A time‐varying process monitoring approach based on iterative‐updated semi‐supervised nonnegative matrix factorizations

Abstract

AbstractThis paper proposes a new time‐varying process monitoring approach based on iterative‐updated semi‐supervised nonnegative matrix factorizations (ISNMFs). ISNMFs are a type of semi‐supervised model that constructs a semi‐nonnegative matrix factorization (SNMF) model of a process using both labelled and unlabelled samples. Compared with the existing nonnegative matrix factorizations (NMFs) where NMFs are referred to as matrix factorization algorithms that factorize a nonnegative matrix into two low‐rank nonnegative matrices whose product can well approximate the original nonnegative matrix, ISNMFs have advantages in terms of the model update and the use of labelled samples. The ISNMFs‐based process monitoring approach concerns fault detection and isolation and updates an SNMF model iteratively using the latest samples to capture the change of statistical property of time‐varying processes. Moreover, the proposed fault detection and isolation approach is supported by the k‐means algorithm in theory. At last, we demonstrate the superiority of ISNMFs over the existing NMFs in terms of fault detection and isolation through a case study on the penicillin fermentation process.