CN103558498B - Based on the insulator pollution flashover leakage current signal sparse representation method of wavelet analysis - Google Patents

Abstract

The invention discloses a kind of insulator pollution flashover leakage current signal sparse representation method based on wavelet analysis in power system signal processing technology field.Comprise and adopt sym8 Orthogonal Wavelets to be sparse base Ψ, wavelet structure sparse transformation orthogonal matrix and obtain the degree of rarefication K of original leakage current signal; Structure gaussian random matrix Φ, it can be used as observing matrix, according to degree of rarefication K computation and measurement number M, is obtained measure vectorial y and sensing matrix Θ by rarefaction representation equation; Under OMP algorithm, original leakage current signal is reconstructed by measurement vectorial y and sensing matrix Θ.The present invention not only reduces the requirement of sensor sample frequency, and under the prerequisite not affecting signal quality, improve collection and the reconstructed velocity of signal, ensure that the accuracy of reconstruct simultaneously.

Description

Based on the insulator pollution flashover leakage current signal sparse representation method of wavelet analysis

Technical field

The invention belongs to power system signal processing technology field, particularly relate to a kind of insulator pollution flashover leakage current signal sparse representation method based on wavelet analysis.

Background technology

In the Real-Time Monitoring of insulator contamination leakage current, pollution flashover leakage current signal sampling rate and processing speed require more and more higher, and huge data volume poses a big pressure to the collect and transmit of leakage current signal and storage.Compressed sensing (CS) can sparse characteristic by what utilize leakage current signal, under the condition much smaller than Nyquist sampling rate, utilizes less measured value to recover original signal, thus alleviates above-mentioned data acquisition transmission and store pressure.

Based on CS thought, in the Its Sparse Decomposition process of sparse signal representation, signal decomposes usually on one group of complete orthogonal basis, mainly contains Fourier transform, Gabor transformation, wavelet transformation etc.But Fourier transform can only time, frequency domain a certain territory on global observing is carried out to signal, also require that signal meets smooth performance.Gabor transformation solves signal Localization Problems, but cannot realize multiresolution analysis.

The present invention proposes the insulator pollution flashover leakage current signal sparse representation method based on wavelet analysis, namely Wavelet Transformation Algorithm is adopted to carry out Its Sparse Decomposition to insulator leakage current on sym8 wavelet basis, and by adopting orthogonal matching pursuit method to be reconstructed, thus achieve the rarefaction representation of signal.The present invention not only reduces the requirement of sensor sample frequency, and under the prerequisite not affecting signal quality, improve collection and the reconstructed velocity of signal, and good basis has been laid in the realization for the Real-Time Monitoring carrying out pollution flashover leakage current.

Summary of the invention

The object of the invention is to, a kind of insulator pollution flashover leakage current signal sparse representation method based on wavelet analysis is provided, in reduction sensor sample frequency with while not affecting signal quality, collection and the reconstructed velocity of leakage current signal can be improved, and improve the accuracy of reconstruct.

To achieve these goals, the technical scheme that the present invention proposes is that a kind of insulator pollution flashover leakage current signal sparse representation method based on wavelet analysis, is characterized in that described method comprises:

Step 1: select sparse base and calculate the degree of rarefication of original leakage current signal;

Step 2: structure gaussian random matrix Φ, and computation and measurement vector y and sensing matrix Θ;

Step 3: utilize measurement vectorial y and sensing matrix Θ to reconstruct original leakage current signal.

Described step 1 comprises:

Step: 11: select sym8 Orthogonal Wavelets as sparse base, design low-pass filter and Hi-pass filter respectively according to sym8 Orthogonal Wavelets;

Step 12: use low-pass filter and Hi-pass filter to carry out from 1 to log initial leak current signal respectively ₂(N) wavelet decomposition of layer, the low-pass filter coefficient of dissociation h and Hi-pass filter coefficient of dissociation g, the N that obtain each layer are the length of initial leak current signal;

Step 13: wavelet structure sparse transformation orthogonal matrix

Step 14: according to formula calculate the small echo sparse coefficient vector of original leakage current signal, wherein x is N × 1 dimensional signal of original leakage current signal in sym8 Orthogonal Wavelets;

Step 15: will the degree of rarefication K of number as original leakage current signal of the small echo sparse coefficient of setting threshold epsilon be greater than.

Described sub-step 13 comprises:

Sub-step 1301: make j=log ₂l+1, L are the length of low-pass filter coefficient of dissociation h, make initial orthogonal matrix for unit matrix I;

Sub-step 1302: utilize the low-pass filter coefficient of dissociation of jth layer to extract the characteristics of low-frequency coefficient of initial leak current signal, obtain characteristics of low-frequency coefficient vector H _j; Utilize the Hi-pass filter coefficient of dissociation of jth layer to extract the high-frequency characteristic coefficient of initial leak current signal, obtain high-frequency characteristic coefficient vector G _j;

Sub-step 1303: make i=1;

Sub-step 1304: to characteristics of low-frequency coefficient vector H _jwith high-frequency characteristic coefficient vector G _jcarry out cyclic extension, namely to characteristics of low-frequency coefficient vector H _jwith high-frequency characteristic coefficient vector G _jincrease by 2 respectively ^j-L row null vector, obtains characteristics of low-frequency matrix of coefficients H _j' and high-frequency characteristic matrix of coefficients G _j';

Sub-step 1305: respectively to characteristics of low-frequency matrix of coefficients H _j' and high-frequency characteristic matrix of coefficients G _j' in column vector carry out single step circumferential displacement;

Sub-step 1306: judge i>2 ^j-1whether set up, if i>2 ^j-1then perform step 1307; Otherwise, make i=i+1, return step 1304;

Sub-step 1307: to characteristics of low-frequency matrix of coefficients H _j' and high-frequency characteristic matrix of coefficients G _j' carry out orthogonalization process, obtain orthogonal matrix

Sub-step 1308: judge j>log ₂whether N sets up, if j>log ₂n, then perform sub-step 1309; Otherwise order and make j=j+1, return sub-step 1302;

Sub-step 1309: the iteration now terminating j, obtains final orthogonal matrix and make be small echo sparse transformation orthogonal matrix.

Described step 2 comprises:

Step 21: according to the degree of rarefication K computation and measurement number M of original leakage current signal; M is the nearest positive integer of distance Klog (N/K);

Step 22: structure exponent number is the gaussian random matrix Φ of M × N, and gaussian random matrix Φ and sparse basis array Ψ is uncorrelated;

Step 23: according to formula y=Φ f computation and measurement vector y; Wherein, f is original leakage current signal;

Step 24: calculate sensing matrix Θ according to formula Θ=Φ Ψ; Wherein, Ψ is sparse basis array;

Described step 3 comprises:

Step 31: set redundancy vector initial value γ respectively ₀, index set initial value Λ ₀with primary iteration number of times t;

Wherein, redundancy vector initial value γ ₀=y;

Index set initial value Λ ₀for empty set;

Primary iteration number of times t=0;

Step 32: according to formula computation index value δ _t, and make Λ _t=Λ _t-1∪ { δ _t;

Wherein, u _jfor related coefficient and u _j=| < γ _t, θ _j>|;

θ _jfor the jth row column vector of sensing matrix Θ;

N is the length of initial leak current signal;

Step 33: according to formula calculating makes residual error y-Θ x _isignal estimation value time minimum wherein, x _ifor time initial leak current signal;

Step 34: according to formula calculate the redundancy vector γ of the t time iteration _t;

Step 35: judge whether t<2 × K sets up, if t<2 × K, then make t=t+1, return step 32; Otherwise, perform sub-step 36;

Step 36: will with small echo sparse transformation orthogonal matrix inverse matrix do the time-domain signal that inverse wavelet transform obtains reconstructing

The present invention by carrying out Its Sparse Decomposition to insulator leakage current signal on sym8 wavelet basis, and is reconstructed by employing orthogonal matching pursuit method, reaches the rarefaction representation of signal; Further, the present invention not only reduces the requirement of sensor sample frequency, and under the prerequisite not affecting signal quality, improve collection and the reconstructed velocity of signal, ensure that the accuracy of reconstruct simultaneously.

Accompanying drawing explanation

Fig. 1 is the insulator pollution flashover leakage current signal sparse representation method process flow diagram based on wavelet analysis;

Fig. 2 is the original leakage current signal figure of insulator that embodiment provides;

Fig. 3 is the restructuring graph of the original leakage current signal of insulator that embodiment provides.

Embodiment

Below in conjunction with accompanying drawing, preferred embodiment is elaborated.It is emphasized that following explanation is only exemplary, instead of in order to limit the scope of the invention and apply.

Embodiment 1

Fig. 1 is the insulator pollution flashover leakage current signal sparse representation method process flow diagram based on wavelet analysis.Below in conjunction with Fig. 1, side's ratio juris provided by the invention is described.As shown in Figure 1, the insulator pollution flashover leakage current signal sparse representation method based on wavelet analysis provided by the invention comprises:

Step 1: select sparse base and calculate the degree of rarefication of original leakage current signal.

The principle of compressed sensing is, is the initial leak current signal f of N, with one group of base vector Ψ=[ψ for length ₁, ψ ₂.., ψ _n] linear combination represent, namely Ψ is N × N sparse basis array.X is the equivalent representation of initial leak current signal f on Ψ territory, when x only has K(K<<N) individual nonzero coefficient time, then signal is sparse, and now title Ψ is the sparse base of signal f, and sparse coefficient number now becomes degree of rarefication K.

Process described in step 1 comprises the steps:

Step 11: select sym8 Orthogonal Wavelets as sparse base, design low-pass filter and Hi-pass filter respectively according to sym8 Orthogonal Wavelets.

Step 12: use low-pass filter and Hi-pass filter to carry out from 1 to log initial leak current signal respectively ₂(N) wavelet decomposition of layer, the low-pass filter coefficient of dissociation h and Hi-pass filter coefficient of dissociation g, the N that obtain each layer are the length of initial leak current signal.

Given wavelet basis is asked resolution filter coefficient had ripe implementation method, in general software for mathematical computing (as MATLAB), all provide this algorithm.Utilize the wfilters function in MATLAB, low-pass filter coefficient of dissociation h and the Hi-pass filter coefficient of dissociation g of sym8 base can be calculated.

Step 13: wavelet structure sparse transformation orthogonal matrix it specifically comprises following sub-step:

Sub-step 1301: make j=log ₂l+1, L are the length of low-pass filter coefficient of dissociation h.Meanwhile, initial orthogonal matrix is made for unit matrix I.

Sub-step 1302: utilize the low-pass filter coefficient of dissociation of jth layer to extract the characteristics of low-frequency coefficient of initial leak current signal, obtain characteristics of low-frequency coefficient vector H _j; Utilize the Hi-pass filter coefficient of dissociation of jth layer to extract the high-frequency characteristic coefficient of initial leak current signal, obtain high-frequency characteristic coefficient vector G _j.

Sub-step 1303: make i=1.

Sub-step 1304: to characteristics of low-frequency coefficient vector H _jwith high-frequency characteristic coefficient vector G _jcarry out cyclic extension, namely to characteristics of low-frequency coefficient vector H _jwith high-frequency characteristic coefficient vector G _jincrease by 2 respectively ^j-L row null vector, obtains characteristics of low-frequency matrix of coefficients H _j' and high-frequency characteristic matrix of coefficients G _j'.

Sub-step 1305: respectively to characteristics of low-frequency matrix of coefficients H _j' and high-frequency characteristic matrix of coefficients G _j' in column vector carry out single step circumferential displacement.Single step circumferential displacement is exactly by (or left) the mobile row to the right of the column vector in matrix, and the rightest (the most left) row move on the most left (or the rightest) row.

Sub-step 1306: judge i>2 ^j-1whether set up, if i>2 ^j-1then perform step 1307; Otherwise, make i=i+1, return step 1304.

Sub-step 1307: to characteristics of low-frequency matrix of coefficients H _j' and high-frequency characteristic matrix of coefficients G _j' carry out orthogonalization process, obtain orthogonal matrix

Sub-step 1308: judge j>log ₂whether N sets up, if j>log ₂n, then perform sub-step 1309; Otherwise order and make j=j+1, return sub-step 1302.

Sub-step 1309: the iteration now terminating j, obtains final orthogonal matrix and make be small echo sparse transformation orthogonal matrix.

Wavelet structure sparse transformation orthogonal matrix in this way to fall decomposing each subband data obtained respectively in the subspace of mutually orthogonal L2 (R), making each subband data correlativity reduce, being conducive to Exact Reconstruction original signal.

Step 14: according to formula calculate the small echo sparse coefficient vector of original leakage current signal, wherein x is N × 1 dimensional signal of original leakage current signal in sym8 Orthogonal Wavelets.

Step 15: will the degree of rarefication K of number as original leakage current signal of the small echo sparse coefficient of setting threshold epsilon be greater than.

The setting of threshold epsilon and the characteristic of signal and change relevant, the present invention is in order to simple computation, and the method for usual employing global threshold, determines a unified threshold value; Meanwhile, in order to make unified threshold value can carry out adaptability selection according to different signal characteristics, present invention employs and divide the interval of sparse coefficient then to get same Interval mean value be the method for threshold value.

Step 2: structure gaussian random matrix Φ, and computation and measurement vector y and sensing matrix Θ.

The implementation procedure of step 2 specifically comprises:

Step 21: be the nearest positive integer of distance Klog (N/K) according to the degree of rarefication K computation and measurement number M of original leakage current signal, M, adopts following formulae discovery:

$M=\left\{\begin{array}{c}\left[K\log (N/K)\right],K\log (N/K)-\left[K\log (N/K)\right]\&le;0.5\\ \left[K\log (N/K)\right]+1,K\log (N/K)-\left[K\log (N/K)\right]>0.5\end{array}\right.$

Wherein, [Klog (N/K)] is the rounding operation of Klog (N/K), namely when Klog (N/K) than its round result large 0.5 time, illustrate Klog (N/K) distance [Klog (N/K)]+1 nearer.Otherwise, illustrate that Klog (N/K) distance [Klog (N/K)] is nearer.

Step 22: structure exponent number is the gaussian random matrix Φ of M × N, and gaussian random matrix Φ and sparse basis array Ψ is uncorrelated.

Step 23: according to formula y=Φ f computation and measurement vector y; Wherein, f is original leakage current signal.

The necessary and sufficient condition recovering original signal due to y meets the equidistant criterion of constraint (RIP), and the condition of equivalence sparse transformation base Ψ of RIP is uncorrelated with observation battle array Φ, and sparse transformation base Ψ has fixed herein, so need observation battle array to meet RIP.There is theoretical proof gaussian random matrix just in time to meet RIP, then set observing matrix Φ to tie up gaussian random matrix as N × M, substitute into expression formula y=Φ Ψ x and obtain linear measurement, namely measure vectorial y.

Step 24: calculate sensing matrix Θ according to formula Θ=Φ Ψ; Wherein, Ψ is sparse basis array.

Step 3: utilize measurement vectorial y and sensing matrix Θ to reconstruct original leakage current signal.

The process of reconstruct initial leak current signal comprises again:

Step 31: set redundancy vector initial value γ respectively ₀, index set initial value Λ ₀with primary iteration number of times t.Wherein, redundancy vector initial value γ ₀=y, index set initial value Λ ₀for empty set, primary iteration number of times t=0;

Step 32: according to formula computation index value δ _t, and make Λ _t=Λ _t-1∪ { δ _t.Wherein, u _jfor related coefficient and u _j=| < γ _t, θ _j>|, the i.e. absolute value of the inner product of redundancy vector and sensing matrix respective column vector, θ _jfor the jth row column vector of sensing matrix Θ, N is the length of initial leak current signal.

Step 33: according to formula adopt least square method to calculate and make residual error y-Θ x _isignal estimation value time minimum wherein, x _ifor time initial leak current signal.

Step 34: according to formula calculate the redundancy vector γ of the t time iteration _t.

Step 35: judge whether t<2 × K sets up, if t<2 × K, then make t=t+1, return step 32; Otherwise, perform sub-step 36.

Step 36: will with small echo sparse transformation orthogonal matrix inverse matrix do the time-domain signal that inverse wavelet transform obtains reconstructing

The present invention is in above-mentioned reconstruction step, iterations is set to the twice of fixing degree of rarefication K, decrease the time in order to solve iterations, and the contradiction between signal degree of accuracy and reconstitution time can be balanced, simplify orthogonal matching pursuit algorithm (OMP).

Embodiment 2

Below for the insulator pollution flashover leakage current signal of reality, implementation process of the present invention is described.What the present invention adopted is salinity (ESDD) be 0.4, gray scale (NSDD) is 2, voltage is use the sample frequency of 10kHz to the pollution flashover leakage current signal of standard form insulator surface under 110KV condition, 2048 points gathered wherein carry out case analysis, and sampled data set is:

[0.863;0.924;1.006;1.22;1.644;2.234;2.854;3.369;3.721;4.01;4.49;...;-0.1]

Unit is milliampere (mA), and the signal graph drawn with MATLAB as shown in Figure 2.

Step 1: select Orthogonal Wavelets to be sparse base Ψ, wavelet structure sparse transformation orthogonal matrix and obtain the degree of rarefication K of original leakage current signal.

The present invention selects sym8 Orthogonal Wavelets, and when being the initial leak current signal f of N by length, with one group of base vector Ψ=[ψ ₁, ψ ₂.., ψ _n] linear combination represent, namely Ψ is N × N matrix, x is the equivalent representation of signal f on Ψ territory, when x only has K(K<<N) individual nonzero coefficient time, then signal is sparse, now title Ψ is the sparse base of signal f, and sparse coefficient number now becomes degree of rarefication K.N=2048 in this example.

Step 11: select sym8 Orthogonal Wavelets as sparse base, design low-pass filter and Hi-pass filter respectively according to sym8 Orthogonal Wavelets.

Step 12: use low-pass filter and Hi-pass filter to carry out from 1 to log initial leak current signal respectively ₂(N) wavelet decomposition of layer, obtain low-pass filter coefficient of dissociation h and the Hi-pass filter coefficient of dissociation g of each layer, wherein N is the length of initial leak current signal, log2(N)=log2(2048)=11.

Obtain respectively after four after retaining radix point:

h=[-0.0034,-0.0005,0.0317,0.0076,-0.1433,-0.0613,0.4814,0.7772,0.3644,-0.0519.-0.0272,0.0491,0.0038,-0.0150.-0.0003,0.0019]，

g=[-0.0019,-0.0003,0.0150,0.0038,-0.0491,-0.0272,0.0519,0.3644,-0.7772,0.4814,0.0613,-0.1433,-0.0076,0.0317,0.0005,-0.0034]。

Wherein sym8 wavelet basis is the symlet small echo with 8 rank vanishing moments, by scaling Equations $\mathrm{\&phi;}\left(x\right)=\sqrt{2}\underset{n\&Element;Z}{\mathrm{\&Sigma;}}h\left(n\right)\mathrm{\&phi;}(2x-n),$ Wavelet basis equationof structure $\mathrm{\&Psi;}\left(x\right)=\sqrt{2}\underset{n\&Element;Z}{\mathrm{\&Sigma;}}{g}_n\mathrm{\&phi;}(2x-n)$ And relational expression g (n)=± (-1) ^1-nh (1-n) can draw wavelet basis function Ψ (x).H (n) can be constructed by equation below:

$\left\{\begin{array}{c}W\left(z\right)=U\left(z\right)\stackrel{\&OverBar;}{U(\frac{1}{z})}={\left[{\cos }^2\left(\frac{w}{2}\right)\right]}^{N}P\left[{\sin }^2\left(\frac{w}{2}\right)\right]\\ P\left(y\right)=\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{C}_k^{N-1+K}{y}^k\end{array}\right.$

Wherein z=e ^iw, ω is angular frequency.When the root of U (z) mould square to be greater than 1 time structure be symlet small echo.

Step 13: wavelet structure sparse transformation orthogonal matrix

Sub-step 1301: make j=log ₂l+1, L are the length of low-pass filter coefficient of dissociation h, and L=16 makes initial orthogonal matrix for unit matrix I.

Sub-step 1302: utilize the low-pass filter coefficient of dissociation of jth layer to extract the characteristics of low-frequency coefficient of initial leak current signal, obtain characteristics of low-frequency coefficient vector H _j; Utilize the Hi-pass filter coefficient of dissociation of jth layer to extract the high-frequency characteristic coefficient of initial leak current signal, obtain high-frequency characteristic coefficient vector G _j.

Sub-step 1303: make i=1.

Sub-step 1304: to characteristics of low-frequency coefficient vector H _jwith high-frequency characteristic coefficient vector G _jcarry out cyclic extension, namely to characteristics of low-frequency coefficient vector H _jwith high-frequency characteristic coefficient vector G _jincrease by 2 respectively ^j-L row null vector, obtains characteristics of low-frequency matrix of coefficients H _j' and high-frequency characteristic matrix of coefficients G _j'.

Sub-step 1305: respectively to characteristics of low-frequency matrix of coefficients H _j' and high-frequency characteristic matrix of coefficients G _j' in column vector carry out single step circumferential displacement.

Sub-step 1306: judge i>2 ^j-1whether set up, if i>2 ^j-1then perform step 1307; Otherwise, make i=i+1, return step 1304.

Sub-step 1307: to characteristics of low-frequency matrix of coefficients H _j' and high-frequency characteristic matrix of coefficients G _j' carry out orthogonalization process, obtain orthogonal matrix

Sub-step 1308: judge j>log ₂whether N sets up, if j>log ₂n, then perform sub-step 1309; Otherwise order and make j=j+1, return sub-step 1302.

Sub-step 1309: the iteration now terminating j, obtains final orthogonal matrix and make be small echo sparse transformation orthogonal matrix.

Because matrix too huge, thus within the rule go out, some programming tool can be used to calculate, such as MATLAB, result directly can substitute into next step.

Step 14: according to formula calculate the small echo sparse coefficient vector of original leakage current signal, wherein x is 2048 × 1 dimensional signals of original leakage current signal in sym8 Orthogonal Wavelets, then XWAVE is 2048 × 1 dimensions:

XWAVE=[0.0177; 0.1378; 0.1823; 0.2183; 0.0045; 0.2838; 0.1165; 0.0354; 0.0243; 0.1461; 6,2695e-4; 3.2671e-5; 4.6706e-5; 3.9453e-7; 2.4082e-6], data are too many, only ten numbers and rear five numbers before this lists XWAVE.

Step 15: the threshold value of setting small echo sparse coefficient is ε, and the coefficient number being greater than threshold epsilon is set to degree of rarefication K, be original leakage current signal degree of rarefication.

The setting of threshold value and the characteristic of signal and change relevant, the present invention is in order to simple computation, and the method for usual employing global threshold, determines a unified threshold value; Meanwhile, in order to make unified threshold value can carry out adaptability selection according to different signal characteristics, present invention employs and divide the interval of sparse coefficient then to get same Interval mean value be the method for threshold value.In this example, the sparse coefficient XWAVE of signal is divided into 20 intervals, and calculate each interval coefficient mean value and the number of coefficient, using the coefficient mean value in interval maximum for coefficient number as threshold epsilon, the coefficient number being greater than threshold epsilon is set to degree of rarefication K, in this example, to contain the interval of 1950 points as coefficient of restitution, threshold value is 0.0248, and degree of rarefication K is 146.

Step 2: structure gaussian random matrix Φ, and computation and measurement vector y and sensing matrix Θ.

Step 21: be the nearest positive integer of distance Klog (N/K) according to the degree of rarefication K computation and measurement number M of original leakage current signal, M.

Step 22: structure exponent number is the gaussian random matrix Φ of M × N, and gaussian random matrix Φ meets and small echo sparse transformation orthogonal matrix independence, signal f is carried out linear projection according to formula y=Φ f, then signal is tieed up by N and is dropped to M dimension, wherein y is that M dimension measures battle array, M is for measuring number, M >=cKlog (N/K).The present embodiment calculates M=386.

Step 23: according to formula y=Φ f computation and measurement vector y; Wherein, f is original leakage current signal.

This example can directly adopt stochastic matrix function randn (M, the N)=randn (386,2048) in MATLAB to construct 386 × 2048 gaussian random matrixes, then calculate the measurement vector of 386 × 1 according to y=Φ Ψ x:

Y=[-2.8229e+3; 1.4013e+3; 4.7197e+3; 223.7540; 5.3618e+3; 4.7203+3; 1.5410e+3;-1.9145e+3;-43.6646;-1.4499e+3;-3.1721e+3; 1.3935e+3; 270.0417;-3.8352e+3; 72.4483], front ten numbers of y and rear five numbers are only listed here.

Step 24: calculate sensing matrix Θ according to formula Θ=Φ Ψ; Wherein, Ψ is sparse basis array.

Step 3: utilize measurement vectorial y and sensing matrix Θ to reconstruct original leakage current signal.

The process of reconstruct initial leak current signal comprises again:

Step 31: set redundancy vector initial value γ respectively ₀, index set initial value Λ ₀with primary iteration number of times t.Wherein, redundancy vector initial value γ ₀=y, index set initial value Λ ₀for empty set, primary iteration number of times t=0;

Step 32: according to formula computation index value δ _t, and make Λ _t=Λ _t-1∪ { δ _t.Wherein, u _jfor related coefficient and u _j=| < γ _t, θ _j>|, the i.e. absolute value of the inner product of redundancy vector and sensing matrix respective column vector, θ _jfor the jth row column vector of sensing matrix Θ, N is the length of initial leak current signal.

Step 33: according to formula adopt least square method to calculate and make residual error y-Θ x _isignal estimation value time minimum wherein, x _ifor time initial leak current signal.

Step 34: according to formula calculate the redundancy vector γ of the t time iteration _t.

In the present embodiment, the final redundancy vector γ calculated _tbe the vector of 386 × 1: γ _t=[-0.5379; 0.0614; 0.2896; 0.2158; 0.3833; 1.6716;-2.2200;-2.0355;-3.1984; 1.4061].

Step 35: due in the present embodiment, degree of rarefication K=146, therefore judges whether t<2 × 146 set up, if t<2 × 146, then makes t=t+1, return step 32; Otherwise, perform sub-step 36.

Iterations is set to the twice of fixing degree of rarefication K, decreases the time solving iterations, and the contradiction between signal degree of accuracy and reconstitution time can be balanced, simplify orthogonal matching pursuit algorithm (OMP).

Step 36: will with small echo sparse transformation orthogonal matrix inverse matrix do the time-domain signal that inverse wavelet transform obtains reconstructing .

The maximum correlation coefficient u finally obtained _tthe Signal estimation of the index position pos at place be then spectral domain to be reconstructed vector r_y, the reconstruct spectral domain vector for the treatment of that this example calculates 1 × 2048 dimension is:

r_y=[1.8551,142.4470,-219.7036,179.3667,0,-283.7255,…,0,50.7893,0,0,0,8.2076]。

By spectral domain vector sum small echo sparse transformation orthogonal matrix to be reconstructed inverse matrix do inverse wavelet transform obtain reconstruct 2048 × 1 dimension time-domain signals be:

$\hat{f}=[22.0010;13.1960;20.5435;19.6215;10.8332;...;-6.6397;1.4932;23.0058;-29.3130;39.8138].$

Draw the signal reconstruction figure that obtains as shown in Figure 3 with MATLAB, can find out and reach good quality reconstruction.

The method that the present invention proposes can under comparatively low sampling rate, and carry out rarefaction representation to pollution flashover leakage current signal, reach rapid and sample accurately and reconstruct, good basis has been laid in the realization for the Real-Time Monitoring carrying out pollution flashover leakage current.

The above; be only the present invention's preferably embodiment, but protection scope of the present invention is not limited thereto, is anyly familiar with those skilled in the art in the technical scope that the present invention discloses; the change that can expect easily or replacement, all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.

Claims (3)

1., based on an insulator pollution flashover leakage current signal sparse representation method for wavelet analysis, it is characterized in that described method comprises:

Step 1: select sparse base and calculate the degree of rarefication of original leakage current signal;

Step 2: structure gaussian random matrix Φ, and computation and measurement vector y and sensing matrix Θ;

Step 3: utilize measurement vectorial y and sensing matrix Θ to reconstruct original leakage current signal;

Described step 2 comprises:

Step 21: according to the degree of rarefication K computation and measurement number M of original leakage current signal; M is the nearest positive integer of distance Klog (N/K), adopts following formulae discovery:

$M=\{\begin{array}{cc}\&lsqb;Klog(N/K)\&rsqb;,& Klog(N/K)-\&lsqb;Klog(N/K)\&rsqb;\&le;0.5\\ \&lsqb;Klog(N/K)\&rsqb;+1,& Klog(N/K)-\&lsqb;Klog(N/K)\&rsqb;>0.5\end{array}$

Wherein, [Klog (N/K)] is the rounding operation of Klog (N/K), namely when Klog (N/K) than its round result large 0.5 time, illustrate Klog (N/K) distance [Klog (N/K)]+1 nearer; Otherwise, illustrate that Klog (N/K) distance [Klog (N/K)] is nearer;

Step 22: structure exponent number is the gaussian random matrix Φ of M × N, and gaussian random matrix Φ and sparse basis array Ψ is uncorrelated;

Step 23: according to formula y=Φ f computation and measurement vector y; Wherein, f is original leakage current signal;

Step 24: calculate sensing matrix Θ according to formula Θ=Φ Ψ; Wherein, Ψ is sparse basis array;

Described step 3 comprises:

Step 31: set redundancy vector initial value γ respectively ₀, index set initial value Λ ₀with primary iteration number of times t;

Wherein, redundancy vector initial value γ ₀=y;

Index set initial value Λ ₀for empty set;

Primary iteration number of times t=0;

Step 32: according to formula computation index value δ _t, and make Λ _t=Λ _t-1∪ { δ _t;

Wherein, u _jfor related coefficient and u _j=| < γ _t, θ _j>|;

θ _jfor the jth row column vector of sensing matrix Θ;

N is the length of initial leak current signal;

Step 33: according to formula calculating makes residual error y-Θ x _isignal estimation value time minimum wherein, x _ifor time initial leak current signal;

Step 34: according to formula calculate the redundancy vector γ of the t time iteration _t;

Step 35: judge whether t<2 × K sets up, if t<2 × K, then make t=t+1, return step 32; Otherwise, perform step 36;

Step 36: will with small echo sparse transformation orthogonal matrix inverse matrix do the time-domain signal that inverse wavelet transform obtains reconstructing

2. method according to claim 1, is characterized in that described step 1 comprises:

Step: 11: select sym8 Orthogonal Wavelets as sparse base, design low-pass filter and Hi-pass filter respectively according to sym8 Orthogonal Wavelets;

Step 12: use low-pass filter and Hi-pass filter to carry out from 1 to log initial leak current signal respectively ₂(N) wavelet decomposition of layer, the low-pass filter coefficient of dissociation h and Hi-pass filter coefficient of dissociation g, the N that obtain each layer are the length of initial leak current signal;

Step 13: wavelet structure sparse transformation orthogonal matrix

Step 14: according to formula calculate the small echo sparse coefficient vector of original leakage current signal, wherein x is N × 1 dimensional signal of original leakage current signal in sym8 Orthogonal Wavelets;

Step 15: will the degree of rarefication K of number as original leakage current signal of the small echo sparse coefficient of setting threshold epsilon be greater than.

3. method according to claim 2, is characterized in that described step 13 comprises:

Step 1301: make j=log ₂l+1, L are the length of low-pass filter coefficient of dissociation h, make initial orthogonal matrix for unit matrix I;

Step 1302: utilize the low-pass filter coefficient of dissociation of jth layer to extract the characteristics of low-frequency coefficient of initial leak current signal, obtain characteristics of low-frequency coefficient vector H _j; Utilize the Hi-pass filter coefficient of dissociation of jth layer to extract the high-frequency characteristic coefficient of initial leak current signal, obtain high-frequency characteristic coefficient vector G _j;

Step 1303: make i=1;

Step 1304: to characteristics of low-frequency coefficient vector H _jwith high-frequency characteristic coefficient vector G _jcarry out cyclic extension, namely to characteristics of low-frequency coefficient vector H _jwith high-frequency characteristic coefficient vector G _jincrease by 2 respectively ^j-L row null vector, obtains characteristics of low-frequency matrix of coefficients H ' _jwith high-frequency characteristic matrix of coefficients G ' _j;

Step 1305: respectively to characteristics of low-frequency matrix of coefficients H ' _jwith high-frequency characteristic matrix of coefficients G ' _jin column vector carry out single step circumferential displacement;

Step 1306: judge i>2 ^j-1whether set up, if i>2 ^j-1then perform step 1307; Otherwise, make i=i+1, return step 1304;

Step 1307: to characteristics of low-frequency matrix of coefficients H ' _jwith high-frequency characteristic matrix of coefficients G ' _jcarry out orthogonalization process, obtain orthogonal matrix

Step 1308: judge j>log ₂whether N sets up, if j>log ₂n, then perform step 1309; Otherwise order and make j=j+1, return step 1302;

Step 1309: the iteration now terminating j, obtains final orthogonal matrix and make be small echo sparse transformation orthogonal matrix.