Fault Detection and Isolation Using Correspondence Analysis

Abstract

In this paper, a new approach to fault detection and diagnosis that is based on correspondence analysis (CA) is proposed. CA is a powerful multivariate technique based on the generalized singular value decomposition. The merits of using CA lie in its ability to depict rows as well as columns as points in the dual lower dimensional vector space. CA has been shown to capture association between various features and events quite effectively.The key strengths of CA, for fault detection and diagnosis, are validated on data involving simulations as well as experimental data obtained from a laboratory-scale setup.

Improved kernel principal component analysis for fault detection

“…Multivariate statistical methods such as principal component analysis (PCA), independent component analysis (ICA) and partial least square (PLS) have been widely applied in chemical industry for fault diagnosis (Chen & Chen, 2006;Detroja, Gudi, Patwardhan, & Roy, 2006;Lee, Han, & Yoon, 2004;Lieftucht, Kruger, & Irwin, 2006;Zuo, Lin, & Fan, 2005). Among these methods, PCA is the most popular one.…”

Polar classification with correspondence analysis for fault isolation

“…It detects row column associations and has also been shown to identify nonlinear dependencies present in the data matrix [1]. For each row point that spans the n-dimensional space and each column point that spans the m-dimensional space, this multivariate technique identifies a set of coordinate axes spanning a lower dimension subspace that represents the joint association between these row and column points.…”

“…The coordinates/score values of row points and column points can be computed by projecting them onto matrices A and B and are given by vectors of F and G matrices [8,1], which represent the score values for the row and column clouds respectively. These are given by…”

“…However, FDA is a supervised algorithm that requires labeling of the training samples and is therefore relatively difficult to use; further PCA and FDA require expansion of the column space to accommodate dynamic or serial correlation in the data. Towards addressing the above problems, correspondence analysis (CA, [5]) was proposed for enhanced discrimination, while retaining the unsupervisory nature of the algorithm [1]. Unlike PCA, CA uses a measure of row-column association to represent the sample-variable relationship and has been shown to be effective at capturing cause and effect relationships present in the data [1].…”

“…Towards addressing the above problems, correspondence analysis (CA, [5]) was proposed for enhanced discrimination, while retaining the unsupervisory nature of the algorithm [1]. Unlike PCA, CA uses a measure of row-column association to represent the sample-variable relationship and has been shown to be effective at capturing cause and effect relationships present in the data [1]. CA also enables the joint projection of variables and samples in a reduced dimensional space called the biplot (for two retained dimensions).…”