CN109141675B - Method for noise reduction of distributed optical fiber temperature measurement system based on binary SVD - Google Patents
Method for noise reduction of distributed optical fiber temperature measurement system based on binary SVD Download PDFInfo
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Abstract
The invention discloses a method for noise reduction of a distributed optical fiber temperature measurement system based on binary SVD (singular value decomposition), which comprises the steps of firstly obtaining two groups of original data to construct two matrixes, wherein the two groups of original data are anti-Stokes and Stokes original data; performing singular value decomposition and reconstruction on the two matrixes respectively to form two matrixes subjected to noise reduction; respectively obtaining noise-reduced data from the noise-reduced matrix, and fusing two groups of data to calculate a temperature measurement result, a maximum deviation, a root mean square error and a smoothness and calculate a result quality coefficient; obtaining a result quality coefficient of a demodulation result of the noise reduction signal after each iteration through multiple iterations of binary singular value decomposition; and finding out the optimal iteration times, and taking the noise reduction data corresponding to the optimal iteration times as an optimal signal. The noise reduction method provided by the invention effectively improves the signal-to-noise ratio of the original acquisition signal, reduces the maximum deviation and the root mean square error of temperature measurement, and improves the smoothness degree of a temperature curve.
Description
Technical Field
The invention relates to a noise reduction method for a temperature measurement system, in particular to a noise reduction method for a distributed optical fiber temperature measurement system based on binary SVD.
Background
With the rapid development of the optical fiber sensing technology, due to the characteristics of electromagnetic interference resistance and distributed continuous measurement, the distributed optical fiber temperature measurement system is widely applied to safety monitoring in specific and severe environments such as power grids, mines and nuclear environments. However, the random noise increase measurement error of the system is a problem that needs to be solved all the time in the distributed optical fiber temperature measurement system. In order to reduce the influence of random noise on the measurement result, researchers respectively adopt improved system hardware and a digital signal processing algorithm to improve the signal-to-noise ratio of the system. Although the method of improving system hardware can effectively suppress system random noise, the method is difficult to implement, expensive in cost and not suitable for large-scale practical application. And the adoption of the data signal processing algorithm can effectively reduce the random noise component of the system without improving the hardware of the system. However, the noise reduction algorithm applied to the distributed optical fiber temperature measurement system at present is complex in implementation process, long in calculation time and not easy to be applied practically.
Disclosure of Invention
The invention aims to provide a method for reducing noise of a distributed optical fiber temperature measurement system based on binary SVD, which can solve the problems, effectively improve the signal-to-noise ratio of an original acquisition signal, reduce the maximum deviation and root-mean-square error of temperature measurement and improve the smoothness degree of a temperature curve.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows: a method for noise reduction of a distributed optical fiber temperature measurement system based on binary SVD comprises the following steps:
(1) acquiring anti-Stokes signals and Stokes signals in an optical fiber temperature measuring system, acquiring anti-Stokes raw data and Stokes raw data, and respectively constructing a 2 gamma (L-1) -dimensional Hankel matrix, wherein L is the length of the raw data;
(2) performing singular value decomposition and reconstruction on the two Hankel matrixes respectively to form two matrixes subjected to noise reduction;
(21) singular value decomposition is carried out on the Hankel matrix to obtain a left singular matrix, a singular value diagonal matrix and a right singular matrix;
(22) reserving a first singular value of the singular value diagonal matrix, and setting other singular values to be 0 to form a new singular value diagonal matrix;
(23) reconstructing the left singular matrix, the right singular matrix and the new singular value diagonal matrix to form a new matrix, and marking the new matrix as a matrix after noise reduction;
(3) acquiring anti-Stokes data and Stokes data from the two de-noised matrixes again, and marking the anti-Stokes data and the Stokes data as anti-Stokes de-noising data and Stokes de-noising data;
(4) acquiring a temperature measurement result according to the anti-Stokes noise reduction data and the Stokes noise reduction data;
(5) calculating three indexes of the temperature measurement result according to the temperature measurement result, wherein the three indexes are maximum deviation, root mean square error and smoothness;
(6) repeating the steps (2) - (5) until the three indexes under the current iteration number are all larger than the three indexes under the previous iteration number, wherein the iteration number at the moment is the maximum iteration number n, and stopping repeating;
(7) sorting the three indexes obtained by each iteration to obtain the bit order h (h is more than 0 and less than or equal to n) of the maximum deviation in the order from large to small in the n iterations, the bit order k (k is more than 0 and less than or equal to n) of the root mean square error in the order from large to small in the n iterations, and the bit order w (w is more than 0 and less than or equal to n) of the smoothness in the order from large to small in the n iterations, wherein j is a positive integer, and j is more than 0 and less than or equal to n
(8) Calculating the result quality coefficient Q of j iterationjThe maximum resulting mass coefficient max { Q } is obtained for h + k + wj}＝QpWherein j is more than 0, p is less than or equal to n, and p is the optimal iteration number;
(9) and acquiring anti-Stokes noise reduction data and Stokes noise reduction data corresponding to the p iteration as best signals of the noise reduction effect.
Preferably, the method comprises the following steps: and (3) acquiring noise reduction data from a noise-reduced matrix by the following steps:
(31) respectively taking the data of the first row and the first column of the noise-reduced matrix and the data of the second row and the L-1 column of the noise-reduced matrix as the first data and the last data of the noise-reduced acquired data;
(32) and adding the data of the 1 st row and the ith column (i is 2,3, …, L-1) of the matrix subjected to noise reduction and the data of the 2 nd row and the ith column of the new matrix, and taking the average value as the ith data of the acquired data subjected to noise reduction.
Preferably, the method comprises the following steps: the step (4) is specifically as follows:
(41) sequentially obtaining the ratio of anti-Stokes signal acquisition data subjected to noise reduction at different temperatures to Stokes signal acquisition data subjected to noise reduction;
(42) obtaining a temperature measurement curve through curve fitting according to the ratio;
(43) and obtaining a temperature measurement result according to the temperature measurement curve.
Preferably, the method comprises the following steps: the three indexes in the step (5) are specifically as follows:
maximum deviation:
in the formula (I), the compound is shown in the specification,
for the temperature measurement result obtained in step (4), TactIs a reference temperature measured by a mercury thermometer; n is the number of effective data of the measurement result;
the root mean square error is the root mean square error between the temperature measurement result and the reference temperature, and the smaller the value of the root mean square error is, the smaller the difference between the overall measurement result and the reference temperature is, and the root mean square error is represented as:
smoothness measures the fluctuation degree of the temperature measurement result, and the smaller the value, the smoother the temperature measurement curve is, the smaller the fluctuation of the measurement result is, and is expressed as:
compared with the prior art, the invention has the advantages that:
firstly, acquiring two groups of raw data to construct two matrixes, wherein the two groups of raw data are anti-Stokes raw data and Stokes raw data; performing singular value decomposition and reconstruction on the two matrixes respectively to form two matrixes subjected to noise reduction; and respectively obtaining the noise-reduced data from the noise-reduced matrix, so that the noise level of the data can be effectively reduced, and the temperature measurement result can be conveniently demodulated.
And demodulating a temperature measurement result according to the two groups of noise reduction data, calculating the maximum deviation, the root mean square error and the smoothness according to the temperature measurement result, and calculating a result quality coefficient according to the three indexes, so that an optimal iteration coefficient can be determined according to the result quality coefficient, a signal with the optimal noise reduction effect can be obtained, and the temperature measurement result with the optimal three indexes can be obtained.
Obtaining a result quality coefficient of a demodulation result of the noise reduction signal after each iteration through multiple iterations of binary singular value decomposition; therefore, the optimal iteration times are found, and the noise reduction data corresponding to the optimal iteration times are used as the optimal signals.
The noise reduction method provided by the invention effectively improves the signal-to-noise ratio of the original acquisition signal, reduces the maximum deviation and the root mean square error of temperature measurement, improves the smoothness degree of a temperature curve, does not need to change the hardware structure of a system, and is convenient to realize.
Drawings
FIG. 1 is a schematic diagram of an optical fiber temperature measurement system;
FIG. 2 is a flow chart of the present invention;
FIG. 3 is a flow chart of singular value decomposition and reconstruction of a Hankel matrix;
FIG. 4 is a graph comparing raw data at 50.0 ℃ with optimal temperature measurements obtained using the present invention;
FIG. 5a is a comparison of noise reduction effects of several noise reduction methods at 42.5 ℃;
FIG. 5b is a comparison of noise reduction effects of several noise reduction methods at 50.0 deg.C;
FIG. 5c is a comparison of noise reduction effects of several noise reduction methods at 55.0 deg.C;
FIG. 5d is a comparison of noise reduction effects of several noise reduction methods at 60.0 deg.C;
FIG. 6a is a three-index plot of 5 iterations at 45.2 ℃;
FIG. 6b is a graph of the resulting quality coefficients of the 5 iterations calculated from FIG. 6 a;
FIG. 7a is a graph of three indices for 5 iterations at 50.0 deg.C;
FIG. 7b is a graph of the resulting quality coefficients for the 5 iterations calculated from FIG. 7 a;
FIG. 8a is a three-index plot for 5 iterations at 55.0 deg.C;
FIG. 8b is a graph of the resulting quality coefficients for the 5 iterations calculated from FIG. 8 a;
FIG. 9a is a three-index plot of 5 iterations at 60.0 deg.C;
FIG. 9b is a graph of the resulting quality coefficients for the 5 iterations calculated from FIG. 9 a;
FIG. 10 is a graph comparing the maximum deviation of the original signal after direct demodulation and demodulation by different methods;
FIG. 11 is a graph of temperature RMS error comparisons of original signal demodulated directly and processed by different methods;
FIG. 12 is a graph of temperature curve smoothness comparison of original signal directly demodulated and demodulated after different processing methods;
FIG. 13 is a comparison graph of smoothness of the temperature profile of FIG. 12 with the original signal removed.
Detailed Description
The invention will be further explained with reference to the drawings.
Example 1: referring to fig. 1 and 2, the optical fiber temperature measuring system includes: the device comprises a laser pulse light source, a wavelength division multiplexer, a sensing optical fiber, an avalanche photodiode, an amplifier and a data acquisition card. The working principle of the device is that a laser pulse light source injects laser pulses into a sensing optical fiber, the laser pulses and a sensing optical fiber medium act to generate backward spontaneous Raman scattering light with temperature information, the backward spontaneous Raman scattering light with the temperature information is divided into anti-Stokes light and Stokes light through a wavelength division multiplexer, two light signals are converted into an anti-Stokes electric signal and a Stokes electric signal through an avalanche photodiode, the two electric signals are amplified through an amplifier, and then the anti-Stokes data and the Stokes data are obtained through a data acquisition card.
A method for noise reduction of a distributed optical fiber temperature measurement system based on binary SVD comprises the following steps:
(1) acquiring anti-Stokes signals and Stokes signals in an optical fiber temperature measuring system, acquiring anti-Stokes raw data and Stokes raw data, and respectively constructing a 2 gamma (L-1) -dimensional Hankel matrix, wherein L is the length of the raw data;
(2) performing singular value decomposition and reconstruction on the two Hankel matrixes respectively to form two matrixes subjected to noise reduction;
(21) singular value decomposition is carried out on the Hankel matrix to obtain a left singular matrix, a singular value diagonal matrix and a right singular matrix;
(22) reserving a first singular value of the singular value diagonal matrix, and setting other singular values to be 0 to form a new singular value diagonal matrix;
(23) reconstructing the left singular matrix, the right singular matrix and the new singular value diagonal matrix to form a new matrix, and marking the new matrix as a matrix after noise reduction;
(3) and for one matrix, acquiring noise reduction data from one noise-reduced matrix by the method that:
(31) respectively taking the data of the first row and the first column of the noise-reduced matrix and the data of the second row and the L-1 column of the noise-reduced matrix as the first data and the last data of the noise-reduced acquired data;
(32) and adding the data of the 1 st row and the ith column (i is 2,3, …, L-1) of the matrix subjected to noise reduction and the data of the 2 nd row and the ith column of the new matrix, and taking the average value as the ith data of the acquired data subjected to noise reduction.
(4) Obtaining a temperature measurement result according to the anti-Stokes noise reduction data and the Stokes noise reduction data, and specifically adopting the following method:
(41) sequentially obtaining the ratio of anti-Stokes signal acquisition data subjected to noise reduction at different temperatures to Stokes signal acquisition data subjected to noise reduction;
(42) obtaining a temperature measurement curve through curve fitting according to the ratio;
(43) and obtaining a temperature measurement result according to the temperature measurement curve.
(5) According to the temperature measurement result, three indexes of the temperature measurement result are calculated, wherein the three indexes are maximum deviation, root mean square error and smoothness, and the calculation method comprises the following steps:
maximum deviation:
in the formula (I), the compound is shown in the specification,
for the temperature measurement result obtained in step (4), TactIs a reference temperature measured by a mercury thermometer; n is the number of effective data of the measurement result;
the root mean square error is the root mean square error between the temperature measurement result and the reference temperature, and the smaller the value of the root mean square error is, the smaller the difference between the overall measurement result and the reference temperature is, and the root mean square error is represented as:
smoothness measures the fluctuation degree of the temperature measurement result, and the smaller the value, the smoother the temperature measurement curve is, the smaller the fluctuation of the measurement result is, and is expressed as:
(6) repeating the steps (2) to (5) until the three indexes under the current iteration number are all larger than the three indexes under the previous iteration number, wherein the iteration number at the moment is the maximum iteration number n, and stopping repeating;
(7) sorting the three indexes obtained by each iteration to obtain the bit order h (h is more than 0 and less than or equal to n) of the maximum deviation in the n iterations in sequence from large to small, the bit order k (k is more than 0 and less than or equal to n) of the root mean square error in the n iterations in sequence from large to small, and the bit order w (w is more than 0 and less than or equal to n) of the smoothness in the n iterations in sequence from large to small, wherein j is a positive integer and is more than 0 and less than or equal to n;
(8) calculating the result quality coefficient Q of j iterationjThe maximum resulting mass coefficient max { Q } is obtained for h + k + wj}＝QpWherein j is more than 0, p is less than or equal to n, and p is the optimal iteration number;
(9) and acquiring anti-Stokes noise reduction data and Stokes noise reduction data corresponding to the p iteration as best signals of the noise reduction effect.
Example 2: referring to fig. 1 to 13, it can be seen that the data acquired by us includes anti-Stokes raw data and Stokes raw data, and in steps (1) - (3), the processing method of the anti-Stokes raw data and the processing method of the Stokes raw data are completely the same. We take the anti-Stokes raw data obtained at an actual temperature of 45.2 ℃ as an example:
constructing anti-Stokes raw data into a 2 gamma (L-1) -dimensional Hankel matrix, wherein L is the length of the raw data;
then, performing singular value decomposition on the Hankel matrix to obtain a left singular matrix, a singular value diagonal matrix and a right singular matrix; reserving a first singular value of the singular value diagonal matrix, and setting other singular values to be 0 to form a new singular value diagonal matrix; reconstructing the left singular matrix, the right singular matrix and the new singular value diagonal matrix to form a new matrix, and marking the new matrix as a matrix after noise reduction; performing matrix reconstruction in the step (2), namely performing a binary SVD denoising process;
then, acquiring anti-Stokes noise reduction data from the matrix subjected to noise reduction again, wherein the processing method of the Stokes original data is the same as that of the anti-Stokes noise reduction data, and finally obtaining a group of Stokes noise reduction data;
demodulating a temperature measurement result according to anti-Stokes denoising data and Stokes denoising data, calculating three indexes of the temperature measurement result under the iteration according to the temperature measurement result, obtaining the maximum iteration times according to the claims 1 and 7, calculating a result quality coefficient under each iteration time, obtaining the optimal iteration times according to the result quality coefficient, obtaining data with the optimal denoising effect according to the optimal iteration times, and obtaining the temperature measurement result with the optimal three indexes according to the data with the optimal denoising effect.
The same principle is that: we repeated the above work at temperatures of 50.0 deg.C, 55.0 deg.C and 60.0 deg.C. Four different sets of measurements were obtained.
Referring to FIG. 4, a graph comparing raw data at 50.0 ℃ and the optimal temperature measurements obtained using the present invention; as can be seen from the figure, the temperature demodulation result of the temperature mutation part subjected to noise reduction by the binary SVD is more gradual than that of the original data.
Referring to fig. 5, fig. 5a, 5b, 5c, and 5d are graphs comparing noise reduction effects of several noise reduction methods at four temperatures; four lines are shown in each graph, which are the comparison of the original data, the wavelet hard threshold denoising, the wavelet soft threshold denoising, and the binary SVD denoising of the present invention.
From fig. 10 to fig. 13, it can be known that the three indexes of the processing result of the binary SVD method are all superior to the processing result of the wavelet threshold method.
In summary, compared with the results obtained by the temperature demodulation of the original data, the maximum deviation of the temperature measurement results of the method is respectively reduced by 1.59 ℃, 2.49 ℃, 1.22 ℃ and 0.87 ℃ at 45.2 ℃, 50.0 ℃, 55.0 ℃ and 60.0 ℃, the root mean square error is respectively reduced by 0.79, 0.95, 0.67 and 0.40, the smoothness degree of the curve is obviously improved, and the three indexes of the maximum deviation, the root mean square error and the smoothness degree of the curve are all superior to the results obtained by the noise reduction of the wavelet threshold method.
Claims (4)
1. A method for noise reduction of a distributed optical fiber temperature measurement system based on binary SVD is characterized by comprising the following steps: the method comprises the following steps:
(1) acquiring anti-Stokes signals and Stokes signals in an optical fiber temperature measuring system, acquiring anti-Stokes raw data and Stokes raw data, and respectively constructing a 2 gamma (L-1) -dimensional Hankel matrix, wherein L is the length of the raw data;
(2) performing singular value decomposition and reconstruction on the two Hankel matrixes respectively to form two matrixes subjected to noise reduction;
(21) singular value decomposition is carried out on the Hankel matrix to obtain a left singular matrix, a singular value diagonal matrix and a right singular matrix;
(22) reserving a first singular value of the singular value diagonal matrix, and setting other singular values to be 0 to form a new singular value diagonal matrix;
(23) reconstructing the left singular matrix, the right singular matrix and the new singular value diagonal matrix to form a new matrix, and marking the new matrix as a matrix after noise reduction;
(3) acquiring anti-Stokes data and Stokes data from the two de-noised matrixes again, and marking the anti-Stokes data and the Stokes data as anti-Stokes de-noising data and Stokes de-noising data;
(4) acquiring a temperature measurement result according to the anti-Stokes noise reduction data and the Stokes noise reduction data;
(5) calculating three indexes of the temperature measurement result according to the temperature measurement result, wherein the three indexes are maximum deviation, root mean square error and smoothness;
(6) performing singular value decomposition and reconstruction on the two noise-reduced matrixes obtained in the step (2) again to form a new noise-reduced matrix which is used as the input of the step (3); repeating the steps (3) - (5) until the three indexes under the current iteration number are all larger than the three indexes under the previous iteration number, wherein the iteration number at the moment is the maximum iteration number n, and stopping repeating;
(7) sorting the three indexes obtained by each iteration to obtain the bit order h (h is more than 0 and less than or equal to n) of the maximum deviation in the n iterations in sequence from large to small, the bit order k (k is more than 0 and less than or equal to n) of the root mean square error in the n iterations in sequence from large to small, and the bit order w (w is more than 0 and less than or equal to n) of the smoothness in the n iterations in sequence from large to small, wherein j is a positive integer and is more than 0 and less than or equal to n;
(8) calculating the result quality coefficient Q of j iterationjThe maximum resulting mass coefficient max { Q } is obtained for h + k + wj}＝QpWherein j is more than 0, p is less than or equal to n, and p is the optimal iteration number;
(9) and acquiring anti-Stokes noise reduction data and Stokes noise reduction data corresponding to the p iteration as best signals of the noise reduction effect.
2. The method for noise reduction of a distributed optical fiber temperature measurement system based on binary SVD of claim 1, wherein: and (3) acquiring noise reduction data from a noise-reduced matrix by the following steps:
(31) respectively taking the data of the first row and the first column of the noise-reduced matrix and the data of the second row and the L-1 th column of the noise-reduced matrix as the first data and the last data of the noise-reduced data;
(32) and adding the data of the ith row and the ith column (i is 2,3, …, L-1) of the matrix after noise reduction and the data of the ith row and the ith column of the matrix after noise reduction to obtain an average value, and taking the average value as the ith data of the noise reduction data.
3. The method for noise reduction of a distributed optical fiber temperature measurement system based on binary SVD of claim 1, wherein: the step (4) is specifically as follows:
(41) sequentially obtaining the ratio of anti-Stokes signal acquisition data subjected to noise reduction at different temperatures to Stokes signal acquisition data subjected to noise reduction;
(42) obtaining a temperature measurement curve through curve fitting according to the ratio;
(43) and obtaining a temperature measurement result according to the temperature measurement curve.
4. The method for noise reduction of a distributed optical fiber temperature measurement system based on binary SVD of claim 1, wherein: the three indexes in the step (5) are specifically as follows:
maximum deviation:
in the formula (I), the compound is shown in the specification,
for the temperature measurement result obtained in step (4), TactIs a reference temperature measured by a mercury thermometer; n is the number of effective data of the measurement result;
the root mean square error is the root mean square error between the temperature measurement result and the reference temperature, and the smaller the value of the root mean square error is, the smaller the difference between the overall measurement result and the reference temperature is, and the root mean square error is represented as:
smoothness measures the fluctuation degree of the temperature measurement result, and the smaller the value, the smoother the temperature measurement curve is, the smaller the fluctuation of the measurement result is, and is expressed as:
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