PSI - Issue 79

Davide D’Andrea et al. / Procedia Structural Integrity 79 (2026) 283–290

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parameter, exhibits a direct correlation with the output. The magnitude of the Spearman coefficients also reveals that the notch opening angle is the most influential variable, with a coefficient of – 0.71. As each input variable was defined to be mutually independent, no correlation among the input parameters has been detected. By analysing Spearman correlation matrix, it can be noted that dimple insertion in the copper layer gives limited advantages if compared to the angle amplitude.

Figure 3. Spearman correlation matrix.

Once this analysis was done, Random Forest algorithm has been employed to obtain a predictive model of SED ratios output. Random Forest algorithm is a supervised ML algorithm which consists of parallel decision trees processing feature from a train dataset (Parmar et al., (2019)). The dataset available composed by 500 results from the independent analysis performed has been split into train set and test set, respectively consisting of the 80% and 20% of the total dataset (Diao et al., (2022)).

Figure 4. Train and Test subsets division

In Figure 4 this division can be observed. Training subset is represented in blue points, while validation subset is represented in red triangles. Coefficient of determination R 2 and Mean Absolute Error (MAE) have been evaluated by equations (2) and (3), where y i is the i-th result deriving from FEM simulations, y î is the i-th predicted value obtained by Random Forest algorithm, y̅ is the average value calculated over the entire test subset composed by n samples.