Bayesian topology identification of linear dynamic networks

TL;DR

This paper introduces a Bayesian model selection approach for identifying the interconnection structure of linear dynamic networks using Gaussian process modeling and hyperparameter estimation, without estimating the transfer functions directly.

Contribution

It proposes a novel Bayesian method employing Gaussian process models and a forward-backward search for network topology identification, avoiding direct transfer function estimation.

Findings

Effective in identifying network connectivity

Uses Gaussian processes for impulse response modeling

Demonstrated through numerical experiments

Abstract

In networks of dynamic systems, one challenge is to identify the interconnection structure on the basis of measured signals. Inspired by a Bayesian approach in [1], in this paper, we explore a Bayesian model selection method for identifying the connectivity of networks of transfer functions, without the need to estimate the dynamics. The algorithm employs a Bayesian measure and a forward-backward search algorithm. To obtain the Bayesian measure, the impulse responses of network modules are modeled as Gaussian processes and the hyperparameters are estimated by marginal likelihood maximization using the expectation-maximization algorithm. Numerical results demonstrate the effectiveness of this method.