Nonlinear system-guided continuous-time generalization for cross-aircraft engine state monitoring

To address multi-distribution perception and temporal generalization challenges in cross-aircraft aero-engine monitoring, the Lyapunov-Schmidt Multi-distributed Perception Network (LSMPNet) is developed as a continuous-time domain generalization framework grounded in improved Lyapunov-Schmidt reduction (LSR). LSMPNet reformulates state monitoring as a continuous nonlinear system, leveraging a T-LSR Decomposer to perform structured decomposition and employing stacked T-LSR Blocks for hierarchical learning of dynamic features. A time-difference-based operator enhances sensitivity to continuous distribution shifts, while complementary manifold topologies strengthen global distribution perception and noise suppression. The linearized operator design ensures low computational complexity and interpretability. Extensive experiments on public benchmarks and real-world cross-aircraft datasets demonstrate superior performance in degradation modeling and water-wash early warning tasks.