Data and Knowledge Dual-Driven Creep Life Prediction for Austenitic Heat-Resistance Steel

Abstract

Traditional creep life prediction methods are generally difficult for researchers to fully consider the key factors affecting the creep performance, which limits their application in the research and development of new alloys. The artificial intelligence method can skip the complex mechanism and directly establish the mathematical correlation between the composition/process and the target performance. The accuracy, universality, and development efficiency of the model are better than the traditional material development strategy. In this study, we collected 216 creep data of austenitic heat-resistant steel, selected a variety of different machine learning algorithms to establish creep life prediction models, calculated and introduced a large amount of physical metallurgy knowledge highly related to creep based on Thermo-Calc, and converted the creep life into the form of the Larson–Miller parameter to optimize the data distribution, which effectively improved the prediction accuracy and interpretability of the model. In addition, the optimal model was combined with a genetic algorithm to obtain the best composition and process scheme with high-creep-performance potential, providing guidance for the design of austenitic heat-resistant steel.

1. Introduction

Austenitic heat-resistant steel is widely used in ultra-supercritical units. Increasing steam temperature and pressure can improve thermal efficiency and reduce coal consumption [1,2]. This more severe service environment puts forward higher requirements for creep resistance of heat-resistant steel. Therefore, it is extremely important to be able to reasonably evaluate the creep behavior and accurately predict the creep life. At present, the commonly used creep endurance experimental evaluation method is expensive and time consuming, and it is difficult to accurately evaluate the creep property of materials in a short time, which greatly limits the research and development efficiency of new materials. Therefore, establishing an accurate creep life prediction model is conducive to improving the efficiency of creep-performance-oriented new material research and development. A variety of creep life prediction models have been established by predecessors, which can be mainly divided into the parametric method and creep damage mechanical model method [3,4,5,6,7,8,9,10,11]. The parameter method is mainly to summarize the general law between material stress, temperature, and the creep life so as to realize the extrapolation of the long-term life at low temperature and low stress from the short-time creep experimental data at high temperature and high stress, which mainly includes the isotherm method and the time–temperature parameter method. Among them, the Larson–Miller parameter method is widely used, but its parameters need to be optimized according to different conditions; it depends on the empirical fitting and extrapolation of a large number of experimental data, which leads to poor prediction accuracy and universality of the model, and it cannot evaluate the current damage status of materials. Therefore, by introducing the “damage variable” to describe the generation, development, and evolution process of microscopic defects, the scholars expounded the process and law leading to material failure and developed the creep life prediction model based on damage mechanics [12]. Examples include Kachanov–Rabotnov, Liu–Murakami, Murakami, and Chaboche damage models. However, this method relies too much on the explicit creep mechanism to constantly modify the model, which leads to too many parameters and complex forms of the model and limits its application value for materials with complex or unclear creep damage mechanisms. In summary, the traditional creep prediction models are generally difficult to fully consider the key factors affecting the performance, and the universality of the models is insufficient, so it is difficult to achieve universal prediction for different composition alloy systems and different damage mechanisms.

With the rise of the concept of material genetic engineering, artificial intelligence (AI) algorithms provide new ideas for solving the above problems, forming the fourth paradigm in the field of material science. Unlike the first paradigm driven by experiments, the second paradigm driven by theory, and the third paradigm driven by computation, the fourth paradigm takes a data-driven approach as its core. By leveraging the powerful data processing and analysis capabilities of artificial intelligence algorithms, it can quickly mine valuable information and patterns from a vast amount of material data, thereby accelerating the development process of new materials. Further incorporating domain knowledge into data-driven models has formed the fifth paradigm of dual data and knowledge drive in the field of material science, effectively improving the interpretability of AI models and their application in the industrial field. The advantage of the AI method is that it can skip the complex and unclear physical mechanism, it can directly establish the mathematical correlation between material properties such as composition and process and target performance, and the prediction of the model is universal [13,14,15,16,17,18,19,20,21]. There are already a large number of application cases in the fields of ultra-high strength steel and high-temperature resistant alloys, which has accelerated the R&D process of key structural materials in power stations and aerospace, such as the creep life of 9Cr-1Mo steel [22], the fatigue life of aluminum alloy [23], the fatigue life of additive manufacturing alloys [24,25], the hardness of D2 steel [26], the yield strength of TWIP steel [27], etc. However, traditional AI models mainly rely on data-driven approaches, making predictions and decisions by mining patterns and regularities in the data, but they often lack an understanding of the physical essence behind the data. By integrating physical metallurgy parameters, it is equivalent to introducing theoretical guidance on the basis of data-driven methods. This enables the model to not only learn data features but also understand and follow the basic principles of physical metallurgy, thereby improving the accuracy and reliability of the model and better capturing the complex relationships between material composition, processes, and properties. Zhao et al. [28] conducted research on the effectiveness of the non-linear three-component (NLTC) model in simulating the accelerated creep behavior of polymer alloys. By combining experimental and numerical simulation methods, they were able to predict the long-term behavior of materials in a relatively short period of time, providing a timely decision-making basis for engineering design. Zhang et al. [29] constructed a creep life prediction model based on a deep neural network for 316 austenitic stainless steel, which accurately constructed the quantitative relationship between the creep life and alloy composition, creep temperature, and stress. This study achieves a universal prediction of the creep life, but the interpretability and rationality of the model are poor because it does not involve any creep damage mechanism. Shin et al. [30] used Thermo-Calc to calculate the physical metallurgical information of AFA austenitic heat-resistant steel, then selected features based on correlation analysis and adopted different algorithms for modeling. This study provides useful insights into the creep prediction model by introducing material science knowledge, but the introduction of a large amount of thermodynamic information does not improve the accuracy of the model because the creep of the alloy is significantly affected by the kinetics of the precipitated phase. In summary, due to the small sample characteristics of creep data and the complex characteristics of the creep mechanism, the modeling results of machine learning generally show overfitting. Moreover, due to the “black box” characteristics of AI, the interpretability of machine learning models applied to an alloy design is particularly important. Therefore, the selection of reasonable machine learning algorithms and the introduction of appropriate physical metallurgy knowledge are the key to improve the accuracy and interpretability of the model.

In this study, we propose a data and knowledge dual-driven creep life prediction model for austenitic heat-resistant steel and establish an alloy design framework in conjunction with a genetic algorithm, the basic process of which is shown in Figure 1a. Specifically, a database is established based on the existing creep data of austenitic heat-resistant steel. A universal prediction of the creep life is realized based on a variety of different machine learning algorithms. Physical metallurgical information highly correlated with creep is calculated by Thermo-Calc and introduced to enhance the interpretability of AI models. The creep life is converted into the Larson–Miller parameter form to optimize the data distribution, thereby further improving the prediction accuracy of the model. Finally, a genetic algorithm is combined to optimize in the reverse direction, obtaining a composition and process scheme with high potential for creep performance, providing preliminary guidance for an alloy design in actual research and development. Therefore, the innovation of this study lies in the application of artificial intelligence and computational material science to the prediction and design of creep properties. It breaks through the limitations of complex and unclear damage mechanisms as well as experimental methods in alloy designs, and it greatly reduces the R&D cost and improves the R&D efficiency, providing alternative solutions for the design of heat-resistant steel.

2. Methods

2.1. Creep Dataset and Machine Learning Algorithms

We collected 216 creep samples of austenitic heat-resistant steel, each of which contained 19 input features and 1 output feature (creep life), and the specific information is shown in

Table 1. The basic information of creep dataset.

	Min	Max	Mean	Std.
Cr/wt%	9.236	19	14.463	1.634
Mn/wt%	0	9.96	2.014	1.952
Ni/wt%	11.92	35.07	23.202	5.903
Cu/wt%	0	3.1	0.854	1.057
Al/wt%	0	5.02	3.171	0.751
Si/wt%	0	0.98	0.149	0.128
Nb/wt%	0	5.014	1.681	1.056
V/wt%	0	0.26	0.035	0.036
Ti/wt%	0	2.88	0.186	0.509
Mo/wt%	0	3.106	1.211	0.97
W/wt%	0	4.04	0.648	0.933
Y/wt%	0	0.044	0.003	0.007
Zr/wt%	0	0.32	0.037	0.092
C/wt%	0.0001	0.452	0.115	0.073
B/wt%	0	0.08	0.009	0.009
P/wt%	0	0.039	0.012	0.01
Creep Stress/MPa	30	300	144.491	63.909
Solutionizing Temp/°C	1093	1250	1186.898	43.252
Creep Temp/°C	600	850	727.894	48.588
Creep Life/h	5.77	11,452	920.068	1685.208

. All the above original creep data were derived from the work of Shin et al. [30,31]. The dataset comprehensively considers the influence of material characteristics, process parameters, and environmental factors on creep life. The material characteristics were 16 dimensional components, such as Cr, Mn, Ni, Cu, Al, Si, Nb, V, Ti, Mo, W, Y, Zr, C, B, and P, and the process parameter was solution temperature. The environmental factors included creep test temperature and stress, which are closely related to the creep process. Different features have different dimensions and magnitudes, and the creep life is between 5.77 and 11,452 h, which is broad and uneven. These data characteristics will significantly affect the decision-making of machine learning models. Therefore, Z-score normalization was used to eliminate the influence of data dimension and improve the stability of the model. Feature analysis is crucial when dealing with datasets with a large number of input features. For creep life prediction, evaluating the relevance and importance of different features for the target variable can help us better understand the factors affecting creep life and build more accurate and interpretable prediction models. The Pearson correlation coefficient (PCC) and Spearman correlation coefficient (SCC) are used to measure the degree of linear correlation and nonlinear correlation between different features, and their values are between −1 and 1. The larger the absolute value of correlation coefficient is, the stronger the correlation between two features is. The mean accuracy decrease (MDA) index based on random forest model was selected to measure the contribution of different features in the creep life prediction process. The principle is to randomly shuffle a certain dimension of the feature data in the database, and the importance of the feature for the model output is judged by the degree of model accuracy decline.

Then, based on different machine learning algorithms, the association of composition, process, creep condition and creep life is constructed, so as to realize the prediction of creep life. In this study, seven different regression algorithms, including Support Vector Regression (SVR), gradient boosting regression (GBR), Linear Regression (LR), random forest (RF), XGBoost (XGB), Multi-layer Perceptron (MLP), and Convolutional Neural Network (CNN), were used, each of which has its specific application scenarios and advantages. A large number of studies have demonstrated the effectiveness of these algorithms in solving problems in material science, which provides a solid foundation for their application in our research. Therefore, different algorithms were selected to build prediction models and compare and analyze them, and finally, the optimal model was selected. SVR is the application of Support Vector Machine (SVM) to regression problems, which minimizes the deviation between the predicted and actual values by finding an optimal hyperplane that maximizes the distance between the data points and the hyperplane. The prediction performance of the SVR model is mainly affected by the penalty coefficient C and the parameter γ. In this study, the parameters C and γ were set in the range of 2⁻¹⁰ to 2¹⁰. GBR is a gradient-boosting-based framework that progressively reduces the prediction error by iteratively training a decision tree and using the residuals of the previous tree as the training target for the next tree. The prediction performance of the GBR model is mainly affected by two parameters: the learning rate (learning_rate) and the number of decision trees (n_estimators). LR is a simple yet effective regression algorithm that makes predictions by finding a line or a linear hyperplane that minimizes the distance between data points and the line. In this study, the radial basis function kernel in the aforementioned SVR model was replaced with a linear kernel to achieve LR. RF is an ensemble learning method that consists of multiple decision trees, each of which is trained by randomly drawing samples and features from the data, and finally predicts the result by voting or averaging. The prediction performance of the RF model is mainly affected by two parameters: the number of decision trees (n_estimators) and the maximum number of features (max_features). XGB is an optimized gradient boosting framework that improves GBR by using second derivatives for optimization and adding regularization terms to reduce overfitting. In addition to the learning rate (learning_rate) and the number of decision trees (n_estimators), XGB is also affected by parameters such as γ, which controls the model complexity, subsample, and colsample_bytree, which control the sampling ratios; max_depth, which controls the maximum depth of the decision trees; and min_child_weight, which controls the minimum weight of the leaf nodes. MLP is a type of feedforward neural network that contains at least three layers (input layer, hidden layer, output layer) and performs feature transformation and prediction through nonlinear activation functions. In this work, the number of hidden layers is set to 4, and the number of neurons ranges from 100 to 500. CNN is a deep learning model that automatically extracts local features of input data through convolutional layers and then makes predictions through fully connected layers. The architecture of the model is shown in Figure 1b.

In this study, we used the Keras framework of Python to construct the CNN model and performed 500 iterations to reduce the model error. Other models were constructed using the scikit-learn library, and grid search with 5-fold cross-validation was employed to find the optimal parameters of the models. Additionally, we employed the squared coefficient of determination (R²) and the mean absolute error (MAE) to assess the predictive accuracy of the models, as shown in Equations (1) and (2), respectively:

$$R^2={\displaystyle \frac{{\left(n\sum _{i=1}^{n}f\left(x_i\right)y_i-\sum _{i=1}^{n}f\left(x_i\right)\sum _{i=1}^n{y}_i\right)}^2}{\left(\sum _{i=1}^n{f\left(x_i\right)}^2-{\left(\sum _{i=1}^{n}f\left(x_i\right)\right)}^2\right)(n\sum _{i=1}^n{y}_i^2-{\left(\sum _{i=1}^n{y}_i\right)}^2)}}$$

(1)

$$MAE={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n|f\left(x_i\right)-y_i|$$

(2)

2.2. Physical Metallurgy Information Calculation

The advantage of the AI method is to skip the complex mechanism and directly establish the correlation between the composition/process and the target performance, and the constructed data-driven model performs well in prediction accuracy and efficiency. However, it often lacks a deep understanding of the underlying logic, and the blind absence of physical mechanisms and the “black box” nature of AI models are likely to lead to alloy design processes that violate the principles of material science. In the process of model training and prediction, the scalability and interpretability of the model can be effectively improved by integrating physical metallurgy information into the machine learning model as prior knowledge. The introduction of physical metallurgy principles as constraints in the alloy design process can prevent the model from output design results that do not conform to physical reality.

In the practical engineering application of austenitic heat-resistant steel, most high-temperature structural materials rely on the second phase precipitation to achieve creep strengthening effect, and the main precipitated phases are M₂₃C₆- and MC-type carbides, Laves, δ-Ni₃Nb, and ${\mathsf{\gamma }}^{\prime }$-Ni₃Al phases. M₂₃C₆-type carbide is mainly Cr carbide, face-centered cubic structure, which mainly exists in austenitic steel without Nb, Ti, and other strong carbide-forming elements. MC-type carbides mainly appear in austenitic steel containing Ti, Nb and other elements, are face-centered cubic structures, mainly NbC, generally nanometer, and have high thermodynamic stability. Therefore, controlling the dispersive precipitation and uniform distribution of nano-scale MC can effectively pin the dislocation motion at high temperature and significantly improve its creep strength. M₇C₃-type carbide in the case of high carbon content will precipitate, so the austenitic steel is generally not easy to form M₇C₃-type carbide. Laves phase is a kind of AB₂-type intermetallic compound. Generally, the Laves phase precipitated in austenitic steel containing Mo or Nb is Fe₂Mo or Fe₂Nb, and its effect on improving the creep resistance of austenitic heat-resistant steel is limited. Ni₃Al in austenitic steel is a geometric dense pile phase with L1₂ structure, but Ni and Al do not precipitate in the form of Ni₃Al in austenitic steel containing Ni and Al, and only the addition of Ti will promote the precipitation of Ni₃Al in austenitic steel. The driving force, equilibrium size, distribution, and volume fraction of these precipitates at creep temperature should be more valuable for creep properties than the composition and process. Therefore, based on the TCFE9 and MOBFE4 databases of Thermo-Calc, we calculated the precipitation driving force and equilibrium volume fraction of the precipitated phase at the solution temperature and creep temperature. Specifically, the precipitation driving force can be represented as the change in the system’s Gibbs free energy before and after the phase transformation. When the second phase precipitates, the system’s Gibbs free energy decreases, and this decrease in Gibbs free energy is the thermodynamic driving force for precipitation. The equilibrium volume fraction refers to the volume proportion of the precipitated phase in the matrix when it reaches thermodynamic equilibrium under given temperature and composition conditions. These parameters are significantly influenced by the alloy’s composition and temperature. In addition, we also considered the thermodynamic concept of element activity in the alloy system, which can reflect the chemical reaction ability and interaction of elements in a specific alloy environment. It can be understood as the effective concentration of elements in the alloy, which can provide more comprehensive information than the element mass fraction. The specific physical metallurgy information is in

Table 2. The abbreviations and detailed descriptions of the physical metallurgical parameters.

Description	Abbreviations
The activity of elements in the alloy system at solutionizing temperature	Cr-ACR-ST, Mn-ACR-ST, Ni-ACR-ST, Cu-ACR-ST, Al-ACR-ST, Si-ACR-ST, Nb-ACR-ST, V-ACR-ST, Ti-ACR-ST, Mo-ACR-ST, W-ACR-ST, Y-ACR-ST, Zr-ACR-ST, C-ACR-ST, B-ACR-ST, P-ACR-ST
The activity of elements in the alloy system at creep temperature	Cr-ACR-CT, Mn-ACR-CT, Ni-ACR-CT, Cu-ACR-CT, Al-ACR-CT, Si-ACR-CT, Nb-ACR-CT, V-ACR-CT, Ti-ACR-CT, Mo-ACR-CTW-ACR-CT, Y-ACR-CT, Zr-ACR-CT, C-ACR-CT, B-ACR-CT, P-ACR-CT
The equilibrium volume frac-tion of the precipitated phase at solutionizing temperature	MC-VF-ST, M23C6-VF-ST, Laves-VF-ST, NbNi3-VF-ST
The equilibrium volume fraction of the precipitated phase at creep temperature	MC-VF-CT, M23C6-VF-CT, Laves-VF-CT, NbNi3-VF-CT
The precipitation driving force of the precipitated phase at solutionizing temperature	MC-DF-ST, M23C6-DF-ST, Laves-DF-ST, NbNi3-DF-ST
The precipitation driving force of the precipitated phase at solutionizing temperature	MC-DF-CT, M23C6-DF-CT, Laves-DF-CT, NbNi3-DF-CT

and Supplementary Materials. For example, the abbreviation Cr-ACR-ST and Cr-ACR-CT represents the activity of chromium in the alloy system at the solutionizing temperature and creep temperature, respectively. The abbreviation MC-VF-ST and MC-VF-CT represents the equilibrium volume fraction of the precipitated phase MC at solutionizing temperature and creep temperature, respectively. The abbreviation MC-DF-ST and MC-DF-CT represents the precipitation driving force of the precipitated phase MC at solutionizing temperature and creep temperature, respectively. Other abbreviations follow the same pattern.

2.3. Alloy Design Results

The composition design of austenitic steel has always been the focus of research in the field. By adjusting the composition range of austenitic steel and expecting the type and distribution of precipitation phase, it can be applied to more severe working temperature and corrosion environment without increasing the cost. In the process of component expansion of austenitic steel, predecessors mainly adjust the content of Cr, Ni, Al, Nb and W, etc., so that the optimized composition can produce thermodynamically stable austenitic single-phase structure at the solution temperature and obtain the room temperature austenitic single-phase structure. However, there is a complex coupling relationship between the composition and process of steel materials; manual screening of the best scheme in such a large combination of austenite steel composition and solution treatment temperature will greatly consume the time and economic components of alloy design, and there will be a large amount of human subjectivity. Genetic algorithm is a computational method that simulates the natural evolution process to search for the optimal solution. It can adaptively explore different combinations of a large number of features in the search space to find the optimal solution and has been widely used in various fields, showing the advantages of simplicity, universality, and robustness. The model construction of genetic algorithm mainly includes five steps: encoding and decoding of chromosome, setting of initial population, calculation of fitness function, crossover and mutation, and setting of control parameters. In this study, the GA used binary encoding to convert creep sample data into vectors to establish a mapping from genotype to phenotype, that is, the association of composition and solution temperature to creep life. The population size of the genetic algorithm was set to 40; the probability of chromosome crossover and mutation was 0.2 and 0.9, respectively; and the number of iterations was 500. The 50 optimal prediction models were used as the objective function of the genetic algorithm to predict the creep life of each component process combination scheme, and the optimal solution with the highest creep life was finally output.

3. Results and Discussion

3.1. Feature Analysis Results

Figure 2a shows the magnitude of the correlation between different characteristics and the creep life. The results show that in addition to environmental factors such as temperature and stress, elements such as Ti, Zr, Ni, Y, and Mo have a large Pearson correlation with the creep life, and elements such as Ti, P, Cr, V, and Mn have a large Spearman correlation with the creep life. The absolute value of the correlation coefficient between any two features is less than 1, which means that all features can be considered independent variables. The absolute value of the correlation coefficient between each characteristic phase and the creep life is greater than 0, which indicates that each characteristic has its own contribution to the creep life. Therefore, it is necessary to further analyze the importance of each characteristic on the creep life separately. Figure 2b shows the contribution of different features in the creep life prediction process, and the results show that environmental factors are the most influential factors on the creep life. In addition, elements such as Cr, Ni, and Zr are ranked highly in importance. Ni can stabilize austenite and expand the austenite zone; with the increase in Ni content, it will reduce the residual ferrite of austenite steel and improve its thermodynamic stability, as the formation of NiAl and Ni₃Al is an important reinforcing phase of austenite steel. However, too much Ni will increase the cost of austenitic steel, generally through the synergy of other elements to improve the creep performance and reduce the use of Ni. Cr is a strong carbide-forming element, which generally forms M₂₃C₆ and M₇C₃ carbides in austenitic steel. Al can form a dense Al₂O₃ oxide film on the surface of austenitic steel and promote the precipitation of NiAl phase, thus hindering the dislocation climbing in the matrix and improving the creep resistance of the material. Ti and Mo can protect the Al₂O₃ oxide film of austenitic steel and improve its high temperature strength. V is a strong carbide-forming element, which can promote the precipitation of carbide in austenitic steel. Mn has a strong stabilizing effect on austenitic structures. According to the action mechanism of alloying elements in austenitic steel, the rationality of the characteristic evaluation results is proven.

Further analyzing the correlation between the thermal dynamic information and the creep life based on the calculation of composition and temperature, Figure 3a shows the magnitude of the correlation between different characteristics and the creep life. For the element activity, Pearson and Spearman coefficients simultaneously suggest that the activity of Ti, Cr, Ni, Al, and Nb has a high correlation with the creep life, focusing on the elements that are more important to the creep life of austenitic heat-resistant steel. The evaluation results of the correlation between the elemental activity and creep life are obviously more reasonable than the aforementioned mass percentage. The activity well considers the interaction of different elements in the alloy and the influence with other elements and can directly affect the microstructure of the material, such as the morphology, distribution, and size of the precipitated phase. In addition, elemental activity will change with temperature and time, and creep tests are usually carried out at high temperature and long-time conditions, which are more in line with the actual situation under creep conditions. For the equilibrium volume fraction and precipitation driving force of the precipitated phase, MC (mainly NbC) and M₂₃C₆ (mainly Cr₂₃C₆) have a great correlation with the creep life, and the correlation of the precipitation driving force is greater than that of the volume fraction. This is because the precipitation driving force directly affects the morphology and distribution of the precipitated phase, thus affecting the creep line of the material. For example, too-coarse precipitated phases may cause the material to be prone to deformation at high temperatures, while finely and uniformly distributed precipitated phases can more effectively hinder the movement of dislocations and thus improve the creep life. In addition, physical metallurgical information is used as additional input features to comprehensively consider the contribution of composition, process, creep condition, and physical metallurgical information in the creep life prediction process. Figure 3b shows the top 30 features ranked by importance. The results show that in addition to temperature and stress features, the precipitation driving force of MC and the activity of Cr elements rank high, and the MDA value is much higher than other features. In summary, the introduction of physical metallurgical information makes the analysis results of feature correlation and importance more reasonable and pays attention to the elements and strengthening phases that are more important for creep performance, which is expected to improve the interpretability of the prediction model and the rationality of the alloy design results.

3.2. Creep Life Prediction Results

First, a creep life prediction model with composition, process, and creep conditions as input was established based on different machine learning algorithms. An appropriate dataset partition ratio can help the model show good generalization ability on unknown data, and different partition ratio will affect the efficiency and accuracy of model training. Figure 4a,b show the influence of four different training and test set ratios of 9:1, 8:2, 7:3, and 6:4 on the prediction results of different models. Under the 9:1 partition ratio, the training set accounts for a large proportion, and the model can learn more data features, thereby obtaining higher accuracy. However, the test set has fewer samples at this time, which may not fully reflect the generalization ability of the model, and the evaluation results may have large fluctuations. Therefore, it is necessary to comprehensively balance the prediction accuracy of the model and the data size of the test set to select the data plan division ratio and finally choose the 8:2 division ratio for subsequent processing. Figure 4c,d show the average prediction results of 50 times with different models under 8:2 ratio, and LR shows the lowest prediction accuracy. This is because the creep life is affected by various factors such as composition, process, temperature, and stress, and the relationships between these factors and the creep life are often complex nonlinear relationships. In addition, there are also complex interactions between the features in the creep dataset, for example, the interactions between elements and between temperature and stress. A simple LR model finds it difficult to automatically capture this interactive effect, which indicates that creep life prediction is a complex issue and cannot be easily solved by simple linear fitting. MLP shows the highest prediction accuracy and the lowest prediction error, and its prediction accuracy is 72%, which is significantly better than other models. However, all the models have serious overfitting phenomenon, and further data augmentation is used to improve the performance of the model, that is, the physical metallurgical information, which is closely related to the creep life, is introduced. Figure 5a,b show the influence of different ways of introducing physical metallurgical parameters on the prediction results of the MLP model. The results show that the introduction of physical metallurgical information improves the prediction performance of the model, and the model with the precipitation driving force of the 4D precipitates under creep temperature and solution temperature shows the highest prediction accuracy and the lowest prediction error, respectively. The above characteristic evaluation results prove the importance of physical metallurgical information for creep properties, which can reflect the precipitation behavior of materials to a certain extent. Incorporating this information into the model can help researchers to better understand the microscopic processes happening inside materials and then improve the prediction accuracy of the model for macroscopic properties.

However, due to the small sample characteristics of the dataset and the wide and uneven distribution of the creep life, there is still room for further optimization of the prediction performance of the model. Wang et al. [32] effectively improved the performance of the creep life prediction model by transforming the creep life into a time–temperature parametric form. As mentioned earlier, the time–temperature parameter method is a classical creep life prediction method based on the extrapolation of creep endurance test. It is a phenomenological model and induces the relationship between temperature, stress, and creep fracture time. Among them, Larson–Miller parametric method is the most widely used in engineering, and it expresses time and temperature as functions of stress, as shown in Equation (3):

$$P_{LM}=T\times (C+lg{t}_f)$$

(3)

Here, P_LM is the Larson–Miller parameter, t_f is the creep fracture time, and C is a constant, which is taken as 20 in the reference [30]. The data distribution results shown in Figure 6a,b indicate that after converting the creep life into the Larson–Miller parameter form, the distribution becomes significantly more uniform and closer to a normal distribution. This distribution characteristic reduces the variance of the data, making it more friendly to most statistical models. As a result, the models can more effectively capture the central tendency and dispersion of the data during the training process, which is expected to improve the prediction accuracy of the models. Subsequently, a creep life prediction model was established based on MLP, using composition, process, temperature, stress, and various physical metallurgy parameters as inputs and the Larson–Miller parameter of the creep life as the output. The prediction results in Figure 6c,d and

Table 3. The results of MLP predictions for the creep life and its Larson–Miller parameter form.

	Mean R2 on Testing SET		Mean MAE on Testing Set
	Larson–Miller Parameter of Creep Life	Creep Life	Larson–Miller Parameter of Creep Life	Creep Life
No-PM	0.87621	0.71626	261.94575	421.7419
All-PM	0.82522	0.70756	295.15915	443.88607
DF-ST	0.87038	0.75262	256.38085	385.36843
DF-CT	0.8532	0.76333	265.00241	393.08826
VF-ST	0.84683	0.75743	272.17425	407.02921
VF-CT	0.86487	0.68146	266.81553	448.90497
ACR-ST	0.86778	0.73474	256.91625	404.9212
ACR-CT	0.85705	0.68496	273.37632	426.25956

indicate that converting the creep life into the Larson–Miller parameter form effectively improves the feature distribution of the original data, and the average prediction accuracy of the model has been significantly enhanced.

3.3. Alloy Optimization Results

The MLP prediction model that introduces the driving force for precipitation and takes the Larson–Miller parameter of the creep life as the output is combined with the genetic algorithm to form an alloy design framework (MLP-DF-GA), and the reverse optimization of alloy composition process is carried out at 750 °C/100 MPa. For the calculation of driving force, if the Thermo-Calc software is directly combined with the genetic algorithm for computation, it will perform 40 × 500 × 50 = 10⁶ calculations, which will consume a huge amount of computing time and resources. Considering the computational efficiency of the alloy design process, this study used a machine learning algorithm to establish the prediction model of precipitation driving force under the solution temperature and creep temperature conditions instead of the direct calculation of Thermo-Calc, and the prediction results are shown in Figure 7. The prediction results of precipitation driving force (DF-ST) at solution temperature show that XGBoost, MLP, MLP, and SVR have the highest average prediction accuracy for the MC, M₂₃C₆, Laves, and NbNi₃ phases, respectively. The prediction results of precipitation driving force (DF-CT) at creep temperature show that GBR, XGBoost, SVR, and SVR have the highest average prediction accuracy for the MC, M₂₃C₆, Laves, and NbNi₃ phases, respectively. The machine learning model achieves a good prediction of the precipitation driving force, which can be used in the next step of alloy design. The design results of the alloy at 750 °C/100 MPa are shown in Figure 8. The predicted values of the creep life of the designed samples are better than those of the optimal samples in the original dataset, indicating that the designed samples are expected to improve the creep performance at 750 °C/100 MPa. In addition, there are not only samples with high similarity to the samples in the original dataset, but also samples with high difference in the design sample, which ensures the novelty of the design alloy. Cr and Ni are the most important alloying elements in austenitic heat-resistant steels. An increase in the content of Al can form a continuous and dense Al₂O₃ oxide film on the surface. This not only improves the high-temperature performance but also reduces the dependence on the expensive Cr and Ni. However, the optimized alloy scheme cannot be directly applied, and the significance of this study lies in providing a more efficient alloy design method to guide the actual creep-performance design.

4. Conclusions

In this paper, the research status of the creep life prediction model of austenitic heat-resistant steel based on machine learning is fully investigated, a small sample creep dataset is established based on literature research, and the physical metallurgical information highly related to creep is fully mined. Based on the correlation and importance of characteristics, the correlation degree between different characteristics and the creep life is evaluated. The traditional Larson–Miller parameter method was used to optimize the data distribution, and the square correlation coefficient and mean absolute error were used to evaluate the performance of the machine learning model. The role of different physical and metallurgical information in the model calculation process was analyzed; finally, the optimal model was selected, and the genetic algorithm was used to reverse design the alloy. The main conclusions are as follows:

(1) The feature evaluation results show that the introduction of physical metallurgical information makes the analysis results of feature correlation and importance more reasonable and pays attention to the elements and strengthening phases that are more important for creep performance, which is expected to improve the interpretability of the prediction model and the rationality of the alloy design results.

(2) The model prediction results show that the introduction of physical metallurgical information effectively improves the prediction accuracy and interpretability of machine learning models, and the kinetic information has a more significant effect on improving the performance of the model than the thermodynamic information. In addition, the traditional Larson–Miller parameter concept is used to optimize the distribution of the target performance of the small sample dataset, which further improves the prediction performance of the model.

(3) Considering the computational efficiency of the alloy design process, the machine learning model prediction is used to replace the direct calculation of Thermo-Calc, and the prediction results of precipitation driving force perform well, which further demonstrates the high correlation between the kinetic information and the composition and temperature. In combination with genetic algorithms for the reverse optimization of the alloy composition/process, the designed samples show the potential for high creep properties with some novelty.

(4) This study makes full use of existing experimental data and builds a prediction framework for the creep performance of austenitic heat-resistant steel and an alloy design framework based on artificial intelligence technology and computational material science methods, which to some extent solves the limitations of traditional orthogonal experimental trial-and-error methods and traditional physical models. However, we should also clearly recognize the scarcity of data in the field of material science (including the quality, quantity, and cost of data), which means that there is room for improvement in both our model predictions and alloy design results. Therefore, the focus of this study is to explore the application value of artificial intelligence technology and computational material science methods in alloy design in order to provide new ideas and methods for accelerating alloy design.