CN113765502B - PD source filtering method based on S domain compact singular value decomposition - Google Patents
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Abstract
The application discloses a PD source filtering method based on S domain compact singular value decomposition, which belongs to the technical field of high voltage and insulation and comprises the following steps: simulating a partial discharge signal PD through a partial discharge simulator, or receiving the partial discharge signal PD at a site where partial discharge occurs through an ultrahigh frequency antenna; introducing adjusting factors alpha and beta to reform S transformation, and obtaining self-adaptive S transformation; performing adaptive S transformation on the received PD source signal by using the adaptive S transformation to acquire a time spectrum of the PD source signal; using a time-frequency grid search method to adaptively filter out a fixed-frequency signal, and obtaining a coefficient matrix; performing compact singular value decomposition on the coefficient matrix to obtain a characteristic value; obtaining optimal singular value parameters by using a fitting interpolation derivative method, and adaptively filtering noise signals; obtaining a PD source time domain waveform PD' through self-adaptive S inverse transformation; and (5) carrying out comprehensive performance evaluation analysis on the result after the feature extraction. The method can be suitable for PD source filtering of complex noise.
Description
Technical Field
The application belongs to the technical field of high voltage and insulation, and particularly relates to a PD source filtering method based on S-domain compact singular value decomposition.
Background
Partial discharge (partial discharge, PD) is one of the main phenomena causing insulation defects of substation power equipment, and serious insulation degradation can cause insulation failure of the equipment. In order to ensure safe and stable operation of the power equipment, partial discharge detection, positioning and diagnosis of the power equipment of the transformer substation are necessary. However, the field detection environment is often very complex, and various background noises are inevitably present. In addition, the influence of communication equipment, such as a broadcast television mobile terminal, can cause a large amount of fixed frequency interference information to be added into the PD source signal. These disturbances all present difficulties in signal detection and feature extraction for the PD source. Therefore, it is necessary to study the PD source filtering method in a complex environment.
In order to filter out periodic narrowband interference noise in a PD source, there are adaptive filtering algorithms based on empirical mode decomposition (Empirical Mode Decomposition, EMD), which are combined with adaptive filtering algorithms and applied in the filtering of single frequency narrowband interference. In order to improve the operation efficiency of the EMD algorithm, parallel analysis of the EMD algorithm is proposed, and the energy parameter and entropy are applied to the filtering of the PD signal as characteristic parameters. But the filtering method considers the filtering of non-stationary signals. In order to perform cable PD fault diagnosis, a feature extraction method based on wavelet transformation and singular value decomposition is provided, and PD fault useful information is extracted by performing singular value decomposition on a signal after wavelet transformation, so that the method is finally successfully applied to cable fault diagnosis.
Aiming at the problem of white noise pollution in the field PD test, a white noise self-adaptive suppression method based on fluctuation is provided. The method utilizes the fluctuation characteristic of the signal to realize noise suppression in the time domain, and simultaneously eliminates the influence of redundant noise on the PD signal through a threshold window. Aiming at noise interference, a multi-source PD signal detection method based on S transformation exists, PD source signals acquired by different sensors are subjected to S transformation, useful features of the PD sources are extracted and combined with random forests, and the method is finally used for PD source space positioning. But the S time-frequency window of this method is not adjustable. Common methods for interference noise in PD signals include adaptive filter processing algorithm, EMD, improved filter method, wavelet transform filter method, and other filter methods. These methods can achieve varying degrees of feature extraction capability for PD signals within a range of applications. But the general filtering method is to filter white noise interference or to filter a single fixed frequency signal. There are several noise pollution problems for PD source, there are few specific filtering methods.
At present, the filtering method aiming at the dyeing noise PD source has single noise filtering type, and the filtering effect is required to be improved.
Disclosure of Invention
Aiming at the problem that various noise signals are difficult to filter simultaneously in the PD source in the prior art, the application provides a PD source filtering method based on S domain compact singular value decomposition, which can be suitable for PD source filtering with complex noise.
In order to achieve the above object, the present application provides a PD source filtering method based on S-domain compact singular value decomposition, including:
s1: the method for acquiring the partial discharge signal PD includes: simulating a partial discharge signal PD through a partial discharge simulator, or receiving the partial discharge signal PD through an ultrahigh frequency antenna on the spot where the partial discharge occurs;
s2: on the basis of S transformation, introducing adjusting factors alpha and beta to transform the S transformation, and obtaining self-adaptive S transformation;
s3: performing self-adaptive S transformation on the acquired PD source signal by utilizing the self-adaptive S transformation to acquire a time spectrum of the PD source signal;
s4: using a time-frequency grid search method to adaptively select adjustment factors alpha and beta, adaptively filtering fixed-frequency signals, and obtaining a coefficient matrix;
s5: performing compact singular value decomposition on the coefficient matrix to obtain a characteristic value;
s6: obtaining optimal singular value parameters by using a fitting interpolation derivative method, and adaptively filtering noise signals;
s7: obtaining a PD source time domain waveform PD' through self-adaptive S inverse transformation;
s8: and (3) carrying out comprehensive performance evaluation analysis on the result PD' after the feature extraction.
In some alternative embodiments, the simulating the partial discharge signal PD by the partial discharge simulator includes:
the ideal partial discharge signal is simulated by means of the double-exponential decay pulse signal P, wherein,a is the intensity of pulse signal, τ 1 And τ 2 All represent decay constants, f c Representing the oscillation frequency;
adding periodic fixed frequency interference signal P to P signal 1 And white noise interference signal P 2 Thereby P and P 1 And P 2 The three signals are superimposed to obtain an analog PD signal x (t), wherein x (t) =P+P 1 +P 2 。
In some alternative embodiments, the adaptive S-transform is:where τ is the time shift factor, f=1/a, a is the scale factor, α is the gaussian window stretching factor, and β is the frequency scale stretching factor.
In some alternative embodiments, step S3 comprises:
s3.1: s (τ, f) is expressed in discrete case as: s is S T (m,n)＝T (mn)1 x[0]+T (mn)2 x[1]+…+T (mn)(N-1) x[N-1]Wherein T is (mn)p Representing an adaptive discrete S-transformed PD signal x [ p ]]The corresponding linear transformation coefficients, m and N are constants, N is the total sampling point number, p=0, 1,2,..;
s3.2: from the following componentsWill S T The elements in (m, n) are converted into a matrix T (mn)p And matrix x [ p ]]Thereby obtaining a time spectrum of the PD source signal, wherein s mn Is S T [m,n]The m-th row and n-th column of the matrix correspond to the elements.
In some alternative embodiments, step S4 comprises:
s4.1: the area corresponding to the time-frequency adjustment factor alpha is set asThe region corresponding to beta is set as phi, and the spatial domain corresponding to alpha and beta is represented by R;
s4.2: when (when)When beta is epsilon phi, the self-adaptive S transformation is utilized to carry out fixed frequency signal filtering on the PD source, and the signal x 'after inverse transformation is obtained' α,β (p)；
S4.3: from x' α,β (p)＝S α,β (x (p)) determining the filtered signal x' α,β (p) and the pre-filtered PD signal x (p)Tying;
s4.4: by root mean square errorRepresenting the error magnitude before and after PD signal feature extraction, where x f (p) represents an ideal PD source signal, p represents a sampling point, and before and after filtering, the RMSE has a corresponding relation with the adjusting factors alpha and beta;
s4.5: performing grid coding on RMSE before and after PD feature extraction, wherein the discretized grid model consists of G grid pointsThe RMSE size in the grid is denoted rmse=f (x' α,β (p),x f (p)), F represents a function of obtaining the RMSE;
s4.6: searching the minimum value point of the RMSE in the grid as the optimal point of feature extraction, and the alpha and beta corresponding to the minimum RMSE as the optimal value of feature extraction effect, thereby obtaining the T-shaped feature extraction result (mn)p Coefficient matrix T of components (mn) 。
In some alternative embodiments, step S5 comprises:
for coefficient matrix T (mn) A compact singular value decomposition is performed and,wherein V is r ＝[υ 1 ,υ 2 ,…,υ r ]∈M m×r ，W r ＝[w 1 ,w 2 ,…,w r ]∈M n×r R is the number of singular values, sigma represents the singular values, V represents V r W represents W r M represents an orthogonal matrix, i represents a singular value parameter, and the sum term +.>The Frobenius inner products are mutually orthogonal.
In some alternative embodiments, step S6 includes:
s6.1: the observed data were (r) i ,σ i ) The objective is to find a simplest functional relation σ=f (r) instead of the original observation, the m algebraic relations being expressed as:a representation;
s6.2: solving forCoefficient a of (a) j (j=0, 1,2, …, m), the observed data (r) in step S6.1 i ,σ i ) Substituted into->Solving n equations;
s6.3: will be located at r by a polynomial i Solution to and observation function sigma of (2) i Differences betweenCalled remainder R i Thereby obtaining n error equations: />
S6.4: according to the least squares fit criterion, n pairs of data (r i ,σ i ) Solving coefficient a j Is to make the remaining term R i Least sum of squares bySolving;
s6.5: in the process of solvingAt minimum, let ∈>A is a minimum value 0 ,a 1 ,…,a m The parameters are required to meet->
S6.6: by means ofSolving m+1 unknowns a j Where j=0, 1,2, …, m,
s6.7: a in step S6.6 j Substituted into step S6.2In the method, a fitting curve polynomial expression +.>
S6.8: deriving the fitted curve polynomial obtained in the step S6.7 to obtain an optimal singular value parameter Sigma λ And adaptively filtering noise signals.
In some alternative embodiments, step S6.8 comprises:
s6.8.1: using h' (r) =dσ i /dr i Solving singular value fitting curveA first derivative curve;
s6.8.2: using h "(r) =d 2 σ i /dr i 2 Solving singular value fitting curveA second derivative curve;
s6.8.3: obtaining a first-order second-order derivative zero crossing point in S6.8.1 and S6.8.2, and obtaining an optimal singular value parameter as sigma assuming that r=lambda at the moment λ Setting the remaining singular value entries of r > λ to zero;
s6.8.4: restoring the S domain coefficient matrix information of PD signals by using CSVD reconstruction algorithm, namely T (λ) ＝V λ ∑ λ W λ * ，V λ ＝[υ 1 ,υ 2 ,…,υ λ ]∈M m×λ ，W λ ＝[w 1 ,w 2 ,…,w λ ]∈M n×λ 。
In some alternative embodiments, the method comprisesThe PD source time domain waveform PD' is obtained by an adaptive inverse S transform, where n=λ.
In some alternative embodiments, step S8 comprises:
s8.1: when the PD signal source is a simulation signal, selecting one or more combinations of waveform similarity parameters NCC, signal-to-noise ratio SNR, transformation trend parameters VTP and standard root mean square error NRMSE before and after feature extraction as evaluation indexes by comprehensive evaluation parameters;
s8.2: when the PD signal source is a field actual measurement signal, the comprehensive evaluation index selects the noise suppression ratio rho NRR And/or amplitude decay ratio ρ ARR These two parameters serve as feature extraction evaluation criteria.
In general, compared with the prior art, the technical scheme designed by the application can achieve the following obvious effects on the PD signals with complex noise: the self-adaptive S transformation can be used for effectively filtering fixed frequency signals and pulse interference signals in the complex noise PD signals, and an introduced adjusting factor enables an S window to be adjustable. The provided time-frequency domain grid searching method can adaptively select the adjusting factors, so that the method is more intelligent and accurate when filtering the fixed-frequency signals. The background noise signals around the main frequency signals can be further filtered by combining a compact truncated singular value decomposition technology, singular value parameters can be accurately found by a fitting derivative method, and noise signals can be filtered in a self-adaptive mode. In conclusion, the PD source filtering method based on S domain compact singular value decomposition can adaptively filter various noise signals in the complex noise PD signals, has very strong adaptability, and has accurate and effective filtering effect.
Drawings
FIG. 1 is a schematic flow chart of a method according to an embodiment of the present application;
FIG. 2 is a simulated ideal PD signal provided by an embodiment of the application;
FIG. 3 is a simulated complex noise PD signal provided by an embodiment of the application;
FIG. 4 is a S-domain 3D time-frequency spectrum diagram of a PD pulse signal after complex noise dyeing provided by the embodiment of the application;
FIG. 5 is a 3D time domain spectrum of a complex noise-dyed PD signal after filtering a fixed frequency signal under a simulated PD signal provided by an embodiment of the application;
FIG. 6 is a solution curve of a singular value interpolation fitted curve under a simulated PD signal provided by an embodiment of the application;
FIG. 7 is a diagram illustrating a solution of a compact singular value parameter at zero crossing points in an emulated PD signal provided by an embodiment of the present application;
fig. 8 is a time domain waveform diagram of a simulated PD signal after filtering noise signals according to an embodiment of the present application;
FIG. 9 is a graph showing performance evaluation after simulated PD signal filtering provided by an embodiment of the application, wherein (a) is the signal-to-noise ratio (SNR) after PD source signal feature extraction; (b) Extracting a post-waveform similarity parameter (NCC) for the PD source signal features; (c) Extracting post-transformation trend parameters (VTP) for PD source signal features; (d) Post-extraction standard root mean square error (NRMSE) for PD source signal features.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application. In addition, the technical features of the embodiments of the present application described below may be combined with each other as long as they do not collide with each other.
In the examples of the present application, "first," "second," etc. are used to distinguish between different objects, and are not used to describe a particular order or sequence.
The application provides a PD source filtering method based on S domain compact singular value decomposition. The method changes the S transformationAn adjustment factor is introduced in order to make the size of the spectral window adjustable at S-transform. And further acquiring spectrum information at the time of PD source. The time-frequency grid search method adaptively selects adjustment factors alpha and beta, and aims to adaptively filter fixed-frequency signals to obtain a coefficient matrix T (mn) . And the influence on the PD source useful signal in the fixed frequency signal is effectively filtered. The introduction of the compact singular value decomposition aims at eliminating noise signals around a main frequency signal and obtaining a characteristic value sigma k . To eliminate the effect of noise on the dominant frequency signal, an optimal singular value parameter Σ λ The method is obtained by using a fitting interpolation derivative method, and white noise signals are filtered in a self-adaptive mode. Finally, the purpose of filtering the PD source complex noise is achieved. The filtering effect is excellent, and a very high feature extraction effect is achieved.
Fig. 1 is a schematic flow chart of a PD source filtering method for S-domain compact singular value decomposition according to an embodiment of the present application, including the following steps:
s1: acquiring a partial discharge signal PD;
in the embodiment of the application, the partial discharge signal PD can be simulated by a partial discharge simulator, or the partial discharge signal PD can be received by an ultrahigh frequency antenna through the site where the partial discharge occurs.
S2: on the basis of S transformation, introducing adjusting factors alpha and beta to transform the S transformation, and obtaining self-adaptive S transformation;
s3: performing self-adaptive S transformation on the acquired PD source signal by utilizing the self-adaptive S transformation to acquire a time spectrum of the PD source signal;
s4: using a time-frequency grid search method to adaptively select adjustment factors alpha and beta, adaptively filtering fixed-frequency signals, and obtaining a coefficient matrix T (mn) ；
S5: for coefficient matrix T (mn) Performing compact singular value decomposition to obtain a characteristic value sigma r ；
S6: obtaining optimal singular value parameter Sigma by fitting interpolation derivative method λ Adaptively filtering noise signals;
s7: obtaining a PD source time domain waveform PD' through self-adaptive S inverse transformation;
s8: and (3) carrying out comprehensive performance evaluation analysis on the result PD' after the feature extraction.
In the embodiment of the present application, the partial discharge signal PD is simulated by the partial discharge simulator, which may be implemented by:
(1.1) simulation of an ideal partial discharge signal by means of a double-exponential-decay-oscillation pulse signal P, can be achieved byWherein A is the intensity of the pulse signal, τ 1 And τ 2 All represent decay constants, f c Representing the oscillation frequency.
(1.2) periodic fixed-frequency interference Signal P added to P Signal 1 White noise interference signal P 2 Automatically generating by a mathematical algorithm, wherein the white noise dyeing intensity is characterized by SNR, wherein P 1 Can pass through P 1 ＝Bsin(2πf c0 t) obtaining, B represents the pulse intensity of the constant frequency signal, f c0 Representing the oscillation frequency of the periodic fixed frequency signal, P 1 Not only such a signal, the signal is aimed at simulating interference signals such as broadcasting, mobile communication, etc. in a real scene; p (P) 2 Can be automatically generated by awgn function, and has adjustable signal-to-noise ratio and P 2 The signals represent various noise signals, so that P and P can be further calculated 1 P 2 The three signals are superimposed to obtain an analog PD signal x (t), and x (t) =P+P can be obtained 1 +P 2 。
As a preferred embodiment, as shown in fig. 2, the embodiment of the present application provides a simulated ideal PD signal, and the partial discharge signal PD is simulated by a partial discharge simulator, which preferably includes the following implementation steps:
initialization ofRelated parameters of (a): the method comprises the steps of pulse amplitude, sampling point number, damping constant and oscillation frequency; as shown in FIG. 2, the time decay constant τ is set at this time 1 And τ 2 Respectively set as 2ns and 3ns, and the oscillation frequency f c Set to 260MHz. Pulse sampling frequency settingSet at 5GHz/s. Pulse intensity a=25 mV, and the number of sampling points is 1600.PD discharge starting Point p 0 PD onset time t 0 ＝(p 0 -1)/f c . Wherein p is 0 ＝461，t 0 ＝92ns。
Setting pulse sampling frequency, periodic noise amplitude and white noise intensity parameter; fig. 3 shows a simulated complex noise-dyeing PD signal diagram provided by an embodiment of the present application. At the moment, the sampling frequency is 5GHz, the amplitude of a periodic fixed frequency signal added in the PD signal is 0.7mV, the white noise interference signal is automatically generated through a mathematical algorithm, and the white noise dyeing intensity is characterized through SNR.
In the embodiment of the application, in step S2, the adjustment factors α and β are introduced on the basis of the S transformation to transform the S transformation, so as to obtain an adaptive S transformation, which can be realized by the following ways:
s-transform for continuous PD signal x (t), specific S-transform S T (τ, f) is:where τ is the time shift factor, f=1/a, a is called the scale factor;
on the basis of S transformation, a Gaussian window function is modified, two adjusting factors alpha and beta are introduced, the Gaussian window can be freely adjusted according to the characteristics of PD signals after the adjusting factors are introduced, the time-frequency resolution after the S transformation can be adjusted by adding the adjusting factors, and the self-adaptive S transformation is obtained, wherein the self-adaptive S transformation after the improvement is as follows:where α is defined as a gaussian window stretching factor and β is a frequency scale stretching factor.
In the embodiment of the present application, in step S3, the adaptive S transform is performed on the acquired PD source signal by using the adaptive S transform, and the time spectrum of the PD source signal is acquired, which may be implemented in the following manner:
s (τ, f) is expressed in discrete case as: s is S T (m,n)＝T (mn)1 x[0]+T (mn)2 x[1]+…+T (mn)(N-1) x[N-1]Wherein T is (mn)p Representing an adaptive discrete S-transformed PD signal x [ p ]]Corresponding linear transformation coefficient, and T (mn)p The method is characterized in that the method is obtained by a fast Fourier calculation method, m and N are constants, N is the total sampling point number, p=0, 1,2, & gt, N-1;
in the adaptive S-transform, the linear transform coefficients are closely related to m, n, the linear transform coefficients corresponding to a two-dimensional matrix of m and n, matrix T (mn)p Represents one transform element of m×n rows and p columns corresponding to the linear transform coefficient, so that S can be expressed as T (m,n)＝T (mn)1 x[0]+T (mn)2 x[1]+…+T (mn)(N-1) x[N-1]Written in the form:
wherein s is mn Is S T [m,n]The M-th row and N-th column of the matrix correspond to the elements, the value range of M is 1, the value range of M and N is 1, the size of N and N is the same as the total sampling point number, and the matrix is composed of S T (m, n) it is known that the elements of the S matrix can be converted into a matrix T (mn)p And matrix x [ p ]]Thereby obtaining the time spectrum of the PD source signal, the resulting time S-domain spectrum is shown in fig. 4.
In the embodiment of the present application, in step S4, the time-frequency grid search method is used to adaptively select the adjustment factors α and β, adaptively filter the fixed frequency signal, and obtain the signal represented by T (mn)p Coefficient matrix T of components (mn) This can be achieved by:
s4.1: the area corresponding to the time-frequency adjustment factor alpha is set asThe region corresponding to beta is set as phi, and the spatial domain corresponding to alpha and beta is represented by R;
s4.2: when (when)When beta is epsilon phi, the self-adaptive S transformation is utilized to perform fixed frequency signal filtering on the PD sourceDividing to obtain inverse transformed signal x' α,β (p)；
S4.3: filtered signal x' α,β (p) and the pre-filtered PD signal x (p) can be expressed as formula x' α,β (p) =sα, β (x (p)) transformation relation;
s4.4: the error before and after the PD signal characteristic extraction can be obtained by root mean square errorRepresentation, where x f (p) represents an ideal PD source signal, p represents a sampling point, and before and after filtering, the RMSE has a corresponding relation with the adjusting factors alpha and beta;
s4.5: performing grid coding on RMSE before and after PD feature extraction, wherein the discretized grid model consists of G grid pointsThe RMSE size in the trellis may be expressed as rmse=f (x' α,β (p),x f (p)) the smaller the errors between the waveform after feature extraction and the ideal waveform, the better the feature extraction effect is, and F represents a function for obtaining RMSE;
s4.6: searching the minimum value point of the RMSE in the grid as the optimal point of the feature extraction, and the alpha and beta corresponding to the minimum RMSE as the optimal value of the feature extraction effect, thereby obtaining a coefficient matrix T (mn) The resulting S-domain time spectrum of the filtered fixed frequency signal is shown in fig. 5.
In the embodiment of the present application, in step S5, the coefficient matrix T is calculated (mn) Performing compact singular value decomposition to obtain a characteristic value sigma r This can be achieved by:
for coefficient matrix T (mn) A compact singular value decomposition is performed and,wherein V is r ＝[υ 1 ,υ 2 ,…,υ r ]∈M m×r ，W r ＝[w 1 ,w 2 ,…,w r ]∈M n×r R is the number of singular values, sigma represents singularValue V represents V r W represents W r M represents an orthogonal matrix, i represents a singular value parameter, and the sum term +.>Regarding the Frobenius inner products being mutually orthogonal, the formula is satisfied:<σ i υ i w i * ,σ j υ j w j * > F ＝tr(σ i σ j w j υ j * υ i w i * )＝σ i σ j δ ij trw j w i * ＝σ i σ j δ ij trw i * w j ＝σ i σ j δ ij ，i,j＝1,2,…,r。
in the embodiment of the present application, in step S6, the optimal singular value parameter Σ is obtained by using a fitting interpolation derivative method λ The adaptive noise signal filtering can be realized by the following ways:
S6.1：T (mn) compact singular value decomposition into (a)The observed data were (r) i ,σ i ) The objective is to find a simplest functional relation sigma=f (r) instead of the original observed data, and the m algebraic relations can be formulated as followsA representation;
s6.2: solving the formulaCoefficient a of (a) j (j=0, 1,2, …, m), the observed data (r) in step S6.1 i ,σ i ) Substituted into->Solving n equations;
s6.3: will be located at r by a polynomial i Solution to and observation function sigma of (2) i Differences betweenCalled remainder R i From this n error equations can be obtained: />
S6.4: according to the least squares fit criterion, n pairs of data (r i ,σ i ) Solving coefficient a j Is to make the remaining term R i The sum of squares of (2) is minimized by the formulaSolving;
s6.5: in solving the formulaAt minimum, let ∈>A is a minimum value 0 ,a 1 ,…,a m The parameters need to satisfy the formula->
S6.6: using the formula:solving m+1 unknowns a j Where j=0, 1,2, …, m, < >>
S6.7: a in step S6.6 j Substituted into step S6.2In (3) obtaining the polynomial expression +.>The fitting curve is shown in fig. 6, and is compared with three fitting algorithms, and the provided interpolation fitting method is the most stable and has the smallest fluctuation;
s6.8: deriving the fitted curve polynomial obtained in the step S6.7 to obtain an optimal singular value parameter Sigma λ And adaptively filtering noise signals.
In the embodiment of the application, in step S6.8, the specific steps of deriving the fitting curve to obtain the zero crossing point include:
s6.8.1: using the formula h' (r) =dσ i /dr i Solving singular value fitting curveA first derivative curve;
s6.8.2: using the formula h "(r) =d 2 σ i /dr i 2 Solving singular value fitting curveA second derivative curve;
s6.8.3: obtaining a first-order second-order derivative zero crossing point in S6.8.1 and S6.8.2, and obtaining an optimal singular value parameter as sigma assuming that r=lambda at the moment λ Setting the remaining singular value entries of r > λ to zero;
s6.8.4: restoring the S domain coefficient matrix information of PD signals by using CSVD reconstruction algorithm, namely T (λ) ＝V λ ∑ λ W λ *，V λ ＝[υ 1 ,υ 2 ,…,υ λ ]∈M m×λ ，W λ ＝[w 1 ,w 2 ,…,w λ ]∈M n×λ . The zero crossing point solves for the compact singular value parameter under the simulated PD signal as given in fig. 7.
In the embodiment of the present application, in step S7, the PD source time domain waveform PD' is obtained by adaptive S inverse transformation, which may be implemented in the following manner:
adaptive S inverse transform pass-through algorithmA kind of electronic device with high-pressure air-conditioning systemSolving, where n=λ, fig. 8 is a time domain waveform diagram of a simulated PD signal provided in an embodiment of the present application after filtering noise signals.
In the embodiment of the present application, in step S8, the comprehensive performance evaluation analysis is performed on the result PD' after feature extraction, which may be implemented in the following manner:
s8.1: when the PD signal source is a simulation signal, the comprehensive evaluation parameters are selected to take waveform similarity parameters NCC, signal-to-noise ratio SNR, transformation trend parameters VTP and standard root mean square error NRMSE before and after feature extraction as evaluation indexes;
s8.2: when the PD signal source is a field actual measurement signal, the comprehensive evaluation index selects the noise suppression ratio rho NRR Amplitude decay ratio ρ ARR These two parameters serve as feature extraction evaluation criteria. FIG. 9 is a simulated PD signal filtered performance evaluation provided by an embodiment of the application, wherein (a) is the signal-to-noise ratio (SNR) after PD source signal feature extraction; (b) Extracting a post-waveform similarity parameter (NCC) for the PD source signal features; (c) Extracting post-transformation trend parameters (VTP) for PD source signal features; (d) Post-extraction standard root mean square error (NRMSE) for PD source signal features.
According to the application, on the basis of S transformation, the adjusting factors alpha and beta are introduced to transform the S transformation, so as to obtain self-adaptive S transformation; and carrying out self-adaptive S conversion on the received PD source signal by utilizing the self-adaptive S conversion to acquire the time spectrum of the PD source signal, and effectively filtering out the fixed frequency signal and the pulse signal. Meanwhile, the influence of Gaussian white noise on PD signals can be effectively filtered by combining a compact truncated singular value decomposition method. Finally, the purpose of filtering complex noise is achieved, the comprehensive performance is greatly improved, and the filtering effect has higher parameter performance.
It should be noted that each step/component described in the present application may be split into more steps/components, or two or more steps/components or part of operations of the steps/components may be combined into new steps/components, according to the implementation needs, to achieve the object of the present application.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the application and is not intended to limit the application, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the application are intended to be included within the scope of the application.
Claims (8)
1. The PD source filtering method based on S domain compact singular value decomposition is characterized by comprising the following steps of:
s1: the method for acquiring the partial discharge signal PD includes: simulating a partial discharge signal PD through a partial discharge simulator, or receiving the partial discharge signal PD through an ultrahigh frequency antenna on the spot where the partial discharge occurs;
s2: on the basis of S transformation, introducing adjusting factors alpha and beta to transform the S transformation, and obtaining self-adaptive S transformation;
s3: performing self-adaptive S transformation on the acquired PD source signal by utilizing the self-adaptive S transformation to acquire a time spectrum of the PD source signal;
s4: using a time-frequency grid search method to adaptively select adjustment factors alpha and beta, adaptively filtering fixed-frequency signals, and obtaining a coefficient matrix;
s5: performing compact singular value decomposition on the coefficient matrix to obtain a characteristic value;
s6: obtaining optimal singular value parameters by using a fitting interpolation derivative method, and adaptively filtering noise signals;
s7: obtaining a PD source time domain waveform PD' through self-adaptive S inverse transformation;
s8: performing comprehensive performance evaluation analysis on the result PD' after feature extraction;
the step S4 includes:
s4.1: the area corresponding to the time-frequency adjustment factor alpha is set asThe region corresponding to beta is set as phi, and the spatial domain corresponding to alpha and beta is represented by R;
s4.2: when (when)When beta is epsilon phi, the self-adaptive S transformation is utilized to carry out fixed frequency signal filtering on the PD source, and the signal x 'after inverse transformation is obtained' α,β (p)；
S4.3: from x' α,β (p)＝S α,β (x (p)) determining the filtered signal x' α,β (p) and the pre-filtered PD signal x (p);
s4.4: by root mean square errorRepresenting the error magnitude before and after PD signal feature extraction, where x f (p) represents an ideal PD source signal, p represents sampling points, a corresponding relation exists between RMSE and adjustment factors alpha and beta before and after filtering, and N is the total sampling points;
s4.5: performing grid coding on RMSE before and after PD feature extraction, wherein the discretized grid model consists of G grid pointsThe RMSE size in the grid is denoted rmse=f (x' α,β (p),x f (p)), F represents a function of obtaining the RMSE;
s4.6: searching the minimum value point of the RMSE in the grid as the optimal point of feature extraction, and the alpha and beta corresponding to the minimum RMSE as the optimal value of feature extraction effect, thereby obtaining the T-shaped feature extraction result (mn)p Coefficient matrix T of components (mn) ，T (mn)p Representing an adaptive discrete S-transformed PD signal x [ p ]]The corresponding linear transformation coefficients, m and n are constants;
the step S5 comprises the following steps:
for coefficient matrix T (mn) A compact singular value decomposition is performed and,wherein V is r ＝[υ 1 ,υ 2 ,…,υ r ]∈M m×r ，W r ＝[w 1 ,w 2 ,…,w r ]∈M n×r R is the number of singular valuesSigma represents singular values, V represents V r W represents W r M represents an orthogonal matrix, i represents a singular value parameter, and the sum term +.>The Frobenius inner products are mutually orthogonal.
2. The method according to claim 1, wherein the simulating of the partial discharge signal PD by the partial discharge simulator comprises:
the ideal partial discharge signal is simulated by means of the double-exponential decay pulse signal P, wherein,a is the intensity of pulse signal, τ 1 And τ 2 All represent decay constants, f c Representing the oscillation frequency;
adding periodic fixed frequency interference signal P to P signal 1 And white noise interference signal P 2 Thereby P and P 1 And P 2 The three signals are superimposed to obtain an analog PD signal x (t), wherein x (t) =P+P 1 +P 2 。
3. The method of claim 2, wherein the adaptive S-transform is:where τ is the time shift factor, f=1a, a is the scale factor, α is the gaussian window stretching factor, and β is the frequency scale stretching factor.
4. A method according to claim 3, wherein step S3 comprises:
s3.1: s (τ, f) is expressed in discrete case as: s is S T (m,n)＝T (mn)1 x[0]+T (mn)2 x[1]+…+T (mn)(N-1) x[N-1]Wherein T is (mn)p Representing adaptive discrete S-transformed PD signalsx[p]The corresponding linear transformation coefficients, m and N are constants, N is the total sampling point number, p=0, 1,2,..;
s3.2: from the following componentsWill S T The elements in (m, n) are converted into a matrix T (mn)p And matrix x [ p ]]Thereby obtaining a time spectrum of the PD source signal, wherein s mn Is S T [m,n]The m-th row and n-th column of the matrix correspond to the elements.
5. The method according to claim 4, wherein step S6 comprises:
s6.1: the observed data were (r) i ,σ i ) The objective is to find a simplest functional relation σ=f (r) instead of the original observation, the m algebraic relations being expressed as:a representation;
s6.2: solving forCoefficient a of (a) j (j=0, 1,2, …, m), the observed data (r) in step S6.1 i ,σ i ) Substituted into->Solving n equations;
s6.3: will be located at r by a polynomial i Solution to and observation function sigma of (2) i Differences betweenCalled remainder R i Thereby obtaining n error equations: />
S6.4: based on least squares fittingCriterion, n pairs of data (r i ,σ i ) Solving coefficient a j Is to make the remaining term R i Least sum of squares bySolving;
s6.5: in the process of solvingAt minimum, let ∈>A is a minimum value 0 ,a 1 ,…,a m The parameters are required to meet->
S6.6: by means ofSolving m+1 unknowns a j Where j=0, 1,2, …, m,
s6.7: a in step S6.6 j Substituted into step S6.2In the method, a fitting curve polynomial expression +.>
S6.8: deriving the fitted curve polynomial obtained in the step S6.7 to obtain an optimal singular value parameter Sigma λ And adaptively filtering noise signals.
6. The method according to claim 5, wherein step S6.8 comprises:
s6.8.1: using h' (r) =dσ i /dr i Solving singular value fitting curveA first derivative curve;
s6.8.2: by means ofSolving singular value fitting curve ∈ ->A second derivative curve;
s6.8.3: obtaining a first-order second-order derivative zero crossing point in S6.8.1 and S6.8.2, and obtaining an optimal singular value parameter as sigma assuming that r=lambda at the moment λ Setting the remaining singular value entries of r > λ to zero;
s6.8.4: restoring the S domain coefficient matrix information of PD signals by using CSVD reconstruction algorithm, namely T (λ) ＝V λ ∑ λ W λ *，V λ ＝[υ 1 ,υ 2 ,…,υ λ ]∈M m×λ ，W λ ＝[w 1 ,w 2 ,…,w λ ]∈M n×λ 。
7. The method according to claim 6, characterized by that, byThe PD source time domain waveform PD' is obtained by an adaptive inverse S transform, where n=λ.
8. The method of claim 7, wherein step S8 comprises:
s8.1: when the PD signal source is a simulation signal, selecting one or more combinations of waveform similarity parameters NCC, signal-to-noise ratio SNR, transformation trend parameters VTP and standard root mean square error NRMSE before and after feature extraction as evaluation indexes by comprehensive evaluation parameters;
s8.2: when the PD signal source is a field actual measurement signal, the comprehensive evaluation index selects the noise suppression ratio rho NRR And/or amplitude decay ratio ρ ARR These two parameters serve as feature extraction evaluation criteria.
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