## 3 Results and Discussions  
### Development of Calibration FTIR-ATR Model  
FTIR calibration model for determination of kinematic viscosity at 100 \({}^{\circ}\)C (KV\({}_{100}\)\({}^{\circ}\)C) of worn-out motor oils, i.e., the procedure of conversion of IR absorption information into viscosity values obtained by laboratory reference method according to CSN EN ISO 3104 [49], was developed by the frequently used regression methods--PLS [50] and PCR [51]. Prior to the creation of calibration models, the experimental data were normalized by the Mean Centering function [52]. This is a procedure that calculates the average spectrum; it was subtracted from the individual measured spectra. In parallel, the average KV\({}_{100}\)\({}^{\circ}\)C values were calculated and these average values were subtracted from the values measured by the standardized method. The resulting normalized (unitless) matrix and normalized vector were used to construct calibration models. A set of 230 samples of worn-out motor oils was used to construct the calibration model. Using Spectrum Outlier diagnostics [52], outliers (a total of 25) were removed during the creation of the calibration model; these were motor oils into which coolant had penetrated as a result of an operational accident and oil samples for which the viscosity value was inaccurately determined. The Spectrum Outlier diagnostics calculates the Mahalanobis distance of the spectrum of each oil calibration sample from the average spectrum and then looks for the spectra that are most different from the other calibration samples. The diagnostics uses the Chauvenet's test [52] to assess whether the difference is significant. The remaining set of 205 standards with a kinematic viscosity in the rangeof 11.340-14.855 mm\({}^{2}\)s\({}^{-1}\) was subsequently divided into two subsets, i.e., 190 calibration samples and 15 samples testing the predictive ability of the calibration model. Figure 1 shows the IR spectra of oils with different kinematic viscosity values in the entire measuring range. The decrease in the viscosity value of oils was mainly affected by the penetration of fuel into the oil filling, which is manifested by an increase in the height of the spectral band with a maximum at 811 cm\({}^{-1}\) belonging to out-of-plane bending = C-H vibrations of aromatics. The cause of the increase in viscosity may be the products of thermal oxidation reactions manifested in the spectrum by valence vibration of the carbonyl group-C=O with a maximum at 1745 cm\({}^{-1}\); this was not proven in the present case. The spectral bands with peaks at 2952, 2920 and 2853 cm\({}^{-1}\) correspond to the CH valence vibrations of saturated n-alkyl groups. Symmetric and asymmetric deformation vibrations of CH bonds exhibiting a band with a peak at 1461 cm\({}^{-1}\) and 1377 cm\({}^{-1}\) belong to the CH\({}_{2}\) and CH\({}_{3}\) groups. According to [PERSON] and [PERSON] [53], the band with a peak at 1706 cm\({}^{-1}\) is shown by polymethacrylate, which is used in motor oils as a viscosity modifier and a pour point depressant. The most effective antioxidant and anti-abrasion additive Zinc Dialkylditiophosphate (ZnDDP) is manifested in the spectrum by a band with a peak at 974 cm\({}^{-1}\) (P-O-C bond) or at 660 cm\({}^{-1}\) (P=S bond). An important step in creating a calibration model is to identify the essential spectral information in the measured spectra of motor oils used for calibration, i.e., to select the part of the spectrum that will be used for the calculation. The diagnostics of statistical spectra [52] identified the highest correlation between the change in spectral information and the change in KV\({}_{100\cdot 0}\) in the wavenumber range of 1750-650 cm\({}^{-1}\). The absorption matrix thus contained 275 data points at a resolution of 4 cm\({}^{-1}\).