Principal component analysis of turbulent combustion data: Data pre-processing and manifold sensitivity

Principal component analysis has demonstrated promise in its ability to identify low-dimensional chemical manifolds in turbulent reacting systems by providing a basis for the a priori parameterization of such systems based on a reduced number of parameterizing variables. Previous studies on PCA have only mentioned the importance of data pre-processing and scaling on the PCA analysis, without detailed consideration. This paper assesses the influence of data-preprocessing techniques on the size-reduction process accomplished through PCA. In particular, a methodology is proposed to identify and remove outlier observations from the datasets on which PCA is performed. Moreover, the effect of centering and scaling techniques on the PCA manifold is assessed and discussed in detail, to investigate how different scalings affect the size of the manifold and the accuracy in the reconstruction of the state-space. Finally, the sensitivity of the chemical manifold to flow characteristics is considered, to investigate its invariance with respect to the Reynolds number. Several high-fidelity experimental datasets from the TNF workshop database are considered in the present work to demonstrate the effectiveness of the proposed methodologies.