Kernel density weighted principal component analysis of combustion processes

Principal component analysis (PCA) has been successfully applied to the analysis of combustion data-sets. However using PCA on a raw direct numerical simulation or an experimental data-set is not straightforward. Indeed, those data-sets usually show non-homogenous data density, hot and cold zones being generally over represented. This can introduce bias in the PCA reconstruction, especially when strong non-linear relationships characterize the data sample. To tackle this problem, a combination of the kernel density method and PCA is introduced here. This new PCA algorithm, called Temperature BAsed KErnel Density weighted PCA (T-BAKED PCA) allows to enhance the PCA accuracy especially in the flame front zone, which is the principal zone of interest. The performance of this new approach is benchmarked against classical PCA. Moreover, a new method called Hybrid T-BAKED PCA or HT-BAKED PCA, combining both classical and T-BAKED PCA, is proposed to provide an optimal representation of all flame regions.