Failure mitigation, vulnerability detection and persistence of network flows in complex systems

Abstract

Finally, the persistence of states is studied in various systems under the respective system dynamics. Lattices in one and two dimensions as well as Complete and E-R graphs are investigated. A contact process and diffusion process are applied to these networks, and the evolution of persistence (being the probability that a site remains in the same state until time t) is investigated. We find the expected and theoretically backed results known in the literature for one and two dimensional lattices. We find non-trivial behavior in E-R graphs, and find the expected trivial behavior in complete graphs. Interestingly, we find that when certain conditions are met, the persistence found for diffusive models and for contact processes yield the same critical decay exponent, suggesting that there are underlying dynamics governing the persistence of the system that are not entirely controlled by the model dynamics.

Complex systems arise in many environments, and can be useful in modeling many aspects of physical and social systems. For many applications the maintenance and operation of these systems is poorly understood. We study the transmission and distribution grids as networks, and we investigate their temporal evolution, including the spread of cascades on such systems. We also analyze the occurrence of anomalies and future outcomes of such anomalies in the distribution grid. In addition, we investigate the persistence of states in lattice systems and networks.

Cascading failures are a critical vulnerability of complex information or infrastructure networks, and are particularly difficult to analyze in the transmission grid. We investigate the properties of load-based cascading failures in real and synthetic spatially-embedded network structures which can be seen as generalizations of power grids, and propose mitigation strategies to reduce the severity of damages caused by such failures. We introduce a stochastic method for optimal heterogeneous distribution of resources (node capacities) subject to a fixed total cost. Additionally, we design and compare the performance of networks with N-stable and (N-1)-stable network-capacity allocations by triggering cascades using various real-world node-attack and node-failure scenarios. We show that failure mitigation through increased node protection can be effectively achieved against single-node failures. However, mitigating against multiple node failures is much more difficult due to the combinatorial increase in possible sets of initially failing nodes in addition to the strongly non-linear dependence of cascade size on the set of initially targeted nodes. We analyze the robustness of the system with increasing protection, and find that a critical tolerance exists at which the system undergoes a phase transition, and above which the network almost completely survives an attack. Moreover, we show that cascade-size distributions measured in this region exhibit a power-law decay indicating that this region holds a critical value. Finally, we find a strong correlation between cascade sizes induced by individual nodes and sets of nodes. We also show that network topology alone is a weak predictor in determining the progression of cascading failures.

On a less theoretical yet more applicable note, we study anomaly occurrences in the distribution grid. We utilize data harvested from phasor measurement units (PMUs) in the distribution grid. The department of energy (DOE) placed these remote sensors in various locations throughout the distribution grid in the past decade in an effort to improve the monitoring, resilience, and efficiency of maintenance, in the distribution grid. The first task is to identify the occurrence of anomalies in the data set. This is performed through a statistical measure indicating the likelihood of an incoming signal. Next the data is classified into one of nine expert-identified classes. Learning algorithms are then trained on this data set that has been labeled by the expert. The performance of the model is investigated.