Beyond Monte Carlo: Analytic Manifold Integration for Time‑Dependent Structural Reliability via Exponential Improper Integrals

Abstract

Traditional structural reliability assessments rely heavily on Monte Carlo simulations (MCS), which often act as black-box estimators for rare-event probabilities while providing limited insight into the geometry of uncertainty and incurring substantial computational cost. This paper proposes Analytic Manifold Integration (AMI), a framework that recasts uncertainty as a geometric failure volume defined by exponential limit-state forms and evaluated through closed-form improper integrals. The approach yields an exact expression for the tail integral via the complementary error function, enabling deterministic assessment of time-dependent reliability when structural resistance degrades over time.