Graph Model for Probabilistic Resilience and Recovery Planning of Multi-Infrastructure Systems

Indirect consequences to shocks and stresses are mounting globally. Estimating and developing plans to treat these risks remains a challenge. The difficulty is determining ahead of time how the losses, and the potential resolutions, might propagate through the interactions of complex connected systems of systems when generally only high-level temporal statistics are available. In this paper, a novel graph model coupled with a maximum entropy likelihood estimator are proposed to map the complex interactions and to assess the statistics resulting from different initiating scenarios. The method involves defining initial conditions from all-hazards effects, followed by generation of event sequences from the high-level statistics, to estimate probabilities of different outcomes after a shock or stress. In this way, a general method is devised to assess indirect consequence in operational loss terms and to assess the merits of risk treatment options. Incorporating these indirect consequence calculations with direct consequence assessments provides a way to support a balance of treatment of these forms of consequence in a multiobjective fashion.