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1. Quantifying the Interdependency Strength Across Critical Infrastructure Systems Using A Dynamic Network Flow Redistribution Model.

   Wang, Y.; Yu, J.; Baroud, H. (July 2020, Proceedings of the 30th European Safety and Reliability Conference and 15th Probabilistic Safety Assessment and Management Conference.)

   Baraldi, P.; null; Zio, E. (Ed.)

   Critical infrastructure networks are becoming increasingly interdependent which adversely impacts their performance through the cascading effect of initial failures. Failing to account for these complex interactions could lead to an underestimation of the vulnerability of interdependent critical infrastructure (ICI). The goal of this research is to assess how important interdependent links are by evaluating the interdependency strength using a dynamic network flow redistribution model which accounts for the dynamic and uncertain aspects of interdependencies. Specifically, a vulnerability analysis is performed considering two scenarios, one with interdependent links and the other without interdependent links. The initial failure is set to be the same under both scenarios. Cascading failure is modeled through a flow redistribution until the entire system reaches a stable state in which cascading failure no longer occurs. The unmet demand of the networks at the stable state over the initial demand is defined as the vulnerability. The difference between the vulnerability of each network under these two scenarios is used as the metric to quantify interdependency strength. A case study of a real power-water-gas system subject to earthquake risk is conducted to illustrate the proposed method. Uncertainty is incorporated by considering failure probability using Monte Carlo simulation. By varying the location and magnitude of earthquake disruptions, we show that interdependency strength is determined not only by the topology and flow of ICIs but also the characteristics of the disruptions. This compound system-disruption effect on interdependency strength can inform the design, assessment, and restoration of ICIs. 

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2. N-k Interdiction Modeling for Natural Gas Networks

   Ahumada-Paras, Mareldi; Sundar, Kaarthik; Bent, Russel; Zlotnik, Anatoly (January 2020, 21st Power Systems Computation Conference (PSCC))

   Although electricity transmission systems are typically very robust, the impacts that arise when they are disrupted motivate methods for analyzing outage risk. For example, N-k interdiction models were developed to characterize disruptions by identifying the sets of k power system components whose failure results in “worst case” outages. While such models have advanced considerably, they generally neglect how failures outside the power system can cause large-scale outages. Specifically, failures in natural gas pipeline networks that provide fuel for gas-fired generators can affect the function of the power grid. In this study, we extend N-k interdiction modeling to gas pipeline networks. We use recently developed convex relaxations for natural gas flow equations to yield tractable formulations for identifying sets of k components whose failure can cause curtailment of natural gas delivery. We then present a novel cutting-plane algorithm to solve these problems. Finally, we use test instances to analyze the performance of the approach in conjunction with simulations of outage effects on electrical power grids. 

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3. Power Grid Cascading Failure Prediction Based on Transformer

   https://doi.org/10.1007/978-3-030-91434-9_15  

   Zhou, Tianxin; Li, Xiang; Lu, Haibing (December 2021, Lecture notes in computer science)

   Smart grids can be vulnerable to attacks and accidents, and any initial failures in smart grids can grow to a large blackout because of cascading failure. Because of the importance of smart grids in modern society, it is crucial to protect them against cascading failures. Simulation of cascading failures can help identify the most vulnerable transmission lines and guide prioritization in protection planning, hence, it is an effective approach to protect smart grids from cascading failures. However, due to the enormous number of ways that the smart grids may fail initially, it is infeasible to simulate cascading failures at a large scale nor identify the most vulnerable lines efficiently. In this paper, we aim at 1) developing a method to run cascading failure simulations at scale and 2) building simplified, diffusion based cascading failure models to support efficient and theoretically bounded identification of most vulnerable lines. The goals are achieved by first constructing a novel connection between cascading failures and natural languages, and then adapting the powerful transformer model in NLP to learn from cascading failure data. Our trained transformer models have good accuracy in predicting the total number of failed lines in a cascade and identifying the most vulnerable lines. We also constructed independent cascade (IC) diffusion models based on the attention matrices of the transformer models, to support efficient vulnerability analysis with performance bounds. 

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4. A Principal-Agent Model of Systems Engineering Processes with Application to Satellite Design

   Safarkhani, Salar; Kattakuri, Vikranth; Bilionis, I.; Panchal, Jitesh H. (July 2018, Council of Engineering Systems Universities (CESUN) Global Conference)

   We present a principal-agent model of a one-shot, shallow, systems engineering process. The process is "one-shot" in the sense that decisions are made during a one-time step and that they are final. The term "shallow" refers to a one-layer hierarchy of the process. Specifically, we assume that the systems engineer has already decomposed the problem in subsystems and that each subsystem is assigned to a different subsystem engineer. Each subsystem engineer works independently to maximize their own expected payoff. The goal of the systems engineer is to maximize the system-level payoff by incentivizing the subsystem engineers. We restrict our attention to requirements-based system-level payoffs, i.e., the systems engineer makes a profit only if all the design requirements are met. We illustrate the model using the design of an Earth-orbiting satellite system where the systems engineer determines the optimum incentive structures and requirements for two subsystems: the propulsion subsystem and the power subsystem. The model enables the analysis of a systems engineer's decisions about optimal passed-down requirements and incentives for sub-system engineers under different levels of task difficulty and associated costs. Sample results, for the case of risk-neutral systems and subsystems engineers, show that it is not always in the best interest of the systems engineer to pass down the true requirements. As expected, the model predicts that for small to moderate task uncertainties the optimal requirements are higher than the true ones, effectively eliminating the probability of failure for the systems engineer. In contrast, the model predicts that for large task uncertainties the optimal requirements should be smaller than the true ones in order to lure the subsystem engineers into participation. 

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5. Recovery coupling in multilayer networks

   https://doi.org/10.1038/s41467-022-28379-5  

   Danziger, Michael M.; Barabási, Albert-László (December 2022, Nature Communications)

   Abstract The increased complexity of infrastructure systems has resulted in critical interdependencies between multiple networks—communication systems require electricity, while the normal functioning of the power grid relies on communication systems. These interdependencies have inspired an extensive literature on coupled multilayer networks, assuming a hard interdependence, where a component failure in one network causes failures in the other network, resulting in a cascade of failures across multiple systems. While empirical evidence of such hard failures is limited, the repair and recovery of a network requires resources typically supplied by other networks, resulting in documented interdependencies induced by the recovery process. In this work, we explore recovery coupling, capturing the dependence of the recovery of one system on the instantaneous functional state of another system. If the support networks are not functional, recovery will be slowed. Here we collected data on the recovery time of millions of power grid failures, finding evidence of universal nonlinear behavior in recovery following large perturbations. We develop a theoretical framework to address recovery coupling, predicting quantitative signatures different from the multilayer cascading failures. We then rely on controlled natural experiments to separate the role of recovery coupling from other effects like resource limitations, offering direct evidence of how recovery coupling affects a system’s functionality. 

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