Quantifying the degradation in thermally treated ceramic matrix composite

Reflectance spectroscopy obtained from a thermally treated silicon nitride carbon based ceramic matrix composite 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 select 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 SiO2 present in the samples which were heat treated for 100 hours compared to 10 hours.