Heteroscedastic Gaussian process regression for the robust design of precast prestressed concrete beams

Abstract

Long-span precast prestressed concrete girders are susceptible to lateral instability during temporary phases such as lifting, transport and placement on bearings. As spans have increased, failures have occurred, driven by initial imperfections from fabrication tolerances, creep, shrinkage and thermal effects. This paper presents a robust optimisation framework that combines a model of hanging beam stability with a most likely heteroscedastic Gaussian process surrogate to identify minimum-weight cross-sections satisfying a probabilistic stress constraint under geometric and material uncertainty. The surrogate learns both the mean stress response and its input-dependent variance, and the resulting optima are validated against Monte Carlo solutions. Decomposing uncertainty into epistemic and aleatoric components distinguishes regions of the design space where the surrogate lacks training data from those where the structural response is inherently sensitive to parameter variability, indicating where additional data or design margin is most required. Results show that the area premium associated with a high target reliability is modest.