Multivariate Seismic Fragility Analysis of Curved Rocking Bridges Using Active Learning‐Enhanced Surrogate Modeling

ABSTRACT Curved bridges with rocking piers offer enhanced seismic resilience but introduce complex interactions among horizontal curvature, bidirectional ground motion, and nonlinear rocking mechanisms, making traditional univariate fragility models insufficient. To address these challenges, the proposed method integrates active learning with Natural Gradient Boosting (AL‐NGB) to construct data‐efficient surrogate models for seismic demand estimation under high‐dimensional uncertainty. A comprehensive dataset comprising 2000 curved rocking bridge models and scaled ground motions is developed to train and validate the surrogate framework. Feature selection via feature importance and correlation analysis identifies S d ,T1 and FI as dominant intensity measures for predicting the average responses of the pier, bearing, shear key, and abutment, which are adopted as the engineering demand parameters. The AL‐NGB framework achieves comparable accuracy to full‐data models using only 10% of the training samples, significantly reducing computational cost. Fragility analyses reveal that system‐level seismic vulnerability of curved rocking bridges is strongly governed by critical components (e.g., shear keys) and is highly sensitive to the directionality of seismic excitation highlighting the need for direction‐aware design. This study demonstrates the potential of combining active learning with probabilistic machine learning for data‐efficient and high‐fidelity seismic risk assessment of complex bridge systems.