PSI - Issue 78

Mirko Calò et al. / Procedia Structural Integrity 78 (2026) 710–717

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AvgSa is the most influential parameter, and higher values (in yellow) are more likely to induce failure, as well as for increasing of the parameter associated with SDL. Longitudinal and transverse reinforcement ratios, ρ L and ρ T respectively, both enhancing flexural capacity of the pier and concrete confinement, contribute to greater energy dissipation resulting in a lower probability of predicting the failure class.

Fig. 2. Description of the trained XGBoost algorithm: (a) Summary of model performance including confusion matrix (Boolean variable here nd atedas1 r“Tr e”and0 r“ alse”, re s n -recall curve, classification metrics (precision, recall, and F1-score), and F1-score as a function of the decision threshold (red dashed line). The optimal threshold was selected as the one maximizing the F1-score; (b) Summary plot reporting input features and related SHAP value (colormap refers to the normalized feature value) considering 10% samples from test set.

Fig. 3. Comparison of average fragility curves between XGBoost algorithm (blue line) and CSM analysis (red line) for different taxonomy branches. μ is the AvgSa level associated with 50% probability of failure.

Results about the application of XGBoost to the taxonomy branches are shown in Fig. 3 and Fig. 4. Before discussing its potential, it is worth noting that the average fragility curves of taxonomic branches derived from XGBoost predictions are very close to those obtained with CSM analysis method, Fig. 3. The fragility curves derived from XGBoost lead to underestimating the AvgSa value associated to a 50% probability of failure, μ , with a difference between 4% (45-80/NS/HS/S) and 7% (80-03/NS/SS/M). These results are related to the use of recall as evaluation metrics in the grid search approach for the hyperparameter tuning and to the calibrated internal threshold. Looking at the results in Fig. 4, the trained XGBoost algorithm allows exploring the influence of independent variables, and a comparison between slender and squat pier is shown in Fig. 4. Referring to μ values ( AvgSa level associated with 50% probability of failure) of 03/S/SS typologies, a slender pier (high H pier / D pier ratios) belonging characterized by a low (L) SDL should be investigated before a squat one (low H pier / D pier ratios) with a medium (M) SDL, Fig. 4(b). On the other hand, a less variability of μ is registered for 45-80/NS/LS typologies, suggesting that the SDL plays a crucial role for this bridge typology regardless of the ratio between H pier and D pier .