Suppressing the Impact of Laser Frequency Drift on φ -OTDR Vibration Detection Based on Improved Variational Mode Decomposition and Its Influencing Factors Investigation

To address the impact of laser frequency drift on measured vibration using phase-sensitive optical time-domain reflectometry (φ-OTDR) systems, an improved variational mode decomposition (VMD) method is proposed in this work to suppress the effects of frequency drift. Based on the Rayleigh backscattering (RBS) signal acquired from vibrating optical fibers, the influence of two key parameters of the VMD method on the demodulated waveform is investigated: the penalty factor α and the number of intrinsic mode functionsk. The results demonstrate that the VMD method can effectively suppress the influence of frequency drift on demodulation. Optimal values of α andkare determined, resulting in a computation time that is only 0.06% to 0.08% of that of the WOA-VMD method, while preserving comparable accuracy. This approach substantially improves the real-time performance by eliminating the need for iterative optimization of α andk. The improved VMD method is realized by applying twice differential (TD) preprocessing to the phase signal after IQ demodulation and phase unwrapping, using fixed optimal parameters set of α andk, and identifying and removing drift-dominated intrinsic mode functions (IMFs) based on their frequency characteristics. Furthermore, the improved VMD method is systematically validated using experimentally acquired RBS signals under different vibration frequencies, vibration types, pulse repetition rates, optical pulse widths, and the sampling duration. Simultaneously, a high-fidelity numerical simulation model of coherent φ-OTDR is employed to investigate the impact of frequency drift rate and frequency drift type on the demodulated waveforms. The results reveal that the improved VMD method can effectively suppress frequency drift effects under different conditions, including different vibration frequencies, vibration types, optical pulse repetition rates, optical pulse widths, sampling duration, frequency drift rates, and frequency drift types. Compared with the original demodulated waveforms, the signal-to-noise ratio (SNR) is improved by 22.56dB to 56.57 dB, demonstrating a wide range of applicability. Moreover, the accuracy of the improved VMD method increases with increasing sampling duration and optical pulse width. In addition, the SNR improvement relative to the original demodulated waveforms increases with increasing pulse repetition rate, optical pulse width, sampling duration, and frequency drift rate. Therefore, the proposed improved VMD method demonstrates high stability under various experimental conditions and can effectively suppress the impact of laser frequency drift on φ-OTDR demodulation.