Direct projection to latent variable space for fault detection

Partial least squares (PLSs) often require many latent variables (LA's) T to describe the variations in process variables X correlated with quality variables Y, which are obtained via the traditional nonlinear iterative PLS (NIPALS) optimal solution based on (X, Y). Total projection to latent structures (T-PLSs) performs further decomposition to extract LVs T-y directly related to Y from T, which are obtained by the PCA optimal solution based on the predicted value of Y. Inspired by T-PLS, combined with practical process characteristics, two fault detection approaches are proposed in this paper to solve problems encountered by T-PLS. Without the NIPALS, (X, Y) are projected into the latent variable space determined by main variations of Y directly. Furthermore, the structure and characteristics of several modified methods in statistical analysis are studied based on calculation procedures of solving PCA. PLS and T-PLS optimization problems, and the geometric significance of the T-PLS model is demonstrated in detail. Simulation analysis and case studies both indicate the effectiveness of the proposed approaches. (C) 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.