# Ultra-High-Cycle Fatigue Life Prediction of Metallic Materials Based on Machine Learning
## 4 Model Evaluation and Comparison
### Evaluation of Model Generalization Ability  
Ultrasonic fatigue tests were performed on GCr15-bearing steel to obtain its fatigue life. The experimentally obtained fatigue lifetimes were then compared with the predicted values to evaluate the generalization abilities of the models. From Figure 1, the S-N curves of GCr15-bearing steel contained five stress levels and its fatigue life was distributed between 10\({}^{4}\) and 10\({}^{8}\) with a total of 12 data points.  
All data in the database were used for model training, and fatigue life prediction was then performed for GCr15 bearing steel. It was found that the predicted life fluctuated greatly. For example, in some cases, the values of R\({}^{2}\) were close to zero, indicating that the models had a certain degree of degradation in their fatigue life prediction ability for new materials. It is already pointed out that training dataset size could significantly affect model accuracy. [PERSON] et al. (2017), in their study on fatigue life prediction under average stress using the RF algorithm and limited learning, also found that prediction ability was significantly improved when local or global similarities were involved between the new material and the material in the training. Therefore, three new experimental datasets of GCr15-bearing steel were added to the training database to expand the training dataset and introduce local similarities. The input parameters of GCr15-bearing steel are listed in Table 3. Ten fatigue life outputs were performed for each stress level, and the output  
With the addition of the three new experimental datasets of GCr15-bearing steel to the training database, the value of R\({}^{2}\) did not appear close to zero, improving the prediction capability of the models. The GB model had only one data point outside the triple error bands, whereas the RF model had only three data points within the triple error bands. The prediction accuracy of the GB model was better than that of the RF model. However, the RF model had better prediction stability than the GB model. Figure 8 compares the fatigue life prediction abilities of the two models for GCr15 bearing steel under 450 MPa for ten times, and it is noticeable that the GB model had two flaw points, whereas the prediction results of the RF model did not have large deviations. Figure 7 reveals that both models had a conservative tendency in making predictions for lifetimes above 10\({}^{7}\) cycles. With the introduction of local similarities, both models could make good predictions for the fatigue life of new materials and maintain their respective advantages. Table 4 presents the relative errors of the predicted and experimental values. The relative error of RF model is larger than GB.  
Therefore, it can be inferred that the prediction ability of the two models for new materials was largely limited by the training database. With the introduction of local similarities, the prediction ability of the models was significantly improved. It is certain that with the progress of ultrasonic fatigue research, more materials will be added to the database and similarities between materials to be predicted and training materials will be further improved.