Inference of dominant modes for linear stochastic processes

For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer (estimate) their dominant modes from observations in real time. The modes can be real or complex. For a real mode (monotone decay), the goal is to infer i...

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Published inRoyal Society open science Vol. 8; no. 4; p. 201442
Main Author MacKay, R S
Format Journal Article
LanguageEnglish
Published England The Royal Society 21.04.2021
Subjects
AC power networks
Gaussian process
inference
Kalman filter
linear stochastic process
Mathematics
mode
AC power networks
mode
linear stochastic process
Gaussian process
inference
Kalman filter
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Summary:For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer (estimate) their dominant modes from observations in real time. The modes can be real or complex. For a real mode (monotone decay), the goal is to infer its damping rate and mode shape. For a complex mode (oscillatory decay), the goal is to infer its frequency, damping rate and (complex) mode shape. Their amplitudes and correlations are encoded in a mode covariance matrix that is also to be inferred. The work is motivated and illustrated by the problem of detection of oscillations in power flow in AC electrical networks. Suggestions of some other applications are given.
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In memory of Professor Sir David John Cameron MacKay FRS (22 April 1967–14 April 2016).
ISSN:2054-5703
2054-5703
DOI:10.1098/rsos.201442