Analysis of Complex Time Series Using a Modified Multiscale Fuzzy Entropy Algorithm

Multiscale fuzzy entropy (MFE) is an effective algorithm which has been successfully applied in many fields for measuring the complexity of a time series. Though, MFE can yield inaccurate entropy estimations as the coarse-graining procedure used by the algorithm reduces the length of the time series under investigation. A modified multiscale fuzzy entropy (MMFE) algorithm is presented in this paper to overcome this problem. In this new approach, the coarse-graining procedure is replaced by a moving-average procedure which constructs template vectors in calculating the fuzzy entropy. The effectiveness of the proposed MMFE algorithm is evaluated on several mixed data (i.e., data mixed with white noise) of various data length. The result shows that the MMFE algorithm can effectively reduce the deviation in entropy estimation as compared to that using MFE algorithm. The MMFE algorithm is further employed in the study to estimate the complexity and irregularity of vibration data of a roller element bearing for fault diagnosis. It is shown that the MMFE algorithm can effectively discriminate the four bearing operation conditions under study.