Optimal-robust selection of a fuel surrogate for homogeneous charge compression ignition modeling

Homogeneous Charge Compression Ignition (HCCI) combustion is a potential candidate for dealing with the stringent regulations on vehicle emissions while still providing very good energy efficiency. Despite the promising results obtained in preliminary studies, the lack of autoignition control has delayed its launch in the engine industry. In the development of the HCCI concept, the availability of reliable computer models has proved extremely valuable, due to their flexibility and lower cost compared with experiments using real engines. In order to obtain the best formulation of a fuel surrogate formulated with n-heptane, toluene and cyclohexane that efficiently estimate the autoignition behaviour, regression adjustments are made to the Root-Mean-Square Errors (RMSE) of experimental Starts of Combustion (SOC) from the modeled SOC. The canonical form of the Scheffé polynomials is widely used to fit the data from mixture experiments, however the experimenter might have only partial knowledge. In this paper we present the adaptation of the robust methodology for possibly misspecified blending model and an algorithm to obtain tailor-made optimal designs for mixture experiments, instead of using standard designs which are indiscriminately employed, to make good estimations of the parameters blending model. We maximize the determinant of the mean squared error matrix of the least square estimator over a realistic neighbourhood of the fitted regression mixture model. The maximized determinant is then minimized over the class of possible designs, yielding an optimal design. Thus, the computed desings are robust to the exact form of the true blending model. Standard mixture designs, as the simplex lattice, are around 25% efficient for estimation purposes compared with the designs obtained in this work when deviances from the considered model occur during the experiments. Once an optimal-robust design was selected (based on the level of certainty about model adequacy), we computed the optimal mixture that best reproduces the combustion property to be imitated. Optimal mixtures obtained when the considered model is inadequate agree with the results achieved in empirical studies, which validates the methodology proposed in this work.