Electromagnetic Inverse Problems Involving Distributions of Dielectric Mechanisms and Parameters

Banks, Harvey Thomas; Gibson, N. L.

doi:10.21236/ada440142

Cited by 3 publications

(1 citation statement)

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“…In that work, a distribution was imposed on the resonance wavenumber and we continue that convention in our current investigation. There is a solid theoretical foundation for the non-parametric estimation of a probability distribution [2,3,6,7,17] under the Prohorov Metric Framework (PMF). The estimation procedure involves approximating the space of admissible probability measures by a finite dimensional space using, for example, either a Dirac approximation method or a linear spline approximation method.…”

Section: Introductionmentioning

confidence: 99%

Method Comparison for Estimation of Distributed Parameters in Permittivity Models Using Reflectance

Banks¹,

Catenacci²,

Hu³

2015

EJMCA

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The use of reflectance spectroscopy is a current area of study for the non-invasive evaluation of complex materials such as ceramic matrix composites. In order to model the reflectance, one must specify a model for the complex permittivity. In this work we compare two methods for modeling the complex permittivity of a heterogenous material. In one approach, we impose a probability distribution on a subset of the dielectric parameters. This approach leads to an infinite dimensional optimization problem over the space of probability measures. We approximate this space with a finite dimensional space by using either a Dirac approximation method or a linear spline approximation method. The second approach is to assume a number of oscillators in the permittivity model, and then use a convolution with a normal distribution. We compare both of these approaches on simulated data sets as well as data obtained from inorganic glasses. Each of these methods are able to fit the data well, yet the ease in interpreting the estimation results of imposing a probability distribution on parameters, as well as the tight mathematical results [2,7] guaranteeing convergence under the Prohorov metric, lead us to favor the first approach.

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Section: Introductionmentioning

confidence: 99%

Method Comparison for Estimation of Distributed Parameters in Permittivity Models Using Reflectance

Banks¹,

Catenacci²,

Hu³

2015

EJMCA

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A comparison of approximation methods for the estimation of probability distributions on parameters

Banks

Davis

2007

Applied Numerical Mathematics

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In this paper, we compare two computationally efficient approximation methods for the estimation of growth rate distributions in size-structured population models. After summarizing the underlying theoretical framework, we present several numerical examples as validation of the theory. Furthermore, we compare the results from a spline based approximation method and a delta function based approximation method for the inverse problem involving the estimation of the distributions of growth rates in size-structured mosquitofish populations. Convergence as well as sensitivity of the estimates with respect to noise in the data are discussed for both approximation methods. 1 Report Documentation PageForm Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

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Time Delay Systems With Distribution Dependent Dynamics

Banks

Dediu

Nguyen

2006

IFAC Proceedings Volumes

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General delay dynamical systems in which uncertainty is present in the form of probability measure dependent dynamics are considered. Several motivating examples arising in biology are discussed. A functional analytic framework for investigating well-posedness (existence, uniqueness and continuous dependence of solutions), inverse problems, sensitivity analysis and approximations of the measures for computational purposes is surveyed.

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Electromagnetic Inverse Problems Involving Distributions of Dielectric Mechanisms and Parameters

Cited by 3 publications

References 39 publications

Method Comparison for Estimation of Distributed Parameters in Permittivity Models Using Reflectance

Method Comparison for Estimation of Distributed Parameters in Permittivity Models Using Reflectance

A comparison of approximation methods for the estimation of probability distributions on parameters

Time Delay Systems With Distribution Dependent Dynamics

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