Considering precision of data in reduction of dimensionality and PCA

Reduction of dimensionality of the data space in process data analysis is considered. A new stepwise collinearity diagnostic (SCD) procedure is presented, which employs indicators based on the estimated signal-to-noise ratio in the data in order to measure the collinearity between the variables. The SCD procedure selects a maximal subset of non-collinear variables and identifies the corresponding collinear subsets of variables. Using SCD, the dimension of the data space is reduced to the dimension of the maximal non-collinear subset. In process monitoring applications, the data associated with the surplus variables can be used for distinguishing between process and sensor failures. Two examples, which demonstrate the advantages of the proposed method over principal component analysis (PCA), are presented. (C) 2000 Elsevier Science Ltd. All rights reserved.