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Abstract
In this study, an optimized localization algorithm is proposed for a dual-Sagnac structure-based fiber optic distributed vibration sensing (DVS) system. Different from the previous localization algorithms, the spectrum peak ratio of the interference signals in the frequency domain is applied for localization calculation, and the localization accuracy is effectively improved for the interference signal with low Signal-Noise-Ratio (SNR). Besides, the proposed optimized algorithm can solve the difficult problem of multi-point vibration localization by employing a continuous low-coherence light source, which largely reduces the system cost. Meanwhile, multi-parameter including the frequency and amplitude of the vibration signal can be retrieved simultaneously except for the vibration position, which is not available for the traditional localization algorithm of the interferometric DVS system. Experimental results verify that the system with the proposed optimized algorithm can realize high-accuracy localization of single-point vibration, multi-point with single-frequency vibration, multi-point with multi-frequency vibration. The corresponding maximum localization errors are only 0.18%, 0.22%, and 0.36% respectively.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fiber optic distributed vibration sensing (DVS) system has been widely used in many applications, such as perimeter intrusion detection [1], aircraft monitoring [2], oil and gas pipeline leaking monitoring [3], etc. Based on the DVS techniques, the external vibrations along the fiber link at any position can be located. The main techniques of DVS fall into two categories [4], one is based on optical backscattering [5–10], and the other is based on optical fiber interferometers [11–17]. When compared with the latter, the optical backscattering technique, such as phase-sensitive OTDR, has been intensively investigated for various DVS applications [7,8]. However, the optical backscattering technique also has several drawbacks. Firstly, for long-distance application, extremely weak scattering light easily generates an insufficient signal-to-noise ratio and further greatly affects the system performance. Secondly, to amplify the weak scattering signal, the optical amplifier and the high-power pulse light source are usually used. This inevitably increases the system cost [18]. Finally, the detectable frequency range of the system is limited. It needs high-frequency modulation and complex data processing to realize the wide-frequency vibration measurement [19].
In contrast, the optical fiber interferometer-based technique usually uses a continuous light source. It has several desirable advantages including low cost, ultra-long sensing, and wide detectable frequency range. Until now, a variety of optical fiber interferometers-based configurations have been proposed for DVS applications, such as single Sagnac interferometer [11], dual Sagnac interferometers [12,17], dual Mach-Zehnder interferometers [13], dual Michelson interferometers [14], merged Sagnac/Michelson interferometers [15], and Sagnac/Mach-Zehnder interferometers [16]. Although many configurations have been proposed, the interference signal in the time domain always keeps continuous, and the difficult problem about how to effectively realize the simultaneous multi-point detection is still quite a challenge [4]. Besides, the traditional localization algorithm can only obtain the position information, while the frequency and amplitude information of vibration signals are hard to be directly obtained with high accuracy. Overcoming these challenges is the objective of the current study.
In this paper, we proposed an optimized localization algorithm for a dual-Sagnac structure-based fiber optic DVS system. By calculating the spectrum peak ratio of the interference signals in the frequency domain, we can effectively improve the localization accuracy. Besides, it solves the difficult problem of simultaneous multi-point localization based on a continuous low-coherence light source, which largely reduces the system cost. Meanwhile, still based on the proposed localization algorithm, multi-parameter such as frequency, and amplitude of the vibration signal can be also retrieved simultaneously except for the vibration position. The experimental tests of single-point vibration, multi-point with single-frequency vibration, multi-point with multi-frequency vibration are conducted respectively to thoroughly evaluate the localization algorithm reliability.
2. Sensing configuration and principle
2.1 Sensing configuration
The distributed sensing system based on the dual-Sagnac structure is shown in Fig. 1. It consists of a broadband source, a polarization beam splitter (PBS), two circulators, two symmetrical 3 × 3 couplers, four polarization beam splitting/combiners (PBS/C1- PBS/C4), and six photo-detectors. A continuous low-coherence broadband source is used as the light source to launch the non-polarized light beam. It is divided into two orthogonal polarized light beams which are aligned to the slow axis (that is the $H{E_{11}}^x$ mode) of the fiber after passing through the PBS. Both polarized light beams form two different Sagnac interferometers independently, and they share the common fiber loop which includes the sensing fiber, conducting fiber, and PBS/C1- PBS/C4. The first Sagnac interferometer consists of the circulator 1, 3×3 coupler C1, common fiber loop, and detectors PD1, PD2, PD3. Correspondingly, the second Sagnac interferometer consists of the circulator 2, 3×3 coupler C2, common fiber loop, and detectors PD4, PD5, PD6. The entire optical path employs the polarization-maintaining (PM) fiber.
Fig. 1. Experimental setup of the fiber optic DVS system based on Dual-Sagnac Interferometer. Inset represents the working principle of the PBS/C.
2.2 Localization algorithm principle based on spectrum peak ratio
Before introducing the optimized algorithm based on spectrum peak ratio, the traditional localization algorithm is described briefly for comparison. For the presented configuration, the sensing fiber and the conducting fiber have the same length L, and the pigtail fiber length is neglected to simplify the following analyses. If the distance between the external vibration and the center of the first Signac loop is defined as ‘Z’, then, the distance between the vibration point and the center of the second Sagnac loop is determined to be ‘L-Z’. According to the previous theory [20,21], the phase differences of the two Sagnac interferometers can be written as $\mathrm{\Delta }{\varphi _1} = \frac{{2Z}}{v}\frac{{d\emptyset }}{{dt}}$ and $\mathrm{\Delta }{\varphi _2} = \frac{{2({L - Z} )}}{v}\frac{{d\emptyset }}{{dt}}$ respectively, where v is the light velocity in the fiber, and $\frac{{d\emptyset }}{{dt}}$ is the time-dependent phase induced by vibration. Besides, 3×3 fiber coupler demodulation algorithm has been widely applied for phase demodulation [22]. The specific techniques can be divided as differential-cross-multiplication and digital arctangent. In this study, the 3×3 coupler demodulation method based on the differential-cross-multiplication demodulator is introduced to recover the phase difference. Then, the vibration localization is determined to be:
where $x(Z)$ is the ratio coefficient of two phase-difference signals, and it can be expressed as:For the traditional algorithm [17,20], $\mathrm{\Delta }{\varphi _1}$ and $\mathrm{\Delta }{\varphi _2}$ are divided directly point-to-point in the time domain to obtain the ratio coefficient x(Z). However, this traditional algorithm cannot provide high-accuracy localization due to the time-dependent phase rate $\frac{{d\emptyset }}{{dt}}$. Particularly, if the phase difference signal has a low SNR due to the weak vibration signal or strong noises induced by PD and the environment, the localization error is gradually obvious.
To solve this problem, an optimized localization algorithm based on spectrum peak ratio is proposed. According to the principle of the vibration spectrum analysis, any complex vibration signal can be decomposed into a linear sum of sinusoidal components with different frequencies. If we assume that a multi-frequency vibration is applied on the sensing fiber with a distance ‘Z’, then, the time-dependent phase is defined as $\emptyset (\textrm{t} )= \mathop \sum \nolimits_{i = 1}^m {\emptyset _i}\textrm{sin}({{w_i}t + {\alpha_i}} )$, where ${\emptyset _i}$, ${w_i}$, and ${\alpha _i}$ are the amplitude, frequency, and initial phase of each sinusoidal component. m is the total number of components. In this study, the initial phase ${\alpha _i}$ is neglected. Then the phase difference of two Sagnac interferometers can be expressed as:
It can be observed from Eqs. (3a) and (3b) that they have similar expressions in the frequency domain. That is to say, if applying Fast Fourier Transform (FFT) on $\mathrm{\Delta }{\varphi _1}$ and $\mathrm{\Delta }{\varphi _2}$, their peak values in the frequency domain c1i, c2i correspond to the amplitudes of the two phase difference signals, which can be written as:
We can see from Eq. (4) that both of the two expressions have the same parameters except for the different position information (Z, L-Z). Thus, we can calculate the peak ratio in the frequency domain to obtain the ratio coefficient x(Z), which can be expressed as:
Then substituting Eq. (5) into Eq. (1), the localization of the vibration can be determined. It should be noticed that, if the vibration is a single-frequency signal, the spectrum peak ratio x(Z) has only one value; if the vibration is a multi-frequency signal, we can get a group of ratios x = [x1, x2, x3…xm], and obviously all elements in this group have equal values, i.e., x1= x2…= xm. In addition, a similar conclusion can be drawn about the multi-point localization. If different positions Z1, Z2, …, ZK are disturbed simultaneously by the different vibration signals ${\emptyset _1}(t ),\; {\emptyset _2}(t ),\; \ldots {\emptyset _k}(t )$ respectively, we can get K groups of peak ratios x1=[x11,…], x2=[x21,…],…, xk=[xk1,…] based on the above method, and the system can also locate these vibrations separately. The block diagram of the proposed algorithm is shown in Fig. 2.
3. Experimental setup
The diagram of the DVS system based on the dual-Sagnac structure is shown in Fig. 3. An amplified spontaneous emission light source (ASE, AQ4315A, Yokogawa) with a wavelength range of 1530nm∼1605nm is selected as the light source. Both the sensing fiber and the conducting fiber use PM fiber with an equal length of 634 m. Four piezoelectric transducers (PZTs) are wrapped with 9 m, 8 m, 8 m, and 11 m PM fibers respectively, and they are placed along with the sensing fiber separately. During the experiments, the distances between four PZTs and the center of the first Saganc loop are fixed as 89 m, 296 m, 334 m, and 444 m respectively. It should be explained that, when the four PZTs are located along the sensing fiber, the wrapped fiber lengths are also considered. Hence the wrapped fiber lengths do not correspond to the spatial resolution of the presented DVS system. The PZTs are driven by arbitrary waveform generators (AWGs, FY6800, Feiyi Technology Co., Ltd) with tunable frequency to simulate the external vibrations. Six InGaAs diode detectors are connected with the data acquisition card (sampling rate: 32.8Kbps) for A/D conversion and data collection. Finally, the data are processed on the computer. Considering the Nyquist sampling theory and frequency multiplication effect due to 3×3 fiber coupler demodulation algorithm, the maximum detectable frequency can achieve one-quarter of the sampling frequency, i.e. 8.2 kHz. This value can be still improved by increasing the sampling rate based on the actual requirements.
4. Experimental results and analyses
4.1 Single-point localization results
Figure 4 shows the effect comparison of the different algorithms when a 20Hz sinusoidal signal with peak-to-peak voltage (Vpp) of 20V is applied on PZT4 at 444m. It can be seen from Fig. 4(a) that the obvious noises are mixed into the phase difference signals $\Delta {\varphi _1}$ and $\Delta {\varphi _2}$. When the two phase difference signals are directly divided point-to-point in the time domain, the result of the ratio coefficient is shown in Fig. 4(b). From the zoom-in view as shown in Fig. 4(c), we can see that if the phase difference signal has a low SNR at a low-frequency of 20 Hz, the ratio coefficients become extremely unstable and difficult for localization. Based on the traditional time-domain localization algorithm, the vibration position is determined to be 156.8 m, which is very far from the actual position. Hence we conclude that the traditional algorithm becomes invalid under this condition. Figure 4(d) shows the phase difference signals after FFT. When compared with the traditional algorithm that is seriously affected by the SNR, the presented algorithm shows better stability and accuracy. When the calculation of the ratio coefficient is converted into the frequency domain, two peaks can be easily located at the modulation frequency with the magnitudes c1 = 0.002936 and c2 = 0.001268, respectively. Then bringing them into Eq. (5) and Eq. (1), the peak ratio x=2.315457 and the corresponding vibration position z=442.8m can be obtained, and the relative error is only 1.2/634 = 0.18%. When compared with the result obtained based on the traditional algorithm, the localization accuracy is obviously improved.
Fig. 4. (a) Demodulated phase difference signals when PZT4 is modulated by a sinusoidal wave with 20Hz frequency. (b) Ratio graph of the two phase difference signals divided point-to-point. (c) Zoom-in view of the ratio graph. (d) Phase difference signals in the frequency domain.
4.2 Multi-point localization results
To verify the simultaneous multipoint localization, four PZTs at 89m, 296m, 334m, and 444m are applied sinusoidal modulation with the amplitude of 20 Vpp and frequencies of 450Hz, 340Hz, 230Hz, and 120Hz, respectively. From Fig. 5(a), it can be seen that, when multiple vibrations occur simultaneously along with the fiber link, the phase difference signals in the time-domain are continuous, and therefore the traditional localization algorithm has failed to distinguish the positions of four PZTs. However, when the phase difference signals are transformed into the frequency domain, as shown in Fig. 5(b), there are four distinct pairs of spectrum peaks at the four modulation frequencies, respectively, which means that four different ratio coefficients can be obtained. By using the “spectrum peak ratio” algorithm, the localization results are 89.4m, 297.4m, 333.9m, and 445.4m, respectively, and the corresponding relative errors are only 0.06%, 0.22%, 0.015%, and 0.22%, which are insignificant. Besides, it should be explained that, in the extreme case, if the signal frequencies of different vibration positions are exactly the same, the proposed localization algorithm fails. It should combine with the other optimized algorithm such as wavelet transform to distinguish the same frequency component at different vibration positions. These will lead to further investigations in the future.
Fig. 5. Demodulated phase difference signals when sinusoidal modulation are applied simultaneously on four PZTs (a) Diagram of the phase difference signals in the time-domain and (b) Diagram of the phase difference signals in the frequency-domain. Inset represents the details of spectrum peak.
In the following experiments, to confirm the simultaneous multipoint localization performance of multi-frequency signal, the modulation waveform changes from sine wave to triangular wave, and the other parameters remain the same. The corresponding result is shown in Fig. 6. When compared with Fig. 5, the phase difference signal shows multiple peaks in the frequency domain, and we can find 16 pairs of peaks at different frequency positions. The peak values, the ratios, and the corresponding localization results of these different frequencies are listed in Table 1. According to the results of peak ratios, 16 pairs of peaks can be divided into 4 groups, which correspond to the four vibration positions. Moreover, the frequency sequences of each group are 1, 3, 5, and 7 times the fundamental modulation frequency, which are consistent with the harmonic frequency component of the triangle wave, and their peak ratios correspond to the same position information. After the average calculation of the four harmonic frequency components in each group, the localization results are determined to be 445.5m, 336.3m, 296.1m, and 90.8m, with relative errors of 0.24%, 0.36%, 0.016%, 0.28% respectively. Besides, although the localization errors vary with the different detection frequencies, there is no fixed relationship between these two parameters. In this case, the localization error depends more on the demodulation capability of the 3×3 coupler algorithm and the noise level of the system instead of detection frequency.
Fig. 6. Demodulated phase difference signals in the frequency domain when four PZTs are modulated by triangular waves with different frequencies.
Table 1. Experimental positioning results of four-point vibration with triangular modulation.
4.3 Measurement of multi-parameter information of vibration events
From the above experiments, we can see that both localization and frequency information of the vibration signal can be retrieved. Next, we still use the “spectrum peak ratio” algorithm to obtain the amplitude information of the vibration signal. Here, we convert Eq. (4) into the following form:
We can see from Eq. (6) that if the position result ‘Z’ and frequency ‘w’ of the vibration signal are known, then, the amplitude of phase ${\phi _i}$ which is induced by the external vibration can be also calculated. Next, we conduct a test to evaluate the relationship between the amplitude of phase ${\phi _i}$ and the voltage applying to the PZT. During the test, a 200Hz sinusoidal voltage with amplitude varying from 5 Vpp to 20 Vpp is applied to the four PZTs, and the corresponding amplitude of the phase at each point is calculated according to Eq. (6). The result is shown in Fig. 7. We can see that for each PZTs, the amplitude of phase shows good linearity with the voltage, and slope coefficients of the linear fitting are 0.56 rad/V, 0.53 rad/V, 0.54 rad/V, and 0.73 rad/V, approximately agree with the ratio of fiber length wrapped on the PZTs (9:8:8:11). Hence, the voltage applying to PZTs can be demodulated based on the calculated ${\phi _i}$ and the slope coefficient.
Finally, we use the experimental results in Fig. 5 as an example to demodulate the voltage applying to the PZTs during this test. Except for the positions and frequencies, the amplitudes of the phases ${\phi _i}$ are calculated based on Eq. (6). The result is shown in Fig. 8. The voltage amplitudes applying to each PZTs are determined to be 18.75 V, 18.90 V, 18.76 V, 18.71 V respectively according to the slope coefficients shown in Fig. 7. When compared with the actual voltage amplitude of 20 V, the averaged error is determined to be 6.1%. The error may be caused by the response instability under different testing frequencies. In conclusion, based on the optimized localization algorithm, simultaneous multi-point detection and multi-parameter (position, frequency, amplitude) retrieval of vibration signals can be realized.
Fig. 8. Multi-parameter 3D reconstruction of vibration signals (x-position, y-frequency, z-amplitude).
5. Conclusion
In summary, an optimized localization algorithm is demonstrated for a dual-Sagnac structure-based fiber optic DVS system. Different from the previous localization algorithms, it can realize high-accuracy localization by calculating the spectrum peak ratio of the interference signals in the frequency domain. Besides, the presented algorithm can also realize simultaneous multi-point localization by employing a continuous low-coherent light source, which largely reduces the system cost. The experimental results solidly support that the proposed algorithm can effectively locate the vibration signal, and the localization accuracy is significantly improved when compared with the traditional algorithm. The relative errors of the single-point localization, multi-point with single-frequency localization, multi-point with multi-frequency localization are 0.18%, 0.22%, 0.36%. Finally, except for the localization, the presented optimized algorithm can also retrieve the amplitude and frequency information of the vibration signal, showing unique advantages when compared with the other DVS techniques. The presented work provides useful experiences to deal with the multi-point localization and multi-parameter retrieval based on the continuous low-coherence light source, and it also lays a good foundation for the non-stationary signal localization.
Funding
National Natural Science Foundation of China (51808347, 61775149, 61805164, U1813207); Natural Science Foundation of SZU (2019109, 860-000002110218).
Disclosures
The authors declare no conflicts of interest.
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