A functional-PCA approach for analyzing and reducing complex chemical mechanisms

In industrial reactive flow systems such as furnaces and gas turbines, there are considerable variations in the temperature and concentrations of species along different spatial directions. Functional principal component analysis (fPCA) can be used to study the temporal (or spatial) evolution of reactions in a reactive flow system, and to develop simplified kinetic models to describe this behaviour. A comprehensive kinetic mechanism for CO oxidation is used to demonstrate application of fPCA to identify important reactions as a function of time. In conventional PCA, the eigenvalue–eigenvector decomposition specifically transforms the variations associated with the time (or spatial directions) and species into loadings that represent only the reactions. However, fPCA produces functional loading vectors ξ→l(t) which are functions of time or distance, whose elements are referred to as functional loadings. The functional loading vectors are the eigenfunctions of the covariance matrix associated with the sensitivity trajectories. The functional loadings are used to identify reactions playing a significant role, possibly as a function of time, and are used to develop a reduced kinetic scheme from a detailed kinetic mechanism.