Resilient critical infrastructure: Bayesian network analysis and contract-Based optimization

Instilling resilience in critical infrastructure (CI) such as dams or power grids is a major challenge for tomorrow’s cities and communities. Resilience, here, pertains to a CI’s ability to adapt or rapidly recover from disruptive events. In this paper, the problem of optimizing and managing the resilience of CIs is studied. In particular, a comprehensive two-fold framework is proposed to improve CI resilience by considering both the individual CIs and their collective contribution to an entire system of multiple CIs. To this end, a novel analytical resilience index is proposed to measure the effect of each CI’s physical components on its probability of failure. In particular, a Markov chain defining each CI’s performance state and a Bayesian network modeling the probability of failure are introduced to infer each CI’s resilience index. Then, to maximize the resilience of a system of CIs, a novel approach for allocating resources, such as drones or maintenance personnel, is proposed. In particular, a comprehensive resource allocation framework, based on the tools of contract theory, is proposed enabling the system operator to optimally allocate resources, such as, redundant components or monitoring devices to each individual CI based on its economic contribution to the entire system. The optimal solution of the contract-based resilience resource allocation problem is analytically derived using dynamic programming. The proposed framework is then evaluated using a case study pertaining to hydropower dams and their interdependence to the power grid. Simulation results, within the case study, show that the system operator can economically benefit from allocating the resources while dams have a 60% average improvement over their initial resilience indices.