Non-Negative Matrix Factorization for Detection and Diagnosis of Plantwide Oscillations

In this paper, we propose the use of non-negative matrix factorization (NMF) of multivariate spectra for plantwide oscillation detection. One of the key features of NMF is that it provides a parts-based representation that allows us to retain the causal basis spectral shapes or parts that constitute the spectra of measurements, unlike the popular principal component analysis (PCA)-based methods. The contributions of this paper are as follows:  (i) a novel measure known as the pseudo-singular value (PSV) to assess the order of the basis space (the PSV is also useful in determining the most dominant features of a data set); (ii) a power decomposition plot that contains the total power (defined in this work) and its decomposition by NMF (the power plot is a useful and compact visual tool that provides overall spectral characteristics of the plant and shows the decomposition of these characteristics into well-localized frequency components); and (iii) a novel measure defined as the strength factor (SF) to ass...