Numerical-Square-Method–Enhanced Ensemble Deep Learning for Accurate Demodulation of FBG Spectra

Abstract

This paper introduces ensemble deep learning (EDL) models for accurate demodulation of Fiber Bragg Grating (FBG) sensor spectra, with input training data enhanced through the numerical square method (NSM) technique. The method combines numerical squaring with EDL to improve prediction accuracy under noisy and overlapping spectral conditions. The proposed system uses an FBG interrogator with sensors embedded in transparent liquid containers to detect liquid level changes via Bragg wavelength shifts. However, changes in the liquid level shift the float position, causing overlap or cross-talk between adjacent sensors. To address this, the NSM enhances signal clarity by boosting authentic FBG responses and minimizing noise. Single, double, and triple NSM operations are applied to the experimental data to sharpen the reflection peaks and enhance overall signal quality, ensuring the data are well-prepared for training the EDL model. The EDL model combines CNNs for spectral feature extraction and LSTMs and GRUs for sequential pattern recognition and efficient learning, effectively capturing both spectral and sequential features. The EDL model is trained on the dataset enhanced by the NSM technique and validated using unseen experimental data to evaluate its performance. The results confirm that NSM efficiently sharpens reflection peaks, improves signal clarity, and reduces noise in FBG spectra, while the EDL model effectively demodulates the overlapping spectra. Experimental results demonstrate that the integrated NSM-EDL approach outperforms traditional machine learning and standalone deep learning models in terms of prediction accuracy, minimal errors, and computational time. The proposed method is cost-effective, hardware-efficient, and ideal for real-time multiplexed FBG sensing applications, such as liquid level monitoring.