Resilient Infrastructure Network: Sparse Edge Change Identification via L1-Regularized Least Squares

TL;DR

This paper introduces a robust L1-regularized least squares method to quickly identify sparse edge changes in infrastructure networks from noisy data, aiding rapid disruption detection.

Contribution

It proposes a novel framework leveraging Laplacian matrix structure to accurately detect sparse network changes under noisy conditions.

Findings

Effective in identifying multiple sparse edge changes

Robust against noisy data in network analysis

Demonstrated success on power network examples

Abstract

Adversarial actions and a rapid climate change are disrupting operations of infrastructure networks (e.g., energy, water, and transportation systems). Unaddressed disruptions lead to system-wide shutdowns, emphasizing the need for quick and robust identification methods. One significant disruption arises from edge changes (addition or deletion) in networks. We present an $\ell_1$-norm regularized least-squares framework to identify multiple but sparse edge changes using noisy data. We focus only on networks that obey equilibrium equations, as commonly observed in the above sectors. The presence or lack of edges in these networks is captured by the sparsity pattern of the weighted, symmetric Laplacian matrix, while noisy data are node injections and potentials. Our proposed framework systematically leverages the inherent structure within the Laplacian matrix, effectively avoiding overparameterization. We demonstrate the robustness and efficacy of the proposed approach through a series of representative examples, with a primary emphasis on power networks.