Probabilistic Monitoring of Correlated Sensors for Nonlinear Processes in State Space

Shunyi Zhao, Yuriy S. Shmaliy, Choon Ki Ahn, Chunhui Zhao

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


To optimize control and/or state estimation of industrial processes, information about measurement quality provided by sensors is required. In this paper, a probabilistic scheme is proposed in discrete-time nonlinear state space with the purpose of sensor monitoring. A quantitative index representing the measurement quality, as well as satisfied state estimates, is obtained by estimating the probability density functions (PDFs) of the states and the measurement noise covariance considered as a random variable using the variational Bayesian approach. To solve the intractable integrals of nonlinear PDFs in real time, a set of weighted particles is generated to overlap an empirical density of state, while the PDF of the measurement noise is still derived analytically. An example of localization and an experiment with a rotary flexible joint are supplied to demonstrate that the proposed algorithm significantly improves the applicability of existing methods and can monitor correlated sensors satisfactorily.

Original languageEnglish
Article number8678661
Pages (from-to)2294-2303
Number of pages10
JournalIEEE Transactions on Industrial Electronics
Issue number3
Publication statusPublished - 2020 Mar

Bibliographical note

Funding Information:
Manuscript received June 18, 2018; revised November 3, 2018, January 3, 2019, and February 13, 2019; accepted March 5, 2019. Date of publication April 1, 2019; date of current version October 31, 2019. This work was supported in part by the National Natural Science Foundation of China under Grant 61833007 and Grant 61603155, in part by the 111 Project under Grant B12018, and in part by the National Research Foundation of Korea through the Ministry of Science, ICT, and Future Planning under Grant NRF-2017R1A1A1A05001325. (Corresponding authors: Shunyi Zhao; Choon Ki Ahn.) S. Zhao is with the Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China (e-mail:,

Publisher Copyright:
© 1982-2012 IEEE.


  • Nonlinear process
  • particle approximation
  • sensor monitoring
  • state estimation
  • variational Bayesian (VB) inference

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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