Compressed multi-scale entropy and its application in mechanical fault diagnosis

Area of Science:

• Engineering
• Data Science
• Signal Processing

Background:

• Multi-scale entropy (MSEn) is a key technique for time series complexity analysis, widely used in mechanical fault diagnosis.
• Traditional MSEn methods suffer from information aliasing during coarse-graining, compromising data reliability and analysis accuracy.
• This limitation hinders the precise identification of faults in mechanical systems.

Purpose of the Study:

• To analyze the information aliasing issue inherent in classical MSEn.
• To propose a novel method, Compressed Multi-scale Entropy (CoMSEn), to overcome these limitations in mechanical fault diagnosis.
• To validate the effectiveness of CoMSEn using benchmark datasets.

Main Methods:

• Introduced random Gaussian matrices for transformation domain projection in the CoMSEn method.
• Utilized varying compression rates as a proxy for different scales in multi-scale analysis.
• Employed the mean of sample entropy from multiple compressions to mitigate Gaussian matrix randomness and ensure result reliability.

Main Results:

• CoMSEn effectively suppresses information aliasing, outperforming classical MSEn by preserving discriminative information.
• The method demonstrates high reliability due to the properties of random Gaussian matrices in sparse signal domains.
• Validation on the CWRU rolling bearing and reciprocating compressor valve datasets confirmed CoMSEn's effectiveness.

Conclusions:

• CoMSEn offers a more reliable approach to complexity measurement in time series for mechanical fault diagnosis.
• The proposed method provides a robust theoretical foundation for entropy calculation, improving fault detection accuracy.
• CoMSEn represents a significant advancement over traditional MSEn techniques in analyzing mechanical system health.