Uncertainty propagation in risk and resilience analysis of hierarchical systems

A novel formulation is proposed for uncertainty propagation in risk and resilience analysis of hierarchical systems. The main challenges are related to the complexity of hierarchical systems’ computational workflow and high-dimensional probability space. The computational workflow in regional risk and resilience analysis consists of many interconnected sub-models to predict future hazards, the reliability and functionality of physical systems, and the recovery of disrupted services. The complexity of the computational workflow limits the number of model evaluations for uncertainty propagation. In contrast, the computational workflow contains many sources of uncertainty that demand extensive model evaluations to accurately estimate their effects. The proposed formulation in this paper consists of a multi-level uncertainty propagation approach to reduce the problem dimensionality and a variables-grouping approach to reduce the number of model evaluations. The idea of the multi-level uncertainty propagation is to break down the high-dimensional problem into several low-dimensional ones, one for each level of the hierarchy in the computational workflow. The proposed variables-grouping approach provides an adaptive refinement of uncertainty propagation to identify the influential uncertain input data and computational sub-models. The paper illustrates the proposed formulation through a well-known academic problem and regional risk and resilience analysis of a community.