CN113378661A - Direct current electric energy signal denoising method based on improved wavelet threshold and related detection - Google Patents
Direct current electric energy signal denoising method based on improved wavelet threshold and related detection Download PDFInfo
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Abstract
A direct current electric energy signal denoising method based on improved wavelet threshold and relevant detection comprises the steps of firstly, utilizing a multi-resolution analysis theory to perform discrete wavelet decomposition on a signal sampled at a fixed frequency, and separating a high-frequency part from a low-frequency part in the signal; then, an improved threshold function is designed to carry out quantization processing on the decomposed wavelet coefficients so as to reduce the influence of noise signals, and a correlation detection method is combined to carry out periodic mean filtering on the wavelet coefficients, so that the extraction effect of periodic signals is improved; and finally, performing inverse wavelet transform on the reconstructed wavelet coefficient to recover a useful signal. Experimental results show that the denoising effect of the new threshold function is superior to that of the traditional method, and the mixed algorithm has a better extraction effect on periodic signals.
Description
Technical Field
The invention relates to a direct current electric energy signal denoising method based on improved wavelet threshold and related detection.
Background
In the process of calibrating and calibrating the direct current electric energy meter by using the standard meter method electric energy calibrating device, an electric energy main standard device is generally required to be configured to measure voltage and current values, and the measured electric energy value is used as an error judgment basis of the to-be-tested meter. Therefore, the metrological accuracy of the master standard is critical to the results of the verification and calibration. Because the signal is in the actual measurement process, calibrating installation receives the influence of the intrinsic noise source of electronic system inside or external disturbance to lead to the electric energy measurement error, so before carrying out the electric energy calculation, it is essential to carry out noise reduction to the sampling signal.
The conventional frequency domain denoising method converts an analysis domain of a signal from a time domain to a frequency domain by fourier transform (FFT), and reduces or eliminates high frequency components of the signal in a frequency spectrum to reduce the influence of noise on a useful signal. However, in real life, the received signals are not all stationary signals, and although the fourier transform can distinguish the frequency components of the signals, the time when the components with different frequencies appear in the signals cannot be known. Short-time fourier transform (STFT) performs fourier transform after segmenting a signal to be analyzed into a plurality of time windows of equal length, and although the signal can be a stationary signal within a limited time width, the selection of the time windows causes a contradiction between time resolution and frequency resolution. Therefore, the traditional denoising method can suppress signal noise and easily lose edge details in a local time range.
The wavelet transform has the characteristic of multi-resolution, and can simultaneously obtain the time-frequency information of signals, so that the wavelet transform is very suitable for being used as a tool for analyzing and processing electric energy signals. Among them, wavelet threshold denoising has become one of the most widely used methods because of its small amount of calculation and easy implementation. In addition, the correlation detection can judge useful signals and noise signals according to the correlation of the values of the signals at different moments, so that the method is widely combined with the wavelet transform technology in the field of digital signal and image denoising.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an improved threshold function to overcome the defects of the traditional function, and utilizes the correlation between an approximation coefficient after wavelet transformation and a useful signal to carry out periodic mean filtering on the basis of signal denoising by a new threshold function, thereby improving the sampling accuracy of an electric energy signal.
The technical scheme proposed for solving the technical problems is as follows:
a direct current electric energy signal denoising method based on improved wavelet threshold and related detection comprises the following steps:
Where σ is the standard deviation of the noise, by
Estimating;
the detail coefficients are detail coefficients of noise-containing signals after the kth wavelet transform of the jth layer, the value range of k is 0-N-1, N is the length of each layer of wavelet coefficient sequence, and media {. is the median of the wavelet coefficient sequence;
In the formula (I), the compound is shown in the specification,
the wavelet coefficient is processed by a threshold value; lambda is a threshold value; m and n are adjustment factors, and values of the m and n are real numbers which are greater than 0; sgn (·) is a sign function;
In the formula (I), the compound is shown in the specification,
is an approximate coefficient of a noise-containing signal after the kth wavelet transform, tau is a time delay serial number,
the approximation coefficient is transformed by the kth-tau wavelet of the jth layer of the noisy signal;
obtaining the periodic characteristics of the approximate coefficients according to the time interval of the appearance of the peak value of the autocorrelation function, and obtaining periodic information corresponding to each layer of coefficients;
In the formula (I), the compound is shown in the specification,
the wavelet coefficient is a wavelet coefficient after the periodic mean filtering processing, beta is a weight factor, and the value is between 0 and 1; w (k) is a wavelet coefficient sequence before filtering; t is the number of periods in the wavelet coefficient sequence; t represents a cycle number; m is the number of coefficients contained in each period;
value of k after complementation of M，
The coefficient of the kth wavelet corresponding to the t period;
and 6, performing inverse wavelet transform on the reconstructed wavelet coefficient to obtain a denoised signal.
The invention has the beneficial effects that: aiming at the situations that the traditional threshold function in the wavelet threshold denoising method has constant deviation and is discontinuous at the threshold, so that the reconstructed signal loses the edge local characteristics of the real signal and additional oscillation occurs, the improved threshold function is provided, the defects of the function are overcome, and the contraction strategy of changing the coefficient outside the threshold range through the adjusting factor is adopted to adapt to the signal denoising processing with different noise intensity. In addition, by performing autocorrelation operation on each layer of approximate coefficients in combination with correlation detection and performing periodic mean filtering on each layer of wavelet coefficients according to detected periodic information, the denoising effect of periodic signals can be further improved.
Drawings
FIG. 1 is a basic flow of the algorithm of the present invention;
FIG. 2 is a graph of the functional characteristics of a conventional soft and hard threshold function and an improved threshold function;
FIG. 3 is a graph of the functional characteristics of an improved threshold function with different values of m;
FIG. 4 is a graph of the functional characteristics of an improved threshold function with different values of n;
FIGS. 5-8 are graphs of the results of noise reduction of a test signal after adding white Gaussian noise of different intensities using 4 threshold functions;
FIG. 9 is a noise-contaminated periodic signal model constructed when the algorithm for checking the correlation combination of coefficients has an effect on the extraction of periodic signals;
FIG. 10 is a diagram of the result of an autocorrelation operation on the approximation coefficients of each layer of wavelet decomposition;
FIG. 11 shows the comparison of denoising using a single wavelet threshold and coefficient dependent combination of denoising methods.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 11, a dc power signal denoising method based on improved wavelet threshold and correlation detection includes the following steps:
Where σ is the standard deviation of the noise, by
Estimating;
the detail coefficients are detail coefficients of noise-containing signals after the kth wavelet transform of the jth layer, the value range of k is 0-N-1, N is the length of each layer of wavelet coefficient sequence, and media {. is the median of the wavelet coefficient sequence;
In the formula (I), the compound is shown in the specification,
the wavelet coefficient is processed by a threshold value; lambda is a threshold value; m and n are adjustment factors, and values of the m and n are real numbers which are greater than 0; sgn (·) is a sign function, and the waveform of the improved threshold function is shown in fig. 2;
the new threshold function has the following characteristics:
(1) when in use
When the distance approaches to the lambda value, the distance is increased,
the new threshold function is therefore continuous at the break point.
(2) When in use
When the distance is approaching to the infinite distance,
the new threshold function is therefore within the defined domain
Is an asymptote, thereby overcoming the problem that the coefficient has constant deviation after being processed by a soft threshold function.
(3) The attenuation of the wavelet coefficient with the absolute value larger than the threshold value can be dynamically adjusted by changing the values of the adjusting factors m and n, so that the loss of the high-frequency signal characteristics is reduced. As shown in fig. 3, the value of m determines the speed at which the function converges to the asymptote: when the value of m is smaller, the convergence speed is faster; otherwise, the speed becomes slow. As shown in fig. 4, the value of n controls the contraction strategy of the wavelet coefficients: when the value of n is larger, the shrinkage rate of the function to the wavelet coefficient is reduced along with the increase of the coefficient, and the function is suitable for processing signals with high signal-to-noise ratio; while the smaller the value of n, the less the wavelet coefficients near the threshold shrink, thereby preserving the local characteristics of the signal.
In summary, the new threshold function not only solves the problems of the three typical functions, but also can flexibly control the denoising strategy by changing the values of the adjustment factors m and n, thereby achieving the purpose of reducing the influence of noise on the useful signal coefficient and simultaneously reserving the local edge of the real signal according to the difference of the signal characteristics.
In the formula (I), the compound is shown in the specification,
is an approximate coefficient of a noise-containing signal after the kth wavelet transform, tau is a time delay serial number,
the approximation coefficient is transformed by the kth-tau wavelet of the jth layer of the noisy signal;
obtaining the periodic characteristics of each layer coefficient according to the time interval of the occurrence of the peak value of the autocorrelation function, and obtaining periodic information corresponding to each layer coefficient;
and 5, carrying out periodic mean filtering on each layer of wavelet coefficients according to the detected periodic information to reduce the interference of noise signals on the wavelet coefficients so as to improve the recovery effect of useful signals, wherein each layer of coefficients after mean filtering is represented as
In the formula (I), the compound is shown in the specification,
the wavelet coefficient is a wavelet coefficient after the periodic mean filtering processing, beta is a weight factor, and the value is between 0 and 1; w (k) is a wavelet coefficient sequence before filtering; t is the number of periods in the wavelet coefficient sequence; t represents a cycle number; m is the number of coefficients contained in each period;
the value of k after the remainder of M,
the coefficient of the kth wavelet corresponding to the t period;
and 6, performing inverse wavelet transform on the reconstructed wavelet coefficient to obtain a denoised signal. .
Experimental verification and results: in order to test the effectiveness of the method provided by the text, the denoising effect of the improved threshold function and coefficient correlation method is verified and analyzed by using a simulation experiment, the signal-to-noise ratio (SNR) and the mean square error (RMSE) are selected as the evaluation indexes of the denoising performance, and the calculation formula is as follows
Wherein y (n) is the original signal,
for the denoised signal, N is the number of sampling points of the signal.
For the denoised signal, if the SNR value is larger and the RMSE value is smaller, the denoising effect is better.
1 improved wavelet threshold function experiment
Using Matlab simulation software, wavelet threshold denoising processing is respectively carried out on the heavisine test signal added with the gaussian white noise by using a traditional wavelet soft threshold function, a hard threshold function, a compromise threshold function (alpha is 0.5) and an improved threshold function (m is 1.2, and n is 0.8) proposed herein. The expressions of the wavelet soft threshold function, the wavelet hard threshold function and the compromise threshold function are respectively (7), (8) and (9):
the threshold values of the wavelet coefficients in the above functions all adopt the local fixed threshold value of the formula (1).
The wavelet basis function selects the db3 wavelet with 5 decomposition levels. Fig. 5-8 show the processing results of noise reduction of a test signal after adding white gaussian noise with different intensities by using 4 threshold functions.
Table 1 shows the snr after signal denoising compared to the mean square error. The result shows that the test signal processed by the soft threshold function is smoother than the hard threshold function, but the signal-to-noise ratio and the mean square error index are both worse than the hard threshold function; the denoising effect of the compromise threshold function is between a soft threshold and a hard threshold, and the theoretical expectation is met; the improved threshold function provided by the invention is superior to other threshold functions in denoising results of test signals. However, as the noise intensity increases, the noise reduction effect of the different functions on the signal decreases.
TABLE 1
Coefficient correlation denoising experiment: in order to examine the effect of the coefficient-dependent algorithm on the periodic signal extraction, a noise-containing periodic signal model x (t) sin (2 π f) was constructed in simulation software1t)+sin(2πf2t) + n (t), where n (t) is white Gaussian noise, f1、f2The signal frequencies are 50Hz and 100Hz, respectively. The noisy periodic signal is shown in fig. 9.
The noisy periodic signal is subjected to 3-layer wavelet decomposition and wavelet threshold denoising by using the improved threshold function provided in the text, and then the autocorrelation operation is performed on the approximation coefficient of each layer of wavelet decomposition, and the operation result is shown in fig. 10.
It can be seen from fig. 10 that the autocorrelation function of each layer of approximation coefficients has obvious periodicity, and the period of each layer of approximation coefficients is 2 after wavelet decomposition of the constructed signal observed according to the time interval of occurrence of the peak in the autocorrelation function5-j(j is the number of layers of approximation coefficients).
And selecting a weight factor beta as 0.8, filtering the wavelet coefficients of each layer by a formula (4), and recovering the signals by using inverse wavelet transform. The results of the denoising method using a single wavelet threshold denoising and coefficient correlation are shown in fig. 11.
Table 2 shows the signal-to-noise ratio and the mean square error of the periodic signal after being processed by the improved threshold denoising and mixing algorithm under the interference of different noise intensities. As can be seen from the table, compared with single wavelet threshold processing, the hybrid algorithm has the advantages that various performance indexes are improved, and the denoising effect is obviously improved along with the increase of the noise intensity, so that the method has a better periodic signal extraction effect.
TABLE 2
While the foregoing has described a preferred embodiment of the invention, it will be appreciated that the invention is not limited to the embodiment described, but is capable of numerous modifications without departing from the basic spirit and scope of the invention as set out in the appended claims. The proposed noise reduction method takes into account both signal smoothing and local characteristics, not only improving the deviation from the original signal, but also improving the signal-to-noise ratio. Meanwhile, the characteristic that the approximation coefficient has correlation after the periodic signal is subjected to wavelet decomposition is utilized, and the extraction effect of the algorithm on the periodic signal is greatly improved.
Claims (1)
1. A direct current electric energy signal denoising method based on improved wavelet threshold and related detection is characterized by comprising the following steps:
step 1, sampling direct current voltage and current signals by using fixed frequency to obtain original sampling data x (t) of electric energy signals, and selectively performing j-layer orthogonal wavelet decomposition on the sampling signals by adopting wavelet basis functions to obtain approximate coefficients of the signals representing low-frequency and high-frequency information on the j-th layer respectively
And detail coefficient
Step 2, setting a threshold value for detail coefficients of each layer after wavelet decomposition, wherein the threshold value adopts a calculation method of a local fixed threshold value, and the calculation formula is
Where σ is the standard deviation of the noise, by
Estimating;
the detail coefficients are detail coefficients of noise-containing signals after the kth wavelet transform of the jth layer, the value range of k is 0-N-1, N is the length of each layer of wavelet coefficient sequence, and media {. is the median of the wavelet coefficient sequence;
step 3, using improved threshold function to carry out quantization processing on detail coefficients of each layer, reducing the influence of noise signals on useful signals, thereby obtaining approximate estimation of the useful signals, wherein the new threshold function expression is
In the formula (I), the compound is shown in the specification,
the wavelet coefficient is processed by a threshold value; lambda is a threshold value; m and n are adjustment factors, and values of the m and n are real numbers which are greater than 0; sgn (·) is a sign function;
step 4, performing autocorrelation operation on each layer of approximate coefficients obtained by decomposition in the step 1, wherein the formula of the autocorrelation operation is
In the formula (I), the compound is shown in the specification,
is an approximate coefficient of a noise-containing signal after the kth wavelet transform, tau is a time delay serial number,
the approximation coefficient is transformed by the kth-tau wavelet of the jth layer of the noisy signal;
obtaining the periodic characteristics of the approximate coefficients according to the time interval of the appearance of the peak value of the autocorrelation function, and obtaining periodic information corresponding to each layer of coefficients;
step 5, according to the period information detected in the step 4, performing average filtering on the periods corresponding to each point in the wavelet coefficient, wherein the formula of the period average filtering is
In the formula (I), the compound is shown in the specification,
the wavelet coefficient is a wavelet coefficient after the periodic mean filtering processing, beta is a weight factor, and the value is between 0 and 1; w (k) is a wavelet coefficient sequence before filtering; t is the number of periods in the wavelet coefficient sequence; t represents a cycle number; m is the number of coefficients contained in each period;
the value of k after the remainder of M,
the coefficient of the kth wavelet corresponding to the t period;
and 6, performing inverse wavelet transform on the reconstructed wavelet coefficient to obtain a denoised signal.
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