  Oscillatory combustion in aero engines and modern gas turbines often has
significant adverse effects on their operation, and accurately recognizing
various oscillation modes is the prerequisite for understanding and controlling
combustion instability. However, the high-dimensional spatial-temporal data of
a complex combustion system typically poses considerable challenges to the
dynamical mode recognition. Based on a two-layer bidirectional long short-term
memory variational autoencoder (Bi-LSTM-VAE) dimensionality reduction model and
a two-dimensional Wasserstein distance-based classifier (WDC), this study
proposes a promising method (Bi-LSTM-VAE-WDC) for recognizing dynamical modes
in oscillatory combustion systems. Specifically, the Bi-LSTM-VAE dimension
reduction model was introduced to reduce the high-dimensional spatial-temporal
data of the combustion system to a low-dimensional phase space; Gaussian kernel
density estimates (GKDE) were computed based on the distribution of phase
points in a grid; two-dimensional WD values were calculated from the GKDE maps
to recognize the oscillation modes. The time-series data used in this study
were obtained from numerical simulations of circular arrays of laminar flame
oscillators. The results show that the novel Bi-LSTM-VAE method can produce a
non-overlapping distribution of phase points, indicating an effective
unsupervised mode recognition and classification. Furthermore, the present
method exhibits a more prominent performance than VAE and PCA (principal
component analysis) for distinguishing dynamical modes in complex flame
systems, implying its potential in studying turbulent combustion.
