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.
In this paper, we propose two metrics, i.e., the optimal repair time and the resilience reduction worth, to measure the criticality of the components of a network system from the perspective of their contribution to system resilience. Specifically, the two metrics quantify: 1) the priority with which a failed component should be repaired and re-installed into the network and 2) the potential loss in the optimal system resilience due to a time delay in the recovery of a failed component, respectively. Given the stochastic nature of disruptive events on infrastructure networks, a Monte Carlo-based method is proposed to generate probability distributions of the two metrics for all of the components of the network; then, a stochastic ranking approach based on the Copeland's pairwise aggregation is used to rank components importance. Numerical results are obtained for the IEEE 30-bus test network and a comparison is made with three classical centrality measures. Critical infrastructure protection (CIP) is envisioned to be one of the most challenging security problems in the coming decade. One key challenge in CIP is the ability to allocate resources, either personnel or cyber, to critical infrastructures with different vulnerability and criticality levels. In this work, a contract- theoretic approach is proposed to solve the problem of resource allocation in critical infrastructure with asymmetric information. A control center (CC) is used to design contracts and offer them to infrastructures' owners. A contract can be seen as an agreement between the CC and infrastructures using which the CC allocates resources and gets rewards in return. Contracts are designed in a way to maximize the CC's benefit and motivate each infrastructure to accept a contract and obtain proper resources for its protection. Infrastructures are defined by both vulnerability levels and criticality levels which are unknown to the CC. Therefore, each infrastructure can claim that it is the most vulnerable or critical to gain more resources. A novel mechanism is developed to handle such an asymmetric information while providing the optimal contract that motivates each infrastructure to reveal its actual type. The necessary and sufficient conditions for such resource allocation contracts under asymmetric information are derived. Simulation results show that the proposed contract-theoretic approach maximizes the CC's utility while ensuring that no infrastructure has an incentive to ask for another contract, despite the lack of exact information at the CC. Abstract This paper proposes a new multi-stage framework to analyze infrastructure resilience. For each stage, a series of resilience-based improvement strategies are highlighted and appropriate correlates of resilience identified, to then be combined for establishing an expected annual resilience metric adequate for both single hazards and concurrent multiple hazard types. Taking the power transmission grid in Harris County, Texas, USA, as a case study, this paper compares an original power grid model with several hypothetical resilience-improved models to quantify their effectiveness at different stages of their response evolution to random hazards and hurricane hazards. Results show that the expected annual resilience is mainly compromised by random hazards due to their higher frequency of occurrence relative to hurricane hazards. In addition, under limited resources, recovery sequences play a crucial role in resilience improvement, while under sufficient availability of resources, deploying redundancy, hardening critical components and ensuring rapid recovery are all effective responses regardless of their ordering. The expected annual resilience of the power grid with all three stage improvements increases 0.034 compared to the original grid. Although the improvement is small in absolute magnitude due to the high reliability of real power grids, it can still save millions of dollars per year as assessed by energy experts. This framework can provide insights to design, maintain, and retrofit resilient infrastructure systems in practice. We consider a cyber-physical system consisting of two interacting networks, i.e., a cyber network overlaying a physical network. It is envisioned that these systems are more vulnerable to attacks since node failures in one network may result in (due to the interdependence) failures in the other network, causing a cascade of failures that would potentially lead to the collapse of the entire infrastructure. The robustness of interdependent systems against this sort of catastrophic failure hinges heavily on the allocation of the (interconnecting) links that connect nodes in one network to nodes in the other network. In this paper, we characterize the optimum inter-link allocation strategy against random attacks in the case where the topology of each individual network is unknown. In particular, we analyze the “regular” allocation strategy that allots exactly the same number of bidirectional internetwork links to all nodes in the system. We show, both analytically and experimentally, that this strategy yields better performance (from a network resilience perspective) compared to all possible strategies, including strategies using random allocation, unidirectional interlinks, etc. Network protection against natural and human-caused hazards has become a topical research theme in engineering and social sciences. This paper focuses on the problem of allocating limited retrofit resources over multiple highway bridges to improve the resilience and robustness of the entire transportation system in question. The main modeling challenges in network retrofit problems are to capture the interdependencies among individual transportation facilities and to cope with the extremely high uncertainty in the decision environment. In this paper, we model the network retrofit problem as a two-stage stochastic programming problem that optimizes a mean-risk objective of the system loss. This formulation hedges well against uncertainty, but also imposes computational challenges due to involvement of integer decision variables and increased dimension of the problem. An efficient algorithm is developed, via extending the well-known L-shaped method using generalized benders decomposition, to efficiently handle the binary integer variables in the first stage and the nonlinear recourse in the second stage of the model formulation. The proposed modeling and solution methods are general and can be applied to other network design problems as well.