Hybrid partial discharge signal separation method

Abstract

The invention relates to the technical field of signal processing, in particular to a mixed partial discharge signal separation method which comprises the following steps: S1, a linear mixed mathematical model is selected to describe the mixing process of partial discharge signals, and a to-be-detected mixed signal x (t) is obtained; s2, performing whitening preprocessing on a mixed signal x (t) to be detected to obtain # imgabs0 # S3, constructing a fourth-order cumulant matrix # imgabs2 # of # imgabs1 # S4, performing joint diagonalization processing on the fourth-order cumulant matrix # imgabs3 # to obtain a unitary matrix U; s5, obtaining a separation matrix W: W = UTQ according to the unitary matrix U and the whitening matrix Q; s6, separating each source signal from the to-be-detected mixed signal x (t) by using the separation matrix W; and S7, correcting the output signal vector of each separated source signal. According to the invention, accurate separation of local mixed discharge signals can be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and more particularly to a mixed partial discharge signal separation method. Background Art

[0002] Partial discharge (PD) is an early manifestation of insulation defects in power system equipment. Once partial discharge occurs, it usually means that there are defects or weaknesses in the insulation system of the power equipment. These defects will lead to the gradual deterioration of insulation performance, and may eventually cause serious equipment failures and power system power outages. Effective monitoring and evaluation of partial discharge phenomena, timely and accurate detection of partial discharge signals and reasonable arrangement of maintenance work can ensure the smooth operation of power equipment. However, various types of high-voltage electrical equipment often have complex structures, which may cause multiple different insulation faults in the same electrical equipment and generate mixed partial discharge signals, which will cause great interference to subsequent signal recognition work. In a complex electromagnetic environment, the accurate separation of mixed partial discharge signals is crucial to assessing the location and severity of insulation defects in power equipment. Selecting a suitable separation algorithm is of great significance to subsequent signal recognition work.

[0003] Traditional methods mainly focus on the identification of single partial discharge signals, and there is relatively little research on multi-source mixed partial discharge signals, which usually makes it difficult to effectively handle such complex situations.

[0004] Therefore, how to achieve accurate separation of mixed discharge signals is a problem that those skilled in the art need to solve urgently. Summary of the invention

[0005] In view of this, the present invention provides a mixed partial discharge signal separation method, which can achieve accurate separation of partial mixed discharge signals.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A mixed partial discharge signal separation method comprises the following steps:

[0008] S1. Select a linear mixed mathematical model to describe the mixing process of the partial discharge signal to obtain the mixed signal x(t) to be detected;

[0009] S2, perform whitening preprocessing on the mixed signal x(t) to be detected, and obtain

[0010] S3. Construction The fourth-order cumulant matrix Q x～ (M);

[0011] S4, for the fourth-order cumulant matrix Perform joint diagonalization to obtain the unitary matrix U;

[0012] S5. Obtain the separation matrix W based on the unitary matrix U and the whitening matrix Q: W = U T Q;

[0013] S6, using the separation matrix W to separate each source signal from the mixed signal x(t) to be detected;

[0014] S7. Correct the output signal vectors of each separated source signal.

[0015] Furthermore, the expression of the linear mixed mathematical model is:

[0016] x(t)=As(t)

[0017] Among them, x(t) represents the mixed signal to be detected; s(t) represents the source signal to be separated; A represents an m×n dimensional mixing matrix, n represents n partial discharge sources, m represents m sensors, and the number of sensors is greater than the number of source signals.

[0018] Furthermore, in S1, y(t) is set as the output signal vector after blind source separation, y(t) = [y1(t), y2(t), ..., y n (t)], then the hybrid mathematical model for blind source separation of partial discharge signals is:

[0019] y(t)=Wx(t)=WAs(t)

[0020] Where W represents the separation matrix.

[0021] Furthermore, in S2, the whitening preprocessing process is expressed as: Where C is the product of the whitening matrix Q and the mixing matrix A, s(t) is The components in are independent and have a variance of 1;

[0022] Assume that the correlation matrix of the multi-channel mixed signal x(t) to be detected is Rx, and perform eigenvalue decomposition R on Rx x =PDP T , where D = diag(d1, d2, ... d m ), a diagonal matrix consisting of m eigenvalues, P represents an orthogonal matrix consisting of eigenvectors corresponding to the eigenvalues, and has PP T =1 orthogonal property; let the whitening matrix formula be: The signal after whitening It is expressed as:

[0023]

[0024] Furthermore, in S3, The fourth-order cumulant matrix It is expressed as:

[0025]

[0026] in, represents the mixed signal after whitening preprocessing; i, j, k, l represent the indexes of different channels in the mixed signal x(t), which are used to represent the statistical relationship of four different mixed signals; 1≤i,j,k,l≤N, N is the number of input mixed signals; M is an N×N-dimensional weight matrix, which is gradually constructed and updated through eigenvalue decomposition and joint diagonalization by estimating the fourth-order cumulant of the mixed signal, m kl is the (k,l)th element in the matrix M.

[0027] Furthermore, in S4, for the fourth-order cumulant matrix Q x～ (M) The process of joint diagonalization is expressed as: F(U) = UQ x～ (M)U T , by finding different fourth-order cumulant matrices Q x～ (M r ), 1≤r≤N, diagonalize F(U) and solve to obtain the unitary matrix U.

[0028] Further, in S7, by constructing a cost function, the sign and amplitude of the output signal vector of each separated source signal are estimated. The cost function is expressed as:

[0029]

[0030] Among them, Z represents the cost function, N represents the number of sampling points, and x i (t) represents the mixed signal collected by the i-th sensor, y(t) represents the output signal vector matrix after blind source separation, and C represents the correction coefficient matrix.

[0031] Furthermore, when Z approaches 0 or is minimized, it means that the amplitude of the separated signal y(t) tends to be equal to the amplitude of the source signal in the corresponding channel, and the amplitude correction is completed.

[0032] Furthermore, the AdaGrad method is used to find the amplitude correction coefficient C that minimizes Z.

[0033] It can be seen from the above technical solutions that, compared with the prior art, the present invention has the following beneficial effects:

[0034] The present invention models the input mixed partial discharge signal as a linear mixed model, performs whitening preprocessing, and then uses a joint approximate diagonalization algorithm to diagonalize the characteristic matrix, thereby solving a unitary matrix, using the unitary matrix and the whitening matrix to calculate a separation matrix and apply it to the mixed signal, ultimately achieving signal separation and source signal estimation, thereby improving the accuracy and robustness of signal separation. By introducing an amplitude correction coefficient matrix, the source signal can be accurately restored from a complex mixed signal, and the positive, negative and amplitude characteristics of the source signal can be effectively extracted.

[0035] The non-Gaussian characteristics of partial discharge signals are effectively processed through the application of high-order statistics (such as JADE), which is independent of the prior information of mixed signals, has strong adaptability, and is applicable to a variety of mixed signal scenarios. The source signal finally separated can provide an accurate analysis basis for power equipment fault diagnosis and monitoring. The application of this technology is expected to significantly improve the effect of partial discharge signal analysis and play an important role in the monitoring, diagnosis and maintenance of power systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0037] Figure 1 The present invention provides a flow chart of the mixed partial discharge signal separation method. DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] like Figure 1 As shown, an embodiment of the present invention discloses a mixed partial discharge signal separation method, comprising the following steps:

[0040] S1. Select a linear mixed mathematical model to describe the mixing process of the partial discharge signal to obtain the mixed signal x(t) to be detected;

[0041] S2, perform whitening preprocessing on the mixed signal x(t) to be detected to obtain x~(t);

[0042] S3. Construct the fourth-order cumulant matrix Q of x~(t)x～ (M);

[0043] S4, the fourth-order cumulant matrix Q x～ (M) Perform joint diagonalization to obtain a unitary matrix U;

[0044] S5. Obtain the separation matrix W based on the unitary matrix U and the whitening matrix Q: W = U T Q;

[0045] S6, using the separation matrix W to separate each source signal from the mixed signal x(t) to be detected;

[0046] S7. Correct the output signal vectors of each separated source signal.

[0047] The above steps are further explained below.

[0048] S1. Select a linear mixed mathematical model to describe the mixing process of partial discharge signals to obtain the mixed signal x(t) to be detected. The expression of the linear mixed mathematical model is:

[0049] x(t)=As(t)

[0050] Among them, x(t) represents the mixed signal to be detected; s(t) represents the source signal to be separated; A represents an m×n dimensional mixing matrix, n represents n partial discharge sources, m represents m sensors, and the number of sensors is greater than the number of source signals.

[0051] The present invention sets the number of sensors to be greater than the number of source signals, not only ensuring that each partial discharge source is monitored by at least one sensor, but also ensuring that the blind source separation process is mathematically solvable and the signal separation effect is better, while enhancing the robustness and adaptability of the system. This setting can: improve the reversibility of the mixing matrix to ensure that the blind source separation problem is solvable; increase redundant information to help suppress noise and improve separation accuracy; capture more signal features to adapt to complex signal propagation environments; enhance the reliability of the system to ensure stable operation in practical applications.

[0052] Let y(t) be the output signal vector after blind source separation, y(t) = [y1(t), y2(t), ..., y n (t)], then the hybrid mathematical model for blind source separation of partial discharge signals is:

[0053] y(t)=Wx(t)=WAs(t)

[0054] Where W represents the separation matrix. The essence of blind source separation is to solve the n×m-order separation matrix W to separate the source signals s(t) from the detection signal x(t).

[0055] S2, perform whitening preprocessing on the mixed signal x(t) to be detected, and obtain The whitening preprocessing process is expressed as: Where C is the product of the whitening matrix Q and the mixing matrix A, s(t) is The components in are independent and have a variance of 1;

[0056] The present invention proposes a method of eigenvalue decomposition to perform signal whitening processing. Assuming that the correlation matrix of the mixed signal x(t) to be detected by the multi-channel is Rx, the eigenvalue decomposition Rx is performed on Rx. x =PDP T , where D = diag(d1, d2, ... d m ), a diagonal matrix consisting of m eigenvalues, P represents an orthogonal matrix consisting of eigenvectors corresponding to the eigenvalues, and has PP T =1 orthogonal characteristics; each eigenvalue represents the energy contribution of the signal in the direction of the corresponding eigenvector. The size of the eigenvalue reflects the strength distribution of the signal in that direction. Larger eigenvalues ​​correspond to the main direction (principal component) of the signal, and smaller eigenvalues ​​may correspond to noise or secondary signal components.

[0057] Let the whitening matrix formula be: The signal after whitening It is expressed as:

[0058] In S3, construct The fourth-order cumulant matrix Specifically include:

[0059] The joint approximate diagonalization algorithm of the characteristic matrix (JADE) is selected to process blind source separation. Based on the assumption that each source signal is statistically independent and the characteristic that the mutual accumulation between independent signals is zero, the algorithm constructs a fourth-order cumulant matrix and performs joint diagonalization on the accumulated matrix to estimate the source signal. The fourth-order cumulant matrix It is expressed as:

[0060]

[0061] in, represents the mixed signal after whitening preprocessing; i, j, k, l represent the indexes of different channels in the mixed signal x(t), which are used to represent the statistical relationship of four different mixed signals; 1≤i,j,k,l≤N, N is the number of input mixed signals; M is an N×N-dimensional weight matrix, which is gradually constructed and updated through eigenvalue decomposition and joint diagonalization by estimating the fourth-order cumulant of the mixed signal, m kl is the (k,l)th element in the matrix M.

[0062] S4, for the fourth-order cumulant matrix Perform joint diagonalization to obtain the unitary matrix U. The joint diagonalization process is expressed as: By finding different fourth-order cumulant matrices Diagonalize F(U) and solve to get the unitary matrix U. Q is known. Diagonalize F as much as possible and use the knowledge of matrix theory to solve the unitary matrix U.

[0063] Joint diagonalization refers to processing a group of matrices so that they can all be diagonalized by the same reversible matrix. The main goal of joint diagonalization is to find a transformation matrix, namely the unitary matrix U, so that multiple matrices are close to diagonalization at the same time. Joint diagonalization means not to diagonalize each cumulant matrix one by one, but to find a unified transformation that makes the non-diagonal elements of all matrices as zero as possible so that the above equation F(U)=UQ is satisfied. x～ (M)U T .

[0064] S5. After solving the unitary matrix U, the separation matrix W is obtained according to the unitary matrix U and the whitening matrix Q: W = U T Q.

[0065] S6. Separate each source signal from the mixed signal x(t) to be detected using the separation matrix W to obtain an output signal vector matrix y(t) of each source signal.

[0066] S7. Next, the positive and negative values ​​and amplitudes of each signal in the output signal vector matrix y(t) of each source signal are estimated, specifically including:

[0067] By constructing a cost function, the positive and negative values ​​and amplitude of the output signal vector of each separated source signal are estimated. The cost function is expressed as:

[0068]

[0069] Among them, Z represents the cost function, N represents the number of sampling points, and x i (t) represents the mixed signal collected by the i-th sensor, y(t) represents the output signal vector matrix after blind source separation, and C represents the correction coefficient matrix.

[0070] The positive or negative estimation of a signal is related to the phase information and waveform of the signal. By analyzing the characteristics of the signal in the time domain or frequency domain, its positive or negative nature can be determined.

[0071] When estimating the amplitude, since the waveform of y(t) is consistent with the waveform of the source signal and there is no phase change, by adjusting the coefficient matrix C, when Z tends to 0 or is minimized, it means that the amplitude of the separated signal y(t) tends to be equal to the amplitude of the source signal in the corresponding channel, and the amplitude correction is completed.

[0072] The AdaGrad method is used to find the amplitude correction coefficient C that minimizes Z. The specific optimization process includes:

[0073] 1. Calculate the gradient of the cost function Z to the amplitude correction coefficient C

[0074] 2. Cumulative Gradient Square

[0075] 3. Parameter update rules

[0076] 4. Check whether the convergence conditions are met: If convergence has not occurred after reaching the maximum number of iterations, return to 2 and continue iterating.

[0077] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0078] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A mixed partial discharge signal separation method, characterized in that: The following steps are involved: S1. Select a linear mixed mathematical model to describe the mixing process of the partial discharge signal to obtain the mixed signal x(t) to be detected; S2, perform whitening preprocessing on the mixed signal x(t) to be detected, and obtain S3. Construction The fourth-order cumulant matrix S4, for the fourth-order cumulant matrix Perform joint diagonalization to obtain the unitary matrix U; S5. Obtain the separation matrix W based on the unitary matrix U and the whitening matrix Q: W = U T Q; S6, using the separation matrix W to separate each source signal from the mixed signal x(t) to be detected; S7. Correct the output signal vectors of each separated source signal.

2. The hybrid partial discharge signal separation method according to claim 1, characterized in that: In S1, the expression of the linear mixed mathematical model is: x(t)=As(t) Among them, x(t) represents the mixed signal to be detected; s(t) represents the source signal to be separated; A represents an m×n dimensional mixing matrix, n represents n partial discharge sources, m represents m sensors, and the number of sensors is greater than the number of source signals.

3. The hybrid partial discharge signal separation method according to claim 1, characterized in that: In S1, let y(t) be the output signal vector after blind source separation, y(t) = [y1(t), y2(t), ..., y n (t)], then the hybrid mathematical model for blind source separation of partial discharge signals is: y(t)=Wx(t)=WAs(t) Where W represents the separation matrix.

4. The hybrid partial discharge signal separation method according to claim 1, characterized in that: In S2, the whitening preprocessing process is expressed as: Where C is the product of the whitening matrix Q and the mixing matrix A, s(t) is The components in are independent and have a variance of 1; Assume that the correlation matrix of the multi-channel mixed signal x(t) to be detected is Rx, and perform eigenvalue decomposition R on Rx x =PDP T , where D = diag(d1, d2, ... d m ), a diagonal matrix consisting of m eigenvalues, P represents an orthogonal matrix consisting of eigenvectors corresponding to the eigenvalues, and has PP T =1 orthogonal property; let the whitening matrix formula be: The signal after whitening It is expressed as:

5. The hybrid partial discharge signal separation method according to claim 1, characterized in that: In S3, The fourth-order cumulant matrix It is expressed as: in, represents the mixed signal after whitening preprocessing; i, j, k, l represent the indexes of different channels in the mixed signal x(t), which are used to represent the statistical relationship of four different mixed signals; 1≤i,j,k,l≤N, N is the number of input mixed signals; M is an N×N-dimensional weight matrix, which is gradually constructed and updated through eigenvalue decomposition and joint diagonalization by estimating the fourth-order cumulant of the mixed signal. kl is the (k,l)th element in the matrix M.

6. The hybrid partial discharge signal separation method according to claim 5, characterized in that: In S4, for the fourth-order cumulant matrix The process of joint diagonalization is expressed as: By finding different fourth-order cumulant matrices 1≤r≤N, diagonalize F(U) and solve to obtain the unitary matrix U.

7. The hybrid partial discharge signal separation method according to claim 1, characterized in that: In S7, the sign and amplitude of the output signal vector of each separated source signal are estimated by constructing a cost function, and the cost function is expressed as: Among them, Z represents the cost function, N represents the number of sampling points, and x i (t) represents the mixed signal collected by the i-th sensor, y(t) represents the output signal vector matrix after blind source separation, and C represents the correction coefficient matrix.

8. The hybrid partial discharge signal separation method according to claim 7, characterized in that: When Z approaches 0 or is minimized, it means that the amplitude of the separated signal y(t) tends to be equal to the amplitude of the source signal in the corresponding channel, and the amplitude correction is completed.

9. The hybrid partial discharge signal separation method according to claim 7, characterized in that: The AdaGrad method is used to find the amplitude correction coefficient C that minimizes Z.

Images