A Sparse Dimensionality Reduction Approach Based on False Nearest Neighbors for Nonlinear Fault Detection

As a newly emerging multivariate statistical process monitoring method, non-negative matrix factorization (NMF) and its variants avoid the positive and negative cancellations between the extracted features because of the purely additive combination of non-negative components. Thus, they make a good match with this reality that the negative values of both observations and decomposed components are physically meaningless in many kinds of industrial processes. However, these methods are effective only for linearly separable problems and are not suitable for dealing with nonlinear process monitoring. In this article, the kernel-based method is integrated into the projective NMF (KPNMF) to improve the accuracy of fault detection, and the appropriate multiplicative update method is proven to be convergent. Furthermore, inspired by the false nearest neighbors (FNNs) method, a new dimensionality reduction approach (KPNMF-FNN) is presented to further reduce the original variables for determining the smallest dimension regression vector needed. Compared with the traditional methods, the proposed approach can greatly reduce the time and storage space required on the premise of maintaining a high fault detection rate and low false alarm rate. The experimental results on the Tennessee Eastman benchmark process and the pumping unit system show that the proposed algorithms have excellent performance and can effectively detect faults under the circumstances of retaining only the top 60% of the original variables.