A scalable multi-step least squares method for network identification with unknown disturbance topology

06/14/2021
by   Stefanie J. M. Fonken, et al.
0

Identification methods for dynamic networks typically require prior knowledge of the network and disturbance topology, and often rely on solving poorly scalable non-convex optimization problems. While methods for estimating network topology are available in the literature, less attention has been paid to estimating the disturbance topology, i.e., the (spatial) noise correlation structure and the noise rank. In this work we present an identification method for dynamic networks, in which an estimation of the disturbance topology precedes the identification of the full dynamic network with known network topology. To this end we extend the multi-step Sequential Linear Regression and Weighted Null Space Fitting methods to deal with reduced rank noise, and use these methods to estimate the disturbance topology and the network dynamics. As a result, we provide a multi-step least squares algorithm with parallel computation capabilities and that rely only on explicit analytical solutions, thereby avoiding the usual non-convex optimizations involved. Consequently we consistently estimate dynamic networks of Box Jenkins model structure, while keeping the computational burden low. We provide a consistency proof that includes path-based data informativity conditions for allocation of excitation signals in the experimental design. Numerical simulations performed on a dynamic network with reduced rank noise clearly illustrate the potential of this method.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/26/2019

Learning sparse linear dynamic networks in a hyper-parameter free setting

We address the issue of estimating the topology and dynamics of sparse l...
research
12/02/2013

Grid Topology Identification using Electricity Prices

The potential of recovering the topology of a grid using solely publicly...
research
10/19/2021

A Unified and Refined Convergence Analysis for Non-Convex Decentralized Learning

We study the consensus decentralized optimization problem where the obje...
research
10/06/2022

Reduced Membrane Model for Liquid Crystal Polymer Networks: Asymptotics and Computation

We examine a reduced membrane model of liquid crystal polymer networks (...
research
10/10/2020

Maximin Optimization for Binary Regression

We consider regression problems with binary weights. Such optimization p...
research
05/31/2017

Learning Graphs with Monotone Topology Properties and Multiple Connected Components

Learning graphs with topology properties is a non-convex optimization pr...

Please sign up or login with your details

Forgot password? Click here to reset