Coded Permutation Entropy: A Measure for Dynamical Changes Based on the Secondary Partitioning of Amplitude Information

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.