Robust design for mixture experiments, an application to solve a real problem for diesel fuel surrogate models

Irene Garcia Camacha Gutierrez

Mixture models are used for analyzing problems where the controlled variables by the experimenter are proportions. The design region turns a constrained region called simplex. Polynomial models have been the most extensively studied in the literature for describing such behaviors. In general, they are appropriate, but no for all mixture systems. We investigate the problem of designing for polynomials models, when the assumed model form is only an approximation to an unknown true model. This approach is based on a notion of the maximum of some scalar-valued function of the mean-squared error matrix of the estimates over a neighborhood of the true model to that which is fitted by the experimenter. For this purpose, it is necessary to develop algorithmic techniques for computing these designs. An improved algorithm based on genetic algorithms is proposed in this work. The selection of the optimal formulation of a diesel surrogate for the prediction of autoignition under HCCI engine conditions motivated the procedures provided.

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