PSI - Issue 78

Gianluca Quinci et al. / Procedia Structural Integrity 78 (2026) 845–851

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4. Machine Learning Implementation and Model Evaluation Following the methodological framework presented earlier, a dataset was assembled using the results of nonlinear static analyses performed on 25 distinct bridge configurations. Each configuration was described using a set of four structural descriptors: total bridge mass, pier height, and the longitudinal reinforcement areas in the upper and lower regions of the pier cross-section. These features were selected based on their relevance to seismic behavior, as they capture the most significant geometric and mechanical aspects influencing the structural response. For each bridge, fragility parameters, namely, the ultimate displacement capacity (d u ), the dispersion coefficient ( β), and the median capacity (μ), were derived from the pushover results using the Cloud Analysis approach previously described (Section 2). Considering the limited size of the available dataset, particular attention was paid to selecting Machine Learning (ML) algorithms that are effective in low-data regimes while being capable of modeling nonlinear relationships. The following five supervised regression models were tested: • 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 model was independently trained to predict one of the fragility curve parameters (μ, β, or d u ) using the geometric inputs described above. To illustrate model behavior, the prediction of the dispersion parameter β is presented as a representative case. The parity plot in Figure 1 compares the predicted values of β to those obtained from the reference cloud analysis.

Fig. 1. Comparison of trained ML models for deriving the β parameter