CN107765347A - A kind of Gaussian process returns and the short-term wind speed forecasting method of particle filter - Google Patents
A kind of Gaussian process returns and the short-term wind speed forecasting method of particle filter Download PDFInfo
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Abstract
The invention discloses a kind of Gaussian process to return the short-term wind speed forecasting method with particle filter, realizes to the dynamic on-line monitoring of exceptional value with correcting and improving forecasting wind speed precision.First, input variable set with moment air speed value correlation maximum to be predicted is determined using partial autocorrelation function, determine state vector and build suitable training sample set, Gaussian process is established in training sample set and returns short-term wind speed forecasting model, and provides training process regression criterion；Then in conjunction with state vector and Gaussian process regression model, particle filter state space equation is established, state estimation is carried out to current measuring value using particle filter algorithm；Finally, the estimate to particle filter and measuring value residual error are analyzed, and are judged according to " 3 σ " principle and corrected exceptional value.Method provided by the invention effectively can be detected and corrected to exceptional value, improve short-term wind speed forecasting precision, can preferably solve the problems, such as power system forecasting wind speed.
Description
Technical field
The present invention relates to a kind of power-system short-term wind speed forecasting method, power system wind speed is predicted, belongs to electricity
Force system technical field.
Background technology
Mainly there are numerical weather forecast and the class method of statistical model two currently used for forecasting wind speed.Numerical weather forecast needs
Physical model is established, the information such as wind speed, wind direction, humiture are obtained by microcosmic meteorological theory and Fluid Mechanics Computation.Statistics
Model method mainly uses the thought of mathematical statistics, is predicted by existing inherent law between mining data.Such method
Main having time sequence, neutral net, SVMs, Kalman filtering etc..Because there is wind speed typical non linear, high-amplitude wave to move
Property and strong random nature, the linear model based on time series analysis be difficult to describe wind speed variation characteristic.Based on BP nerve nets
The short-term wind speed forecasting model of network has preferable precision of prediction, but process is based on "black box" principle, it is difficult to establishes dominant number
Learn expression.SVMs (support vector machines, SVM) model replaces nerve using structural risk minimization
The empirical risk minimization of network, so as to have more preferable generalization ability, it is adapted to processing small sample, higher-dimension, nonlinear regression
Problem, but time-consuming for model hyper parameter training process, limits its extensive use to a certain extent.Passage time sequence analysis
Kalman's forecasting wind speed model of foundation, achieves preferable precision of prediction.But kalman filter method is applied to linear math
Model, it is weak for non-linear process disposal ability.It is defeated that Gaussian process returns (Gaussian process regression, GPR)
Go out with probability distribution feature, compared with SVM and BP neural network model, GPR has more preferable precision of prediction.Therefore, it is of the invention
Establish the short-term wind speed forecasting model based on GPR.
Meanwhile often there are two major issues in short-term wind speed forecasting：1) influence of noise that historical wind speed sequence mixes
Precision of forecasting model.Wind series are during collection, transmission, storage etc. inevitably by the shadow of various noise factors
Ring, loss of data in such as measurement equipment collection mistake, data transmission procedure.When training forecast model, these exceptional values will
Cause predicted value to deviate actual value, even be difficult to provide prediction result under shortage of data serious conditions.Meanwhile model parameter is not
Accurate estimation also reduces precision of prediction.Statistical method is pointed out：In the training process, match value much deviates the sample of actual value
This point is outlier.Thus, the rejecting outliers method based on deviation is generated.This method main process is：It is sharp first
With given data founding mathematical models, judge whether data are abnormal according to the residual error between fitting data and actual value.It is assumed
Condition is the Gaussian Profile that regression criterion obeys that average is zero.2) hysteresis quality existing for statistical model method mechanism itself,
Cause predicted value variation tendency to lag behind wind speed actual value, especially undergone mutation the moment in wind speed, forecast model output valve is often
It is difficult to reflect actual value, it is necessary to be modified predicted value.
For existing first problem during forecasting wind speed, the present invention uses the rejecting outliers side based on deviation
Method.During using GPR fitting actual values, strong randomness and uncertain, forecast model itself hysteresis due to wind speed
Property so that match value and actual value have relatively large deviation, so as to the deviation " flooded " at exceptional value, cause rejecting outliers difficult
Or cause flase drop, missing inspection.To eliminate deviation larger at normal value, invention introduces nonlinear and non-Gaussian filtering method-grain
Son filtering (particle filter, PF), so as to propose to return what is be combined with particle filter (GPR-PF) based on Gaussian process
Short-term wind speed forecasting model, realize exceptional value dynamic on-line monitoring and amendment.The inventive method can by Example Verification
Effectively exceptional value is detected and corrected.
The content of the invention
Goal of the invention：The problem of influenceing forecasting wind speed precision for noise existing for historical wind speed sequence or shortage of data,
The present invention provides a kind of short-term wind speed forecasting method returned based on Gaussian process with particle filter, realizes to the online of exceptional value
Dynamic detection and amendment, so as to accurately estimate model parameter and improve forecasting wind speed precision.For effectively select with it is to be predicted when
The larger input variable set of air speed value correlation is carved, the present invention uses partial autocorrelation function to measure the correlation between two variables simultaneously
Training sample set is determined, further determines state vector.Concentrate to return by Gaussian process in training sample and establish state
Space equation, state estimation is carried out to current measuring value using particle filter algorithm, estimate and the residual error of measuring value are carried out
Analysis, and exceptional value is judged according to " 3 σ " principle.Then, exceptional value is corrected, and height is re-established to the wind series after cleaning
This process regressive prediction model.When carrying out 15 minutes forecasting wind speeds in advance, equally using particle filter algorithm to newest measurement
Value carries out state estimation, realizes exceptional value on-line checking and corrects.Finally, sample calculation analysis result shows, particle filter algorithm
Can effective detection go out abnormal air speed value, reduce forecasting wind speed error.
Technical scheme：A kind of short-term wind speed forecasting method returned based on Gaussian process with particle filter, including following step
Suddenly：
1) master data needed for power-system short-term forecasting wind speed is obtained, and initial data is carried out at zero averaging
Reason；
(2) the input variable set with moment air speed value correlation maximum to be predicted is determined using partial autocorrelation function, really
Determine state vector and build suitable training sample set；
(3) Gaussian process is established in training sample set and returns short-term wind speed forecasting model, and provides training process plan
Close residual error；
(4) bonding state vector sum Gaussian process regression model, particle filter state space equation is established, is filtered using particle
Ripple algorithm carries out state estimation to current measuring value；
(5) estimate to particle filter and measuring value residual error are analyzed, and are judged and corrected different according to " 3 σ " principle
Constant value；
(6) Gaussian process regressive prediction model is re-established to the wind series after cleaning.Carrying out 15 minutes wind in advance
During speed prediction, state estimation is equally carried out to newest measuring value using particle filter algorithm, exceptional value on-line checking is realized and repaiies
Just.
Further, zero averaging processing, the zero averaging formula are carried out to original wind speed time series in step (1)
For：
In formula：X (t) is original wind speed time series,For sequence x (t) average value.
Further, step (2) is determined defeated with moment air speed value correlation maximum to be predicted using partial autocorrelation function
Enter variables collection, and determine that state vector is with building suitable training sample set, the partial autocorrelation function computational methods：
3.1 assume xiIt is output variable, when lag order is k, PARCOR coefficients value is in 95% confidential intervalIt is interior, then xi-kOne of input vector can be used as, if all PARCOR coefficients values exist
In 95% confidential interval, then it is assumed that xi-1It is input variable；
3.2 for time series { x1,x2,L,xn, covariance when lag order is k is defined as γk, (during k=0, γ
For variance), calculation formula is as follows：
In formula：K=0,1,2, L, M,It is the average of time series；M=n/4 is maximum lag order；
3.3 lag orders are that k auto-correlation function (autocorrelation function, ACF) is defined as ρk：
In formula：For lag order k=0 when covariance.
PACF when then lag order is k is defined as αkk：
In formula：K=1,2, L, M.
Further, step (3) establishes Gaussian process in training sample set and returns short-term wind speed forecasting model, and gives
Go out training process regression criterion, the Gaussian process forecast of regression model process is：
4.1 hypothesis training sample sets are combined into D={ (xi,yi) | i=1,2,3, n }=(X, y), wherein：xi∈Rm
For m dimensional input vectors, m × n dimension input matrixes are then represented by X=[x1,x2,···,xn], n represents training sample points
Amount, yi∈ R are corresponding to xiOutput scalar；
4.2 defined function space f (x)=Φ (x)Tω, f (x(1))、f(x(2))、…、f(x(n)) form the one of stochastic variable
Individual set, and Joint Gaussian distribution is obeyed, Gaussian process model can is expressed as：
In formula：It is 0 that independent white Gaussian noise, which obeys average, variance σ2Gaussian Profile, be denoted as ε:N(0,σ2)；δijFor
Kronecker delta functions, as i=j, function δij=1；M (x) is the mean value function of family of finite-dimensional distribution, describes wind speed
Average output result；K (x, x ') is covariance function, portrays wind speed variance size；
4.3GPR forecast models establish prior distribution in n dimension training sets D, in n*Tie up test set D*={ (xi,yi) | i=n
+1,L,n+n*Under be changed into Posterior distrbutionp, then the training sample observation y and output vector f of test data*Between form joint
Gaussian Profile
Wherein, K (X, X)=KnRepresent N × N nuclear matrix, its element Kij=k (xi,xj)；K(X,X*)=K (X*,X)TTo survey
Try data X*Covariance matrix between the input X of training set；K(X*,X*) it is X*The covariance of itself；
Thus 4.4 draw predicted value f*Posterior distrbutionp is
Wherein
Mean vectorFor GPR model forecasting wind speed averages, exported corresponding to point prediction,For corresponding to
Variance, thus can obtain the wind speed interval prediction result with probability distribution meaning.
Further, bonding state vector sum Gaussian process regression model in step (4), establishes particle filter state space
Equation, state estimation is carried out to current measuring value using particle filter algorithm.Described particle filter state space equation is：
In formula：H=[1 00 0]；Nonlinear state transfer function GP (g) reflects by k moment states XkObtain the k+1 moment
Wind speed value, the function is by training sample set by training GPR model parameters to obtain；WkAnd Vk+1Respectively systematic procedure
Noise and observation noise；X (k)=[X1(k)X2(k)X3(k)X4(k)]T。
Further, the estimate and measuring value residual error of particle filter are analyzed in step (5), and it is former according to " 3 σ "
Then judge and correct exceptional value, " 3 σ " the principle detailed process is：
6.1 for test data r1,r2,L,rn, take its arithmetic mean of instantaneous value
And residual error valueThus obtaining its root-mean-square-deviation is
6.2 exceptional value distinguishing rules are：IfThe value is abnormal data；IfThen riFor normal number
According to.
Beneficial effect：The present invention establishes the short-term wind speed forecasting method based on Gaussian process recurrence with particle filter, profit
With particle filter is non-linear, non-gaussian filter capacity is realized and exceptional value present in original wind series is detected and repaiied
Just, while using partial autocorrelation function optimal input variable set and state vector are determined, avoids artificial experience and choose input
The deficiency of variable.Sample calculation analysis result shows that wind speed forecasting method of the invention can realize the dynamic on-line monitoring of exceptional value
With amendment, short-term wind speed forecasting model is established to the time series after cleaning, further enhancing the estimated performance of model.This hair
Bright method provides a kind of wind speed time series exceptional value dynamic on-line monitoring and modification method, improves short-term wind speed forecasting
Precision, there is certain engineer applied meaning.
Brief description of the drawings
Fig. 1 is auto-correlation and partial autocorrelation function figure；
Fig. 2 is wind speed fitting result；
Fig. 3 is wind speed fitting result partial enlarged drawing；
Fig. 4 is different models fitting residual errors；
Fig. 5 is 15min forecasting wind speeds result in advance；
Fig. 6 is the flow chart of Forecasting Methodology of the present invention.
Embodiment
With reference to specific embodiment, the present invention is furture elucidated, it should be understood that these embodiments are merely to illustrate the present invention
Rather than limitation the scope of the present invention, after the present invention has been read, various equivalences of the those skilled in the art to the present invention
The modification of form falls within the application appended claims limited range.
The thinking of the present invention is that the non-linear of particle filter, non-gaussian filtering characteristics are used for original historical wind speed sequence
Present in exceptional value carry out dynamic on-line monitoring and amendment, so that the data after cleaning are established with forecasting wind speed model, improve
Precision of prediction.First, to determine input variable set and state vector, using the correlation between partial autocorrelation function gauge variable
Property.Secondly, concentrate to return by Gaussian process in training sample and establish state space equation, using particle filter algorithm to current
Measuring value carries out state estimation, the residual error of estimate and measuring value is analyzed, and judge exceptional value according to " 3 σ " principle.So
Afterwards, exceptional value is corrected, and Gaussian process regressive prediction model is re-established to the wind series after cleaning.Carrying out 15 points in advance
During clock forecasting wind speed, state estimation is equally carried out to newest measuring value using particle filter algorithm, exceptional value is realized and examines online
Survey and correct.Finally, the validity of the inventive method is shown by sample calculation analysis result.
The present invention establishes short-term wind speed forecasting model using GPR, and GPR is using bayesian theory and Statistical Learning Theory as base
Plinth, has that easy programming is realized, hyper parameter adaptively obtains when handling high dimension, small sample and the complicated regression problem such as non-linear
And output probability the advantages that being distributed, so as to multi-field be obtained in time series analysis, dynamic system model identification, system control etc.
Obtained extensive use.
When carrying out short-term wind speed forecasting modeling using GPR, it is assumed that training sample set is combined into D={ (xi,yi) | i=1,2,
3, n }=(X, y), wherein：xi∈RmFor m dimensional input vectors, m × n dimension input matrixes are then represented by X=[x1,
x2,···,xn], n represents training sample point quantity, yi∈ R are corresponding to xiOutput scalar.Wind speed is described with mathematical linguistics
Prediction process is：
Defined function space f (x)=Φ (x)Tω, f (x(1))、f(x(2))、…、f(x(n)) form one of stochastic variable
Set, and Joint Gaussian distribution is obeyed, Gaussian process model can is expressed as
In formula：It is 0 that independent white Gaussian noise, which obeys average, variance σ2Gaussian Profile, be denoted as ε:N(0,σ2)；δijFor
Kroneckerdelta functions, as i=j, function δij=1；M (x) is the mean value function of family of finite-dimensional distribution, and description wind speed is equal
It is worth output result；K (x, x ') is covariance function, portrays wind speed variance size.
Derived to simplify, wind speed average m (x) carries out data prediction and is allowed to as 0.GPR forecast models are in n dimension training sets D
Prior distribution is inside established, in n*Tie up test set D*={ (xi,yi) | i=n+1, L, n+n*Under be changed into Posterior distrbutionp, then train sample
This observation y and test data output vector f*Between form Joint Gaussian distribution
Wherein, K (X, X)=KnRepresent N × N nuclear matrix, its element Kij=k (xi,xj)；K(X,X*)=K (X*,X)TFor
Test data X*Covariance matrix between the input X of training set；K(X*,X*) it is X*The covariance of itself.
Thus predicted value f is drawn*Posterior distrbutionp is
Wherein
Mean vectorFor GPR model forecasting wind speed averages, exported corresponding to point prediction,For corresponding to
Variance, thus can obtain the wind speed interval prediction result with probability distribution meaning.
PF algorithms have good nonlinear and non-Gaussian system mode filter capacity, and random quantity need not meet Gauss point
The restriction condition of cloth, thus applied in fields such as signal transacting, communication, artificial intelligence.Present invention selection particle filter is calculated
Method is handled exceptional value existing for wind series, proposes the short-term wind speed forecasting model based on GPR-PF.
PF basic thoughts are with the Posterior probability distribution of one group of particle approximate representation system, are then approximately represented with this
Estimate the state of nonlinear system.Describing particle filter process with nonlinear system dynamical state space model is
In formula：xkAnd zkRespectively k moment system mode vector and measuring value；F (g) and h (g) is respectively that system mode turns
Move function and measurement model function；wk-1And νkRespectively systematic procedure noise and observation noise；From the importance density function q (xk|
x1:k-1,zk) sampling obtains N number of sample, and these samples are expressed as：The predicted value at state k moment isI.e.
In formula：It is to sample the obtained independent sample corresponding to particle i in the distribution of system known noise.Complete prediction
All particles in stage just form the prior probability sample at k moment, are expressed asPriori probability density p is namely obtained
(xk|Zk-1).Obtaining new observed quantity zkAfterwards, each particleIt is updated according to weights formula
Weights are normalized
Overcome sample degeneracy phenomenon using method for resampling.Weights are normalized to sample resampling according to each particle,
The larger particle of weights is replicated, deletes the less particle of weights, obtains waiting weights particle collection, you can obtain a posteriori distribution density letter
Number
In formula：δ (g) is dirac Kronecker delta functions, and a loop iteration process terminates.
State optimization under minimum mean square error criterion meaning is estimated as
Auto-correlation function and partial autocorrelation function have great importance during identification model type and estimation exponent number.
The present invention weighs X according to auto-correlation function and partial autocorrelation functionkWith Xk-τBetween dependency relation, so as to effectively analyzing the time
Delay, and determine input variable set and state vector.Wherein, τ is time delay.
It is pre- that Jiangsu Province's wind power plant actual measurement wind speed (data sampling time is at intervals of 15min) is used for the short-term wind speed of GPR-PF
Modeling is surveyed, Fig. 1 is the autocorrelation function graph and partial autocorrelation function figure of time series analysis.It can be seen that auto-correlation
Function has hangover feature, and partial autocorrelation function truncation, so as to which wind series meet AR models.With reference to partial autocorrelation function
Figure, 4 input variables are chosen herein, that is, predict the wind speed X at k+1 momentk+1When, by k, k-1, k-2, the wind speed X at k-3 momentk,
Xk-1,Xk-2,Xk-3As input variable.Make X1(k)=X (k), X2(k)=X (k-1), X3(k)=X (k-2), X4(k)=X (k-
3), then k moment state vector is X (k)=[X1(k)X2(k)X3(k)X4(k)]T。
When carrying out wind series rejecting outliers with amendment using particle filter, worked as first using the prediction of historical wind speed value
Preceding moment gustiness, then predicted value is modified according to current time wind speed measuring value, measured so as to obtain this moment
The optimal estimation of value, and obtain the residual error between wind estimation value and measuring value.
The state vector determined with reference to partial autocorrelation function, GPR-PF short-term wind speed forecasting state-space models of the invention
For：
In formula：H=[1 00 0]；Nonlinear state transfer function GP (g) reflects by k moment states XkObtain the k+1 moment
Wind speed value, the function is by training sample set by training GPR model parameters to obtain.
Particle filter estimates to obtain k+1 moment wind estimation values by the state to the k moment, and is measured according to the k+1 moment
Measured value amendment estimate, so as to wind speed optimal estimation value after being filtered.
The present invention is detected and corrected present in original wind series using the data exception value detection method based on deviation
Exceptional value, judge by analyzing existing residual error r between GPR-PF wind estimations value and measuring value, and then according to " 3 σ " criterion
Exceptional value.
For test data r1,r2,L,rn, take its arithmetic mean of instantaneous value
And residual error valueThus obtaining its root-mean-square-deviation is
Then exceptional value distinguishing rule is：IfThe value is abnormal data；IfThen riFor normal number
According to.
Degree for quantitative prediction value close to actual value, mean absolute percentage error (mean absolute are selected herein
Percentage error, MAPE) and root-mean-square error (root mean square error, RMSE) as model prediction imitate
Fruit evaluation index, calculation formula are respectively：
In formula：T is future position number, yiFor i-th of future position wind speed actual value,For i-th of future position model prediction
Value.
The present invention is using certain wind power plant 14 days 12 May in 2008:00 up to 25 days 23 May:When 45 totally 1104 actual measurement wind
Speed value is used as training sample sequence, and data sampling time establishes GPR-PF forecasting wind speed models, to May 26 at intervals of 15min
96 air speed values propose back (shift to an earlier date 15min) prediction.
First, GPR short-term wind speed forecastings model and solving model hyper parameter are established by training sample set, establishes state space
Equation, the residual error between analysis model match value and measuring value, so as to carry out rejecting outliers using the method based on deviation.Fig. 2
For the prediction result for using GPR to be obtained with two methods of GPR-PF in training process.It can be seen that using GPR models
When carrying out short-term wind speed forecasting, due to the strong fluctuation of wind speed and randomness so that GPR models are difficult to track wind speed change well
Trend, certain hysteresis quality be present, so as to produce larger deviation.And GPR-PF models use current time measuring value to wind speed
Estimate enters Mobile state renewal, can be good at estimating the time of day of wind speed.Can be with from Fig. 3 prediction results partial enlarged drawing
The fitting effect of more careful two kinds of models of comparison.Residual analysis is carried out to wind speed value and actual measuring value, Fig. 4 is respectively to adopt
Residual result when being fitted with GPR and GPR-PF models.When individually using GPR models, it can be seen that residual distribution relatively divides
Dissipate, be unfavorable for the analysis and detection of exceptional value.And when using GPR-PF mixed methods, residual distribution is relatively concentrated, can be easier
Exceptional value is judged using " 3 σ " criterion.
By to residual distribution analysis and " 3 σ " criterion, it is as shown in table 1 with correction result to rejecting outliers.
The rejecting outliers of table 1 and correction result
Wind series after cleaning are re-established with GPR forecast models, and carries out the short-term wind speed forecasting of 15min in advance.
Fig. 5 is the forecasting wind speed result using tetra- kinds of BP neural network, SVM, GPR and GPR-PF models.Forecast model quantitative assessment refers to
It is as shown in table 2 to mark result.As can be seen that relative to two kinds of BP neural network, SVM forecast models, GPR can provide preferably pre-
Survey precision.After being modified by using particle filter algorithm to exceptional value, GPR-PF forecasting wind speeds model of the invention weakens
Influence of noise, so as to obtaining optimum prediction result.
Table 2 shifts to an earlier date 15min forecasting wind speed errors
In summary, the present invention is returned with the short-term wind speed forecasting method of particle filter with following excellent based on Gaussian process
Gesture：1) input variable collection is chosen using partial autocorrelation function and merges determination state vector, it is defeated so as to avoid artificial experience selection
Enter the deficiency of variable.2) state space equation based on particle filter is established, is realized to abnormal present in historical wind speed sequence
Value carries out dynamic on-line monitoring and amendment, and Gaussian process is established to the wind speed time series after cleaning and returns short-term wind speed forecasting mould
Type, so as to further increase precision of prediction.3) used relative to SVMs and BP neural network Forecasting Methodology, the present invention
Gaussian process returns and establishes short-term wind speed forecasting model, has the performance of more preferable estimated performance, its model hyper parameter can be with adaptive
It should obtain.The inventive method can carry out dynamic on-line monitoring and amendment to exceptional value present in original time series, so as to
Short-term wind speed forecasting precision is improved, the plan of wind power output is arranged power system and ensures that power network safety operation has
Certain reference value.
Claims (6)
1. a kind of Gaussian process returns and the short-term wind speed forecasting method of particle filter, it is characterised in that：Comprise the following steps：
(1) master data needed for power-system short-term forecasting wind speed is obtained, and zero-mean is carried out to original wind speed time series
Change is handled；
(2) the input variable set with moment air speed value correlation maximum to be predicted is determined using partial autocorrelation function, determines shape
State vector simultaneously builds suitable training sample set；
(3) Gaussian process is established in training sample set and returns short-term wind speed forecasting model, and it is residual to provide training process fitting
Difference；
(4) bonding state vector sum Gaussian process regression model, particle filter state space equation is established, is calculated using particle filter
Method carries out state estimation to current measuring value；
(5) estimate to particle filter and measuring value residual error are analyzed, and are judged according to " 3 σ " principle and corrected exceptional value；
(6) Gaussian process regressive prediction model is re-established to the wind series after cleaning, 15 minutes in advance wind speed are pre- carrying out
During survey, state estimation is equally carried out to newest measuring value using particle filter algorithm, exceptional value on-line checking is realized and corrects.
2. returned as claimed in claim 1 based on Gaussian process and the short-term wind speed forecasting method of particle filter, its feature exist
In：Zero averaging processing is carried out to original wind speed time series in step (1), the zero averaging formula is：
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In formula：X (t) is original wind speed time series,For sequence x (t) average value.
3. returned as claimed in claim 1 based on Gaussian process and the short-term wind speed forecasting method of particle filter, its feature exist
In：Step (2) determines the input variable set with moment air speed value correlation maximum to be predicted using partial autocorrelation function, and really
Determining state vector with building suitable training sample set, the partial autocorrelation function computational methods is：
3.1 assume xiIt is output variable, when lag order is k, PARCOR coefficients value is in 95% confidential intervalIt is interior, then xi-kOne of input vector can be used as, if all PARCOR coefficients values exist
In 95% confidential interval, then it is assumed that xi-1It is input variable；
3.2 for time series { x1,x2,L,xn, covariance when lag order is k is defined as γk, (during k=0, γ is side
Difference), calculation formula is as follows：
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In formula：K=0,1,2, L, M,It is the average of time series；M=n/4 is maximum lag order；
3.3 lag orders are that k auto-correlation function is defined as ρk：
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In formula：For lag order k=0 when covariance；
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<mn>11</mn>
</msub>
<mo>=</mo>
<msub>
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<mi>&rho;</mi>
<mo>^</mo>
</mover>
<mn>1</mn>
</msub>
</mrow>
</mtd>
</mtr>
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<mi>&alpha;</mi>
<mo>^</mo>
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</mrow>
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<mo>^</mo>
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</mtd>
</mtr>
</mtable>
</mfenced>
In formula：K=1,2, L, M.
4. returned as claimed in claim 1 based on Gaussian process and the short-term wind speed forecasting method of particle filter, its feature exist
In：Step (3) establishes Gaussian process in training sample set and returns short-term wind speed forecasting model, and provides training process fitting
Residual error, the Gaussian process forecast of regression model process are：
4.1 hypothesis training sample sets are combined into D={ (xi,yi) i=1,2,3 ..., n=(X, y), wherein：xi∈RmTie up and input for m
Vector, m × n dimension input matrixes are then represented by X=[x1,x2,···,xn], n represents training sample point quantity, yi∈ R are
Corresponding to xiOutput scalar；
4.2 defined function space f (x)=Φ (x)Tω, f (x(1))、f(x(2))、…、f(x(n)) form one of stochastic variable collection
Close, and obey Joint Gaussian distribution, Gaussian process model can is expressed as：
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<mi>y</mi>
<mo>~</mo>
<mi>GP</mi>
<mrow>
<mo>(</mo>
<mi>m</mi>
<mrow>
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<mo>)</mo>
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<mi>ij</mi>
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</mrow>
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In formula：It is 0 that independent white Gaussian noise, which obeys average, variance σ2Gaussian Profile, be denoted as ε:N(0,σ2)；δijFor
Kroneckerdelta functions, as i=j, function δij=1；M (x) is the mean value function of family of finite-dimensional distribution, and description wind speed is equal
It is worth output result；K (x, x ') is covariance function, portrays wind speed variance size；
4.3GPR forecast models establish prior distribution in n dimension training sets D, in n*Tie up test set D*={ (xi,yi) | i=n+1, L,
n+n*Under be changed into Posterior distrbutionp, then the training sample observation y and output vector f of test data*Between form joint Gauss
Distribution
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<mo>)</mo>
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</mrow>
Wherein, K (X, X)=KnRepresent N × N nuclear matrix, its element Kij=k (xi,xj)；K (X, X*)=K (X*, X)TTo test number
According to the covariance matrix between X* and the input X of training set；K (X*, X*) is X* itself covariance；
Thus 4.4 show that predicted value f* Posterior distrbutionps are
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Wherein
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Mean vectorFor GPR model forecasting wind speed averages, exported corresponding to point prediction,For corresponding toSide
Difference, it thus can obtain the wind speed interval prediction result with probability distribution meaning.
5. returned as claimed in claim 1 based on Gaussian process and the short-term wind speed forecasting method of particle filter, its feature exist
In：Bonding state vector sum Gaussian process regression model, establishes particle filter state space equation, using particle in step (4)
Filtering algorithm carries out state estimation to current measuring value.Described particle filter state space equation is：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msub>
<mi>X</mi>
<mrow>
<mi>k</mi>
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</mrow>
</msub>
<mo>=</mo>
<mi>G</mi>
<mi>P</mi>
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<mi>k</mi>
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<mrow>
<mi>k</mi>
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</mrow>
</msub>
<mo>=</mo>
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<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>V</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula：H=[1 00 0]；Nonlinear state transfer function GP (g) reflects by k moment states XkObtain k+1 moment wind speed
Predicted value, the function is by training sample set by training GPR model parameters to obtain；WkAnd Vk+1Respectively systematic procedure noise
And observation noise；X (k)=[X1(k) X2(k) X3(k) X4(k)]T。
6. returned as claimed in claim 1 based on Gaussian process and the short-term wind speed forecasting method of particle filter, its feature exist
In：The estimate and measuring value residual error of particle filter are analyzed in step (5), and judges and corrects different according to " 3 σ " principle
Constant value, " 3 σ " the principle detailed process are：
6.1 for test data r1,r2,L,rn, take its arithmetic mean of instantaneous value
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</msub>
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And residual error valueThus obtaining its root-mean-square-deviation is
<mrow>
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<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mrow>
6.2 exceptional value distinguishing rules are：IfThe value is abnormal data；IfThen ri is normal data.
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