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Description
Vector Fitting (VF) is a recent macromodeling method that has been popularized by its use in many commercial software for extracting equivalent circuit's of simulated networks. Specifically for material measurement applications, VF is shown to estimate either the permittivity or permeability of a multi-Debye material accurately, even when measured in the presence of noise and interferences caused by test setup imperfections. A brief history and survey of methods utilizing VF for material measurement will be introduced in this work. It is shown how VF is useful for macromodeling dielectric materials after being measured with standard transmission line and free-space methods. The sources of error in both an admittance tunnel test device and stripline resonant cavity test device are identified and VF is employed for correcting these errors. Full-wave simulations are performed to model the test setup imperfections and the sources of interference they cause are further verified in actual hardware measurements. An accurate macromodel is attained as long as the signal-to-interference-ratio (SIR) in the measurement is sufficiently high such that the Debye relaxations are observable in the data. Finally, VF is applied for macromodeling the time history of the total fields scattering from a perfectly conducting wedge. This effort is an initial test to see if a time domain theory of diffraction exists, and if the diffraction coefficients may be exactly modeled with VF. This section concludes how VF is not only useful for applications in material measurement, but for the solution of modeling fields and interactions in general.
ContributorsRichards, Evan (Author) / Diaz, Rodolfo E (Thesis advisor) / Tsakalis, Konstantinos (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2013
Description
This thesis describes an approach to system identification based on compressive sensing and demonstrates its efficacy on a challenging classical benchmark single-input, multiple output (SIMO) mechanical system consisting of an inverted pendulum on a cart. Due to its inherent non-linearity and unstable behavior, very few techniques currently exist that are capable of identifying this system. The challenge in identification also lies in the coupled behavior of the system and in the difficulty of obtaining the full-range dynamics. The differential equations describing the system dynamics are determined from measurements of the system's input-output behavior. These equations are assumed to consist of the superposition, with unknown weights, of a small number of terms drawn from a large library of nonlinear terms. Under this assumption, compressed sensing allows the constituent library elements and their corresponding weights to be identified by decomposing a time-series signal of the system's outputs into a sparse superposition of corresponding time-series signals produced by the library components. The most popular techniques for non-linear system identification entail the use of ANN's (Artificial Neural Networks), which require a large number of measurements of the input and output data at high sampling frequencies. The method developed in this project requires very few samples and the accuracy of reconstruction is extremely high. Furthermore, this method yields the Ordinary Differential Equation (ODE) of the system explicitly. This is in contrast to some ANN approaches that produce only a trained network which might lose fidelity with change of initial conditions or if facing an input that wasn't used during its training. This technique is expected to be of value in system identification of complex dynamic systems encountered in diverse fields such as Biology, Computation, Statistics, Mechanics and Electrical Engineering.
ContributorsNaik, Manjish Arvind (Author) / Cochran, Douglas (Thesis advisor) / Kovvali, Narayan (Committee member) / Kawski, Matthias (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2011
Description
The reconstruction of piecewise smooth functions from non-uniform Fourier data arises in sensing applications such as magnetic resonance imaging (MRI). This thesis presents a new polynomial based resampling method (PRM) for 1-dimensional problems which uses edge information to recover the Fourier transform at its integer coefficients, thereby enabling the use of the inverse fast Fourier transform algorithm. By minimizing the error of the PRM approximation at the sampled Fourier modes, the PRM can also be used to improve on initial edge location estimates. Numerical examples show that using the PRM to improve on initial edge location estimates and then taking of the PRM approximation of the integer frequency Fourier coefficients is a viable way to reconstruct the underlying function in one dimension. In particular, the PRM is shown to converge more quickly and to be more robust than current resampling techniques used in MRI, and is particularly amenable to highly irregular sampling patterns.
ContributorsGutierrez, Alexander Jay (Author) / Platte, Rodrigo (Thesis director) / Gelb, Anne (Committee member) / Viswanathan, Adityavikram (Committee member) / Barrett, The Honors College (Contributor) / School of International Letters and Cultures (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-05