## 3 Results
### Thermal Response and Sensibility Tests  
Tests investigated the range of temperatures of 30 to 70 \({}^{\circ}\)C, considering that the material of the 3D-printed device exhibits a melting point at 75 \({}^{\circ}\)C. This property, in real operation, might help in visualizing the effect of temperature since the melt thermoplastic resin adds white color to water and, thus, the operator can receive an additional visual warning of the risk of excessive heating. The use of water might even help in perceiving the achievement of 100 \({}^{\circ}\)C as soon as it starts boiling. The cooling water jets applied to rolls, for instance, assures the availability of water at room temperature.  
The temperature has been increased by a rate of 0.02 \({}^{\circ}\)C/s. Ten tests allowed extracting the main properties of the FBG sensor as follows:  
\[\{\lambda_{i}\}=K_{T}\{T_{i}\}+a \tag{8}\]  
i.e., a linear regression based on the minimum squares method allowed finding the relation between measurement and temperature, considering parameter '\(a\)' the wavelength at 0 \({}^{\circ}\)C.  
To validate the numerical approach, the determination coefficient \(R^{2}\) is defined as:  
\[R^{2}=\frac{\sum_{i=1}^{n}\left(\widetilde{\lambda}_{i}-\overline{\lambda} \right)^{2}}{\sum_{i=1}^{n}\left(\lambda_{i}-\overline{\lambda}\right)^{2}} \tag{9}\]  
has been calculated by comparing measured values \(\lambda_{i}\), their average value \(\overline{\lambda}\), and values \(\widetilde{\lambda}_{i}\) obtained by the linear regression.  
The uncertainties related to experimental parameters required resorting to the Monte Carlo method [68; 69] to check the reliability of numerical values extracted by the linear regression. Both the temperature and wavelength signals are subject to measurement errors due to the sensitivity of the measuring instruments. In particular, the uncertainty of the measuring equipment was used to define the standard deviation (s) of the temperature signal, \(s(T_{i})=0.01\)\({}^{\circ}\)C, and wavelength signal, \(s(\lambda_{i})=8\times 10^{-4}\) nm. In order to evaluate the standard deviation of the linear regression coefficients, \(s(K_{T})\) and \(s(a)\), using a Monte Carlo simulation, 5000 runs were carried out for each test, randomly varying each of the measured values within the uncertainty interval (represented by plus or minus one standard deviation from the experimentally measured value), according to a uniform distribution. The five thousand linear correlation values thus obtained were used to evaluate the standard deviation of both linear regression coefficients, obtaining \(s(K_{T})=1\times 10^{-5}\) nm/\({}^{\circ}\)C and \(s(a)=1\times 10^{-3}\) nm. Therefore, for each test, the temperature sensibility coefficient \(K_{T}\) can be considered correct up to the fourth decimal place, while the parameter '\(a\)' can be considered certain up to the second.  
Tests lead to evaluate main parameters varying within a narrow range of values, since \(K_{T}=0.01207\) to 0.01272 (nm/\({}^{\circ}\)C) with \(a=1564.913\) to 1564.960 (nm), \(R^{2}=0.9979\) to 0.9997, \(\lambda_{0}=1565.292\) to 1565.326 (nm). The average value of \(K_{T}\) is 0.01232 nm/\({}^{\circ}\)C with variance \(\sigma^{2}=3.661\times 10^{-8}\) (pm/\({}^{\circ}\)C)\({}^{2}\). This result demonstrates the suitable reliability of that identification. It can be noticed that the interrogator can measure changes in temperature corresponding to \(\Delta\lambda_{min}=0.0008\) nm. Therefore, the minimum change of temperature to be detected is \(\Delta T_{min}=0.0008/K_{T}=0.065\)\({}^{\circ}\)C, i.e., 100 times the precision of the controller TEC equipped with thermocouple PT-100. The correspondence between the regression function and experimental results has been checked as well as the linearity of the dynamic behavior of the FBG sensor (Figure 8).