PSI - Issue 84

Marianna Crognale et al. / Procedia Structural Integrity 84 (2026) 898–905

902

Fig. 3. Moment–curvature responses of the pier section corresponding to different combinations of concrete and steel degradation levels.

3. Machine–Learning Surrogates for Degradation Prediction The fiber-section dataset described in Section 2.3 is used to train machine-learning (ML) surrogates that approximate the degradation of stiffness and strength in reinforced-concrete pier sections. The objective is to replace repeated fiber-based simulations with fast, data-driven predictions while preserving the underlying physical trends observed in nonlinear section analyses. Two degradation indicators are defined based on the moment–curvature response: ( )= ( ) 0 , ( )= ( ) 0 where sec is the secant stiffness at ductility , is the resisting moment, and subscript u and 0 denote the ultimate and undegraded reference state, respectively. Each data sample is characterized by physically meaningful input features, including material degradation levels, axial load, and curvature (or equivalent ductility). Tree-based regression models (XGBoost) are adopted due to their accuracy, robustness, and efficiency in handling nonlinear relationships in tabular structural data. In detail, XGBoost (eXtreme Gradient Boosting) is a highly efficient, scalable implementation of gradient boosted decision trees (GBDT): for regression tasks, it predicts a continuous numerical target by combining an ensemble of weak learners (typically shallow decision trees) into a single strong predictor (Chen and Guestrin, 2016). The trained surrogates reproduce the fiber-based moment–curvature response with high fidelity across the considered degradation scenarios and axial load levels. Prediction accuracy is assessed using standard regression metrics, indicating that the ML models provide reliable approximations of stiffness and strength degradation over the relevant deformation range. Fig. 4 shows a fiber-computed versus ML-predicted moment degradation factor as a function of curvature for a representative degraded pier section (C2–S0, =15 MN). Table 2 shows the obtained R² (Coefficient of Determination) and MAE (Mean Absolute Error) , where the first measures how well a model explains the variance of the target variable (it ranges from minus infinity to 1, where higher values indicate better model fit and a value of 1 means the model perfectly explains the data), and the second measures the average absolute difference between predicted and actual values (and it is expressed in the same units as the target variable, with lower values indicating better predictive accuracy). The close agreement demonstrates the ability of the trained surrogate to reproduce section level degradation laws conditioned on material state and axial load.