Heuristic extraction of rules in pruned artificial neural networks models used for quantifying highly overlapping chromatographic peaks

The suitability of an approach for extracting heuristic rules from trained artificial neural networks (ANNs) pruned by a regularization method and with architectures designed by evolutionary computation for quantifying highly overlapping chromatographic peaks is demonstrated. The ANN input data are estimated by the Levenberg-Marquardt method in the form of a four-parameter Weibull curve associated with the profile of the chromatographic band. To test this approach, two N-methylcarbamate pesticides, carbofuran and propoxur, were quantified using a classic peroxyoxalate chemiluminescence reaction as a detection system for chromatographic analysis. Straightforward network topologies (one and two outputs models) allow the analytes to be quantified in concentration ratios ranging from 1:7 to 5:1 with an average standard error of prediction for the generalization test of 2.7 and 2.3% for carbofuran and propoxur, respectively. The reduced dimensions of the selected ANN architectures, especially those obtained after using heuristic rules, allowed simple quantification equations to be developed that transform the input variables into output variables. These equations can be easily interpreted from a chemical point of view to attain quantitative analytical information regarding the effect of both analytes on the characteristics of chromatographic bands, namely profile, dispersion, peak height, and residence time.