Iterative Observer-based Estimation Algorithms for Steady-State Elliptic Partial Differential Equation Systems

Handle URI:
http://hdl.handle.net/10754/625240
Title:
Iterative Observer-based Estimation Algorithms for Steady-State Elliptic Partial Differential Equation Systems
Authors:
Majeed, Muhammad Usman ( 0000-0001-6296-2158 )
Abstract:
Steady-state elliptic partial differential equations (PDEs) are frequently used to model a diverse range of physical phenomena. The source and boundary data estimation problems for such PDE systems are of prime interest in various engineering disciplines including biomedical engineering, mechanics of materials and earth sciences. Almost all existing solution strategies for such problems can be broadly classified as optimization-based techniques, which are computationally heavy especially when the problems are formulated on higher dimensional space domains. However, in this dissertation, feedback based state estimation algorithms, known as state observers, are developed to solve such steady-state problems using one of the space variables as time-like. In this regard, first, an iterative observer algorithm is developed that sweeps over regular-shaped domains and solves boundary estimation problems for steady-state Laplace equation. It is well-known that source and boundary estimation problems for the elliptic PDEs are highly sensitive to noise in the data. For this, an optimal iterative observer algorithm, which is a robust counterpart of the iterative observer, is presented to tackle the ill-posedness due to noise. The iterative observer algorithm and the optimal iterative algorithm are then used to solve source localization and estimation problems for Poisson equation for noise-free and noisy data cases respectively. Next, a divide and conquer approach is developed for three-dimensional domains with two congruent parallel surfaces to solve the boundary and the source data estimation problems for the steady-state Laplace and Poisson kind of systems respectively. Theoretical results are shown using a functional analysis framework, and consistent numerical simulation results are presented for several test cases using finite difference discretization schemes.
Advisors:
Laleg-Kirati, Taous-Meriem ( 0000-0001-5944-0121 )
Committee Member:
Shamma, Jeff S. ( 0000-0001-5638-9551 ) ; Keyes, David E. ( 0000-0002-4052-7224 ) ; Wu, Ying ( 0000-0002-7919-1107 ) ; Smith, Ralph
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
19-Jul-2017
Type:
Dissertation
Description:
A recording of the defense presentation for this dissertation is available at: http://hdl.handle.net/10754/625197
Additional Links:
http://hdl.handle.net/10754/625197
Appears in Collections:
Dissertations

Full metadata record

DC FieldValue Language
dc.contributor.advisorLaleg-Kirati, Taous-Meriemen
dc.contributor.authorMajeed, Muhammad Usmanen
dc.date.accessioned2017-07-20T08:58:18Z-
dc.date.available2017-07-20T08:58:18Z-
dc.date.issued2017-07-19-
dc.identifier.urihttp://hdl.handle.net/10754/625240-
dc.descriptionA recording of the defense presentation for this dissertation is available at: http://hdl.handle.net/10754/625197en
dc.description.abstractSteady-state elliptic partial differential equations (PDEs) are frequently used to model a diverse range of physical phenomena. The source and boundary data estimation problems for such PDE systems are of prime interest in various engineering disciplines including biomedical engineering, mechanics of materials and earth sciences. Almost all existing solution strategies for such problems can be broadly classified as optimization-based techniques, which are computationally heavy especially when the problems are formulated on higher dimensional space domains. However, in this dissertation, feedback based state estimation algorithms, known as state observers, are developed to solve such steady-state problems using one of the space variables as time-like. In this regard, first, an iterative observer algorithm is developed that sweeps over regular-shaped domains and solves boundary estimation problems for steady-state Laplace equation. It is well-known that source and boundary estimation problems for the elliptic PDEs are highly sensitive to noise in the data. For this, an optimal iterative observer algorithm, which is a robust counterpart of the iterative observer, is presented to tackle the ill-posedness due to noise. The iterative observer algorithm and the optimal iterative algorithm are then used to solve source localization and estimation problems for Poisson equation for noise-free and noisy data cases respectively. Next, a divide and conquer approach is developed for three-dimensional domains with two congruent parallel surfaces to solve the boundary and the source data estimation problems for the steady-state Laplace and Poisson kind of systems respectively. Theoretical results are shown using a functional analysis framework, and consistent numerical simulation results are presented for several test cases using finite difference discretization schemes.en
dc.language.isoenen
dc.relation.urlhttp://hdl.handle.net/10754/625197en
dc.subjectobserver designen
dc.subjectInverse problemsen
dc.subjectBoundary Estimationen
dc.subjectsource localizationen
dc.subjectelliptic PDEsen
dc.subjectkalman filteren
dc.titleIterative Observer-based Estimation Algorithms for Steady-State Elliptic Partial Differential Equation Systemsen
dc.typeDissertationen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen
dc.contributor.committeememberShamma, Jeff S.en
dc.contributor.committeememberKeyes, David E.en
dc.contributor.committeememberWu, Yingen
dc.contributor.committeememberSmith, Ralphen
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameDoctor of Philosophyen
dc.person.id118534en
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