CN103902844A - Transformer vibration signal de-noising method based on EEMD kurtosis threshold value - Google Patents
Transformer vibration signal de-noising method based on EEMD kurtosis threshold value Download PDFInfo
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Abstract
The invention discloses a transformer vibration signal de-noising method based on an EEMD kurtosis threshold value. Many methods have been put forward by domestic and foreign scholars for de-noising of non-stationary signals and are roughly divided into three major types of time-frequency analysis methods based on time domain statistics, Fourier transform and wavelet transform. All the methods have respective advantages and disadvantages, for instance, the theory of the frequency domain method is mature, but signals with overlapped frequency are difficult to separate; although the wavelet transform method has the multi-resolution performance, the de-noising effect of the method usually depends on selection of a wavelet base and a threshold value. The method includes the steps that first, random signals are subjected to EEMD, then, each intrinsic mode function is subjected to autocorrelation function calculation, the kurtosis coefficient of each IMF is solved, next, the IMFs are differentiated through the threshold value, and therefore noisy signals can be removed. The method is used for de-noising of transformer vibration signals.
Description
Technical field:
The present invention relates to a kind of transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value.
Background technology:
Transformer is as hinge equipment important in electric system, and not only price is very expensive for it, acts on also very importantly, guarantees that its safe and reliable operation is the key of whole electric power netting safe running, and it is very necessary therefore its running status being carried out detecting in real time.At present, the Diagnosis Method of Transformer Faults based on analysis of vibration signal is as a kind of novel diagnostic method, and it has the feature of real-time and on-line operation, now in electric system, extensively adopts.But in engineering, the signal of actual acquisition all contains much noise, as: when transformer equipment breaks down in early days, in the vibration signal gathering, contain random noise, make the effective information that can react fault signature become very faint, therefore how can effectively extract useful signal, suppress noise raising signal to noise ratio (S/N ratio) is precondition and the necessary links that carries out fault diagnosis based on vibration signal.
For the noise reduction of non-stationary signal, Chinese scholars has proposed many methods, is broadly divided into based on time domain statistics, based on Fourier transform and the Time-Frequency Analysis Method three major types based on wavelet transformation.These methods have relative merits separately, as: frequency domain method is theoretical ripe, but is difficult to the signal of cross frequence lap; Though small wave converting method has multi-resolution analysis energy, its noise reduction often depends on the selection of wavelet basis and threshold value.Empirical mode decomposition (EMD) is the method that many component signals is resolved into multiple natural mode components (IMF) that the people such as Huang propose for 1997.Instantaneous frequency in these IMF components has actual physical significance, and frequency is by height distribution successively on earth, has a very strong frequency choosing layer performance, is a kind of complete adaptive decomposition method.Generalized case the method can obtain good noise reduction, if but in signal, there is abnormal sudden change, be subject to the impact of the shortcoming such as EMD method mode aliasing and breakpoint effect, noise reduction is by variation.
The set empirical mode decomposition method (EEMD) proposing for 2008 Deng people is that white noise is added in the signal that contains singular point and decomposed to promote to resist to mix, and has effectively suppressed mode mixing phenomenon.Scholars are also attempting utilizing EEMD method to carry out noise reduction process to signal at present, as each component energy density and the average period of utilizing white noise to decompose through EEMD are this features of constant, the noise component satisfying condition is rejected, but the component of rejecting likely contains useful signal, does not provide solution in literary composition; Also the method having is to utilize the otherness of white noise and normal signal autocorrelation function, first signals and associated noises is carried out to EMD decomposition, then artificially judge which IMF is noise component, again noise component is carried out to soft-threshold processing, though the method can effectively suppress noise, but the differentiation of noise component and useful component can only judge to have certain subjectivity artificially.
Summary of the invention:
The object of this invention is to provide a kind of transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value.
Above-mentioned object realizes by following technical scheme:
A kind of transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value, the method comprises the steps: first the transformer vibration signal collecting to be carried out to EEMD decomposition, then carry out autocorrelation function calculating and ask its coefficient of kurtosis for each intrinsic mode functions IMF, then utilize threshold value that these intrinsic mode functions IMF is distinguished, and then cancelling noise signal.
The described transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value, described signal is carried out to EEMD decomposes is the equally distributed characteristic of frequency spectrum of having utilized white noise, and white noise signal automatic average after EMD decomposes is decomposed on different time yardstick; Due to white noise zero mean characteristic, after average the intrinsic mode functions IMF after repeatedly decomposing, eliminate noise effect completely, obtain the finally intrinsic mode functions IMF component without aliasing effect, specific algorithm is as follows:
The first step: in original signal
in add
inferior average is zero, the white noise that standard variance is constant
;
Second step: to adding the signal of white noise
carry out EMD decomposition, obtain
individual intrinsic mode functions IMF component and a 1 remaining component
,
（2）；
The 3rd step: utilize the feature that white noise statistical nature average is zero, the intrinsic mode functions IMF component and the remaining component that decompose are averaged respectively to computing at every turn, eliminate the impact of the white noise at every turn adding, and then also offset the aliasing that singular point causes;
Wherein,
for final signal decompose the
individual intrinsic mode functions IMF component,
for the remaining component of final signal decomposition;
The 4th step: utilize intrinsic mode functions IMF component obtained above and remaining component to carry out the reconstruct of original signal:
The described transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value, the autocorrelation function of described random signal has reacted signal and himself degree of correlation in different time points, is a kind of statistical measures method of time domain, and it is defined as:
（7），
In formula:
for the time interval,
represent signal with from the correlation function value of synchronization, obviously, for any random signal, this value is all maximum; Autocorrelation function is the function in sigtnal interval, is separated with positive and negative interval, so length is
signal, have
individual auto-correlation function value, what describe respectively is the similarity degree at unlike signal interval, has also embodied the symmetry of autocorrelation function.
The described transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value, the coefficient of kurtosis of described autocorrelation function is used for metric data at center aggregation extent, in normal distribution situation, coefficient of kurtosis value is 0, positive coefficient of kurtosis explanation observed quantity is more concentrated, has the afterbody longer than normal distribution; Negative coefficient of kurtosis explanation observed quantity is not exclusively concentrated, has the afterbody shorter than normal distribution, and the standard error of coefficient of kurtosis is used for judging the normality of distribution, and it is defined as:
（8）
Kurtosis is the index for reflecting the high and steep or flat degree of distribution curve top point, is worth more precipitous.
Beneficial effect:
The present invention carries out EEMD decomposition in order to overcome EMD mode mixing shortcoming to signal, and EEMD method repeatedly joins white noise in original signal, with the impact of this next level and smooth singular point.
The present invention's application EEMD method realizes the decomposition of signals and associated noises, then utilize the feature that random noise is not identical with the autocorrelation function distribution characteristics of generic function, utilize each IMF component of kurtosis value quantitative description from light function distribution characteristics mutually, and then passing threshold judges the method for cancelling noise picking up signal useful signal.
The present invention proposes a kind of method of utilizing coefficient of kurtosis to measure white noise and normal signal autocorrelation function otherness.First algorithm carries out EEMD decomposition to signal, carries out autocorrelation function calculating and asks its coefficient of kurtosis for each IMF, then utilizes threshold value that these IMF are distinguished, and then cancelling noise signal.In experiment, the inventive method is applied to simulate signal and transformer actual vibration signal carries out noise reduction process and compares with additive method, result shows that the performance of this paper method is better than other noise-reduction methods.
Accompanying drawing explanation:
Accompanying drawing 1 is structural representation of the present invention.
Accompanying drawing 2 is stack general signal time domain waveform figure of 20Hz and 30Hz sine and cosine.
Accompanying drawing 3 is autocorrelation function shape schematic diagram of the stack general signal of 20Hz and 30Hz sine and cosine.
Accompanying drawing 4 is that variance is 0.1 noise signal time domain waveform figure.
Accompanying drawing 6 is that frequency is the cosine signal time domain waveform figure of 10Hz.
Accompanying drawing 7 is that to add variance be the cosine signal time domain waveform figure that 0.1 random noise frequency is 10Hz.
Accompanying drawing 8 is the 1st intrinsic mode functions IMF component schematic diagram of noisy simulate signal.
Accompanying drawing 9 is the 2nd intrinsic mode functions IMF component schematic diagram of noisy simulate signal.
Accompanying drawing 11 is the 4th intrinsic mode functions IMF component schematic diagram of noisy simulate signal.
Accompanying drawing 12 is spectrograms of the 1st intrinsic mode functions IMF of noisy simulate signal.
Accompanying drawing 13 is spectrograms of the 2nd intrinsic mode functions IMF of noisy simulate signal.
Accompanying drawing 14 is spectrograms of the 3rd intrinsic mode functions IMF of noisy simulate signal.
Accompanying drawing 15 is spectrograms of the 4th intrinsic mode functions IMF of noisy simulate signal.
Accompanying drawing 16 is autocorrelation function graphs of the 1st IMF of noisy simulate signal.
Accompanying drawing 17 is autocorrelation function graphs of the 2nd IMF of noisy simulate signal.
Accompanying drawing 18 is autocorrelation function graphs of the 3rd IMF of noisy simulate signal.
Accompanying drawing 19 is autocorrelation function graphs of the 4th IMF of noisy simulate signal.
Accompanying drawing 20 is the signal to noise ratio (S/N ratio) schematic diagram after the denoising of different variance noise.
Accompanying drawing 21 is that the wave-form similarity after the denoising of different variance noise compares schematic diagram.
Accompanying drawing 22 is vibration signal curve synoptic diagrams.
Accompanying drawing 23 is through the inventive method reconstruction signal curve synoptic diagram.
Accompanying drawing 24 is that EEMD decomposition adds 0.05 standard variance noise, the 1st intrinsic mode functions IMF component schematic diagram in the situation that integrated number is 50.
Accompanying drawing 26 is that EEMD decomposition adds 0.05 standard variance noise, the 3rd intrinsic mode functions IMF component schematic diagram in the situation that integrated number is 50.
Accompanying drawing 27 is that EEMD decomposition adds 0.05 standard variance noise, the 4th intrinsic mode functions IMF component schematic diagram in the situation that integrated number is 50.
Accompanying drawing 28 is that EEMD decomposition adds 0.05 standard variance noise, the spectrogram of the 1st intrinsic mode functions IMF in the situation that integrated number is 50.
Accompanying drawing 29 is that EEMD decomposition adds 0.05 standard variance noise, the spectrogram of the 2nd intrinsic mode functions IMF in the situation that integrated number is 50.
Accompanying drawing 30 is that EEMD decomposition adds 0.05 standard variance noise, the spectrogram of the 3rd intrinsic mode functions IMF in the situation that integrated number is 50.
Accompanying drawing 31 is that EEMD decomposition adds 0.05 standard variance noise, the spectrogram of the 4th intrinsic mode functions IMF in the situation that integrated number is 50.
Embodiment:
Embodiment 1:
A kind of transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value, the method comprises the steps: first the transformer vibration signal collecting to be carried out to EEMD decomposition, then carry out autocorrelation function calculating and ask its coefficient of kurtosis for each intrinsic mode functions IMF, then utilize threshold value that these intrinsic mode functions IMF is distinguished, and then cancelling noise signal.
Embodiment 2:
According to the transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value described in embodiment 1, described signal is carried out to EEMD decomposes is the equally distributed characteristic of frequency spectrum of having utilized white noise, and white noise signal automatic average after EMD decomposes is decomposed on different time yardstick; Due to white noise zero mean characteristic, after average the intrinsic mode functions IMF after repeatedly decomposing, eliminate noise effect completely, obtain the finally intrinsic mode functions IMF component without aliasing effect, specific algorithm is as follows:
The first step: in original signal
in add
inferior average is zero, the white noise that standard variance is constant
;
（1）；
Second step: to adding the signal of white noise
carry out EMD decomposition, obtain
individual intrinsic mode functions IMF component and a 1 remaining component
,
（2）；
The 3rd step: utilize the feature that white noise statistical nature average is zero, the intrinsic mode functions IMF component and the remaining component that decompose are averaged respectively to computing at every turn, eliminate the impact of the white noise at every turn adding, and then also offset the aliasing that singular point causes;
Wherein,
for final signal decompose the
individual intrinsic mode functions IMF component,
for the remaining component of final signal decomposition;
The 4th step: utilize intrinsic mode functions IMF component obtained above and remaining component to carry out the reconstruct of original signal:
Embodiment 3:
According to the transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value described in embodiment 1, the autocorrelation function of described random signal has reacted signal and himself degree of correlation in different time points, be a kind of statistical measures method of time domain, it is defined as:
In formula:
for the time interval,
represent signal with from the correlation function value of synchronization, obviously, for any random signal, this value is all maximum; Autocorrelation function is the function in sigtnal interval, is separated with positive and negative interval, so length is
signal, have
individual auto-correlation function value, what describe respectively is the similarity degree at unlike signal interval, has also embodied the symmetry of autocorrelation function.
Embodiment 4:
According to the transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value described in embodiment 1, the coefficient of kurtosis of described autocorrelation function is used for metric data at center aggregation extent, in normal distribution situation, coefficient of kurtosis value is 0, positive coefficient of kurtosis explanation observed quantity is more concentrated, has the afterbody longer than normal distribution; Negative coefficient of kurtosis explanation observed quantity is not exclusively concentrated, has the afterbody shorter than normal distribution, and the standard error of coefficient of kurtosis is used for judging the normality of distribution, and it is defined as:
Kurtosis is the index for reflecting the high and steep or flat degree of distribution curve top point, is worth more precipitous.
As the autocorrelation function shape contrast of accompanying drawing 2,3,4,5 random noises and general signal, the kurtosis value of the general signal autocorrelation function in upper example is 4.0622, and the kurtosis value of random signal autocorrelation function is 114.0381.Visible, the distribution of the autocorrelation function of random signal is extremely precipitous.
As shown in Figure 1, the noise-reduction method flow process based on EEMD autocorrelation function kurtosis threshold value is described below:
First this algorithm carries out EEMD decomposition to signal, then calculates the autocorrelation function of each intrinsic mode functions IMF and tries to achieve its kurtosis value, judges whether to meet the auto-correlation function characteristics of random noise according to kurtosis value.To be greater than the intrinsic mode functions IMF component rejection of threshold value, retain non-noise intrinsic mode functions IMF component and its reconstruct is obtained to the signal after denoising, only appear at HFS because the method does not require noise, therefore can remain with the high frequency component signal of use.Wherein threshold value be set as 10.
Embodiment 5:
The above-mentioned transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value, said method emulation is evaluated and tested to data: the cosine signal that simulate signal proportion is 10Hz, wherein
second, sample frequency is 1000Hz.Adding average is 0, after the random noise that standard deviation is 0.1, carries out EEMD decomposition and (makes white noise number of times M=5, standard deviation 0.05), as shown in Figure 6,7, front 4 IMF and spectrogram thereof are as shown in Fig. 8-15 for original signal and noisy signal, and front 4 autocorrelation function graphs are as shown in Figure 16-19.Wherein their kurtosis value is respectively 314.8461,104.2123, and 80.3738,2.7018.According to threshold value known first three be all noise, only having the 4th IMF is useful signal.Frequency spectrum from accompanying drawing 16-19 can find out to only have IMF4 in 10HZ left and right.
In order further to verify the validity of noise-reduction method herein, in simulation process, add the random noise that standard deviation is different, observe and result of calculation, and by adding variance to be noise reduction result and small echo db8 soft-threshold noise reduction and the comparison of EMD noise-reduction method of 0.3 noise signal, as shown in table 1.Wherein anti-acoustic capability index: output signal-to-noise ratio and input-output wave shape similarity.
Output signal-to-noise ratio as shown in the formula:
Wherein
for the variance of reconstruction signal,
for reconstruction signal deducts the variance of former beginning and end plus noise signal.Input-output wave shape similarity formula:
Wherein
for output signal value,
for former beginning and end plus noise signal value.
Table 1 noise-reduction method of the present invention and wavelet soft-threshold and EMD noise reduction comparing result
| 0.3 | Db8 wavelet de-noising | EMD method | The inventive method |
| Signal to noise ratio (S/N ratio) | 15.451 | 20.672 | 26.267 |
| Similarity | 0.883 | 0.940 | 0.999 |
In table 1, data show, noise-reduction method has obvious advantage with respect to small echo db8 soft-threshold noise reduction and EMD noise-reduction method herein.
Embodiment 5:
The above-mentioned transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value, example laboratory:
Experimental data utilizes vibration acceleration sensor to gather casing vibration signal from transformer-cabinet.Signal sampling frequency is 10 kHz, 1000 of sampling numbers, and vibration data is delivered on PC and processed.Vibration signal and reconstruction signal are as shown in Figure 22-23, and EEMD decomposes and adds 0.05 standard variance noise, and integrated number is 50.Front four IMF and frequency spectrum thereof, as shown in Figure 24-31, can find out that first IMF presents noisiness, and the kurtosis value of its autocorrelation function is: 80.6.
Further we that this paper method is compared to experimental result with wavelet method and EMD method is as shown in table 2.The noise reduction that can find out this paper method from result is better than other two kinds of methods equally.
Table 2 noise-reduction method of the present invention and wavelet soft-threshold and EMD noise reduction comparing result
| 0.6 | Db8 wavelet de-noising | EMD method | This paper method |
| Signal to noise ratio (S/N ratio) | 4.677 | 5.221 | 6.432 |
| Similarity | 0.803 | 0.810 | 0.8248 |
Claims (4)
1. the transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value, it is characterized in that: the method comprises the steps: first the transformer vibration signal collecting to be carried out to EEMD decomposition, then carry out autocorrelation function calculating and ask its coefficient of kurtosis for each intrinsic mode functions IMF, then utilize threshold value that these intrinsic mode functions IMF is distinguished, and then cancelling noise signal.
2. the transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value according to claim 1, it is characterized in that: described signal is carried out to EEMD decomposes is the equally distributed characteristic of frequency spectrum of having utilized white noise, and white noise signal automatic average after EMD decomposes is decomposed on different time yardstick; Due to white noise zero mean characteristic, after average the intrinsic mode functions IMF after repeatedly decomposing, eliminate noise effect completely, obtain the finally intrinsic mode functions IMF component without aliasing effect, specific algorithm is as follows:
The first step: in original signal
in add
inferior average is zero, the white noise that standard variance is constant
;
Second step: to adding the signal of white noise
carry out EMD decomposition, obtain
individual intrinsic mode functions IMF component and a 1 remaining component
,
The 3rd step: utilize the feature that white noise statistical nature average is zero, the intrinsic mode functions IMF component and the remaining component that decompose are averaged respectively to computing at every turn, eliminate the impact of the white noise at every turn adding, and then also offset the aliasing that singular point causes;
（3）
（4）
Wherein,
for final signal decompose the
individual intrinsic mode functions IMF component,
for the remaining component of final signal decomposition;
The 4th step: utilize intrinsic mode functions IMF component obtained above and remaining component to carry out the reconstruct of original signal:
3. the transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value according to claim 1 and 2, it is characterized in that: the autocorrelation function of described random signal has reacted signal and himself degree of correlation in different time points, be a kind of statistical measures method of time domain, it is defined as:
In formula:
for the time interval,
represent signal with from the correlation function value of synchronization, obviously, for any random signal, this value is all maximum; Autocorrelation function is the function in sigtnal interval, is separated with positive and negative interval, so length is
signal, have
individual auto-correlation function value, what describe respectively is the similarity degree at unlike signal interval, has also embodied the symmetry of autocorrelation function.
4. according to the transformer vibration signal noise-reduction method based on EEMD kurtosis threshold value described in claim 1 or 2 or 3, it is characterized in that: the coefficient of kurtosis of described autocorrelation function is used for metric data at center aggregation extent, in normal distribution situation, coefficient of kurtosis value is 0, positive coefficient of kurtosis explanation observed quantity is more concentrated, has the afterbody longer than normal distribution; Negative coefficient of kurtosis explanation observed quantity is not exclusively concentrated, has the afterbody shorter than normal distribution, and the standard error of coefficient of kurtosis is used for judging the normality of distribution, and it is defined as:
representative sample number,
for sample average,
represent the standard variance of sample set;
Kurtosis is the index for reflecting the high and steep or flat degree of distribution curve top point, is worth more precipitous.
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