CN112528853B - Improved dual-tree complex wavelet transform denoising method - Google Patents

Improved dual-tree complex wavelet transform denoising method Download PDF

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CN112528853B
CN112528853B CN202011452278.4A CN202011452278A CN112528853B CN 112528853 B CN112528853 B CN 112528853B CN 202011452278 A CN202011452278 A CN 202011452278A CN 112528853 B CN112528853 B CN 112528853B
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姜毅
张国荣
张兴霖
李锐
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Zhaotong Power Supply Bureau of Yunnan Power Grid Co Ltd
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Abstract

The invention discloses an improved dual-tree complex wavelet transform denoising method, and belongs to the technical field of power equipment power quality signal processing. The method comprises the steps of power quality signal acquisition, filtering processing, dual-tree complex wavelet transformation, threshold function improvement, dual-tree complex wavelet combination of the improved threshold function and the like. The method effectively analyzes and processes the common parameter fluctuation of the power quality, makes targeted improvement, effectively processes the noise of the power quality by using the factors such as voltage fluctuation, frequency change, load imbalance, flicker and the like, greatly simplifies the operation amount, improves the analysis precision, greatly improves the signal quality of the power quality, reduces the influence of the noise on the operation of later equipment and signal processing, and lays a solid foundation for further processing and analysis in the future.

Description

Improved dual-tree complex wavelet transform denoising method
Technical Field
The invention belongs to the technical field of power quality signal processing of power equipment, and particularly relates to an improved dual-tree complex wavelet transform denoising method.
Background
The method comprises the following steps that the power quality signal processing of the power equipment adopts a wavelet threshold denoising method traditionally, wherein the wavelet threshold denoising method comprises a soft threshold method and a hard threshold method, but the hard threshold method is discontinuous, and the soft threshold method has constant deviation.
The traditional wavelet threshold denoising method is to perform wavelet transformation on a noisy signal by utilizing the multi-scale characteristics of wavelet analysis, then perform threshold processing on the obtained wavelet coefficient, and then reconstruct the processed wavelet coefficient, thus obtaining a denoised signal.
The specific steps for denoising noisy transponder signals are as follows:
1) selecting a proper wavelet basis function, and performing N-layer wavelet decomposition on the signal of the noisy responder to obtain a wavelet coefficient;
2) and selecting a threshold to perform threshold quantization processing on the 1-N layers of high-frequency coefficients to obtain a wavelet coefficient estimation value of the original signal. The traditional wavelet threshold quantization processing adopts soft and hard threshold methods. The hard threshold method is to set the coefficient with the absolute value smaller than the threshold value after wavelet decomposition as zero, and the coefficient larger than or equal to the threshold value is kept unchanged, and the hard threshold value determines that the discontinuity of the hard threshold value has a pseudo Gibbs phenomenon.
Therefore, how to overcome the defects of the prior art is a problem to be solved in the technical field of power quality signal processing of power equipment.
Disclosure of Invention
The invention aims to solve the defects of the prior art and provides an improved dual-tree complex wavelet transform denoising method, which combines the characteristics of 35kV-500kV electric energy quality signals and effectively processes the noise of the electric energy quality by using the factors such as voltage fluctuation, frequency change, load imbalance and flicker, thereby greatly simplifying the operation amount and improving the analysis precision.
In order to achieve the purpose, the invention adopts the following technical scheme:
the improved dual-tree complex wavelet transform denoising method comprises the following steps:
step (1), acquiring an electric energy quality original signal, and performing dual-tree complex wavelet decomposition on the signal;
s＝f(i)+ε×e(i)，i＝0，1，2，…，N-1；
wherein f (i) is the original transponder signal; e (i) is noise; s (i) is a noisy transponder signal; ε is the noise level coefficient; n is the number of signal sampling points;
step (2), calculating the noise variance after the dual-tree wavelet decomposition:
Figure BDA0002827532760000021
σ is the noise variance of the signal; w is aj，kDecomposing k for j layers in the original transponder signal matrixAnA threshold function of the sequence;
step (3), calculating a wavelet threshold:
Figure BDA0002827532760000022
wherein λ represents a threshold value, j represents the number of decomposition layers, a is a constant and 0 < a < 1;
step (4), decomposing k for j layers in all original transponder signal matrixesAnThe threshold function of the sequence is processed using the following formula and then using the processed coefficientsDouble-tree complexPerforming inverse wave transformation to obtain a noise-reduced electric energy quality signal;
Figure BDA0002827532760000023
in the formula (I), the compound is shown in the specification,
Figure BDA0002827532760000024
for improved threshold coefficient, ωj，kAs an original threshold function, λ is a threshold, j represents the number of decomposition layers, and k is 1j-1。
Further, it is preferable that the power quality bus voltage range is 35kV to 500 kV.
Further, the range of the decomposition layer number of the dual-tree complex wavelet is preferably 1-5.
Further, it is preferable that the number of decomposition layers of the dual-tree complex wavelet is 4.
Further, it is preferable that the raw signal of the power quality includes an amplitude, a phase angle and a frequency.
Aiming at the defects of a soft threshold method and a hard threshold method, the invention provides an improved threshold function aiming at the characteristics of a 35kV-500kV electric energy quality signal, mainly solves the problem of denoising when the signal has strong noise, enables an estimated signal after quantization processing to be closer to an original signal by the improved threshold function, and verifies the effectiveness of the method through simulation.
Compared with the prior art, the invention has the following effects:
the invention combines the characteristics of the electric energy quality signal of 35kV-500kV, and effectively processes the noise of the electric energy quality by the factors of voltage fluctuation, frequency variation, unbalanced load, flicker and the like, thereby greatly simplifying the operation amount and improving the analysis precision. By comparing the processing results of the hard threshold denoising image (figure 8), the soft threshold denoising image (figure 9) and the ITF-DTCTWT denoising image (figure 10) of the same signal, the method can obtain the method, and the method avoids the discontinuity of the traditional hard threshold method and the constant deviation of the soft threshold method, and lays a solid foundation for further processing of the signal.
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FIG. 1 is a flow chart of a one-dimensional DTCTWT decomposition process in the method of the present invention;
FIG. 2 is a flow chart of a DTCTWT-based PQDS denoising method according to the present invention;
FIG. 3 is a waveform of a sinusoidal signal de-noising; wherein, (a) is a noiseless original signal waveform, (b) is a noiseless original signal waveform, (c) is a reconstructed signal waveform after denoising (HTF algorithm), (d) is a reconstructed signal waveform after denoising (STF algorithm), and (e) is a reconstructed signal waveform after denoising (ITF-DTCTWT algorithm);
FIG. 4 is a harmonic signal de-noising waveform; wherein, (a) is a noiseless original signal waveform, (b) is a noiseless original signal waveform, (c) is a reconstructed signal waveform after denoising (HTF algorithm), (d) is a reconstructed signal waveform after denoising (STF algorithm), and (e) is a reconstructed signal waveform after denoising (ITF-DTCTWT algorithm);
FIG. 5 illustrates a denoised waveform of an oscillation signal; wherein, (a) is a noiseless original signal waveform, (b) is a noiseless original signal waveform, (c) is a reconstructed signal waveform after denoising (HTF algorithm), (d) is a reconstructed signal waveform after denoising (STF algorithm), and (e) is a reconstructed signal waveform after denoising (ITF-DTCTWT algorithm);
FIG. 6 is a graph of power quality raw signals;
FIG. 7 is a graph of an original signal after superimposing noise;
FIG. 8 is a graph after hard threshold denoising;
FIG. 9 is a diagram after soft threshold denoising;
FIG. 10 is a diagram after ITF-DTCTWT denoising;
FIG. 11 is a flowchart of an improved dual-tree complex wavelet transform denoising method according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples. The examples are given solely for the purpose of illustration and are not to be construed as limitations of the present invention.
It will be appreciated by those skilled in the art that the following examples are illustrative of the invention only and should not be taken as limiting the scope of the invention. The examples do not specify particular techniques or conditions, and are performed according to the techniques or conditions described in the literature in the art or according to the product specifications. The materials or equipment used are not indicated by manufacturers, and all are conventional products available by purchase.
The terms involved in the present invention are as follows:
a Power Quality Disturbance Signal (PQDS);
improved Threshold Function (ITF);
dual-tree complex wavelet transform (DTCWT);
soft Threshold Function (STF);
signal to noise ratio (SNR);
root Mean Square Error (MSE);
an improved dual-tree complex wavelet transform denoising method (ITF-DTCTWT).
The improved dual-tree complex wavelet transform denoising method comprises the following steps:
step (1), acquiring an electric energy quality original signal, and performing dual-tree complex wavelet decomposition on the signal;
s(i)＝f(i)+ε×e(i)，i＝0，1，2，...，N-1；
wherein f (i) is the original transponder signal; e (a)i) Is noise; s (i) Is a noisy transponder signal; ε is the noise level coefficient; n is the number of signal sampling points;
step (2), calculating the noise variance after the dual-tree wavelet decomposition:
Figure BDA0002827532760000041
σ is the noise variance of the signal; w is aj，kDecomposing k for j layers in the original transponder signal matrixAnA threshold function of the sequence;
step (3), calculating a wavelet threshold:
Figure BDA0002827532760000042
wherein λ represents a threshold value, j represents the number of decomposition layers, a is a constant and 0 < a < 1;
step (4), decomposing k for j layers in all original transponder signal matrixesAnThe threshold function of the sequence is processed using the following formula and then using the processed coefficientsDouble-tree complexPerforming inverse wave transformation to obtain a noise-reduced electric energy quality signal;
Figure BDA0002827532760000043
in the formula (I), the compound is shown in the specification,
Figure BDA0002827532760000044
for improved threshold coefficient, ωj，kAs an original threshold function, λ is a threshold, j represents the number of decomposition layers, and k is 1j-1。
Preferably, the voltage range of the power quality bus is 35kV-500 kV.
Preferably, the range of the decomposition layer number of the dual-tree complex wavelet is 1-5.
Preferably, the number of layers of the dual-tree complex wavelet decomposition is 4.
Preferably, the power quality original signal comprises amplitude, phase angle and frequency.
1. A flow chart of a conventional dual-tree complex wavelet algorithm, such as a one-dimensional DTCWT decomposition process, is shown in figure 1. The one-dimensional DTCWT is mainly composed of two parallel wavelet transforms, where a tree is a real wavelet coefficient obtained by decomposing a signal with conjugate orthogonal filters (h0(n), h1(n)), and contains high-frequency and low-frequency components. The tree b is an imaginary wavelet coefficient obtained by decomposing a signal using conjugate integration filters (g0(n), g1(n)), which also contains high-frequency and low-frequency components. Additionally ↓2in fig. 1 represents alternate 2 samples.
As known from the one-dimensional DTCWT decomposition process, both the tree a and the tree b are filtered and then extracted, and if the delays of the upper tree and the lower tree are set to a sampling interval, the obtained data form a complementary relationship, so that the loss of the original signal characteristic information can be reduced. For each subsequent layer decomposition, if the group delay of half a sampling period between the two-tree filter groups is set, the respective filter lengths of the tree a and the tree b are consistent, and the total delay generated by the layer and all previous layers is ensured to be one period. Meanwhile, the biorthogonal wavelet transformation has the characteristic of linear phase, if the filter length of the tree a is set to be an odd number, and the filter length of the tree b is set to be an even number, or vice versa, the linear phase of the transformation is ensured.
2. De-noising process
The noisy power quality signal may be expressed as:
z＝s+n (1)
where z represents a noisy signal and n represents random noise, the purpose of denoising the signal is to reduce the noisy signal z to a true signal s by using wavelet transform or the like.
The wavelet transform of equation (1) can be used to obtain:
Wz W W (2)
in the formula, WzIs the wavelet transform coefficient of signal z; w is the wavelet transform coefficient of signal s; w is the wavelet transform coefficient of the signal n.
A flowchart of a Power Quality Disturbance Signal (PQDS) denoising method based on DTCWT is shown in fig. 2.
The implementation steps of the PQDS denoising method based on DTCTT are as follows:
(1) and (3) complex wavelet transformation: performing two-path parallel wavelet decomposition on the original PQDS containing noise, filtering and then extracting to obtain real part wavelet coefficients and imaginary part wavelet coefficients;
(2) threshold processing: processing the corresponding real and imaginary wavelet coefficients in the wavelet domain using ITF;
(3) inverse complex wavelet transform: and performing inverse wavelet transform on the processed real part wavelet coefficients and imaginary part wavelet coefficients, and performing interpolation and filtering to obtain the denoised PQDS.
3. Determination of thresholds and threshold functions
In the denoising method based on wavelet transformation, the most critical step is the selection of the threshold value size, which directly influences the final denoising effect of the algorithm. When the threshold is selected too small, the wavelet coefficients smaller than the threshold will be set to zero, i.e. it is possible that signal components other than noise are mistakenly filtered out as noise. When the threshold is selected to be too large, the wavelet coefficients larger than the threshold will be retained, i.e. it is possible that noise components other than the signal are mistakenly retained as a signal. The traditional wavelet threshold is generally determined according to the statistical rule of the noise variance and the number of wavelet coefficients, and the expression is as follows:
Figure BDA0002827532760000061
wherein σ is the noise variance of the signal; n is the number of wavelet coefficients; lambda [ alpha ]0Is a threshold value;
wherein the calculation of the noise variance can useDonohoThe median estimation formula proposed by the et al based on the threshold estimation risk theorem:
Figure BDA0002827532760000062
ωj，kas an original threshold function, λ is a threshold, j represents the number of decomposition layers, and k is 0j-1；
In the formula, σ and | ω are shownj，kThe median value in | is proportional, i.e. once the signal is determined, the wavelet coefficient obtained by decomposition is constant, and σ and the threshold value are constant values. According to the noise, in the wavelet decomposition process, the corresponding wavelet coefficient value decreases with the increase of the decomposition layer number, and obviously, the determination of the threshold value is different with the difference of the wavelet decomposition layer number.
Therefore, the invention provides a determination method for improving a threshold, which is shown in formula (5):
Figure BDA0002827532760000063
in the formula, λ represents a threshold value, j represents the number of decomposition layers, a is a constant and 0 < a < 1. The formula (5) is increased by a factor of 1/a compared to the formula (3)-The characteristic that the wavelet coefficient can change along with the decomposition scale is adapted, so that the improved threshold lambda can be used for distinguishing the noise signal from the useful signal.
The method for processing wavelet coefficients by using a preselected threshold is called a threshold function, and conventionally comprises a Hard Threshold (HTF) and a Soft Threshold (STF), which are respectively expressed as (6) and (7):
Figure BDA0002827532760000064
Figure BDA0002827532760000065
where λ represents an empirically selected threshold, λ being the same in both HTF and STF; omegaj，kRepresenting an original threshold function, which is mainly a wavelet coefficient of a high-frequency part of a signal according to the distribution condition of noise frequency;
Figure BDA0002827532760000066
the wavelet coefficient obtained after the judgment of the signal component or the noise component through the HTF algorithm and the STF algorithm and the processing is shown.
Both HTF and STF algorithms have achieved good results in practical applicationNoise removal effect ofThere are also deficiencies:
(1) for HTF, the wavelet coefficient which is larger than or equal to a threshold lambda is not changed, the wavelet coefficient which is smaller than the threshold lambda is directly set to zero, the function is discontinuous at the threshold lambda and is shown as mutation or singularity, and some oscillation is easily generated after a denoising signal is reconstructed;
(2) for STF, it can be known from equation (7) that the wavelet coefficients greater than or equal to the threshold λ undergo a certain shrinkage (minus λ), and the wavelet coefficients smaller than the threshold λ are directly set to zero, so that there is no discontinuity at the threshold λ, but because the wavelet coefficients have a certain shrinkage, ω and ω have a constant deviation, which inevitably causes the energy of the de-noised signal to be attenuated and affects the approximation degree.
On the basis of HTF and STF algorithms, the invention provides an improved threshold function, which is characterized in that the denoising effect is ensured, and the characteristic information in the original signal is kept as much as possible, wherein the expression is (8):
Figure BDA0002827532760000071
in equation (8), the size of the subtrahend represents one statistical value of the noise size, and is obtained by different statistics.
From the formula (8), the ITF of the present invention has the following characteristics:
(1) continuity at threshold λ: when | ω, | λ, ω, ═ 0; when ω, → ∞ ω, → 0; it is clear that the occurrence of a sudden change or singularity at the threshold λ can be avoided; when | ω, | → ∞ is ω, → ω, i.e., ω, → ω, which is an asymptote, it can be seen that the difference between the wavelet coefficients ω,, ω, becomes smaller and smaller as | ω, | increases, i.e., a constant deviation between the two is reduced and the approximation between the two is improved.
(2) The formula (8) has no uncertain factor, and the determined omega can be directly obtained from omega and a threshold lambda, so that the stability of the denoising process is ensured; the threshold function includes a decomposition level variable j, which varies with j, and is obviously adaptive.
The core step is therefore to calculate the threshold λ from equation (5) and then to process the corresponding wavelet coefficients according to equation (8).
4. Improved algorithm experiments and results
In order to verify the effectiveness and the denoising effect of the ITF-DTCTWT denoising method in the power quality disturbance signal denoising application, firstly, taking a plurality of simulated power quality disturbance signals as an example, the ITF-DTCTWT algorithm is verified and compared with the traditional hard and soft threshold algorithm, and then the actual power quality disturbance signals are utilized to perform comparison tests on the hard threshold function, the soft threshold function and the ITF-DTCTWT algorithm.
At present, two methods are mainly used for evaluating the denoising effect of the algorithm, firstly, subjective evaluation is carried out, namely, human eyes are used for observing the waveform change conditions before and after denoising to evaluate the denoising effect, so that time is consumed, the evaluation standard is difficult to unify, and the method is rarely applied in practice at present. Secondly, the index is used for evaluation, and the commonly used indexes are signal to noise ratio (SNR) and Mean Squared Error (MSE), which are respectively shown in formulas (9) and (10):
Figure BDA0002827532760000081
Figure BDA0002827532760000082
in the formula: n is the number of signal sampling points; i isThe serial number of the signal sampling point; s (i) isi pieces ofReal values of sampling points;
Figure BDA0002827532760000084
is as followsi pieces ofSampling pointAfter denoisingAn estimate of (d).
The relation between SNR and MSE is equation (11):
Figure BDA0002827532760000083
it can be seen that the SNR and MSE values are calculated by the signals before and after denoising through the equations (9) and (10) to judge the denoising effect.
4.1 comparison of denoising Effect for simulation signals
In order to test the effectiveness and the denoising effect of the ITF-DTCTWT algorithm and simultaneously carry out verification comparison with a hard threshold algorithm and a soft threshold algorithm, the experiment firstly selects 3 power quality disturbance simulation signals of sine, harmonic and oscillation to test.
The signal length is 10 cycles (50Hz), the sampling frequency is 51.2kHz, and the frequency amplitude is a per unit value (pu). FIGS. 3, 4 and 5 are waveforms of sinusoidal, harmonic and oscillating power quality signals respectively denoised when the standard deviation sigma of the noise is 0.01,
in order to further verify the adaptability, effectiveness and denoising effect of the ITF-DTCTWT algorithm on various types of PQDS denoising, the ITF-DTCTWT algorithm is verified and compared with the traditional algorithm. Nine common PQDS such as standard sinusoidal voltage, voltage harmonic (harmonics), voltage flicker (flicker), voltage notch (notch), voltage interruption (interruption), voltage dip (sag), voltage rise (swell), voltage oscillation (oscillation), voltage pulse (impulse) and the like are selected. To avoid random effects in the test, all signals were repeated 5 times per noise standard deviation σ and the SNR average was taken. Table 1 shows the experimental comparison results of the hard threshold algorithm, the soft threshold algorithm and the method of the present invention when the noise standard deviation is 0.01, 0.03, 0.05, 0.1, 0.2, respectively. Wherein, the algorithm 1 represents the HTF denoising algorithm, the algorithm 2 represents the STF denoising algorithm, and the algorithm 3 represents the ITF-DTCTWT denoising algorithm. It can be seen from the table that under the condition of different noise standard deviations σ, the SNR index of the denoised signal obtained by the algorithm is better than that of the traditional HTF and STF denoising algorithms, which indicates that the denoising effect is improved.
TABLE 1 three algorithms for nine PQDS denoising test results (SNR)
Figure BDA0002827532760000091
4.2 comparison of denoising Effect for actual signals
The actual signal is from a power quality disturbance signal collected from a power grid, and the disturbance signal is tested. The length of the perturbation signal is 6 cycles (50Hz), the sampling frequency is 12.8kHz, and the frequency amplitude value is per unit (pu) as shown in fig. 6-10.
As is clear from the waveforms before and after denoising shown in fig. 6 to 10, the overall denoising effect and the detail characteristics at the mutation point are better in the ITF-dtctt algorithm than the conventional HTF and STF algorithms, and the retaining effect on the information of the mutation point is the best.
The invention provides a PQDS denoising method of ITF-DTCTWT aiming at the change characteristic of wavelet coefficients of noise signals along with different decomposition layer numbers. The method mainly works by firstly improving the selection of the threshold value, then designing a threshold function which not only ensures the denoising effect, but also improves the retaining effect of the detail characteristics of the catastrophe points, and then combining DTCTWT processing wavelet coefficients, thereby overcoming some defects of the traditional denoising method. The HTF, STF and ITF-DTCTWT 3 algorithms are verified and compared through simulation and actual PQDS, and experimental results show that the adaptability, effectiveness and denoising effect of the ITF-DTCTWT algorithm are superior to those of the traditional HTF and STF denoising algorithms.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (5)

1. The improved dual-tree complex wavelet transform denoising method is characterized by comprising the following steps:
step (1), acquiring an electric energy quality original signal, and performing dual-tree complex wavelet decomposition on the signal;
s(i)＝f(i)+ε×e(i)，i＝0，1，2，...，N-1；
wherein f (i) is the original transponder signal; e (i) is noise; s (i) is a noisy transponder signal; ε is the noise level coefficient; n is the number of signal sampling points;
step (2), calculating the noise variance after the dual-tree wavelet decomposition:
Figure FDA0002827532750000011
σ is the noise variance of the signal; w is aj，kDecomposing a threshold function of k sequences for j layers in the original transponder signal matrix;
step (3), calculating a wavelet threshold:
Figure DEST_PATH_BDA0002827532760000022
wherein λ represents a threshold value, j represents the number of decomposition layers, a is a constant and 0 < a < 1;
step (4), a threshold function of j layers of decomposed k sequences in all original responder signal matrixes is processed by adopting the following formula, and then dual-tree complex wavelet inverse transformation is carried out by adopting the processed coefficients to obtain denoised electric energy quality signals;
Figure FDA0002827532750000013
in the formula (I), the compound is shown in the specification,
Figure FDA0002827532750000014
for improved threshold coefficient, ωj，kAs an original threshold function, λ is a threshold, j represents the number of decomposition layers, and k is 1j-1。
2. The improved dual-tree complex wavelet transform denoising method of claim 1, wherein the power quality bus voltage range is 35kV-500 kV.
3. The improved dual-tree complex wavelet transform denoising method of claim 1, wherein the number of decomposition layers of the dual-tree complex wavelet is in the range of 1-5.
4. The improved dual-tree complex wavelet transform denoising method of claim 1, wherein the number of dual-tree complex wavelet decomposition layers is 4.
5. The improved dual-tree complex wavelet transform denoising method of claim 1, wherein the power quality original signal comprises amplitude, phase angle and frequency.
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