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Assessing the complexity of signals or dynamical systems is important in disease diagnosis, mechanical system defect, astronomy analysis, and many other fields. Although entropy measures as complexity estimators have greatly improved, the majority of these measures are quite sensitive to specified parameters and are impacted by short data lengths. This paper proposes a novel entropy algorithm to enhance the existing complexity assessment methods based on classical dispersion entropy (DE) and Rényi entropy (RE) by introducing refined composite multiscale coarse-grained treatment and phase transformation. The proposed refined composite multiscale phase Rényi dispersion entropy (PRRCMDE) addresses the flaws of various existing entropy approaches while still incorporating their merits. Several simulated signals from logistic mapping, AR model, MIX process, and additive WGN periodic signals are adopted to examine the performance of PRRCMDE from multiple perspectives. It demonstrates that the efficacy of the suggested algorithm can be increased by modifying the DE and RE parameters to a reasonable range. As a real-world application, the bearings' varied fault types and levels can also be recognized clearly. [ABSTRACT FROM AUTHOR]

Permutation entropy (PE) has been regarded as a most successful measure for the complexity of the time series. To overcome the undeniable shortcomings of PE is some cases, this paper designs a novel complexity algorithm called multiscale weighted phase permutation entropy (MWPPE). The proposed MWPPE adopts phase transformation, weight influence and multiscale information to improve PE, which can help us understand the complexity of nonlinear time series in depth. The method is also further extended to fractional order to obtain fractional multiscale phase permutation entropy (FMPPE). Based on the simulation sequence, a deep and systematic discussion is carried out on the effectiveness of the proposed two complexity measure algorithms, and results show that the proposed algorithms can amplify the detection effect of dynamic changes. Aiming at the financial markets of many countries and regions, the dynamic properties of financial time series with stock index are analyzed. It is concluded that compared with the MWPPE method, the FMPPE strategy can distinguish developed country stock index and emerging country stock index more effectively. • Two novel measure methods to quantify the complexity of nonlinear time series are proposed. • These models not only consider the amplitude information of the original time series, but also encode the phase, multiscale and fractional information. • These algorithms can reduce the variability of the entropy measurement on the long time scale, thus making the results more reliable and stable. • The model is applied to different time series, which proves the good performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]