Browsing by Author "Hien Tran, Committee Member"

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Analysis and Computation for a Fluid Mixture Model of Tissue Deformations
(2008-06-17) Jiang, Qunlei; Xiaobiao Lin, Committee Member; Kazufumi Ito, Committee Member; Hien Tran, Committee Member; Zhilin Li, Committee Chair; Sharon R. Lubkin, Committee Co-Chair
A fluid mixture model of tissue deformations in one and two dimensions has been studied in this dissertation. The model is a mixed system of nonlinear hyperbolic and elliptic partial differential equations with interfaces. Both theoretical and numerical analysis are presented. We found the relationship between physical parameters and the resulting pattern of tissue deformations via linear stability analysis. Several numerical experiments support our theoretical analysis. The solution of the system exhibits non-smoothness and discontinuities at the interfaces. The conventional high order finite difference methods (FDM), such as the WENO scheme and TVD Runge Kutta method, for the hyperbolic equation, coupled with the central FDM for the elliptic equation, give spurious oscillations near the interfaces in our problem. By enforcing the jump conditions across the interfaces, our approach, the immersed interface method (IIM), eliminates non-physical oscillations, improves the accuracy of the solution, and maintains the sharp interface as time evolves. The IIM has been applied to solve a one dimensional linear advection equation with discontinuous initial conditions. By building the jump conditions into a conventional finite difference method, the Lax-Wendroff method, solutions of second order accuracy are observed. The IIM showed its robustness in solving the linear advection equation with nonhomogeneous jump conditions across the moving interface. The two dimensional fluid mixture model has been derived asymptotically from the three dimensional model so that the thickness of the gel is taken into account. Many numerical examples have been completed using Clawpack and qualitatively reasonable numerical solutions have been obtained.
Auxiliary Signal Design for Fault Detection in Nonlinear Systems
(2008-04-03) Sweetingham, Kelly Ann; Stephen L. Campbell, Committee Chair; Negash Medhin, Committee Member; Ralph Smith, Committee Member; Hien Tran, Committee Member
Recently, research has developed in the area of active fault detection and model identification algorithms for linear systems. These algorithms compute an auxiliary input signal which guarantees fault detection, assuming a bounded noise. This dissertation addresses the question of when the previous linear theory can be applied to nonlinear systems. Several case studies are presented to verify that linearizations can in fact produce results in the nonlinear case. Two results are proven about the use of linearizations. The first result gives a parameter which scales the entire problem. Using this parameter, the scaled auxiliary signal, along with a scaled noise bound, will guarantee fault detection in the nonlinear problem. The second result shows how to compute the acceptable noise bound for the nonlinear problem using the exact auxiliary signal from the linearized problem. Also presented is a computational study to verify these two results. Two secondary projects are also presented in this dissertation. The first is a comparison of two different linear algorithms used to compute the optimal auxiliary signal. The second is a port of one of the existing pieces of fault detection software into Matlab. This new software is included, as well as a discuss of the complications of the port.
Distributed and Collaborative Processing in Wireless Sensor Networks
(2007-08-21) Li, Wenjun; Huaiyu Dai, Committee Chair; Brian Hughes, Committee Member; Alexandra Duel-Hallen, Committee Member; Hamid Krim, Committee Member; Hien Tran, Committee Member
Exploring the Inverse Problem with Infectious Disease Models.
(2010-07-01) Capaldi, Alexander; Alun Lloyd, Committee Chair; Kevin Gross, Committee Member; James Selgrade, Committee Member; Hien Tran, Committee Member
Model Development for Shape Memory Polymers
(2008-08-01) Siskind, Ryan David; Stefan Seelecke, Committee Member; Hien Tran, Committee Member; Mansoor Haider, Committee Member; Ralph Smith, Committee Chair
Model-Based Robust Control Designs for High Performance Magnetostrictive Transducers
(2003-09-03) Nealis, James Matthew; Fen Wu, Committee Member; Kazufumi Ito, Committee Member; Hien Tran, Committee Member; Ralph C. Smith, Committee Chair
The increasing employment of smart structures in industrial processes necessitates the study of materials exhibiting constitutive nonlinearities and hysteresis. The high performance and high speed demands of such processes can often be met by transducers utilizing piezoceramic, shape memory alloy, or magnetostrictive elements.Here, the focus is place on magnetostrictive materials. These material provide several benefits such as the ability to generate large forces and strains and provide precision placement. However, to achieve the full potential of magnetostrictive materials, models and control laws which accommodate the inherent nonlinearities and hysteresis must be employed. An emphasis has been placed on the design of models for magnetostrictive transducers and control strategies that are implementable in real time and incorporate realistic operating conditions. To this end, models of the nonlinearities and hysteresis exhibited by magnetostrictive materials are developed considering not only accuracy, but the computational efficiency and the existence of an inverse or partial inverse as well. To attenuate the nonlinear and hysteretic behaviors, we employ the inverses of the material models as filters of the input to the transducer. The models describing the nonlinearities and hysteresis for the smart materials, contain several material dependent parameters which must be identified in order to effectively utilize resulting inverse compensators. A nonlinear adaptive parameter estimation algorithm is developed to identify nonlinearly occurring parameters which may not be identified by physical measurements or may be slowly varying. Once an inverse filter has been developed and the material parameters identified, feedback control laws are designed to meet the performance specifications. A successful controller must provide accurate tracking of a reference signal while accommodating the hysteretic behavior and other external disturbances such as sensor noise. Several initial feedback control methods are considered to motivate the investigation of robust control designs. Robust techniques including H₂ and H[subscript ∞] optimal control as well as multiple objective control designs are employed to control a magnetostrictive transducer and the performance is illustrated through simulations.
Modeling Shear Wave Propagation in Biotissue: An Internal Variable Approach to Dissipation
(2006-08-07) Luke, Nicholas Stephen; H.T. Banks, Committee Chair; Negash Medhin, Committee Member; Hien Tran, Committee Member; Mansoor Haider, Committee Member
The ability to reliably detech artery disease based on the acoustic noises produced by a stenosis can provide a simple, non-invasive technique for diagnosis. Current research exploits the shear wave fields in body tissue to detect and analyze coronary stenoses. A mathematical model of this system, utilizing an internal strain variable approximation to the quasi-linear viscoelastic constitutive equation proposed by Fung, was previously presented. The methods an ideas outlined in that presentation are expanded upon in this work. As an initial investigation, a homogeneous two-dimensional viscoelastic geometry is considered. Being uniform in theta, this geometry behaves as a one dimensional model, and the results generated from it are compared to the one dimensional results. Several variations of the model are considered, to allow for different assumptions about the elastic response. A statistical significance test is employed to determine if the extra parameters needed for certain variations of the model are necessary in modeling efforts. After validating the model with the comparison to previous findings, more complicated geometries are developed. Simulations involving a heterogeneous geometry with a uniform ring running through the originam medium, a theta dependent model which considers a rigid occlusion formed along the inner radius of the geometry, and a model which combines the ring and occlusion are presented. In an attempt to move towards the ultimate goal of detecting the location of a stenosis from the data gathered at the chestwall, an inverse problem methodology is introduced and results from the inverse problem are shown.
Optimization Problems in the Presence of Uncertainty
(2007-09-17) Grove, Sarah Lynn; Mansoor Haider, Committee Member; Hien Tran, Committee Member; H.T. Banks, Committee Chair; Kazufumi Ito, Committee Member
We consider optimization problems in the presence of uncertainty for three different scientific examples. The first optimization problem addressed is in the area of parameter estimation. We review the asymptotic theory for standard errors in classical ordinary least squares (OLS) inverse or parameter estimation problems involving general nonlinear dynamical systems where sensitivity matrices can be used to compute the asymptotic covariance matrices. We discuss possible pitfalls in computing standard errors in regions of low parameter sensitivity and/or near a steady state solution of the underlying dynamical system. Next we consider electromagnetic evasion-interrogation games where the evader can use ferroelectric material coatings to avoid detection while the interrogator can manipulate the interrogating frequencies and angles of incidence to enhance detection. Each player in this two-player game wishes to change the amount of reflected signal created in a way that will benefit them the most. Thus both players will attempt to optimize their chances of either remaining undetected or detecting their opponent. With the introduction of uncertainty, the resulting game is carried out over spaces of probability measures. Finally, a one player dynamical game is formulated. The premise here is for the evader to manipulate the ferroelectric material coatings to avoid detection based upon updated information about the frequencies being sent out. The uncertainty is found in the frequencies that the interrogator will employ. We incorporate both drift and diffusion into this optimization problem.