Fiche détaillée  Thèses 
Université de VersaillesSaint Quentin en Yvelines (05/12/2011), Michel Sorine (Dir.) 
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Some inverse scattering problems on starshaped graphs: application to fault detection on electrical transmission line networks 
Filippo Visco Comandini^{1} 
In this thesis, having in mind applications to the faultdetection/diagnosis of electrical networks, we consider some inverse scattering problems for the ZakharovShabat equations and timeindependent Schrödinger operators over starshaped graphs. The first chapter is devoted to describe reflectometry methods applied to electrical networks as an inverse scattering problems on the starshaped network. Reflectometry methods are presented and modeled by the telegrapher's equations. Reflectometry experiments can be written as inverse scattering problems for Schrödinger operator in the lossless case and for ZakharovShabat system for the lossy transmission network. In chapter 2 we introduce some elements of the inverse scattering theory for 1 d Schrödinger equations and the ZakharovShabat system. We recall the basic results for these two systems and we present the state of art of scattering theory on network. The third chapter deals with some inverse scattering for the Schrödinger operators. We prove the identifiability of the geometry of the starshaped graph: the number of the edges and their lengths. Next, we study the potential identification problem by inverse scattering. In the last chapter we focus on the inverse scattering problems for lossy transmission starshaped network. We prove the identifiability of some geometric informations by inverse scattering and we present a result toward the identification of the heterogeneities, showing the identifiability of the loss line factor. 
1 :  INRIA Rocquencourt  SISYPHE (SIgnals and SYstems in PHysiology and Engineering) 
Transmission Line Network – Reflectometry – Inverse scattering – Schrodinger operators – ZakharovShabat equations 
In this thesis, having in mind applications to the faultdetection/diagnosis of electrical networks, we consider some inverse scattering problems for the ZakharovShabat equations and timeindependent Schrödinger operators over starshaped graphs. The first chapter is devoted to describe reflectometry methods applied to electrical networks as an inverse scattering problems on the starshaped network. Reflectometry methods are presented and modeled by the telegrapher's equations. Reflectometry experiments can be written as inverse scattering problems for Schrödinger operator in the lossless case and for ZakharovShabat system for the lossy transmission network. In chapter 2 we introduce some elements of the inverse scattering theory for 1 d Schrödinger equations and the ZakharovShabat system. We recall the basic results for these two systems and we present the state of art of scattering theory on network. The third chapter deals with some inverse scattering for the Schrödinger operators. We prove the identifiability of the geometry of the starshaped graph: the number of the edges and their lengths. Next, we study the potential identification problem by inverse scattering. In the last chapter we focus on the inverse scattering problems for lossy transmission starshaped network. We prove the identifiability of some geometric informations by inverse scattering and we present a result toward the identification of the heterogeneities, showing the identifiability of the loss line factor. 
Transmission Line Network – Reflectometry – Inverse scattering – Schrodinger operators – ZakharovShabat equations 
tel00748216, version 1  
http://tel.archivesouvertes.fr/tel00748216  
oai:tel.archivesouvertes.fr:tel00748216  
Contributeur : Filippo Visco Comandini  
Soumis le : Lundi 5 Novembre 2012, 10:31:38  
Dernière modification le : Lundi 5 Novembre 2012, 10:50:51 