Nonlinear latent variable regression

Many operations, such as monitoring and control, require the availability of some key process variables. When these variables are difficult to measure, it is usually relied on inferential models that can be used to estimate these variables from other easier-to-measure variables. Latent variable regression (LVR) techniques, such as principal component regression (PCR), partial least square (PLS), and regularized canonical correlation analysis (RCCA), are commonly used as inferential models. In this paper, these linear LVR modeling techniques are first reviewed, and then a new algorithm that extends these LVR modeling techniques to nonlinear processes is presented. The developed nonlinear LVR (NLLVR) modeling algorithm utilizes nonlinear functions in the form of polynomials to capture the nonlinear relationships between the latent variables are the model output. The structures of these polynomials as well as the number of latent variables used are optimized using cross validation. The performances of the developed NLLVR modeling techniques are illustrated and compared with those the conventional linear LVR techniques (PCR, PLS, and RCCA). This comparison is performed using two examples, one using synthetic data and the other using simulated distillation column data. The results of both examples show that a significant improvement in model predictions can be achieved using the NLLVR modeling methods.