Robust dynamic experiments for the precise estimation of respiration and fermentation parameters of fruit and vegetables

Dynamic models based on non-linear differential equations are increasingly being used in many biological applications. Highly informative dynamic experiments are valuable for the identification of these dynamic models. The storage of fresh fruit and vegetables is one such application where dynamic experimentation is gaining momentum. In this paper, we construct optimal O2 and CO2 gas input profiles to estimate the respiration and fermentation kinetics of pear fruit. The optimal input profiles, however, depend on the true values of the respiration and fermentation parameters. Locally optimal design of input profiles, which uses a single initial guess for the parameters, is the traditional method to deal with this issue. This method, however, is very sensitive to the initial values selected for the model parameters. Therefore, we present a robust experimental design approach that can handle uncertainty on the model parameters.Author summary: Fruit and vegetables need to be stored at low temperature and oxygen conditions as well as slightly heightened carbon dioxide conditions so that they remain fresh throughout the entire year. The exact storage conditions are different for each cultivated variety. Optimizing these storage conditions typically requires a lot of experimentation. Traditionally, this was done by independently storing the fruit of vegetable product at many different combinations of temperature as well as oxygen and carbon dioxide conditions, and by tracking the quality of the product and choosing the best of these conditions. This, however, is a very wasteful approach as the quality tracking at certain conditions do not inform us about the quality at different storage conditions. Instead, we adopt a model-based approach, where the product is described as a dynamic system with inputs and outputs. This model has parameters that must be estimated from experimental data. But once the model has been calibrated it can be used to make predictions at any storage condition. We develop the experimental design methodology required to precisely estimate the model parameters. We do this in a robust manner, meaning we are able to discover the true model parameter values no matter their specific value.