Cross-Entropy-Based Adaptive Concurrent Importance Sampling for Probabilistic Seismic Loss Analysis of Spatially Distributed Multistate Systems

Spatially distributed infrastructure systems are crucial assets of a community, and thus assessing their risk under seismic hazards is essential. These assessments should be system-wide, regional, and probabilistic to provide comprehensive insights for decision-makers. Monte Carlo simulation is often used owing to its straightforward application but can be computationally inefficient for rare, high-impact events. While importance sampling can improve computational efficiency by focusing on significant outcomes, it may struggle with computing multiple probabilities simultaneously as it is usually optimized for single-event scenarios. To address these issues, we propose a novel approach termed cross-entropy-based “concurrent” adaptive importance sampling (CE-CAIS). This method efficiently samples multistate systems by concurrently estimating multiple system failure probabilities using a single near-optimal importance sampling density. The effectiveness of CE-CAIS is demonstrated using the Sioux Falls traffic network example consisting of 11 system states and a large-scale regional analysis. In the latter, dimensionality reduction techniques, such as principal component analysis, and the central limit theorem are additionally employed to assess the loss of Shelby County, Tennessee, which includes 305,694 buildings. These results highlight the potential of CE-CAIS in risk assessment of complex systems, paving the way for more effective and scalable approaches to evaluating regional impacts of seismic hazards on spatially distributed infrastructure systems.