Multimode Process Monitoring with Bayesian Inference-Based Finite Gaussian Mixture Models

Jie YU*, S. Joe QIN

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

498 Citations (Scopus)


For complex industrial processes with multiple operating conditions, the traditional multivariate process monitoring techniques such as principal component analysis (PCA) and partial least squares (PLS) are ill-suited because the fundamental assumption that the operating data follow a unimodal Gaussian distribution usually becomes invalid. In this article, a novel multimode process monitoring approach based on finite Gaussian mixture model (FGMM) and Bayesian inference strategy is proposed. First the process data are assumed to be from a number of different clusters, each of which corresponds to an operating mode and can be characterized by a Gaussian component. In the absence of a priori process knowledge, the Figueiredo-Jain (F-J) algorithm is then adopted to automatically optimize the number of Gaussian components and estimate their statistical distribution parameters. With the obtained FGMM, a Bayesian inference strategy is further utilized to compute the posterior probabilities of each monitored sample belonging to the multiple components and derive an integrated global probabilistic index for fault detection of multimode processes. The validity and effectiveness of the proposed monitoring approach are illustrated through three examples: (1) a simple multivariate linear system, (2) a simulated continuous stirred tank heater (CSTH) process, and (3) the Tennessee Eastman challenge problem. The comparison of monitoring results demonstrates that the proposed approach is superior to the conventional PCA method and can achieve accurate and early detection of various types of faults in multimode processes. © 2008 American Institute of Chemical Engineers.
Original languageEnglish
Pages (from-to)1811-1829
Number of pages19
JournalAICHE Journal
Issue number7
Early online date9 May 2008
Publication statusPublished - Jul 2008
Externally publishedYes


  • Bayesian inference
  • Fault detection
  • Finite Gaussian mixture model
  • Global probabilistic index
  • Mahalanobis distance
  • Multimode process monitoring
  • Tennessee Eastman chemical process


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