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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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
2009
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| Online Access: | https://hdl.handle.net/10356/18737 |
| _version_ | 1811683299341369344 |
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| author | Khanmohamadi, Omid |
| author2 | Xu Daolin |
| author_facet | Xu Daolin Khanmohamadi, Omid |
| author_sort | Khanmohamadi, Omid |
| collection | NTU |
| 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. |
| first_indexed | 2024-10-01T04:10:32Z |
| format | Thesis |
| id | ntu-10356/18737 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:10:32Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | ntu-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 |
| spellingShingle | DRNTU::Science::Mathematics::Applied mathematics::Simulation and modeling Khanmohamadi, Omid Spatiotemporal system identification with spectral methods |
| title | 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_short | Spatiotemporal system identification with spectral methods |
| title_sort | spatiotemporal system identification with spectral methods |
| topic | DRNTU::Science::Mathematics::Applied mathematics::Simulation and modeling |
| url | https://hdl.handle.net/10356/18737 |
| work_keys_str_mv | AT khanmohamadiomid spatiotemporalsystemidentificationwithspectralmethods |