Gaussian process models for proces monitoring and control

Abstract

One problem of special interest both in industry and the engineering community is that of using the enormous amounts of data routinely generated and recorded in e cient process monitoring and control strategies. In statistical terms this is related to identifying those variables which exhibit unwanted or unusual process variability so that remedial action can be taken. To this end, a common approach in the literature is to reduce the problem dimensionality by using latent variable models. Customarily, the latent variables are a function of all of the original variables and monitoring is carried out in the reduced space. Within this context, this thesis explores the development of models in which the latent factors are a function of a subset, only, of the original observations. By doing that, the advantages of monitoring in a reduced subspace are retained but there there are also additional gains in model interpretability. The idea arises from the sparse representation of the mapping matrix between latent and original variables in a linear factor analysis (FA) model. An extension of principal component analysis (PCA) to monitor nonlinear systems is proposed by using a a Gaussian Process Latent Variable model [Lawrence, 2005], GPLVM, as a starting point. Its application in a process control problem is also introduced. Using a Gaussian process, GP, as the backbone, we de ne a Gaussian Process Functional Factor Analysis model which maps subsets of the latent variables to the observed data-space; a study of the model asymptotic properties is given. Several parameter inference methods as well as a model selection procedure via penalty functions are also proposed. There are several scienti c disciplines involved in the problem at hand. Chemical engineers refer to it as a sub- eld of Process Control known as Multivariate Statistical Process Control. It is also an area of tremendous success in process Chemometrics where it has grown very rapidly over the last two decades. In Statistics, it touches the topics of latent variable models and variable selection methods. And within the Machine Learning community is classi ed as an Unsupervised Learning problem.