Extraction of nonlinear feature parameters based on multi-channel dataset

Phase space reconstruction plays a pivotal role in calculating features of nonlinear systems. By mapping one-dimensional time series onto a high-dimensional phase space using phase space reconstruction techniques, the dynamical characteristics of nonlinear systems can be revealed. However, existing nonlinear analysis methods are primarily based on phase space reconstruction of single-channel data and cannot directly utilize the rich information contained in multi-channel array data. The reconstructed data matrix shows the structural similarities with multi-channel array data. The relationship between phase space reconstruction and array data structure, as well as the gain in nonlinear features brought by array data, has not been sufficiently studied. In this paper, two classical nonlinear features: multiscale sample entropy and multiscale permutation entropy are adopted. The array multi-channel data are used to replace the phase space reconstruction step in algorithms so as to enhance the algorithmic performance. Initially, the relationship between phase space reconstruction parameters and actual array structures is analyzed, and conversion relationships are established. Then, multiple sets of simulated and real-world array data are used to evaluate the performances of the two entropy algorithms. The results show that substituting array data for phase space reconstruction effectively improves the performances of both entropy algorithms. Specifically, the multiscale sample entropy algorithm, when applied to array data, allows for distinguishing between noisy target signals from background noise at low signal-to-noise ratios. At the same time, the multiscale permutation entropy algorithm using array data reveals the complex structure of signals on different time scales more accurately.