PSI - Issue 46

Nithin Konda et al. / Procedia Structural Integrity 46 (2023) 87–93 Nithin Konda et al. / Structural Integrity Procedia 00 (2019) 000–000

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1. When the R2 score for train data is higher and incomparable with R2 score of test data, then the model is said to be overfitting, whereas if the R2 score for test data is higher and incomparable with train data, then the model is said to be under fitting. So, the R2 scores of both the train and the test data should be almost similar and comparable. The performance metrics are plotted with respect to the algorithms used to understand which of the algorithms performed better on this fatigue dataset of Ti6Al4V alloy. The performance metrics obtained are shown in Table 5 and the plots, Fig.1(a-c) are shown below:

Fig. 1. (a) MSE and MAE Compared for RF and XGB; (b) Test and Train R 2 scores are compared for RF; (c) Test and Train R 2 scores are compared for XGB.

Table 5. Performance Metrics Metric R2 Score for Test data using RF R2 Score for Train Data using RF R2 score for Test data using XGB

Value

0.76 0.78 0.83 0.82 0.38 0.27 0.56 0.44

R2 score for Train data using XGB Mean squared error for test data using RF Mean squared error for test data using XGB Mean Absolute error for test data using RF Mean Absolute error for test data using XGB

By looking at the above figures and table, it is clear that mean squared error, mean absolute error are smaller and R2 score for train and test dataset is higher for XGB algorithm which makes it superior for this dataset. Since the residuals of the preceding regression tree are trained to the succeeding regression tree, the residuals are shrinking to zero, due to which the patterns in the data are identified. However, there is higher chance of overfitting when higher number of trees are trained. In this case, R2 score for both the test and train data set are comparable from Figure 1(c) hence model is not overfitted. For both the algorithms, R2 scores for train and test datasets are similar and R2 scores of XGB are slightly higher than RF, which indicates that XGB is performing better.