3.5.   Variable Selection by Brute Force

The problem of finding the best 2-sensor combination for the discrimination of the two analytes is a typical variable selection problem. The rather low number of 2 variables out of 6 allows a brute force variable selection, as according to equation (15) only 15 combinations are possible. The RMSE of these 15 combinations, which are listed in row 3 to row 17 of table 1, confirm the conclusion drawn when analyzing the sensitivities of the sensors for the pure analytes. The best combination with the lowest mean RMSE of the test data is the PDMS + UE 2010 20% layer and the second best combination is the PUT + UE 2010 20% layer. The combinations with the 6 lowest mean RMSE of the test data in between 0.00440 and 0.00612 consist all of one polar polymer and one microporous polymer, which showed the biggest differences of the sensitivity patterns in figure 8. The combination of two different interaction principles seems to be optimal for the discrimination of the two refrigerants as the combinations of 2 polar or 2 microporous polymers all showed significantly higher errors.