CN114330445A - Wavelet threshold denoising method based on transformer vibration signal sensitive IMF - Google Patents
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Abstract
The invention discloses a wavelet threshold denoising method based on transformer vibration signal sensitive IMF, relating to the technical field of transformer signal processing; the method of the invention comprises the following steps: and carrying out VMD decomposition on the transformer body vibration signal after the band-pass filtering, and screening out the sensitive IMF by using the sensitive factors of each IMF component. The method is characterized in that a wavelet threshold method is adopted to perform denoising processing on non-sensitive IMF components, and an improved wavelet threshold function is utilized to perform threshold processing on wavelet coefficients, so that the denoising capability of the wavelet threshold method is improved, noise interference is reduced, and more effective information of original vibration signals of the transformer is reserved. The wavelet threshold denoising method based on the transformer vibration signal sensitive IMF effectively improves the denoising capability of the transformer body vibration signal denoising method, improves the denoising efficiency, and meanwhile retains effective information in original signals.
Description
Technical Field
The invention relates to the technical field of transformer signal processing, in particular to a wavelet threshold denoising method based on transformer vibration signal sensitive IMF.
Background
The power transformer is an important device in the power system, and the operation reliability of the power transformer is directly related to the safety and stability of the whole power system. In the running process of the transformer, faults can occur inevitably, the faults can be found and eliminated as soon as possible, and the method has important significance for improving the running safety of the transformer.
The existing transformer fault detection methods include a vibration signal detection method, an infrared imaging monitoring method, an ultrasonic detection method and the like. Wherein the vibration signal detection is widely applied because of the advantages of no direct contact with the power system, easy acquisition, no influence on the normal operation of the whole power system, sensitive response to the defects of the mechanical structure and the like,
however, the vibration sensor collects the sound signals of the running state of the transformer and also has environmental noise, so that effective running state information is submerged in various interferences and effective subsequent processing is difficult to perform. Therefore, how to effectively extract the vibration signal of the transformer becomes the key for accurately judging the fault of the transformer in the follow-up process.
The vibration analysis method analyzes the vibration signal of the transformer body and monitors the mechanical states of the transformer iron core, the winding and the like. The vibration signal of the normal operation transformer body is mainly concentrated in a low frequency band, 100Hz is used as a fundamental frequency, and rich high-order harmonics are contained. However, the noise background of the transformer working site is complex, and the monitored data can be mixed with various noises, wherein other interference noises below 50Hz, small noises above 1000Hz and white noises are taken as main noises. The interference of these noises can reduce the effectiveness of the signal and affect the analysis of the vibration signal.
Therefore, there is a need for an effective method for reducing noise interference in the vibration signal of the transformer body.
Disclosure of Invention
In order to solve the above problems, the present invention provides a wavelet threshold denoising method based on transformer vibration signal sensitive IMF.
In order to achieve the purpose, the invention is realized by the following technical scheme:
a wavelet threshold denoising method based on transformer vibration signal sensitive IMF comprises the following steps:
step A: VMD decomposition is carried out on the transformer body vibration signal subjected to median filtering, the sensitive factor of each IMF component is calculated, and the sensitive IMF components are screened by utilizing the sensitive factor;
and B: improving a wavelet threshold function, and denoising the screened non-sensitive IMF component by using the improved wavelet threshold function; and combining and reconstructing the sensitive IMF component and the denoised non-sensitive IMF component to obtain a complete denoised signal.
A wavelet threshold denoising method based on transformer vibration signal sensitive IMF specifically comprises the following steps:
inputting an original signal s (t) into a band-pass filter, and filtering interference signals below 50Hz and above 1000Hz to obtain a filtered signal s' (t);
decomposing the filtered vibration signal s' (t) into k IMF components by using a VMD algorithm;
thirdly, calculating a sensitive factor, and screening out a sensitive IMF component, wherein the sensitive IMF component specifically comprises the following steps:
calculating a correlation coefficient Cf between each IMF component and the filtered vibration signal s' (t)i；
In the formula, mui、σiRespectively, the ith IMF component xi(t) mean and standard deviation; μ and σ are the mean and standard deviation, respectively, of the filtered vibration signal s' (t);
② calculating the sensitivity factor Sf of each IMF componenti。
Selecting sensitive IMF component.
According to the sensitivity factor Sf calculated in (2)iSequencing IMF from large to small to obtain a new IMF sequence and a sensitive factor sequence (Sf)i' }, calculating the difference d between the sensitivity factors of two adjacent IMFsiAnd the subscript corresponding to the maximum difference is i, the first i IMFs are the screened sensitive IMF components.
di＝Sfi'-Sfi+1' (3)
Fourthly, denoising the screened (k-i) non-sensitive IMF components by utilizing an improved wavelet threshold function, and specifically comprises the following steps:
a, selecting a proper wavelet basis function, determining the number m of decomposition layers to decompose (k-i) non-sensitive IMF components respectively, and obtaining respective wavelet decomposition coefficients w;
b, constructing an improved wavelet threshold function as shown in a formula (4), and determining the optimal value of a parameter n of the improved wavelet threshold function;
wherein w is the wavelet decomposition coefficient obtained in the step one,
the value range of the wavelet coefficient and the parameter n after the wavelet coefficient is processed by the threshold function (4) is (0, ∞).
c, solving a wavelet threshold lambda in the formula (4) by adopting a self-adaptive unified threshold method, and performing threshold processing on the wavelet coefficient by using the formula (4), wherein the wavelet threshold solving formula is as follows:
in the formula, m is the number of decomposition layers, N is the signal length, and σ is the standard deviation of the noise signal, and the solving formula is:
where madian (·) is the median function, w1,allAll wavelet coefficients of the first layer, 0.6754 is an adjustment coefficient.
And d, performing signal reconstruction by using the wavelet coefficient subjected to wavelet threshold processing to obtain (k-i) denoising signals.
Fifthly, combining and reconstructing i sensitive IMF components in the third step and (k-i) denoised non-sensitive IMF components in the fourth step to obtain a complete denoised signal
Compared with the prior art, the invention has the following advantages:
the wavelet threshold denoising method based on the transformer vibration signal sensitive IMF screens a sensitive Intrinsic Mode Function (IMF) through Variable Modal Decomposition (VMD), utilizes an improved wavelet threshold method to denoise a non-sensitive IMF component, and reduces noise interference in a transformer body vibration signal. Aiming at the problems of incomplete denoising, noise residue, oscillation and the like existing in the original wavelet threshold denoising, the method improves the threshold function, not only retains the advantages of small mean square error of a hard threshold function and smooth processing of a soft threshold function in the traditional wavelet threshold, but also overcomes the defects of discontinuity of the hard threshold function and deviation of the soft threshold function.
The wavelet threshold denoising method based on the transformer vibration signal sensitive IMF adopts a dynamic selection mode in wavelet threshold selection. Because the wavelet coefficient of noise decreases with increasing scale, when de-noising a signal, the thresholds of different decomposition layers should be selected differently, and the thresholds should decrease with increasing decomposition scale. The threshold selection mode used by the invention enables the threshold to be changed along with the decomposition scale, and the threshold is correspondingly reduced when the decomposition scale is larger, so that the fact that the coefficients of different decomposition layers after wavelet decomposition are different in the proportion distribution of signals and noise is relatively met, the practicability of the threshold can be increased, and the deviation caused by wavelet coefficient threshold error breakage is reduced.
The invention discloses a wavelet threshold denoising method based on transformer vibration signal sensitive IMF, aiming at the interference noise components in the transformer body vibration signal: the method combines three denoising methods, namely band-pass filtering, VMD decomposition and improved wavelet threshold denoising, and effectively improves the denoising capability of the transformer body vibration signal denoising method, improves the denoising efficiency, and simultaneously retains effective information in original signals.
Drawings
FIG. 1 is a schematic diagram of an improved threshold function compared to a conventional threshold function;
FIG. 2 is a flow chart of a wavelet threshold denoising method based on transformer vibration signal sensitive IMF;
FIG. 3 is a time domain waveform of the filtered signal s' (t);
FIG. 4 is a signal s' (t) VMD decomposition;
FIG. 5 is an IMF4 waveform after wavelet threshold denoising;
FIG. 6 shows a signal after wavelet threshold denoising based on sensitive IMF
FIG. 7 is a time domain waveform of the filtered signal x' (t);
FIG. 8 shows a signal after wavelet threshold denoising based on sensitive IMF
Detailed Description
The invention aims to provide a wavelet threshold denoising method based on transformer vibration signal sensitive IMF, which is realized by the following technical scheme:
a wavelet threshold denoising method based on transformer vibration signal sensitive IMF comprises the following steps:
inputting an original signal s (t) into a band-pass filter, and filtering interference signals below 50Hz and above 1000Hz to obtain a filtered signal s' (t);
decomposing the filtered vibration signal s' (t) into k IMF components by using a VMD algorithm;
thirdly, calculating a sensitive factor, and screening out a sensitive IMF component, wherein the sensitive IMF component specifically comprises the following steps:
calculating a correlation coefficient Cf between each IMF component and the filtered vibration signal s' (t)i；
In the formula, mui、σiRespectively, the ith IMF component xi(t) mean and standard deviation; μ and σ are the mean and standard deviation, respectively, of the filtered vibration signal s' (t);
② calculating the sensitivity factor Sf of each IMF componenti。
Selecting sensitive IMF component.
According to the sensitivity factor Sf calculated in (2)iSequencing IMF from large to small to obtain a new IMF sequence and a sensitive factor sequence (Sf)i' }, calculating the difference d between the sensitivity factors of two adjacent IMFsiAnd the subscript corresponding to the maximum difference is i, the first i IMFs are the screened sensitive IMF components.
di＝Sfi'-Sfi+1' (3)
Fourthly, denoising the screened (k-i) non-sensitive IMF components by utilizing an improved wavelet threshold function, and specifically comprises the following steps:
a, selecting a proper wavelet basis function, determining the number m of decomposition layers to decompose (k-i) non-sensitive IMF components respectively, and obtaining respective wavelet decomposition coefficients w;
b, constructing an improved wavelet threshold function as shown in a formula (4), and determining the optimal value of a parameter n of the improved wavelet threshold function;
wherein w is the wavelet decomposition coefficient obtained in the step one,
the value range of the wavelet coefficient and the parameter n after the wavelet coefficient is processed by the threshold function (4) is (0, ∞).
c, solving a wavelet threshold lambda in the formula (4) by adopting a self-adaptive unified threshold method, and performing threshold processing on the wavelet coefficient by using the formula (4), wherein the wavelet threshold solving formula is as follows:
in the formula, m is the number of decomposition layers, N is the signal length, and σ is the standard deviation of the noise signal, and the solving formula is:
where madian (·) is the median function, w1,allAll wavelet coefficients of the first layer, 0.6754 is an adjustment coefficient.
And d, performing signal reconstruction by using the wavelet coefficient subjected to wavelet threshold processing to obtain (k-i) denoising signals.
Fifthly, combining and reconstructing i sensitive IMF components in the third step and (k-i) denoised non-sensitive IMF components in the fourth step to obtain a complete denoised signal
In the traditional wavelet threshold denoising, due to the properties of discontinuity and large variance of a hard threshold function (formula 7), the problem of denoised signal oscillation can occur, and the problem of low similarity between a soft threshold (formula 8) denoised signal and an original signal is solved, and an improved threshold function is provided, as shown in formula (4).
For the improvement threshold function (4):
from equation (9), the modified threshold function is continuous at λ, i.e. the modified threshold function is continuous within its domain, overcoming the disadvantage of discontinuous hard threshold function. As can be seen from equation (10), as w gradually increases and approaches positive infinity, the improved threshold function value approaches the original wavelet coefficient infinitely, and the deviation from the true coefficient is reduced. Comparison of the three threshold functions, as shown in FIG. 1.
The invention is further described with reference to specific examples.
Example 1
A wavelet threshold denoising method based on transformer vibration signal sensitive IMF is disclosed, the flow of the method is shown in FIG. 2, and the method comprises the following steps:
firstly, inputting an original signal s (t) into a band-pass filter, filtering out interference signals below 50Hz and above 1000Hz, and obtaining a filtered signal s' (t), wherein the time domain waveform of the filtered signal is shown in fig. 3.
Secondly, the VMD algorithm is used to decompose the filtered vibration signal s' (t) into 10 IMF components, as shown in fig. 4.
Thirdly, calculating a sensitive factor, and screening out a sensitive IMF component, and the specific steps are as follows:
according toEquation (1) calculates a correlation coefficient Cf between each IMF component and the filtered vibration signal x' (t)i。
In the formula, mui、σiRespectively, the ith IMF component xi(t) mean and standard deviation; μ and σ are the mean and standard deviation, respectively, of the filtered vibration signal s' (t).
Secondly, calculating the sensitivity factor Sf of each IMF component according to the formula (2)iThe results are shown in Table 1.
TABLE 1 sensitivity factor for each IMF component
| IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | IMF8 | IMF9 | IMF10 | |
| Sf | 1 | 0.8599 | 0.4451 | 0.0242 | 0.01 | 0.0081 | 0.0041 | 0.0037 | 0.0007 | 0 |
Selecting sensitive IMF component.
According to the sensitivity factor Sf calculated in 2iSequencing IMF from large to small to obtain a new IMF sequence and a sensitive factor sequence (Sf)i' }, calculating the difference d between the sensitivity factors of two adjacent IMFsiAs shown in table 2. The subscript corresponding to the maximum difference is 3, then the first 3 IMFs are the screened-out sensitive IMF components.
TABLE 2 difference between sensitivity factors of two adjacent IMFs
| d1 | d2 | d3 | d4 | d5 | d6 | d7 | d8 | d9 |
| 0.1401 | 0.4148 | 0.4209 | 0.0142 | 0.019 | 0.0040 | 0.0004 | 0.0029 | 0.0007 |
Fourthly, denoising the screened 7 non-sensitive IMF components by utilizing an improved wavelet threshold function, and specifically comprises the following steps:
selecting a wavelet basis function coif5, decomposing 5 layers, and decomposing 7 non-sensitive IMF components respectively to obtain respective wavelet decomposition coefficients wi(i＝1,2...5)。
Taking IMF4 as an example to show a specific process, calculating a standard deviation of a noise signal according to equation (5):
the wavelet threshold calculation result is:
and constructing an improved wavelet threshold function, wherein the parameter n is 8, and as shown in formula (11), processing the wavelet coefficient after IMF4 wavelet decomposition by using a wavelet threshold.
Thirdly, signal reconstruction is carried out by using the wavelet coefficient after wavelet threshold processing, and IMF4 after wavelet threshold denoising is obtained, as shown in FIG. 5.
Fourthly, after the same processing is carried out on other 6 IMF components, the IMF components and the 3 sensitive IMF components in the third step are combined and reconstructed to obtain a complete de-noising signal
As shown in fig. 6.
In order to further prove the denoising effect of the invention, the denoising effect of the improved threshold function of the invention is compared and evaluated with the denoising effect of the traditional soft threshold function and the traditional hard threshold function. Evaluation indexes selected signal-to-noise ratio (SNR), Root Mean Square Error (RMSE), and signal correlation Coefficient (COR), and the comparison results are shown in table 3.
TABLE 3 comparative evaluation result table of evaluation indexes
According to the evaluation indexes in table 3, the denoising effect of the denoising algorithm provided by the invention is obviously superior to that of the conventional wavelet threshold denoising, and the reduction degree of the effective information of the original signal is higher.
Example 2
A wavelet threshold denoising method based on transformer vibration signal sensitive IMF is disclosed, the flow of the method is shown in FIG. 2, and the method comprises the following steps:
firstly, inputting an original signal x (t) into a band-pass filter, filtering out interference signals below 50Hz and above 1000Hz, and obtaining a filtered signal x' (t), wherein the time domain waveform of the filtered signal is shown in fig. 7.
And secondly, decomposing the filtered vibration signal x' (t) into 6 IMF components by utilizing a VMD algorithm.
Thirdly, calculating a sensitive factor, and screening out a sensitive IMF component, and the specific steps are as follows:
calculating a correlation coefficient Cf between each IMF component and the filtered vibration signal x' (t) according to equation (1)i。
In the formula, mui、σiRespectively, the ith IMF component xi(t) mean and standard deviation; μ and σ are the mean and standard deviation, respectively, of the filtered vibration signal s' (t).
Calculating the sensitivity factor Sf of each IMF component according to the formula (2)i。
Sensitivity factor Sf calculated according to equation (2)iSequencing IMF from large to small to obtain a new IMF sequence and a sensitive factor sequence (Sf)i' }, calculating the difference d between the sensitivity factors of two adjacent IMFsi. The subscript corresponding to the maximum difference is 2, then the first 2 IMFs are the screened-out sensitive IMF components.
Fourthly, denoising the screened 4 non-sensitive IMF components by utilizing an improved wavelet threshold function, and specifically comprises the following steps:
selecting a wavelet basis function coif5, decomposing the 4 non-sensitive IMF components with 10 decomposition layers respectively to obtain respective wavelet decomposition coefficients wi(i＝1,2...10)。
And (5) calculating the standard deviation of the noise signal according to the formula (5) to obtain a wavelet threshold calculation result.
Wherein m is the number of decomposition layers, N is the signal length, and sigma is the standard deviation of the noise signal;
and constructing an improved wavelet threshold function, wherein the parameter n is 4, and processing the wavelet coefficients after IMF4 wavelet decomposition by using a wavelet threshold. And performing signal reconstruction by using the wavelet coefficient subjected to wavelet threshold processing to obtain an IMF component subjected to wavelet threshold denoising.
The combined reconstruction is carried out with 2 sensitive IMF components in the third step to obtain a complete de-noising signal
As shown in fig. 8.
As can be seen from the comparison between FIG. 7 and FIG. 8, the denoising algorithm provided by the present invention has a good denoising effect.
Claims (4)
1. A wavelet threshold denoising method based on transformer vibration signal sensitive IMF is characterized by comprising the following steps: the method comprises the following steps:
step A: VMD decomposition is carried out on the transformer body vibration signal subjected to median filtering, the sensitive factor of each IMF component is calculated, and the sensitive IMF components are screened by utilizing the sensitive factor;
and B: improving a wavelet threshold function, and denoising the screened non-sensitive IMF component by using the improved wavelet threshold function; and combining and reconstructing the sensitive IMF component and the denoised non-sensitive IMF component to obtain a complete denoised signal.
2. The wavelet threshold denoising method based on transformer vibration signal sensitive IMF as claimed in claim 1, wherein: the step A comprises the following steps:
inputting an original signal s (t) into a band-pass filter, and filtering interference signals below 50Hz and above 1000Hz to obtain a filtered signal s' (t);
decomposing the filtered vibration signal s' (t) into k IMF components by using a VMD algorithm;
thirdly, calculating a sensitive factor, and screening out a sensitive IMF component, wherein the sensitive IMF component specifically comprises the following steps:
calculating a correlation coefficient Cf between each IMF component and the filtered vibration signal s' (t)i；
In the formula, mui、σiRespectively, the ith IMF component xi(t) mean and standard deviation; μ and σ are the mean and standard deviation, respectively, of the filtered vibration signal s' (t);
② calculating the sensitivity factor Sf of each IMF componenti：
Selecting sensitive IMF component:
according to the sensitivity factor Sf calculated in (2)iSequencing IMF from large to small to obtain a new IMF sequence and a sensitive factor sequence (Sf)i' }, calculating the difference d between the sensitivity factors of two adjacent IMFsiAnd the subscript corresponding to the maximum difference is i, then the first i IMFs are the screened sensitive IMF components:
di＝Sfi'-Sfi+1' (3)。
3. the wavelet threshold denoising method based on transformer vibration signal sensitive IMF as claimed in claim 1, wherein: the step B comprises the following steps:
denoising the screened (k-i) non-sensitive IMF components by using an improved wavelet threshold function, and specifically comprising the following steps:
a, selecting a proper wavelet basis function, determining the number m of decomposition layers to decompose (k-i) non-sensitive IMF components respectively, and obtaining respective wavelet decomposition coefficients w;
b, constructing an improved wavelet threshold function as shown in a formula (4), and determining the optimal value of a parameter n of the improved wavelet threshold function;
wherein w is the wavelet decomposition coefficient obtained in the step one,
the value range of the wavelet coefficient and the parameter n after the wavelet coefficient and the parameter n are processed by the threshold function (4) is (0, ∞);
c, performing signal reconstruction by using the wavelet coefficient subjected to wavelet threshold processing to obtain (k-i) denoising signals;
d, performing signal reconstruction by using the wavelet coefficient subjected to wavelet threshold processing to obtain (k-i) denoising signals;
then, combining and reconstructing the screened i sensitive IMF components and the (k-i) denoised non-sensitive IMF components to obtain a complete denoising signal
4. The wavelet threshold denoising method based on transformer vibration signal sensitive IMF as claimed in claim 3, wherein: c, performing signal reconstruction by using the wavelet coefficient subjected to wavelet threshold processing to obtain (k-i) denoising signals, specifically comprising the following steps:
solving a wavelet threshold lambda in the formula (4) by adopting a self-adaptive unified threshold method, and performing threshold processing on the wavelet coefficient by using the formula (4), wherein the wavelet threshold solving formula is as follows:
in the formula, m is the number of decomposition layers, N is the signal length, and σ is the standard deviation of the noise signal, and the solving formula is:
where madian (·) is the median function, w1,allAll wavelet coefficients of the first layer, 0.6754 is an adjustment coefficient.
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| CN117786333A (en) * | 2024-01-08 | 2024-03-29 | 江苏省家禽科学研究所 | Broiler chicken breeding behavior data acquisition device |
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| CN117332221A (en) * | 2023-09-26 | 2024-01-02 | 国网江苏省电力有限公司南通供电分公司 | Noise reduction method and system for oil leakage ultrasonic signals of hydraulic mechanism |
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