Statistical Process Monitoring Based on General Semi–Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a widely applied method for feature extraction and dimensionality reduction. However, existing NMF-like methods primarily focus on deriving a subspace representation based on partial bases from the original data, overlooking the inter-sample correlations. In this paper, a new method, named general semi–nonnegative matrix factorization (GSNMF), is proposed for statistical process monitoring. This method relieves the nonnegativity constraint on the original data, expanding its applicability, and is capable of capturing the primary variations in the data. Furthermore, by extracting the common features of the data in a low dimensional space, it preserves the specific and significant features of the data. Two test statistical metrics and kernel density estimation (KDE) are employed for fault detection. Finally, the superiority of the proposed method is validated by taking common public datasets as examples.