Hybrid Partial Least Squares Models for Batch Processes: Integrating Data with Process Knowledge

This paper presents a unique strategy for integrating fundamental process knowledge with measurement data to build a partial least squares (PLS) model with improved estimation capability. To this end, variables from two different sources are combined to create the predictor data matrix for the PLS model. Measurement data from sensors is stored and used as inputs to a modified first-principles model to generate trajectory data of unmeasured variables. Then the traditional X data matrix (built with measured data) is augmented with batch trajectory data of the calculated variables. The PLS model built with this augmented matrix is referred to as hybrid/augmented PLS, and this proposed methodology is tested on a seeded batch crystallization process to illustrate this straightforward but powerful approach to estimate the final crystal size distribution. The efficacy of the proposed approach is demonstrated using simulation studies by comparing the results with the standard PLS and subspace based quality model.