Adaptive decomposition of nonlinear and noisy signals using a dual-criterion symplectic framework

Accurate extraction of informative components from nonlinear, nonstationary, and noisy signals remains a challenging task. While symplectic geometric mode decomposition (SGMD) effectively preserves intrinsic dynamical structures, its conventional framework may suffer from over-decomposition and redundant modes. To overcome these limitations, this study proposes an adaptive symplectic geometric mode decomposition (ASGMD), which integrates a termination criterion based on ternary Lempel–Ziv Complexity (TLZC) to adaptively determine suitable stopping points and prevent over-decomposition, together with a hybrid time–frequency (HTF)-based similarity decision that extracts features from the HTF domain and applies density-based spatial clustering of applications with noise (DBSCAN) to automatically identify and merge correlated components. Simulation results show that ASGMD achieves superior noise robustness, decomposition stability, and accuracy compared with jump plus AM-FM mode decomposition, feature mode decomposition, successive variational mode decomposition, and conventional SGMD. Real-world validation using gear vibration signals and ship-radiated noise data further demonstrates its effectiveness in extracting physically meaningful components and improving both fault diagnosis and acoustic target recognition. Overall, the proposed ASGMD provides a reliable and adaptive framework for nonlinear signal analysis, enhancing interpretability and robustness across diverse real-world applications.