Time Series Analysis Using Composite Multiscale Entropy

TLDR

Multiscale entropy evaluates time‑series complexity across scales, but its sample‑entropy estimates become statistically unreliable as the scale factor increases. This study proposes composite multiscale entropy to address the reliability problem of multiscale entropy at large time scales. The authors introduce CMSE and apply it to fault‑bearing vibration data to extract features. Simulations on white and 1/f noise and experiments on fault‑bearing vibration data show that CMSE yields more reliable entropy estimates at large scales and better feature separability than MSE.

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.