PSI - Issue 84

Gianluca Quinci et al. / Procedia Structural Integrity 84 (2026) 199–206

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As a final outcome, the trained ML regressors were able to estimate the bridge-specific seismic fragility characteristics μ, β, and d_u directly from structural features, supporting efficient preliminary screening of seismic vulnerability across extended bridge networks. 4. Machine Learning Implementation and Model Evaluation Building on the methodological workflow described in the previous sections, a dedicated dataset was created from the outcomes of nonlinear static analyses carried out on 25 different bridge configurations. Each bridge was represented through four key descriptors: the overall bridge mass, the pier height, and the longitudinal reinforcement areas located in the top and bottom portions of the pier section. These variables were intentionally selected because they condense the most influential geometric and mechanical characteristics governing seismic response, thereby providing a compact yet meaningful description of the structural system. For every bridge configuration, the parameters required to define fragility behavior—namely the ultimate displacement capacity d u , the dispersion term β, and the median capacity μ —were extracted from pushover-based results using the Cloud Analysis procedure previously introduced (Section 2). Given the limited number of available samples, the ML stage focused on supervised regression techniques known to perform reliably in low-data settings and, at the same time, able to capture nonlinear dependencies between inputs and targets. Five models were therefore investigated: • Linear Regression – used as a baseline to identify potential linear trends in the data, Maulud et al. 2020; • Decision Tree Regression – effective for capturing nonlinear behavior through recursive feature space partitioning, and robust with small datasets Somvanshi et al. 2016; • Support Vector Regression (SVR) – well suited to small sample sizes and high-dimensional feature spaces, offering good generalization, Smola et al. 2004; • Gaussian Process Regression (GPR) – a non-parametric Bayesian model ideal for small datasets, with built-in uncertainty estimation, Rasmussen et al. 2006; • Random Forest Regression – an ensemble method aggregating multiple decision trees to improve accuracy and reduce overfitting Breiman et al. 2001. Each algorithm was trained separately to predict one fragility parameter at a time (μ, β, or d u ), using the four structural descriptors as inputs. To provide a clear example of model performance, the dispersion coefficient β is discussed as a representative output. Figure 1 shows the parity plot comparing predicted β values against those computed from the reference cloud analysis. Among the evaluated regressors, Gaussian Process Regression achieved the highest predictive performance, with a determination coefficient of R² = 0.82, which indicates a strong agreement between estimates and targets and highlights the ability of GPR to learn effectively from sparse information while maintaining stability and accuracy. For brevity, Table 1 summarizes the best-performing model identified for each fragility parameter. In all three cases, GPR delivered the top results, consistently outperforming the remaining methods in terms of robustness and generalization. To further assess practical usability, the fragility curve estimated via GPR for a previously unseen bridge (excluded from the training set) was compared with a reference curve derived from a full nonlinear time-history analysis. The comparison in Figure 2 shows a close correspondence between the two functions, with a mean absolute error (MAE) below 2% over the investigated PGA interval. This level of agreement suggests that, while approximate by construction, the proposed ML-based procedure can provide sufficient accuracy for early-stage seismic risk screening. In particular, it enables fragility curves to be generated rapidly over large inventories, substantially reducing computational demand and supporting network-level prioritization and decision-making.