A new simplex-based approach predicting olive oil blend compositions from fatty acid data

Olive oils represent complex matrices varying from pure to heterogeneous varietal contents. Quantitative analysis of co-occurring components is fundamental for conformity checking and adulteration alerting (fighting) of commercial oils. Proportions of co-occurring components are governed by additive-dilutive processes which obey to simplex rule. Using simplex rule, we developed an original computational approach to predict proportions of different co-occurring oil varieties from quantitative chemical features of blends. The approach consisted in applying a complete set of N mixtures between different olive oil varieties by gradually varying their proportions. The N simulated mixtures were characterized by N average fatty acid (FA) profiles calculated from N combinations of randomly sampled individual profiles. After k iterations of the mixture design, the k sets of N FA average profiles were used as input in a discriminant analysis to predict proportions of co-occurring olive oil varieties in different blends. Illustrative application concerned blends made by three main French mono-varietal virgin olive oils (Aglandau, Grossane and Salonenque) and benefiting from Protected Designation of Origin label. Predictive model was validated on outside blends and showed prediction errors with an order of 10% susceptible of reduction by applying a larger mixture design.