Enhanced time series analysis using improved symplectic geometric mode decomposition and refined ordinal pattern network

The analysis of time series data is pivotal in numerous domains, yet it is frequently hindered by challenges such as non-stationarity, noise, and the presence of outliers. This paper presents a novel methodology that integrates an improved symplectic geometric mode decomposition (ISGMD) with a refined ordinal pattern network (ROPN) for advanced time series analysis. ISGMD enhances traditional decomposition techniques by incorporating a dispersion entropy-based Lempel–Ziv complexity method. This integration significantly boosts robustness and noise resilience, thereby improving the accuracy of signal characterization. Concurrently, ROPN advances the ordinal pattern network approach by including both ordinal and absolute amplitude information, which results in more precise network construction and dynamic feature extraction. The synthetic signal experimental results demonstrate that ISGMD substantially outperforms existing methods, such as time-varying filter approach for empirical mode decomposition (TVF-EMD) and successive variational mode decomposition (SVMD), in terms of noise reduction and computational efficiency. Comparative analyses using chaotic maps and amplitude-modulated chirp signals underscore ROPN's superior capability in handling noisy datasets and capturing intricate temporal dynamics. Furthermore, the effectiveness of ISGMD and ROPN is validated through practical applications on measured underwater acoustic signals, achieving a recognition rate consistently above 90%. This outperforms traditional methods, such as SGMD, TVF-EMD, and SVMD combined with ROPN by over 6%, and exceeds ISGMD combined with OPN by more than 4%. These results highlight the superiority of the ISGMD-ROPN, advancing the accuracy and efficiency of time series analysis in practical applications.