CN110034767A - A kind of electric energy quality signal self-adapting reconstruction method - Google Patents
A kind of electric energy quality signal self-adapting reconstruction method Download PDFInfo
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Abstract
The present invention provides a kind of electric energy quality signal self-adapting reconstruction method, belong to electric energy quality signal identification technology field, in the case where degree of rarefication is unknown, pass through the sparse Adaptive matching tracking of one variable step size of setting, it can be to avoid unnecessary iteration, gradually signal degree of rarefication is assessed, is finally reached the purpose of signal reconstruction；Variable parameter, which is adjusted, by redundancy vector realizes accurate reconstruction signal.Electric energy quality signal self-adapting reconstruction method of the present invention, compared with orthogonal matching pursuit method (OMP), compression sampling match tracing method (CoSaMP), degree of rarefication may be implemented adaptively to adjust, signal reconstruction effect is good, rebuilds speed is fast, suitable for electric power system data signal compression and decompression reconstruction.
Description
Technical field
The invention belongs to electric energy quality signal identification technology fields, and in particular to a kind of electric energy quality signal self-adapting reconstruction
Method.
Background technique
In recent years, power quality problem becomes increasingly conspicuous, and causes the most attention of power supply department and vast power consumer, grinds
Study carefully the various factors for influencing power quality, the various problems that discovery causes power quality to decline in time, and these problems are realized
Effectively classification is of great immediate significance to the final power quality problem that solves.With the development and life of modern science and technology
The flat raising of running water, a large amount of non-linear, impact load and power electronic equipment access in power grid, cause power quality problem
It gets worse, and requirement of the very widely used today various accurate electrical equipments to power quality is higher and higher.Power quality
Accurately identifying for disturbing signal is that electrical energy power quality disturbance is administered and the premise of electrical energy power quality disturbance analysis and basis.Traditional electric energy
Mass analysis method includes two steps, passes through Fourier transformation, Short Time Fourier Transform, wavelet transformation, dq transformation, S first
Transformation etc. digital signal processing methods, to electrical energy power quality disturbance carry out feature extraction, then by artificial neural network, support to
The methods of amount machine, decision tree classify to electrical energy power quality disturbance.
Donoho and Candes et al. propose compressive sensing theory (CS), provide to reduce power quality mass data
A kind of new thinking.Compressed sensing, also known as compression sampling, in the development of compressed sensing, compressed sensing can reduce sampling frequency
The characteristic of rate, is widely used in every field, as radar detection, geological prospecting, imaging of medical, signal denoising, image are super
Resolution reconstruction etc..Compressive sensing theory keeps the prototype structure of signal using non-adaptive linear projection, to compressible
Signal can carry out data sampling by the standard far below nyquist frequency in a manner of stochastical sampling, and the data of acquisition are
The data of compression.Current restructing algorithm mainly has three categories: greedy algorithm, convex optimized algorithm and combinational algorithm etc..Wherein covet
Greedy algorithm is most widely used, and main thought is by iterative calculation selection locally optimal solution come Step wise approximation original signal.Packet
Include matching pursuit algorithm (MP) and orthogonal matching pursuit algorithm (OMP), segmentation orthogonal matching pursuit algorithm (StOMP), regularization
Orthogonal matching pursuit algorithm (ROMP), compression sampling matching pursuit algorithm (CoSaMP) and quick Bayesian matching tracking (FBMP)
Deng.But above-mentioned algorithm requires the degree of rarefication of known signal, and electric energy quality signal cannot obtain preferably in practical power distribution network
Quality reconstruction brings very big inconvenience to practical application.
(1) the technical issues of solving
It cannot be obtained under electric energy quality signal degree of rarefication unknown situation in practical power distribution network for existing matching pursuit algorithm
Preferable signal reconstruction effect defect problem, propose it is a kind of quickly, simply based on the electric energy quality signal of compressive sensing theory
Self-adapting reconstruction method.
(2) technical solution
In order to achieve the above object, the present invention is achieved by the following technical programs:
A kind of electric energy quality signal self-adapting reconstruction method, comprising the following steps:
The compression sampling vector y of S1, inputing power quality signal；Choose compressed sensing observing matrix Φ, sparse transformation base
Matrix Ψ；
S2, initial original sparse signal s0=0；Initial redundancy vector r0=y；Initial sparse degree K0=1；Primary iteration system
Number k=1；Indexed setΓ0∈ Γ, wherein Γ0For maximum K corresponding in vector g0(1≤K0≤ N) a element is corresponding
Indexed set, vector g meet g=ΦTY, KSFor the initial value of degree of rarefication K；Supported collection
S3, pass through formula g=ΦTY obtains K0A element maximum value, by K0The element index of a maximum value is stored in indexed set
Γ0In；IfWherein (0 < δ < 1), incrementally increases K0, K can be used0=K0+ 1, untilObtain degree of rarefication estimated value KS=K0；
S4, pass through formulaIt calculates signal and acts on behalf of u=ΦTR, the number of winning the confidence act on behalf of u
Middle 2KSA greatest member corresponds to the composition set omega of the index value in Φ, expands supported collection Tk, Tk=Tk-1+Ω；
S5, supported collection T is takenkMiddle index element is mapped as Φ in ΦT, s is calculated by least square methodk=(ΦTΦ)-1
ΦTy；
S6, redundancy vector r is updatedk- 1=rk, rk=y- Φ sk；If | | rk||2> ε1, ε1To control phase transition threshold value,
Then stop iteration and enter step S8, otherwise carries out S7；
If S7, | | rk-rk-1||2≥ε2, ε2To control the number of iterations threshold value, K=K+ Δ step, Δ step are adaptive
Adjusting step, k=k+1 carry out step S4, otherwise exit and be recycled into step S8；
S8, reconstruct original signal
An embodiment according to the present invention, the electric energy quality signal compressed sensing observing matrix of the step S1 random measurement
Φ makes great efforts matrix for random shellfish；Constructing a size is that each element independently obeys shellfish effort in M × N-dimensional matrix Φ, Φ
Distribution, it may be assumed that
Or
An embodiment according to the present invention, the sparse transformation base believe electrical energy power quality disturbance using dct basis
Number carry out rarefaction representation, sparse transformation basic matrixWherein i ∈ 0 ..., N-
1 } and j ∈ { 0 ..., N-1 } be respectively sparse transformation basic matrix Ψ row and column, as i=0,As i ≠ 0,
An embodiment according to the present invention, the sparse transformation basic matrix Ψ are orthogonal matrix, sparse transformation basic matrix Ψ
Inverse matrix and transposed matrix it is equal, i.e. Ψ-1=ΨT。
The dimension M of an embodiment according to the present invention, the step S1 compressed sensing observing matrix Φ is equal to 100.
An embodiment according to the present invention, the dimension N are equal to 600.
(3) beneficial effect
Beneficial effects of the present invention: a kind of electric energy quality signal self-adapting reconstruction method, in the case where degree of rarefication is unknown,
It, can be to avoid unnecessary iteration, gradually to signal degree of rarefication by the sparse Adaptive matching tracking of one variable step size of setting
It is assessed, is finally reached the purpose of signal reconstruction；Variable parameter, which is adjusted, by redundancy vector realizes accurate reconstruction signal；This hair
Degree of rarefication may be implemented compared with orthogonal matching pursuit method (OMP), compression sampling match tracing method (CoSaMP) in bright method
Adaptive adjustment, signal reconstruction effect is good, reconstruction speed is fast, compression and decompression weight suitable for electric power system data signal
It builds.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 is the method for the present invention flow chart.
Fig. 2 is reconstructed error with measurement dimension trend chart.
Fig. 3 is the reconstruct probability correlation curve under different degree of rarefication K.
Fig. 4 is the reconstruct probability correlation curve under different measurement dimension M.
Fig. 5 is the signal-to-noise ratio correlation curve under different degree of rarefication K.
Fig. 6 is the Mean Time To Recovery correlation curve under different degree of rarefication K.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
Every other embodiment obtained without creative efforts, shall fall within the protection scope of the present invention.
When being carried out to Band-Limited Signal Sampling, it is desirable to which the signal sampled has the duplicate letter of original band-limited signal
Breath to the limitation of sample frequency requires that original band-limited signal must be at least up to using Shannon/nyquist sampling theorem
2 times of frequency.In order to reduce sample frequency, compressed sensing is put forward for the first time by Donoho and Candes et al., compressed sensing makes
It is sparse (sparse) with premise signal, the sampling that sparse signal is able to achieve lower than that Qwest's frequency obtains signal, and transports
It is gone to rebuild original signal with gained signal.
Compressive sensing theory by signal can this attribute of rarefaction representation realize the compression of signal.In compressive sensing theory
In, the compression sampling of electric energy quality signal is realized by compressed sensing observing matrix Φ.The compression sampling value of electric energy quality signal x
It indicates are as follows:
Y=Φ x=Φ Ψ s=Θ s, y is the compression sampling value for the electric energy quality signal that M × 1 is tieed up in formula, and x is that N × 1 is tieed up
Electric energy quality signal, Φ is M × N-dimensional compressed sensing observing matrix, and Ψ is N × N-dimensional sparse transformation basic matrix, s be N ×
The sparse transformation signal of 1 dimension, only K (K < < N) a nonzero element, Θ are M × N-dimensional perception matrixes in s.Compression sampling value y's
Dimension M realizes that high dimensional data f (dimension of N × 1) arrives the throwing of low-dimensional data (dimension of M × 1) well below original signal dimension N, i.e. y
Shadow realizes the compression process of data.If under the premise of y includes enough reconstruction signal information, projection matrix meets constraint etc.
Restore sparse vector from compression sampling value y with restructing algorithm away from conditionTo Accurate Reconstruction original signalI.e.
The y and perception matrix Θ of projection can reconstruct original signal, complete the decompression process of compression sampling data.
In conjunction with Fig. 1, a kind of electric energy quality signal self-adapting reconstruction method, comprising the following steps:
The compression sampling vector y of S1, inputing power quality signal；Choose compressed sensing observing matrix Φ, sparse transformation base
Matrix Ψ.
The electric energy quality signal compressed sensing observing matrix Φ of random measurement makes great efforts matrix for random shellfish；Construct a size
Shellfish, which is independently obeyed, for each element in M × N-dimensional matrix Φ, Φ makes great efforts distribution, it may be assumed that
Sparse transformation base carries out rarefaction representation, sparse transformation base to Power Quality Disturbance using dct basis
MatrixWherein i ∈ { 0 ..., N-1 } and j ∈ { 0 ..., N-1 } are respectively
The row and column of sparse transformation basic matrix Ψ, as i=0,As i ≠ 0,Sparse transformation basic matrix Ψ is
Orthogonal matrix, the inverse matrix and transposed matrix of sparse transformation basic matrix Ψ is equal, i.e. Ψ-1=ΨT。
S2, initial original sparse signal s0=0；Initial redundancy vector r0=y；Initial sparse degree K0=1；Primary iteration system
Number k=1；Indexed setΓ0∈ Γ, wherein Γ0For maximum K corresponding in vector g0(1≤K0≤ N) a element is corresponding
Indexed set, vector g meet g=ΦTY, KSFor the initial value of degree of rarefication K；Supported collection
S3, pass through formula g=ΦTY obtains K0A element maximum value, by K0The element index of a maximum value is stored in indexed set
Γ0In；IfWherein (0 < δ < 1), incrementally increases K0, K can be used0=K0+ 1, untilObtain degree of rarefication estimated value KS=K0。
S4, pass through formulaIt calculates signal and acts on behalf of u=ΦTR, the number of winning the confidence are acted on behalf of in u
2KSA greatest member corresponds to the composition set omega of the index value in Φ, expands supported collection Tk, Tk=Tk-1+Ω；
S5, supported collection T is takenkMiddle index element is mapped as Φ in ΦT, s is calculated by least square methodk=(ΦTΦ)-1
ΦTy。
S6, redundancy vector r is updatedk-1=rk, rk=y- Φ sk；If | | rk||2> ε1, ε1To control phase transition threshold value,
Then stop iteration and enter step S8, otherwise carries out S7.
If S7, | | rk-rk-1||2≥ε2, ε2To control the number of iterations threshold value, K=K+ Δ step, Δ step are adaptive
Adjusting step, k=k+1 carry out step S4, otherwise exit and be recycled into step S8.
S8, reconstruct original signal
Embodiment:
A kind of electric energy quality signal self-adapting reconstruction method, comprising the following steps:
The compression sampling vector y of S1, inputing power quality signal；Choose compressed sensing observing matrix Φ, sparse transformation base
Matrix Ψ.
The electric energy quality signal compressed sensing observing matrix Φ of random measurement makes great efforts matrix for random shellfish；Construct a size
Shellfish, which is independently obeyed, for each element in M × N-dimensional matrix Φ, Φ makes great efforts distribution, it may be assumed that
Or
For various Power Quality Disturbances in the case where different mappings measure dimension M, repeats 30 experiments and average.With
For due to voltage spikes, as shown in Figure 2, as the increase reconstructed error of M gradually decreases, when M is more than or equal to 100, reconstructed error
Less than 5% and tend towards stability.Comprehensively consider Sampling Compression ratio and reconstruction accuracy, selection measurement dimension M is equal to 100, and dimension N is equal to
600。
Sparse transformation base carries out rarefaction representation, sparse transformation base to Power Quality Disturbance using dct basis
MatrixWherein i ∈ { 0 ..., N-1 } and j ∈ { 0 ..., N-1 } are respectively
The row and column of sparse transformation basic matrix Ψ, as i=0,As i ≠ 0,Sparse transformation basic matrix Ψ is
Orthogonal matrix, the inverse matrix and transposed matrix of sparse transformation basic matrix Ψ is equal, i.e. Ψ-1=ΨT。
S2, initial original sparse signal s0=0；Initial redundancy vector r0=y；Initial sparse degree K0=1；Primary iteration system
Number k=1；Indexed setΓ0∈ Γ, wherein Γ0For maximum K corresponding in vector g0(1≤K0≤ N) a element is corresponding
Indexed set, vector g meet g=ΦTY, KSFor the initial value of degree of rarefication K；Supported collection
S3, pass through formula g=ΦTY obtains K0A element maximum value, by K0The element index of a maximum value is stored in indexed set
Γ0In；If(δ=0.1) wherein is chosen, incrementally increases K0, K can be used0=K0+ 1, untilObtain degree of rarefication estimated value KS=K0。
S4, pass through formulaIt calculates signal and acts on behalf of u=ΦTR, the number of winning the confidence are acted on behalf of in u
2KSA greatest member corresponds to the composition set omega of the index value in Φ, expands supported collection Tk, Tk=Tk-1+Ω；
S5, supported collection T is takenkMiddle index element is mapped as Φ in ΦT, s is calculated by least square methodk=(ΦTΦ)-1
ΦTy。
S6, redundancy vector r is updatedk-1=rk, rk=y- Φ sk；If | | rk||2> ε1, take ε1=10-4, then stop iteration
S8 is entered step, S7 is otherwise carried out.
If S7, | | rk-rk-1||2≥ε2, take ε2=5 × 10-4, K=K+ Δ step, Δ step=5, k=k+1 are carried out
Otherwise step S4 is exited and is recycled into step S8.
S8, reconstruct original signal
Common Power Quality Disturbance have voltage dip, voltage swell, due to voltage spikes, Voltage notches, voltage oscillation,
Voltage harmonic, voltage interruption, voltage pulse and 9 kinds of voltage flicker, sample frequency 6400Hz, voltage fundamental frequency are
100Hz.Establish electric energy quality signal self-adapting reconstruction method of the present invention and orthogonal matching pursuit side respectively using simulation software
Method (OMP), compression sampling match tracing method (CoSaMP) model.Table 1 gives three kinds of methods to 9 kinds of common power qualities
The reconstruction SNR (dB) of disturbing signal respectively carries out experiment 50 times, takes average experimental result.
1: three kind of method reconstruction SNR experimental data comparison of table
| Method | The method of the present invention | CoSaMP | OMP |
| Voltage dip | 59.35 | 41.22 | 39.71 |
| Voltage swell | 57.38 | 42.51 | 40.12 |
| Due to voltage spikes | 48.31 | 31.55 | 29.64 |
| Voltage notches | 46.75 | 31.98 | 30.35 |
| Voltage oscillation | 54.41 | 34.18 | 32.51 |
| Voltage harmonic | 50.51 | 34.21 | 33.01 |
| Voltage interruption | 45.88 | 27.18 | 23.81 |
| Voltage pulse | 61.43 | 45.13 | 40.72 |
| Voltage flicker | 59.98 | 41.75 | 37.98 |
By taking due to voltage spikes as an example, by emulation, Fig. 3 gives reconstruct probability pair of three kinds of methods at different degree of rarefication K
Than curve, three kinds of method degree of rarefication K increase to 70 from 10, and reconstruct probability is gradually reduced to 0 from 1, it can be seen that originally from curve
Inventive method is better than orthogonal matching pursuit method (OMP), compression sampling match tracing method (CoSaMP).Fig. 4 gives three kinds
Reconstruct probability correlation curve of the method at different measurement dimension M, three kinds of methods measure dimension M and increase to 120 from 40, and reconstruct is general
Rate is gradually increased to 1, it can be seen that the method for the present invention is better than orthogonal matching pursuit method (OMP), compression sampling from curve
With method for tracing (CoSaMP).Fig. 5 gives signal-to-noise ratio correlation curve of three kinds of methods at different degree of rarefication K, can from figure
To find out that the signal-to-noise ratio of signal after the method for the present invention reconstructs compared with orthogonal matching pursuit method (OMP) improves 10-20dB, this
The signal-to-noise ratio of signal improves 3-8dB after inventive method reconstructs compared with compression sampling match tracing method (CoSaMP).Fig. 6 gives
Mean Time To Recovery correlation curve of three kinds of methods at different degree of rarefication K is gone out, as can be seen from the figure orthogonal matching pursuit
Method (OMP) reconstruction signal Mean Time To Recovery is 10 times of the method for the present invention Mean Time To Recovery or more, compression sampling matching
Method for tracing (CoSaMP) reconstruction signal Mean Time To Recovery is 4 times of the method for the present invention Mean Time To Recovery or more.By imitative
Very it can be seen that the method for the present invention performance is substantially better than orthogonal matching pursuit method (OMP), compression sampling match tracing method
(CoSaMP)。
In conclusion the embodiment of the present invention, electric energy quality signal self-adapting reconstruction method, in the situation that degree of rarefication is unknown
Under, it is tracked by the sparse Adaptive matching of one variable step size of setting, it can be gradually sparse to signal to avoid unnecessary iteration
Degree is assessed, and the purpose of signal reconstruction is finally reached；Variable parameter, which is adjusted, by redundancy vector realizes accurate reconstruction signal；This
Inventive method may be implemented sparse compared with orthogonal matching pursuit method (OMP), compression sampling match tracing method (CoSaMP)
The adaptive adjustment of degree, signal reconstruction effect is good, reconstruction speed is fast, compression and decompression weight suitable for electric power system data signal
It builds.
The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although with reference to the foregoing embodiments
Invention is explained in detail, those skilled in the art should understand that: it still can be to aforementioned each implementation
Technical solution documented by example is modified or equivalent replacement of some of the technical features；And these modification or
Replacement, the spirit and scope for technical solution of various embodiments of the present invention that it does not separate the essence of the corresponding technical solution.
Claims (6)
1. a kind of electric energy quality signal self-adapting reconstruction method, it is characterised in that: the following steps are included:
The compression sampling vector y of S1, inputing power quality signal；Choose compressed sensing observing matrix Φ, sparse transformation basic matrix
Ψ；
S2, initial original sparse signal s0=0；Initial redundancy vector r0=y；Initial sparse degree K0=1；Primary iteration coefficient k=
1；Indexed setΓ0∈ Γ, wherein Γ0For maximum K corresponding in vector g0(1≤K0≤ N) the corresponding index of a element
Collection, vector g meet g=ΦTY, KSFor the initial value of degree of rarefication K；Supported collection
S3, pass through formula g=ΦTY obtains K0A element maximum value, by K0The element index of a maximum value is stored in indexed set Γ0
In；IfWherein (0 < δ < 1), incrementally increases K0K can be used0=K0+ 1, untilObtain degree of rarefication estimated value KS=K0；
S4, pass through formulaIt calculates signal and acts on behalf of u=ΦTR, the number of winning the confidence act on behalf of 2K in uS
A greatest member corresponds to the composition set omega of the index value in Φ, expands supported collection Tk, Tk=Tk-1+Ω；
S5, supported collection T is takenkMiddle index element is mapped as Φ in ΦT, s is calculated by least square methodk=(ΦTΦ)-1ΦTy；
S6, redundancy vector r is updatedk-1=rk, rk=y- Φ sk；If | | rk||2> ε1, ε1To control phase transition threshold value, then stop
Only iteration enters step S8, otherwise carries out S7；
If S7, | | rk-rk-1||2≥ε2, ε2To control the number of iterations threshold value, K=K+ Δ step, Δ step are adaptive adjustment
Step-length, k=k+1 carry out step S4, otherwise exit and be recycled into step S8；
S8, reconstruct original signal
2. a kind of electric energy quality signal self-adapting reconstruction method according to claim 1, it is characterised in that: the step S1
The electric energy quality signal compressed sensing observing matrix Φ of random measurement makes great efforts matrix for random shellfish；Constructing a size is M × N-dimensional
Matrix Φ, Φ in each element independently obey shellfish make great efforts distribution, it may be assumed that
Or
3. a kind of electric energy quality signal self-adapting reconstruction method according to claim 2, it is characterised in that: the sparse change
It changes base and rarefaction representation, sparse transformation basic matrix is carried out to Power Quality Disturbance using dct basisWherein i ∈ { 0 ..., N-1 } and j ∈ { 0 ..., N-1 } are respectively sparse change
The row and column for changing basic matrix Ψ, as i=0,As i ≠ 0,
4. a kind of electric energy quality signal self-adapting reconstruction method according to claim 3, it is characterised in that: the sparse change
Changing basic matrix Ψ is orthogonal matrix, and the inverse matrix and transposed matrix of sparse transformation basic matrix Ψ is equal, i.e. Ψ-1=ΨT。
5. a kind of electric energy quality signal self-adapting reconstruction method according to claim 2, it is characterised in that: the step S1
The dimension M of compressed sensing observing matrix Φ is equal to 100.
6. a kind of electric energy quality signal self-adapting reconstruction method according to claim 5, it is characterised in that: the dimension N
Equal to 600.
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| CN113395181A (en) * | 2021-06-11 | 2021-09-14 | 中国人民解放军陆军勤务学院 | Signal measurement method and device, and state monitoring method and device of Internet of things network |
| CN117318730A (en) * | 2023-11-30 | 2023-12-29 | 山东大学 | Ionosphere data real-time acquisition and compression method, device, chip and system |
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| CN113395181A (en) * | 2021-06-11 | 2021-09-14 | 中国人民解放军陆军勤务学院 | Signal measurement method and device, and state monitoring method and device of Internet of things network |
| CN117318730A (en) * | 2023-11-30 | 2023-12-29 | 山东大学 | Ionosphere data real-time acquisition and compression method, device, chip and system |
| CN117318730B (en) * | 2023-11-30 | 2024-02-23 | 山东大学 | Ionosphere data real-time acquisition and compression method, device, chip and system |
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