Identifiability of linear dynamic networks

TL;DR

This paper introduces the concept of network identifiability for linear dynamic networks, focusing on conditions under which network models can be uniquely distinguished from data, including scenarios with reduced-rank disturbances and noise-free nodes.

Contribution

It defines network identifiability as a property of model sets, extending classical parameter identifiability to structured network transfer functions, and provides conditions for different disturbance and excitation scenarios.

Findings

Defines network identifiability for dynamic networks.

Establishes conditions for model distinguishability based on excitation and disturbance signals.

Includes reduced-rank disturbance scenarios and noise-free nodes.

Abstract

Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we need to make sure that the network model set is identifiable. We introduce the notion of network identifiability, as a property of a parameterized model set, that ensures that different network models can be distinguished from each other when performing identification on the basis of measured data. Different from the classical notion of (parameter) identifiability, we focus on the distinction between network models in terms of their transfer functions. For a given structured model set with a pre-chosen topology, identifiability typically requires conditions on the presence and location of excitation signals, and on presence, location and correlation of disturbance signals. Because in a dynamic network, disturbances cannot always be considered to be of full-rank, the reduced-rank situation is also covered, meaning that the number of driving white noise processes can be strictly less than the number of disturbance variables. This includes the situation of having noise-free nodes.