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Title: Optimal designs for Antoine's equation Authors:  Carlos de la Calle-Arroyo - Universidad de Castilla-La Mancha (Spain) [presenting]
Jesus Lopez-Fidalgo - University of Navarra (Spain)
Licesio Rodriguez-Aragon - University of Castilla-La Mancha (Spain)
Abstract: The influence of temperature in the vapour pressure of liquid or gas is derived from a class of semi-empiric equations known as Antoine's Equation. It represents the relationship between vapour pressure and temperature for distillation or pharmacological processes, in which a precise estimation of the parameters is required. The model has three unknown parameters for which, as a non-linear model, previous best guesses are required. These best guesses vary for different pure substances, and between the state of the substance, which establishes the space of the design for practical matters. To improve the accuracy of the experimental experiences with this model, optimal designs have been proposed. The analytical expression for the D-optimal design is included. Optimal designs have been calculated numerically for Ds-optimality, which has focused on estimating with least variance a subset of the parameters, A-optimality, that minimises the average of the variances, and I-optimality, to minimize the variance of the prediction over an interest region. Comparisons between some common designs and optimal designs are shown, to benchmark usual choices in this kind of experiments. Also, a class of designs with a compromise between both has been computed. An online tool to calculate Antoine's optimal designs for the considered criteria has been developed.