In recent years, fiber Bragg grating (FBG) sensors have been widely used in structural health monitoring (SHM) of aerospace structures due to their advantages, such as compact structure, electromagnetic interference resistance, and quasi-distributed integration. However, when exposed to harsh environments for a long time, they are susceptible to temperature, vibration, and other factors, resulting in problems such as spectral noise and baseline drift, which reduce the signal-to-noise ratio (SNR) and seriously affect demodulation accuracy. Traditional denoising algorithms, such as Savitzky-Golay filter and wavelet transform, rely on manual parameter setting in low-SNR scenarios, resulting in poor adaptability and difficulty in meeting high-precision monitoring requirements. This article proposes a novel DSC-U-Net deep neural network model, which integrates the feature extraction capability of the U-Net architecture and the lightweight advantage of depthwise separable convolution (DSC), enabling effective removal of noise and baseline distortion. Based on the coupled-mode theory and transfer matrix method, 90 000 spectral samples covering an SNR range of -20 dB to 20 dB are simulated for model training and testing. Subsequently, the data volume required for model training and the model training results were discussed. Test results show that the model trained with the full dataset can improve the SNR of 0 dB spectra to 13.266 dB, with a similarity of 0.892 to pure spectra and a root mean square error (RMSE) of only 0.05, outperforming traditional algorithms such as arPLS combined with window functions. An experimental system for harsh environments (-55℃~150℃) is established for experimental data collection, and verification is conducted using the model trained with simulated data. The demodulation algorithm combining DSC-U-Net and MLP reduces the demodulation error from 0.297 pm to 0.023 pm, with an accuracy improvement of 92.26%. Model training using simulated data can significantly reduce training costs. The DSC-U-Net deep neural network model requires no manual intervention, featuring both high precision and efficient computation. It solves the demodulation problem of FBG signals under low SNR and provides a reliable solution for long-term stable monitoring in harsh aerospace environments.