The sum of weighted normalized square envelope: A unified framework for kurtosis, negative entropy, Gini index and smoothness index for machine health monitoring

• Published in: Mechanical systems and signal processing 2020-06, Vol.140, p.106725, Article 106725
• Main Authors: Wang, Dong, Peng, Zhike, Xi, Lifeng
• Format: Article
• Language: English
• Subjects: Degradation; Entropy; Failure analysis; Gini index; Health monitoring; Kurtosis; Negative entropy; Smoothness; Smoothness index; Spectra; Unified framework
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2020.106725

•A unified framework for kurtosis, entropy, smoothness index and Gini index was discovered.•Soft thresholding used in calculating kurtosis and negative entropy was discovered.•The main difference between spectral kurtosis and spectral negative entropy was discovered.•Weight designs by domain knowledge and a data-driven method were respectively presented. Machine health monitoring aims to use monitoring data collected from a machine to assess machine degradation and prevent unexpected machine failures. Spectral kurtosis, spectral negative entropy, spectral Gini index and spectral smoothness index are well-known indices for characterizing the impulsiveness of repetitive transients caused by early machine faults. In this paper, it is discovered that all of these indices fall into the sum of weighted normalized square envelope. The main difference among these indices is that different weights are respectively applied to normalized square envelope. Further, weight designs by domain knowledge and a data-driven method are respectively presented. Then, the proposed unified framework is applied to analyze bearing run to failure degradation data. The proposed framework can be easily extended to other health monitoring situations in which repetitive transients and fault frequencies are of concern.