## 4 Experiments and Discussion
### Results and Discussion
The \(R^{2}\) closer to one implies that the generalization performance and fitting effect of DNN are optimal. Moreover, combining the proposed GAN for data augmentation with LR, SVR, GPR, and DNN provides better performance than when used individually. The proposed sensor demodulation neural network (GAN+DNN) achieves optimal results. These doubly confirm the effectiveness of GAN in the proposed demodulation system and the excellent performance of this system. The wide demodulation range of the proposed system is reflected in the LPG sensor's rising and falling edge range of nearly 56.1 nm. However, we could not measure more offset data in that range due to the specifications and experimental conditions of the FBG sensor used. Second, deploying the well-trained sensor demodulation neural network model on a neural network-enabled development board (e.g., FPGA) can replace the optical spectrum analyzer in actual measurements, which significantly reduces the overall cost and complexity of the system and makes large-scale measurements possible. In addition, the rich scalability of the system allows users to directly consider increasing the size of the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Min. (nm)** & **Max. (nm)** & **Ave. (nm)** \\ \hline LR (Linear) & 0.0390 & 0.4852 & 0.2309 \\ GAN + LR (Linear) & 0.0020 & 0.2998 & 0.0714 \\ SVR (RBF) & 0.0185 & 0.6002 & 0.2931 \\ GAN + SVR (RBF) & 0.0009 & 0.2974 & 0.0720 \\ SVR (matern) & 0.0266 & 0.7012 & 0.3122 \\ GAN + SVR (matern) & 0.0042 & 0.3780 & 0.0757 \\ GPR (RBF) & 0.0021 & 0.5664 & 0.3776 \\ GAN + GPR (RBF) & 0.0003 & 0.2226 & 0.0401 \\ DNN & 0.0031 & 0.0298 & 0.0144 \\
**GAN + DNN** & **0** & **0.0059** & **0.0030** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Error statistics for the central wavelength interrogation of different demodulation mode, in which the Linear, RBF, and matern denotes the kernel function of these machine learning algorithms. Figure 6: Histogram of wavelength demodulation error distribution. (**a**) Error distribution of the DNN. (**b**) Error distribution of the DNN + GAN (our proposal). neural network model to improve the demodulation precision, but this will be accompanied by more resource utilization. In terms of algorithms, we have compared and analyzed our proposed algorithm with existing algorithms in terms of demodulation metrics and algorithm properties, as shown in Table 4. In terms of interrogation precision, compared to the particle-swarm-optimization-based simulated annealing (PSO-SA) demodulation proposed by [PERSON] et al. [33], variable-step-size & cross-correlation demodulation presented by et al. [34], and cascaded CNN & BPNN demodulation proposed by [PERSON] et al. and [PERSON] et al. [18; 35], our proposed models of cascaded GAN and DNN and traditional algorithms of distributed estimation algorithm (EDA) [36] and dynamic calibration algorithm [5] can achieve the same interrogation precision. However, our proposed model significantly outperforms other algorithms regarding algorithmic complexity and data. In terms of algorithmic complexity, the proposed model is based on neural networks, meaning that physical constraints between variables can be ignored to model the complex nonlinear relationship between transmission intensity and central wavelength. In contrast, traditional algorithms must model complex physical relationships between variables on this basis. In terms of data, the optimization calculations of the traditional algorithms [5; 33; 34; 36] and the two mentioned NN-based algorithms [18; 35] rely on a large amount of measurement data, which can be unacceptably expensive to collect. In contrast, based on generative adversarial networks, the proposed model achieves excellent performance based on a preliminary small-scale data set, significantly reducing the data collection cost. In addition, the proposed model has significant advantages in generalization performance and scalability due to the customizable design of the scale of the generated data.