Abstract
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.
Highlights
Quantifying the amount of regularity for a time series is an essential task in understanding the behavior of a system
The effectiveness of the composite multiscale entropy (CMSE) algorithm is evaluated through two synthetic noise signals and a real vibration data set provided by Case Western Reserve University (CWRU) [17]
These results indicate that the entropy values calculated by the conventional multiscale entropy (MSE) and CMSE algorithms are almost the same, but the CMSE can estimate entropy values more accurate than the MSE
Summary
Quantifying the amount of regularity for a time series is an essential task in understanding the behavior of a system. The MSE has been successfully applied to different research fields in the past decades These applications include the analyses of the human gait dynamics [2], heart rate variability [3,4], electroencephalogram [5], postural control [6], vibration of rotary machine [7,8], rainfall time series [9], time series of river flow [10], electroseismic time series [11], time series of traffic flow [12], social dynamics [13], chatter in the milling process [14], and vibrations of a vehicle [15], etc. The effectiveness of the CMSE algorithm is evaluated through two synthetic noise signals and a real vibration data set provided by Case Western Reserve University (CWRU) [17]
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