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 PDFInfo
- 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
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
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:
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,is the phase;
the probability density function for Middleton Class a noise is as follows:
where z is the impulse noise sample,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:
The wavelet transform at this scale is called binary wavelet transform:
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:
subtracting the two ends of the formula (12) and simplifying to obtain the formula (13):
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 asThe reconstructed signal is then noted as:
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:
In the algorithm calculation flow: r istRepresenting the residual, t is the number of iterations,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:
(2) Find index lambdatSo that λt=arg maxj=1,2...N|<rt-1,aj>|;
(3) Let Λt=Λt-1∪{λt},At=At-1∪aλ;
(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 resultantAt ΛtWith non-zero terms having values obtained in the last iteration
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:
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:
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,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:
where z is the impulse noise sample,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:
where the coefficients of the binomial equation are:
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:
The wavelet transform at this scale is called a binary wavelet transform, as follows:
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:
subtracting the two ends of the formula (12) and simplifying to obtain the formula (13):
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 asThe reconstructed signal is then noted as:
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:
Referring to fig. 3, in the following algorithm calculation flow: r istRepresenting the residual, t is the number of iterations,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:
(2) Find index lambdatSo that λt=arg maxj=1,2...N|<rt-1,aj>|;
(3) Let Λt=Λt-1∪{λt},At=At-1∪aλ;
(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 resultantAt ΛtWith non-zero terms having values obtained in the last iteration
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:
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,is the phase;
the probability density function for Middleton Class a noise is as follows:
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:
The wavelet transform at this scale is called binary wavelet transform:
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:
subtracting the two ends of the formula (12) and simplifying to obtain the formula (13):
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 asThen the reconstructed messageThe numbers are recorded as:
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:
In the algorithm calculation flow: r istRepresenting the residual, t is the number of iterations,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:
(2) Find index lambdatSo that λt=arg maxj=1,2…N|<rt-1,aj>|;
(3) Let Λt=Λt-1∪{λt},At=At-1∪aλ;
(6) if t is equal to or less than K, returning to the step (2), otherwise, stopping iteration and entering the step (7);
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).
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)
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 |
-
2020
- 2020-12-03 CN CN202011395928.6A patent/CN112737636B/en active Active
Patent Citations (6)
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)
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 |