An efficient approach to optimal interpolation of experimental data

In this work, a computational method is proposed in order to choose the best interpolation function for experimental data. The optimal interpolation function follows the natural tendency of data, suffers a minimal influence by removing one data point, does not present over fitting and yields the best representation for large or rough data sets. High pressure Px data of binary mixtures containing ionic liquid were used as case studies: supercritical CO2 + 1-hexyl-3-methyl imidazolium hexafluorophosphate {[hmim][PF6]}, supercritical CO2 + 1-butyl-3-methyl imidazolium tetrafluoroborate {[bmim][BF4]} and supercritical CHF3 + 1-butyl-3-methyl imidazolium hexafluorophosphate {[bmim][PF6]}. The common practice of using the correlation coefficient to analyze the accuracy of the interpolation model is critically discussed. As a validation of the method, a thermodynamic consistency test is applied to the interpolated data. The results show that the mean values of the interpolation error for CO2 + [hmim][PF6], CO2 + [bmim][BF4] and CHF3 + [bmim][PF6] are 0.47%, 0.33% and 0.13%, respectively. These values are within the reported experimental error, which has a range from 0.04% to 1.7%.