Graph Signal Processing for Infrastructure Resilience: Suitability and Future Directions

TL;DR

This paper evaluates the application of graph signal processing (GSP) to infrastructure resilience, analyzing power and water systems to determine their suitability for GSP techniques and proposing future research directions.

Contribution

It assesses the spectral structure of infrastructure signals, relates these to system properties, and explores a data-driven approach to enhance GSP applicability in resilience analysis.

Findings

Many systems are well-structured for GSP techniques

Significant variability in signal structure across systems

A data-driven approach can improve GSP metrics

Abstract

Graph signal processing (GSP) is an emerging field developed for analyzing signals defined on irregular spatial structures modeled as graphs. Given the considerable literature regarding the resilience of infrastructure networks using graph theory, it is not surprising that a number of applications of GSP can be found in the resilience domain. GSP techniques assume that the choice of graphical Fourier transform (GFT) imparts a particular spectral structure on the signal of interest. We assess a number of power distribution systems with respect to metrics of signal structure and identify several correlates to system properties and further demonstrate how these metrics relate to performance of some GSP techniques. We also discuss the feasibility of a data-driven approach that improves these metrics and apply it to a water distribution scenario. Overall, we find that many of the candidate systems analyzed are properly structured in the chosen GFT basis and amenable to GSP techniques, but identify considerable variability and nuance that merits future investigation.