Transformer vibration signal blind source separation method

Abstract

The invention provides a transformer vibration signal blind source separation method comprising the following steps: S1, obtaining a transformer box surface vibration mixed signal, and preprocessing the vibration mixed signal; s2, constructing a vibration mixed signal blind source separation mathematical model: X (t) = AS (t); s3, constructing a signal reconstruction model: Y (t) = WX (t); and S4, constructing a target function based on reconstruction source signal non-Gaussian maximization, acquiring an optimal value of a separation matrix based on an information acquisition optimizer and a fast independent component analysis method, and substituting the optimal value into the signal reconstruction model to obtain a vibration signal blind source separation result.

Description

Technical Field

[0001] The present invention relates to a method for acquiring electric power equipment signals, and in particular to a method for blind source separation of transformer vibration signals. Background Art

[0002] As an important electrical equipment, transformers are of great significance to the reliability of electric energy conversion, transmission and distribution. Among them, winding and core failures are the main reasons for abnormal working conditions of large transformers, and their operating conditions directly affect the stability of oil-immersed power equipment.

[0003] The vibration method is widely used to diagnose abnormal transformer working conditions. That is, the vibration signal on the surface of the box is collected to realize the live fault diagnosis of the transformer. The vibration signal of the transformer oil tank wall is mainly coupled by the winding and core vibration transmitted to the box surface through multiple paths. Therefore, in order to improve the mixed signal of the box vibration, obtaining the winding and core source signals is the key to improving the accuracy of fault diagnosis.

[0004] Existing blind source separation methods for transformer vibration signals primarily combine independent component analysis (ICA) for related expansion and analysis. This method relies on establishing an objective function based on an independence criterion and employing an optimization algorithm to optimize the parameters of the separation matrix within the objective function, thereby maximizing the reconstructed signal's approximation to the statistically independent source signals. The objective function is a functional of the source signal's probability density function. Methods include mutual information minimization, information maximization, non-Gaussianity maximization, and maximum likelihood estimation. Non-Gaussianity maximization can be measured using higher-order statistics, the most representative of which is negative entropy. Optimization algorithms include stochastic gradient method, natural gradient method and fixed point algorithm. After reasonably selecting the initial value of the separation matrix, the stochastic gradient method calculates the gradient value of the separation matrix of the objective function and shifts it in the gradient direction to update the separation matrix. When the dimension of the separation matrix is ​​large, the computational efficiency and robustness of this method decrease; the natural gradient method effectively makes up for the shortcomings of the stochastic gradient method from the perspective of Riemannian geometry, but the convergence speed of this method is slow during iterative calculation; the fixed point algorithm is also known as the fast independent component analysis method. This method uses a large amount of sample data for calculation in each iteration through batch processing, and achieves rapid convergence based on the Newton iteration method. However, since the Newton iteration direction is not necessarily the gradient direction, and the convergence of this method is affected by the initial value, the objective function may not converge after multiple iterations.

[0005] Therefore, in order to solve the above technical problems, it is urgent to propose a new technical means. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide a blind source separation method for transformer vibration signals, which optimizes the separation matrix by establishing a separation model and determining the negative entropy of the separation matrix based on the non-Gaussian maximization objective function, and obtains relevant parameters through an information acquisition optimizer to perform global search and local optimization. It can effectively solve the limitations of low robustness and slow convergence speed in the existing technology, and can accurately determine the separation matrix to ensure that the final reconstructed signal accurately reflects the fault state of the transformer.

[0007] The present invention provides a method for blind source separation of transformer vibration signals, comprising the following steps:

[0008] S1 obtains the transformer tank surface vibration mixed signal, and preprocesses the vibration mixed signal;

[0009] S2. Construct a mathematical model for blind source separation of vibration mixed signals:

[0010] X(t) = AS(t) (1), where S(t) is the N × 1 dimensional preprocessed source signal vector and A is the mixing matrix;

[0011] S3. Build signal reconstruction model:

[0012] Y(t)=WX(t)(2), where: Y(t)=[y1(t),y2(t),…,y i (t),…,y N (t)] T For N×1 dimensional reconstruction of the source signal, W=(w ij ) N×M is an N×M dimensional separation matrix;

[0013] S4. Construct an objective function based on maximizing the non-Gaussianity of the reconstructed source signal, and obtain the optimal value of the separation matrix based on the information acquisition optimizer and the fast independent component analysis method, and substitute it into the signal reconstruction model to obtain the blind source separation result of the vibration signal.

[0014] Furthermore, the objective function based on maximizing the non-Gaussianity of the reconstructed source signal is constructed as follows:

[0015] J∝F(w i )=[E{G(w i X(t))}-E{G(v)}] 2 (3);

[0016] Among them, y i represents the i-th reconstructed source signal, y i =w i X(t); G(·) represents a non-quadratic function, E{·} represents the mathematical expectation, ∝ represents proportional to, and v represents the difference between y and iGaussian random variables with the same variance, w i is the i-th column vector of the separation matrix W;

[0017] Among them, when the variable obeys the super Gaussian distribution:

[0018]

[0019] When the variable follows a sub-Gaussian distribution:

[0020] G(x)=-exp(-x 2 / 2);

[0021] When a variable has both super-Gaussian and sub-Gaussian distributions:

[0022]

[0023] Furthermore, the optimal value of the separation matrix is ​​obtained based on the information acquisition optimizer and the fast independent component analysis method, specifically including:

[0024] Take the column vector w of the separation matrix W i Construct an information body status update model for the information body:

[0025]

[0026] Where: T represents the current number of iterations, θ is a random number in the range [0,1], and Represents two randomly generated information bodies at the Tth iteration;

[0027]

[0028] Among them, r1 is a random number in the range of [0,1], Δ i is the error factor of subjective factors;

[0029]

[0030] Where: Λ is the control factor, is the optimal information body generated at the Tth iteration, ε, κ and ω are both random numbers in the range [0,1];

[0031] The information body state is updated by formula (4)-formula (6) respectively, and the updated results are substituted into formula (3) respectively. The information body when the non-Gaussian maximization objective function obtains the maximum value is taken as the optimal result.

[0032] Furthermore, the error factor Δ of the subjective factor is determined by the following method: i

[0033]

[0034] Where: Γ represents the reliability factor, σ represents the subjective influence factor;

[0035] σ=2mod(3.468v(1-β)(a·cos(γ·10 4 )),1);

[0036]

[0037] Where: Φ represents the information quality factor, T max represents the maximum number of iterations, v, β, a, γ, and δ are random numbers in the range [0,1].

[0038] Furthermore, the control factor Λ is:

[0039]

[0040] Furthermore, the vibration mixed signal is preprocessed including signal centering processing and whitening processing.

[0041] The beneficial effects of the present invention are as follows: through the present invention, the separation matrix is ​​optimized by establishing a separation model and determining the negative entropy of the separation matrix based on the non-Gaussian maximization objective function, and the relevant parameters are obtained through the information acquisition optimizer to perform global search and local optimization. The limitations of low robustness and slow convergence speed in the existing technology can be effectively solved, and the separation matrix can be accurately determined to ensure that the final reconstructed signal accurately reflects the fault state of the transformer. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0043] Figure 1 Flowchart of the present invention.

[0044] Figure 2 This is a layout diagram of a 110KV transformer vibration acceleration sensor according to a specific example of the present invention.

[0045] Figure 3 This is the time domain diagram of the winding and core signals at measuring point 4 of 110KV in the specific example of the present invention.

[0046] Attachment Figure 4 It is the time domain and frequency domain diagram of the 110kV transformer vibration mixed signal;

[0047] Attachment Figure 5 It is the time domain and frequency domain diagram of the reconstructed source signal obtained based on the IAO-ICA method;

[0048] Attachment Figure 6These are the time domain and frequency domain images of the reconstructed source signal obtained based on the FastICA method. DETAILED DESCRIPTION

[0049] The present invention is further described in detail below:

[0050] The present invention provides a method for blind source separation of transformer vibration signals, comprising the following steps:

[0051] S1. Obtain the mixed vibration signal of the transformer box surface and preprocess the mixed vibration signal; Figure 2 As shown, in practice, the existing vibration acceleration sensor is arranged on the transformer housing and then the vibration mixed signal is obtained. Figure 2 The circle represents the vibration acceleration sensor, and the number represents the measurement point number.

[0052] S2. Construct a mathematical model for blind source separation of vibration mixed signals:

[0053] X(t) = AS(t) (1), where S(t) is the N × 1 dimensional preprocessed source signal vector and A is the mixing matrix;

[0054] S3. Build signal reconstruction model:

[0055] Y(t)=WX(t)(2), where: Y(t)=[y1(t),y2(t),…,y i (t),…,y N (t)] T For N×1 dimensional reconstruction of the source signal, W=(w ij ) N×M is an N×M dimensional separation matrix;

[0056] S4. Construct an objective function based on maximizing the non-Gaussianity of the reconstructed source signal, and obtain the optimal value of the separation matrix based on the information acquisition optimizer and the fast independent component analysis method (abbreviated as IAO-ICA method), and substitute it into the signal reconstruction model to obtain the blind source separation result of the vibration signal.

[0057] Among them, the preprocessing of the vibration mixed signal includes signal centering processing and whitening processing, among which the signal centering processing is to perform mean value removal processing on the signal:

[0058]

[0059] Where E(x) is the mean of signal x.

[0060] After the mixed signal is centered, whitening is required to remove the correlation between the components of the signal, thereby reducing the complexity of the ICA problem. M(t)] T , where x k (t) is an n-dimensional column vector, and the whitening process can be achieved by linearly transforming it using the whitening matrix T:

[0061] Z(t) = TX(t);

[0062]

[0063] T=G -1 Q T ;

[0064] R X is the estimated value of the covariance matrix of the mixed signal X, P 2 R X The diagonal matrix obtained after eigenvalue decomposition has diagonal elements R X The eigenvalues ​​of the matrix Q are R X The orthogonal eigenvectors of .

[0065] Through the above method, the separation model is established and the negative entropy of the separation matrix is ​​determined based on the non-Gaussian maximization objective function to optimize the separation matrix. The relevant parameters are obtained through the information acquisition optimizer to perform global search and local optimization. This can effectively solve the limitations of low robustness and slow convergence speed in the existing technology, and can accurately determine the separation matrix to ensure that the final reconstructed signal accurately reflects the fault state of the transformer.

[0066] In this embodiment, the non-Gaussian maximization objective function based on the separation matrix is ​​constructed as follows:

[0067] J∝F(w i )=[E{G(w i X(t))}-E{G(v)}] 2 (3);

[0068] Among them, y i represents the i-th reconstructed source signal, y i =w i X(t); G(·) represents a non-quadratic function, E{·} represents the mathematical expectation, ∝ represents proportional to, that is, J and F(w i ) is proportional to, when F(w i ) reaches its maximum value, J also reaches its maximum value, v represents the maximum value with y i Gaussian random variables with the same variance, w iis the i-th column vector of the separation matrix W; when multiple independent source signals are transmitted to the sensor through linear superposition, the non-Gaussianity of the source signal is stronger than the received mixed signal. Therefore, the non-Gaussianity of the reconstructed source signal can be used as the criterion for the blind source separation problem, and the negative entropy is used to evaluate the non-Gaussianity of the signal, where the negative entropy is a non-negative value, and the larger the negative entropy value, the stronger the non-Gaussianity.

[0069] Among them, when the variable y i When it obeys the super Gaussian distribution:

[0070]

[0071] When the variable y i When it obeys the sub-Gaussian distribution:

[0072] G(x)=-exp(-x 2 / 2);

[0073] When the variable y i When there is both super-Gaussian and sub-Gaussian distribution:

[0074]

[0075] In this embodiment, obtaining the optimal value of the separation matrix based on the information acquisition optimizer and the fast independent component analysis method specifically includes:

[0076] During initialization, the maximum number of iterations T needs to be set max , the number of information bodies n and the number of optimization parameters M;

[0077] Take the column vector w of the separation matrix W i Construct an information body status update model for the information body:

[0078]

[0079] Where: T represents the current number of iterations, θ is a random number in the range [0,1], and Represents two randomly generated information bodies at the Tth iteration; when T is 0, it represents the initial state,

[0080]

[0081] Among them, r1 is a random number in the range of [0,1], Δ i is the error factor of subjective factors; Formula (5) represents the information filtering and evaluation stage, which is the key process for individuals to quickly identify effective information. The purpose of this stage is to eliminate misleading information and improve information quality;

[0082]

[0083] Where: Λ is the control factor, is the optimal information body generated at the Tth iteration, ε, κ and ω are both random numbers in the range of [0,1]. Formula (6) is the information analysis and organization stage, the purpose of which is to identify available information and convert part of the information into usable information, thereby increasing the probability of obtaining the optimal information body.

[0084] The information body state is updated by formula (4)-formula (6) respectively, and the updated results are substituted into formula (3) respectively. The information body when the objective function of maximizing non-Gaussianity obtains the maximum value is regarded as the optimal result.

[0085] Where: The error factor Δ of the subjective factor is determined by the following method i

[0086]

[0087] Where: Γ represents the reliability factor, σ represents the subjective influence factor;

[0088] σ=2mod(3.468v(1-β)(a·cos(γ·10 4 )),1);

[0089]

[0090] Where: Φ represents the information quality factor, T max represents the maximum number of iterations, v, β, a, γ, and δ are random numbers in the range [0,1].

[0091] The control factor Λ is:

[0092]

[0093] After completing the above process, use the following method to verify:

[0094] The average waveform similarity coefficient and Amari error rate are used to analyze and evaluate the blind source separation method. The specific steps are as follows:

[0095] The waveform similarity coefficient is defined as:

[0096]

[0097] Where K is the waveform length, λ ij To reconstruct the source signal y i (t) and the source signal s j (t) similarity relationship, λ ij The value range is [0,1], i,j∈N, N is the number of source signals and reconstructed source signals.i =as j (a is a constant), λ ij =1, then the i-th reconstructed source signal y i (t) and the j-th source signal s j (t) differs only in amplitude, and the waveforms are exactly the same; when λ ij = 0, the two signals do not have similar features, that is, λ ij The closer it is to 1, the greater the similarity between the reconstructed source signal and the source signal waveform. Since the results of blind source separation have uncertainty in signal amplitude and order, the order of the reconstructed source signal and the source signal may be inconsistent, so the average correlation coefficient is defined as:

[0098]

[0099] The Amari error rate, defined as

[0100]

[0101] Where, f ij =|T| ij , T=WA is the global matrix; W is the separation matrix; A is the mixing matrix. err ∈[0,2], the smaller the value, the better the blind source separation effect.

[0102] by Figure 2 The present invention is further explained at test point 4:

[0103] The source signal waveform and spectrum at measuring point 4 are shown in the attached figure. Figure 3 As shown. Randomly generate the mixing matrix A, whose parameters are:

[0104]

[0105] Combine the source signal and the mixing matrix to generate a mixed vibration signal. The waveform and spectrum of the mixed signal at measuring point 4 are shown in the attached figure. Figure 4 In order to verify the superiority of the blind source separation method of transformer vibration signal based on information acquisition optimizer and independent component analysis proposed in this invention, the mixed signal is blindly separated by the method proposed in this invention and the classic algorithm Fast Independent Component Analysis (Fast-ICA) method, and the obtained separation matrix estimation value is Its parameters are:

[0106]

[0107] according to and Get the reconstructed source signal y w (t) and y c(t), wherein the time domain and frequency domain diagrams of the reconstructed source signal obtained by the method proposed by the present invention and the FastICA method are shown in the attached figure respectively. Figure 5 and attached Figure 6 In order to further compare the advantages and disadvantages of the two algorithms, the average waveform similarity coefficient and Amari error rate were calculated respectively, and the results are shown in Table 1.

[0108] Table 1 Performance comparison of two independent component analysis methods

[0109]

[0110] By the attached Figure 5 and attached Figure 6 It can be seen that the reconstructed source signal obtained using the method proposed in this invention is more similar to the time domain and frequency domain characteristics of the source signal. As shown in Table 1, compared with the FastICA algorithm, the method proposed in this invention has a higher average similarity coefficient and a lower error rate. In other words, the blind source separation of multichannel signals based on the IAO-ICA method is more effective. Therefore, using the IAO algorithm to optimize the independent component analysis method based on negentropy maximization can effectively improve the robustness and accuracy of the method.

[0111] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for blind source separation of transformer vibration signals, characterized in that: The following steps are involved: S1 obtains the transformer tank surface vibration mixed signal, and preprocesses the vibration mixed signal; S2. Construct a mathematical model for blind source separation of vibration mixed signals: X(t) = AS(t) (1), where S(t) is the N × 1 dimensional preprocessed source signal vector and A is the mixing matrix; S3. Build signal reconstruction model: Y(t)=WX(t)(2), where: Y(t)=[y1(t),y2(t),…,y i (t),…,y N (t)] T For N×1 dimensional reconstruction of the source signal, W=(w ij ) N×M is an N×M dimensional separation matrix; S4. Construct an objective function based on maximizing the non-Gaussianity of the reconstructed source signal, and obtain the optimal value of the separation matrix based on the information acquisition optimizer and the fast independent component analysis method, and substitute it into the signal reconstruction model to obtain the blind source separation result of the vibration signal.

2. The blind source separation method for transformer vibration signals according to claim 1, characterized in that: The objective function based on maximizing the non-Gaussianity of the reconstructed source signal is constructed as follows: J∝F(w i )=[E{G(w i X(t))}-E{G(v)}] 2 (3); Among them, y i represents the i-th reconstructed source signal, y i =w i X(t); G(·) represents a non-quadratic function, E{·} represents the mathematical expectation, ∝ represents proportional to, and v represents the difference between y and i Gaussian random variables with the same variance, w i is the i-th column vector of the separation matrix W; Among them, when the variable obeys the super Gaussian distribution: When the variable follows a sub-Gaussian distribution: G(x)=-exp(-x 2 / 2); When a variable has both super-Gaussian and sub-Gaussian distributions:

3. The method for blind source separation of transformer vibration signals according to claim 2, wherein: The optimal value of the separation matrix is ​​obtained based on the information acquisition optimizer and the fast independent component analysis method, specifically including: Take the column vector w of the separation matrix W i Construct an information body status update model for the information body: Where: T represents the current number of iterations, θ is a random number in the range [0,1], and Represents two randomly generated information bodies at the Tth iteration; Among them, r1 is a random number in the range of [0,1], Δ i is the error factor of subjective factors; Where: Λ is the control factor, is the optimal information body generated at the Tth iteration, ε, κ and ω are both random numbers in the range [0,1]; The information body state is updated by formula (4)-formula (6) respectively, and the updated results are substituted into formula (3) respectively. The information body when the non-Gaussian maximization objective function obtains the maximum value is taken as the optimal result.

4. The method for blind source separation of transformer vibration signals according to claim 3, wherein: The error factor Δ of the subjective factor is determined by the following method i Where: Γ represents the reliability factor, σ represents the subjective influence factor; σ=2mod(3.468v(1-β)(a·cos(γ·10 4 )),1); Where: Φ represents the information quality factor, T max represents the maximum number of iterations, v, β, a, γ, and δ are random numbers in the range [0,1].

5. The method for blind source separation of transformer vibration signals according to claim 4, characterized in that: The control factor Λ is:

6. The method for blind source separation of transformer vibration signals according to claim 1, characterized in that: Preprocessing the vibration mixed signal includes signal centering and whitening.

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