CN111046791A - Current signal filtering and denoising method based on generalized S transform containing variable factors - Google Patents

Current signal filtering and denoising method based on generalized S transform containing variable factors Download PDF

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CN111046791A
CN111046791A CN201911264865.8A CN201911264865A CN111046791A CN 111046791 A CN111046791 A CN 111046791A CN 201911264865 A CN201911264865 A CN 201911264865A CN 111046791 A CN111046791 A CN 111046791A
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卫志农
毛玥萱
殷志华
孙国强
臧海祥
刘玲
刘雨琦
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Hohai University HHU
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Abstract

The invention discloses a current signal filtering and denoising method based on generalized S-transform containing variable factors, which comprises the steps of firstly converting a discrete sampling sequence of a group of continuous time domain current signals into a two-dimensional time-frequency complex matrix through the generalized S-transform containing variable factors; secondly, performing threshold filtering method processing on the two-dimensional time-frequency matrix, then processing by using a time-frequency filter based on time-frequency spectrum distribution, retaining effective signals in a time-frequency domain, and extracting effective current signal components; and finally, obtaining a one-dimensional time domain current signal with noise removed through the generalized inverse S transform. The invention can effectively extract the current pure signal under the noise background, thereby analyzing and processing the current signal under various working conditions.

Description

Current signal filtering and denoising method based on generalized S transform containing variable factors
Technical Field
The invention belongs to the technical field of signal filtering and denoising processing, and particularly relates to a current signal filtering and denoising method based on generalized S-transform containing variable factors.
Background
In engineering practice, the influence of noise on the actual measured values is almost unavoidable. When a small-current single-phase earth fault occurs in a power distribution network, a large amount of noise signals easily submerge weak fault characteristic signals, so that effective fault signals are more difficult to extract, and the problem of fault positioning is difficult to solve. On one hand, with the rapid development of urban power grids, the proportion of cables in a distribution line is higher and higher, and noise pollution is aggravated; on the other hand, due to the error of the measuring device, the fault current and voltage sensors applied in the existing engineering have certain measuring errors due to the limitations of cost, technical conditions and the like. Therefore, the filtering and denoising processing method of the current signal becomes important.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a current signal filtering and denoising method based on generalized S-transform containing variable factors aiming at the condition that the effective signals are submerged by the widely existing noise background, so as to achieve the purpose of extracting the effective signals from the noise background under various working condition environments.
The technical scheme is as follows: the invention relates to a current signal filtering and denoising method based on generalized S transform containing variable factors, which comprises the following steps:
(1) inputting a discrete sampling sequence of a group of continuous time domain current signals;
(2) obtaining a two-dimensional time-frequency complex matrix through generalized S transformation containing variable factors;
(3) processing signals by using a threshold filtering method;
(4) performing signal processing by using a time-frequency filter based on time-frequency spectrum distribution;
(5) and obtaining a one-dimensional time domain current signal with noise removed through the generalized inverse S transform, and comparing the signal.
Further, the generalized S transformation algorithm with variable factors in the step (2) introduces variable factors sigma adjusted along with frequency variationfThe gaussian window function with variable factors is as follows:
Figure BDA0002312543370000011
where f is frequency, t is time, σfAs a variable factor having an argument f, e.g. sigmaf(f)＝kf+b,σf(f)＝k/f+b,σf(f)＝(kf+b)aEtc., k, a, b are all constants.
Substitution of sigmaf(f) Kf + b, the generalized S transform function with variable factors is:
Figure BDA0002312543370000021
when f → n/NT, τ → kT, the discrete generalized S transform function is:
Figure BDA0002312543370000022
wherein the content of the first and second substances,
Figure BDA0002312543370000023
is the discrete fourier transform of a discrete sequence of time domain signals, N is the number of sample points, T is the sample time interval, k represents time, and N represents frequency.
The two-dimensional time-frequency complex matrix of the time domain signal obtained after the generalized S transformation is as follows:
Figure BDA0002312543370000024
wherein A (k, n) is the amplitude matrix of the signal after the generalized S transformation,
Figure BDA0002312543370000025
is a phase angle matrix of the signal after the generalized S transform.
Further, the threshold filtering method in step (3) includes the following steps:
(31) after obtaining generalized S transformation containing variable factorsMaximum value GST of signal dataHMax (GST (k, n)) and minimum GSTL＝min(GST(k,n))；
(32) Quantizing the transformed signal data, and selecting K-2nWhen n is 7 or 8 as the quantization level, the quantization interval is obtained as:
Figure BDA0002312543370000026
thus, each quantization interval is obtained as:
σ＝(GSTL+Δp(K-1),GSTL+Δp·K)
(33) selecting a threshold α capable of filtering noise range, and determining a filtering factor of threshold filtering:
Figure BDA0002312543370000027
(34) and (3) extracting effective signals in a time-frequency domain through processing by a threshold filtering method:
GST1(k,n)＝GST(k,n)*H1(k,n)
further, the time-frequency filter signal processing based on the time-frequency spectrum distribution in the step (4) comprises the following steps:
(41) determining the instantaneous frequency of the signal according to the signal characteristics in the time-frequency domain;
(42) analyzing the time-frequency distribution of the signals, determining the noise time-frequency range, reserving the time-frequency range of the effective signals, and performing a time-frequency filter function based on the time-frequency spectrum distribution as follows:
Figure BDA0002312543370000031
(43) and extracting effective signals in a time-frequency domain through time-frequency filter method processing based on time-frequency spectrum distribution:
GST2(k,n)＝GST1(k,n)*H2(k,n)
further, the function of the generalized inverse S transform described in step (5) is as follows:
x(t)＝GST-1[GST2(k,n)]
has the advantages that: compared with the prior art, the method has the following remarkable technical effects that on one hand, variable factors which can change along with frequency change are introduced into the Gaussian window function of the generalized S transform algorithm containing the variable factors, and the local frequency band time-frequency resolution of the full-time signal is improved. On the other hand, the invention combines the threshold filtering method with the time-frequency filter method based on the time-frequency spectrum distribution, better realizes the functions of extracting effective signals and inhibiting noise, and has more excellent filtering and denoising effects.
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FIG. 1 is a schematic flow chart of a processing method of a current signal filtering and denoising method according to the present invention;
FIG. 2 is a schematic diagram of effective signal extraction by a time-frequency filter method based on time-frequency spectrum distribution;
fig. 3 is a comparison graph of effects of four filtering and denoising methods for line transient zero-sequence current based on 100 Ω transition resistance single-phase ground fault of a power distribution network.
Detailed Description
For the purpose of illustrating the technical solutions disclosed in the present invention in detail, the following description is further provided with reference to the accompanying drawings and specific embodiments.
The invention provides a current signal filtering and denoising method based on generalized S transform containing variable factors aiming at the condition that the widely existing noise background submerges effective signals. The invention can carry out filtering and denoising processing on the signal by a threshold filtering method containing variable factor generalized S transformation and a filtering and denoising method combining a time-frequency filter based on time-frequency spectrum distribution, thereby realizing the purpose of extracting effective signals from noise backgrounds under various working condition environments.
As shown in FIG. 1, the method comprises the following steps:
step one, inputting a group of discrete sampling sequences of continuous time domain current signals.
And step two, obtaining a two-dimensional time-frequency complex matrix through generalized S transformation containing variable factors.
Variable factor sigma adjusted along with frequency change is introduced into generalized S transformation algorithm containing variable factorfThe gaussian window function with variable factors is as follows:
Figure BDA0002312543370000041
where f is frequency, t is time, σfAs a variable factor having an argument f, e.g. sigmaf(f)＝kf+b,σf(f)＝k/f+b,σf(f)＝(kf+b)aEtc., k, a, b are all constants.
Substitution of sigmaf(f) Kf + b, the generalized S transform function with variable factors is:
Figure BDA0002312543370000042
when f tends towards n/NT and τ tends towards kT, the discrete generalized S transform function is:
Figure BDA0002312543370000043
wherein the content of the first and second substances,
Figure BDA0002312543370000044
is the discrete fourier transform of a discrete sequence of time domain signals, N is the number of sample points, T is the sample time interval, k represents time, and N represents frequency.
The two-dimensional time-frequency complex matrix of the time domain signal obtained after the generalized S transformation is as follows:
Figure BDA0002312543370000045
wherein A (k, n) is the amplitude matrix of the signal after the generalized S transformation,
Figure BDA0002312543370000046
is a phase angle matrix of the signal after the generalized S transform.
And step three, performing signal processing by using a threshold filtering method.
Determining the maximum GST of the signal data after the generalized S-transform with variable factorsHMax (GST (k, n)) and minimum GSTL＝min(GST(k,n))。
Quantizing the transformed signal data, and selecting K-2nAs the quantization series, n is generally 7 or 8, and the quantization interval is obtained as:
Figure BDA0002312543370000051
thus, each quantization interval is obtained as:
σ＝(GSTL+Δp(K-1),GSTL+Δp·K)
selecting an appropriate threshold α, determining a filtering factor of threshold filtering:
Figure BDA0002312543370000052
and (3) extracting effective signals in a time-frequency domain through processing by a threshold filtering method:
GST1(k,n)＝GST(k,n)*H1(k,n)
where k represents time and n represents frequency.
And step four, performing signal processing by using a time-frequency filter based on time-frequency spectrum distribution.
The instantaneous frequency of the signal is determined according to the signal characteristics in the time-frequency domain, and for a noisy signal, the following can be described:
h(t)＝x(t)+n(t)
wherein x (t) is the effective signal, and n (t) is the noise signal.
The generalized S transform of this signal can be expressed as:
GSTh(k,n)＝GSTx(k,n)+GSTn(k,n)
when GST is allowed to reactnIf (k, n) ═ 0, the valid signal can be extracted.
As shown in fig. 2, the time-frequency distribution of the signal is analyzed to determine the noise time-frequency range, and the time-frequency range of the effective signal is retained, and the time-frequency filter function based on the time-frequency spectral distribution is as follows:
Figure BDA0002312543370000053
wherein [ tk-1,tk]And [ fn-1,fn]Representing the time range and frequency range of the valid signal, respectively.
And extracting effective signals in a time-frequency domain through time-frequency filter method processing based on time-frequency spectrum distribution:
GST2(k,n)＝GST1(k,n)*H2(k,n)
and step five, obtaining a one-dimensional time domain current signal with noise removed through the generalized S inverse transformation, and comparing the signal.
The function of the generalized inverse S transform is as follows:
x(t)＝GST-1[GST2(k,n)]
specifically, as shown in fig. 3, when a 100 Ω transition resistance single-phase ground fault occurs in the power distribution network, the current waveform filtering effects are compared for the mathematical morphology adaptive filtering method, the wavelet threshold filtering method, the S-transform adaptive filtering method and the current signal filtering and denoising method based on the generalized S-transform with variable factors proposed by the present invention. The effect shown in fig. 3 is known that the filtering and denoising method provided by the present invention has the most significant effect, and obviously removes the noise signal in the original signal, thereby effectively extracting the pure current signal.
Table 1 provides specific numerical value comparisons between the mathematical morphology adaptive filtering method, the wavelet threshold filtering method, the S-transform adaptive filtering method, and the filtering method proposed by the present invention under four fault conditions, where a signal-to-noise ratio (SNR) and a Mean Square Error (MSE) reflect the denoising performance of the filtering method, and the larger the SNR is, the smaller the MSE is, the better the denoising performance of the filtering method is reflected. Analysis table 1 shows that the filtering and denoising method provided by the invention is obviously better than other three methods in terms of SNR and MSE indexes.
Table, denoising performance comparison of fault simulation transient current signals containing noise in 110kV resonant grounding system under four different filtering denoising methods
Figure BDA0002312543370000061
The invention provides a current signal filtering and denoising method based on generalized S transform containing variable factors aiming at the condition that the widely existing noise background submerges effective signals. The invention can carry out filtering and denoising processing on the signal by a threshold filtering method containing variable factor generalized S transformation and a filtering and denoising method combining a time-frequency filter based on time-frequency spectrum distribution, thereby realizing the purpose of extracting effective signals from noise backgrounds under various working condition environments.

Claims (5)

1. A current signal filtering and denoising method based on generalized S transform containing variable factors is characterized in that: the method comprises the following steps:
(1) collecting a discrete sampling sequence of a group of continuous time domain current signals;
(2) obtaining a two-dimensional time-frequency complex matrix through generalized S transformation containing variable factors;
(3) processing signals by using a threshold filtering method;
(4) performing signal processing by using a time-frequency filter based on time-frequency spectrum distribution;
(5) and obtaining a one-dimensional time domain current signal with noise removed through the generalized inverse S transform, and comparing the signal.
2. The method for filtering and denoising current signals based on generalized S-transform with variable factors according to claim 1, wherein: introducing variable factor sigma adjusted along with frequency change into generalized S transformation algorithm containing variable factors in step (2)fThe method comprises the following steps:
the expression of the Gaussian window function containing the variable factors is as follows:
Figure FDA0002312543360000011
where f is frequency, t is time, σfThe independent variable is a variable factor with f, and k, a and b are constants;
substitution of sigmaf(f) Kf + b, the generalized S transform function with variable factors is:
Figure FDA0002312543360000012
when f tends to n/NT and τ tends to kT, the discrete generalized S transform function is:
Figure FDA0002312543360000013
wherein the content of the first and second substances,
Figure FDA0002312543360000014
the method comprises the steps of discrete Fourier transform of a time domain signal discrete sequence, wherein N is the number of sampling points, T is a sampling time interval, k represents time, and N represents frequency;
the two-dimensional time-frequency complex matrix of the time domain signal obtained after the generalized S transformation is as follows:
Figure FDA0002312543360000015
wherein A (k, n) is the amplitude matrix of the signal after the generalized S transformation,
Figure FDA0002312543360000016
is a phase angle matrix of the signal after the generalized S transform.
3. The method for filtering and denoising current signals based on generalized S-transform with variable factors according to claim 1, wherein: the threshold filtering method in the step (3) comprises the following steps:
(31) calculating the maximum GST of the signal data after the generalized S transformation with variable factorsHMax (GST (k, n)) and maxSmall value GSTL＝min(GST(k,n))；
(32) Quantizing the transformed signal data, and selecting K-2nWhen n is 7 or 8 as the quantization level, the quantization interval is:
Figure FDA0002312543360000021
thus, each quantization interval is obtained as:
σ＝(GSTL+Δp(K-1),GSTL+Δp·K)
(33) determining α a threshold for rejecting noise, determining a filter factor for the threshold filtering, and calculating the expression:
Figure FDA0002312543360000022
(34) and extracting effective signals in a time-frequency domain after the processing of a threshold filtering method, wherein the calculation expression is as follows:
GST1(k,n)＝GST(k,n)*H1(k,n)
where k represents time and n represents frequency.
4. The method for filtering and denoising current signals based on generalized S-transform with variable factors according to claim 1, wherein: the time-frequency filter signal processing based on the time-frequency spectrum distribution in the step (4) comprises the following steps:
(41) determining the instantaneous frequency of the signal according to the signal characteristics in the time-frequency domain;
(42) analyzing the time-frequency distribution of the signals, determining the noise time-frequency range, reserving the time-frequency range of the effective signals, and expressing the function expression of a time-frequency filter based on the time-frequency spectrum distribution as follows:
Figure FDA0002312543360000023
wherein [ tk-1,tk]And [ fn-1,fn]Individual watchShowing the time range and frequency range of the valid signal;
(43) and extracting effective signals in a time-frequency domain through time-frequency filter method processing based on time-frequency spectrum distribution:
GST2(k,n)＝GST1(k,n)*H2(k,n)。
5. the method for filtering and denoising current signals based on generalized S-transform with variable factors according to claim 1, wherein: the function of the generalized inverse S transform in the step (5) is specifically as follows:
x(t)＝GST-1[GST2(k,n)]。
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CN111711586A (en) * 2020-06-15 2020-09-25 吉林大学 Time-frequency collaborative filtering method and system applied to communication modulation mode identification
CN112083327A (en) * 2020-09-08 2020-12-15 广东电网有限责任公司广州供电局 Mechanical fault diagnosis method and system for high-voltage vacuum circuit breaker
CN113017640A (en) * 2021-02-23 2021-06-25 安徽省立医院(中国科学技术大学附属第一医院) Magnetocardiogram signal background noise S transform domain removing method and system
CN115267548A (en) * 2022-07-22 2022-11-01 苏州元启动力科技有限公司 Lithium battery voltage sampling method, system and readable storage medium
CN113017640B (en) * 2021-02-23 2024-06-04 安徽省立医院(中国科学技术大学附属第一医院) Method and system for removing S transform domain of background noise of magnetocardiogram signals

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Publication number Priority date Publication date Assignee Title
CN111711586A (en) * 2020-06-15 2020-09-25 吉林大学 Time-frequency collaborative filtering method and system applied to communication modulation mode identification
CN111711586B (en) * 2020-06-15 2021-07-13 吉林大学 Time-frequency collaborative filtering method and system applied to communication modulation mode identification
CN112083327A (en) * 2020-09-08 2020-12-15 广东电网有限责任公司广州供电局 Mechanical fault diagnosis method and system for high-voltage vacuum circuit breaker
CN113017640A (en) * 2021-02-23 2021-06-25 安徽省立医院(中国科学技术大学附属第一医院) Magnetocardiogram signal background noise S transform domain removing method and system
CN113017640B (en) * 2021-02-23 2024-06-04 安徽省立医院(中国科学技术大学附属第一医院) Method and system for removing S transform domain of background noise of magnetocardiogram signals
CN115267548A (en) * 2022-07-22 2022-11-01 苏州元启动力科技有限公司 Lithium battery voltage sampling method, system and readable storage medium

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