Ensemble Improved Permutation Entropy: A New Approach for Time Series Analysis

Entropy quantification approaches have gained considerable attention in engineering applications. However, certain limitations persist, including the strong dependence on parameter selection, limited discriminating power, and low robustness to noise. To alleviate these issues, this paper introduces two novel algorithms for time series analysis: the ensemble improved permutation entropy (EIPE) and multiscale EIPE (MEIPE). Our approaches employ a new symbolization process that considers both permutation relations and amplitude information. Additionally, the ensemble technique is utilized to reduce the dependence on parameter selection. We performed a comprehensive evaluation of the proposed methods using various synthetic and experimental signals. The results illustrate that EIPE is capable of distinguishing white, pink, and brown noise with a smaller number of samples compared to traditional entropy algorithms. Furthermore, EIPE displays the potential to discriminate between regular and non-regular dynamics. Notably, when compared to permutation entropy, weighted permutation entropy, and dispersion entropy, EIPE exhibits superior robustness against noise. In practical applications, such as RR interval data classification, bearing fault diagnosis, marine vessel identification, and electroencephalographic (EEG) signal classification, the proposed methods demonstrate better discriminating power compared to conventional entropy measures. These promising findings validate the effectiveness and potential of the algorithms proposed in this paper.