Functional Data Analysis and Design of Experiments as Efficient Tools to Determine the Dynamical Design Space of Food and Biotechnological Batch Processes

A dynamical design space for the batch milling process of a hazelnut-and-cocoa-based paste in a stirred ball mill was obtained through functional data analysis (FDA) combined with design of experiments (DOE). A face-centred central composited design with two functional responses, fineness and energy, and three factors (rotational speed, mass of balls and ball diameter) was used. The functional responses were pre-processed, smoothed through B-spline approximation and subjected to functional principal component analysis (FPCA). The scores of the FPCA were modelled as a function of the experimental factors through response surface models and used to build a final model for the functional responses including only one principal component for energy and two for fineness. The developed models were able to predict with good accuracy the functional responses as a function of the experimental factors and time and allowed to build a dynamical design space. FDA combined with DOE appears to be an efficient and easy-to-use tool to model batch processes and obtain their dynamical design space.