Generalized fined-grained multiscale information entropy with multi-feature extraction and its application in phase space reconstruction

Phase space reconstruction plays an indispensable role in nonlinear engineering applications, and the quality of the reconstructed attractor depends on the optimal estimation of delay time and embedding dimension. This study mainly proposes a novel solution strategy for optimal delay time, which can lead to statistically equivalent reconstructions. First, a novel generalized fined-grained multiscale information entropy with multi-feature extraction (GFMIEME) is proposed, which exhibits excellent separability for various noises and chaotic signals. GFMIEME can preserve more original information and features of the target signals while ensuring processing efficiency. The design of multi-feature extraction helps to solve the problem that the mutation features are smoothed in multi-scale analysis, such as the violent fluctuations of signal amplitude and frequency are weakened. Then, based on GFMIEME, an improved mutual information method is developed to estimate delay time precisely. This method ensures the optimal estimation of the delay time for target signals through multiscale and multi-feature analysis. Final, phase space reconstruction is performed on the chaotic signals generated by the Lorenz and Liu systems to evaluate the effectiveness of the GFMIEME-based mutual information method to estimate the optimal delay time. Moreover, the robustness of the proposed method to noise under different signal-to-noise ratios (SNRs) is analyzed. The simulation results illustrate that the improved mutual information method can extract multiscale and multi-feature information from chaotic signals, and estimate the optimal delay time. The reconstructed attractors have a topological structure similar to the original system. Compared with the traditional delay time estimation methods, the proposed GFMIEME-based mutual information method exhibits better robustness to noise. When the SNR reaches -25 dB, the optimal delay times of the Lorenz and Liu attractors can still be estimated successfully.