Advanced regression methods for combustion modelling using principal components

Modelling the physics of combustion remains a challenge due to a large range of temporal and physical scales which are important in these systems. Detailed chemical kinetic mechanisms are used to describe the chemistry involved in the combustion process yielding highly coupled partial differential equations for each of the chemical species used in the mechanism. Recently, Principal Components Analysis (PCA) has shown promise in its ability to identify a low-dimensional manifold describing the reacting system. Several PCA-based models have been developed which may be well-suited for combustion problems; however, several challenging aspects of the model must be addressed. In this paper, the parameterization of state-space variables and PC-transport equation source terms are investigated. The ability to achieve highly accurate mapping through various nonlinear regression methods is shown. In addition, the effect of PCA-scaling on the ability to regress the surface is investigated. Finally, the present work demonstrates the capabilities of the model by solving a reduced system represented by several PC-transport equations for a perfectly stirred reactor (PSR) configuration.