Nonlinear process monitoring using kernel nonnegative matrix factorization

Abstract

This paper focuses on developing an advanced nonlinear process monitoring technique involving fault detection and identification methods. The new monitoring methods are proposed based on two nonlinear matrix factorization algorithms. Both factorizations use the kernel method to replace lower-dimensional nonlinearity using higher-dimensional linearity by nonlinearly mapping the data onto a high-dimensional linear space. In the high-dimensional linear space, also known as feature space, the first factorization decomposes the data matrix into two low-rank matrix products, in which the first matrix factor is restricted to being orthogonal and non-negative leading to a good performance in the subspace approximation of the original data. In the second factorization, a matrix consisting of all types of fault samples is decomposed into two low-rank matrix products, in which the second matrix factor is restricted to being orthogonal and non-negative providing a clear K-means clustering interpretation. On the basis of the above two factorizations, the corresponding fault detection and identification methods are developed. Finally, the proposed approaches are used to monitor the penicillin fermentation process (PFP), and encouraging experimental results are achieved.

Deep neural network based recursive feature learning for nonlinear dynamic process monitoring

“…In order to address nonlinear problems, several algorithms have been proposed . Kernel techniques, such as kernel principal component analysis (KPCA), kernel partial least squares (KPLS), and kernel independent component analysis (KICA), are the most popular methods.…”

Simultaneous Fault Detection and Isolation Based on Transfer Semi-Nonnegative Matrix Factorization

“…The time duration for the simulation is 300 h, and the sampling time interval is 1 h. System initial conditions and set points of variables are given by Tables and , respectively . A total of 16 process variables, as listed in Table , are monitored.…”

Simultaneous fault detection and isolation using semi‐supervised kernel nonnegative matrix factorization

“…As illustrated above, both NMF and KNMF have similar decomposition forms with k ‐means. That is, NMF and KNMF can be applied to the data clustering with a mild constraint that allows the cluster indicators vary between interval [0, + ) instead of the data set {0,1} . In such a case, we can regard both factorizations as the mild version of k ‐means.…”

“…Simulation time lasts for 400 h and sampling time is 1 h. The monitored variables are given by Table . The initial conditions are given by Table . In addition, the set points of the variables are given by Table …”

“…The initial conditions are given by Table . In addition, the set points of the variables are given by Table …”