CN105117593A - Wavelet transform and particle swarm optimized grey model-based short-term wind speed forecasting method - Google Patents

Abstract

The invention discloses a wavelet transform and particle swarm optimized grey model-based short-term wind speed forecasting method. The method comprises the following steps: decomposing and analyzing wind speed data by utilizing wavelet decomposition and reconstruction; inputting the reconstructed data into a particle swarm optimized grey wind speed forecasting model one by one to obtain forecasting values; adding the forecasting values to obtain a wind speed forecasting value; and finally evaluating the wind speed forecasting ability. According to the method provided by the invention, the problem of high-frequency component overfitting is solved on the basis of ensuring the low-frequency component fitting; and less information is required and the forecasting can be completed under the condition of being relatively lack of data, so that the precision and stability of the method is higher than that of the traditional grey model forecasting method.

Description

Based on the short-term wind speed forecasting method of wavelet transformation and population updated gray correlation analysis

Technical field

Invention relates to a kind of short-term wind speed forecasting method based on wavelet transformation and population updated gray correlation analysis, belongs to short-term wind speed forecasting field.

Background technology

The dual-pressure of world energy sources crisis and environmental protection, impels countries in the world man area more to pay attention to the exploitation of sustainable development source and clean energy resource.Wherein wind energy cleanliness without any pollution, energy is large, and prospect of the application is wide.Nowadays day by day deeply, scope also becomes wide increasingly, comprises Large-scale Wind Turbines, wind-powered electricity generation penetrates the aspects such as power in the domestic and international research for wind-power electricity generation.Generated energy is determined by wind energy size.The size of wind energy is then subject to the impact of wind speed size.Can draw thus, the size of wind speed has close contact with wind power generation efficiency.When generating just devoted oneself to work by blower fan, the value of wind speed has been referred to as incision wind speed, also referred to as threshold wind velocity.The speed of wind when this moment is blower fan for determining rated power.It is a value determined.Now the power of blower fan reaches maximal value.When wind speed is some numerical value---during cut-out wind speed, wind turbine continues operation and has certain danger.Now wind speed is a maximum value.The situation that may occur has damages machinery, significantly unstable output etc.These all require that we will have a relatively accurate prediction to following wind speed.

The method being suitable for wind speed short-term forecasting at present has a lot.Some of them statistical method includes linear regression, multiple regression analysis, ARMA (auto regressive moving average), based on Kalman filter technique method, and Bock this and Jenkins model.Increasing intelligent algorithm is also employed for this simultaneously, as utilized expert system, and ANN (artificial neural network), fuzzy logic, ESN (echo state network).By multiple Combination of Methods, as the built-up pattern based on fuzzy reasoning and Artificial Neural Network, based on WT (wavelet transformation), artificial neural network, the built-up pattern of EA (evolution algorithm), based on the built-up pattern of ARMAX (exogenous variable of autoregression (AR) and moving average (MA)) and PSO (particle swarm optimization), and the built-up pattern of ANN and ANFIS is in daily use.The superiority of built-up pattern is apparent.GM (gray model) independently carries out predicting that the short-term wind speed forecasting result obtained is sometimes accurate not, thus needs in conjunction with additive method to improve its performance.

Summary of the invention

The present invention is directed to the needs of domestic wind energy turbine set short-term wind speed forecasting application, propose a kind of short-term wind speed forecasting method based on wavelet transformation and population updated gray correlation analysis, can be applicable to scientific research and the engineer applied of wind energy association area.

For achieving the above object, the present invention adopts following technical scheme:

Based on the short-term wind speed forecasting method of wavelet transformation and population updated gray correlation analysis, comprise the following steps:

1) input air speed data, data prediction is carried out to the original series that air speed data is formed;

2) wavelet function feedback is carried out to pretreated wind series;

3) the forecasting wind speed model based on gray theory is set up;

4) particle swarm optimization algorithm improved grey model forecasting wind speed model is utilized;

5) wind series is carried out each component after wavelet function feedback to predict as the grey forecasting wind speed model after input one by one input particle group optimizing;

6) forecasting wind speed value is obtained;

7) error of calculation index, assesses forecasting wind speed;

8) forecasting wind speed value and error criterion is exported.

Aforesaid step 1) in, carry out data prediction and refer to when predicting that the air speed data in moment and the air speed data size of previous moment differ by more than 10%, based on following equation, pre-service is carried out to air speed data:

$X_s(m+1)=X_s\left(m\right)+\left(X_s\right(m+1)-\frac{X_s\left(m\right)}{3})---\left(1\right)$

Wherein, X _s(m+1) air speed data in m+1 moment is represented, X _sm () represents the air speed data in m moment.

Aforesaid step 2) in, choose 3 layers of wavelet decomposition, then wavelet decomposition and reconstruct after, original series is expressed as:

X _s＝G ₁+G ₂+G ₃+X ₃(2)

Wherein, X _sfor original series, G ₁, G ₂, G ₃be respectively the high-frequency signal after ground floor to third layer reconstruct, X ₃for the low frequency signal of third layer reconstruct,

Original series X _sin i-th element can be expressed as follows:

X _s,i＝G _1,i+G _2,i+G _3,i+X _3,i(3)

Wherein, G _{1, i}, G _{2, i}, G _{3, i}be respectively X _sin i-th element ground floor to third layer reconstruct after high-frequency signal, X _{3, i}for X _sin i-th element third layer reconstruct low frequency signal.

Aforesaid step 3) in, set up the forecasting wind speed model based on gray theory, comprise the following steps:

3-1) accumulated generating operation is carried out to the component after reconstruct, as follows:

By described step 2) wavelet decomposition and reconstruct after component G ₁, G ₂, G ₃and X ₃respectively as the list entries X in forecasting wind speed model ⁽⁰⁾, carry out accumulated generating operation, and the air speed data choosing front 5 moment can predict the wind speed of subsequent time,

Order, X ⁽¹⁾x ⁽⁰⁾single order Accumulating generation, its element can be determined by the following:

X ⁽⁰⁾(1)＝X ⁽¹⁾(1)(4)

$X^{\left(1\right)}\left(k\right)=\underset{m=1}{\overset{k}{\Σ}}{X}^{\left(0\right)}\left(m\right),k=2,3,...5---\left(5\right)$

Wherein, X ⁽⁰⁾k () represents list entries X ⁽⁰⁾in the data in front k moment;

Background value 3-2) calculating grey forecasting wind speed model is as follows:

Z ⁽¹⁾(k)＝gX ⁽¹⁾(k)+(1-g)X ⁽¹⁾(k-1),k＝2,3...5(6)

Wherein, Z ⁽¹⁾k () represents background value, g generates coefficient;

Equation 3-3) setting up grey forecasting wind speed model is as follows:

X ⁽⁰⁾(k)+aZ ⁽¹⁾(k)＝bX ⁽¹⁾(k)(7)

Wherein, a is development coefficient, and b is the grey input coefficient obtained by least square method;

Definition matrix B and Y _nas follows:

$B=\left[\begin{array}{cc}-Z^{\left(1\right)}\left(2\right)& 1\\ -Z^{\left(1\right)}\left(3\right)& 1\\ -Z^{\left(1\right)}\left(4\right)& 1\\ -Z^{\left(1\right)}\left(5\right)& 1\end{array}\right]---\left(8\right)$

$Y_N=\left[\begin{array}{c}{X}^{\left(0\right)}\left(2\right)\\ X^{\left(0\right)}\left(3\right)\\ X^{\left(0\right)}\left(4\right)\\ X^{\left(0\right)}\left(5\right)\end{array}\right]---\left(9\right)$

The value of coefficient a, b is determined by following equation:

$\left[\begin{array}{c}a\\ b\end{array}\right]={\left(B^{T}B\right)}^{-1}*B^T*Y_N---\left(10\right);$

3-4) determine that the differential equation of grey forecasting wind speed model is as follows:

$\frac{{\mathrm{dX}}^{\left(1\right)}}{dt}+{\mathrm{aX}}^{\left(1\right)}\left(t\right)=b---\left(11\right)$

The solution of the above-mentioned differential equation is as follows:

${\hat{X}}^{\left(1\right)}(k+1)=\{X^{\left(0\right)}\left(1\right)-b/a\}*e^{-at}+b/a,k\≥1---\left(12\right)$

Wherein, the X being ⁽¹⁾k the estimated value of (), is equaled first element of this sequence, determines following relation by first element estimated value of the single order Accumulating generation of a sequence:

${\hat{X}}^{\left(1\right)}\left(1\right)=X^{\left(0\right)}\left(1\right)---\left(13\right);$

3-5) carry out inverse accumulated generating operation, determine forecasting wind speed value:

${\hat{X}}^{\left(0\right)}\left(k\right)={\hat{X}}^{\left(1\right)}\left(k\right)-{\hat{X}}^{\left(1\right)}(k-1),k\≥2---\left(14\right)$

Wherein, original series X ⁽⁰⁾the estimated value of (k).

Aforesaid step 4) in, utilize particle swarm optimization algorithm improved grey model forecasting wind speed model to refer to determine the optimum value generating coefficient, meet minimum mean absolute percentage error:

$\underset{i=1}{\overset{10}{\Σ}}{\mathrm{MAPE}}_i,$ Obey 0≤g≤1;

Wherein, MAPE is mean absolute percentage error;

Particle swarm optimization algorithm searching process is as follows:

Stochastic choice one group of particle carrys out matching particle swarm optimization algorithm model as initial value.These particle goal seeking spaces, in k iteration in object space, by describe position and the speed of each particle respectively, each particle records their best positions in k+1 iteration, the speed of particle obtained by equation below:

$V_{k+1}^i=\mathrm{\ω}\·V_k^i+c_1\·r_1(P_{lbest}^i-X_k^i)+c_2\·r_2(P_{global}^i-X_k^i)---\left(15\right)$

Wherein, r ₁and r ₂be the random number between 0 and 1 respectively, ω is inertia weight coefficient, c ₁and c ₂training coefficient, it is global optimum position;

The computing formula of ω is as follows:

$\mathrm{\ω}={\mathrm{\ω}}_{max}-\frac{({\mathrm{\ω}}_{max}-{\mathrm{\ω}}_{min})}{k_{\max }}\×k---\left(16\right)$

Wherein, k _maxmaximum iteration time, ω _maxbe 0.9, ω _minbe 0.4, in each iteration, the reposition of each particle is obtained, as following formula by its original position and its current speed addition:

$X_{k+1}^i=X_k^i+V_{k+1}^i---\left(17\right).$

Aforesaid step 5) wind series carried out each component after wavelet function feedback and predict as the grey forecasting wind speed model after input drops into particle group optimizing one by one, specifically refer to, by original series X _shigh fdrequency component G ₁, G ₂, G ₃, low frequency component X ₃and described step 4) generation coefficient g after optimizing as input, be input to described step 3) grey forecasting wind speed model predict, the output obtained is exactly that each component is in the result of carrying out short-term wind speed forecasting.

Aforesaid step 6) obtain forecasting wind speed value and refer to described step 5) the predicting the outcome of each component that obtain superpose, thus obtain forecasting wind speed value,

Original series X _s, M element prediction value after the k moment be expressed as follows:

$\stackrel{\‾}{X_{s,M+k}}=\stackrel{\‾}{G_{1,M+k}}+\stackrel{\‾}{G_{2,M+k}}+\stackrel{\‾}{G_{3,M+k}}+\stackrel{\‾}{X_{3,M+k}}---\left(18\right)$

Wherein, represent original series X respectively _sm element X _s,Mground floor after reconstruct is to third layer high-frequency signal G _{1, M}, G _{2, M}, G _{3, M}with the low frequency signal X of third layer reconstruct _{3, M}the k moment after predict the outcome.

Aforesaid step 7) in, error criterion adopts mean absolute percentage error MAPE, and mean absolute error MAE, average relative error MPE, be defined as follows:

$MAPE=\left(\frac{1}{n}\right)\underset{i=1}{\overset{n}{\Σ}}\left(\frac{|L_f-L_a|}{L_a}\right)---\left(19\right)$

$MAE=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}|L_f-L_a|---\left(20\right)$

$MPE=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}\frac{L_f-L_a}{L_a}\×100---\left(21\right)$

Wherein, L _fand L _abe forecasting wind speed value and actual wind speed value respectively, i represents hour, and n represents moment number.

The present invention uses particle swarm optimization algorithm to be optimized gray model, secondly, the wavelet transformation of the good reputation that utilization has " digital microscope " carrys out the air speed data of analysis of history record, by using wavelet transformation, level discharge rating is carried out to the wind series of a certain wind energy turbine set, population updated gray correlation analysis is used to predict the signal after an every part single reconstruct respectively, then each predicted value is superposed, obtain predicting the outcome of original wind series, last coding, realizes above algorithm.The present invention solves the problem of high fdrequency component over-fitting on the basis that ensure that low frequency component matching, and the information of needs is less, can complete prediction, had raising relative to the precision and stability of traditional Grey Model when data relative absence.

Accompanying drawing explanation

Fig. 1 is the inventive method process flow diagram;

Fig. 2 is the process flow diagram of wavelet function feedback process;

Fig. 3 is that the present invention PSO optimizes the process flow diagram generating coefficient g;

Fig. 4 is applied to the predicted value and actual value that wind series obtains in embodiments of the invention.

Embodiment

Below in conjunction with the drawings and specific embodiments, invention is described in detail.

As shown in Figure 1, the gray prediction method improved based on wavelet transformation and population of the present invention, comprises the following steps:

1. first input air speed data, data prediction carried out to the original series that air speed data is formed:

The selection of input variable is all one of most important part for often kind of method, and it affects the accuracy of prediction.Input variable is a full and accurate explanatory variable in the ideal case, and air speed data a few days ago, for forecasting wind speed, is exactly a highly full and accurate explanatory variable.In this model, the numerical value of continuous two moment wind speed can be very different sometimes, and this species diversity can cause forecasting wind speed error.When predicting that the air speed data (m+1 moment) in moment differs by more than 10% with the size of previous moment (m moment), based on following equation, partial data is finely tuned:

$X_s(m+1)=X_s\left(m\right)+\left(X_s\right(m+1)-\frac{X_s\left(m\right)}{3})---\left(1\right)$

Wherein, X _s(m+1) air speed data in m+1 moment is represented, X _sm () represents the air speed data in m moment.

2. the sequence after pair adjustment carries out wavelet function feedback:

During wavelet decomposition, the very important point is the number needing to determine Decomposition order.The degree of decomposition of small echo, the careful degree that namely frequency range of signal divides decides flatness, the stability of low frequency term and high frequency item, and this is the feature that small echo self possesses.But Decomposition order is not The more the better, at signal in decomposable process yet, how much have some errors calculated and produce.More down decompose, Decomposition order is more, and error also can accumulate larger.Therefore, when selecting Decomposition order, be generally advisable with 2 ~ 4 layers.What the present invention chose is 3 layers of decomposition.

Small echo ' db3 ' is selected one-dimensional signal to be carried out to the wavelet decomposition of N (N=3) layer.First wavelet function feedback is utilized to process non-stationary series.Then high-frequency signal and low frequency signal are separated, drop into model respectively and predict.What high-frequency signal was corresponding is fluctuation item, the details coefficients of original signal that what its embodied is, what low frequency signal was corresponding is trend term, the general trend of original signal that what its embodied is.Like this each component is carried out to the method for modeling, can reach and divide and rule, non-interference prediction effect, accurately independent in the hope of what predict.Its process as shown in Figure 2.

Make X _sfor the short-term wind series of non-stationary, this sequence is that tool is tactic.After wavelet decomposition is carried out to this sequence, the more each layer time series after decomposing is reconstructed respectively, original series can be expressed as:

X _s＝G ₁+G ₂+G ₃+X ₃(2)

Wherein, X _sfor original series, G ₁, G ₂, G ₃be respectively the high-frequency signal after ground floor to third layer reconstruct, X ₃for the low frequency signal of third layer reconstruct,

Original series X _sin i-th element can be expressed as follows:

X _s,i＝G _1,i+G _2,i+G _3,i+X _3,i(3)

Wherein, G _{1, i}, G _{2, i}, G _{3, i}be respectively X _sin i-th element ground floor to third layer reconstruct after high-frequency signal, X _{3, i}for X _sin i-th element third layer reconstruct low frequency signal.

3. set up the forecasting wind speed model based on gray theory, the component after ream weight structure is one by one as input.

In the present invention, the wind speed in front 5 moment can predict the wind speed of subsequent time.Component after ream weight structure is one by one as input, and note list entries is X ⁽⁰⁾, by the component G after step 2 wavelet decomposition and reconstruct ₁, G ₂, G ₃and X ₃respectively as the X in forecasting wind speed model ⁽⁰⁾sequence, its concrete algorithm and step as follows:

3.1 accumulated generating operations (AGO)

The AGO (Accumulating generation) of each list entries of grey forecasting wind speed model is as follows:

X ⁽¹⁾x ⁽⁰⁾single order AGO, its element can be determined by the following:

X ⁽⁰⁾(1)＝X ⁽¹⁾(1)(4)

$X^{\left(1\right)}\left(k\right)=\underset{m=1}{\overset{k}{\Σ}}{X}^{\left(0\right)}\left(m\right),k=2,3,...5---\left(5\right)$

It should be noted that, subscript 1 represents the single order AGO of original series, X ⁽⁰⁾k () represents list entries X ⁽⁰⁾in the data in front k moment, k=5 represents front 5 moment.

The background value of 3.2 calculating grey forecasting wind speed models

In this stage, the background value of grey forecasting wind speed model is determined as follows:

Z ⁽¹⁾(k)＝gX ⁽¹⁾(k)+(1-g)X ⁽¹⁾(k-1),k＝2,3...5(6)

Wherein, Z ⁽¹⁾k () represents background value, g generates coefficient, and not yet determine its optimal value herein, thus background value is also not yet determined.Without in the model optimized, the usual use experience formula of calculating of background value.Optimized model specifically determines that the method for optimal value is shown in next step.

The determination of 3.3 grey forecasting wind speed model equations

The equation set up between the value of known, unknown system is as follows:

X ⁽⁰⁾(k)+aZ ⁽¹⁾(k)＝bX ⁽¹⁾(k)(7)

Wherein, a is development coefficient, and b is the grey input coefficient obtained by least square method.For determining these coefficients, matrix B and Y _nbe defined as follows:

$B=\left[\begin{array}{cc}-Z^{\left(1\right)}\left(2\right)& 1\\ -Z^{\left(1\right)}\left(3\right)& 1\\ -Z^{\left(1\right)}\left(4\right)& 1\\ -Z^{\left(1\right)}\left(5\right)& 1\end{array}\right]---\left(8\right)$

$Y_N=\left[\begin{array}{c}{X}^{\left(0\right)}\left(2\right)\\ X^{\left(0\right)}\left(3\right)\\ X^{\left(0\right)}\left(4\right)\\ X^{\left(0\right)}\left(5\right)\end{array}\right]---\left(9\right)$

The value of coefficient a, b is determined by following equation:

$\left[\begin{array}{c}a\\ b\end{array}\right]={\left(B^{T}B\right)}^{-1}*B^T*Y_N---\left(10\right).$

3.4 determine the differential equation

For determining coefficient a and b, the differential equation of grey forecasting wind speed model can be determined as follows:

$\frac{{\mathrm{dX}}^{\left(1\right)}}{dt}+{\mathrm{aX}}^{\left(1\right)}\left(t\right)=b---\left(11\right)$

The solution of the above-mentioned differential equation is as follows:

${\hat{X}}^{\left(1\right)}(k+1)=\{X^{\left(0\right)}\left(1\right)-b/a\}*e^{-at}+b/a,k\≥1---\left(12\right)$

Wherein, the X being ⁽¹⁾the estimated value of (k).Equaled first element of this sequence by first element estimated value of the single order AGO of a sequence, determine following relation:

${\hat{X}}^{\left(1\right)}\left(1\right)=X^{\left(0\right)}\left(1\right)---\left(13\right).$

3.5 inverse accumulated generatings operation (IAGO)

Finally, in order to predict the element of original series, inverse accumulated generating operation should be carried out.Therefore, predicted value can be determined as follows:

${\hat{X}}^{\left(0\right)}\left(k\right)={\hat{X}}^{\left(1\right)}\left(k\right)-{\hat{X}}^{\left(1\right)}(k-1),k\≥2---\left(14\right)$

Wherein, original series X ⁽⁰⁾k the estimated value of (), this is also the output that we expect.When it should be noted that grey forecasting wind speed model GM (1,1) carries out forecasting wind speed, using the input of the air speed data in front 5 moment as gray model.

4. utilize particle swarm optimization algorithm (PSO) improved grey model forecasting wind speed model:

4.1 fitness functions determining PSO

Particle cluster algorithm is used for determining to generate coefficient optimum value.The optimum value generating coefficient is determined by the error farthest reduced between the wind speed of 5 moment predictions in advance and actual wind speed.For this reason, the present invention determines by particle swarm optimization algorithm the optimal value generating coefficient, at utmost reduces MAPE (mean absolute percentage error):

Minimum obey 0≤g≤1

Here, the diagram of the generation coefficient optimal value process determining grey forecasting wind speed model is we illustrated.

4.2 searching process

PSO algorithm searching process as shown in Figure 3.Stochastic choice one group of particle carrys out matching particle swarm optimization algorithm model as initial value.These particle goal seeking spaces, thus find new solution.In k iteration in object space, by describe position and the speed of each particle respectively, each particle records their best positions then, in k+1 iteration, the speed of particle obtained by equation below:

$V_{k+1}^i=\mathrm{\ω}\·V_k^i+c_1\·r_1(P_{lbest}^i-X_k^i)+c_2\·r_2(P_{global}^i-X_k^i)---\left(15\right)$

Wherein, r ₁and r ₂be the random number between 0 and 1 respectively, ω is inertia weight coefficient, c ₁and c ₂training coefficient, it is global optimum position.

This equation is made up of following three parts.

(1) initial value of particle rapidity.Its value is large, contributes to global search; Its value is little, then contribute to Local Search.Its value can make global search and Local Search present a relative suitable state.

(2) orientation of particle self.Its value is along with c ₁, r ₁change change.The experience that its value is inclined to according to current search, strengthens the ability of global search.

(3) intersection study between population.Its value is along with c ₂, r ₂change change.Its value means that the information in population is intersected shared, common learning experience, multidirectional transmission.This is also that particle cluster algorithm is with genetic algorithm significant difference.

Three parts of above-mentioned equation make population according to the orientation of self, i.e. the experience of self search, and the experience of intersection study mutually constantly changes oneself position and speed, finally reaches an optimal value.

Wherein r ₁and r ₂span is 0 ~ 1, and they are all the numbers of stochastic generation, and the value mode of their stochastic generation means that function is also stochastic generation; ω is inertia weight coefficient, c ₁, c ₂for training coefficient.Especially, ω drops to 0.4 from 0.9 straight line.

The computing formula of ω is as follows:

$\mathrm{\ω}={\mathrm{\ω}}_{max}-\frac{({\mathrm{\ω}}_{max}-{\mathrm{\ω}}_{min})}{k_{\max }}\×k---\left(16\right)$

Wherein, k _maxmaximum iteration time, ω _maxbe 0.9, ω _minbe 0.4.In each iteration, the reposition of each particle is obtained, as following formula by its original position and its current speed addition:

$X_{k+1}^i=X_k^i+V_{k+1}^i---\left(17\right).$

5. the prediction of each component:

This step is by high fdrequency component G ₁, G ₂, G ₃, low frequency component X ₃predict as the grey forecasting wind speed model after input drops into particle group optimizing one by one.The grey forecasting wind speed model training optimized by PSO determines the optimal value generating coefficient g, now can be predicted by the present wind speed to future time instance.Input needed for test phase is called test set.The test set that this process need is used is the air speed data G in front several moment ₁, G ₂, G ₃and X ₃the optimal value (in step 4 optimizing gained) of (processing gained in step 2) and generation coefficient g.Using the input of these data as short-term wind speed forecasting gray model (shown in step 3), the output obtained is exactly the result that each component carries out short-term wind speed forecasting in GMIPSO model.

6. the acquisition of forecasting wind speed value:

The predicting the outcome of each component that step 5 obtains by this step superposes, thus obtains predicting the outcome of wind series.Original series X _s, M element prediction value after the k moment can be expressed as follows:

$\stackrel{\‾}{X_{s,M+k}}=\stackrel{\‾}{G_{1,M+k}}+\stackrel{\‾}{G_{2,M+k}}+\stackrel{\‾}{G_{3,M+k}}+\stackrel{\‾}{X_{3,M+k}}---\left(18\right)$

Wherein, represent original series X respectively _sm element X _s,Mground floor after reconstruct is to third layer high-frequency signal G _{1, M}, G _{2, M}, G _{3, M}with the low frequency signal X of third layer reconstruct _{3, M}the k moment after predict the outcome.

7. the assessment of forecasting wind speed ability:

Error of calculation index, thus the performance of forecast model is assessed.Existed at present much to the mode error of forecasting wind speed assessment, such as MAPE (mean absolute percentage error), MAE (mean absolute error), MPE (average relative error), it is defined as follows:

$MAPE=\left(\frac{1}{n}\right)\underset{i=1}{\overset{n}{\Σ}}\left(\frac{|L_f-L_a|}{L_a}\right)---\left(19\right)$

$MAE=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}|L_f-L_a|---\left(20\right)$

$MPE=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}\frac{L_f-L_a}{L_a}\×100---\left(21\right)$

Wherein, L _fand L _aforecasting wind speed value and actual wind speed value respectively.I represents hour, and n represents moment number.

8. export forecasting wind speed value and error criterion.

Embodiment

For checking effect of the present invention, for a certain wind energy turbine set, a kind of specific implementation process based on wavelet transformation and population improved grey model prognoses system is described.This wind energy turbine set has installed DATA REASONING instrument, and observation station has recorded the data to July in 2009 4 months.The order of data according to the time arranged, the training sample selected is the record data of front 1158 moment observation stations, is approximately the air speed data amount of 4 days.Test sample book is the record data of 288 moment observation stations thereafter.With Matlab, the example of structure is programmed, and result is analyzed, as shown in Figure 4.In order to contrast, employ traditional gray model GM and predicting as reference merely through the GMIPSO of parameter optimization.

The MAE (mean absolute error) of GM is 0.4948, and its MAPE (mean absolute percentage error) is 9.0012%; The MAE (mean absolute error) of GMIPSO is 0.4836, and the MAPE (mean absolute percentage error) of its model is 8.8045%; The MAE (mean absolute error) of the WGMIPSO improved based on wavelet transformation and population of the present invention is 0.1283, and the MAPE (mean absolute percentage error) of its model is 8.1678%.

The error evaluation data that GM model, GMIPSO model are relevant with WGMIPSO model are as shown in table 1, no matter be MAE or MAPE, all gradually reduced to WGMIPSO model by GM model, GMIPSO model, therefore when carrying out short-term wind speed forecasting, particle swarm optimization algorithm determination parameter effectively improves traditional gray model.High-frequency signal and low frequency signal separate by the inventive method, drop into model respectively to predict, like this at utmost alleviating on the basis to the over-fitting of high fdrequency component, improve the fitting degree to low frequency component as far as possible, this disposal route effectively can improve the accuracy of prediction.

It is worth mentioning that, the MAE of WGMIPSO model is very large compared with other two kinds of method differences.Even if this can show that WGMIPSO is not obvious in the high precision of most moment prediction, but for certain individually point occur that the contingency of big error can be smaller, the stability namely predicted can be higher, further illustrates the advantage of this invention.

Table 1

Claims (8)

1., based on the short-term wind speed forecasting method of wavelet transformation and population updated gray correlation analysis, it is characterized in that, comprise the following steps:

1) input air speed data, data prediction is carried out to the original series that air speed data is formed;

2) wavelet function feedback is carried out to pretreated wind series;

3) the forecasting wind speed model based on gray theory is set up;

4) particle swarm optimization algorithm improved grey model forecasting wind speed model is utilized;

5) wind series is carried out each component after wavelet function feedback to predict as the grey forecasting wind speed model after input one by one input particle group optimizing;

6) forecasting wind speed value is obtained;

7) error of calculation index, assesses forecasting wind speed;

8) forecasting wind speed value and error criterion is exported.

2. the short-term wind speed forecasting method based on wavelet transformation and population updated gray correlation analysis according to claim 1, it is characterized in that, described step 1) in, carrying out data prediction to refer to when predicting that the air speed data in moment and the air speed data size of previous moment differ by more than 10%, based on following equation, pre-service being carried out to air speed data:

$X_s(m+1)=X_s\left(m\right)+\left(X_s\right(m+1)-\frac{X_s\left(m\right)}{3})---\left(1\right)$

Wherein, X _s(m+1) air speed data in m+1 moment is represented, X _sm () represents the air speed data in m moment.

3. the short-term wind speed forecasting method based on wavelet transformation and population updated gray correlation analysis according to claim 1, is characterized in that, described step 2) in, choose 3 layers of wavelet decomposition, then, after wavelet decomposition and reconstruct, original series is expressed as:

X _s＝G ₁+G ₂+G ₃+X ₃(2)

Wherein, X _sfor original series, G ₁, G ₂, G ₃be respectively the high-frequency signal after ground floor to third layer reconstruct, X ₃for the low frequency signal of third layer reconstruct,

Original series X _sin i-th element can be expressed as follows:

X _s,i＝G _1,i+G _2,i+G _3,i+X _3,i(3)

Wherein, G _{1, i}, G _{2, i}, G _{3, i}be respectively X _sin i-th element ground floor to third layer reconstruct after high-frequency signal, X _{3, i}for X _sin i-th element third layer reconstruct low frequency signal.

4. the short-term wind speed forecasting method based on wavelet transformation and population updated gray correlation analysis according to claim 3, is characterized in that, described step 3) in, set up the forecasting wind speed model based on gray theory, comprise the following steps:

3-1) accumulated generating operation is carried out to the component after reconstruct, as follows:

By described step 2) wavelet decomposition and reconstruct after component G ₁, G ₂, G ₃and X ₃respectively as the list entries X in forecasting wind speed model ⁽⁰⁾, carry out accumulated generating operation, and the air speed data choosing front 5 moment can predict the wind speed of subsequent time,

Order, X ⁽¹⁾x ⁽⁰⁾single order Accumulating generation, its element can be determined by the following:

X ⁽⁰⁾(1)＝X ⁽¹⁾(1)(4)

$X^{\left(1\right)}\left(k\right)=\underset{m=1}{\overset{k}{\Σ}}{X}^{\left(0\right)}\left(m\right),k=2,3,...5---\left(5\right)$

Wherein, X ⁽⁰⁾k () represents list entries X ⁽⁰⁾in the data in front k moment;

Background value 3-2) calculating grey forecasting wind speed model is as follows:

Z ⁽¹⁾(k)＝gX ⁽¹⁾(k)+(1-g)X ⁽¹⁾(k-1),k＝2,3...5(6)

Wherein, Z ⁽¹⁾k () represents background value, g generates coefficient;

Equation 3-3) setting up grey forecasting wind speed model is as follows:

X ⁽⁰⁾(k)+aZ ⁽¹⁾(k)＝bX ⁽¹⁾(k)(7)

Wherein, a is development coefficient, and b is the grey input coefficient obtained by least square method;

Definition matrix B and Y _nas follows:

$B=\left[\begin{array}{cc}-Z^{\left(1\right)}\left(2\right)& 1\\ -Z^{\left(1\right)}\left(3\right)& 1\\ -Z^{\left(1\right)}\left(4\right)& 1\\ -Z^{\left(1\right)}\left(5\right)& 1\end{array}\right]---\left(8\right)$

$Y_N=\left[\begin{array}{c}{X}^{\left(0\right)}\left(2\right)\\ X^{\left(0\right)}\left(3\right)\\ X^{\left(0\right)}\left(4\right)\\ X^{\left(0\right)}\left(5\right)\end{array}\right]---\left(9\right)$

The value of coefficient a, b is determined by following equation:

$\left[\begin{array}{c}a\\ b\end{array}\right]={\left(B^{T}B\right)}^{-1}*B^T*Y_N---\left(10\right);$

3-4) determine that the differential equation of grey forecasting wind speed model is as follows:

$\frac{{\mathrm{dX}}^{\left(1\right)}}{dt}+{\mathrm{aX}}^{\left(1\right)}\left(t\right)=b---\left(11\right)$

The solution of the above-mentioned differential equation is as follows:

${\hat{X}}^{\left(1\right)}(k+1)=\{X^{\left(0\right)}\left(1\right)-b/a\}*e^{-at}+b/a,k\≥1---\left(12\right)$

Wherein, the X being ⁽¹⁾k the estimated value of (), is equaled first element of this sequence, determines following relation by first element estimated value of the single order Accumulating generation of a sequence:

${\hat{X}}^{\left(1\right)}\left(1\right)=X^{\left(0\right)}\left(1\right)---\left(13\right);$

3-5) carry out inverse accumulated generating operation, determine forecasting wind speed value:

${\hat{X}}^{\left(0\right)}\left(k\right)={\hat{X}}^{\left(1\right)}\left(k\right)-{\hat{X}}^{\left(1\right)}(k-1),k\≥2---\left(14\right)$

Wherein, original series X ⁽⁰⁾the estimated value of (k).

5. the short-term wind speed forecasting method based on wavelet transformation and population updated gray correlation analysis according to claim 1, it is characterized in that, described step 4) in, utilize particle swarm optimization algorithm improved grey model forecasting wind speed model to refer to determine the optimum value generating coefficient, meet minimum mean absolute percentage error:

obey 0≤g≤1;

Wherein, MAPE is mean absolute percentage error;

Particle swarm optimization algorithm searching process is as follows:

Stochastic choice one group of particle carrys out matching particle swarm optimization algorithm model as initial value.These particle goal seeking spaces, in k iteration in object space, by describe position and the speed of each particle respectively, each particle records their best positions in k+1 iteration, the speed of particle obtained by equation below:

$V_{k+1}^i=\mathrm{\ω}\·V_k^i+c_1\·r_1(P_{lbest}^i-X_k^i)+c_2\·r_2(P_{global}^i-X_k^i)---\left(15\right)$

Wherein, r ₁and r ₂be the random number between 0 and 1 respectively, ω is inertia weight coefficient, c ₁and c ₂training coefficient, it is global optimum position;

The computing formula of ω is as follows:

$\mathrm{\ω}={\mathrm{\ω}}_{max}-\frac{({\mathrm{\ω}}_{max}-{\mathrm{\ω}}_{min})}{k_{\max }}\×k---\left(16\right)$

Wherein, k _maxmaximum iteration time, ω _maxbe 0.9, ω _minbe 0.4, in each iteration, the reposition of each particle is obtained, as following formula by its original position and its current speed addition:

$X_{k+1}^i=X_k^i+V_{k+1}^i---\left(17\right).$

6. the short-term wind speed forecasting method based on wavelet transformation and population updated gray correlation analysis according to claim 3, it is characterized in that, described step 5) wind series carried out each component after wavelet function feedback and predict as the grey forecasting wind speed model after input drops into particle group optimizing one by one, specifically refer to, by original series X _shigh fdrequency component G ₁, G ₂, G ₃, low frequency component X ₃and described step 4) generation coefficient g after optimizing as input, be input to described step 3) grey forecasting wind speed model predict, the output obtained is exactly that each component is in the result of carrying out short-term wind speed forecasting.

7. the short-term wind speed forecasting method based on wavelet transformation and population updated gray correlation analysis according to claim 1, it is characterized in that, described step 6) obtain forecasting wind speed value and refer to described step 5) the predicting the outcome of each component that obtain superpose, thus obtain forecasting wind speed value

Original series X _s, M element prediction value after the k moment be expressed as follows:

$\stackrel{\‾}{X_{s,M+k}}=\stackrel{\‾}{G_{1,M+k}}+\stackrel{\‾}{G_{2,M+k}}+\stackrel{\‾}{G_{3,M+k}}+\stackrel{\‾}{X_{3,M+k}}---\left(18\right)$

Wherein, represent original series X respectively _sm element X _s,Mground floor after reconstruct is to third layer high-frequency signal G _{1, M}, G _{2, M}, G _{3, M}with the low frequency signal X of third layer reconstruct _{3, M}the k moment after predict the outcome.

8. the short-term wind speed forecasting method based on wavelet transformation and population updated gray correlation analysis according to claim 1, is characterized in that, described step 7) in, error criterion adopts mean absolute percentage error MAPE, mean absolute error MAE, average relative error MPE, be defined as follows:

$MAPE=\left(\frac{1}{n}\right)\underset{i=1}{\overset{n}{\Σ}}\left(\frac{|L_f-L_a|}{L_a}\right)---\left(19\right)$

$MAE=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}|L_f-L_a|---\left(20\right)$

$MPE=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}\frac{L_f-L_a}{L_a}\×100---\left(21\right)$

Wherein, L _fand L _abe forecasting wind speed value and actual wind speed value respectively, i represents hour, and n represents moment number.