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Abstract
We have proposed and demonstrated a weak acoustic signal detection technology based on phase-sensitive optical time-domain reflectometry (Φ-OTDR). Non-contact acoustic signals transmitting through air gap between the sound source and the receiver are difficult to detect due to fast attenuation. In order to improve the detection ability of non-contact weak acoustic signals, we demonstrate that multi-mode fiber (MMF) is a better solution than single-mode fiber (SMF) benefiting from its larger core and higher Rayleigh backscattering (RBS) capture coefficient. The frequency signal-to-noise ratio (SNR) has been enhanced by 9.26 dB. Then, with the help of 3D printing technology, elastomers have been designed to further enhance the detection ability due to the high-sensitive response to acoustic signals. Compared with the previous reported “I” type elastomer, the location and frequency SNR enhancement caused by our new proposed “n” type elastomer are 8.39 dB and 11.02 dB in SMF based system. The values are further improved to 10.51 dB and 13.38 dB in MMF and “n” type elastomer integrated system. And a phase-pressure sensitivity of -94.62 dB re rad/µPa has been achieved at 2.5 kHz. This non-contact weak acoustic signal detection technique has great application potential in the quasi-distributed partial discharge (PD) detection of smart grid.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Weak acoustic detection is urgently needed in many fields, such as intrusion detection [1], oil exploration [2], pipeline security [3], marine optics [4] and partial discharge (PD) in smart grid [5–7]. At present, a number of points sensing methods have been reported for weak acoustic signal detection. In 2018, G. M. Ma, et al. proposed a PD detection system based on phase-shifted fiber Bragg gratings to overcome the low sensitivity of power transformer PD detection [6]. In 2019, Quan. Y, et al. proposed an auxiliary Mach-Zehnder interferometer method to compensate for the influences of laser-frequency-drift in order to raise the recognition sensitivity of weak acoustic signals [8]. However, such point sensing methods are limited in the application where the remote sensing or locating is needed [9].
On the other hand, distributed optical fiber sensing technology based on Φ-OTDR with merits of remote sensing and high sensitivity has been explored in locating and monitoring acoustic signals [10,11]. However, the SNR of acoustic signal with standard SMF is fundamentally limited due to the relatively weak RBS light [12] and inherent signal fading [13]. Recently, specialty fibers integrated Φ-OTDR have attracted much attention in distributed acoustic sensing (DAS) [14]. With the assist of the specialty fibers, either the SNR of detected signal can be enhanced or the fading problem can be mitigated. In general, these specialty fibers can be classified into two catalogs by the process of fiber fabrication: the fiber that is directly fabricated from the fiber drawing process, and the fiber that requires an additional post-processing. For the directly fabricated fiber, it mainly includes multi-core fiber (MCF) [15], few-mode fiber (FMF) [16], and MMF [17]. In 2020, Y. Mao, et al. achieved a simultaneous distributed acoustic and temperature sensing based on a MMF based distributed optical fiber sensing with a 12.98-dB SNR and temperature measurements of an ±1 °C accuracy. For the fibers with additional post-processing, it mainly consists of weak fiber Bragg grating (FBG) arrays [18], microstructure optical fibers (MOFs) [19,20], cladding softened fiber [21], UV irradiation fiber [22], etc. For example, D. Liu, et al. proposed the DAS system with MOF, in which the SNR of sensing signal is increased by enhancing the microstructure light scattering. In 2021, J. Yao et al. demonstrated a phase sensitivity improvement technology of DAS by softening sensing fiber cladding. Although the aforementioned specialty fibers can improve the performance of DAS, most of fibers might not be compatible with the standard fiber communication link. High cost and the sophisticated preparation process still have to be taken into consideration. Among the aforementioned specialty fibers, MMF has been more commonly used, especially for short-distance applications [23]. Furthermore, MMF owns its inherent merits, such as high nonlinear threshold, large core for power transmission and relative low cost. Driven by the above advantages, MMF is very attractive to practical application for improving the performance of DAS.
In addition to the specialty fibers, the integration of elastomer in Φ-OTDR for weak acoustic signal detection is of great interest. In 2016, T. Zhang et al. demonstrated a Michelson interferometer-based fiber sensor with a compact and high sensitivity cylindrical elastomer for detecting acoustic emission generated from the PD [24]. However, they are lack of distributed sensing. In 2020, Z. Chen et al. realized sensitivity enhancement of acoustic emission detection during breakdown discharge process by a “I” type elastomer based on 3D printing technology incorporating with a SMF [25]. Most of the above proposed elastomers are actually sensing when they are in contact with the sound source. However, when non-contact monitoring is required, space interval exists between the detection configuration and the sound source. The current elastomer sensing technology is still not sensitive enough for this non-contact DAS application. DAS system with higher acoustic-phase response and larger SNR is still in urgent need for weak acoustic signal detection.
In recent years, high sensitized optical cable has been designed and used for underwater acoustic wave detection [26]. Different from their work, we used the commercial telecommunication MMF for quasi-distributed fiber sensing. As shown in Fig. 1, such MMF with elastomer can enhance the sensitivity and SNR of weak acoustic signal detection, and has great potential in building up the integrated communication and sensing networks. In our experiment, we induce different-intensity acoustic signals between 0.04 Pa to 0.16 Pa. Among the testing experiments, MMF based system enhances 9.26 dB frequency SNR than SMF based system. The “n” type elastomer enhances the location and frequency SNR by 8.39 dB and 11.02 dB in a SMF based system. The values have been further improved to 10.51 dB and 13.38 dB in a MMF based system. Finally, the combine of the “n” type elastomer and the MMF makes the system achieve 19.85 dB location SNR and 32.25 dB frequency SNR. The new proposed sensing link greatly expands the weak acoustic signal detection ability of the Φ-OTDR system, which will benefit the application of quasi-distributed PD detection of smart grid.
Fig. 1. Illustration of sensing head for weak acoustic signal detection by the combined scheme of a MMF and an “n” type elastomer.
2. Principles and elastomer design
2.1 Rayleigh backscattering in MMF
In MMF-based DAS system, the RBS signal received into a certain mode is a superposition result of the signals scattered back to this mode from all transmission modes, which is called signal aliasing phenomenon [27]. The RBS received at the input end can be derived by the following Eq. (1), when an optical pulse with a width of Δτ, a power of ${P_0}$ is launched to the MMF. Without launching limitations, the RBS light will couple to all the allowed modes. Considering light power ${P_0}$ launched into forward-propagating mode m at the input end, the temporal power of the RBS power in mode n can be expressed as [28]
It can be deducted that the ${F_{mn}}$ is maximized when $m = n$ . Based on (1) and (2), the maximum RBS power in MMF can be received when the RBS mode is the same as mode injected to the input end. Since the fundamental mode (FM) is non-degenerate, it is barely coupled to the other modes and kept FM to the end of MMF. Single mode circulator has been proved to be an effect method for exciting the FM into the MMF and only pick the FM of the RBS signal at the receiving end. Therefore, the MMF-based DAS system can act similarly as the SMF-based system, which can be called quasi-single-mode state (QSM) operation [17].
If only take the scattering and attenuation effect in to account, the maximum sensing length ${L^{max}}$ of MMF can be expressed as (3), where ${\alpha _m}$ and ${\alpha _n}$ represent the attenuation constant of mode m and n, respectively [28]. As a result, the maximum sensing length of MMF is 17 km with an attenuation of ${\alpha _m}$ = 0.058 /km (0.25 dB/km) when $m = n$. In addition, for a graded-index MMF based DAS system in which dispersion induced influence on space resolution can be alleviated, the maximum sensing length is mainly determined by the signal frequency response bandwidth [32].
However, high order modes still exist due to bending or other disturbance. If we take the FM as the main mode of the injection light by a SMF circulator launching to MMF, $m = 1$ and ${E_m}$ can be approximately fixed, but ${E_n}$ may suffer from multimode interference. Though FM can be picked by spatial filtering, the optical field indeed composes of a summation of many modes [29]
2.2 Elastomer design
In order to further enhance the SNR of weak acoustic signal detection, the acoustic sensitive elastomer is explored in this work. According to the Hooke’s law, the relationship of the stress and strain of our proposed “n” type elastomer can be expressed as (4) and (5) [20]:
Here we propose an “n” type elastomer as shown in Fig. 2(a), which is different from previous reported “I” type elastomer (as Refs. [25]) as shown in Fig. 2(b). In the simulation, an acoustic-structure coupling model has been built up. Specifically, the sound source is arranged at 10 mm above the top face of the elastomer. The meshing size is 1/6 of the acoustic wavelength. A reference section is selected in the center of the elastomer side wall to quantitatively calibrate the sensitivity. Given by (6), (7) and (8), we firstly investigate the relationship between material characteristics ($Y$, $\mu $) and S with fixed structural parameters. Figure 2(c) shows that the sensitivity is inversely proportional to the Young’s Modulus, the lower the Young’s Modulus, the higher the sensitivity. But it does not exhibit a simple proportional or inversely proportional relationship between the sensitivity and Poisson’s ratio. And the sensitivity is slightly influenced by the Poisson’s ratio sensitivity. Limited by characteristics of the exist material, a flexible material which owns 500 MPa Young’s Modulus and 0.48 Poisson’s ratio has been chosen.
Fig. 2. The structure of the (a) “n” type elastomer and (b) “I” type elastomer. The sensitivity optimizing procedure in (c) material and (d) structural parameters of “n” type elastomer in simulation.
Then, we have explored neural network (NN) algorithms for fast multi-parameters (T, R, H) structural optimization. Firstly, the outliers that have existed physically but do not exist logically should be removed. Here, based on the density method, the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) clustering algorithm is used to define objects in low density regions as outliers [34]. Here, the density around an object is defined as the number of objects within a specified distance d. When d = 5 pm/Pa, we set the lower limit of the value density to 8, that is, within the range interval of 5 pm/Pa, data points less than 8 will be regarded as outlier, and they will be deleted directly. After sorting, data with sensitivity results greater than 135 pm/Pa will be deleted. Secondly, in the multi-layer perceptron (MLP) algorithm, 3543 sets of data (70%, stratified sampling) are used for training the model, and 1519 sets of data (30%, stratified sampling) are used for evaluating the results. The prediction model uses the perceptron neural network, in which each layer consists of the perceptron layer and Rectified Linear Unit (ReLU) layer. There are four layers in total. The numbers of middle layers are 256, 512 and 32, respectively. The model takes the T, R, H as inputs, S as labels. The loss function uses Mean Absolute Error (MAE), and the optimizer uses Adaptive Moment Estimation (Adam) for training. At the same time, cross validation and hyperparameter regulation training are carried out. After training is completed, the reconstruction parameters are stored in the network, and fast elastomer-sensitivity prediction can be achieved by simply inputting the structural parameters. It is worth mentioning that the MLP algorithm saves 99.76% calculation time from 4247 minutes to 10 minutes (including training time). Figure 2(d) shows the optimization result. In order to balance the manufacturing process and sensitivity performance, the truely optimized “n” type elastomer is shown in Fig. 2(a), with T of 3.0 mm, H of 3.0 mm and R of 15.0 mm.
Taking the occurring low frequency band inside the partial discharge into consideration, the sensitivity between 2.0 kHz to 2.9 kHz has been discussed. In particular, our proposed “n” type elastomer obtains 6.94 dB sensitivity gain at 2.5 kHz as shown in Fig. 3. It is worth mentioning that the resonant frequency of the elastomer is out of the simulation and experiment bandwidth.
Fig. 3. The sensitivity comparison of the optimized “n” type elastomer and the corresponding “I” type elastomer. The color of the insert figures represents the radial displacement field distribution.
3. Experimental setup
Figure 4 shows the experimental setup of Φ-OTDR system for weak acoustic signal detection. Highly coherent light is produced by a narrow linewidth continuous-wave laser (NLL) source at 1550 nm with an isolator for protection. An optical fiber coupler with power ratio of 99:1 is used to separate the light into two parts. The part with 1% ratio is the reference path. The path with 99% light is launched to an acousto-optic modulator (AOM) which is driven by an arbitrary waveform generator (AWG). Continuous light is modulated into optical pulse with a 200-MHz frequency shift by the AOM. The output pulse has pulse width of 60 ns and a repetition rate of 25 kHz. An erbium-doped fiber amplifier (EDFA) with an amplifier spontaneous emission (ASE) noise filter is used to power boost. An optical fiber circulator is used to collect RBS signal, followed by a pre-EDFA. Mixing with the 1% reference light through a 50:50 optical fiber coupler, RBS light is converted to electrical signal by a balanced photo-detector (BPD) with a detection bandwidth of 350 MHz. Differential frequency component is recorded by a high-speed data acquisition card (DAQ) with 1 GHz for data analysis. A buzzer is induced to produce different acoustic signals.
Fig. 4. Experimental setup of the Φ-OTDR system. AOM: acousto-optic modulator; EDFA: erbium doped fiber amplifier; SMF: single mode fiber; MMF: multi-mode fiber; BPD: balanced photo-detector; DAQ: data acquisition card; PC: personal computer. Insert figure (a) is “I” type elastomer and (b) is “n” type elastomer.
In the experiment, a sound level meter is used to calibrate the acoustic signal intensity of the buzzer as the variable. The corresponding sound pressure level (SPL) changes from 0.04 Pa to 0.16 Pa. In order to prove that MMF has higher SNR for weak acoustic signal detection than SMF, the performance of Φ-OTDR system with 2 spans of 1.1-km-long SMF and 2 spans of 1.2-km-long MMF without elastomers are compared in the experiment. Furthermore, both “I” type and “n” type elastomers have been inserted to the middle of the SMF and MMF fiber link, to compare and evaluate the SNR enhancement of the Φ-OTDR system.
4. Results and analysis
Based on a heterodyne coherent Φ-OTDR system, we firstly applied a 1.1-km-long SMF as the fiber under test (FUT). About 1.98 m of the fiber end has been wrapped in 7 circles. Different intervals away from the buzzer are used to simulate the contact and non-contact conditions, as shown in the insert figure of Fig. 5 (a). The buzzer emits 0.16-Pa acoustic signal at 5 kHz. Then a contact signal with the fiber circles bonding close to the buzzer and a non-contact signal with 10-mm space away from the fiber circles have been applied. The non-contact signal is extremely weak and hard to detect. Here, demodulation of the amplitude is used for location [35,36]. In details, the location SNR of the non-contact signal is 4.89 dB lower than the contact one, as shown in Fig. 5(a). And the frequency SNR of the non-contact signal is 8.12 dB lower than the contact one, as shown in Fig. 5(b). In order to obtain more accurate phase recovery, higher detection ability is needed.
Fig. 5. (a) Location and (b) frequency demodulation of contact and non-contact acoustic signals in same condition. Insert figure in (a) shows the contact and non-contact conditions.
4.1 SNR enhancement of weak acoustic signal by MMF based Φ-OTDR system
Based on (1) and (2), the MMF is expected to have better SNR compared with SMF [30,31]. Here the comparison experiment for weak acoustic signal detection is developed. Both of the SMF and the MMF are bent in 9-cm diameters for 7 turns as the disturbance area. As shown in Fig. 6(a), when a 0.07-Pa, 2.5 kHz acoustic signal is emitted by a buzzer, the time domain acoustic signal demodulated by MMF based system shows better phase-recovery compared to SMF based system. Frequency domain acoustic signal obtained by Fourier transform achieves 9.90-dB higher SNR in MMF based system, as shown in the insert figure in Fig. 6(a). In order to evaluate different-intensity acoustic detection performance, we do the repeat experiments. The SNR of both systems under 0.04-Pa to 0.16-Pa acoustic signals detection has been investigated in Fig. 6(b). Each of the discrete point shows the mean value of 5 times experiments, and the lengths of the vertical lines shows the standard deviations. In the whole SPL range under test, MMF based system achieves higher frequency SNR. In the area SPL lower than 0.12 Pa, the SMF based system can hardly demodulate the acoustic frequency. Obviously, the MMF based system obtains wider detection range. MMF based system achieves the highest frequency SNR enhancement of 9.26 dB when the SPL is 0.07 Pa.
Fig. 6. (a) Time domain of a 0.07-Pa, 2.5 kHz signal by SMF and MMF based Φ-OTDR system without elastomer. Insert figure is frequency domain signal. (b)Frequency SNR of SMF and MMF based Φ-OTDR system with error bar.
4.2 Acoustic frequency response sensitivity enhancement based on “n” type elastomer
The comparison experiment of the previous reported “I” type elastomer and our new proposed “n” type elastomer begins with the SMF-combined system. The same setup of disturbance has been induced. Besides, the middle of the 2 spans of 1.1-km-long SMF has been wound 6 turns for each of the elastomer. As shown in Fig. 7(a), maintaining the repetition frequency, the pulse width, and the input laser power, the “I” type elastomer integrated Φ-OTDR system is hard to locate the disturbance based on amplitude demodulation, while “n” type elastomer integrated Φ-OTDR system locates the position clearly. According to Fig. 7(b), we demonstrate the frequency-demodulation ability by analyzing the frequency SNR with error bar. With the help of the elastomers, both fiber links successfully demodulate the frequency of the acoustic signal. Among them, the “n” type elastomer helps the SMF based Φ-OTDR system to achieve 8.39 dB for location SNR and 11.02 dB for frequency SNR enhancement in maximum when the SPL is 0.16 Pa, specifically.
Fig. 7. (a) Location and (b) frequency SNR of SMF integrated with “I” and “n” type elastomers based Φ-OTDR system with error bar.
4.3 Frequency response sensitivity enhancement scheme based on MMF combined with “n” type elastomer
We further combine the MMF and the “n” type elastomer to enhance the SNR. The experimental setup is the same as the comparison experiment in section B. MMF combined with both of the elastomers locates the disturbance area and demodulates the acoustic frequency clearly as shown in Figs. 8(a) and (b). The “n” type elastomer improves the location SNR and the frequency SNR of the MMF based Φ-OTDR system for 10.51 dB and 13.38 dB in maximum when the SPL is 0.10 Pa. After taking a polynomial fitting to the whole range of the existed data between 0.04 Pa to 0.16 Pa, the lower limit intensity of the proposed system can reach 0.01 Pa.
Fig. 8. (a) Location and (b) frequency SNR of MMF integrated with “I” and “n” type elastomers based Φ-OTDR system with error bar.
Phase change can be calculated by differential phase of 40 consecutive pulses [37]. As shown in Fig. 9(a), MMF combined with “n” type elastomer system recovers the acoustic wave most precisely. Compared with the result shown in Fig. 6(a), the new proposed system proposed in this paper achieves significant improvement. It is worth mentioning that the MMF achieves phase recovery enhancement under serious bending conditions due to its higher sensitive refractive index change with bending radius than SMF. The acoustic pressure sensitivity is key point for phase enhancement. As illustrated in Fig. 9(b), a phase-pressure sensitivity of 18.57 rad/Pa (i.e., -94.62 dB re rad/µPa) has been achieved at 2.5 kHz by linear fitting. Besides, the integration of the “n” type elastomer can also be flexibly applied along the fiber link according to the demand of locally sensitivity enhancement. We confirm the feasibility of a MMF and an “n” type elastomer integrated Φ-OTDR system and illustrate a more stable SNR enhancement performance.
Fig. 9. (a) Time domain 0.16-Pa, 2.5 kHz acoustic signal detected by SMF and MMF integrated with “I” and “n” type elastomers based Φ-OTDR system. (b) Sensitivity of MMF integrated with “I” and “n” type elastomers based Φ-OTDR system.
5. Conclusion
In order to overcome the difficulty of weak non-contact acoustic signals detection in DAS, a MMF integrated with an optimized “n” type elastomer based Φ-OTDR system has been proposed. On one hand, the power intensity of the RBS light along the whole fiber has been improved by inducing a MMF as the FUT. Firstly, the frequency SNR obtained 9.26-dB gain in MMF based system compared with SMF based system. Secondly, compared with the previous proposed “I” type elastomer, the new proposed “n” type elastomer obtains 8.39 dB and 11.02 dB on location and frequency SNR enhancement specifically by SMF based Φ-OTDR system. Then, these two values improve to be 10.51 dB and 13.38 dB by MMF and elastomers based Φ-OTDR system. Finally, a phase-pressure sensitivity of -94.62 dB re rad/µPa has been achieved at 2.5 kHz. MMF expands the range of acoustic detection intensity to a wider range. The “n” type elastomer further enhances the acoustic frequency response and phase recover ability. The adequate analysis proved that the proposed system will not perform competently in sensitivity enhancement of DAS without any of them. We indicate its great potential for weak acoustic signal detection. With a view of the present and future, highly sensitive quasi-distributed weak acoustic signal detection will show practical value in many applications.
Funding
National Natural Science Foundation of China (62220106006); Natural Science Foundation of Guangdong Province (No. 2022A1515011434); Stable Support Program for Higher Education Institutions from Shenzhen Science, Technology & Innovation Commission (20200925162216001); Basic and Applied Basic Research Foundation of Guangdong Province (2021B1515120013); Open Fund State Key Laboratory of Information Photonics and Optical Communications Beijing University of Posts and Telecommunications (No.IPOC2020A002); Open Projects Foundation of State Key Laboratory of Optical Fiber and Cable Manufacture Technology (No. SKLD2105); General Program of Shenzhen Science, Technology & Innovation Commission (JCYJ20220530113811026); Shenzhen Research Foundation (JCYJ20220818101206015, JSGG20220831103402004).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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