Abstract
An improved permutation entropy (PE) algorithm named coded permutation entropy (CPE) is proposed in this paper to optimize the problems existing in PE based on the secondary partitioning. The principle of CPE algorithm is given, and the performance of it for dynamical change detection is analyzed using synthetic signal, logistic map and Lorenz map. The detection ability of CPE algorithm in different signal-to-noise ratios (SNR) is studied and the algorithm complexity is discussed. The results show that CPE can accurately capture minor feature information and amplify the detection results of dynamical changes compared with PE, weighted permutation entropy (WPE) and amplitude-aware permutation entropy (AAPE), but it has less robustness to noise and requires a higher computation cost than the others. Finally, we use the new algorithm to analyze the rolling bearing fault signals. The application of actual signals illustrates that CPE performs better in detecting abnormal pulse of the rolling bearing when the embedded dimension is small. From all the analyses in this paper, we find that CPE has a better performance for dynamical change detection compared with the other three algorithms when there is a larger repetition rate of permutation pattern in the position sequences.
Highlights
Detecting the dynamical changes of complex systems and distinguishing the complexity of output time series offer great practical significance in physics, biomedicine, engineering and economics
A synthetic signal, a discrete standard model and a continuous standard model are applied to verify the limitations of permutation entropy (PE), weighted permutation entropy (WPE) and aware permutation entropy (AAPE), and illustrate the advantage of coded permutation entropy (CPE)
The dynamical change detection performance of these four algorithms are studied when the signal contains the noise, and the algorithm complexity is analyzed from the running time and time complexity
Summary
Detecting the dynamical changes of complex systems and distinguishing the complexity of output time series offer great practical significance in physics, biomedicine, engineering and economics. In 2002, Bandt and Pompe proposed permutation entropy (PE) to measure the natural complexity of time series [4] After that, this algorithm has attracted the attention of many researchers because it has superior robustness and requires less computation [14,15,16]. In Reference [25], He et al proposed a concept which has the intention of secondary partitioning, and they applied their idea in the multivariate system and presented multivariate permutation entropy (MvPE) In their concept, each permutation pattern in PE is divided into three sub-patterns according to where the intermediate element is. We make a secondary partitioning, which improving the accuracy of partitioning based on permutation pattern and overcoming the incompatibility of MvPE algorithm for m, and propose coded permutation entropy (CPE).
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