Probabilistic vehicle speed prediction and reliability-based design optimization of mountainous freeway renovation using Transformer and active learning surrogates.

Accurate characterization of vehicle speed distributions is essential for evaluating driving safety and supporting reliability-based geometric design of mountainous freeways. Conventional deterministic approaches based on design speed fail to capture the variability of driver behavior under complex road and terrain conditions, leading to insufficient safety margins. This study proposes a reliability-based design optimization (RBDO) framework that integrates probabilistic vehicle speed prediction with safety-oriented geometric design when freeway plans to be renovated. A Transformer-based architecture is developed to establish the mapping between freeway alignment and affiliated facilities and vehicle speed distributions, enabling accurate probabilistic characterization of driving behavior. Driving safety reliability is quantified through three indicators-lateral stability, speed harmonization, and stopping sight distance sufficiency-formulated as stochastic limit state functions. To balance safety and renovation cost, the RBDO problem is solved using an active learning Kriging surrogate model, which enhances computational efficiency while maintaining accuracy. Numerical experiments on a typical mountainous freeway demonstrate that the proposed approach outperforms conventional regression and recurrent models in capturing multimodal speed distributions, and that modest adjustments to longitudinal slopes and curve radii can substantially improve driving safety reliability with limited renovation costs. The findings highlight the potential of combining deep learning and surrogate-based RBDO to support data-driven, safety-oriented design optimization of transportation infrastructure.