Cross-Entropy-based Stationary Proposal Importance Sampling for life-cycle structural reliability and seismic risk assessment

Life-cycle reliability assessment of deteriorating systems may involve the modeling of complex stochastic processes, further propagating uncertainties and exacerbating computational efforts. This paper discusses a novel simulation-based framework to estimate the time-variant failure probabilities based on Importance Sampling (IS) with Stationary Proposal (SP) distribution. IS methodologies allow to improve computational efficiency and estimate accuracy of simulation-based failure probabilities. The proposed methodology extends adaptive numerical approaches traditionally developed for time-invariant problems, in which the Kullback–Leibler Cross-Entropy is minimized to find a near-optimal simulation density from a chosen family of parametric distributions. The proposed framework is applied to typical reliability problems extended to account for a life-cycle perspective and time-variant seismic risk of deteriorating bridge networks.