CN113765502A - PD source filtering method based on S-domain compact singular value decomposition - Google Patents
PD source filtering method based on S-domain compact singular value decomposition Download PDFInfo
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Abstract
The invention 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 on a partial discharge site through an ultrahigh frequency antenna; introducing regulating factors alpha and beta to reform S transformation to obtain self-adaptive S transformation; carrying out self-adaptive S conversion on the received PD source signal by utilizing the self-adaptive S conversion to obtain a time frequency spectrum of the PD source signal; using a time-frequency grid search method to adaptively filter out fixed-frequency signals and obtain a coefficient matrix; carrying out compact singular value decomposition on the coefficient matrix to obtain a characteristic value; obtaining optimal singular value parameters by using a fitting interpolation derivation method, and filtering noise signals in a self-adaptive manner; obtaining a PD source time domain waveform PD' through self-adaptive S inverse transformation; and carrying out comprehensive performance evaluation analysis on the result after the characteristic extraction. The invention can be suitable for the PD source filtering of complex noise pollution.
Description
Technical Field
The invention 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 (PD) is one of the main phenomena causing insulation defects of substation power equipment, and serious insulation degradation causes insulation failure of the equipment. In order to ensure the safe and stable operation of the power equipment, it is necessary to perform partial discharge detection, positioning and diagnosis on the power equipment of the transformer substation. However, the field detection environment is very complex, and various background noises are inevitably existed. In addition, the influence of communication equipment, such as a broadcast television mobile terminal, etc., may cause a great amount of fixed frequency interference information to be added to the PD source signal. These interferences can cause difficulties in signal detection and feature extraction of PD sources. Therefore, it is necessary to research a PD source filtering method in a complex environment.
In order to filter out periodic narrow-band interference noise in the PD source, there is an adaptive filtering algorithm based on Empirical Mode Decomposition (EMD), which is combined with the adaptive filtering algorithm and applied to filtering out single-frequency narrow-band interference. In order to improve the operation efficiency of the EMD algorithm, parallel analysis is carried out on the EMD algorithm, and the energy parameter and the entropy are used as characteristic parameters to be applied to the filtering of the PD signal. But the filtering method considers filtering of non-stationary signals. In order to carry out cable PD fault diagnosis, a characteristic extraction method based on wavelet transformation and singular value decomposition is provided, useful PD fault information is extracted by carrying out singular value decomposition on signals after wavelet transformation, and the method is finally successfully applied to cable fault diagnosis.
Aiming at the problem of white noise pollution in field PD test, a white noise self-adaptive suppression method based on fluctuation is provided. The method realizes the suppression of noise by using the fluctuation characteristic of the signal in a 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, the PD source signals obtained by different sensors are subjected to S transformation, useful features of the PD source are extracted to be combined with random forests, and finally the method is used for PD source space positioning. But the S time-frequency window of the method is not adjustable. Currently, common methods for the interference noise in the PD signal include adaptive filtering processing algorithm, EMD and its improved filtering method, wavelet transform filtering method, and other filtering methods. The methods can realize different degrees of feature extraction capability on PD signals within a certain application range. But the general filtering method is to filter out white noise interference or to filter out single fixed frequency signal. Aiming at the problems of various noise pollution of PD sources, a special filtering method is rarely available.
The existing filtering method for the noise-contaminated PD source has the defects that the type of noise to be filtered is single, and the filtering effect needs to be improved.
Disclosure of Invention
Aiming at the problem that multiple noise signals are difficult to filter in the PD source in the prior art, the invention provides a PD source filtering method based on S-domain compact singular value decomposition, which can be applied to the complex noise-polluted PD source filtering.
In order to achieve the above object, the present invention provides a PD source filtering method based on S-domain compact singular value decomposition, including:
s1: acquiring a partial discharge signal PD, wherein the manner of acquiring the partial discharge signal PD comprises the following steps: simulating a partial discharge signal PD through a partial discharge simulator, or receiving the partial discharge signal PD by using an ultrahigh frequency antenna through a partial discharge site;
s2: on the basis of S transformation, adjusting factors alpha and beta are introduced to reform the S transformation to obtain self-adaptive S transformation;
s3: carrying out self-adaptive S conversion on the obtained PD source signal by utilizing the self-adaptive S conversion to obtain a time frequency spectrum of the PD source signal;
s4: self-adaptively selecting adjustment factors alpha and beta by using a time-frequency grid search method, and filtering fixed-frequency signals in a self-adaptive manner to obtain a coefficient matrix;
s5: carrying out compact singular value decomposition on the coefficient matrix to obtain a characteristic value;
s6: obtaining optimal singular value parameters by using a fitting interpolation derivation method, and filtering noise signals in a self-adaptive manner;
s7: obtaining a PD source time domain waveform PD' through self-adaptive S inverse transformation;
s8: and (4) carrying out comprehensive performance evaluation analysis on the result PD' after the characteristic extraction.
In some optional embodiments, the simulating the partial discharge signal PD by the partial discharge simulator includes:
an ideal partial discharge signal is simulated by using a dual-exponential ringing pulse signal P, wherein,
a is the intensity of the pulse signal, τ1And τ2All represent the attenuation constant, fcRepresents the oscillation frequency;
adding periodic fixed frequency interference signal P to P signal1And a white noise interference signal P2Further combine P with P1And P2Superposing the three signals to obtain an analog PD signal x (t), wherein x (t) is P + P1+P2。
In some alternative embodiments, the adaptive S transform is:
where τ is a time shift factor, f is 1/a, a is called a scale factor, α is a gaussian window stretching factor, and β is a frequency scale stretching factor.
In some alternative embodiments, step S3 includes:
s3.1: in the discrete case, S (τ, f) is expressed as: sT(m,n)＝T(mn)1x[0]+T(mn)2x[1]+…+T(mn)(N-1)x[N-1]Wherein, T(mn)pRepresenting an adaptive discrete S-transform PD signal x [ p ]]Corresponding linear transformation coefficients, wherein m and N are constants, N is the total number of sampling points, and p is 0,1, 2.
S3.2: by
Will STConversion of the elements in (m, n) into a matrix T(mn)pAnd matrix x [ p ]]Thereby obtaining a time spectrum of the PD source signal, where smnIs ST[m,n]The mth row and the nth column of the matrix.
In some alternative embodiments, step S4 includes:
s4.1: the region corresponding to the time-frequency adjustment factor alpha is set as
The region corresponding to beta is set as phi, and the spatial domain corresponding to alpha and beta is represented by R;
s4.2: when in use
When beta belongs to phi, the PD source is filtered by the fixed frequency signal by utilizing the self-adaptive S transformation, and the inverse transformed signal x 'is obtained'α,β(p)；
S4.3: from x'α,β(p)＝Sα,β(x (p)) determining the filtered signal x'α,β(p) a transformation relation with the PD signal x (p) before filtering;
s4.4: from root mean square error
Representing the error before and after PD signal feature extraction, wherein xf(p) represents an ideal PD source signal, p represents a sampling point, and the RMSE before and after filtering has a corresponding relation with the adjustment factors alpha and beta;
s4.5: carrying out grid coding on RMSE before and after PD feature extraction, wherein the discretization grid model is composed of G grid points
The RMSE size in the mesh is expressed as RMSE ═ F (x'α,β(p),xf(p)), F represents a function to solve RMSE;
s4.6: searching the minimum point of RMSE in the grid as the optimal point of feature extraction, and obtaining the optimal value of the feature extraction effect by alpha and beta corresponding to the minimum RMSE(mn)pComposed coefficient matrix T(mn)。
In some alternative embodiments, step S5 includes:
for coefficient matrix T(mn)The compact singular value decomposition is carried out to obtain the singular value,
wherein, Vr＝[υ1,υ2,…,υr]∈Mm×r，Wr＝[w1,w2,…,wr]∈Mn×rR is the number of singular values, sigma is the singular value, upsilon is VrW represents WrM denotes an orthogonal matrix, i denotes a singular value parameter, sum term
The Frobenius inner products are orthogonal to each other.
In some alternative embodiments, step S6 includes:
s6.1: the observed data are (r)i,σi) The objective is to find a simplest functional relation σ ═ f (r) instead of the original observed data, and the m-degree algebraic relation is expressed as:
represents;
s6.2: solve out
Coefficient a of (1)j(j is 0,1,2, …, m), and the observed data (r) in step S6.1 is compared with the observed data (r) in step S2i,σi) Substitution into
Solving n equations;
s6.3: will be located at r by a polynomialiSolution of and observation function σiDifference therebetween
Referred to as the residue term RiThus, n error equations are obtained:
s6.4: n pairs of data (r) according to a least squares fitting criterioni,σi) Solving the coefficient ajIs such that the residue term RiHas the smallest sum of squares, by
Solving;
s6.5: in the request of
At a minimum value, such that
A is a minimum value0,a1,…,amEach parameter needs to be satisfied
S6.6: by using
Solving m +1 unknowns ajWhere j is 0,1,2, …, m,
s6.7: a in step S6.6jSubstituted in step S6.2
In (1), obtaining fitting curve polynomial expression
S6.8: the fitting curve polynomial obtained in the step S6.7 is subjected to derivation to obtain the optimal singular value parameter sigmaλAnd adaptively filtering the noise signal.
In some alternative embodiments, step S6.8 comprises:
s6.8.1: using h' (r) ═ d σi/driSolving a singular value fitting curve
A first derivative curve;
s6.8.2: using h' (r) ═ d2σi/dri 2Solving a singular value fitting curve
A second derivative curve;
s6.8.3: the zero crossing point of the first-order second derivative in S6.8.1 and S6.8.2 is obtained, and the optimal singular value parameter is sigma when r is lambdaλSetting the residual singular value items of r & gt lambda to zero;
s6.8.4: restoring S-domain coefficient matrix information of PD signals, namely T, by using CSVD reconstruction algorithm(λ)＝Vλ∑λWλ *，Vλ＝[υ1,υ2,…,υλ]∈Mm×λ，Wλ＝[w1,w2,…,wλ]∈Mn×λ。
In some alternative embodiments, the composition is prepared by
And obtaining a PD source time domain waveform PD' through adaptive inverse S transform, wherein N is lambda.
In some alternative embodiments, step S8 includes:
s8.1: when the PD signal source is a simulation signal, the comprehensive evaluation parameter selects one or more combinations of a waveform similarity parameter NCC, a signal-to-noise ratio SNR, a transformation trend parameter VTP and a standard root mean square error NRMSE before and after feature extraction as an evaluation index;
s8.2: when the PD signal source is a field actual measurement signal, the noise suppression ratio rho is selected according to the comprehensive evaluation indexNRRAnd/or amplitude attenuation ratio pARRThese two parameters serve as feature extraction evaluation criteria.
In general, compared with the prior art, the technical scheme of the invention can achieve the following obvious effects on complex noise-contaminated PD signals: fixed frequency signals and pulse interference signals in the complex noise-contaminated PD signals can be effectively filtered by utilizing self-adaptive S conversion, and the S window is adjustable by the introduced adjusting factors. The provided time-frequency domain grid searching method can adaptively select the adjustment factors, so that the fixed-frequency signals are more intelligently and accurately filtered. By combining with the technology of compact truncation singular value decomposition, background noise signals around the main frequency signal can be further filtered, and the fitting derivation method can accurately find singular value parameters and adaptively filter noise signals. In conclusion, the PD source filtering method based on S-domain compact singular value decomposition can adaptively filter various noise signals in complex noise-contaminated PD signals, and has very strong adaptivity and accurate and effective filtering effect.
Drawings
FIG. 1 is a schematic flow chart of a method provided by an embodiment of the present invention;
FIG. 2 is a diagram illustrating an exemplary simulated ideal PD signal according to an embodiment of the present invention;
fig. 3 is a simulated complex noise-contaminated PD signal provided by an embodiment of the present invention;
fig. 4 is an S-domain 3D time-frequency spectrogram of a PD pulse signal after complex noise contamination according to an embodiment of the present invention;
fig. 5 is a 3D time domain spectrum of a complex noise-contaminated PD signal with a fixed-frequency signal filtered out, in a simulated PD signal according to an embodiment of the present invention;
fig. 6 is a singular value interpolation fitting curve solving curve under a simulated PD signal according to an embodiment of the present invention;
fig. 7 is a diagram illustrating a zero-crossing point for solving compact singular value parameters under a simulated PD signal according to an embodiment of the present invention;
fig. 8 is a time domain waveform diagram of a simulated PD signal after noise signals are filtered out according to an embodiment of the present invention;
fig. 9 is a performance evaluation after filtering of a simulated PD signal according to an embodiment of the present invention, where (a) a signal-to-noise ratio (SNR) is extracted for PD source signal features; (b) extracting a post-waveform similarity parameter (NCC) for the PD source signal characteristics; (c) transforming trend parameters (VTP) after PD source signal feature extraction; (d) and extracting the standard root mean square error (NRMSE) of the PD source signal characteristics.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
In the present examples, "first", "second", etc. are used for distinguishing different objects, and are not used for describing a specific order or sequence.
The invention provides a PD source filtering method based on S-domain compact singular value decomposition. The method introduces an adjustment factor by improving the S transformation, and aims to enable the size of a frequency spectrum window to be adjustable during the S transformation. And further acquiring PD source time-frequency spectrum information. The time-frequency grid search method adaptively selects the adjustment factors alpha and beta, and aims to adaptively filter the fixed-frequency signals and obtain a coefficient matrix T(mn). The influence on useful signals of a PD source in fixed-frequency signals is effectively filtered. The introduction of the compact singular value decomposition aims at eliminating noise signals around the main frequency signal and obtaining a characteristic value sigmak. For eliminating the influence of noise on the main frequency signal, the optimal singular value parameter sigmaλThe white noise signal is obtained by utilizing a fitting interpolation derivation method and is filtered in a self-adaptive mode. Finally, the purpose of filtering the complex noise of the PD source is achieved. The filtering effect is superior, and a high characteristic 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 invention, which includes the following steps:
s1: acquiring a partial discharge signal PD;
in the embodiment of the invention, the partial discharge signal PD can be simulated through a partial discharge simulator, or the partial discharge signal PD can be received by using an ultrahigh frequency antenna through a partial discharge site.
S2: on the basis of S transformation, adjusting factors alpha and beta are introduced to reform the S transformation to obtain self-adaptive S transformation;
s3: carrying out self-adaptive S conversion on the obtained PD source signal by utilizing the self-adaptive S conversion to obtain a time frequency spectrum of the PD source signal;
s4: self-adaptively selecting adjustment factors alpha and beta by using a time-frequency grid search method, filtering fixed-frequency signals in a self-adaptive manner, and acquiring a coefficient matrix T(mn)；
S5: for coefficient matrix T(mn)Carrying out compact singular value decomposition to obtain a characteristic value sigmar；
S6: obtaining optimal singular value parameter sigma by fitting interpolation derivation methodλAdaptively filtering noise signals;
s7: obtaining a PD source time domain waveform PD' through self-adaptive S inverse transformation;
s8: and (4) carrying out comprehensive performance evaluation analysis on the result PD' after the characteristic extraction.
In the embodiment of the present invention, the partial discharge signal PD is simulated by a partial discharge simulator, and the simulation can be implemented in the following manner:
(1.1) the ideal partial discharge signal is simulated by using the double-exponential decaying oscillation pulse signal P, and the ideal partial discharge signal can be obtained by
Wherein A is the intensity of the pulse signal, τ1And τ2All represent the attenuation constant, fcRepresenting the oscillation frequency.
(1.2) periodic fixed-frequency interference signal P added to P signal1White noise interference signal P2Automatically generated by a mathematical algorithm, and the white noise pollution intensity is characterized by SNR, wherein P1Can pass through P1＝Bsin(2πfc0t) acquisition, B represents the pulse intensity of the fixed frequency signal, fc0Representing the oscillation frequency, P, of a periodic fixed-frequency signal1Not only to such a signal, which is intended to simulate an interference signal of broadcasting, mobile communication, etc. in an actual scene; p2Can be automatically generated through an awgn function, the signal-to-noise ratio is adjustable, and P2The signal represents various noise signals, and P can be further combined1And P2The three signals are superposed to obtain an analog PD signal x (t), and x (t) is P + P1+P2。
As a preferred implementation manner, as shown in fig. 2, the simulation of the ideal PD signal provided in the embodiment of the present invention simulates a partial discharge signal PD through a partial discharge simulator, and the preferred implementation steps are as follows:
initialization
The relevant parameters in (1): the method comprises the steps of pulse amplitude, sampling point number, attenuation constant and oscillation frequency; as shown in FIG. 2, the time decay constant τ is set at this time1And τ2Set to 2ns and 3ns, respectively, oscillation frequency fcSet to 260 MHz. The pulse sampling frequency was set to 5 GHz/s. The pulse intensity A is 25mV, and the number of sampling points is 1600. PD discharge starting point is p0PD starting time is t0＝(p0-1)/fc. Wherein p is0＝461，t0＝92ns。
Setting pulse sampling frequency, periodic noise amplitude and white noise intensity parameters; fig. 3 is a diagram illustrating a simulated complex noise-contaminated PD signal according to an embodiment of the present invention. The sampling frequency is 5GHz, the amplitude of a periodic fixed frequency signal added in the PD signal is 0.7mV, a white noise interference signal is automatically generated through a mathematical algorithm, and the white noise pollution intensity is represented through an SNR.
In the embodiment of the present invention, in step S2, the adjustment factors α and β are introduced on the basis of the S transform to reform the S transform, so as to obtain the adaptive S transform, which may be implemented by:
performing S transformation on continuous PD signals x (t), specifically S transformation ST(τ, f) is:
where τ is a time shift factor, f is 1/a, and a is called a scale factor;
on the basis of S transformation, a Gaussian window function is transformed, two regulating factors alpha and beta are introduced, the Gaussian window can be freely adjusted according to the characteristics of PD signals after the regulating factors are introduced, and the time-frequency resolution after the S transformation can be regulated by adding the regulating factors, so that self-adaptive S transformation is obtained, wherein the improved self-adaptive S transformation is as follows:
where α is defined as the gaussian window stretch factor and β is the frequency scale stretch factor.
In the embodiment of the present invention, in step S3, the obtained PD source signal is subjected to adaptive S transform by using adaptive S transform, and a time-frequency spectrum of the PD source signal is obtained, which may be implemented by:
in the discrete case, S (τ, f) is expressed as: sT(m,n)＝T(mn)1x[0]+T(mn)2x[1]+…+T(mn)(N-1)x[N-1]Wherein, T(mn)pRepresenting an adaptive discrete S-transform PD signal x [ p ]]Corresponding linear transform coefficient, and T(mn)pThe method is obtained by a fast Fourier calculation method, wherein m and N are constants, N is the total number of sampling points, and p is 0,1, 2.
In the adaptive S-transform, linear transform coefficients are closely related to m, n, and correspond to a two-dimensional matrix about m and n, matrix T(mn)pOne transform element representing m × n rows and p columns to which the linear transform coefficient corresponds, and thus S may be setT(m,n)＝T(mn)1x[0]+T(mn)2x[1]+…+T(mn)(N-1)x[N-1]Written as follows:
wherein s ismnIs ST[m,n]The value range of M is 1, the value range of M, N is 1, the value range of N is the same as the total sampling point number, and S is ST(m, n) it is known that the elements of the S matrix can be converted into a matrix T(mn)pAnd matrix x [ p ]]Thereby obtaining a time-frequency spectrum of the PD source signal, the resulting time-S domain spectrum being shown in fig. 4.
In step S4, adjusting factors α and β are adaptively selected by using a time-frequency grid search method, and the fixed-frequency signal is adaptively filtered to obtain a filtered signal T(mn)pComposed coefficient matrix T(mn)The method can be realized by the following steps:
s4.1: the region corresponding to the time-frequency adjustment factor alpha is set as
The region corresponding to beta is set as phi, and the spatial domain corresponding to alpha and beta is represented by R;
s4.2: when in use
When beta belongs to phi, the PD source is filtered by the fixed frequency signal by utilizing the self-adaptive S transformation, and the inverse transformed signal x 'is obtained'α,β(p)；
S4.3: filtered signal x'α,β(p) and the PD signal x (p) before filtering can be expressed as formula x'α,β(p) ═ S α, β (x (p)) transform relationships;
s4.4: the error before and after PD signal feature extraction can be calculated by root mean square error
Is represented by, wherein xf(p) represents an ideal PD source signal, p represents a sampling point, and the RMSE before and after filtering has a corresponding relation with the adjustment factors alpha and beta;
s4.5: carrying out grid coding on RMSE before and after PD feature extraction, wherein the discretization grid model is composed of G grid points
The RMSE size in the mesh may be expressed as RMSE ═ F (x'α,β(p),xf(p)), the smaller the error between the waveform after feature extraction and the ideal waveform is, the better the feature extraction effect is, and F represents the function of solving RMSE;
s4.6: searching a minimum value point of RMSE in the grid as an optimal point of feature extraction, and obtaining a coefficient matrix T by taking alpha and beta corresponding to the minimum RMSE as optimal values of feature extraction effect(mn)The resulting S-domain time-frequency spectrum of the filtered fixed-frequency signal is shown in fig. 5.
In the embodiment of the present invention, in step S5, coefficient matrix T is processed(mn)Carrying out compact singular value decomposition to obtain a characteristic value sigmarThe method can be realized by the following steps:
for coefficient matrix T(mn)The compact singular value decomposition is carried out to obtain the singular value,
wherein, Vr＝[υ1,υ2,…,υr]∈Mm×r，Wr＝[w1,w2,…,wr]∈Mn×rR is the number of singular values, sigma is the singular value, upsilon is VrW represents WrM denotes an orthogonal matrix, i denotes a singular value parameter, sum term
Regarding Frobenius inner products are mutually orthogonal, the formula is satisfied:<σiυiwi *,σjυjwj *>F＝tr(σiσjwjυj *υiwi *)＝σiσjδijtrwjwi *＝σiσjδijtrwi *wj＝σiσjδij，i,j＝1,2,…,r。
in the embodiment of the invention, in step S6, the optimal singular value parameter Σ is obtained by using the fitting interpolation derivation methodλThe adaptive noise signal filtering can be realized by the following steps:
S6.1：T(mn)is decomposed into compact singular values
The observed data are (r)i,σi) The objective is to find a simplest functional relation σ ═ f (r) instead of the original observed data, and the m-degree algebraic relation can be represented by a formula
Represents;
s6.2: find out a publicFormula (II)
Coefficient a of (1)j(j is 0,1,2, …, m), and the observed data (r) in step S6.1 is compared with the observed data (r) in step S2i,σi) Substitution into
Solving n equations;
s6.3: will be located at r by a polynomialiSolution of and observation function σiDifference therebetween
Referred to as the residue term RiFrom this, n error equations can be obtained:
s6.4: n pairs of data (r) according to a least squares fitting criterioni,σi) Solving the coefficient ajIs such that the residue term RiThe sum of squares of (a) and (b) is minimized, can be represented by the formula
Solving;
s6.5: in the solution of formula
At a minimum value, such that
A is a minimum value0,a1,…,amEach parameter needs to satisfy the formula
S6.6: using the formula:
solving m +1 unknowns ajWhere j is 0,1,2, …, m,
s6.7: a in step S6.6jSubstituted in step S6.2
In the method, a fitting curve polynomial expression can be obtained
The fitting curve is shown in FIG. 6, and is compared with three fitting algorithms at the same time, the interpolation fitting method is most stable, and the volatility is minimum;
s6.8: the fitting curve polynomial obtained in the step S6.7 is subjected to derivation to obtain the optimal singular value parameter sigmaλAnd adaptively filtering the noise signal.
In the embodiment of the present invention, in step S6.8, the step of obtaining the zero-crossing point by fitting curve derivation specifically includes:
s6.8.1: using the formula h' (r) ═ d σi/driSolving a singular value fitting curve
A first derivative curve;
s6.8.2: using the formula h' (r) ═ d2σi/dri 2Solving a singular value fitting curve
A second derivative curve;
s6.8.3: the zero crossing point of the first-order second derivative in S6.8.1 and S6.8.2 is obtained, and the optimal singular value parameter is sigma when r is lambdaλSetting the residual singular value items of r & gt lambda to zero;
s6.8.4: restoring S-domain coefficient matrix information of PD signals, namely T, by using CSVD reconstruction algorithm(λ)＝Vλ∑λWλ*，Vλ＝[υ1,υ2,…,υλ]∈Mm×λ，Wλ＝[w1,w2,…,wλ]∈Mn×λ. Under the simulated PD signal, the zero-crossing point is used for solving compact singular value parameters, as shown in FIG. 7.
In the embodiment of the present invention, in step S7, a PD source time-domain waveform PD' is obtained through adaptive inverse S transform, which may be implemented as follows:
adaptive inverse S transform pass formula
And solving, where N ═ λ, fig. 8 is a time domain waveform diagram of the simulated PD signal after noise signals are filtered out, according to the embodiment of the present invention.
In the embodiment of the present invention, in step S8, the overall performance evaluation analysis of the result PD' after feature extraction may be implemented by:
s8.1: when the PD signal source is a simulation signal, the comprehensive evaluation parameters select a waveform similarity parameter NCC, a signal-to-noise ratio SNR, a transformation trend parameter VTP and a 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 noise suppression ratio rho is selected as the comprehensive evaluation indexNRRAnd amplitude attenuation ratio ρARRThese two parameters serve as feature extraction evaluation criteria. Fig. 9 is a performance evaluation of a simulated PD signal after filtering according to an embodiment of the present invention, where (a) a signal-to-noise ratio (SNR) after extracting PD source signal features; (b) extracting a post-waveform similarity parameter (NCC) for the PD source signal characteristics; (c) transforming trend parameters (VTP) after PD source signal feature extraction; (d) and extracting the standard root mean square error (NRMSE) of the PD source signal characteristics.
On the basis of S transformation, adjusting factors alpha and beta are introduced to reform the S transformation to obtain self-adaptive S transformation; and the received PD source signal is subjected to self-adaptive S conversion by utilizing the self-adaptive S conversion to obtain a time frequency spectrum of the PD source signal, and a fixed frequency signal and a pulse signal are effectively filtered. Meanwhile, the influence of Gaussian white noise on the PD signal 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, according to the implementation requirement, each step/component described in the present application can be divided into more steps/components, and two or more steps/components or partial operations of the steps/components can be combined into new steps/components to achieve the purpose of the present invention.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A PD source filtering method based on S-domain compact singular value decomposition is characterized by comprising the following steps:
s1: acquiring a partial discharge signal PD, wherein the manner of acquiring the partial discharge signal PD comprises the following steps: simulating a partial discharge signal PD through a partial discharge simulator, or receiving the partial discharge signal PD by using an ultrahigh frequency antenna through a partial discharge site;
s2: on the basis of S transformation, adjusting factors alpha and beta are introduced to reform the S transformation to obtain self-adaptive S transformation;
s3: carrying out self-adaptive S conversion on the obtained PD source signal by utilizing the self-adaptive S conversion to obtain a time frequency spectrum of the PD source signal;
s4: self-adaptively selecting adjustment factors alpha and beta by using a time-frequency grid search method, and filtering fixed-frequency signals in a self-adaptive manner to obtain a coefficient matrix;
s5: carrying out compact singular value decomposition on the coefficient matrix to obtain a characteristic value;
s6: obtaining optimal singular value parameters by using a fitting interpolation derivation method, and filtering noise signals in a self-adaptive manner;
s7: obtaining a PD source time domain waveform PD' through self-adaptive S inverse transformation;
s8: and (4) carrying out comprehensive performance evaluation analysis on the result PD' after the characteristic extraction.
2. The method of claim 1, wherein simulating a partial discharge signal PD by a partial discharge simulator comprises:
an ideal partial discharge signal is simulated by using a dual-exponential ringing pulse signal P, wherein,
a is the intensity of the pulse signal, τ1And τ2All represent the attenuation constant, fcRepresents the oscillation frequency;
adding periodic fixed frequency interference signal P to P signal1And a white noise interference signal P2Further combine P with P1And P2Superposing the three signals to obtain an analog PD signal x (t), wherein x (t) is P + P1+P2。
3. The method of claim 2, wherein the adaptive S-transform is to:
where τ is a time shift factor, f is 1/a, a is called a scale factor, α is a gaussian window stretching factor, and β is a frequency scale stretching factor.
4. The method according to claim 3, wherein step S3 includes:
s3.1: in the discrete case, S (τ, f) is expressed as: sT(m,n)＝T(mn)1x[0]+T(mn)2x[1]+…+T(mn)(N-1)x[N-1]Wherein, T(mn)pRepresenting an adaptive discrete S-transform PD signal x [ p ]]Corresponding linear transformation coefficients, wherein m and N are constants, N is the total number of sampling points, and p is 0,1, 2.
S3.2: by
Will STConversion of the elements in (m, n) into a matrix T(mn)pAnd matrix x [ p ]]Thereby obtaining a time spectrum of the PD source signal,wherein s ismnIs ST[m,n]The mth row and the nth column of the matrix.
5. The method according to claim 4, wherein step S4 includes:
s4.1: the region corresponding to the time-frequency adjustment factor alpha is set as
The region corresponding to beta is set as phi, and the spatial domain corresponding to alpha and beta is represented by R;
s4.2: when in use
When beta belongs to phi, the PD source is filtered by the fixed frequency signal by utilizing the self-adaptive S transformation, and the inverse transformed signal x 'is obtained'α,β(p)；
S4.3: from x'α,β(p)＝Sα,β(x (p)) determining the filtered signal x'α,β(p) a transformation relation with the PD signal x (p) before filtering;
s4.4: from root mean square error
Representing the error before and after PD signal feature extraction, wherein xf(p) represents an ideal PD source signal, p represents a sampling point, and the RMSE before and after filtering has a corresponding relation with the adjustment factors alpha and beta;
s4.5: carrying out grid coding on RMSE before and after PD feature extraction, wherein the discretization grid model is composed of G grid points
The RMSE size in the mesh is expressed as RMSE ═ F (x'α,β(p),xf(p)), F represents a function to solve RMSE;
s4.6: searching the minimum point of RMSE in the grid as the optimal point of feature extraction, and obtaining the optimal value of the feature extraction effect by alpha and beta corresponding to the minimum RMSE(mn)pComposed coefficient matrix T(mn)。
6. The method according to claim 5, wherein step S5 includes:
for coefficient matrix T(mn)The compact singular value decomposition is carried out to obtain the singular value,
wherein, Vr＝[υ1,υ2,…,υr]∈Mm×r，Wr＝[w1,w2,…,wr]∈Mn×rR is the number of singular values, sigma is the singular value, upsilon is VrW represents WrM denotes an orthogonal matrix, i denotes a singular value parameter, sum term
The Frobenius inner products are orthogonal to each other.
7. The method according to claim 6, wherein step S6 includes:
s6.1: the observed data are (r)i,σi) The objective is to find a simplest functional relation σ ═ f (r) instead of the original observed data, and the m-degree algebraic relation is expressed as:
represents;
s6.2: solve out
Coefficient a of (1)j(j is 0,1,2, …, m), and the observed data (r) in step S6.1 is compared with the observed data (r) in step S2i,σi) Substitution into
Solving n equations;
s6.3: will be located at r by a polynomialiSolution of and observation function σiDifference therebetween
Referred to as the residue term RiThus, n error equations are obtained:
s6.4: n pairs of data (r) according to a least squares fitting criterioni,σi) Solving the coefficient ajIs such that the residue term RiHas the smallest sum of squares, by
Solving;
s6.5: in the request of
At a minimum value, such that
A is a minimum value0,a1,…,amEach parameter needs to be satisfied
S6.6: by using
Solving m +1 unknowns ajWhere j is 0,1,2, …, m,
s6.7: a in step S6.6jSubstituted in step S6.2
In (1), obtaining fitting curve polynomial expression
S6.8: the fitting curve polynomial obtained in the step S6.7 is subjected to derivation to obtain the optimal singular value parameter sigmaλAnd adaptively filtering the noise signal.
8. The method according to claim 7, characterized in that step S6.8 comprises:
s6.8.1: using h' (r) ═ d σi/driSolving a singular value fitting curve
A first derivative curve;
s6.8.2: using h' (r) ═ d2σi/dri 2Solving a singular value fitting curve
A second derivative curve;
s6.8.3: the zero crossing point of the first-order second derivative in S6.8.1 and S6.8.2 is obtained, and the optimal singular value parameter is sigma when r is lambdaλSetting the residual singular value items of r & gt lambda to zero;
s6.8.4: restoring S-domain coefficient matrix information of PD signals, namely T, by using CSVD reconstruction algorithm(λ)＝Vλ∑λWλ*，Vλ＝[υ1,υ2,…,υλ]∈Mm×λ，Wλ＝[w1,w2,…,wλ]∈Mn×λ。
9. The method of claim 8, wherein the method is performed by
And obtaining a PD source time domain waveform PD' through adaptive inverse S transform, wherein N is lambda.
10. The method according to claim 9, wherein step S8 includes:
s8.1: when the PD signal source is a simulation signal, the comprehensive evaluation parameter selects one or more combinations of a waveform similarity parameter NCC, a signal-to-noise ratio SNR, a transformation trend parameter VTP and a standard root mean square error NRMSE before and after feature extraction as an evaluation index;
s8.2: when the PD signal source is a field actual measurement signal, the noise suppression ratio rho is selected according to the comprehensive evaluation indexNRRAnd/or amplitude attenuation ratio pARRThese two parameters serve as feature extraction evaluation criteria.
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