# Machine Learning-Based Framework for Predicting Creep Rupture Life of Modified 9 Cr-1 Mo Steel
## 3 Results and Discussion  
### Feature Screening Results  
Figure 3 displays the heat map of the Pearson correlation coefficient of all variables in the current dataset. Yellow indicates the positive correlation between features, while blue represents the negative correlation. It is clear that there is a significant nonlinear link between features because the correlation coefficient between any two features is always less than 0.95. This indicates that all the features in the current dataset can be considered independent variables. Consequently, it is reasonable and necessary to examine the effect and importance of each feature on creep rupture life. Using a game-theoretic method known as the SHAP value, the individual contribution of each feature to the prediction of the model is revealed. The global effects of the features are shown in a bar plot, as can be seen in Figure 4a. The features are ordered from highest to lowest importance according to the absolute mean SHAP value. On the other hand, the local feature contribution for each sample is depicted by the beeswarm plot, as shown in Figure 4b. Each data point in this plot corresponds to a single observation in the dataset, and it is colored either in red or blue according to the feature value. Positive SHAP valuesindicate that the creep life is increased because of the feature value, while negative SHAP values suggest a negative influence. As expected, the test stress is shown to be the most crucial feature. The feature value of the test stress is high when the SHAP value is smaller than 0. This indicates that the stress with a high value corresponds to a lower predicted creep rupture life, whereas higher creep life can be obtained by applying lower stress. The second important feature is the test temperature, followed by the tempering time and S content. Higher values of these features also tend to negatively contribute to the creep rupture life. These key features also exhibit strong Pearson correlation coefficient values with creep life, as shown in Figure 3, indicating the compatibility of SHAP and correlation analysis. In addition, other features including the material form have a negligible contribution to the creep life because the SHAP values are distributed near 0, whether their values are high or low. Figure 5 shows the results of sequential forward selection with the aid of GPR and SVR models. As the selection process proceeds, the GPR model achieves the highest \(R^{2}\) and lowest \(RMSE\) when there are five features. The error values also  
Figure 4: Results of SHAP value: (**a**) Importance of input features, and (**b**) summary plot of SHAP value. Figure 3: Heat map of the Pearson correlation coefficient. five-feature SVR model, as shown in Figure 5b. These facts show that selecting more than five features has a negligible impact on the predicted creep rupture life. Additionally, it can be seen in Figure 5b that there is a clear rise in error when the SVR model is trained using more than eleven features, demonstrating that the addition of redundant features has a detrimental effect on modeling accuracy. Therefore, feature screening must be conducted before a machine learning model is trained and validated in order to improve the robustness of the model. The test stress, test temperature, tempering time, and the contents of S and Cr are determined as the five crucial features in order of the contribution of each feature to the model. According to Figure 4a, the importance of test stress and test temperature is about five times greater than that of tempering time, which is ranked third. This shows that environmental factors should be given far more attention in creep-oriented alloy design because they are substantially more significant than alloy constituents and processing conditions. The tempering time is the third most important feature, and a higher value has a negative impact on creep rupture life, as shown in Figure 4b.