TY - JOUR

T1 - Identification of Edge Disconnections in Networks Based on Graph Filter Outputs

AU - Shaked, Shlomit

AU - Routtenberg, Tirza

N1 - Funding Information:
Manuscript received February 3, 2021; revised June 27, 2021; accepted August 15, 2021. Date of publication August 30, 2021; date of current version September 16, 2021. This work was supported in part by the Israeli Ministry of National Infrastructure, Energy and Water Resources and in part by BGU Cyber Security Research Center. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Siheng Chen. (Corresponding author: Tirza Routtenberg.) The authors are with the School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel (e-mail: shlomsh@post.bgu.ac.il; tirzar@bgu.ac.il). Digital Object Identifier 10.1109/TSIPN.2021.3107628
Publisher Copyright:
© 2015 IEEE.

PY - 2021/8/30

Y1 - 2021/8/30

N2 - Graphs are fundamental mathematical structures used in various fields to model statistical and physical relationships between data, signals, and processes. In some applications, such as data processing in graphs that represent physical networks, the initial network topology is known. However, disconnections of edges in the network change the topology and may affect the signals and processes over the network. In this paper, we consider the problem of edge disconnection identification in networks by using concepts from graph signal processing (GSP). We assume that the graph signals measured over the vertices of the network can be represented as white noise that has been filtered on the graph topology by a smooth graph filter. We develop the likelihood ratio test (LRT) to detect a specific set of edge disconnections. Then, we provide the maximum likelihood (ML) decision rule for identifying general scenarios of edge disconnections in the network. It is shown that the sufficient statistics of the LRT and ML decision rule are the graph frequency energy levels in the graph spectral domain. However, the ML decision rule leads to a high-complexity exhaustive search over the edges in the network and is practically infeasible. Thus, we propose a low-complexity greedy method that identifies a single disconnected edge at each iteration. Moreover, by using the smoothness of the considered graph filter, we suggest a local implementation of the decision rule, which is based solely on the measurements at neighboring vertices. Simulation results demonstrate that the proposed methods outperform existing detection and identification methods on a synthetic dataset and for line outage identification in power systems from the IEEE 118-bus test case.

AB - Graphs are fundamental mathematical structures used in various fields to model statistical and physical relationships between data, signals, and processes. In some applications, such as data processing in graphs that represent physical networks, the initial network topology is known. However, disconnections of edges in the network change the topology and may affect the signals and processes over the network. In this paper, we consider the problem of edge disconnection identification in networks by using concepts from graph signal processing (GSP). We assume that the graph signals measured over the vertices of the network can be represented as white noise that has been filtered on the graph topology by a smooth graph filter. We develop the likelihood ratio test (LRT) to detect a specific set of edge disconnections. Then, we provide the maximum likelihood (ML) decision rule for identifying general scenarios of edge disconnections in the network. It is shown that the sufficient statistics of the LRT and ML decision rule are the graph frequency energy levels in the graph spectral domain. However, the ML decision rule leads to a high-complexity exhaustive search over the edges in the network and is practically infeasible. Thus, we propose a low-complexity greedy method that identifies a single disconnected edge at each iteration. Moreover, by using the smoothness of the considered graph filter, we suggest a local implementation of the decision rule, which is based solely on the measurements at neighboring vertices. Simulation results demonstrate that the proposed methods outperform existing detection and identification methods on a synthetic dataset and for line outage identification in power systems from the IEEE 118-bus test case.

KW - Graph signal processing (GSP)

KW - identification of edge disconnections

KW - likelihood ratio test (LRT)

KW - network topology

KW - smooth graph filters

UR - http://www.scopus.com/inward/record.url?scp=85115448627&partnerID=8YFLogxK

U2 - 10.1109/TSIPN.2021.3107628

DO - 10.1109/TSIPN.2021.3107628

M3 - Article

SN - 2373-776X

VL - 7

SP - 578

EP - 594

JO - IEEE Transactions on Signal and Information Processing over Networks

JF - IEEE Transactions on Signal and Information Processing over Networks

ER -