Log Likelihood Monitoring for Multimode Process Using Variational Bayesian Mixture Factor Analysis Model

Fan Wang,Yixin Yin,Sen Zhang

doi:10.1109/access.2019.2925884

Fan Wang, Yixin Yin + Show 1 more

Open Access

https://doi.org/10.1109/access.2019.2925884

Copy DOI

Journal: IEEE Access	Publication Date: Jan 1, 2019
Citations: 2	License type: CC BY 4.0

Affiliation: University of Science and Technology Beijing

Abstract

When a traditional mixture factor analysis (MFA) model is used for multimode process monitoring, the determination of parameter is complex, and the construction of monitoring statistics only considers the expectation in probability distributions of factor space and residual space. In this paper, a novel fault detection method based on a variational Bayesian MFA model for multimode process is introduced. The parameters of the MFA model structure, namely the number of local factor analyzer and the reduced dimensionality inside each factor analyzer, can be easily obtained through the birth-and-death Markov chain Monte Carlo algorithm and the variational inference technique. After parameter estimation for the Bayesian MFA model is done, a new monitoring index called negative variational log likelihood is developed by utilizing the whole information in probability distribution functions of all parameters. At last, two case studies, including a numerical example and the Tennessee Eastman (TE) process, verify the effectiveness and feasibility of the proposed monitoring scheme.

Highlights

Process monitoring, including fault detection and fault diagnosis, plays critical role in the successful and safe operation of complex chemical processes
Demonstrate more satisfactory monitoring performance. This is because the probabilistic manner has following advantages: (1) the latent variable model is achieved in probability density space so that statistical decisions can be made; (2) random noises existing in process variables are considered; (3) missing values in data set can be handled
principal component analysis (PPCA), maximum likelihood PCA (MLPCA) and factor analysis (FA) have been employed for process monitoring and good monitoring performance has been gained [8]–[15]

Summary

INTRODUCTION

Process monitoring, including fault detection and fault diagnosis, plays critical role in the successful and safe operation of complex chemical processes. F. Wang et al.: Log Likelihood Monitoring for Multimode Process Using Variational Bayesian MFA Model (such as GMM) pay no attention to dimensionality reduction and random noise of process variables. Zhu et al [28] proposed a Bayesian robust mixture factor analyzer to characterize multimode process data with outliers by using student distribution but fault detection part is not given. Given training data set Y , the parameters of MFA model can be estimated via maximizing the log likelihood function: N. In this case, it is difficult to deal with the complex nonlinear optimization problem.

VARIATIONAL INFERENCE

Findings

THE PROCEDURE OF MULTIMODE PROCESS MONITORING