CN109946518A - Electric harmonic signal analysis method and analytical equipment based on bayes method - Google Patents
Electric harmonic signal analysis method and analytical equipment based on bayes method Download PDFInfo
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Abstract
The electric harmonic signal analysis method and electric harmonic signal analysis equipment that the present invention provides a kind of based on bayes method, different from existing strip method harmonic wave method, use the time domain sparse features of electric system complexity harmonic signal, and harmonic signal analysis mathematical model is established using Bayesian model, and then be by the maximum algorithm Recursive Solution problem of expectation while the amplitude and frequency of signal can be obtained.Wherein electric harmonic signal analysis method includes: setting Bayesian Estimation initial value and convergence parameter；Harmonic frequency analysis section is obtained, and harmonic frequency analysis Interval Discrete is turned into setting quantity analysis subinterval, forms harmonic wave measurement matrix；The sampled signal of signal to be analyzed is obtained, and establishes the probability density function of harmonic signal according to Bayesian formula；And calculating is iterated to probability density function using desired maximum calculated method, estimation obtains the frequency and amplitude of the harmonic component in signal to be analyzed.
Description
Technical field
The present invention relates to power technologies, more particularly to the electric harmonic signal analysis method based on bayes method and divide
Desorption device.
Background technique
In recent years, as the increase of interference load and equipment increase the sensitivity of harmonic wave, harmonic wave is to power train
The influence of system is also more serious, and harmonic pollution has become one the problem of urgently paying close attention to.It is generally believed that the frequency of integral frequency harmonizing wave
Rate is the integral multiple of fundamental frequency.In addition to this, there is also non-integer harmonics abundant, i.e. m-Acetyl chlorophosphonazo, frequencies for power grid
It is not the integral multiple of fundamental frequency, and discrete form or conitnuous forms may be presented in its frequency spectrum.Contain harmonic wave/monochromatic wave letter
Number it can be collectively referred to as complicated harmonic wave.
Many harmonic analysis methods have been provided in the prior art, but these analysis methods are mostly based on FFT (Fast
Fourier Transformation, Fast Fourier Transform (FFT)), IEC standard 61000-4-7 also recommends FFT as harmonic measure
Most basic method.Really, these methods are simple and to calculate cost small, under the conditions of synchronized sampling, can be realized to harmonic wave
High accuracy analysis, however these are sensitive to frequency shift (FS) based on the method for FFT, harsher to the condition of sampling and exist
The problems such as spectral leakage and fence effect, while the method for parameter estimation based on FFT is all by the Fourier of uncertainty principle point
The limitation of resolution.Particularly, difference on the frequency is two sine wave signals of Δ ω, needs data length longer than 2 π/Δ ω, this
A little defects become apparent from when the analysis to m-Acetyl chlorophosphonazo.Therefore, the method that the limitation of FFT resolution ratio can be avoided by finding has ten
Divide important value.
Summary of the invention
It is an object of the present invention to provide it is a kind of at least solve one side in above-mentioned technical problem based on Bayes
The electric harmonic signal analysis method and analytical equipment of method.
A further object of the present invention is to spectral leakage phenomenons to be avoided, and improve the precision of frequency analysis.
Another further object of the present invention is to want can to estimate the frequency and phase of harmonic wave.
Particularly, the present invention provides a kind of electric harmonic signal analysis method based on bayes method, comprising: setting
Bayesian Estimation initial value and convergence parameter；Harmonic frequency analysis section is obtained, and harmonic frequency analysis Interval Discrete is turned to
It sets quantity and analyzes subinterval, form harmonic wave measurement matrix；The sampled signal of signal to be analyzed is obtained, and according to Bayes's public affairs
Formula establishes the probability density function of harmonic signal；And calculating is iterated to probability density function using desired maximum calculated method,
Estimation obtains the frequency and amplitude of the harmonic component in signal to be analyzed.
Optionally, Bayesian Estimation initial value includes: the number of iterations t=0, and harmonic signal obeys the normal distribution x of zero-mean
~N (0, Λ), variances sigma=0.01, the initial value Λ of model parameter Λ0=diag (γi=0, i=1,2 ..., N), γiIt is humorous
The element of wave train vector, N are the quantity for analyzing subinterval；Convergence parameter includes: iteration convergence threshold value δ=10-5, sparse component sentences
Disconnected threshold gamma '=10-4。
Optionally, the step of harmonic frequency analysis Interval Discrete being turned to setting quantity analysis subinterval includes: will be humorous
Wave frequency rate analystal section [f0, f1] discretization is divided into N number of analysis subinterval, and meetsM is signal
Sampling number；
Harmonic wave measurement matrix isWherein
Δ T is signal sampling time interval.
Optionally, sampled signalAnd probability density function isAnd abbreviation
ForWherein b is the scale of laplacian distribution
Parameter, and b > 0.
Optionally, the step of being iterated calculating to probability density function using desired maximum calculated method includes: to carry out t times
E step estimation iteration, i.e. calculating p (x | y, Λt)=N (μ, ∑x), wherein μ=β ∑xATY, ∑x=([Λt]-1+βHTH)-1, β=
σ-2, ΛtIt is the parameter of t-1 step estimation；T M step estimation iteration is carried out, updates harmonic amplitude parameter Λ, more new formula is
Λt+1=diag (γi, i=1,2 ... N), wherein∑X, iiIndicate ∑x(i, i)-diagonal element, μi
It is i-th of the element for the μ that E step estimates.
Meeting | μt-1-μt| when the condition of < δ, terminate iteration；
It obtains
?In to find amplitude be corresponding value greater than i-th of element in the indexed set S, S of γ ' is si, andIn corresponding siCapable and siColumn are z, then and i-th
The corresponding frequency values of a harmonic component are fz, corresponding amplitude is
Optionally, after the frequency and amplitude for estimating the harmonic component in signal to be analyzed further include: obtain next group
Sampled signal is simultaneously iterated calculating again, compares to obtain the phase of harmonic component using the result of iteration again.
Optionally, the step of obtaining next group of sampled signal and being iterated calculating again further include: obtain next group and adopt
Sample signal isIt repeats it is expected that the iterative calculation of maximum algorithm obtains the harmonic signal amplitude of this group of sampled signalIf it is s that i-th of element, which is corresponding value, in Si, then the phase of i-th of component are as follows:
According to another aspect of the present invention, a kind of electric harmonic signal analysis equipment is additionally provided comprising processor
And memory, computer program is stored in memory, for realizing according to right when computer program is executed by processor
It is required that any one of 1 to the 7 electric harmonic signal analysis method based on bayes method.
Optionally, above-mentioned electric harmonic signal analysis equipment further include: signal sampling device, for signal to be analyzed into
Row samples and is provided to processor.
The solution of the present invention utilizes electric system complexity harmonic signal different from the method for existing strip method harmonic wave
Time domain sparse features, and harmonic signal analysis mathematical model is established using Bayesian model, and then by it is expected maximum algorithm
(EM algorithm) Recursive Solution, while the amplitude and frequency of signal can be obtained.Overcome frequency domain and spectral leakage and non-synchronous sampling
Give computational accuracy bring influence, and can simultaneously estimated amplitude harmonic wave amplitude and frequency, frequency resolution with higher and
Analysis precision.
Further, the solution of the present invention realizes Harmonious Waves in Power Systems and humorous using sliding window and Semidefinite Programming
The analysis of wave signal, overcomes the spectral leakage and fence effect of FFT, the phase of sophisticated signal can also be obtained by way of sliding window
Position.
According to the following detailed description of specific embodiments of the present invention in conjunction with the accompanying drawings, those skilled in the art will be brighter
The above and other objects, advantages and features of the present invention.
Detailed description of the invention
Some specific embodiments of the present invention is described in detail by way of example and not limitation with reference to the accompanying drawings hereinafter.
Identical appended drawing reference denotes same or similar part or part in attached drawing.It should be appreciated by those skilled in the art that these
What attached drawing was not necessarily drawn to scale.In attached drawing:
Fig. 1 is the signal of the electric harmonic signal analysis method according to an embodiment of the invention based on bayes method
Figure；
Fig. 2 is phase in the electric harmonic signal analysis method according to an embodiment of the invention based on bayes method
The schematic diagram of sliding window used in estimation；
Fig. 3 is the schematic diagram of electric harmonic signal analysis equipment according to an embodiment of the invention.
Specific embodiment
Fourier transformation is a kind of complete Orthogonal Decomposition method in the prior art, and there are spectral leakage phenomenons, reduce
The precision of frequency analysis, in addition Fourier transformation also can not simultaneously estimated amplitude harmonic wave frequency and phase, for this purpose, the present embodiment
Method the atom of minimum (rather than most complete in Fourier's variation) is found to indicate that harmonic wave is believed by continuous parameter space
Breath further can carry out recurrence estimation using bayes method by sparse modeling, in order to improve Parameter Estimation Precision.This
The principle of the electric harmonic signal analysis method based on bayes method of embodiment is as follows:
If shown in the stable state complexity harmonic signal such as formula (1) of k steady state power harmonic wave, m-Acetyl chlorophosphonazo composition:
Wherein { fi}I=1,2 ... kFor harmonic wave/m-Acetyl chlorophosphonazo frequency, { φi}I=1,2 ... kFor harmonic wave/m-Acetyl chlorophosphonazo phase, y (m) table
Show m-th of sampled signal.I is serial number, AiIt is the amplitude of i-th of component,
Above-mentioned signal also can be expressed as the form of formula (2):
Wherein M be signal sampling total number, N be dictionary frequency number, N > > k,It is frequency dictionary,
WhenWhen,Otherwise
Since the number of harmonic wave in the signal of practical power systems, m-Acetyl chlorophosphonazo is all limited, this meaning vectorIn
Most elements are zero, or the element most elements very big relative to small part are all very small, therefore the vector is necessarily
The sparse vector of a height, this is that the method for an important priori knowledge and the present embodiment is different from existing Fourier
The theoretical basis of transform method.
In view of various noises, formula (2) can write a Chinese character in simplified form into formula (3):
Y=Hx+e (3)
Wherein y ∈ RN×1Indicate harmonic wave sampled value, H ∈ RM×NIndicate harmonic wave measurement matrix, e∈RN×1For harmonic wave acquisition
Noise column vector, obeying mean value is 0, and variance is the normal distribution of σ.
In view of x ∈ RN×1It is a sparse vector, it is independent identically distributed to can consider that its element is obeyed in the present embodiment
Laplace is distributed (laplacian distribution):
Wherein b > 0 is the scale parameter of Laplace distribution, and Laplace distribution has bigger trailing phenomenon, therefore energy
Sparse vector is induced, this just describes the sparsity of x.
According to the posterior probability density function of Bayesian formula x are as follows:
Further abbreviation are as follows:
Therefore, because harmonic wave is sparse, then the form of the posterior probability density function of frequency analysis problem is very multiple
Miscellaneous, the posteriority statistic mean value (i.e. harmonic amplitude) for calculating x all refers to Higher Dimensional Integration, can not effectively calculate, in order to solve this
Problem, the present embodiment is using bayes method research harmonic parameters estimation.
Bayesian Estimation theory is a kind of very effective sparse learning method, acquires signal using known priori knowledge
Posterior density function, belong to non-convex optimization class algorithm.Bayesian Estimation theory is applied to solve frequency analysis problem, specifically
Process establishes compressed sensing model, in the case where the distribution of the priori probability density of known sparse signal, using Bayesian Estimation
Method estimates signal maximum a posteriori probability Density Distribution, obtains approximate mean value and variance, and variance can be used as tradeoff and rebuild accurately
The standard of degree, mean value can be used as the estimated value of original signal recovery.
If x obeys the normal distribution of zero-mean, i.e. x~N (0, Λ), wherein Λ=diag (γi, i=1,2 ..., N),
So:
It is further assumed that γi, i=1,2 ..., N independent same distribution obedience Gamma distribution (Gamma distribution):
Wherein
Theory shows that the x for obeying Laplace distribution can be distributed by parameterized Gaussian and derives.
For this purpose, the present embodiment solves harmonic wave hidden variable x and model parameter Λ using EM (it is expected maximum algorithm) algorithm, according to
E step estimation calculation formula can be obtained in the basic principle of EM algorithm:
Wherein.ΛtIndicate calculated value when EM algorithm t step iteration, ln p in above formula (x | Λ) and p (x | y,
Λt) calculation formula be respectively as follows:
Wherein: μ=β ∑xHTY, ∑x=([Λt]-1+βHTH)-1, β=σ-2
Bring above-mentioned two formula into formula (9):It can obtain:
Wherein ∑X, iiIndicate ∑x(i, i)-diagonal element.
By the basic principle of EM algorithm, the M of t+1 step walks calculation formula are as follows:
Λt+1=argmaxΛ L(Y|Λ) (13)
(12) substitution (13) can be obtained:
Greatest hope Bayesian Estimation algorithm does not need to obtain harmonic signal degree of rarefication (i.e. harmonic wave/simple harmonic quantity wave component in advance
Number), over-fitting error is reduced, has the advantages that reconstruction accuracy is high, computation complexity is lower.
Fig. 1 is the signal of the electric harmonic signal analysis method according to an embodiment of the invention based on bayes method
Figure, this method generally may include:
Bayesian Estimation initial value and convergence parameter is arranged in step S101；Wherein, Bayesian Estimation initial value includes: iteration
Number t=0, harmonic signal obey normal distribution x~N (0, Λ) of zero-mean, and variances sigma=0.01, model parameter Λ's is initial
Value Λ0=diag (γi=0, i=1,2 ..., N), γiFor the element of harmonic wave column vector, N is the quantity for analyzing subinterval；It receives
Holding back parameter includes: iteration convergence threshold value δ=10-5, sparse component judgment threshold γ '=10-4。
Step S102 obtains harmonic frequency analysis section, and harmonic frequency analysis Interval Discrete is turned to setting quantity
Subinterval is analyzed, harmonic wave measurement matrix is formed；Such as harmonic frequency analysis section [f0, f1], by N equal part, obtain N number of
Subinterval is analyzed, and is metM is signal sampling points.
And harmonic wave measurement matrix isIts
Middle Δ T is signal sampling time interval.
Step S103 obtains the sampled signal of signal to be analyzed, and the probability of harmonic signal is established according to Bayesian formula
Density function；Such as sampled signalAnd probability density function is And abbreviation
ForWherein b is the scale of laplacian distribution
Parameter, and b > 0.
Step S104 is iterated calculating to probability density function using desired maximum calculated method, and estimation obtains letter to be analyzed
The frequency and amplitude of harmonic component in number.Specifically calculating process can be with are as follows: the E step estimation iteration for carrying out t time calculates p
(x | y, Λt)=N (μ, ∑x), wherein μ=β ∑xATY, ∑x=([Λt]-1+βHTH)-1, β=σ-2, ΛtIt is t-1 step estimation
Parameter；T M step estimation iteration is carried out, updates harmonic amplitude parameter Λ, more new formula is Λt+1=diag (γi, i=1,
2 ... N), wherein∑X, iiIndicate ∑x(i, i)-diagonal element, μiIt is the i-th of the μ that E step estimates
A element.
Meeting | μt-1-μt| when the condition of < δ, terminate iteration.
It obtains?In find amplitude greater than γ ' indexed set S, S in i-th of element be corresponding
Value be si, andIn corresponding siCapable and siColumn
It is z, then the corresponding frequency values of i-th of harmonic component are fz, corresponding amplitude is
It is subsequent to utilize the result of iteration again by obtaining next group of sampled signal and being iterated calculating again
Comparison obtains the phase of harmonic component.Specifically, next group of sampled signal isIt repeats it is expected maximum algorithm
Iterative calculation obtains the harmonic signal amplitude of this group of sampled signalIf it is s that i-th of element, which is corresponding value, in Si, then
The phase of i-th of component are as follows:
The execution process of the electric harmonic signal analysis method based on bayes method of above-described embodiment can be summarised
Are as follows:
Step S201: setting parameter Bayesian Estimation initial value:
T=0, Λ0, p (x | y, Λ0)
σ=0.01, Λ0=diag (γi=0, i=1,2 ..., N)
Convergence threshold δ=10-5, sparse component judgment threshold γ=10-4。
Step S202: according to harmonic frequency analysis section [f0, f1], its discretization is divided into N number of section, at discretization
When sparse domain is divided into uniform grid by reason, grid is finer, and the error between actual parameter and mesh point is with regard to smaller, usually
It needs to guaranteeHere M is the total sampling number of signal, forms harmonic wave measurement matrix on this basisΔ T is signal equal interval sampling frequency.
Step S203: sampled signal is obtainedAnd the E for carrying out the t times iteration walks estimation, i.e. calculating p (x | y, Λt)
=N (μ, ∑x), wherein μ=β ∑xATY, ∑x=([Λt]-1+βHTH)-1, β=σ-2；Λ hereintIt is the ginseng of t-1 step estimation
Number, y are harmonic wave sampled signal values.
Step S204: the M for carrying out the t times iteration walks estimation, i.e. update harmonic amplitude parameter Λ, update method Λt+1=
diag(γi, i=1,2 ... N), whereinHere ∑X, iiIndicate ∑x(i, i)-diagonal element, μiIt is E
Walk i-th of element of the μ estimated.
Step S205: when t-1 step and t step | μt-1-μt| < δ, iteration terminate；
Step S206: harmonic signal amplitude
Step S207: frequency, Amplitude Estimation
?In find the indexed set S that amplitude is greater than γ, if it is s that i-th of element, which is corresponding value, in Si, andIn corresponding siCapable and siColumn are for z then
The corresponding frequency values of i harmonic signal components are fz, corresponding amplitude isRemaining component is not deposited in complicated harmonic signal
Each component frequencies and amplitude of complicated harmonic frequency so can be obtained；
Step 8: phase estimation
Obtain sampled signalStep S203 to step S2055 is repeated to obtain under new sample sequenceIf it is s that i-th of element, which is corresponding value, in Si, then the phase of i-th of component are as follows:
Frequency domain and spectral leakage and non-synchronous sampling are overcome to calculating compared to the method in Time Domain Processing, the present embodiment
Precision bring influences, and the amplitude and frequency of energy while estimated amplitude harmonic wave, frequency resolution with higher and analysis essence
Degree.
The estimation of phase is carried out by postponing a window in above-mentioned steps, it is clear that can also use the shape of sliding window
Formula is estimated every a fixed sample interval, can improve the precision of estimation in this way.Fig. 2 is according to an embodiment of the present invention
The electric harmonic signal analysis method based on bayes method in sliding window used in phase estimation schematic diagram.Wherein first
Window 30 includesAnd the second window 40 includesAlong the glide direction of arrow, slided with sliding window available
Multiple windows, are estimated respectively, and available multiple groups are as a result, to improve precision.
Fig. 3 is the schematic diagram of electric harmonic signal analysis equipment 50 according to an embodiment of the invention, the electric harmonic
Signal analysis equipment 50 includes processor 51 and memory 52, is stored with computer program 53, computer journey in memory 52
It is analyzed when sequence 53 is executed by processor 51 for realizing according to the electric harmonic signal based on bayes method of above-described embodiment
Method.Electric harmonic signal analysis equipment 50 can further include: signal sampling device 54, for signal to be analyzed into
Row samples and is provided to processor 51.
Processor 51 can be a central processing unit (CPU), or be digital processing element (DSP) etc..Storage
Device 52 is used for the program that storage processor 51 executes.Memory 52 can be used for carrying or storing have instruction or data
The desired program code of structure type and can by any medium of computer access, but not limited to this.Memory 52 can also
To be the combination of various memories.
Each process of above method embodiment is realized when being executed due to computer program 53 by processor 51, and can be reached
Identical technical effect, to avoid repeating, which is not described herein again.
So far, although those skilled in the art will appreciate that present invention has been shown and described in detail herein multiple shows
Example property embodiment still without departing from the spirit and scope of the present invention, still can according to the present disclosure directly
Determine or deduce out many other variations or modifications consistent with the principles of the invention.Therefore, the scope of the present invention is understood that and recognizes
It is set to and covers all such other variations or modifications.
Claims (9)
1. a kind of electric harmonic signal analysis method based on bayes method, comprising:
Bayesian Estimation initial value and convergence parameter are set；
Harmonic frequency analysis section is obtained, and the harmonic frequency analysis Interval Discrete is turned into setting quantity analysis sub-district
Between, form harmonic wave measurement matrix；
The sampled signal of signal to be analyzed is obtained, and establishes the probability density function of harmonic signal according to Bayesian formula；And
Calculating is iterated to the probability density function using desired maximum calculated method, estimation obtains in the signal to be analyzed
The frequency and amplitude of harmonic component.
2. according to the method described in claim 1, wherein,
The Bayesian Estimation initial value includes: the number of iterations t=0, harmonic signal obey zero-mean normal distribution x~N (0,
Λ), variances sigma=0.01, the initial value Λ of model parameter Λ0=diag (γi=0, i=1,2 ..., N), γiFor harmonic wave arrange to
The element of amount, N are the quantity in the analysis subinterval；
Convergence parameter includes: iteration convergence threshold value δ=10-5, sparse component judgment threshold γ '=10-4。
3. according to the method described in claim 2, wherein
The step of harmonic frequency analysis Interval Discrete is turned to setting quantity analysis subinterval includes: by the harmonic wave frequency
Rate analystal section [f0, f1] discretization is divided into N number of analysis subinterval, and meetsM is
Signal sampling points；
The harmonic wave measurement matrix isWherein
Δ T is signal sampling time interval.
4. according to the method described in claim 3, wherein
The sampled signalAnd the probability density function isAnd abbreviation isWherein b is the scale of laplacian distribution
Parameter, and b > 0.
5. according to the method described in claim 4, being iterated calculating to the probability density function using desired maximum calculated method
The step of include:
The E step estimation iteration that progress is t times, i.e. calculating p (x | y, Λt)=N (μ, ∑x), wherein μ=β ∑xATY, ∑x=([Λt]-1
+βHTH)-1, β=σ-2, ΛtIt is the parameter of t-1 step estimation；
T M step estimation iteration is carried out, updates harmonic amplitude parameter Λ, more new formula is Λt+1=diag (γi, i=1,2,
... N), wherein∑X, iiIndicate ∑x(i, i)-diagonal element, μiIt is i-th of the μ that E step estimates
Element；
Meeting | μt-1-μt| when the condition of < δ, terminate iteration；
It obtains
?In to find amplitude be corresponding value greater than i-th of element in the indexed set S, S of γ ' is si, andIn corresponding siCapable and siColumn are z, then and
The corresponding frequency values of i harmonic component are fz, corresponding amplitude is
6. the method according to any one of claims 1 to 5, wherein estimating the harmonic component in the signal to be analyzed
Frequency and amplitude after further include:
It obtains next group of sampled signal and is iterated calculating again, compare to obtain the harmonic wave point using the result of iteration again
The phase of amount.
7. method according to any one of claim 1 to 6, wherein obtaining next group of sampled signal and being iterated again
The step of calculating further include:
Obtaining next group of sampled signal isIt repeats it is expected that the iterative calculation of maximum algorithm obtains group sampling letter
Number harmonic signal amplitudeIf it is s that i-th of element, which is corresponding value, in Si, then the phase of i-th of component are as follows:
8. a kind of electric harmonic signal analysis equipment, including processor and memory, computer is stored in the memory
Program, for realizing base according to any one of claim 1 to 7 when the computer program is executed by the processor
In the electric harmonic signal analysis method of bayes method.
9. electric harmonic signal analysis equipment according to claim 8, further includes:
Signal sampling device, for being sampled to signal to be analyzed and being provided to the processor.
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| CN113852605B (en) * | 2021-08-29 | 2023-09-22 | 北京工业大学 | Protocol format automatic inference method and system based on relation reasoning |
| CN114236236A (en) * | 2021-12-17 | 2022-03-25 | 福州大学 | Harmonic source positioning method based on interval dynamic state estimation |
| CN114236236B (en) * | 2021-12-17 | 2024-02-06 | 福州大学 | Harmonic source positioning method based on interval dynamic state estimation |
| CN114859115A (en) * | 2022-07-08 | 2022-08-05 | 四川大学 | Broadband dense frequency signal analysis method based on rapid alternation algorithm |
| CN114859115B (en) * | 2022-07-08 | 2022-09-16 | 四川大学 | Broadband dense frequency signal analysis method based on rapid alternation algorithm |
| CN116191679A (en) * | 2023-04-24 | 2023-05-30 | 南京恺隆电力科技有限公司 | High-stability power monitoring system and monitoring method thereof |
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