Phase-sensitive optical time-domain reflectometry (Φ-OTDR), owing to its unique advantages in the sensor domain, has received significant attention. Among the pivotal advancements in this field, the introduction of frequency-division multiplexing (FDM) is notable as it significantly enhances the system’s frequency-response bandwidth and overcomes the limitations imposed by the fiber length on the maximum response frequency. This breakthrough has considerably expanded the utility of FDM Φ-OTDR, particularly in applications requiring high-frequency vibration monitoring and ultrasonic sensing for partial-discharge detection. However, the practical deployment of FDM Φ-OTDR systems is typically accompanied by substantial challenges, including interference from external environmental factors and phase noise from the light source, which severely compromises the accuracy of high-frequency detection. Addressing these issues is critical for the advancement and broader application of Φ-OTDR. Previous attempts to mitigate noise interference, such as wavelet denoising and variational-mode decomposition, indicate limitations, including dependence on base functions and the inability to achieve a satisfactory signal-to-noise ratio (SNR) in nonstationary environments. This study proposes an innovative approach, i.e., an improved singular value decomposition (SVD) method for noise reduction, which addresses the specific challenges encountered by FDM Φ-OTDR systems in high-frequency signal detection. By constructing a Hankel singular-value matrix to distinguish between signal and noise components and employing a thresholding method to identify significant singular values, this method not only effectively suppresses noise but also preserves essential high-frequency information. This study aims to provide a novel perspective and a robust solution for noise suppression in FDM Φ-OTDR systems, thus enhancing their performance in critical applications such as infrastructure monitoring and the diagnosis of electrical-cable faults.

In this study, the operational principles and demodulation process of an FDM Φ-OTDR system are presented, along with the introduction of an improved SVD methodology for noise suppression within the functioning framework of the sensor. The principle of the noise-reduction technique is the strategic selection of a threshold, as depicted in Fig. 5, where each frequency signal yields a pair of closely matched singular values following SVD. These pairs serve as the foundation for establishing equivalence between the frequency differential outcomes and singular values, which is crucial for effective noise mitigation. The proposed method begins with the demodulation of high-frequency signals via the FDM Φ-OTDR system, followed by the transformation of these signals into a Hankel-matrix configuration. This transformation facilitates the differentiation between the primary-signal components and secondary-noise elements within the signal matrix. By employing a thresholding approach, we delineate the principal singular values, which are instrumental to noise reduction while preserving essential high-frequency details. This procedure involves: 1) band-pass filtering to segregate Rayleigh backscattering (RBS) light from various channels and performing alignment to form a three-dimensional RBS matrix; 2) orthogonally demodulating RBS light from different channels to extract phase components followed by concatenating these components based on their sensing sequence to achieve phase restoration; 3) employing the Hankel matrix to execute SVD, thereby isolating noisy singular values; 4) utilizing established formulas to select an optimal threshold, thus nullifying noise-related singular values; 5) reconstructing data with the refined singular-value matrix, which culminates in noise attenuation in the high-frequency signals. This comprehensive approach underpins our improved SVD-based noise-suppression strategy, thus offering a new perspective and solution for high-frequency signal monitoring in FDM Φ-OTDR systems.

An FDM Φ-OTDR system as an acoustic or vibrational sensor was developed and implemented in this study, which achieved a maximum responsive frequency-band range of 62.5 kHz. As shown in Fig. 7, this system accurately reconstructs sinusoidal vibrations at 25.0 kHz, thereby highlighting its proficiency in discerning external disturbances. Subsequently, the system was employed to detect subtle acoustic signals using an improved SVD method for the precise reconstruction of nonstationary sound signals ranging from 0 to 3.5 kHz. Initial experiments validated the accuracy and reliability of the system for vibration and acoustic-signal detection, along with the feasibility of the enhanced SVD method for noise suppression. Further application of the improved SVD method to the system facilitated the detection of partial-discharge signals. The construction of the Hankel matrix for denoising, as shown in Fig. 11, coupled with the power differential spectrum depicted in Fig. 12, enabled the elimination of periodic narrowbands and white noise in partial-discharge signals. A comparative analysis of the wavelet-threshold-denoising and variational-mode decomposition methods demonstrates the superior denoising capability of the improved SVD approach. As indicated in Table 1, after denoising, the waveform similarity of the effective partial-discharge signal reaches 0.963, with the root-mean-square error reducing to 0.0099, and the SNR increasing from 13.118 dB to 29.300 dB, i.e., an increase by 16.182 dB in the SNR. This signifies a significant advancement in noise suppression and signal clarity for FDM Φ-OTDR systems.

This study introduces an improved SVD denoising method devised for suppressing background noise in high-frequency signal detection using FDM Φ-OTDR systems. By deconstructing the Hankel singular-value matrix and employing a threshold method to discern significant singular values, the method effectively distinguishes between primary and secondary noise elements, thus facilitating noise-component elimination. Empirical validation of the FDM Φ-OTDR system shows a broad frequency-response range, which signifies its ability to detect high frequencies. The system adeptly identifies nonstationary acoustic signals within the 0?3.5 kHz range in environmental settings, thus ultimately achieving the detection and denoising of partial-discharge signals in 10 kV power cables. Compared with the original signals, the denoised signals exhibit a waveform similarity of 0.963, with a lower root-mean-square error of 0.0099 and an improved SNR of 16.182 dB. The proposed method not only expands the measurable frequency response of FDM Φ-OTDR systems to 62.5 kHz, thus significantly enhancing the frequency-response range of distributed fiber-optic sensors, but also signifies a novel and meaningful attempt in monitoring nonstationary acoustic and partial-discharge signals. This approach provides a new perspective and solution for high-frequency signal monitoring within FDM Φ-OTDR systems, thus expanding the boundaries of current applications and inspiring further innovations in the field.