Spatiotemporal system identification with spectral methods

In inverse problem theory, the identification of nonlinear spatiotemporal systems is still an underdeveloped topic. This work aims to introduce a means for spatiotemporal system identification based on spectral methods. To achieve this goal, a continuous black-box model class is proposed and paramet...

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Main Author: Khanmohamadi, Omid
Other Authors: Xu Daolin
Format: Theses and Dissertations
Language:English
Published: 2009
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Online Access:https://hdl.handle.net/10356/18737
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-187372023-03-11T17:46:25Z Spatiotemporal system identification with spectral methods Khanmohamadi, Omid Xu Daolin School of Mechanical and Aerospace Engineering DRNTU::Science::Mathematics::Applied mathematics::Simulation and modeling In inverse problem theory, the identification of nonlinear spatiotemporal systems is still an underdeveloped topic. This work aims to introduce a means for spatiotemporal system identification based on spectral methods. To achieve this goal, a continuous black-box model class is proposed and parameterized to obtain a model structure whose proper discretization yields a regression form, giving the unknown parameters based on the maximum likelihood estimation. An orthogonal system simplification algorithm is devised to eliminate the redundant parameters. Spectral differentiation operators are extended to inverse problems for proper discretization of the continuous model structure. Trigonometric and algebraic spectral operators are introduced for periodic and non-periodic system identifications and for their practical implementation, wavenumber reordering and roundoff attenuation methods are proposed. The main contribution of this work is to introduce a methodology, namely spectral spatiotemporal system identification, for one-dimensional periodic/non-periodic inverse problems and analyze its superior accuracy and robustness compared with its finite difference counterparts, through the numerical analysis of the method and experiments on indentifying Kuramoto-Sivashinsky (in chaotic regime), Burgers and Allen-Cahn spatiotemporal systems. MASTER OF ENGINEERING (MAE) 2009-07-07T06:31:10Z 2009-07-07T06:31:10Z 2009 2009 Thesis Khanmohamadi, O. (2009). Spatiotemporal system identification with spectral methods. Master’s thesis, Nanyang Technological University, Singapore. https://hdl.handle.net/10356/18737 10.32657/10356/18737 en 137 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Mathematics::Applied mathematics::Simulation and modeling
spellingShingle DRNTU::Science::Mathematics::Applied mathematics::Simulation and modeling
Khanmohamadi, Omid
Spatiotemporal system identification with spectral methods
description In inverse problem theory, the identification of nonlinear spatiotemporal systems is still an underdeveloped topic. This work aims to introduce a means for spatiotemporal system identification based on spectral methods. To achieve this goal, a continuous black-box model class is proposed and parameterized to obtain a model structure whose proper discretization yields a regression form, giving the unknown parameters based on the maximum likelihood estimation. An orthogonal system simplification algorithm is devised to eliminate the redundant parameters. Spectral differentiation operators are extended to inverse problems for proper discretization of the continuous model structure. Trigonometric and algebraic spectral operators are introduced for periodic and non-periodic system identifications and for their practical implementation, wavenumber reordering and roundoff attenuation methods are proposed. The main contribution of this work is to introduce a methodology, namely spectral spatiotemporal system identification, for one-dimensional periodic/non-periodic inverse problems and analyze its superior accuracy and robustness compared with its finite difference counterparts, through the numerical analysis of the method and experiments on indentifying Kuramoto-Sivashinsky (in chaotic regime), Burgers and Allen-Cahn spatiotemporal systems.
author2 Xu Daolin
author_facet Xu Daolin
Khanmohamadi, Omid
format Theses and Dissertations
author Khanmohamadi, Omid
author_sort Khanmohamadi, Omid
title Spatiotemporal system identification with spectral methods
title_short Spatiotemporal system identification with spectral methods
title_full Spatiotemporal system identification with spectral methods
title_fullStr Spatiotemporal system identification with spectral methods
title_full_unstemmed Spatiotemporal system identification with spectral methods
title_sort spatiotemporal system identification with spectral methods
publishDate 2009
url https://hdl.handle.net/10356/18737
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