DOI
https://doi.org/10.11606/T.3.2005.tde-16072024-100326
Documento
Autor
Nome completo
Flavio Celso Trigo
Área do Conhecimento
Data de Defesa
Imprenta
São Paulo, 2005
Lima, Raúl González (Presidente)
Amato, Marcelo Britto Passos
Donha, Decio Crisol
Fleury, Agenor de Toledo
Rios Neto, Atair

Título em português
Estimação não linear de parâmetros através dos filtros de Kalman na tomografia por impedância elétrica.
Palavras-chave em português
Estimação não linear
Filtros de Kalman
Tomografia
Resumo em português

Título em inglês
Untitled in english
Palavras-chave em inglês
Kalman filters
Nonlinear estimation
Tomography
Resumo em inglês
Electrical Impedance Tomography (EIT) attempts to estimate dielectrical properties of a medium in which currents are injected and voltages measured (or vice-versa) through lead electrodes attached around its border. Reconstructed images from the estimated conductivities/resistivities show the distribution of those parameters inside the medium. Research towards applications of EIT in medicine and industrial processes has currently been carried out. The conductivities/resistivities are parameters of a model of the phantom under evaluation. Those parameters result from the solution of the Laplace partial derivatives differential equation with known potential and proper boundary conditions. However, the dielectric properties of the medium that generated the above-mentioned potential are unknown. Mathematical problems of that kind are called inverse problems. Solutions for an inverse problem are often obtained through numerical procedures. This work evaluates the performance of one of those procedures, the Kalman filter, as an estimator for the conductivity/resistivity distribution in EIT. In order to accomplish the task, the problem is described in a state-space form. The medium is discretized in triangle finite elements with uniform conductivity/resistivity distribution. The conductivity/resistivity of each finite element is assigned to a state variable. The observation equation is directly obtained from linearization of the finite element model, whereas for thetime evolution of the system a random-walk model is assumed. Three versions of the Kalman filter are implemented: the extended (EKF), the iterated extended (IEKF), and the adaptive iterated extended (AIEKF); the IEKF and the AIEKF are new in this kind of application. In addition, the paradigm of sequential data processing through the EKF (SEKF), is approached. ) The performance of each method is evaluated through numerical simulations and experimental data from a test rig. One of the novelties presented in this Thesis is the estimation of medium-electrode contact parameters with the help of FEK using data from the test rig. Subsequently, using the medium electrode contact impedances as prior information, the presence and localization of an object inserted in the phantom, acting as a step function perturbation on the previously homogeneous medium, is estimated by the EKF and by the IEKF. The estimates obtained through the IEKF are 70% more accurate than those from the EKF and SEKF, whose performance is equivalent. Furthermore, the influence of regularization procedures is quantitatively investigated. Aiming at simultaneously identifying medium and contact parameters, a new approach called Two-phase identification is proposed. Using data from the phantom, the two-phase identification method is effective in determining both electrode contact impedances and medium resistivity distribution with the perturbation, when used in association with the IEKF or the AIEKF. The state estimates present normalized observation residuals whose statistics is consistent with the expected values, thus ensuring convergence of the estimation process.

AVISO - A consulta a este documento fica condicionada na aceitação das seguintes condições de uso:
Este trabalho é somente para uso privado de atividades de pesquisa e ensino. Não é autorizada sua reprodução para quaisquer fins lucrativos. Esta reserva de direitos abrange a todos os dados do documento bem como seu conteúdo. Na utilização ou citação de partes do documento é obrigatório mencionar nome da pessoa autora do trabalho.
Data de Publicação
2024-07-16

AVISO: Saiba o que são os trabalhos decorrentes clicando aqui.
Todos os direitos da tese/dissertação são de seus autores.
CeTI-SC/STI
© 2001-2024. Biblioteca Digital de Teses e Dissertações da USP.