Adaptive noise suppression for Sagnac interferometric system with variable step-size LSTM-LMS method

Fiber–optic vibration sensing based on the Sagnac interferometer offers great potential for non–contact monitoring of human vital signs owing to its high sensitivity and immunity to electromagnetic interference. Nevertheless, system–induced noise severely corrupts weak respiratory and ballistocardiogram (BCG) signals acquired by such sensing systems, degrading signal quality and detection performance. To address this challenge, this paper proposes an adaptive noise suppression approach combining Long Short-Term Memory (LSTM) and Least Mean Square (LMS) with dynamic step-size regulation, termed LSTM-LMS. The proposed workflow consists of time–series feature extraction, LSTM network training, and subsequent adaptive filtering. Training samples are constructed by extracting temporal characteristics from error signals. The well–trained LSTM network is used to dynamically predict and adjust the step–size factor of the LMS, so as to improve overall noise–reduction performance. A Sagnac interferometric fiber–optic sensing system adopting a 3 × 3 fiber coupler demodulation scheme is established, and a flexible sensing pad is designed for capturing human vital sign signals. Comparative experiments are performed on five human participants. Experimental results demonstrate that the proposed LSTM–LMS method achieves an average signal–to–noise ratio (SNR) improvement of 17.39 dB, with an average convergence time of 0.14 s and an average steady–state mean–square error of 0.007. The method can effectively suppress system noise while preserving the characteristics of BCG waveforms. It provides a reliable noise–suppression solution for interferometric fiber–optic vibration sensing applied to flexible vital sign monitoring scenarios.