Deriving early warning signals of turbulent thermoacoustic system using principal component analysis

In modern combustors, predicting thermoacoustic instability is critical for preventing potentially catastrophic system failures. Recent research on turbulent thermoacoustic systems has revealed an underlying universality in the self-organization behavior observed during transitions, where ordered patterns emerge from initially disordered states. Inspired by these studies, our work identifies the principles governing the topology change of phase trajectories in high-dimensional space as turbulent thermoacoustic systems transition from combustion noise to periodic oscillation. The phase space is reconstructed using the Hankel matrix. We decompose the dynamics in phase-space topology into orthogonal modes by employing principal component analysis (PCA). Our investigation reveals that as the system transitions from low-amplitude aperiodic oscillation to thermoacoustic instability, significant changes in phase space modes occur before the root mean square of the pressure fluctuation reaches its maximum value, providing early warning signals of impending instability. Subsequently, the relative changes in the principal components will be analyzed by providing scaling relations. We will show that the topology change of the phase space trajectories, quantified by the aspect ratio, follows a power law across multiple systems.