Affiliations: [a] Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, USA | [b] Materials and Manufacturing Directorate, Air Force Research Labs, Wright-Patterson Air Force Base, OH, USA
Correspondence:
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Corresponding author: H.T. Banks, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8212, USA. E-mail:htbanks@ncsu.edu
Abstract: Reflectance spectroscopy obtained from thermally treated silicon nitride carbon based ceramic matrix composites is used to quantity the oxidation products SiO_2 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 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 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, including a piecewise asymptotic confidence band for the estimated probability density. 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.
