Fault detection and isolation with Interval Principal Component Analysis

Diagnosis method based on Principal Component Analysis (PCA) has been widely developed. However, this method deals only with data which are described by single-valued variables. The purpose of the present paper is to generalize the diagnosis method to interval PCA. The fault detection is performed using the new indicator [SPE]. To identify the faulty variables, this work proposes a new method based on the reconstruction principle to this indicator. It aims to solve an interval linear system to obtain the reconstructed variables. The analysis of the reconstruction conditions permits to determine the useful directions. Then, the residuals structuring according to these directions allows to identify the set of faulty variables. This new diagnosis method based on interval PCA model is validated by a simulation example.

[1]  S. Rump.  Verification methods for dense and sparse systems of equations , 1994 .

[2]  E. Diday,et al.  Extension de l'analyse en composantes principales à des données de type intervalle , 1997 .

[3]  J. Ragot,et al.  Fault detection and isolation with robust principal component analysis , 2008, MED 2008.

[4]  Luc Jaulin,et al.  Applied Interval Analysis , 2001, Springer London.

[5]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[6]  Ahlame Douzal-Chouakria.  Extension des méthodes d'analyse factorielles à des données de type intervalle , 1998 .

[7]  Didier Maquin,et al.  Fault Detection and Isolation with Robust Principal Component Analysis , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[8]  Götz Alefeld,et al.  The Cholesky method for interval data , 1993 .

[9]  Si-Zhao Joe Qin,et al.  Reconstruction-based contribution for process monitoring , 2009, Autom..

[10]  G. William Walster,et al.  Global Optimization Using Interval Analysis: Revised and Expanded , 2007 .

[11]  S. Joe Qin,et al.  Subspace approach to multidimensional fault identification and reconstruction , 1998 .

[12]  Gene H. Golub,et al.  Matrix computations , 1983 .

[13]  M. Hladík.  A Contractor for the Symmetric Solution Set , 2010 .

[14]  Masayuki Tamura,et al.  A study on the number of principal components and sensitivity of fault detection using PCA , 2007, Comput. Chem. Eng..

[15]  S. Joe Qin,et al.  Statistical process monitoring: basics and beyond , 2003 .

[16]  Christian Jansson,et al.  Interval linear systems with symmetric matrices, skew-symmetric matrices and dependencies in the right hand side , 1991, Computing.

[17]  A. Neumaier.  Interval methods for systems of equations , 1990 .