Soft sensors are powerful tools for the implementation of process analytical technology (PAT). They are categorized into white-box (first-principle), black-box (statistical), and gray-box models. Gray-box models integrate white-box and black-box models to address each drawback, i.e., prediction accuracy and intuitiveness. Although they have been applied to various industrial processes, their applicability to water content monitoring in fluidized bed granulation has not been reported. In this study, we evaluated three types of gray-box models, i.e., parallel, serial, and combined gray-box models, in terms of prediction accuracy using real operating data on a commercial scale with two formulations. The gray-box models were constructed by integrating the heat and mass balance model (white-box model) and locally weighted partial least squares regression (LW-PLSR) model (black-box model). LW-PLSR was utilized to cope with collinearity and nonlinearity. In the serial gray-box models, LW-PLSR models adjusted the fitting parameters of the white-box model depending on the process parameters for each query. In the parallel gray-box or combined gray-box models, LW-PLSR models compensated for the output error of the white-box or serial gray-box models, respectively. The results demonstrated that all three types of gray-box models improved the prediction accuracy of the white-box models regardless of the formulation. Besides, we proposed the assessment method based on Hotelling's T2 and Q residual for gray-box models using LW-PLSR, which contributes decision support to select gray-box or white-box model. The accurate and descriptive gray-box models are expected to enhance process understanding and precise quality control in fluidized bed granulation.
Keywords: fluidized bed granulation; gray-box model; heat and mass balance model; locally weighted partial least squares regression (LW-PLSR); process analytical technology (PAT); soft sensor.