## 5 Results and Discussions  
The different parameters, such as epochs, hidden layers, batch sizes, and optimizer and activation functions, were adjusted until an optimal or well-trained model was obtained. The optimal parameters for the well-trained DBN model are crucial in achieving high accuracy in peak wavelength detection. Thus, the optimal parameters used for training the proposed DBN included 3 hidden layers, 32 batch sizes, 150 epochs, the Adam optimizer, and ReLU activation functions in the hidden layers that introduced non-linearity, improving the network's ability to model complex relationships in the data. Figure 6a shows the DBN's training performance evaluated through its training and validation losses, as well as training and validation accuracy using these optimal parameters. The training loss and validation loss curves provide insights into the model's performance during training and on unseen data, respectively. The training loss quickly declined and stabilized near zero at epoch 150 on the bottom x-axis, indicating effective learning of training data patterns. The validation loss also decreased significantly early on and remains stable, showing good generalization to unseen data without overfitting. The training accuracy reached nearly 1.0 (100%) by epoch 150 at the top x-axis, and the validation accuracy also approached 1.0 (100%), though with some variability. In general, the DBN demonstrated strong performance, effectively learning and generalizing from the data, with high accuracy and low loss metrics. Figure 6b shows that the performance of the DBN for peak wavelength detection of FBG strain sensors was evaluated in terms of prediction error, measured as MSE, MAE, and RMSE, and training time, measured in seconds per epoch. As shown in the figure, the training process showed stabilization of training time after initial fluctuations, indicating computational efficiency. Key error metrics, including MSE, MAE, and RMSE, at epoch 0 were relatively high. However, as training progressed, all significantly decreased, remaining close to zero at 150 epochs, which signifies that the model effectively minimized prediction errors and indicates the DBN's ability to accurately learn and predict peak wavelengths, demonstrating its reliability and effectiveness for this application. Furthermore, to determine the best optimizer, the model was trained and tested with different optimizers, and their performance was compared based on MSE, MAE, and RMSE. According to Figure 7, Adam achieved lower MSE, MAE, and RMSE values of 0.0012, 0.015, and 0.0187 compared to other optimizers. This was due to its computational efficiency and noise minimization. As a result, the proposed DBN model was trained and tested using the Adam optimizer. Figure 6: (**a**) Training performance of the DBN model in terms of loss and accuracy. (**b**) Performance of DBN in terms of prediction error and compilation time. Figure 7: Performance comparison with different optimizers. Figure 8 shows the predicted peak wavelengths of the strained FBGs, fixed FBGs, and three different interferences. In Figure 8a, the x-axis represents the peak wavelength of the strained FBGs in reality, while the y-axis represents the peak wavelength of the strained FBGs predicted by the DBN model. The yellow symbols on the graph show the ideal values, indicating where the predicted values should be if they exactly match the ideal values. Along this line, 15 randomly selected prediction data points are positioned to demonstrate the accuracy of the DBN model. The closer these points are to yellow symbols, the more accurate the prediction becomes, suggesting that the DBN model is very effective in accurately predicting the peak wavelength of the strained FBG in the case of overlap with the FBG and interferences. The x-axis of Figure 8b is the marked peak wavelength of fixed FBG and three different interferences, which are 1545.1 nm, 1546.88 nm (interference 1), 1547.11 nm (interference 2), and 1547.39 nm (interference 3), respectively.