Statistical‐based monitoring of multivariate non‐Gaussian systems

TLDR

Existing work advocates using independent component analysis to extract underlying non‑Gaussian data structure. The study addresses monitoring of multivariate systems with non‑Gaussian behavior, proposes PCA to capture both Gaussian and non‑Gaussian source signals, and uses support vector data description to set confidence limits. The method applies PCA, then ICA on retained PCs to extract non‑Gaussian components, and develops a statistical test to determine the number of such components and define monitoring statistics. The scheme’s utility is shown through a simulation example and analysis of data from an industrial melter. © 2008 American Institute of Chemical Engineers AIChE J, 2008.

Abstract

Abstract The monitoring of multivariate systems that exhibit non‐Gaussian behavior is addressed. Existing work advocates the use of independent component analysis (ICA) to extract the underlying non‐Gaussian data structure. Since some of the source signals may be Gaussian, the use of principal component analysis (PCA) is proposed to capture the Gaussian and non‐Gaussian source signals. A subsequent application of ICA then allows the extraction of non‐Gaussian components from the retained principal components (PCs). A further contribution is the utilization of a support vector data description to determine a confidence limit for the non‐Gaussian components. Finally, a statistical test is developed for determining how many non‐Gaussian components are encapsulated within the retained PCs, and associated monitoring statistics are defined. The utility of the proposed scheme is demonstrated by a simulation example, and the analysis of recorded data from an industrial melter. © 2008 American Institute of Chemical Engineers AIChE J, 2008