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

This 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.