Design space of the formulation process of a food suspension by D-optimal mixture experiment and functional data analysis

Functional data analysis (FDA) was applied to a D-optimal mixture design for the formulation process of a food suspension. The design included two functional responses characterizing the solid particle size distribution and the flow behaviour, namely oversize vs. class size and apparent viscosity vs. shear rate, and three components (flour, lipidic phase and icing sugar). The functional responses were transformed, smoothed through B-spline approximation, and subjected to functional principal component analysis (FPCA). The first component of the FPCA analysis explained about 99% and 88.5% of the variance for the oversize and apparent viscosity, respectively, and greatly simplified the interpretation of the system behaviour. The corresponding scores were regressed as a function of the component proportions through response surface models and used to build a final model for the functional responses. The developed models were able to predict both the oversize and apparent viscosity curves as a function of suspension composition and allowed to develop the design space of the process. FDA combined with design of experiments (DOE) offer an efficient and easy to use strategy to model particle size distribution functions and apparent viscosity curves of food suspensions as a function of formulation variables.