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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
Description
Finite element simulations modeling the hydrodynamic impact loads subjected to an elastomeric coating were performed to develop an understanding of the performance and failure mechanisms of protective coatings for cavitating environments.
In this work, two major accomplishments were achieved: 1) scaling laws were developed from hydrodynamic principles and numerical simulations to allow conversion of measured distributions of pressure peaks in a cavitating flow to distributions of microscopic impact loadings modeling individual bubble collapse events, and 2) a finite strain, thermo-mechanical material model for polyurea-based elastomers was developed using a logarithmic rate formulation and implemented into an explicit finite element code.
Combining the distribution of microscopic impact loads and finite element modeling, a semi-quantitative predictive framework is created to calculate the energy dissipation within the coating which can further the understanding of temperature induced coating failures.
The influence of coating thickness and elastomer rheology on the dissipation of impact energies experienced in cavitating flows has also been explored.
The logarithmic formulation has many desired features for the polyurea constitutive model, such as objectivity, integrability, and additive decomposition compatibility.
A review and discussion on the kinematics in large deformation, including a comparison between Lagrangian and Eulerian descriptions, are presented to explain the issues in building rate-dependent constitutive models in finite strains.
When comparing the logarithmic rate with other conventional rates in test examples, the logarithmic rate shows a better conservation of objectivity and integrability.
The modeling framework was validated by comparing predictions against temperatures measured within coatings subjected to a cavitating jet.
Both the experiments and models show that the temperatures generated, even under mild flow conditions, raise the coating temperature by a significant amount, suggesting that the failure of these coatings under more aggressive flows is thermally induced.
The models show that thin polyurea coatings synthesized with shorter molecular weight soft segments dissipate significantly less energy per impact and conduct heat more efficiently.
This work represents an important step toward understanding thermally induced failure in elastomers subjected to cavitating flows, which provides a foundation for design and optimization of coatings with enhanced erosion resistance.
In this work, two major accomplishments were achieved: 1) scaling laws were developed from hydrodynamic principles and numerical simulations to allow conversion of measured distributions of pressure peaks in a cavitating flow to distributions of microscopic impact loadings modeling individual bubble collapse events, and 2) a finite strain, thermo-mechanical material model for polyurea-based elastomers was developed using a logarithmic rate formulation and implemented into an explicit finite element code.
Combining the distribution of microscopic impact loads and finite element modeling, a semi-quantitative predictive framework is created to calculate the energy dissipation within the coating which can further the understanding of temperature induced coating failures.
The influence of coating thickness and elastomer rheology on the dissipation of impact energies experienced in cavitating flows has also been explored.
The logarithmic formulation has many desired features for the polyurea constitutive model, such as objectivity, integrability, and additive decomposition compatibility.
A review and discussion on the kinematics in large deformation, including a comparison between Lagrangian and Eulerian descriptions, are presented to explain the issues in building rate-dependent constitutive models in finite strains.
When comparing the logarithmic rate with other conventional rates in test examples, the logarithmic rate shows a better conservation of objectivity and integrability.
The modeling framework was validated by comparing predictions against temperatures measured within coatings subjected to a cavitating jet.
Both the experiments and models show that the temperatures generated, even under mild flow conditions, raise the coating temperature by a significant amount, suggesting that the failure of these coatings under more aggressive flows is thermally induced.
The models show that thin polyurea coatings synthesized with shorter molecular weight soft segments dissipate significantly less energy per impact and conduct heat more efficiently.
This work represents an important step toward understanding thermally induced failure in elastomers subjected to cavitating flows, which provides a foundation for design and optimization of coatings with enhanced erosion resistance.
ContributorsLiao, Xiao (Author) / Oswald, Jay (Thesis advisor) / Liu, Yongming (Committee member) / Jiang, Hanqing (Committee member) / Rajan, Subramaniam D. (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2016