Ultralow-Frequency Vibration Sensing in Phase-Sensitive OTDR Using Multiscale VMD

Abstract

Laser frequency drift (LFD) restricts the low-frequency vibration sensing ability of phase-sensitive optical time-domain reflectometer ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula> -OTDR). In this study, we propose a self-diagnosis structure combining Mach–Zehnder interference and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula> -OTDR is first designed to realize LFD measurement and vibration sensing simultaneously. A multiscale variational mode decomposition (VMD) with the judgment at different amplitude scales, time scales, and modal scales is proposed to suppress the influence of LFD at low-frequency vibration demodulation. Experimental results show a long-time continuous LFD measurement and vibration sensing along the sensing fiber of 10040 m. After the parameter optimization of iteration and mode decomposition with multiscale VMD, infrasonic and sub-Hertz vibration signals can be detected with improved SNR. The ultralow-frequency vibration signal as low as 0.04 Hz is also demodulated under a long-time continuous detection of more than 40 min. The fitting coefficient between the recovered vibration frequency and the actual vibration frequency is 0.99966. This self-diagnostic structure, based on multiscale VMD, effectively suppresses the influence of LFD on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula> -OTDR and reliably recovers ultralow-frequency vibrations during long-term detection.