An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach

Handle URI:
http://hdl.handle.net/10754/292839
Title:
An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach
Authors:
Asiri, Sharefa M. ( 0000-0001-9602-9462 )
Abstract:
Observers are well known in the theory of dynamical systems. They are used to estimate the states of a system from some measurements. However, recently observers have also been developed to estimate some unknowns for systems governed by Partial differential equations. Our aim is to design an observer to solve inverse source problem for a one dimensional wave equation. Firstly, the problem is discretized in both space and time and then an adaptive observer based on partial field measurements (i.e measurements taken form the solution of the wave equation) is applied to estimate both the states and the source. We see the effectiveness of this observer in both noise-free and noisy cases. In each case, numerical simulations are provided to illustrate the effectiveness of this approach. Finally, we compare the performance of the observer approach with Tikhonov regularization approach.
Advisors:
Laleg-Kirati, Taous-Meriem ( 0000-0001-5944-0121 )
Committee Member:
Claudel, Christian G. ( 0000-0003-0702-6548 ) ; Wu, Ying ( 0000-0002-7919-1107 )
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
25-May-2013
Type:
Thesis
Appears in Collections:
Applied Mathematics and Computational Science Program; Theses; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.advisorLaleg-Kirati, Taous-Meriemen
dc.contributor.authorAsiri, Sharefa M.en
dc.date.accessioned2013-05-26T12:13:04Z-
dc.date.available2013-05-26T12:13:04Z-
dc.date.issued2013-05-25en
dc.identifier.urihttp://hdl.handle.net/10754/292839en
dc.description.abstractObservers are well known in the theory of dynamical systems. They are used to estimate the states of a system from some measurements. However, recently observers have also been developed to estimate some unknowns for systems governed by Partial differential equations. Our aim is to design an observer to solve inverse source problem for a one dimensional wave equation. Firstly, the problem is discretized in both space and time and then an adaptive observer based on partial field measurements (i.e measurements taken form the solution of the wave equation) is applied to estimate both the states and the source. We see the effectiveness of this observer in both noise-free and noisy cases. In each case, numerical simulations are provided to illustrate the effectiveness of this approach. Finally, we compare the performance of the observer approach with Tikhonov regularization approach.en
dc.language.isoenen
dc.subjectInverse Problemen
dc.subjectWave Equationen
dc.subjectTikhonov Regularizationen
dc.subjectObserveren
dc.titleAn Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approachen
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberClaudel, Christian G.en
dc.contributor.committeememberWu, Yingen
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameMaster of Scienceen
dc.person.id117658en
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