A Brillouin frequency shift error estimation method

Abstract

The purpose of the present invention is to estimate the temperature / strain measurement error in fiber distributed sensing based on Brillouin scattering, and to provide a fast and accurate method for estimating the Brillouin frequency shift error. The technical solution of the present invention is: pulse light is incident into the optical fiber, the Brillouin spectrum of the scattered light is detected at the incident end of the optical fiber, the measured Brillouin spectrum is fitted using a fitting algorithm based on the pseudo-Voigt model, and the line width and the signal-to-noise ratio within a line width are calculated. The Brillouin frequency shift error #imgabs0# is estimated according to the following formula, where #imgabs1# is the Brillouin frequency shift error, R is the ratio of the sweep range to the line width, SNR is the signal-to-noise ratio within a line width, N is the number of sweep points, and Δv B is the line width. Since the relevant parameters can be easily obtained, the Brillouin frequency shift error can be conveniently, quickly and accurately calculated based on the above formula. At the same time, the influence of various factors on the error can be qualitatively analyzed according to the estimation formula, which provides a reference for selecting appropriate parameters in actual measurement to further reduce the error of Brillouin frequency shift.

Description

Technical Field

[0001] The invention relates to a method for estimating Brillouin frequency shift error in optical fiber distributed sensing, and belongs to the technical field of measurement. Background Art

[0002] In addition to the advantages of general optical fiber sensors such as anti-electromagnetic interference, corrosion resistance, and good electrical insulation, distributed optical fiber sensors also have unique advantages such as only one measurement is needed to obtain the distribution information of the measured field along the entire optical fiber. In addition, they have high measurement accuracy, accurate positioning, and a sensing distance of up to hundreds of kilometers. Therefore, the application field is very wide. Among them, the distributed sensing technology based on optical fiber Brillouin scattering has advantages in measurement accuracy, measurement range, and spatial resolution in temperature and strain measurement, and has therefore attracted widespread attention and research at home and abroad. Using this technology to conduct online monitoring of temperature and strain of oil and gas pipelines, large-scale water conservancy and hydropower engineering structures, and power cables, etc., can achieve rapid and accurate positioning of potential faults and fault points.

[0003] The research on temperature and strain sensing based on Brillouin scattering mainly focuses on the accuracy of temperature and strain measurement, simultaneous measurement of temperature and strain, improvement of spatial resolution, and improvement of temperature and strain measurement range. Measurement accuracy is the basis of all other measurement indicators. Temperature and strain will affect the Brillouin gain spectrum. By detecting the characteristic parameters of the Brillouin gain spectrum, it is hoped that temperature and strain can be measured. Since the Brillouin frequency shift has a linear relationship with temperature and strain and has the highest stability, the most commonly used of these characteristic parameters is the Brillouin frequency shift. Once the temperature and strain coefficients are determined, the accuracy of temperature and strain measurements will directly depend on the accuracy of the Brillouin frequency shift measurement. In order to estimate the Brillouin frequency shift error, a well-known Brillouin frequency shift minimum detectable error estimation formula has been proposed, as follows

[0004]

[0005] Among them, δv B is the minimum detectable error of the Brillouin frequency shift; Δv B is the line width; is the SNR signal-to-noise ratio.

[0006] This formula has been widely cited. As long as the signal-to-noise ratio and line width are known, the temperature and strain measurement errors in many real-life situations can be estimated. However, in real-life situations, the number of sweep points and sweep range may be different, which will also affect the Brillouin frequency shift error, and thus affect the accuracy of the Brillouin frequency shift error estimation. The original formula does not take these two points into account. As a result, there may be errors in the estimation results. In addition, no literature has publicly reported the process of obtaining this formula, which reduces its credibility. Summary of the invention

[0007] The purpose of the present invention is to effectively estimate the temperature / strain measurement error of optical fiber distributed sensing based on Brillouin scattering. Considering that temperature / strain is linearly related to Brillouin frequency shift, a fast and accurate Brillouin frequency shift error estimation method is proposed.

[0008] The technical solution of the present invention is: pulse light is incident into an optical fiber, light propagates in the optical fiber and Brillouin scattering occurs, and the Brillouin spectrum of the scattered light is detected at the incident end. A fitting algorithm based on a pseudo-Voigt model is used to fit the measured Brillouin spectrum, and the line width and the signal-to-noise ratio within a line width are calculated. A Brillouin frequency shift error estimation formula based on the signal-to-noise ratio, sweep range, number of sweep points and line width is proposed, and the Brillouin frequency shift error is estimated according to the signal-to-noise ratio within a line width of the Brillouin spectrum, the sweep range, number of sweep points and the line width combined with the formula.

[0009] The advantages of the present invention are:

[0010] (1) High accuracy

[0011] By analyzing the influence of each factor on the Brillouin frequency shift error, we obtain the influence law of each factor on the Brillouin frequency shift error, and then combine the actual situation to obtain the Brillouin frequency shift error estimation formula considering multiple factors. The results are tested by a large number of actual spectrum data under different circumstances, and the error is only about 10%.

[0012] (2) Easy to use and fast

[0013] The estimation formula of Brillouin frequency shift error is given directly. Once the line width, signal-to-noise ratio within a line width, sweep range and number of sweep points are known, the Brillouin frequency shift error can be directly estimated in a very short time. At the same time, line width, signal-to-noise ratio, sweep range and number of sweep points are very easy to obtain.

[0014] (3) Ability to qualitatively analyze the influence of various factors on errors

[0015] The estimation formula of Brillouin frequency shift error can be used to qualitatively analyze the influence of various factors on the error, which can be used to select appropriate parameters to further reduce the Brillouin frequency shift error. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is the relationship between signal-to-noise ratio and Brillouin frequency shift error and the fitting situation;

[0017] Figure 2 The relationship and fitting between the sweep frequency range and the Brillouin frequency shift error;

[0018] Figure 3 is the relationship between line width and Brillouin frequency shift error and the fitting situation;

[0019] Figure 4The relationship between the number of frequency sweep points and the Brillouin frequency shift error and the fitting situation;

[0020] Figure 5 The estimation results and fitting of the proposed Brillouin frequency shift error estimation formula are shown below;

[0021] Figure 6 is a flow chart of the present invention;

[0022] Figure 7 The average number of superpositions is 2 18 The relationship between the Brillouin frequency shift and the fiber position;

[0023] Figure 8 The Brillouin frequency shift error and the estimated result of the present invention under different pulse widths and superposition average times when the frequency sweep range is 10.52 to 10.92 GHz and the frequency sweep interval is 1 MHz;

[0024] Fig. 9 The Brillouin frequency shift error and the estimated result of the present invention under different pulse widths and superposition average times when the line width and the sweep interval are 2 MHz.

[0025] The present invention is further described below in conjunction with the accompanying drawings:

[0026] 1. Influence of related factors on Brillouin frequency shift error

[0027] 1.1 Signal-to-Noise Ratio

[0028] Without loss of generality, g0,v B and Δv B are the peak gain, Brillouin frequency shift and linewidth, which are set to 0.9, 10.8 GHz and 0.03 GHz respectively. The Lorentz model shown in equation (1) is used to generate the Brillouin spectrum.

[0029]

[0030] Where v is the frequency.

[0031] The sweep frequency range is v B -Δv B to v B +Δv B . A Gaussian white noise with a zero mean normal distribution is applied to the generated signal, and the signal-to-noise ratio varies from 0dB to 50dB. The signal-to-noise ratio is the result within one line width. The number of sweep points is 61. In order to reflect the influence of randomness, each combination signal of the above parameters is randomly generated 10,000 times. is the average of 10,000 Brillouin frequency shift error amplitudes. The relationship between the signal-to-noise ratio and the average Brillouin frequency shift error amplitude (hereinafter referred to as Brillouin frequency shift error) is as follows: Figure 1The figure also shows the fitting results of the signal-to-noise ratio and the Brillouin frequency shift error. The fitting formula is:

[0032]

[0033] The excessive noise at 0 dB causes the Brillouin frequency shift obtained by fitting the Lorentz model to exceed the frequency sweep range. The error is taken as a random value within the frequency sweep range, so the error law is different from other cases. The prediction error of formula (3) is slightly larger. In addition, the maximum values ​​of the fitting error and the relative fitting error are 1.66×10 -5 GHz and 2.21%. The average values ​​of the fitting error amplitude and relative error amplitude are 4.34×10 -6 GHz and 1.19%. It can be seen that the error decreases exponentially with the increase of signal-to-noise ratio (in dB).

[0034] 1.2 Frequency sweep range

[0035] Without loss of generality, the signal-to-noise ratio is set to 10dB. The frequency sweep range is from v B -RΔv B / 2 to v B +RΔv B / 2, R is the ratio of the sweep range to the line width, which varies from 0.3 to 10. Other parameters are consistent with Section 1.1. The relationship between the sweep range and the Brillouin frequency shift error is obtained as follows: Figure 2 The figure also shows the fitting results of Brillouin frequency shift error and R. The fitting formula is:

[0036]

[0037] Depend on Figure 2 It can be seen that if the number of sweep points remains unchanged, the Brillouin frequency shift calculation error first decreases and then increases as the sweep range increases from a smaller value. B to 2Δv B Within the range, the sweep frequency range has little effect on the Brillouin frequency shift error, and it can be approximately considered that the Brillouin frequency calculation error remains unchanged within this range. B To 10Δv B When the frequency shift error changes within the range, the ratio of the maximum frequency shift error to the minimum frequency shift error is 3. Therefore, the frequency sweep range needs to be given when the Brillouin frequency shift error estimation formula is given, otherwise the applicability of the formula will decrease or a large error will be generated.

[0038] 1.3 Line Width

[0039] Without loss of generality, the signal-to-noise ratio is set to 10 dB. The line width varies from 0.03 GHz to 0.15 GHz. Other parameters are consistent with Section 1.1. The relationship between the Brillouin frequency shift error and the line width is obtained as follows: Figure 3 The figure also shows the fitting results of Brillouin frequency shift error and line width. The fitting formula is:

[0040]

[0041] The maximum values ​​of fitting error and relative fitting error are 8.87×10 -6 GHz and 5.25×10 -1 % The mean values ​​of fitting error amplitude and relative error amplitude are 6.70×10 -6 GHz and 2.93×10 -1 %. It can be seen that the error increases linearly with the increase of line width.

[0042] 1.4 Sweep points

[0043] Without loss of generality, the signal-to-noise ratio is set to 10 dB. The number of sweep points varies from 11 to 12001. Other parameters are the same as in Section 1.1. The relationship is as Figure 4 The figure also shows the fitting results of Brillouin frequency shift error and the number of sweep points. The fitting formula is:

[0044]

[0045] Where N is the number of frequency sweep points.

[0046] The maximum values ​​of fitting error and relative fitting error are 4.21×10 -5 GHz and 4.64%. The average values ​​of the fitting error amplitude and relative error amplitude are 1.18×10 -5 That is to say, with the increase of the number of sweep points, the Brillouin frequency shift error decreases in a power function law, and the exponent is approximately -0.5.

[0047] 2 Brillouin frequency shift error estimation formula

[0048] According to formulas (4)-(6) and the mechanism analysis of the influence of relevant factors on the error, the Brillouin frequency shift error estimation formula can be expressed as

[0049]

[0050] The subsequent goal is to verify whether formula (7) can effectively estimate the Brillouin frequency shift error, and on this basis determine b, c, d, f, g and h in formula (7). To achieve this goal, we perform a sweep frequency range of v B -Δv B to v B +Δv B, the number of sweep points varies from 11 to 601, the signal-to-noise ratio varies from 2dB to 52dB, the linewidth varies from 0.03GHz to 0.15GHz, and the numerical value generates 35750000 sets of Brillouin gain spectrum signals. Then, according to the least squares fitting, the optimal b, c, d, f, g and h are 1.00, -1.52, 6.73×10 -1 , 2.88×10 -1 , -5.10×10 -1 and -1.18×10 -1 The calculated Brillouin frequency shift error, fitting result and fitting error are shown in Figure 5 As shown. Note that the Brillouin frequency shift errors have been sorted by size. The maximum values ​​of the fitting error and the fitting relative error are -8.07×10 -3 GHz and -24.30%. The average values ​​of the fitting error amplitude and the fitting relative error amplitude are 7.51×10 -5 GHz and 4.26%. The Brillouin frequency shift error estimation formula is obtained as

[0051]

[0052] Once the Brillouin frequency shift error is known, the measurement error of temperature or strain along the optical fiber can be estimated using equations (9) to (10):

[0053]

[0054]

[0055] Among them, E T For E ε are the errors of temperature and strain, C vT and C ε are the sensitivity coefficients of temperature and strain, respectively. DETAILED DESCRIPTION

[0056] See attached Figure 6 , the steps of applying the present invention are:

[0057] 1) Inject pulsed light into the optical fiber;

[0058] 2) Detect the Brillouin spectrum of scattered light at the fiber incident end;

[0059] 3) Fitting the measured Brillouin spectrum using a fitting algorithm based on the pseudo-Voigt model to calculate the line width and the signal-to-noise ratio within a line width;

[0060] 4) Estimate the Brillouin frequency shift error based on the linewidth of the Brillouin spectrum, the signal-to-noise ratio within one linewidth, the sweep range, and the number of sweep points.

[0061] The Brillouin spectrum of a 9 / 125μm single-mode optical fiber with a length of about 1km was measured using the AV6419 Brillouin optical time domain reflectometer based on Brillouin scattering (integrated with pulse signal generation, incident and spectrum detection modules), and the wavelength of the incident light was 1550nm. In order to measure more spectra and more fully verify the effectiveness of the present invention, the sampling resolution was selected to be 0.1m. The sweep range is 10.52-10.92GHz, and the sweep interval is 1MHz, that is, the number of sweep points is 401. The incident pulse widths are selected to be 10ns, 20ns, 50ns, 100ns and 200ns. The number of superposition averages is 2 10 , 2 12 , 2 14 , 2 16 and 2 18 .

[0062] After the experiment, 9650 sets of Brillouin spectra were collected for any combination of pulse width and superposition averaging number. 18 The Brillouin frequency shift obtained by the fitting algorithm based on the Lorentz model (abbreviated as LFA) is as follows: Figure 7 shown.

[0063] Although Figure 7 The Brillouin spectra under different pulse widths are the measurement results at the same temperature, but the strain caused by fiber winding causes the Brillouin frequency shift to gradually change along the line. The Brillouin frequency shift under different pulse widths shows a very similar law, which basically verifies the reliability of the calculation results. Formula (8) needs to involve the signal-to-noise ratio and line width when calculating the Brillouin frequency shift error. Considering that the Brillouin spectrum under different pulse widths approximately satisfies the Voigt model, and this model can be approximated by the pseudo-Voigt model. Therefore, an algorithm based on the pseudo-Voigt model (abbreviated as PVFA) is used to separate the Brillouin spectrum and noise and extract the Brillouin spectrum parameters. The signal-to-noise ratio and line width obtained by PVFA are shown in Table 1. Note that the signal-to-noise ratio and line width are the average values ​​of the corresponding results of all points on an optical fiber.

[0064] Table 1 Signal-to-noise ratio and line width of the measured Brillouin spectra at different pulse widths and superposition average times

[0065]

[0066] From Table 1, we can see that the average number of superpositions is 2 18When the signal has a line width range of about 40 dB, the signal-to-noise ratio is quite high. At the same time, the number of sweep points reaches 401. It can be considered that the fitting algorithm based on the Lorentz model has a sufficiently high accuracy. At the same time, although the measurement environment is approximately constant temperature, the average value of the Brillouin frequency shift on the entire optical fiber under different conditions still differs by several hundred kHz. This is caused by the ambient temperature rather than the noise. We corrected the average Brillouin frequency shift of the entire optical fiber under different conditions to the same value. In this way, the difference between the Brillouin frequency shift at the same pulse width and different superposition average times and the superposition average times of 218 can be considered to be mainly caused by noise. The Brillouin frequency shift error calculated by the above method under different pulse widths and superposition average times is plotted with the calculation result of formula (8) Figure 8 middle.

[0067] The prediction results based on the formula (8) proposed by the present invention in the above 160 cases are close to the calculation results of the actual spectrum using the fitting algorithm based on the Lorentz model. The average difference amplitude and the average relative difference amplitude of the two are only 0.02MHz and 13.55% respectively.

[0068] In order to analyze the results under different sweep ranges and sweep conditions, we intercepted a part of the spectrum signal from the Brillouin spectrum measured above for analysis. The sweep range of the intercepted signal was selected as 1 and 2 line widths, and the sweep interval was selected as 1, 2, 5, and 10 MHz. According to the similar method as before, the Brillouin frequency shift error calculated by LFA and the prediction results of the corresponding formula (8) were obtained under 160 different sweep ranges, sweep points, and signal-to-noise ratios. The average of the difference amplitude and the average of the relative difference amplitude were 0.03 MHz and 11.26%, respectively. The results when two typical line widths and a sweep interval of 2 MHz are selected are shown in Figure 1. Fig. 9 shown.

[0069] In order to further verify the accuracy of the method proposed in this invention, three measurement configurations were selected. The test fibers were a multimode 50 / 125μm fiber with a length of 1km, a single-mode 9 / 125μm fiber with a length of 1km, and a single-mode 9 / 125μm fiber with a length of 1km. The incident pulse width was 10ns, and the average number of superpositions was 2. 10 , 2 10 and 2 13The number of measurement groups were 223, 84 and 25 respectively, the sweep intervals were 2, 1 and 1 MHz respectively, and the sweep ranges were 10.06-10.46 GHz, 10.471-10.969 GHz and 10.471-10.969 GHz respectively. In order to measure more spectra and make the analysis results more reliable, the measurement resolution was deliberately selected to be higher than the spatial resolution, i.e. 0.5m, 0.05m and 0.05m. Other measurement parameters and measurement equipment are introduced in the first paragraph of this section. The Brillouin spectrum signal-to-noise ratio under different conditions is calculated using an algorithm based on the pseudo-Voigt model, and the signal-to-noise ratio SNR, sweep range coefficient R, number of sweep points N and linewidth Δv under different conditions are calculated. B As shown in Table 2, the calculated Brillouin frequency shift error and the estimation result of equation (8) are listed together in Table 2.

[0070] Table 2 Brillouin spectrum parameters and Brillouin frequency shift error and calculation results of formula (8)

[0071]

[0072] The average values ​​of the prediction error amplitude and the average values ​​of the relative error amplitude in the above three cases are 0.06 MHz and 9.99% respectively.

[0073] In summary, the Brillouin frequency shift error estimation formula proposed in the present invention has an estimation error of about 10% under different circumstances, and the accuracy is guaranteed.

Claims

1. A fast and accurate method for estimating Brillouin frequency shift errors, characterized in that: The steps of the present invention are: 1) Inject pulsed light into the optical fiber; 2) Detect the Brillouin spectrum of scattered light at the fiber incident end; 3) Fitting the measured Brillouin spectrum using a fitting algorithm based on the pseudo-Voigt model to calculate the line width and the signal-to-noise ratio within a line width; 4) According to the line width of the Brillouin spectrum, the signal-to-noise ratio within a line width, the sweep range and the number of sweep points, the formula Estimate the Brillouin frequency shift error, where is the Brillouin frequency shift error, R is the ratio of the sweep range to the line width, SNR is the signal-to-noise ratio within a line width, N is the number of sweep points and Δv B is the line width.

2. A fast and accurate Brillouin frequency shift error estimation method according to claim 1, characterized in that: The signal-to-noise ratio and line width used for calculation are the average values ​​of the corresponding results of all points on an optical fiber.

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