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Quantifying Degradation in Ceramic Matrix Composites Through Electromagnetic Interrogation and the Related Estimation Techniques.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Quantifying Degradation in Ceramic Matrix Composites Through Electromagnetic Interrogation and the Related Estimation Techniques./
Author:	Catenacci, Jared William.
Description:	1 online resource (168 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
Contained By:	Dissertation Abstracts International78-08B(E).
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369620351

Quantifying Degradation in Ceramic Matrix Composites Through Electromagnetic Interrogation and the Related Estimation Techniques.
Catenacci, Jared William.

Quantifying Degradation in Ceramic Matrix Composites Through Electromagnetic Interrogation and the Related Estimation Techniques. - 1 online resource (168 pages)

Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

Re ectance spectroscopy obtained from thermally treated silicon nitride carbon based ceramic matrix composites is used to quantity the oxidation products SiO2 and SiN. The data collection is described in detail in order to point out the potential biasing present in the data processing. A probability distribution is imposed on selected dielectric model parameters, and then non-parametrically estimated. A non-parametric estimation is chosen since the exact composition of the material is unknown due to the inherent heterogeneity of ceramic composites. The probability distribution is estimated using the Prohorov metric framework (PMF) in which the infinite dimensional optimization is reduced to a finite dimensional optimization using an approximating space composed of linear splines. A weighted least squares estimation is carried out, and uncertainty quantification is performed on the model parameters. Our estimation results indicate a distinguishable increase in the SiO 2 present in the samples which were heat treated for 100 hours compared to those treated for 10 hours.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369620351Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Quantifying Degradation in Ceramic Matrix Composites Through Electromagnetic Interrogation and the Related Estimation Techniques.
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100 1 $a Catenacci, Jared William. $3 1180810
245 1 0 $a Quantifying Degradation in Ceramic Matrix Composites Through Electromagnetic Interrogation and the Related Estimation Techniques.
264 0 $c 2016
300 $a 1 online resource (168 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
500 $a Adviser: Amanda Criner.
502 $a Thesis (Ph.D.) $c North Carolina State University $d 2016.
504 $a Includes bibliographical references
520 $a Re ectance spectroscopy obtained from thermally treated silicon nitride carbon based ceramic matrix composites is used to quantity the oxidation products SiO2 and SiN. The data collection is described in detail in order to point out the potential biasing present in the data processing. A probability distribution is imposed on selected dielectric model parameters, and then non-parametrically estimated. A non-parametric estimation is chosen since the exact composition of the material is unknown due to the inherent heterogeneity of ceramic composites. The probability distribution is estimated using the Prohorov metric framework (PMF) in which the infinite dimensional optimization is reduced to a finite dimensional optimization using an approximating space composed of linear splines. A weighted least squares estimation is carried out, and uncertainty quantification is performed on the model parameters. Our estimation results indicate a distinguishable increase in the SiO 2 present in the samples which were heat treated for 100 hours compared to those treated for 10 hours.
520 $a To establish probability measure estimation in a nonparametric model using the Prohorov Metric Framework, we first summarize the computational methods and related convergence results that were recently developed by our group. Results are presented on the bias and the variance due to the approximation and the pointwise asymptotic normality of the approximated probability measure estimator is established. We propose use of a model selection criterion to balance the bias and the variance, and compare the pointwise confidence bands constructed using the asymptotic normality results with that obtained by Monte Carlo simulations. Additionally, we propose a method in which the information provided by difference based approximations of the measurement errors is used as a way of determining the presence of statistical model discrepancy. A number of numerical examples are given to illustrate the effectiveness of these proposed methods.
520 $a Additionally, we investigate the feasibility of quantifying properties of a composite dielectric material through the re ectance in which we estimate an unknown probability measure by means of the PMF. We point out the limitation of the existing computational algorithms for this particular application. We then improve the algorithms, and demonstrate the feasibility of our proposed methods by numerical results obtained for both simulated data and experimental data for inorganic glass. We compare this with a second, more classical approach, where it is assumed that the permittivity is composed of a number of oscillators, and then a convolution is taken with a normal distribution. Each of these methods are able to fit the data well, yet the ease in interpreting the estimation results in using the PMF approach, as well as the tight mathematical results guaranteeing convergence under the Prohorov metric, lead us to favor this approach.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a North Carolina State University. $3 845424
773 0 $t Dissertation Abstracts International $g 78-08B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10583340 $z click for full text (PQDT)