CN112737636A - Compressed sensing and reconstruction method based on power signal transmission singularity measurement - Google Patents

Compressed sensing and reconstruction method based on power signal transmission singularity measurement Download PDF

Info

Publication number
CN112737636A
CN112737636A CN202011395928.6A CN202011395928A CN112737636A CN 112737636 A CN112737636 A CN 112737636A CN 202011395928 A CN202011395928 A CN 202011395928A CN 112737636 A CN112737636 A CN 112737636A
Authority
CN
China
Prior art keywords
signal
maximum value
noise
modulus maximum
modulus
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202011395928.6A
Other languages
Chinese (zh)
Other versions
CN112737636B (en
Inventor
邢砾云
杨淼
金基良
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beihua University
Original Assignee
Beihua University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beihua University filed Critical Beihua University
Priority to CN202011395928.6A priority Critical patent/CN112737636B/en
Publication of CN112737636A publication Critical patent/CN112737636A/en
Application granted granted Critical
Publication of CN112737636B publication Critical patent/CN112737636B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B3/00—Line transmission systems
    • H04B3/54—Systems for transmission via power distribution lines
    • H04B3/544—Setting up communications; Call and signalling arrangements
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/148—Wavelet transforms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B3/00—Line transmission systems
    • H04B3/02—Details
    • H04B3/04—Control of transmission; Equalising
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
    • Y04S10/52—Outage or fault management, e.g. fault detection or location

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Data Mining & Analysis (AREA)
  • Signal Processing (AREA)
  • Mathematical Analysis (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Theoretical Computer Science (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computational Mathematics (AREA)
  • Algebra (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Compression, Expansion, Code Conversion, And Decoders (AREA)

Abstract

The invention belongs to the field of compression and denoising of power line signals, and relates to a compression sensing and reconstruction method based on power signal transmission singularity measurement. The method comprises the following steps: constructing a low-voltage three-phase power transmission line model; collecting voltage data of power lines of each phase of line; adding noise to the collected voltage data; selecting a proper wavelet base; decomposing the voltage data added with the noise by using binary wavelet transform to obtain a modulus maximum value of each layer of the voltage signal; judging the modulus maximum value of the useful signal and the modulus maximum value of the noise according to the Lee's index, removing the modulus maximum value of the noise and improving the sparsity of the modulus maximum value of the signal; compressing and sensing the modulus maximum value reserved after denoising by utilizing an OMP algorithm; and reconstructing the signal at a receiving end by utilizing the received signal modulus maximum value restored by the OMP algorithm and reserved. The accuracy of power signal transmission is effectively improved. The method overcomes the defect of unstable denoising effect of the common given threshold method and combines the advantage of small compressed sensing calculation amount.

Description

Compressed sensing and reconstruction method based on power signal transmission singularity measurement
Technical Field
The invention belongs to the field of compression and denoising of power line signals, and relates to a compressed sensing and reconstruction method based on power signal transmission anisotropy measurement.
Background
With the continuous development of information technology and the accelerated popularization of broadband, the explosive growth of data traffic inevitably brings about the large-scale construction of communication infrastructure. The low-voltage power lines which are widely distributed at present save the trouble of re-laying lines, save communication cost, have firm structures and low price, and are focused by researchers, so that power line carrier communication (PLC) is developed. However, as the related art is continuously developed, the information transmission rate of the PLC is rapidly increased, and a large amount of noise accompanying the power line signal transmission seriously affects the accuracy of the information transmission. To address the problems associated with PLC, researchers have introduced compressed sensing techniques that have emerged in recent years into this area.
The current applications of compressed sensing in power signal processing are mainly as follows: the method comprises the steps of completing missing data of the power load, compressing a large amount of power quality data, positioning line faults, finding harmonic sources and the like. Therefore, the compression sensing is mainly used for compressing massive power data in the power system, high-efficiency transmission is achieved, and power signal denoising is rarely involved. While denoising for power signals is mainly used at present: the method comprises the steps of variable step size adaptive filtering, combination of threshold and translation invariant wavelet and an improved threshold translation invariant method, wherein the denoising effect of the method depends on the selection of the threshold, but the selection of the threshold does not have a uniform standard, so the denoising effect is unstable, and the calculation amount is huge.
It can be seen that the current research mainly utilizes compressed sensing to reduce the data processing amount of the power line signal, but rarely involves compressing and denoising the power line signal containing noise at the same time. The denoising method represented by a given threshold value method has large calculation amount and low efficiency.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a compression sensing and reconstruction method based on power line signal transmission singularity measurement, which takes the Lipschitz index as a noise removal basis to remove the module maximum value of noise, and then compresses and senses the denoised module maximum value, thereby effectively improving the accuracy of power line signal transmission. The method overcomes the defect of unstable denoising effect of the common given threshold method and combines the advantage of small computational complexity of compressed sensing.
The invention is realized in such a way that a compression sensing and reconstruction method based on power signal transmission singularity measurement comprises the following steps:
1) constructing a low-voltage three-phase power transmission line model;
2) collecting voltage data of power lines of each phase of line;
3) adding noise to the collected voltage data;
4) selecting a proper wavelet base;
5) decomposing the voltage data added with the noise in the step 3 by using binary wavelet transform to obtain a modulus maximum value of each layer of the voltage signal;
6) judging the modulus maximum value of the useful signal and the modulus maximum value of the noise according to the Lee's index, removing the modulus maximum value of the noise and improving the sparsity of the modulus maximum value of the signal;
7) compressing and sensing the modulus maximum value reserved after denoising by utilizing an OMP algorithm;
8) and reconstructing the signal at a receiving end by utilizing the received signal modulus maximum value restored by the OMP algorithm and reserved.
Further, in the step 3), adding narrow-band noise and Middleton Class a noise respectively, where the narrow-band noise is a result of superposition of independent sinusoidal signals:
Figure BDA0002814874350000021
wherein A isiIs the amplitude of the signal, which is uniformly normalized and the amplitude is randomly generated in the background noise range, fiIs the frequency of the radio,
Figure BDA0002814874350000031
is the phase;
the probability density function for Middleton Class a noise is as follows:
Figure BDA0002814874350000032
Figure BDA0002814874350000033
Figure BDA0002814874350000034
Figure BDA0002814874350000035
where z is the impulse noise sample,
Figure BDA0002814874350000036
is the noise variance, a determines the impulse degree of the noise, and Γ is the gaussian pulse power ratio.
Further, in the step 5), the collected voltage data is decomposed by using binary wavelet transform, so as to obtain a modulus maximum value of each layer of the voltage signal, which is specifically as follows:
given a basis function:
Figure BDA0002814874350000037
where a is the scale and b is the displacement, discretizing a
Figure BDA0002814874350000038
a0>0, j ∈ Z then a0＝2，
Figure BDA0002814874350000039
The wavelet transform at this scale is called binary wavelet transform:
Figure BDA00028148743500000310
and decomposing the noisy power signal by using binary wavelet transform to obtain the modulus maximum value of each layer.
Further, the step 6) of distinguishing the mode maximum value of the useful signal and the mode maximum value of the noise according to the lees index, removing the mode maximum value of the noise, and improving the sparsity of the mode maximum value of the signal includes: calculating the maximum value of the wavelet mode of the voltage signal to calculate the Lee index;
if the signal is disconnected at a certain point or the derivative of a certain order is discontinuous, the point of the signal is singular, and in the singularity analysis of the signal, a Lipschitz index is introduced to express singularity characteristics;
given a function f (x) e R, there is 0 ≦ α ≦ 1, k is a constant, at x0To x0Such that:
|f(x)-f(x0)|≤k|x-x0|α (9)
then it is said that f (x) is in x0Is Lipschitz α if the wavelet transform of f (x) is at point(s)0，x0) Satisfies the following conditions:
|Wf(s0，x)|≤|Wf(s0，x0)| (10)
when f (x) is subjected to binary wavelet transform over the interval [ a, b ], equation (10) satisfies:
|Wf(2j，x)|≤k(2j)α (11)
wherein k is a constant and α is a Lipschitz index;
when W isf(2jX) is a modulus maximum, on both sides of equation (11) at two different scales sj，sj+1The modulus maximum with base 2 is taken up:
Figure BDA0002814874350000041
subtracting the two ends of the formula (12) and simplifying to obtain the formula (13):
Figure BDA0002814874350000042
as can be seen from equation (13), when α >0, the modulus maximum of the wavelet transform is proportional to the scale j, whereas inversely proportional, and when α is 0, the modulus maximum is unchanged;
according to the standard that the Lee index of the mode maximum value of the noise is smaller than zero, removing the point that the Lee index of the mode maximum value of the signal is smaller than zero, namely, removing the mode maximum value of the noise and reserving the mode maximum value of the useful signal, and improving the sparsity of the mode maximum value.
Further, in the step 7), the modulus maximum value retained after denoising is compressed and sensed by using an OMP algorithm, which is specifically as follows:
assuming that the original signal is a one-dimensional signal with a length of N and the sparsity k is unknown, the measurement matrix phi is a matrix of M x N, the sparse matrix psi is a matrix of N x N, and theta is a sparse decomposition coefficient, x is psi theta, and the observation vector y is a matrix of M x 1:
y＝φψθ (14)
let the perceptual matrix a be phi ψ, then equation (14) at this time is:
y＝Aθ (15)
the compressed sensing mainly solves the underdetermined linear equation y as A theta, and in the case that y is unknown to A, the compressed sensing solves theta,
solving theta by using an OMP algorithm, and recording the solved theta as
Figure BDA0002814874350000051
The reconstructed signal is then noted as:
Figure BDA0002814874350000052
further, the flow of the OMP algorithm is as follows:
inputting:
a M × N sensing matrix a ═ phi ψ;
an observation vector y of nx 1;
3. sparsity K;
and (3) outputting:
1. signal sparse representation coefficient obtained through algorithm calculation
Figure BDA0002814874350000053
Residual error of Nx 1
Figure BDA0002814874350000054
In the algorithm calculation flow: r istRepresenting the residual, t is the number of iterations,
Figure BDA0002814874350000055
represents the empty set, ΛtSet of indices, λ, representing t iterationstRepresenting the index found in the t-th iteration, ajRepresents the jth column of matrix A, AtRepresentative by index ΛtSelected set of columns, θ, of matrix AtIs a column vector of t x 1, the symbol @ denotes a set merging operation,<■，■>the inner product is calculated as follows:
(1) initialization r0＝y，
Figure BDA0002814874350000056
t＝1；
(2) Find index lambdatSo that λt＝arg maxj＝1，2...N|＜rt-1，aj＞|；
(3) Let Λt＝Λt-1∪{λt}，At＝At-1∪aλ；
(4) Finding y as AtθtLeast squares solution of (c):
Figure BDA0002814874350000061
(5) and (3) residual error updating:
Figure BDA0002814874350000062
(6) if t is equal to or less than K, returning to the step (2), otherwise, stopping iteration and entering the step (7);
(7) reconstructing the resultant
Figure BDA0002814874350000063
At ΛtWith non-zero terms having values obtained in the last iteration
Figure BDA0002814874350000064
Further, in step 8), the receiving end reconstructs the signal by using the retained signal modulus maximum recovered by the received OMP algorithm, which is specifically as follows:
receiving a reserved modulus maximum value recovered by the OMP algorithm;
reconstructing a signal according to the abscissa of the modulus maximum value, the modulus maximum value and the profile of the last stage; wherein:
in binary wavelet transform, the minimum value of j is 1, the assumed maximum scale j is large enough, and information with the scale larger than j is concentrated in low-frequency aj(t) at which time aj(t) is a j-th level profile; let tj，nTransforming WT for binary waveletsxThe abscissa when taking the modulus maximum, then | WTx(j，tj，n) I is the modulo maximum value of the matrix,
at an arbitrary point t for the signal0The method comprises the following steps:
|WTx(j，t0)|＝＜x(t)，ψj(t0-t)＞ (17)
and satisfies the following conditions:
＜h(t)，ψj(tj，n-t)＞＝<x(t)，ψj(tj，n-t)＞ (18)
where x (t) is the original signal, h (t) is the set of assumed signals, i.e., the approximate signal of x (t), tj，nIs the abscissa of the maximum of the x (t) wavelet transform mode, from tj，nModulo maximum valueAnd a final level of profile aj(t) to reconstruct the signal x (t).
Compared with the prior art, the invention has the beneficial effects that:
the method combines the advantage of small compressed sensing calculation amount and overcomes the defect of unstable denoising effect of the commonly used given threshold value method, achieves good denoising effect while realizing power line signal compression, is simple to realize, and is easy to realize in practical engineering application.
The invention improves the noise removal effect of the power line, takes the Leersian exponent as the basis for removing the noise, and overcomes the instability of the noise removal effect caused by the uncertainty of threshold selection in the traditional given threshold method. The data processing amount is reduced, the transmission efficiency of power line signals is improved, the compression sensing is utilized to compress and transmit the modulus maximum value which has sparsity after denoising, and the data processing efficiency is greatly improved. Theoretical analysis shows that the method achieves good denoising effect while achieving high-efficiency voltage of the power signal, and can reconstruct an original signal without noise well when the compressibility of a modulus maximum value reserved after signal denoising reaches 40%. The invention combines compressed sensing and opposite sex detection, thereby improving the data compression efficiency of the transmission signal while ensuring the quality and accuracy of the signal. Moreover, the method can greatly save the transmission cost, is easy to implement and has high engineering application value.
Drawings
FIG. 1 is a general flow diagram of a method of compressed sensing and reconstruction based on power signal transmission singularity metrics;
FIG. 2 is a flow chart for removing noise modulus maxima from the Lee index;
FIG. 3 is a flow chart of the OMP algorithm;
fig. 4 is a flow of compressing, sensing, and reconstructing the original signal using the modulus maxima restored by the OMP algorithm.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention combines the compressed sensing with the singularity detection of the power line signal, overcomes the problem that the denoising effect is unstable in the currently commonly applied method taking a threshold value as a core, and simultaneously combines the compressed sensing to realize the high-efficiency compression of the power line signal while denoising, thereby realizing the accuracy of the power line signal transmission and saving the storage space.
(1) Discrete binary wavelet transform is carried out on the collected power line signals, the modulus maximum value of each layer is obtained, and the li's index is used as an index to remove the modulus maximum value of noise.
The wavelet transform is a continuous wavelet transform, and a binary discrete wavelet is formed after the binary discrete is performed on the scale of the continuous wavelet transform. And decomposing the noisy power line signal by using binary wavelet transformation to obtain a modulus maximum value of each layer, and removing the modulus maximum value of the noise by using the Lee index as a judgment standard.
Firstly, binary wavelet transform is carried out on signals to obtain decomposition coefficients of each layer, and a module maximum value of each layer is calculated;
secondly, removing the mode maximum value of the noise according to the difference between the noise and the Lee's index of the useful information.
(2) And compressing and sensing the reserved module maximum value by using an Orthogonal Matching Pursuit (OMP) algorithm, and reconstructing an original signal by using the module maximum value restored by the OMP.
The OMP algorithm is a typical representation of the greedy algorithm in the compressive perceptual reconstruction algorithm. The premise of compressed sensing is that the signal has certain sparsity, and the modulus maximum has obvious sparsity, so that the requirement is well met.
Compressing the reserved module maximum value of each layer by using an OMP algorithm;
and secondly, reconstructing the original signal at the receiving end by using the modulus maximum value recovered by the OMP.
Referring to fig. 1 to 4, in the embodiment, a method for compressed sensing and reconstruction based on power signal transmission singularity measurement includes the following specific steps:
1) and constructing a power transmission model according to the parameters of the actual low-voltage power line. The mathematical model of the real three-phase transmission line is as follows:
Figure BDA0002814874350000091
wherein u isa、ub、ucThe phase voltage is respectively the phase A, the phase B and the phase C of the three-phase circuit. w is the angular frequency and α is the phase angle.
2) Collecting voltage data of power lines of each phase of line;
3) adding noise to the collected voltage data;
narrow-band noise, the frequency spectrum of which is found by research is composed of a series of narrow-band signals with a plurality of impacts, and therefore can be considered as a result of superposition of several independent sinusoidal signals:
Figure BDA0002814874350000092
wherein A isiIs the amplitude of the signal, which is uniformly normalized and the amplitude is randomly generated within the background noise range. f. ofiIs the frequency of the radio,
Figure BDA0002814874350000093
is the phase.
Model II, a typical model of Middleton Class A noise and power line impulse noise. This is an impulse noise modeling method based on physical statistical analysis, since its model derivation is based entirely on the statistical analysis of the sequence in which the power line noise is actually generated. The probability density function is as follows:
Figure BDA0002814874350000094
Figure BDA0002814874350000095
Figure BDA0002814874350000096
Figure BDA0002814874350000097
where z is the impulse noise sample,
Figure BDA0002814874350000098
is the noise variance, a determines the impulse degree of the noise, and Γ is the gaussian pulse power ratio.
4) A suitable wavelet basis is selected. According to the characteristics of the power signal and the waveform characteristics of the dbN wavelet, a db4 wavelet is selected as a wavelet basis, which has no explicit expression, but the square of the modulus of the transfer function is determined:
Figure BDA0002814874350000101
where the coefficients of the binomial equation are:
Figure BDA0002814874350000102
Figure BDA0002814874350000103
5) decomposing the acquired voltage data by using binary wavelet transform to obtain the modulus maximum value of each layer of the voltage signal, which is as follows:
given a basis function:
Figure BDA0002814874350000104
where a is the dimension and b is the displacement. Discretizing a, making
Figure BDA0002814874350000105
a0>0, j ∈ Z then a0＝2，
Figure BDA0002814874350000106
The wavelet transform at this scale is called a binary wavelet transform, as follows:
Figure BDA0002814874350000107
and decomposing the noisy power signal by using binary wavelet transform to obtain the modulus maximum value of each layer.
6) And judging the modulus maximum value of the useful signal and the modulus maximum value of the noise according to the Lee index, removing the modulus maximum value of the noise and improving the sparsity of the modulus maximum value of the signal.
Firstly, constructing a low-voltage three-phase power transmission line model according to the step 1);
collecting voltage data of the power line with noise in each phase line according to the step 2);
thirdly, adding noise to the collected voltage data according to the step 3)
Selecting proper wavelet base according to the step 4);
according to step 5), decomposing the acquired voltage data by utilizing binary wavelet transform to obtain a modulus maximum value of each layer of the voltage signal;
calculating the Lee index according to the maximum value of the wavelet mode of the calculated voltage signal;
the signal is singular if the signal is broken at a certain point or the derivative of a certain order is discontinuous, and in the singularity analysis of the signal, a Lipschitz index is introduced to express the singularity feature.
Given a function f (x) epsilon R, there is 0 ≦ α ≦ 1, k isConstant at x0To x0Such that:
|f(x)-f(x0)|≤k|x-x0|α (9)
then it is said that f (x) is in x0Is Lipschitz α. If the wavelet transform of f (x) is at point(s)0，x0) Satisfies the following conditions:
|Wf(s0，x)|≤|Wf(s0，x0)| (10)
when f (x) is subjected to binary wavelet transform over the interval [ a, b ], equation (10) satisfies:
|Wf(2j，x)|≤k(2j)α (11)
where k is a constant and α is the Lipschitz index.
When W isf(2jX) is the modulus maximum, on both sides of equation (15) at two different scales sj，sj+1The modulus maximum with base 2 is taken up:
Figure BDA0002814874350000111
subtracting the two ends of the formula (12) and simplifying to obtain the formula (13):
Figure BDA0002814874350000112
as can be seen from equation (13), when α >0, the modulus maximum of the wavelet transform is proportional to the scale j, whereas inversely proportional, and when α is 0, the modulus maximum is unchanged.
According to the standard that the Lee's index of the mode maximum value of the noise is smaller than zero, removing the point that the Lee's index of the mode maximum value of the signal is smaller than zero, namely removing the mode maximum value of the noise, reserving the mode maximum value of the useful signal, and improving the sparsity of the mode maximum value.
7) And compressing and sensing the modulus maximum value reserved after denoising by utilizing an OMP algorithm.
The assumed signal is a one-dimensional signal with the length of N, and the sparsity k is unknown. The measurement matrix phi is a matrix of M x N, the sparse matrix psi is a matrix of N x N, theta is a sparse decomposition coefficient, x is psi theta, and the observation vector y is a matrix of M x 1:
y＝φψθ (14)
let the sensing matrix Λ ═ Φ ψ, then equation (14) at this time can be:
y＝Aθ (15)
the compressed sensing mainly solves the underdetermined linear equation y as a θ, that is, when y is unknown to a, θ is obtained. The invention uses OMP algorithm to solve theta, and records the solved theta as
Figure BDA0002814874350000121
The reconstructed signal is then noted as:
Figure BDA0002814874350000122
the flow of the OMP algorithm is as follows:
inputting:
a M × N sensing matrix a ═ phi ψ;
an observation vector y of nx 1;
3. sparsity K;
and (3) outputting:
1. signal sparse representation coefficient obtained through algorithm calculation
Figure BDA0002814874350000123
Residual error of Nx 1
Figure BDA0002814874350000124
Referring to fig. 3, in the following algorithm calculation flow: r istRepresenting the residual, t is the number of iterations,
Figure BDA0002814874350000125
represents the empty set, ΛtSet of indices, λ, representing t iterationstRepresenting the t-th iterationTo index (column number), ajRepresents the j column, Λ, of matrix AtRepresentative by index ΛtThe selected column set of matrix A (M x t matrix), θtIs a column vector of t × 1, and the symbol @ represents a union operation.<■，■>The inner product is calculated as follows:
(1) initialization r0＝y，
Figure BDA0002814874350000131
t＝1；
(2) Find index lambdatSo that λt＝arg maxj＝1，2...N|<rt-1，aj>|；
(3) Let Λt＝Λt-1∪{λt}，At＝At-1∪aλ；
(4) Finding y as AtθtLeast squares solution of (c):
Figure BDA0002814874350000132
(5) and (3) residual error updating:
Figure BDA0002814874350000133
(6) if t is equal to or less than K, returning to the step (2), otherwise, stopping iteration and entering the step (7);
(7) reconstructing the resultant
Figure BDA0002814874350000134
At ΛtWith non-zero terms having values obtained in the last iteration
Figure BDA0002814874350000135
According to the characteristic that the modulus maximum value has certain sparsity, the unit matrix is selected as a sparse base, and the Gaussian matrix is selected as a measurement matrix. And then compressing and sensing the denoised module maximum value by using an OMP algorithm.
8) And reconstructing the signal at the receiving end by utilizing the received reserved signal modulus maximum value recovered by the OMP algorithm.
Receiving a reserved modulus maximum value recovered by an OMP algorithm;
secondly, reconstructing a signal according to the abscissa of the modulus maximum value, the modulus maximum value and the final level of the profile;
in binary wavelet transform, the minimum value of j is 1. Assuming that the maximum dimension j is large enough, information with a dimension larger than j is concentrated in a low frequencyj(t) at which time aj(t) is a j-th level profile. Let (t)j，n) Transforming WT for binary waveletsxThe abscissa when taking the modulus maximum, then | WTx(j，tj，n) I is the modulo maximum.
At an arbitrary point t for the signal0The method comprises the following steps:
|WTx(j，t0)|＝＜x(t)，ψj(t0-t)＞ (17)
and satisfies the following conditions:
＜h(t)，ψj(tj，n-t)＞＝<x(t)，ψj(tj，n-t)＞ (18)
where x (t) is the original signal, and h (t) is the approximate signal of the hypothetical signal set, i.e., x (h). t is tj，nIs the abscissa of the x (t) wavelet transform mode maximum. From tj，nModulo maximum and last level profile aj(t) to reconstruct the signal x (t).
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (7)

1. A compressed sensing and reconstruction method based on power signal transmission singularity measurement is characterized by comprising the following steps:
1) constructing a low-voltage three-phase power transmission line model;
2) collecting voltage data of power lines of each phase of line;
3) adding noise to the collected voltage data;
4) selecting a proper wavelet base;
5) decomposing the voltage data added with the noise in the step 3 by using binary wavelet transform to obtain a modulus maximum value of each layer of the voltage signal;
6) judging the modulus maximum value of the useful signal and the modulus maximum value of the noise according to the Lee's index, removing the modulus maximum value of the noise and improving the sparsity of the modulus maximum value of the signal;
7) compressing and sensing the modulus maximum value reserved after denoising by utilizing an OMP algorithm;
8) and reconstructing the signal at a receiving end by utilizing the received signal modulus maximum value restored by the OMP algorithm and reserved.
2. The method as claimed in claim 1, wherein the step 3) adds narrowband noise and Middleton Class a noise separately, wherein the narrowband noise is a result of superposition of independent sinusoidal signals:
Figure FDA0002814874340000011
wherein A isiIs the amplitude of the signal, which is uniformly normalized and the amplitude is randomly generated in the background noise range, fiIs the frequency of the radio,
Figure FDA0002814874340000012
is the phase;
the probability density function for Middleton Class a noise is as follows:
Figure FDA0002814874340000021
Figure FDA0002814874340000022
Figure FDA0002814874340000023
Figure FDA0002814874340000024
where z is the impulse noise sample,
Figure FDA0002814874340000025
is the noise variance, a determines the impulse degree of the noise, and Γ is the gaussian pulse power ratio.
3. The method as claimed in claim 1, wherein in step 5), the collected voltage data is decomposed by using binary wavelet transform to obtain the modulus maxima of each layer of the voltage signal, and the method includes:
given a basis function:
Figure FDA0002814874340000026
where a is the scale and b is the displacement, discretizing a
Figure FDA0002814874340000027
a0>0, j ∈ Z then a0＝2，
Figure FDA0002814874340000028
The wavelet transform at this scale is called binary wavelet transform:
Figure FDA0002814874340000029
and decomposing the noisy power signal by using binary wavelet transform to obtain the modulus maximum value of each layer.
4. The method as claimed in claim 3, wherein the step 6) of discriminating between the modulo maximum of the useful signal and the modulo maximum of the noise according to the lee's index, removing the modulo maximum of the noise, and increasing the sparsity of the modulo maximum of the signal includes: calculating the maximum value of the wavelet mode of the voltage signal to calculate the Lee index;
if the signal is disconnected at a certain point or the derivative of a certain order is discontinuous, the point of the signal is singular, and in the singularity analysis of the signal, a Lipschitz index is introduced to express singularity characteristics;
given a function f (x) e R, there is 0 ≦ α ≦ 1, k is a constant, at x0To x0Such that:
|f(x)-f(x0)|≤k|x-x0|α (9)
then it is said that f (x) is in x0Is Lipschitz α if the wavelet transform of f (x) is at point(s)0，x0) Satisfies the following conditions:
|Wf(s0，x)|≤|Wf(s0，x0)| (10)
when f (x) is subjected to binary wavelet transform over the interval [ a, b ], equation (10) satisfies:
|Wf(2j，x)|≤k(2j)α (11)
wherein k is a constant and α is a Lipschitz index;
when W isf(2jX) is a modulus maximum, on both sides of equation (11) at two different scales sj，sj+1The modulus maximum with base 2 is taken up:
Figure FDA0002814874340000031
subtracting the two ends of the formula (12) and simplifying to obtain the formula (13):
Figure FDA0002814874340000032
as can be seen from equation (13), when α >0, the modulus maximum of the wavelet transform is proportional to the scale j, whereas inversely proportional, and when α is 0, the modulus maximum is unchanged;
according to the standard that the Lee's index of the mode maximum value of the noise is smaller than zero, removing the point that the Lee's index of the mode maximum value of the signal is smaller than zero, namely removing the mode maximum value of the noise and reserving the mode maximum value of the useful signal, and improving the sparsity of the mode maximum value.
5. The method according to claim 1, wherein in step 7), the modulus maxima retained after denoising are compressed and sensed by using an OMP algorithm, and specifically, the following steps are performed:
assuming that the original signal is a one-dimensional signal with a length of N and the sparsity k is unknown, the measurement matrix phi is a matrix of M × N, the sparse matrix psi is a matrix of N × N, and θ is a sparse decomposition coefficient, x is ψ θ, and the observation vector y is a matrix of M × 1:
y＝φψθ (14)
let the perceptual matrix a be phi ψ, then equation (14) at this time is:
y＝Aθ (15)
the compressed sensing mainly solves the underdetermined linear equation y as A theta, and in the case that y is unknown to A, the compressed sensing solves theta,
solving theta by using an OMP algorithm, and recording the solved theta as
Figure FDA0002814874340000041
Then the reconstructed messageThe numbers are recorded as:
Figure FDA0002814874340000042
6. the method of claim 5, wherein the OMP algorithm is performed as follows:
inputting:
a M × N sensing matrix a ═ phi ψ;
an observation vector y of nx 1;
3. sparsity K;
and (3) outputting:
1. signal sparse representation coefficient obtained through algorithm calculation
Figure FDA0002814874340000043
Residual error of Nx 1
Figure FDA0002814874340000044
In the algorithm calculation flow: r istRepresenting the residual, t is the number of iterations,
Figure FDA0002814874340000045
represents the empty set, ΛtSet of indices, λ, representing t iterationstRepresenting the index found in the t-th iteration, ajRepresents the jth column of matrix A, AtRepresentative by index ΛtSelected set of columns, θ, of matrix AtIs a column vector of t × 1, the symbol @ represents a union operation,<■，■>the inner product is calculated as follows:
(1) initialization r0＝y，
Figure FDA0002814874340000051
t＝1；
(2) Find index lambdatSo that λt＝arg maxj＝1，2…N|<rt-1，aj>|；
(3) Let Λt＝Λt-1∪{λt}，At＝At-1∪aλ；
(4) Finding y as AtθtLeast squares solution of (c):
Figure FDA0002814874340000052
(5) and (3) residual error updating:
Figure FDA0002814874340000053
(6) if t is equal to or less than K, returning to the step (2), otherwise, stopping iteration and entering the step (7);
(7) reconstructing the resultant
Figure FDA0002814874340000054
At ΛtWith non-zero terms having values obtained in the last iteration
Figure FDA0002814874340000055
7. The method according to claim 1, wherein in step 8), the retained signal modulus maximum restored by the received OMP algorithm is used at the receiving end to reconstruct the signal, and the method includes:
receiving a reserved modulus maximum value recovered by the OMP algorithm;
reconstructing a signal according to the abscissa of the modulus maximum value, the modulus maximum value and the profile of the last stage; wherein:
in binary wavelet transform, the minimum value of j is 1, the assumed maximum scale j is large enough, and information with the scale larger than j is concentrated in low-frequency aj(t) at which time aj(t) is a j-th level profile; let tj，nTransforming WT for binary waveletsxThe abscissa when taking the modulus maximum, then | WTx(j，tj，n) I is the modulo maximum value of the matrix,
at an arbitrary point t for the signal0The method comprises the following steps:
|WTx(j，t0)|＝<x(t)，ψj(t0-t)> (17)
and satisfies the following conditions:
<h(t)，ψj(tj，n-t)>＝<x(t)，ψj(tj，n-t)> (18)
where x (t) is the original signal, h (t) is the set of assumed signals, i.e., the approximate signal of x (t), tj，nIs the abscissa of the modulus maximum of the x (t) wavelet transform, denoted by tj，nModulo maximum and last level profile aj(t) to reconstruct the signal x (t).
CN202011395928.6A 2020-12-03 2020-12-03 Compressed sensing and reconstruction method based on power signal transmission singularity measurement Active CN112737636B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011395928.6A CN112737636B (en) 2020-12-03 2020-12-03 Compressed sensing and reconstruction method based on power signal transmission singularity measurement

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011395928.6A CN112737636B (en) 2020-12-03 2020-12-03 Compressed sensing and reconstruction method based on power signal transmission singularity measurement

Publications (2)

Publication Number Publication Date
CN112737636A true CN112737636A (en) 2021-04-30
CN112737636B CN112737636B (en) 2023-03-24

Family

ID=75598420

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011395928.6A Active CN112737636B (en) 2020-12-03 2020-12-03 Compressed sensing and reconstruction method based on power signal transmission singularity measurement

Country Status (1)

Country Link
CN (1) CN112737636B (en)

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104034939A (en) * 2014-06-06 2014-09-10 河海大学 Voltage signal sampling and reconstructing method for photovoltaic power generation system
US20170041166A1 (en) * 2015-08-05 2017-02-09 National Taiwan University Compressive sensing system based on personalized basis and method thereof
EP3154022A1 (en) * 2015-10-07 2017-04-12 Univerza v Ljubljani A method of compressive sensing-based image filtering and reconstruction, and a device for carrying out said method
CN107360111A (en) * 2017-06-01 2017-11-17 宁波大学 Impulsive Noise Mitigation Method in a kind of power line communication based on compressed sensing
CN109067433A (en) * 2018-09-04 2018-12-21 国网四川省电力公司电力科学研究院 Low-voltage powerline carrier communication noise suppressing method suitable for intelligent electric energy meter
CN111181891A (en) * 2019-10-21 2020-05-19 浙江万胜智能科技股份有限公司 Improved power line impulse noise suppression method based on compressed sensing

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104034939A (en) * 2014-06-06 2014-09-10 河海大学 Voltage signal sampling and reconstructing method for photovoltaic power generation system
US20170041166A1 (en) * 2015-08-05 2017-02-09 National Taiwan University Compressive sensing system based on personalized basis and method thereof
EP3154022A1 (en) * 2015-10-07 2017-04-12 Univerza v Ljubljani A method of compressive sensing-based image filtering and reconstruction, and a device for carrying out said method
CN107360111A (en) * 2017-06-01 2017-11-17 宁波大学 Impulsive Noise Mitigation Method in a kind of power line communication based on compressed sensing
CN109067433A (en) * 2018-09-04 2018-12-21 国网四川省电力公司电力科学研究院 Low-voltage powerline carrier communication noise suppressing method suitable for intelligent electric energy meter
CN111181891A (en) * 2019-10-21 2020-05-19 浙江万胜智能科技股份有限公司 Improved power line impulse noise suppression method based on compressed sensing

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
李树强: "电力线通信噪声信号压缩与重构方法与效果评价", 《信息通信》 *
滕文海: "电力线通信噪声信号压缩与重构方法与效果评价研究", 《中国新通信》 *

Also Published As

Publication number Publication date
CN112737636B (en) 2023-03-24

Similar Documents

Publication Publication Date Title
CN102427527B (en) Method for reconstructing non key frame on basis of distributed video compression sensing system
CN112134567B (en) Self-adaptive real-time compression method and system for absorption spectrum data
CN105741844B (en) A kind of digital audio watermarking algorithm based on DWT-SVD-ICA
CN111967508A (en) Time series abnormal point detection method based on saliency map
CN104301728A (en) Compressed video capture and reconstruction system based on structured sparse dictionary learning
CN105206277A (en) Voice compression method base on monobit compression perception
CN102915735A (en) Noise-containing speech signal reconstruction method and noise-containing speech signal device based on compressed sensing
CN111010191B (en) Data acquisition method, system, equipment and storage medium
CN102025998B (en) Code book designing method for vector quantization of digital image signal
CN112737636B (en) Compressed sensing and reconstruction method based on power signal transmission singularity measurement
Alsayyh et al. A Novel Fused Image Compression Technique Using DFT, DWT, and DCT.
CN113556132B (en) Novel improved electric power signal compressed sensing method based on signal singularity detection
CN102509268B (en) Immune-clonal-selection-based nonsubsampled contourlet domain image denoising method
Prasetyo et al. Integrating Companding and Deep Learning on Bandwidth-Limited Image Transmission
Raj et al. Audio signal quality enhancement using multi-layered convolutional neural network based auto encoder–decoder
CN107689797B (en) Compressed sensing signal reconstruction method based on block Hadamard measurement matrix with arbitrary dimension
CN111475768A (en) Observation matrix construction method based on low coherence unit norm tight frame
CN116520277B (en) Radar target recognition method and system based on separated convolution network
CN115798517B (en) Commodity searching method and system based on voice information characteristic data
Chatterjee et al. Image compression and resizing using vector quantization and other efficient algorithms
Babu et al. Image compression and reconstruction using improved Stockwell transform for quality enhancement.
Soraghan et al. ECG signal compression using classified gain-shape vector quantisation in the wavelet transform domain
Sridhar et al. Performance Evaluation of CS Based Speech Enhancement using Adaptive and Sparse Dictionaries
CN115065367A (en) Low-complexity sparse signal sampling reconstruction system and method
Glorindal A Simplified Fractal Texture Analysis Approach using Quadtree Decomposition with Huffman Coding Technique

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant