Theoretical Investigations on Kurtosis and Entropy and Their Improvements for System Health Monitoring

Jingjing Zhong, Dong Wang, Ju'e Guo, Diego Cabrera, Chuan Li

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


System health monitoring as the basis of prognostics and health management (PHM) aims to explore health indices/features for PHM to do condition monitoring, perform abnormal detection, and provide degradation trends for prognostic models. Kurtosis and negative entropy are two classic and popular indices to measure the sparsity of impulsive transients, and they are prone to be affected by impulsive noise. The purpose of this article is twofold. Theoretically, new propositions and their proofs are proposed to illustrate how kurtosis and negative entropy can help to characterize impulsive transients and why they are affected by impulsive noise. Next, a weighted residual regression-based index is proposed to relieve the sensitivity of kurtosis and entropy to impulsive noise and to provide monotonic trends for gear and bearing degradation assessment. Theoretical results show that kurtosis and negative entropy are changed with the length of nonimpulsive regions of impulsive transients. Experimental results demonstrate that the proposed method has better incipient fault detection ability and monotonic trending ability than kurtosis and negative entropy for bearing and gear health monitoring and degradation assessment.

Original languageEnglish
Article number9223728
JournalIEEE Transactions on Instrumentation and Measurement
StatePublished - 2021

Bibliographical note

Funding Information:
Manuscript received July 31, 2020; revised September 15, 2020; accepted October 8, 2020. Date of publication October 14, 2020; date of current version December 24, 2020. This work was supported by the National Natural Science Foundation of China under Grant 51975355 and Grant 71774130. The Associate Editor coordinating the review process was Eduardo Cabal-Yepez. (Corresponding author: Chuan Li.) Jingjing Zhong and Chuan Li are with the College of Mechanical Engineering, Dongguan University of Technology, Dongguan 523808, China (e-mail:;

Publisher Copyright:
© 1963-2012 IEEE.


  • Condition monitoring
  • fault diagnosis
  • prognostics and health management (PHM)
  • system health monitoring
  • weighted residual regression


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