CN114330445A - Wavelet threshold denoising method based on transformer vibration signal sensitive IMF - Google Patents

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

A Wavelet Threshold Denoising Method Based on Sensitive IMF of Transformer Vibration Signal

technical field

The invention relates to the technical field of transformer signal processing, in particular to a wavelet threshold denoising method based on a transformer vibration signal sensitive IMF.

Background technique

Power transformer is an important equipment in the power system, and its operational reliability is directly related to the safety and stability of the entire power system. In the process of transformer operation, faults will inevitably occur, and early detection and elimination of faults are of great significance to improve the operational safety of transformers.

Existing transformer fault detection methods include vibration signal detection method, infrared imaging monitoring method and ultrasonic detection method. Among them, vibration signal detection is widely used because it has no direct contact with the power system, is easy to collect, has no impact on the normal operation of the entire power system, and is sensitive to mechanical structural defects.

However, in addition to the acoustic signal of the transformer operating state collected by the vibration sensor, there is also environmental noise, which makes the effective operating state information submerged in various disturbances, and it is difficult to carry out effective follow-up processing. Therefore, how to effectively extract the transformer vibration signal becomes the key to correctly judge the transformer fault in the future.

The vibration analysis method monitors the mechanical state of the transformer core and windings by analyzing the vibration signal of the transformer body. The vibration signal of the transformer body in normal operation is mainly concentrated in the low frequency band, with 100Hz as the fundamental frequency, and contains rich high-order harmonics. However, the noise background of the transformer work site is complex, and the monitored data will be mixed with various noises, among which other interference noises below 50Hz, a small amount of noise above 1000Hz and white noise are the main ones. The interference of these noises can reduce the validity of the signal and affect the analysis of the vibration signal.

Therefore, there is an urgent need for an effective method for reducing the noise interference in the vibration signal of the transformer body.

SUMMARY OF THE INVENTION

In order to solve the above problems, the purpose of the present invention is to provide a wavelet threshold denoising method based on the sensitive IMF of the transformer vibration signal.

The present invention is achieved by the following technical solutions in order to achieve the above object:

A wavelet threshold denoising method based on sensitive IMF of transformer vibration signal, comprising the following steps:

Step A: perform VMD decomposition on the vibration signal of the transformer body after median filtering, calculate the sensitive factor of each IMF component, and use the sensitive factor to screen the sensitive IMF component;

Step B: Improve the wavelet threshold function, and use the improved wavelet threshold function to denoise the selected insensitive IMF components; combine and reconstruct the sensitive IMF components and the denoised insensitive IMF components to obtain a complete denoised signal.

A wavelet threshold denoising method based on the sensitive IMF of transformer vibration signal, which specifically includes the following steps:

1. Input the original signal s(t) into the band-pass filter, filter out the interference signal below 50Hz and above 1000Hz, and obtain the filtered signal s'(t);

2. Use VMD algorithm to decompose the filtered vibration signal s'(t) into k IMF components;

3. Calculate sensitive factors and screen out sensitive IMF components, including:

① Calculate the correlation coefficient Cf _i between each IMF component and the filtered vibration signal s'(t);

where μ _i and σ _i are the mean and standard deviation of the i-th IMF component x _i (t), respectively; μ and σ are the mean and standard deviation of the filtered vibration signal s'(t), respectively;

② Calculate the sensitivity factor _Sfi of each IMF component.

③Select the sensitive IMF component.

According to the sensitive factors Sfi calculated in (2), sort the IMFs from large to small to obtain a new IMF sequence and a sensitive factor sequence {Sf _i '}, and calculate the difference d _i of the sensitive factors of two adjacent IMFs _, corresponding to The subscript of the largest difference is i, then the first i IMFs are the selected sensitive IMF components.

d _i =Sf _i '-Sf _i+1 ' (3)

4. Use the improved wavelet threshold function to denoise the (k-i) non-sensitive IMF components selected. The specific steps are as follows:

a Select the appropriate wavelet basis function, determine the decomposition level m to decompose the (k-i) insensitive IMF components respectively, and obtain their respective wavelet decomposition coefficients w;

b Construct an improved wavelet threshold function, as shown in formula (4), and determine the optimal value of its parameter n;

经过阈值函数(4)处理后的小波系数，参数n，取值范围为(0,∞)。In the formula, w is the wavelet decomposition coefficient obtained in step 1,

The wavelet coefficient processed by the threshold function (4), the parameter n, the value range is (0, ∞).

c Use the adaptive unified threshold method to solve the wavelet threshold λ in the formula (4), and use the formula (4) to perform threshold processing on the wavelet coefficients. The wavelet threshold solution formula is:

In the formula, m is the number of decomposition layers, N is the signal length, σ is the standard deviation of the noise signal, and the solution formula is:

In the formula, madian( ) is the median function, w _1,all is all the wavelet coefficients of the first layer, and 0.6754 is the adjustment coefficient.

d Use the wavelet coefficients processed by the wavelet threshold to reconstruct the signal to obtain (k-i) denoised signals.

5. Combine and reconstruct the i sensitive IMF components in step 3 and the (ki) denoised non-sensitive IMF components in step 4 to obtain a complete denoised signal

Compared with the prior art, the present invention has the following advantages:

A wavelet threshold denoising method based on the sensitive IMF of the transformer vibration signal of the present invention, the sensitive intrinsic mode function (IMF) is screened through variational modal decomposition (Variational Modal Decomposition, VMD), and the improved wavelet threshold is used. The non-sensitive IMF component is denoised by the method to reduce the noise interference in the vibration signal of the transformer body. Aiming at the problems of incomplete denoising, residual noise and oscillation in the original wavelet threshold denoising, the present invention improves the threshold function, which not only retains the small mean square error of the hard threshold function and the smooth processing of the soft threshold function in the traditional wavelet threshold. It also overcomes the shortcomings of discontinuous hard threshold function and deviation of soft threshold function.

A wavelet threshold denoising method based on the sensitive IMF of the transformer vibration signal of the present invention adopts a dynamic selection method in the selection of the wavelet threshold. Because the wavelet coefficient of the noise decreases with the increase of the scale, when denoising the signal, the selection of the threshold value of different decomposition layers should also be different, and the threshold value should decrease with the increase of the decomposition scale. The threshold selection method used in the present invention makes the threshold change with the decomposition scale, and the larger the decomposition scale, the corresponding reduction of the threshold, which is more in line with the coefficients of different decomposition layers after wavelet decomposition. The fact that the difference is different can increase the practicability of the threshold and reduce the deviation caused by the false thresholding of the wavelet coefficients.

The wavelet threshold denoising method based on the sensitive IMF of the transformer vibration signal of the present invention is aimed at the components of the interference noise in the vibration signal of the transformer body: the low frequency noise lower than 50Hz, the high frequency noise higher than 1000Hz and the white noise. The combination of three denoising methods, filtering, VMD decomposition and improved wavelet threshold denoising, can effectively improve the noise reduction ability of the vibration signal denoising method of the transformer body, improve the denoising efficiency, and at the same time retain the effective information in the original signal.

Description of drawings

Fig. 1 is the contrast schematic diagram of improved threshold function and traditional threshold function;

Fig. 2 is a kind of wavelet threshold denoising method flow chart based on sensitive IMF of transformer vibration signal;

Figure 3 is the time domain waveform of the filtered signal s'(t);

Fig. 4 is signal s'(t) VMD decomposition;

Figure 5 is the IMF4 waveform after wavelet threshold denoising;

Figure 6 is the signal after wavelet threshold denoising based on sensitive IMF

Fig. 7 is the time-domain waveform of the filtered signal x'(t);

Figure 8 is the signal after wavelet threshold denoising based on sensitive IMF

Detailed ways

The object of the present invention is to provide a kind of wavelet threshold denoising method based on the sensitive IMF of transformer vibration signal, which is realized by the following technical solutions:

A wavelet threshold denoising method based on sensitive IMF of transformer vibration signal, comprising the following steps:

1. Input the original signal s(t) into the band-pass filter, filter out the interference signal below 50Hz and above 1000Hz, and obtain the filtered signal s'(t);

2. Use VMD algorithm to decompose the filtered vibration signal s'(t) into k IMF components;

3. Calculate sensitive factors and screen out sensitive IMF components, including:

① Calculate the correlation coefficient Cf _i between each IMF component and the filtered vibration signal s'(t);

where μ _i and σ _i are the mean and standard deviation of the i-th IMF component x _i (t), respectively; μ and σ are the mean and standard deviation of the filtered vibration signal s'(t), respectively;

② Calculate the sensitivity factor _Sfi of each IMF component.

③Select the sensitive IMF component.

According to the sensitive factors Sfi calculated in (2), sort the IMFs from large to small to obtain a new IMF sequence and a sensitive factor sequence {Sf _i '}, and calculate the difference d _i of the sensitive factors of two adjacent IMFs _, corresponding to The subscript of the largest difference is i, then the first i IMFs are the selected sensitive IMF components.

d _i =Sf _i '-Sf _i+1 ' (3)

4. Use the improved wavelet threshold function to denoise the (k-i) non-sensitive IMF components selected. The specific steps are as follows:

a Select the appropriate wavelet basis function, determine the decomposition level m to decompose the (k-i) insensitive IMF components respectively, and obtain their respective wavelet decomposition coefficients w;

b Construct an improved wavelet threshold function, as shown in formula (4), and determine the optimal value of its parameter n;

经过阈值函数(4)处理后的小波系数，参数n，取值范围为(0,∞)。In the formula, w is the wavelet decomposition coefficient obtained in step 1,

The wavelet coefficient processed by the threshold function (4), the parameter n, the value range is (0, ∞).

c Use the adaptive unified threshold method to solve the wavelet threshold λ in the formula (4), and use the formula (4) to perform threshold processing on the wavelet coefficients. The wavelet threshold solution formula is:

In the formula, m is the number of decomposition layers, N is the signal length, σ is the standard deviation of the noise signal, and the solution formula is:

In the formula, madian( ) is the median function, w _1,all is all the wavelet coefficients of the first layer, and 0.6754 is the adjustment coefficient.

d Use the wavelet coefficients processed by the wavelet threshold to reconstruct the signal to obtain (k-i) denoised signals.

5. Combine and reconstruct the i sensitive IMF components in step 3 and the (ki) denoised non-sensitive IMF components in step 4 to obtain a complete denoised signal

In traditional wavelet threshold denoising, due to the discontinuous and large variance of the hard threshold function (Equation 7), the denoising signal oscillation problem will occur, while the soft threshold (Equation 8) denoising signal has a low similarity to the original signal, An improved threshold function is proposed, as shown in equation (4).

For the improved threshold function (4):

It can be seen from equation (9) that the improved threshold function is continuous at λ, that is, the improved threshold function is continuous in its definition domain, which overcomes the discontinuity of the hard threshold function. It can be seen from equation (10) that as w increases gradually and approaches positive infinity, the value of the improved threshold function infinitely approaches the original wavelet coefficient, reducing the deviation from the true coefficient. The comparison of the three threshold functions is shown in Figure 1.

The present invention will be further described below in conjunction with specific embodiments.

Example 1

A wavelet threshold denoising method based on the sensitive IMF of transformer vibration signal, the method flow is shown in Figure 2, including the following steps:

1. Input the original signal s(t) into the band-pass filter, filter out the interference signal below 50Hz and above 1000Hz, and obtain the filtered signal s'(t), whose time domain waveform is shown in Figure 3.

2. Using the VMD algorithm to decompose the filtered vibration signal s'(t) into 10 IMF components, as shown in Figure 4.

3. Calculate the sensitivity factor and filter out the sensitive IMF components. The specific steps are as follows:

① Calculate the correlation coefficient Cf _i between each IMF component and the filtered vibration signal x'(t) according to formula (1).

In the formula, μ _i and σ _i are the mean and standard deviation of the i-th IMF component x _i (t), respectively; μ and σ are the mean and standard deviation of the filtered vibration signal s'(t).

② Calculate the sensitivity factor _Sfi of each IMF component according to formula (2). The results are shown in Table 1.

Table 1 Sensitivity factors of 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

③Select the sensitive IMF component.

Sort the IMFs from large to small according to the sensitive factors Sfi calculated in 2, obtain a new IMF sequence and a sensitive factor sequence {Sf _i '}, and calculate the difference d _i of the sensitive factors of two adjacent IMFs _, as shown in Table 2. Show. The subscript corresponding to the maximum difference is 3, and the first three IMFs are the selected sensitive IMF components.

Table 2 The difference between the 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

4. Use the improved wavelet threshold function to denoise the 7 non-sensitive IMF components screened out. The specific steps are as follows:

The wavelet basis function coif5 is selected, the number of decomposition layers is 5, and the 7 non-sensitive IMF components are decomposed respectively to obtain their respective wavelet decomposition coefficients w _i (i=1, 2...5).

① Take IMF4 as an example to show the specific process, and calculate the standard deviation of the noise signal according to formula (5):

Then the wavelet threshold calculation result is:

②Construct an improved wavelet threshold function, whose parameter n=8, as shown in formula (11), use the wavelet threshold to process the wavelet coefficients after IMF4 wavelet decomposition.

③Use the wavelet coefficients processed by the wavelet threshold to reconstruct the signal, and obtain the IMF4 after denoising by the wavelet threshold, as shown in Figure 5.

如图6所示。④ After the other 6 IMF components are processed in the same way, they are combined with the 3 sensitive IMF components in step 3 to reconstruct to obtain a complete denoising signal.

As shown in Figure 6.

In order to further prove the denoising effect of the present invention, the denoising effects of the improved threshold function of the present invention and the traditional soft threshold function and hard threshold function are compared and evaluated. The evaluation indicators select signal-to-noise ratio (SNR), root mean square error (RMSE) and signal correlation coefficient (COR). The comparison results are shown in Table 3.

Table 3 Comparative evaluation results of evaluation indicators

According to the evaluation indicators in Table 3, the denoising effect of the denoising algorithm proposed by the present invention is obviously better than that of the traditional wavelet threshold denoising, and the degree of restoration of the effective information of the original signal is higher.

Example 2

A wavelet threshold denoising method based on the sensitive IMF of transformer vibration signal, the method flow is shown in Figure 2, including the following steps:

1. Input the original signal x(t) into the band-pass filter, filter out the interference signals below 50Hz and above 1000Hz, and obtain the filtered signal x'(t). Its time domain waveform is shown in Figure 7.

Second, use VMD algorithm to decompose the filtered vibration signal x'(t) into 6 IMF components.

3. Calculate the sensitivity factor and filter out the sensitive IMF components. The specific steps are as follows:

The correlation coefficient Cf _i between each IMF component and the filtered vibration signal x'(t) is calculated according to equation (1).

In the formula, μ _i and σ _i are the mean and standard deviation of the i-th IMF component x _i (t), respectively; μ and σ are the mean and standard deviation of the filtered vibration signal s'(t).

The sensitivity factor Sf _i of each IMF component is calculated according to formula (2).

According to the sensitivity factor Sfi calculated in formula (2), sort the IMFs from large to small, obtain a new IMF sequence and a sensitive factor sequence {Sf _i '}, and calculate the difference d _i of the sensitive factors of two adjacent IMFs _. The subscript corresponding to the maximum difference is 2, then the first two IMFs are the selected sensitive IMF components.

4. Use the improved wavelet threshold function to denoise the 4 non-sensitive IMF components screened out. The specific steps are as follows:

The wavelet basis function coif5 is selected, the number of decomposition layers is 10, and the four non-sensitive IMF components are decomposed respectively to obtain their respective wavelet decomposition coefficients w _i (i=1, 2...10).

Calculate the standard deviation of the noise signal according to formula (5), and obtain the calculation result of the wavelet threshold.

where m is the number of decomposition layers, N is the signal length, and σ is the standard deviation of the noise signal;

An improved wavelet threshold function is constructed, its parameter n=4, and the wavelet coefficients after IMF4 wavelet decomposition are processed by the wavelet threshold. Using the wavelet coefficients after wavelet thresholding to reconstruct the signal, the IMF components after wavelet thresholding denoising are obtained.

如图8所示。Combined with the two sensitive IMF components in step 3 for reconstruction to obtain a complete denoised signal

As shown in Figure 8.

It can be seen from the comparison between FIG. 7 and FIG. 8 that the denoising algorithm proposed 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, mu_i、σ_iRespectively, the ith IMF component x_i(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 component_i：

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 IMFs_iAnd the subscript corresponding to the maximum difference is i, then the first i IMFs are the screened sensitive IMF components:

d_i＝Sf_i'-Sf_i+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, w_1,allAll wavelet coefficients of the first layer, 0.6754 is an adjustment coefficient.

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