Topology Learning of Radial Dynamical Systems with Latent Nodes

TL;DR

This paper introduces a method to accurately reconstruct the topology of radial dynamical systems with hidden nodes using spectral analysis, enabling identification of both observed and unobserved nodes in electrical grids.

Contribution

It presents a novel spectral-based algorithm with provable guarantees for topology learning in partially observed radial networks, including unobserved node localization.

Findings

Successfully reconstructs network topology from time-series data.

Identifies unobserved nodes and eliminates spurious links.

Validated on a real electric distribution system.

Abstract

In this article, we present a method to reconstruct the topology of a partially observed radial network of linear dynamical systems with bi-directional interactions. Our approach exploits the structure of the inverse power spectral density matrix and recovers edges involving nodes up to four hops away in the underlying topology. We then present an algorithm with provable guarantees, which eliminates the spurious links obtained and also identifies the location of the unobserved nodes in the inferred topology. The algorithm recovers the exact topology of the network by using only time-series of the states at the observed nodes. The effectiveness of the method developed is demonstrated by applying it on a typical distribution system of the electric grid.