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Spring 2010 Seminars

Wednesday, February 10, 2010
Inverse Problems Seminar
Speaker: Mourad Zeghal, Civil and Environmental Engineering, RPI
Title: Development of a Multiscale Monitoring and Health Assessment Framework for Effective Management of Levees and Flood-Control Infrastructure Systems       
Location: Amos Eaton Rm 402
Time: 4:00 PM

Abstract:
The integrity and reliability of levees, earthen dams and flood-control infrastructure are essential components of homeland safety.  The failure of such systems due to a natural or man-made hazard such as a (hurricane) storm surge, flood, earthquake, deterioration, or terrorist attack can have monumental repercussions, sometimes with dramatic and unanticipated consequences on human life, property and the country’s economy.
This presentation will introduce and discuss a recently started project to develop a new health assessment framework to monitor, manage and ensure the safety of levees and other systems of a flood-control infrastructure. The proposed framework includes a comprehensive multiscale monitoring and analysis for real time health assessment of this infrastructure. This framework relies on long term continuous monitoring techniques that are minimally-intrusive and inexpensive. They include: (1) satellite-based interferometric synthetic aperture radar (InSAR) measurements, (2) a new high resolution GPS sensor with millimeter level accuracy, and (3) a new high resolution shape-acceleration-pore pressure (SAPP) arrays. The InSAR satellite measurements will be employed to obtain high resolution (millimeter accuracy) estimates of the global displacement and changes in near-surface moisture content of flood-control systems (levees and dams).  Model-based analysis and inverse problem tools will be developed to continuously assess the global health of the system of levees and identify critical or degrading segments of this system.  The SAPP arrays will be judiciously installed into the ground at critical segments. They will provide high resolution (in space and time) measurements to monitor the local response of these segments. In turn, the local measurements will be used along with inverse problem analyses to assess the health of the critical segments and determine an updated assessment of the health status of the whole system of flood-control levees. The network of high resolution GPS sensors will provide information that bridges the gap between the global (InSAR) and local (SAPP) measurements.
The proposed new health assessment framework will be implemented and benchmarked through an ambitious field implementation plan in the New Orleans area. The benchmark plan includes a $5,000,000 full-scale test of a levee that will be loaded until failure (i.e., levee breach) fully funded by the US Army Corps of Engineers.


Tuesday, January 26, 2010
Inverse Problems Seminar
Speaker: Samuli Siltanen, Professor of Industrial Mathematics, University of Helsinki
Title: Regularized D-bar method for the inverse conductivity problem
Location: Amos Eaton Rm 402
Time: 4:00 PM

Abstract:
The inverse conductivity problem formulated by Calderon in 1980 is the mathematical model of the emerging medical imaging method called Electrical Impedance Tomography (EIT). The idea of EIT is to feed harmless electric currents to the patient through electrodes attached to the skin, measure the resulting voltages at the electrodes, and form an image of the inner organs of the patient based on the measurement data. This image reconstruction task is a nonlinear and severely ill-posed inverse problem.
A strategy for regularizing the inversion procedure for the two- dimensional D-bar reconstruction algorithm for EIT is presented. The strategy utilizes truncation of a boundary integral equation and a scattering transform. It is shown that this leads to a stable reconstruction of the conductivity; an explicit rate of convergence in appropriate
Banach spaces is derived as well. Numerical results are also included, demonstrating the convergence of the reconstructed conductivity to the true conductivity as the noise level tends to zero.
The results provide a link between two traditions of inverse problems research: theory of regularization and inversion methods based on complex geometrical optics. Also, the procedure is a novel regularized imaging method for electrical
impedance tomography. The results can be seen as the essentially final step of a project aiming to implement practically Nachman's reconstruction method introduced for infinite-precision EIT data in 1996.

 

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