(674a) Hybrid Modeling Approach Integrating PLS Models with First Principles Knowledge

Projection to latent spaces (PLS) is a widely used statistical modeling approach and has found excellent applicability in modeling, monitoring and control [1-2] of complex batch processes. In batch processes, the quality of the final product is of utmost importance and predicting the quality of products well in advance is essential to move the process towards the desired objective. The simple PLS models built with data from previous batches have demonstrated great success in this regard. However, use of process knowledge in developing these models have not been explored in sufficient detail. Motivated by these considerations, in the present work, a hybrid PLS model built with recorded measurement data and data based on first principles model is proposed. A batch crystallization process is chosen as the motivating example where the particle size distribution at batch end is our desired quality variable.

Measuring quality related variables, such as particle size, in a lab during batch runs is an expensive and time intensive task thus motivating the use of good models to predict time evolution of the process variable trajectories and the final quality attributes at the end of the batch. Detailed first principles models of these processes are often available which can predict such final quality attributes with reasonable precision. However, to do so they need to be calibrated to existing plant data by estimating key parameters in the model. Furthermore, to be used in on-line monitoring and control, where disturbances are present, these models need to be run in the form of an observer, Extended Kalman Filter (EKF) or incorporated into a Moving Horizon Estimator (MHE), all of which require considerable expertise and effort to build and maintain. As a result, fundamental models rarely find application in on-line monitoring, optimization and control.. However, these first principles models can provide much useful information that can augment on-line process data to potentially provide improved final quality attribute predictions.

This work addresses the problem of integrating fundamental process knowledge with measurement data to build hybrid PLS models with better predictive ability. This is done by considering the process measurements of historical batches as inputs to the first principles model to predict batch trajectories of variables which are not directly measured. The X block matrix is then augmented with this valuable information once the data of these variables is generated. The first principles models do not have to be calibrated to plant data. Rather, they only need to help in predicting changes in the direction of the process during its duration. The hybrid batch PLS models will accommodate for any biases in the trajectory predictions of the incorporated first principles model, and, in an on-line monitoring mode, will provide the time varying adaptation of the predictions that might be afforded by an EKF or MHE implementation of a first principles only model.

This hybrid PLS methodology approach is used to illustrate this straightforward but powerful approach to predict the final crystal size distribution for the batch crystallization process and is compared with the standard PLS approach based only on plant data, and to subspace based quality models. The simulation results show the improved predictive capability of the proposed approach over the other modeling techniques considered.

[1] Paul Nomikos, John F. MacGregor, Multi-way partial least squares in monitoring batch processes, Chemometrics and Intelligent Laboratory Systems, Volume 30, Issue 1, 1995, Pages 97-108, ISSN 0169-7439

[2] Latent variable MPC for trajectory tracking in batch processes, Journal of Process Control, Volume 15, Issue 6, 2005, Pages 651-663, ISSN 0959-1524

[3] Dan Shi, Nael H. El-Farra, Mingheng Li, Prashant Mhaskar, Panagiotis D. Christofides, Predictive control of particle size distribution in particulate processes, Chemical Engineering Science, Volume 61, Issue 1, 2006, Pages 268-281, ISSN 0009-2509