Fault detection based on Gaussian process latent variable models

Gaussian processes, GPsGPs, can be used to approximate complex non-linear functions with relative simplicity. Their regression performance is, at least, comparable to that achieved via artificial neural networks (ANN) and, in fact, both methods are intrinsically related. They are both non-parametric and, as Neal (1994) [1] has shown, when the number of nodes in the hidden layer of a neural network tends to infinity the ANN converge to a Gaussian process.In most of the cases, the GPGP will map a multivariate input into a univariate response. In this paper, however, we present an approach to process monitoring that combines several GPsGPs so that multivariate responses can be appropriately modeled. We review a similar approach recently proposed in the literature and highlight some concerns related to it that needs to be taken into consideration. Additionally, we propose an alternative procedure to the way in which new observations are mapped into the non-linear model. A simulation study is provided that will help understand the method flexibility. Furthermore, results from a real example are also discussed.

► A Gaussian process latent variable model is used for fault detection.
► We propose a general method for projecting new observations onto the latent space.
► The model uncovers the true underlying dimensionality of the system.
► The method can be used to monitor non-linear systems.
► In our study, the model outperforms kernel PCA in terms of preventing false alarms.