## 4 Experiments and Discussion  
### Experimental Setup  
We completed the experiments using the system shown in Figure 1. The FBG sensor was fixed as a stress sensor on a motorized translation table driven by a stepper motor that stretched the sensor in different steps to apply horizontal stress. The experiments were conducted at a constant room temperature of 26 \({}^{\circ}\)C. The initial state of the FBG sensor used is shown in Figure 3a. During the stretching process, the motorized translation table stretched the FBG sensor fixed on it once every three seconds. The stretching process can be divided into two stages, and the ranges and stretching lengths of the two processes are shown in the Table 1. In the first stage, the motorized translation table worked at a progression of 5 \(\upmu\)m per stretch. In the second stage, the motorized translation table worked at an advance of 10 \(\upmu\)m per stretch, allowing data diversity to improve the generalization performance of the subsequent training model. The drift of the FBG reflection spectra during the whole stretching process is shown in Figure 3b. The reflection spectrum of the LPG sensor used as a linear filter is shown in Figure 3c. The change in the transmitted intensity of the LPG was due to the change in the FBG reflection spectrum caused by the stress application, and the value was recorded by an optical power meter. The optical spectrum analyzer (YOKOGAWA, OSA AQ6370D) recorded the actual spectral change of the FBG sensor while the FBG sensor was stretched to serve as a reference value. The real spectra and transmitted intensity were recorded point to point to construct the dataset. Figure 2: Architecture of the proposed sensor demodulation neural network. (**a**) Overall architecture of the GAN. The shape of the random noise vector is consistent with the generation. (**b**) Detailed architecture of the generator network (\(G\)) and discriminator network (\(D\)). \(G\) consists of three Linear Leaky ReLu sequences and one Linear Tanh sequence, and the number of neurons in the linear layer is 128-256-512-1024. \(D\) consists of two Linear Leaky ReLu sequences and one Linear Sigmoid sequence, and the number of neurons in the linear layer is 512-256-1, and Leaky ReLu, Tanh, and Sigmoid are the activation functions. (**c**) Detailed architecture of the DNN consists of an input layer, four hidden layers, and an output layer. The number of neurons in the hidden layers is 64-128-256-512, and the activation function is ReLu–ReLu–Tanh. The dataset generated from the above information was first fed into the GAN for training to perform data augmentation. Before training the GAN, these data were divided into the training, test, and validation dataset after being randomly disrupted in the ratio of 80%, 10%, and 10%, with no overlapping part. During the training of the GAN, _RMSprop_ and _Adam_ were selected as the optimizers for the \(G\) and \(D\), respectively, and the initial learning rates (LR) of \(G\) and \(D\) were preset to 0.001. A learning rate decay strategy was adopted to prevent them from overfitting, which can be formulated as Equation (5). \[LR^{\prime}=LR*e^{\frac{-\alpha}{N}}, \tag{5}\]  
where the \(LR^{\prime}\) and \(LR\) denotes the learning rate after decay and before decay, respectively, \(\alpha\) is the factor of decaying that is a constant, and \(N\) represents the total number of model iterations. In addition, the strategy of alternate training of \(G\) and \(D\) was adopted, i.e., \(G\) was trained once every five times of \(D\) training to ensure that \(G\) could generate data distributions closer to the ground truth. After that, the data generated by the GAN were fed into the DNN for training along with the data generated by the optical system. The dataset was randomly disrupted between 80% and 20%, divided into training and validation datasets. Furthermore, the test dataset was collected and built by collecting data from additional continuous stretching experiments with no overlap between them.