Improvement of Statistical Performance of Ordinal Multiscale Entropy Techniques Using Refined Composite Downsampling...

Area of Science:

• Complexity Science
• Time Series Analysis
• Information Theory

Background:

• Multiscale Permutation Entropy (MPE) is a key method for quantifying time series information content.
• Existing refinements like Composite MPE (cMPE) and Refined Composite MPE (rcMPE) enhance precision but lack theoretical grounding.
• There is a need for a robust theoretical framework and improved methods for entropy estimation.

Purpose of the Study:

• To develop the statistical theory underpinning cMPE and rcMPE.
• To introduce Refined Composite Downsampling Permutation Entropy (rcDPE) as a novel method for enhanced entropy estimation precision.
• To compare the performance of MPE, cMPE, rcMPE, and rcDPE in signal analysis applications.

Main Methods:

• Theoretical development of the statistical underpinnings for cMPE and rcMPE.
• Algorithmic design and implementation of the proposed Refined Composite Downsampling Permutation Entropy (rcDPE).
• Application of MPE, cMPE, rcMPE, and rcDPE to classify faults in bearing vibration signals.

Main Results:

• While cMPE and rcMPE showed improvements over MPE on uncorrelated noise, their performance exceeded predictions due to algorithm-inherent redundancies.
• The proposed rcDPE method aligned with theoretical predictions and significantly outperformed MPE, cMPE, and rcMPE.
• rcDPE demonstrated the smallest bias and variance in entropy estimation, leading to enhanced discrimination between faulty and non-faulty bearing vibration signals when combined with appropriate filtering.

Conclusions:

• The statistical theory for cMPE and rcMPE has been established.
• rcDPE offers superior precision and reduced bias/variance in entropy estimation compared to existing multiscale permutation entropy methods.
• rcDPE shows significant potential for improving fault diagnosis in mechanical systems by enhancing the analysis of vibration signals.