State and parameter estimators in ï¬‚uid-structure interaction for data assimilation in large arteries
vendredi 11 février 2011, 11h00 - 12h00
Medical imaging data is increasingly getting interest not only for patient speciï¬c geometry generation, but also for estimating uncertain parameters of the governing equations. However, parameter estimation in dynamical systems coming, e.g., from the discretization of partial differential equations requires not only efï¬cient numerical methods but also to reduce other uncertainties coming from the modeling and discretization errors and initial condition. This is called « Data Assimilation » (DA).
Typically, DA of distributed mechanical systems is performed within a variational approach, that is, by minimizing a least square criterion which balances the error between observations and model prediction, and a regularization based on a priori estimation of the solution. One of the main difficulties related to this approach lies in the iterative evaluation of the criterion (involving many solutions of the direct problem) and its gradient, typically adjoint-based.
Another fashion to perform DA is by means of sequential approaches, e.g. Kalman ï¬ltering. Even though we can formulate fully-discrete ï¬‚uid-structure interaction problems in a Kalman ï¬lter way, it becomes intractable on large distributed parameter systems.
Therefore, for the state estimation (i.e., assuming only an error in the initial condition), we analyze the performance of physical ï¬lters (e.g., Luenberger observers) in the ï¬‚uid-structure system under physiological conditions. For the parameter estimation, we will also present some results concerning the application of reduced order, non-linear Kalman filters.