Row-Column Overcomplete Structured Dictionary Learning for Enhanced Fault Detection and Isolation

Abstract

To improve the monitoring performance of dictionary learning based methods, this article proposes a row-column overcomplete structured dictionary learning (RCOSDL) method for fault detection and isolation of industrial processes. Unlike conventional dictionary learning approaches which are overcomplete column-wise, the proposed method involves a dictionary that is overcomplete both row- and column-wise. The introduction of row-column overcomplete dictionary results in monitoring statistics that are more sensitive to incipient faults. In order to incorporate structured information, two graph Laplacian regularization terms, namely, manifold graph Laplacian and full graph Laplacian are considered. Whilst the inherent local geometric structure in the data is preserved in the sparse representation by the manifold graph Laplacian term, the correlation structure between process variables is preserved by using the full graph Laplacian term. Hence violation in the geometric or correlation structure will be promptly detected. To pinpoint faulty variables, a fault isolation method is developed by imposing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}$</tex-math></inline-formula> / <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{2,1}$</tex-math></inline-formula> -norm constraint on the sparse coefficients. In addition, theoretical property involving the condition for guaranteed fault isolation is presented in Theorem 1. The contributions of this article include the introduction of monitoring statistics based on RCOSDL that are suitable for incipient faults, a new fault isolation scheme as well as theoretical analysis on the condition of guaranteed fault isolation. The better performance of the proposed method is illustrated by applications to numerical studies and practical industrial cases.