Optimization of reinforced concrete bridge girders using reliability-based design and active learning to ensure long-term serviceability

Abstract Bridges play a critical role in ensuring the safe and continuous movement of people and goods, making their structural integrity over time a key concern in civil engineering. This study introduces a novel two-stage Reliability-Based Design Optimization (RBDO) approach for optimizing the cross-sectional dimensions of reinforced concrete bridge girders at the end of their service life. The method explicitly accounts for key time-dependent degradation mechanisms-creep, shrinkage, corrosion, and traffic growth-often neglected or treated in isolation in prior research. The first stage involves a deterministic optimization to provide a cost-effective initial design. The second stage applies an active learning-based RBDO using a hybrid surrogate model that combines artificial neural networks (ANN), radial basis functions (RBF), and support vector regression (SVR). This adaptive strategy significantly reduces the number of full-model evaluations required to estimate failure probabilities, ensuring both computational efficiency and accuracy. Validation against benchmark problems confirms the robustness of the proposed framework in terms of both reliability estimation and optimization. When applied to a real bridge case, the method achieved convergence in only 11 deterministic and 15 RBDO iterations, resulting in a 47% reduction in computational cost compared to a standard Adaptive Kriging Monte Carlo Simulation (AK-MCS)-based approach. Overall, the proposed methodology enables a more realistic, economical, and computationally efficient design of bridge structures over their entire lifespan.