Process Modeling by Bayesian Latent Variable Regression

Process Modeling by Bayesian Latent Variable Regression Mohamed N. Nounou, Bhavik R. Bakshi Prem K. Goel, Xiaotong Shen Department of Chemical Engineering Department of Statistics The Ohio State University, Columbus, OH 43210, USA Abstract Large quantities of measured data are being routinely collected in a variety of industries and used for extracting linear models for tasks such as, process control, fault diagnosis and process monitoring. However, existing linear modeling methods do not fully utilize all the information contained in the measurements. This paper presents a new approach for linear process modeling that makes maximum use of available process data and process knowledge. This approach, called Bayesian Latent Variable Regression (BLVR), permits extraction and incorporation of knowledge about the statistical behavior of measurements in developing linear process models. Furthermore, unlike existing methods, BLVR is able to handle noise in inputs and outputs, collinear variables, and incorporate prior knowledge about the regression parameters and measured variables. The resulting model is usually more accurate than that obtained by existing methods including, OLS, PCR and PLS. In this paper, BLVR considers a univariate output, and assumes the underlying variables and noise to be Gaussian, but the approach may be easily used for multivariate outputs and other distributions. An empirical Bayes approach is developed to extract the prior information from historical data or from the maximum likelihood solution of available data. Illustrative 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 the proposed framework are also discussed.