A study of the fourth order joint statistical moment for dimensionality reduction of combustion datasets

Principal Component Analysis (PCA) is a widely used dimensionality reduction technique that uses the eigenvectors of the second-order joint statistical moment, i.e., the covariance matrix to transform thethermochemical state space. However, combustion simulations are often characterized by thin reaction zones that occupy small fractions of the computational domain. These zones are, statistically speaking, represented by a small set of samples which can be viewed as extreme valued events that break the assumption of an underlying Gaussian distribution. Furthermore, it is also reasonable that the underlying distribution of the thermochemical scalars be considered as non-Gaussian. Thus, it can be conjectured that the ability of PCA based reduced manifolds to capture important local chemical dynamics may not be optimal. In this work, the principal vectors needed for dimensionality reduction are obtained through a singular value decomposition of a matricized representation of the fourth order joint statistical moment, namely the Co-Kurtosis tensor. The performance of the proposed dimensionality reduction procedure is evaluated, and compared against PCA, for two combustion datasets namely the spontaneous ignition of premixed ethylene in a homogeneous reactor and that of a homogeneous charge compression ignition, for two reduced manifolds and the linear reconstruction technique. It is found that the proposed method captures the chemical dynamics, as represented by the heat release rate, approximately 1.85 times better (averaged over all results) than PCA.