Early detection of Hopf bifurcation in a solid rocket motor via transfer learning

Hopf bifurcation, a prevalent phenomenon in solid rocket motors (SRMs), signifies a critical transition from a fixed point to a limit cycle. The detection of early warning signals (EWSs) for Hopf bifurcation is significant for preventing or mitigating potentially dangerous self-excited states. However, conventional data-driven EWSs are hindered by the lack of a consistent threshold, yielding mainly qualitative judgments when solely pre-bifurcation data are available. In this study, we introduce a transfer learning (TL) framework designed to estimate the system growth rate as an EWS utilizing pre-bifurcation data. The framework is initially trained on the correlation between dynamical features and growth rate within a source domain, generated by a reduced-order model proposed by Culick. Subsequently, it is applied to the target domain from the SRM system. This TL-based EWS exhibits remarkable sensitivity when applied to the SRM system, providing consistent threshold values for quantitative predictions based on pre-bifurcation data exclusively. Our findings present a promising path for detecting the EWSs of Hopf bifurcations in SRMs and affirm the feasibility and tremendous potential of utilizing TL in scenarios where real data are limited.