CN114544009A - High-precision fiber grating demodulation method and system - Google Patents

High-precision fiber grating demodulation method and system Download PDF

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CN114544009A
CN114544009A CN202210190063.2A CN202210190063A CN114544009A CN 114544009 A CN114544009 A CN 114544009A CN 202210190063 A CN202210190063 A CN 202210190063A CN 114544009 A CN114544009 A CN 114544009A
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fbg
demodulation
spectrum
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孙博钰
曹晨
保宏
蒋柏峰
杨明焕
胡瑞贤
王伟
冷国俊
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
    • G—PHYSICS
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    • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D5/00—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable
    • G01D5/26—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light
    • G01D5/32—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light
    • G01D5/34—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light the beams of light being detected by photocells
    • G01D5/353—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light the beams of light being detected by photocells influencing the transmission properties of an optical fibre

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Abstract

The invention discloses a high-precision fiber grating demodulation method and a system, which comprises the following steps: acquiring a plurality of FBG spectrum sampling points by using an FBG sensor; interpolating sampling points of the FBG spectrum; and fitting and demodulating by using the interpolated sampling point of the FBG spectrum by utilizing an LM iterative algorithm to complete demodulation of the FBG sensor.

Description

High-precision fiber grating demodulation method and system
Technical Field
The invention belongs to the field of sensor demodulation, and relates to a high-precision fiber grating demodulation method and system.
Background
Fiber Bragg gratings (Fiber Bragg gratings) use the photosensitivity of Fiber materials to form a spatial phase Grating in the core, which essentially forms a narrow-band mirror in the core. FBGs have been widely used in the field of optical fiber sensing technology, and sensing information is obtained based on the modulation of the central wavelength of the FBG reflection spectrum by external parameters (such as stress, temperature, etc.). Therefore, the key technology of the FBG sensing demodulation system is to detect the shift of the center wavelength thereof, and therefore, it is important to accurately extract the center wavelength value of the FBG reflection spectrum to improve the accuracy and resolution of the wavelength detection of the sensing system. The FBG reflection spectrum sampling signal collected by the spectrometer contains various noise sources, the peak value directly obtained from the sampling signal and the corresponding central wavelength have larger error, and the currently commonly used spectrum fitting peak searching algorithm comprises a direct peak searching method, a polynomial fitting method, a Gaussian fitting method or a Gaussian polynomial fitting method and the like.
The most widely applied is the Gaussian fitting algorithm which integrates all indexes to ensure the demodulation precision, but the demodulation speed is greatly reduced due to the increase of the number of sampling points in the experiment, the memory allocation is increased, and a large amount of experimental data allocation is occupied, so that each spectrum peak cannot be sampled by more than 100 points.
Disclosure of Invention
The present invention is directed to overcome the above-mentioned shortcomings of the prior art, and provides a high-precision fiber grating demodulation method and system, which can guarantee the demodulation speed while guaranteeing the precision.
In order to achieve the above purpose, the high-precision fiber grating demodulation method of the present invention comprises the following steps:
acquiring a plurality of FBG spectrum sampling points by using an FBG sensor;
interpolating sampling points of the FBG spectrum;
and performing fitting demodulation by using the interpolated sampling point of the FBG spectrum by using an LM iterative algorithm to complete the demodulation of the FBG sensor.
The specific process of interpolating the sampling point of the FBG spectrum is as follows: the sampling points of the FBG spectrum are interpolated by NURBS curves.
In the fitting demodulation by using the interpolated sampling point of the FBG spectrum by using the LM iterative algorithm, the iterative rule of the LM iterative algorithm is as follows:
Xn+1＝Xn-Hn -1Gn (4)
Hn＝J(r(Xn))TJ(r(Xn))+λI (5)
Figure BDA0003524216790000021
wherein H is calculated by the formula (5)nInstead of the blacksen matrix, j (x) is a jacobian matrix and λ is a variable.
The Jacobian matrix J (X) is:
Figure BDA0003524216790000031
Figure BDA0003524216790000032
Figure BDA0003524216790000033
Figure BDA0003524216790000034
Ji,4＝1 (11)
the process of fitting and demodulating the sampling points of the FBG spectrum after interpolation by utilizing an LM iterative algorithm is as follows:
11) estimating the collected sampling points to obtain an initial vector X;
12) setting the needed iteration number n, delta lambda being 0.001, determining the target error, and calculating the square sum e of the initial error0Setting the current sum of squared errors E-E0；
13) When E is less than or equal to g or n is more than or equal to l, turning to the step 14), otherwise, ending the iteration;
14) calculating the sum of squares of errors enWhen e isn> E, will set λ ← 10 λ, n ← n-1, and Xn+1If the calculated value is invalid, the step 13) is carried out, otherwise, the step 15) is carried out;
15) set λ ← 0.1 λ, E ═ EnAnd then to step 13).
The high-precision fiber grating demodulation system comprises:
the acquisition module is used for acquiring a plurality of FBG spectrum sampling points by utilizing the FBG sensor;
the interpolation module is used for interpolating sampling points of the FBG spectrum;
and the demodulation module is used for performing fitting demodulation by using the interpolated sampling point of the FBG spectrum by utilizing an LM iterative algorithm to complete the demodulation of the FBG sensor.
The invention has the following beneficial effects:
when the high-precision fiber bragg grating demodulation method and the system are specifically operated, sampling points of a basic FBG spectrum are used for interpolation, a small number of original sampling points are expanded to about 100 sampling points, and LM algorithm fitting demodulation is carried out by using the interpolated sampling points, so that a large amount of sampling data is not needed, the demodulation speed can be ensured, the precision of a fitting algorithm can be improved, and the precision of center wavelength demodulation is improved.
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FIG. 1 is a full spectrum of a set of four FBG sensors at 20 ℃;
FIG. 2 is a graph of the distribution of the fundamental sampling points of the FBG spectrum;
FIG. 3 is a plot of experimental spectral points after expansion using NURBS;
FIG. 4 is a basic flow diagram of the LM algorithm;
FIGS. 5 and 6 are comparative graphs of spectral peaks fitted using Gaussian fitting and the Gaussian LM algorithm;
FIG. 7 is a graph of the error contrast of the modified Gaussian-LM algorithm and the Gaussian fitting algorithm.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments, and are not intended to limit the scope of the present disclosure. Moreover, in the following description, descriptions of well-known structures and techniques are omitted so as to not unnecessarily obscure the concepts of the present disclosure. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
There is shown in the drawings a schematic block diagram of a disclosed embodiment in accordance with the invention. The figures are not drawn to scale, wherein certain details are exaggerated and possibly omitted for clarity of presentation. The shapes of various regions, layers and their relative sizes and positional relationships shown in the drawings are merely exemplary, and deviations may occur in practice due to manufacturing tolerances or technical limitations, and a person skilled in the art may additionally design regions/layers having different shapes, sizes, relative positions, according to actual needs.
The expression of the Gaussian curve model is integrally similar to the FBG reflected spectrum signal obtained by sampling, and the noise is removed through Gaussian fitting to obtain a more optimal spectrum signal, so that the peak wavelength characteristic of the spectrum is accurately obtained, the principle of the Gaussian fitting is to minimize the mean square error of the Gaussian fitting, when the window size, the wavelength resolution and the signal-to-noise ratio are the same, the Gaussian fitting method is an algorithm with the minimum error change and the most stable, the Gaussian function is approximately expressed as a power density spectrum curve of the FBG reflected spectrum, and the specific form is as follows:
Figure BDA0003524216790000051
therefore, the selection of appropriate values of the gaussian fit coefficients a0, a1, and a2 is crucial to the accuracy of the gaussian fit, and theoretically, a0 corresponds to the peak intensity of the real FBG reflection spectrum, a1 corresponds to the central wavelength value, a2 corresponds to the 3db bandwidth of the reflection spectrum,the Gaussian fitting curve can accurately fit a real spectrum curve through the sampling spectrum, and the error mean value and the standard deviation both reach the minimum value. However, in practice, three parameters of the reflectance spectrum are unknown, and are interfered by instrument noise and background noise, real coefficients cannot be directly obtained from sampled data points, and a general peak searching method adopts gaussian fitting coefficient values a0, a1 and a2 obtained by direct peak searching, but the coefficients obtained by direct peak searching are influenced by noise in the spectrum to generate large errors. In order to solve the problem, the conventional technology generally acquires a large amount of original spectral data to estimate the true value more accurately, but the data acquired in the spectral processing is limited, and when the acquired data is excessive, the speed of information processing is affected. The selection of the Gaussian fitting coefficient values a0, a1 and a2 is optimized by using an LM algorithm, the Gaussian fitting coefficient obtained by directly searching peaks is used as an initial value of the LM algorithm, the LM algorithm selects the information of a secondary derivative capable of utilizing a Gaussian function by combining a Gaussian curve model, so that the iterative step length is adaptively adjusted to quickly converge to an optimal solution, and the mixed algorithm of the two is called a Gaussian algorithm.
When the Gaussian fitting algorithm is used, the number of the spectrum sampling points can be controlled within 10 points, so that the experimental sampling time is greatly reduced, and the speed of the overall demodulation algorithm is improved. After the LM algorithm is combined, the number of spectrum sampling points required by the experiment needs to be increased, and in order to ensure that the fitting precision after iteration is improved, the spectrum sampling needs to be relatively dense, and the result is relatively good. When one wave peak in the sampling spectrum has 100 sampling points, the precision of the LM algorithm can be ensured. However, in the experiment, the increased number of sampling points can greatly reduce the demodulation speed, and the allocation of memory can also be increased, so that a large amount of experimental data allocation is occupied, and therefore, each spectrum peak cannot be sampled by more than 100 points, the basic FBG spectrum sampling points can be used for NURBS curve interpolation, the original ones sampling points are expanded to about 100 sampling points, and then the sampling points are used for carrying out LM algorithm solution, so that a large amount of sampling data is not needed, the demodulation speed is ensured, the precision of a fitting algorithm can be improved, and the demodulation precision of the center wavelength is improved.
Based on the above analysis, the high-precision fiber grating demodulation method of the present invention comprises the following steps:
1) acquiring a plurality of FBG spectrum sampling points by using an FBG sensor;
2) interpolating the sampling point of the FBG spectrum through a NURBS curve;
3) and performing fitting demodulation by using the interpolated sampling point of the FBG spectrum by using an LM iterative algorithm to complete the demodulation of the FBG sensor.
It should be noted that, the original FBG sampled spectrum is close to gaussian distribution, one peak represents the sampled data of one sensor, and each peak can be plotted as spectral data by about 10 sampling points, as shown in fig. 2. FBG (fiber Bragg Grating) fiber Bragg grating; LM (Levenberg-Marquardt) Levenberg-Marquardt algorithm; NURBS (Non-Uniform Rational B-Splines)
NURBS curves are commonly referred to as non-uniform rational B-splines, given a set of data points, i.e., type value points, through three steps: a) calculating a node vector; b) calculating a boundary condition; c) back-computing the control vertices performs a back-computation of the curve to generate a NURBS curve through these shaped points. The number of sampling points is increased through NURBS curve interpolation, so that the reflection spectrum is more complete, the sampling points are denser, the center wavelength is solved by using an LM algorithm, and the curve interpolation result is shown in figures 2 and 3.
The improved FBG reflection spectrum is close to gaussian distribution. Therefore, after the wave curve is cut, the approximate Gaussian function can be used to represent:
Figure BDA0003524216790000071
where G0 is the peak power of the light reflection spectrum, λ 0 is the center wavelength, and Δ λ is the bandwidth of the reflection spectrum that drops by 3 dB.
The error function is expressed as:
Figure BDA0003524216790000072
according to the least square method, the sum of errors should be as small as possible, i.e. the problem of error minimization is solved as follows:
Figure BDA0003524216790000073
when the error is minimal, λ 0 is the center wavelength of the fit.
X is solved according to the LM algorithm rule, and the iteration rule of the LM algorithm is as follows:
Xn+1＝Xn-Hn -1Gn (4)
Hn＝J(r(Xn))TJ(r(Xn))+λI (5)
Figure BDA0003524216790000081
wherein H is calculated by the formula (5)nInstead of the Hessian matrix, to prevent Hn from deviating too much from the actual Hessian matrix, the variables λ, j (x) are introduced as jacobian matrices, wherein,
Figure BDA0003524216790000082
Figure BDA0003524216790000083
Figure BDA0003524216790000084
Figure BDA0003524216790000085
Ji,4＝1 (11)
the key of the LM algorithm is to find a suitable lambda in each iteration, and when the lambda is too large, the formula (13) is approximate to a Gauss-Newton algorithm; when λ is too small, equation (13) is similar to the gradient descent algorithm, so that the LM algorithm can combine the advantages of the gauss-newton algorithm and the gradient descent algorithm, and the gaussian fitting process based on the L-M algorithm is as follows:
11) estimating the acquired sampling points to obtain an initial vector X of the LM algorithm needing iteration;
12) setting the needed iteration number n, delta lambda being 0.001, determining a target error and the iteration number I, and calculating the square sum e of the initial error0Setting the current sum of squared errors E-E0；
13) When E is less than or equal to g or n is more than or equal to l, turning to the step 14), otherwise, ending the iteration;
14) calculating the sum of squares of errors enWhen e isn> E, will set λ 10 λ, n-1, and Xn+1If the calculated value is invalid, the step 13) is carried out, otherwise, the step 15) is carried out;
15) setting λ 0.1 λ, E ═ EnAnd then to step 13).
Referring to fig. 4, the initial vector X0 is substituted into equation (13) for multiple iterations until the sum of the squares of the errors is less than the target parameter set or the number of iterations is greater than the maximum set of iterations, at which point the vector is the desired gaussian function parameter.
Simulation experiment
The MOI demodulator is used for measuring four FBG sensors in a single channel, and the experiment is as follows, in the experiment, a grating is placed in a constant-temperature high-low temperature experiment box, after the temperature is regulated to 20 ℃ and stabilized, full spectrum data and peak wavelength of the corresponding sensors are recorded, and then the full spectrum data and the peak wavelength are respectively collected at 25 ℃, 30 ℃ and 35 ℃, wherein the full spectrum collected at 20 ℃ is shown in figure 1, as can be seen from figure 1, the single-peak curve has good symmetry and high signal-to-noise ratio, so that the peak position can be obtained through Gaussian fitting, and in the experiment, four groups of full spectrum data are obtained by the four FBG sensors at four temperatures and are used for peak search.
From the above results, 4 sets of data can be truncated in each full spectrum data, and thus, under four temperature conditions, a total of 16 sets of data are obtained for fitting.
When the LM algorithm is adopted for peak searching, the selection of the initial value is very important, and if the deviation of the initial value is large, the error of the final peak value result is also large. For example, the actual center wavelength is 1550.5 nm. The initial value λ 0 was set to 1550nm and the fitting results are shown in fig. 1. Therefore, in the experiment, the abscissa corresponding to the maximum optical power sampling point is used as the initial value λ 0 of the fitting, and the full spectrum data at different temperatures is processed according to the above method. Comparing the central wavelength obtained by LM algorithm fitting and the central wavelength obtained by Gaussian fitting algorithm with the wavelength measured by MOI to obtain a peak error, wherein the result is as follows:
as shown in table 1 at 20 ℃:
TABLE 1
True value LM fitting value Error of the measurement Gaussian fitting Error of the measurement
FBG1 1550.4999 1550.4984 0.0015 1550.1974 0.0025
FBG2 1553.0496 1553.0481 0.0015 1553.0469 0.0027
FBG3 1555.2199 1555.2201 0.0002 1555.2190 0.0009
FBG4 1558.0036 1558.0031 0.0005 1558.0021 0.0015
As shown in table 2 at 25 ℃:
TABLE 2
True value LM fitting value Error of the measurement Gaussian fitting Error of
FBG1 1550.5505 1550.5486 0.0019 1550.5473 0.0032
FBG2 1553.0983 1553.0965 0.0018 1553.0954 0.0029
FBG3 1555.2719 1555.2702 0.0017 1555.2684 0.0035
FBG4 1558.0520 1558.0522 0.0002 1558.0500 0.0020
As shown in table 3 at 30 ℃:
TABLE 3
True value LM fitting value Error of the measurement Gaussian fitting Error of the measurement
FBG1 1550.6051 1550.6041 0.0010 1550.6025 0.0026
FBG2 1553.1481 1553.1455 0.0026 1553.1440 0.0041
FBG3 1555.3255 1555.3241 0.0014 1555.3227 0.0028
FBG4 1558.1023 1558.1008 0.0015 1558.0993 0.0030
As shown in table 4 at 35 ℃:
TABLE 4
True value LM fitting value Error of the measurement Gaussian fitting Error of the measurement
FBG1 1550.6533 1550.6519 0.0014 1550.6505 0.0028
FBG2 1553.1972 1553.1956 0.0016 1553.1941 0.0031
FBG3 1555.3735 1555.3724 0.0011 1555.3703 0.0032
FBG4 1558.1526 1558.1506 0.0020 1558.1496 0.0030
The experimental data show that for the Gaussian fitting algorithm, the maximum error of the center wavelength obtained by solving is 4.1pm, the minimum error is 0.9pm, and the average error is 2.73pm, while for the Gaussian-LM algorithm, the maximum error is 2.6pm, the minimum error is 0.2pm, and the average error is 1.33 pm. It can be seen from the data that the average error of the center wavelength obtained by the Gaussian-LM algorithm is much smaller than that of the Gaussian fitting algorithm, and the error is kept within 3pm, and it can be seen from fig. 7 that the Gaussian-LM is an improvement on the Gaussian fitting algorithm, thereby successfully reducing the error and improving the demodulation precision. The algorithm has good stability, can control the error within a small range, and has higher consistency with the central wavelength obtained by an MOI demodulator.

Claims (6)

1. A high-precision fiber grating demodulation method is characterized by comprising the following steps:
acquiring a plurality of FBG spectrum sampling points by using an FBG sensor;
interpolating sampling points of the FBG spectrum;
and performing fitting demodulation by using the interpolated sampling point of the FBG spectrum by using an LM iterative algorithm to complete the demodulation of the FBG sensor.
2. The demodulation method of the fiber bragg grating with high precision as claimed in claim 1, wherein the specific process of interpolating the sampling points of the FBG spectrum is as follows: the sampling points of the FBG spectrum are interpolated by NURBS curves.
3. The demodulation method of the fiber bragg grating of claim 1, wherein in the fitting demodulation using the interpolated sampling points of the FBG spectrum by using an LM iterative algorithm, an iterative rule of the LM iterative algorithm is as follows:
Xn+1＝Xn-Hn -1Gn (4)
Hn＝J(r(Xn))TJ(r(Xn))+λI (5)
Figure FDA0003524216780000011
wherein H is calculated by the formula (5)nInstead of the blacksen matrix, j (x) is a jacobian matrix and λ is a variable.
4. The demodulation method of claim 3 wherein the Jacobian matrix J (X) is:
Figure FDA0003524216780000012
Figure FDA0003524216780000021
Figure FDA0003524216780000022
Figure FDA0003524216780000023
Ji,4＝1 (11) 。
5. the demodulation method of the fiber bragg grating with high precision as claimed in claim 1, wherein the fitting demodulation process using the interpolated sampling points of the FBG spectrum by the LM iterative algorithm is as follows:
11) estimating the collected sampling points to obtain an initial vector X;
12) setting the needed iteration number n, delta lambda being 0.001, determining the target error, and calculating the square sum e of the initial error0Setting the current sum of squared errors E-E0；
13) When E is less than or equal to g or n is more than or equal to l, turning to the step 14), otherwise, ending the iteration;
14) calculating the sum of squares of errors enWhen e isn> E, will set λ ← 10 λ, n ← n-1, and Xn+1If the calculated value is invalid, the step 13) is carried out, otherwise, the step 15) is carried out;
15) set λ ← 0.1 λ, E ═ EnAnd then to step 13).
6. A high-precision fiber grating demodulation system, comprising:
the acquisition module is used for acquiring a plurality of FBG spectrum sampling points by utilizing the FBG sensor;
the interpolation module is used for interpolating sampling points of the FBG spectrum;
and the demodulation module is used for performing fitting demodulation by using the interpolated sampling point of the FBG spectrum by utilizing an LM iterative algorithm to complete the demodulation of the FBG sensor.
CN202210190063.2A 2022-02-28 2022-02-28 High-precision fiber grating demodulation method and system Pending CN114544009A (en)

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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113290558A (en) * 2021-05-24 2021-08-24 南京航空航天大学 NURBS curve speed interpolation method based on parameter densification
CN113358239A (en) * 2021-05-24 2021-09-07 长春工业大学 FBG-based wavelength feature identification method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113290558A (en) * 2021-05-24 2021-08-24 南京航空航天大学 NURBS curve speed interpolation method based on parameter densification
CN113358239A (en) * 2021-05-24 2021-09-07 长春工业大学 FBG-based wavelength feature identification method

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