Interpretation and characterization of MILD combustion systems using unsupervised VQPCA clustering

Abstract

In this study, we have used an unsupervised clustering algorithm called Vec- tor Quantization Principal Component Analysis (VQPCA) to identify vari- able(s) for characterizing different Moderate and Intense Low-oxygen Dilu- tion (MILD) combustion systems. Two direct numerical simulation (DNS) datasets of non-premixed MILD combustion are used and they differ primar- ily in the oxygen (O2) dilution levels. Maximum volume fraction of O2 for Case-AZ1 is 3.5% (lower dilution) and for Case-BZ1 it is 2.0% (higher dilu- tion). The set of DNS grid points with thermo-chemical information is fed as input to VQPCA which partitions this set into a few clusters. Qualita- tive and quantitative comparison between VQPCA clusters and structures of physical variables such as mixture-fraction, Z, and heat-release rate, HRR, are used to identify variable for system-level characterization. While qualita- tive comparison is based on visualization, quantitative comparison is newly developed in this study and is based on Boolean logic. Subsequently, a new physics-based method is then proposed to rank important features (or vari- ables) for each cluster. This is useful for a fine-grained characterization of a system. This method is based on calculating the Hellinger distance be- tween the probability density functions (PDF) of each feature conditioned over a cluster and the region outside it. The outcome of physics-based feature ranking method is compared with several feature selection methods based on PCA. Finally, we also demonstrate that through careful selection of features we can tailor clustering outcomes in systems, like BZ1, where initially no system-level variable was recognized.