CN106788697A - A kind of noise-reduction method of phase sensitive OTDR signals - Google Patents
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Abstract
The present invention relates to a kind of noise-reduction method of phase sensitive OTDR signals.The present invention carries out multi collect and is superimposed to phase-sensitive OTDR sensing curves, it is process object with the two-dimensional matrix for constituting, its direct circulation is translated, the signal after cycle spinning is aligned using fast discrete curvelet transform carries out multiple dimensioned decomposition, to being reconstructed after the analysis of each scale component and threshold process, so as to suppress ambient noise, the effect of noise reduction is reached, the position of true disturbance is observed with this.The noise-reduction method of phase sensitive OTDR signals of the present invention, according to sensing curve threshold value size in itself, and uses different threshold values for each scale layer, can be very good random noise attenuation；Separation method between signal and noise is realized to greatest extent.
Description
Technical Field
The invention relates to a noise reduction method of a phase-sensitive OTDR signal, belonging to the technical field of optical fiber sensing detection.
Background
The safety of national defense, military, civil facilities and the lives and properties of people is a big matter related to the national civilians, so that China has great technical requirements in the fields of perimeter security, long-distance pipeline safety, large-scale structure health monitoring and the like. The phase-sensitive OTDR (optical time domain reflectometer) is used as an emerging representative of a distributed optical fiber sensing technology, and has the advantages of high sensitivity, light weight, small volume, no electromagnetic interference and capability of continuously detecting the spatial distribution and time variation information of parameters such as strain, vibration and the like on a transmission path. In recent years, the vibration measuring device has been widely used for vibration measurement in the fields of petroleum, traffic, structures and the like.
The phase-sensitive OTDR mainly detects the interference effect of the backward rayleigh scattered light, and needs to avoid the rapid change of the optical power. In fact, a slight disturbance from the outside causes a change in the optical phase and thus a drastic change in the detected optical power, resulting in the real signal being buried in noise. Meanwhile, random variation of detection results caused by polarization fading in the optical fiber can also be identified by the OTDR as a real signal. Therefore, identifying real signals, reducing background noise and improving detection performance are problems which need to be solved urgently by the application of the phase-sensitive OTDR.
Chinese patent CN102946271A discloses a method and an apparatus for reducing noise of an OTDR test curve, which perform discrete fourier transform of time domain transform frequency domain on a point sequence of the OTDR test curve through a time domain transform frequency domain module, perform low-pass filtering on the OTDR curve through a low-pass filtering module in the frequency domain, filter a high-frequency part in the curve to obtain a curve of a low-frequency part, then perform inverse discrete fourier transform on the filtered curve through a frequency domain inverse time domain module, and restore the curve to the OTDR curve in the time domain, so that noise in the OTDR test curve is reduced. The processing object of the method and the device disclosed in the patent document is a sensing curve, and the accidental occurrence exists in the actual process, so that false alarm or false alarm can be easily caused. Secondly, the method and the device have relatively simple processing on the sensing curve, and are easy to lose the effective part of the signal under the conditions of high frequency and low frequency to reduce the signal-to-noise ratio, even the signal can not be detected.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a noise reduction method of a phase-sensitive OTDR signal.
Description of terms:
backward rayleigh scattering: in the optical fiber, the random fluctuation of the fiber density causes local fluctuation of the refractive index, which causes scattering of light in various directions, the wavelength of the rayleigh scattered light is equal to the wavelength of the incident light without frequency change, and the backward rayleigh scattering refers to scattered light directed toward the incident end.
Fast discrete curvelet transform: the method belongs to the second generation curvelet transform theory, divides the frequency domain of a processing object by utilizing a concentric square area, and processes each sub-block respectively.
Summary of the invention:
the invention adopts the following technical scheme: the method comprises the steps of collecting and superposing phase-sensitive OTDR sensing curves for multiple times, taking a formed two-dimensional matrix as a processing object, carrying out positive cyclic translation on the two-dimensional matrix, carrying out multi-scale decomposition on signals subjected to positive cyclic translation by utilizing rapid discrete curvelet transformation, carrying out reconstruction after analyzing components of each scale and processing a threshold value, and thus inhibiting background noise, achieving the effect of noise reduction, and observing the position of real disturbance.
The technical scheme of the invention is as follows:
a noise reduction method of phase sensitive OTDR signal is used for removing noise of backward Rayleigh scattering light signal, comprising the following steps:
1) the process of 'forward cyclic translation, fast discrete curvelet transformation, threshold processing, fast discrete curvelet inverse transformation and inverse cyclic translation' is repeated, and the specific formula is as follows:
wherein,is a sensing curve matrix after noise reduction treatment, S is a sensing curve matrix, Fn,nFor positive cyclic translation operators, F-n,-nFor the inverse cyclic translation operator, I and I-1Respectively a fast dispersion curvelet transform operator and a fast dispersion curvelet inverse transform operator, T being a threshold reconstruction operator, n1And n2Respectively the amount of translation of the matrix of the sensing curve in the row and column directions, N1For the range of translation of the matrix of the sensing curve in the row direction, N2The translation range of the sensing curve matrix in the column direction is defined; and translating the sensing curve matrix in the row and column directions, moving one row and one column every time, wherein the maximum translation time is the number of rows multiplied by the number of columns, denoising and inversely translating the translated signals, and averaging after multiple times of cyclic translation, thereby effectively eliminating the ringing effect.
The translation of the sensing curve matrix in the row and column directions corresponds to the translation of the superposed sensing curves in the horizontal and vertical directions; because the curvelet transform does not have translation invariance, the phenomenon of pseudo Gibbs is generated at the adjacent position of the discontinuous point of the effective signal, and the phenomenon of pseudo Gibbs is effectively inhibited by positive cycle translation.
According to a preferred embodiment of the present invention, the method for reducing noise of a phase-sensitive OTDR signal includes the following steps:
1.1) collecting and superposing the phase-sensitive OTDR signal curve for 100-1000 times (collecting the superposition result of 1000 times in the example), and expressing the superposed sensing curve as an MXN sensing curve matrix;
1.2) carrying out positive cycle translation on the sensing curve matrix; translating the sensing curve matrix in the row and column directions, moving one row and one column every time, wherein the maximum translation time is the number of rows multiplied by the number of columns; positive cyclic translation is a data processing means well known to those skilled in the art.
1.3) carrying out scale decomposition on the sensing curve matrix subjected to positive cycle translation by adopting rapid discrete curvelet transformation to obtain a curvelet coefficient matrix C (j, l, k); wherein j is a decomposed scale parameter, l is a direction parameter corresponding to each scale parameter, and k is a position parameter corresponding to each direction parameter;
1.4) carrying out threshold processing on curvelet transform coefficients corresponding to different scale layers, and inhibiting background noise:
wherein, Cr(j, l, k) is a curvelet coefficient matrix after threshold processing, and T is a threshold coefficient; for the coefficient matrix C (j, l, k), different scale layers represent different frequency components, different threshold coefficients are adopted for processing each scale layer, signal components are reserved, and noise components are removed.
The curvelet transform can be divided into three scale layers: the search layer, the detect layer and the FINE layer, wherein the detect layer can be further subdivided into a plurality of layers, and the ceil (log2(min (M, N)) -3) is generally divided into the plurality of layers by default (M, N is the matrix size). The innermost layer, the coarse layer, mainly contains some low frequency information, and is not directional. The outermost fine layer is mainly some high frequency information. Each layer of the device also comprises a plurality of directions, and the directions are divided into more fine parts as the number of the layers is more.
1.5) carrying out fast discrete curvelet inverse transformation and inverse cyclic translation on the curvelet coefficient matrix after threshold processing; wherein, the fast discrete curvelet inverse transformation and the inverse cyclic translation are respectively the inverse processes of the fast discrete curvelet transformation and the forward cyclic translation.
1.6) repeating the steps 1.2) -1.5) (4 times in the example) to obtain a sensing curve matrix after noise reduction treatment. The number of times of repeating steps 1.2) -1.4) is determined according to the range of cyclic translation.
Further preferably, in the step 1.3), a specific method for obtaining the curvelet coefficient matrix C (j, l, k) by performing scale decomposition by using fast discrete curvelet transformation includes: carrying out rapid discrete curvelet transformation on the sensing curve matrix by using the conventional curvelet tool box of matlab to obtain a curve coefficient matrix C (j, l, k); the method for realizing the rapid dispersion curvelet inverse transformation is realized by utilizing the existing curvelet tool box of matlab. The use of matlab for fast discrete curvelet transformation and fast discrete curvelet inverse transformation is a well-known technique in the art.
Further preferably, in the step 1.3), the number of layers for the scale decomposition is:
[J]＝log2(M,N)-3
wherein [ J ] represents the integer part of J; the first layer is a Coarse scale layer and is a matrix consisting of low-frequency coefficients; the outermost layer is a Fine scale layer and is a matrix consisting of high-frequency coefficients; the middle layer is a Detail scale layer and is a matrix composed of medium and high frequency coefficients.
Still further preferably, in step 1.4), the threshold coefficient is calculated by using a monte carlo threshold method to obtain:
T＝k·ej·e
wherein e isjAfter fast discrete curvelet transformation is carried out on Gaussian white noise with the mean value of 0 and the variance of 1, a Monte Carlo test is carried out to obtain a coefficient standard deviation; e is the noise standard deviation in the phase sensitive OTDR signal;
j＝1,2,3…[J]；Ljis a rulerThe number of directions of the degree layer; k is a scale-dependent coefficient, and for different scales, k takes different values to meet the needs. The specific process of the coefficient standard deviation obtained by the monte carlo test is to obtain the norm of the coefficient matrix in each scale and each direction, and then divide the norm by the number of elements contained in the matrix.
According to the present invention, the step 1) is preferably followed by a step of performing a difference processing on the noise reduction result:
wherein, x (N) represents the phase-sensitive OTDR curve after noise reduction, y (N) represents the phase-sensitive OTDR curve after differential processing, and N represents the total number of the phase-sensitive OTDR curves. The difference processing can more intuitively see the location of the disturbance.
Further preferably, the number of times of collecting and superimposing the phase-sensitive OTDR signal curves in step 1.1) is 100 to 1000.
The invention has the beneficial effects that:
1. the noise reduction method of the phase-sensitive OTDR signal determines the size of the threshold according to the sensing curve, and uses different thresholds for each scale layer, so that random noise can be well attenuated; the separation of signals and noise is realized to the maximum extent;
2. the noise reduction method of the phase-sensitive OTDR signal has no requirement on the frequency of the processed signal, effectively avoids the loss of the effective part of the signal, enhances the signal-to-noise ratio and improves the accuracy of positioning an external disturbance vibration source;
3. according to the noise reduction method of the phase-sensitive OTDR signal, the phase-sensitive OTDR curve is collected for multiple times and is subjected to noise reduction processing after being superposed, so that the contingency in the actual process is greatly reduced, and the phenomenon of false alarm or false alarm omission is effectively avoided;
4. the noise reduction method of the phase-sensitive OTDR signal effectively improves the accuracy of disturbance detection based on the phase-sensitive OTDR system, improves the detection performance of working in a complex noise environment, and can be widely applied to the fields of pipeline transportation, bridge detection and the like.
Drawings
Fig. 1 is a flowchart illustrating a method for noise reduction of a phase-sensitive OTDR signal according to the present invention;
fig. 2 is a schematic diagram of the phase-sensitive OTDR device described in embodiment 2;
FIG. 3 is a superimposed graph of signal curves of piezoelectric ceramic simulated vibration;
FIG. 4 is a graph showing the superposition of the signal curves after curvelet transform noise reduction;
fig. 5 is a superimposed graph of the signal curves after the difference processing.
Fig. 6 is a superimposed graph of signal curves obtained by directly performing the difference processing without performing the noise reduction processing.
Detailed Description
The invention is further described below, but not limited thereto, with reference to the following examples and the accompanying drawings.
Example 1
As shown in fig. 1.
A noise reduction method of phase sensitive OTDR signal is used for removing noise of backward Rayleigh scattering light signal, comprising the following steps:
1) the process of 'forward cyclic translation, fast discrete curvelet transformation, threshold processing, fast discrete curvelet inverse transformation and inverse cyclic translation' is repeated, and the specific formula is as follows:
wherein,is a sensing curve matrix after noise reduction treatment, S is a sensing curve matrix, Fn,nFor positive cyclic translation operators, F-n,-nFor the inverse cyclic translation operator, I and I-1Respectively a fast dispersion curvelet transform operator and a fast dispersion curvelet inverse transform operator, T being a threshold reconstruction operator, n1And n2Respectively the amount of translation of the matrix of the sensing curve in the row and column directions, N1For the range of translation of the matrix of the sensing curve in the row direction, N2The translation range of the sensing curve matrix in the column direction is defined; and translating the sensing curve matrix in the row and column directions, moving one row and one column every time, wherein the maximum translation time is the number of rows multiplied by the number of columns, denoising and inversely translating the translated signals, and averaging after multiple times of cyclic translation, thereby effectively eliminating the ringing effect.
The translation of the sensing curve matrix in the row and column directions corresponds to the translation of the superposed sensing curves in the horizontal and vertical directions; because the curvelet transform does not have translation invariance, the phenomenon of pseudo Gibbs is generated at the adjacent position of the discontinuous point of the effective signal, and the phenomenon of pseudo Gibbs is effectively inhibited by positive cycle translation.
Example 2
The method for reducing noise of a phase-sensitive OTDR signal according to embodiment 1, except that the method for reducing noise of a phase-sensitive OTDR signal includes the following steps:
1.1) collecting and superposing phase-sensitive OTDR signal curves for 1000 times, and representing the superposed sensing curves as a 1000 multiplied by 1000 sensing curve matrix;
1.2) carrying out positive cycle translation on the sensing curve matrix; and translating the sensing curve matrix in the row and column directions, wherein the maximum translation time is the number of rows multiplied by the number of columns when moving one row and one column at a time.
1.3) carrying out scale decomposition on the sensing curve matrix subjected to positive cycle translation by adopting rapid discrete curvelet transformation to obtain a curvelet coefficient matrix C (j, l, k); wherein j is a decomposed scale parameter, l is a direction parameter corresponding to each scale parameter, and k is a position parameter corresponding to each direction parameter;
1.4) carrying out threshold processing on curvelet transform coefficients corresponding to different scale layers, and inhibiting background noise:
wherein, Cr(j, l, k) is a curvelet coefficient matrix after threshold processing, and T is a threshold coefficient; for the coefficient matrix C (j, l, k), different scale layers represent different frequency components, different threshold coefficients are adopted for processing each scale layer, signal components are reserved, and noise components are removed.
1.5) carrying out fast discrete curvelet inverse transformation and inverse cyclic translation on the curvelet coefficient matrix after threshold processing; wherein, the fast discrete curvelet inverse transformation and the inverse cyclic translation are respectively the inverse processes of the fast discrete curvelet transformation and the forward cyclic translation.
1.6) repeating the steps 1.2) -1.5)4 times to obtain a sensing curve matrix after noise reduction treatment.
In this embodiment, a schematic diagram of the phase-sensitive OTDR device is shown in fig. 2, where the number of acquisition times is 1000, the length of the optical fiber is 1Km, and the analog vibration signal is a sinusoidal signal of 200HZ and is set at a position of 880 m. The superposition of the signal curves of the simulated vibration of the piezoelectric ceramic is shown in fig. 3. And (3) performing positive cyclic translation on the matrix, wherein the matrix of the sensing signal curve is a 1000 multiplied by 1000 matrix, and the cycle number is 4, namely translating two rows and two columns to obtain the matrix after the positive cyclic translation.
The superposition of the signal curves after the curvelet transform noise reduction is shown in fig. 4.
Example 3
The method for reducing noise of a phase-sensitive OTDR signal according to embodiment 2, except that, in step 1.3), the specific method for obtaining the curved-wave coefficient matrix C (j, l, k) by performing scale decomposition through fast discrete curved-wave transformation includes: carrying out rapid discrete curvelet transformation on the sensing curve matrix by using the conventional curvelet tool box of matlab to obtain a curve coefficient matrix C (j, l, k); the method for realizing the rapid dispersion curvelet inverse transformation is realized by utilizing the existing curvelet tool box of matlab.
The fast discrete curvelet inverse transformation is realized by wrapping algorithm:
A. for two-dimensional objective functionAnd (3) performing two-dimensional Fourier transform to obtain representation of a two-dimensional frequency domain of the frequency domain:
B. in the frequency domain, for each pair of scale and angle (j, l), the solution is obtainedAndthe product of (a);
C. performing wrap on the data obtained in the previous step around the origin to obtain
D. To pairAnd performing two-dimensional inverse Fourier transform to obtain a curvelet coefficient matrix C (j, l, k).
Example 4
The method for reducing noise of a phase-sensitive OTDR signal according to embodiment 2, except that, in the step 1.3), the number of layers of the scale decomposition:
[J]＝log2(M,N)-3
wherein [ J ] represents the integer part of J; the first layer is a Coarse scale layer and is a matrix consisting of low-frequency coefficients; the outermost layer is a Fine scale layer and is a matrix consisting of high-frequency coefficients; the middle layer is a Detail scale layer and is a matrix composed of medium and high frequency coefficients.
In this embodiment, the sensing curve matrix is decomposed by 7-layer fast discrete curved wave transformation. For a j-1 scale layer, the direction parameter l-1, i.e. no direction information; for a 2-scale layer, the direction parameter l is {1,2, …,16}, i.e., contains 16 directional subbands; for a 3-scale layer, the directional parameter l is {1,2, …,32}, i.e., contains 32 directional subbands; for a 4-scale layer, the directional parameter l is {1,2, …,32}, i.e., contains 32 directional subbands; for a 5-scale layer, the direction parameter l is {1,2, …,64}, i.e., contains 64 directional subbands; for a 6-scale layer, the direction parameter l is {1,2, …,64}, i.e., contains 64 directional subbands; for a 7-scale layer, the direction parameter l is {1,2, …,128}, i.e., contains 128 directional subbands.
Example 5
The method for reducing noise of a phase-sensitive OTDR signal according to embodiment 4, except that, in the step 1.4), the threshold coefficient is calculated by using a monte carlo threshold method to obtain:
T＝k·ej·e
wherein e isjAfter fast discrete curvelet transformation is carried out on Gaussian white noise with the mean value of 0 and the variance of 1, a Monte Carlo test is carried out to obtain a coefficient standard deviation; e is the noise standard deviation in the phase sensitive OTDR signal;
j＝1,2,3…[J]；Ljthe number of directions of the scale layer; k is a scale-dependent coefficient, and for different scales, k takes different values to meet the needs. The specific process of the coefficient standard deviation obtained by the monte carlo test is to obtain the norm of the coefficient matrix in each scale and each direction, and then divide the norm by the number of elements contained in the matrix.
Example 6
The method of reducing noise in a phase sensitive OTDR signal according to embodiment 1, except that said step 1) is followed by
The method comprises the following steps of carrying out differential processing on a noise reduction result:
wherein, x (N) represents the phase-sensitive OTDR curve after noise reduction, y (N) represents the phase-sensitive OTDR curve after differential processing, and N represents the total number of the phase-sensitive OTDR curves. The difference processing can more intuitively see the location of the disturbance.
In this embodiment, the total number of the sensing curves is 1000, the difference processing process is to make a difference between the 1 st sensing curve and the 2 nd sensing curve, the result is used as the 1 st column of the new matrix, the difference between the 2 nd sensing curve and the 3 rd sensing curve is made, the result is used as the 2 nd column of the new matrix, and so on, the difference between the 1000 th sensing curve and the 1 st sensing curve is made, the result is used as the 1000 th column of the new matrix, and the result is shown in fig. 5.
Comparative example:
for the signal curve of the piezoelectric ceramic analog vibration, the differential processing is directly carried out without noise reduction processing; the difference processing procedure is the same as that of embodiment 6; the resulting overlay of the signal curves is shown in fig. 6.
As can be seen by comparing fig. 5 to fig. 6: the result after denoising is processed by the curvelet transform threshold, so that the existence of vibration information at 880m can be obviously seen, random noise is filtered, and the signal-to-noise ratio is higher. And as a result of not performing denoising processing, the noise component is obvious, the signal is submerged in the noise, and the vibration information is completely invisible. Therefore, the method has the advantages of reducing random noise, improving the signal-to-noise ratio and accurately positioning disturbance in the process of processing the phase-sensitive OTDR signal.
Claims (7)
1. A method for noise reduction of a phase sensitive OTDR signal, comprising the steps of:
1) the process of 'forward cyclic translation, fast discrete curvelet transformation, threshold processing, fast discrete curvelet inverse transformation and inverse cyclic translation' is repeated, and the specific formula is as follows:
wherein,is a sensing curve matrix after noise reduction treatment, S is a sensing curve matrix, Fn,nFor positive cyclic translation operators, F-n,-nFor the inverse cyclic translation operator, I and I-1Respectively a fast dispersion curvelet transform operator and a fast dispersion curvelet inverse transform operator, T being a threshold reconstruction operator, n1And n2Respectively the amount of translation of the matrix of the sensing curve in the row and column directions, N1For the range of translation of the matrix of the sensing curve in the row direction, N2The translation range of the sensing curve matrix in the column direction is shown.
2. The method of claim 1, wherein the method of reducing noise in a phase-sensitive OTDR signal comprises the following steps:
1.1) carrying out multiple acquisition and superposition on a phase-sensitive OTDR signal curve, and representing the superposed sensing curve as an MXN sensing curve matrix;
1.2) carrying out positive cycle translation on the sensing curve matrix;
1.3) carrying out scale decomposition on the sensing curve matrix subjected to positive cycle translation by adopting rapid discrete curvelet transformation to obtain a curvelet coefficient matrix C (j, l, k); wherein j is a decomposed scale parameter, l is a direction parameter corresponding to each scale parameter, and k is a position parameter corresponding to each direction parameter;
1.4) carrying out threshold processing on curvelet transform coefficients corresponding to different scale layers, and inhibiting background noise:
wherein, Cr(j, l, k) is a curvelet coefficient matrix after threshold processing, and T is a threshold coefficient;
1.5) carrying out fast discrete curvelet inverse transformation and inverse cyclic translation on the curvelet coefficient matrix after threshold processing;
1.6) repeating the steps 1.2) -1.5) to obtain a sensing curve matrix after noise reduction treatment.
3. The method for reducing noise of a phase-sensitive OTDR signal according to claim 2, characterized in that, in said step 1.3), the specific method for obtaining the curvelet coefficient matrix C (j, l, k) by performing the scale decomposition using the fast discrete curvelet transform is: carrying out rapid discrete curvelet transformation on the sensing curve matrix by using the conventional curvelet tool box of matlab to obtain a curve coefficient matrix C (j, l, k); the method for realizing the rapid dispersion curvelet inverse transformation is realized by utilizing the existing curvelet tool box of matlab.
4. A method of noise reduction of a phase sensitive OTDR signal according to claim 2, characterized in that, in said step 1.3), the number of layers of the scale decomposition:
[J]＝log2(M,N)-3
wherein [ J ] represents the integer part of J; the first layer is a Coarse scale layer and is a matrix consisting of low-frequency coefficients; the outermost layer is a Fine scale layer and is a matrix consisting of high-frequency coefficients; the middle layer is a Detail scale layer and is a matrix composed of medium and high frequency coefficients.
5. A method for noise reduction of phase sensitive OTDR signals according to claim 4, wherein in step 1.4), said threshold coefficients are calculated using a Monte Carlo threshold method:
T＝k·ej·e
wherein e isjAfter fast discrete curvelet transformation is carried out on Gaussian white noise with the mean value of 0 and the variance of 1, a Monte Carlo test is carried out to obtain a coefficient standard deviation; e is the noise standard deviation in the phase sensitive OTDR signal;
j＝1,2,3…[J]；Ljis the number of directions of the scale layer.
6. A method of noise reduction of a phase sensitive OTDR signal according to claim 1, characterized in that, after said step 1), it further comprises the step of performing a difference processing on the noise reduction result:
wherein, x (N) represents the phase-sensitive OTDR curve after noise reduction, y (N) represents the phase-sensitive OTDR curve after differential processing, and N represents the total number of the phase-sensitive OTDR curves.
7. The method for reducing noise of a phase-sensitive OTDR signal according to claim 2, characterized in that, the number of times of collecting and superimposing the phase-sensitive OTDR signal curve in step 1.1) is 100-1000.
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| CN109391321A (en) * | 2018-11-20 | 2019-02-26 | 山东大学 | Disturbance positioning method in a kind of phase sensitive OTDR sensing |
| CN113987843A (en) * | 2021-12-27 | 2022-01-28 | 四川创智联恒科技有限公司 | Method for inhibiting Gibbs effect in digital signal processing system |
| CN118424350A (en) * | 2024-07-05 | 2024-08-02 | 吉林大学 | Phase unwrapping error recovery method based on phase sensitive optical time domain reflectometer |
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| CN109391321B (en) * | 2018-11-20 | 2021-05-18 | 山东大学 | Disturbance positioning method in phase-sensitive OTDR (optical time Domain reflectometer) sensing |
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| CN118424350A (en) * | 2024-07-05 | 2024-08-02 | 吉林大学 | Phase unwrapping error recovery method based on phase sensitive optical time domain reflectometer |
| CN118424350B (en) * | 2024-07-05 | 2024-09-03 | 吉林大学 | Phase unwrapping error recovery method based on phase sensitive optical time domain reflectometer |
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