Original title: TESTING THE METHOD OF MULTIPLE SCALES AND THE AVERAGING PRINCIPLE FOR MODEL PARAMETER ESTIMATION OF QUASIPERIODIC TWO TIME-SCALE MODELS
Authors: Papáček, Štěpán ; Matonoha, Ctirad
Document type: Papers
Conference/Event: Programs and Algorithms of Numerical Mathematics 21, PANM 21 /2022/, Jablonec nad Nisou (CZ), 20220619
Year: 2023
Language: eng
Abstract: Some dynamical systems are characterized by more than one timescale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slow-fast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of the solution of associated forward problem: (i) the multiple time-scales method, and (ii) the method of averaging. On a case study, being an under-damped harmonic oscillator containing two state variables and two parameters, the method of averaging gives well (theoretically predicted) results, while the use of multiple time-scales method is not suitable for our purposes.
Keywords: Averaging; Damped oscillations; Dynamical system; Parameter estimation; Singular perturbation; Slow-fast decomposition
Project no.: GA21-03689S (CEP)
Funding provider: GA ČR
Host item entry: Programs and Algorithms of Numerical Mathematics 21 : Proceedings of Seminar, ISBN 978-80-85823-73-8

Institution: Institute of Information Theory and Automation AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://library.utia.cas.cz/separaty/2023/TR/papacek-0566289.pdf
Original record: https://hdl.handle.net/11104/0337768

Permalink: http://www.nusl.cz/ntk/nusl-512278


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