Estimating the make-up of a blend in terms of its parent mixtures (e.g., reverse-engineering a wine blend) based on chemical fingerprints

<jats:p>In the chemical, food &amp; beverage, agricultural, and pharmaceutical industries, non-reacting complex mixtures are often blended to tune the properties of a finished product. Herein, we tackle the inverse problem of reconstructing the unknown make-up of a blend in terms of its parent mixtures based on chemical fingerprints. As an experimental case study, we estimate the volume percentages of Cabernet Sauvignon, Merlot, and Cabernet Franc composing a Bordeaux red wine blend. For chemical fingerprinting, we measure the ethanol, sugar, and acid concentrations in the blend and each pure-varietal wine. A mass balance on each constituent over mixing (neglecting chemical reactions, evaporation, and excess volume) gives a system of linear equations, subject to a sum-to-one constraint, governing the make-up of the blend. To find the best approximate solution to this overdetermined system, we solve a constrained, scaled total least squares optimization problem, thereby explicitly accounting for measurement errors in all of the chemical fingerprints. We predicted the Cabernet Sauvignon, Merlot, and Cabernet Franc content in four different blends with an average error of &lt;5 vol. %. Monte Carlo sampling and propagation of measurement errors provided uncertainty quantification. Such “computational unmixing” of a blend is useful for authenticity verification, fraud detection, forensics, quality control, and routing of blends across many different industries.</jats:p>