Dispersion entropy (DE) can effectively detect the chaotic features in ordered sequences. However, DE is only defined by the probability distribution of static dispersion patterns, ignoring the dynamic transitions between pairwise dispersion patterns. Therefore, in this paper, by introducing the transition probability between pairwise dispersion patterns, we propose the transfer dispersion entropy (TDE) to detect the chaotic characteristics of the system. Additionally, based on both the difference in the number of each dispersion patterns and the difference in the transfer probability matrix, we define a dissimilarity measure for different sequences, namely transfer dissimilarity based on dispersion patterns (TDDP). Then, the proposed methods are verified on numerical simulation data and NASA-CMAPSS aero-engine simulation data.Compared with the existing entropy algorithms, the results show that TDE can not only capture more detailed chaotic changes, but also identify the early degradation of gas path components by detecting abnormal shifts in pattern transition behaviors, enabling more timely fault warnings.Finally, the combination of TDDP and multidimensional scaling can be used for similarity classification of aero-engine simulation time series.
Zhang et al. (Wed,) studied this question.