {F1,F2,F3,...,F...). last Then, using the first classification algorithm, machine learning models are constructed based on each initial feature subset, meaning each initial feature subset corresponds to a machine learning model, resulting in the following... Figure 3 The model consists of Model-1, Model-2, ..., Model-last. Finally, the accuracy of Model-1, Model-2, ..., Model-last in predicting the first classification target is compared, and the initial feature subset corresponding to the machine learning model with the highest prediction accuracy is determined as the first optimal feature subset.

[0099] (2) When a feature is deleted from the initial feature set, the first best feature subset is reduced by the semi-exhaustive iterative feature elimination method to obtain the second best feature subset. The second best feature subset is then used as the initial feature set for the next iteration. The process jumps to step (1) above and continues until no feature is deleted from the initial feature set, thus obtaining the first best feature set.

[0100] In this embodiment of the invention, it can be determined whether any features in the initial feature set have been deleted by comparing the number of features in the first optimal feature subset with the number of features in the initial feature set. When any features in the initial feature set have been deleted, a semi-exhaustive iterative feature elimination method is used to reduce the first optimal feature subset to obtain a second optimal feature subset. The second optimal feature subset is then used as the initial feature set for the next iteration, and the process jumps to step (1) above to continue until no features in the initial feature set have been deleted. The initial feature set at this point is then used as the first optimal feature set. Figure 3 The iterative principles of the recursive feature addition method and the semi-exhaustive iterative feature elimination method are shown.

[0101] In another feasible embodiment, the specific implementation of the semi-exhaustive iterative feature elimination method for reducing the first optimal feature subset is described in the following embodiment three, and will not be repeated here.

[0102] By implementing the above steps (1)-(2), the initial feature set of the first training dataset is reduced, thereby improving the prediction performance and accuracy of the model built with the reduced training dataset.

[0103] In another feasible embodiment, after obtaining the first optimal feature set, a final classification model is constructed on the first training dataset with the first optimal feature set after feature reduction using a first classification algorithm, in order to predict the first classification target. For ease of description, this model is referred to as the first target classification model.

[0104] In step S203, based on the second classification algorithm, a feature reduction strategy is used to reduce the initial feature set of the second training dataset to obtain the second optimal feature set.

[0105] In this embodiment of the invention, based on the second classification algorithm, a feature reduction strategy is adopted to reduce the initial feature set of the second training dataset, so as to select representative features from the initial feature set of the second training dataset to construct the final classification model. All the selected representative features constitute the second optimal feature set.

[0106] In a feasible embodiment, the implementation principle of using a feature reduction strategy to reduce the initial feature set of the second training dataset is the same as that of step S202. For details of its implementation, please refer to the description of step S202, which will not be repeated here.

[0107] As an example, Figure 4 The diagram illustrates the entire filtering process and final results of using a feature reduction strategy to reduce features in datasets A and B. The filtering process first uses Method 1 (recursive feature addition) to reduce features in both datasets A and B, decreasing the number of features from 42 to 28 and 34 respectively. Next, Method 2 (semi-exhaustive iterative feature elimination) is used, reducing the number of features to 27 and 31 respectively. Then, Method 1 is used again, reducing the number of features to 24 and 20 respectively. In other words, after using the feature reduction strategy to reduce features in datasets A and B, dataset A has 24 optimal features, which constitute the optimal feature set for dataset A, and dataset B has 20 optimal features, which constitute the optimal feature set for dataset B.

[0108] In another feasible embodiment, after obtaining the second optimal feature set, the second classification algorithm is used to construct the final classification model on the second training dataset with the second optimal feature set after feature reduction, so as to predict the second classification target. For ease of description, this model is called the second target classification model.

[0109] To verify the predictive performance and reliability of the first and second target classification models in predicting the phase formation of MPESAs, target classification model A was constructed using the GBC algorithm on dataset A with 24 optimal features, and target classification model B was constructed using the XGBC algorithm on dataset B with 20 optimal features. Ten-fold cross-validation was used to verify the prediction accuracy of target classification models A and B, respectively. The prediction results are shown below. Figure 5 The confusion matrices (a) and (b) are shown. Figure 5 As shown in the confusion matrix (a), the target classification model A achieves prediction accuracies of 97.42% and 92.95% for Have-L12-phase and None-L12-phase binary classification, respectively, with an overall accuracy of 95.42%. This is a slight improvement over the 95.12% accuracy of the initial classification model built on dataset A with 42 initial features. Figure 5 (b) The confusion matrix shows that the target classification model B achieves classification accuracies of 76.02% and 91.35% for Have-other-phases and None-other-phases, respectively, with an overall accuracy of 85.82%, which is 1.66% higher than the 84.16% accuracy of the initial classification model built on dataset B with 42 initial features. Meanwhile, Figure 5 Figures (c) and (d) show the 10-fold cross-validation ROC curves (Receiver Operating Characteristic Curve) for target classification model A and target classification model B, respectively. The average AUC (Area Under the Curve) of target classification model A reaches 0.98, indicating that target classification model A has good overall performance. The average AUC of target classification model B also reaches 0.9, indicating that target classification model B has sufficient reliability. Experimental results show that the constructed final target classification model is robust and reliable in predicting the phase formation of MPESAs.

[0110] In step S204, the Shapley additive interpretation analysis method is used to calculate the SHAP value of each best feature in the first best feature set and the SHAP value of each best feature in the second best feature set.

[0111] In this embodiment of the invention, Shapley additive explanations (SHAP) analysis is used to transform the knowledge learned by the first target classification model and the second target classification model into understandable material knowledge, so as to obtain design strategies for the formation of multi-principal high-temperature alloy phases. These strategies are then used for alloy design to achieve the same purpose as the model prediction. Specifically, SHAP analysis is used to calculate the SHAP value of each best feature in the first best feature set and the SHAP value of each best feature in the second best feature set, so as to quantify the contribution of each feature to the model prediction through each SHAP value.

[0112] In step S205, based on the SHAP values ​​of all the best features in the first best feature set and the SHAP values ​​of all the best features in the second best feature set, a first rule and a second rule that promote the formation of the microstructure of multi-principal element superalloys are obtained.

[0113] In this embodiment of the invention, the microstructure of the multi-principal element superalloy is a "FCC+L12" two-phase microstructure. First, based on the SHAP values, common features that significantly contribute to model prediction are determined from all optimal features in the first and second optimal feature sets (these common features are called principal features). These principal features are the main elements and preset empirical parameters of the alloy that promote the formation of the "FCC+L12" two-phase microstructure. Then, in the first training dataset, based on the SHAP values ​​of the principal features, positively influential feature values ​​are determined from all feature values ​​corresponding to the principal features; these positively influential feature values ​​promote L12 precipitation. All determined positively influential feature values ​​constitute the optimal range of the principal feature that promotes L12 precipitation. For ease of description, this optimal range is called the first optimal range. In the second training dataset, based on the SHAP values ​​of the principal features, positively influential feature values ​​are determined from all feature values ​​corresponding to the principal features. Among all the corresponding eigenvalues, the positive eigenvalues ​​with a positive influence are determined, that is, eigenvalues ​​in which no other phases besides the L12 phase precipitate. All the determined positive eigenvalues ​​constitute the optimal range of the main feature in which no other phases besides the L12 phase precipitate. For ease of description, this optimal range is called the second optimal range. Then, the first optimal range and the second optimal range corresponding to the same main feature are superimposed. The overlapping area of ​​the first optimal range and the second optimal range is the optimal range corresponding to the main feature that promotes the formation of the "FCC+L12" dual-phase microstructure. Thus, the reasonable range of element content for forming the "FCC+L12" dual-phase microstructure and the optimal range of preset empirical parameters are obtained. Finally, the first rule is determined according to the reasonable range of element content, and the second rule is determined according to the optimal range of preset empirical parameters. The first rule and the second rule form a design strategy for the formation of multi-principal element high-temperature alloy phases.

[0114] When obtaining the first and second rules for promoting the formation of microstructures in multi-principal superalloys based on the SHAP values ​​of all optimal features in the first and second optimal feature sets, specifically, a visual relationship diagram between each optimal feature and its corresponding SHAP value is drawn. Based on this visual relationship diagram, the reasonable range of element content for forming the "FCC+L12" dual-phase microstructure and the optimal range of preset empirical parameters can be intuitively obtained. For example, as shown... Figure 6 and Figure 7 As shown, blue and orange are the SHAP values ​​output by the target classification model A built on dataset A, where orange represents a positive influence. Gray and yellow are the SHAP values ​​output by the target classification model B built on dataset B, where gray represents a negative influence. This means that gray eigenvalues ​​often lead to the precipitation of phases other than L12. By superimposing the SHAP values ​​of target classification model A and target classification model B, a common region between orange and yellow can be delineated. This region represents the optimal range of the "FCC+L12" biphasic microstructure.

[0115] in addition, Figure 6 The results show that to obtain the "FCC+L12" dual-phase microstructure, the content of each element needs to be within a reasonable range. For example, the content of Co and Ni needs to be relatively high because they are the main elements forming the L12 phase; the ranges for Al and Ti are narrower, at 3.5 at.%–8 at.% and 3.1 at.%–6 at.%, respectively, or appropriately relaxed to 1.5 at.%–8.5 at.% and 1.4 at.%–9.1 at.%, respectively. This result is consistent with experimental reports. Excess Al will form a brittle (Ni,Co)2AlHeusler phase, and too high a Ti content will lead to the formation of the Co2TiLaves phase and η-Ni3Ti phase by combining Ti with Co, Ni, or Fe. The hexagonal phase or Fe2TiLaves phase; Cr and Fe are also common elements in MPESAs. Model results show that the Cr content is best less than 15 at.%, which is beneficial for the formation of the L12 phase. However, excessively high Cr content will lead to a decrease in the volume fraction of the L12 phase. Studies have also shown that excessively high Cr content can lead to the formation of brittle phases such as σ, μ, and Laves. If Fe is added, the Fe content should be less than 10 at.%, and further increasing the Fe content will lead to the precipitation of Laves and NiAl phases. Figure 7 This demonstrates the optimal range for the "FCC+L12" dual-phase microstructure, a set of empirical parameters commonly used to determine alloy phase formation. For example... Figure 7 As shown, the average valence electron concentration of the alloy The value should be greater than 8 to promote the formation of the "FCC+L12" dual-phase microstructure; the enthalpy of mixing of the alloy (ΔH)mix The concentration should be controlled between -15.35 and -9.73 kJ·mol⁻¹. -1 Within the range; the radius difference of the alloy (δ) r The optimal range for δ is 3.53–4.7, but it can be appropriately relaxed to 3.53–5.38. Other studies have shown that δ r Less than 6.5 and ΔH mix Between -15 and 5 kJ·mol -1 Within this range, the formation of multi-component alloy solid solutions is favorable, and our research shows that the "FCC+L12" dual-phase microstructure influences the δ... r and ΔH mix The required range is relatively narrow; the mixing entropy (ΔS) of the alloy mix The range of ) is not ideal, but it is between 5.3 and 13.4 J·mol⁻¹ -1 ·K -1 Relatively suitable within the range; average melting point of the alloy The optimal range is between 1723.63 and 1822.3 K, which can be appropriately extended to 1682.71 to 1822.3 K. Using these rules, novel MPESAs with an ideal "FCC+L12" dual-phase microstructure can be designed reasonably and quickly.

[0116] To verify the usability of the design strategy for phase formation in multi-principal superalloys, the obtained design strategy was used to evaluate the phase formation of samples in datasets A and B. Dataset A contains 983 samples, of which 543 are in the Have-L12-phase state and 440 are in the None-L12-phase state (accounting for 44.76%). and -15.35 < ΔH mix <-9.73kJ·mol -1 After screening according to the criteria, 235 samples were retained, including 214 Have-L12-phase and 21 None-L12-phase. Subsequently, based on... Further refined screening resulted in the retention of 159 samples, including 153 Have-L12-phase and 6 None-L12-phase (5.73%). The Co content of the 6 None-L12-phase alloys did not fall between 31% and 72%. In dataset B, 347 were None-other-phases and 196 were Have-other-phases (36.1%). After screening based on the three empirical parameters mentioned above, 152 samples remained, including 119 None-other-phases and 33 Have-other-phases (21.71%). Among the 33 Have-other-phase alloys, 28 had Co contents exceeding the 31%-72% range. Of the remaining 5 alloys, one had an Fe content of 25%, significantly exceeding 10%, and two had an Al content of 14.2%, exceeding 9.1%. After screening the two experimental datasets, it was found that the elemental content (especially the Co content) has a great influence on the formation of the “FCC+L12” biphase microstructure.

[0117] To further evaluate these rules in the design strategy, we generated 15,390 candidate MPESAs based on the optimal content ranges of some key elements. We then used the final target classification model A / B, constructed with the optimal feature set, to predict their phase formation, and further filtered them using these rules. The prediction results for Target-A showed that out of the 15,390 candidate MPESAs, 15,201 candidates were predicted as Have-L12-phase (98.77%), and 189 candidates were predicted as None-L12-phase. The prediction results for Target-B showed that out of the 15,390 candidate MPESAs, 10,947 candidates were classified as None-other-phases (71.13%), and 4,443 candidates were classified as Have-other-phases. This demonstrates that after setting optimal content ranges for some key elements, a considerable proportion (71.13%) of the generated candidate MPESAs met the specified requirements. Next, according to... and -15.35 < ΔH mix <-9.73kJ·mol -1 Based on the selection criteria, 5438 candidate MPESAs were retained. Prediction results for Target-A showed that all of them belonged to the Have-L12-phase. For Target-B, 5167 were classified as None-other-phases, and 271 were classified as Have-other-phases. Subsequently, according to... Based on the established criteria, 3260 candidate MPESAs were retained. In the Target-B prediction, 3215 (98.62%) were classified as None-other-phases, and 45 were classified as Have-other-phases. The Δχ² values ​​of these 45 Have-other-phase candidate MPESAs were all greater than 0.12, and the δ... r The value exceeds 5.38. The results indicate that the combination... The rules outlined in this application allow for the rapid and highly accurate (>98%) design of MPESAs with a "FCC+L12" dual-phase microstructure. Furthermore, by incorporating other empirical parameters (such as Δχ<0.12) into the screening process, further refined design is possible. The experimental results demonstrate that the obtained design strategy for multi-principal element superalloy phase formation is usable, and the empirical parameters required for calculation are readily available (low cost), computationally fast, and provide highly accurate specified ranges, thus enabling the rapid, efficient, and low-cost design of MPESAs microstructures. Moreover, the method for obtaining the design strategy presented in this application is universal, and any materials designer can reasonably utilize it.

[0118] In this embodiment of the invention, based on a first training dataset and a second training dataset, a first classification algorithm for predicting a first classification target and a second classification algorithm for predicting a second classification target are determined, respectively. Based on the first classification algorithm, a feature reduction strategy is used to reduce the initial feature set of the first training dataset to obtain a first optimal feature set. Based on the second classification algorithm, a feature reduction strategy is used to reduce the initial feature set of the second training dataset to obtain a second optimal feature set. The Shapley additive interpretation analysis method is used to calculate the SHAP value of each optimal feature in the first optimal feature set and the SHAP value of each optimal feature in the second optimal feature set, respectively. Based on the SHAP values ​​of all optimal features in the first optimal feature set and the SHAP values ​​of all optimal features in the second optimal feature set, a first rule and a second rule that promote the formation of the microstructure of multi-principal element high-temperature alloys are obtained. This realizes the transformation of the knowledge learned by the machine learning model into understandable material knowledge, so as to use the learned material knowledge rules for alloy design without relying on model prediction.

[0119] Example 3:

[0120] Figure 8 The implementation flow of the method for determining the formation of multi-principal element high-temperature alloy phases provided in Embodiment 3 of the present invention is shown. For ease of explanation, only the parts related to the embodiments of the present invention are shown, and are described in detail below:

[0121] The following steps are used to reduce the first optimal feature subset in step S202 of Embodiment 2 by employing a semi-exhaustive iterative feature elimination method:

[0122] In step S801, the importance score of each best feature in the first best feature subset is obtained using the first classification algorithm;

[0123] In step S802, a machine learning model is constructed based on the first optimal feature subset to obtain the first model;

[0124] In step S803, based on the importance scores, the currently traversed feature to be deleted is selected from the first optimal feature subset, and a machine learning model is constructed based on the other features in the first optimal feature subset excluding the currently deleted feature, to obtain the second model;

[0125] In this embodiment of the invention, all the best features in the first best feature subset are sorted in descending order of importance score. In each traversal, one best feature is selected from the first best feature subset as the current feature to be deleted. Specifically, the traversal starts from the best feature with the lowest importance score. If the current traversal is not the first time, and the feature to be deleted in the previous traversal was not removed from the first best feature subset, then the next low-scoring feature is selected as the current feature to be deleted according to the sorting. If the feature to be deleted in the previous traversal was removed from the first best feature subset, then the best feature with the lowest importance score in the current first best feature subset is selected as the current feature to be deleted.

[0126] In step S804, it is determined whether the prediction accuracy of the second model is higher than that of the first model.

[0127] In this embodiment of the invention, when the prediction accuracy of the second model is higher than that of the first model, step S805 is executed; when the prediction accuracy of the second model is lower than that of the first model, the current feature to be deleted is not removed, but the process jumps to step S803 for the next iteration.

[0128] In step S805, the features to be deleted are removed from the first optimal feature subset.

[0129] In this embodiment of the invention, the current feature to be deleted is removed from the first best feature subset to obtain the first best feature subset after removal, and then the process jumps to step S802 to continue execution for the next traversal.

[0130] In embodiments of the present invention, such as Figure 3The diagram illustrates the principle of the semi-exhaustive iterative feature elimination method. First, the importance score of each best feature in the first best feature subset is obtained using a first classification algorithm. All best features in the first best feature subset are sorted in descending order of importance score, and a model is built on the initial first best feature subset. Then, the feature with the lowest score is removed, and a new model is built using the remaining features. If the accuracy of the new model is higher than that of the previous model, the feature is deleted; otherwise, if the accuracy is lower, the feature is put back. The process continues to remove the next low-scoring feature according to the sorting, and the previous step is repeated until all remaining features are traversed. After this process, if any feature is removed, the remaining features will enter the next iteration. This process continues until no feature is removed, thereby improving the prediction performance and accuracy of the model built on the pruned training dataset.

[0131] Example 4:

[0132] Figure 9 The structure of the apparatus for determining the formation of multi-principal-element high-temperature alloy phases provided in Embodiment 4 of the present invention is shown. For ease of explanation, only the parts related to the embodiments of the present invention are shown, including:

[0133] Alloy generation unit 91 is used to generate candidate alloys according to the first rule in the design strategy for phase formation of multi-principal high-temperature alloys during the design process of multi-principal high-temperature alloys.

[0134] Phase formation determination unit 92 is used to screen candidate alloys according to the second rule in the design strategy, and determine whether the phase of the multi-principal element high-temperature alloy is formed based on the screening results.

[0135] Preferably, the apparatus for determining the formation of multi-principal-element high-temperature alloy phases in embodiments of the present invention further includes:

[0136] The classification algorithm determination unit is used to determine, based on the first training dataset and the second training dataset, a first classification algorithm for predicting a first classification target and a second classification algorithm for predicting a second classification target, respectively.

[0137] The first feature reduction unit is used to reduce the initial feature set of the first training dataset based on the first classification algorithm and the feature reduction strategy to obtain the first optimal feature set.

[0138] The second feature reduction unit is used to reduce the initial feature set of the second training dataset based on the second classification algorithm and the feature reduction strategy to obtain the second optimal feature set.

[0139] The SHAP value calculation unit is used to calculate the SHAP value of each best feature in the first best feature set and the SHAP value of each best feature in the second best feature set using the Shapley additive interpretation analysis method.

[0140] The design strategy determination unit is used to obtain a first rule and a second rule that promote the formation of microstructures of multi-principal element superalloys based on the SHAP values ​​of all best features in the first best feature set and the SHAP values ​​of all best features in the second best feature set.

[0141] In this embodiment of the invention, each unit of the device for determining the formation of multi-principal-element high-temperature alloy phases can be implemented by corresponding hardware or software units. Each unit can be an independent hardware or software unit, or it can be integrated into a single hardware or software unit, which is not intended to limit the invention. Specifically, the implementation methods of each unit can be referred to the description of the foregoing method embodiments, and will not be repeated here.

[0142] Example 5:

[0143] Figure 10 The structure of the computing device provided in Embodiment 5 of the present invention is shown. For ease of explanation, only the parts related to the embodiments of the present invention are shown.

[0144] The computing device 10 of this embodiment includes a processor 100, a memory 101, and a computer program 102 stored in the memory 101 and executable on the processor 100. When the processor 100 executes the computer program 102, it implements the steps in the above-described embodiment of the method for determining the formation of multi-principal element high-temperature alloy phases, for example... Figure 1 The steps S101 to S102 are shown. Alternatively, when the processor 100 executes the computer program 102, it implements the functions of each unit in the above-described device embodiments, for example... Figure 9 The functions of units 91 to 92 are shown.

[0145] In this embodiment of the invention, candidate alloys are generated according to the first rule in the design strategy for phase formation of multi-principal high-temperature alloys, and the candidate alloys are screened according to the second rule in the design strategy. Based on the screening results, it is determined whether the phase of the multi-principal high-temperature alloy has formed. This enables the determination of phase formation of multi-principal high-temperature alloys to be free from the dependence on machine learning models, improves the judgment speed and accuracy, and reduces the implementation cost.

[0146] The computing device in this embodiment of the invention can be a personal computer or a server. The steps implemented by the processor 100 in the computing device 10 when executing the computer program 102 to determine the formation of a multi-principal element high-temperature alloy phase can be referred to the description of the foregoing method embodiments, and will not be repeated here.

[0147] Example 6:

[0148] In this embodiment of the invention, a computer-readable storage medium is provided, which stores a computer program. When executed by a processor, the computer program implements the steps in the above-described embodiment of the method for determining the formation of multi-principal element high-temperature alloy phases. For example... Figure 1 The steps S101 to S102 are shown. Alternatively, when the computer program is executed by the processor, it implements the functions of each unit in the above-described device embodiments, for example... Figure 9 The functions of units 91 to 92 are shown.

[0149] In this embodiment of the invention, candidate alloys are generated according to the first rule in the design strategy for phase formation of multi-principal high-temperature alloys, and the candidate alloys are screened according to the second rule in the design strategy. Based on the screening results, it is determined whether the phase of the multi-principal high-temperature alloy has formed. This enables the determination of phase formation of multi-principal high-temperature alloys to be free from the dependence on machine learning models, improves the judgment speed and accuracy, and reduces the implementation cost.

[0150] The computer-readable storage medium in embodiments of the present invention may include any entity or device capable of carrying computer program code, a recording medium, such as ROM / RAM, disk, optical disk, flash memory, etc.

[0151] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for determining the formation of multi-principal element high-temperature alloy phases, characterized in that, The method includes the following steps: Based on the first training dataset and the second training dataset, a first classification algorithm for predicting the first classification target and a second classification algorithm for predicting the second classification target are determined respectively. Based on the first classification algorithm, a feature reduction strategy is used to reduce the initial feature set of the first training dataset to obtain the first optimal feature set; Based on the second classification algorithm, the feature reduction strategy is used to reduce the initial feature set of the second training dataset to obtain the second optimal feature set; The Shapley additive interpretation analysis method was used to calculate the SHAP value of each best feature in the first best feature set and the SHAP value of each best feature in the second best feature set. Based on the SHAP values ​​of all the best features in the first optimal feature set and the SHAP values ​​of all the best features in the second optimal feature set, a first rule and a second rule are obtained to promote the formation of the microstructure of multi-principal element superalloys. The second rule includes the optimal range of preset empirical parameters, which include the average valence electron concentration, the mixing enthalpy, and the average melting point. Candidate alloys are generated according to the first rule in the design strategy for the formation of multi-principal-element high-temperature alloy phases. According to the second rule in the design strategy, the candidate alloys are screened, and based on the screening results, it is determined whether the phase of the multi-principal element high-temperature alloy has formed. Specifically, this includes: calculating the average valence electron concentration, mixing enthalpy, and average melting point of the candidate alloys respectively; determining whether the average valence electron concentration, mixing enthalpy, and average melting point of the candidate alloys respectively meet the optimal range of average valence electron concentration, optimal range of mixing enthalpy, and optimal range of average melting point in the design strategy; if yes, it is determined that the phase of the multi-principal element high-temperature alloy has formed; otherwise, it is determined that the phase of the multi-principal element high-temperature alloy has not formed.

2. The method as described in claim 1, characterized in that, Based on the first classification algorithm, the step of reducing the initial feature set of the first training dataset using a feature reduction strategy to obtain the first optimal feature set includes: The initial feature set of the first training dataset is reduced by using a recursive feature addition method to obtain the first optimal feature subset; When a feature is deleted from the initial feature set, the first optimal feature subset is reduced using a semi-exhaustive iterative feature elimination method to obtain a second optimal feature subset. The second optimal feature subset is then used as the initial feature set for the next iteration. The process then jumps to the step of reducing the initial feature set of the first training dataset using a recursive feature addition method until no feature is deleted from the initial feature set, thus obtaining the first optimal feature set.

3. The method as described in claim 2, characterized in that, The step of reducing the initial feature set of the first training dataset using a recursive feature addition method to obtain the first optimal feature subset includes: The importance score of each initial feature in the initial feature set of the first training dataset is obtained using the first classification algorithm. Based on the importance scores, a series of initial feature subsets are constructed; Machine learning models are constructed based on each of the initial feature subsets, wherein all of the machine learning models employ the first classification algorithm to predict the first classification target; Based on the prediction accuracy of all the machine learning models, the initial feature subset corresponding to the machine learning model with the highest prediction accuracy is determined as the first optimal feature subset.

4. The method as described in claim 2, characterized in that, The steps of reducing the first optimal feature subset to obtain the second optimal feature subset using a semi-exhaustive iterative feature elimination method include: The importance score of each best feature in the first best feature subset is obtained using the first classification algorithm. A machine learning model is constructed based on the first optimal feature subset to obtain the first model; Based on the importance scores, the currently traversed feature to be deleted is selected from the first optimal feature subset, and a machine learning model is constructed based on the other features in the first optimal feature subset excluding the currently deleted feature, to obtain the second model; Determine whether the prediction accuracy of the second model is higher than that of the first model; If so, the current feature to be deleted is removed from the first optimal feature subset, and execution continues to the step of building a machine learning model based on the first optimal feature subset; otherwise, execution continues to the step of selecting the currently traversed current feature to be deleted from the first optimal feature subset according to the order of importance scores.

5. A device for determining the formation of multi-principal-element high-temperature alloy phases, characterized in that, The device includes: The classification algorithm determination unit is used to determine, based on the first training dataset and the second training dataset, a first classification algorithm for predicting a first classification target and a second classification algorithm for predicting a second classification target, respectively. The first feature reduction unit is used to reduce the initial feature set of the first training dataset based on the first classification algorithm and using a feature reduction strategy to obtain the first optimal feature set. The second feature reduction unit is used to reduce the initial feature set of the second training dataset based on the second classification algorithm and the feature reduction strategy to obtain the second optimal feature set. The SHAP value calculation unit is used to calculate the SHAP value of each best feature in the first best feature set and the SHAP value of each best feature in the second best feature set using the Shapley additive interpretation analysis method. The design strategy determination unit is used to obtain a first rule and a second rule that promote the formation of microstructures of multi-principal element superalloys based on the SHAP values ​​of all best features in the first best feature set and the SHAP values ​​of all best features in the second best feature set. The second rule includes the optimal range of preset empirical parameters, which include the average valence electron concentration, mixing enthalpy and average melting point. An alloy generation unit is used to generate candidate alloys according to the first rule in the design strategy for the formation of multi-principal-element high-temperature alloy phases; The phase formation determination unit is used to screen the candidate alloys according to the second rule in the design strategy, and determine whether the phase of the multi-principal element high-temperature alloy has formed based on the screening results. Specifically, it includes: calculating the average valence electron concentration, mixing enthalpy, and average melting point of the candidate alloys respectively; determining whether the average valence electron concentration, mixing enthalpy, and average melting point of the candidate alloys respectively meet the optimal range of average valence electron concentration, optimal range of mixing enthalpy, and optimal range of average melting point in the design strategy; if yes, it determines that the phase of the multi-principal element high-temperature alloy has formed; otherwise, it determines that the phase of the multi-principal element high-temperature alloy has not formed.

6. The apparatus as claimed in claim 5, characterized in that, When the first feature reduction unit reduces the initial feature set of the first training dataset based on the first classification algorithm and employs a feature reduction strategy to obtain a first optimal feature set, it includes: The initial feature set of the first training dataset is reduced by using a recursive feature addition method to obtain the first optimal feature subset; When a feature is deleted from the initial feature set, the first optimal feature subset is reduced using a semi-exhaustive iterative feature elimination method to obtain a second optimal feature subset. The second optimal feature subset is then used as the initial feature set for the next iteration. The process then jumps to the step of reducing the initial feature set of the first training dataset using a recursive feature addition method until no feature is deleted from the initial feature set, thus obtaining the first optimal feature set.

7. The apparatus as claimed in claim 6, characterized in that, When the first feature reduction unit reduces the initial feature set of the first training dataset using a recursive feature addition method to obtain the first optimal feature subset, it includes: The importance score of each initial feature in the initial feature set of the first training dataset is obtained using the first classification algorithm. Based on the importance scores, a series of initial feature subsets are constructed; Machine learning models are constructed based on each of the initial feature subsets, wherein all of the machine learning models employ the first classification algorithm to predict the first classification target; Based on the prediction accuracy of all the machine learning models, the initial feature subset corresponding to the machine learning model with the highest prediction accuracy is determined as the first optimal feature subset.

8. The apparatus as claimed in claim 6, characterized in that, When the first feature reduction unit reduces the first optimal feature subset using a semi-exhaustive iterative feature elimination method to obtain a second optimal feature subset, it includes: The importance score of each best feature in the first best feature subset is obtained using the first classification algorithm. A machine learning model is constructed based on the first optimal feature subset to obtain the first model; Based on the importance scores, the currently traversed feature to be deleted is selected from the first optimal feature subset, and a machine learning model is constructed based on the other features in the first optimal feature subset excluding the currently deleted feature, to obtain the second model; Determine whether the prediction accuracy of the second model is higher than that of the first model; If so, the current feature to be deleted is removed from the first optimal feature subset, and execution continues to the step of building a machine learning model based on the first optimal feature subset; otherwise, execution continues to the step of selecting the currently traversed current feature to be deleted from the first optimal feature subset according to the order of importance scores.

9. A computing device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 4.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 4.

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