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Entropy 2013, 15(3), 1069-1084; doi:10.3390/e15031069

Time Series Analysis Using Composite Multiscale Entropy

1 Department of Mechatronic Technology, National Taiwan Normal University, Taipei 10610, Taiwan 2 Department of Communication, Navigation and Control Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan 3 Mechanical and Systems Research Laboratories, Industrial Technology Research Institute, Hsinchu 31040, Taiwan 4 Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei 10617, Taiwan
* Author to whom correspondence should be addressed.
Received: 4 February 2013 / Revised: 25 February 2013 / Accepted: 13 March 2013 / Published: 18 March 2013
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Multiscale entropy (MSE) was recently developed to evaluate the complexity of time series over different time scales. Although the MSE algorithm has been successfully applied in a number of different fields, it encounters a problem in that the statistical reliability of the sample entropy (SampEn) of a coarse-grained series is reduced as a time scale factor is increased. Therefore, in this paper, the concept of a composite multiscale entropy (CMSE) is introduced to overcome this difficulty. Simulation results on both white noise and 1/f noise show that the CMSE provides higher entropy reliablity than the MSE approach for large time scale factors. On real data analysis, both the MSE and CMSE are applied to extract features from fault bearing vibration signals. Experimental results demonstrate that the proposed CMSE-based feature extractor provides higher separability than the MSE-based feature extractor.
Keywords: composite multiscale entropy; multiscale entropy; fault diagnosis composite multiscale entropy; multiscale entropy; fault diagnosis
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Wu, S.-D.; Wu, C.-W.; Lin, S.-G.; Wang, C.-C.; Lee, K.-Y. Time Series Analysis Using Composite Multiscale Entropy. Entropy 2013, 15, 1069-1084.

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