Gasoline quality prediction using the alternating conditional expectation (ACE) algorithm and ATR-FTIR

Accurate estimation of oxygenates is a critical issue in the quality evaluation of gasoline samples. This work aims to examine the nonparametric robust principal component analysis-alternating conditional expectation (rPCA-ACE) algorithm combined with FTIR spectroscopy as a rapid and accurate analytical method for predicting the quality of gasoline samples based on oxygenates content (methanol, methyl tert-butyl ether, and isobutanol). In the ACE algorithm, a set of optimal transformations is estimated for both the independent and dependent variables. These transformations reveal their non-linear relationships and generate a maximum linear effect between the transformed independent variables and the transformed response variable. In this study, the ACE algorithm was applied to an empirical gasoline dataset and considered a series of possible transformations of the independent and dependent variables to find the best transformations. Among all possible transformations, the ACE algorithm identified a series of polynomials and a nearly linear transformation as the best transformations for the independent and dependent variables, respectively. The regression statistics for calibration and prediction, including the correlation coefficient (R_cal² = 0.9692), root mean square error of calibration (RMSEC = 2.8638), and root mean square error of prediction (RMSEP = 4.0498) (%v/v) for oxygenates content, were calculated. The ACE model showed improved regression results compared to the linear PLS model (R_cal² = 0.9550, RMSEC = 3.9052, RMSEP = 5.1342) and PCR model (R_cal² = 0.9160, RMSEC = 6.5330, RMSEP = 7.0270). By applying the ACE technique to the synthetic fully non-linear dataset obtained from the equation y^'=exp(y) for the response variable, we demonstrated the power of the ACE algorithm in multivariate analysis and its ability to identify the exact functional relationship between independent and dependent variables to solve fully non-linear problems.