Process modeling by Bayesian latent variable regression

Large quantities of measured data are being routinely collected in various industries and used for extracting linear models for tasks such as process control, fault diagnosis, and process monitoring. Existing linear modeling methods, however, do not fully utilize all the information contained in the measurements. A new approach for linear process modeling makes maximum use of available process data and process knowledge. Bayesian latent-variable regression (BLVR) permits extraction and incorporation of knowledge about the statistical behavior of measurements in developing linear process models. Furthermore, BLVR can handle noise in inputs and outputs, collinear variables, and incorporate prior knowledge about regression parameters and measured variables. The model is usually more accurate than those of existing methods, including OLS, PCR, and PLS. BLVR considers a univariate output and assumes the underlying variables and noise to be Gaussian, but it can be used for multivariate outputs and other distributions. An empirical Bayes approach is developed to extract the prior information from historical data or maximum-likelihood solution of available data. Examples of steady-state, dynamic and inferential modeling demonstrate the superior accuracy of BLVR over existing methods even when the assumptions of Gaussian distributions are violated. The relationship between BLVR and existing methods and opportunities for future work based on this framework are also discussed.