Estimation and visualization of process states using latent variable models based on Gaussian process

The estimation and visualization of process states are important for process control in chemical and industrial plants. Since industrial processes are related to Gaussian distributions theoretically, this study focused on Gaussian process latent variable models. Process state estimation and visualization methods are proposed using two latent variables based on the Bayesian Gaussian process latent variable model (BGPLVM), infinite warped mixture model (iWMM), and Gaussian process dynamical models (GPDM). The Tennessee Eastman process dataset was analyzed and it was confirmed that the performance of estimating the process states was highest in the order of GPDM, iWMM, and BGPLVM. Moreover, time-delayed process variables were added to the process variables to consider the process dynamics, which further improved the performance of estimating the process states. Particularly in the case of GPDM, only two latent variables could estimate the process states, with approximately 100% accuracy for four process states. Additionally, even 10 process states could be estimated with approximately 90% accuracy, and it was confirmed that the process state estimation and process state visualization could be achieved simultaneously.