Reliability analysis for structures with topological variations induced by geometric uncertainty through segmented regression

• Geometric uncertainty can cause variations in structural topological configurations. • A segmented regression-assisted reliability analysis scheme is proposed. • Reliability analysis for structures with topological changes is fully investigated. • Segmented regression is extended to multi-segment, multi-variable, nonlinear tasks. This research addresses a class of practice-driven problems where geometric uncertainty induces discrete topological changes, producing non-smooth or discontinuous response surfaces. Representative scenarios include additively manufactured materials with tolerance-induced changes in strut connectivity, porous biomedical scaffolds with altered pore networks, cracked or perforated plates crossing predefined geometric thresholds, and deployment mechanisms such as folded satellite antennas, origami-inspired devices, or morphing wings with configuration transitions. In many of these cases, the boundaries between topological configurations can be predicted a priori from measurable geometric criteria. To mitigate the adverse impact of such discontinuities on surrogate modelling accuracy, we propose a Segmented Extended Support Vector Regression (Seg-X-SVR) framework. This method embeds physical insights to predefine segmentation boundaries and, within each segment, formulates and solves a convex optimization problem to construct accurate surrogate models. By bypassing repeated calls to computationally expensive physical models, the framework enables efficient large-scale sampling for structural reliability analysis under geometric uncertainty. It is broadly applicable across engineering domains, accommodates diverse uncertainty models, and provides rich statistical information on quantities of interest.