## 4 Experiments and Discussion
### Results and Discussion  
Before completing the demodulation of the FBG sensor center wavelength, the data generated by the GAN needs to be input to the DNN along with the original data for training. The results of data augmentation using GAN are shown in Figure 4. The data generated using GAN does not affect the original dataset, and the intensity and wavelength distributions in the generated dataset are consistent with those in original dataset, which were 3.5-4.5 nW and 1544-1551 nm, respectively, as shown in Figure 4a,b. In addition, the dataset generated by GAN is highly diverse, and the number of samples is much more significant than in the original dataset. Specifically, the size of the generated dataset is one hundred times larger than that of the original dataset, as shown in Figure 4c,d. The dataset acquired in the additional continuous stretching experiments was selected as a test dataset for the well-trained model, and the test results are shown in Figure 5. In addition, the wavelength demodulation error distribution using DNN alone and the combination of GAN and DNN are shown in Figure 6. The demodulation error was used to reflect the system's precision, defined as the difference between the wavelength interrogated by the system and the wavelength measured by the OSA. The wavelength interrogation of the FBG sensor using DNN alone has a demodulation error distribution in the range of \(\pm\)0.03 nm. The demodulation error is within \(\pm\)0.006 nm when the GAN and DNN were combined, which means that the combination of GAN+DNN can achieve pm-level wavelength interrogation precision. In summary, the superiority of the proposed demodulation system in demodulation performance was demonstrated. The demodulation errors of DNN as well as traditional machine learning algorithms such as support vector regression (SVR), linear regression (LR), and Gaussian regression (GPR), and the errors using GAN for demodulation on top of them are quantified as shown in Table 2. During the training of these algorithms, a training dataset consistent with the training of the proposed neural network algorithm was used. The model with data augmentation using GAN was significantly lower than the original model without GAN in terms of maximum, minimum, and average errors, which implies that our proposed GAN for demodulation data augmentation has a significant advantage in improving the model's interrogation precision. Moreover, the proposed system (GAN + DNN) can achieve wavelength interrogation with precision of at least \(\pm 3\) pm. Figure 4: Data augmentation results of the GAN. (**a,b**) are the original dataset and the GAN-enhanced dataset, respectively, with the intensity in the LPG spectrum on the \(x\)-axis and the central wavelength of the FBG on the \(y\)-axis. (**c,d**) are the original dataset and the GAN-augmented dataset, respectively, with the number of dataset samples on the \(x\)-axis and the central wavelength of the FBG sensor on the \(y\)-axis. Figure 5: Demodulation results in the test dataset. The solid brown line is the actual central wavelength value of the FBG sensor measured by OSA, and the solid red line and solid blue represent the demodulation results of the proposed system when DNN acts alone and when GAN and DNN act together, respectively. The four performance evaluation metrics mentioned in Section 4.2 were utilized to evaluate their performance comprehensively and verify the superiority of the proposed neural network model. In addition, the performance of these traditional machine learning methods combined with the proposed GAN was also calculated to evaluate their effectiveness fully. The statistics of the evaluation metrics are shown in Table 3. DNN performs significantly better than LR, SVR, and GPR when used alone as a sensor demodulation neural network, as reflected by the nearly tenfold difference in RMSE, MSE, MAE, and corresponding metrics of DNN on the test dataset and the machine learning model used as a reference.