Fault Detection with Bayesian Network

The purpose of this chapter is to present a method for the fault detection in multivariate process, with a bayesian network. In this context, the detection is viewed as a classification task like the discriminant analysis, which can be transposed in a bayesian network. We prove mathematically the equivalence between the usual detection methods that are the multivariate control charts (Hotelling's T², MEWMA) and the quadratic discriminant analysis (in a bayesian network). So, this makes possible the fault detection with a bayesian network. An application on the Tennessee Eastman Process is given in order to demonstrate the approach.

[1]  Arthur B. Yeh,et al.  A multivariate exponentially weighted moving average control chart for monitoring process variability , 2003 .

[2]  Theodora Kourti,et al.  Multivariate SPC Methods for Process and Product Monitoring , 1996 .

[3]  Peter E. Hart,et al.  Nearest neighbor pattern classification , 1967, IEEE Trans. Inf. Theory.

[4]  Pedro M. Domingos,et al.  Beyond Independence: Conditions for the Optimality of the Simple Bayesian Classifier , 1996, ICML.

[5]  Solomon Kullback,et al.  Approximating discrete probability distributions , 1969, IEEE Trans. Inf. Theory.

[6]  Charles W. Champ,et al.  A multivariate exponentially weighted moving average control chart , 1992 .

[7]  Manabu Kano,et al.  Comparison of multivariate statistical process monitoring methods with applications to the Eastman challenge problem , 2002 .

[8]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[9]  Theodora Kourti,et al.  Statistical Process Control of Multivariate Processes , 1994 .

[10]  Nir Friedman,et al.  Bayesian Network Classifiers , 1997, Machine Learning.

[11]  David Heckerman,et al.  Knowledge Representation and Inference in Similarity Networks and Bayesian Multinets , 1996, Artif. Intell..

[12]  D. Hawkins Multivariate quality control based on regression-adjusted variables , 1991 .

[13]  Abdessamad Kobi,et al.  Fault diagnosis of industrial systems with bayesian networks and mutual information , 2007, 2007 European Control Conference (ECC).

[14]  Lakhmi C. Jain,et al.  Introduction to Bayesian Networks , 2008 .

[15]  I Inza,et al.  Representing the behaviour of supervised classification learning algorithms by Bayesian networks , 1999, Pattern Recognit. Lett..

[16]  Douglas C. Montgomery,et al.  Introduction to Statistical Quality Control , 1986 .

[17]  C. N. Liu,et al.  Approximating discrete probability distributions with dependence trees , 1968, IEEE Trans. Inf. Theory.

[18]  Vladimir Cherkassky,et al.  The Nature Of Statistical Learning Theory , 1997, IEEE Trans. Neural Networks.

[19]  Mehran Sahami,et al.  Learning Limited Dependence Bayesian Classifiers , 1996, KDD.

[20]  Pat Langley,et al.  An Analysis of Bayesian Classifiers , 1992, AAAI.

[21]  H. Hotelling,et al.  Multivariate Quality Control , 1947 .

[22]  George C. Runger,et al.  Comparison of multivariate CUSUM charts , 1990 .

[23]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[24]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[25]  B. Bakshi Multiscale PCA with application to multivariate statistical process monitoring , 1998 .

[26]  Abdessamad Kobi,et al.  A new procedure based on mutual information for fault diagnosis of industrial systems , 2006 .

[27]  Richard D. Braatz,et al.  Fault Detection and Diagnosis in Industrial Systems , 2001 .

[28]  Igor Kononenko,et al.  Semi-Naive Bayesian Classifier , 1991, EWSL.

[29]  W. A. Wallis,et al.  Techniques of Statistical Analysis. , 1950 .

[30]  David G. Stork,et al.  Pattern classification, 2nd Edition , 2000 .

[31]  Robert P. W. Duin,et al.  Combining One-Class Classifiers , 2001, Multiple Classifier Systems.

[32]  A. R. Crathorne,et al.  Economic Control of Quality of Manufactured Product. , 1933 .