Assimilation de données par filtrage pour les systèmes hyperboliques du second ordre - Applications à la mécanique cardiaque

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.
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https://pastel.archives-ouvertes.fr/tel-00358582
Contributor : Philippe Moireau <>
Submitted on : Tuesday, February 3, 2009 - 5:32:27 PM
Last modification on : Friday, May 25, 2018 - 12:02:03 PM
Long-term archiving on : Friday, October 12, 2012 - 10:40:11 AM

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  • HAL Id : tel-00358582, version 1

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Philippe Moireau. Assimilation de données par filtrage pour les systèmes hyperboliques du second ordre - Applications à la mécanique cardiaque. Modélisation et simulation. Ecole Polytechnique X, 2008. Français. ⟨tel-00358582⟩

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