Transformer pressure signal denoising method based on multi-precision variational modal decomposition algorithm

Abstract

The application discloses a transformer pressure signal denoising method based on a multi-precision variational mode decomposition algorithm, adopts an improved empirical mode decomposition algorithm (EMD) and a multi-precision variational mode decomposition algorithm (VMD), and is suitable for signal denoising processing of pressure sensors of power transformers of various voltage grades. The multi-precision adaptive variational mode decomposition method can be used in a transformer pressure abnormality early warning device to remove electromagnetic interference influence, so that interference on the pressure signal is filtered out, and the method has a good market application prospect.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of online monitoring of power transformers, and in particular to a transformer pressure signal denoising method based on a multi-precision variational mode decomposition algorithm. BACKGROUND

[0002] A transformer is an important power equipment in a power facility. A transformer in a long-term operation process will cause faults due to various reasons. When the transformer oil encounters a malignant fault, the insulating material and the transformer oil are cracked by high temperature or electric arc, and a large amount of gas is generated. The malignant fault continues to occur, the oil temperature continues to rise, the pressure in the fault bubble continues to rise, and due to the expansion inertia of the liquid insulating oil near the fault point, a significant pressure rise will occur at the gas-liquid interface between the fault bubble and the surrounding liquid insulating oil, and the pressure wave will propagate in the transformer oil tank in the form of a pressure wave, causing the overall oil pressure in the oil tank to rise suddenly, and even causing an explosion and fire.

[0003] In addition, there are many devices in a transformer substation, especially a high-voltage and high-current primary system. When performing related operations, such as switching a high-voltage bus, an unloaded line, an unloaded transformer, an isolating switch, a bus loop current, and a high-low voltage reactor switching operation, a transient electromagnetic field will inevitably be generated around the device, which is very easy to couple into an electromagnetic sensitive electronic component, thereby affecting the secondary equipment in operation and causing measurement errors of the secondary equipment. For a transformer pressure abnormality monitoring and early warning device, the internal multiple high-precision pressure sensors and data processing chips will also be affected by electromagnetic interference. However, the existing monitoring device for transformer pressure abnormalities does not consider electromagnetic interference. Once false alarms occur due to electromagnetic interference signals, the safety of the transformer operation will be seriously affected. SUMMARY

[0004] In order to overcome the above technical problems, the present application provides a method for filtering out the interference of the pressure signal by using an improved empirical mode decomposition algorithm (EMD) and a multi-precision variational mode decomposition algorithm (VMD).

[0005] The technical scheme adopted by the present application to overcome the technical problems is as follows:

[0006] A transformer pressure signal denoising method based on a multi-precision variational mode decomposition algorithm, comprising the following steps: a) collecting an original signal x(t) from a pressure sensor, and converting the original signal x(t) into a frequency domain signal x(f);

[0007] b) calculating an optimal modal function K;

[0008] c) using a variational mode decomposition algorithm VMD to perform coarse denoising on the frequency domain signal x(f) to obtain a pressure signal xc (f);

[0009] d) using empirical mode decomposition algorithm EMD to decompose the pressure signal x c (f) into N intrinsic mode functions c n (f) is the nth intrinsic mode function, n = {1, 2, …, N}, N = K, and the intrinsic mode function with the lowest frequency is denoted as c trend ;

[0010] e) calculating a weighted multi-index correlation coefficient CWC, if CWC > P, the corresponding intrinsic mode function c n (f) is an effective intrinsic mode function, if CWC≤P, the corresponding intrinsic mode function c n (f) is a noisy intrinsic mode function that needs to be filtered out;

[0011] f) the effective intrinsic mode function c n (f) is obtained by the formula to obtain a fine denoising pressure signal x f .

[0012] Preferably, the original signal x(t) in time domain is converted into a frequency domain signal x(f) by using fast Fourier transform in step a).

[0013] Further, step b) comprises the following steps:

[0014] b-1) the maximum frequency of the frequency domain signal x(f) is f m , and the selected range d(K) of the average bandwidth of each mode is calculated by the formula , K is the mode function;

[0015] b-2) the frequency corresponding to the maximum amplitude of the pressure signal collected by the pressure sensor is denoted as f d , the frequency corresponding to the minimum amplitude before the maximum amplitude of the pressure signal is denoted as f n , and the difference between the frequency f d and the frequency f n is defined as Δf nd , and the value of the selected mode function K corresponds to d(K) satisfying d(K) ∈ [2Δf nd , 3Δf ndb-3) The joint function MI(x,y) is calculated using the formula MI(x,y)=H(x)+H(y)-H(x,y). H(x) is the information entropy function of the original signal x(t), H(y) is the information entropy function of the mode function corresponding to the intermediate oscillation frequency, and H(x,y) is the joint information entropy function of the original signal x(t) and the mode function corresponding to the intermediate oscillation frequency. When the joint function MI(x,y) reaches its maximum value, the optimal K value is obtained.

[0016] Furthermore, in step b-3), the formula is used. The information entropy function H(x) of the original signal x(t) is calculated, p x (x i Let x be the probability mass function. i For the i-th original signal, the formula is used... The information entropy function H(y), p, corresponding to the intermediate oscillation frequency, is calculated. y (y j Let y be the probability mass function. j The modal function number corresponding to the j-th intermediate oscillation frequency is obtained through the formula. The joint information entropy function H(x,y) is calculated, p xy (x i ,y j ) is the probability mass function.

[0017] Furthermore, step c) includes the following steps:

[0018] c-1) Decompose the frequency domain signal x(f) into K finite bandwidth mode functions, where k is the k-th finite bandwidth mode function, k = {1, 2, ..., K};

[0019] c-2) Through formula The mode function u of the k-th finite bandwidth is calculated. k The oscillation capability loss is greater than e k In the formula A r (x) represents the spectral amplitude of the original signal x(t) at its own oscillation frequency, A r (u k Let u be the mode function with finite bandwidth. k Spectral amplitude at its own oscillation frequency; c-3) the ratio of oscillation capability loss to e k The pressure signal x is obtained by combining the residual with the coarsely denoised signal. c (f). Further, step e) includes the following steps:

[0020] e-1) calculating a weighted multi-index correlation coefficient CWC by the formula CWC = wr(n) + (1-w)g(n), wherein w is a weight, r(n) is a linear correlation coefficient, wherein Q = K, x c (q) is the qth completed coarse denoising pressure signal, c n (q) is the qth eigenmode function, is the expectation of x c (q), is the expectation of c n (q), g(n) is a geometric correlation coefficient,

[0021] x c (0) (Q) = x c (q) - x c (1), x c (1) is the 1st completed coarse denoising pressure signal, c n (1) is the 1st eigenmode function.

[0022] Preferably, P = 0.5 in step e).

[0023] The present application has the beneficial effects that: by using the improved empirical mode decomposition algorithm (EMD) and multi-precision variational mode decomposition algorithm (VMD), the present application is suitable for signal denoising processing of pressure sensors of power transformers of various voltage levels, and can be used in a transformer pressure abnormality early warning device to remove the influence of electromagnetic interference, thereby filtering out the interference received by the pressure signal, and having a good market application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 is a flow chart of the method of the present application. DETAILED DESCRIPTION

[0025] The present application will be further described below with reference to the accompanying drawings. Figure 1 The present application will be further described below with reference to the accompanying drawings.

[0026] A transformer pressure signal denoising method based on a multi-precision variational mode decomposition algorithm, comprising the following steps: a) collecting an original signal x(t) from a pressure sensor, and converting the original signal x(t) into a frequency domain signal x(f); b) calculating an optimal modal function K. Coarse denoising is performed using an adaptive variational mode decomposition method. First, the optimal value of the modal number K is adaptively determined according to the frequency domain characteristics of the pressure signal, an information entropy function and a joint information entropy function. If the set K is less than the number of useful components in the signal to be decomposed (under-decomposition), insufficient decomposition will occur, resulting in modal aliasing. If the set K value is greater than the number of useful components in the signal to be decomposed (over-decomposition), some useless false components will be generated. Therefore, the determination of the K value is very important for variational mode decomposition.

[0027] c) Coarse denoising of the frequency domain signal x(f) is performed using a variational mode decomposition algorithm VMD to obtain a pressure signal x c (f) after coarse denoising.

[0028] d) In order to remove the remaining low-frequency noise components from the coarse denoised pressure signal x c (f), an empirical mode decomposition algorithm EMD is used to decompose the pressure signal x c (f) into N intrinsic mode functions (IMFs), c n (f) is the nth intrinsic mode function, n={1,2,...,N}, N=K, and the intrinsic mode function with the lowest frequency is denoted as c trend Therefore, the relevant intrinsic mode functions IMFs should be obtained according to appropriate indicators.

[0029] e) The correlation coefficient is a commonly used method for selecting effective IMFs from EMD results. However, in pressure signals, the results are easily affected by low-frequency noise. To solve this problem, a method CWC (comprehensive weighted correlative) based on a linear correlation coefficient (r(n)) and a geometric correlation coefficient (g(n)) is proposed to cluster effective IMFs. Specifically, the weighted multi-index correlation coefficient is CWC, if CWC>P, then the corresponding intrinsic mode function c n (f) is an effective intrinsic mode function. The larger the value of the weighted multi-index correlation coefficient CWC, the greater the correlation, and if CWC≤P, then the corresponding intrinsic mode function c n (f) is a noisy intrinsic mode function that needs to be filtered out. f) The effective intrinsic mode function c n (f) is calculated by the formula to obtain a fine denoised pressure signal x f .

[0030] Example 1:

[0031] In step a), the original signal x(t) in time domain is converted into a signal x(f) in frequency domain by using fast Fourier transform.

[0032] Embodiment 2

[0033] For the pressure signal, especially the signal when the pressure abnormally fluctuates, it has the characteristics of short action time, rapid mutation and wide frequency spectrum range, but the low frequency signal occupies the main part of the energy, and there are a large number of mutations and peaks in the signal. Step b) includes the following steps:

[0034] b-1) The maximum frequency of the frequency domain signal x(f) is f m , and the selection range d(K) of the average bandwidth of each mode function K is calculated by the formula .

[0035] b-2) The frequency corresponding to the maximum amplitude of the pressure signal collected by the pressure sensor is f d , and the frequency corresponding to the minimum amplitude before the maximum amplitude of the pressure signal appears is f n , and the difference between the frequency f d and the frequency f n is defined as Δf nd . For the pressure signal, the maximum value of the pressure can indicate whether an abnormal pressure condition occurs, therefore, in order to effectively remove the noise components near the frequency of the maximum amplitude of the pressure signal, and without insufficient decomposition and over-decomposition, the value of the mode function K selected corresponds to d(K) satisfying d(K) ∈ [2Δf nd , 3Δf nd ].

[0036] b-3) In order to further determine the final value of K from the above possible value range of K, a joint function MI(x, y) needs to be constructed, therefore the joint function MI(x, y) is calculated by the formula MI(x, y) = H(x) + H(y) - H(x, y), H(x) is the information entropy function of the original signal x(t), H(y) is the information entropy function of the mode function corresponding to the intermediate oscillation frequency, and H(x, y) is the joint information entropy function of the original signal x(t) and the mode function corresponding to the intermediate oscillation frequency. A larger MI(x, y) means that more oscillation information is transmitted from the pressure signal. Therefore, when MI(x, y) reaches the maximum value, the optimal K value can be determined.

[0037] Embodiment 3

[0038] In step b-3), the information entropy function H(x) of the original signal x(t) is calculated by the formula , and p x (xi ) is the probability mass function, x i is the i-th original signal, which is calculated by formula y (y j ) is the probability mass function, y j is the j-th intermediate oscillation frequency corresponding to the modal function number, which is calculated by formula xy (x i ,y j ) is the probability mass function.

[0039] Embodiment 4:

[0040] Step c) includes the following steps:

[0041] c-1) decompose the frequency domain signal x(f) into K finite bandwidth modal functions, u

[0042] c-2) In order to eliminate the high frequency noise components close to the oscillation frequency of the pressure signal itself and part of the low frequency noise components at the same time, to prevent the modal mixing problem, an index called oscillation energy loss ratio e k is proposed to cluster the relevant modes obtained by the sub-modal decomposition algorithm. Specifically, the oscillation energy loss ratio e k of the k-th finite bandwidth modal function u k is calculated by formula , in which A r (x) is the spectral amplitude of the original signal x(t) at its own oscillation frequency, and A r (u k ) is the spectral amplitude of the k-th finite bandwidth modal function u k at its own oscillation frequency. The e k of the effective finite bandwidth modal function (i.e. the one that can contain most of the oscillation components) should be much smaller than that of the noisy finite bandwidth modal function, so as to select the effective finite bandwidth modal function.

[0043] c-3) combine the oscillation energy loss ratio e k and the residual to obtain the pressure signal x c (f) after rough denoising. Since the variational modal decomposition algorithm VMD has poor decomposition performance on wideband pressure signals, it contains part of the low frequency noise. Therefore, the rough denoising result x c (f) still contains part of the low frequency noise that is difficult to filter out.

[0044] ​​Embodiment 5

[0045] Step e) comprises the following steps:

[0046] e-1) calculating a weighted multi-index correlation coefficient CWC by the formula CWC = wr(n) + (1-w)g(n), wherein w is a weight, the weight w is used to adjust the weight of the linear correlation coefficient r(n) and the geometric correlation coefficient g(n), so as to obtain the modal function x c (q) and c n (q) are analyzed for correlation, wherein Q = K, x c (q) is the qth pressure signal after rough denoising, c n (q) is the qth eigenmodal function, is the expectation of x c (q), and g(n) is a geometric correlation coefficient, is the expectation of c n (q), g(n) is a geometric correlation coefficient,

[0047] x c (1) is the 1st pressure signal after rough denoising, c n (1) is the 1st eigenmodal function.

[0048] Embodiment 6

[0049] In step e), P = 0.5.

[0050] Finally, it should be noted that the above only describes the preferred embodiments of the present application and is not intended to limit the present application. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent replacements to some technical features. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for denoising transformer pressure signals based on a multi-precision variational mode decomposition algorithm, characterized in that, Includes the following steps: a) Acquire the raw signal x(t) from the pressure sensor and convert the raw signal x(t) into a frequency domain signal x(f); b) Calculate the optimal mode function K; c) The frequency domain signal x(f) is coarsely denoised using the Variational Mode Decomposition (VMD) algorithm to obtain the coarsely denoised pressure signal x. c (f); d) Use the Empirical Mode Decomposition (EMD) algorithm to analyze the pressure signal x. c (f) Decomposed into N eigenmode functions, c n (f) is the nth eigenmode function, n = {1, 2, ..., N}, N = K. The eigenmode function with the lowest frequency is denoted as c. trend ; e) Calculate the weighted multi-index correlation coefficient CWC. If CWC > P, then the corresponding intrinsic mode function c n (f) is a valid eigenmode function if CWC ≤ P, then the corresponding eigenmode function c n (f) represents the noisy intrinsic mode functions that need to be filtered out; f) The effective intrinsic mode functions c n (f) By formula The calculated and refined denoised pressure signal x f ; Step e) includes the following steps: e-1) The weighted multi-indicator correlation coefficient CWC is calculated using the formula CWC=wr(n)+(1-w)g(n), where w is the weight and r(n) is the linear correlation coefficient. In the formula, Q = K, x c (q) represents the q-th pressure signal that has undergone coarse denoising, c n (q) is the q-th intrinsic mode function. For x c The expectation of (q), For c n The expected value of (q), and g(n) is the geometric correlation coefficient. x c (1) The first pressure signal to complete coarse denoising c n (1) The first intrinsic mode function.

2. The transformer pressure signal denoising method based on multi-precision variational mode decomposition algorithm according to claim 1, characterized in that: In step a), the original time-domain signal x(t) is transformed into the frequency-domain signal x(f) using the Fast Fourier Transform.

3. The transformer pressure signal denoising method based on multi-precision variational mode decomposition algorithm according to claim 1, characterized in that, Step b) includes the following steps: b-1) The maximum frequency of the frequency domain signal x(f) is f m Through formula The selection range d(K) of the average bandwidth per mode is calculated, where K is the mode function; b-2) The frequency corresponding to the maximum amplitude of the pressure signal collected by the pressure sensor is denoted as f. d The frequency corresponding to the minimum amplitude before the maximum amplitude of the suppression signal appears is only f. n Frequency f d With frequency f n The difference is defined as Δf nd The selected modal function K corresponds to the value of d(K) satisfying d(K)∈[2Δf nd ,3Δf nd b-3) The joint function MI(x,y) is calculated using the formula MI(x,y)=H(x)+H(y)-H(x,y). H(x) is the information entropy function of the original signal x(t), H(y) is the information entropy function of the mode function corresponding to the intermediate oscillation frequency, and H(x,y) is the joint information entropy function of the original signal x(t) and the mode function corresponding to the intermediate oscillation frequency. When the joint function MI(x,y) reaches its maximum value, the optimal K value is obtained.

4. The transformer pressure signal denoising method based on multi-precision variational mode decomposition algorithm according to claim 3, characterized in that: In step b-3), the formula is used. The information entropy function H(x) of the original signal x(t) is calculated, p x (x i Let x be the probability mass function. i For the i-th original signal, the formula is used. The information entropy function H(y), p, corresponding to the intermediate oscillation frequency, is calculated. y (y j Let y be the probability mass function. j The modal function number corresponding to the j-th intermediate oscillation frequency is obtained through the formula. The joint information entropy function H(x,y) is calculated, p xy (x i ,y j ) is the probability mass function.

5. The transformer pressure signal denoising method based on multi-precision variational mode decomposition algorithm according to claim 1, characterized in that, Step c) includes the following steps: c-1) Decompose the frequency domain signal x(f) into K finite bandwidth mode functions, where k is the k-th finite bandwidth mode function, k = {1, 2, ..., K}; c-2) Through formula The mode function u of the k-th finite bandwidth is calculated. k The loss of oscillation capability is greater than e k In the formula A r (x) represents the spectral amplitude of the original signal x(t) at its own oscillation frequency, A r (u k Let u be the mode function with finite bandwidth. k Spectral amplitude at its own oscillation frequency; c-3) The oscillation capability loss ratio is e k The pressure signal x is obtained by combining the residual with the coarsely denoised signal. c (f).

6. The transformer pressure signal denoising method based on multi-precision variational mode decomposition algorithm according to claim 1, characterized in that: In step e), P = 0.5.

Images