Browsing by Author "H.T. Tran, Member"

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An Application of a Reduced Order Computational Methodology for Eddy Current Based Nondestructive Evaluation Techniques
(2001-06-11) Joyner, Michele Lynn; H.T. Banks, Chair; H.T. Tran, Member; Pierre A. Gremaud, Member; Kazufumi Ito, Member
In the field of nondestructive evaluation, new and improved techniques are constantly being sought to facilitate the detection of hidden corrosion and flaws in structures such as airplanes and pipelines. In this dissertation, we explore the feasibility of detecting such damages by application of an eddy current based technique and reduced order modeling. We begin by developing a model for a specific eddy current method in which we make some simplifying assumptions reducing the three-dimensional problem to a two-dimensional problem. (We do this for proof-of-concept.) Theoretical results are then presented which establish the existence and uniqueness of solutions as well as continuous dependence of the solution on the parameters which represent the damage. We further discuss theoretical issues concerning the least squares parameter estimation problem used in identifying the geometry of the damage. To solve the identification problem, an optimization algorithm is employed which requires solving the forward problem numerous times. To implement these methods in a practical setting, the forward algorithm must be solved with extremely fast and accurate solution methods. Therefore in constructing these computational methods, we employ reduced order Proper Orthogonal Decomposition (POD) techniques which allows one to create a set of basis elements spanning a data set consisting of either numerical simulations or experimental data. We investigate two different approaches in forming the POD approximation, a POD/Galerkin technique and a POD/Interpolation technique. We examine the error in the approximation using one approach versus the other as well as present results of the parameter estimation problem for both techniques. Finally, results of the parameter estimation problem are given using both simulated data with relative noise added as well as experimental data obtained using a giant magnetoresistive (GMR) sensor. The experimental results are based on successfully using actual experimental data to form the POD basis elements (instead of numerical simulations) thus illustrating the effectiveness of this method on a wide range of applications. In both instances the methods are found to be efficient and robust. Furthermore, the methods were fast; our findings suggest a significant reduction in computational time.
Computational Methods for Feedback Control in Structural Systems
(1998-11-05) Rosario, Ricardo C.H.; H.T. Banks, Chair; R.C. Smith, Member; K. Ito, Member; H.T. Tran, Member
Numerical methods, LQR control, an abstract formulation andreduced basis techniques for a system consisting of a thin cylindrical shellwith surface-mounted piezoceramic actuators are investigated.Donnell-Mushtari equations,modified to include Kelvin-Voigt damping and passive patch contributions,are used to model the system dynamics. The voltage-induced piezoceramicpatch contributions, used as input inthe control regime, enter the equations as externalforces and moments. Existence and uniqueness of solutions are demonstratedthrough variational and semigroup formulations of the system equations.The semigroup formulation is also used to establish theoretical controlresults and illustrate convergence of the finite dimensional controlsand Riccati operators.The spatial components of the state arediscretized using a Galerkin expansion resulting in an ordinarydifferential equation that can be readily marched in time by existingordinary differential equationsolvers.Full order approximation methods which employ standard basiselements such as cubic or linear splines result in large matrixdimensions rendering the system computationally expensive for real-timesimulations. To lessen on-line computational requirements, reducedbasis methods employing snapshots of the full order model as basisfunctions are investigated. As a first step in validating the model, a shell with obtainable analyticnatural frequencies and modes was considered. The derived frequenciesand modeswere then compared with numerical approximations using full order basisfunctions. Further testing on the static and dynamic performance of the fullorder model was carried out through the following steps:(i) choose true state solutions, (ii) solve for the forces in theequations that would lead to these known solutions, and (iii) comparenumerical results excited by the derived forces with the true solutions.Reduced order methods employing the Lagrange and theKarhunen-Loève proper orthogonal decomposition (POD)basis functions are implemented on the model. Finally, a statefeedback method was developed and investigated computationally for both the full order and reduced ordermodels.
Fault Detection and Model Identification in Linear Dynamical Systems
(2001-04-05) Horton, Kirk Gerritt; S.L. Campbell, Chair; R. Smith, Member; K. Ito, Member; H.T. Tran, Member; E. Chukwu, Member
Linear dynamical systems, Ex'+Fx=f(t), in which E is singular, are useful in a wide variety of applications. Because of this wide spread applicability, much research has been done recently to develop theory for the design of linear dynamical systems. A key aspect of system design is fault detection and isolation (FDI). One avenue of FDI is via the multi-model approach, in which the parameters of the nominal, unfailed model of the system are known, as well as the parameters of one or more fault models. The design goal is to obtain an indicator for when a fault has occurred, and, when more than one type is possible, which type of fault it is. A choice that must be made in the system design is how to model noise. One way is as a bounded energy signal. This approach places very few restrictions on the types of noisy systems which can be addressed, requiring no complex modeling requirement. This thesis applies the multi-model approach to FDI in linear dynamical systems, modeling noise as bounded energy signals. A complete algorithm is developed, requiring very little on-line computation, with which nearly perfect fault detection and isolation over a finite horizon is attained. The algorithm applies techniques to convert complex system relationships into necessary and sufficient conditions for the solutions to optimal control problems. The first such problem provides the fault indicator via the minimum energy detection signal, while the second problem provides for fault isolation via the separating hyperplane. The algorithm is implemented and tested on a suite of examples in commercial optimization software. The algorithm is shownto have promise in nonlinear problems, time varying problems, and certain types of linear problems for which existing theory is not suitable.
Physiologically Based Pharmacokinetic Models for the Systemic Transport of Trichloroethylene
(2001-05-17) Potter, Laura Kay; H.T Banks, Chair; J. Bishir, Member; M.V. Evans, Member; K. Ito, Member; H.T. Tran, Member
Three physiologically based pharmacokinetic (PBPK) models for thesystemic transport of inhaled trichloroethylene (TCE) are presented.The major focus ofthese modeling efforts is the disposition of TCE in the adiposetissue, where TCE is known to accumulate. Adipose tissue is highly heterogeneous, with wide variations in fat cell size, lipid composition, blood flow rates and cellpermeability. Since TCE is highly lipophilic, the uneven distributionof lipids in the adipose tissue may lead to an uneven distribution of TCEwithin the fat. These physiological characteristics suggest that thedynamics of TCE in the adipose tissue may depend on spatial variations within the tissue itself. The first PBPK model for inhaled TCE presented here is a system ofordinary differential equations which includes the standardperfusion-limited compartmental model for each of the adipose, brain,kidney, liver, muscle and remaining tissue compartments.Model simulations predict relatively rapiddecreases in TCE fat concentrations following exposure, which may notreflect the accumulation and relative persistence of TCE inside the fattissue. The second PBPK model is identical to the first except forthe adipose tissue compartment, which is modeled as a diffusion-limited compartment.Although this model yields various concentration profiles for TCE inthe adipose tissue depending on the value of the permeabilitycoefficient, this model may not be physically appropriate for TCE,which is highly lipophilic and has a low molecular weight. Moreover,neither of these two PBPK models is able to capture spatialvariation of TCE concentrations in adipose tissue as suggested bythe physiology. The third model we present is a hybrid PBPK model with adispersion-type model for the transport of TCE in the adipose tissue. Thedispersion model is designed to account for the heterogeneities within fattissue, as well as the corresponding spatial variation of TCE concentrationsthat may occur. This partial differential equation model is based onthe dispersion model of Roberts and Rowland for hepatic uptake andelimination, adapted here for the specific physiology of adipose tissue. Theoretical results are given for the well-posedness of a generalclass of abstract nonlinear parabolic systems which includes the TCEPBPK-hybrid model as a special case. Moreover, theoretical issues related to associated general least squares estimation problems are addressed,including the standard type of deterministic problem and aprobability-based identification problem that incorporates variability inparameters across a population. We also establish thetheoretical convergence of the Galerkin approximations used in our numericalschemes. The qualitative behavior of the TCE PBPK-hybrid model is studied usingmodel simulations and parameter estimation techniques. In general, theTCE PBPK-hybrid model can generate various predictions of the dynamicsof TCE in adipose tissue by varying the adipose model parameters.These predictions include simulations that are similar to the expectedbehavior of TCE in the adipose tissue, which involves a rapid increaseof TCE adipocyte concentrations during the exposure period, followed by aslow decay of TCE levels over several hours. Results are presented for several types of parameter estimationproblems associatedwith the TCE PBPK-hybrid model. We test theseestimation strategies using two types of simulated data: observationsrepresenting TCE concentrations from a single individual, andobservations that simulateinter-individual variability. The latter type of data, which iscommonly found in experiments related to toxicokinetics, assumesvariability in the parameters across a population, and may includeobservations from multiple individuals. Using both deterministic andprobability-based estimation techniques, we demonstrate thatthe probability-based estimation strategiesthat incorporate variability in the parameters may be best suited forestimating adipose model parameters that vary across the population.