## 5 Verification  
To verify the neural network model, we used an algorithm consisting of a series of steps similar to the training algorithm, except for the error back propagation part of the algorithm:  
1. Modeling of the FBG reflection spectrum at a wavelength arbitrarily selected from the range [\(\lambda_{\text{B}}-0.5\) nm; \(\lambda_{\text{B}}+0.5\) nm], where \(\lambda_{\text{B}}\) is the central value of the wavelength within the controlled wavelength interval \(\Delta\). The resulting spectrum \(\{R_{i}\}\) is discretized at \(\Delta\lambda\) intervals. The amplitude values \(\{R_{i}\}\) and the central wavelength \(\lambda_{\text{B}}\) are normalized using (1). 2. Calculation of the neural network response \(\overline{\lambda}\) using (6). 3. Calculation of the error in FBG central wavelength determination using (3). Figure 5 shows the neural network response's dependence on the values of the FBG central wavelength \(\lambda\) for \(10^{4}\) iterations of the verification algorithm. The red line represents the dependence corresponding to the neural network model's response; the blue line (along the additional axis) represents the magnitude of the error in the central wavelength determination \(\left(\lambda-\overline{\lambda}\right)\). When the sensor system was in real-time operation, the profile of the FBG reflection spectrum serving as a sensor sensing element hardly changed. Consequently, it was intriguing to investigate the magnitude of the absolute error in determining the central wavelength that resulted from a plane-parallel shift of the same spectrum across the entire controlled wavelength section. Two approaches were of interest here. The first involved determining the FBG reflection spectrum central wavelength in the wavelength range with an interval \(\Delta\) and fixed left \(\lambda_{\text{L}}\) and right \(\lambda_{\text{R}}\) boundaries. The second approach involved determining the FBG reflection spectrum central wavelength in the wavelength range with an interval \(\Delta\) but with variable left \(\lambda_{\text{L}}\) and right \(\lambda_{\text{R}}\) boundaries. Here the boundary was determined according to a rule that ensured that the wavelength \(\lambda_{\text{Max}}\) corresponding to the maximum value in the discretely obtained spectrum \(\lambda_{\text{Max}}=\text{max}(\mathbf{R})\) was always located in the center of the wavelength range [\(\lambda_{\text{L}}\), \(\lambda_{\text{R}}\)]. Figures 6 and 7 show the absolute errors in determining wavelengths using the first and second range control approaches, respectively. Figure 4: FBG spectral response: a bar chart at a discretization interval of 167 pm and a flat line at an infinitesimal discretization interval, where \(\lambda\) is the central wavelength. Comparing the errors in determining the central wavelength with fixed (Figure 6) and variable (Figure 7) boundaries revealed that the errors in the latter case were smaller and had an almost periodic dependence on the location of the FBG reflection spectrum maximum. It is also worth noting that the quasi-periodic dependence of errors in Figure 7 was caused by the errors belonging to the interval [1549.917, 1550.083] nm in Figure 6 (green area). The distribution density of errors in determining the FBG central wavelength for each approach (fixed and variable boundaries) is shown in Figures 8 and 9, respectively. Figure 5: Dependence of the neural network response (\(\overline{\lambda}\)) on the FBG wavelength (\(\lambda\)) (red line) and absolute error in the wavelength determination (\(\overline{\lambda}-\lambda\)). Figure 6: Error in determining the FBG central wavelength at a fixed-boundary interval. Figure 7: Error in determining the FBG central wavelength at a variable-boundary interval. In addition, the value of the FBG central wavelength error corresponding to the central wavelength shift for \(\lambda_{\text{B}}\) is plotted on the abscissa axis (on the additional ordinate axis).