Probabilistic Seismic Risk Assessment of Lifeline Networks Using Cross-entropy- Based Adaptive Importance Sampling

Because of its complexity, reliability analysis of lifeline-network usually employs a sampling-based approach. MonteCarlo simulation (MCS) provides a straightforward method to deal with interdependence between structural components and their cascading failures in the lifeline network system, but its computational cost might be expensive if the probability of the event of interest is too low. To overcome this issue, an adaptive importance sampling (AIS) method was recently developed to identify a near-optimal sampling density by minimizing Kullback–Leibler cross entropy (CE) measuring the difference between the best importance sampling (IS) density and the sampling density model in use. This cross-entropy-based adaptive importance sampling (CE-AIS) drastically improves efficiency of MCS by using the near-optimal sampling density. To facilitate its applications to probabilistic seismic risk assessment (PSRA) for lifeline-network, we propose a sophisticated sampling technique which is suitable to evaluate the probabilities of multiple network performance states caused by earthquake. The proposed method does not rely on any heuristic intuition to perform importance sampling, and concurrently obtains the probabilities of multiple post-disaster consequences of the lifeline network in a way that they converge in a speedy manner. The results of the numerical example demonstrate that our approach, termed as CE-based “concurrent” AIS (CE-CAIS) make the probabilities of multiple system events converge to the exact values evenly well in terms of the level of coefficients of variation of the estimates. The proposed method is expected to be useful for a variety of hazard risk assessment for complex systems and provide new insights into the simulation-based PSRA.