In recent years, the demand for high-precision sensing technologies has grown substantially across critical sectors such as industrial monitoring and medical applications. Within these domains, shape sensing emerges as a pivotal challenge that forms the foundation for device and process monitoring. While fiber Bragg grating (FBG) sensors demonstrate significant potential for shape sensing applications, they are confronted with three primary error sources: manufacturing inconsistencies, insufficient demodulation accuracy, and spectral drift. These errors collectively compromise reconstruction accuracy, with spectral drift being particularly exacerbated by material creep and prolonged sensor operation. To address this challenge, we propose a novel spectral drift correction method employing a hybrid bi-directional long short-term memory-long short-term memory (BiLSTM-LSTM) neural network architecture. The developed approach aims to enhance both the accuracy and operational stability of FBG-based shape sensing systems through effective drift compensation and precision optimization in shape reconstruction.

The proposed correction method strategically integrates BiLSTM and LSTM networks through a sequential processing architecture. The BiLSTM layer extracts bidirectional temporal features from FBG sensor data, establishing comprehensive temporal dependencies through its dual-directional processing capability. These features are subsequently refined by the LSTM layer to enhance spectral-curvature relationship modeling efficiency. Training data consists of 2690 samples with curvature variation of 0.05?0.15 m^-1 obtained from a dedicated FBG sensing platform. Preprocessing incorporates Gaussian smoothing, controlled noise injection, and spectral drift simulation to emulate operational disturbances. Critical parameters including network units, dropout rate, and learning rate are optimized via particle swarm optimization (PSO).

Results demonstrate significant performance enhancement in FBG shape sensing through the proposed BiLSTM-LSTM architecture. Curvature reconstruction errors decreased from [15.7609,14.4787,20.5649,18.2307] mm to [0.1391,2.5222,1.7354,1.2951] mm across various configurations, achieving 44% average accuracy improvement over benchmark models: Frenet, convolutional neural network (CNN), LSTM-SelfAttention. As evidenced in Figs. 8 and 9, the correlation between predicted and actual curvature values exhibits exceptional consistency with a mean R2 of 0.9918. Residual analysis in Fig. 8(b) confirms normally distributed errors (mean is about 0), validating the model’s precision and stability. Comparative evaluations highlight the model’s dual advantages: surpassing Frenet-based methods in baseline accuracy while outperforming CNN and LSTM-SelfAttention architectures in error minimization: mean absolute error/total error (MAE/TE) reduction. By resisting long-term spectral drift, this capability enables sustained high-precision reconstruction. Such reliability is critical for structural health inspection and industrial monitoring applications.

We present a hybrid BiLSTM-LSTM network addressing FBG spectral drift through temporal dependency modeling and spectral-curvature nonlinear mapping. Experimental validation shows 44% accuracy improvement over traditional methods (e.g., Frenet framework) and other deep learning models. This study paves the way for more accurate and reliable FBG shape sensing systems, with potential applications in structural health inspection and industrial pipeline inspection.