CN103995950A - Wavelet coefficient partial discharge signal noise elimination method based on related space domain correction threshold values - Google Patents

Abstract

The invention belongs to the field of industrial signal processing, and particularly relates to a wavelet coefficient partial discharge signal noise elimination method based on related space domain correction threshold values. The method includes the steps that wavelet transformation is carried out on partial discharge signals containing white noise; an initial value and an estimated value of a wavelet coefficient are extracted; size correlation coefficients are solved; correlation values are obtained after normalization; discrete wavelet transform is recorded and signals after noise elimination are obtained. A wavelet threshold value selection method is improved, a space domain related optimizing partial reestablishment weight matrix is introduced, and therefore, influences of noise points on sample data are reduced, the algorithm convergence rate is improved, and the noise elimination speed and precision of the partial discharge signals are improved.

Description

Change wavelet coefficient local discharge signal noise-eliminating method based on the relevant correction threshold in spatial domain

Technical field

The invention belongs to industrial signal process field, be specifically related to a kind of change wavelet coefficient local discharge signal noise-eliminating method based on the relevant correction threshold in spatial domain.

Background technology

Along with the widespread use of various organic insulations in power equipment, effective extraction problem of local discharge signal in power equipment (Partial Discharge, PD made in brief note) becomes more and more outstanding.Utilize local discharge signal can carry out the determining of diagnosis, degree of discharge and type of insulation fault, apparatus insulated deteriorated judgement etc., these all play vital effect to the safety and steady operation of power equipment.Yet, in the actual motion environment of power equipment, exist electromagnetic interference (EMI), cause local discharge signal to be submerged in noise, and then impact utilize the accuracy of local discharge signal to Electric Power Equipment Insulation fault diagnosis.Therefore, by effective filtering technique, remove the interference of noise information, and the essential information feature that retains local discharge signal is one of PD key issue of detecting research.

Local discharge signal belongs to transient signal, and the white noise in interference belongs to non-stationary signal, and the time-frequency domain characteristic of the two there are differences.In order to realize effective detection of two kinds of signals simultaneously, wavelet transformation (Wavelet Transform in recent years, WT made in brief note) method owing to taking full advantage of the local characteristics of signal, by regulating the different wavelet coefficients of local discharge signal and white noise, can realize the detection of two kinds of signal with different type.

For local discharge signal and white noise signal, after wavelet transformation, the wavelet coefficient amplitude that local discharge signal produces is larger, but number is less, and wavelet coefficient number corresponding to white noise is more, amplitude is less.The two is carried out after wavelet decomposition simultaneously, and the amplitude of the wavelet coefficient of local discharge signal is greater than the coefficient amplitude of white noise.Therefore, by select suitable threshold value on different scale, will be less than the wavelet coefficient zero setting of this threshold value, and retain, be greater than the wavelet coefficient of threshold value, thereby the white noise in local signal is suppressed.

Wavelet thresholding method is a kind of nonlinear noise signal elimination method, its essence is that signal is described to essence by thick according to resolution height, recycling different decomposition scale factor is done the bandpass filter of filtering to signal, by being set, reasonable threshold value selects wavelet basis, the detection of realization to singularity characteristics information in signal, thus realize the de-noising of signal.Threshold value back-and-forth method (Threshold Elimination Method, TEM made in brief note) be a kind of in wavelet thresholding method, it is that Donoho DL is at a kind of nonlinear noise-eliminating method of 1995 propositions, its basic thought for local discharge signal de-noising is that after utilization is decomposed, the amplitude size of each layer of wavelet coefficient is according to the threshold value of estimating the filter factor of local discharge signal, makes filtered data keep the essential characteristic of original signal.

At present, to threshold value, system of selection is studied many scholars both domestic and external, and general method is the global threshold system of selection that the people such as Shim propose, and utilizes signal length and noise variance to estimate global threshold, in this method, the threshold value of each decomposition layer is identical, and treatment effect is undesirable.Conventional threshold value system of selection also has Stein without inclined to one side evaluation of risk method and minimax principle method etc., and its Research on threshold selection need to be estimated noise, belongs to semi-automatic semiempirical threshold value system of selection, and de-noising effect is not very good in actual applications.In wavelet noise threshold value selection algorithm, most crucial problem is the differentiation of signal and noise, is about to compared with amplitude coefficient of dissociation, to be defined as signal on each yardstick, utilizes coefficient of dissociation amplitude size directly as the standard of distinguishing, and carries out threshold process.Yet, this algorithm is that the local data for signal operates, and in being mixed with the local discharge signal of white noise, the signal amplitude of white noise is far longer than the amplitude of local discharge signal, this makes this algorithm very sensitive to the threshold amplitude in sample, in the situation that interference is stronger, the de-noising effect of threshold method is also unstable.

Spatial domain related algorithm (Spatial Correlation Filtering Method, SCFM made in brief note) be to utilize the correlativity of coefficient of wavelet decomposition corresponding point on different scale to carry out the choice of wavelet basis coefficient, edge that can also sharpening signal when effectively suppressing noise, algorithm performance is comparatively stable.But up to the present, also nobody selects this algorithm application the optimization aspect of de-noising in threshold value.

For the problems referred to above, the present invention utilizes threshold value selection algorithm coefficient wavelet transformation between data, searching makes to convert rear wavelet coefficient and the immediate threshold value of local discharge signal, has reached and has effectively utilized the resolution characteristic of signal and white noise on different scale effectively to distinguish the two.Meanwhile, the essence of spatial domain related algorithm has determined the threshold value that not exclusively depends on wavelet conversion coefficient of determining of weight, thereby can reduce the impact of noise spot on sample data, and improves algorithm travelling speed.

Summary of the invention

The object of the present invention is to provide a kind of reduction noise effect, improve the change wavelet coefficient local discharge signal noise-eliminating method based on the relevant correction threshold in spatial domain of de-noising speed and precision.

The object of the present invention is achieved like this:

(1) local discharge signal that contains white noise is carried out to wavelet transformation, the decomposition number of plies in wavelet transformation process is M, obtains the wavelet coefficient initial value W of the signals and associated noises f of position n place in yardstick j _f(j, n);

(2) extract wavelet coefficient initial value W _fthe detail section coefficient D of (j, n) each layer ₁-D _mapproximation coefficient A with last one deck _mthe maximal value d of absolute value _1max-d _mmaxand a _mmaxas initial threshold; By wavelet coefficient initial value W _f(j, n) coefficient and threshold value compare, and retain the wavelet coefficient initial value be less than threshold value, the estimated value W' of the wavelet coefficient that obtains containing white noise local discharge signal _f(j, n);

(3) ask between signal the yardstick related coefficient C at position n place in yardstick j ₂' (j, n),

C′ ₂(j,n)=W′ _f(j,n)W′ _f(j+1,n)

(4) by yardstick related coefficient C ₂' obtain correlation C after (j, n) normalization _{2, new}' (j, n),

$C_{2,\mathrm{new}}^{\′}(j,n)=C_2^{\′}(j,n)\sqrt{P_W\left(j\right)/P_{C2}\left(j\right)},$

Wherein, n=1,2 ..., N, $P_{C2}\left(j\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{C}_2^{\′}{(j,n)}^2,P_W\left(j\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{W}_f^{\′}{(j,n)}^2;$

If | C _{2, new}' (j, n) |>=W _f' (j, n) n point place wavelet coefficient belong to the local discharge signal that contains white noise, W' _f(j, n) is assigned to filtered wavelet transform W _g, W _ginitial value is zero, simultaneously by W' _f(j, n) and C ₂' (j, n) zero setting, otherwise W' _f(j, n) is judged as noise, retains former filtered wavelet transform W _g;

(5) repeated execution of steps (4) is to the energy value P of white noise _w(j) be less than the threshold value of noise energy;

(6) record wavelet transform W _g, then by W _gcarry out discrete wavelet inverse transformation and obtain the signal after denoising.

Beneficial effect of the present invention is: in the present invention, to wavelet threshold, system of selection improves, introduce the relevant partial reconstruction weight matrix of optimizing in spatial domain, thereby reduced the impact of noise spot on sample data, improve method speed of convergence, improved local discharge signal de-noising speed and precision.

Accompanying drawing explanation

Fig. 1. the local discharge signal noise-eliminating method process flow diagram of spatial domain dependent thresholds correction wavelet threshold;

Fig. 2 is local discharge signal noise-canceling system schematic diagram;

Fig. 3 is single bilateral damped oscillation pulse simulate signal schematic diagram;

Fig. 4 is white noise simulate signal;

Fig. 5 is for containing noisy local discharge signal emulation schematic diagram;

Fig. 6 is wavelet noise result;

Fig. 7 is the de-noising effect of 10 pulse local discharge signals.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described further.

1. the system of selection of wavelet threshold

The data acquisition of wavelet threshold selection algorithm has a hypotheses: sampled data during lower than starting potential, is recorded noise signal at impressed voltage; Along with impressed voltage raises gradually, when higher than starting potential, record is containing noisy local discharge signal.

Threshold value selection algorithm (Threshold Elimination Method, TEM made in brief note) in first to select base small echo and decompose the number of plies, the signal of a Noise is carried out to wavelet transformation, select the maximal value of every layer of detail section and the approximate part wavelet coefficient of last one deck and record, this maximal value has represented the feature of maximum noise.When estimating the wavelet coefficient of local discharge signal, any all irrelevant with noise higher than this peaked wavelet coefficient, only may be caused by local discharge signal, therefore the threshold value using this maximal value as this one deck.Secondly, signals and associated noises is carried out to wavelet transformation, base small echo is identical while all decomposing with noise with the decomposition number of plies, and before the wavelet coefficient of every layer is used, selected threshold value is processed, and the wavelet coefficient after threshold process is exactly the estimation coefficient of local discharge signal.Finally, utilize and estimate that wavelet coefficient carrys out reconstruct original signal.The concrete steps of wavelet threshold selection algorithm are as follows:

(1) noise signal is carried out to wavelet decomposition, the decomposition number of plies is M, obtains the coefficient of wavelet decomposition W of noise _n(j, n).

(2) for W _nthe detail section coefficient D of (j, n) each layer ₁-D _mapproximation coefficient A with last one deck _m, by the maximal value d of coefficient of dissociation absolute value in each layer coefficients _1max-d _mmaxand a _mmaxrecord, as initial threshold.

(3) will carry out wavelet decomposition containing noisy PD signal, the decomposition number of plies is M, obtains coefficient of wavelet decomposition W _pD(j, n).

(4) to W _pDeach of (j, n) layer wavelet coefficient respectively with each layer of initial threshold d _1max-d _mmaxand a _mmaxrelatively, when wavelet coefficient is greater than initial threshold, change record value, thereby obtain the estimated value W' of PD wavelet coefficient _pD(j, n).

(5) use the wavelet coefficient estimated value W' of local discharge signal _pD(j, n) reconstruction signal, the signal obtaining is the signal after de-noising.

Algorithm has been considered the difference of different scale wavelet decomposition characteristic when calculated threshold, is a kind of gradient threshold system of selection, and, on different decomposition scales, threshold value value is different.

2. the relevant correction algorithm in spatial domain

Spatial domain correlation theory thinks that signal is after wavelet transformation, and its wavelet coefficient has stronger correlativity on each yardstick, and especially, near the edge of signal, its correlativity is more obvious; And wavelet coefficient corresponding to noise do not have this obvious correlativity between yardstick.Therefore, can consider to utilize the correlativity of wavelet coefficient corresponding point position on different scale to determine it is signal coefficient or noise figure, the wavelet coefficient after processing is like this corresponding the edge of signal substantially.

Spatial domain related algorithm points out that the catastrophe point of signal has larger peak value to occur at the same position of different scale, and noise energy but reduces along with the increase of yardstick.Therefore, the wavelet coefficient that can get adjacent yardstick directly multiplies each other and carries out correlation computations, thereby suppresses noise in sharpening signal edge and other key character, and can improve the positioning precision at the main edge of signal.

Defining between two signals the yardstick related coefficient at n place, position in yardstick j is C ₂(j, n), as shown in Equation 1.

C ₂(j,n)=W _f(j,n)W _f(j+1,n) （1）

In formula, W _fconversion coefficient in (j, n) expression yardstick j after the discrete wavelet of the signals and associated noises f of n place, position.For making yardstick related coefficient and wavelet coefficient have comparability, definition standard yardstick related coefficient is shown in formula 2.

$C_{2,\mathrm{new}}(j,n)=C_2(j,n)\sqrt{P_w\left(j\right)/P_{C2}\left(j\right)}---\left(2\right)$

In formula, n=1,2 ..., N; Its correlativity can be passed through the marginal probability of yardstick related coefficient marginal probability density with wavelet transformation further describe.In algorithm, pass through relatively | C _{2, new}(j, n) | and | W _f(j, n) | the important edges of big or small distinguishing signal, if | C _{2, new}(j, n) | >W _f(j, n) |, think the edge of this respective signal, storage W _fthe position of (j, n) and amplitude size, and by C _{2, new}(j, n) and W _fin (j, n), relevant position sets to 0, otherwise this is put to corresponding noise.Then remaining data is designated as to W ' _f(j, n) and C ' _{2, new}(j, n), differentiates signal time important edges by said method.Repeat said process, work as W _fwhen the energy of the point not being extracted in (j, n) is less than the noise energy on this yardstick, stop extracting.

The concrete steps of the relevant correction algorithm in spatial domain are as follows:

(1) to carrying out wavelet transformation containing noisy signal, obtain W _f(j, n), asks for each yardstick related coefficient C ₂(j, n).

(2) calculate C ₂correlation C after (j, n) normalization _{2, new}(j, n).If | C _{2, new}(j, n) |>=W _f(j, n) |, think that n point place wavelet coefficient belongs to PD signal.By W _f(j, n) assignment is to W _g(W _gbe filtered value, initial value is zero), simultaneously by W _f(j, n) and C ₂(j, n) zero setting.If | C _{2, new}(j, n) |≤| W _f(j, n) |, think this W _f(j, n) belongs to noise, and wavelet coefficient is retained.

(3) repeating step 2, until P _w(j) be less than the critical value of noise energy, at this moment obtain W _gthe estimation wavelet coefficient of the PD signal of middle reservation, finally utilizes and estimates wavelet coefficient renewal value reconstruct local discharge signal.

3. ripple Coefficient Algorithm diminishes

Local discharge signal shows different resolution characteristics on different scale from white noise signal.In wavelet transformation threshold theory point out local discharge signal be decomposed on each yardstick compared with amplitude.Therefore, coefficient of dissociation amplitude size, directly as the standard of distinguishing, is carried out to threshold process.All wavelet conversion coefficients that are greater than threshold value are all remained, yet this part is compared with in the coefficient of dissociation of amplitude, generally having a small amount of coefficient of dissociation is to decompose gained by noise signal.

In actual test, use separately the method for wavelet threshold can make noise effectively be suppressed, but have unavoidably the residual of a small amount of noise after de-noising, Partial Discharge Detection equipment is conventionally in compared with strong electromagnetic interference environment, and this has also increased the difficulty of de-noising.Therefore, consider to utilize the correlativity of coefficient of wavelet decomposition corresponding point on different scale to carry out the choice of wavelet coefficient with spatial domain related algorithm, edge that can also sharpening signal in effective inhibition noise, algorithm performance is comparatively stable.But spatial domain related algorithm needs repeatedly iteration, and calculated amount is very large, result of use is unsatisfactory separately.

Therefore, during de-noising of the present invention, wavelet threshold selection algorithm (TEM) is combined with spatial domain related algorithm (SCFM), be defined as based on the relevant local discharge signal denoising algorithm (TSCFM) of revising wavelet threshold in spatial domain, to containing noisy local discharge signal de-noising.

Therefore, during denoising of the present invention, wavelet threshold selection algorithm (TEM) is combined with spatial domain related algorithm (SCFM), be defined as based on the relevant local discharge signal denoising algorithm (TSCFM) of revising wavelet threshold in spatial domain containing noisy local discharge signal de-noising, concrete steps are as follows:

First adopt the method for wavelet transformation to obtain wavelet coefficient initial value W the local discharge signal that contains white noise _f(j, n);

To the concentrated coefficient of wavelet coefficient respectively with each layer of threshold value d _1max-d _mmaxand a _mmaxprocess the estimated value W' of the wavelet coefficient that obtains containing white noise local discharge signal _f(j, n), using it as obtaining new wavelet coefficient;

To new wavelet coefficient W' _fthe sparse W' of new small echo in the set that (j, n) forms _f(j, n) asks between signal the yardstick related coefficient C at position n place in yardstick j ₂' (j, n);

By yardstick related coefficient C ₂' obtain correlation C after (j, n) normalization _{2, new}' (j, n).If | C _{2, new}' (j, n) |>=W _f' (j, n) think that n point place wavelet coefficient belongs to the local discharge signal that contains white noise, W' _f(j, n) is assigned to W _gbe filtered value, initial value is zero, simultaneously by W' _f(j, n) and C ₂' (j, n) zero setting.Otherwise, W' _f(j, n) is judged as noise, retains former W _g;

Repeating step (4), the energy value P that iteration stopping condition is white noise _w(j) be less than the threshold value of noise energy;

The wavelet transform W of signal after recording processing _g, then by W _gcarry out discrete wavelet inverse transformation and obtain the signal after denoising.

The present invention is directed to the white noise that the local discharge signal in electric system is mixed with and carry out de-noising research, choose 2 kinds of local discharge signals (exponential damping and concussion decay) and carry out emulation, by average, be 1 again, variance is 0 white Gaussian noise and its stack, and it is input in system as the local discharge signal that contains white Gaussian noise.The algorithm flow chart of system as shown in Figure 1.In denoising Processing, first by user, by signaling interface, propose de-noising request (target data), denoising Processing module adopts the mode of wavelet transform that the local discharge signal with gaussian random noise is converted according to request, records wavelet coefficient; Then threshold value selection is carried out in set wavelet coefficient being formed, and obtains new wavelet coefficient collection, by spatial domain related algorithm, obtains Optimum wavelet coefficient value; Finally, according to the Optimal Wavelet Transform coefficient obtaining, carry out inverse transformation, obtain the local discharge signal after de-noising, it is fed back to user as output signal.As shown in Figure 2, specific implementation method is as follows for system architecture diagram:

1. signal simulation and multiresolution wavelet resolution characteristic

(1) partial discharge pulse's emulation

Consider partial discharge pulse's signal duration extremely short (approximately several ns), the wave head rise time is 1ns left and right only, Maetal proposes to use exponential damping pulsed D EP(the damped exponential pulse) and concussion decaying pulse DOP(the damped oscillatory pulse) be mathematical model simulation local discharge signal, in the present invention, adopt bilateral damped oscillation pulse signal to simulate actual local discharge signal, expression formula as shown in Equation 3.

$\mathrm{DOP}\left(t\right)=A\sin \left(2\mathrm{\π}{f}_{c}t\right)(e^{-\frac{t}{{\mathrm{\τ}}_1}}-e^{-\frac{t}{{\mathrm{\τ}}_2}})---\left(3\right)$

In formula, A represents peak value, τ ₁, τ ₂be time constant, determined the parameters such as rise time, f _cit is the concussion frequency of DOP signal.

The damped oscillation pulse signal of two pulses of take is example, and shelf depreciation simulate signal as shown in Figure 3.

Multiresolution analysis (Multi Resolution Analysis, MRA) is proposed by Mallat, and algorithm has provided the building method of orthogonal wavelet, and has provided on this basis fast algorithm-Mallat algorithm of wavelet transformation.Arthmetic statement is as follows:

$d_j\left(n\right)=\underset{k}{\mathrm{\Σ}}\stackrel{\‾}{g}(k-2n)c_{j-1}\left(k\right)=[c_{j-1}\left(n\right)*\stackrel{\‾}{g}(-n)]{\↓}_2---\left(4\right)$

$c_j\left(n\right)=\underset{k}{\mathrm{\Σ}}\stackrel{\‾}{h}(k-2n)c_{j-1}\left(k\right)=[c_{j-1}\left(n\right)*\stackrel{\‾}{h}(-n)]{\↓}_2---\left(5\right)$

In formula, n is sampled point, d _j(n) represent the coefficient sequence of the detail section that original signal resolves into, c _j(n) represent the coefficient sequence of approximate part, h (n) is low-pass filter coefficients, and g (n) is Hi-pass filter coefficient, and " * " represents convolution, and " ↓ 2 " represent to extract even number of samples point from filtered sequence.

Function f (x) is at certain 1 x ₀the regularity at place can be portrayed by Lipschitz index α, if Lipschitz index α is larger, function shape is just relatively smooth.

Theorem 1: establish 0≤α≤1, f (x) ∈ L ²(R), [a, b] is an interval on R, and and if only if for any x ∈ [a, b], has a constant k, makes | W _f(s, x) |≤ks ^αset up, claim that f (x) is the consistent Lipschitz index α at interval [a, b].

The modulus maximum of signal coefficient of wavelet decomposition on each yardstick and Lipschitz index α have corresponding relation, if Lipschitz index α is >0, with the increase of yardstick j, modulus maximum should increase, if Lipschitz index α=0, modulus maximum on each yardstick without significant change, if Lipschitz index α is <0, the modulus maximum characteristic of wavelet transformation should be just in time contrary with the situation of α >0, when decomposition scale increases, modulus maximum is corresponding to be reduced.

The Lipschitz index α of local discharge signal meets: 0< α <1.Therefore the modulus maximum of PD signal, in decomposition scale j increase process, increases gradually, and number is also substantially equal on each yardstick.

Adopt multi-scale wavelet to decompose the local discharge signal of simulation, in Multiscale Wavelet Decomposition process, the decomposition of every one deck all can produce the approximate component of a low frequency and the details component of a high frequency, in the decomposition of lower one deck, only the approximate component of low frequency is decomposed again, office puts simulate signal and after db4 wavelet transformation, obtains the coefficient of dissociation of each layer, the coefficient of wavelet decomposition that it has comprised each layer of low frequency component, and in the process increasing at decomposition scale, wavelet coefficient amplitude is corresponding increase also.Therefore, along with the increase of decomposition scale, the low-frequency approximation of signal partly has certain energy loss, and this is that the reduction of decomposition scale temporal resolution that increase causes causes, and the energy of this part loss is being embodied in corresponding high fdrequency component.

(2) white noise signal emulation

White noise is a kind of common interference, and its frequency spectrum is very wide, is almost distributed in whole frequency range, and the simulating signal of white noise is generally normal distribution, is the random signal that average is 0, variance is constant, is the simulate signal of white noise shown in Fig. 4.If white noise n (k) is an average, be zero, the wide stationary signal that variance is ξ, W _n(j, k) is the wavelet transformation of n on j yardstick (k), and to establish small echo ψ (k) be real-number function, ψ _j(k)=2 ^jψ (2 ^jk), thus have:

W _n(j,k)=∫ _Rn(u)ψ _j(k-u)du （6）

Can obtain:

$\begin{array}{c}E\left\{{\left|W_n(j,k)\right|}^2\right\}=\&Integral;\underset{R}{\&Integral;}E\left\{n\left(u\right)n\left(v\right)\right\}{\mathrm{\&psi;}}_j(k-u){\mathrm{\&psi;}}_j(k-v)\mathrm{dudv}\\ =\mathrm{\&xi;}\&Integral;\underset{R}{\&Integral;}(u-v){\mathrm{\&psi;}}_j(k-u){\mathrm{\&psi;}}_j(k-v)\mathrm{dudv}\\ =\mathrm{\&xi;}{\left|\right|\mathrm{\&psi;}\left|\right|}^2\&times;2^{-j}\end{array}---\left(7\right)$

This shows W _nthe average power of (j, k) and yardstick j are inversely proportional to, and that is to say that the modulus maximum of white noise, when decomposition scale j increases, reduces.

Therefore, the Lipschitz index α of white noise is: α=-0.5-ε, ε >0.Modulus maximum, in decomposition scale j increase process, reduces gradually.

The coefficient of wavelet decomposition that comprises low frequency component and high fdrequency component in the wavelet decomposition of white noise, in the process increasing at decomposition scale, coefficient of dissociation all obviously diminishes, and this is contrary with the wavelet conversion characteristics of Partial discharge signal.

(3) the local discharge signal emulation that contains white noise

For the ease of observing de-noising simulation result, signal amplitude is normalized to 1, simulate signal and white noise signal stack are put in damped oscillation simulation office, obtain the shelf depreciation simulate signal that contains white noise, its expression formula is suc as formula shown in (8), and simulation waveform as shown in Figure 5.

$y\left(t\right)=A\sin \left(2\mathrm{\&pi;}{f}_{c}t\right)(e^{-\frac{t}{{\mathrm{\&tau;}}_1}}-e^{-\frac{t}{\mathrm{\&tau;}2}})+\underset{k=-\&infin;}{\overset{t}{\mathrm{\&Sigma;}}}n\left(k\right)---\left(8\right)$

In formula, A represents peak value, τ ₁, τ ₂be time constant, determined the parameters such as rise time, f _cbe the concussion frequency of DOP signal, n (k) is that an average is zero, the broadband stationary white noise signal that variance is ξ.

Therefore, will carry out wavelet transformation containing noisy local discharge signal, the low-frequency approximation part of signal is in decomposition scale increase process, and amplitude is increasing, and obviously reduces in the process that the amplitude of noise coefficient of dissociation increases at yardstick.

Local discharge signal Lipschitz index α >0 and the Lipschitz index α <0 of white noise, both modulus maximums are when decomposition scale j becomes large, show contrary characteristic, the wavelet coefficient of white noise local discharge signal is along with the increase of yardstick j is distinguished significantly.

2. the selection of base small echo

Wavelet noise process generally comprises following three steps:

1) select a base small echo with handled Signal Matching, selected decomposition number of plies N, calculates the wavelet conversion coefficient of every layer.

2) use certain method criterion, wavelet coefficient is judged, obtain the estimation wavelet coefficient of signal.

3) with the wavelet coefficient reconstruction signal of estimating, the signal obtaining is exactly the signal after de-noising.

First the problem that will consider in de-noising is the selection of base small echo, and Mallat proposes to judge with the cross-correlation coefficient γ of whole sample the matching degree of base small echo and PD signal.The computing formula of γ is shown in formula 7:

$\mathrm{\&gamma;}=\frac{\left(\mathrm{\&Sigma;}(X-\stackrel{\&OverBar;}{X})(Y-\stackrel{\&OverBar;}{Y})\right)}{\sqrt{\mathrm{\&Sigma;}{(X-\stackrel{\&OverBar;}{X})}^2{(Y-\stackrel{\&OverBar;}{Y})}^2}}---\left(9\right)$

In formula, X is Partial Discharge Data, be the mean value of X, Y is wavelet data, the mean value of Y.When signal is carried out to wavelet transformation, need to select the suitable decomposition number of plies, if decompose the number of plies too conference make distorted signals, the too little noise reduction object that do not reach again.Decompose the number of plies also has certain relation with sample frequency simultaneously, can make correspondingly and adjusting according to the concrete condition of de-noising in actual applications.

Visible, in de-noising process base small echo choose very importantly, selected base small echo will just can extract useful signal with the Waveform Matching of local discharge signal.The conventional wavelet function of shelf depreciation comprises " db ", " bior " and " coif " small echo.Mallat proposes to judge with cross-correlation coefficient γ the whole matching degree of base small echo and local discharge signal, and db4 small echo and local discharge signal related coefficient are 1.72, therefore in invention, adopts db4 small echo as the wavelet basis of de-noising.The wavelet decomposition of local discharge signal when base small echo is db4 small echo, therefore, db4 small echo can be portrayed the details of signal preferably.

3. be correlated with and revise wavelet threshold in spatial domain

Noisy shelf depreciation simulate signal wavelet transformation is obtained to wavelet coefficient W _f(j, n), threshold method deal with data obtains W' _f(j, n), estimates small echo global threshold according to formula (10).

$\mathrm{\&lambda;}=\mathrm{\&sigma;}\sqrt{2\log \left(n\right)}---\left(10\right)$

Wherein, the global threshold that λ is each layer, n is that signal length σ is noise criteria variance.λ is global threshold, and the threshold value of each decomposition layer is identical.And then to W' _f(j, n) utilizes following steps to carry out interative computation, and concrete steps are as follows:

(1) to carrying out wavelet transformation containing noisy signal, obtain W _f(j, n), asks for each yardstick related coefficient C ₂(j, n).

(2) calculate C ₂correlation C after (j, n) normalization _{2, new}(j, n).If | C _{2, new}(j, n) |>=| W _f(j, n) |, think that n point place wavelet coefficient belongs to PD signal.By W _f(j, n) assignment is to W _g(W _gbe filtered value, initial value is zero), simultaneously by W _f(j, n) and C ₂(j, n) zero setting.If | C _{2, new}(j, n) |≤| W _f(j, n) |, think this W _f(j, n) belongs to noise, and wavelet coefficient is retained.

(3) repeating step 2, until P _w(j) be less than the critical value of noise energy, at this moment obtain W _gthe middle estimation wavelet coefficient that retains PD signal, finally utilizes and estimates wavelet coefficient reconstruct PD signal.

Until P _w(j) be less than the threshold value of noise energy, obtain W _g, to W _gcarry out wavelet inverse transformation and obtain the signal after de-noising.

When having the signal processing of partial discharge of attenuation characteristic, this method can suppress the energy loss producing in damped oscillation process in local discharge signal, realizes effective de-noising of local discharge signal.Adopt this method de-noising effect figure as shown in Figure 6.

4. the performance evaluation of method

The present invention disturbs mainly for the white noise in local discharge signal, adopts the de-noising ability of signal to noise ratio (S/N ratio) and Y-PSNR describing system.Usually, signal to noise ratio (S/N ratio) is described effective local discharge signal and is extracted situation, and Y-PSNR has reflected the reservation situation of characteristic spikes point.Therefore, general noise-canceling system requires these two evaluatings all to obtain reasonable numerical value.

In the present invention, adopt conventional de-noising performance evaluation formula in signal processing to evaluate the de-noising performance of system, establishing s (i) is useful signal, and n (i) is noise signal.Now provide the local discharge signal s (i) of emulation, (i=1,2, ..., N), N is the predefined local discharge signal sampled point of test macro de-noising performance number, (the Signal to Noise Ratio of the signal to noise ratio (S/N ratio) after de-noising, SNR) be the major criterion of weighing de-noising effect, be defined as:

$\mathrm{SNR}=20\lg \frac{\underset{i=1}{\overset{N}{\max }}\left\{s\left(i\right)\right\}}{\underset{i=1}{\overset{N}{\max }}\left\{n\left(i\right)\right\}}---\left(11\right)$

When signal to noise ratio (S/N ratio) is greater than 0, show that useful signal is stronger than noise; When signal to noise ratio (S/N ratio) is greater than 10, illustrate that de-noising effect is good, local discharge signal can effectively be identified.Therefore, signal to noise ratio (S/N ratio) has guaranteed that useful signal extracts effectively.

After local discharge signal denoising Processing, the distortion degree of signal is little, to meet the needs of subsequent treatment.In invention, adopt Y-PSNR (Peak Signal to Noise Ratio, PSNR) as evaluating, to describe the distortion degree of the waveform after de-noising, be defined as:

$\mathrm{PSNR}=20\lg \frac{\max \left(s\left(i\right)\right)}{\sqrt{\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}|s\left(i\right)-n\left(i\right)|}}---\left(12\right)$

In formula, max (s (i)) is the maximum amplitude of signal, the reserving degree of the characteristic spikes point of PSNR reflection original signal.

In order further to analyze the whole structure of method in the actual local discharge signal that contains white noise, adopt 10 pulses as the local discharge signal of one group of simulation, adopt the method in the present invention, add up respectively corresponding signal to noise ratio (S/N ratio) and Y-PSNR.

Through statistics, show after de-noising, to only have the SNR of a signal lower than 10, the SNR of all the other 9 signals all can reach more than 10, and variance 2.9380 is visible, and the method obviously improves inhibition ability and the stability of noise.Data from table 1 can find out, in the peak amplitude conversion of the de-noising in this method, to only have the Y-PSNR of a signal more serious, and all the other are all in 15%.

Claims (1)

1. the change wavelet coefficient local discharge signal noise-eliminating method based on the relevant correction threshold in spatial domain, is characterized in that:

(1) local discharge signal that contains white noise is carried out to wavelet transformation, the decomposition number of plies in wavelet transformation process is M, obtains the wavelet coefficient initial value W of the signals and associated noises f of position n place in yardstick j _f(j, n);

(2) extract wavelet coefficient initial value W _fthe detail section coefficient D of (j, n) each layer ₁-D _mapproximation coefficient A with last one deck _mthe maximal value d of absolute value _1max-d _mmaxand a _mmaxas initial threshold; By wavelet coefficient initial value W _f(j, n) coefficient and threshold value compare, and retain the wavelet coefficient initial value be less than threshold value, the estimated value W' of the wavelet coefficient that obtains containing white noise local discharge signal _f(j, n);

(3) ask between signal the yardstick related coefficient C at position n place in yardstick j ₂' (j, n),

C′ ₂(j,n)＝W′ _f(j,n)W′ _f(j+1,n)

(4) by yardstick related coefficient C ₂' obtain correlation C after (j, n) normalization _{2, new}' (j, n),

$C_{2,\mathrm{new}}^{\&prime;}(j,n)=C_2^{\&prime;}(j,n)\sqrt{P_W\left(j\right)/P_{C2}\left(j\right)},$

Wherein, n=1,2 ..., N, $P_{C2}\left(j\right)=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{C}_2^{\&prime;}{(j,n)}^2,P_W\left(j\right)=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{W}_f^{\&prime;}{(j,n)}^2;$

If | C _{2, new}' (j, n) |>=W _f' (j, n) n point place wavelet coefficient belong to the local discharge signal that contains white noise, W' _f(j, n) is assigned to filtered wavelet transform W _g, W _ginitial value is zero, simultaneously by W' _f(j, n) and C ₂' (j, n) zero setting, otherwise W' _f(j, n) is judged as noise, retains former filtered wavelet transform W _g;

(5) repeated execution of steps (4) is to the energy value P of white noise _w(j) be less than the threshold value of noise energy;

(6) record wavelet transform W _g, then by W _gcarry out discrete wavelet inverse transformation and obtain the signal after denoising.