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Entropy 2019, 21(3), 238; https://doi.org/10.3390/e21030238

Extreme Interval Entropy Based on Symbolic Analysis and a Self-Adaptive Method

1
Faculty of Printing Packaging Engineering and Digital Media Technology, Xi’an University of Technology, Xi’an 710048, China
2
School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an 710048, China
*
Author to whom correspondence should be addressed.
Received: 6 January 2019 / Revised: 22 February 2019 / Accepted: 26 February 2019 / Published: 2 March 2019
(This article belongs to the Section Signal and Data Analysis)
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Abstract

Self-adaptive methods are recognized as important tools in signal process and analysis. A signal can be decomposed into a serious of new components with these mentioned methods, thus the amount of information is also increased. In order to use these components effectively, a feature set is used to describe them. With the development of pattern recognition, the analysis of self-adaptive components is becoming more intelligent and depend on feature sets. Thus, a new feature is proposed to express the signal based on the hidden property between extreme values. In this investigation, the components are first simplified through a symbolization method. The entropy analysis is incorporated into the establishment of the characteristics to describe those self-adaptive decomposition components according to the relationship between extreme values. Subsequently, Extreme Interval Entropy is proposed and used to realize the pattern recognition, with two typical self-adaptive methods, based on both Empirical Mode Decomposition (EMD) and Empirical Wavelet Transform (EWT). Later, extreme interval entropy is applied in two fault diagnosis experiments. One experiment is the fault diagnosis for rolling bearings with both different faults and damage degrees, the other experiment is about rolling bearing in a printing press. The effectiveness of the proposed method is evaluated in both experiments with K-means cluster. The accuracy rate of the fault diagnosis in rolling bearing is in the range of 75% through 100% using EMD, 95% through 100% using EWT. In the printing press experiment, the proposed method can reach 100% using EWT to distinguish the normal bearing (but cannot distinguish normal samples at different speeds), with fault bearing in 4r/s and in 8r/s. The fault samples are identified only according to a single proposed feature with EMD and EWT. Therefore, the extreme interval entropy is proved to be a reliable and effective tool for fault diagnosis and other similar applications. View Full-Text
Keywords: empirical mode decomposition; empirical wavelet transform; intrinsic mode functions; symbolization; extreme interval entropy empirical mode decomposition; empirical wavelet transform; intrinsic mode functions; symbolization; extreme interval entropy
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Xu, Z.; Shi, Y.; Zhao, Q.; Li, W.; Liu, K. Extreme Interval Entropy Based on Symbolic Analysis and a Self-Adaptive Method. Entropy 2019, 21, 238.

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