Statistical process monitoring via generalized non-negative matrix projection

Abstract

As a famous dimension reduction technique, non-negative matrix factorization (NMF) has been used in diverse scientific fields since its appearance. In this work, we aim to propose a new statistical monitoring method based on NMF framework. Considering that the projection method is standardly used in conventional methods such as principal component analysis (PCA), a new variant of NMF method based on positively constrained projections is presented here. This algorithm also relieves the non-negative restriction for original data. Hence it can be called generalized non-negative matrix projection (GNMP). Then, we use GNMP to extract the latent variables that drive a process and to combine them with process monitoring techniques for fault detection. Kernel density estimation (KDE) is adopted to calculate the confidence limits of defined statistical metrics. In addition, corresponding contribution plots are defined for fault isolation. Afterwards, the proposed method is applied to the Tennessee Eastman process to evaluate the monitoring performance. The experiment results clearly illustrate the feasibility of the proposed method.