## 3 Results and Discussions
### Development of Calibration FTIR-ATR Model
In the area of the so-called fingerprint [54], in addition to the spectral bands already mentioned which are related to the change in viscosity, there are also indistinct spectral bands belonging to detergent-dispersant additives, which are calcium and magnesium salts of organic acids; alkylthiophosphates, sulfonates, phenolates [46]. Among other things, these additives play  
Figure 1: FTIR spectra in the measured range 4000–650 cm\({}^{-1}\), (1) new motor oil with KV100 \({}^{\circ}\)C = 13.950 mm\({}^{2}\)s\({}^{-1}\), (2) worm-out oil with KV\({}_{100\cdot 0}\)C = 10.743 mm\({}^{2}\)s\({}^{-1}\). an important role in neutralizing acidic fuel combustion products or acidic products of oxidative degradation of oil. Thus, the increase in oil viscosity caused by the oxidation products of oil degradation may correlate with the loss of these additives. The change in viscosity was apparently not affected by soot contamination of motor oil, which is reflected in an overall shift of the spectrum to higher absorbances in the region of about 2000 cm\({}^{-1}\); this spectral region did not significantly correlate with the change in kinematic viscosity. A correlation of R = 0.34 between KV\({}_{100}\)\({}_{\text{C}}\) and soot in worn-out motor oils operated in large-volume diesel engines was published in [55]. When creating the FTIR-PLS and FTIR-PCR calibration models, a mathematical description of the dependence between the spectral data matrix X (190 \(\times\) 275) of the calibration samples and the matrix Y, i.e., the unit standard vector of samples of used motor oils with determined values of KV\({}_{100}\)\({}_{\text{C}}\) according to CSN EN ISO 3104, was created. During the creation of calibration PLS and PCR models, the matrix of spectral data was transformed by Principal Components Analysis (PCA) [50] from the original variables to a significantly smaller number of latent variables-Principal Components (PCs), which in the present case are linear combinations of original absorbances at 4 cm\({}^{-1}\) and are mutually uncorrelated, i.e., the basic characteristic of each PCs is its degree of variability-of variance. Therefore, the real calibration result is not only affected by the height or the area of the bands, but also the slope and curvature of the spectrum. It was the substantial change in the spectrum due to the penetration of the coolant into some of the samples of monitored oil fillings that caused the evaluation of these spectra by program diagnostics as atypical spectra (outliers) and therefore unsuitable for creating calibration models. The PRESS (Prediction Residual Error Sum of Square) diagnostics was used in TQ analyst to determine the optimal number of principal components [39]. The criteria for selecting a suitable calibration model are the Root Mean Square Error of Calibration (RMSEC) [33,42] and the Correlation Coefficient (R) [39]. Equation (1) is used to calculate RMSEC and Equation (2) is used to calculate the Correlation Coefficient,  
\[RMSEC=\sqrt{\frac{\sum\limits_{i=1}^{m}\left(c_{ir}-\overline{c}_{r}\right) ^{2}}{m_{c}}} \tag{1}\]  
\[R=\frac{\sum\limits_{i=1}^{m}\left(c_{ir}-\overline{c}_{r}\right)\left(c_{ie}- \overline{c}_{e}\right)}{\sqrt{\sum\limits_{i=1}^{m}\left(c_{ir}-\overline{c} _{r}\right)^{2}\sum\limits_{i=1}^{m}\left(c_{ie}-\overline{c}_{e}\right)^{2}}} \tag{2}\]  
where: \(c_{ie}\) is a predicted value of an \(i\)-th calibration sample, \(\overline{c}_{e}\) is an average predicted value, \(c_{ir}\) stands for a value of a parameter of the \(i\)-th calibration sample defined based on a standardized method, \(\overline{c}_{r}\) is an average value of the parameter determined using a standardized method and \(m_{c}\) is a total number of calibration samples. The Correlation Coefficient R indicates the strength of the regression dependence between the laboratory values and the values predicted by FTIR spectrometry; it should be as close to one as possible.