Surrogate-assisted design optimization of cable-stayed bridges with dynamic trust threshold-based active learning

The design optimization of cable-stayed bridges (DOC) is particularly challenging due to the involvement of prestress variables, which strongly couple with structural parameters and exhibit high sensitivity in constraint verification. These characteristics make it difficult for conventional optimization frameworks to efficiently identify reliable preliminary design schemes, while the high computational cost of repeated prestress tuning further limits practical applicability. To address this challenge, this paper proposes a dynamic trust-threshold-based active learning strategy (DGPR) within a surrogate-assisted decoupled optimization framework. The decoupled framework transforms the original problem into sub-problems with reduced cross-variable nonlinearity, while the surrogate model alleviates the computational burden introduced by the decoupling. A novel trust-based active learning strategy is then introduced: trusted predictions are directly passed to the subsequent finite element analysis, whereas cable force optimization by direct finite element analyses is performed for distrusted ones. The new samples obtained from these high-fidelity evaluations are then used to update the surrogate model. The proposed dynamic trust threshold combines bending strain energy, prediction uncertainty, and a relaxation function to incorporate both physical and stochastic information. The proposed DGPR framework is tested through three cases with an increasing number of design variables and more restrictive constraints: a benchmark function, a 20-m cable-stayed cantilever, and an 818-m three-span cable-stayed bridge. The results demonstrate that the proposed framework can efficiently optimize structural parameters and prestress designs, significantly reducing computational cost and trial-and-error efforts while maintaining high reliability. These features make the proposed method a practical and useful tool for bridge engineers, especially at the preliminary design stages of cable-stayed bridges.