Total projection to latent structures for process monitoring

Abstract

Partial least squares or projection to latent structures (PLS) has been used in multivariate statistical process monitoring similar to principal component analysis. Standard PLS often requires many components or latent variables (LVs), which contain variations orthogonal to Y and useless for predicting Y. Further, the X-residual of PLS usually has quite large variations, thus is not proper to monitor with the Q-statistic. To reduce false alarm and missing alarm rates of faults related to Y, a total projection to latent structures (T-PLS) algorithm is proposed in this article. The new structure divides the X-space into four parts instead of two parts in standard PLS. The properties of T-PLS are studied in detail, including its relationship to the orthogonal PLS. Further study shows the space decomposition on X-space induced by T-PLS. Fault detection policy is developed based on the T-PLS. Case studies on two simulation examples show the effectiveness of the T-PLS based fault detection methods.

Simultaneous determination by NIR spectroscopy of the roasting degree and Arabica/Robusta ratio in roasted and ground coffee

“…With the aim to evaluate if some samples of the validation set were statistically different from the regression model, the Hotelling's T 2 and Q residual statistics were evaluated (Choi & Lee, 2005;Mason & Young, 2002;Zhou, Li, & Qin 2010). These statistical parameters were originally developed for PLS-based process control to detect the presence of special causes of variation.…”

Quality-relevant fault detection and diagnosis for hot strip mill process with multi-specification and multi-batch measurements

“…When the latter is carried out, for one thing, it separates the significant variations claimed to be completely irrelevant to Y, for the other thing, the residuals of Xŷ are thought to possibly affect Y and serve quality-relevant monitoring. Actually, we include the additional part for interpreting Y, which is partially sparked by Zhou et al [36] and Qin et al [37]'s works. The PCA in step 1 does not consider the impact of Y, thus the abandoned T res may possibly influence Y.…”

Online process operating performance assessment and nonoptimal cause identification for industrial processes

“…(2), t y represents the output-related variations in score matrix T of original PLS model, T o represents the output-unrelated variations in T, T r is the major part of original E, and E r is the residual part of X. More details about T-PLS can be found in [13].…”

“…T-PLS [13] is considered as an improved version of PLS. Through further decomposition, the output-unrelated and output-related part can be separated in PLS systematic subspace, and large process variations are separated from noise in residual subspace, which provides more accurate information for those who are more concerned with certain aspects of the whole information.…”

“…Recently, Zhou et al [13,14] proposed a total projection to latent structures (T-PLS) for process monitoring and fault diagnosis. They analyzed the problem of conventional PLS which only divides the measured variable space into two subspaces and indicated that the output-unrelated variations are also included by PLS scores while PLS residuals do not necessarily cover only small process variations.…”