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10.1038/s44172-024-00274-5
Article
Achieving precise multiparameter measurements with distributed optical fiber sensor using wavelength diversity and deep neural networks
http://orcid.org/0000-0002-5652-0449
Lalam Nageswara nageswara.lalam@netl.doe.gov

12
Bukka Sandeep 12
http://orcid.org/0000-0001-7966-3621
Bhatta Hari 13
Buric Michael 4
http://orcid.org/0000-0003-2115-0692
Ohodnicki Paul 5
Wright Ruishu 1
1 https://ror.org/01x26mz03 grid.451363.6 0000 0001 2206 3094 National Energy Technology Laboratory, Pittsburgh, PA USA
2 grid.451363.6 0000 0001 2206 3094 NETL Research Support Contractor, Pittsburgh, PA USA
3 https://ror.org/040vxhp34 0000 0000 9696 3282 Oak Ridge Institute for Science and Education, Oak Ridge, TN USA
4 https://ror.org/01x26mz03 grid.451363.6 0000 0001 2206 3094 National Energy Technology Laboratory, Morgantown, WV USA
5 https://ror.org/01an3r305 grid.21925.3d 0000 0004 1936 9000 Mechanical Engineering & Materials Science, University of Pittsburgh, Pittsburgh, PA USA
31 8 2024
31 8 2024
2024
3 12129 2 2024
22 8 2024
© The Author(s) 2024
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The development of advanced distributed optical fiber sensing systems that are capable of performing accurate and spatially resolved multiparameter measurements is of great interest to a wide range of scientific and industrial applications. Here, we propose and experimentally demonstrate a wavelength diversity based advanced distributed optical fiber sensor system to accomplish multiparameter sensing while greatly enhancing measurement accuracy. A suite of deep neural network (DNN) algorithms are developed and verified for data denoising, rapid Brillouin frequency shift estimation, and vibration data event classification. As a proof-of-concept, we demonstrate the effectiveness of the proposed advanced wavelength diversity distributed fiber sensor system assisted by DNN for simultaneous, independent measurements of static strain, temperature, and acoustic vibrations over a 25 km long sensing fiber at 3 m spatial resolution. These results suggest the potential for an intelligent multiparameter monitoring system with enhanced performance in advanced structural health monitoring applications.

Nageswara Lalam and colleagues demonstrate a multiparameter distributed optical fibre sensing. They employ the wavelength multiplexing technique in Brillouin and Rayleigh scattering with the deep neural networks and achieve an improved performance of strain, temperature and vibration detection.

Subject terms

Applied optics
Optical physics
issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Distributed optical fiber sensors (DOFS) have emerged as cutting-edge technologies with the potential to transform monitoring and sensing industries. By utilizing the properties of light propagation through optical fibers, these sensors offer numerous advantages over traditional sensors, including spatially resolved measurement, immunity to electromagnetic interference, harsh environmental capability, and extensive sensing coverage along the entire length of the fiber1. These sensors utilize the inherent properties of optical fibers, such as Rayleigh, Brillouin, and Raman scattering, to extract valuable data on parameters such as temperature, strain, pressure, vibration, and acoustic signals. These sensors can provide crucial insights into diverse application fields such as oil and gas, marine, aerospace, civil engineering, and environmental monitoring2,3. However, conventional DOFS use a single scattering process, which provides limited sensing parameters such as static strain, temperature, or acoustic vibrations. Therefore, they are unable to give sufficient insight into the measurements, which can lead to inaccuracies and false alarms that could have a detrimental impact on current industrial applications. In contrast, multi-parameter monitoring is vital for industrial applications. For example, pipeline monitoring frequently requires simultaneous temperature, static strain, and vibration measurements to identify, distinguish, and successfully classify early cracks, leaks, and third-party intrusion events.

The integration of Rayleigh and Brillouin scattering in optical fibers has revolutionized the field of distributed fiber-optic sensing4,5. By combining the strengths of both scattering phenomena, this sensor system offers a powerful and comprehensive solution for monitoring various physical parameters along the length of optical fibers. Rayleigh scattering-based phase-optical time-domain reflectometry (Φ-OTDR), often called a distributed acoustic sensor (DAS), provides dynamic strain/acoustic vibrations, while the Brillouin scattering component enables the measurement of temperature and static strain. The approach of combining Rayleigh and Brillouin methods using a single interrogator system overcomes the limitations of individual sensing techniques and provides a more robust, cost-effective, and versatile sensing system. This proactive approach to maintenance and monitoring can prevent costly downtimes, improve safety, and enhance operational efficiency. A few research groups have demonstrated the utilization of Rayleigh and Brillouin scattering for the multiparameter monitoring of vibration and temperature/strain. In 2016, Zhang et al.6 demonstrated a hybrid system by integrating BOTDR and Φ-OTDR with modulated light pulses for standard 10 km long single-mode fiber. Nevertheless, the measurement accuracy, data processing speed for static strain/temperature of BOTDR and fading noise in Φ-OTDR remains challenging. In 2018, Fu et al.7 demonstrated a long-distance hybrid Brillouin optical time-domain analyzer (BOTDR) and Φ-OTDR at a spatial resolution of 30 m. Thereafter, Coscetta et al.8 presented a hybrid Brillouin optical time-domain analysis (BOTDA) and Φ-OTDR for multiparameter sensing. Although this system can detect temperature, static strain, and vibrations, it cannot monitor multiple measurements simultaneously with discrimination. In 20235, the authors proposed a multiparameter system that discriminates between temperature and strain measurements. Although all of these studies took advantage of two scattering mechanisms, simultaneous strain, temperature, and vibration sensing at the same time were not demonstrated since an optical switch was employed to change between BOTDA/BOTDR and Φ-OTDR systems. Moreover, owing to the immense system noise, the static strain, temperature, and vibration measurements have large measurement errors with slow processing speeds, which require advanced signal processing techniques. In 20239, the authors proposed a scanning-free hybrid Rayleigh–Brillouin system and conducted measurements on a 9.52 km single-mode fiber (SMF) with a 10 m spatial resolution and Brillouin frequency shift (BFS) accuracy of 0.74 MHz. The methods that were previously proposed have a low measurement accuracy of static strain and temperature, and low data processing speed is another challenge. It has never been reported that the hybrid DOFS system can achieve high measurement accuracy and rapid data processing speed with advanced denoising algorithms including vibration classifications.

The primary drawbacks of DOFS include susceptibility to cross-sensitivity due to sensitive multiple physical parameters, substantial volume of data generation, slow data processing, signal-to-noise ratio (SNR) degradation along the fiber length, and high cost of sensor and interrogator systems. These obstacles can be overcome by developing advanced data analytics engines utilizing recent breakthroughs in machine-learning (ML) deep neural networks (DNN) and utilizing the proposed advanced DOFS, leveraging wavelength diversity and DNN for precise multiparameter monitoring. Several works have already been proposed in the literature that integrate ML and DNN algorithms with DOFS technologies. Venketeswaran et al.10, provided a comprehensive review of fiber optic sensors integrated with ML and DNN algorithms. L Yang et al.11 proposed a convolutional neural network (CNN) to minimize the noise from earthquake and micro-seismic events data and recover weak DAS signals. In 2023, S. Lapins et al.12 demonstrated a supervised ML method (named DAS-Noise2Noise) for suppressing random noise in DAS data. This approach shows an effective method than the conventional band pass and white noise filtering procedures. In addition to DAS data denoising, vibration classification is essential to categorize the events13,14. PD Hernández et al.15 developed CNN models for an early warning earthquake with an accuracy of 96.94%. However, there hasn’t been much research on using classification models and DAS data denoising together. Wang et al.16 demonstrated a temperature and static strain extraction with enhanced accuracy by using DNN. In 2021, Soto et al.17 suggested an image-denoising method for BOTDA data and calculated the uncertainty of the Brillouin frequency shift (BFS) that results from image denoising.

In this work, we propose a single-end access hybrid DOFS system integrated with wavelength diversity, allowing multi-parameter monitoring, and simultaneous monitoring of static strain, temperature, and vibration with enhanced performance. The wavelength diversity technique reduces the BFS error (also referred to as BFS uncertainty) in the BOTDR system, whereas the Φ–OTDR system reduces the fading locations leading to a fading-free system. Additionally, we applied a suite of DNN algorithms for data denoising, rapid BFS estimation, and vibration event classification, leading to improved system performance with rapid data processing speed. To overcome the cross-sensitivity between the static strain, and temperature in the BOTDR system, we utilized a multi-Brillouin peak fiber for simultaneous and discriminative monitoring of static strain, temperature, and vibration over a 25 km long sensing fiber at 3 m spatial resolution. The schematic illustration of an improved performance advanced distributed fiber sensor system assisted by DNN for multi-parameter monitoring along with a selection of example applications is shown in Fig. 1.Fig. 1 Overall schematic of deep neural network (DNN)-assisted enhanced distributed fiber sensor system for multi-parameter monitoring.

A sensing optical fiber cable connected to an intelligent multi-parameter interrogator incorporating DNN technologies can be used for various applications.

Methods

Experimental Setup

The multi-parameter DOFS system involving a wavelength diversity technique relies on spontaneous Brillouin and Rayleigh backscattering signals. Both these methods send a narrow-bandwidth laser pulse, both need access to only one end, and backscattered light is analyzed to retrieve the physical stimuli information along the entire fiber length with spatial resolutions dictated by the interrogating optical pulse width18. In both conventional BOTDR and Φ-OTDR, a limited SNR is evident, and a tradeoff exists between spatial resolution and SNR. For BOTDR, the accuracy of the BFS measurements is severely affected by the low SNR, whereas in Φ-OTDR, the fading errors adversely affect the minimum vibration frequency that can be measured19. Therefore, to minimize the BFS errors while enhancing the vibration-sensing performance, a wavelength-diversity technique was employed in the multi-parameter DOFS system. The following considerations must be made while applying the wavelength diversity method: (i) the frequency spacing between the various pump wavelengths must be twice as large as the Brillouin gain spectrum (BGS) linewidth (~30 MHz); (ii) moreover, the frequency spacing must be larger than the photodetector (PD) bandwidth to avoid interference; and (iii) large frequency spacing can cause a beat spectral widening, which will lead to very severe BFS errors. The complete set of operating principles can be found in Supplementary Information, Supplementary Note 1.

The experimental setup of the single-end access multi-parameter DOFS system employing the wavelength diversity technique is illustrated in Fig. 2. A narrow-linewidth laser (~2 kHz) operating at a wavelength of 1550 nm with an output power of 30 mW was used as the light source. The wavelength diversity technique involved injecting several wavelengths into the sensor fiber. An external frequency synthesizer controls both the number of wavelengths and the frequency separation between wavelengths. An external frequency synthesizer operating at 500 MHz powered an intensity Mach-Zehnder modulator (MZM) that modulated the single wavelength laser output. To get the most optical power output from the MZM, a polarization controller (PC) is used before it. Three pump wavelengths (i.e., the carrier and two sidebands) can be set at identical peak power levels by adjusting the DC bias of the intensity MZM. In order to stabilize the frequency spacing and the power balance of the pump wavelengths, an automatic bias controller circuit is used to ensure stable operation over time. After that, coupler 1 divided the light into two branches. The bottom branch is utilized for the local oscillator, while the higher branch is used to generate pulses. The light wave in the upper branch is modulated by a semiconductor optical amplifier (SOA) to create high extinction ratio (>45 dB) optical pump pulses. Following the amplification and control of these pulses by an erbium-doped fiber amplifier (EDFA 1), the ASE noise is removed from the EDFA using an amplified spontaneous emission (ASE) bandpass filter. The pulse repetition frequency was fixed at 4 kHz, while the peak power and pulse width were established at 17 dBm and 30 ns, respectively. The circulator port 3 collects the backscattered signal that is amplified by EDFA2 and then splits it into two signals using 50/50 coupler 2. One branch of coupler 2 output beats with a local oscillator which maintains high SNR of BOTDR beat signal in the heterodyne detection process, whereas the other branch is used for Rayleigh signal detection. To reduce the signal fluctuations caused by polarization in BOTDR, a polarization scrambler (PS) was incorporated into the local oscillator. The beat signal was detected by the photodetector (PD1, bandwidth:12 GHz) and analyzed by a vector network analyzer (VNA). The detected electrical signals from the PD1 consist of the summed contribution of the Brillouin gain spectra generated by the three pump wavelengths. Whereas, the Rayleigh signal is separately detected by another PD2 (bandwidth:600 MHz) and displayed on the benchtop VNA. A small footprint, compact USB-based VNA or DAQ can be used in portable real-world application instrumentation.Fig. 2 Schematic representation of experimental setup of proposed multi-parameter distributed optical fiber sensors (DOFS) system employing wavelength diversity technique assisted by deep neural network-based data processing and classification.

ISO isolator, PC polarization controller, MZM Mach-Zehnder modulator, SOA semiconductor optical modulator, EDFA erbium-doped fiber amplifier, ASE amplified spontaneous emission, DC direct current power supply, PS polarization scrambler, PD photodetector, BGS Brillouin gain spectrum, Φ-OTDR phase-optical time-domain reflectometry, PDNN probabilistic deep neural network, CNN convolutional neural network, BFS Brillouin frequency shift, and CI confidence intervals.

Deep Neural Network-Based Signal Processing

The problems of inherent noise from the measured BGSs20,21, and vibration data22,23, lengthy processing time for BFS peak estimation with confidence intervals (C.I)24, and event classification of measured vibrations are addressed via DNN algorithms. The overall efficiency of data processing is improved and accelerated by using ML models. Due to access to the cleaner and noisy data versions of the BGSs, we applied a supervised denoising autoencoder to map the noisy data to clean data over a range of temperatures. This trained network is used to denoise the data for unknown temperatures. Whereas, for the case of acoustic vibration data from a proposed DOFS system, the unavailability of cleaner data motivated us to apply a more efficient self-supervised denoising algorithm, Noise to Noise (Noise2Noise)25,26 for vibration data denoising. Our research team proposed a probabilistic deep neural network (PDNN) for BFS estimation and further improved this work to estimate the multi-peak LEAF fiber BFSs27. The training and BFS peak estimation using the PDNN framework is described in Supplementary Information, Supplementary Note 3. Finally, a vanilla CNN is built and trained for the classification of events from the acoustic vibration data. Table 1 outlines all the proposed DNN models used in this study with brief notes on their architecture, tasks addressed, and learning paradigm, respectively. Comprehensive insights into the training methodologies and discussions on data denoising are expounded in Supplementary Information, Supplementary Note 2. In the case of BGS data, we considered a five-layer autoencoder network with the first two encoder layers containing 64 and 32 neurons, the middle bottleneck layer containing 16 neurons, and the last decoder layers containing 32 and 64 neurons. Rectified linear unit (Relu) is used as activation across all layers. The training is carried out for 100 epochs with a learning rate of 0.001 and ADAM optimizer. For the Φ-OTDR vibration data denoising, the Noise2Noise self-supervised denoising algorithm was applied. Finally, CNNs are used for the vibration event classification for various third-party intrusion events.Table 1 Summary of different deep neural network (DNN) models used for various tasks in the hybrid Rayleigh/Brillouin system

Model name	Neural network architecture	Task	Learning paradigm	
Autoencoder	Multi-layer feed-forward networks with bottleneck layer	Denoising of BOTDR data	Supervised	
PDNN	One-dimensional CNN with Gaussian layers towards the end	BFS estimation	Supervised	
Noise2Noise	Deep U-Net model with 20 layers	Denoising of Φ-OTDR data	Self-supervised	
CNN	Two-dimensional CNN with 6 layers	Classification of Φ-OTDR data	Supervised	

Results and Discussions

Experimental Results

Initially, we attained Brillouin spectral mappings for standard single-mode fiber by using conventional single wavelength (N = 1), and then by wavelength diversity method with three wavelengths (N = 3). We swept the VNA frequencies from 10.7 to 11 GHz with a step of 2 MHz and by using 1000 trace averages. The obtained Brillouin spectral mapping with three wavelengths (N = 3) is illustrated in Fig. 3a. The measured raw data fitted with a quadratic curve and the extracted BFS distribution over the sensing fiber are shown in Fig. 3a. inset. We evaluated the BFS errors over the fiber distance in both cases. Figure 3b shows measured BFS uncertainties over the sensing fiber length28. Here, the BFS uncertainty was calculated as a function of Brillouin spectrum linewidth, SNR of the trace at the peak Brillouin gain, and the frequency scanning step28. It is important to mention that we measured both the Brillouin spectrums with N = 1 and 3 at the same set of conditions, such as number of trace averages (2000), pulse width (30 ns), and optimized input peak power (~17 dBm) to the sensing fiber. At the end of the 25 km long sensing fiber, the frequency errors were 0.73 MHz, and 0.41 MHz for conventional single wavelength (N = 1), and wavelength diversity with three wavelengths, respectively. Based on these frequency errors, the estimated strain, and temperature accuracies at the far end of the sensing fiber were, ~18 µε, and ~0.71 °C for a single wavelength, and ~10 µε, and ~0.39 °C for three wavelengths.Fig. 3 Brillouin detection employing wavelength diversity technique.

a Three-dimensional Brillouin spectrum along the fiber with three wavelengths (N = 3). Inset: calculated Brillouin frequency shift (BFS) distribution over the fiber length. b Calculated BFS uncertainty over the fiber distance for N = 1 (red), and N = 3 (blue) wavelengths. c The zoom-in top view of 3D distribution near temperature effect of 75 °C. d Zoom-in BFS distribution around the heated temperature section.

Thereafter, we demonstrated a temperature sensing of the proposed multi-parameter DOFS system employing the wavelength diversity method. A 10 m fiber segment towards the end of a 25 km fiber was placed inside the temperature chamber, and the rest of the fiber was at ambient room temperature and kept strain-free. The temperatures were varied from room temperature (~21 °C) to up to 75 °C. Figure 3c shows the magnified top view of measured Brillouin spectra over the sensing fiber when the fiber section inside the temperature chamber was set at 75 °C, and a clear spectral shift was observed. The BFS distribution was calculated at various temperatures and illustrated in Fig. 3d. A spatial resolution of 3 m (measured from 10% to 90% response distance) was observed, as shown in Fig. 3d inset. This confirms the 30 ns pulse width used in the proposed advanced multi-parameter DOFS system.

Then, we measured a Φ-OTDR trace from the same ~25 km long single-mode fiber with N = 1 and three pump wavelengths. In Φ-OTDR, typically the fading effect refers to the noise dominated intensity fluctuations in the detected trace from the fiber under test such that at certain locations it is difficult to realize the distortion free amplitude/phase demodulation. This is due to a random distribution of Rayleigh scattering points and interference of these scattered light within a pulse width duration as that may result in low-intensity areas close to the level of the system noise floor. Particularly, due to destructive interference, the detected amplitude has weak amplitude (falls within the noise floor limit) at several locations over the fiber under test, significantly impacts the accuracy, and leads to false alarms. In conventional single wavelength Φ-OTDR, the fading effect severely degrades the vibration sensing performance. As the fading positions (dead zones) of Φ-OTDR traces are optical frequency dependent, the proposed wavelength diversity technique eliminates fading points significantly. Therefore, the fading noise properties are shared and self-canceled by utilizing the wavelength-diversity scheme. Taking advantage of wavelength-dependent fading noise locations, the proposed method reduces the possibility of dead zones and measured Φ-OTDR traces with N = 1, and three pump wavelengths are shown in the Supplementary Information Figure S2. It is worth noting that, the peak power of all three wavelengths was equally adjusted by tuning the DC bias of the MZM modulator. Each wavelength peak power was below the nonlinear threshold level to avoid nonlinear effects, such as modulation instability and stimulated Brillouin scattering29. To confirm the improvement in fading suppression, the aggregated phase-OTDR traces were obtained using single wavelength (N = 1) and multi-wavelength (N = 3) including vibration performance. Figure 4, shows the vibration performance comparison in both cases of N = 1 and N = 3. At the end of the fiber around 24 km location, a 20 m fiber was wrapped around the piezoelectric (PZT) cylinder using adhesive glue. The PZT cylinder was then excited at a 500 Hz sinusoidal frequency using an external arbitrary waveform generator and a low-frequency RF amplifier. As shown in Fig. 4a, measured superimposed 11,600 successive traces, the dead zones were significant using conventional single wavelength and the vibrations cannot be demodulated at those locations. The dead zones were significantly minimized using three wavelengths as shown in Fig. 4c. The corresponding extracted fast Fourier transform (FFT) spectra of single and three wavelengths were illustrated in Fig. 4b, and d, respectively. The SNR of the frequency spectra measured by the N = 1 is 22.8 dB, while the SNR of the N = 3 case is 30.1 dB. These results clearly show that the SNR is moderately higher than that of the single wavelength (which could be due to the reduced noise) in addition to minimizing the fading errors.Fig. 4 Comparison of fading noise and vibration detection in conventional and wavelength diversity phase-optical time-domain reflectometry (Φ-OTDR).

a Aggregated differential traces of conventional single wavelength (N = 1), (b) extracted frequency spectra (c) wavelength diversity (N = 3) technique, and (d) corresponding extracted frequency spectra at a vibration frequency of 500 Hz applied around 24 km location.

To validate the vibration sensing using a proposed sensor system, the frequencies were swept from 250 Hz up to 1250 Hz. At a 5 Vpp and 1 kHz excitation frequency, the zoom-in view of raw Φ-OTDR traces is shown in Fig. 5a. It is noticeable that the amplitude experiences substantial changes around the vibration excitation location (highlighted red dashed line in Fig. 5a) among different traces, where the rest of the fiber amplitude is relatively unchanged. The zoom-in reconstructed spatial-temporal density plot is illustrated in Fig. 5b, which shows the spatial information in the x-axis, and the y-axis shows the temporal information with noticeable vibration events around the 24 km fiber location. Figure 5c shows the extracted time-domain signal at 1 kHz frequency. The sensor system clearly recorded a clean sinusoidal signal at 1 kHz frequency, whereas the PZT cylinder was driven by an external arbitrary waveform generator set at 1 kHz sinusoidal frequency. Thereafter, the frequency ranged from 250 Hz to 1250 Hz and measured FFT spectra at each measurement are displayed in Fig. 5d. The recorded spectrum has high SNR (>20 dB) peaks at all test frequencies that are easily identified.Fig. 5 Vibration measurements using the proposed hybrid sensor system.

a Magnified view of consecutive overlapped Rayleigh raw traces obtained from the proposed sensing system with N = 3 wavelengths. b Differential spatial-temporal spectrogram plot of the retrieved Rayleigh backscattered amplitude traces. The red dashed line corresponds to the intrusion location on the fiber. The vibration tests at the end of the sensing fiber. c Extracted time domain signal at 1 kHz frequency. (d) Frequency spectra for an applied vibration from 250 Hz to 1250 Hz.

Although the proposed DOFS system monitors the strain, temperature, and vibrations, the cross-sensitivity between static measurements of strain and temperature is still challenging. Therefore, to overcome the cross-sensitivity problem and the feasibility of simultaneous strain, and temperature measurement, we used a multi-Brillouin peak large-effective area fiber (LEAF). We utilized a 25 km long LEAF fiber and interrogated using a proposed multi-parameter DOFS system. The measured Φ-OTDR traces using N = 1 and N = 3 wavelengths are illustrated in Fig. 6a. In the case of a single wavelength (N = 1), the Φ-OTDR trace intensities are found to be very weak in many places, sometimes even below the noise level due to interference fading, which causes repeated trigger false alarms. The three-dimensional Brillouin gain spectrum, which contains multiple gain spectrums originated from the complex triangle refractive index profile of the core. The measured three-dimensional Brillouin gain spectrum of LEAF at ambient room temperature and strain-free conditions is illustrated in Fig. 6b, where the frequencies were swept from 10.55 to 11.1 GHz with a step of 2 MHz. Thereafter, the BFS dependence of temperature and strain was explored for peaks 1 and 2 with linear curve fitting illustrated in Fig. 6c and d. The measured temperature coefficients for peaks 1 and 2 are 1.018 MHz/°C, and 0.918 MHz/°C, respectively. On the other hand, the strain coefficients for peaks 1 and 2 are 0.03774 MHz/µε and 0.03748 MHz/µε, respectively. It is evident that, due to distinct temperature, and strain coefficients of peaks 1 and 2, discriminative simultaneous measurement can be achieved while measuring the acoustic vibrations from the same LEAF fiber. Our most recent research work30 provides a detailed strain and temperature discriminative measurement using multi-Brillouin peak fiber.Fig. 6 Validation of multiparameter sensing performance using large-effective area fiber (LEAF).

a Measured phase-optical time-domain reflectometry (Φ-OTDR) traces using N = 1 (black), and N = 3 (red) pump wavelengths. b Three-dimensional Brillouin spectrum along the LEAF with three wavelengths (N = 3). Measured Brillouin frequency shift dependence for LEAF fiber’s peak 1 and peak 2 for c temperature and d strain.

To validate the multi-parameter sensing at the same time, a translation stage with a 4 m long fiber, and a PZT cylinder wrapped with 20 m long fiber were placed inside a temperature oven. The PZT cylinder was excited using an external arbitrary waveform generator and a low-frequency RF amplifier. The schematic setup is shown in Fig. 7a, where the LEAF fiber is used as fiber under test to discriminate strain and temperature. Initially, we measured baseline BFSs at room temperature (~23°C) and strain-free. Thereafter, 200 µε was applied using a translation stage, while the PZT was driven at a 1 kHz sinusoidal frequency. The measured Φ-OTDR spatial-temporal density zoomed-in plot is illustrated in Fig. 7b, where the red dashed line indicates the vibration location. Subsequently, the oven temperature was changed to 35, and 45 °C from the ambient room temperature of ~23°C. Baseline BFS was subtracted from each new measurement to determine the relative BFS for peaks 1 and 2. A linear matrix equation was then applied to compute the resulting strain and temperature variations. The procedure for strain and temperature separation using linear equations is described in Supplementary Information, Supplementary Note 4. The simultaneously extracted temperature and strain are shown in Fig. 7c and d, respectively.Fig. 7 Simultaneous multiparameter monitoring using the proposed hybrid sensor system.

a Schematic setup of monitoring strain, temperature, and vibrations at the end of the LEAF sensing fiber using multi-parameter distributed optical fiber sensors (DOFS) sensor system, b spatial-temporal spectrogram of the retrieved differential traces. At a fixed strain of 200 µε with varied temperatures, the simultaneously measured c temperature and d strain distribution.

Denoising of BGS and Φ-OTDR Data

After experimental validation, DNN-based signal processing algorithms are established for data denoising and rapid BFS peak estimation. The comparison of noisy, denoised, and BGS spectrum at the 12 km location of sensing fiber at 30 °C temperature dataset for configuration 1 is depicted in Fig. 8a. Quadratic fitting is performed on the noisy data obtained at 100 averages and denoised data to extract the BFS peaks 1 and 2 simultaneously28. Thereafter, we measured the SNR, and BFS uncertainty over the sensing fiber length, illustrated in Fig. 8b. The SNR was calculated for the peak-gain trace of the BGS along the fiber. Peak gain trace was first normalized to the maximum value, local SNR at each location is then calculated as a ratio of the gain value to noise. Here, gain is calculated as the mean, and noise as the standard deviation among the nearest 50 gain points in the temporal domain which was chosen not to degrade the spatial resolution of the system. The SNR improvement of ~4 dB is found for both peaks 1 and 2 compared to noisy raw data. It is evident that the measured BFS uncertainty is consistent with the improved SNR and demonstrates a growing pattern along the fiber’s length. The measurement accuracy improved noticeably after DNN-based data denoising, as indicated by the BFS uncertainties for peaks 1 and 2 at the end of the sensing fiber. The BFS uncertainty for peak 1 is significantly lower, reduced from 3 MHz to 1.2 MHz, indicating a significant increase in measurement accuracy. Similarly, for peak 2, the BFS uncertainty reduced from 6.5 MHz to 3 MHz, reflecting a substantial enhancement in measurement accuracy as well. The associated strain and temperature accuracies are ±60 µε and ±3 °C based on the observed coefficients displayed in Fig. 6c and d. After denoising, these values have been improved to ±12 µε and ±1.2 °C, respectively, for peak 1. For peak 2, the initial measurement accuracies are ±130 µε and ±6.5 °C have been enhanced to ±60 µε and ±3 °C, respectively. The supervised ML with autoencoder networks is quite robust and promising for the problem of denoising. It can learn the mapping between lower and higher ensemble average data from the interrogator quite efficiently across unseen parameters. The autoencoder model can be easily scaled with much larger datasets acquired from laboratory experiments and field demonstration measurements. Furthermore, we compared performances between the DNN based denoising with the conventional optimized non-local means (NLM) filter based denoising, we found that DNN based denoising results in very less processing times (0.02 s) and remains robust also in SNR enhancement and BFS error reductions with respect to NLM filter based method as shown in Table 2.Fig. 8 Brillouin gain spectrums (BGSs) data denoising based on deep neural network (DNN) algorithm.

Comparison of a noisy raw data, denoised data, and Brillouin gain spectrum (BGS) at the 12 km location of the fiber. b Signal-to-noise ratio (SNR) and Brillouin frequency shift (BFS) uncertainty for noisy raw data, and denoised data obtained at 30 oC temperature along the fiber length.

Table 2 Comparison of non-local means (NLM) based denoising with deep neural network (DNN)-based denoising technique at a 12 km location

Data type	Peak 1 - SNR (dB)	Peak 2 - SNR (dB)	Peak 1 - BFS uncertainty (MHz)	Peak 2 - BFS uncertainty (MHz)	Processing time for denoising (seconds)	
Original raw data without denoising	7.8	4.8	2.8	5.75	NA	
Denoising with NLM	10.52	8.2	1.46	2.66	2.29	
Denoising with DNN (this work)	12.1	8.87	1.15	2.64	0.02	

In contrast to the previous results where access to clean BGS data is available, it is not the case for the Φ-OTDR data. The dominant noises in Φ-OTDR traces are intensity and polarization fading noises, and low Rayleigh backscattered signal strength, the measured traces suffer from fading errors and excessive noise. Although, our proposed wavelength diversity technique reduces the fading errors, the extracted vibration data still contains inherent noise due to the low SNR of the measured Φ-OTDR traces. An alternative method to improve the Rayleigh backscattering strength is to use enhanced Rayleigh scattering fibers thus improving SNR over the sensing fiber31,32. However, the specialty enhanced Rayleigh scattering fibers are expensive and have a complicated fabrication process, which limits their usage in practical applications. This motivated us to apply self-supervised denoising algorithms such as Noise2Noise26 for the measured Φ-OTDR vibrations from the proposed next-generation multiparameter DOFS interrogator. For more mathematical justification and operating principles of Noise2Noise training, readers can refer to25,26. The same acoustic dataset generated for third-party intrusion event classification was used for the denoising problem. The measured noisy vibration data input and target pairs were created from the Φ-OTDR dataset generated from a strictly regulated soundproof environment by adding an uncorrelated white noise to underlying clean data. In this way, the two conditions required for the Noise2Noise training were met. This demonstration was valid since the trained denoising network can be directly applied to noisy acoustic data collected in real-world or lab environment without any soundproof system to compute the denoised signal. The details of the 20-layered deep complex U-net architecture are outlined in ref. 25 and the corresponding code is taken from the GitHub repository33. We have directly used the above code for our dataset and trained the DCU-net model for 4 epochs on a local Macbook m1 pro. The results are displayed in Supplementary Fig. S4, which shows an SNR improvement of over 8 dB was achieved by training for just 4 epochs. This demonstrates the ability of Noise2Noise’s self-supervised training strategy using the DCU-net model.

Brillouin Frequency Shift (BFS) Estimation Using PDNN

DNN-based data processing provides faster processing speed in comparison to traditional nonlinear curve fitting algorithms, which have slow processing speeds for estimating BFS peaks. Venketeswaran et al.27, introduced a PDNN for BFS estimation with C.I. However, the authors demonstrated only for a standard single-mode fiber that has only a single BGS peak and needs further optimization for multi-peak BGS originating from LEAF fiber used in this proposed work. Therefore, the same framework was further optimized and applied to solve the problem of simultaneous estimation of BGS peaks. The overall schematic of this framework with its training procedure is outlined in Supplementary Information, Supplementary Note 3. To give a brief summary of the architecture of PDNN, the input layer is composed of two channels corresponding to frequency and Brillouin gain spectrum, respectively, followed by a series of three convolutional and max-pooling layers with channels of 64, 32, and 16, and a kernel size of 5 for convolutional layers and 3 for max pooling layers. The final three layers consist of a flattened, dense layer with 64 units and an output probability layer with 4 units corresponding to BFS peak 1 and peak 2 with their respective C.I. By output probability layer, we mean that layer has a Gaussian random variable wrapped inside it and outputs the mean and standard deviation. Further, a learning rate schedule and early stopping criterion are implemented to automate the number of epochs used for training. The network is trained for 50,000 samples of simulated noisy BGS data with varying BFS peaks 1 and 2 and different noise levels.

The results for different inputs BGS data are outlined in Fig. 9. The BGS data was obtained by sweeping the Brillouin frequencies from 10.5 to 11.1 GHz with a frequency step of 3 MHz. Initially, the data was obtained at 100 ensemble averages and applied DNN-denoising algorithm. Whereas, the clean data was obtained at 15,000 ensemble averages. These predictions were compared with the conventional Lorentzian curve fitting with their processing speed as shown in Fig. 9. In general, the fluctuations in the BFS profile are not caused by the noise but rather are produced by the nonuniform strain in the fiber spool, resulting in oscillations in the BFS profile. In addition to data denoising, the data processing time to extract the BFS profile is another important factor. In our experiments, 201 scanning frequency steps were used to cover both BGS spectrums of the LEAF fiber, and the pulse period of 250 µs was used to cover the 25 km long LEAF fiber. Theoretically, the data acquisition time for each measurement with 1000 averages is 201 × 1000 × 2 × 250µs = 1.6 minutes34. This acquisition time increases significantly with increased average values. As expected, the PDNN predictions for denoised and clean data are similar, which is quantified by the similar standard deviation values of BFSs across the fiber length. When lower ensemble averaged data is considered, the inherent noise in the data manifests in the higher standard C.I by the PDNN predictions and higher BFS standard deviation values across the fiber length. The quantitative performance of PDNN is also in line with traditional Lorentzian curve fitting. This is expected since PDNN is trained on the data from the Lorentzian curve. However, for enormously noisy and unstable data that which as produced 10 ensemble averages from BOTDA, one cannot produce any results from curve fitting as it fails to fit but PDNN can infer the BFSs even for this highly noisy data with higher C.I. This indicates the presence of significant noise in the data, the trained PDNN model able to predict the BFSs. As a result of the large amount of noise as well as the shape of the BGS that deviates from a Lorentzian curve, the nonlinear least squares method for Lorentzian curve fitting failed to converge and therefore failed to estimate the peak BFSs of 10 average data35,36. The PDNN model processed the 40,000 BGS spectra across the whole fiber length in just under 4 seconds whereas the curve fitting procedure took around 45 seconds to do the same. The PDNN model outperforms traditional curve fitting in computational time by achieving a speedup of a factor above 10. The ability to predict BFS for highly noisy data and the high computational speed offered by PDNN demonstrate the ability of deep neural networks to achieve more efficient and accelerated signal processing for data coming from fiber optic sensors.Fig. 9 Comparison of probabilistic deep neural network (PDNN)’s Brillouin frequency shift (BFS) predictions including standard deviation (σ) and computational efficiency for different average data.

Classification of third-party vibration events

CNNs are used for the event classification of Φ-OTDR’s vibration data, related to various third-party intrusion events. Identification and classification of third-party intrusion events have paramount importance for infrastructure monitoring, and it has real-world applications across a diverse set of industries varying from civil, offshore, aerospace, defense, mechanical, and automotive. In this work, we have chosen specific pipeline third-party intrusion signatures, such as excavation, pipe spill, gas leak, digging, etc. Approximately 13 typical third-party events were obtained from open-source audio repositories. All these audio files were resampled to 50 kHz with each sample length of ten seconds. For the sake of demonstration, we assume the vibration data that we receive from the Φ-OTDR experiments are the original clean data. To ensure minimal noise in the Φ-OTDR data, the acoustic experiments were conducted in a clean laboratory environment. A 10 m long fiber at the end of the fiber under test was looped and glued with acoustically conductive epoxy on an aluminum foil to enhance the acoustic sensitivity. A loudspeaker was positioned underneath the sensing fiber, and each audio file was played ten times consecutively with a silent gap of ten seconds between each sample. The acoustic waves from the speaker excited the fiber and a specific signature was recorded by the Φ-OTDR interrogator for each event. An outline for the experimental setup is provided in Fig. 10. In total, 200 such signatures were collected from the Φ-OTDR, and they are labeled with their corresponding classes. The step by step process of third-party intrusion classification is outlined in Fig. 11. A few samples from this dataset were set aside for blind testing. This labeled dataset of 200 vibration signatures was divided into train/test with a ratio of 80/20. Thereafter, a CNN was trained using the labeled training dataset. The parameters of the CNN model trained are outlined in Table 3. A set of data pre-processing steps were conducted on the raw traces collected from the interrogator and normalized, masked mel spectrograms were generated and fed into the CNN model for the training. The training is carried out for 100 epochs with a constant learning rate of 0.001 and ADAM optimizer. Standard binary cross entropy was used as the loss function for the optimizer. A sample acoustic signature related to excavation from the test dataset is shown in Fig. 11a. A confusion matrix for the predictions on the whole test dataset is also plotted in Fig. 11e, we were able to achieve 97% accuracy on the test dataset.Fig. 10 Schematic setup of third-party intrusion detection through a loudspeaker and multi-parameter distributed optical fiber sensors (DOFS) interrogator in a laboratory environment.

Fig. 11 Classification of third-party intrusion events of phase-optical time-domain reflectometry (Φ-OTDR) data with a convolutional neural network (CNN).

a Raw signal from third-party intrusion event of excavator, (b) 12 b Mel-spectrogram of the raw signal, c Mel-spectrogram of the raw signal with data pre-processing such as normalization, time and frequency masks, d Schematic of the CNN, and e Confusion matrix with 97% accuracy predicted by the classification model.

Table 3 Network parameters of the CNN used in the classification model

CNN network parameters	
Layer	kernel	Input size	Output size	
Conv2D	5 × 5	1 x 128 x 977	8 x 64 x 489	
Conv2D	3 × 3	8 x 64 x 489	16 x 32 x 245	
Conv2D	3 × 3	16 x 32 x 245	32 x 16 x 123	
Conv2D	3 × 3	3216 x 23	64 x 8 x 62	
AdaptiveAvgPool2d	–	64 x 8 x 62	64 x 1 x 1	
Dense	–	64	13	
Optimizer parameters	
Activation	Relu	
Optimizer	Adam	
Learning rate	0.001	
Batch size	16	
Num epochs	100	

Conclusion

In conclusion, this study proposed and demonstrated a wavelength diversity multi-parameter distributed fiber sensor system integrated with DNN-based data denoising, BFS estimation, and vibration event classification. The DNN-based signal processing for a multi-parameter distributed sensor system helping to achieve improved accuracy in simultaneous strain, temperature, and vibration measurements. Moreover, the wavelength diversity approach enhanced the SNR significantly, which benefits Brillouin detection by reducing BFS uncertainty while avoiding fading errors in Rayleigh detection. The problems of data denoising and slow processing speed of BFS estimation with confidence intervals and event classification of third-party intrusion events were addressed via DNN. For the denoising of BGS data, supervised learning using fully connected feed-forward autoencoder networks is carried out. The performance of autoencoder networks for denoising has significant improvement in SNR and BFS uncertainty reductions. A self-supervised denoising approach using the algorithm Noise2Noise was used for denoising the Φ-OTDR vibration signatures. Probabilistic DNN was used for the BFS estimation with C.I., quantifying the amount of noise in the data. PDNN model is shown to be more efficient for highly noisy data and has a significant computational speedup compared to traditional curve fitting. Finally, a database of 200 Φ-OTDR signatures was generated for real-world third-party intrusion events in the lab and a CNN model was trained to achieve 97% accuracy for the classification of these events. We will be integrating all the above DNN models into a single suite of signal processing frameworks for fiber optic sensor data. This framework will be further improved with more complex models and will be tested for real-world field data. With its high accuracy and intelligent multi-parameter sensing capability, the proposed sensor system holds great potential for various practical applications where multi-parameter sensing with enhanced accuracy is critical. Future work will focus on a comprehensive investigation of wavelength diversity technique in Brillouin and Rayleigh detection, investigation of ultra-long distance with hybrid amplification techniques, and field demonstration of natural gas pipeline integrity monitoring.

Supplementary information

Supplementary Information

Supplementary information

The online version contains supplementary material available at 10.1038/s44172-024-00274-5.

Acknowledgements

This work was performed in support of the U.S. Department of Energy’s (DOE) Fossil Energy and Carbon Management and executed through the National Energy Technology Laboratory (NETL) Research & Innovation Center’s Natural Gas Infrastructure Field Work Proposal. Research performed by Leidos Research Support Team (LRST) staff was conducted under the RSS contract. This project was funded by the U.S. Department of Energy, National Energy Technology Laboratory, in part, through a site support contract. Neither the United States Government nor any agency thereof, nor any of their employees, nor the support contractor, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Author contributions

N.L. designed the experimental setup and collected the data, H.B. designed the multiparameter sensing capability and performed the strain, temperature, and vibration sensing experiments, S.B. performed deep neural network-based data analytics, M.B., P.O, and R.W. provided useful discussion and overseen the project.

Peer review

Peer review information

Communications Engineering thanks Daniele Tosi, Ioannis Matthaiou, and the other, anonymous, reviewer for their contribution to the peer review of this work. Primary Handling Editors: Anastasiia Vasylchenkova and Saleem Denholme.

Data availability

The datasets generated during this research study are available upon request. The data are not publicly available due to export control regulations.

Code availability

All codes used in this study are available from the corresponding authors upon request.

Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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References

1. Wijaya H Rajeev P Gad E Distributed optical fibre sensor for infrastructure monitoring: Field applications Opt. Fiber Technol. 2021 64 102577 10.1016/j.yofte.2021.102577
Wijaya, H., Rajeev, P. & Gad, E. Distributed optical fibre sensor for infrastructure monitoring: Field applications. Opt. Fiber Technol. 64, 102577 (2021).10.1016/j.yofte.2021.102577
2. Pendão C Silva I Optical fiber sensors and sensing networks: overview of the main principles and applications Sensors 2022 22 7554 10.3390/s22197554 36236653
Pendão, C. & Silva, I. Optical fiber sensors and sensing networks: overview of the main principles and applications. Sensors 22, 7554 (2022).36236653 10.3390/s22197554
3. Lu, P. et al. Distributed optical fiber sensing: Review and perspective. Appl. Phys. Rev. 6, 15–26 (2019).
4. Miah K Potter DK A review of hybrid fiber-optic distributed simultaneous vibration and temperature sensing technology and its geophysical applications Sensors 2017 17 2511 10.3390/s17112511 29104259
Miah, K. & Potter, D. K. A review of hybrid fiber-optic distributed simultaneous vibration and temperature sensing technology and its geophysical applications. Sensors 17, 2511 (2017).29104259 10.3390/s17112511
5. Murray MJ Murray JB Ogden HM Redding B Dynamic temperature-strain discrimination using a hybrid distributed fiber sensor based on Brillouin and Rayleigh scattering Opt. Express 2023 31 287 300 10.1364/OE.477481 36606967
Murray, M. J., Murray, J. B., Ogden, H. M. & Redding, B. Dynamic temperature-strain discrimination using a hybrid distributed fiber sensor based on Brillouin and Rayleigh scattering. Opt. Express 31, 287–300 (2023).36606967 10.1364/OE.477481
6. Zhang J High spatial resolution distributed fiber system for multi-parameter sensing based on modulated pulses Opt. Express 2016 24 27482 27493 10.1364/OE.24.027482 27906320
Zhang, J. et al. High spatial resolution distributed fiber system for multi-parameter sensing based on modulated pulses. Opt. Express 24, 27482–27493 (2016).27906320 10.1364/OE.24.027482
7. Fu Y Ultra-long-distance hybrid BOTDA/Ф-OTDR Sensors 2018 18 976 10.3390/s18040976
Fu, Y. et al. Ultra-long-distance hybrid BOTDA/Ф-OTDR. Sensors 18, 976 (2018).10.3390/s18040976
8. Coscetta A Hybrid Brillouin/Rayleigh sensor for multiparameter measurements in optical fibers Opt. Express 2021 29 24025 24031 10.1364/OE.426427 34614655
Coscetta, A. et al. Hybrid Brillouin/Rayleigh sensor for multiparameter measurements in optical fibers. Opt. Express 29, 24025–24031 (2021).34614655 10.1364/OE.426427
9. Huang L Fan X He Z Scanning-free hybrid Rayleigh–Brillouin distributed fiber-optic sensing system Opt. Lett. 2023 48 4629 4632 10.1364/OL.499635 37656572
Huang, L., Fan, X. & He, Z. Scanning-free hybrid Rayleigh–Brillouin distributed fiber-optic sensing system. Opt. Lett. 48, 4629–4632 (2023).37656572 10.1364/OL.499635
10. Venketeswaran A Recent advances in machine learning for fiber optic sensor applications Adv. Intell. Syst. 2022 4 2100067 10.1002/aisy.202100067
Venketeswaran, A. et al. Recent advances in machine learning for fiber optic sensor applications. Adv. Intell. Syst. 4, 2100067 (2022).10.1002/aisy.202100067
11. Yang L Denoising of distributed acoustic sensing data using supervised deep learning Geophysics 2022 88 WA91 WA104 10.1190/geo2022-0138.1
Yang, L. et al. Denoising of distributed acoustic sensing data using supervised deep learning. Geophysics 88, WA91–WA104 (2022).10.1190/geo2022-0138.1
12. Lapins S DAS-N2N: machine learning distributed acoustic sensing (DAS) signal denoising without clean data Geophys. J. Int. 2023 236 1026 1041 10.1093/gji/ggad460
Lapins, S. et al. DAS-N2N: machine learning distributed acoustic sensing (DAS) signal denoising without clean data. Geophys. J. Int. 236, 1026–1041 (2023).10.1093/gji/ggad460
13. Matthaiou I., Masoudi A., Modafferi S., Brambilla G. Classifying space-time images obtained from distributed acoustic sensing. In: Optica Sensing Congress 2023). Optica Publishing Group (2023).
14. Gonzalez-Herraez, M. et al. Underwater seismic tomography with unprecedented resolution using fiber optics. In: OSA Optical Sensors and Sensing Congress 2021). Optica Publishing Group (2021).
15. Hernández PD Ramírez JA Soto MA Deep-learning-based earthquake detection for fiber-optic distributed acoustic sensing J. Lightw. Technol. 2022 40 2639 2650 10.1109/JLT.2021.3138724
Hernández, P. D., Ramírez, J. A. & Soto, M. A. Deep-learning-based earthquake detection for fiber-optic distributed acoustic sensing. J. Lightw. Technol. 40, 2639–2650 (2022).10.1109/JLT.2021.3138724
16. Wang B Deep neural networks assisted BOTDA for simultaneous temperature and strain measurement with enhanced accuracy Opt. Express 2019 27 2530 2543 10.1364/OE.27.002530 30732290
Wang, B. et al. Deep neural networks assisted BOTDA for simultaneous temperature and strain measurement with enhanced accuracy. Opt. Express 27, 2530–2543 (2019).30732290 10.1364/OE.27.002530
17. Soto MA Yang Z Ramírez JA Zaslawski S Thévenaz L Evaluating measurement uncertainty in Brillouin distributed optical fibre sensors using image denoising Nat. Commun. 2021 12 4901 10.1038/s41467-021-25114-4 34385426
Soto, M. A., Yang, Z., Ramírez, J. A., Zaslawski, S. & Thévenaz, L. Evaluating measurement uncertainty in Brillouin distributed optical fibre sensors using image denoising. Nat. Commun. 12, 4901 (2021).34385426 10.1038/s41467-021-25114-4
18. Boyd R. Nonlinear optics 3rd edn, ed RW Boyd (Burlington: Academic). (2008).
19. Karapanagiotis C Krebber K MachinE LEARNING APproaches in Brillouin DISTRIBUTED FIBER OPTIC SEnsors Sensors 2023 23 6187 10.3390/s23136187 37448034
Karapanagiotis, C. & Krebber, K. MachinE LEARNING APproaches in Brillouin DISTRIBUTED FIBER OPTIC SEnsors. Sensors 23, 6187 (2023).37448034 10.3390/s23136187
20. Wang S Yang Z Soto MA Thévenaz L Study on the signal-to-noise ratio of Brillouin optical-time domain analyzers Opt. Express 2020 28 19864 19876 10.1364/OE.393928 32680057
Wang, S., Yang, Z., Soto, M. A. & Thévenaz, L. Study on the signal-to-noise ratio of Brillouin optical-time domain analyzers. Opt. Express 28, 19864–19876 (2020).32680057 10.1364/OE.393928
21. Qian X Noise level estimation of BOTDA for optimal non-local means denoising Appl Opt. 2017 56 4727 4734 10.1364/AO.56.004727 29047608
Qian, X. et al. Noise level estimation of BOTDA for optimal non-local means denoising. Appl Opt. 56, 4727–4734 (2017).29047608 10.1364/AO.56.004727
22. Wang Z Lu B Ye Q Cai H Recent progress in distributed fiber acoustic sensing with Φ-OTDR Sensors 2020 20 6594 10.3390/s20226594 33218051
Wang, Z., Lu, B., Ye, Q. & Cai, H. Recent progress in distributed fiber acoustic sensing with Φ-OTDR. Sensors 20, 6594 (2020).33218051 10.3390/s20226594
23. Li T Zhang F Lin J Bai X Liu H Fading noise suppression method of Ф-OTDR system based on non-local means filtering Opt. Fiber Technol. 2023 81 103572 10.1016/j.yofte.2023.103572
Li, T., Zhang, F., Lin, J., Bai, X. & Liu, H. Fading noise suppression method of Ф-OTDR system based on non-local means filtering. Opt. Fiber Technol. 81, 103572 (2023).10.1016/j.yofte.2023.103572
24. Xu Z Zhao L Investigation of Brillouin frequency shift error estimated by quadratic fitting and the improved algorithm Optik 2021 241 166456 10.1016/j.ijleo.2021.166456
Xu, Z. & Zhao, L. Investigation of Brillouin frequency shift error estimated by quadratic fitting and the improved algorithm. Optik 241, 166456 (2021).10.1016/j.ijleo.2021.166456
25. Kashyap M., Tambwekar A., Manohara K., Subramanyam N. Speech Denoising Without Clean Training Data: A Noise2Noise Approach (2021).
26. Lehtinen, J. et al. Noise2Noise: Learning Image Restoration without Clean Data. In: 35th International Conference on Machine Learning. pp. 2965-2974, PMLR (2018).
27. Venketeswaran A Robust vector BOTDA signal processing with probabilistic machine learning Sensors 2023 23 6064 10.3390/s23136064 37447912
Venketeswaran, A. et al. Robust vector BOTDA signal processing with probabilistic machine learning. Sensors 23, 6064 (2023).37447912 10.3390/s23136064
28. Soto MA Thévenaz L Modeling and evaluating the performance of Brillouin distributed optical fiber sensors Opt. Express 2013 21 31347 31366 10.1364/OE.21.031347 24514710
Soto, M. A. & Thévenaz, L. Modeling and evaluating the performance of Brillouin distributed optical fiber sensors. Opt. Express 21, 31347–31366 (2013).24514710 10.1364/OE.21.031347
29. Alahbabi MN Cho YT Newson TP Wait PC Hartog AH Influence of modulation instability on distributed optical fiber sensors based on spontaneous Brillouin scattering J. Opt. Soc. Am. B 2004 21 1156 1160 10.1364/JOSAB.21.001156
Alahbabi, M. N., Cho, Y. T., Newson, T. P., Wait, P. C. & Hartog, A. H. Influence of modulation instability on distributed optical fiber sensors based on spontaneous Brillouin scattering. J. Opt. Soc. Am. B 21, 1156–1160 (2004).10.1364/JOSAB.21.001156
30. Lalam N Pilot-scale testing of natural gas pipeline monitoring based on phase-OTDR and enhanced scatter optical fiber cable Sci. Rep. 2023 13 14037 10.1038/s41598-023-41338-4 37640901
Lalam, N. et al. Pilot-scale testing of natural gas pipeline monitoring based on phase-OTDR and enhanced scatter optical fiber cable. Sci. Rep. 13, 14037 (2023).37640901 10.1038/s41598-023-41338-4
31. Westbrook PS Enhanced optical fiber for distributed acoustic sensing beyond the limits of Rayleigh backscattering iScience 2020 23 101137 10.1016/j.isci.2020.101137 32454447
Westbrook, P. S. et al. Enhanced optical fiber for distributed acoustic sensing beyond the limits of Rayleigh backscattering. iScience 23, 101137 (2020).32454447 10.1016/j.isci.2020.101137
32. Wang, F. et al. The Impact of Rayleigh Scattering in UWFBG Array-Based Φ-OTDR and Its Suppression Method. Sensors 23, (2023).
33. Kashyap M. M., Tambwekar A., Manohara K., Natarajan S. Noise2Noise-audio_denoising_without_clean_training_data) (2021). https://github.com/madhavmk/Noise2Noise-audio_denoising_without_clean_training_data (2021).
34. Wu H Real-time denoising of Brillouin optical time domain analyzer with high data fidelity using convolutional neural networks J. Lightw. Technol. 2019 37 2648 2653 10.1109/JLT.2018.2876909
Wu, H. et al. Real-time denoising of Brillouin optical time domain analyzer with high data fidelity using convolutional neural networks. J. Lightw. Technol. 37, 2648–2653 (2019).10.1109/JLT.2018.2876909
35. Farahani MA Castillo-Guerra E Colpitts BG Accurate estimation of Brillouin frequency shift in Brillouin optical time domain analysis sensors using cross correlation Opt. Lett. 2011 36 4275 4277 10.1364/OL.36.004275 22048389
Farahani, M. A., Castillo-Guerra, E. & Colpitts, B. G. Accurate estimation of Brillouin frequency shift in Brillouin optical time domain analysis sensors using cross correlation. Opt. Lett. 36, 4275–4277 (2011).22048389 10.1364/OL.36.004275
36. Zhang, C., Yang, Y. & Li, A. Application of Levenberg-Marquardt algorithm in the Brillouin spectrum fitting. In: Seventh International Symposium on Instrumentation and Control Technology). SPIE (2008).
