Moireau, Philippe (2008) Filtering based data assimilation for second order hyperbolic PDEs - Applications in cardiac mechanics. PhD thesis Mathématiques Appliquées, EP/X p.320.
Full text available as:
|
|
Alternative Locations: http://www-c.inria.fr/MACS/article.php3?id_article=162
Abstract
The objective is to formulate data assimilation methodologies adapted to the simulation of the heart mechanical behavior over a complete beat. The motivation is to benefit from both the development of medical imaging and the increased interest of clinicians for numerical simulation. We present an original filtering strategy to perform estimation for mechanical systems, and more generally for second-order hyperbolic equations, with uncertain initial conditions and parameters. The trajectory estimation is performed with effective Luenberger observers which use feedback control strategies for estimation purposes. Unlike the classical Kalman approach, these filters can be computationally tractable for numerical systems arising from the discretization of PDEs, and the exponential stability of the corresponding controlled system gives exponential convergence of the estimator. In this respect, we more specifically analyze the "Direct Velocity Feedback" collocated strategy arising in the control of mechanical structures. We then formulate an original observer when the available measurements are positions, and by extension contours in images. With uncertain parameters, we extend the estimator by incorporating the parameters in an augmented dynamical system. The previous state observers then circumscribe the uncertainty to the parameter space and allow an H2 or Hinfinity reduced rank filter in this space. The convergence of the resulting joint state-parameter estimator is mathematically established, and illustrated by identifying localized stiffness and contractility, with the perspective of diagnosis assistance for infarcted regions in the cardiac tissue.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| Additional Information: | Laboratoire d'accueil : Equipe-projet MACS, INRIA |
| PhD Supervisor: | Chapelle, Dominique and Le Tallec, Patrick |
| Date: | 12 December 2008 |
| Board of examiners: | Allaire, Grégoire and Bensoussan, Alain and Blum, Jacques and Bourquin, Frédéric and Lorenz, Cristian and Raoult, Annie and Sorine, Michel |
| Ecole Doctorale: | ED 447 ECOLE DOCTORALE DE L'ECOLE POLYTECHNIQUE |
| Discipline: | Mathématiques Appliquées |
| Collection (Fonds): | Ecole Polytechnique (EP/X) |
| Institution: | EP/X |
| Subjects: | 1. Mathematics and Applications |
| Uncontrolled Keywords: | Solid mechanics, Mécanique du solide, Data assimilation, Assimilation de données, Identification, Identification, Filtering, Filtrage, Cardiac modeling, Modélisation cardiaque, Estimation, Estimation, Luenberger observer, Observateur de Luenberger, Reduced-order filtering, Filtrage réduit |
| ID Code: | 4681 |
| Deposited By: | Philippe Moireau |
| Deposited On: | 09 February 2009 |
Table of content
Chap 1: Least-square estimation principles
Chap 2: Cardiac modeling
Chap 3: State estimation for a class of hyperbolic systems
Chap 4: Joint state-parameter estimation for distributed systems
Repository Staff Only: edit this item