Dynamical mode recognition of coupled flame oscillators by supervised and unsupervised learning approaches

Combustion instability in gas turbines and rocket engines, as one of the most challenging problems in combustion research, arises from the complex interactions among flames influenced by chemical reactions, heat and mass transfer, and acoustics. Identifying and understanding combustion instability is essential for ensuring the safe and reliable operation of many combustion systems, where exploring and classifying the dynamical behaviors of complex flame systems is a core task. To facilitate fundamental studies, the present work concerned dynamical mode recognition of coupled flame oscillators made of flickering buoyant diffusion flames, which have gained increasing attention in recent years but are not sufficiently understood. The time series data of flame oscillators were generated through fully validated reacting flow simulations. Due to the limitations of expertise-based models, a data-driven approach was adopted. In this study, a nonlinear dimensional reduction model of variational autoencoder (VAE) was used to project the high dimensional data onto a 2-dimensional latent space. Based on phase trajectories in the latent space, both supervised and unsupervised classifiers were proposed for datasets with and without well-known labeling, respectively. For labeled datasets, we established the Wasserstein-distance-based classifier (WDC) for mode recognition; for unlabeled datasets, we developed a novel unsupervised classifier (GMM-DTW) combining dynamic time warping (DTW) and Gaussian mixture model (GMM). Through comparing with conventional approaches for dimensionality reduction and classification, the proposed supervised and unsupervised VAE-based approaches exhibit a prominent performance across seven assessment metrics for distinguishing dynamical modes, implying their potential extension to dynamical mode recognition in complex combustion problems. © 2024